Artificial Epigenetic Networks: Automatic Decomposition of Dynamical Control Tasks Using Topological Self-Modification.

PubMed

Turner, Alexander P; Caves, Leo S D; Stepney, Susan; Tyrrell, Andy M; Lones, Michael A

2017-01-01

This paper describes the artificial epigenetic network, a recurrent connectionist architecture that is able to dynamically modify its topology in order to automatically decompose and solve dynamical problems. The approach is motivated by the behavior of gene regulatory networks, particularly the epigenetic process of chromatin remodeling that leads to topological change and which underlies the differentiation of cells within complex biological organisms. We expected this approach to be useful in situations where there is a need to switch between different dynamical behaviors, and do so in a sensitive and robust manner in the absence of a priori information about problem structure. This hypothesis was tested using a series of dynamical control tasks, each requiring solutions that could express different dynamical behaviors at different stages within the task. In each case, the addition of topological self-modification was shown to improve the performance and robustness of controllers. We believe this is due to the ability of topological changes to stabilize attractors, promoting stability within a dynamical regime while allowing rapid switching between different regimes. Post hoc analysis of the controllers also demonstrated how the partitioning of the networks could provide new insights into problem structure.

Resource Allocation and Cross Layer Control in Wireless Networks

DTIC Science & Technology

2006-08-25

arrival rates lies within the capacity region of the network. The notion of controlling the system to maximize its stability region and the following...optimization problem (4.5) that must be solved at the beginning of 48 Dynamic Control for Network Stability each time slot requires in general knowledge...Dynamic Control for Network Stability ~ (c) ab (t) those of any other feasible algorithm, then for any time t 0; X ic U (c) i (t) "X b ~ (c) ab (t) X

Interval stability for complex systems

NASA Astrophysics Data System (ADS)

Klinshov, Vladimir V.; Kirillov, Sergey; Kurths, Jürgen; Nekorkin, Vladimir I.

2018-04-01

Stability of dynamical systems against strong perturbations is an important problem of nonlinear dynamics relevant to many applications in various areas. Here, we develop a novel concept of interval stability, referring to the behavior of the perturbed system during a finite time interval. Based on this concept, we suggest new measures of stability, namely interval basin stability (IBS) and interval stability threshold (IST). IBS characterizes the likelihood that the perturbed system returns to the stable regime (attractor) in a given time. IST provides the minimal magnitude of the perturbation capable to disrupt the stable regime for a given interval of time. The suggested measures provide important information about the system susceptibility to external perturbations which may be useful for practical applications. Moreover, from a theoretical viewpoint the interval stability measures are shown to bridge the gap between linear and asymptotic stability. We also suggest numerical algorithms for quantification of the interval stability characteristics and demonstrate their potential for several dynamical systems of various nature, such as power grids and neural networks.

Optimum Design of High-Speed Prop-Rotors

NASA Technical Reports Server (NTRS)

Chattopadhyay, Aditi; McCarthy, Thomas Robert

1993-01-01

An integrated multidisciplinary optimization procedure is developed for application to rotary wing aircraft design. The necessary disciplines such as dynamics, aerodynamics, aeroelasticity, and structures are coupled within a closed-loop optimization process. The procedure developed is applied to address two different problems. The first problem considers the optimization of a helicopter rotor blade and the second problem addresses the optimum design of a high-speed tilting proprotor. In the helicopter blade problem, the objective is to reduce the critical vibratory shear forces and moments at the blade root, without degrading rotor aerodynamic performance and aeroelastic stability. In the case of the high-speed proprotor, the goal is to maximize the propulsive efficiency in high-speed cruise without deteriorating the aeroelastic stability in cruise and the aerodynamic performance in hover. The problems studied involve multiple design objectives; therefore, the optimization problems are formulated using multiobjective design procedures. A comprehensive helicopter analysis code is used for the rotary wing aerodynamic, dynamic and aeroelastic stability analyses and an algorithm developed specifically for these purposes is used for the structural analysis. A nonlinear programming technique coupled with an approximate analysis procedure is used to perform the optimization. The optimum blade designs obtained in each case are compared to corresponding reference designs.

Flatness-based adaptive fuzzy control of chaotic finance dynamics

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Loia, V.; Tommasetti, A.; Troisi, O.

2017-11-01

A flatness-based adaptive fuzzy control is applied to the problem of stabilization of the dynamics of a chaotic finance system, describing interaction between the interest rate, the investment demand and the price exponent. By proving that the system is differentially flat and by applying differential flatness diffeomorphisms, its transformation to the linear canonical (Brunovsky) is performed. For the latter description of the system, the design of a stabilizing state feedback controller becomes possible. A first problem in the design of such a controller is that the dynamic model of the finance system is unknown and thus it has to be identified with the use neurofuzzy approximators. The estimated dynamics provided by the approximators is used in the computation of the control input, thus establishing an indirect adaptive control scheme. The learning rate of the approximators is chosen from the requirement the system's Lyapunov function to have always a negative first-order derivative. Another problem that has to be dealt with is that the control loop is implemented only with the use of output feedback. To estimate the non-measurable state vector elements of the finance system, a state observer is implemented in the control loop. The computation of the feedback control signal requires the solution of two algebraic Riccati equations at each iteration of the control algorithm. Lyapunov stability analysis demonstrates first that an H-infinity tracking performance criterion is satisfied. This signifies elevated robustness against modelling errors and external perturbations. Moreover, the global asymptotic stability is proven for the control loop.

Analytical stability criteria for the Caledonian Symmetric Four and Five Body Problems

NASA Astrophysics Data System (ADS)

Steves, Bonnie; Shoaib Afridi, Mohammad; Sweatman, Winston

2017-06-01

Analytical studies of the stability of three or more body gravitational systems are difficult because of the greater number of variables involved with the increasing number of bodies and the limitation of 10 integrals that exist in the gravitational n-body problem. Utilisation of symmetries or the neglecting of the masses of some of the bodies compared to others can simplify the dynamical problem and enable global analytical stability solutions to be derived. These symmetric and restricted few body systems with their analytical stability criterion can then provide useful information on the stability of the general few body system when near symmetry or the restricted situation. Even with symmetrical reductions, analytical stability derivations for four and five body problems are rare. In this paper, we develop an analytical stability criterion for the Caledonian Symmetric Five Body Problem (CS5BP) , a dynamically symmetrical planar problem with two pairs of equal masses and a fifth mass located at the centre of mass. Sundman’s inequality is applied to derive boundary surfaces to the allowed real motion of the system. This enables the derivation of a stability criterion valid for all time for the hierarchical stability of the CS5BP and its subset the Caledonian Symmetric Four Body Problem (CSFBP), where the central mass is taken to be equal to zero. We show that the hierarchical stability depends solely on the Szebehely constant C0, which is a function of the total energy H and angular momentum c. The critical value Ccrit at which the system becomes hierarchically stable for all time depends only on the two mass ratios of the symmetric five body system. We then explore the effect on the stability of the whole system of adding an increasing massive central body. It is shown both analytically and numerically that all CS5BPs and CSFBPs of different mass ratios are hierarchically stable if C0 > 0.0659 and C0 > 0.0465, respectively. The Caledonian Symmetric Four and Five Body gravitational models are relevant to the study of the stability and evolution of symmetric quadruple/quintuple stellar clusters and symmetric exoplanetary systems of two planets orbiting a binary/triplet of stars.

Robustness and cognition in stabilization problem of dynamical systems based on asymptotic methods

NASA Astrophysics Data System (ADS)

Dubovik, S. A.; Kabanov, A. A.

2017-01-01

The problem of synthesis of stabilizing systems based on principles of cognitive (logical-dynamic) control for mobile objects used under uncertain conditions is considered. This direction in control theory is based on the principles of guaranteeing robust synthesis focused on worst-case scenarios of the controlled process. The guaranteeing approach is able to provide functioning of the system with the required quality and reliability only at sufficiently low disturbances and in the absence of large deviations from some regular features of the controlled process. The main tool for the analysis of large deviations and prediction of critical states here is the action functional. After the forecast is built, the choice of anti-crisis control is the supervisory control problem that optimizes the control system in a normal mode and prevents escape of the controlled process in critical states. An essential aspect of the approach presented here is the presence of a two-level (logical-dynamic) control: the input data are used not only for generating of synthesized feedback (local robust synthesis) in advance (off-line), but also to make decisions about the current (on-line) quality of stabilization in the global sense. An example of using the presented approach for the problem of development of the ship tilting prediction system is considered.

On the stabilization of decentralized control systems.

NASA Technical Reports Server (NTRS)

Wang, S.-H.; Davison, E. J.

1973-01-01

This paper considers the problem of stabilizing a linear time-variant multivariable system by using several local feedback control laws. Each local feedback control law depends only on partial system outputs. A necessary and sufficient condition for the existence of local control laws with dynamic compensation to stabilize a given system is derived. This condition is stated in terms of a new notion, called fixed modes, which is a natural generalization of the well-known concept of uncontrollable modes and unobservable modes that occur in centralized control system problems. A procedure that constructs a set of stabilizing feedback control laws is given.

Application of a Modal Approach in Solving the Static Stability Problem for Electric Power Systems

NASA Astrophysics Data System (ADS)

Sharov, J. V.

2017-12-01

Application of a modal approach in solving the static stability problem for power systems is examined. It is proposed to use the matrix exponent norm as a generalized transition function of the power system disturbed motion. Based on the concept of a stability radius and the pseudospectrum of Jacobian matrix, the necessary and sufficient conditions for existence of the static margins were determined. The capabilities and advantages of the modal approach in designing centralized or distributed control and the prospects for the analysis of nonlinear oscillations and rendering the dynamic stability are demonstrated.

A general method to determine the stability of compressible flows

NASA Technical Reports Server (NTRS)

Guenther, R. A.; Chang, I. D.

1982-01-01

Several problems were studied using two completely different approaches. The initial method was to use the standard linearized perturbation theory by finding the value of the individual small disturbance quantities based on the equations of motion. These were serially eliminated from the equations of motion to derive a single equation that governs the stability of fluid dynamic system. These equations could not be reduced unless the steady state variable depends only on one coordinate. The stability equation based on one dependent variable was found and was examined to determine the stability of a compressible swirling jet. The second method applied a Lagrangian approach to the problem. Since the equations developed were based on different assumptions, the condition of stability was compared only for the Rayleigh problem of a swirling flow, both examples reduce to the Rayleigh criterion. This technique allows including the viscous shear terms which is not possible in the first method. The same problem was then examined to see what effect shear has on stability.

A study of aeroelastic and structural dynamic effects in multi-rotor systems with application to hybrid heavy lift vehicles

NASA Technical Reports Server (NTRS)

Friedmann, P. P.

1984-01-01

An aeroelastic model suitable for the study of aeroelastic and structural dynamic effects in multirotor vehicles simulating a hybrid heavy lift vehicle was developed and applied to the study of a number of diverse problems. The analytical model developed proved capable of modeling a number of aeroelastic problems, namely: (1) isolated blade aeroelastic stability in hover and forward flight, (2) coupled rotor/fuselage aeromechanical problem in air or ground resonance, (3) tandem rotor coupled rotor/fuselage problems, and (4) the aeromechanical stability of a multirotor vehicle model representing a hybrid heavy lift airship (HHLA). The model was used to simulate the ground resonance boundaries of a three bladed hingeless rotor model, including the effect of aerodynamic loads, and the theoretical predictions compared well with experimental results. Subsequently the model was used to study the aeromechanical stability of a vehicle representing a hybrid heavy lift airship, and potential instabilities which could occur for this type of vehicle were identified. The coupling between various blade, supporting structure and rigid body modes was identified.

Formulation of the aeroelastic stability and response problem of coupled rotor/support systems

NASA Technical Reports Server (NTRS)

Warmbrodt, W.; Friedmann, P.

1979-01-01

The consistent formulation of the governing nonlinear equations of motion for a coupled rotor/support system is presented. Rotor/support coupling is clearly documented by enforcing dynamic equilibrium between the rotor and the moving flexible support. The nonlinear periodic coefficient equations of motion are applicable to both coupled rotor/fuselage aeroelastic problems of helicopters in hover or forward flight and coupled rotor/tower dynamics of a large horizontal axis wind turbine (HAWT). Finally, the equations of motion are used to study the influence of flexible supports and nonlinear terms on rotor aeroelastic stability and response of a large two-bladed HAWT.

Perspectives on the geographic stability and mobility of people in cities

PubMed Central

Hanson, Susan

2005-01-01

A class of questions in the human environment sciences focuses on the relationship between individual or household behavior and local geographic context. Central to these questions is the nature of people's geographic mobility as well as the duration of their locational stability at varying spatial and temporal scales. The problem for researchers is that the processes of mobility/stability are temporally and spatially dynamic and therefore difficult to measure. Whereas time and space are continuous, analysts must select levels of aggregation for both length of time in place and spatial scale of place that fit with the problem in question. Previous work has emphasized mobility and suppressed stability as an analytic category. I focus here on stability and show how analyzing individuals' stability requires also analyzing their mobility. Through an empirical example centered on the relationship between entrepreneurship and place, I demonstrate how a spotlight on stability illuminates a resolution to the measurement problem by highlighting the interdependence between the time and space dimensions of stability/mobility. PMID:16230616

NL(q) Theory: A Neural Control Framework with Global Asymptotic Stability Criteria.

PubMed

Vandewalle, Joos; De Moor, Bart L.R.; Suykens, Johan A.K.

1997-06-01

In this paper a framework for model-based neural control design is presented, consisting of nonlinear state space models and controllers, parametrized by multilayer feedforward neural networks. The models and closed-loop systems are transformed into so-called NL(q) system form. NL(q) systems represent a large class of nonlinear dynamical systems consisting of q layers with alternating linear and static nonlinear operators that satisfy a sector condition. For such NL(q)s sufficient conditions for global asymptotic stability, input/output stability (dissipativity with finite L(2)-gain) and robust stability and performance are presented. The stability criteria are expressed as linear matrix inequalities. In the analysis problem it is shown how stability of a given controller can be checked. In the synthesis problem two methods for neural control design are discussed. In the first method Narendra's dynamic backpropagation for tracking on a set of specific reference inputs is modified with an NL(q) stability constraint in order to ensure, e.g., closed-loop stability. In a second method control design is done without tracking on specific reference inputs, but based on the input/output stability criteria itself, within a standard plant framework as this is done, for example, in H( infinity ) control theory and &mgr; theory. Copyright 1997 Elsevier Science Ltd.

Dynamical analysis of Lorenz System on traffic problem in Yogyakarta, Indonesia

NASA Astrophysics Data System (ADS)

Hartono; Saptaningtyas, F. Y.; Krisnawan, K. P.

2018-03-01

The traffic congestion becomes a routine problem which occurs in Yogyakarta. This study was to develop a mathematical model of traffic congestion using Lorenz System. This system was used to analyze the traffic condition in Yogyakarta road. The data was taken from the observation of the road and it had been validated. Routh Hourwith used to analyse the stability of free jamm equlibrium. The dynamic analysis showed that the system was stabil. Numerical solution showed that the bigger value of ratio of the distance relaxsation time to velocity relaxsation time resulting the more time to reach the stabil condition. It showed that more and more time to reach optimal velocity, needed more and more time as well to reach equilibrium. Traffic condition at the time of observation was ideal and there was no transition of traffic jam.

Normalization of Hamiltonian and nonlinear stability of the triangular equilibrium points in non-resonance case with perturbations

NASA Astrophysics Data System (ADS)

Kishor, Ram; Kushvah, Badam Singh

2017-09-01

For the study of nonlinear stability of a dynamical system, normalized Hamiltonian of the system is very important to discuss the dynamics in the vicinity of invariant objects. In general, it represents a nonlinear approximation to the dynamics, which is very helpful to obtain the information as regards a realistic solution of the problem. In the present study, normalization of the Hamiltonian and analysis of nonlinear stability in non-resonance case, in the Chermnykh-like problem under the influence of perturbations in the form of radiation pressure, oblateness, and a disc is performed. To describe nonlinear stability, initially, quadratic part of the Hamiltonian is normalized in the neighborhood of triangular equilibrium point and then higher order normalization is performed by computing the fourth order normalized Hamiltonian with the help of Lie transforms. In non-resonance case, nonlinear stability of the system is discussed using the Arnold-Moser theorem. Again, the effects of radiation pressure, oblateness and the presence of the disc are analyzed separately and it is observed that in the absence as well as presence of perturbation parameters, triangular equilibrium point is unstable in the nonlinear sense within the stability range 0<μ<μ1=\\bar{μc} due to failure of the Arnold-Moser theorem. However, perturbation parameters affect the values of μ at which D4=0, significantly. This study may help to analyze more generalized cases of the problem in the presence of some other types of perturbations such as P-R drag and solar wind drag. The results are limited to the regular symmetric disc but it can be extended in the future.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuzmina, L.K.

The research deals with different aspects of mathematical modelling and the analysis of complex dynamic non-linear systems as a consequence of applied problems in mechanics (in particular those for gyrosystems, for stabilization and orientation systems, control systems of movable objects, including the aviation and aerospace systems) Non-linearity, multi-connectedness and high dimensionness of dynamical problems, that occur at the initial full statement lead to the need of the problem narrowing, and of the decomposition of the full model, but with safe-keeping of main properties and of qualitative equivalence. The elaboration of regular methods for modelling problems in dynamics, the generalization ofmore » reduction principle are the main aims of the investigations. Here, uniform methodology, based on Lyapunov`s methods, founded by N.G.Ohetayev, is developed. The objects of the investigations are considered with exclusive positions, as systems of singularly perturbed class, treated as ones with singular parametrical perturbations. It is the natural extension of the statements of N.G.Chetayev and P.A.Kuzmin for parametrical stability. In paper the systematical procedures for construction of correct simplified models (comparison ones) are developed, the validity conditions of the transition are determined the appraisals are received, the regular algorithms of engineering level are obtained. Applicabilitelly to the stabilization and orientation systems with the gyroscopic controlling subsystems, these methods enable to build the hierarchical sequence of admissible simplified models; to determine the conditions of their correctness.« less

Stability and periodicity in the Sitnikov three-body problem when primaries are oblate spheroids

NASA Astrophysics Data System (ADS)

Rahman, M. A.; Garain, D. N.; Hassan, M. R.

2015-05-01

This paper deals with the effect of oblateness of the primaries of equal masses on the series solutions of the Sitnikov problem of three bodies. Effects of oblateness have also been shown on the stability of libration points and Poincare surface of section. Here series solutions have been developed with the help of iteration process of Green's function and by the Lindstedt-Poincare method. Following Murray and Dermott (Solar System Dynamics, Cambridge University Press, Cambridge, 1999) we have checked the stability of the equilibrium points in the Sitnikov problem. Periodicity and quasi-periodicity have been examined by drawing the Poincare surfaces of section using the mathematical software.

Dynamical theory of stability for elastic rods with nonlinear curvature and twist

NASA Technical Reports Server (NTRS)

Wauer, J.

1977-01-01

Considering non-linear terms in the curvature as well as in the twist, the governing boundary value problem for lateral bending of elastic, transverse loaded rods is formulated by means of Hamilton's principle. Using the method of small vibrations, the associated linearized equations of stability are derived, which complete the currently accepted relations. The example of the simplest lateral bending problem illustrates the improved effect of the proposed equations.

Aeroelasticity and mechanical stability report, 0.27 Mach scale model of the YAH-64 advanced attack helicopter

NASA Technical Reports Server (NTRS)

Straub, F. K.; Johnston, R. A.

1987-01-01

A 27% dynamically scaled model of the YAH-64 Advanced Attack Helicopter main rotor and hub has been designed and fabricated. The model will be tested in the NASA Langley Research Center V/STOL wind tunnel using the General Rotor Model System (GRMS). This report documents the studies performed to ensure dynamic similarity of the model with its full scale parent. It also contains a preliminary aeroelastic and aeromechanical substantiation for the rotor installation in the wind tunnel. From the limited studies performed no aeroelastic stability or load problems are projected. To alleviate a projected ground resonance problem, a modification of the roll characteristics of the GRMS is recommended.

Parachute dynamics and stability analysis. [using nonlinear differential equations of motion

NASA Technical Reports Server (NTRS)

Ibrahim, S. K.; Engdahl, R. A.

1974-01-01

The nonlinear differential equations of motion for a general parachute-riser-payload system are developed. The resulting math model is then applied for analyzing the descent dynamics and stability characteristics of both the drogue stabilization phase and the main descent phase of the space shuttle solid rocket booster (SRB) recovery system. The formulation of the problem is characterized by a minimum number of simplifying assumptions and full application of state-of-the-art parachute technology. The parachute suspension lines and the parachute risers can be modeled as elastic elements, and the whole system may be subjected to specified wind and gust profiles in order to assess their effects on the stability of the recovery system.

Development and application of a time-history analysis for rotorcraft dynamics based on a component approach

NASA Technical Reports Server (NTRS)

Sopher, R.; Hallock, D. W.

1985-01-01

A time history analysis for rotorcraft dynamics based on dynamical substructures, and nonstructural mathematical and aerodynamic components is described. The analysis is applied to predict helicopter ground resonance and response to rotor damage. Other applications illustrate the stability and steady vibratory response of stopped and gimballed rotors, representative of new technology. Desirable attributes expected from modern codes are realized, although the analysis does not employ a complete set of techniques identified for advanced software. The analysis is able to handle a comprehensive set of steady state and stability problems with a small library of components.

Dynamical control of a quantum Kapitza pendulum in a spin-1 BEC

NASA Astrophysics Data System (ADS)

Hoang, Thai; Gerving, Corey; Land, Ben; Anquez, Martin; Hamley, Chris; Chapman, Michael

2013-05-01

We demonstrate dynamic stabilization of an unstable strongly interacting quantum many-body system by periodic manipulation of the phase of the collective states. The experiment employs a spin-1 atomic Bose condensate that has spin dynamics analogous to a non-rigid pendulum in the mean-field limit. The condensate spin is initialized to an unstable (hyperbolic) fixed point of the phase space, where subsequent free evolution gives rise to spin-nematic squeezing and quantum spin mixing. To stabilize the system, periodic microwave pulses are applied that manipulate the spin-nematic fluctuations and limit their growth. The range of pulse periods and phase shifts with which the condensate can be stabilized is measured and compares well with a linear stability analysis of the problem. C.D. Hamley, et al., ``Spin-Nematic Squeezed Vacuum in a Quantum Gas,'' Nature Physics 8, 305-308 (2012).

Research on H2 speed governor for diesel engine of marine power station

NASA Astrophysics Data System (ADS)

Huang, Man-Lei

2007-09-01

The frequency stability of a marine power system is determined by the dynamic characteristic of the diesel engine speed regulation system in a marine power station. In order to reduce the effect of load disturbances and improve the dynamic precision of a diesel engine speed governor, a controller was designed for a diesel engine speed regulation system using H2 control theory. This transforms the specifications of the system into a standard H2 control problem. Firstly, the mathematical model of a diesel engine speed regulation system using an H2 speed governor is presented. To counter external disturbances and model uncertainty, the design of an H2 speed governor rests on the problem of mixed sensitivity. Computer simulation verified that the H2 speed governor improves the dynamic precision of a system and the ability to adapt to load disturbances, thus enhancing the frequency stability of marine power systems.

Dynamics and stability of mechanical systems with follower forces

NASA Technical Reports Server (NTRS)

Herrmann, G.

1971-01-01

A monograph on problems of stability of equilibrium of mechanical systems with follower forces is presented. Concepts of stability and criteria of stability are reviewed briefly, together with means of analytical specification of follower forces. Nondissipative systems with two degrees of freedom are discussed, and destabilizing effects due to various types of dissipative forces both in discrete and continuous systems, are treated. The analyses are accompanied by some quantative experiments and observations on demonstrational laboratory models.

Dynamics of family economic hardship and the progression of health problems of husbands and wives during the middle years: a perspective from rural Mid-West.

PubMed

Wickrama, K A S; Hwa Kwag, Kyung; Lorenz, Federick O; Conger, Rand D; Surjadi, Florensia F

2010-12-01

The objective of this study was to investigate the influence of theoretically important dimensions of stability and change in economic hardship during early middle years on decade-long health problems of husbands and wives. The study used prospective data collected from 360 middle-aged husbands and wives during a 12-year period. The variables included self-reported economic hardship (22 items), mental and physical health, and physical impairment. The results supported the hypothesis that the dynamics of family economic hardship (in terms of stability and change) during the early middle years contribute to subsequent onset of health problems of middle-aged husbands and wives. These health problems in turn progress as an interrelated process through intrahealth-domain continuities, cross-health domain proliferations, and dyadic associations as they pass through midlife. A better understanding of these processes may aid in the formation and effective implementation of health promotion programs for middle-aged husbands and wives.

A Study on a Centralized Under-Voltage Load Shedding Scheme Considering the Load Characteristics

NASA Astrophysics Data System (ADS)

Deng, Jiyu; Liu, Junyong

Under-voltage load shedding is an important measure for maintaining voltage stability.Aiming at the optimal load shedding problem considering the load characteristics,firstly,the traditional under-voltage load shedding scheme based on a static load model may cause the analysis inaccurate is pointed out on the equivalent Thevenin circuit.Then,the dynamic voltage stability margin indicator is derived through local measurement.The derived indicator can reflect the voltage change of the key area in a myopia linear way.Dimensions of the optimal problem will be greatly simplified using this indicator.In the end,mathematical model of the centralized load shedding scheme is built with the indicator considering load characteristics.HSPPSO is introduced to slove the optimal problem.Simulation results on IEEE-39 system show that the proposed scheme display a good adaptability in solving the under-voltage load shedding considering dynamic load characteristics.

Vibration characteristics of the HPOTP (High-Pressure Oxygen Turbopump) of the SSME (Space Shuttle Main Engine)

NASA Technical Reports Server (NTRS)

Childs, D. W.; Moyer, D. S.

1984-01-01

Attention is given to rotor dynamic problems that have been encountered and eliminated in the course of Space Shuttle Main Engine (SSME) development, as well as continuing, subsynchronous problems which are being encountered in the development of a 109-percent power level engine. The basic model for the SSME's High Pressure Oxygen Turbopump (HPOTP) encompasses a structural dynamic model for the rotor and housing, and component models for the liquid and gas seals, turbine clearance excitation forces, and impeller diffuser forces. Linear model results are used to examine the synchronous response and stability characteristics of the HPOTP, with attention to bearing load and stability problems associated with the second critical speed. Differences between linear and nonlinear model results are discussed and explained in terms of simple models. Simulation results indicate that while synchronous bearing loads can be reduced, subsynchronous motion is not eliminated by seal modifications.

Well-posed and stable transmission problems

NASA Astrophysics Data System (ADS)

Nordström, Jan; Linders, Viktor

2018-07-01

We introduce the notion of a transmission problem to describe a general class of problems where different dynamics are coupled in time. Well-posedness and stability are analysed for continuous and discrete problems using both strong and weak formulations, and a general transmission condition is obtained. The theory is applied to the coupling of fluid-acoustic models, multi-grid implementations, adaptive mesh refinements, multi-block formulations and numerical filtering.

Improving stability margins in discrete-time LQG controllers

NASA Technical Reports Server (NTRS)

Oranc, B. Tarik; Phillips, Charles L.

1987-01-01

Some of the problems are discussed which are encountered in the design of discrete-time stochastic controllers for problems that may adequately be described by the Linear Quadratic Gaussian (LQG) assumptions; namely, the problems of obtaining acceptable relative stability, robustness, and disturbance rejection properties. A dynamic compensator is proposed to replace the optimal full state feedback regulator gains at steady state, provided that all states are measurable. The compensator increases the stability margins at the plant input, which may possibly be inadequate in practical applications. Though the optimal regulator has desirable properties the observer based controller as implemented with a Kalman filter, in a noisy environment, has inadequate stability margins. The proposed compensator is designed to match the return difference matrix at the plant input to that of the optimal regulator while maintaining the optimality of the state estimates as directed by the measurement noise characteristics.

Sparse Reconstruction of Regional Gravity Signal Based on Stabilized Orthogonal Matching Pursuit (SOMP)

NASA Astrophysics Data System (ADS)

Saadat, S. A.; Safari, A.; Needell, D.

2016-06-01

The main role of gravity field recovery is the study of dynamic processes in the interior of the Earth especially in exploration geophysics. In this paper, the Stabilized Orthogonal Matching Pursuit (SOMP) algorithm is introduced for sparse reconstruction of regional gravity signals of the Earth. In practical applications, ill-posed problems may be encountered regarding unknown parameters that are sensitive to the data perturbations. Therefore, an appropriate regularization method needs to be applied to find a stabilized solution. The SOMP algorithm aims to regularize the norm of the solution vector, while also minimizing the norm of the corresponding residual vector. In this procedure, a convergence point of the algorithm that specifies optimal sparsity-level of the problem is determined. The results show that the SOMP algorithm finds the stabilized solution for the ill-posed problem at the optimal sparsity-level, improving upon existing sparsity based approaches.

Stability of Shapes Held by Surface Tension and Subjected to Flow

NASA Technical Reports Server (NTRS)

Chen, Yi-Ju; Robinson, Nathaniel D.; Steen, Paul H.

1999-01-01

Results of three problems are summarized in this contribution. Each involves the fundamental capillary instability of an interfacial bridge and is an extension of previous work. The first two problems concern equilibrium shapes of liquid bridges near the stability boundary corresponding to maximum length (Plateau-Rayleigh limit). For the first problem, a previously formulated nonlinear theory to account for imposed gravity and interfacial shear disturbances in an isothermal environment is quantitatively tested in experiment. For the second problem, the liquid bridge is subjected to a shear that models the effect of a thermocapillary flow generated by a ring heater in a liquid encapsulated float-zone configuration. In the absence of gravity, this symmetric perturbation can stabilize the bridge to lengths on the order of 30 percent beyond the Plateau-Rayleigh limit, which is on the order of heretofore unexplained Shuttle observations. The third problem considers the dynamics of collapse and pinchoff of a film bridge (no gravity), which happens in the absence of stabilization. Here, we summarize experimental efforts to measure the self-similar cone-and-crater structure predicted by a previous theory.

Research in Structures and Dynamics, 1984

NASA Technical Reports Server (NTRS)

Hayduk, R. J. (Compiler); Noor, A. K. (Compiler)

1984-01-01

A symposium on advanced and trends in structures and dynamics was held to communicate new insights into physical behavior and to identify trends in the solution procedures for structures and dynamics problems. Pertinent areas of concern were (1) multiprocessors, parallel computation, and database management systems, (2) advances in finite element technology, (3) interactive computing and optimization, (4) mechanics of materials, (5) structural stability, (6) dynamic response of structures, and (7) advanced computer applications.

Discrete time modeling and stability analysis of TCP Vegas

NASA Astrophysics Data System (ADS)

You, Byungyong; Koo, Kyungmo; Lee, Jin S.

2007-12-01

This paper presents an analysis method for TCP Vegas network model with single link and single source. Some papers showed global stability of several network models, but those models are not a dual problem where dynamics both exist in sources and links such as TCP Vegas. Other papers studied TCP Vegas as a dual problem, but it did not fully derive an asymptotic stability region. Therefore we analyze TCP Vegas with Jury's criterion which is necessary and sufficient condition. So we use state space model in discrete time and by using Jury's criterion, we could find an asymptotic stability region of TCP Vegas network model. This result is verified by ns-2 simulation. And by comparing with other results, we could know our method performed well.

Information flow dynamics in the brain

NASA Astrophysics Data System (ADS)

Rabinovich, Mikhail I.; Afraimovich, Valentin S.; Bick, Christian; Varona, Pablo

2012-03-01

Timing and dynamics of information in the brain is a hot field in modern neuroscience. The analysis of the temporal evolution of brain information is crucially important for the understanding of higher cognitive mechanisms in normal and pathological states. From the perspective of information dynamics, in this review we discuss working memory capacity, language dynamics, goal-dependent behavior programming and other functions of brain activity. In contrast with the classical description of information theory, which is mostly algebraic, brain flow information dynamics deals with problems such as the stability/instability of information flows, their quality, the timing of sequential processing, the top-down cognitive control of perceptual information, and information creation. In this framework, different types of information flow instabilities correspond to different cognitive disorders. On the other hand, the robustness of cognitive activity is related to the control of the information flow stability. We discuss these problems using both experimental and theoretical approaches, and we argue that brain activity is better understood considering information flows in the phase space of the corresponding dynamical model. In particular, we show how theory helps to understand intriguing experimental results in this matter, and how recent knowledge inspires new theoretical formalisms that can be tested with modern experimental techniques.

Dynamic stability and bifurcation analysis in fractional thermodynamics

NASA Astrophysics Data System (ADS)

Béda, Péter B.

2018-02-01

In mechanics, viscoelasticity was the first field of applications in studying geomaterials. Further possibilities arise in spatial non-locality. Non-local materials were already studied in the 1960s by several authors as a part of continuum mechanics and are still in focus of interest because of the rising importance of materials with internal micro- and nano-structure. When material instability gained more interest, non-local behavior appeared in a different aspect. The problem was concerned to numerical analysis, because then instability zones exhibited singular properties for local constitutive equations. In dynamic stability analysis, mathematical aspects of non-locality were studied by using the theory of dynamic systems. There the basic set of equations describing the behavior of continua was transformed to an abstract dynamic system consisting of differential operators acting on the perturbation field variables. Such functions should satisfy homogeneous boundary conditions and act as indicators of stability of a selected state of the body under consideration. Dynamic systems approach results in conditions for cases, when the differential operators have critical eigenvalues of zero real parts (dynamic stability or instability conditions). When the critical eigenvalues have non-trivial eigenspace, the way of loss of stability is classified as a typical (or generic) bifurcation. Our experiences show that material non-locality and the generic nature of bifurcation at instability are connected, and the basic functions of the non-trivial eigenspace can be used to determine internal length quantities of non-local mechanics. Fractional calculus is already successfully used in thermo-elasticity. In the paper, non-locality is introduced via fractional strain into the constitutive relations of various conventional types. Then, by defining dynamic systems, stability and bifurcation are studied for states of thermo-mechanical solids. Stability conditions and genericity conditions are presented for constitutive relations under consideration.

A class of stabilizing controllers for flexible multibody systems

NASA Technical Reports Server (NTRS)

Joshi, Suresh M.; Kelkar, Atul G.; Maghami, Peiman G.

1995-01-01

The problem of controlling a class of nonlinear multibody flexible space systems consisting of a flexible central body to which a number of articulated appendages are attached is considered. Collocated actuators and sensors are assumed, and global asymptotic stability of such systems is established under a nonlinear dissipative control law. The stability is shown to be robust to unmodeled dynamics and parametric uncertainties. For a special case in which the attitude motion of the central body is small, the system, although still nonlinear, is shown to be stabilized by linear dissipative control laws. Two types of linear controllers are considered: static dissipative (constant gain) and dynamic dissipative. The static dissipative control law is also shown to provide robust stability in the presence of certain classes of actuator and sensor nonlinearities and actuator dynamics. The results obtained for this special case can also be readily applied for controlling single-body linear flexible space structures. For this case, a synthesis technique for the design of a suboptimal dynamic dissipative controller is also presented. The results obtained in this paper are applicable to a broad class of multibody and single-body systems such as flexible multilink manipulators, multipayload space platforms, and space antennas. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems.

A Study of Longitudinal Control Problems at Low and Negative Damping and Stability with Emphasis on Effects of Motion Cues

NASA Technical Reports Server (NTRS)

Sadoff, Melvin; McFadden, Norman M.; Heinle, Donovan R.

1961-01-01

As part of a general investigation to determine the effects of simulator motions on pilot opinion and task performance over a wide range of vehicle longitudinal dynamics, a cooperative NASA-AMAL program was conducted on the centrifuge at Johnsville, Pennsylvania. The test parameters and measurements for this program duplicated those of earlier studies made at Ames Research Center with a variable-stability airplane and with a pitch-roll chair flight simulator. Particular emphasis was placed on the minimum basic damping and stability the pilots would accept and on the minimum dynamics they considered controllable in the event of stability-augmentation system failure. Results of the centrifuge-simulator program indicated that small positive damping was required by the pilots over most of the frequency range covered for configurations rated acceptable for emergency conditions only (e.g., failure of a pitch damper). It was shown that the pilot's tolerance for unstable dynamics was dependent primarily on the value of damping. For configurations rated acceptable for emergency operation only, the allowable instability and damping corresponded to a divergence time to double amplitude of about 1 second. Comparisons were made of centrifuge, pitch-chair and fixed-cockpit simulator tests with flight tests. Pilot ratings indicated that the effects of incomplete or spurious motion cues provided by these three modes of simulation were important only for high-frequency, lightly damped dynamics or unstable, moderately damped dynamics. The pitch- chair simulation, which provided accurate angular-acceleration cues to the pilot, compared most favorably with flight. For the centrifuge simulation, which furnished accurate normal accelerations but spurious pitching and longitudinal accelerations, there was a deterioration of pilots' opinion relative to flight results. Results of simulator studies with an analog pilot replacing the human pilot illustrated the adaptive capability of human pilots in coping with the wide range of vehicle dynamics and the control problems covered in this study. It was shown that pilot-response characteristics, deduced by the analog-pilot method, could be related to pilot opinion. Possible application of these results for predicting flight-control problems was illustrated by means of an example control-problem analysis. The results of a brief evaluation of a pencil-type side-arm controller in the centrifuge showed a considerable improvement in the pilots' ability to cope with high-frequency, low-damping dynamics, compared to results obtained with the center stick. This improvement with the pencil controller was attributed primarily to a marked reduction in the adverse effects of large and exaggerated pitching and longitudinal accelerations on pilot control precision.

Dynamic aeroelastic stability of vertical-axis wind turbines under constant wind velocity

NASA Astrophysics Data System (ADS)

Nitzsche, Fred

1994-05-01

The flutter problem associated with the blades of a class of vertical-axis wind turbines called Darrieus is studied in detail. The spinning blade is supposed to be initially curved in a particular shape characterized by a state of pure tension at the blade cross section. From this equilibrium position a three-dimensional linear perturbation pattern is superimposed to determine the dynamic aeroelastic stability of the blade in the presence of free wind speed by means of the Floquet-Lyapunov theory for periodic systems.

Orbital motion (3rd revised and enlarged edition)

NASA Astrophysics Data System (ADS)

Roy, A. E.

The fundamental principles of celestial mechanics are discussed in an introduction for students of astronomy, aerospace engineering, and geography. Chapters are devoted to the dynamic structure of the universe, coordinate and timekeeping systems, the reduction of observational data, the two-body problem, the many-body problem, general and special perturbations, and the stability and evolution of the solar system. Consideration is given to lunar theory, artificial satellites, rocket dynamics and transfer orbits, interplanetary and lunar trajectories, orbit determination and interplanetary navigation, binaries and other few-body systems, and many-body systems of stars. Diagrams, graphs, tables, and problems with solutions are provided.

Evaluation of constraint stabilization procedures for multibody dynamical systems

NASA Technical Reports Server (NTRS)

Park, K. C.; Chiou, J. C.

1987-01-01

Comparative numerical studies of four constraint treatment techniques for the simulation of general multibody dynamic systems are presented, and results are presented for the example of a classical crank mechanism and for a simplified version of the seven-link manipulator deployment problem. The staggered stabilization technique (Park, 1986) is found to yield improved accuracy and robustness over Baumgarte's (1972) technique, the singular decomposition technique (Walton and Steeves, 1969), and the penalty technique (Lotstedt, 1979). Furthermore, the staggered stabilization technique offers software modularity, and the only data each solution module needs to exchange with the other is a set of vectors plus a common module to generate the gradient matrix of the constraints, B.

Dynamics of an SAITS alcoholism model on unweighted and weighted networks

NASA Astrophysics Data System (ADS)

Huo, Hai-Feng; Cui, Fang-Fang; Xiang, Hong

2018-04-01

A novel SAITS alcoholism model on networks is introduced, in which alcoholics are divided into light problem alcoholics and heavy problem alcoholics. Susceptible individuals can enter into the compartment of heavy problem alcoholics directly by contacting with light problem alcoholics or heavy problem alcoholics and the heavy problem alcoholics who receive treatment can relapse into the compartment of heavy problem alcoholics are also considered. First, the dynamics of our model on unweighted networks, including the basic reproduction number, existence and stability of equilibria are studied. Second, the models with fixed weighted and adaptive weighted networks are introduced and investigated. At last, some simulations are presented to illustrate and extend our results. Our results show that it is very important to treat alcoholics to quit the drinking.

Control of linear uncertain systems utilizing mismatched state observers

NASA Technical Reports Server (NTRS)

Goldstein, B.

1972-01-01

The control of linear continuous dynamical systems is investigated as a problem of limited state feedback control. The equations which describe the structure of an observer are developed constrained to time-invarient systems. The optimal control problem is formulated, accounting for the uncertainty in the design parameters. Expressions for bounds on closed loop stability are also developed. The results indicate that very little uncertainty may be tolerated before divergence occurs in the recursive computation algorithms, and the derived stability bound yields extremely conservative estimates of regions of allowable parameter variations.

Robust ADP Design for Continuous-Time Nonlinear Systems With Output Constraints.

PubMed

Fan, Bo; Yang, Qinmin; Tang, Xiaoyu; Sun, Youxian

2018-06-01

In this paper, a novel robust adaptive dynamic programming (RADP)-based control strategy is presented for the optimal control of a class of output-constrained continuous-time unknown nonlinear systems. Our contribution includes a step forward beyond the usual optimal control result to show that the output of the plant is always within user-defined bounds. To achieve the new results, an error transformation technique is first established to generate an equivalent nonlinear system, whose asymptotic stability guarantees both the asymptotic stability and the satisfaction of the output restriction of the original system. Furthermore, RADP algorithms are developed to solve the transformed nonlinear optimal control problem with completely unknown dynamics as well as a robust design to guarantee the stability of the closed-loop systems in the presence of unavailable internal dynamic state. Via small-gain theorem, asymptotic stability of the original and transformed nonlinear system is theoretically guaranteed. Finally, comparison results demonstrate the merits of the proposed control policy.

State-of-the-Art Study for High-speed Deceleration and Stabilization Devices

NASA Technical Reports Server (NTRS)

Alexander, W. C.; Lau, R. A.

1966-01-01

Documented aerodynamic deployable decelerator performance data above Mach 1. 0 is presented. The state of the art of drag and stability characteristics for reentry and recovery applications is defined for a wide range of decelerator configurations. Structural and material data and other design information also are presented. Emphasis is given to presentation of basic aero, thermal, and structural design data, which points out basic problem areas and voids in existing technology. The basic problems and voids include supersonic "buzzing" of towed porous decelerators in the wake of the forebody, the complete lack of dynamic stability data, and the general lack of aerothermal data at speeds above Mach 5.

Stability of power systems coupled with market dynamics

NASA Astrophysics Data System (ADS)

Meng, Jianping

This Ph.D. thesis presented here spans two relatively independent topics. The first part, Chapter 2 is self-contained, and is dedicated to studies of new algorithms for power system state estimation. The second part, encompassing the remaining chapters, is dedicated to stability analysis of power system coupled with market dynamics. The first part of this thesis presents improved Newton's methods employing efficient vectorized calculations of higher order derivatives in power system state estimation problems. The improved algorithms are proposed based on an exact Newton's method using the second order terms. By efficiently computing an exact gain matrix, combined with a special optimal multiplier method, the new algorithms show more reliable convergence compared with the existing methods of normal equations, orthogonal decomposition, and Hachtel's sparse tableau. Our methods are able to handle ill-conditioned problems, yet show minimal penalty in computational cost for well-conditioned cases. These claims are illustrated through the standard IEEE 118 and 300 bus test examples. The second part of the thesis focuses on stability analysis of market/power systems. The work presented is motivated by an emerging problem. As the frequency of market based dispatch updates increases, there will inevitably be interaction between the dynamics of markets determining the generator dispatch commands, and the physical response of generators and network interconnections, necessitating the development of stability analysis for such coupled systems. We begin with numeric tests using different market models, with detailed machine/exciter/turbine/governor dynamics, in the New England 39 bus test system. A progression of modeling refinements are introduced, including such non-ideal effects as time delays. Electricity market parameter identification algorithms are also studied based on real time data from the PJM electricity market. Finally our power market model is augmented by optimal power flow constraints, allowing study of the so-called congestion problem. These studies show that understanding of potential modes of instability in such coupled systems is of crucial importance both in designing suitable rules for power markets, and in designing physical generator controls that are complementary to market-based dispatch.

The Next Generation of High-Speed Dynamic Stability Wind Tunnel Testing (Invited)

NASA Technical Reports Server (NTRS)

Tomek, Deborah M.; Sewall, William G.; Mason, Stan E.; Szchur, Bill W. A.

2006-01-01

Throughout industry, accurate measurement and modeling of dynamic derivative data at high-speed conditions has been an ongoing challenge. The expansion of flight envelopes and non-conventional vehicle design has greatly increased the demand for accurate prediction and modeling of vehicle dynamic behavior. With these issues in mind, NASA Langley Research Center (LaRC) embarked on the development and shakedown of a high-speed dynamic stability test technique that addresses the longstanding problem of accurately measuring dynamic derivatives outside the low-speed regime. The new test technique was built upon legacy technology, replacing an antiquated forced oscillation system, and greatly expanding the capabilities beyond classic forced oscillation testing at both low and high speeds. The modern system is capable of providing a snapshot of dynamic behavior over a periodic cycle for varying frequencies, not just a damping derivative term at a single frequency.

Topics in Modeling of Cochlear Dynamics: Computation, Response and Stability Analysis

NASA Astrophysics Data System (ADS)

Filo, Maurice G.

This thesis touches upon several topics in cochlear modeling. Throughout the literature, mathematical models of the cochlea vary according to the degree of biological realism to be incorporated. This thesis casts the cochlear model as a continuous space-time dynamical system using operator language. This framework encompasses a wider class of cochlear models and makes the dynamics more transparent and easier to analyze before applying any numerical method to discretize space. In fact, several numerical methods are investigated to study the computational efficiency of the finite dimensional realizations in space. Furthermore, we study the effects of the active gain perturbations on the stability of the linearized dynamics. The stability analysis is used to explain possible mechanisms underlying spontaneous otoacoustic emissions and tinnitus. Dynamic Mode Decomposition (DMD) is introduced as a useful tool to analyze the response of nonlinear cochlear models. Cochlear response features are illustrated using DMD which has the advantage of explicitly revealing the spatial modes of vibrations occurring in the Basilar Membrane (BM). Finally, we address the dynamic estimation problem of BM vibrations using Extended Kalman Filters (EKF). Due to the limitations of noninvasive sensing schemes, such algorithms are inevitable to estimate the dynamic behavior of a living cochlea.

Robust control with structured perturbations

NASA Technical Reports Server (NTRS)

Keel, Leehyun

1988-01-01

Two important problems in the area of control systems design and analysis are discussed. The first is the robust stability using characteristic polynomial, which is treated first in characteristic polynomial coefficient space with respect to perturbations in the coefficients of the characteristic polynomial, and then for a control system containing perturbed parameters in the transfer function description of the plant. In coefficient space, a simple expression is first given for the l(sup 2) stability margin for both monic and non-monic cases. Following this, a method is extended to reveal much larger stability region. This result has been extended to the parameter space so that one can determine the stability margin, in terms of ranges of parameter variations, of the closed loop system when the nominal stabilizing controller is given. The stability margin can be enlarged by a choice of better stabilizing controller. The second problem describes the lower order stabilization problem, the motivation of the problem is as follows. Even though the wide range of stabilizing controller design methodologies is available in both the state space and transfer function domains, all of these methods produce unnecessarily high order controllers. In practice, the stabilization is only one of many requirements to be satisfied. Therefore, if the order of a stabilizing controller is excessively high, one can normally expect to have a even higher order controller on the completion of design such as inclusion of dynamic response requirements, etc. Therefore, it is reasonable to have a lowest possible order stabilizing controller first and then adjust the controller to meet additional requirements. The algorithm for designing a lower order stabilizing controller is given. The algorithm does not necessarily produce the minimum order controller; however, the algorithm is theoretically logical and some simulation results show that the algorithm works in general.

Existence and Stability of Compressible Current-Vortex Sheets in Three-Dimensional Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Chen, Gui-Qiang; Wang, Ya-Guang

2008-03-01

Compressible vortex sheets are fundamental waves, along with shocks and rarefaction waves, in entropy solutions to multidimensional hyperbolic systems of conservation laws. Understanding the behavior of compressible vortex sheets is an important step towards our full understanding of fluid motions and the behavior of entropy solutions. For the Euler equations in two-dimensional gas dynamics, the classical linearized stability analysis on compressible vortex sheets predicts stability when the Mach number M > sqrt{2} and instability when M < sqrt{2} ; and Artola and Majda’s analysis reveals that the nonlinear instability may occur if planar vortex sheets are perturbed by highly oscillatory waves even when M > sqrt{2} . For the Euler equations in three dimensions, every compressible vortex sheet is violently unstable and this instability is the analogue of the Kelvin Helmholtz instability for incompressible fluids. The purpose of this paper is to understand whether compressible vortex sheets in three dimensions, which are unstable in the regime of pure gas dynamics, become stable under the magnetic effect in three-dimensional magnetohydrodynamics (MHD). One of the main features is that the stability problem is equivalent to a free-boundary problem whose free boundary is a characteristic surface, which is more delicate than noncharacteristic free-boundary problems. Another feature is that the linearized problem for current-vortex sheets in MHD does not meet the uniform Kreiss Lopatinskii condition. These features cause additional analytical difficulties and especially prevent a direct use of the standard Picard iteration to the nonlinear problem. In this paper, we develop a nonlinear approach to deal with these difficulties in three-dimensional MHD. We first carefully formulate the linearized problem for the current-vortex sheets to show rigorously that the magnetic effect makes the problem weakly stable and establish energy estimates, especially high-order energy estimates, in terms of the nonhomogeneous terms and variable coefficients. Then we exploit these results to develop a suitable iteration scheme of the Nash Moser Hörmander type to deal with the loss of the order of derivative in the nonlinear level and establish its convergence, which leads to the existence and stability of compressible current-vortex sheets, locally in time, in three-dimensional MHD.

Stability analysis of an implicitly defined labor market model

NASA Astrophysics Data System (ADS)

Mendes, Diana A.; Mendes, Vivaldo M.

2008-06-01

Until very recently, the pervasive existence of models exhibiting well-defined backward dynamics but ill-defined forward dynamics in economics and finance has apparently posed no serious obstacles to the analysis of their dynamics and stability, despite the problems that may arise from possible erroneous conclusions regarding theoretical considerations and policy prescriptions from such models. A large number of papers have dealt with this problem in the past by assuming the existence of symmetry between forward and backward dynamics, even in the case when the map cannot be invertible either forward or backwards. However, this procedure has been seriously questioned over the last few years in a series of papers dealing with implicit difference equations and inverse limit spaces. This paper explores the search and matching labor market model developed by Bhattacharya and Bunzel [J. Bhattacharya, H. Bunzel, Chaotic Planning Solution in the Textbook Model of Equilibrium Labor Market Search and Matching, Mimeo, Iowa State University, 2002; J. Bhattacharya, H. Bunzel, Economics Bulletin 5 (19) (2003) 1-10], with the following objectives in mind: (i) to show that chaotic dynamics may still be present in the model for acceptable parameter values, (ii) to clarify some open questions related with the admissible dynamics in the forward looking setting, by providing a rigorous proof of the existence of cyclic and chaotic dynamics through the application of tools from symbolic dynamics and inverse limit theory.

Control of nonlinear systems with applications to constrained robots and spacecraft attitude stabilization

NASA Technical Reports Server (NTRS)

Krishnan, Hariharan

1993-01-01

This thesis is organized in two parts. In Part 1, control systems described by a class of nonlinear differential and algebraic equations are introduced. A procedure for local stabilization based on a local state realization is developed. An alternative approach to local stabilization is developed based on a classical linearization of the nonlinear differential-algebraic equations. A theoretical framework is established for solving a tracking problem associated with the differential-algebraic system. First, a simple procedure is developed for the design of a feedback control law which ensures, at least locally, that the tracking error in the closed loop system lies within any given bound if the reference inputs are sufficiently slowly varying. Next, by imposing additional assumptions, a procedure is developed for the design of a feedback control law which ensures that the tracking error in the closed loop system approaches zero exponentially for reference inputs which are not necessarily slowly varying. The control design methodologies are used for simultaneous force and position control in constrained robot systems. The differential-algebraic equations are shown to characterize the slow dynamics of a certain nonlinear control system in nonstandard singularly perturbed form. In Part 2, the attitude stabilization (reorientation) of a rigid spacecraft using only two control torques is considered. First, the case of momentum wheel actuators is considered. The complete spacecraft dynamics are not controllable. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but a discontinuous feedback control strategy is constructed. Next, the case of gas jet actuators is considered. If the uncontrolled principal axis is not an axis of symmetry, the complete spacecraft dynamics are small time locally controllable. However, the spacecraft attitude cannot be asymptotically stabilized using continuous feedback, but a discontinuous stabilizing feedback control strategy is constructed. If the uncontrolled principal axis is an axis of symmetry, the complete spacecraft dynamics cannot be stabilized. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but again a discontinuous feedback control strategy is constructed.

The numerical dynamic for highly nonlinear partial differential equations

NASA Technical Reports Server (NTRS)

Lafon, A.; Yee, H. C.

1992-01-01

Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.

Asymptotic theory of neutral stability of the Couette flow of a vibrationally excited gas

NASA Astrophysics Data System (ADS)

Grigor'ev, Yu. N.; Ershov, I. V.

2017-01-01

An asymptotic theory of the neutral stability curve for a supersonic plane Couette flow of a vibrationally excited gas is developed. The initial mathematical model consists of equations of two-temperature viscous gas dynamics, which are used to derive a spectral problem for a linear system of eighth-order ordinary differential equations within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the "inviscid" and "viscous" parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. In particular, the critical Reynolds number increases with excitation enhancement, and the neutral stability curve is shifted toward the domain of higher wave numbers. This is also confirmed by means of solving an asymptotic equation for the critical Reynolds number at the Mach number M ≤ 4.

Comprehensive rotorcraft analysis methods

NASA Technical Reports Server (NTRS)

Stephens, Wendell B.; Austin, Edward E.

1988-01-01

The development and application of comprehensive rotorcraft analysis methods in the field of rotorcraft technology are described. These large scale analyses and the resulting computer programs are intended to treat the complex aeromechanical phenomena that describe the behavior of rotorcraft. They may be used to predict rotor aerodynamics, acoustic, performance, stability and control, handling qualities, loads and vibrations, structures, dynamics, and aeroelastic stability characteristics for a variety of applications including research, preliminary and detail design, and evaluation and treatment of field problems. The principal comprehensive methods developed or under development in recent years and generally available to the rotorcraft community because of US Army Aviation Research and Technology Activity (ARTA) sponsorship of all or part of the software systems are the Rotorcraft Flight Simulation (C81), Dynamic System Coupler (DYSCO), Coupled Rotor/Airframe Vibration Analysis Program (SIMVIB), Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dynamics (CAMRAD), General Rotorcraft Aeromechanical Stability Program (GRASP), and Second Generation Comprehensive Helicopter Analysis System (2GCHAS).

The dynamics and control of a spherical robot with an internal omniwheel platform

NASA Astrophysics Data System (ADS)

Karavaev, Yury L.; Kilin, Alexander A.

2015-03-01

This paper deals with the problem of a spherical robot propelled by an internal omniwheel platform and rolling without slipping on a plane. The problem of control of spherical robot motion along an arbitrary trajectory is solved within the framework of a kinematic model and a dynamic model. A number of particular cases of motion are identified, and their stability is investigated. An algorithm for constructing elementary maneuvers (gaits) providing the transition from one steady-state motion to another is presented for the dynamic model. A number of experiments have been carried out confirming the adequacy of the proposed kinematic model.

Active synchronization between two different chaotic dynamical system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maheri, M.; Arifin, N. Md; Ismail, F.

2015-05-15

In this paper we investigate on the synchronization problem between two different chaotic dynamical system based on the Lyapunov stability theorem by using nonlinear control functions. Active control schemes are used for synchronization Liu system as drive and Rossler system as response. Numerical simulation by using Maple software are used to show effectiveness of the proposed schemes.

Results of the Workshop on Two-Phase Flow, Fluid Stability and Dynamics: Issues in Power, Propulsion, and Advanced Life Support Systems

NASA Technical Reports Server (NTRS)

McQuillen, John; Rame, Enrique; Kassemi, Mohammad; Singh, Bhim; Motil, Brian

2003-01-01

The Two-phase Flow, Fluid Stability and Dynamics Workshop was held on May 15, 2003 in Cleveland, Ohio to define a coherent scientific research plan and roadmap that addresses the multiphase fluid problems associated with NASA s technology development program. The workshop participants, from academia, industry and government, prioritized various multiphase issues and generated a research plan and roadmap to resolve them. This report presents a prioritization of the various multiphase flow and fluid stability phenomena related primarily to power, propulsion, fluid and thermal management and advanced life support; and a plan to address these issues in a logical and timely fashion using analysis, ground-based and space-flight experiments.

A study analysis of cable-body systems totally immersed in a fluid stream

NASA Technical Reports Server (NTRS)

Delaurier, J. D.

1972-01-01

A general stability analysis of a cable-body system immersed in a fluid stream is presented. The analytical portion of this analysis treats the system as being essentially a cable problem, with the body dynamics giving the end conditions. The mathematical form of the analysis consists of partial differential wave equations, with the end and auxiliary conditions being determined from the body equations of motion. The equations uncouple to give a lateral problem and a longitudinal problem as in first order airplane dynamics. A series of tests on a tethered wind tunnel model provide a comparison of the theory with experiment.

Application of GRASP (General Rotorcraft Aeromechanical Stability Program) to nonlinear analysis of a cantilever beam

NASA Technical Reports Server (NTRS)

Hinnant, Howard E.; Hodges, Dewey H.

1987-01-01

The General Rotorcraft Aeromechanical Stability Program (GRASP) was developed to analyse the steady-state and linearized dynamic behavior of rotorcraft in hovering and axial flight conditions. Because of the nature of problems GRASP was created to solve, the geometrically nonlinear behavior of beams is one area in which the program must perform well in order to be of any value. Numerical results obtained from GRASP are compared to both static and dynamic experimental data obtained for a cantilever beam undergoing large displacements and rotations caused by deformations. The correlation is excellent in all cases.

Missile Interceptor Guidance System Technology (La Technologie Pour Les Systemes De Guidage Des Missiles Intercepteurs (DE Missiles Ou D’Aeronefs)

DTIC Science & Technology

1990-01-01

robustness of feedback systems with structured uncertainty. Theorem: Robust Stability Fu(G,A) stable V AA iff suP (Gll(JW))Sl. Theorem: Robust ...through a gain KR. The addition of other dynamics and feedback paths creates stabilization problems for this simple roll attitude feedback control...characteristics are most useful to the designer when examined in the frequency domain. Both relative stability and robustness can be determined from an

Damping seals for turbomachinery

NASA Technical Reports Server (NTRS)

Vonpragenau, G. L.

1985-01-01

Rotor whirl stabilization of high performance turbomachinery which operates at supercritical speed is discussed. Basic whirl driving forces are reviewed. Stabilization and criteria are discussed. Damping seals are offered as a solution to whirl and high vibration problems. Concept, advantages, retrofitting, and limits of damping seals are explained. Dynamic and leakage properties are shown to require a rough stator surface for stability and efficiency. Typical seal characteristics are given for the case of the high pressure oxidizer turbopump of the Space Shuttle. Ways of implementation and bearing load effects are discussed.

Selected Problems in Nonlinear Dynamics and Sociophysics

NASA Astrophysics Data System (ADS)

Westley, Alexandra Renee

This Ph.D. dissertation focuses on a collection of problems on the dynamical behavior of nonlinear many-body systems, drawn from two substantially different areas. First, the dynamical behavior seen in strongly nonlinear lattices such as in the Fermi-Pasta-Ulam-Tsingou (FPUT) system (part I) and second, time evolution behavior of interacting living objects which can be broadly considered as sociophysics systems (part II). The studies on FPUT-like systems will comprise of five chapters, dedicated to the properties of solitary and anti-solitary waves in the system, how localized nonlinear excitations decay and spread throughout these lattices, how two colliding solitary waves can precipitate highly localized and stable excitations, a possible alternative way to view these localized excitations through Duffing oscillators, and finally an exploration of parametric resonance in an FPUT-like lattice. Part II consists of two problems in the context of sociophysics. I use molecular dynamics inspired simulations to study the size and the stability of social groups of chimpanzees (such as those seen in central Africa) and compare the results with existing observations on the stability of chimpanzee societies. Secondly, I use an agent-based model to simulate land battles between an intelligent army and an insurgency when both have access to equally powerful weaponry. The study considers genetic algorithm based adaptive strategies to infer the strategies needed for the intelligent army to win the battles.

Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

NASA Astrophysics Data System (ADS)

Lukyanenko, D. V.; Shishlenin, M. A.; Volkov, V. T.

2018-01-01

We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. I - The dynamics of time discretization and its implications for algorithm development in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.; Griffiths, D. F.

1991-01-01

Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

Dynamic Stability Analysis of Linear Time-varying Systems via an Extended Modal Identification Approach

NASA Astrophysics Data System (ADS)

Ma, Zhisai; Liu, Li; Zhou, Sida; Naets, Frank; Heylen, Ward; Desmet, Wim

2017-03-01

The problem of linear time-varying(LTV) system modal analysis is considered based on time-dependent state space representations, as classical modal analysis of linear time-invariant systems and current LTV system modal analysis under the "frozen-time" assumption are not able to determine the dynamic stability of LTV systems. Time-dependent state space representations of LTV systems are first introduced, and the corresponding modal analysis theories are subsequently presented via a stability-preserving state transformation. The time-varying modes of LTV systems are extended in terms of uniqueness, and are further interpreted to determine the system's stability. An extended modal identification is proposed to estimate the time-varying modes, consisting of the estimation of the state transition matrix via a subspace-based method and the extraction of the time-varying modes by the QR decomposition. The proposed approach is numerically validated by three numerical cases, and is experimentally validated by a coupled moving-mass simply supported beam experimental case. The proposed approach is capable of accurately estimating the time-varying modes, and provides a new way to determine the dynamic stability of LTV systems by using the estimated time-varying modes.

ISS method for coordination control of nonlinear dynamical agents under directed topology.

PubMed

Wang, Xiangke; Qin, Jiahu; Yu, Changbin

2014-10-01

The problems of coordination of multiagent systems with second-order locally Lipschitz continuous nonlinear dynamics under directed interaction topology are investigated in this paper. A completely nonlinear input-to-state stability (ISS)-based framework, drawing on ISS methods, with the aid of results from graph theory, matrix theory, and the ISS cyclic-small-gain theorem, is proposed for the coordination problem under directed topology, which can effectively tackle the technical challenges caused by locally Lipschitz continuous dynamics. Two coordination problems, i.e., flocking with a virtual leader and containment control, are considered. For both problems, it is assumed that only a portion of the agents can obtain the information from the leader(s). For the first problem, the proposed strategy is shown effective in driving a group of nonlinear dynamical agents reach the prespecified geometric pattern under the condition that at least one agent in each strongly connected component of the information-interconnection digraph with zero in-degree has access to the state information of the virtual leader; and the strategy proposed for the second problem can guarantee the nonlinear dynamical agents moving to the convex hull spanned by the positions of multiple leaders under the condition that for each agent there exists at least one leader that has a directed path to this agent.

Dynamic remedial action scheme using online transient stability analysis

NASA Astrophysics Data System (ADS)

Shrestha, Arun

Economic pressure and environmental factors have forced the modern power systems to operate closer to their stability limits. However, maintaining transient stability is a fundamental requirement for the operation of interconnected power systems. In North America, power systems are planned and operated to withstand the loss of any single or multiple elements without violating North American Electric Reliability Corporation (NERC) system performance criteria. For a contingency resulting in the loss of multiple elements (Category C), emergency transient stability controls may be necessary to stabilize the power system. Emergency control is designed to sense abnormal conditions and subsequently take pre-determined remedial actions to prevent instability. Commonly known as either Remedial Action Schemes (RAS) or as Special/System Protection Schemes (SPS), these emergency control approaches have been extensively adopted by utilities. RAS are designed to address specific problems, e.g. to increase power transfer, to provide reactive support, to address generator instability, to limit thermal overloads, etc. Possible remedial actions include generator tripping, load shedding, capacitor and reactor switching, static VAR control, etc. Among various RAS types, generation shedding is the most effective and widely used emergency control means for maintaining system stability. In this dissertation, an optimal power flow (OPF)-based generation-shedding RAS is proposed. This scheme uses online transient stability calculation and generator cost function to determine appropriate remedial actions. For transient stability calculation, SIngle Machine Equivalent (SIME) technique is used, which reduces the multimachine power system model to a One-Machine Infinite Bus (OMIB) equivalent and identifies critical machines. Unlike conventional RAS, which are designed using offline simulations, online stability calculations make the proposed RAS dynamic and adapting to any power system configuration and operating state. The generation-shedding cost is calculated using pre-RAS and post-RAS OPF costs. The criteria for selecting generators to trip is based on the minimum cost rather than minimum amount of generation to shed. For an unstable Category C contingency, the RAS control action that results in stable system with minimum generation shedding cost is selected among possible candidate solutions. The RAS control actions update whenever there is a change in operating condition, system configuration, or cost functions. The effectiveness of the proposed technique is demonstrated by simulations on the IEEE 9-bus system, the IEEE 39-bus system, and IEEE 145-bus system. This dissertation also proposes an improved, yet relatively simple, technique for solving Transient Stability-Constrained Optimal Power Flow (TSC-OPF) problem. Using the SIME method, the sets of dynamic and transient stability constraints are reduced to a single stability constraint, decreasing the overall size of the optimization problem. The transient stability constraint is formulated using the critical machines' power at the initial time step, rather than using the machine rotor angles. This avoids the addition of machine steady state stator algebraic equations in the conventional OPF algorithm. A systematic approach to reach an optimal solution is developed by exploring the quasi-linear behavior of critical machine power and stability margin. The proposed method shifts critical machines active power based on generator costs using an OPF algorithm. Moreover, the transient stability limit is based on stability margin, and not on a heuristically set limit on OMIB rotor angle. As a result, the proposed TSC-OPF solution is more economical and transparent. The proposed technique enables the use of fast and robust commercial OPF tool and time-domain simulation software for solving large scale TSC-OPF problem, which makes the proposed method also suitable for real-time application.

New broadband square-law detector

NASA Technical Reports Server (NTRS)

Reid, M. S.; Gardner, R. A.; Stelzried, C. T.

1975-01-01

Compact device has wide dynamic range, accurate square-law response, good thermal stability, high-level dc output with immunity to ground-loop problems, ability to insert known time constants for radiometric applications, and fast response times compatible with computer systems.

Stability of Contact Lines in Fluids: 2D Stokes Flow

NASA Astrophysics Data System (ADS)

Guo, Yan; Tice, Ian

2018-02-01

In an effort to study the stability of contact lines in fluids, we consider the dynamics of an incompressible viscous Stokes fluid evolving in a two-dimensional open-top vessel under the influence of gravity. This is a free boundary problem: the interface between the fluid in the vessel and the air above (modeled by a trivial fluid) is free to move and experiences capillary forces. The three-phase interface where the fluid, air, and solid vessel wall meet is known as a contact point, and the angle formed between the free interface and the vessel is called the contact angle. We consider a model of this problem that allows for fully dynamic contact points and angles. We develop a scheme of a priori estimates for the model, which then allow us to show that for initial data sufficiently close to equilibrium, the model admits global solutions that decay to equilibrium exponentially quickly.

Nonlinear neural control with power systems applications

NASA Astrophysics Data System (ADS)

Chen, Dingguo

1998-12-01

Extensive studies have been undertaken on the transient stability of large interconnected power systems with flexible ac transmission systems (FACTS) devices installed. Varieties of control methodologies have been proposed to stabilize the postfault system which would otherwise eventually lose stability without a proper control. Generally speaking, regular transient stability is well understood, but the mechanism of load-driven voltage instability or voltage collapse has not been well understood. The interaction of generator dynamics and load dynamics makes synthesis of stabilizing controllers even more challenging. There is currently increasing interest in the research of neural networks as identifiers and controllers for dealing with dynamic time-varying nonlinear systems. This study focuses on the development of novel artificial neural network architectures for identification and control with application to dynamic electric power systems so that the stability of the interconnected power systems, following large disturbances, and/or with the inclusion of uncertain loads, can be largely enhanced, and stable operations are guaranteed. The latitudinal neural network architecture is proposed for the purpose of system identification. It may be used for identification of nonlinear static/dynamic loads, which can be further used for static/dynamic voltage stability analysis. The properties associated with this architecture are investigated. A neural network methodology is proposed for dealing with load modeling and voltage stability analysis. Based on the neural network models of loads, voltage stability analysis evolves, and modal analysis is performed. Simulation results are also provided. The transient stability problem is studied with consideration of load effects. The hierarchical neural control scheme is developed. Trajectory-following policy is used so that the hierarchical neural controller performs as almost well for non-nominal cases as they do for the nominal cases. The adaptive hierarchical neural control scheme is also proposed to deal with the time-varying nature of loads. Further, adaptive neural control, which is based on the on-line updating of the weights and biases of the neural networks, is studied. Simulations provided on the faulted power systems with unknown loads suggest that the proposed adaptive hierarchical neural control schemes should be useful for practical power applications.

How can periodic orbits puzzle out the coexistence of terrestrial planets with giant eccentric ones?

NASA Astrophysics Data System (ADS)

Antoniadou, K. I.; Libert, A.-S.

2017-09-01

Hitherto unprecedented detections of exoplanets have been triggered by missions and ground based telescopes. The quest of ``exo-Earths'' has become intriguing and the long-term stability of planetary orbits is a crucial factor for the biosphere to evolve. Planets in mean-motion resonances (MMRs) prompt the investigation of the dynamics in the framework of the three-body problem, where the families of stable periodic orbits constitute the backbone of stability domains in phase space. In this talk, we address the question of the possible coexistence of terrestrial planets with a giant companion on circular or eccentric orbit and explore the extent of the stability regions, when both the eccentricity of the outer giant planet and the semi-major axis of the inner terrestrial one vary, i.e. we investigate both non-resonant and resonant configurations. The families of periodic orbits in the restricted three-body problem are computed for the 3/2, 2/1, 5/2, 3/1, 4/1 and 5/1 MMRs. We then construct maps of dynamical stability (DS-maps) to identify the boundaries of the stability domains where such a coexistence is allowed. Guided by the periodic orbits, we delve into regular motion in phase space and propose the essential values of the orbital elements, in order for such configurations to survive long time spans and hence, for observations to be complemented or revised.

Intelligent on-line fault tolerant control for unanticipated catastrophic failures.

PubMed

Yen, Gary G; Ho, Liang-Wei

2004-10-01

As dynamic systems become increasingly complex, experience rapidly changing environments, and encounter a greater variety of unexpected component failures, solving the control problems of such systems is a grand challenge for control engineers. Traditional control design techniques are not adequate to cope with these systems, which may suffer from unanticipated dynamic failures. In this research work, we investigate the on-line fault tolerant control problem and propose an intelligent on-line control strategy to handle the desired trajectories tracking problem for systems suffering from various unanticipated catastrophic faults. Through theoretical analysis, the sufficient condition of system stability has been derived and two different on-line control laws have been developed. The approach of the proposed intelligent control strategy is to continuously monitor the system performance and identify what the system's current state is by using a fault detection method based upon our best knowledge of the nominal system and nominal controller. Once a fault is detected, the proposed intelligent controller will adjust its control signal to compensate for the unknown system failure dynamics by using an artificial neural network as an on-line estimator to approximate the unexpected and unknown failure dynamics. The first control law is derived directly from the Lyapunov stability theory, while the second control law is derived based upon the discrete-time sliding mode control technique. Both control laws have been implemented in a variety of failure scenarios to validate the proposed intelligent control scheme. The simulation results, including a three-tank benchmark problem, comply with theoretical analysis and demonstrate a significant improvement in trajectory following performance based upon the proposed intelligent control strategy.

Spectral analysis of point-vortex dynamics: first application to vortex polygons in a circular domain

NASA Astrophysics Data System (ADS)

Speetjens, M. F. M.; Meleshko, V. V.; van Heijst, G. J. F.

2014-06-01

The present study addresses the classical problem of the dynamics and stability of a cluster of N-point vortices of equal strength arranged in a polygonal configuration (‘N-vortex polygons’). In unbounded domains, such N-vortex polygons are unconditionally stable for N\\leqslant 7. Confinement in a circular domain tightens the stability conditions to N\\leqslant 6 and a maximum polygon size relative to the domain radius. This work expands on existing studies on stability and integrability by a first giving an exploratory spectral analysis of the dynamics of N vortex polygons in circular domains. Key to this is that the spectral signature of the time evolution of vortex positions reflects their qualitative behaviour. Expressing vortex motion by a generic evolution operator (the so-called Koopman operator) provides a rigorous framework for such spectral analyses. This paves the way to further differentiation and classification of point-vortex behaviour beyond stability and integrability. The concept of Koopman-based spectral analysis is demonstrated for N-vortex polygons. This reveals that conditional stability can be seen as a local form of integrability and confirms an important generic link between spectrum and dynamics: discrete spectra imply regular (quasi-periodic) motion; continuous (sub-)spectra imply chaotic motion. Moreover, this exposes rich nonlinear dynamics as intermittency between regular and chaotic motion and quasi-coherent structures formed by chaotic vortices. Dedicated to the memory of Slava Meleshko, a dear friend and inspiring colleague.

Adaptive Fuzzy Control Design for Stochastic Nonlinear Switched Systems With Arbitrary Switchings and Unmodeled Dynamics.

PubMed

Li, Yongming; Sui, Shuai; Tong, Shaocheng

2017-02-01

This paper deals with the problem of adaptive fuzzy output feedback control for a class of stochastic nonlinear switched systems. The controlled system in this paper possesses unmeasured states, completely unknown nonlinear system functions, unmodeled dynamics, and arbitrary switchings. A state observer which does not depend on the switching signal is constructed to tackle the unmeasured states. Fuzzy logic systems are employed to identify the completely unknown nonlinear system functions. Based on the common Lyapunov stability theory and stochastic small-gain theorem, a new robust adaptive fuzzy backstepping stabilization control strategy is developed. The stability of the closed-loop system on input-state-practically stable in probability is proved. The simulation results are given to verify the efficiency of the proposed fuzzy adaptive control scheme.

Event-Based Robust Control for Uncertain Nonlinear Systems Using Adaptive Dynamic Programming.

PubMed

Zhang, Qichao; Zhao, Dongbin; Wang, Ding

2018-01-01

In this paper, the robust control problem for a class of continuous-time nonlinear system with unmatched uncertainties is investigated using an event-based control method. First, the robust control problem is transformed into a corresponding optimal control problem with an augmented control and an appropriate cost function. Under the event-based mechanism, we prove that the solution of the optimal control problem can asymptotically stabilize the uncertain system with an adaptive triggering condition. That is, the designed event-based controller is robust to the original uncertain system. Note that the event-based controller is updated only when the triggering condition is satisfied, which can save the communication resources between the plant and the controller. Then, a single network adaptive dynamic programming structure with experience replay technique is constructed to approach the optimal control policies. The stability of the closed-loop system with the event-based control policy and the augmented control policy is analyzed using the Lyapunov approach. Furthermore, we prove that the minimal intersample time is bounded by a nonzero positive constant, which excludes Zeno behavior during the learning process. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed control scheme.

Decentralized Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Robotic Walking.

PubMed

Hamed, Kaveh Akbari; Gregg, Robert D

2016-07-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg.

Decentralized Feedback Controllers for Robust Stabilization of Periodic Orbits of Hybrid Systems: Application to Bipedal Walking.

PubMed

Hamed, Kaveh Akbari; Gregg, Robert D

2017-07-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially and robustly stabilize periodic orbits for hybrid dynamical systems against possible uncertainties in discrete-time phases. The algorithm assumes a family of parameterized and decentralized nonlinear controllers to coordinate interconnected hybrid subsystems based on a common phasing variable. The exponential and [Formula: see text] robust stabilization problems of periodic orbits are translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities. By investigating the properties of the Poincaré map, some sufficient conditions for the convergence of the iterative algorithm are presented. The power of the algorithm is finally demonstrated through designing a set of robust stabilizing local nonlinear controllers for walking of an underactuated 3D autonomous bipedal robot with 9 degrees of freedom, impact model uncertainties, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg.

Decentralized Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Robotic Walking*

PubMed Central

Hamed, Kaveh Akbari; Gregg, Robert D.

2016-01-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg. PMID:27990059

Decentralized Feedback Controllers for Robust Stabilization of Periodic Orbits of Hybrid Systems: Application to Bipedal Walking

PubMed Central

Hamed, Kaveh Akbari; Gregg, Robert D.

2016-01-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially and robustly stabilize periodic orbits for hybrid dynamical systems against possible uncertainties in discrete-time phases. The algorithm assumes a family of parameterized and decentralized nonlinear controllers to coordinate interconnected hybrid subsystems based on a common phasing variable. The exponential and H2 robust stabilization problems of periodic orbits are translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities. By investigating the properties of the Poincaré map, some sufficient conditions for the convergence of the iterative algorithm are presented. The power of the algorithm is finally demonstrated through designing a set of robust stabilizing local nonlinear controllers for walking of an underactuated 3D autonomous bipedal robot with 9 degrees of freedom, impact model uncertainties, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg. PMID:28959117

Use of satellite data and modeling to assess the influence of stratospheric processes on the troposphere

NASA Astrophysics Data System (ADS)

Nathan, Terrence

1991-09-01

Over the past forty years, numerous linear stability studies have been performed in order to explain the origin and structure of observed waves in the atmosphere. Of these studies, only a small fraction have considered the stability of time-dependent, zonally varying flow or the influence of radiative-photochemical feedbacks on the stability of zonally uniform flow. The stability of such flows is described, and these flows may yield important information concerning the origin, structure, and transient time scales of free waves in the atmosphere. During the period 1990 to 1991, a beta-plane model that couples radiative transfer, ozone advection, and ozone photochemistry with the quasigeostrophic dynamical circulation was developed in order to study the diabatic effects of Newtonian cooling and ozone-dynamics interaction on the linear stability of free planetary waves in the atmosphere. The stability of a basic state consisting of a westward-moving wave and a zonal mean jet was examined using a linearized, nondivergent barotropic model on sphere. The sensitivity of the stability of the flow to the strength and structure of the zonal jet was emphasized. The current research is focused on the following problems: (1) examination of the finite amplitude interactions among radiation, ozone, and dynamics; and (2) examination of the role of seasonal forcing in short-term climate variability. The plans for next year are presented.

A dynamic feedforward neural network based on gaussian particle swarm optimization and its application for predictive control.

PubMed

Han, Min; Fan, Jianchao; Wang, Jun

2011-09-01

A dynamic feedforward neural network (DFNN) is proposed for predictive control, whose adaptive parameters are adjusted by using Gaussian particle swarm optimization (GPSO) in the training process. Adaptive time-delay operators are added in the DFNN to improve its generalization for poorly known nonlinear dynamic systems with long time delays. Furthermore, GPSO adopts a chaotic map with Gaussian function to balance the exploration and exploitation capabilities of particles, which improves the computational efficiency without compromising the performance of the DFNN. The stability of the particle dynamics is analyzed, based on the robust stability theory, without any restrictive assumption. A stability condition for the GPSO+DFNN model is derived, which ensures a satisfactory global search and quick convergence, without the need for gradients. The particle velocity ranges could change adaptively during the optimization process. The results of a comparative study show that the performance of the proposed algorithm can compete with selected algorithms on benchmark problems. Additional simulation results demonstrate the effectiveness and accuracy of the proposed combination algorithm in identifying and controlling nonlinear systems with long time delays.

A Technique for Measuring Rotocraft Dynamic Stability in the 40 by 80 Foot Wind Tunnel

NASA Technical Reports Server (NTRS)

Gupta, N. K.; Bohn, J. G.

1977-01-01

An on-line technique is described for the measurement of tilt rotor aircraft dynamic stability in the Ames 40- by 80-Foot Wind Tunnel. The technique is based on advanced system identification methodology and uses the instrumental variables approach. It is particulary applicable to real time estimation problems with limited amounts of noise-contaminated data. Several simulations are used to evaluate the algorithm. Estimated natural frequencies and damping ratios are compared with simulation values. The algorithm is also applied to wind tunnel data in an off-line mode. The results are used to develop preliminary guidelines for effective use of the algorithm.

Stability of Solutions to Classes of Traveling Salesman Problems.

PubMed

Niendorf, Moritz; Kabamba, Pierre T; Girard, Anouck R

2016-04-01

By performing stability analysis on an optimal tour for problems belonging to classes of the traveling salesman problem (TSP), this paper derives margins of optimality for a solution with respect to disturbances in the problem data. Specifically, we consider the asymmetric sequence-dependent TSP, where the sequence dependence is driven by the dynamics of a stack. This is a generalization of the symmetric non sequence-dependent version of the TSP. Furthermore, we also consider the symmetric sequence-dependent variant and the asymmetric non sequence-dependent variant. Amongst others these problems have applications in logistics and unmanned aircraft mission planning. Changing external conditions such as traffic or weather may alter task costs, which can render an initially optimal itinerary suboptimal. Instead of optimizing the itinerary every time task costs change, stability criteria allow for fast evaluation of whether itineraries remain optimal. This paper develops a method to compute stability regions for the best tour in a set of tours for the symmetric TSP and extends the results to the asymmetric problem as well as their sequence-dependent counterparts. As the TSP is NP-hard, heuristic methods are frequently used to solve it. The presented approach is also applicable to analyze stability regions for a tour obtained through application of the k -opt heuristic with respect to the k -neighborhood. A dimensionless criticality metric for edges is proposed, such that a high criticality of an edge indicates that the optimal tour is more susceptible to cost changes in that edge. Multiple examples demonstrate the application of the developed stability computation method as well as the edge criticality measure that facilitates an intuitive assessment of instances of the TSP.

Interface stability in a slowly rotating low-gravity tank Theory

NASA Technical Reports Server (NTRS)

Gans, R. F.; Leslie, F. W.

1986-01-01

The equilibrium configuration of a bubble in a rotating liquid confined by flat axial boundaries (baffles) is found. The maximum baffle spacing assuring bubble confinement is bounded from above by the natural length of a bubble in an infinite medium under the same conditions. Effects of nonzero contact angle are minimal. The problem of dynamic stability is posed. It can be solved in the limit of rapid rotation, for which the bubble is a long cylinder. Instability is to axisymmetric perturbations; nonaxisymmetric perturbations are stable. The stability criterion agrees with earlier results.

Study of the Dynamics of a Pressurized Reactor as Integral Unit for Naval Propulsion; STUDIO DELLA DINAMICA DI UN REATTORE PRESSURIZZATO AD UNITA INTEGRALE PER PROPULSIONE NAVALE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gilardi, E.; Cimorelli, L.

1963-07-01

The dynamic behavior of an integrated, pressurizedwater reactor with natural circulation was investigated both by analog computer techniques and a simplified analytical approach. Hydraulic instabilities due to the core or riser were considered, as well as overall stability and problems arising from heavy sea conditions. (auth)

Synchronization in dynamical networks with unconstrained structure switching

NASA Astrophysics Data System (ADS)

del Genio, Charo I.; Romance, Miguel; Criado, Regino; Boccaletti, Stefano

2015-12-01

We provide a rigorous solution to the problem of constructing a structural evolution for a network of coupled identical dynamical units that switches between specified topologies without constraints on their structure. The evolution of the structure is determined indirectly from a carefully built transformation of the eigenvector matrices of the coupling Laplacians, which are guaranteed to change smoothly in time. In turn, this allows one to extend the master stability function formalism, which can be used to assess the stability of a synchronized state. This approach is independent from the particular topologies that the network visits, and is not restricted to commuting structures. Also, it does not depend on the time scale of the evolution, which can be faster than, comparable to, or even secular with respect to the dynamics of the units.

A unified perspective on robot control - The energy Lyapunov function approach

NASA Technical Reports Server (NTRS)

Wen, John T.

1990-01-01

A unified framework for the stability analysis of robot tracking control is presented. By using an energy-motivated Lyapunov function candidate, the closed-loop stability is shown for a large family of control laws sharing a common structure of proportional and derivative feedback and a model-based feedforward. The feedforward can be zero, partial or complete linearized dynamics, partial or complete nonlinear dynamics, or linearized or nonlinear dynamics with parameter adaptation. As result, the dichotomous approaches to the robot control problem based on the open-loop linearization and nonlinear Lyapunov analysis are both included in this treatment. Furthermore, quantitative estimates of the trade-offs between different schemes in terms of the tracking performance, steady state error, domain of convergence, realtime computation load and required a prior model information are derived.

Non-Static error tracking control for near space airship loading platform

NASA Astrophysics Data System (ADS)

Ni, Ming; Tao, Fei; Yang, Jiandong

2018-01-01

A control scheme based on internal model with non-static error is presented against the uncertainty of the near space airship loading platform system. The uncertainty in the tracking table is represented as interval variations in stability and control derivatives. By formulating the tracking problem of the uncertainty system as a robust state feedback stabilization problem of an augmented system, sufficient condition for the existence of robust tracking controller is derived in the form of linear matrix inequality (LMI). Finally, simulation results show that the new method not only has better anti-jamming performance, but also improves the dynamic performance of the high-order systems.

Two-craft Coulomb formation study about circular orbits and libration points

NASA Astrophysics Data System (ADS)

Inampudi, Ravi Kishore

This dissertation investigates the dynamics and control of a two-craft Coulomb formation in circular orbits and at libration points; it addresses relative equilibria, stability and optimal reconfigurations of such formations. The relative equilibria of a two-craft tether formation connected by line-of-sight elastic forces moving in circular orbits and at libration points are investigated. In circular Earth orbits and Earth-Moon libration points, the radial, along-track, and orbit normal great circle equilibria conditions are found. An example of modeling the tether force using Coulomb force is discussed. Furthermore, the non-great-circle equilibria conditions for a two-spacecraft tether structure in circular Earth orbit and at collinear libration points are developed. Then the linearized dynamics and stability analysis of a 2-craft Coulomb formation at Earth-Moon libration points are studied. For orbit-radial equilibrium, Coulomb forces control the relative distance between the two satellites. The gravity gradient torques on the formation due to the two planets help stabilize the formation. Similar analysis is performed for along-track and orbit-normal relative equilibrium configurations. Where necessary, the craft use a hybrid thrusting-electrostatic actuation system. The two-craft dynamics at the libration points provide a general framework with circular Earth orbit dynamics forming a special case. In the presence of differential solar drag perturbations, a Lyapunov feedback controller is designed to stabilize a radial equilibrium, two-craft Coulomb formation at collinear libration points. The second part of the thesis investigates optimal reconfigurations of two-craft Coulomb formations in circular Earth orbits by applying nonlinear optimal control techniques. The objective of these reconfigurations is to maneuver the two-craft formation between two charged equilibria configurations. The reconfiguration of spacecraft is posed as an optimization problem using the calculus of variations approach. The optimality criteria are minimum time, minimum acceleration of the separation distance, minimum Coulomb and electric propulsion fuel usage, and minimum electrical power consumption. The continuous time problem is discretized using a pseudospectral method, and the resulting finite dimensional problem is solved using a sequential quadratic programming algorithm. The software package, DIDO, implements this approach. This second part illustrates how pseudospectral methods significantly simplify the solution-finding process.

A Gait Generation for an Unlocked Joint Failure of the Quadruped Robot with Balance Weight

NASA Astrophysics Data System (ADS)

Cho, C. H.; Min, B. C.; Kim, D. H.

Assurance of a stability margin for a stabilized gait is the most important issue for the quadruped robot. Although various studies for dynamic stability of the quadruped robot have been studied, problems in which one of the legs has an unlocked joint failure haven’t been relatively studied so far. In this paper, assurance of stability margin for the unlocked joint failure of the quadruped robot is suggested by using gait stabilization and a control method of the moment of inertia. Then, efficiency of BW (balance weight) will be experimentally verified by comparing the two types of robot; one is equipped with the BW, the other is not equipped with BW.

Control-oriented modeling and adaptive backstepping control for a nonminimum phase hypersonic vehicle.

PubMed

Ye, Linqi; Zong, Qun; Tian, Bailing; Zhang, Xiuyun; Wang, Fang

2017-09-01

In this paper, the nonminimum phase problem of a flexible hypersonic vehicle is investigated. The main challenge of nonminimum phase is the prevention of dynamic inversion methods to nonlinear control design. To solve this problem, we make research on the relationship between nonminimum phase and backstepping control, finding that a stable nonlinear controller can be obtained by changing the control loop on the basis of backstepping control. By extending the control loop to cover the internal dynamics in it, the internal states are directly controlled by the inputs and simultaneously serve as virtual control for the external states, making it possible to guarantee output tracking as well as internal stability. Then, based on the extended control loop, a simplified control-oriented model is developed to enable the applicability of adaptive backstepping method. It simplifies the design process and releases some limitations caused by direct use of the no simplified control-oriented model. Next, under proper assumptions, asymptotic stability is proved for constant commands, while bounded stability is proved for varying commands. The proposed method is compared with approximate backstepping control and dynamic surface control and is shown to have superior tracking accuracy as well as robustness from the simulation results. This paper may also provide a beneficial guidance for control design of other complex systems. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. Part 1: The ODE connection and its implications for algorithm development in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.; Griffiths, D. F.

1990-01-01

Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

Stochastic Adaptive Estimation and Control.

DTIC Science & Technology

1994-10-26

Marcus, "Language Stability and Stabilizability of Discrete Event Dynamical Systems ," SIAM Journal on Control and Optimization, 31, September 1993...in the hierarchical control of flexible manufacturing systems ; in this problem, the model involves a hybrid process in continuous time whose state is...of the average cost control problem for discrete- time Markov processes. Our exposition covers from finite to Borel state and action spaces and

The research of the coupled orbital-attitude controlled motion of celestial body in the neighborhood of the collinear libration point L1

NASA Astrophysics Data System (ADS)

Shmyrov, A.; Shmyrov, V.; Shymanchuk, D.

2017-10-01

This article considers the motion of a celestial body within the restricted three-body problem of the Sun-Earth system. The equations of controlled coupled attitude-orbit motion in the neighborhood of collinear libration point L1 are investigated. The translational orbital motion of a celestial body is described using Hill's equations of circular restricted three-body problem of the Sun-Earth system. Rotational orbital motion is described using Euler's dynamic equations and quaternion kinematic equation. We investigate the problem of stability of celestial body rotational orbital motion in relative equilibrium positions and stabilization of celestial body rotational orbital motion with proposed control laws in the neighborhood of collinear libration point L1. To study stabilization problem, Lyapunov function is constructed in the form of the sum of the kinetic energy and special "kinematic function" of the Rodriguez-Hamiltonian parameters. Numerical modeling of the controlled rotational motion of a celestial body at libration point L1 is carried out. The numerical characteristics of the control parameters and rotational motion are given.

Stability and sensitivity of ABR flow control protocols

NASA Astrophysics Data System (ADS)

Tsai, Wie K.; Kim, Yuseok; Chiussi, Fabio; Toh, Chai-Keong

1998-10-01

This tutorial paper surveys the important issues in stability and sensitivity analysis of ABR flow control of ATM networks. THe stability and sensitivity issues are formulated in a systematic framework. Four main cause of instability in ABR flow control are identified: unstable control laws, temporal variations of available bandwidth with delayed feedback control, misbehaving components, and interactions between higher layer protocols and ABR flow control. Popular rate-based ABR flow control protocols are evaluated. Stability and sensitivity is shown to be the fundamental issues when the network has dynamically-varying bandwidth. Simulation result confirming the theoretical studies are provided. Open research problems are discussed.

Contributions to the understanding of large-scale coherent structures in developing free turbulent shear flows

NASA Technical Reports Server (NTRS)

Liu, J. T. C.

1986-01-01

Advances in the mechanics of boundary layer flow are reported. The physical problems of large scale coherent structures in real, developing free turbulent shear flows, from the nonlinear aspects of hydrodynamic stability are addressed. The presence of fine grained turbulence in the problem, and its absence, lacks a small parameter. The problem is presented on the basis of conservation principles, which are the dynamics of the problem directed towards extracting the most physical information, however, it is emphasized that it must also involve approximations.

Direct heuristic dynamic programming for damping oscillations in a large power system.

PubMed

Lu, Chao; Si, Jennie; Xie, Xiaorong

2008-08-01

This paper applies a neural-network-based approximate dynamic programming method, namely, the direct heuristic dynamic programming (direct HDP), to a large power system stability control problem. The direct HDP is a learning- and approximation-based approach to addressing nonlinear coordinated control under uncertainty. One of the major design parameters, the controller learning objective function, is formulated to directly account for network-wide low-frequency oscillation with the presence of nonlinearity, uncertainty, and coupling effect among system components. Results include a novel learning control structure based on the direct HDP with applications to two power system problems. The first case involves static var compensator supplementary damping control, which is used to provide a comprehensive evaluation of the learning control performance. The second case aims at addressing a difficult complex system challenge by providing a new solution to a large interconnected power network oscillation damping control problem that frequently occurs in the China Southern Power Grid.

Stability results for multi-layer radial Hele-Shaw and porous media flows

NASA Astrophysics Data System (ADS)

Gin, Craig; Daripa, Prabir

2015-01-01

Motivated by stability problems arising in the context of chemical enhanced oil recovery, we perform linear stability analysis of Hele-Shaw and porous media flows in radial geometry involving an arbitrary number of immiscible fluids. Key stability results obtained and their relevance to the stabilization of fingering instability are discussed. Some of the key results, among many others, are (i) absolute upper bounds on the growth rate in terms of the problem data; (ii) validation of these upper bound results against exact computation for the case of three-layer flows; (iii) stability enhancing injection policies; (iv) asymptotic limits that reduce these radial flow results to similar results for rectilinear flows; and (v) the stabilizing effect of curvature of the interfaces. Multi-layer radial flows have been found to have the following additional distinguishing features in comparison to rectilinear flows: (i) very long waves, some of which can be physically meaningful, are stable; and (ii) eigenvalues can be complex for some waves depending on the problem data, implying that the dispersion curves for one or more waves can contact each other. Similar to the rectilinear case, these results can be useful in providing insight into the interfacial instability transfer mechanism as the problem data are varied. Moreover, these can be useful in devising smart injection policies as well as controlling the complexity of the long-term dynamics when drops of various immiscible fluids intersperse among each other. As an application of the upper bound results, we provide stabilization criteria and design an almost stable multi-layer system by adding many layers of fluid with small positive jumps in viscosity in the direction of the basic flow.

Numerical solution of problems concerning the thermal convection of a variable-viscosity liquid

NASA Astrophysics Data System (ADS)

Zherebiatev, I. F.; Lukianov, A. T.; Podkopaev, Iu. L.

A stabilizing-correction scheme is constructed for integrating the fourth-order equation describing the dynamics of a viscous incompressible liquid. As an example, a solution is obtained to the problem of the solidification of a liquid in a rectangular region with allowance for convective energy transfer in the liquid phase as well as temperature-dependent changes of viscosity. It is noted that the proposed method can be used to study steady-state problems of thermal convection in ingots obtained through continuous casting.

Sitnikov cyclic configuration of N+1-body problem

NASA Astrophysics Data System (ADS)

Shahbaz Ullah, M.; Hassan, M. R.

2014-12-01

This manuscript deals with the generalisation of all previous works on series solutions and linear stability of equilibrium points of the Sitnikov problem. Following Giacaglia (1967), in Sect. 2 we have derived the equation of motion of the infinitesimal mass moving along the z-axis about which the plane of motion is rotating with unit angular velocity. In Sects. 3, 4 and 5 the series solutions of the Sitnikov problem have been developed by the method of MacMillan, Lindstedt-Poincaré and iteration of Green's function respectively. In Sect. 6 the three series solutions have been compared graphically by putting N=2, 3, 4. In Sect. 7 the coordinates of equilibrium points have been calculated. In Sect. 8 the linear stability of equilibrium points has been examined by the method of Murray and Dermott (Solar System Dynamics, Cambridge University Press, Cambridge, 1999) and it was found that the equilibrium points are stable in Sitnikov problem.

Application of the Hughes-LIU algorithm to the 2-dimensional heat equation

NASA Technical Reports Server (NTRS)

Malkus, D. S.; Reichmann, P. I.; Haftka, R. T.

1982-01-01

An implicit explicit algorithm for the solution of transient problems in structural dynamics is described. The method involved dividing the finite elements into implicit and explicit groups while automatically satisfying the conditions. This algorithm is applied to the solution of the linear, transient, two dimensional heat equation subject to an initial condition derived from the soluton of a steady state problem over an L-shaped region made up of a good conductor and an insulating material. Using the IIT/PRIME computer with virtual memory, a FORTRAN computer program code was developed to make accuracy, stability, and cost comparisons among the fully explicit Euler, the Hughes-Liu, and the fully implicit Crank-Nicholson algorithms. The Hughes-Liu claim that the explicit group governs the stability of the entire region while maintaining the unconditional stability of the implicit group is illustrated.

An Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations

PubMed Central

Mirzaev, Inom; Byrne, Erin C.; Bortz, David M.

2016-01-01

We investigate the inverse problem of identifying a conditional probability measure in measure-dependent evolution equations arising in size-structured population modeling. We formulate the inverse problem as a least squares problem for the probability measure estimation. Using the Prohorov metric framework, we prove existence and consistency of the least squares estimates and outline a discretization scheme for approximating a conditional probability measure. For this scheme, we prove general method stability. The work is motivated by Partial Differential Equation (PDE) models of flocculation for which the shape of the post-fragmentation conditional probability measure greatly impacts the solution dynamics. To illustrate our methodology, we apply the theory to a particular PDE model that arises in the study of population dynamics for flocculating bacterial aggregates in suspension, and provide numerical evidence for the utility of the approach. PMID:28316360

Full load shop testing of 18,000-hp gas turbine driven centrifugal compressor for offshore platform service: Evaluation of rotor dynamics performance

NASA Technical Reports Server (NTRS)

Kirk, R. G.; Simpson, M.

1985-01-01

The results for in-plant full load testing of a 13.4 MW (18000 HP) gas turbine driven centrifugal compressor are presented and compared to analytical predictions of compressor rotor stability. Unique problems from both oil seals and labyrinth gas seals were encountered during the testing. The successful resolution of these problems are summarized.

Robust adaptive cruise control of high speed trains.

PubMed

Faieghi, Mohammadreza; Jalali, Aliakbar; Mashhadi, Seyed Kamal-e-ddin Mousavi

2014-03-01

The cruise control problem of high speed trains in the presence of unknown parameters and external disturbances is considered. In particular a Lyapunov-based robust adaptive controller is presented to achieve asymptotic tracking and disturbance rejection. The system under consideration is nonlinear, MIMO and non-minimum phase. To deal with the limitations arising from the unstable zero-dynamics we do an output redefinition such that the zero-dynamics with respect to new outputs becomes stable. Rigorous stability analyses are presented which establish the boundedness of all the internal states and simultaneously asymptotic stability of the tracking error dynamics. The results are presented for two common configurations of high speed trains, i.e. the DD and PPD designs, based on the multi-body model and are verified by several numerical simulations. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Stable H(infinity) Controller Design for the Longitudinal Dynamics of an Aircraft

NASA Technical Reports Server (NTRS)

Oezbay, Hitay; Garg, Sanjay

1995-01-01

This report discusses different approaches to stable H infinity controller design applied to the problem of augmenting the longitudinal dynamics of an aircraft. Stability of the H infinity controller is investigated by analyzing the effects of changes in the performance index weights, and modifications in the measured outputs. The existence of a stable suboptimal controller is also investigated. It is shown that this is equivalent to finding a stable controller, whose infinity norm is less than a specified bound, for an unstable plant which is determined from parametrization of all H infinity controllers. Examples are given for a gust alleviation and a command tracking problem.

An embedded mesh method using piecewise constant multipliers with stabilization: mathematical and numerical aspects

DOE PAGES

Puso, M. A.; Kokko, E.; Settgast, R.; ...

2014-10-22

An embedded mesh method using piecewise constant multipliers originally proposed by Puso et al. (CMAME, 2012) is analyzed here to determine effects of the pressure stabilization term and small cut cells. The approach is implemented for transient dynamics using the central difference scheme for the time discretization. It is shown that the resulting equations of motion are a stable linear system with a condition number independent of mesh size. Furthermore, we show that the constraints and the stabilization terms can be recast as non-proportional damping such that the time integration of the scheme is provably stable with a critical timemore » step computed from the undamped equations of motion. Effects of small cuts are discussed throughout the presentation. A mesh study is conducted to evaluate the effects of the stabilization on the discretization error and conditioning and is used to recommend an optimal value for stabilization scaling parameter. Several nonlinear problems are also analyzed and compared with comparable conforming mesh results. Finally, we show several demanding problems highlighting the robustness of the proposed approach.« less

Neurodynamics in the Sensorimotor Loop: Representing Behavior Relevant External Situations

PubMed Central

Pasemann, Frank

2017-01-01

In the context of the dynamical system approach to cognition and supposing that brains or brain-like systems controlling the behavior of autonomous systems are permanently driven by their sensor signals, the paper approaches the question of neurodynamics in the sensorimotor loop in a purely formal way. This is carefully done by addressing the problem in three steps, using the time-discrete dynamics of standard neural networks and a fiber space representation for better clearness. Furthermore, concepts like meta-transients, parametric stability and dynamical forms are introduced, where meta-transients describe the effect of realistic sensor inputs, parametric stability refers to a class of sensor inputs all generating the “same type” of dynamic behavior, and a dynamical form comprises the corresponding class of parametrized dynamical systems. It is argued that dynamical forms are the essential internal representatives of behavior relevant external situations. Consequently, it is suggested that dynamical forms are the basis for a memory of these situations. Finally, based on the observation that not all brain process have a direct effect on the motor activity, a natural splitting of neurodynamics into vertical (internal) and horizontal (effective) parts is introduced. PMID:28217092

Performance Characterization, Development, and Application of Artificial Potential Function Guidance Methods

DTIC Science & Technology

2014-03-01

to determine if a system is stabilizable with feedback. 12 that asymptotic stability is guaranteed by Lyapunov theory. The advantage of this method are...discretized dynamics are a sufficient representation of the continuous system . Given these assumptions, the optimal control problem for minimum transit time is...tion (APF) guidance performance when applied to systems with limited control au- thority in a dynamic environment and then to use the findings to

Developmentally dynamic genome: Evidence of genetic influences on increases and decreases in conduct problems from early childhood to adolescence.

PubMed

Pingault, Jean-Baptiste; Rijsdijk, Frühling; Zheng, Yao; Plomin, Robert; Viding, Essi

2015-05-06

The development of conduct problems in childhood and adolescence is associated with adverse long-term outcomes, including psychiatric morbidity. Although genes constitute a proven factor of stability in conduct problems, less is known regarding their role in conduct problems' developmental course (i.e. systematic age changes, for instance linear increases or decreases).Mothers rated conduct problems from age 4 to 16 years in 10,038 twin pairs from the Twins Early Development Study. Individual differences in the baseline level (.78; 95% CI: .68-.88) and the developmental course of conduct problems (.73; 95% CI: .60-.86) were under high and largely independent additive genetic influences. Shared environment made a small contribution to the baseline level but not to the developmental course of conduct problems. These results show that genetic influences not only contribute to behavioural stability but also explain systematic change in conduct problems. Different sets of genes may be associated with the developmental course versus the baseline level of conduct problems. The structure of genetic and environmental influences on the development of conduct problems suggests that repeated preventive interventions at different developmental stages might be necessary to achieve a long-term impact.

Stabilization of model-based networked control systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miranda, Francisco; Instituto Politécnico de Viana do Castelo, Viana do Castelo; Abreu, Carlos

2016-06-08

A class of networked control systems called Model-Based Networked Control Systems (MB-NCSs) is considered. Stabilization of MB-NCSs is studied using feedback controls and simulation of stabilization for different feedbacks is made with the purpose to reduce the network trafic. The feedback control input is applied in a compensated model of the plant that approximates the plant dynamics and stabilizes the plant even under slow network conditions. Conditions for global exponential stabilizability and for the choosing of a feedback control input for a given constant time between the information moments of the network are derived. An optimal control problem to obtainmore » an optimal feedback control is also presented.« less

The mathematical model of dynamic stabilization system for autonomous car

NASA Astrophysics Data System (ADS)

Saikin, A. M.; Buznikov, S. E.; Shabanov, N. S.; Elkin, D. S.

2018-02-01

Leading foreign companies and domestic enterprises carry out extensive researches and developments in the field of control systems for autonomous cars and in the field of improving driver assistance systems. The search for technical solutions, as a rule, is based on heuristic methods and does not always lead to satisfactory results. The purpose of this research is to formalize the road safety problem in the terms of modern control theory, to construct the adequate mathematical model for solving it, including the choice of software and hardware environment. For automatic control of the object, it is necessary to solve the problem of dynamic stabilization in the most complete formulation. The solution quality of the problem on a finite time interval is estimated by the value of the quadratic functional. Car speed, turn angle and additional yaw rate (during car drift or skidding) measurements are performed programmatically by the original virtual sensors. The limit speeds at which drift, skidding or rollover begins are calculated programmatically taking into account the friction coefficient identified in motion. The analysis of the results confirms both the adequacy of the mathematical models and the algorithms and the possibility of implementing the system in the minimal technical configuration.

Aerodynamic characteristics of airplanes at high angles of attack

NASA Technical Reports Server (NTRS)

Chambers, J. R.; Grafton, S. B.

1977-01-01

An introduction to, and a broad overiew of, the aerodynamic characteristics of airplanes at high angles of attack are provided. Items include: (1) some important fundamental phenomena which determine the aerodynamic characteristics of airplanes at high angles of attack; (2) static and dynamic aerodynamic characteristics near the stall; (3) aerodynamics of the spin; (4) test techniques used in stall/spin studies; (5) applications of aerodynamic data to problems in flight dynamics in the stall/spin area; and (6) the outlook for future research in the area. Although stalling and spinning are flight dynamic problems of importance to all aircraft, including general aviation aircraft, commercial transports, and military airplanes, emphasis is placed on military configurations and the principle aerodynamic factors which influence the stability and control of such vehicles at high angles of attack.

Study of stability of the difference scheme for the model problem of the gaslift process

NASA Astrophysics Data System (ADS)

Temirbekov, Nurlan; Turarov, Amankeldy

2017-09-01

The paper studies a model of the gaslift process where the motion in a gas-lift well is described by partial differential equations. The system describing the studied process consists of equations of motion, continuity, equations of thermodynamic state, and hydraulic resistance. A two-layer finite-difference Lax-Vendroff scheme is constructed for the numerical solution of the problem. The stability of the difference scheme for the model problem is investigated using the method of a priori estimates, the order of approximation is investigated, the algorithm for numerical implementation of the gaslift process model is given, and the graphs are presented. The development and investigation of difference schemes for the numerical solution of systems of equations of gas dynamics makes it possible to obtain simultaneously exact and monotonic solutions.

Spectral collocation methods

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Kopriva, D. A.; Patera, A. T.

1987-01-01

This review covers the theory and application of spectral collocation methods. Section 1 describes the fundamentals, and summarizes results pertaining to spectral approximations of functions. Some stability and convergence results are presented for simple elliptic, parabolic, and hyperbolic equations. Applications of these methods to fluid dynamics problems are discussed in Section 2.

Effects of shock on hypersonic boundary layer stability

NASA Astrophysics Data System (ADS)

Pinna, F.; Rambaud, P.

2013-06-01

The design of hypersonic vehicles requires the estimate of the laminar to turbulent transition location for an accurate sizing of the thermal protection system. Linear stability theory is a fast scientific way to study the problem. Recent improvements in computational capabilities allow computing the flow around a full vehicle instead of using only simplified boundary layer equations. In this paper, the effect of the shock is studied on a mean flow provided by steady Computational Fluid Dynamics (CFD) computations and simplified boundary layer calculations.

Developmentally dynamic genome: Evidence of genetic influences on increases and decreases in conduct problems from early childhood to adolescence

PubMed Central

Pingault, Jean-Baptiste; Rijsdijk, Frühling; Zheng, Yao; Plomin, Robert; Viding, Essi

2015-01-01

The development of conduct problems in childhood and adolescence is associated with adverse long-term outcomes, including psychiatric morbidity. Although genes constitute a proven factor of stability in conduct problems, less is known regarding their role in conduct problems’ developmental course (i.e. systematic age changes, for instance linear increases or decreases).Mothers rated conduct problems from age 4 to 16 years in 10,038 twin pairs from the Twins Early Development Study. Individual differences in the baseline level (.78; 95% CI: .68-.88) and the developmental course of conduct problems (.73; 95% CI: .60-.86) were under high and largely independent additive genetic influences. Shared environment made a small contribution to the baseline level but not to the developmental course of conduct problems. These results show that genetic influences not only contribute to behavioural stability but also explain systematic change in conduct problems. Different sets of genes may be associated with the developmental course versus the baseline level of conduct problems. The structure of genetic and environmental influences on the development of conduct problems suggests that repeated preventive interventions at different developmental stages might be necessary to achieve a long-term impact. PMID:25944445

The rectilinear three-body problem as a basis for studying highly eccentric systems

NASA Astrophysics Data System (ADS)

Voyatzis, G.; Tsiganis, K.; Gaitanas, M.

2018-01-01

The rectilinear elliptic restricted three-body problem (TBP) is the limiting case of the elliptic restricted TBP when the motion of the primaries is described by a Keplerian ellipse with eccentricity e'=1, but the collision of the primaries is assumed to be a non-singular point. The rectilinear model has been proposed as a starting model for studying the dynamics of motion around highly eccentric binary systems. Broucke (AIAA J 7:1003-1009, 1969) explored the rectilinear problem and obtained isolated periodic orbits for mass parameter μ =0.5 (equal masses of the primaries). We found that all orbits obtained by Broucke are linearly unstable. We extend Broucke's computations by using a finer search for symmetric periodic orbits and computing their linear stability. We found a large number of periodic orbits, but only eight of them were found to be linearly stable and are associated with particular mean motion resonances. These stable orbits are used as generating orbits for continuation with respect to μ and e'<1. Also, continuation of periodic solutions with respect to the mass of the small body can be applied by using the general TBP. FLI maps of dynamical stability show that stable periodic orbits are surrounded in phase space with regions of regular orbits indicating that systems of very highly eccentric orbits can be found in stable resonant configurations. As an application we present a stability study for the planetary system HD7449.

Discontinuous Galerkin finite element method for solving population density functions of cortical pyramidal and thalamic neuronal populations.

PubMed

Huang, Chih-Hsu; Lin, Chou-Ching K; Ju, Ming-Shaung

2015-02-01

Compared with the Monte Carlo method, the population density method is efficient for modeling collective dynamics of neuronal populations in human brain. In this method, a population density function describes the probabilistic distribution of states of all neurons in the population and it is governed by a hyperbolic partial differential equation. In the past, the problem was mainly solved by using the finite difference method. In a previous study, a continuous Galerkin finite element method was found better than the finite difference method for solving the hyperbolic partial differential equation; however, the population density function often has discontinuity and both methods suffer from a numerical stability problem. The goal of this study is to improve the numerical stability of the solution using discontinuous Galerkin finite element method. To test the performance of the new approach, interaction of a population of cortical pyramidal neurons and a population of thalamic neurons was simulated. The numerical results showed good agreement between results of discontinuous Galerkin finite element and Monte Carlo methods. The convergence and accuracy of the solutions are excellent. The numerical stability problem could be resolved using the discontinuous Galerkin finite element method which has total-variation-diminishing property. The efficient approach will be employed to simulate the electroencephalogram or dynamics of thalamocortical network which involves three populations, namely, thalamic reticular neurons, thalamocortical neurons and cortical pyramidal neurons. Copyright © 2014 Elsevier Ltd. All rights reserved.

Efficient and stable exponential time differencing Runge-Kutta methods for phase field elastic bending energy models

NASA Astrophysics Data System (ADS)

Wang, Xiaoqiang; Ju, Lili; Du, Qiang

2016-07-01

The Willmore flow formulated by phase field dynamics based on the elastic bending energy model has been widely used to describe the shape transformation of biological lipid vesicles. In this paper, we develop and investigate some efficient and stable numerical methods for simulating the unconstrained phase field Willmore dynamics and the phase field Willmore dynamics with fixed volume and surface area constraints. The proposed methods can be high-order accurate and are completely explicit in nature, by combining exponential time differencing Runge-Kutta approximations for time integration with spectral discretizations for spatial operators on regular meshes. We also incorporate novel linear operator splitting techniques into the numerical schemes to improve the discrete energy stability. In order to avoid extra numerical instability brought by use of large penalty parameters in solving the constrained phase field Willmore dynamics problem, a modified augmented Lagrange multiplier approach is proposed and adopted. Various numerical experiments are performed to demonstrate accuracy and stability of the proposed methods.

Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES

NASA Astrophysics Data System (ADS)

Marras, Simone; Nazarov, Murtazo; Giraldo, Francis X.

2015-11-01

The high order spectral element approximation of the Euler equations is stabilized via a dynamic sub-grid scale model (Dyn-SGS). This model was originally designed for linear finite elements to solve compressible flows at large Mach numbers. We extend its application to high-order spectral elements to solve the Euler equations of low Mach number stratified flows. The major justification of this work is twofold: stabilization and large eddy simulation are achieved via one scheme only. Because the diffusion coefficients of the regularization stresses obtained via Dyn-SGS are residual-based, the effect of the artificial diffusion is minimal in the regions where the solution is smooth. The direct consequence is that the nominal convergence rate of the high-order solution of smooth problems is not degraded. To our knowledge, this is the first application in atmospheric modeling of a spectral element model stabilized by an eddy viscosity scheme that, by construction, may fulfill stabilization requirements, can model turbulence via LES, and is completely free of a user-tunable parameter. From its derivation, it will be immediately clear that Dyn-SGS is independent of the numerical method; it could be implemented in a discontinuous Galerkin, finite volume, or other environments alike. Preliminary discontinuous Galerkin results are reported as well. The straightforward extension to non-linear scalar problems is also described. A suite of 1D, 2D, and 3D test cases is used to assess the method, with some comparison against the results obtained with the most known Lilly-Smagorinsky SGS model.

Convergence of the standard RLS method and UDUT factorisation of covariance matrix for solving the algebraic Riccati equation of the DLQR via heuristic approximate dynamic programming

NASA Astrophysics Data System (ADS)

Moraes Rêgo, Patrícia Helena; Viana da Fonseca Neto, João; Ferreira, Ernesto M.

2015-08-01

The main focus of this article is to present a proposal to solve, via UDUT factorisation, the convergence and numerical stability problems that are related to the covariance matrix ill-conditioning of the recursive least squares (RLS) approach for online approximations of the algebraic Riccati equation (ARE) solution associated with the discrete linear quadratic regulator (DLQR) problem formulated in the actor-critic reinforcement learning and approximate dynamic programming context. The parameterisations of the Bellman equation, utility function and dynamic system as well as the algebra of Kronecker product assemble a framework for the solution of the DLQR problem. The condition number and the positivity parameter of the covariance matrix are associated with statistical metrics for evaluating the approximation performance of the ARE solution via RLS-based estimators. The performance of RLS approximators is also evaluated in terms of consistence and polarisation when associated with reinforcement learning methods. The used methodology contemplates realisations of online designs for DLQR controllers that is evaluated in a multivariable dynamic system model.

Robust Neural Sliding Mode Control of Robot Manipulators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nguyen Tran Hiep; Pham Thuong Cat

2009-03-05

This paper proposes a robust neural sliding mode control method for robot tracking problem to overcome the noises and large uncertainties in robot dynamics. The Lyapunov direct method has been used to prove the stability of the overall system. Simulation results are given to illustrate the applicability of the proposed method.

Robustness enhancement of neurocontroller and state estimator

NASA Technical Reports Server (NTRS)

Troudet, Terry

1993-01-01

The feasibility of enhancing neurocontrol robustness, through training of the neurocontroller and state estimator in the presence of system uncertainties, is investigated on the example of a multivariable aircraft control problem. The performance and robustness of the newly trained neurocontroller are compared to those for an existing neurocontrol design scheme. The newly designed dynamic neurocontroller exhibits a better trade-off between phase and gain stability margins, and it is significantly more robust to degradations of the plant dynamics.

Identical synchronization of nonidentical oscillators: when only birds of different feathers flock together

NASA Astrophysics Data System (ADS)

Zhang, Yuanzhao; Motter, Adilson E.

2018-01-01

An outstanding problem in the study of networks of heterogeneous dynamical units concerns the development of rigorous methods to probe the stability of synchronous states when the differences between the units are not small. Here, we address this problem by presenting a generalization of the master stability formalism that can be applied to heterogeneous oscillators with large mismatches. Our approach is based on the simultaneous block diagonalization of the matrix terms in the variational equation, and it leads to dimension reduction that simplifies the original equation significantly. This new formalism allows the systematic investigation of scenarios in which the oscillators need to be nonidentical in order to reach an identical state, where all oscillators are completely synchronized. In the case of networks of identically coupled oscillators, this corresponds to breaking the symmetry of the system as a means to preserve the symmetry of the dynamical state— a recently discovered effect termed asymmetry-induced synchronization (AISync). Our framework enables us to identify communication delay as a new and potentially common mechanism giving rise to AISync, which we demonstrate using networks of delay-coupled Stuart-Landau oscillators. The results also have potential implications for control, as they reveal oscillator heterogeneity as an attribute that may be manipulated to enhance the stability of synchronous states.

Computer program system for dynamic simulation and stability analysis of passive and actively controlled spacecraft. Volume 1. Theory

NASA Technical Reports Server (NTRS)

Bodley, C. S.; Devers, D. A.; Park, C. A.

1975-01-01

A theoretical development and associated digital computer program system is presented. The dynamic system (spacecraft) is modeled as an assembly of rigid and/or flexible bodies not necessarily in a topological tree configuration. The computer program system may be used to investigate total system dynamic characteristics including interaction effects between rigid and/or flexible bodies, control systems, and a wide range of environmental loadings. Additionally, the program system may be used for design of attitude control systems and for evaluation of total dynamic system performance including time domain response and frequency domain stability analyses. Volume 1 presents the theoretical developments including a description of the physical system, the equations of dynamic equilibrium, discussion of kinematics and system topology, a complete treatment of momentum wheel coupling, and a discussion of gravity gradient and environmental effects. Volume 2, is a program users' guide and includes a description of the overall digital program code, individual subroutines and a description of required program input and generated program output. Volume 3 presents the results of selected demonstration problems that illustrate all program system capabilities.

Cyclic public goods games: Compensated coexistence among mutual cheaters stabilized by optimized penalty taxation

NASA Astrophysics Data System (ADS)

Griffin, Christopher; Belmonte, Andrew

2017-05-01

We study the problem of stabilized coexistence in a three-species public goods game in which each species simultaneously contributes to one public good while freeloading off another public good ("cheating"). The proportional population growth is governed by an appropriately modified replicator equation, depending on the returns from the public goods and the cost. We show that the replicator dynamic has at most one interior unstable fixed point and that the population becomes dominated by a single species. We then show that by applying an externally imposed penalty, or "tax" on success can stabilize the interior fixed point, allowing for the symbiotic coexistence of all species. We show that the interior fixed point is the point of globally minimal total population growth in both the taxed and untaxed cases. We then formulate an optimal taxation problem and show that it admits a quasilinearization, resulting in novel necessary conditions for the optimal control. In particular, the optimal control problem governing the tax rate must solve a certain second-order ordinary differential equation.

Cyclic public goods games: Compensated coexistence among mutual cheaters stabilized by optimized penalty taxation.

PubMed

Griffin, Christopher; Belmonte, Andrew

2017-05-01

We study the problem of stabilized coexistence in a three-species public goods game in which each species simultaneously contributes to one public good while freeloading off another public good ("cheating"). The proportional population growth is governed by an appropriately modified replicator equation, depending on the returns from the public goods and the cost. We show that the replicator dynamic has at most one interior unstable fixed point and that the population becomes dominated by a single species. We then show that by applying an externally imposed penalty, or "tax" on success can stabilize the interior fixed point, allowing for the symbiotic coexistence of all species. We show that the interior fixed point is the point of globally minimal total population growth in both the taxed and untaxed cases. We then formulate an optimal taxation problem and show that it admits a quasilinearization, resulting in novel necessary conditions for the optimal control. In particular, the optimal control problem governing the tax rate must solve a certain second-order ordinary differential equation.

Stability of wave processes in a rotating electrically conducting fluid

NASA Astrophysics Data System (ADS)

Peregudin, S. I.; Peregudina, E. S.; Kholodova, S. E.

2018-05-01

The paper puts forward a mathematical model of dynamics of spatial large-scale motions in a rotating layer of electrically conducting incompressible perfect fluid of variable depth with due account of dissipative effects. The resulting boundary-value problem is reduced to a vector system of partial differential equations for any values of the Reynolds number. Theoretical analysis of the so-obtained analytical solution reveals the effect of the magnetic field diffusion on the stability of the wave mode — namely, with the removed external magnetic field, the diffusion of the magnetic field promotes its damping. Besides, a criterion of stability of a wave mode is obtained.

Wavelength-switched phase interrogator for EFPI sensors with polarization self-calibrated

NASA Astrophysics Data System (ADS)

Xia, Ji; Wang, Fuyin; Luo, Hong; Xiong, Shuidong

2017-10-01

The stability of the demodulation system for extrinsic Fabry-Perot interferometric(EFPI) sensors is significant to dynamic signal recovery. In the wavelength-switched demodulation system, a phase interrogation with a wavelength-switched structure has been presented. Two reflected peaks were in perpendicular polarization direction and switched in the time-domain. However, the operation point of system affected output of the linearly-polarized beams seriously, and the stability of the system decreased and even failed to work. In order to solve this problem, a polarization control unit is added into the system in this paper. The modified demodulation system has been demonstrated to have a higher stability.

On the nonlinear stability of mKdV breathers

NASA Astrophysics Data System (ADS)

Alejo, Miguel A.; Muñoz, Claudio

2012-11-01

Breather modes of the mKdV equation on the real line are known to be elastic under collisions with other breathers and solitons. This fact indicates very strong stability properties of breathers. In this communication we describe a rigorous, mathematical proof of the stability of breathers under a class of small perturbations. Our proof involves the existence of a nonlinear equation satisfied by all breather profiles, and a new Lyapunov functional which controls the dynamics of small perturbations and instability modes. In order to construct such a functional, we work in a subspace of the energy one. However, our proof introduces new ideas in order to attack the corresponding stability problem in the energy space. Some remarks about the sine-Gordon case are also considered.

The availability of diltiazem: a study on the sorption by intravenous delivery systems and on the stability of the drug.

PubMed

De Vroe, C; De Muynck, C; Remon, J P; Scheldewaert, R; Colardyn, F

1989-04-01

The stability and the sorption by intravenous delivery systems of the calcium antagonist diltiazem dissolved into either 5% dextrose or 0.9% sodium chloride solutions have been investigated, under conditions simulating current clinical practice. Static experiments showed an excellent stability and no sorption after 48 h. Dynamic experiments, at a perfusion rate of 20 mg h-1, showed no sorption of the drug by infusion fluid containers, burettes or administration sets. For end-line filters a temporary decrease of the recovered amount of diltiazem was observed but only with the 0.9% NaCl solution. It is concluded that the stability and the sorption of diltiazem offers no problem with regard to clinical efficacy.

A new delay-independent condition for global robust stability of neural networks with time delays.

PubMed

Samli, Ruya

2015-06-01

This paper studies the problem of robust stability of dynamical neural networks with discrete time delays under the assumptions that the network parameters of the neural system are uncertain and norm-bounded, and the activation functions are slope-bounded. By employing the results of Lyapunov stability theory and matrix theory, new sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point for delayed neural networks are presented. The results reported in this paper can be easily tested by checking some special properties of symmetric matrices associated with the parameter uncertainties of neural networks. We also present a numerical example to show the effectiveness of the proposed theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.

Small Body GN&C Research Report: A Robust Model Predictive Control Algorithm with Guaranteed Resolvability

NASA Technical Reports Server (NTRS)

Acikmese, Behcet A.; Carson, John M., III

2005-01-01

A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees the resolvability of the associated finite-horizon optimal control problem in a receding-horizon implementation. The control consists of two components; (i) feedforward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives, and derivatives in polytopes. An illustrative numerical example is also provided.

A robust model predictive control algorithm for uncertain nonlinear systems that guarantees resolvability

NASA Technical Reports Server (NTRS)

Acikmese, Ahmet Behcet; Carson, John M., III

2006-01-01

A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees resolvability. With resolvability, initial feasibility of the finite-horizon optimal control problem implies future feasibility in a receding-horizon framework. The control consists of two components; (i) feed-forward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives and derivatives in polytopes. An illustrative numerical example is also provided.

Generalized Hill-stability criteria for hierarchical three-body systems at arbitrary inclinations

NASA Astrophysics Data System (ADS)

Grishin, Evgeni; Perets, Hagai B.; Zenati, Yossef; Michaely, Erez

2017-04-01

A fundamental aspect of the three-body problem is its stability. Most stability studies have focused on the co-planar three-body problem, deriving analytic criteria for the dynamical stability of such pro/retrograde systems. Numerical studies of inclined systems phenomenologically mapped their stability regions, but neither complement it by theoretical framework, nor provided satisfactory fit for their dependence on mutual inclinations. Here we present a novel approach to study the stability of hierarchical three-body systems at arbitrary inclinations, which accounts not only for the instantaneous stability of such systems, but also for the secular stability and evolution through Lidov-Kozai cycles and evection. We generalize the Hill-stability criteria to arbitrarily inclined triple systems, explain the existence of quasi-stable regimes and characterize the inclination dependence of their stability. We complement the analytic treatment with an extensive numerical study, to test our analytic results. We find excellent correspondence up to high inclinations (˜120°), beyond which the agreement is marginal. At such high inclinations, the stability radius is larger, the ratio between the outer and inner periods becomes comparable and our secular averaging approach is no longer strictly valid. We therefore combine our analytic results with polynomial fits to the numerical results to obtain a generalized stability formula for triple systems at arbitrary inclinations. Besides providing a generalized secular-based physical explanation for the stability of non-co-planar systems, our results have direct implications for any triple systems and, in particular, binary planets and moon/satellite systems; we briefly discuss the latter as a test case for our models.

Constrained dynamics approach for motion synchronization and consensus

NASA Astrophysics Data System (ADS)

Bhatia, Divya

In this research we propose to develop constrained dynamical systems based stable attitude synchronization, consensus and tracking (SCT) control laws for the formation of rigid bodies. The generalized constrained dynamics Equations of Motion (EOM) are developed utilizing constraint potential energy functions that enforce communication constraints. Euler-Lagrange equations are employed to develop the non-linear constrained dynamics of multiple vehicle systems. The constraint potential energy is synthesized based on a graph theoretic formulation of the vehicle-vehicle communication. Constraint stabilization is achieved via Baumgarte's method. The performance of these constrained dynamics based formations is evaluated for bounded control authority. The above method has been applied to various cases and the results have been obtained using MATLAB simulations showing stability, synchronization, consensus and tracking of formations. The first case corresponds to an N-pendulum formation without external disturbances, in which the springs and the dampers connected between the pendulums act as the communication constraints. The damper helps in stabilizing the system by damping the motion whereas the spring acts as a communication link relaying relative position information between two connected pendulums. Lyapunov stabilization (energy based stabilization) technique is employed to depict the attitude stabilization and boundedness. Various scenarios involving different values of springs and dampers are simulated and studied. Motivated by the first case study, we study the formation of N 2-link robotic manipulators. The governing EOM for this system is derived using Euler-Lagrange equations. A generalized set of communication constraints are developed for this system using graph theory. The constraints are stabilized using Baumgarte's techniques. The attitude SCT is established for this system and the results are shown for the special case of three 2-link robotic manipulators. These methods are then applied to the formation of N-spacecraft. Modified Rodrigues Parameters (MRP) are used for attitude representation of the spacecraft because of their advantage of being a minimum parameter representation. Constrained non-linear equations of motion for this system are developed and stabilized using a Proportional-Derivative (PD) controller derived based on Baumgarte's method. A system of 3 spacecraft is simulated and the results for SCT are shown and analyzed. Another problem studied in this research is that of maintaining SCT under unknown external disturbances. We use an adaptive control algorithm to derive control laws for the actuator torques and develop an estimation law for the unknown disturbance parameters to achieve SCT. The estimate of the disturbance is added as a feed forward term in the actual control law to obtain the stabilization of a 3-spacecraft formation. The disturbance estimates are generated via a Lyapunov analysis of the closed loop system. In summary, the constrained dynamics method shows a lot of potential in formation control, achieving stabilization, synchronization, consensus and tracking of a set of dynamical systems.

Pollution source localization in an urban water supply network based on dynamic water demand.

PubMed

Yan, Xuesong; Zhu, Zhixin; Li, Tian

2017-10-27

Urban water supply networks are susceptible to intentional, accidental chemical, and biological pollution, which pose a threat to the health of consumers. In recent years, drinking-water pollution incidents have occurred frequently, seriously endangering social stability and security. The real-time monitoring for water quality can be effectively implemented by placing sensors in the water supply network. However, locating the source of pollution through the data detection obtained by water quality sensors is a challenging problem. The difficulty lies in the limited number of sensors, large number of water supply network nodes, and dynamic user demand for water, which leads the pollution source localization problem to an uncertainty, large-scale, and dynamic optimization problem. In this paper, we mainly study the dynamics of the pollution source localization problem. Previous studies of pollution source localization assume that hydraulic inputs (e.g., water demand of consumers) are known. However, because of the inherent variability of urban water demand, the problem is essentially a fluctuating dynamic problem of consumer's water demand. In this paper, the water demand is considered to be stochastic in nature and can be described using Gaussian model or autoregressive model. On this basis, an optimization algorithm is proposed based on these two dynamic water demand change models to locate the pollution source. The objective of the proposed algorithm is to find the locations and concentrations of pollution sources that meet the minimum between the analogue and detection values of the sensor. Simulation experiments were conducted using two different sizes of urban water supply network data, and the experimental results were compared with those of the standard genetic algorithm.

Continuous-time mean-variance portfolio selection with value-at-risk and no-shorting constraints

NASA Astrophysics Data System (ADS)

Yan, Wei

2012-01-01

An investment problem is considered with dynamic mean-variance(M-V) portfolio criterion under discontinuous prices which follow jump-diffusion processes according to the actual prices of stocks and the normality and stability of the financial market. The short-selling of stocks is prohibited in this mathematical model. Then, the corresponding stochastic Hamilton-Jacobi-Bellman(HJB) equation of the problem is presented and the solution of the stochastic HJB equation based on the theory of stochastic LQ control and viscosity solution is obtained. The efficient frontier and optimal strategies of the original dynamic M-V portfolio selection problem are also provided. And then, the effects on efficient frontier under the value-at-risk constraint are illustrated. Finally, an example illustrating the discontinuous prices based on M-V portfolio selection is presented.

Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jin, Tao; Mourad, Hashem M.; Bronkhorst, Curt A.

Here, we present an explicit finite element formulation designed for the treatment of strain localization under highly dynamic conditions. We also used a material stability analysis to detect the onset of localization behavior. Finite elements with embedded weak discontinuities are employed with the aim of representing subsequent localized deformation accurately. The formulation and its algorithmic implementation are described in detail. Numerical results are presented to illustrate the usefulness of this computational framework in the treatment of strain localization under highly dynamic conditions, and to examine its performance characteristics in the context of two-dimensional plane-strain problems.

Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions

DOE PAGES

Jin, Tao; Mourad, Hashem M.; Bronkhorst, Curt A.; ...

2017-09-13

Here, we present an explicit finite element formulation designed for the treatment of strain localization under highly dynamic conditions. We also used a material stability analysis to detect the onset of localization behavior. Finite elements with embedded weak discontinuities are employed with the aim of representing subsequent localized deformation accurately. The formulation and its algorithmic implementation are described in detail. Numerical results are presented to illustrate the usefulness of this computational framework in the treatment of strain localization under highly dynamic conditions, and to examine its performance characteristics in the context of two-dimensional plane-strain problems.

A comprehensive analytical model of rotorcraft aerodynamics and dynamics. Part 3: Program manual

NASA Technical Reports Server (NTRS)

Johnson, W.

1980-01-01

The computer program for a comprehensive analytical model of rotorcraft aerodynamics and dynamics is described. This analysis is designed to calculate rotor performance, loads, and noise; the helicopter vibration and gust response; the flight dynamics and handling qualities; and the system aeroelastic stability. The analysis is a combination of structural, inertial, and aerodynamic models that is applicable to a wide range of problems and a wide class of vehicles. The analysis is intended for use in the design, testing, and evaluation of rotors and rotorcraft and to be a basis for further development of rotary wing theories.

A proposed new generation of intact stability criteria for assessment of ship stability in longitudinal waves

NASA Astrophysics Data System (ADS)

Andrei, C.

2017-08-01

Intact ship stability assessment to prevent stability failure in heavy weather conditions is of paramount importance on board vessel. The possibility of assessment the causes that can lead to loss of ship’s stability as well as the assessment of intact stability in heavy seas is a important problem and has attracted a huge interest of the national and international regulatory authorities. Despite the regulations in force, referring to intact ship stability, many ships continued to lose the stability and or capsize due to failure modes that presently are not covered by such regulations. Based on this aspect has been identified the necessity of modelling an updated criteria for assessment of ship’s stability taking into consideration actual possible situations for loss of stability in heavy seas as a measure of increasing she safety of ships. In this respect, the goal of this paper is to illustrate a possible criteria for assessment ship’s stability in heavy seas through a method of determination the possible problems in a form of dynamic stability criteria. A new intact stability criteria is proposed and developed based on separate levels for assessment of vulnerability and susceptibility of ships in situations of parametric rolling and pure loss of stability encountered in extreme sea conditions. Mathematical models correlated with ship’s construction particulars and weather conditions were developed for every separate level in order to assess the ship’s stability. The objective of the proposed criteria is to bring to officers on board ships the possibility of assessment the ship’s intact stability, as a measure of prevention and improvement of safety during the voyage.

Better, Cheaper, Faster Molecular Dynamics

NASA Technical Reports Server (NTRS)

Pohorille, Andrew; DeVincenzi, Donald L. (Technical Monitor)

2001-01-01

Recent, revolutionary progress in genomics and structural, molecular and cellular biology has created new opportunities for molecular-level computer simulations of biological systems by providing vast amounts of data that require interpretation. These opportunities are further enhanced by the increasing availability of massively parallel computers. For many problems, the method of choice is classical molecular dynamics (iterative solving of Newton's equations of motion). It focuses on two main objectives. One is to calculate the relative stability of different states of the system. A typical problem that has' such an objective is computer-aided drug design. Another common objective is to describe evolution of the system towards a low energy (possibly the global minimum energy), "native" state. Perhaps the best example of such a problem is protein folding. Both types of problems share the same difficulty. Often, different states of the system are separated by high energy barriers, which implies that transitions between these states are rare events. This, in turn, can greatly impede exploration of phase space. In some instances this can lead to "quasi non-ergodicity", whereby a part of phase space is inaccessible on time scales of the simulation. To overcome this difficulty and to extend molecular dynamics to "biological" time scales (millisecond or longer) new physical formulations and new algorithmic developments are required. To be efficient they should account for natural limitations of multi-processor computer architecture. I will present work along these lines done in my group. In particular, I will focus on a new approach to calculating the free energies (stability) of different states and to overcoming "the curse of rare events". I will also discuss algorithmic improvements to multiple time step methods and to the treatment of slowly decaying, log-ranged, electrostatic effects.

Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology

NASA Astrophysics Data System (ADS)

Pitton, Giuseppe; Quaini, Annalisa; Rozza, Gianluigi

2017-09-01

We focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier-Stokes equations for a Newtonian and viscous fluid in contraction-expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator. An alternative to this approach is the direct simulation of the flow to characterize the asymptotic behavior of the solution. Both approaches can be extremely expensive in terms of computational time. We propose to apply Reduced Order Modeling (ROM) techniques to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the regurgitant mitral valve orifice shape.

Dynamical habitability of planetary systems.

PubMed

Dvorak, Rudolf; Pilat-Lohinger, Elke; Bois, Eric; Schwarz, Richard; Funk, Barbara; Beichman, Charles; Danchi, William; Eiroa, Carlos; Fridlund, Malcolm; Henning, Thomas; Herbst, Tom; Kaltenegger, Lisa; Lammer, Helmut; Léger, Alain; Liseau, René; Lunine, Jonathan; Paresce, Francesco; Penny, Alan; Quirrenbach, Andreas; Röttgering, Huub; Selsis, Frank; Schneider, Jean; Stam, Daphne; Tinetti, Giovanna; White, Glenn J

2010-01-01

The problem of the stability of planetary systems, a question that concerns only multiplanetary systems that host at least two planets, is discussed. The problem of mean motion resonances is addressed prior to discussion of the dynamical structure of the more than 350 known planets. The difference with regard to our own Solar System with eight planets on low eccentricity is evident in that 60% of the known extrasolar planets have orbits with eccentricity e > 0.2. We theoretically highlight the studies concerning possible terrestrial planets in systems with a Jupiter-like planet. We emphasize that an orbit of a particular nature only will keep a planet within the habitable zone around a host star with respect to the semimajor axis and its eccentricity. In addition, some results are given for individual systems (e.g., Gl777A) with regard to the stability of orbits within habitable zones. We also review what is known about the orbits of planets in double-star systems around only one component (e.g., gamma Cephei) and around both stars (e.g., eclipsing binaries).

Analysis of friction and instability by the centre manifold theory for a non-linear sprag-slip model

NASA Astrophysics Data System (ADS)

Sinou, J.-J.; Thouverez, F.; Jezequel, L.

2003-08-01

This paper presents the research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. Indeed, the impact of unstable oscillations can be catastrophic. It can cause vehicle control problems and component degradation. Accordingly, complex stability analysis is required. This paper outlines stability analysis and centre manifold approach for studying instability problems. To put it more precisely, one considers brake vibrations and more specifically heavy trucks judder where the dynamic characteristics of the whole front axle assembly is concerned, even if the source of judder is located in the brake system. The modelling introduces the sprag-slip mechanism based on dynamic coupling due to buttressing. The non-linearity is expressed as a polynomial with quadratic and cubic terms. This model does not require the use of brake negative coefficient, in order to predict the instability phenomena. Finally, the centre manifold approach is used to obtain equations for the limit cycle amplitudes. The centre manifold theory allows the reduction of the number of equations of the original system in order to obtain a simplified system, without loosing the dynamics of the original system as well as the contributions of non-linear terms. The goal is the study of the stability analysis and the validation of the centre manifold approach for a complex non-linear model by comparing results obtained by solving the full system and by using the centre manifold approach. The brake friction coefficient is used as an unfolding parameter of the fundamental Hopf bifurcation point.

Dynamic modeling and ascent flight control of Ares-I Crew Launch Vehicle

NASA Astrophysics Data System (ADS)

Du, Wei

This research focuses on dynamic modeling and ascent flight control of large flexible launch vehicles such as the Ares-I Crew Launch Vehicle (CLV). A complete set of six-degrees-of-freedom dynamic models of the Ares-I, incorporating its propulsion, aerodynamics, guidance and control, and structural flexibility, is developed. NASA's Ares-I reference model and the SAVANT Simulink-based program are utilized to develop a Matlab-based simulation and linearization tool for an independent validation of the performance and stability of the ascent flight control system of large flexible launch vehicles. A linearized state-space model as well as a non-minimum-phase transfer function model (which is typical for flexible vehicles with non-collocated actuators and sensors) are validated for ascent flight control design and analysis. This research also investigates fundamental principles of flight control analysis and design for launch vehicles, in particular the classical "drift-minimum" and "load-minimum" control principles. It is shown that an additional feedback of angle-of-attack can significantly improve overall performance and stability, especially in the presence of unexpected large wind disturbances. For a typical "non-collocated actuator and sensor" control problem for large flexible launch vehicles, non-minimum-phase filtering of "unstably interacting" bending modes is also shown to be effective. The uncertainty model of a flexible launch vehicle is derived. The robust stability of an ascent flight control system design, which directly controls the inertial attitude-error quaternion and also employs the non-minimum-phase filters, is verified by the framework of structured singular value (mu) analysis. Furthermore, nonlinear coupled dynamic simulation results are presented for a reference model of the Ares-I CLV as another validation of the feasibility of the ascent flight control system design. Another important issue for a single main engine launch vehicle is stability under mal-function of the roll control system. The roll motion of the Ares-I Crew Launch Vehicle under nominal flight conditions is actively stabilized by its roll control system employing thrusters. This dissertation describes the ascent flight control design problem of Ares-I in the event of disabled or failed roll control. A simple pitch/yaw control logic is developed for such a technically challenging problem by exploiting the inherent versatility of a quaternion-based attitude control system. The proposed scheme requires only the desired inertial attitude quaternion to be re-computed using the actual uncontrolled roll angle information to achieve an ascent flight trajectory identical to the nominal flight case with active roll control. Another approach that utilizes a simple adjustment of the proportional-derivative gains of the quaternion-based flight control system without active roll control is also presented. This approach doesn't require the re-computation of desired inertial attitude quaternion. A linear stability criterion is developed for proper adjustments of attitude and rate gains. The linear stability analysis results are validated by nonlinear simulations of the ascent flight phase. However, the first approach, requiring a simple modification of the desired attitude quaternion, is recommended for the Ares-I as well as other launch vehicles in the event of no active roll control. Finally, the method derived to stabilize a large flexible launch vehicle in the event of uncontrolled roll drift is generalized as a modified attitude quaternion feedback law. It is used to stabilize an axisymmetric rigid body by two independent control torques.

Ares-I Bending Filter Design using a Constrained Optimization Approach

NASA Technical Reports Server (NTRS)

Hall, Charles; Jang, Jiann-Woei; Hall, Robert; Bedrossian, Nazareth

2008-01-01

The Ares-I launch vehicle represents a challenging flex-body structural environment for control system design. Software filtering of the inertial sensor output is required to ensure adequate stable response to guidance commands while minimizing trajectory deviations. This paper presents a design methodology employing numerical optimization to develop the Ares-I bending filters. The design objectives include attitude tracking accuracy and robust stability with respect to rigid body dynamics, propellant slosh, and flex. Under the assumption that the Ares-I time-varying dynamics and control system can be frozen over a short period of time, the bending filters are designed to stabilize all the selected frozen-time launch control systems in the presence of parameter uncertainty. To ensure adequate response to guidance command, step response specifications are introduced as constraints in the optimization problem. Imposing these constrains minimizes performance degradation caused by the addition of the bending filters. The first stage bending filter design achieves stability by adding lag to the first structural frequency to phase stabilize the first flex mode while gain stabilizing the higher modes. The upper stage bending filter design gain stabilizes all the flex bending modes. The bending filter designs provided here have been demonstrated to provide stable first and second stage control systems in both Draper Ares Stability Analysis Tool (ASAT) and the MSFC MAVERIC 6DOF nonlinear time domain simulation.

Ares I Flight Control System Design

NASA Technical Reports Server (NTRS)

Jang, Jiann-Woei; Alaniz, Abran; Hall, Robert; Bedrossian, Nazareth; Hall, Charles; Ryan, Stephen; Jackson, Mark

2010-01-01

The Ares I launch vehicle represents a challenging flex-body structural environment for flight control system design. This paper presents a design methodology for employing numerical optimization to develop the Ares I flight control system. The design objectives include attitude tracking accuracy and robust stability with respect to rigid body dynamics, propellant slosh, and flex. Under the assumption that the Ares I time-varying dynamics and control system can be frozen over a short period of time, the flight controllers are designed to stabilize all selected frozen-time launch control systems in the presence of parametric uncertainty. Flex filters in the flight control system are designed to minimize the flex components in the error signals before they are sent to the attitude controller. To ensure adequate response to guidance command, step response specifications are introduced as constraints in the optimization problem. Imposing these constraints minimizes performance degradation caused by the addition of the flex filters. The first stage bending filter design achieves stability by adding lag to the first structural frequency to phase stabilize the first flex mode while gain stabilizing the higher modes. The upper stage bending filter design gain stabilizes all the flex bending modes. The flight control system designs provided here have been demonstrated to provide stable first and second stage control systems in both Draper Ares Stability Analysis Tool (ASAT) and the MSFC 6DOF nonlinear time domain simulation.

Invariant Tori in the Secular Motions of the Three-body Planetary Systems

NASA Astrophysics Data System (ADS)

Locatelli, Ugo; Giorgilli, Antonio

We consider the problem of the applicability of KAM theorem to a realistic problem of three bodies. In the framework of the averaged dynamics over the fast angles for the Sun-Jupiter-Saturn system we can prove the perpetual stability of the orbit. The proof is based on semi-numerical algorithms requiring both explicit algebraic manipulations of series and analytical estimates. The proof is made rigorous by using interval arithmetics in order to control the numerical errors.

Problem reporting management system performance simulation

NASA Technical Reports Server (NTRS)

Vannatta, David S.

1993-01-01

This paper proposes the Problem Reporting Management System (PRMS) model as an effective discrete simulation tool that determines the risks involved during the development phase of a Trouble Tracking Reporting Data Base replacement system. The model considers the type of equipment and networks which will be used in the replacement system as well as varying user loads, size of the database, and expected operational availability. The paper discusses the dynamics, stability, and application of the PRMS and addresses suggested concepts to enhance the service performance and enrich them.

Qualitative and quantitative behaviour of planetary systems; Proceedings of the 3rd Alexander von Humboldt Colloquium on Celestial Mechanics, Ramsau, Austria, Mar. 29-Apr. 4, 1992

NASA Astrophysics Data System (ADS)

Dvorak, R.; Henrard, J.

1993-06-01

Topics addressed include planetary theories, the Sitnikov problem, asteroids, resonance, general dynamical systems, and chaos and stability. Particular attention is given to recent progress in the theory and application of symplectic integrators, a computer-aided analysis of the Sitnikov problem, the chaotic behavior of trajectories for the asteroidal resonances, and the resonant motion in the restricted three-body problem. Also discussed are the second order long-period motion of Hyperion, meteorites from the asteroid 6 Hebe, and least squares parameter estimation in chaotic differential equations.

A Topology Control Strategy with Reliability Assurance for Satellite Cluster Networks in Earth Observation

PubMed Central

Chen, Qing; Zhang, Jinxiu; Hu, Ze

2017-01-01

This article investigates the dynamic topology control problem of satellite cluster networks (SCNs) in Earth observation (EO) missions by applying a novel metric of stability for inter-satellite links (ISLs). The properties of the periodicity and predictability of satellites’ relative position are involved in the link cost metric which is to give a selection criterion for choosing the most reliable data routing paths. Also, a cooperative work model with reliability is proposed for the situation of emergency EO missions. Based on the link cost metric and the proposed reliability model, a reliability assurance topology control algorithm and its corresponding dynamic topology control (RAT) strategy are established to maximize the stability of data transmission in the SCNs. The SCNs scenario is tested through some numeric simulations of the topology stability of average topology lifetime and average packet loss rate. Simulation results show that the proposed reliable strategy applied in SCNs significantly improves the data transmission performance and prolongs the average topology lifetime. PMID:28241474

Robustness analysis of uncertain dynamical neural networks with multiple time delays.

PubMed

Senan, Sibel

2015-10-01

This paper studies the problem of global robust asymptotic stability of the equilibrium point for the class of dynamical neural networks with multiple time delays with respect to the class of slope-bounded activation functions and in the presence of the uncertainties of system parameters of the considered neural network model. By using an appropriate Lyapunov functional and exploiting the properties of the homeomorphism mapping theorem, we derive a new sufficient condition for the existence, uniqueness and global robust asymptotic stability of the equilibrium point for the class of neural networks with multiple time delays. The obtained stability condition basically relies on testing some relationships imposed on the interconnection matrices of the neural system, which can be easily verified by using some certain properties of matrices. An instructive numerical example is also given to illustrate the applicability of our result and show the advantages of this new condition over the previously reported corresponding results. Copyright © 2015 Elsevier Ltd. All rights reserved.

A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances.

PubMed

Pashaei, Shabnam; Badamchizadeh, Mohammadali

2016-07-01

This paper investigates the stabilization and disturbance rejection for a class of fractional-order nonlinear dynamical systems with mismatched disturbances. To fulfill this purpose a new fractional-order sliding mode control (FOSMC) based on a nonlinear disturbance observer is proposed. In order to design the suitable fractional-order sliding mode controller, a proper switching surface is introduced. Afterward, by using the sliding mode theory and Lyapunov stability theory, a robust fractional-order control law via a nonlinear disturbance observer is proposed to assure the existence of the sliding motion in finite time. The proposed fractional-order sliding mode controller exposes better control performance, ensures fast and robust stability of the closed-loop system, eliminates the disturbances and diminishes the chattering problem. Finally, the effectiveness of the proposed fractional-order controller is depicted via numerical simulation results of practical example and is compared with some other controllers. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Trimethylamine-N-oxide switches from stabilizing nature: A mechanistic outlook through experimental techniques and molecular dynamics simulation

NASA Astrophysics Data System (ADS)

Rani, Anjeeta; Jayaraj, Abhilash; Jayaram, B.; Pannuru, Venkatesu

2016-03-01

In adaptation biology of the discovery of the intracellular osmolytes, the osmolytes are found to play a central role in cellular homeostasis and stress response. A number of models using these molecules are now poised to address a wide range of problems in biology. Here, a combination of biophysical measurements and molecular dynamics (MD) simulation method is used to examine the effect of trimethylamine-N-oxide (TMAO) on stem bromelain (BM) structure, stability and function. From the analysis of our results, we found that TMAO destabilizes BM hydrophobic pockets and active site as a result of concerted polar and non-polar interactions which is strongly evidenced by MD simulation carried out for 250 ns. This destabilization is enthalpically favourable at higher concentrations of TMAO while entropically unfavourable. However, to the best of our knowledge, the results constitute first detailed unambiguous proof of destabilizing effect of most commonly addressed TMAO on the interactions governing stability of BM and present plausible mechanism of protein unfolding by TMAO.

Stability analysis of confined V-shaped flames in high-velocity streams.

PubMed

El-Rabii, Hazem; Joulin, Guy; Kazakov, Kirill A

2010-06-01

The problem of linear stability of confined V-shaped flames with arbitrary gas expansion is addressed. Using the on-shell description of flame dynamics, a general equation governing propagation of disturbances of an anchored flame is obtained. This equation is solved analytically for V-flames anchored in high-velocity channel streams. It is demonstrated that dynamics of the flame disturbances in this case is controlled by the memory effects associated with vorticity generated by the perturbed flame. The perturbation growth rate spectrum is determined, and explicit analytical expressions for the eigenfunctions are given. It is found that the piecewise linear V structure is unstable for all values of the gas expansion coefficient. Despite the linearity of the basic pattern, however, evolutions of the V-flame disturbances are completely different from those found for freely propagating planar flames or open anchored flames. The obtained results reveal strong influence of the basic flow and the channel walls on the stability properties of confined V-flames.

On the impact index of synchronous generator displaced by DFIG on power system small-signal stability

NASA Astrophysics Data System (ADS)

Bi, J. T.; Du, W. J.; Wang, H. F.; Song, Y. T.; Wang, Q.; Ding, J.; Chen, D. Z.; Wei, W.

2017-05-01

As the maturity of wind power technology and the ageing and retirement of conventional synchronous generators, the displacement of synchronous generators by wind power generators would be a trend in the next few decades. The power system small-signal angular stability caused by the displacement is an urgent problem to be studied. The displacement of the SG by the DFIG includes withdrawing the dynamic interactions of the displaced SG and adding the dynamic interactions of the displacing DFIG. Based on this fact, a new index is proposed to predict the impact of the SG to be displaced by the DFIG on power system oscillation modes. The sensitivity index of the oscillation modes to the constant inertia of the displaced SGs, proposed in early literatures to estimate the dynamic impact of the SG being displaced by the DFIG, is also compared with the proposed index. The modified New England power system is adopted to show various results and conclusions. The proposed index can correctly identify the most dangerous and beneficial displacement to power system small-signal angular stability, and is very useful in practical applications.

Stabilization of a programmed rotation mode for a satellite with electrodynamic attitude control system

NASA Astrophysics Data System (ADS)

Aleksandrov, A. Yu.; Aleksandrova, E. B.; Tikhonov, A. A.

2018-07-01

The paper deals with a dynamically symmetric satellite in a circular near-Earth orbit. The satellite is equipped with an electrodynamic attitude control system based on Lorentz and magnetic torque properties. The programmed satellite attitude motion is such that the satellite slowly rotates around the axis of its dynamical symmetry. Unlike previous publications, we consider more complex and practically more important case where the axis is fixed in the orbital frame in an inclined position with respect to the local vertical axis. The satellite stabilization in the programmed attitude motion is studied. The gravitational disturbing torque acting on the satellite attitude dynamics is taken into account since it is the largest disturbing torque. The novelty of the proposed approach is based on the usage of electrodynamic attitude control system. With the aid of original construction of a Lyapunov function, new conditions under which electrodynamic control solves the problem are obtained. Sufficient conditions for asymptotic stability of the programmed motion are found in terms of inequalities for the values of control parameters. The results of a numerical simulation are presented to demonstrate the effectiveness of the proposed approach.

Adaptive control of an exoskeleton robot with uncertainties on kinematics and dynamics.

PubMed

Brahmi, Brahim; Saad, Maarouf; Ochoa-Luna, Cristobal; Rahman, Mohammad H

2017-07-01

In this paper, we propose a new adaptive control technique based on nonlinear sliding mode control (JSTDE) taking into account kinematics and dynamics uncertainties. This approach is applied to an exoskeleton robot with uncertain kinematics and dynamics. The adaptation design is based on Time Delay Estimation (TDE). The proposed strategy does not necessitate the well-defined dynamic and kinematic models of the system robot. The updated laws are designed using Lyapunov-function to solve the adaptation problem systematically, proving the close loop stability and ensuring the convergence asymptotically of the outputs tracking errors. Experiments results show the effectiveness and feasibility of JSTDE technique to deal with the variation of the unknown nonlinear dynamics and kinematics of the exoskeleton model.

Synthesis of a controller for stabilizing the motion of a rigid body about a fixed point

NASA Astrophysics Data System (ADS)

Zabolotnov, Yu. M.; Lobanov, A. A.

2017-05-01

A method for the approximate design of an optimal controller for stabilizing the motion of a rigid body about a fixed point is considered. It is assumed that rigid body motion is nearly the motion in the classical Lagrange case. The method is based on the common use of the Bellman dynamic programming principle and the averagingmethod. The latter is used to solve theHamilton-Jacobi-Bellman equation approximately, which permits synthesizing the controller. The proposed method for controller design can be used in many problems close to the problem of motion of the Lagrange top (the motion of a rigid body in the atmosphere, the motion of a rigid body fastened to a cable in deployment of the orbital cable system, etc.).

Acknowledging the Elephant in the Room: How Stressful Environmental Contexts Shape Relationship Dynamics

PubMed Central

Neff, Lisa A.; Karney, Benjamin R.

2016-01-01

Compared to affluent marriages, lower income marriages develop within a context filled with negative stressors that may prove quite toxic for marital stability. The current paper argues that stressful contexts may undermine marital well-being through two routes. First, external stressors create additional problems within the marriage by diverting time and attention away from activities that promote intimacy between partners. Second, external stress may render spouses ill-equipped to cope with this increase in problems by draining spouses of the energy and resources necessary for responding to marital challenges in a constructive manner. In acknowledging the role of the marital context for relationship dynamics, this model suggests new directions for interventions designed to strengthen the marriages of lower income couples. PMID:27766285

Importance of stability study of continuous systems for ethanol production.

PubMed

Paz Astudillo, Isabel Cristina; Cardona Alzate, Carlos Ariel

2011-01-10

Fuel ethanol industry presents different problems during bioreactors operation. One of them is the unexpected variation in the output ethanol concentration from the bioreactor or a drastic fall in the productivity. In this paper, a compilation of concepts and relevant results of several experimental and theoretical studies about dynamic behavior of fermentation systems for bioethanol production with Saccharomyces cerevisiae and Zymomonas mobilis is done with the purpose of understanding the stability phenomena that could affect the productivity of industries producing fuel ethanol. It is shown that the design of high scale biochemical processes for fuel ethanol production must be done based on stability studies. © 2010 Elsevier B.V. All rights reserved.

Sensor fusion for structural tilt estimation using an acceleration-based tilt sensor and a gyroscope

NASA Astrophysics Data System (ADS)

Liu, Cheng; Park, Jong-Woong; Spencer, B. F., Jr.; Moon, Do-Soo; Fan, Jiansheng

2017-10-01

A tilt sensor can provide useful information regarding the health of structural systems. Most existing tilt sensors are gravity/acceleration based and can provide accurate measurements of static responses. However, for dynamic tilt, acceleration can dramatically affect the measured responses due to crosstalk. Thus, dynamic tilt measurement is still a challenging problem. One option is to integrate the output of a gyroscope sensor, which measures the angular velocity, to obtain the tilt; however, problems arise because the low-frequency sensitivity of the gyroscope is poor. This paper proposes a new approach to dynamic tilt measurements, fusing together information from a MEMS-based gyroscope and an acceleration-based tilt sensor. The gyroscope provides good estimates of the tilt at higher frequencies, whereas the acceleration measurements are used to estimate the tilt at lower frequencies. The Tikhonov regularization approach is employed to fuse these measurements together and overcome the ill-posed nature of the problem. The solution is carried out in the frequency domain and then implemented in the time domain using FIR filters to ensure stability. The proposed method is validated numerically and experimentally to show that it performs well in estimating both the pseudo-static and dynamic tilt measurements.

Adaptive robust control of a class of non-affine variable-speed variable-pitch wind turbines with unmodeled dynamics.

PubMed

Bagheri, Pedram; Sun, Qiao

2016-07-01

In this paper, a novel synthesis of Nussbaum-type functions, and an adaptive radial-basis function neural network is proposed to design controllers for variable-speed, variable-pitch wind turbines. Dynamic equations of the wind turbine are highly nonlinear, uncertain, and affected by unknown disturbance sources. Furthermore, the dynamic equations are non-affine with respect to the pitch angle, which is a control input. To address these problems, a Nussbaum-type function, along with a dynamic control law are adopted to resolve the non-affine nature of the equations. Moreover, an adaptive radial-basis function neural network is designed to approximate non-parametric uncertainties. Further, the closed-loop system is made robust to unknown disturbance sources, where no prior knowledge of disturbance bound is assumed in advance. Finally, the Lyapunov stability analysis is conducted to show the stability of the entire closed-loop system. In order to verify analytical results, a simulation is presented and the results are compared to both a PI and an existing adaptive controllers. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Robust H∞ cost guaranteed integral sliding mode control for the synchronization problem of nonlinear tele-operation system with variable time-delay.

PubMed

Al-Wais, Saba; Khoo, Suiyang; Lee, Tae Hee; Shanmugam, Lakshmanan; Nahavandi, Saeid

2018-01-01

This paper is devoted to the synchronization problem of tele-operation systems with time-varying delay, disturbances, and uncertainty. Delay-dependent sufficient conditions for the existence of integral sliding surfaces are given in the form of Linear Matrix Inequalities (LMIs). This guarantees the global stability of the tele-operation system with known upper bounds of the time-varying delays. Unlike previous work, in this paper, the controller gains are designed but not chosen, which increases the degree of freedom of the design. Moreover, Wirtinger based integral inequality and reciprocally convex combination techniques used in the constructed Lypunove-Krasoviskii Functional (LKF) are deemed to give less conservative stability condition for the system. Furthermore, to relax the analysis from any assumptions regarding the dynamics of the environment and human operator forces, H ∞ design method is used to involve the dynamics of these forces and ensure the stability of the system against these admissible forces in the H ∞ sense. This design scheme combines the strong robustness of the sliding mode control with the H ∞ design method for tele-operation systems which is coupled using state feedback controllers and inherit variable time-delays in their communication channels. Simulation examples are given to show the effectiveness of the proposed method. Copyright © 2017 ISA. All rights reserved.

Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks.

PubMed

Chen, Wu-Hua; Lu, Xiaomei; Zheng, Wei Xing

2015-04-01

This paper investigates the problems of impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks (DDNNs). Two types of DDNNs with stabilizing impulses are studied. By introducing the time-varying Lyapunov functional to capture the dynamical characteristics of discrete-time impulsive delayed neural networks (DIDNNs) and by using a convex combination technique, new exponential stability criteria are derived in terms of linear matrix inequalities. The stability criteria for DIDNNs are independent of the size of time delay but rely on the lengths of impulsive intervals. With the newly obtained stability results, sufficient conditions on the existence of linear-state feedback impulsive controllers are derived. Moreover, a novel impulsive synchronization scheme for two identical DDNNs is proposed. The novel impulsive synchronization scheme allows synchronizing two identical DDNNs with unknown delays. Simulation results are given to validate the effectiveness of the proposed criteria of impulsive stabilization and impulsive synchronization of DDNNs. Finally, an application of the obtained impulsive synchronization result for two identical chaotic DDNNs to a secure communication scheme is presented.

How Positive Affect Modulates Cognitive Control: Reduced Perseveration at the Cost of Increased Distractibility

ERIC Educational Resources Information Center

Dreisbach, Gesine; Goschke, Thomas

2004-01-01

A fundamental problem that organisms face in a changing environment is how to regulate dynamically the balance between stable maintenance and flexible switching of goals and cognitive sets. The authors show that positive affect plays an important role in the regulation of this stability-flexibility balance. In a cognitive set-switching paradigm,…

Existence and uniqueness of steady state solutions of a nonlocal diffusive logistic equation

NASA Astrophysics Data System (ADS)

Sun, Linan; Shi, Junping; Wang, Yuwen

2013-08-01

In this paper, we consider a dynamical model of population biology which is of the classical Fisher type, but the competition interaction between individuals is nonlocal. The existence, uniqueness, and stability of the steady state solution of the nonlocal problem on a bounded interval with homogeneous Dirichlet boundary conditions are studied.

Dynamic Stability and Gravitational Balancing of Multiple Extended Bodies

NASA Technical Reports Server (NTRS)

Quadrelli, Marco

2008-01-01

Feasibility of a non-invasive compensation scheme was analyzed for precise positioning of a massive extended body in free fall using gravitational forces influenced by surrounding source masses in close proximity. The N-body problem of classical mechanics is a paradigm used to gain insight into the physics of the equivalent N-body problem subject to control forces. The analysis addressed how a number of control masses move around the proof mass so that the proof mass position can be accurately and remotely compensated when exogenous disturbances are acting on it, while its sensitivity to gravitational waves remains unaffected. Past methods to correct the dynamics of the proof mass have considered active electrostatic or capacitive methods, but the possibility of stray capacitances on the surfaces of the proof mass have prompted the investigation of other alternatives, such as the method presented in this paper. While more rigorous analyses of the problem should be carried out, the data show that, by means of a combined feedback and feed-forward control approach, the control masses succeeded in driving the proof mass along the specified trajectory, which implies that the proof mass can, in principle, be balanced via gravitational forces only while external perturbations are acting on it. This concept involves the dynamic stability of a group of massive objects interacting gravitationally under active control, and can apply to drag-free control of spacecraft during missions, to successor gravitational wave space borne sensors, or to any application requiring flying objects to be precisely controlled in position and attitude relative to another body via gravitational interactions only.

The addition of body armor diminishes dynamic postural stability in military soldiers.

PubMed

Sell, Timothy C; Pederson, Jonathan J; Abt, John P; Nagai, Takashi; Deluzio, Jennifer; Wirt, Michael D; McCord, Larry J; Lephart, Scott M

2013-01-01

Poor postural stability has been identified as a risk factor for lower extremity musculoskeletal injury. The additional weight of body armor carried by Soldiers alters static postural stability and may predispose Soldiers to lower extremity musculoskeletal injuries. However, static postural stability tasks poorly replicate the dynamic military environment, which places considerable stress on the postural control system during tactical training and combat. Therefore, the purpose of this study was to examine the effects of body armor on dynamic postural stability during single-leg jump landings. Thirty-six 101st Airborne Division (Air Assault) Soldiers performed single-leg jump landings in the anterior direction with and without wearing body armor. The dynamic postural stability index and the individual stability indices (medial-lateral stability index, anterior-posterior stability index, and vertical stability index) were calculated for each condition. Paired sample t-tests were performed to determine differences between conditions. Significant differences existed for the medial-lateral stability index, anterior-posterior stability index, vertical stability index, and dynamic postural stability index (p < 0.05). The addition of body armor resulted in diminished dynamic postural stability, which may result in increased lower extremity injuries. Training programs should address the altered dynamic postural stability while wearing body armor in attempts to promote adaptations that will result in safer performance during dynamic tasks.

A time delay controller for magnetic bearings

NASA Technical Reports Server (NTRS)

Youcef-Toumi, K.; Reddy, S.

1991-01-01

The control of systems with unknown dynamics and unpredictable disturbances has raised some challenging problems. This is particularly important when high system performance needs to be guaranteed at all times. Recently, the Time Delay Control has been suggested as an alternative control scheme. The proposed control system does not require an explicit plant model nor does it depend on the estimation of specific plant parameters. Rather, it combines adaptation with past observations to directly estimate the effect of the plant dynamics. A control law is formulated for a class of dynamic systems and a sufficient condition is presented for control systems stability. The derivation is based on the bounded input-bounded output stability approach using L sub infinity function norms. The control scheme is implemented on a five degrees of freedom high speed and high precision magnetic bearing. The control performance is evaluated using step responses, frequency responses, and disturbance rejection properties. The experimental data show an excellent control performance despite the system complexity.

Information spread in networks: Games, optimal control, and stabilization

NASA Astrophysics Data System (ADS)

Khanafer, Ali

This thesis focuses on designing efficient mechanisms for controlling information spread in networks. We consider two models for information spread. The first one is the well-known distributed averaging dynamics. The second model is a nonlinear one that describes virus spread in computer and biological networks. We seek to design optimal, robust, and stabilizing controllers under practical constraints. For distributed averaging networks, we study the interaction between a network designer and an adversary. We consider two types of attacks on the network. In Attack-I, the adversary strategically disconnects a set of links to prevent the nodes from reaching consensus. Meanwhile, the network designer assists the nodes in reaching consensus by changing the weights of a limited number of links in the network. We formulate two problems to describe this competition where the order in which the players act is reversed in the two problems. Although the canonical equations provided by the Pontryagin's Maximum Principle (MP) seem to be intractable, we provide an alternative characterization for the optimal strategies that makes connection to potential theory. Further, we provide a sufficient condition for the existence of a saddle-point equilibrium (SPE) for the underlying zero-sum game. In Attack-II, the designer and the adversary are both capable of altering the measurements of all nodes in the network by injecting global signals. We impose two constraints on both players: a power constraint and an energy constraint. We assume that the available energy to each player is not sufficient to operate at maximum power throughout the horizon of the game. We show the existence of an SPE and derive the optimal strategies in closed form for this attack scenario. As an alternative to the "network designer vs. adversary" framework, we investigate the possibility of stabilizing unknown network diffusion processes using a distributed mechanism, where the uncertainty is due to an attack on the network. To this end, we propose a distributed version of the classical logic-based supervisory control scheme. Given a network of agents whose dynamics contain unknown parameters, the distributed supervisory control scheme is used to assist the agents to converge to a certain set-point without requiring them to have explicit knowledge of that set-point. Unlike the classical supervisory control scheme where a centralized supervisor makes switching decisions among the candidate controllers, in our scheme, each agent is equipped with a local supervisor that switches among the available controllers. The switching decisions made at a certain agent depend only on the information from its neighboring agents. We provide sufficient conditions for stabilization and apply our framework to the distributed averaging problem in the presence of large modeling uncertainty. For infected networks, we study the stability properties of a susceptible-infected-susceptible (SIS) diffusion model, so-called the n-intertwined Markov model, over arbitrary network topologies. Similar to the majority of infection spread dynamics, this model exhibits a threshold phenomenon. When the curing rates in the network are high, the all-healthy state is the unique equilibrium over the network. Otherwise, an endemic equilibrium state emerges, where some infection remains within the network. Using notions from positive systems theory, we provide conditions for the global asymptotic stability of the equilibrium points in both cases over strongly and weakly connected directed networks based on the value of the basic reproduction number, a fundamental quantity in the study of epidemics. Furthermore, we demonstrate that the n-intertwined Markov model can be viewed as a best-response dynamical system of a concave game among the nodes. This characterization allows us to cast new infection spread dynamics; additionally, we provide a sufficient condition, for the global convergence to the all-healthy state, that can be checked in a distributed fashion. Moreover, we investigate the problem of stabilizing the network when the curing rates of a limited number of nodes can be controlled. In particular, we characterize the number of controllers required for a class of undirected graphs. We also design optimal controllers capable of minimizing the total infection in the network at minimum cost. Finally, we outline a set of open problems in the area of information spread control.

Temporal stability of pathological scratchcard gambling among adult scratchcard buyers two years later.

PubMed

DeFuentes-Merillas, Laura; Koeter, Maarten W J; Schippers, Gerard M; van den Brink, Wim

2004-01-01

To estimate the 2-year cumulative incidence of pathological scratchcard gambling (PSG) among a representative sample of high-risk scratchcard buyers, to assess the 2-year temporal stability of PSG and scratchcard-related problems and to estimate the adjusted 1-year prevalence for PSG taking into account the temporal dynamics of this diagnosis. A prospective study with two assessments was applied to a non-proportional stratified random sample of 12,222 adult scratchcard buyers in the Netherlands. A cost-effective design was used and only those scratchcard buyers (n=201) who had already experienced some scratchcard-related problems at initial assessment were followed-up 2 years later. Two independent cohorts of buyers with scratchcard-related problems were followed-up: a cohort of 173 potential problematic scratchcard gamblers (PPSG) at increased risk for PSG and a cohort of 28 pathological scratchcard gamblers. Incidence and prevalence estimates were calculated for the total sample of adult scratchcard buyers and for the Dutch adult population. Of the PPSG group 6.72% (95% CI 2.30-8.90%) became addicted to scratchcards during the 2-year period. The 2-year cumulative incidence of PSG among Dutch adult scratchcard players was 0.24% (95% CI 0.16-0.34%). The stability of the Diagnostic and Statistical Manual 4th edition (DSM-IV) diagnosis of PSG ranged from 11.1% to 42.9%, depending on whether or not those lost to follow-up were considered to be cases of PSG. Taking into account the dynamics of this disorder, using the most conservative assumption, the adjusted 1-year prevalence of PSG for the total sample of adult scratchcard buyers was 0.33% (95% CI 0.23-0.45%). PSG proves to be a rare phenomenon among adult scratchcard buyers in the Netherlands. Both incidence and prevalence of the DSM-IV diagnosis PSG were low. Stability of the DSM-IV diagnosis PSG, DSM-IV criteria and South Oaks Gambling Screening-S (SOGS-S) problems were low. Prevalence was stable over the time because incidence and recovery rates were very similar.

Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model

NASA Astrophysics Data System (ADS)

Ni, Wenjie; Shi, Junping; Wang, Mingxin

2018-06-01

A diffusive Lotka-Volterra competition model with nonlocal intraspecific and interspecific competition between species is formulated and analyzed. The nonlocal competition strength is assumed to be determined by a diffusion kernel function to model the movement pattern of the biological species. It is shown that when there is no nonlocal intraspecific competition, the dynamics properties of nonlocal diffusive competition problem are similar to those of classical diffusive Lotka-Volterra competition model regardless of the strength of nonlocal interspecific competition. Global stability of nonnegative constant equilibria are proved using Lyapunov or upper-lower solution methods. On the other hand, strong nonlocal intraspecific competition increases the system spatiotemporal dynamic complexity. For the weak competition case, the nonlocal diffusive competition model may possess nonconstant positive equilibria for some suitably large nonlocal intraspecific competition coefficients.

A review and guidance for pattern selection in spatiotemporal system

NASA Astrophysics Data System (ADS)

Wang, Chunni; Ma, Jun

2018-03-01

Pattern estimation and selection in media can give important clues to understand the collective response to external stimulus by detecting the observable variables. Both reaction-diffusion systems (RDs) and neuronal networks can be treated as multi-agent systems from molecular level, intrinsic cooperation, competition. An external stimulus or attack can cause collapse of spatial order and distribution, while appropriate noise can enhance the consensus in the spatiotemporal systems. Pattern formation and synchronization stability can bridge isolated oscillators and the network by coupling these nodes with appropriate connection types. As a result, the dynamical behaviors can be detected and discussed by developing different spatial patterns and realizing network synchronization. Indeed, the collective response of network and multi-agent system depends on the local kinetics of nodes and cells. It is better to know the standard bifurcation analysis and stability control schemes before dealing with network problems. In this review, dynamics discussion and synchronization control on low-dimensional systems, pattern formation and synchronization stability on network, wave stability in RDs and neuronal network are summarized. Finally, possible guidance is presented when some physical effects such as polarization field and electromagnetic induction are considered.

The Effect of Systematic Error in Forced Oscillation Testing

NASA Technical Reports Server (NTRS)

Williams, Brianne Y.; Landman, Drew; Flory, Isaac L., IV; Murphy, Patrick C.

2012-01-01

One of the fundamental problems in flight dynamics is the formulation of aerodynamic forces and moments acting on an aircraft in arbitrary motion. Classically, conventional stability derivatives are used for the representation of aerodynamic loads in the aircraft equations of motion. However, for modern aircraft with highly nonlinear and unsteady aerodynamic characteristics undergoing maneuvers at high angle of attack and/or angular rates the conventional stability derivative model is no longer valid. Attempts to formulate aerodynamic model equations with unsteady terms are based on several different wind tunnel techniques: for example, captive, wind tunnel single degree-of-freedom, and wind tunnel free-flying techniques. One of the most common techniques is forced oscillation testing. However, the forced oscillation testing method does not address the systematic and systematic correlation errors from the test apparatus that cause inconsistencies in the measured oscillatory stability derivatives. The primary objective of this study is to identify the possible sources and magnitude of systematic error in representative dynamic test apparatuses. Sensitivities of the longitudinal stability derivatives to systematic errors are computed, using a high fidelity simulation of a forced oscillation test rig, and assessed using both Design of Experiments and Monte Carlo methods.

Dynamics of Orbits near 3:1 Resonance in the Earth-Moon System

NASA Technical Reports Server (NTRS)

Dichmann, Donald J.; Lebois, Ryan; Carrico, John P., Jr.

2013-01-01

The Interstellar Boundary Explorer (IBEX) spacecraft is currently in a highly elliptical orbit around Earth with a period near 3:1 resonance with the Moon. Its orbit is oriented so that apogee does not approach the Moon. Simulations show this orbit to be remarkably stable over the next twenty years. This article examines the dynamics of such orbits in the Circular Restricted 3-Body Problem (CR3BP). We look at three types of periodic orbits, each exhibiting a type of symmetry of the CR3BP. For each of the orbit types, we assess the local stability using Floquet analysis. Although not all of the periodic solutions are stable in the mathematical sense, any divergence is so slow as to produce practical stability over several decades. We use Poincare maps with twenty-year propagations to assess the nonlinear stability of the orbits, where the perturbation magnitudes are related to the orbit uncertainty for the IBEX mission. Finally we show that these orbits belong to a family of orbits connected in a bifurcation diagram that exhibits exchange of stability. The analysis of these families of period orbits provides a valuable starting point for a mission orbit trade study.

Influence of different types of seals on the stability behavior of turbopumps

NASA Technical Reports Server (NTRS)

Diewald, W.; Nordmann, R.

1989-01-01

One of the main problems in designing a centrifugal pump is to achieve a good efficiency while not neglecting the dynamic performance of the machine. The first aspect leads to the design of grooved seals in order to minimize the leakage flow. But the influence of these grooves to the dynamic behavior is not well known. Experimental and theoretical results of the rotordynamic coefficients for different groove shapes and depths in seals is presented. In addition, the coefficients are applied to a simple pump model.

Fluid Dynamics of Three-Dimensional Turbulent Shear Flows and Transition: Conference Proceedings of the Symposium of the Fluid Dynamics Panel Held in Cesme (Turkey) on 3-6 October 1988

DTIC Science & Technology

1989-04-01

1984), Herbert (1985, 1988), Singer ct al . (1986, 1987), and Saic (1985a,b, 1986). A renewed interest in problems of stability and transio iii swcpt...1981), Montoya et at. (1981), Harvey & Pride (1982), Pearce (1982a,b), Pearce et al . (1982), Tuttle & Maddalon (1982), Boeing Commercial Airplane...Company (1982, 1984), Etchberger (1983), Hanks et al . (1983), Wagner & Fischer (1983, 1984), Douglas Aircraft Company (1984), Holmes (1984), Runyan Ct al

Effect of Footwear on Dynamic Stability during Single-leg Jump Landings.

PubMed

Bowser, Bradley J; Rose, William C; McGrath, Robert; Salerno, Jilian; Wallace, Joshua; Davis, Irene S

2017-06-01

Barefoot and minimal footwear running has led to greater interest in the biomechanical effects of different types of footwear. The effect of running footwear on dynamic stability is not well understood. The purpose of this study was to compare dynamic stability and impact loading across 3 footwear conditions; barefoot, minimal footwear and standard running shoes. 25 injury free runners (21 male, 4 female) completed 5 single-leg jump landings in each footwear condition. Dynamic stability was assessed using the dynamic postural stability index and its directional components (mediolateral, anteroposterior, vertical). Peak vertical ground reaction force and vertical loadrates were also compared across footwear conditions. Dynamic stability was dependent on footwear type for all stability indices (ANOVA, p<0.05). Post-hoc tests showed dynamic stability was greater when barefoot than in running shoes for each stability index (p<0.02) and greater than minimal footwear for the anteroposterior stability index (p<0.01). Peak vertical force and average loadrates were both dependent on footwear (p≤0.05). Dynamic stability, peak vertical force, and average loadrates during single-leg jump landings appear to be affected by footwear type. The results suggest greater dynamic stability and lower impact loading when landing barefoot or in minimal footwear. © Georg Thieme Verlag KG Stuttgart · New York.

Automatic generation of the non-holonomic equations of motion for vehicle stability analysis

NASA Astrophysics Data System (ADS)

Minaker, B. P.; Rieveley, R. J.

2010-09-01

The mathematical analysis of vehicle stability has been utilised as an important tool in the design, development, and evaluation of vehicle architectures and stability controls. This paper presents a novel method for automatic generation of the linearised equations of motion for mechanical systems that is well suited to vehicle stability analysis. Unlike conventional methods for generating linearised equations of motion in standard linear second order form, the proposed method allows for the analysis of systems with non-holonomic constraints. In the proposed method, the algebraic constraint equations are eliminated after linearisation and reduction to first order. The described method has been successfully applied to an assortment of classic dynamic problems of varying complexity including the classic rolling coin, the planar truck-trailer, and the bicycle, as well as in more recent problems such as a rotor-stator and a benchmark road vehicle with suspension. This method has also been applied in the design and analysis of a novel three-wheeled narrow tilting vehicle with zero roll-stiffness. An application for determining passively stable configurations using the proposed method together with a genetic search algorithm is detailed. The proposed method and software implementation has been shown to be robust and provides invaluable conceptual insight into the stability of vehicles and mechanical systems.

Dynamic large eddy simulation: Stability via realizability

NASA Astrophysics Data System (ADS)

Mokhtarpoor, Reza; Heinz, Stefan

2017-10-01

The concept of dynamic large eddy simulation (LES) is highly attractive: such methods can dynamically adjust to changing flow conditions, which is known to be highly beneficial. For example, this avoids the use of empirical, case dependent approximations (like damping functions). Ideally, dynamic LES should be local in physical space (without involving artificial clipping parameters), and it should be stable for a wide range of simulation time steps, Reynolds numbers, and numerical schemes. These properties are not trivial, but dynamic LES suffers from such problems over decades. We address these questions by performing dynamic LES of periodic hill flow including separation at a high Reynolds number Re = 37 000. For the case considered, the main result of our studies is that it is possible to design LES that has the desired properties. It requires physical consistency: a PDF-realizable and stress-realizable LES model, which requires the inclusion of the turbulent kinetic energy in the LES calculation. LES models that do not honor such physical consistency can become unstable. We do not find support for the previous assumption that long-term correlations of negative dynamic model parameters are responsible for instability. Instead, we concluded that instability is caused by the stable spatial organization of significant unphysical states, which are represented by wall-type gradient streaks of the standard deviation of the dynamic model parameter. The applicability of our realizability stabilization to other dynamic models (including the dynamic Smagorinsky model) is discussed.

Mapped Chebyshev Pseudo-Spectral Method for Dynamic Aero-Elastic Problem of Limit Cycle Oscillation

NASA Astrophysics Data System (ADS)

Im, Dong Kyun; Kim, Hyun Soon; Choi, Seongim

2018-05-01

A mapped Chebyshev pseudo-spectral method is developed as one of the Fourier-spectral approaches and solves nonlinear PDE systems for unsteady flows and dynamic aero-elastic problem in a given time interval, where the flows or elastic motions can be periodic, nonperiodic, or periodic with an unknown frequency. The method uses the Chebyshev polynomials of the first kind for the basis function and redistributes the standard Chebyshev-Gauss-Lobatto collocation points more evenly by a conformal mapping function for improved numerical stability. Contributions of the method are several. It can be an order of magnitude more efficient than the conventional finite difference-based, time-accurate computation, depending on the complexity of solutions and the number of collocation points. The method reformulates the dynamic aero-elastic problem in spectral form for coupled analysis of aerodynamics and structures, which can be effective for design optimization of unsteady and dynamic problems. A limit cycle oscillation (LCO) is chosen for the validation and a new method to determine the LCO frequency is introduced based on the minimization of a second derivative of the aero-elastic formulation. Two examples of the limit cycle oscillation are tested: nonlinear, one degree-of-freedom mass-spring-damper system and two degrees-of-freedom oscillating airfoil under pitch and plunge motions. Results show good agreements with those of the conventional time-accurate simulations and wind tunnel experiments.

A Practice-Oriented Bifurcation Analysis for Pulse Energy Converters: A Stability Margin

NASA Astrophysics Data System (ADS)

Kolokolov, Yury; Monovskaya, Anna

The popularity of systems of pulse energy conversion (PEC-systems) for practical applications is due to the heightened efficiency of energy conversion processes with comparatively simple realizations. Nevertheless, a PEC-system represents a nonlinear object with a variable structure, and the bifurcation analysis remains the basic tool to describe PEC dynamics evolution. The paper is devoted to the discussion on whether the scientific viewpoint on the natural nonlinear dynamics evolution can be involved in practical applications. We focus on the problems connected with stability boundaries of an operating regime. The results of both small-signal analysis and computational bifurcation analysis are considered in the parametrical space in comparison with the results of the experimental identification of the zonal heterogeneity of the operating process. This allows to propose an adapted stability margin as a sufficiently safe distance before the point after which the operating process begins to lose the stability. Such stability margin can extend the permissible operating domain in the parametrical space at the expense of using cause-and-effect relations in the context of natural regularities of nonlinear dynamics. Reasoning and discussion are based on the experimental and computational results for a synchronous buck converter with a pulse-width modulation. The presented results can be useful, first of all, for PEC-systems with significant variation of equivalent inductance and/or capacity. We believe that the discussion supports a viewpoint by which the contemporary methods of the computational and experimental bifurcation analyses possess both analytical abilities and experimental techniques for promising solutions which could be practice-oriented for PEC-systems.

Asymptotic stability of shear-flow solutions to incompressible viscous free boundary problems with and without surface tension

NASA Astrophysics Data System (ADS)

Tice, Ian

2018-04-01

This paper concerns the dynamics of a layer of incompressible viscous fluid lying above a rigid plane and with an upper boundary given by a free surface. The fluid is subject to a constant external force with a horizontal component, which arises in modeling the motion of such a fluid down an inclined plane, after a coordinate change. We consider the problem both with and without surface tension for horizontally periodic flows. This problem gives rise to shear-flow equilibrium solutions, and the main thrust of this paper is to study the asymptotic stability of the equilibria in certain parameter regimes. We prove that there exists a parameter regime in which sufficiently small perturbations of the equilibrium at time t=0 give rise to global-in-time solutions that return to equilibrium exponentially in the case with surface tension and almost exponentially in the case without surface tension. We also establish a vanishing surface tension limit, which connects the solutions with and without surface tension.

Post-Newtonian Circular Restricted 3-Body Problem: Schwarzschild primaries

NASA Astrophysics Data System (ADS)

Dubeibe, F. L.; Lora-Clavijo, F. D.; González, G. A.

2017-07-01

The restricted three-body problem (RTBP) has been extensively studied to investigate the stability of the solar system, extra-solar subsystems, asteroid capture, and the dynamics of two massive black holes orbited by a sun. In the present work, we study the stability of the planar circular restricted three-body problem in the context of post-Newtonian approximations. First of all, we review the results obtained from the post-Newtonian equations of motion calculated in the framework of the Einstein-Infeld-Hoffmann formalism (EIH). Therefore, using the Fodor-Hoenselers-Perjes formalism (FHP), we have performed an expansion of the gravitational potential for two primaries, deriving a new system of equations of motion, which unlike the EIH-approach, preserves the Jacobian integral of motion. Additionally, we have obtained approximate expressions for the Lagrange points in terms of a mass parameter μ, where it is found that the deviations from the classical regime are larger for the FHP than for the EIH equations.

Changes of instability thresholds of rotor due to bearing misalignments

NASA Technical Reports Server (NTRS)

Springer, H.; Ecker, H.; Gunter, E. J.

1985-01-01

The influence of bearing misalignment upon the dynamic characteristics of statistically indeterminant rotor bearing systems is investigated. Both bearing loads and stability speed limits of a rotor may be changed significantly by magnitude and direction of bearing misalignment. The useful theory of short journal bearings is introduced and simple analytical expressions, governing the misalignment problem, are carried out. Polar plots for the bearing load capacities and stability maps, describing the speed limit in terms of misalignment, are presented. These plots can be used by the designer to estimate deviations between calculation and experimental data due to misalignment effects.

Influence of nonlinear interactions on the development of instability in hydrodynamic wave systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romanova, N. N.; Chkhetiani, O. G., E-mail: ochkheti@mx.iki.rssi.ru, E-mail: ochkheti@gmail.ru; Yakushkin, I. G.

2016-05-15

The problem of the development of shear instability in a three-layer medium simulating the flow of a stratified incompressible fluid is considered. The hydrodynamic equations are solved by expanding the Hamiltonian in a small parameter. The equations for three interacting waves, one of which is unstable, have been derived and solved numerically. The three-wave interaction is shown to stabilize the instability. Various regimes of the system’s dynamics, including the stochastic ones dependent on one of the invariants in the problem, can arise in this case. It is pointed out that the instability development scenario considered differs from the previously consideredmore » scenario of a different type, where the three-wave interaction does not stabilize the instability. The interaction of wave packets is considered briefly.« less

Stability Analysis of Continuous-Time and Discrete-Time Quaternion-Valued Neural Networks With Linear Threshold Neurons.

PubMed

Chen, Xiaofeng; Song, Qiankun; Li, Zhongshan; Zhao, Zhenjiang; Liu, Yurong

2018-07-01

This paper addresses the problem of stability for continuous-time and discrete-time quaternion-valued neural networks (QVNNs) with linear threshold neurons. Applying the semidiscretization technique to the continuous-time QVNNs, the discrete-time analogs are obtained, which preserve the dynamical characteristics of their continuous-time counterparts. Via the plural decomposition method of quaternion, homeomorphic mapping theorem, as well as Lyapunov theorem, some sufficient conditions on the existence, uniqueness, and global asymptotical stability of the equilibrium point are derived for the continuous-time QVNNs and their discrete-time analogs, respectively. Furthermore, a uniform sufficient condition on the existence, uniqueness, and global asymptotical stability of the equilibrium point is obtained for both continuous-time QVNNs and their discrete-time version. Finally, two numerical examples are provided to substantiate the effectiveness of the proposed results.

Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier–Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balajewicz, Maciej; Tezaur, Irina; Dowell, Earl

For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based fluid ROMs in which truncated modes are accounted for a priori via a minimal rotation of the projection subspace. Attention is focused on the full non-linear compressible Navier–Stokes equations in specific volume form as a step toward a more general formulation for problems with generic non-linearities. Unlike traditional approaches, no empirical turbulence modeling terms are required, and consistency between the ROM and themore » Navier–Stokes equation from which the ROM is derived is maintained. Mathematically, the approach is formulated as a trace minimization problem on the Stiefel manifold. As a result, the reproductive as well as predictive capabilities of the method are evaluated on several compressible flow problems, including a problem involving laminar flow over an airfoil with a high angle of attack, and a channel-driven cavity flow problem.« less

Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier–Stokes equations

DOE PAGES

Balajewicz, Maciej; Tezaur, Irina; Dowell, Earl

2016-05-25

For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based fluid ROMs in which truncated modes are accounted for a priori via a minimal rotation of the projection subspace. Attention is focused on the full non-linear compressible Navier–Stokes equations in specific volume form as a step toward a more general formulation for problems with generic non-linearities. Unlike traditional approaches, no empirical turbulence modeling terms are required, and consistency between the ROM and themore » Navier–Stokes equation from which the ROM is derived is maintained. Mathematically, the approach is formulated as a trace minimization problem on the Stiefel manifold. As a result, the reproductive as well as predictive capabilities of the method are evaluated on several compressible flow problems, including a problem involving laminar flow over an airfoil with a high angle of attack, and a channel-driven cavity flow problem.« less

Direct Adaptive Control of Systems with Actuator Failures: State of the Art and Continuing Challenges

NASA Technical Reports Server (NTRS)

Tao, Gang; Joshi, Suresh M.

2008-01-01

In this paper, the problem of controlling systems with failures and faults is introduced, and an overview of recent work on direct adaptive control for compensation of uncertain actuator failures is presented. Actuator failures may be characterized by some unknown system inputs being stuck at some unknown (fixed or varying) values at unknown time instants, that cannot be influenced by the control signals. The key task of adaptive compensation is to design the control signals in such a manner that the remaining actuators can automatically and seamlessly take over for the failed ones, and achieve desired stability and asymptotic tracking. A certain degree of redundancy is necessary to accomplish failure compensation. The objective of adaptive control design is to effectively use the available actuation redundancy to handle failures without the knowledge of the failure patterns, parameters, and time of occurrence. This is a challenging problem because failures introduce large uncertainties in the dynamic structure of the system, in addition to parametric uncertainties and unknown disturbances. The paper addresses some theoretical issues in adaptive actuator failure compensation: actuator failure modeling, redundant actuation requirements, plant-model matching, error system dynamics, adaptation laws, and stability, tracking, and performance analysis. Adaptive control designs can be shown to effectively handle uncertain actuator failures without explicit failure detection. Some open technical challenges and research problems in this important research area are discussed.

Maximum likelihood identification and optimal input design for identifying aircraft stability and control derivatives

NASA Technical Reports Server (NTRS)

Stepner, D. E.; Mehra, R. K.

1973-01-01

A new method of extracting aircraft stability and control derivatives from flight test data is developed based on the maximum likelihood cirterion. It is shown that this new method is capable of processing data from both linear and nonlinear models, both with and without process noise and includes output error and equation error methods as special cases. The first application of this method to flight test data is reported for lateral maneuvers of the HL-10 and M2/F3 lifting bodies, including the extraction of stability and control derivatives in the presence of wind gusts. All the problems encountered in this identification study are discussed. Several different methods (including a priori weighting, parameter fixing and constrained parameter values) for dealing with identifiability and uniqueness problems are introduced and the results given. The method for the design of optimal inputs for identifying the parameters of linear dynamic systems is also given. The criterion used for the optimization is the sensitivity of the system output to the unknown parameters. Several simple examples are first given and then the results of an extensive stability and control dervative identification simulation for a C-8 aircraft are detailed.

The Sheperd equation and chaos identification.

PubMed

Gregson, Robert A M

2010-04-01

An equation created by Sheperd (1982) to model stability in exploited fish populations has been found to have a wider application, and it exhibits complicated internal dynamics, including phases of strict periodicity and of chaos. It may be potentially applicable to other psychophysiological contexts. The problems of determining goodness-of fit, and the comparative performance of alternative models including the Shephed model, are briefly addressed.

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

NASA Astrophysics Data System (ADS)

Chróścielewski, Jacek; Schmidt, Rüdiger; Eremeyev, Victor A.

2018-05-01

This paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite rotations of the normal. The finite element model can be applied to static, stability, and transient analysis of smart structures consisting of a master structure and integrated piezoelectric actuator layers or patches attached to the upper and lower surfaces. Two problems are studied extensively: (i) FE analyses of a clamped semicircular ring shell that has been used as a benchmark problem for linear vibration control in several recent papers are critically reviewed and extended to account for the effects of structural nonlinearity and (ii) a smart circular arch subjected to a hydrostatic pressure load is investigated statically and dynamically in order to study the shift of bifurcation and limit points, eigenfrequencies, and eigenvectors, as well as vibration control for loading conditions which may lead to dynamic loss of stability.

Linear State-Space Representation of the Dynamics of Relative Motion, Based on Restricted Three Body Dynamics

NASA Technical Reports Server (NTRS)

Luquette,Richard J.; Sanner, Robert M.

2004-01-01

Precision Formation Flying is an enabling technology for a variety of proposed space-based observatories, including the Micro-Arcsecond X-ray Imaging Mission (MAXIM) , the associated MAXIM pathfinder mission, Stellar Imager (SI) and the Terrestrial Planet Finder (TPF). An essential element of the technology is the control algorithm, requiring a clear understanding of the dynamics of relative motion. This paper examines the dynamics of relative motion in the context of the Restricted Three Body Problem (RTBP). The natural dynamics of relative motion are presented in their full nonlinear form. Motivated by the desire to apply linear control methods, the dynamics equations are linearized and presented in state-space form. The stability properties are explored for regions in proximity to each of the libration points in the Earth/Moon - Sun rotating frame. The dynamics of relative motion are presented in both the inertial and rotating coordinate frames.

Theoretical study and control optimization of an integrated pest management predator-prey model with power growth rate.

PubMed

Sun, Kaibiao; Zhang, Tonghua; Tian, Yuan

2016-09-01

This work presents a pest control predator-prey model, where rate of change in prey density follows a scaling law with exponent less than one and the control is by an integrated management strategy. The aim is to investigate the change in system dynamics and determine a pest control level with minimum control price. First, the dynamics of the proposed model without control is investigated by taking the exponent as an index parameter. And then, to determine the frequency of spraying chemical pesticide and yield releases of the predator, the existence of the order-1 periodic orbit of the control system is discussed in cases. Furthermore, to ensure a certain robustness of the adopted control, i.e., for an inaccurately detected species density or a deviation, the control system could be stabilized at the order-1 periodic orbit, the stability of the order-1 periodic orbit is verified by an stability criterion for a general semi-continuous dynamical system. In addition, to minimize the total cost input in pest control, an optimization problem is formulated and the optimum pest control level is obtained. At last, the numerical simulations with a specific model are carried out to complement the theoretical results. Copyright © 2016 Elsevier Inc. All rights reserved.

Thermodiffusion as a means to manipulate liquid film dynamics on chemically patterned surfaces

PubMed Central

Kalpathy, Sreeram K.; Shreyes, Amrita Ravi

2017-01-01

The model problem examined here is the stability of a thin liquid film consisting of two miscible components, resting on a chemically patterned solid substrate and heated from below. In addition to surface tension gradients, the temperature variations also induce gradients in the concentration of the film by virtue of thermodiffusion/Soret effects. We study the stability and dewetting behaviour due to the coupled interplay between thermal gradients, Soret effects, long-range van der Waals forces, and wettability gradient-driven flows. Linear stability analysis is first employed to predict growth rates and the critical Marangoni number for chemically homogeneous surfaces. Then, nonlinear simulations are performed to unravel the interfacial dynamics and possible locations of the film rupture on chemically patterned substrates. Results suggest that appropriate tuning of the Soret parameter and its direction, in conjunction with either heating or cooling, can help manipulate the location and time scales of the film rupture. The Soret effect can either potentially aid or oppose film instability depending on whether the thermal and solutal contributions to flow are cooperative or opposed to each other. PMID:28595391

Linear and nonlinear dynamic analysis by boundary element method. Ph.D. Thesis, 1986 Final Report

NASA Technical Reports Server (NTRS)

Ahmad, Shahid

1991-01-01

An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons with available analytical and numerical results, the stability and high accuracy of these dynamic analysis techniques are established.

Polaritonic Rabi and Josephson Oscillations

PubMed Central

Rahmani, Amir; Laussy, Fabrice P.

2016-01-01

The dynamics of coupled condensates is a wide-encompassing problem with relevance to superconductors, BECs in traps, superfluids, etc. Here, we provide a unified picture of this fundamental problem that includes i) detuning of the free energies, ii) different self-interaction strengths and iii) finite lifetime of the modes. At such, this is particularly relevant for the dynamics of polaritons, both for their internal dynamics between their light and matter constituents, as well as for the more conventional dynamics of two spatially separated condensates. Polaritons are short-lived, interact only through their material fraction and are easily detuned. At such, they bring several variations to their atomic counterpart. We show that the combination of these parameters results in important twists to the phenomenology of the Josephson effect, such as the behaviour of the relative phase (running or oscillating) or the occurence of self-trapping. We undertake a comprehensive stability analysis of the fixed points on a normalized Bloch sphere, that allows us to provide a generalized criterion to identify the Rabi and Josephson regimes in presence of detuning and decay. PMID:27452872

Radiation Pressure Cooling as a Quantum Dynamical Process

NASA Astrophysics Data System (ADS)

He, Bing; Yang, Liu; Lin, Qing; Xiao, Min

2017-06-01

One of the most fundamental problems in optomechanical cooling is how small the thermal phonon number of a mechanical oscillator can be achieved under the radiation pressure of a proper cavity field. Different from previous theoretical predictions, which were based on an optomechanical system's time-independent steady states, we treat such cooling as a dynamical process of driving the mechanical oscillator from its initial thermal state, due to its thermal equilibrium with the environment, to a stabilized quantum state of higher purity. We find that the stabilized thermal phonon number left in the end actually depends on how fast the cooling process could be. The cooling speed is decided by an effective optomechanical coupling intensity, which constitutes an essential parameter for cooling, in addition to the sideband resolution parameter that has been considered in other theoretical studies. The limiting thermal phonon number that any cooling process cannot surpass exhibits a discontinuous jump across a certain value of the parameter.

The Effect of Dynamic Wetting on the Stability of a Gas-Liquid Interface Subjected to Vertical Oscillations

NASA Astrophysics Data System (ADS)

Kraynik, Andrew M.; Romero, Louis; Torczynski, John R.; Brooks, Carlton F.; O'Hern, Timothy J.; Jepson, Richard A.; Benavides, Gilbert L.

2009-11-01

The stability of an interface in a container partially filled with silicone oil and subjected to gravity and vertical oscillations has been examined theoretically and computationally. An exact theory for the onset of a parametric instability producing Faraday-like waves was developed for arbitrary liquid viscosity, stress-free walls, and deep two-dimensional or axisymmetric containers. Finite-element simulations for stress-free walls are in excellent agreement with the theory, which predicts instability in discrete frequency bands. These simpler calculations are a departure point for examining the more realistic problem, which involves no-slip at the walls and dynamic wetting modeled with a Blake condition. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Process-driven inference of biological network structure: feasibility, minimality, and multiplicity

NASA Astrophysics Data System (ADS)

Zeng, Chen

2012-02-01

For a given dynamic process, identifying the putative interaction networks to achieve it is the inference problem. In this talk, we address the computational complexity of inference problem in the context of Boolean networks under dominant inhibition condition. The first is a proof that the feasibility problem (is there a network that explains the dynamics?) can be solved in polynomial-time. Second, while the minimality problem (what is the smallest network that explains the dynamics?) is shown to be NP-hard, a simple polynomial-time heuristic is shown to produce near-minimal solutions, as demonstrated by simulation. Third, the theoretical framework also leads to a fast polynomial-time heuristic to estimate the number of network solutions with reasonable accuracy. We will apply these approaches to two simplified Boolean network models for the cell cycle process of budding yeast (Li 2004) and fission yeast (Davidich 2008). Our results demonstrate that each of these networks contains a giant backbone motif spanning all the network nodes that provides the desired main functionality, while the remaining edges in the network form smaller motifs whose role is to confer stability properties rather than provide function. Moreover, we show that the bioprocesses of these two cell cycle models differ considerably from a typically generated process and are intrinsically cascade-like.

The Realization and Analysis of Capacitance Self Tracing (CST) Method for Wide Band Response Measurement of Carrier Type Dynamic Strain Amplifier

NASA Astrophysics Data System (ADS)

Kubodera, Shinji; Tanzawa, Tsutomu; Morisawa, Masayuki; Kiyohiro, Noriaki

Carrier type dynamic strain amplifiers are frequently used for stress measurement with strain gages. That is because the carrier type dynamic strain amplifier can conduct high precision measurement since it is highly resistant against hum noise from the power supply frequency in principle and is free from the thermoelectomotive force even if a metal contact is used in wiring to a Wheatstone bridge for measuring. A problem of the carrier type dynamic strain amplifier is generation of Capacitive component (hereinafter referred to as the C component) in an input cable connecting from the amplifier to the input sensor (Wheatstone bridge for measuring). The C component varies with cable length, cable materials, or ambient temperature change. The aforementioned changing adversely affects the stability of the amplifier. In this paper, we realize and analyze the method that increases the stability of amplifier by detecting, eliminating and self tracking the above C component constantly. Used carrier frequency at 12kHz and 28kHz. We made amplifiers with noise resistant and wide band frequency of measurement range and verified the theory of the Capacitance Self Tracing with the above amplifiers.

Buckling Instabilities and Complex Dynamics in a Model of Uniflagellar Bacterial Locomotion

NASA Astrophysics Data System (ADS)

Nguyen, Frank; Graham, Michael

2015-11-01

Locomotion of microorganisms at low Reynolds number is a long studied problem. Of particular interest are organisms using a single flagellum to undergo a wide range of motions: pushing, pulling, and tumbling or flicking. Recent experiments have connected the stability of the hook protein, connecting cell motor and flagellum, to deviations from typical straight swimming trajectories. We seek physical explanations to these phenomena by developing a computationally inexpensive, rigid-body dynamic model of a uniflagellated organism with a flexible hook connection that captures the fundamental dynamics, kinematics, and configurations. Furthermore, the model addresses the effects of hook loading and geometry on the stability of the system. Simulations with low hook flexibility produce the classic straight trajectory, but a large flexibility produces helical trajectories, leading to directional changes when coupled with transient hook stiffening. Minima for critical flexibilities are found in certain subsets of parameter space, implying preferred geometries for certain swimming dynamics. The model verifies proposed mechanisms for swimming in various modes and highlights the role of flexibility in the biology of real organisms and the engineering of artificial microswimmers. This work was supported by NSF grant PHY-1304942.

Tibiotalocalcaneal arthrodesis using a dynamically locked retrograde intramedullary nail.

PubMed

Pelton, Kevin; Hofer, Jason K; Thordarson, David B

2006-10-01

Tibiotalocalcaneal arthrodesis is an important salvage method for patients with complex hindfoot problems, including Charcot arthropathy, osteonecrosis of the talus, combined arthritis of the ankle and subtalar joint, and failed total ankle arthroplasty. This study evaluated the results of a dynamic retrograde intramedullary nail for fixation with posterior to anterior distal interlocking screws placed through the calcaneus for tibiotalocalcaneal fusion. Thirty-three consecutive tibiotalocalcaneal fusions were done by a single surgeon (DBT) and were stabilized with a dynamic retrograde intramedullary nail. Time to fusion, impaction of the nail relative to the intramedullary canal, nail-tibial angle, and complications were noted. Average followup was 14 months. Twenty-nine of 33 feet (88%) fused at an average of 3.7 months after surgery. Average impaction of the nail was 2.3 (0.5 to 5.0) mm. Cortical hypertrophy at the tip of the rod or at the proximal interlocking screw was noted in 13 of 27 patients. A trend toward a higher nonunion rate was noted in patients with an increased nail-tibial angle. Dynamic retrograde intramedullary nailing for fixation of the tibiotalocalcaneal fusions is a good method of stabilizing this complex fusion construct.

Dynamics and stability of light-like tachyon condensation

NASA Astrophysics Data System (ADS)

Barnaby, Neil; Mulryne, David J.; Nunes, Nelson J.; Robinson, Patrick

2009-03-01

Recently, Hellerman and Schnabl considered the dynamics of unstable D-branes in the background of a linear dilaton. Remarkably, they were able to construct light-like tachyon solutions which interpolate smoothly between the perturbative and nonperturbative vacua, without undergoing the wild oscillations that plague time-like solutions. In their analysis, however, the full structure of the initial value problem for the nonlocal dynamical equations was not considered. In this paper, therefore, we reexamine the nonlinear dynamics of light-like tachyon condensation using a combination of numerical and analytical techniques. We find that for the p-adic string the monotonic behaviour obtained previously relied on a special choice of initial conditions near the unstable maximum. For generic initial conditions the wild oscillations come back to haunt us. Interestingly, we find an ``island of stability'' in initial condition space that leads to sensible evolution at late times. For the string field theory case, on the other hand, we find that the evolution is completely stable for generic choices of initial data. This provides an explicit example of a string theoretic system that admits infinitely many initial data but is nevertheless nonperturbatively stable. Qualitatively similar dynamics are obtained in nonlocal cosmologies where the Hubble damping plays a role very analogous to the dilaton gradient.

Robust Stability of Scaled-Four-Channel Teleoperation with Internet Time-Varying Delays

PubMed Central

Delgado, Emma; Barreiro, Antonio; Falcón, Pablo; Díaz-Cacho, Miguel

2016-01-01

We describe the application of a generic stability framework for a teleoperation system under time-varying delay conditions, as addressed in a previous work, to a scaled-four-channel (γ-4C) control scheme. Described is how varying delays are dealt with by means of dynamic encapsulation, giving rise to mu-test conditions for robust stability and offering an appealing frequency technique to deal with the stability robustness of the architecture. We discuss ideal transparency problems and we adapt classical solutions so that controllers are proper, without single or double differentiators, and thus avoid the negative effects of noise. The control scheme was fine-tuned and tested for complete stability to zero of the whole state, while seeking a practical solution to the trade-off between stability and transparency in the Internet-based teleoperation. These ideas were tested on an Internet-based application with two Omni devices at remote laboratory locations via simulations and real remote experiments that achieved robust stability, while performing well in terms of position synchronization and force transparency. PMID:27128914

Trojan resonant dynamics, stability, and chaotic diffusion, for parameters relevant to exoplanetary systems

NASA Astrophysics Data System (ADS)

Páez, Rocío Isabel; Efthymiopoulos, Christos

2015-02-01

The possibility that giant extrasolar planets could have small Trojan co-orbital companions has been examined in the literature from both viewpoints of the origin and dynamical stability of such a configuration. Here we aim to investigate the dynamics of hypothetical small Trojan exoplanets in domains of secondary resonances embedded within the tadpole domain of motion. To this end, we consider the limit of a massless Trojan companion of a giant planet. Without other planets, this is a case of the elliptic restricted three body problem (ERTBP). The presence of additional planets (hereafter referred to as the restricted multi-planet problem, RMPP) induces new direct and indirect secular effects on the dynamics of the Trojan body. The paper contains a theoretical and a numerical part. In the theoretical part, we develop a Hamiltonian formalism in action-angle variables, which allows us to treat in a unified way resonant dynamics and secular effects on the Trojan body in both the ERTBP or the RMPP. In both cases, our formalism leads to a decomposition of the Hamiltonian in two parts, . , called the basic model, describes resonant dynamics in the short-period (epicyclic) and synodic (libration) degrees of freedom, while contains only terms depending trigonometrically on slow (secular) angles. is formally identical in the ERTBP and the RMPP, apart from a re-definition of some angular variables. An important physical consequence of this analysis is that the slow chaotic diffusion along resonances proceeds in both the ERTBP and the RMPP by a qualitatively similar dynamical mechanism. We found that this is best approximated by the paradigm of `modulational diffusion'. In the paper's numerical part, we then focus on the ERTBP in order to make a detailed numerical demonstration of the chaotic diffusion process along resonances. Using color stability maps, we first provide a survey of the resonant web for characteristic mass parameter values of the primary, in which the secondary resonances from 1:5 to 1:12 (ratio of the short over the synodic period), as well as their transverse resonant multiplets, appear. We give numerical examples of diffusion of weakly chaotic orbits in the resonant web. We finally make a statistics of the escaping times in the resonant domain, and find power-law tails of the distribution of the escaping times for the slowly diffusing chaotic orbits. Implications of resonant dynamics in the search for Trojan exoplanets are discussed.

Big Data-Based Approach to Detect, Locate, and Enhance the Stability of an Unplanned Microgrid Islanding

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, Huaiguang; Li, Yan; Zhang, Yingchen

In this paper, a big data-based approach is proposed for the security improvement of an unplanned microgrid islanding (UMI). The proposed approach contains two major steps: the first step is big data analysis of wide-area monitoring to detect a UMI and locate it; the second step is particle swarm optimization (PSO)-based stability enhancement for the UMI. First, an optimal synchrophasor measurement device selection (OSMDS) and matching pursuit decomposition (MPD)-based spatial-temporal analysis approach is proposed to significantly reduce the volume of data while keeping appropriate information from the synchrophasor measurements. Second, a random forest-based ensemble learning approach is trained to detectmore » the UMI. When combined with grid topology, the UMI can be located. Then the stability problem of the UMI is formulated as an optimization problem and the PSO is used to find the optimal operational parameters of the UMI. An eigenvalue-based multiobjective function is proposed, which aims to improve the damping and dynamic characteristics of the UMI. Finally, the simulation results demonstrate the effectiveness and robustness of the proposed approach.« less

Stable architectures for deep neural networks

NASA Astrophysics Data System (ADS)

Haber, Eldad; Ruthotto, Lars

2018-01-01

Deep neural networks have become invaluable tools for supervised machine learning, e.g. classification of text or images. While often offering superior results over traditional techniques and successfully expressing complicated patterns in data, deep architectures are known to be challenging to design and train such that they generalize well to new data. Critical issues with deep architectures are numerical instabilities in derivative-based learning algorithms commonly called exploding or vanishing gradients. In this paper, we propose new forward propagation techniques inspired by systems of ordinary differential equations (ODE) that overcome this challenge and lead to well-posed learning problems for arbitrarily deep networks. The backbone of our approach is our interpretation of deep learning as a parameter estimation problem of nonlinear dynamical systems. Given this formulation, we analyze stability and well-posedness of deep learning and use this new understanding to develop new network architectures. We relate the exploding and vanishing gradient phenomenon to the stability of the discrete ODE and present several strategies for stabilizing deep learning for very deep networks. While our new architectures restrict the solution space, several numerical experiments show their competitiveness with state-of-the-art networks.

Cancellation control law for lateral-directional dynamics of a supermaneuverable aircraft

NASA Technical Reports Server (NTRS)

Snell, Antony

1993-01-01

Cancellation control laws are designed which reduce the high levels of lateral acceleration encountered during aggressive rolling maneuvers executed at high angle of attack. Two independent problem are examined. One is to reduce lateral acceleration at the mass center, while the other focuses on lateral acceleration at the pilot's station, located 7.0 m forward of the mass center. Both of these problems are challenging and somewhat different in their limitations. In each case the design is based on a linearization of the lateral-directional dynamics about a high angle of attack condition. The controllers incorporate dynamic inversion inner loops to provide control of stability-axis roll- and yaw-rates and then employ cancellation filters in both feed-forward and feed-back signal paths. The relative simplicity of the control laws should allow nonlinear generalizations to be devised. Although it is shown that lateral acceleration can be reduced substantially by such control laws, this is at the cost of slowed roll response, poor dutch-roll damping or a combination of the two.

Association schemes perspective of microbubble cluster in ultrasonic fields.

PubMed

Behnia, S; Yahyavi, M; Habibpourbisafar, R

2018-06-01

Dynamics of a cluster of chaotic oscillators on a network are studied using coupled maps. By introducing the association schemes, we obtain coupling strength in the adjacency matrices form, which satisfies Markov matrices property. We remark that in general, the stability region of the cluster of oscillators at the synchronization state is characterized by Lyapunov exponent which can be defined based on the N-coupled map. As a detailed physical example, dynamics of microbubble cluster in an ultrasonic field are studied using coupled maps. Microbubble cluster dynamics have an indicative highly active nonlinear phenomenon, were not easy to be explained. In this paper, a cluster of microbubbles with a thin elastic shell based on the modified Keller-Herring equation in an ultrasonic field is demonstrated in the framework of the globally coupled map. On the other hand, a relation between the microbubble elements is replaced by a relation between the vertices. Based on this method, the stability region of microbubbles pulsations at complete synchronization state has been obtained analytically. In this way, distances between microbubbles as coupling strength play the crucial role. In the stability region, we thus observe that the problem of study of dynamics of N-microbubble oscillators reduce to that of a single microbubble. Therefore, the important parameters of the isolated microbubble such as applied pressure, driving frequency and the initial radius have effective behavior on the synchronization state. Copyright © 2018 Elsevier B.V. All rights reserved.

On regulators with a prescribed degree of stability. M.S. Thesis

NASA Technical Reports Server (NTRS)

Ng, P. T. P.

1981-01-01

Several important aspects of the Regulator with a Prescribed Degree of Stability (RPDS) methodology and its applications are considered. The solution of the time varying RPDS problem as well as the characterization of RPDS closed loop eigenstructure properties are obtained. Based on the asymptotic behavior of RPDS root loci, a one step algorithm for designing Regulators with Prescribed Damping Ratio (RPDR) is developed. The robustness properties of RPDS are characterized in terms of the properties of the return difference and the inverse return difference matrices for the RPDS state feedback loop. This class of regulators is found to possess excellent multiloop margins with respect to stability and degree of stability properties. The ability of RPDS design to tolerate changing operating conditions and unmodelled dynamics are illustrated with a multiterminal dc/ac power system example. The output feedback realization of RPDS requires the use of Linear Quadratic Gaussian (LQG) methodology.

Wind-tunnel static and free-flight investigation of high-angle-of-attack stability and control characteristics of a model of the EA-6B airplane

NASA Technical Reports Server (NTRS)

Jordan, Frank L., Jr.; Hahne, David E.

1992-01-01

An investigation was conducted in the Langley 30- by 60-Foot Tunnel and the Langley 12-Foot Low-Speed Tunnel to identify factors contributing to a directional divergence at high angles of attack for the EA-6B airplane. The study consisted of static wind-tunnel tests, smoke and tuft flow-visualization tests, and free-flight tests of a 1/8.5-scale model of the airplane. The results of the investigation indicate that the directional divergence of the airplane is brought about by a loss of directional stability and effective dihedral at high angles of attack. Several modifications were tested that significantly alleviate the stability problem. The results of the free-flight study show that the modified configuration exhibits good dynamic stability characteristics and could be flown at angles of attack significantly higher than those of the unmodified configuration.

Application of the comparison principle to analysis of nonlinear systems. [using Lipschitz condition and differential equations

NASA Technical Reports Server (NTRS)

Gunderson, R. W.

1975-01-01

A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.

Theoretical and Experimental Methods in the Solution of Missile Nonlinear Roll Problems

DTIC Science & Technology

1978-03-01

OF ILLUSTRATIONS (Continued) 34 Typical Effect of Slot on Induced Rolling Moment .............. 35 35 Effect of Slot on Amplitude of Induced Rolling...Characteristics of Slotted Fill Vehicle .............. 40 41 Effects of Fin Configuration on Stability ..................... 41 42 Release Envelope...missiles depended strongly upon roll rate. The concept of Magnus instability had been developed earlier from the linear theory of missile dynamics, and

The Dynamics of Finite-Dimensional Systems Under Nonconservative Position Forces

NASA Astrophysics Data System (ADS)

Lobas, L. G.

2001-01-01

General theorems on the stability of stationary states of mechanical systems subjected to nonconservative position forces are presented. Specific mechanical problems on gyroscopic systems, a double-link pendulum with a follower force and elastically fixed upper tip, multilink pneumowheel vehicles, a monorail car, and rail-guided vehicles are analyzed. Methods for investigation of divergent bifurcations and catastrophes of stationary states are described

Approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays: a robust stability problem.

PubMed

Pandiselvi, S; Raja, R; Cao, Jinde; Rajchakit, G; Ahmad, Bashir

2018-01-01

This work predominantly labels the problem of approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays. Here we design a linear estimator in such a way that the absorption of mRNA and protein can be approximated via known measurement outputs. By utilizing a Lyapunov-Krasovskii functional and some stochastic analysis execution, we obtain the stability formula of the estimation error systems in the structure of linear matrix inequalities under which the estimation error dynamics is robustly exponentially stable. Further, the obtained conditions (in the form of LMIs) can be effortlessly solved by some available software packages. Moreover, the specific expression of the desired estimator is also shown in the main section. Finally, two mathematical illustrative examples are accorded to show the advantage of the proposed conceptual results.

Trojans in habitable zones.

PubMed

Schwarz, Richard; Pilat-Lohinger, Elke; Dvorak, Rudolf; Erdi, Balint; Sándor, Zsolt

2005-10-01

With the aid of numerical experiments we examined the dynamical stability of fictitious terrestrial planets in 1:1 mean motion resonance with Jovian-like planets of extrasolar planetary systems. In our stability study of the so-called "Trojan" planets in the habitable zone, we used the restricted three-body problem with different mass ratios of the primary bodies. The application of the three-body problem showed that even massive Trojan planets can be stable in the 1:1 mean motion resonance. From the 117 extrasolar planetary systems only 11 systems were found with one giant planet in the habitable zone. Out of this sample set we chose four planetary systems--HD17051, HD27442, HD28185, and HD108874--for further investigation. To study the orbital behavior of the stable zone in the different systems, we used direct numerical computations (Lie Integration Method) that allowed us to determine the escape times and the maximum eccentricity of the fictitious "Trojan planets."

Bouncing ball problem: stability of the periodic modes.

PubMed

Barroso, Joaquim J; Carneiro, Marcus V; Macau, Elbert E N

2009-02-01

Exploring all its ramifications, we give an overview of the simple yet fundamental bouncing ball problem, which consists of a ball bouncing vertically on a sinusoidally vibrating table under the action of gravity. The dynamics is modeled on the basis of a discrete map of difference equations, which numerically solved fully reveals a rich variety of nonlinear behaviors, encompassing irregular nonperiodic orbits, subharmonic and chaotic motions, chattering mechanisms, and also unbounded nonperiodic orbits. For periodic motions, the corresponding conditions for stability and bifurcation are determined from analytical considerations of a reduced map. Through numerical examples, it is shown that a slight change in the initial conditions makes the ball motion switch from periodic to chaotic orbits bounded by a velocity strip v=+/-Gamma(1-epsilon) , where Gamma is the nondimensionalized shaking acceleration and epsilon the coefficient of restitution which quantifies the amount of energy lost in the ball-table collision.

Robustness of delayed multistable systems with application to droop-controlled inverter-based microgrids

NASA Astrophysics Data System (ADS)

Efimov, Denis; Schiffer, Johannes; Ortega, Romeo

2016-05-01

Motivated by the problem of phase-locking in droop-controlled inverter-based microgrids with delays, the recently developed theory of input-to-state stability (ISS) for multistable systems is extended to the case of multistable systems with delayed dynamics. Sufficient conditions for ISS of delayed systems are presented using Lyapunov-Razumikhin functions. It is shown that ISS multistable systems are robust with respect to delays in a feedback. The derived theory is applied to two examples. First, the ISS property is established for the model of a nonlinear pendulum and delay-dependent robustness conditions are derived. Second, it is shown that, under certain assumptions, the problem of phase-locking analysis in droop-controlled inverter-based microgrids with delays can be reduced to the stability investigation of the nonlinear pendulum. For this case, corresponding delay-dependent conditions for asymptotic phase-locking are given.

Quadruped Robot Locomotion using a Global Optimization Stochastic Algorithm

NASA Astrophysics Data System (ADS)

Oliveira, Miguel; Santos, Cristina; Costa, Lino; Ferreira, Manuel

2011-09-01

The problem of tuning nonlinear dynamical systems parameters, such that the attained results are considered good ones, is a relevant one. This article describes the development of a gait optimization system that allows a fast but stable robot quadruped crawl gait. We combine bio-inspired Central Patterns Generators (CPGs) and Genetic Algorithms (GA). CPGs are modelled as autonomous differential equations, that generate the necessar y limb movement to perform the required walking gait. The GA finds parameterizations of the CPGs parameters which attain good gaits in terms of speed, vibration and stability. Moreover, two constraint handling techniques based on tournament selection and repairing mechanism are embedded in the GA to solve the proposed constrained optimization problem and make the search more efficient. The experimental results, performed on a simulated Aibo robot, demonstrate that our approach allows low vibration with a high velocity and wide stability margin for a quadruped slow crawl gait.

Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment

NASA Astrophysics Data System (ADS)

Khan, Muhammad Altaf; Khan, Yasir; Islam, Saeed

2018-03-01

In this paper, we describe the dynamics of an SEIR epidemic model with saturated incidence, treatment function, and optimal control. Rigorous mathematical results have been established for the model. The stability analysis of the model is investigated and found that the model is locally asymptotically stable when R0 < 1. The model is locally as well as globally asymptotically stable at endemic equilibrium when R0 > 1. The proposed model may possess a backward bifurcation. The optimal control problem is designed and obtained their necessary results. Numerical results have been presented for justification of theoretical results.

Application of Krylov exponential propagation to fluid dynamics equations

NASA Technical Reports Server (NTRS)

Saad, Youcef; Semeraro, David

1991-01-01

An application of matrix exponentiation via Krylov subspace projection to the solution of fluid dynamics problems is presented. The main idea is to approximate the operation exp(A)v by means of a projection-like process onto a krylov subspace. This results in a computation of an exponential matrix vector product similar to the one above but of a much smaller size. Time integration schemes can then be devised to exploit this basic computational kernel. The motivation of this approach is to provide time-integration schemes that are essentially of an explicit nature but which have good stability properties.

Gesellschaft fuer angewandte Mathematik und Mechanik, Scientific Annual Meeting, Universitaet Hannover, Hanover, Federal Republic of Germany, Apr. 8-12, 1990, Reports

NASA Astrophysics Data System (ADS)

Various papers on applied mathematics and mechanics are presented. Among the individual topics addressed are: dynamical systems with time-varying or unsteady structure, micromechanical modeling of creep rupture, forced vibrations of elastic sandwich plates with thick surface layers, postbuckling of a complete spherical shell under a line load, differential-geometric approach to the multibody system dynamics, stability of an oscillator with stochastic parametric excitation, identification strategies for crack-formation in rotors, identification of physical parameters of FEMs, impact model for elastic and partly plastic impacts on objects, varying delay and stability in dynamical systems. Also discussed are: parameter identification of a hybrid model for vibration analysis using the FEM, vibration behavior of a labyrinth seal with through-flow, similarities in the boundary layer of fiber composite materials, distortion parameter in shell theories, elastoplastic crack problem at finite strain, algorithm for computing effective stiffnesses of plates with periodic structure, plasticity of metal-matrix composites in a mixed stress-strain space formation, constitutive equations in directly formulated plate theories, microbuckling and homogenization for long fiber composites.

Dynamics and stability of thin liquid films

NASA Astrophysics Data System (ADS)

Craster, R. V.; Matar, O. K.

2009-07-01

The dynamics and stability of thin liquid films have fascinated scientists over many decades: the observations of regular wave patterns in film flows down a windowpane or along guttering, the patterning of dewetting droplets, and the fingering of viscous flows down a slope are all examples that are familiar in daily life. Thin film flows occur over a wide range of length scales and are central to numerous areas of engineering, geophysics, and biophysics; these include nanofluidics and microfluidics, coating flows, intensive processing, lava flows, dynamics of continental ice sheets, tear-film rupture, and surfactant replacement therapy. These flows have attracted considerable attention in the literature, which have resulted in many significant developments in experimental, analytical, and numerical research in this area. These include advances in understanding dewetting, thermocapillary- and surfactant-driven films, falling films and films flowing over structured, compliant, and rapidly rotating substrates, and evaporating films as well as those manipulated via use of electric fields to produce nanoscale patterns. These developments are reviewed in this paper and open problems and exciting research avenues in this thriving area of fluid mechanics are also highlighted.

On Flexible Tubes Conveying Fluid: Geometric Nonlinear Theory, Stability and Dynamics

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Putkaradze, Vakhtang

2015-08-01

We derive a fully three-dimensional, geometrically exact theory for flexible tubes conveying fluid. The theory also incorporates the change of the cross section available to the fluid motion during the dynamics. Our approach is based on the symmetry-reduced, exact geometric description for elastic rods, coupled with the fluid transport and subject to the volume conservation constraint for the fluid. We first derive the equations of motion directly, by using an Euler-Poincaré variational principle. We then justify this derivation with a more general theory elucidating the interesting mathematical concepts appearing in this problem, such as partial left (elastic) and right (fluid) invariance of the system, with the added holonomic constraint (volume). We analyze the fully nonlinear behavior of the model when the axis of the tube remains straight. We then proceed to the linear stability analysis and show that our theory introduces important corrections to previously derived results, both in the consistency at all wavelength and in the effects arising from the dynamical change of the cross section. Finally, we derive and analyze several analytical, fully nonlinear solutions of traveling wave type in two dimensions.

Overview of Orion Crew Module and Launch Abort Vehicle Dynamic Stability

NASA Technical Reports Server (NTRS)

Owens, Donald B.; Aibicjpm. Vamessa V.

2011-01-01

With the retirement of the Space Shuttle, NASA is designing a new spacecraft, called Orion, to fly astronauts to low earth orbit and beyond. Characterization of the dynamic stability of the Orion spacecraft is important for the design of the spacecraft and trajectory construction. Dynamic stability affects the stability and control of the Orion Crew Module during re-entry, especially below Mach = 2.0 and including flight under the drogues. The Launch Abort Vehicle is affected by dynamic stability as well, especially during the re-orientation and heatshield forward segments of the flight. The dynamic stability was assessed using the forced oscillation technique, free-to-oscillate, ballistic range, and sub-scale free-flight tests. All of the test techniques demonstrated that in heatshield-forward flight the Crew Module and Launch Abort Vehicle are dynamically unstable in a significant portion of their flight trajectory. This paper will provide a brief overview of the Orion dynamic aero program and a high-level summary of the dynamic stability characteristics of the Orion spacecraft.

User's manual for MMLE3, a general FORTRAN program for maximum likelihood parameter estimation

NASA Technical Reports Server (NTRS)

Maine, R. E.; Iliff, K. W.

1980-01-01

A user's manual for the FORTRAN IV computer program MMLE3 is described. It is a maximum likelihood parameter estimation program capable of handling general bilinear dynamic equations of arbitrary order with measurement noise and/or state noise (process noise). The theory and use of the program is described. The basic MMLE3 program is quite general and, therefore, applicable to a wide variety of problems. The basic program can interact with a set of user written problem specific routines to simplify the use of the program on specific systems. A set of user routines for the aircraft stability and control derivative estimation problem is provided with the program.

Spreadsheet analysis of stability and meta-stability of low-dimensional magnetic particles using the Ising approach

NASA Astrophysics Data System (ADS)

Ehrmann, Andrea; Blachowicz, Tomasz; Zghidi, Hafed

2015-05-01

Modelling hysteresis behaviour, as it can be found in a broad variety of dynamical systems, can be performed in different ways. An elementary approach, applied for a set of elementary cells, which uses only two possible states per cell, is the Ising model. While such Ising models allow for a simulation of many systems with sufficient accuracy, they nevertheless depict some typical features which must be taken into account with proper care, such as meta-stability or the externally applied field sweeping speed. This paper gives a general overview of recent results from Ising models from the perspective of a didactic model, based on a 2D spreadsheet analysis, which can be used also for solving general scientific problems where direct next-neighbour interactions take place.

Adaptive nearly optimal control for a class of continuous-time nonaffine nonlinear systems with inequality constraints.

PubMed

Fan, Quan-Yong; Yang, Guang-Hong

2017-01-01

The state inequality constraints have been hardly considered in the literature on solving the nonlinear optimal control problem based the adaptive dynamic programming (ADP) method. In this paper, an actor-critic (AC) algorithm is developed to solve the optimal control problem with a discounted cost function for a class of state-constrained nonaffine nonlinear systems. To overcome the difficulties resulting from the inequality constraints and the nonaffine nonlinearities of the controlled systems, a novel transformation technique with redesigned slack functions and a pre-compensator method are introduced to convert the constrained optimal control problem into an unconstrained one for affine nonlinear systems. Then, based on the policy iteration (PI) algorithm, an online AC scheme is proposed to learn the nearly optimal control policy for the obtained affine nonlinear dynamics. Using the information of the nonlinear model, novel adaptive update laws are designed to guarantee the convergence of the neural network (NN) weights and the stability of the affine nonlinear dynamics without the requirement for the probing signal. Finally, the effectiveness of the proposed method is validated by simulation studies. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Algorithms for sum-of-squares-based stability analysis and control design of uncertain nonlinear systems

NASA Astrophysics Data System (ADS)

Ataei-Esfahani, Armin

In this dissertation, we present algorithmic procedures for sum-of-squares based stability analysis and control design for uncertain nonlinear systems. In particular, we consider the case of robust aircraft control design for a hypersonic aircraft model subject to parametric uncertainties in its aerodynamic coefficients. In recent years, Sum-of-Squares (SOS) method has attracted increasing interest as a new approach for stability analysis and controller design of nonlinear dynamic systems. Through the application of SOS method, one can describe a stability analysis or control design problem as a convex optimization problem, which can efficiently be solved using Semidefinite Programming (SDP) solvers. For nominal systems, the SOS method can provide a reliable and fast approach for stability analysis and control design for low-order systems defined over the space of relatively low-degree polynomials. However, The SOS method is not well-suited for control problems relating to uncertain systems, specially those with relatively high number of uncertainties or those with non-affine uncertainty structure. In order to avoid issues relating to the increased complexity of the SOS problems for uncertain system, we present an algorithm that can be used to transform an SOS problem with uncertainties into a LMI problem with uncertainties. A new Probabilistic Ellipsoid Algorithm (PEA) is given to solve the robust LMI problem, which can guarantee the feasibility of a given solution candidate with an a-priori fixed probability of violation and with a fixed confidence level. We also introduce two approaches to approximate the robust region of attraction (RROA) for uncertain nonlinear systems with non-affine dependence on uncertainties. The first approach is based on a combination of PEA and SOS method and searches for a common Lyapunov function, while the second approach is based on the generalized Polynomial Chaos (gPC) expansion theorem combined with the SOS method and searches for parameter-dependent Lyapunov functions. The control design problem is investigated through a case study of a hypersonic aircraft model with parametric uncertainties. Through time-scale decomposition and a series of function approximations, the complexity of the aircraft model is reduced to fall within the capability of SDP solvers. The control design problem is then formulated as a convex problem using the dual of the Lyapunov theorem. A nonlinear robust controller is searched using the combined PEA/SOS method. The response of the uncertain aircraft model is evaluated for two sets of pilot commands. As the simulation results show, the aircraft remains stable under up to 50% uncertainty in aerodynamic coefficients and can follow the pilot commands.

Neuromechanics: an integrative approach for understanding motor control.

PubMed

Nishikawa, Kiisa; Biewener, Andrew A; Aerts, Peter; Ahn, Anna N; Chiel, Hillel J; Daley, Monica A; Daniel, Thomas L; Full, Robert J; Hale, Melina E; Hedrick, Tyson L; Lappin, A Kristopher; Nichols, T Richard; Quinn, Roger D; Satterlie, Richard A; Szymik, Brett

2007-07-01

Neuromechanics seeks to understand how muscles, sense organs, motor pattern generators, and brain interact to produce coordinated movement, not only in complex terrain but also when confronted with unexpected perturbations. Applications of neuromechanics include ameliorating human health problems (including prosthesis design and restoration of movement following brain or spinal cord injury), as well as the design, actuation and control of mobile robots. In animals, coordinated movement emerges from the interplay among descending output from the central nervous system, sensory input from body and environment, muscle dynamics, and the emergent dynamics of the whole animal. The inevitable coupling between neural information processing and the emergent mechanical behavior of animals is a central theme of neuromechanics. Fundamentally, motor control involves a series of transformations of information, from brain and spinal cord to muscles to body, and back to brain. The control problem revolves around the specific transfer functions that describe each transformation. The transfer functions depend on the rules of organization and operation that determine the dynamic behavior of each subsystem (i.e., central processing, force generation, emergent dynamics, and sensory processing). In this review, we (1) consider the contributions of muscles, (2) sensory processing, and (3) central networks to motor control, (4) provide examples to illustrate the interplay among brain, muscles, sense organs and the environment in the control of movement, and (5) describe advances in both robotics and neuromechanics that have emerged from application of biological principles in robotic design. Taken together, these studies demonstrate that (1) intrinsic properties of muscle contribute to dynamic stability and control of movement, particularly immediately after perturbations; (2) proprioceptive feedback reinforces these intrinsic self-stabilizing properties of muscle; (3) control systems must contend with inevitable time delays that can simplify or complicate control; and (4) like most animals under a variety of circumstances, some robots use a trial and error process to tune central feedforward control to emergent body dynamics.

Brief analysis of Jiangsu grid security and stability based on multi-infeed DC index in power system

NASA Astrophysics Data System (ADS)

Zhang, Wenjia; Wang, Quanquan; Ge, Yi; Huang, Junhui; Chen, Zhengfang

2018-02-01

The impact of Multi-infeed HVDC has gradually increased to security and stability operating in Jiangsu power grid. In this paper, an appraisal method of Multi-infeed HVDC power grid security and stability is raised with Multi-Infeed Effective Short Circuit Ratio, Multi-Infeed Interaction Factor and Commutation Failure Immunity Index. These indices are adopted in security and stability simulating calculation of Jiangsu Multi-infeed HVDC system. The simulation results indicate that Jiangsu power grid is operating with a strong DC system. It has high level of power grid security and stability, and meet the safety running requirements. Jinpin-Suzhou DC system is located in the receiving end with huge capacity, which is easily leading to commutation failure of the transmission line. In order to resolve this problem, dynamic reactive power compensation can be applied in power grid near Jinpin-Suzhou DC system. Simulation result shows this method is feasible to commutation failure.

Stability switches of arbitrary high-order consensus in multiagent networks with time delays.

PubMed

Yang, Bo

2013-01-01

High-order consensus seeking, in which individual high-order dynamic agents share a consistent view of the objectives and the world in a distributed manner, finds its potential broad applications in the field of cooperative control. This paper presents stability switches analysis of arbitrary high-order consensus in multiagent networks with time delays. By employing a frequency domain method, we explicitly derive analytical equations that clarify a rigorous connection between the stability of general high-order consensus and the system parameters such as the network topology, communication time-delays, and feedback gains. Particularly, our results provide a general and a fairly precise notion of how increasing communication time-delay causes the stability switches of consensus. Furthermore, under communication constraints, the stability and robustness problems of consensus algorithms up to third order are discussed in details to illustrate our central results. Numerical examples and simulation results for fourth-order consensus are provided to demonstrate the effectiveness of our theoretical results.

Rotordynamic Characteristics of the HPOTP (High Pressure Oxygen Turbopump) of the SSME (Space Shuttle Main Engine)

NASA Technical Reports Server (NTRS)

Childs, D. W.

1984-01-01

Rotational stability of turbopump components in the space shuttle main engine was studied via analysis of component and structural dynamic models. Subsynchronous vibration caused unacceptable migration of the rotor/housing unit with unequal load sharing of the synchronous bearings that resulted in the failure of the High Pressure Oxygen Turbopump. Linear analysis shows that a shrouded inducer eliminates the second critical speed and the stability problem, a stiffened rotor improves the rotordynamic characteristics of the turbopump, and installing damper boost/impeller seals reduces bearing loads. Nonlinear analysis shows that by increasing the "dead band' clearances, a marked reduction in peak bearing loads occurs.

Adaptive fixed-time control for cluster synchronisation of coupled complex networks with uncertain disturbances

NASA Astrophysics Data System (ADS)

Jiang, Shengqin; Lu, Xiaobo; Cai, Guoliang; Cai, Shuiming

2017-12-01

This paper focuses on the cluster synchronisation problem of coupled complex networks with uncertain disturbances under an adaptive fixed-time control strategy. To begin with, complex dynamical networks with community structure which are subject to uncertain disturbances are taken into account. Then, a novel adaptive control strategy combined with fixed-time techniques is proposed to guarantee the nodes in the communities to desired states in a settling time. In addition, the stability of complex error systems is theoretically proved based on Lyapunov stability theorem. At last, two examples are presented to verify the effectiveness of the proposed adaptive fixed-time control.

New class of control laws for robotic manipulators. I - Nonadaptive case. II - Adaptive case

NASA Technical Reports Server (NTRS)

Wen, John T.; Bayard, David S.

1988-01-01

A new class of exponentially stabilizing control laws for joint level control of robot arms is discussed. Closed-loop exponential stability has been demonstrated for both the set point and tracking control problems by a slight modification of the energy Lyapunov function and the use of a lemma which handles third-order terms in the Lyapunov function derivatives. In the second part, these control laws are adapted in a simple fashion to achieve asymptotically stable adaptive control. The analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and uses a parameterization based on physical (time-invariant) quantities.

Astrophysical fluid dynamics

NASA Astrophysics Data System (ADS)

Ogilvie, Gordon I.

2016-06-01

> These lecture notes and example problems are based on a course given at the University of Cambridge in Part III of the Mathematical Tripos. Fluid dynamics is involved in a very wide range of astrophysical phenomena, such as the formation and internal dynamics of stars and giant planets, the workings of jets and accretion discs around stars and black holes and the dynamics of the expanding Universe. Effects that can be important in astrophysical fluids include compressibility, self-gravitation and the dynamical influence of the magnetic field that is `frozen in' to a highly conducting plasma. The basic models introduced and applied in this course are Newtonian gas dynamics and magnetohydrodynamics (MHD) for an ideal compressible fluid. The mathematical structure of the governing equations and the associated conservation laws are explored in some detail because of their importance for both analytical and numerical methods of solution, as well as for physical interpretation. Linear and nonlinear waves, including shocks and other discontinuities, are discussed. The spherical blast wave resulting from a supernova, and involving a strong shock, is a classic problem that can be solved analytically. Steady solutions with spherical or axial symmetry reveal the physics of winds and jets from stars and discs. The linearized equations determine the oscillation modes of astrophysical bodies, as well as their stability and their response to tidal forcing.

Proceedings of the 8th Annual Conference on Manual Control

NASA Technical Reports Server (NTRS)

Pew, R. W.

1972-01-01

The volume presents recent developments in the field of manual control theory and applications. The papers give analytical methods as well as examples of the important interplay between man and machine, such as how man controls and stabilizes machine dynamics, and how machines extend man's capability. Included in the broad range of subjects are procedures to evaluate and identify display systems, controllers, manipulators, human operators, aircraft, and non-flying vehicles. Of particular interest is the continuing trend of applying control theory to problems in medicine and psychology, as well as to problems in vehicle control.

Algorithm For Hypersonic Flow In Chemical Equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

Implicit, finite-difference, shock-capturing algorithm calculates inviscid, hypersonic flows in chemical equilibrium. Implicit formulation chosen because overcomes limitation on mathematical stability encountered in explicit formulations. For dynamical portion of problem, Euler equations written in conservation-law form in Cartesian coordinate system for two-dimensional or axisymmetric flow. For chemical portion of problem, equilibrium state of gas at each point in computational grid determined by minimizing local Gibbs free energy, subject to local conservation of molecules, atoms, ions, and total enthalpy. Major advantage: resulting algorithm naturally stable and captures strong shocks without help of artificial-dissipation terms to damp out spurious numerical oscillations.

Dynamic stability of passive dynamic walking on an irregular surface.

PubMed

Su, Jimmy Li-Shin; Dingwell, Jonathan B

2007-12-01

Falls that occur during walking are a significant health problem. One of the greatest impediments to solve this problem is that there is no single obviously "correct" way to quantify walking stability. While many people use variability as a proxy for stability, measures of variability do not quantify how the locomotor system responds to perturbations. The purpose of this study was to determine how changes in walking surface variability affect changes in both locomotor variability and stability. We modified an irreducibly simple model of walking to apply random perturbations that simulated walking over an irregular surface. Because the model's global basin of attraction remained fixed, increasing the amplitude of the applied perturbations directly increased the risk of falling in the model. We generated ten simulations of 300 consecutive strides of walking at each of six perturbation amplitudes ranging from zero (i.e., a smooth continuous surface) up to the maximum level the model could tolerate without falling over. Orbital stability defines how a system responds to small (i.e., "local") perturbations from one cycle to the next and was quantified by calculating the maximum Floquet multipliers for the model. Local stability defines how a system responds to similar perturbations in real time and was quantified by calculating short-term and long-term local exponential rates of divergence for the model. As perturbation amplitudes increased, no changes were seen in orbital stability (r(2)=2.43%; p=0.280) or long-term local instability (r(2)=1.0%; p=0.441). These measures essentially reflected the fact that the model never actually "fell" during any of our simulations. Conversely, the variability of the walker's kinematics increased exponentially (r(2)>or=99.6%; p<0.001) and short-term local instability increased linearly (r(2)=88.1%; p<0.001). These measures thus predicted the increased risk of falling exhibited by the model. For all simulated conditions, the walker remained orbitally stable, while exhibiting substantial local instability. This was because very small initial perturbations diverged away from the limit cycle, while larger initial perturbations converged toward the limit cycle. These results provide insight into how these different proposed measures of walking stability are related to each other and to risk of falling.

Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems

NASA Technical Reports Server (NTRS)

Murthy, V. R.; Shultz, Louis A.

1994-01-01

The goal of this research is to develop the transfer matrix method to treat nonlinear autonomous boundary value problems with multiple branches. The application is the complete nonlinear aeroelastic analysis of multiple-branched rotor blades. Once the development is complete, it can be incorporated into the existing transfer matrix analyses. There are several difficulties to be overcome in reaching this objective. The conventional transfer matrix method is limited in that it is applicable only to linear branch chain-like structures, but consideration of multiple branch modeling is important for bearingless rotors. Also, hingeless and bearingless rotor blade dynamic characteristics (particularly their aeroelasticity problems) are inherently nonlinear. The nonlinear equations of motion and the multiple-branched boundary value problem are treated together using a direct transfer matrix method. First, the formulation is applied to a nonlinear single-branch blade to validate the nonlinear portion of the formulation. The nonlinear system of equations is iteratively solved using a form of Newton-Raphson iteration scheme developed for differential equations of continuous systems. The formulation is then applied to determine the nonlinear steady state trim and aeroelastic stability of a rotor blade in hover with two branches at the root. A comprehensive computer program is developed and is used to obtain numerical results for the (1) free vibration, (2) nonlinearly deformed steady state, (3) free vibration about the nonlinearly deformed steady state, and (4) aeroelastic stability tasks. The numerical results obtained by the present method agree with results from other methods.

High Performance Parallel Analysis of Coupled Problems for Aircraft Propulsion

NASA Technical Reports Server (NTRS)

Felippa, C. A.; Farhat, C.; Lanteri, S.; Maman, N.; Piperno, S.; Gumaste, U.

1994-01-01

In order to predict the dynamic response of a flexible structure in a fluid flow, the equations of motion of the structure and the fluid must be solved simultaneously. In this paper, we present several partitioned procedures for time-integrating this focus coupled problem and discuss their merits in terms of accuracy, stability, heterogeneous computing, I/O transfers, subcycling, and parallel processing. All theoretical results are derived for a one-dimensional piston model problem with a compressible flow, because the complete three-dimensional aeroelastic problem is difficult to analyze mathematically. However, the insight gained from the analysis of the coupled piston problem and the conclusions drawn from its numerical investigation are confirmed with the numerical simulation of the two-dimensional transient aeroelastic response of a flexible panel in a transonic nonlinear Euler flow regime.

Shake, Rattle, and Roll: Nonlinear Dynamics in Mechanical Engineering

NASA Astrophysics Data System (ADS)

Shaw, Steven

1997-03-01

This presentation will focus on three mechanical engineering applications in which methods from nonlinear dynamics have been applied with success. Each topic will be briefly surveyed by outlining the development of a mathematical model, providing a description of the analysis tools employed, and showing the main results obtained. The applications are: vibration reduction in internal combustion engines, impact dynamics of mechanical components, and the dynamics of ship capsize. The first topic demonstrates a novel arrangement of dynamic absorbers that can be used for attenuating torsional vibrations in rotating machinery. The operation of this device takes advantage of a purely nonlinear system response that results from a period doubling bifurcation. This configuration is more effective than existing absorbers and it cannot be imagined by using naive extensions of linear vibration theory. The second topic deals with the dynamics of mechanical systems in which components make intermittent contact with each another. Such dynamics are often the source of undesirable noise and wear in machinery and can be extremely complicated. Results obtained from simple predictive models and some application areas will be presented for these impacting systems. The final topic deals with the gross motions of seagoing vessels and their stability against capsize. Existing safety regulations for ship stability are based on purely static measures, whereas capsize is an inherently nonlinear dynamic event. An overview will be given that considers some basic modeling issues, dynamic analysis techniques (based on the concept of chaotic phase-space transport), and the resulting predictive tools that have been developed for this class of problems.

A study of helicopter stability and control including blade dynamics

NASA Technical Reports Server (NTRS)

Zhao, Xin; Curtiss, H. C., Jr.

1988-01-01

A linearized model of rotorcraft dynamics has been developed through the use of symbolic automatic equation generating techniques. The dynamic model has been formulated in a unique way such that it can be used to analyze a variety of rotor/body coupling problems including a rotor mounted on a flexible shaft with a number of modes as well as free-flight stability and control characteristics. Direct comparison of the time response to longitudinal, lateral and directional control inputs at various trim conditions shows that the linear model yields good to very good correlation with flight test. In particular it is shown that a dynamic inflow model is essential to obtain good time response correlation, especially for the hover trim condition. It also is shown that the main rotor wake interaction with the tail rotor and fixed tail surfaces is a significant contributor to the response at translational flight trim conditions. A relatively simple model for the downwash and sidewash at the tail surfaces based on flat vortex wake theory is shown to produce good agreement. Then, the influence of rotor flap and lag dynamics on automatic control systems feedback gain limitations is investigated with the model. It is shown that the blade dynamics, especially lagging dynamics, can severly limit the useable values of the feedback gain for simple feedback control and that multivariable optimal control theory is a powerful tool to design high gain augmentation control system. The frequency-shaped optimal control design can offer much better flight dynamic characteristics and a stable margin for the feedback system without need to model the lagging dynamics.

Local Dynamic Stability Associated with Load Carrying

PubMed Central

Lockhart, Thurmon E

2013-01-01

Objectives Load carrying tasks are recognized as one of the primary occupational factors leading to slip and fall injuries. Nevertheless, the mechanisms associated with load carrying and walking stability remain illusive. The objective of the current study was to apply local dynamic stability measure in walking while carrying a load, and to investigate the possible adaptive gait stability changes. Methods Current study involved 25 young adults in a biomechanics research laboratory. One tri-axial accelerometer was used to measure three-dimensional low back acceleration during continuous treadmill walking. Local dynamic stability was quantified by the maximum Lyapunov exponent (maxLE) from a nonlinear dynamics approach. Results Long term maxLE was found to be significant higher under load condition than no-load condition in all three reference axes, indicating the declined local dynamic stability associated with load carrying. Conclusion Current study confirmed the sensitivity of local dynamic stability measure in load carrying situation. It was concluded that load carrying tasks were associated with declined local dynamic stability, which may result in increased risk of fall accident. This finding has implications in preventing fall accidents associated with occupational load carrying. PMID:23515183

Comparison of dynamic postural stability scores between athletes with and without chronic ankle instability during lateral jump landing.

PubMed

Shiravi, Zeinab; Shadmehr, Azadeh; Moghadam, Saeed Talebian; Moghadam, Behrouz Attarbashi

2017-01-01

Many ankle injuries occur while participating in sports that require jumping and landing such as basketball, volleyball and soccer. Most recent studies have investigated dynamic postural stability of patients with chronic ankle instability after landing from a forward jump. The present study aimed to investigate the dynamic postural stability of the athletes who suffer from chronic ankle sprain while landing from a lateral jump. Twelve athletes with self-reported unilateral chronic ankle instability (4 females and 8 males) and 12 matched controls (3 females and 9 males) voluntarily participated in the study. Dynamic postural stability index and its directional indices were measured while performing lateral jump landing test. No differences were found between athletes with and without chronic ankle instability during our landing protocol by means of the dynamic postural stability index and its directional indices. Findings showed that in each group, medial/lateral stability index is significantly higher than anterior/posterior and vertical stability indexes. Findings showed that dynamic postural stability was not significantly different between the two groups. Future studies should examine chronic ankle instability patients with more severe disabilities and expose them to more challenging dynamic balance conditions to further explore postural stability. IIIa.

Adaptive fuzzy wavelet network control of second order multi-agent systems with unknown nonlinear dynamics.

PubMed

Taheri, Mehdi; Sheikholeslam, Farid; Najafi, Majddedin; Zekri, Maryam

2017-07-01

In this paper, consensus problem is considered for second order multi-agent systems with unknown nonlinear dynamics under undirected graphs. A novel distributed control strategy is suggested for leaderless systems based on adaptive fuzzy wavelet networks. Adaptive fuzzy wavelet networks are employed to compensate for the effect of unknown nonlinear dynamics. Moreover, the proposed method is developed for leader following systems and leader following systems with state time delays. Lyapunov functions are applied to prove uniformly ultimately bounded stability of closed loop systems and to obtain adaptive laws. Three simulation examples are presented to illustrate the effectiveness of the proposed control algorithms. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Milestones in Rotorcraft Aeromechanics

NASA Technical Reports Server (NTRS)

Johnson, Wayne

2011-01-01

The subject of this paper is milestones in rotorcraft aeromechanics. Aeromechanics covers much of what the engineer needs: performance, loads, vibration, stability, flight dynamics, noise. These topics cover many of the key performance attributes, and many of the often-encountered problems in rotorcraft designs. A milestone is a critical achievement, a turning point, an event marking a significant change or stage in development. The milestones identified and discussed include the beginnings of aeromechanics with autogyro analysis, ground resonance, aeromechanics books, unsteady aerodynamics and airloads, nonuniform inflow and wakes, beams and dynamics, comprehensive analysis, computational fluid dynamics, and rotor airloads tests. The focus on milestones limits the scope of the history, but allows the author to acknowledge his choices for key steps in the development of the science and engineering of rotorcraft.

Effects of predation efficiencies on the dynamics of a tritrophic food chain.

PubMed

Cassinari, Maria Paola; Groppi, Maria; Tebaldi, Claudio

2007-07-01

In this paper the dynamics of a tritrophic food chain (resource, consumer, top predator) is investigated, with particular attention not only to equilibrium states but also to cyclic behaviours that the system may exhibit. The analysis is performed in terms of two bifurcation parameters, denoted by p and q, which measure the efficiencies of the interaction processes. The persistence of the system is discussed, characterizing in the (p; q) plane the regions of existence and stability of biologically significant steady states and those of existence of limit cycles. The bifurcations occurring are discussed, and their implications with reference to biological control problems are considered. Examples of the rich dynamics exhibited by the model, including a chaotic regime, are described.

Estimation of Attitude and External Acceleration Using Inertial Sensor Measurement During Various Dynamic Conditions

PubMed Central

Lee, Jung Keun; Park, Edward J.; Robinovitch, Stephen N.

2012-01-01

This paper proposes a Kalman filter-based attitude (i.e., roll and pitch) estimation algorithm using an inertial sensor composed of a triaxial accelerometer and a triaxial gyroscope. In particular, the proposed algorithm has been developed for accurate attitude estimation during dynamic conditions, in which external acceleration is present. Although external acceleration is the main source of the attitude estimation error and despite the need for its accurate estimation in many applications, this problem that can be critical for the attitude estimation has not been addressed explicitly in the literature. Accordingly, this paper addresses the combined estimation problem of the attitude and external acceleration. Experimental tests were conducted to verify the performance of the proposed algorithm in various dynamic condition settings and to provide further insight into the variations in the estimation accuracy. Furthermore, two different approaches for dealing with the estimation problem during dynamic conditions were compared, i.e., threshold-based switching approach versus acceleration model-based approach. Based on an external acceleration model, the proposed algorithm was capable of estimating accurate attitudes and external accelerations for short accelerated periods, showing its high effectiveness during short-term fast dynamic conditions. Contrariwise, when the testing condition involved prolonged high external accelerations, the proposed algorithm exhibited gradually increasing errors. However, as soon as the condition returned to static or quasi-static conditions, the algorithm was able to stabilize the estimation error, regaining its high estimation accuracy. PMID:22977288

Orbit Determination Using Vinti’s Solution

DTIC Science & Technology

2016-09-15

Surveillance Network STK Systems Tool Kit TBP Two Body Problem TLE Two-line Element Set xv Acronym Definition UKF Unscented Kalman Filter WPAFB Wright...simplicity, stability, and speed. On the other hand, Kalman filters would be best suited for sequential estimation of stochastic or random components of a...be likened to how an Unscented Kalman Filter samples a system’s nonlinearities directly, avoiding linearizing the dynamics in the partials matrices

Hypersonic Aeroelastic Analysis

DTIC Science & Technology

1975-09-30

Interaction", WADC TR-58-95. July 1960. 6 Blessing, A. H., and Honawalt, A. J., "Thermal Effects on Static Aero- elastlc Stability and Control, Part I...Problems in Multilayer Plato Cylinders and Spheres Subject to Arbitrary Aerodynamic Heat Transfer". TN 4061-124, N.W.C. China Lake, July ...547-553. 64 Orlik-Rlickemann, K. J., "Dynamic Viscous Pressure-Interaction in Hyper- Flow", Aeronautical Report LR-525, July 1970, National Research

Pseudosatellite technologies based on the use of functionally stable complexes of remote-piloted aircrafts

NASA Astrophysics Data System (ADS)

Mashkov, O. A.; Samborskiy, I. I.

2009-10-01

A bundle of papers dealing with functionally stable systems requires the necessity of analyzing of obtained results and their understanding in a general context of cybernetic's development and applications. Description of this field of science, main results and perspectives of the new theory of functionally stability of dynamical systems concerning the problem of remote-piloted aircrafts engineering using pseudosatellite technologies are proposed in the paper.

Bifurcation and Nonlinear Oscillations.

DTIC Science & Technology

1980-09-28

Structural stability and bifurcation theory. pp. 549-560 in Dinamical Systems (Ed. MI. Peixoto), Academic Press, 1973. [211 J. Sotomayor, Generic one...Dynamical Systems Brown University ELECTP" 71, Providence, R. I. 02912 1EC 2 4 1980j //C -*)’ Septabe-4., 1980 / -A + This research was supported in...problems are discussed. The first one deals with the characterization of the flow for a periodic planar system which is the perturbation of an autonomous

Important factors in the maximum likelihood analysis of flight test maneuvers

NASA Technical Reports Server (NTRS)

Iliff, K. W.; Maine, R. E.; Montgomery, T. D.

1979-01-01

The information presented is based on the experience in the past 12 years at the NASA Dryden Flight Research Center of estimating stability and control derivatives from over 3500 maneuvers from 32 aircraft. The overall approach to the analysis of dynamic flight test data is outlined. General requirements for data and instrumentation are discussed and several examples of the types of problems that may be encountered are presented.

Nonlinear relative-proportion-based route adjustment process for day-to-day traffic dynamics: modeling, equilibrium and stability analysis

NASA Astrophysics Data System (ADS)

Zhu, Wenlong; Ma, Shoufeng; Tian, Junfang; Li, Geng

2016-11-01

Travelers' route adjustment behaviors in a congested road traffic network are acknowledged as a dynamic game process between them. Existing Proportional-Switch Adjustment Process (PSAP) models have been extensively investigated to characterize travelers' route choice behaviors; PSAP has concise structure and intuitive behavior rule. Unfortunately most of which have some limitations, i.e., the flow over adjustment problem for the discrete PSAP model, the absolute cost differences route adjustment problem, etc. This paper proposes a relative-Proportion-based Route Adjustment Process (rePRAP) maintains the advantages of PSAP and overcomes these limitations. The rePRAP describes the situation that travelers on higher cost route switch to those with lower cost at the rate that is unilaterally depended on the relative cost differences between higher cost route and its alternatives. It is verified to be consistent with the principle of the rational behavior adjustment process. The equivalence among user equilibrium, stationary path flow pattern and stationary link flow pattern is established, which can be applied to judge whether a given network traffic flow has reached UE or not by detecting the stationary or non-stationary state of link flow pattern. The stability theorem is proved by the Lyapunov function approach. A simple example is tested to demonstrate the effectiveness of the rePRAP model.

Dual-user nonlinear teleoperation subjected to varying time delay and bounded inputs.

PubMed

Zakerimanesh, Amir; Hashemzadeh, Farzad; Ghiasi, Amir Rikhtehgar

2017-05-01

A novel trilateral control architecture for Dual-master/Single-slave teleoperation system with taking account of saturation in actuators, nonlinear dynamics for telemanipulators and bounded varying time delay which affects the transmitted signals in the communication channels, is proposed in this paper. In this research, we will address the stability and desired position coordination problem of trilateral teleoperation system by extension of (nP+D) controller that is used for Single-master/Single-slave teleoperation system. Our proposed controller is weighted summation of nonlinear Proportional plus Damping (nP+D) controller that incorporate gravity compensation and the weights are specified by the dominance factor, which determines the supremacy of each user over the slave robot and over the other user. The asymptotic stability of closed loop dynamics is studied using Lyapunov-Krasovskii functional under conditions on the controller parameters, the actuator saturation characteristics and the maximum values of varying time delays. It is shown that these controllers satisfy the desired position coordination problem in free motion condition. To show the effectiveness of the proposed method, a number of simulations have been conducted on a varying time delay Dual-master/Single-slave teleoperation system using 3-DOF planar robots for each telemanipulator subjected to actuator saturation. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Steady states and linear stability analysis of precipitation pattern formation at geothermal hot springs.

PubMed

Chan, Pak Yuen; Goldenfeld, Nigel

2007-10-01

A dynamical theory of geophysical precipitation pattern formation is presented and applied to irreversible calcium carbonate (travertine) deposition. Specific systems studied here are the terraces and domes observed at geothermal hot springs, such as those at Yellowstone National Park, and speleothems, particularly stalactites and stalagmites. The theory couples the precipitation front dynamics with shallow water flow, including corrections for turbulent drag and curvature effects. In the absence of capillarity and with a laminar flow profile, the theory predicts a one-parameter family of steady state solutions to the moving boundary problem describing the precipitation front. These shapes match the measured shapes near the vent at the top of observed travertine domes well. Closer to the base of the dome, the solutions deviate from observations and circular symmetry is broken by a fluting pattern, which we show is associated with capillary forces causing thin film break-up. We relate our model to that recently proposed for stalactite growth, and calculate the linear stability spectrum of both travertine domes and stalactites. Lastly, we apply the theory to the problem of precipitation pattern formation arising from turbulent flow down an inclined plane and identify a linear instability that underlies scale-invariant travertine terrace formation at geothermal hot springs.

Steady states and linear stability analysis of precipitation pattern formation at geothermal hot springs

NASA Astrophysics Data System (ADS)

Chan, Pak Yuen; Goldenfeld, Nigel

2007-10-01

A dynamical theory of geophysical precipitation pattern formation is presented and applied to irreversible calcium carbonate (travertine) deposition. Specific systems studied here are the terraces and domes observed at geothermal hot springs, such as those at Yellowstone National Park, and speleothems, particularly stalactites and stalagmites. The theory couples the precipitation front dynamics with shallow water flow, including corrections for turbulent drag and curvature effects. In the absence of capillarity and with a laminar flow profile, the theory predicts a one-parameter family of steady state solutions to the moving boundary problem describing the precipitation front. These shapes match the measured shapes near the vent at the top of observed travertine domes well. Closer to the base of the dome, the solutions deviate from observations and circular symmetry is broken by a fluting pattern, which we show is associated with capillary forces causing thin film break-up. We relate our model to that recently proposed for stalactite growth, and calculate the linear stability spectrum of both travertine domes and stalactites. Lastly, we apply the theory to the problem of precipitation pattern formation arising from turbulent flow down an inclined plane and identify a linear instability that underlies scale-invariant travertine terrace formation at geothermal hot springs.

Structural Stability of Mathematical Models of National Economy

NASA Astrophysics Data System (ADS)

Ashimov, Abdykappar A.; Sultanov, Bahyt T.; Borovskiy, Yuriy V.; Adilov, Zheksenbek M.; Ashimov, Askar A.

2011-12-01

In the paper we test robustness of particular dynamic systems in a compact regions of a plane and a weak structural stability of one dynamic system of high order in a compact region of its phase space. The test was carried out based on the fundamental theory of dynamical systems on a plane and based on the conditions for weak structural stability of high order dynamic systems. A numerical algorithm for testing the weak structural stability of high order dynamic systems has been proposed. Based on this algorithm we assess the weak structural stability of one computable general equilibrium model.

Dynamic inverse models in human-cyber-physical systems

NASA Astrophysics Data System (ADS)

Robinson, Ryan M.; Scobee, Dexter R. R.; Burden, Samuel A.; Sastry, S. Shankar

2016-05-01

Human interaction with the physical world is increasingly mediated by automation. This interaction is characterized by dynamic coupling between robotic (i.e. cyber) and neuromechanical (i.e. human) decision-making agents. Guaranteeing performance of such human-cyber-physical systems will require predictive mathematical models of this dynamic coupling. Toward this end, we propose a rapprochement between robotics and neuromechanics premised on the existence of internal forward and inverse models in the human agent. We hypothesize that, in tele-robotic applications of interest, a human operator learns to invert automation dynamics, directly translating from desired task to required control input. By formulating the model inversion problem in the context of a tracking task for a nonlinear control system in control-a_ne form, we derive criteria for exponential tracking and show that the resulting dynamic inverse model generally renders a portion of the physical system state (i.e., the internal dynamics) unobservable from the human operator's perspective. Under stability conditions, we show that the human can achieve exponential tracking without formulating an estimate of the system's state so long as they possess an accurate model of the system's dynamics. These theoretical results are illustrated using a planar quadrotor example. We then demonstrate that the automation can intervene to improve performance of the tracking task by solving an optimal control problem. Performance is guaranteed to improve under the assumption that the human learns and inverts the dynamic model of the altered system. We conclude with a discussion of practical limitations that may hinder exact dynamic model inversion.

14 CFR 23.181 - Dynamic stability.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Dynamic stability. 23.181 Section 23.181... STANDARDS: NORMAL, UTILITY, ACROBATIC, AND COMMUTER CATEGORY AIRPLANES Flight Stability § 23.181 Dynamic... that the function of a stability augmentation system, reference § 23.672, is needed to meet the flight...

Optimal harvesting for a predator-prey agent-based model using difference equations.

PubMed

Oremland, Matthew; Laubenbacher, Reinhard

2015-03-01

In this paper, a method known as Pareto optimization is applied in the solution of a multi-objective optimization problem. The system in question is an agent-based model (ABM) wherein global dynamics emerge from local interactions. A system of discrete mathematical equations is formulated in order to capture the dynamics of the ABM; while the original model is built up analytically from the rules of the model, the paper shows how minor changes to the ABM rule set can have a substantial effect on model dynamics. To address this issue, we introduce parameters into the equation model that track such changes. The equation model is amenable to mathematical theory—we show how stability analysis can be performed and validated using ABM data. We then reduce the equation model to a simpler version and implement changes to allow controls from the ABM to be tested using the equations. Cohen's weighted κ is proposed as a measure of similarity between the equation model and the ABM, particularly with respect to the optimization problem. The reduced equation model is used to solve a multi-objective optimization problem via a technique known as Pareto optimization, a heuristic evolutionary algorithm. Results show that the equation model is a good fit for ABM data; Pareto optimization provides a suite of solutions to the multi-objective optimization problem that can be implemented directly in the ABM.

Model-Free Adaptive Control for Unknown Nonlinear Zero-Sum Differential Game.

PubMed

Zhong, Xiangnan; He, Haibo; Wang, Ding; Ni, Zhen

2018-05-01

In this paper, we present a new model-free globalized dual heuristic dynamic programming (GDHP) approach for the discrete-time nonlinear zero-sum game problems. First, the online learning algorithm is proposed based on the GDHP method to solve the Hamilton-Jacobi-Isaacs equation associated with optimal regulation control problem. By setting backward one step of the definition of performance index, the requirement of system dynamics, or an identifier is relaxed in the proposed method. Then, three neural networks are established to approximate the optimal saddle point feedback control law, the disturbance law, and the performance index, respectively. The explicit updating rules for these three neural networks are provided based on the data generated during the online learning along the system trajectories. The stability analysis in terms of the neural network approximation errors is discussed based on the Lyapunov approach. Finally, two simulation examples are provided to show the effectiveness of the proposed method.

Learning-Based Adaptive Optimal Tracking Control of Strict-Feedback Nonlinear Systems.

PubMed

Gao, Weinan; Jiang, Zhong-Ping; Weinan Gao; Zhong-Ping Jiang; Gao, Weinan; Jiang, Zhong-Ping

2018-06-01

This paper proposes a novel data-driven control approach to address the problem of adaptive optimal tracking for a class of nonlinear systems taking the strict-feedback form. Adaptive dynamic programming (ADP) and nonlinear output regulation theories are integrated for the first time to compute an adaptive near-optimal tracker without any a priori knowledge of the system dynamics. Fundamentally different from adaptive optimal stabilization problems, the solution to a Hamilton-Jacobi-Bellman (HJB) equation, not necessarily a positive definite function, cannot be approximated through the existing iterative methods. This paper proposes a novel policy iteration technique for solving positive semidefinite HJB equations with rigorous convergence analysis. A two-phase data-driven learning method is developed and implemented online by ADP. The efficacy of the proposed adaptive optimal tracking control methodology is demonstrated via a Van der Pol oscillator with time-varying exogenous signals.

Control of Flexible Structures (COFS) Flight Experiment Background and Description

NASA Technical Reports Server (NTRS)

Hanks, B. R.

1985-01-01

A fundamental problem in designing and delivering large space structures to orbit is to provide sufficient structural stiffness and static configuration precision to meet performance requirements. These requirements are directly related to control requirements and the degree of control system sophistication available to supplement the as-built structure. Background and rationale are presented for a research study in structures, structural dynamics, and controls using a relatively large, flexible beam as a focus. This experiment would address fundamental problems applicable to large, flexible space structures in general and would involve a combination of ground tests, flight behavior prediction, and instrumented orbital tests. Intended to be multidisciplinary but basic within each discipline, the experiment should provide improved understanding and confidence in making design trades between structural conservatism and control system sophistication for meeting static shape and dynamic response/stability requirements. Quantitative results should be obtained for use in improving the validity of ground tests for verifying flight performance analyses.

Seeking the chemical roots of darwinism: bridging between chemistry and biology.

PubMed

Pross, Addy

2009-08-24

Chemistry and biology are intimately connected sciences yet the chemistry-biology interface remains problematic and central issues regarding the very essence of living systems remain unresolved. In this essay we build on a kinetic theory of replicating systems that encompasses the idea that there are two distinct kinds of stability in nature-thermodynamic stability, associated with "regular" chemical systems, and dynamic kinetic stability, associated with replicating systems. That fundamental distinction is utilized to bridge between chemistry and biology by demonstrating that within the parallel world of replicating systems there is a second law analogue to the second law of thermodynamics, and that Darwinian theory may, through scientific reductionism, be related to that second law analogue. Possible implications of these ideas to the origin of life problem and the relationship between chemical emergence and biological evolution are discussed.

Designing Liquid Rocket Engine Injectors for Performance, Stability, and Cost

NASA Technical Reports Server (NTRS)

Westra, Douglas G.; West, Jeffrey S.

2014-01-01

NASA is developing the Space Launch System (SLS) for crewed exploration missions beyond low Earth orbit. Marshall Space Flight Center (MSFC) is designing rocket engines for the SLS Advanced Booster (AB) concepts being developed to replace the Shuttle-derived solid rocket boosters. One AB concept uses large, Rocket-Propellant (RP)-fueled engines that pose significant design challenges. The injectors for these engines require high performance and stable operation while still meeting aggressive cost reduction goals for access to space. Historically, combustion stability problems have been a critical issue for such injector designs. Traditional, empirical injector design tools and methodologies, however, lack the ability to reliably predict complex injector dynamics that often lead to combustion stability. Reliance on these tools alone would likely result in an unaffordable test-fail-fix cycle for injector development. Recently at MSFC, a massively parallel computational fluid dynamics (CFD) program was successfully applied in the SLS AB injector design process. High-fidelity reacting flow simulations were conducted for both single-element and seven-element representations of the full-scale injector. Data from the CFD simulations was then used to significantly augment and improve the empirical design tools, resulting in a high-performance, stable injector design.

Dynamic Stability of a Cylindrical Shell Stiffened with a Cylinder and Longitudinal Diaphragms at External Pressure

NASA Astrophysics Data System (ADS)

Bakulin, V. N.; Danilkin, E. V.; Nedbai, A. Ya.

2018-05-01

A study has been made of the dynamic stability of a cylindrical orthotropic shell stiffened with a hollow cylinder and inhomogeneous longitudinal diaphragms under the action of axial forces and pulsating external pressure. The influence of the cylinder and diaphragms on the stability of the shell was taken account of in the form of elastic foundations whose moduli of subgrade reaction are determined from the equations of a three-dimensional theory of elasticity and the Timoshenko model respectively. A solution to the equation of motion of the shell has been found in the form of a trigonometric circumferential-coordinate series. To construct the principal region of instability of the shell, a binomial approximation was used in the obtained Mathieu-Hill equations. As a result, the problem was reduced to a system of two algebraic equations for normal displacement of the shell at diaphragm installation sites. For uniformly spaced identical diaphragms, a solution has been obtained in explicit form. The dependences of the principal region of instability of the shell on the number and rigidity of the diaphragms have been determined at different radii of the cylinder channel.

Efficient stabilization and acceleration of numerical simulation of fluid flows by residual recombination

NASA Astrophysics Data System (ADS)

Citro, V.; Luchini, P.; Giannetti, F.; Auteri, F.

2017-09-01

The study of the stability of a dynamical system described by a set of partial differential equations (PDEs) requires the computation of unstable states as the control parameter exceeds its critical threshold. Unfortunately, the discretization of the governing equations, especially for fluid dynamic applications, often leads to very large discrete systems. As a consequence, matrix based methods, like for example the Newton-Raphson algorithm coupled with a direct inversion of the Jacobian matrix, lead to computational costs too large in terms of both memory and execution time. We present a novel iterative algorithm, inspired by Krylov-subspace methods, which is able to compute unstable steady states and/or accelerate the convergence to stable configurations. Our new algorithm is based on the minimization of the residual norm at each iteration step with a projection basis updated at each iteration rather than at periodic restarts like in the classical GMRES method. The algorithm is able to stabilize any dynamical system without increasing the computational time of the original numerical procedure used to solve the governing equations. Moreover, it can be easily inserted into a pre-existing relaxation (integration) procedure with a call to a single black-box subroutine. The procedure is discussed for problems of different sizes, ranging from a small two-dimensional system to a large three-dimensional problem involving the Navier-Stokes equations. We show that the proposed algorithm is able to improve the convergence of existing iterative schemes. In particular, the procedure is applied to the subcritical flow inside a lid-driven cavity. We also discuss the application of Boostconv to compute the unstable steady flow past a fixed circular cylinder (2D) and boundary-layer flow over a hemispherical roughness element (3D) for supercritical values of the Reynolds number. We show that Boostconv can be used effectively with any spatial discretization, be it a finite-difference, finite-volume, finite-element or spectral method.

Hybrid Instrumentation in Lumbar Spinal Fusion: A Biomechanical Evaluation of Three Different Instrumentation Techniques.

PubMed

Obid, Peter; Danyali, Reza; Kueny, Rebecca; Huber, Gerd; Reichl, Michael; Richter, Alexander; Niemeyer, Thomas; Morlock, Michael; Püschel, Klaus; Übeyli, Hüseyin

2017-02-01

Ex vivo human cadaveric study. The development or progression of adjacent segment disease (ASD) after spine stabilization and fusion is a major problem in spine surgery. Apart from optimal balancing of the sagittal profile, dynamic instrumentation is often suggested to prevent or impede ASD. Hybrid instrumentation is used to gain stabilization while allowing motion to avoid hypermobility in the adjacent segment. In this biomechanical study, the effects of two different hybrid instrumentations on human cadaver spines were evaluated and compared with a rigid instrumentation. Eighteen human cadaver spines (T11-L5) were subdivided into three groups: rigid, dynamic, and hook comprising six spines each. Clinical parameters and initial mechanical characteristics were consistent among groups. All specimens received rigid fixation from L3-L5 followed by application of a free bending load of extension and flexion. The range of motion (ROM) for every segment was evaluated. For the rigid group, further rigid fixation from L1-L5 was applied. A dynamic Elaspine system (Spinelab AG, Winterthur, Switzerland) was applied from L1 to L3 for the dynamic group, and the hook group was instrumented with additional laminar hooks at L1-L3. ROM was then evaluated again. There was no significant difference in ROM among the three instrumentation techniques. Based on this data, the intended advantage of a hybrid or dynamic instrumentation might not be achieved.

Feedback control by online learning an inverse model.

PubMed

Waegeman, Tim; Wyffels, Francis; Schrauwen, Francis

2012-10-01

A model, predictor, or error estimator is often used by a feedback controller to control a plant. Creating such a model is difficult when the plant exhibits nonlinear behavior. In this paper, a novel online learning control framework is proposed that does not require explicit knowledge about the plant. This framework uses two learning modules, one for creating an inverse model, and the other for actually controlling the plant. Except for their inputs, they are identical. The inverse model learns by the exploration performed by the not yet fully trained controller, while the actual controller is based on the currently learned model. The proposed framework allows fast online learning of an accurate controller. The controller can be applied on a broad range of tasks with different dynamic characteristics. We validate this claim by applying our control framework on several control tasks: 1) the heating tank problem (slow nonlinear dynamics); 2) flight pitch control (slow linear dynamics); and 3) the balancing problem of a double inverted pendulum (fast linear and nonlinear dynamics). The results of these experiments show that fast learning and accurate control can be achieved. Furthermore, a comparison is made with some classical control approaches, and observations concerning convergence and stability are made.

Designing Adaptive Low Dissipative High Order Schemes

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjoegreen, B.; Parks, John W. (Technical Monitor)

2002-01-01

Proper control of the numerical dissipation/filter to accurately resolve all relevant multiscales of complex flow problems while still maintaining nonlinear stability and efficiency for long-time numerical integrations poses a great challenge to the design of numerical methods. The required type and amount of numerical dissipation/filter are not only physical problem dependent, but also vary from one flow region to another. This is particularly true for unsteady high-speed shock/shear/boundary-layer/turbulence/acoustics interactions and/or combustion problems since the dynamics of the nonlinear effect of these flows are not well-understood. Even with extensive grid refinement, it is of paramount importance to have proper control on the type and amount of numerical dissipation/filter in regions where it is needed.

Calculation of the lateral-dynamic stability of aircraft

NASA Technical Reports Server (NTRS)

Raikh, A

1952-01-01

Graphs and formulas are given with the aid of which all the aerodynamic coefficients required for computing the lateral dynamic stability can be determined. A number of numerical examples are given for obtaining the stability derivatives and solving the characteristic-stability equation. Approximate formulas are derived with the aid of which rapid preliminary computations may be made and the stability coefficients corrected for certain modifications of the airplane. A derivation of the lateral-dynamic-stability equations is included.

A mathematical model of Chagas disease transmission

NASA Astrophysics Data System (ADS)

Hidayat, Dayat; Nugraha, Edwin Setiawan; Nuraini, Nuning

2018-03-01

Chagas disease is a parasitic infection caused by protozoan Trypanosoma cruzi which is transmitted to human by insects of the subfamily Triatominae, including Rhodnius prolixus. This disease is a major problem in several countries of Latin America. A mathematical model of Chagas disease with separate vector reservoir and a neighboring human resident is constructed. The basic reproductive ratio is obtained and stability analysis of the equilibria is shown. We also performed sensitivity populations dynamics of infected humans and infected insects based on migration rate, carrying capacity, and infection rate parameters. Our findings showed that the dynamics of the infected human and insect is mostly affected by carrying capacity insect in the settlement.

Multiphase Fluid Dynamics for Spacecraft Applications

NASA Astrophysics Data System (ADS)

Shyy, W.; Sim, J.

2011-09-01

Multiphase flows involving moving interfaces between different fluids/phases are observed in nature as well as in a wide range of engineering applications. With the recent development of high fidelity computational techniques, a number of challenging multiphase flow problems can now be computed. We introduce the basic notion of the main categories of multiphase flow computation; Lagrangian, Eulerian, and Eulerian-Lagrangian techniques to represent and follow interface, and sharp and continuous interface methods to model interfacial dynamics. The marker-based adaptive Eulerian-Lagrangian method, which is one of the most popular methods, is highlighted with microgravity and space applications including droplet collision and spacecraft liquid fuel tank surface stability.

Nonlinear travelling waves in rotating Hagen–Poiseuille flow

NASA Astrophysics Data System (ADS)

Pier, Benoît; Govindarajan, Rama

2018-03-01

The dynamics of viscous flow through a rotating pipe is considered. Small-amplitude stability characteristics are obtained by linearizing the Navier–Stokes equations around the base flow and solving the resulting eigenvalue problems. For linearly unstable configurations, the dynamics leads to fully developed finite-amplitude perturbations that are computed by direct numerical simulations of the complete Navier–Stokes equations. By systematically investigating all linearly unstable combinations of streamwise wave number k and azimuthal mode number m, for streamwise Reynolds numbers {{Re}}z ≤slant 500 and rotational Reynolds numbers {{Re}}{{Ω }} ≤slant 500, the complete range of nonlinear travelling waves is obtained and the associated flow fields are characterized.

Numerical stability analysis of two-dimensional solute transport along a discrete fracture in a porous rock matrix

NASA Astrophysics Data System (ADS)

Watanabe, Norihiro; Kolditz, Olaf

2015-07-01

This work reports numerical stability conditions in two-dimensional solute transport simulations including discrete fractures surrounded by an impermeable rock matrix. We use an advective-dispersive problem described in Tang et al. (1981) and examine the stability of the Crank-Nicolson Galerkin finite element method (CN-GFEM). The stability conditions are analyzed in terms of the spatial discretization length perpendicular to the fracture, the flow velocity, the diffusion coefficient, the matrix porosity, the fracture aperture, and the fracture longitudinal dispersivity. In addition, we verify applicability of the recently developed finite element method-flux corrected transport (FEM-FCT) method by Kuzmin () to suppress oscillations in the hybrid system, with a comparison to the commonly utilized Streamline Upwinding/Petrov-Galerkin (SUPG) method. Major findings of this study are (1) the mesh von Neumann number (Fo) ≥ 0.373 must be satisfied to avoid undershooting in the matrix, (2) in addition to an upper bound, the Courant number also has a lower bound in the fracture in cases of low dispersivity, and (3) the FEM-FCT method can effectively suppress the oscillations in both the fracture and the matrix. The results imply that, in cases of low dispersivity, prerefinement of a numerical mesh is not sufficient to avoid the instability in the hybrid system if a problem involves evolutionary flow fields and dynamic material parameters. Applying the FEM-FCT method to such problems is recommended if negative concentrations cannot be tolerated and computing time is not a strong issue.

Identification of Synchronous Machine Stability - Parameters: AN On-Line Time-Domain Approach.

NASA Astrophysics Data System (ADS)

Le, Loc Xuan

1987-09-01

A time-domain modeling approach is described which enables the stability-study parameters of the synchronous machine to be determined directly from input-output data measured at the terminals of the machine operating under normal conditions. The transient responses due to system perturbations are used to identify the parameters of the equivalent circuit models. The described models are verified by comparing their responses with the machine responses generated from the transient stability models of a small three-generator multi-bus power system and of a single -machine infinite-bus power network. The least-squares method is used for the solution of the model parameters. As a precaution against ill-conditioned problems, the singular value decomposition (SVD) is employed for its inherent numerical stability. In order to identify the equivalent-circuit parameters uniquely, the solution of a linear optimization problem with non-linear constraints is required. Here, the SVD appears to offer a simple solution to this otherwise difficult problem. Furthermore, the SVD yields solutions with small bias and, therefore, physically meaningful parameters even in the presence of noise in the data. The question concerning the need for a more advanced model of the synchronous machine which describes subtransient and even sub-subtransient behavior is dealt with sensibly by the concept of condition number. The concept provides a quantitative measure for determining whether such an advanced model is indeed necessary. Finally, the recursive SVD algorithm is described for real-time parameter identification and tracking of slowly time-variant parameters. The algorithm is applied to identify the dynamic equivalent power system model.

Dynamic modeling and hierarchical compound control of a novel 2-DOF flexible parallel manipulator with multiple actuation modes

NASA Astrophysics Data System (ADS)

Liang, Dong; Song, Yimin; Sun, Tao; Jin, Xueying

2018-03-01

This paper addresses the problem of rigid-flexible coupling dynamic modeling and active control of a novel flexible parallel manipulator (PM) with multiple actuation modes. Firstly, based on the flexible multi-body dynamics theory, the rigid-flexible coupling dynamic model (RFDM) of system is developed by virtue of the augmented Lagrangian multipliers approach. For completeness, the mathematical models of permanent magnet synchronous motor (PMSM) and piezoelectric transducer (PZT) are further established and integrated with the RFDM of mechanical system to formulate the electromechanical coupling dynamic model (ECDM). To achieve the trajectory tracking and vibration suppression, a hierarchical compound control strategy is presented. Within this control strategy, the proportional-differential (PD) feedback controller is employed to realize the trajectory tracking of end-effector, while the strain and strain rate feedback (SSRF) controller is developed to restrain the vibration of the flexible links using PZT. Furthermore, the stability of the control algorithm is demonstrated based on the Lyapunov stability theory. Finally, two simulation case studies are performed to illustrate the effectiveness of the proposed approach. The results indicate that, under the redundant actuation mode, the hierarchical compound control strategy can guarantee the flexible PM achieves singularity-free motion and vibration attenuation within task workspace simultaneously. The systematic methodology proposed in this study can be conveniently extended for the dynamic modeling and efficient controller design of other flexible PMs, especially the emerging ones with multiple actuation modes.

Fuzzy Model-based Pitch Stabilization and Wing Vibration Suppression of Flexible Wing Aircraft.

NASA Technical Reports Server (NTRS)

Ayoubi, Mohammad A.; Swei, Sean Shan-Min; Nguyen, Nhan T.

2014-01-01

This paper presents a fuzzy nonlinear controller to regulate the longitudinal dynamics of an aircraft and suppress the bending and torsional vibrations of its flexible wings. The fuzzy controller utilizes full-state feedback with input constraint. First, the Takagi-Sugeno fuzzy linear model is developed which approximates the coupled aeroelastic aircraft model. Then, based on the fuzzy linear model, a fuzzy controller is developed to utilize a full-state feedback and stabilize the system while it satisfies the control input constraint. Linear matrix inequality (LMI) techniques are employed to solve the fuzzy control problem. Finally, the performance of the proposed controller is demonstrated on the NASA Generic Transport Model (GTM).

Asymptotic Stability of Interconnected Passive Non-Linear Systems

NASA Technical Reports Server (NTRS)

Isidori, A.; Joshi, S. M.; Kelkar, A. G.

1999-01-01

This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.

A loosely-coupled scheme for the interaction between a fluid, elastic structure and poroelastic material

NASA Astrophysics Data System (ADS)

Bukač, M.

2016-05-01

We model the interaction between an incompressible, viscous fluid, thin elastic structure and a poroelastic material. The poroelastic material is modeled using the Biot's equations of dynamic poroelasticity. The fluid, elastic structure and the poroelastic material are fully coupled, giving rise to a nonlinear, moving boundary problem with novel energy estimates. We present a modular, loosely coupled scheme where the original problem is split into the fluid sub-problem, elastic structure sub-problem and poroelasticity sub-problem. An energy estimate associated with the stability of the scheme is derived in the case where one of the coupling parameters, β, is equal to zero. We present numerical tests where we investigate the effects of the material properties of the poroelastic medium on the fluid flow. Our findings indicate that the flow patterns highly depend on the storativity of the poroelastic material and cannot be captured by considering fluid-structure interaction only.

Geometrical analysis of the LiCN vibrational dynamics: a stability geometrical indicator.

PubMed

Vergel, A; Benito, R M; Losada, J C; Borondo, F

2014-02-01

The vibrational dynamics of the LiNC/LiCN molecular system is examined making use of the Riemannian geometry. Stability and chaoticity are analyzed, in this context, by means of the Jacobi-Levi-Civita equations, derived from the Jacobi metric, and its solutions. A dynamical indicator, called stability geometrical indicator, is introduced in order to ascertain the dynamical characteristics of stability and chaos in the molecule under study.

Comprehensive helicopter analysis: A state of the art review

NASA Technical Reports Server (NTRS)

Johnson, W.

1978-01-01

An assessment of the status of helicopter theory and analysis is presented. The technology level embodied in available design tools (computer programs) is examined, considering the problem areas of performance, loads and vibration, handling qualities and simulation, and aeroelastic stability. The effectiveness of the present analyses is discussed. The characteristics of the technology in the analyses are reviewed, including the aerodynamics technology, induced velocity and wake geometry, dynamics technology, and machine limitations.

Decentralized regulation of dynamic systems. [for controlling large scale linear systems

NASA Technical Reports Server (NTRS)

Chu, K. C.

1975-01-01

A special class of decentralized control problem is discussed in which the objectives of the control agents are to steer the state of the system to desired levels. Each agent is concerned about certain aspects of the state of the entire system. The state and control equations are given for linear time-invariant systems. Stability and coordination, and the optimization of decentralized control are analyzed, and the information structure design is presented.

A method of intentional movement estimation of oblique small-UAV videos stabilized based on homography model

NASA Astrophysics Data System (ADS)

Guo, Shiyi; Mai, Ying; Zhao, Hongying; Gao, Pengqi

2013-05-01

The airborne video streams of small-UAVs are commonly plagued with distractive jittery and shaking motions, disorienting rotations, noisy and distorted images and other unwanted movements. These problems collectively make it very difficult for observers to obtain useful information from the video. Due to the small payload of small-UAVs, it is a priority to improve the image quality by means of electronic image stabilization. But when small-UAV makes a turn, affected by the flight characteristics of it, the video is easy to become oblique. This brings a lot of difficulties to electronic image stabilization technology. Homography model performed well in the oblique image motion estimation, while bringing great challenges to intentional motion estimation. Therefore, in this paper, we focus on solve the problem of the video stabilized when small-UAVs banking and turning. We attend to the small-UAVs fly along with an arc of a fixed turning radius. For this reason, after a series of experimental analysis on the flight characteristics and the path how small-UAVs turned, we presented a new method to estimate the intentional motion in which the path of the frame center was used to fit the video moving track. Meanwhile, the image sequences dynamic mosaic was done to make up for the limited field of view. At last, the proposed algorithm was carried out and validated by actual airborne videos. The results show that the proposed method is effective to stabilize the oblique video of small-UAVs.

Decentralized Fuzzy MPC on Spatial Power Control of a Large PHWR

NASA Astrophysics Data System (ADS)

Liu, Xiangjie; Jiang, Di; Lee, Kwang Y.

2016-08-01

Reliable power control for stabilizing the spatial oscillations is quite important for ensuring the safe operation of a modern pressurized heavy water reactor (PHWR), since these spatial oscillations can cause “flux tilting” in the reactor core. In this paper, a decentralized fuzzy model predictive control (DFMPC) is proposed for spatial control of PHWR. Due to the load dependent dynamics of the nuclear power plant, fuzzy modeling is used to approximate the nonlinear process. A fuzzy Lyapunov function and “quasi-min-max” strategy is utilized in designing the DFMPC, to reduce the conservatism. The plant-wide stability is achieved by the asymptotically positive realness constraint (APRC) for this decentralized MPC. The solving optimization problem is based on a receding horizon scheme involving the linear matrix inequalities (LMIs) technique. Through dynamic simulations, it is demonstrated that the designed DFMPC can effectively suppress spatial oscillations developed in PHWR, and further, shows the advantages over the typical parallel distributed compensation (PDC) control scheme.

Free Energy Perturbation Calculations of the Thermodynamics of Protein Side-Chain Mutations.

PubMed

Steinbrecher, Thomas; Abel, Robert; Clark, Anthony; Friesner, Richard

2017-04-07

Protein side-chain mutation is fundamental both to natural evolutionary processes and to the engineering of protein therapeutics, which constitute an increasing fraction of important medications. Molecular simulation enables the prediction of the effects of mutation on properties such as binding affinity, secondary and tertiary structure, conformational dynamics, and thermal stability. A number of widely differing approaches have been applied to these predictions, including sequence-based algorithms, knowledge-based potential functions, and all-atom molecular mechanics calculations. Free energy perturbation theory, employing all-atom and explicit-solvent molecular dynamics simulations, is a rigorous physics-based approach for calculating thermodynamic effects of, for example, protein side-chain mutations. Over the past several years, we have initiated an investigation of the ability of our most recent free energy perturbation methodology to model the thermodynamics of protein mutation for two specific problems: protein-protein binding affinities and protein thermal stability. We highlight recent advances in the field and outline current and future challenges. Copyright © 2017 Elsevier Ltd. All rights reserved.

A new smooth robust control design for uncertain nonlinear systems with non-vanishing disturbances

NASA Astrophysics Data System (ADS)

Xian, Bin; Zhang, Yao

2016-06-01

In this paper, we consider the control problem for a general class of nonlinear system subjected to uncertain dynamics and non-varnishing disturbances. A smooth nonlinear control algorithm is presented to tackle these uncertainties and disturbances. The proposed control design employs the integral of a nonlinear sigmoid function to compensate the uncertain dynamics, and achieve a uniformly semi-global practical asymptotic stable tracking control of the system outputs. A novel Lyapunov-based stability analysis is employed to prove the convergence of the tracking errors and the stability of the closed-loop system. Numerical simulation results on a two-link robot manipulator are presented to illustrate the performance of the proposed control algorithm comparing with the layer-boundary sliding mode controller and the robust of integration of sign of error control design. Furthermore, real-time experiment results for the attitude control of a quadrotor helicopter are also included to confirm the effectiveness of the proposed algorithm.

Interfacial fluid instabilities and Kapitsa pendula.

PubMed

Krieger, Madison S

2017-07-01

The onset and development of instabilities is one of the central problems in fluid mechanics. Here we develop a connection between instabilities of free fluid interfaces and inverted pendula. When acted upon solely by the gravitational force, the inverted pendulum is unstable. This position can be stabilized by the Kapitsa phenomenon, in which high-frequency low-amplitude vertical vibrations of the base creates a fictitious force which opposes the gravitational force. By transforming the dynamical equations governing a fluid interface into an appropriate pendulum-type equation, we demonstrate how stability can be induced in fluid systems by properly tuned vibrations. We construct a "dictionary"-type relationship between various pendula and the classical Rayleigh-Taylor, Kelvin-Helmholtz, Rayleigh-Plateau and the self-gravitational instabilities. This makes several results in control theory and dynamical systems directly applicable to the study of tunable fluid instabilities, where the critical wavelength depends on the external forces or the instability is suppressed entirely. We suggest some applications and instances of the effect ranging in scale from microns to the radius of a galaxy.

Seasonally forced disease dynamics explored as switching between attractors

NASA Astrophysics Data System (ADS)

Keeling, Matt J.; Rohani, Pejman; Grenfell, Bryan T.

2001-01-01

Biological phenomena offer a rich diversity of problems that can be understood using mathematical techniques. Three key features common to many biological systems are temporal forcing, stochasticity and nonlinearity. Here, using simple disease models compared to data, we examine how these three factors interact to produce a range of complicated dynamics. The study of disease dynamics has been amongst the most theoretically developed areas of mathematical biology; simple models have been highly successful in explaining the dynamics of a wide variety of diseases. Models of childhood diseases incorporate seasonal variation in contact rates due to the increased mixing during school terms compared to school holidays. This ‘binary’ nature of the seasonal forcing results in dynamics that can be explained as switching between two nonlinear spiral sinks. Finally, we consider the stability of the attractors to understand the interaction between the deterministic dynamics and demographic and environmental stochasticity. Throughout attention is focused on the behaviour of measles, whooping cough and rubella.

Dynamics of Numerics & Spurious Behaviors in CFD Computations. Revised

NASA Technical Reports Server (NTRS)

Yee, Helen C.; Sweby, Peter K.

1997-01-01

The global nonlinear behavior of finite discretizations for constant time steps and fixed or adaptive grid spacings is studied using tools from dynamical systems theory. Detailed analysis of commonly used temporal and spatial discretizations for simple model problems is presented. The role of dynamics in the understanding of long time behavior of numerical integration and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in computational fluid dynamics (CFD) is explored. The study is complemented with examples of spurious behavior observed in steady and unsteady CFD computations. The CFD examples were chosen to illustrate non-apparent spurious behavior that was difficult to detect without extensive grid and temporal refinement studies and some knowledge from dynamical systems theory. Studies revealed the various possible dangers of misinterpreting numerical simulation of realistic complex flows that are constrained by available computing power. In large scale computations where the physics of the problem under study is not well understood and numerical simulations are the only viable means of solution, extreme care must be taken in both computation and interpretation of the numerical data. The goal of this paper is to explore the important role that dynamical systems theory can play in the understanding of the global nonlinear behavior of numerical algorithms and to aid the identification of the sources of numerical uncertainties in CFD.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koniges, A.E.; Craddock, G.G.; Schnack, D.D.

The purpose of the workshop was to assemble workers, both within and outside of the fusion-related computations areas, for discussion regarding the issues of dynamically adaptive gridding. There were three invited talks related to adaptive gridding application experiences in various related fields of computational fluid dynamics (CFD), and nine short talks reporting on the progress of adaptive techniques in the specific areas of scrape-off-layer (SOL) modeling and magnetohydrodynamic (MHD) stability. Adaptive mesh methods have been successful in a number of diverse fields of CFD for over a decade. The method involves dynamic refinement of computed field profiles in a waymore » that disperses uniformly the numerical errors associated with discrete approximations. Because the process optimizes computational effort, adaptive mesh methods can be used to study otherwise the intractable physical problems that involve complex boundary shapes or multiple spatial/temporal scales. Recent results indicate that these adaptive techniques will be required for tokamak fluid-based simulations involving the diverted tokamak SOL modeling and MHD simulations problems related to the highest priority ITER relevant issues.Individual papers are indexed separately on the energy data bases.« less

Development and application of a local linearization algorithm for the integration of quaternion rate equations in real-time flight simulation problems

NASA Technical Reports Server (NTRS)

Barker, L. E., Jr.; Bowles, R. L.; Williams, L. H.

1973-01-01

High angular rates encountered in real-time flight simulation problems may require a more stable and accurate integration method than the classical methods normally used. A study was made to develop a general local linearization procedure of integrating dynamic system equations when using a digital computer in real-time. The procedure is specifically applied to the integration of the quaternion rate equations. For this application, results are compared to a classical second-order method. The local linearization approach is shown to have desirable stability characteristics and gives significant improvement in accuracy over the classical second-order integration methods.

Bifurcation approach to a logistic elliptic equation with a homogeneous incoming flux boundary condition

NASA Astrophysics Data System (ADS)

Umezu, Kenichiro

In this paper, we consider a semilinear elliptic boundary value problem in a smooth bounded domain, having the so-called logistic nonlinearity that originates from population dynamics, with a nonlinear boundary condition. Although the logistic nonlinearity has an absorption effect in the problem, the nonlinear boundary condition is induced by the homogeneous incoming flux on the boundary. The objective of our study is to analyze the existence of a bifurcation component of positive solutions from trivial solutions and its asymptotic behavior and stability. We perform this analysis using the method developed by Lyapunov and Schmidt, based on a scaling argument.

Effect of damping on excitability of high-order normal modes. [for a large space telescope spacecraft

NASA Technical Reports Server (NTRS)

Merchant, D. H.; Gates, R. M.; Straayer, J. W.

1975-01-01

The effect of localized structural damping on the excitability of higher-order large space telescope spacecraft modes is investigated. A preprocessor computer program is developed to incorporate Voigt structural joint damping models in a finite-element dynamic model. A postprocessor computer program is developed to select critical modes for low-frequency attitude control problems and for higher-frequency fine-stabilization problems. The selection is accomplished by ranking the flexible modes based on coefficients for rate gyro, position gyro, and optical sensor, and on image-plane motions due to sinusoidal or random PSD force and torque inputs.

Dyadic flexibility and positive affect in parent–child coregulation and the development of child behavior problems

PubMed Central

LUNKENHEIMER, ERIKA S.; OLSON, SHERYL L.; HOLLENSTEIN, TOM; SAMEROFF, ARNOLD J.; WINTER, CHARLOTTE

2018-01-01

Parent–child dyadic rigidity and negative affect contribute to children’s higher levels of externalizing problems. The present longitudinal study examined whether the opposite constructs of dyadic flexibility and positive affect predicted lower levels of externalizing behavior problems across the early childhood period. Mother–child (N = 163) and father–child (n = 94) dyads engaged in a challenging block design task at home when children were 3 years old. Dynamic systems methods were used to derive dyadic positive affect and three indicators of dyadic flexibility (range, dispersion, and transitions) from observational coding. We hypothesized that the interaction between dyadic flexibility and positive affect would predict lower levels of externalizing problems at age 5.5 years as rated by mothers and teachers, controlling for stability in externalizing problems, task time, child gender, and the child’s effortful control. The hypothesis was supported in predicting teacher ratings of child externalizing from both mother–child and father–child interactions. There were also differential main effects for mothers and fathers: mother–child flexibility was detrimental and father–child flexibility was beneficial for child outcomes. Results support the inclusion of adaptive and dynamic parent–child coregulation processes in the study of children’s early disruptive behavior. PMID:23786697

Randomly Sampled-Data Control Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Han, Kuoruey

1990-01-01

The purpose is to solve the Linear Quadratic Regulator (LQR) problem with random time sampling. Such a sampling scheme may arise from imperfect instrumentation as in the case of sampling jitter. It can also model the stochastic information exchange among decentralized controllers to name just a few. A practical suboptimal controller is proposed with the nice property of mean square stability. The proposed controller is suboptimal in the sense that the control structure is limited to be linear. Because of i. i. d. assumption, this does not seem unreasonable. Once the control structure is fixed, the stochastic discrete optimal control problem is transformed into an equivalent deterministic optimal control problem with dynamics described by the matrix difference equation. The N-horizon control problem is solved using the Lagrange's multiplier method. The infinite horizon control problem is formulated as a classical minimization problem. Assuming existence of solution to the minimization problem, the total system is shown to be mean square stable under certain observability conditions. Computer simulations are performed to illustrate these conditions.

ECCD-induced tearing mode stabilization in coupled IPS/NIMROD/GENRAY HPC simulations

NASA Astrophysics Data System (ADS)

Jenkins, Thomas; Kruger, S. E.; Held, E. D.; Harvey, R. W.; Elwasif, W. R.

2012-03-01

We summarize ongoing developments toward an integrated, predictive model for determining optimal ECCD-based NTM stabilization strategies in ITER. We demonstrate the capability of the SWIM Project's Integrated Plasma Simulator (IPS) framework to choreograph multiple executions of, and data exchanges between, physics codes modeling various spatiotemporal scales of this coupled RF/MHD problem on several thousand HPC processors. As NIMROD evolves fluid equations to model bulk plasma behavior, self-consistent propagation/deposition of RF power in the ensuing plasma profiles is calculated by GENRAY. Data from both codes is then processed by computational geometry packages to construct the RF-induced quasilinear diffusion tensor; moments of this tensor (entering as additional terms in NIMROD's fluid equations due to the disparity in RF/MHD spatiotemporal scales) influence the dynamics of current, momentum, and energy evolution as well as the MHD closures. Initial results are shown to correctly capture the physics of magnetic island stabilization; we also discuss the development of a numerical plasma control system for active feedback stabilization of tearing modes.

Neuromechanic: a computational platform for simulation and analysis of the neural control of movement

PubMed Central

Bunderson, Nathan E.; Bingham, Jeffrey T.; Sohn, M. Hongchul; Ting, Lena H.; Burkholder, Thomas J.

2015-01-01

Neuromusculoskeletal models solve the basic problem of determining how the body moves under the influence of external and internal forces. Existing biomechanical modeling programs often emphasize dynamics with the goal of finding a feed-forward neural program to replicate experimental data or of estimating force contributions or individual muscles. The computation of rigid-body dynamics, muscle forces, and activation of the muscles are often performed separately. We have developed an intrinsically forward computational platform (Neuromechanic, www.neuromechanic.com) that explicitly represents the interdependencies among rigid body dynamics, frictional contact, muscle mechanics, and neural control modules. This formulation has significant advantages for optimization and forward simulation, particularly with application to neural controllers with feedback or regulatory features. Explicit inclusion of all state dependencies allows calculation of system derivatives with respect to kinematic states as well as muscle and neural control states, thus affording a wealth of analytical tools, including linearization, stability analyses and calculation of initial conditions for forward simulations. In this review, we describe our algorithm for generating state equations and explain how they may be used in integration, linearization and stability analysis tools to provide structural insights into the neural control of movement. PMID:23027632

Neuromechanic: a computational platform for simulation and analysis of the neural control of movement.

PubMed

Bunderson, Nathan E; Bingham, Jeffrey T; Sohn, M Hongchul; Ting, Lena H; Burkholder, Thomas J

2012-10-01

Neuromusculoskeletal models solve the basic problem of determining how the body moves under the influence of external and internal forces. Existing biomechanical modeling programs often emphasize dynamics with the goal of finding a feed-forward neural program to replicate experimental data or of estimating force contributions or individual muscles. The computation of rigid-body dynamics, muscle forces, and activation of the muscles are often performed separately. We have developed an intrinsically forward computational platform (Neuromechanic, www.neuromechanic.com) that explicitly represents the interdependencies among rigid body dynamics, frictional contact, muscle mechanics, and neural control modules. This formulation has significant advantages for optimization and forward simulation, particularly with application to neural controllers with feedback or regulatory features. Explicit inclusion of all state dependencies allows calculation of system derivatives with respect to kinematic states and muscle and neural control states, thus affording a wealth of analytical tools, including linearization, stability analyses and calculation of initial conditions for forward simulations. In this review, we describe our algorithm for generating state equations and explain how they may be used in integration, linearization, and stability analysis tools to provide structural insights into the neural control of movement. Copyright © 2012 John Wiley & Sons, Ltd.

A flatness-based control approach to drug infusion for cardiac function regulation

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Zervos, Nikolaos; Melkikh, Alexey

2016-12-01

A new control method based on differential flatness theory is developed in this article, aiming at solving the problem of regulation of haemodynamic parameters, Actually control of the cardiac output (volume of blood pumped out by heart per unit of time) and of the arterial blood pressure is achieved through the administered infusion of cardiovascular drugs, such as dopamine and sodium nitroprusside. Time delays between the control inputs and the system's outputs are taken into account. Using the principle of dynamic extension, which means that by considering certain control inputs and their derivatives as additional state variables, a state-space description for the heart's function is obtained. It is proven that the dynamic model of the heart is a differentially flat one. This enables its transformation into a linear canonical and decoupled form, for which the design of a stabilizing feedback controller becomes possible. The proposed feedback controller is of proven stability and assures fast and accurate tracking of the reference setpoints by the outputs of the heart's dynamic model. Moreover, by using a Kalman Filter-based disturbances' estimator, it becomes possible to estimate in real-time and compensate for the model uncertainty and external perturbation inputs that affect the heart's model.

Fractional Stability of Trunk Acceleration Dynamics of Daily-Life Walking: Toward a Unified Concept of Gait Stability

PubMed Central

Ihlen, Espen A. F.; van Schooten, Kimberley S.; Bruijn, Sjoerd M.; Pijnappels, Mirjam; van Dieën, Jaap H.

2017-01-01

Over the last decades, various measures have been introduced to assess stability during walking. All of these measures assume that gait stability may be equated with exponential stability, where dynamic stability is quantified by a Floquet multiplier or Lyapunov exponent. These specific constructs of dynamic stability assume that the gait dynamics are time independent and without phase transitions. In this case the temporal change in distance, d(t), between neighboring trajectories in state space is assumed to be an exponential function of time. However, results from walking models and empirical studies show that the assumptions of exponential stability break down in the vicinity of phase transitions that are present in each step cycle. Here we apply a general non-exponential construct of gait stability, called fractional stability, which can define dynamic stability in the presence of phase transitions. Fractional stability employs the fractional indices, α and β, of differential operator which allow modeling of singularities in d(t) that cannot be captured by exponential stability. The fractional stability provided an improved fit of d(t) compared to exponential stability when applied to trunk accelerations during daily-life walking in community-dwelling older adults. Moreover, using multivariate empirical mode decomposition surrogates, we found that the singularities in d(t), which were well modeled by fractional stability, are created by phase-dependent modulation of gait. The new construct of fractional stability may represent a physiologically more valid concept of stability in vicinity of phase transitions and may thus pave the way for a more unified concept of gait stability. PMID:28900400

Dynamics and Self-consistent Chaos in a Mean Field Hamiltonian Model

NASA Astrophysics Data System (ADS)

del-Castillo-Negrete, Diego

We study a mean field Hamiltonian model that describes the collective dynamics of marginally stable fluids and plasmas in the finite N and N-> infty kinetic limit (where N is the number of particles). The linear stability of equilibria in the kinetic model is studied as well as the initial value problem including Landau damping . Numerical simulations show the existence of coherent, rotating dipole states. We approximate the dipole as two macroparticles and show that the N=2 limit has a family of rotating integrable solutions that provide an accurate description of the dynamics. We discuss the role of self-consistent Hamiltonian chaos in the formation of coherent structures, and discuss a mechanism of "violent" mixing caused by a self-consistent elliptic-hyperbolic bifurcation in phase space.

An integrated collision prediction and avoidance scheme for mobile robots in non-stationary environments

NASA Technical Reports Server (NTRS)

Kyriakopoulos, K. J.; Saridis, G. N.

1993-01-01

A formulation that makes possible the integration of collision prediction and avoidance stages for mobile robots moving in general terrains containing moving obstacles is presented. A dynamic model of the mobile robot and the dynamic constraints are derived. Collision avoidance is guaranteed if the distance between the robot and a moving obstacle is nonzero. A nominal trajectory is assumed to be known from off-line planning. The main idea is to change the velocity along the nominal trajectory so that collisions are avoided. A feedback control is developed and local asymptotic stability is proved if the velocity of the moving obstacle is bounded. Furthermore, a solution to the problem of inverse dynamics for the mobile robot is given. Simulation results verify the value of the proposed strategy.

Dynamics of Equilibrium Points in a Uniformly Rotating Second-Order and Degree Gravitational Field

NASA Astrophysics Data System (ADS)

Feng, Jinglang; Hou, Xiyun

2017-07-01

Using tools such as periodic orbits and invariant manifolds, the global dynamics around equilibrium points (EPs) in a rotating second-order and degree gravitational field are studied. For EPs on the long axis, planar and vertical periodic families are computed, and their stability properties are investigated. Invariant manifolds are also computed, and their relation to the first-order resonances is briefly discussed. For EPs on the short axis, planar and vertical periodic families are studied, with special emphasis on the genealogy of the planar periodic families. Our studies show that the global dynamics around EPs are highly similar to those around libration points in the circular restricted three-body problem, such as spatial halo orbits, invariant manifolds, and the genealogy of planar periodic families.

Using waveform information in nonlinear data assimilation

NASA Astrophysics Data System (ADS)

Rey, Daniel; Eldridge, Michael; Morone, Uriel; Abarbanel, Henry D. I.; Parlitz, Ulrich; Schumann-Bischoff, Jan

2014-12-01

Information in measurements of a nonlinear dynamical system can be transferred to a quantitative model of the observed system to establish its fixed parameters and unobserved state variables. After this learning period is complete, one may predict the model response to new forces and, when successful, these predictions will match additional observations. This adjustment process encounters problems when the model is nonlinear and chaotic because dynamical instability impedes the transfer of information from the data to the model when the number of measurements at each observation time is insufficient. We discuss the use of information in the waveform of the data, realized through a time delayed collection of measurements, to provide additional stability and accuracy to this search procedure. Several examples are explored, including a few familiar nonlinear dynamical systems and small networks of Colpitts oscillators.

Stochastic sensitivity analysis of the variability of dynamics and transition to chaos in the business cycles model

NASA Astrophysics Data System (ADS)

Bashkirtseva, Irina; Ryashko, Lev; Ryazanova, Tatyana

2018-01-01

A problem of mathematical modeling of complex stochastic processes in macroeconomics is discussed. For the description of dynamics of income and capital stock, the well-known Kaldor model of business cycles is used as a basic example. The aim of the paper is to give an overview of the variety of stochastic phenomena which occur in Kaldor model forced by additive and parametric random noise. We study a generation of small- and large-amplitude stochastic oscillations, and their mixed-mode intermittency. To analyze these phenomena, we suggest a constructive approach combining the study of the peculiarities of deterministic phase portrait, and stochastic sensitivity of attractors. We show how parametric noise can stabilize the unstable equilibrium and transform dynamics of Kaldor system from order to chaos.

[On the problems of the evolutionary optimization of life history. II. To justification of optimization criterion for nonlinear Leslie model].

PubMed

Pasekov, V P

2013-03-01

The paper considers the problems in the adaptive evolution of life-history traits for individuals in the nonlinear Leslie model of age-structured population. The possibility to predict adaptation results as the values of organism's traits (properties) that provide for the maximum of a certain function of traits (optimization criterion) is studied. An ideal criterion of this type is Darwinian fitness as a characteristic of success of an individual's life history. Criticism of the optimization approach is associated with the fact that it does not take into account the changes in the environmental conditions (in a broad sense) caused by evolution, thereby leading to losses in the adequacy of the criterion. In addition, the justification for this criterion under stationary conditions is not usually rigorous. It has been suggested to overcome these objections in terms of the adaptive dynamics theory using the concept of invasive fitness. The reasons are given that favor the application of the average number of offspring for an individual, R(L), as an optimization criterion in the nonlinear Leslie model. According to the theory of quantitative genetics, the selection for fertility (that is, for a set of correlated quantitative traits determined by both multiple loci and the environment) leads to an increase in R(L). In terms of adaptive dynamics, the maximum R(L) corresponds to the evolutionary stability and, in certain cases, convergent stability of the values for traits. The search for evolutionarily stable values on the background of limited resources for reproduction is a problem of linear programming.

Thermostability of In Vitro Evolved Bacillus subtilis Lipase A: A Network and Dynamics Perspective

PubMed Central

Srivastava, Ashutosh; Sinha, Somdatta

2014-01-01

Proteins in thermophilic organisms remain stable and function optimally at high temperatures. Owing to their important applicability in many industrial processes, such thermostable proteins have been studied extensively, and several structural factors attributed to their enhanced stability. How these factors render the emergent property of thermostability to proteins, even in situations where no significant changes occur in their three-dimensional structures in comparison to their mesophilic counter-parts, has remained an intriguing question. In this study we treat Lipase A from Bacillus subtilis and its six thermostable mutants in a unified manner and address the problem with a combined complex network-based analysis and molecular dynamic studies to find commonality in their properties. The Protein Contact Networks (PCN) of the wild-type and six mutant Lipase A structures developed at a mesoscopic scale were analyzed at global network and local node (residue) level using network parameters and community structure analysis. The comparative PCN analysis of all proteins pointed towards important role of specific residues in the enhanced thermostability. Network analysis results were corroborated with finer-scale molecular dynamics simulations at both room and high temperatures. Our results show that this combined approach at two scales can uncover small but important changes in the local conformations that add up to stabilize the protein structure in thermostable mutants, even when overall conformation differences among them are negligible. Our analysis not only supports the experimentally determined stabilizing factors, but also unveils the important role of contacts, distributed throughout the protein, that lead to thermostability. We propose that this combined mesoscopic-network and fine-grained molecular dynamics approach is a convenient and useful scheme not only to study allosteric changes leading to protein stability in the face of negligible over-all conformational changes due to mutations, but also in other molecular networks where change in function does not accompany significant change in the network structure. PMID:25122499

Some remarks on the attractor behaviour in ELKO cosmology

NASA Astrophysics Data System (ADS)

Pereira, S. H.; A. Pinho S., S.; Hoff da Silva, J. M.

2014-08-01

Recent results on the dynamical stability of a system involving the interaction of the ELKO spinor field with standard matter in the universe have been reanalysed, and the conclusion is that such system does not exhibit isolated stable points that could alleviate the cosmic coincidence problem. When a constant parameter δ related to the potential of the ELKO field is introduced in the system however, stable fixed points are found for some specific types of interaction between the ELKO field and matter. Although the parameter δ is related to an unknown potential, in order to satisfy the stability conditions and also that the fixed points are real, the range of the constant parameter δ can be constrained for the present time and the coincidence problem can be alleviated for some specific interactions. Such restriction on the ELKO potential opens possibility to apply the ELKO field as a candidate to dark energy in the universe, and so explain the present phase of acceleration of the universe through the decay of the ELKO field into matter.

Control-structure interaction in precision pointing servo loops

NASA Technical Reports Server (NTRS)

Spanos, John T.

1989-01-01

The control-structure interaction problem is addressed via stability analysis of a generic linear servo loop model. With the plant described by the rigid body mode and a single elastic mode, structural flexibility is categorized into one of three types: (1) appendage, (2) in-the-loop minimum phase, and (3) in-the-loop nonminimum phase. Closing the loop with proportional-derivative (PD) control action and introducing sensor roll-off dynamics in the feedback path, stability conditions are obtained. Trade studies are conducted with modal frequency, modal participation, modal damping, loop bandwidth, and sensor bandwidth treated as free parameters. Results indicate that appendage modes are most likely to produce instability if they are near the sensor rolloff, whereas in-the-loop modes are most dangerous near the loop bandwidth. The main goal of this paper is to provide a fundamental understanding of the control-structure interaction problem so that it may benefit the design of complex spacecraft and pointing system servo loops. In this framework, the JPL Pathfinder gimbal pointer is considered as an example.

Optimal placement of FACTS devices using optimization techniques: A review

NASA Astrophysics Data System (ADS)

Gaur, Dipesh; Mathew, Lini

2018-03-01

Modern power system is dealt with overloading problem especially transmission network which works on their maximum limit. Today’s power system network tends to become unstable and prone to collapse due to disturbances. Flexible AC Transmission system (FACTS) provides solution to problems like line overloading, voltage stability, losses, power flow etc. FACTS can play important role in improving static and dynamic performance of power system. FACTS devices need high initial investment. Therefore, FACTS location, type and their rating are vital and should be optimized to place in the network for maximum benefit. In this paper, different optimization methods like Particle Swarm Optimization (PSO), Genetic Algorithm (GA) etc. are discussed and compared for optimal location, type and rating of devices. FACTS devices such as Thyristor Controlled Series Compensator (TCSC), Static Var Compensator (SVC) and Static Synchronous Compensator (STATCOM) are considered here. Mentioned FACTS controllers effects on different IEEE bus network parameters like generation cost, active power loss, voltage stability etc. have been analyzed and compared among the devices.

Robust, nonlinear, high angle-of-attack control design for a supermaneuverable vehicle

NASA Technical Reports Server (NTRS)

Adams, Richard J.

1993-01-01

High angle-of-attack flight control laws are developed for a supermaneuverable fighter aircraft. The methods of dynamic inversion and structured singular value synthesis are combined into an approach which addresses both the nonlinearity and robustness problems of flight at extreme operating conditions. The primary purpose of the dynamic inversion control elements is to linearize the vehicle response across the flight envelope. Structured singular value synthesis is used to design a dynamic controller which provides robust tracking to pilot commands. The resulting control system achieves desired flying qualities and guarantees a large margin of robustness to uncertainties for high angle-of-attack flight conditions. The results of linear simulation and structured singular value stability analysis are presented to demonstrate satisfaction of the design criteria. High fidelity nonlinear simulation results show that the combined dynamics inversion/structured singular value synthesis control law achieves a high level of performance in a realistic environment.

Adaptive dynamic surface control of flexible-joint robots using self-recurrent wavelet neural networks.

PubMed

Yoo, Sung Jin; Park, Jin Bae; Choi, Yoon Ho

2006-12-01

A new method for the robust control of flexible-joint (FJ) robots with model uncertainties in both robot dynamics and actuator dynamics is proposed. The proposed control system is a combination of the adaptive dynamic surface control (DSC) technique and the self-recurrent wavelet neural network (SRWNN). The adaptive DSC technique provides the ability to overcome the "explosion of complexity" problem in backstepping controllers. The SRWNNs are used to observe the arbitrary model uncertainties of FJ robots, and all their weights are trained online. From the Lyapunov stability analysis, their adaptation laws are induced, and the uniformly ultimately boundedness of all signals in a closed-loop adaptive system is proved. Finally, simulation results for a three-link FJ robot are utilized to validate the good position tracking performance and robustness against payload uncertainties and external disturbances of the proposed control system.

Vibration waveform effects on dynamic stabilization of ablative Rayleigh-Taylor instability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Piriz, A. R.; Lucchio, L. Di; Rodriguez Prieto, G.

2011-08-15

An analysis of dynamic stabilization of Rayleigh-Taylor instability in an ablation front is performed by considering a general square wave for modulating the vertical acceleration of the front. Such a kind of modulation allows for clarifying the role of thermal conduction in the mechanism of dynamic stabilization. In addition, the study of the effect of different modulations by varying the duration and amplitude of the square wave in each half-period provides insight on the optimum performance of dynamic stabilization.

Robust Dynamic Multi-objective Vehicle Routing Optimization Method.

PubMed

Guo, Yi-Nan; Cheng, Jian; Luo, Sha; Gong, Dun-Wei

2017-03-21

For dynamic multi-objective vehicle routing problems, the waiting time of vehicle, the number of serving vehicles, the total distance of routes were normally considered as the optimization objectives. Except for above objectives, fuel consumption that leads to the environmental pollution and energy consumption was focused on in this paper. Considering the vehicles' load and the driving distance, corresponding carbon emission model was built and set as an optimization objective. Dynamic multi-objective vehicle routing problems with hard time windows and randomly appeared dynamic customers, subsequently, were modeled. In existing planning methods, when the new service demand came up, global vehicle routing optimization method was triggered to find the optimal routes for non-served customers, which was time-consuming. Therefore, robust dynamic multi-objective vehicle routing method with two-phase is proposed. Three highlights of the novel method are: (i) After finding optimal robust virtual routes for all customers by adopting multi-objective particle swarm optimization in the first phase, static vehicle routes for static customers are formed by removing all dynamic customers from robust virtual routes in next phase. (ii)The dynamically appeared customers append to be served according to their service time and the vehicles' statues. Global vehicle routing optimization is triggered only when no suitable locations can be found for dynamic customers. (iii)A metric measuring the algorithms' robustness is given. The statistical results indicated that the routes obtained by the proposed method have better stability and robustness, but may be sub-optimum. Moreover, time-consuming global vehicle routing optimization is avoided as dynamic customers appear.

Quantitative local analysis of nonlinear systems

NASA Astrophysics Data System (ADS)

Topcu, Ufuk

This thesis investigates quantitative methods for local robustness and performance analysis of nonlinear dynamical systems with polynomial vector fields. We propose measures to quantify systems' robustness against uncertainties in initial conditions (regions-of-attraction) and external disturbances (local reachability/gain analysis). S-procedure and sum-of-squares relaxations are used to translate Lyapunov-type characterizations to sum-of-squares optimization problems. These problems are typically bilinear/nonconvex (due to local analysis rather than global) and their size grows rapidly with state/uncertainty space dimension. Our approach is based on exploiting system theoretic interpretations of these optimization problems to reduce their complexity. We propose a methodology incorporating simulation data in formal proof construction enabling more reliable and efficient search for robustness and performance certificates compared to the direct use of general purpose solvers. This technique is adapted both to region-of-attraction and reachability analysis. We extend the analysis to uncertain systems by taking an intentionally simplistic and potentially conservative route, namely employing parameter-independent rather than parameter-dependent certificates. The conservatism is simply reduced by a branch-and-hound type refinement procedure. The main thrust of these methods is their suitability for parallel computing achieved by decomposing otherwise challenging problems into relatively tractable smaller ones. We demonstrate proposed methods on several small/medium size examples in each chapter and apply each method to a benchmark example with an uncertain short period pitch axis model of an aircraft. Additional practical issues leading to a more rigorous basis for the proposed methodology as well as promising further research topics are also addressed. We show that stability of linearized dynamics is not only necessary but also sufficient for the feasibility of the formulations in region-of-attraction analysis. Furthermore, we generalize an upper bound refinement procedure in local reachability/gain analysis which effectively generates non-polynomial certificates from polynomial ones. Finally, broader applicability of optimization-based tools stringently depends on the availability of scalable/hierarchial algorithms. As an initial step toward this direction, we propose a local small-gain theorem and apply to stability region analysis in the presence of unmodeled dynamics.

On periodic motions of an orbital dumbbell-shaped body with a cabin-elevator

NASA Astrophysics Data System (ADS)

Burov, A. A.; Kosenko, I. I.; Troger, H.

2012-05-01

The motion of a dumbbell-shaped body (a pair of massive points connected with each other by a weightless rod along which the elevator, i.e., a third point, is moving according to a given law) in an attractive Newtonian central field is considered. In particular, such a mechanical system can be considered as a simplified model of an orbital cable system equipped with an elevator. The practically most interesting case where the cabin performs periodic "shuttle"motions is studied. Under the assumption that the elevator mass is small compared with the dumbbell mass, the Poincaré theory is used to determine the conditions for the existence of families of system periodic motions analytically depending on the arising small parameter and passing into some stable radial steady-state motion of the unperturbed problem as the small parameter tends to zero. It is also proved that, for sufficiently small parameter values, each of the radial relative equilibria generates exactly one family of such periodic motions. The stability of the obtained periodic solutions is studied in the linear approximation, and these solutions themselves are calculated up to terms of the firstorder in the small parameter. The contemporary studies of the motion of orbital dumbbell systems apparently originated in Okunev's papers [1, 2]. These studies were continued in [3], where plane motions of an orbit tether (represented as a dumbbell-shaped satellite) in a circular orbit were considered in the satellite approximation. In [4], in the case of equal masses and in the unbounded statement, the energy-momentum method was used to perform the dynamic reduction of the problem and analyze the stability of relative equilibria. A similar technique was used in [5], where, in contrast to the above-mentioned problems, the massive points were connected by an elastic spring resisting to compression and forming a dumbbell with elastic properties. Under such assumptions, the stability of radial configurations was investigated in that paper. The bifurcations and stability of steady-state configurations of a deformable elastic dumbbell were also studied in [6]. Various obstacles arising in the construction of orbital cable systems, in particular, the strong deformability of known materials, were discussed in [7]. In [8], the problem of orbital motion of a pair of massive points connected by an inextensible weightless cable was considered in the exact statement. In other words, it was assumed that a unilateral constraint is imposed on themassive points. The conditions of stability of vertical positions of the relative equilibria of the cable system, which were obtained in [8], can be used for any ratio of the subsatellite and station masses. In turn, these results agree well with the results obtained earlier in the studies of stability of vertical configurations in the case of equal masses of the system end bodies [3, 4]. One of the basic papers in the dynamics of three-body orbital cable systems is the paper [9]. The steady-state motions and their bifurcations and stability were studied depending on the elevator cabin position in [10].

Fluctuating interaction network and time-varying stability of a natural fish community

NASA Astrophysics Data System (ADS)

Ushio, Masayuki; Hsieh, Chih-Hao; Masuda, Reiji; Deyle, Ethan R.; Ye, Hao; Chang, Chun-Wei; Sugihara, George; Kondoh, Michio

2018-02-01

Ecological theory suggests that large-scale patterns such as community stability can be influenced by changes in interspecific interactions that arise from the behavioural and/or physiological responses of individual species varying over time. Although this theory has experimental support, evidence from natural ecosystems is lacking owing to the challenges of tracking rapid changes in interspecific interactions (known to occur on timescales much shorter than a generation time) and then identifying the effect of such changes on large-scale community dynamics. Here, using tools for analysing nonlinear time series and a 12-year-long dataset of fortnightly collected observations on a natural marine fish community in Maizuru Bay, Japan, we show that short-term changes in interaction networks influence overall community dynamics. Among the 15 dominant species, we identify 14 interspecific interactions to construct a dynamic interaction network. We show that the strengths, and even types, of interactions change with time; we also develop a time-varying stability measure based on local Lyapunov stability for attractor dynamics in non-equilibrium nonlinear systems. We use this dynamic stability measure to examine the link between the time-varying interaction network and community stability. We find seasonal patterns in dynamic stability for this fish community that broadly support expectations of current ecological theory. Specifically, the dominance of weak interactions and higher species diversity during summer months are associated with higher dynamic stability and smaller population fluctuations. We suggest that interspecific interactions, community network structure and community stability are dynamic properties, and that linking fluctuating interaction networks to community-level dynamic properties is key to understanding the maintenance of ecological communities in nature.

Control design for robust stability in linear regulators: Application to aerospace flight control

NASA Technical Reports Server (NTRS)

Yedavalli, R. K.

1986-01-01

Time domain stability robustness analysis and design for linear multivariable uncertain systems with bounded uncertainties is the central theme of the research. After reviewing the recently developed upper bounds on the linear elemental (structured), time varying perturbation of an asymptotically stable linear time invariant regulator, it is shown that it is possible to further improve these bounds by employing state transformations. Then introducing a quantitative measure called the stability robustness index, a state feedback conrol design algorithm is presented for a general linear regulator problem and then specialized to the case of modal systems as well as matched systems. The extension of the algorithm to stochastic systems with Kalman filter as the state estimator is presented. Finally an algorithm for robust dynamic compensator design is presented using Parameter Optimization (PO) procedure. Applications in a aircraft control and flexible structure control are presented along with a comparison with other existing methods.

Optimization of block-floating-point realizations for digital controllers with finite-word-length considerations.

PubMed

Wu, Jun; Hu, Xie-he; Chen, Sheng; Chu, Jian

2003-01-01

The closed-loop stability issue of finite-precision realizations was investigated for digital controllers implemented in block-floating-point format. The controller coefficient perturbation was analyzed resulting from using finite word length (FWL) block-floating-point representation scheme. A block-floating-point FWL closed-loop stability measure was derived which considers both the dynamic range and precision. To facilitate the design of optimal finite-precision controller realizations, a computationally tractable block-floating-point FWL closed-loop stability measure was then introduced and the method of computing the value of this measure for a given controller realization was developed. The optimal controller realization is defined as the solution that maximizes the corresponding measure, and a numerical optimization approach was adopted to solve the resulting optimal realization problem. A numerical example was used to illustrate the design procedure and to compare the optimal controller realization with the initial realization.

Dissipativity and stability analysis of fractional-order complex-valued neural networks with time delay.

PubMed

Velmurugan, G; Rakkiyappan, R; Vembarasan, V; Cao, Jinde; Alsaedi, Ahmed

2017-02-01

As we know, the notion of dissipativity is an important dynamical property of neural networks. Thus, the analysis of dissipativity of neural networks with time delay is becoming more and more important in the research field. In this paper, the authors establish a class of fractional-order complex-valued neural networks (FCVNNs) with time delay, and intensively study the problem of dissipativity, as well as global asymptotic stability of the considered FCVNNs with time delay. Based on the fractional Halanay inequality and suitable Lyapunov functions, some new sufficient conditions are obtained that guarantee the dissipativity of FCVNNs with time delay. Moreover, some sufficient conditions are derived in order to ensure the global asymptotic stability of the addressed FCVNNs with time delay. Finally, two numerical simulations are posed to ensure that the attention of our main results are valuable. Copyright © 2016 Elsevier Ltd. All rights reserved.

Stability analysis of spacecraft power systems

NASA Technical Reports Server (NTRS)

Halpin, S. M.; Grigsby, L. L.; Sheble, G. B.; Nelms, R. M.

1990-01-01

The problems in applying standard electric utility models, analyses, and algorithms to the study of the stability of spacecraft power conditioning and distribution systems are discussed. Both single-phase and three-phase systems are considered. Of particular concern are the load and generator models that are used in terrestrial power system studies, as well as the standard assumptions of load and topological balance that lead to the use of the positive sequence network. The standard assumptions regarding relative speeds of subsystem dynamic responses that are made in the classical transient stability algorithm, which forms the backbone of utility-based studies, are examined. The applicability of these assumptions to a spacecraft power system stability study is discussed in detail. In addition to the classical indirect method, the applicability of Liapunov's direct methods to the stability determination of spacecraft power systems is discussed. It is pointed out that while the proposed method uses a solution process similar to the classical algorithm, the models used for the sources, loads, and networks are, in general, more accurate. Some preliminary results are given for a linear-graph, state-variable-based modeling approach to the study of the stability of space-based power distribution networks.

Unifying perspective: Solitary traveling waves as discrete breathers in Hamiltonian lattices and energy criteria for their stability

NASA Astrophysics Data System (ADS)

Cuevas-Maraver, Jesús; Kevrekidis, Panayotis G.; Vainchtein, Anna; Xu, Haitao

2017-09-01

In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pasta-Ulam and the Toda lattice are prototypical examples. One is as an eigenvalue problem for a stationary solution in a cotraveling frame, while the other is as a periodic orbit modulo shifts. We connect the eigenvalues of the former with the Floquet multipliers of the latter and using this formulation derive an energy-based spectral stability criterion. It states that a sufficient (but not necessary) condition for a change in the wave stability occurs when the functional dependence of the energy (Hamiltonian) H of the model on the wave velocity c changes its monotonicity. Moreover, near the critical velocity where the change of stability occurs, we provide an explicit leading-order computation of the unstable eigenvalues, based on the second derivative of the Hamiltonian H''(c0) evaluated at the critical velocity c0. We corroborate this conclusion with a series of analytically and numerically tractable examples and discuss its parallels with a recent energy-based criterion for the stability of discrete breathers.

Attitude stability of a spinning spacecraft during appendage deployment/retraction

NASA Technical Reports Server (NTRS)

Fitz-Coy, Norman; Fullerton, Wayne

1994-01-01

The work presented is motivated by the need for a national satellite rescue policy, not the ad hoc policy now in place. In studying different approaches for a national policy, the issue of capture and stabilization of a tumbling spacecraft must be addressed. For a rescue mission involving a tumbling spacecraft, it may be advantageous to have a rescue vehicle which is compact and 'rigid' during the rendezvous/capture phase. After capture, passive stabilization techniques could be utilized as an efficient means of detumbling the resulting system (i.e., both the rescue vehicle and captures spacecraft). Since the rescue vehicle is initially compact and 'rigid,' significant passive stabilization through energy dissipation can only be achieved through the deployment of flexible appendages. Once stabilization is accomplished, retraction of the appendages before maneuvering the system to its final destination may also prove advantageous. It is therefore of paramount interest that we study the effect of appendage deployment/retraction on the attitude stability of a spacecraft. Particular interest should be paid to appendage retraction, since if this process is destabilizing, passive stabilization as proposed may not be useful. Over the past three decades, it has been an 'on-again-off-again affair' with the problem of spacecraft appendage deployment. In most instances, these studies have been numerical simulations of specific spacecraft configurations for which there were specific concerns. The primary focus of these studies was the behavior of the appendage during deployment; the effects of appendage retraction was considered only in one of these studies. What is missing in the literature is a thorough study of the effects of appendage deployment/retraction on the attitude stability of a spacecraft. This paper presents a rigorous analysis of the stability of a spinning spacecraft during the deployment or the retraction of an appendage. The analysis is simplified such that meaningful insights into the problem can be inferred; it is not overly simplified such that critical dynamical behavior is neglected. The system is analyzed assuming that the spacecraft hub is rigid. The appendage deployment mechanism is modeled as a point mass on a massless rod whose length undergoes prescribed changes. Simplified flexibility effects of the appendage are included. The system is examined for stability by linearizing the equations in terms of small deviations from steady, noninterfering coning motion. Routh's procedure for analyzing small deviations from steady motion in dynamical systems is utilized in the analysis. The system of equations are nondimensionalized to facilitate parametric studies. The results are presented in terms of a reduced number of nondimensional parameters so that some general conclusions may be drawn. Verification of the linear analysis is presented through numerical simulations of the complete nonlinear, nonautonomous, coupled equations.

Dynamic Stability Experiment of Maglev Systems,

DTIC Science & Technology

1995-04-01

This report summarizes the research performed on maglev vehicle dynamic stability at Argonne National Laboratory during the past few years. It also... maglev system, it is important to consider this phenomenon in the development of all maglev systems. This report presents dynamic stability experiments...on maglev systems and compares their numerical simulation with predictions calculated by a nonlinear dynamic computer code. Instabilities of an

Stability of Dynamical Systems with Discontinuous Motions:

NASA Astrophysics Data System (ADS)

Michel, Anthony N.; Hou, Ling

In this paper we present a stability theory for discontinuous dynamical systems (DDS): continuous-time systems whose motions are not necessarily continuous with respect to time. We show that this theory is not only applicable in the analysis of DDS, but also in the analysis of continuous dynamical systems (continuous-time systems whose motions are continuous with respect to time), discrete-time dynamical systems (systems whose motions are defined at discrete points in time) and hybrid dynamical systems (HDS) (systems whose descriptions involve simultaneously continuous-time and discrete-time). We show that the stability results for DDS are in general less conservative than the corresponding well-known classical Lyapunov results for continuous dynamical systems and discrete-time dynamical systems. Although the DDS stability results are applicable to general dynamical systems defined on metric spaces (divorced from any kind of description by differential equations, or any other kinds of equations), we confine ourselves to finite-dimensional dynamical systems defined by ordinary differential equations and difference equations, to make this paper as widely accessible as possible. We present only sample results, namely, results for uniform asymptotic stability in the large.

Designing Inter-Organisational Collectivities for Dynamic Fit: Stability, maneuvrability and Application in Disaster Relief Endeavours

DTIC Science & Technology

2011-01-01

changed consumer preferences . Hence, static stability limits initial performance deviation (e.g., maintaining desired airplane altitude, maintaining...by changed consumer preferences . Hence, dynamic stability limits the duration of performance deviation (e.g., maintaining desired airplane altitude...altitude from wind gust. Initial resistance to deviation in profit level from change in consumer preferences . Dynamic stability Quickness of a

DYNAMIC NEUROMUSCULAR STABILIZATION & SPORTS REHABILITATION

PubMed Central

Kobesova, Alena; Kolar, Pavel

2013-01-01

Dynamic neuromuscular (core) stability is necessary for optimal athletic performance and is not achieved purely by adequate strength of abdominals, spinal extensors, gluteals or any other musculature; rather, core stabilization is accomplished through precise coordination of these muscles and intra‐abdominal pressure regulation by the central nervous system. Understanding developmental kinesiology provides a framework to appreciate the regional interdependence and the inter‐linking of the skeleton, joints, musculature during movement and the importance of training both the dynamic and stabilizing function of muscles in the kinetic chain. The Dynamic Neuromuscular Stabilization (DNS) approach provides functional tools to assess and activate the intrinsic spinal stabilizers in order to optimize the movement system for both pre‐habilitation and rehabilitation of athletic injuries and performance. Level of Evidence: 5 PMID:23439921

Running interfacial waves in a two-layer fluid system subject to longitudinal vibrations.

PubMed

Goldobin, D S; Pimenova, A V; Kovalevskaya, K V; Lyubimov, D V; Lyubimova, T P

2015-05-01

We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of quasistationary states of free interface in fluid dynamical systems subject to vibrations, revealed the existence of standing periodic waves and solitons in this system. However, this approach does not provide regular means for dealing with evolutionary problems: neither stability problems nor ones associated with propagating waves. In this work, we rigorously derive the evolution equations for long waves in the system, which turn out to be identical to the plus (or good) Boussinesq equation. With these equations one can find all the time-independent-profile solitary waves (standing solitons are a specific case of these propagating waves), which exist below the linear instability threshold; the standing and slow solitons are always unstable while fast solitons are stable. Depending on initial perturbations, unstable solitons either grow in an explosive manner, which means layer rupture in a finite time, or falls apart into stable solitons. The results are derived within the long-wave approximation as the linear stability analysis for the flat-interface state [D.V. Lyubimov and A.A. Cherepanov, Fluid Dynamics 21, 849 (1986)] reveals the instabilities of thin layers to be long wavelength.

Stability-Constrained Aerodynamic Shape Optimization with Applications to Flying Wings

NASA Astrophysics Data System (ADS)

Mader, Charles Alexander

A set of techniques is developed that allows the incorporation of flight dynamics metrics as an additional discipline in a high-fidelity aerodynamic optimization. Specifically, techniques for including static stability constraints and handling qualities constraints in a high-fidelity aerodynamic optimization are demonstrated. These constraints are developed from stability derivative information calculated using high-fidelity computational fluid dynamics (CFD). Two techniques are explored for computing the stability derivatives from CFD. One technique uses an automatic differentiation adjoint technique (ADjoint) to efficiently and accurately compute a full set of static and dynamic stability derivatives from a single steady solution. The other technique uses a linear regression method to compute the stability derivatives from a quasi-unsteady time-spectral CFD solution, allowing for the computation of static, dynamic and transient stability derivatives. Based on the characteristics of the two methods, the time-spectral technique is selected for further development, incorporated into an optimization framework, and used to conduct stability-constrained aerodynamic optimization. This stability-constrained optimization framework is then used to conduct an optimization study of a flying wing configuration. This study shows that stability constraints have a significant impact on the optimal design of flying wings and that, while static stability constraints can often be satisfied by modifying the airfoil profiles of the wing, dynamic stability constraints can require a significant change in the planform of the aircraft in order for the constraints to be satisfied.

Investigation of biomechanical behavior of lumbar vertebral segments with dynamic stabilization device using finite element approach

NASA Astrophysics Data System (ADS)

Deoghare, Ashish B.; Kashyap, Siddharth; Padole, Pramod M.

2013-03-01

Degenerative disc disease is a major source of lower back pain and significantly alters the biomechanics of the lumbar spine. Dynamic stabilization device is a remedial technique which uses flexible materials to stabilize the affected lumbar region while preserving the natural anatomy of the spine. The main objective of this research work is to investigate the stiffness variation of dynamic stabilization device under various loading conditions under compression, axial rotation and flexion. Three dimensional model of the two segment lumbar spine is developed using computed tomography (CT) scan images. The lumbar structure developed is analyzed in ANSYS workbench. Two types of dynamic stabilization are considered: one with stabilizing device as pedicle instrumentation and second with stabilization device inserted around the inter-vertebral disc. Analysis suggests that proper positioning of the dynamic stabilization device is of paramount significance prior to the surgery. Inserting the device in the posterior region indicates the adverse effects as it shows increase in the deformation of the inter-vertebral disc. Analysis executed by positioning stabilizing device around the inter-vertebral disc yields better result for various stiffness values under compression and other loadings. [Figure not available: see fulltext.

Feedforward Tracking Control of Flat Recurrent Fuzzy Systems

NASA Astrophysics Data System (ADS)

Gering, Stefan; Adamy, Jürgen

2014-12-01

Flatness based feedforward control has proven to be a feasible solution for the problem of tracking control, which may be applied to a broad class of nonlinear systems. If a flat output of the system is known, the control is often based on a feedforward controller generating a nominal input in combination with a linear controller stabilizing the linearized error dynamics around the trajectory. We show in this paper that the very same idea may be incorporated for tracking control of MIMO recurrent fuzzy systems. Their dynamics is given by means of linguistic differential equations but may be converted into a hybrid system representation, which then serves as the basis for controller synthesis.

Hybrid Instrumentation in Lumbar Spinal Fusion

PubMed Central

Danyali, Reza; Kueny, Rebecca; Huber, Gerd; Reichl, Michael; Richter, Alexander; Niemeyer, Thomas; Morlock, Michael; Püschel, Klaus; Übeyli, Hüseyin

2017-01-01

Study Design Ex vivo human cadaveric study. Objective The development or progression of adjacent segment disease (ASD) after spine stabilization and fusion is a major problem in spine surgery. Apart from optimal balancing of the sagittal profile, dynamic instrumentation is often suggested to prevent or impede ASD. Hybrid instrumentation is used to gain stabilization while allowing motion to avoid hypermobility in the adjacent segment. In this biomechanical study, the effects of two different hybrid instrumentations on human cadaver spines were evaluated and compared with a rigid instrumentation. Methods Eighteen human cadaver spines (T11–L5) were subdivided into three groups: rigid, dynamic, and hook comprising six spines each. Clinical parameters and initial mechanical characteristics were consistent among groups. All specimens received rigid fixation from L3–L5 followed by application of a free bending load of extension and flexion. The range of motion (ROM) for every segment was evaluated. For the rigid group, further rigid fixation from L1–L5 was applied. A dynamic Elaspine system (Spinelab AG, Winterthur, Switzerland) was applied from L1 to L3 for the dynamic group, and the hook group was instrumented with additional laminar hooks at L1–L3. ROM was then evaluated again. Results There was no significant difference in ROM among the three instrumentation techniques. Conclusion Based on this data, the intended advantage of a hybrid or dynamic instrumentation might not be achieved. PMID:28451509

Detailed Multidimensional Simulations of the Structure and Dynamics of Flames

NASA Technical Reports Server (NTRS)

Patnaik, G.; Kailasanath, K.

1999-01-01

Numerical simulations in which the various physical and chemical processes can be independently controlled can significantly advance our understanding of the structure, stability, dynamics and extinction of flames. Therefore, our approach has been to use detailed time-dependent, multidimensional, multispecies numerical models to perform carefully designed computational experiments of flames on Earth and in microgravity environments. Some of these computational experiments are complementary to physical experiments performed under the Microgravity Program while others provide a fundamental understanding that cannot be obtained from physical experiments alone. In this report, we provide a brief summary of our recent research highlighting the contributions since the previous microgravity combustion workshop. There are a number of mechanisms that can cause flame instabilities and result in the formation of dynamic multidimensional structures. In the past, we have used numerical simulations to show that it is the thermo-diffusive instability rather than an instability due to preferential diffusion that is the dominant mechanism for the formation of cellular flames in lean hydrogen-air mixtures. Other studies have explored the role of gravity on flame dynamics and extinguishment, multi-step kinetics and radiative losses on flame instabilities in rich hydrogen-air flames, and heat losses on burner-stabilized flames in microgravity. The recent emphasis of our work has been on exploring flame-vortex interactions and further investigating the structure and dynamics of lean hydrogen-air flames in microgravity. These topics are briefly discussed after a brief discussion of our computational approach for solving these problems.

Introduction: demography and cultural macroevolution.

PubMed

Steele, James; Shennan, Stephen

2009-04-01

The papers in this special issue of Human Biology, which derive from a conference sponsored by the Arts and Humanities Research Council (AHRC) Center for the Evolution of Cultural Diversity, lay some of the foundations for an empirical macroevolutionary analysis of cultural dynamics. Our premise here is that cultural dynamics-including the stability of traditions and the rate of origination of new variants-are influenced by independently occurring demographic processes (population size, structure, and distribution as these vary over time as a result of changes in rates of fertility, mortality, and migration). The contributors focus on three sets of problems relevant to empirical studies of cultural macroevolution: large-scale reconstruction of past population dynamics from archaeological and genetic data; juxtaposition of models and evidence of cultural dynamics using large-scale archaeological and historical data sets; and juxtaposition of models and evidence of cultural dynamics from large-scale linguistic data sets. In this introduction we outline some of the theoretical and methodological issues and briefly summarize the individual contributions.

Complex Dynamics in a Model of Common Fishery Resource Harvested by Multiagents with Heterogeneous Strategy

NASA Astrophysics Data System (ADS)

Gu, En-Guo

In this paper, we formulate a dynamical model of common fishery resource harvested by multiagents with heterogeneous strategy: profit maximizers and gradient learners. Special attention is paid to the problem of heterogeneity of strategic behaviors. We mainly study the existence and the local stability of non-negative equilibria for the model through mathematical analysis. We analyze local bifurcations and complex dynamics such as coexisting attractors by numerical simulations. We also study the local and global dynamics of the exclusive gradient learners as a special case of the model. We discover that when adjusting the speed to be slightly high, the increasing ratio of gradient learners may lead to instability of the fixed point and makes the system sink into complicated dynamics such as quasiperiodic or chaotic attractor. The results reveal that gradient learners with high adjusting speed may ultimately be more harmful to the sustainable use of fish stock than the profit maximizers.

PDEMOD: Software for control/structures optimization

NASA Technical Reports Server (NTRS)

Taylor, Lawrence W., Jr.; Zimmerman, David

1991-01-01

Because of the possibility of adverse interaction between the control system and the structural dynamics of large, flexible spacecraft, great care must be taken to ensure stability and system performance. Because of the high cost of insertion of mass into low earth orbit, it is prudent to optimize the roles of structure and control systems simultaneously. Because of the difficulty and the computational burden in modeling and analyzing the control structure system dynamics, the total problem is often split and treated iteratively. It would aid design if the control structure system dynamics could be represented in a single system of equations. With the use of the software PDEMOD (Partial Differential Equation Model), it is now possible to optimize structure and control systems simultaneously. The distributed parameter modeling approach enables embedding the control system dynamics into the same equations for the structural dynamics model. By doing this, the current difficulties involved in model order reduction are avoided. The NASA Mini-MAST truss is used an an example for studying integrated control structure design.

Early Universe Higgs dynamics in the presence of the Higgs-inflaton and non-minimal Higgs-gravity couplings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ema, Yohei; Karčiauskas, Mindaugas; Lebedev, Oleg

Apparent metastability of the electroweak vacuum poses a number of cosmological questions. These concern evolution of the Higgs field to the current vacuum, and its stability during and after inflation. Higgs-inflaton and non-minimal Higgs-gravity interactions can make a crucial impact on these considerations potentially solving the problems. In this work, we allow for these couplings to be present simultaneously and study their interplay. We find that different combinations of the Higgs-inflaton and non-minimal Higgs-gravity couplings induce effective Higgs mass during and after inflation. This crucially affects the Higgs stability considerations during preheating. In particular, a wide range of the couplingsmore » leading to stable solutions becomes allowed.« less

Employing static excitation control and tie line reactance to stabilize wind turbine generators

NASA Technical Reports Server (NTRS)

Hwang, H. H.; Mozeico, H. V.; Guo, T.

1978-01-01

An analytical representation of a wind turbine generator is presented which employs blade pitch angle feedback control. A mathematical model was formulated. With the functioning MOD-0 wind turbine serving as a practical case study, results of computer simulations of the model as applied to the problem of dynamic stability at rated load are also presented. The effect of the tower shadow was included in the input to the system. Different configurations of the drive train, and optimal values of the tie line reactance were used in the simulations. Computer results revealed that a static excitation control system coupled with optimal values of the tie line reactance would effectively reduce oscillations of the power output, without the use of a slip clutch.

Calculation of Linear Stability of a Stratified Gas-Liquid Flow in an Inclined Plane Channel

NASA Astrophysics Data System (ADS)

Trifonov, Yu. Ya.

2018-01-01

Linear stability of liquid and gas counterflows in an inclined channel is considered. The full Navier-Stokes equations for both phases are linearized, and the dynamics of periodic disturbances is determined by means of solving a spectral problem in wide ranges of Reynolds numbers for the liquid and vapor velocity. Two unstable modes are found in the examined ranges: surface mode (corresponding to the Kapitsa waves at small velocities of the gas) and shear mode in the gas phase. The wave length and the phase velocity of neutral disturbances of both modes are calculated as functions of the Reynolds number for the liquid. It is shown that these dependences for the surface mode are significantly affected by the gas velocity.

Estimation of mountain slope stability depending on ground consistency and slip-slide resistance changes on impact of dynamic forces

NASA Astrophysics Data System (ADS)

Hayroyan, H. S.; Hayroyan, S. H.; Karapetyan, K. A.

2018-04-01

In this paper, three types of clayish soils with different consistency and humidity properties and slip-slide resistance indexes are considered on impact of different cyclic shear stresses. The side-surface deformation charts are constructed on the basis of experimental data obtained testing cylindrical soil samples. It is shown that the fluctuation amplitude depends on time and the consistency index depends on the humidity condition in the soil inner contact and the connectivity coefficients. Consequently, each experiment is interpreted. The main result of this research is that it is necessary to make corrections in the currently active schemes of slip-hazardous slopes stability estimation, which is a crucial problem requiring ASAP solution.

Lattice Boltzmann model for numerical relativity.

PubMed

Ilseven, E; Mendoza, M

2016-02-01

In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.

Dynamic Stabilization of a Quantum Many-Body Spin System

NASA Astrophysics Data System (ADS)

Hoang, T. M.; Gerving, C. S.; Land, B. J.; Anquez, M.; Hamley, C. D.; Chapman, M. S.

2013-08-01

We demonstrate dynamic stabilization of a strongly interacting quantum spin system realized in a spin-1 atomic Bose-Einstein condensate. The spinor Bose-Einstein condensate is initialized to an unstable fixed point of the spin-nematic phase space, where subsequent free evolution gives rise to squeezing and quantum spin mixing. To stabilize the system, periodic microwave pulses are applied that rotate the spin-nematic many-body fluctuations and limit their growth. The stability diagram for the range of pulse periods and phase shifts that stabilize the dynamics is measured and compares well with a stability analysis.

Controls for space structures

NASA Astrophysics Data System (ADS)

Balas, Mark

1991-11-01

Assembly and operation of large space structures (LSS) in orbit will require robot-assisted docking and berthing of partially-assembled structures. These operations require new solutions to the problems of controls. This is true because of large transient and persistent disturbances, controller-structure interaction with unmodeled modes, poorly known structure parameters, slow actuator/sensor dynamical behavior, and excitation of nonlinear structure vibrations during control and assembly. For on-orbit assembly, controllers must start with finite element models of LSS and adapt on line to the best operating points, without compromising stability. This is not easy to do, since there are often unmodeled dynamic interactions between the controller and the structure. The indirect adaptive controllers are based on parameter estimation. Due to the large number of modes in LSS, this approach leads to very high-order control schemes with consequent poor stability and performance. In contrast, direct model reference adaptive controllers operate to force the LSS to track the desirable behavior of a chosen model. These schemes produce simple control algorithms which are easy to implement on line. One problem with their use for LSS has been that the model must be the same dimension as the LSS - i.e., quite large. A control theory based on the command generator tracker (CGT) ideas of Sobel, Mabins, Kaufman and Wen, Balas to obtain very low-order models based on adaptive algorithms was developed. Closed-loop stability for both finite element models and distributed parameter models of LSS was proved. In addition, successful numerical simulations on several LSS databases were obtained. An adaptive controller based on our theory was also implemented on a flexible robotic manipulator at Martin Marietta Astronautics. Computation schemes for controller-structure interaction with unmodeled modes, the residual mode filters or RMF, were developed. The RMF theory was modified to compensate slow actuator/sensor dynamics. These new ideas are being applied to LSS simulations to demonstrate the ease with which one can incorporate slow actuator/sensor effects into our design. It was also shown that residual mode filter compensation can be modified for small nonlinearities to produce exponentially stable closed-loop control.

Controls for space structures

NASA Technical Reports Server (NTRS)

Balas, Mark

1991-01-01

Assembly and operation of large space structures (LSS) in orbit will require robot-assisted docking and berthing of partially-assembled structures. These operations require new solutions to the problems of controls. This is true because of large transient and persistent disturbances, controller-structure interaction with unmodeled modes, poorly known structure parameters, slow actuator/sensor dynamical behavior, and excitation of nonlinear structure vibrations during control and assembly. For on-orbit assembly, controllers must start with finite element models of LSS and adapt on line to the best operating points, without compromising stability. This is not easy to do, since there are often unmodeled dynamic interactions between the controller and the structure. The indirect adaptive controllers are based on parameter estimation. Due to the large number of modes in LSS, this approach leads to very high-order control schemes with consequent poor stability and performance. In contrast, direct model reference adaptive controllers operate to force the LSS to track the desirable behavior of a chosen model. These schemes produce simple control algorithms which are easy to implement on line. One problem with their use for LSS has been that the model must be the same dimension as the LSS - i.e., quite large. A control theory based on the command generator tracker (CGT) ideas of Sobel, Mabins, Kaufman and Wen, Balas to obtain very low-order models based on adaptive algorithms was developed. Closed-loop stability for both finite element models and distributed parameter models of LSS was proved. In addition, successful numerical simulations on several LSS databases were obtained. An adaptive controller based on our theory was also implemented on a flexible robotic manipulator at Martin Marietta Astronautics. Computation schemes for controller-structure interaction with unmodeled modes, the residual mode filters or RMF, were developed. The RMF theory was modified to compensate slow actuator/sensor dynamics. These new ideas are being applied to LSS simulations to demonstrate the ease with which one can incorporate slow actuator/sensor effects into our design. It was also shown that residual mode filter compensation can be modified for small nonlinearities to produce exponentially stable closed-loop control. A theory for disturbance accommodating controllers based on reduced order models of structures was developed, and stability results for these controllers in closed-loop with large-scale finite element models of structures were obtained.

Control and stabilization of decentralized systems

NASA Technical Reports Server (NTRS)

Byrnes, Christopher I.; Gilliam, David; Martin, Clyde F.

1989-01-01

Proceeding from the problem posed by the need to stabilize the motion of two helicopters maneuvering a single load, a methodology is developed for the stabilization of classes of decentralized systems based on a more algebraic approach, which involves the external symmetries of decentralized systems. Stabilizing local-feedback laws are derived for any class of decentralized systems having a semisimple algebra of symmetries; the helicopter twin-lift problem, as well as certain problems involving the stabilization of discretizations of distributed parameter problems, have just such algebras of symmetries.

Gravity-oriented satellite dynamics subject to gravitational and active damping torques

NASA Astrophysics Data System (ADS)

Sarychev, V. A.; Gutnik, S. A.

2018-01-01

The dynamics of the rotational motion of a satellite moving in the central Newtonian field of force over a circular orbit under the effect of gravitational and active damping torques, which depend on the satellite angular velocity projections, has been investigated. The paper proposes a method of determining all equilibrium positions (equilibrium orientations) of a satellite in the orbital coordinate system for specified values of damping coefficients and principal central moments of inertia. The conditions of their existence have been obtained. For a zero equilibrium position where the axes of the satellite-centered coordinate system coincide with the axes of the orbital coordinate system, the necessary and sufficient conditions for asymptotic stability are obtained using the Routh-Hurwitz criterion. A detailed analysis of the regions where the conditions of the asymptotic stability of a zero equilibrium position are fulfilled have been obtained depending on three dimensionless parameters of the problem, and the numerical study of the process of attenuation of satellite's spatial oscillations for various damping coefficients has been carried out. It has been shown that there is a wide range of damping parameters from which, by choosing the necessary values, one can provide the asymptotic stability of satellite's zero equilibrium position in the orbital coordinate system.

Application of dynamic programming to evaluate the slope stability of a vertical extension to a balefill.

PubMed

Kremen, Arie; Tsompanakis, Yiannis

2010-04-01

The slope-stability of a proposed vertical extension of a balefill was investigated in the present study, in an attempt to determine a geotechnically conservative design, compliant with New Jersey Department of Environmental Protection regulations, to maximize the utilization of unclaimed disposal capacity. Conventional geotechnical analytical methods are generally limited to well-defined failure modes, which may not occur in landfills or balefills due to the presence of preferential slip surfaces. In addition, these models assume an a priori stress distribution to solve essentially indeterminate problems. In this work, a different approach has been applied, which avoids several of the drawbacks of conventional methods. Specifically, the analysis was performed in a two-stage process: (a) calculation of stress distribution, and (b) application of an optimization technique to identify the most probable failure surface. The stress analysis was performed using a finite element formulation and the location of the failure surface was located by dynamic programming optimization method. A sensitivity analysis was performed to evaluate the effect of the various waste strength parameters of the underlying mathematical model on the results, namely the factor of safety of the landfill. Although this study focuses on the stability investigation of an expanded balefill, the methodology presented can easily be applied to general geotechnical investigations.

Electrorheological Fluids with High Shear Stress Based on Wrinkly Tin Titanyl Oxalate.

PubMed

Wu, Jinghua; Zhang, Lei; Xin, Xing; Zhang, Yang; Wang, Hui; Sun, Aihua; Cheng, Yuchuan; Chen, Xinde; Xu, Gaojie

2018-02-21

Electrorheological (ER) fluids are considered as a type of smart fluids because their rheological characteristics can be altered through an electric field. The discovery of giant ER effect revived the researchers' interest in the ER technological area. However, the poor stability including the insufficient dynamic shear stress, the large leakage current density, and the sedimentation tendency still hinders their practical applications. Herein, we report a facile and scalable coprecipitation method for synthesizing surfactant-free tin titanyl oxalate (TTO) particles with tremella-like wrinkly microstructure (W-TTO). The W-TTO-based ER fluids exhibit enhanced ER activity compared to that of the pristine TTO because of the improved wettability between W-TTO and the silicone oil. In addition, the static yield stress and leakage current of W-TTO ER fluids also show a fine time stability during the 30 day tests. More importantly, the dynamic shear stress of W-TTO ER fluids can remain stable throughout the shear rate range, which is valuable for their use in engineering applications. The results in this work provided a promising strategy to solving the long-standing problem of ER fluid stability. Moreover, this convenient route of synthesis may be considered a green approach for the mass production of giant ER materials.

Unifying dynamical and structural stability of equilibria

NASA Astrophysics Data System (ADS)

Arnoldi, Jean-François; Haegeman, Bart

2016-09-01

We exhibit a fundamental relationship between measures of dynamical and structural stability of linear dynamical systems-e.g. linearized models in the vicinity of equilibria. We show that dynamical stability, quantified via the response to external perturbations (i.e. perturbation of dynamical variables), coincides with the minimal internal perturbation (i.e. perturbations of interactions between variables) able to render the system unstable. First, by reformulating a result of control theory, we explain that harmonic external perturbations reflect the spectral sensitivity of the Jacobian matrix at the equilibrium, with respect to constant changes of its coefficients. However, for this equivalence to hold, imaginary changes of the Jacobian's coefficients have to be allowed. The connection with dynamical stability is thus lost for real dynamical systems. We show that this issue can be avoided, thus recovering the fundamental link between dynamical and structural stability, by considering stochastic noise as external and internal perturbations. More precisely, we demonstrate that a linear system's response to white-noise perturbations directly reflects the intensity of internal white-noise disturbance that it can accommodate before becoming stochastically unstable.

Unifying dynamical and structural stability of equilibria.

PubMed

Arnoldi, Jean-François; Haegeman, Bart

2016-09-01

We exhibit a fundamental relationship between measures of dynamical and structural stability of linear dynamical systems-e.g. linearized models in the vicinity of equilibria. We show that dynamical stability, quantified via the response to external perturbations (i.e. perturbation of dynamical variables), coincides with the minimal internal perturbation (i.e. perturbations of interactions between variables) able to render the system unstable. First, by reformulating a result of control theory, we explain that harmonic external perturbations reflect the spectral sensitivity of the Jacobian matrix at the equilibrium, with respect to constant changes of its coefficients. However, for this equivalence to hold, imaginary changes of the Jacobian's coefficients have to be allowed. The connection with dynamical stability is thus lost for real dynamical systems. We show that this issue can be avoided, thus recovering the fundamental link between dynamical and structural stability, by considering stochastic noise as external and internal perturbations. More precisely, we demonstrate that a linear system's response to white-noise perturbations directly reflects the intensity of internal white-noise disturbance that it can accommodate before becoming stochastically unstable.

Assessment of Walking Stability of Elderly by Means of Nonlinear Time-Series Analysis and Simple Accelerometry

NASA Astrophysics Data System (ADS)

Ohtaki, Yasuaki; Arif, Muhammad; Suzuki, Akihiro; Fujita, Kazuki; Inooka, Hikaru; Nagatomi, Ryoichi; Tsuji, Ichiro

This study presents an assessment of walking stability in elderly people, focusing on local dynamic stability of walking. Its main objectives were to propose a technique to quantify local dynamic stability using nonlinear time-series analyses and a portable instrument, and to investigate their reliability in revealing the efficacy of an exercise training intervention for elderly people for improvement of walking stability. The method measured three-dimensional acceleration of the upper body, and computation of Lyapunov exponents, thereby directly quantifying the local stability of the dynamic system. Straight level walking of young and elderly subjects was investigated in the experimental study. We compared Lyapunov exponents of young and the elderly subjects, and of groups before and after the exercise intervention. Experimental results demonstrated that the exercise intervention improved local dynamic stability of walking. The proposed method was useful in revealing effects and efficacies of the exercise intervention for elderly people.

Finite-time and fixed-time leader-following consensus for multi-agent systems with discontinuous inherent dynamics

NASA Astrophysics Data System (ADS)

Ning, Boda; Jin, Jiong; Zheng, Jinchuan; Man, Zhihong

2018-06-01

This paper is concerned with finite-time and fixed-time consensus of multi-agent systems in a leader-following framework. Different from conventional leader-following tracking approaches where inherent dynamics satisfying the Lipschitz continuous condition is required, a more generalised case is investigated: discontinuous inherent dynamics. By nonsmooth techniques, a nonlinear protocol is first proposed to achieve the finite-time leader-following consensus. Then, based on fixed-time stability strategies, the fixed-time leader-following consensus problem is solved. An upper bound of settling time is obtained by using a new protocol, and such a bound is independent of initial states, thereby providing additional options for designers in practical scenarios where initial conditions are unavailable. Finally, numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

Dynamics of Equilibrium Points in a Uniformly Rotating Second-Order and Degree Gravitational Field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Feng, Jinglang; Hou, Xiyun, E-mail: jinglang@nju.edu.cn, E-mail: silence@nju.edu.cn

2017-07-01

Using tools such as periodic orbits and invariant manifolds, the global dynamics around equilibrium points (EPs) in a rotating second-order and degree gravitational field are studied. For EPs on the long axis, planar and vertical periodic families are computed, and their stability properties are investigated. Invariant manifolds are also computed, and their relation to the first-order resonances is briefly discussed. For EPs on the short axis, planar and vertical periodic families are studied, with special emphasis on the genealogy of the planar periodic families. Our studies show that the global dynamics around EPs are highly similar to those around libration points in the circularmore » restricted three-body problem, such as spatial halo orbits, invariant manifolds, and the genealogy of planar periodic families.« less

Persistent model order reduction for complex dynamical systems using smooth orthogonal decomposition

NASA Astrophysics Data System (ADS)

Ilbeigi, Shahab; Chelidze, David

2017-11-01

Full-scale complex dynamic models are not effective for parametric studies due to the inherent constraints on available computational power and storage resources. A persistent reduced order model (ROM) that is robust, stable, and provides high-fidelity simulations for a relatively wide range of parameters and operating conditions can provide a solution to this problem. The fidelity of a new framework for persistent model order reduction of large and complex dynamical systems is investigated. The framework is validated using several numerical examples including a large linear system and two complex nonlinear systems with material and geometrical nonlinearities. While the framework is used for identifying the robust subspaces obtained from both proper and smooth orthogonal decompositions (POD and SOD, respectively), the results show that SOD outperforms POD in terms of stability, accuracy, and robustness.

Coupling Dynamics in Aircraft: A Historical Perspective

NASA Technical Reports Server (NTRS)

Day, Richard E.

1997-01-01

Coupling dynamics can produce either adverse or beneficial stability and controllability, depending on the characteristics of the aircraft. This report presents archival anecdotes and analyses of coupling problems experienced by the X-series, Century series, and Space Shuttle aircraft. The three catastrophic sequential coupling modes of the X-2 airplane and the two simultaneous unstable modes of the X-15 and Space Shuttle aircraft are discussed. In addition, the most complex of the coupling interactions, inertia roll coupling, is discussed for the X-2, X-3, F-100A, and YF-102 aircraft. The mechanics of gyroscopics, centrifugal effect, and resonance in coupling dynamics are described. The coupling modes discussed are interacting multiple degrees of freedom of inertial and aerodynamic forces and moments. The aircraft are assumed to be rigid bodies. Structural couplings are not addressed. Various solutions for coupling instabilities are discussed.

Study of Nanocomposites of Amino Acids and Organic Polyethers by Means of Mass Spectrometry and Molecular Dynamics Simulation

NASA Astrophysics Data System (ADS)

Zobnina, V. G.; Kosevich, M. V.; Chagovets, V. V.; Boryak, O. A.

A problem of elucidation of structure of nanomaterials based on combination of proteins and polyether polymers is addressed on the monomeric level of single amino acids and oligomers of PEG-400 and OEG-5 polyethers. Efficiency of application of combined approach involving experimental electrospray mass spectrometry and computer modeling by molecular dynamics simulation is demonstrated. It is shown that oligomers of polyethers form stable complexes with amino acids valine, proline, histidine, glutamic, and aspartic acids. Molecular dynamics simulation has shown that stabilization of amino acid-polyether complexes is achieved due to winding of the polymeric chain around charged groups of amino acids. Structural motives revealed for complexes of single amino acids with polyethers can be realized in structures of protein-polyether nanoparticles currently designed for drug delivery.

Applications of fidelity measures to complex quantum systems

PubMed Central

2016-01-01

We revisit fidelity as a measure for the stability and the complexity of the quantum motion of single-and many-body systems. Within the context of cold atoms, we present an overview of applications of two fidelities, which we call static and dynamical fidelity, respectively. The static fidelity applies to quantum problems which can be diagonalized since it is defined via the eigenfunctions. In particular, we show that the static fidelity is a highly effective practical detector of avoided crossings characterizing the complexity of the systems and their evolutions. The dynamical fidelity is defined via the time-dependent wave functions. Focusing on the quantum kicked rotor system, we highlight a few practical applications of fidelity measurements in order to better understand the large variety of dynamical regimes of this paradigm of a low-dimensional system with mixed regular–chaotic phase space. PMID:27140967

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Freels, J. D.

1989-01-01

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

Model and controller reduction of large-scale structures based on projection methods

NASA Astrophysics Data System (ADS)

Gildin, Eduardo

The design of low-order controllers for high-order plants is a challenging problem theoretically as well as from a computational point of view. Frequently, robust controller design techniques result in high-order controllers. It is then interesting to achieve reduced-order models and controllers while maintaining robustness properties. Controller designed for large structures based on models obtained by finite element techniques yield large state-space dimensions. In this case, problems related to storage, accuracy and computational speed may arise. Thus, model reduction methods capable of addressing controller reduction problems are of primary importance to allow the practical applicability of advanced controller design methods for high-order systems. A challenging large-scale control problem that has emerged recently is the protection of civil structures, such as high-rise buildings and long-span bridges, from dynamic loadings such as earthquakes, high wind, heavy traffic, and deliberate attacks. Even though significant effort has been spent in the application of control theory to the design of civil structures in order increase their safety and reliability, several challenging issues are open problems for real-time implementation. This dissertation addresses with the development of methodologies for controller reduction for real-time implementation in seismic protection of civil structures using projection methods. Three classes of schemes are analyzed for model and controller reduction: nodal truncation, singular value decomposition methods and Krylov-based methods. A family of benchmark problems for structural control are used as a framework for a comparative study of model and controller reduction techniques. It is shown that classical model and controller reduction techniques, such as balanced truncation, modal truncation and moment matching by Krylov techniques, yield reduced-order controllers that do not guarantee stability of the closed-loop system, that is, the reduced-order controller implemented with the full-order plant. A controller reduction approach is proposed such that to guarantee closed-loop stability. It is based on the concept of dissipativity (or positivity) of linear dynamical systems. Utilizing passivity preserving model reduction together with dissipative-LQG controllers, effective low-order optimal controllers are obtained. Results are shown through simulations.

Compressor stability management

NASA Astrophysics Data System (ADS)

Dhingra, Manuj

Dynamic compressors are susceptible to aerodynamic instabilities while operating at low mass flow rates. These instabilities, rotating stall and surge, are detrimental to engine life and operational safety, and are thus undesirable. In order to prevent stability problems, a passive technique, involving fuel flow scheduling, is currently employed on gas turbines. The passive nature of this technique necessitates conservative stability margins, compromising performance and/or efficiency. In the past, model based active control has been proposed to enable reduction of margin requirements. However, available compressor stability models do not predict the different stall inception patterns, making model based control techniques practically infeasible. This research presents active stability management as a viable alternative. In particular, a limit detection and avoidance approach has been used to maintain the system free of instabilities. Simulations show significant improvements in the dynamic response of a gas turbine engine with this approach. A novel technique has been developed to enable real-time detection of stability limits in axial compressors. It employs a correlation measure to quantify the chaos in the rotor tip region. Analysis of data from four axial compressors shows that the value of the correlation measure decreases as compressor loading is increased. Moreover, sharp drops in this measure have been found to be relevant for stability limit detection. The significance of these drops can be captured by tracking events generated by the downward crossing of a selected threshold level. It has been observed that the average number of events increases as the stability limit is approached in all the compressors studied. These events appear to be randomly distributed in time. A stochastic model for the time between consecutive events has been developed and incorporated in an engine simulation. The simulation has been used to highlight the importance of the threshold level to successful stability management. The compressor stability management concepts have also been experimentally demonstrated on a laboratory axial compressor rig. The fundamental nature of correlation measure has opened avenues for its application besides limit detection. The applications presented include stage load matching in a multi-stage compressor and monitoring the aerodynamic health of rotor blades.

A dynamic model for generating actuator specifications for small arms barrel active stabilization

NASA Astrophysics Data System (ADS)

Pathak, Anupam; Brei, Diann; Luntz, Jonathan; Lavigna, Chris

2006-03-01

Due to stresses encountered in combat, it is known that soldier marksmanship noticeably decreases regardless of prior training. Active stabilization systems in small arms have potential to address this problem to increase soldier survivability and mission effectiveness. The key to success is proper actuator design, but this is highly dependent on proper specification which is challenging due to the human/weapon interaction. This paper presents a generic analytical dynamic model which is capable of defining the necessary actuation specifications for a wide range of small arms platforms. The model is unique because it captures the human interface--shoulder and arm--that introduces the jitter disturbance in addition to the geometry, inertial properties and active stabilization stiffness of the small arms platform. Because no data to date is available for actual shooter-induced disturbance in field conditions, a method is given using the model to back-solve from measured shooting range variability data the disturbance amplitude information relative to the input source (arm or shoulder). As examples of the applicability of the model to various small arms systems, two different weapon systems were investigated: the M24 sniper weapon and the M16 assault rifle. In both cases, model based simulations provided valuable insight into impact on the actuation specifications (force, displacement, phase, frequency) due to the interplay of the human-weapon-active stabilization interface including the effect of shooter-disturbance frequency, disturbance location (shoulder vs. arm), and system parameters (stiffness, barrel rotation).

Design of Launch Vehicle Flight Control Augmentors and Resulting Flight Stability and Control (Center Director's Discretionary Fund Project 93-05, Part III)

NASA Technical Reports Server (NTRS)

Barret, C.

1997-01-01

This publication presents the control requirements, the details of the designed Flight Control Augmentor's (FCA's), the static stability and dynamic stability wind tunnel test programs, the static stability and control analyses, the dynamic stability characteristics of the experimental Launch Vehicle (LV) with the designed FCA's, and a consideration of the elastic vehicle. Dramatic improvements in flight stability have been realized with all the FCA designs; these ranged from 41 percent to 72 percent achieved by the blunt TE design. The control analysis showed that control increased 110 percent with only 3 degrees of FCA deflection. The dynamic stability results showed improvements with all FCA designs tested at all Mach numbers tested. The blunt TE FCA's had the best overall dynamic stability results. Since the lowest elastic vehicle frequency must be well separated from that of the control system, the significant frequencies and modes of vibration have been identified, and the response spectra compared for the experimental LV in both the conventional and the aft cg configuration. Although the dynamic response was 150 percent greater in the aft cg configuration, the lowest bending mode frequency decreased by only 2.8 percent.

Comparative modeling of coevolution in communities of unicellular organisms: adaptability and biodiversity.

PubMed

Lashin, Sergey A; Suslov, Valentin V; Matushkin, Yuri G

2010-06-01

We propose an original program "Evolutionary constructor" that is capable of computationally efficient modeling of both population-genetic and ecological problems, combining these directions in one model of required detail level. We also present results of comparative modeling of stability, adaptability and biodiversity dynamics in populations of unicellular haploid organisms which form symbiotic ecosystems. The advantages and disadvantages of two evolutionary strategies of biota formation--a few generalists' taxa-based biota formation and biodiversity-based biota formation--are discussed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, R.; Harrison, D. E. Jr.

A variable time step integration algorithm for carrying out molecular dynamics simulations of atomic collision cascades is proposed which evaluates the interaction forces only once per time step. The algorithm is tested on some model problems which have exact solutions and is compared against other common methods. These comparisons show that the method has good stability and accuracy. Applications to Ar/sup +/ bombardment of Cu and Si show good accuracy and improved speed to the original method (D. E. Harrison, W. L. Gay, and H. M. Effron, J. Math. Phys. /bold 10/, 1179 (1969)).

Anticontrol of Hopf bifurcation and control of chaos for a finance system through washout filters with time delay.

PubMed

Zhao, Huitao; Lu, Mengxia; Zuo, Junmei

2014-01-01

A controlled model for a financial system through washout-filter-aided dynamical feedback control laws is developed, the problem of anticontrol of Hopf bifurcation from the steady state is studied, and the existence, stability, and direction of bifurcated periodic solutions are discussed in detail. The obtained results show that the delay on price index has great influences on the financial system, which can be applied to suppress or avoid the chaos phenomenon appearing in the financial system.

A new finite element formulation for computational fluid dynamics. IX - Fourier analysis of space-time Galerkin/least-squares algorithms

NASA Technical Reports Server (NTRS)

Shakib, Farzin; Hughes, Thomas J. R.

1991-01-01

A Fourier stability and accuracy analysis of the space-time Galerkin/least-squares method as applied to a time-dependent advective-diffusive model problem is presented. Two time discretizations are studied: a constant-in-time approximation and a linear-in-time approximation. Corresponding space-time predictor multi-corrector algorithms are also derived and studied. The behavior of the space-time algorithms is compared to algorithms based on semidiscrete formulations.

Flocking with connectivity preservation for disturbed nonlinear multi-agent systems by output feedback

NASA Astrophysics Data System (ADS)

Li, Ping; Zhang, Baoyong; Ma, Qian; Xu, Shengyuan; Chen, Weimin; Zhang, Zhengqiang

2018-05-01

This paper considers the problem of flocking with connectivity preservation for a class of disturbed nonlinear multi-agent systems. In order to deal with the nonlinearities in the dynamic of all agents, some auxiliary variables are introduced into the state observer for stability analysis. By proposing a bounded potential function and using adaptive theory, a novel output feedback consensus algorithm is developed to guarantee that the states of all agents achieve flocking with connectivity preservation.

System analysis of vehicle active safety problem

NASA Astrophysics Data System (ADS)

Buznikov, S. E.

2018-02-01

The problem of the road transport safety affects the vital interests of the most of the population and is characterized by a global level of significance. The system analysis of problem of creation of competitive active vehicle safety systems is presented as an interrelated complex of tasks of multi-criterion optimization and dynamic stabilization of the state variables of a controlled object. Solving them requires generation of all possible variants of technical solutions within the software and hardware domains and synthesis of the control, which is close to optimum. For implementing the task of the system analysis the Zwicky “morphological box” method is used. Creation of comprehensive active safety systems involves solution of the problem of preventing typical collisions. For solving it, a structured set of collisions is introduced with its elements being generated also using the Zwicky “morphological box” method. The obstacle speed, the longitudinal acceleration of the controlled object and the unpredictable changes in its movement direction due to certain faults, the road surface condition and the control errors are taken as structure variables that characterize the conditions of collisions. The conditions for preventing typical collisions are presented as inequalities for physical variables that define the state vector of the object and its dynamic limits.

On the optimization of discrete structures with aeroelastic constraints

NASA Technical Reports Server (NTRS)

Mcintosh, S. C., Jr.; Ashley, H.

1978-01-01

The paper deals with the problem of dynamic structural optimization where constraints relating to flutter of a wing (or other dynamic aeroelastic performance) are imposed along with conditions of a more conventional nature such as those relating to stress under load, deflection, minimum dimensions of structural elements, etc. The discussion is limited to a flutter problem for a linear system with a finite number of degrees of freedom and a single constraint involving aeroelastic stability, and the structure motion is assumed to be a simple harmonic time function. Three search schemes are applied to the minimum-weight redesign of a particular wing: the first scheme relies on the method of feasible directions, while the other two are derived from necessary conditions for a local optimum so that they can be referred to as optimality-criteria schemes. The results suggest that a heuristic redesign algorithm involving an optimality criterion may be best suited for treating multiple constraints with large numbers of design variables.

Formation tracker design of multiple mobile robots with wheel perturbations: adaptive output-feedback approach

NASA Astrophysics Data System (ADS)

Yoo, Sung Jin

2016-11-01

This paper presents a theoretical design approach for output-feedback formation tracking of multiple mobile robots under wheel perturbations. It is assumed that these perturbations are unknown and the linear and angular velocities of the robots are unmeasurable. First, adaptive state observers for estimating unmeasurable velocities of the robots are developed under the robots' kinematics and dynamics including wheel perturbation effects. Then, we derive a virtual-structure-based formation tracker scheme according to the observer dynamic surface design procedure. The main difficulty of the output-feedback control design is to manage the coupling problems between unmeasurable velocities and unknown wheel perturbation effects. These problems are avoided by using the adaptive technique and the function approximation property based on fuzzy logic systems. From the Lyapunov stability analysis, it is shown that point tracking errors of each robot and synchronisation errors for the desired formation converge to an adjustable neighbourhood of the origin, while all signals in the controlled closed-loop system are semiglobally uniformly ultimately bounded.

Least square based sliding mode control for a quad-rotor helicopter and energy saving by chattering reduction

NASA Astrophysics Data System (ADS)

Sumantri, Bambang; Uchiyama, Naoki; Sano, Shigenori

2016-01-01

In this paper, a new control structure for a quad-rotor helicopter that employs the least squares method is introduced. This proposed algorithm solves the overdetermined problem of the control input for the translational motion of a quad-rotor helicopter. The algorithm allows all six degrees of freedom to be considered to calculate the control input. The sliding mode controller is applied to achieve robust tracking and stabilization. A saturation function is designed around a boundary layer to reduce the chattering phenomenon that is a common problem in sliding mode control. In order to improve the tracking performance, an integral sliding surface is designed. An energy saving effect because of chattering reduction is also evaluated. First, the dynamics of the quad-rotor helicopter is derived by the Newton-Euler formulation for a rigid body. Second, a constant plus proportional reaching law is introduced to increase the reaching rate of the sliding mode controller. Global stability of the proposed control strategy is guaranteed based on the Lyapunov's stability theory. Finally, the robustness and effectiveness of the proposed control system are demonstrated experimentally under wind gusts, and are compared with a regular sliding mode controller, a proportional-differential controller, and a proportional-integral-differential controller.

Enhancing the stabilization of aircraft pitch motion control via intelligent and classical method

NASA Astrophysics Data System (ADS)

Lukman, H.; Munawwarah, S.; Azizan, A.; Yakub, F.; Zaki, S. A.; Rasid, Z. A.

2017-12-01

The pitching movement of an aircraft is very important to ensure passengers are intrinsically safe and the aircraft achieve its maximum stability. The equations governing the motion of an aircraft are a complex set of six nonlinear coupled differential equations. Under certain assumptions, it can be decoupled and linearized into longitudinal and lateral equations. Pitch control is a longitudinal problem and thus, only the longitudinal dynamics equations are involved in this system. It is a third order nonlinear system, which is linearized about the operating point. The system is also inherently unstable due to the presence of a free integrator. Because of this, a feedback controller is added in order to solve this problem and enhance the system performance. This study uses two approaches in designing controller: a conventional controller and an intelligent controller. The pitch control scheme consists of proportional, integral and derivatives (PID) for conventional controller and fuzzy logic control (FLC) for intelligent controller. Throughout the paper, the performance of the presented controllers are investigated and compared based on the common criteria of step response. Simulation results have been obtained and analysed by using Matlab and Simulink software. The study shows that FLC controller has higher ability to control and stabilize the aircraft's pitch angle as compared to PID controller.

Stability and Optimal Harvesting of Modified Leslie-Gower Predator-Prey Model

NASA Astrophysics Data System (ADS)

Toaha, S.; Azis, M. I.

2018-03-01

This paper studies a modified of dynamics of Leslie-Gower predator-prey population model. The model is stated as a system of first order differential equations. The model consists of one predator and one prey. The Holling type II as a predation function is considered in this model. The predator and prey populations are assumed to be beneficial and then the two populations are harvested with constant efforts. Existence and stability of the interior equilibrium point are analysed. Linearization method is used to get the linearized model and the eigenvalue is used to justify the stability of the interior equilibrium point. From the analyses, we show that under a certain condition the interior equilibrium point exists and is locally asymptotically stable. For the model with constant efforts of harvesting, cost function, revenue function, and profit function are considered. The stable interior equilibrium point is then related to the maximum profit problem as well as net present value of revenues problem. We show that there exists a certain value of the efforts that maximizes the profit function and net present value of revenues while the interior equilibrium point remains stable. This means that the populations can live in coexistence for a long time and also maximize the benefit even though the populations are harvested with constant efforts.

Parameter estimation for stiff deterministic dynamical systems via ensemble Kalman filter

NASA Astrophysics Data System (ADS)

Arnold, Andrea; Calvetti, Daniela; Somersalo, Erkki

2014-10-01

A commonly encountered problem in numerous areas of applications is to estimate the unknown coefficients of a dynamical system from direct or indirect observations at discrete times of some of the components of the state vector. A related problem is to estimate unobserved components of the state. An egregious example of such a problem is provided by metabolic models, in which the numerous model parameters and the concentrations of the metabolites in tissue are to be estimated from concentration data in the blood. A popular method for addressing similar questions in stochastic and turbulent dynamics is the ensemble Kalman filter (EnKF), a particle-based filtering method that generalizes classical Kalman filtering. In this work, we adapt the EnKF algorithm for deterministic systems in which the numerical approximation error is interpreted as a stochastic drift with variance based on classical error estimates of numerical integrators. This approach, which is particularly suitable for stiff systems where the stiffness may depend on the parameters, allows us to effectively exploit the parallel nature of particle methods. Moreover, we demonstrate how spatial prior information about the state vector, which helps the stability of the computed solution, can be incorporated into the filter. The viability of the approach is shown by computed examples, including a metabolic system modeling an ischemic episode in skeletal muscle, with a high number of unknown parameters.

Factors Affecting Lateral Stability and Controllability

NASA Technical Reports Server (NTRS)

Campbell, John P; Toll, Thomas A

1948-01-01

The effects on dynamic lateral stability and controllability of some of the important aerodynamic and mass characteristics are discussed and methods are presented for estimating the various stability parameters to be used in the calculation of the dynamic lateral stability of airplanes with swept and low-aspect-ratio wings.

Monoamine oxidase A polymorphism moderates stability of attention problems and susceptibility to life stress during adolescence.

PubMed

Zohsel, K; Bianchi, V; Mascheretti, S; Hohm, E; Schmidt, M H; Esser, G; Brandeis, D; Banaschewski, T; Nobile, M; Laucht, M

2015-11-01

Attention problems affect a substantial number of children and adolescents and are predictive of academic underachievement and lower global adaptive functioning. Considerable variability has been observed with regard to the individual development of attention problems over time. In particular, the period of adolescence is characterized by substantial maturation of executive functioning including attentional processing, with the influence of genetic and environmental factors on individual trajectories not yet well understood. In the present investigation, we evaluated whether the monoamine oxidase A functional promoter polymorphism, MAOA-LPR, plays a role in determining continuity of parent-rated attention problems during adolescence. At the same time, a potential effect of severe life events (SLEs) was taken into account. A multi-group path analysis was used in a sample of 234 adolescents (149 males, 85 females) who took part in an epidemiological cohort study at the ages of 11 and 15 years. Attention problems during early adolescence were found to be a strong predictor of attention problems in middle adolescence. However, in carriers of the MAOA-LPR low-activity variant (MAOA-L), stability was found to be significantly higher than in carriers of the high-activity variant (MAOA-H). Additionally, only in MAOA-L carriers did SLEs during adolescence significantly impact on attention problems at the age of 15 years, implying a possible gene × environment interaction. To conclude, we found evidence that attention problems during adolescence in carriers of the MAOA-L allele are particularly stable and malleable to life stressors. The present results underline the usefulness of applying a more dynamic GxE perspective. © 2015 John Wiley & Sons Ltd and International Behavioural and Neural Genetics Society.

The importance of steady and dynamic inflow on the stability of rotor-body systems

NASA Technical Reports Server (NTRS)

Peters, David A.

1988-01-01

The induced flow field of a rotor responds in a dynamic fashion to oscillations in rotor lift. This was long known to affect the stability and control derivatives of the rotor. More recently, however, it was also shown that this dynamic inflow also affects rotor and rotor-body aeroelastic stability. Thus, both the steady and unsteady inflow have pronounced effects on air resonance. Recent theoretical developments were made in the modeling of dynamic inflow, and these were verified experimentally. Thus, there is now a simple, verified dynamic inflow model for use in dynamic analyses.

Oscillatory Protein Expression Dynamics Endows Stem Cells with Robust Differentiation Potential

PubMed Central

Kaneko, Kunihiko

2011-01-01

The lack of understanding of stem cell differentiation and proliferation is a fundamental problem in developmental biology. Although gene regulatory networks (GRNs) for stem cell differentiation have been partially identified, the nature of differentiation dynamics and their regulation leading to robust development remain unclear. Herein, using a dynamical system modeling cell approach, we performed simulations of the developmental process using all possible GRNs with a few genes, and screened GRNs that could generate cell type diversity through cell-cell interactions. We found that model stem cells that both proliferated and differentiated always exhibited oscillatory expression dynamics, and the differentiation frequency of such stem cells was regulated, resulting in a robust number distribution. Moreover, we uncovered the common regulatory motifs for stem cell differentiation, in which a combination of regulatory motifs that generated oscillatory expression dynamics and stabilized distinct cellular states played an essential role. These findings may explain the recently observed heterogeneity and dynamic equilibrium in cellular states of stem cells, and can be used to predict regulatory networks responsible for differentiation in stem cell systems. PMID:22073296

Lévy targeting and the principle of detailed balance.

PubMed

Garbaczewski, Piotr; Stephanovich, Vladimir

2011-07-01

We investigate confining mechanisms for Lévy flights under premises of the principle of detailed balance. In this case, the master equation of the jump-type process admits a transformation to the Lévy-Schrödinger semigroup dynamics akin to a mapping of the Fokker-Planck equation into the generalized diffusion equation. This sets a correspondence between above two stochastic dynamical systems, within which we address a (stochastic) targeting problem for an arbitrary stability index μ ε (0,2) of symmetric Lévy drivers. Namely, given a probability density function, specify the semigroup potential, and thence the jump-type dynamics for which this PDF is actually a long-time asymptotic (target) solution of the master equation. Here, an asymptotic behavior of different μ-motion scenarios ceases to depend on μ. That is exemplified by considering Gaussian and Cauchy family target PDFs. A complementary problem of the reverse engineering is analyzed: given a priori a semigroup potential, quantify how sensitive upon the choice of the μ driver is an asymptotic behavior of solutions of the associated master equation and thus an invariant PDF itself. This task is accomplished for so-called μ family of Lévy oscillators.

Evaluation of a Hybrid Dynamic Stabilization and Fusion System in the Lumbar Spine: A 10 Year Experience.

PubMed

Kashkoush, Ahmed; Agarwal, Nitin; Paschel, Erin; Goldschmidt, Ezequiel; Gerszten, Peter C

2016-06-10

The development of adjacent-segment disease is a recognized consequence of lumbar fusion surgery. Posterior dynamic stabilization, or motion preservation, techniques have been developed which theoretically decrease stress on adjacent segments following fusion. This study presents the experience of using a hybrid dynamic stabilization and fusion construct for degenerative lumbar spine pathology in place of rigid arthrodesis. A clinical cohort investigation was conducted of 66 consecutive patients (31 female, 35 male; mean age: 53 years, range: 25 - 76 years) who underwent posterior lumbar instrumentation with the Dynesys Transition Optima (DTO) implant (Zimmer-Biomet Spine, Warsaw, IN) hybrid dynamic stabilization and fusion system over a 10-year period. The median length of follow-up was five years. DTO consists of pedicle screw fixation coupled to a rigid rod as well as a flexible longitudinal connecting system. All patients had symptoms of back pain and neurogenic claudication refractory to non-surgical treatment. Patients underwent lumbar arthrodesis surgery in which the hybrid system was used for stabilization instead of arthrodesis of the stenotic adjacent level. Indications for DTO instrumentation were primary degenerative disc disease (n = 52) and failed back surgery syndrome (n = 14). The most common dynamically stabilized and fused segments were L3-L4 (n = 37) and L5-S1 (n = 33), respectively. Thirty-eight patients (56%) underwent decompression at the dynamically stabilized level, and 57 patients (86%) had an interbody device placed at the level of arthrodesis. Complications during the follow-up period included a single case of screw breakage and a single case of pseudoarthrosis. Ten patients (15%) subsequently underwent conversion of the dynamic stabilization portion of their DTO instrumentation to rigid spinal arthrodesis. The DTO system represents a novel hybrid dynamic stabilization and fusion construct. This 10-year experience found the device to be highly effective as well as safe. The technique may serve as an alternative to multilevel arthrodesis. Implantation of a motion-preserving dynamic stabilization device immediately adjacent to a fused level instead of extending a rigid construct may reduce the subsequent development of adjacent-segment disease in this patient population.

Safety assurance of non-deterministic flight controllers in aircraft applications

NASA Astrophysics Data System (ADS)

Noriega, Alfonso

Loss of control is a serious problem in aviation that primarily affects General Aviation. Technological advancements can help mitigate the problem, but the FAA certification process makes certain solutions economically unfeasible. This investigation presents the design of a generic adaptive autopilot that could potentially lead to a single certification for use in several makes and models of aircraft. The autopilot consists of a conventional controller connected in series with a robust direct adaptive model reference controller. In this architecture, the conventional controller is tuned once to provide outer-loop guidance and navigation to a reference model. The adaptive controller makes unknown aircraft behave like the reference model, allowing the conventional controller to successfully provide navigation without the need for retuning. A strong theoretical foundation is presented as an argument for the safety and stability of the controller. The stability proof of direct adaptive controllers require that the plant being controlled has no unstable transmission zeros and has a nonzero high frequency gain. Because most conventional aircraft do not readily meet these requirements, a process known as sensor blending was used. Sensor blending consists of using a linear combination of the plant's outputs that has no unstable transmission zeros and has a nonzero high frequency gain to drive the adaptive controller. Although this method does not present a problem for regulators, it can lead to a steady state error in tracking applications. The sensor blending theory was expanded to take advantage of the system's dynamics to allow for zero steady state error tracking. This method does not need knowledge of the specific system's dynamics, but instead uses the structure of the A and B matrices to perform the blending for the general case. The generic adaptive autopilot was tested in two high-fidelity nonlinear simulators of two typical General Aviation aircraft. The results show that the autopilot was able to adapt appropriately to the different aircraft and was able to perform three-dimensional navigation and an ILS approach, without any modification to the controller. The autopilot was tested in moderate atmospheric turbulence, using consumer-grade sensors and actuators currently available in General Aviation aircraft. The generic adaptive autopilot was shown to be robust to atmospheric turbulence and sensor and actuator random noise. In both aircraft simulators, the autopilot adapted successfully to changes in airspeed, altitude, and configuration. This investigation proves the feasibility of a generic autopilot using direct adaptive controller. The autopilot does not need a priori information of the specific aircraft's dynamics to maintain its safety and stability arguments. Real-time parameter estimation of the aircraft dynamics are not needed. Recommendations for future work are provided.

Robust H∞ control of active vehicle suspension under non-stationary running

NASA Astrophysics Data System (ADS)

Guo, Li-Xin; Zhang, Li-Ping

2012-12-01

Due to complexity of the controlled objects, the selection of control strategies and algorithms in vehicle control system designs is an important task. Moreover, the control problem of automobile active suspensions has been become one of the important relevant investigations due to the constrained peculiarity and parameter uncertainty of mathematical models. In this study, after establishing the non-stationary road surface excitation model, a study on the active suspension control for non-stationary running condition was conducted using robust H∞ control and linear matrix inequality optimization. The dynamic equation of a two-degree-of-freedom quarter car model with parameter uncertainty was derived. The H∞ state feedback control strategy with time-domain hard constraints was proposed, and then was used to design the active suspension control system of the quarter car model. Time-domain analysis and parameter robustness analysis were carried out to evaluate the proposed controller stability. Simulation results show that the proposed control strategy has high systemic stability on the condition of non-stationary running and parameter uncertainty (including suspension mass, suspension stiffness and tire stiffness). The proposed control strategy can achieve a promising improvement on ride comfort and satisfy the requirements of dynamic suspension deflection, dynamic tire loads and required control forces within given constraints, as well as non-stationary running condition.

Dynamic learning from adaptive neural network control of a class of nonaffine nonlinear systems.

PubMed

Dai, Shi-Lu; Wang, Cong; Wang, Min

2014-01-01

This paper studies the problem of learning from adaptive neural network (NN) control of a class of nonaffine nonlinear systems in uncertain dynamic environments. In the control design process, a stable adaptive NN tracking control design technique is proposed for the nonaffine nonlinear systems with a mild assumption by combining a filtered tracking error with the implicit function theorem, input-to-state stability, and the small-gain theorem. The proposed stable control design technique not only overcomes the difficulty in controlling nonaffine nonlinear systems but also relaxes constraint conditions of the considered systems. In the learning process, the partial persistent excitation (PE) condition of radial basis function NNs is satisfied during tracking control to a recurrent reference trajectory. Under the PE condition and an appropriate state transformation, the proposed adaptive NN control is shown to be capable of acquiring knowledge on the implicit desired control input dynamics in the stable control process and of storing the learned knowledge in memory. Subsequently, an NN learning control design technique that effectively exploits the learned knowledge without re-adapting to the controller parameters is proposed to achieve closed-loop stability and improved control performance. Simulation studies are performed to demonstrate the effectiveness of the proposed design techniques.

Robustness of linear quadratic state feedback designs in the presence of system uncertainty. [application to Augmentor Wing Jet STOL Research Aircraft flare control autopilot design

NASA Technical Reports Server (NTRS)

Patel, R. V.; Toda, M.; Sridhar, B.

1977-01-01

The paper deals with the problem of expressing the robustness (stability) property of a linear quadratic state feedback (LQSF) design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices so that the closed-loop system remains stable. Nonlinear time-varying and linear time-invariant perturbations are considered. The only computation required in obtaining a measure of the robustness of an LQSF design is to determine the eigenvalues of two symmetric matrices determined when solving the algebraic Riccati equation corresponding to the LQSF design problem. Results are applied to a complex dynamic system consisting of the flare control of a STOL aircraft. The design of the flare control is formulated as an LQSF tracking problem.

Application of circular dichroism and magnetic circular dichroism for assessing biopharmaceuticals formulations photo-stability and small ligands binding properties.

PubMed

Longo, Edoardo; Hussain, Rohanah; Siligardi, Giuliano

2015-03-01

Synchrotron radiation circular dichroism (SRCD) is a powerful tool for photo-stability assessment of proteins. Recently our research has been interested in applying SRCD to develop screening methodologies for accelerated photo-stability assessment of monoclonal antibody formulations. Despite it was proven to be reliable and applicable within a wide range of salts and excipients containing solutions, the presence of far-UV (<260nm) strong absorbing species (e.g., sodium chloride, histidine, arginine) in common formulations completely prevent the analysis. Herein, we propose a new method based on CD coupled with magnetic CD (MCD) to address the problem and offer an additional versatile tool for monitoring the photo-stability. This is done by assessing the stability of the samples by looking at the near-UV band, as well as giving insights in the denaturation mechanism. We applied this method to four mAbs formulations and correlated the results with dynamic light scattering data. Finally, we applied MCD in ligand interaction to key proteins such as lysozyme, comparing the human with the hen enzyme in the binding of N,N',N''-triacetylchitotriose. Copyright © 2015 The Authors. Published by Elsevier B.V. All rights reserved.

Robot body self-modeling algorithm: a collision-free motion planning approach for humanoids.

PubMed

Leylavi Shoushtari, Ali

2016-01-01

Motion planning for humanoid robots is one of the critical issues due to the high redundancy and theoretical and technical considerations e.g. stability, motion feasibility and collision avoidance. The strategies which central nervous system employs to plan, signal and control the human movements are a source of inspiration to deal with the mentioned problems. Self-modeling is a concept inspired by body self-awareness in human. In this research it is integrated in an optimal motion planning framework in order to detect and avoid collision of the manipulated object with the humanoid body during performing a dynamic task. Twelve parametric functions are designed as self-models to determine the boundary of humanoid's body. Later, the boundaries which mathematically defined by the self-models are employed to calculate the safe region for box to avoid the collision with the robot. Four different objective functions are employed in motion simulation to validate the robustness of algorithm under different dynamics. The results also confirm the collision avoidance, reality and stability of the predicted motion.

A game theoretic controller for a linear time-invariant system with parameter uncertainty and its application to the Space Station

NASA Technical Reports Server (NTRS)

Rhee, Ihnseok; Speyer, Jason L.

1990-01-01

A game theoretic controller is developed for a linear time-invariant system with parameter uncertainties in system and input matrices. The input-output decomposition modeling for the plant uncertainty is adopted. The uncertain dynamic system is represented as an internal feedback loop in which the system is assumed forced by fictitious disturbance caused by the parameter uncertainty. By considering the input and the fictitious disturbance as two noncooperative players, a differential game problem is constructed. It is shown that the resulting time invariant controller stabilizes the uncertain system for a prescribed uncertainty bound. This game theoretic controller is applied to the momentum management and attitude control of the Space Station in the presence of uncertainties in the moments of inertia. Inclusion of the external disturbance torque to the design procedure results in a dynamical feedback controller which consists of conventional PID control and cyclic disturbance rejection filter. It is shown that the game theoretic design, comparing to the LQR design or pole placement design, improves the stability robustness with respect to inertia variations.

Atomic dynamics and the problem of the structural stability of free clusters of solidified inert gases

NASA Astrophysics Data System (ADS)

Verkhovtseva, É. T.; Gospodarev, I. A.; Grishaev, A. V.; Kovalenko, S. I.; Solnyshkin, D. D.; Syrkin, E. S.; Feodos'ev, S. B.

2003-05-01

The dependence of the rms amplitudes of atoms in free clusters of solidified inert gases on the cluster size is investigated theoretically and experimentally. Free clusters are produced by homogeneous nucleation in an adiabatically expanding supersonic stream. Electron diffraction is used to measure the rms amplitudes of the atoms; the Jacobi-matrix method is used for theoretical calculations. A series of distinguishing features of the atomic dynamics of microclusters was found. This was necessary to determine the character of the formation and the stability conditions of the crystal structure. It wass shown that for clusters consisting of less than N˜103 atoms, as the cluster size decreases, the rms amplitudes grow much more rapidly than expected from the increase in the specific contribution of the surface. It is also established that an fcc structure of a free cluster, as a rule, contains twinning defects (nuclei of an hcp phase). One reason for the appearance of such defects is the so-called vertex instability (anomalously large oscillation amplitudes) of the atoms in coordination spheres.

Logic Dynamics for Deductive Inference -- Its Stability and Neural Basis

NASA Astrophysics Data System (ADS)

Tsuda, Ichiro

2014-12-01

We propose a dynamical model that represents a process of deductive inference. We discuss the stability of logic dynamics and a neural basis for the dynamics. We propose a new concept of descriptive stability, thereby enabling a structure of stable descriptions of mathematical models concerning dynamic phenomena to be clarified. The present theory is based on the wider and deeper thoughts of John S. Nicolis. In particular, it is based on our joint paper on the chaos theory of human short-term memories with a magic number of seven plus or minus two.

ECCD-induced tearing mode stabilization in coupled IPS/NIMROD/GENRAY HPC simulations

NASA Astrophysics Data System (ADS)

Jenkins, Thomas; Kruger, S. E.; Held, E. D.; Harvey, R. W.; Elwasif, W. R.; Schnack, D. D.; SWIM Project Team

2011-10-01

We present developments toward an integrated, predictive model for determining optimal ECCD-based NTM stabilization strategies in ITER. We demonstrate the capability of the SWIM Project's Integrated Plasma Simulator (IPS) framework to choreograph multiple executions of, and data exchanges between, physics codes modeling various spatiotemporal scales of this coupled RF/MHD problem on several thousand HPC processors. As NIMROD evolves fluid equations to model bulk plasma behavior, self-consistent propagation/deposition of RF power in the ensuing plasma profiles is calculated by GENRAY. A third code (QLCALC) then interfaces with computational geometry packages to construct the RF-induced quasilinear diffusion tensor from NIMROD/GENRAY data, and the moments of this tensor (entering as additional terms in NIMROD's fluid equations due to the disparity in RF/MHD spatiotemporal scales) influence the dynamics of current, momentum, and energy evolution. Initial results are shown to correctly capture the physics of magnetic island stabilization [Jenkins et al., PoP 17, 012502 (2010)]; we also discuss the development of a numerical plasma control system for active feedback stabilization of tearing modes. Funded by USDoE SciDAC.

A nonlinear optimal control approach to stabilization of a macroeconomic development model

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Ghosh, T.; Sarno, D.

2017-11-01

A nonlinear optimal (H-infinity) control approach is proposed for the problem of stabilization of the dynamics of a macroeconomic development model that is known as the Grossman-Helpman model of endogenous product cycles. The dynamics of the macroeconomic development model is divided in two parts. The first one describes economic activities in a developed country and the second part describes variation of economic activities in a country under development which tries to modify its production so as to serve the needs of the developed country. The article shows that through control of the macroeconomic model of the developed country, one can finally control the dynamics of the economy in the country under development. The control method through which this is achieved is the nonlinear H-infinity control. The macroeconomic model for the country under development undergoes approximate linearization round a temporary operating point. This is defined at each time instant by the present value of the system's state vector and the last value of the control input vector that was exerted on it. The linearization is based on Taylor series expansion and the computation of the associated Jacobian matrices. For the linearized model an H-infinity feedback controller is computed. The controller's gain is calculated by solving an algebraic Riccati equation at each iteration of the control method. The asymptotic stability of the control approach is proven through Lyapunov analysis. This assures that the state variables of the macroeconomic model of the country under development will finally converge to the designated reference values.

A Study of Fixed-Order Mixed Norm Designs for a Benchmark Problem in Structural Control

NASA Technical Reports Server (NTRS)

Whorton, Mark S.; Calise, Anthony J.; Hsu, C. C.

1998-01-01

This study investigates the use of H2, p-synthesis, and mixed H2/mu methods to construct full-order controllers and optimized controllers of fixed dimensions. The benchmark problem definition is first extended to include uncertainty within the controller bandwidth in the form of parametric uncertainty representative of uncertainty in the natural frequencies of the design model. The sensitivity of H2 design to unmodelled dynamics and parametric uncertainty is evaluated for a range of controller levels of authority. Next, mu-synthesis methods are applied to design full-order compensators that are robust to both unmodelled dynamics and to parametric uncertainty. Finally, a set of mixed H2/mu compensators are designed which are optimized for a fixed compensator dimension. These mixed norm designs recover the H, design performance levels while providing the same levels of robust stability as the u designs. It is shown that designing with the mixed norm approach permits higher levels of controller authority for which the H, designs are destabilizing. The benchmark problem is that of an active tendon system. The controller designs are all based on the use of acceleration feedback.

The need for higher-order averaging in the stability analysis of hovering, flapping-wing flight.

PubMed

Taha, Haithem E; Tahmasian, Sevak; Woolsey, Craig A; Nayfeh, Ali H; Hajj, Muhammad R

2015-01-05

Because of the relatively high flapping frequency associated with hovering insects and flapping wing micro-air vehicles (FWMAVs), dynamic stability analysis typically involves direct averaging of the time-periodic dynamics over a flapping cycle. However, direct application of the averaging theorem may lead to false conclusions about the dynamics and stability of hovering insects and FWMAVs. Higher-order averaging techniques may be needed to understand the dynamics of flapping wing flight and to analyze its stability. We use second-order averaging to analyze the hovering dynamics of five insects in response to high-amplitude, high-frequency, periodic wing motion. We discuss the applicability of direct averaging versus second-order averaging for these insects.

Advanced computational techniques for incompressible/compressible fluid-structure interactions

NASA Astrophysics Data System (ADS)

Kumar, Vinod

2005-07-01

Fluid-Structure Interaction (FSI) problems are of great importance to many fields of engineering and pose tremendous challenges to numerical analyst. This thesis addresses some of the hurdles faced for both 2D and 3D real life time-dependent FSI problems with particular emphasis on parachute systems. The techniques developed here would help improve the design of parachutes and are of direct relevance to several other FSI problems. The fluid system is solved using the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) finite element formulation for the Navier-Stokes equations of incompressible and compressible flows. The structural dynamics solver is based on a total Lagrangian finite element formulation. Newton-Raphson method is employed to linearize the otherwise nonlinear system resulting from the fluid and structure formulations. The fluid and structural systems are solved in decoupled fashion at each nonlinear iteration. While rigorous coupling methods are desirable for FSI simulations, the decoupled solution techniques provide sufficient convergence in the time-dependent problems considered here. In this thesis, common problems in the FSI simulations of parachutes are discussed and possible remedies for a few of them are presented. Further, the effects of the porosity model on the aerodynamic forces of round parachutes are analyzed. Techniques for solving compressible FSI problems are also discussed. Subsequently, a better stabilization technique is proposed to efficiently capture and accurately predict the shocks in supersonic flows. The numerical examples simulated here require high performance computing. Therefore, numerical tools using distributed memory supercomputers with message passing interface (MPI) libraries were developed.

Expendable launch vehicle studies

NASA Technical Reports Server (NTRS)

Bainum, Peter M.; Reiss, Robert

1995-01-01

Analytical support studies of expendable launch vehicles concentrate on the stability of the dynamics during launch especially during or near the region of maximum dynamic pressure. The in-plane dynamic equations of a generic launch vehicle with multiple flexible bending and fuel sloshing modes are developed and linearized. The information from LeRC about the grids, masses, and modes is incorporated into the model. The eigenvalues of the plant are analyzed for several modeling factors: utilizing diagonal mass matrix, uniform beam assumption, inclusion of aerodynamics, and the interaction between the aerodynamics and the flexible bending motion. Preliminary PID, LQR, and LQG control designs with sensor and actuator dynamics for this system and simulations are also conducted. The initial analysis for comparison of PD (proportional-derivative) and full state feedback LQR Linear quadratic regulator) shows that the split weighted LQR controller has better performance than that of the PD. In order to meet both the performance and robustness requirements, the H(sub infinity) robust controller for the expendable launch vehicle is developed. The simulation indicates that both the performance and robustness of the H(sub infinity) controller are better than that for the PID and LQG controllers. The modelling and analysis support studies team has continued development of methodology, using eigensensitivity analysis, to solve three classes of discrete eigenvalue equations. In the first class, the matrix elements are non-linear functions of the eigenvector. All non-linear periodic motion can be cast in this form. Here the eigenvector is comprised of the coefficients of complete basis functions spanning the response space and the eigenvalue is the frequency. The second class of eigenvalue problems studied is the quadratic eigenvalue problem. Solutions for linear viscously damped structures or viscoelastic structures can be reduced to this form. Particular attention is paid to Maxwell and Kelvin models. The third class of problems consists of linear eigenvalue problems in which the elements of the mass and stiffness matrices are stochastic. dynamic structural response for which the parameters are given by probabilistic distribution functions, rather than deterministic values, can be cast in this form. Solutions for several problems in each class will be presented.

Origin and continuation of 3/2, 5/2, 3/1, 4/1 and 5/1 resonant periodic orbits in the circular and elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Antoniadou, Kyriaki I.; Libert, Anne-Sophie

2018-06-01

We consider a planetary system consisting of two primaries, namely a star and a giant planet, and a massless secondary, say a terrestrial planet or an asteroid, which moves under their gravitational attraction. We study the dynamics of this system in the framework of the circular and elliptic restricted three-body problem, when the motion of the giant planet describes circular and elliptic orbits, respectively. Originating from the circular family, families of symmetric periodic orbits in the 3/2, 5/2, 3/1, 4/1 and 5/1 mean-motion resonances are continued in the circular and the elliptic problems. New bifurcation points from the circular to the elliptic problem are found for each of the above resonances, and thus, new families continued from these points are herein presented. Stable segments of periodic orbits were found at high eccentricity values of the already known families considered as whole unstable previously. Moreover, new isolated (not continued from bifurcation points) families are computed in the elliptic restricted problem. The majority of the new families mainly consists of stable periodic orbits at high eccentricities. The families of the 5/1 resonance are investigated for the first time in the restricted three-body problems. We highlight the effect of stable periodic orbits on the formation of stable regions in their vicinity and unveil the boundaries of such domains in phase space by computing maps of dynamical stability. The long-term stable evolution of the terrestrial planets or asteroids is dependent on the existence of regular domains in their dynamical neighbourhood in phase space, which could host them for long-time spans. This study, besides other celestial architectures that can be efficiently modelled by the circular and elliptic restricted problems, is particularly appropriate for the discovery of terrestrial companions among the single-giant planet systems discovered so far.

Static and dynamic stability analysis of the space shuttle vehicle-orbiter

NASA Technical Reports Server (NTRS)

Chyu, W. J.; Cavin, R. K.; Erickson, L. L.

1978-01-01

The longitudinal static and dynamic stability of a Space Shuttle Vehicle-Orbiter (SSV Orbiter) model is analyzed using the FLEXSTAB computer program. Nonlinear effects are accounted for by application of a correction technique in the FLEXSTAB system; the technique incorporates experimental force and pressure data into the linear aerodynamic theory. A flexible Orbiter model is treated in the static stability analysis for the flight conditions of Mach number 0.9 for rectilinear flight (1 g) and for a pull-up maneuver (2.5 g) at an altitude of 15.24 km. Static stability parameters and structural deformations of the Orbiter are calculated at trim conditions for the dynamic stability analysis, and the characteristics of damping in pitch are investigated for a Mach number range of 0.3 to 1.2. The calculated results for both the static and dynamic stabilities are compared with the available experimental data.

Decomposition-aggregation stability analysis. [for large scale dynamic systems with application to spinning Skylab control system

NASA Technical Reports Server (NTRS)

Siljak, D. D.; Weissenberger, S.; Cuk, S. M.

1973-01-01

This report presents the development and description of the decomposition aggregation approach to stability investigations of high dimension mathematical models of dynamic systems. The high dimension vector differential equation describing a large dynamic system is decomposed into a number of lower dimension vector differential equations which represent interconnected subsystems. Then a method is described by which the stability properties of each subsystem are aggregated into a single vector Liapunov function, representing the aggregate system model, consisting of subsystem Liapunov functions as components. A linear vector differential inequality is then formed in terms of the vector Liapunov function. The matrix of the model, which reflects the stability properties of the subsystems and the nature of their interconnections, is analyzed to conclude over-all system stability characteristics. The technique is applied in detail to investigate the stability characteristics of a dynamic model of a hypothetical spinning Skylab.

Damage instability and Earthquake nucleation

NASA Astrophysics Data System (ADS)

Ionescu, I. R.; Gomez, Q.; Campillo, M.; Jia, X.

2017-12-01

Earthquake nucleation (initiation) is usually associated to the loss of the stability of the geological structure under a slip-weakening friction acting on the fault. The key parameters involved in the stability of the fault are the stress drop, the critical slip distance but also the elastic stiffness of the surrounding materials (rocks). We want to explore here how the nucleation phenomena are correlated to the material softening during damage accumulation by dynamic and/or quasi-static processes. Since damage models are describing micro-cracks growth, which is generally an unstable phenomenon, it is natural to expect some loss of stability on the associated micro-mechanics based models. If the model accurately captures the material behavior, then this can be due to the unstable nature of the brittle material itself. We obtained stability criteria at the microscopic scale, which are related to a large class of damage models. We show that for a given continuous strain history the quasi-static or dynamic problems are instable or ill-posed (multiplicity of material responses) and whatever the selection rule is adopted, shocks (time discontinuities) will occur. We show that the quasi-static equilibria chosen by the "perfect delay convention" is always stable. These stability criteria are used to analyze how NIC (Non Interacting Crack) effective elasticity associated to "self similar growth" model work in some special configurations (one family of micro-cracks in mode I, II and III and in plane strain or plain stress). In each case we determine a critical crack density parameter and critical micro-crack radius (length) which distinguish between stable and unstable behaviors. This critical crack density depends only on the chosen configuration and on the Poisson ratio.

Unstable behaviour of RPT when testing turbine characteristics in the laboratory

NASA Astrophysics Data System (ADS)

Nielsen, T. K.; Fjørtoft Svarstad, M.

2014-03-01

A reversible pump turbine is a machine that can operate in three modes of operation i.e. in pumping mode. in turbine mode and in phase compensating mode (idle speed). Reversible pump turbines have an increasing importance for regulation purposes for obtaining power balance in electric power systems. Especially in grids dominated by thermal energy. reversible pump turbines improve the overall power regulating ability. Increased use of renewables (wind-. wave- and tidal power plants) will utterly demand better regulation ability of the traditional water power systems. enhancing the use of reversible pump turbines. A reversible pump turbine is known for having incredible steep speed - flow characteristics. As the speed increases the flow decreases more than that of a Francis turbines with the same specific speed. The steep characteristics might cause severe stability problems in turbine mode of operation. Stability in idle speed is a necessity for phasing in the generator to the electric grid. In the design process of a power plant. system dynamic simulations must be performed in order to check the system stability. The turbine characteristics will have to be modelled with certain accuracy even before one knows the exact turbine design and have measured characteristics. A representation of the RPT characteristics for system dynamic simulation purposes is suggested and compared with measured characteristics. The model shows good agreement with RPT characteristics measured in The Waterpower Laboratory. Because of the S-shaped characteristics. there is a stability issue involved when measuring these characteristics. Without special measures. it is impossible to achieve stable conditions in certain operational points. The paper discusses the mechanism when using a throttle to achieve system stability. even if the turbine characteristics imply instability.

Rotating Space Elevators: Classical and Statistical Mechanics

NASA Astrophysics Data System (ADS)

Knudsen, Steven

We investigate a novel and unique dynamical system, the Rotating Space Elevator (RSE). The RSE is a multiply rotating system of strings reaching beyond the Earth geo-synchronous satellite orbit. Objects sliding along the RSE string ("climbers") do not require internal engines or propulsion to be transported far away from the Earth's surface. The RSE thus solves a major problem in the space elevator technology which is how to supply the energy to the climbers moving along the string. The RSE is a double rotating floppy string. The RSE can be made in various shapes that are stabilized by an approximate equilibrium between the gravitational and inertial forces acting in the double rotating frame. The RSE exhibits a variety of interesting dynamical phenomena studied in this thesis.

Spontaneously Broken Neutral Symmetry in an Ecological System

NASA Astrophysics Data System (ADS)

Borile, C.; Muñoz, M. A.; Azaele, S.; Banavar, Jayanth R.; Maritan, A.

2012-07-01

Spontaneous symmetry breaking plays a fundamental role in many areas of condensed matter and particle physics. A fundamental problem in ecology is the elucidation of the mechanisms responsible for biodiversity and stability. Neutral theory, which makes the simplifying assumption that all individuals (such as trees in a tropical forest)—regardless of the species they belong to—have the same prospect of reproduction, death, etc., yields gross patterns that are in accord with empirical data. We explore the possibility of birth and death rates that depend on the population density of species, treating the dynamics in a species-symmetric manner. We demonstrate that dynamical evolution can lead to a stationary state characterized simultaneously by both biodiversity and spontaneously broken neutral symmetry.

Twirling and Whirling: Viscous Dynamics of Rotating Elastica

NASA Astrophysics Data System (ADS)

Wolgemuth, Charles; Powers, Thomas; Goldstein, Raymond

1999-10-01

The stability of forced elastic filaments arise in several important biological settings involving bend and twist elasticity at low Reynolds number. Examples include DNA transcription and replication and bacterial flagellar motion. In order to elucidate fundamental processes common to these systems, we consider the model problem of a rotationally forced filament with twist and bend elasticity. Competition between twist injection, twist diffusion, and writhing instabilities is described by a novel pair of PDEs for twist and bend evolution. Analytical and numerical methods elucidate the twist/bend coupling and reveal two dynamical regimes seperated by a Hopf bifurcation: (i) diffusion-dominated axial rotation, or twirling, and (ii) steady-state crankshafting motion, or whirling. Experiments are proposed to examine these phenomena and the consequences for swimming investigated.

Study of iron structure stability in high temperature molten lead-bismuth eutectic with oxygen injection using molecular dynamics simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arkundato, Artoto; Su'ud, Zaki; Sudarko

2014-09-30

Corrosion of structural materials in high temperature molten lead-bismuth eutectic is a major problem for design of PbBi cooled reactor. One technique to inhibit corrosion process is to inject oxygen into coolant. In this paper we study and focus on a way of inhibiting the corrosion of iron using molecular dynamics method. For the simulation results we concluded that effective corrosion inhibition of iron may be achieved by injection 0.0532 wt% to 0.1156 wt% oxygen into liquid lead-bismuth. At this oxygen concentration the structure of iron material will be maintained at about 70% in bcc crystal structure during interaction withmore » liquid metal.« less

Alternative experiments using the geophysical fluid flow cell

NASA Technical Reports Server (NTRS)

Hart, J. E.

1984-01-01

This study addresses the possibility of doing large scale dynamics experiments using the Geophysical Fluid Flow Cell. In particular, cases where the forcing generates a statically stable stratification almost everywhere in the spherical shell are evaluated. This situation is typical of the Earth's atmosphere and oceans. By calculating the strongest meridional circulation expected in the spacelab experiments, and testing its stability using quasi-geostrophic stability theory, it is shown that strongly nonlinear baroclinic waves on a zonally symmetric modified thermal wind will not occur. The Geophysical Fluid Flow Cell does not have a deep enough fluid layer to permit useful studies of large scale planetary wave processes arising from instability. It is argued, however, that by introducing suitable meridional barriers, a significant contribution to the understanding of the oceanic thermocline problem could be made.

Effect of thermal expansion on the stability of two-reactant flames

NASA Technical Reports Server (NTRS)

Jackson, T. L.

1986-01-01

The full problem of flame stability for the two-reactant model, which takes into account thermal expansion effects for all disturbance wave lengths, is examined. It is found that the stability problem for the class of two-reactant flames is equivalent to the stability problem for the class of one-reactant flames with an appropriate interpretation of Lewis numbers.

Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Parsani, Matteo; Fisher, Travis C.; Nielsen, Eric J.

2016-01-01

Entropy stable (SS) discontinuous spectral collocation formulations of any order are developed for the compressible Navier-Stokes equations on hexahedral elements. Recent progress on two complementary efforts is presented. The first effort is a generalization of previous SS spectral collocation work to extend the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to tensor product Legendre-Gauss (LG) points. The LG and LGL point formulations are compared on a series of test problems. Although being more costly to implement, it is shown that the LG operators are significantly more accurate on comparable grids. Both the LGL and LG operators are of comparable efficiency and robustness, as is demonstrated using test problems for which conventional FEM techniques suffer instability. The second effort generalizes previous SS work to include the possibility of p-refinement at non-conforming interfaces. A generalization of existing entropy stability machinery is developed to accommodate the nuances of fully multi-dimensional summation-by-parts (SBP) operators. The entropy stability of the compressible Euler equations on non-conforming interfaces is demonstrated using the newly developed LG operators and multi-dimensional interface interpolation operators.

Hypersonic vehicle control law development using H infinity and mu-synthesis

NASA Technical Reports Server (NTRS)

Gregory, Irene M.; Chowdhry, Rajiv S.; Mcminn, John D.; Shaughnessy, John D.

1992-01-01

Applicability and effectiveness of robust control techniques to a single-stage-to-orbit (SSTO) airbreathing hypersonic vehicle on an ascent accelerating path and their effectiveness are explored in this paper. An SSTO control system design problem, requiring high accuracy tracking of velocity and altitude commands while limiting angle of attack oscillations, minimizing control power usage and stabilizing the vehicle all in the presence of atmospheric turbulence and uncertainty in the system, was formulated to compare results of the control designs using H infinity and mu-synthesis procedures. The math model, an integrated flight/propulsion dynamic model of a conical accelerator class vehicle, was linearized as the vehicle accelerated through Mach 8. Controller analysis was conducted using the singular value technique and the mu-analysis approach. Analysis results were obtained in both the frequency and the time domains. The results clearly demonstrate the inherent advantages of the structured singular value framework for this class of problems. Since payload performance margins are so critical for the SSTO mission, it is crucial that adequate stability margins be provided without sacrificing any payload mass.

Observer-based robust finite time H∞ sliding mode control for Markovian switching systems with mode-dependent time-varying delay and incomplete transition rate.

PubMed

Gao, Lijun; Jiang, Xiaoxiao; Wang, Dandan

2016-03-01

This paper investigates the problem of robust finite time H∞ sliding mode control for a class of Markovian switching systems. The system is subjected to the mode-dependent time-varying delay, partly unknown transition rate and unmeasurable state. The main difficulty is that, a sliding mode surface cannot be designed based on the unknown transition rate and unmeasurable state directly. To overcome this obstacle, the set of modes is firstly divided into two subsets standing for known transition rate subset and unknown one, based on which a state observer is established. A component robust finite-time sliding mode controller is also designed to cope with the effect of partially unknown transition rate. It is illustrated that the reachability, finite-time stability, finite-time boundedness, finite-time H∞ state feedback stabilization of sliding mode dynamics can be ensured despite the unknown transition rate. Finally, the simulation results verify the effectiveness of robust finite time control problem. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

An Inverse Neural Controller Based on the Applicability Domain of RBF Network Models

PubMed Central

Alexandridis, Alex; Stogiannos, Marios; Papaioannou, Nikolaos; Zois, Elias; Sarimveis, Haralambos

2018-01-01

This paper presents a novel methodology of generic nature for controlling nonlinear systems, using inverse radial basis function neural network models, which may combine diverse data originating from various sources. The algorithm starts by applying the particle swarm optimization-based non-symmetric variant of the fuzzy means (PSO-NSFM) algorithm so that an approximation of the inverse system dynamics is obtained. PSO-NSFM offers models of high accuracy combined with small network structures. Next, the applicability domain concept is suitably tailored and embedded into the proposed control structure in order to ensure that extrapolation is avoided in the controller predictions. Finally, an error correction term, estimating the error produced by the unmodeled dynamics and/or unmeasured external disturbances, is included to the control scheme to increase robustness. The resulting controller guarantees bounded input-bounded state (BIBS) stability for the closed loop system when the open loop system is BIBS stable. The proposed methodology is evaluated on two different control problems, namely, the control of an experimental armature-controlled direct current (DC) motor and the stabilization of a highly nonlinear simulated inverted pendulum. For each one of these problems, appropriate case studies are tested, in which a conventional neural controller employing inverse models and a PID controller are also applied. The results reveal the ability of the proposed control scheme to handle and manipulate diverse data through a data fusion approach and illustrate the superiority of the method in terms of faster and less oscillatory responses. PMID:29361781

Containment control of networked autonomous underwater vehicles: A predictor-based neural DSC design.

PubMed

Peng, Zhouhua; Wang, Dan; Wang, Wei; Liu, Lu

2015-11-01

This paper investigates the containment control problem of networked autonomous underwater vehicles in the presence of model uncertainty and unknown ocean disturbances. A predictor-based neural dynamic surface control design method is presented to develop the distributed adaptive containment controllers, under which the trajectories of follower vehicles nearly converge to the dynamic convex hull spanned by multiple reference trajectories over a directed network. Prediction errors, rather than tracking errors, are used to update the neural adaptation laws, which are independent of the tracking error dynamics, resulting in two time-scales to govern the entire system. The stability property of the closed-loop network is established via Lyapunov analysis, and transient property is quantified in terms of L2 norms of the derivatives of neural weights, which are shown to be smaller than the classical neural dynamic surface control approach. Comparative studies are given to show the substantial improvements of the proposed new method. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Amplification without instability: applying fluid dynamical insights in chemistry and biology

NASA Astrophysics Data System (ADS)

McCoy, Jonathan H.

2013-11-01

While amplification of small perturbations often arises from instability, transient amplification is possible locally even in asymptotically stable systems. That is, knowledge of a system's stability properties can mislead one's intuition for its transient behaviors. This insight, which has an interesting history in fluid dynamics, has more recently been rediscovered in ecology. Surprisingly, many nonlinear fluid dynamical and ecological systems share linear features associated with transient amplification of noise. This paper aims to establish that these features are widespread in many other disciplines concerned with noisy systems, especially chemistry, cell biology and molecular biology. Here, using classic nonlinear systems and the graphical language of network science, we explore how the noise amplification problem can be reframed in terms of activatory and inhibitory interactions between dynamical variables. The interaction patterns considered here are found in a great variety of systems, ranging from autocatalytic reactions and activator-inhibitor systems to influential models of nerve conduction, glycolysis, cell signaling and circadian rhythms.

Dynamic Assessment of Water Quality Based on a Variable Fuzzy Pattern Recognition Model

PubMed Central

Xu, Shiguo; Wang, Tianxiang; Hu, Suduan

2015-01-01

Water quality assessment is an important foundation of water resource protection and is affected by many indicators. The dynamic and fuzzy changes of water quality lead to problems for proper assessment. This paper explores a method which is in accordance with the water quality changes. The proposed method is based on the variable fuzzy pattern recognition (VFPR) model and combines the analytic hierarchy process (AHP) model with the entropy weight (EW) method. The proposed method was applied to dynamically assess the water quality of Biliuhe Reservoir (Dailan, China). The results show that the water quality level is between levels 2 and 3 and worse in August or September, caused by the increasing water temperature and rainfall. Weights and methods are compared and random errors of the values of indicators are analyzed. It is concluded that the proposed method has advantages of dynamism, fuzzification and stability by considering the interval influence of multiple indicators and using the average level characteristic values of four models as results. PMID:25689998

Dynamic assessment of water quality based on a variable fuzzy pattern recognition model.

PubMed

Xu, Shiguo; Wang, Tianxiang; Hu, Suduan

2015-02-16

Water quality assessment is an important foundation of water resource protection and is affected by many indicators. The dynamic and fuzzy changes of water quality lead to problems for proper assessment. This paper explores a method which is in accordance with the water quality changes. The proposed method is based on the variable fuzzy pattern recognition (VFPR) model and combines the analytic hierarchy process (AHP) model with the entropy weight (EW) method. The proposed method was applied to dynamically assess the water quality of Biliuhe Reservoir (Dailan, China). The results show that the water quality level is between levels 2 and 3 and worse in August or September, caused by the increasing water temperature and rainfall. Weights and methods are compared and random errors of the values of indicators are analyzed. It is concluded that the proposed method has advantages of dynamism, fuzzification and stability by considering the interval influence of multiple indicators and using the average level characteristic values of four models as results.

Detecting dynamical boundaries from kinematic data in biomechanics

NASA Astrophysics Data System (ADS)

Ross, Shane D.; Tanaka, Martin L.; Senatore, Carmine

2010-03-01

Ridges in the state space distribution of finite-time Lyapunov exponents can be used to locate dynamical boundaries. We describe a method for obtaining dynamical boundaries using only trajectories reconstructed from time series, expanding on the current approach which requires a vector field in the phase space. We analyze problems in musculoskeletal biomechanics, considered as exemplars of a class of experimental systems that contain separatrix features. Particular focus is given to postural control and balance, considering both models and experimental data. Our success in determining the boundary between recovery and failure in human balance activities suggests this approach will provide new robust stability measures, as well as measures of fall risk, that currently are not available and may have benefits for the analysis and prevention of low back pain and falls leading to injury, both of which affect a significant portion of the population.

Wavelet-based spectral finite element dynamic analysis for an axially moving Timoshenko beam

NASA Astrophysics Data System (ADS)

Mokhtari, Ali; Mirdamadi, Hamid Reza; Ghayour, Mostafa

2017-08-01

In this article, wavelet-based spectral finite element (WSFE) model is formulated for time domain and wave domain dynamic analysis of an axially moving Timoshenko beam subjected to axial pretension. The formulation is similar to conventional FFT-based spectral finite element (SFE) model except that Daubechies wavelet basis functions are used for temporal discretization of the governing partial differential equations into a set of ordinary differential equations. The localized nature of Daubechies wavelet basis functions helps to rule out problems of SFE model due to periodicity assumption, especially during inverse Fourier transformation and back to time domain. The high accuracy of WSFE model is then evaluated by comparing its results with those of conventional finite element and SFE results. The effects of moving beam speed and axial tensile force on vibration and wave characteristics, and static and dynamic stabilities of moving beam are investigated.

Unbalance Response Analysis and Experimental Validation of an Ultra High Speed Motor-Generator for Microturbine Generators Considering Balancing

PubMed Central

Hong, Do-Kwan; Joo, Dae-Suk; Woo, Byung-Chul; Koo, Dae-Hyun; Ahn, Chan-Woo

2014-01-01

The objective of the present study was to deal with the rotordynamics of the rotor of an ultra-high speed PM type synchronous motor-generator for a 500 W rated micro gas turbine generator. This paper introduces dynamic analysis, and experiments on the motor-generator. The focus is placed on an analytical approach considering the mechanical dynamic problems. It is essential to deal with dynamic stability at ultra-high speeds. Unbalance response analysis is performed by calculating the unbalance with and without balancing using a balancing machine. Critical speed analysis is performed to determine the operating speed with sufficient separation margin. The unbalance response analysis is compared with the experimental results considering the balancing grade (ISO 1940-1) and predicted vibration displacement with and without balancing. Based on these results, a high-speed motor-generator was successfully developed. PMID:25177804

Distributed neural network control for adaptive synchronization of uncertain dynamical multiagent systems.

PubMed

Peng, Zhouhua; Wang, Dan; Zhang, Hongwei; Sun, Gang

2014-08-01

This paper addresses the leader-follower synchronization problem of uncertain dynamical multiagent systems with nonlinear dynamics. Distributed adaptive synchronization controllers are proposed based on the state information of neighboring agents. The control design is developed for both undirected and directed communication topologies without requiring the accurate model of each agent. This result is further extended to the output feedback case where a neighborhood observer is proposed based on relative output information of neighboring agents. Then, distributed observer-based synchronization controllers are derived and a parameter-dependent Riccati inequality is employed to prove the stability. This design has a favorable decouple property between the observer and the controller designs for nonlinear multiagent systems. For both cases, the developed controllers guarantee that the state of each agent synchronizes to that of the leader with bounded residual errors. Two illustrative examples validate the efficacy of the proposed methods.

Epicyclic helical channels for parametric resonance ionization cooling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johson, Rolland Paul; Derbenev, Yaroslav

Proposed next-generation muon colliders will require major technical advances to achieve rapid muon beam cooling requirements. Parametric-resonance Ionization Cooling (PIC) is proposed as the final 6D cooling stage of a high-luminosity muon collider. In PIC, a half-integer parametric resonance causes strong focusing of a muon beam at appropriately placed energy absorbers while ionization cooling limits the beam’s angular spread. Combining muon ionization cooling with parametric resonant dynamics in this way should then allow much smaller final transverse muon beam sizes than conventional ionization cooling alone. One of the PIC challenges is compensation of beam aberrations over a sufficiently wide parametermore » range while maintaining the dynamical stability with correlated behavior of the horizontal and vertical betatron motion and dispersion. We explore use of a coupling resonance to reduce the dimensionality of the problem and to shift the dynamics away from non-linear resonances. PIC simulations are presented.« less

Dynamic stabilization of an optomechanical oscillator

DTIC Science & Technology

2014-10-20

respectively. The proper frequency of the pendulum is ω0 = √ g/, where g is the gravitational acceleration and is the length of the pendulum . The...controlled experiments. In this paper we discuss one such situation, the dynamic stabilization of a mechanical system such as an inverted pendulum . The...quantumoptomechanics, macroscopic quantum system, dynamic stabilization, Kapitza pendulum REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S REPORT NUMBER(S

Loss of Consciousness Is Associated with Stabilization of Cortical Activity

PubMed Central

Solovey, Guillermo; Alonso, Leandro M.; Yanagawa, Toru; Fujii, Naotaka; Magnasco, Marcelo O.; Cecchi, Guillermo A.

2015-01-01

What aspects of neuronal activity distinguish the conscious from the unconscious brain? This has been a subject of intense interest and debate since the early days of neurophysiology. However, as any practicing anesthesiologist can attest, it is currently not possible to reliably distinguish a conscious state from an unconscious one on the basis of brain activity. Here we approach this problem from the perspective of dynamical systems theory. We argue that the brain, as a dynamical system, is self-regulated at the boundary between stable and unstable regimes, allowing it in particular to maintain high susceptibility to stimuli. To test this hypothesis, we performed stability analysis of high-density electrocorticography recordings covering an entire cerebral hemisphere in monkeys during reversible loss of consciousness. We show that, during loss of consciousness, the number of eigenmodes at the edge of instability decreases smoothly, independently of the type of anesthetic and specific features of brain activity. The eigenmodes drift back toward the unstable line during recovery of consciousness. Furthermore, we show that stability is an emergent phenomenon dependent on the correlations among activity in different cortical regions rather than signals taken in isolation. These findings support the conclusion that dynamics at the edge of instability are essential for maintaining consciousness and provide a novel and principled measure that distinguishes between the conscious and the unconscious brain. SIGNIFICANCE STATEMENT What distinguishes brain activity during consciousness from that observed during unconsciousness? Answering this question has proven difficult because neither consciousness nor lack thereof have universal signatures in terms of most specific features of brain activity. For instance, different anesthetics induce different patterns of brain activity. We demonstrate that loss of consciousness is universally and reliably associated with stabilization of cortical dynamics regardless of the specific activity characteristics. To give an analogy, our analysis suggests that loss of consciousness is akin to depressing the damper pedal on the piano, which makes the sounds dissipate quicker regardless of the specific melody being played. This approach may prove useful in detecting consciousness on the basis of brain activity under anesthesia and other settings. PMID:26224868

Loss of Consciousness Is Associated with Stabilization of Cortical Activity.

PubMed

Solovey, Guillermo; Alonso, Leandro M; Yanagawa, Toru; Fujii, Naotaka; Magnasco, Marcelo O; Cecchi, Guillermo A; Proekt, Alex

2015-07-29

What aspects of neuronal activity distinguish the conscious from the unconscious brain? This has been a subject of intense interest and debate since the early days of neurophysiology. However, as any practicing anesthesiologist can attest, it is currently not possible to reliably distinguish a conscious state from an unconscious one on the basis of brain activity. Here we approach this problem from the perspective of dynamical systems theory. We argue that the brain, as a dynamical system, is self-regulated at the boundary between stable and unstable regimes, allowing it in particular to maintain high susceptibility to stimuli. To test this hypothesis, we performed stability analysis of high-density electrocorticography recordings covering an entire cerebral hemisphere in monkeys during reversible loss of consciousness. We show that, during loss of consciousness, the number of eigenmodes at the edge of instability decreases smoothly, independently of the type of anesthetic and specific features of brain activity. The eigenmodes drift back toward the unstable line during recovery of consciousness. Furthermore, we show that stability is an emergent phenomenon dependent on the correlations among activity in different cortical regions rather than signals taken in isolation. These findings support the conclusion that dynamics at the edge of instability are essential for maintaining consciousness and provide a novel and principled measure that distinguishes between the conscious and the unconscious brain. What distinguishes brain activity during consciousness from that observed during unconsciousness? Answering this question has proven difficult because neither consciousness nor lack thereof have universal signatures in terms of most specific features of brain activity. For instance, different anesthetics induce different patterns of brain activity. We demonstrate that loss of consciousness is universally and reliably associated with stabilization of cortical dynamics regardless of the specific activity characteristics. To give an analogy, our analysis suggests that loss of consciousness is akin to depressing the damper pedal on the piano, which makes the sounds dissipate quicker regardless of the specific melody being played. This approach may prove useful in detecting consciousness on the basis of brain activity under anesthesia and other settings. Copyright © 2015 the authors 0270-6474/15/3510866-12$15.00/0.

Lateral Stability of a Dynamic Ram Air Cushion Vehicle

DOT National Transportation Integrated Search

1974-08-01

The lateral stability derivatives of a dynamic ram air cushion vehicle in a rectangular guideway were measured using a ship model towing tank. Lift and pitching moment are also reported. The primary lateral derivatives are all stabilizing, with signi...

Distributed formation control of nonholonomic autonomous vehicle via RBF neural network

NASA Astrophysics Data System (ADS)

Yang, Shichun; Cao, Yaoguang; Peng, Zhaoxia; Wen, Guoguang; Guo, Konghui

2017-03-01

In this paper, RBF neural network consensus-based distributed control scheme is proposed for nonholonomic autonomous vehicles in a pre-defined formation along the specified reference trajectory. A variable transformation is first designed to convert the formation control problem into a state consensus problem. Then, the complete dynamics of the vehicles including inertia, Coriolis, friction model and unmodeled bounded disturbances are considered, which lead to the formation unstable when the distributed kinematic controllers are proposed based on the kinematics. RBF neural network torque controllers are derived to compensate for them. Some sufficient conditions are derived to accomplish the asymptotically stability of the systems based on algebraic graph theory, matrix theory, and Lyapunov theory. Finally, simulation examples illustrate the effectiveness of the proposed controllers.

Nonlinear dynamics of mini-satellite respinup by weak internal controllable torques

NASA Astrophysics Data System (ADS)

Somov, Yevgeny

2014-12-01

Contemporary space engineering advanced new problem before theoretical mechanics and motion control theory: a spacecraft directed respinup by the weak restricted control internal forces. The paper presents some results on this problem, which is very actual for energy supply of information mini-satellites (for communication, geodesy, radio- and opto-electronic observation of the Earth et al.) with electro-reaction plasma thrusters and gyro moment cluster based on the reaction wheels or the control moment gyros. The solution achieved is based on the methods for synthesis of nonlinear robust control and on rigorous analytical proof for the required spacecraft rotation stability by Lyapunov function method. These results were verified by a computer simulation of strongly nonlinear oscillatory processes at respinuping of a flexible spacecraft.

Precise computer controlled positioning of robot end effectors using force sensors

NASA Technical Reports Server (NTRS)

Shieh, L. S.; Mcinnis, B. C.; Wang, J. C.

1988-01-01

A thorough study of combined position/force control using sensory feedback for a one-dimensional manipulator model, which may count for the spacecraft docking problem or be extended to the multi-joint robot manipulator problem, was performed. The additional degree of freedom introduced by the compliant force sensor is included in the system dynamics in the design of precise position control. State feedback based on the pole placement method and with integral control is used to design the position controller. A simple constant gain force controller is used as an example to illustrate the dependence of the stability and steady-state accuracy of the overall position/force control upon the design of the inner position controller. Supportive simulation results are also provided.

Homeostatic Agent for General Environment

NASA Astrophysics Data System (ADS)

Yoshida, Naoto

2018-03-01

One of the essential aspect in biological agents is dynamic stability. This aspect, called homeostasis, is widely discussed in ethology, neuroscience and during the early stages of artificial intelligence. Ashby's homeostats are general-purpose learning machines for stabilizing essential variables of the agent in the face of general environments. However, despite their generality, the original homeostats couldn't be scaled because they searched their parameters randomly. In this paper, first we re-define the objective of homeostats as the maximization of a multi-step survival probability from the view point of sequential decision theory and probabilistic theory. Then we show that this optimization problem can be treated by using reinforcement learning algorithms with special agent architectures and theoretically-derived intrinsic reward functions. Finally we empirically demonstrate that agents with our architecture automatically learn to survive in a given environment, including environments with visual stimuli. Our survival agents can learn to eat food, avoid poison and stabilize essential variables through theoretically-derived single intrinsic reward formulations.

Instabilities and Turbulence Generation by Pick-Up Ion Distributions in the Outer Heliosheath

NASA Astrophysics Data System (ADS)

Weichman, K.; Roytershteyn, V.; Delzanno, G. L.; Pogorelov, N.

2017-12-01

Pick-up ions (PUIs) play a significant role in the dynamics of the heliosphere. One problem that has attracted significant attention is the stability of ring-like distributions of PUIs and the electromagnetic fluctuations that could be generated by PUI distributions. For example, PUI stability is relevant to theories attempting to identify the origins of the IBEX ribbon. PUIs have previously been investigated by linear stability analysis of model (e.g. Gaussian) rings and corresponding computer simulations. The majority of these simulations utilized particle-in-cell methods which suffer from accuracy limitations imposed by the statistical noise associated with representing the plasma by a relatively small number of computational particles. In this work, we utilize highly accurate spectral Vlasov simulations conducted using the fully kinetic implicit code SPS (Spectral Plasma Solver) to investigate the PUI distributions inferred from a global heliospheric model (Heerikhuisen et al., 2016). Results are compared with those obtained by hybrid and fully kinetic particle-in-cell methods.

Transient Cognitive Dynamics, Metastability, and Decision Making

PubMed Central

Rabinovich, Mikhail I.; Huerta, Ramón; Varona, Pablo; Afraimovich, Valentin S.

2008-01-01

The idea that cognitive activity can be understood using nonlinear dynamics has been intensively discussed at length for the last 15 years. One of the popular points of view is that metastable states play a key role in the execution of cognitive functions. Experimental and modeling studies suggest that most of these functions are the result of transient activity of large-scale brain networks in the presence of noise. Such transients may consist of a sequential switching between different metastable cognitive states. The main problem faced when using dynamical theory to describe transient cognitive processes is the fundamental contradiction between reproducibility and flexibility of transient behavior. In this paper, we propose a theoretical description of transient cognitive dynamics based on the interaction of functionally dependent metastable cognitive states. The mathematical image of such transient activity is a stable heteroclinic channel, i.e., a set of trajectories in the vicinity of a heteroclinic skeleton that consists of saddles and unstable separatrices that connect their surroundings. We suggest a basic mathematical model, a strongly dissipative dynamical system, and formulate the conditions for the robustness and reproducibility of cognitive transients that satisfy the competing requirements for stability and flexibility. Based on this approach, we describe here an effective solution for the problem of sequential decision making, represented as a fixed time game: a player takes sequential actions in a changing noisy environment so as to maximize a cumulative reward. As we predict and verify in computer simulations, noise plays an important role in optimizing the gain. PMID:18452000

Stabilization of dynamics of oscillatory systems by nonautonomous perturbation.

PubMed

Lucas, Maxime; Newman, Julian; Stefanovska, Aneta

2018-04-01

Synchronization and stability under periodic oscillatory driving are well understood, but little is known about the effects of aperiodic driving, despite its abundance in nature. Here, we consider oscillators subject to driving with slowly varying frequency, and investigate both short-term and long-term stability properties. For a phase oscillator, we find that, counterintuitively, such variation is guaranteed to enlarge the Arnold tongue in parameter space. Using analytical and numerical methods that provide information on time-variable dynamical properties, we find that the growth of the Arnold tongue is specifically due to the growth of a region of intermittent synchronization where trajectories alternate between short-term stability and short-term neutral stability, giving rise to stability on average. We also present examples of higher-dimensional nonlinear oscillators where a similar stabilization phenomenon is numerically observed. Our findings help support the case that in general, deterministic nonautonomous perturbation is a very good candidate for stabilizing complex dynamics.

Stabilization of dynamics of oscillatory systems by nonautonomous perturbation

NASA Astrophysics Data System (ADS)

Lucas, Maxime; Newman, Julian; Stefanovska, Aneta

2018-04-01

Synchronization and stability under periodic oscillatory driving are well understood, but little is known about the effects of aperiodic driving, despite its abundance in nature. Here, we consider oscillators subject to driving with slowly varying frequency, and investigate both short-term and long-term stability properties. For a phase oscillator, we find that, counterintuitively, such variation is guaranteed to enlarge the Arnold tongue in parameter space. Using analytical and numerical methods that provide information on time-variable dynamical properties, we find that the growth of the Arnold tongue is specifically due to the growth of a region of intermittent synchronization where trajectories alternate between short-term stability and short-term neutral stability, giving rise to stability on average. We also present examples of higher-dimensional nonlinear oscillators where a similar stabilization phenomenon is numerically observed. Our findings help support the case that in general, deterministic nonautonomous perturbation is a very good candidate for stabilizing complex dynamics.

Falling, flapping, flying, swimming,...: High-Re fluid-solid interactions with vortex shedding

NASA Astrophysics Data System (ADS)

Michelin, Sebastien Honore Roland

The coupling between the motion of a solid body and the dynamics of the surrounding flow is essential to the understanding of a large number of engineering and physical problems, from the stability of a slender structure exposed to the wind to the locomotion of insects, birds and fishes. Because of the strong coupling on a moving boundary of the equations for the solid and fluid, the simulation of such problems is computationally challenging and expensive. This justifies the development of simplified models for the fluid-solid interactions to study their physical properties and behavior. This dissertation proposes a reduced-order model for the interaction of a sharp-edged solid body with a strongly unsteady high Reynolds number flow. In such a case, viscous forces in the fluid are often negligible compared to the fluid inertia or the pressure forces, and the thin boundary layers separate from the solid at the edges, leading to the shedding of large and persistent vortices in the solid's wake. A general two-dimensional framework is presented based on complex potential flow theory. The formation of the solid's vortical wake is accounted for by the shedding of point vortices with unsteady intensity from the solid's sharp edges, and the fluid-solid problem is reformulated exclusively as a solid-vortex interaction problem. In the case of a rigid solid body, the coupled problem is shown to reduce to a set of non-linear ordinary differential equations. This model is used to study the effect of vortex shedding on the stability of falling objects. The solid-vortex model is then generalized to study the fluttering instability and non-linear flapping dynamics of flexible plates or flags. The uttering instability and resulting flapping motion result from the competing effects of the fluid forcing and of the solid's flexural rigidity and inertia. Finally, the solid-vortex model is applied to the study of the fundamental effect of bending rigidity on the flapping performance of flapping appendages such as insect wings or fish fins.

Molecular dynamics study of thermodynamic stability and dynamics of [Li(glyme)]+ complex in lithium-glyme solvate ionic liquids

NASA Astrophysics Data System (ADS)

Shinoda, Wataru; Hatanaka, Yuta; Hirakawa, Masashi; Okazaki, Susumu; Tsuzuki, Seiji; Ueno, Kazuhide; Watanabe, Masayoshi

2018-05-01

Equimolar mixtures of glymes and organic lithium salts are known to produce solvate ionic liquids, in which the stability of the [Li(glyme)]+ complex plays an important role in determining the ionic dynamics. Since these mixtures have attractive physicochemical properties for application as electrolytes, it is important to understand the dependence of the stability of the [Li(glyme)]+ complex on the ion dynamics. A series of microsecond molecular dynamics simulations has been conducted to investigate the dynamic properties of these solvate ionic liquids. Successful solvate ionic liquids with high stability of the [Li(glyme)]+ complex have been shown to have enhanced ion dynamics. Li-glyme pair exchange rarely occurs: its characteristic time is longer than that of ion diffusion by one or two orders of magnitude. Li-glyme pair exchange most likely occurs through cluster formation involving multiple [Li(glyme)]+ pairs. In this process, multiple exchanges likely take place in a concerted manner without the production of energetically unfavorable free glyme or free Li+ ions.

Chatter reduction in boring process by using piezoelectric shunt damping with experimental verification

NASA Astrophysics Data System (ADS)

Yigit, Ufuk; Cigeroglu, Ender; Budak, Erhan

2017-09-01

Chatter is a self-excited type of vibration that develops during machining due to process-structure dynamic interactions resulting in modulated chip thickness. Chatter is an important problem as it results in poor surface quality, reduced productivity and tool life. The stability of a cutting process is strongly influenced by the frequency response function (FRF) at the cutting point. In this study, the effect of piezoelectric shunt damping on chatter vibrations in a boring process is studied. In piezoelectric shunt damping method, an electrical impedance is connected to a piezoelectric transducer which is bonded on cutting tool. Electrical impedance of the circuit consisting of piezoceramic transducer and passive shunt is tuned to the desired natural frequency of the cutting tool in order to maximize damping. The optimum damping is achieved in analytical and finite element models (FEM) by using a genetic algorithm focusing on the real part of the tool point FRF rather than the amplitude. Later, a practical boring bar is considered where the optimum circuit parameters are obtained by the FEM. Afterwards, the effect of the optimized piezoelectric shunt damping on the dynamic rigidity and absolute stability limit of the cutting process are investigated experimentally by modal analysis and cutting tests. It is both theoretically and experimentally shown that application of piezoelectric shunt damping results in a significant increase in the absolute stability limit in boring operations.

Dynamics of a distributed drill string system: Characteristic parameters and stability maps

NASA Astrophysics Data System (ADS)

Aarsnes, Ulf Jakob F.; van de Wouw, Nathan

2018-03-01

This paper involves the dynamic (stability) analysis of distributed drill-string systems. A minimal set of parameters characterizing the linearized, axial-torsional dynamics of a distributed drill string coupled through the bit-rock interaction is derived. This is found to correspond to five parameters for a simple drill string and eight parameters for a two-sectioned drill-string (e.g., corresponding to the pipe and collar sections of a drilling system). These dynamic characterizations are used to plot the inverse gain margin of the system, parametrized in the non-dimensional parameters, effectively creating a stability map covering the full range of realistic physical parameters. This analysis reveals a complex spectrum of dynamics not evident in stability analysis with lumped models, thus indicating the importance of analysis using distributed models. Moreover, it reveals trends concerning stability properties depending on key system parameters useful in the context of system and control design aiming at the mitigation of vibrations.

Biomechanical assessment of dynamic balance: Specificity of different balance tests.

PubMed

Ringhof, Steffen; Stein, Thorsten

2018-04-01

Dynamic balance is vitally important for most sports and activities of daily living, so the assessment of dynamic stability has become an important issue. In consequence, a large number of balance tests have been developed. However, it is not yet known whether these tests (i) measure the same construct and (ii) can differentiate between athletes with different balance expertise. We therefore studied three common dynamic balance tests: one-leg jump landings, Posturomed perturbations and simulated forward falls. Participants were 24 healthy young females in regular training in either gymnastics (n = 12) or swimming (n = 12). In each of the tests, the participants were instructed to recover balance as quickly as possible. Dynamic stability was computed by time to stabilization and margin of stability, deduced from force plates and motion capture respectively. Pearson's correlations between the dynamic balance tests found no significant associations between the respective dynamic stability measures. Furthermore, independent t-tests indicated that only jump landings could properly distinguish between both groups of athletes. In essence, the different dynamic balance tests applied did not measure the same construct but rather task-specific skills, each of which depends on multifactorial internal and external constraints. Our study therefore contradicts the traditional view of considering balance as a general ability, and reinforces that dynamic balance measures are not interchangeable. This highlights the importance of selecting appropriate balance tests. Copyright © 2018 Elsevier B.V. All rights reserved.

The Discriminant Value of Phase-Dependent Local Dynamic Stability of Daily Life Walking in Older Adult Community-Dwelling Fallers and Nonfallers

PubMed Central

Ihlen, Espen A. F.; Weiss, Aner; Helbostad, Jorunn L.; Hausdorff, Jeffrey M.

2015-01-01

The present study compares phase-dependent measures of local dynamic stability of daily life walking with 35 conventional gait features in their ability to discriminate between community-dwelling older fallers and nonfallers. The study reanalyzes 3D-acceleration data of 3-day daily life activity from 39 older people who reported less than 2 falls during one year and 31 who reported two or more falls. Phase-dependent local dynamic stability was defined for initial perturbation at 0%, 20%, 40%, 60%, and 80% of the step cycle. A partial least square discriminant analysis (PLS-DA) was used to compare the discriminant abilities of phase-dependent local dynamic stability with the discriminant abilities of 35 conventional gait features. The phase-dependent local dynamic stability λ at 0% and 60% of the step cycle discriminated well between fallers and nonfallers (AUC = 0.83) and was significantly larger (p < 0.01) for the nonfallers. Furthermore, phase-dependent λ discriminated as well between fallers and nonfallers as all other gait features combined. The present result suggests that phase-dependent measures of local dynamic stability of daily life walking might be of importance for further development in early fall risk screening tools. PMID:26491669

Dynamic postural stability for double-leg drop landing.

PubMed

Niu, Wenxin; Zhang, Ming; Fan, Yubo; Zhao, Qinping

2013-01-01

Dynamic postural stability has been widely studied for single-leg landing, but seldom considered for double-leg landing. This study aimed to evaluate the dynamic postural stability and the influence mechanism of muscle activities during double-leg drop landing. Eight recreationally active males and eight recreationally active females participated in this study and dropped individually from three heights (0.32 m, 0.52 m, and 0.72 m). Ground reaction force was recorded to calculate the time to stabilisation. Electromyographic activities were recorded for selected lower-extremity muscles. A multivariate analysis of variance was carried out and no significant influence was found in time to stabilisation between genders or limb laterals (P > 0.05). With increasing drop height, time to stabilisation decreased significantly in two horizontal directions and the lower-extremity muscle activities were enhanced. Vertical time to stabilisation was not significantly influenced by drop height. Dynamic postural stability improved by neuromuscular change more than that required due to the increase of drop height. Double-leg landing on level ground is a stable movement, and the body would often be injured before dynamic postural stability is impaired. It is understandable to protect tissues from mechanical injuries by the sacrifice of certain dynamic postural stability in the design of protective devices or athlete training.

Investigations Into Internal and External Aspects of Dynamic Agent-Environment Couplings

NASA Astrophysics Data System (ADS)

Dautenhahn, Kerstin

This paper originates from my work on `social agents'. An issue which I consider important to this kind of research is the dynamic coupling of an agent with its social and non-social environment. I hypothesize `internal dynamics' inside an agent as a basic step towards understanding. The paper therefore focuses on the internal and external dynamics which couple an agent to its environment. The issue of embodiment in animals and artifacts and its relation to `social dynamics' is discussed first. I argue that embodiment is linked to a concept of a body and is not necessarily given when running a control program on robot hardware. I stress the individual characteristics of an embodied cognitive system, as well as its social embeddedness. I outline the framework of a physical-psychological state space which changes dynamically in a self-modifying way as a holistic approach towards embodied human and artificial cognition. This framework is meant to discuss internal and external dynamics of an embodied, natural or artificial agent. In order to stress the importance of a dynamic memory I introduce the concept of an `autobiographical agent'. The second part of the paper gives an example of the implementation of a physical agent, a robot, which is dynamically coupled to its environment by balancing on a seesaw. For the control of the robot a behavior-oriented approach using the dynamical systems metaphor is used. The problem is studied through building a complete and co-adapted robot-environment system. A seesaw which varies its orientation with one or two degrees of freedom is used as the artificial `habitat'. The problem of stabilizing the body axis by active motion on a seesaw is solved by using two inclination sensors and a parallel, behavior-oriented control architecture. Some experiments are described which demonstrate the exploitation of the dynamics of the robot-environment system.

Dynamic water patterns change the stability of the collapsed filter conformation of the KcsA K+ channel

PubMed Central

2017-01-01

The selectivity filter of the KcsA K+ channel has two typical conformations—the conductive and the collapsed conformations, respectively. The transition from the conductive to the collapsed filter conformation can represent the process of inactivation that depends on many environmental factors. Water molecules permeating behind the filter can influence the collapsed filter stability. Here we perform the molecular dynamics simulations to study the stability of the collapsed filter of the KcsA K+ channel under the different water patterns. We find that the water patterns are dynamic behind the collapsed filter and the filter stability increases with the increasing number of water molecules. In addition, the stability increases significantly when water molecules distribute uniformly behind the four monomeric filter chains, and the stability is compromised if water molecules only cluster behind one or two adjacent filter chains. The altered filter stabilities thus suggest that the collapsed filter can inactivate gradually under the dynamic water patterns. We also demonstrate how the different water patterns affect the filter recovery from the collapsed conformation. PMID:29049423

Dynamic water patterns change the stability of the collapsed filter conformation of the KcsA K+ channel.

PubMed

Wu, Di

2017-01-01

The selectivity filter of the KcsA K+ channel has two typical conformations-the conductive and the collapsed conformations, respectively. The transition from the conductive to the collapsed filter conformation can represent the process of inactivation that depends on many environmental factors. Water molecules permeating behind the filter can influence the collapsed filter stability. Here we perform the molecular dynamics simulations to study the stability of the collapsed filter of the KcsA K+ channel under the different water patterns. We find that the water patterns are dynamic behind the collapsed filter and the filter stability increases with the increasing number of water molecules. In addition, the stability increases significantly when water molecules distribute uniformly behind the four monomeric filter chains, and the stability is compromised if water molecules only cluster behind one or two adjacent filter chains. The altered filter stabilities thus suggest that the collapsed filter can inactivate gradually under the dynamic water patterns. We also demonstrate how the different water patterns affect the filter recovery from the collapsed conformation.

STARS: An integrated general-purpose finite element structural, aeroelastic, and aeroservoelastic analysis computer program

NASA Technical Reports Server (NTRS)

Gupta, Kajal K.

1991-01-01

The details of an integrated general-purpose finite element structural analysis computer program which is also capable of solving complex multidisciplinary problems is presented. Thus, the SOLIDS module of the program possesses an extensive finite element library suitable for modeling most practical problems and is capable of solving statics, vibration, buckling, and dynamic response problems of complex structures, including spinning ones. The aerodynamic module, AERO, enables computation of unsteady aerodynamic forces for both subsonic and supersonic flow for subsequent flutter and divergence analysis of the structure. The associated aeroservoelastic analysis module, ASE, effects aero-structural-control stability analysis yielding frequency responses as well as damping characteristics of the structure. The program is written in standard FORTRAN to run on a wide variety of computers. Extensive graphics, preprocessing, and postprocessing routines are also available pertaining to a number of terminals.

Numerical study of the geometry of the phase space of the Augmented Hill Three-Body problem

NASA Astrophysics Data System (ADS)

Farrés, Ariadna; Jorba, Àngel; Mondelo, Josep-Maria

2017-09-01

The Augmented Hill Three-Body problem is an extension of the classical Hill problem that, among other applications, has been used to model the motion of a solar sail around an asteroid. This model is a 3 degrees of freedom (3DoF) Hamiltonian system that depends on four parameters. This paper describes the bounded motions (periodic orbits and invariant tori) in an extended neighbourhood of some of the equilibrium points of the model. An interesting feature is the existence of equilibrium points with a 1:1 resonance, whose neighbourhood we also describe. The main tools used are the computation of periodic orbits (including their stability and bifurcations), the reduction of the Hamiltonian to centre manifolds at equilibria, and the numerical approximation of invariant tori. It is remarkable how the combination of these techniques allows the description of the dynamics of a 3DoF Hamiltonian system.

A space-frequency multiplicative regularization for force reconstruction problems

NASA Astrophysics Data System (ADS)

Aucejo, M.; De Smet, O.

2018-05-01

Dynamic forces reconstruction from vibration data is an ill-posed inverse problem. A standard approach to stabilize the reconstruction consists in using some prior information on the quantities to identify. This is generally done by including in the formulation of the inverse problem a regularization term as an additive or a multiplicative constraint. In the present article, a space-frequency multiplicative regularization is developed to identify mechanical forces acting on a structure. The proposed regularization strategy takes advantage of one's prior knowledge of the nature and the location of excitation sources, as well as that of their spectral contents. Furthermore, it has the merit to be free from the preliminary definition of any regularization parameter. The validity of the proposed regularization procedure is assessed numerically and experimentally. It is more particularly pointed out that properly exploiting the space-frequency characteristics of the excitation field to identify can improve the quality of the force reconstruction.

Nonlinear problems of the theory of heterogeneous slightly curved shells

NASA Technical Reports Server (NTRS)

Kantor, B. Y.

1973-01-01

An account if given of the variational method of the solution of physically and geometrically nonlinear problems of the theory of heterogeneous slightly curved shells. Examined are the bending and supercritical behavior of plates and conical and spherical cupolas of variable thickness in a temperature field, taking into account the dependence of the elastic parameters on temperature. The bending, stability in general and load-bearing capacity of flexible isotropic elastic-plastic shells with different criteria of plasticity, taking into account compressibility and hardening. The effect of the plastic heterogeneity caused by heat treatment, surface work hardening and irradiation by fast neutron flux is investigated. Some problems of the dynamic behavior of flexible shells are solved. Calculations are performed in high approximations. Considerable attention is given to the construction of a machine algorithm and to the checking of the convergence of iterative processes.

Research on Optimization of Pooling System and Its Application in Drug Supply Chain Based on Big Data Analysis

PubMed Central

2017-01-01

Reform of drug procurement is being extensively implemented and expanded in China, especially in today's big data environment. However, the pattern of supply mode innovation lags behind procurement improvement. Problems in financial strain and supply break frequently occur, which affect the stability of drug supply. Drug Pooling System is proposed and applied in a few pilot cities to resolve these problems. From the perspective of supply chain, this study analyzes the process of setting important parameters and sets out the tasks of involved parties in a pooling system according to the issues identified in the pilot run. The approach is based on big data analysis and simulation using system dynamic theory and modeling of Vensim software to optimize system performance. This study proposes a theoretical framework to resolve problems and attempts to provide a valuable reference for future application of pooling systems. PMID:28293258

The Incidence of Adjacent Segment Degeneration after the Use of a Versatile Dynamic Hybrid Stabilization Device in Lumbar Stenosis: Results of a 5–8-Year Follow-up

PubMed Central

Dobran, Mauro; Esposito, Domenico Paolo; Gladi, Maurizio; Scerrati, Massimo; Iacoangeli, Maurizio

2018-01-01

Study Design Retrospective study with long-term follow-up. Purpose To evaluate the long-term incidence of adjacent segment degeneration (ASD) and clinical outcomes in a consecutive series of patients who underwent spinal decompression associated with dynamic or hybrid stabilization with a Flex+TM stabilization system (SpineVision, Antony, France) for lumbar spinal stenosis. Overview of Literature The incidence of ASD and clinical outcomes following dynamic or hybrid stabilization with the Flex+TM system used for lumbar spinal stenosis have not been well investigated. Methods Twenty-one patients with lumbar stenosis and probable post-decompressive spinal instability underwent decompressive laminectomy followed by spinal stabilization using the Flex+TM stabilization system. The indication for a mono-level dynamic stabilization was a preoperative magnetic resonance imaging (MRI) demonstrating evidence of severe disc disease associated with severe spinal stenosis. The hybrid stabilization (rigid-dynamic) system was used for multilevel laminectomies with associated initial degenerative scoliosis, first-grade spondylolisthesis, or rostral pathology. Results The improvement in Visual Analog Scale and Oswestry Disability Index scores at follow-up were statistically significant (p<0.0001 and p<0.0001, respectively). At the 5–8-year follow-up, clinical examination, MRI, and X-ray findings showed an ASD complication with pain and disability in one of 21 patients. The clinical outcomes were similar in patients treated with dynamic or hybrid fixation. Conclusions Patients treated with laminectomy and Flex+TM stabilization presented a satisfactory clinical outcome after 5–8 years of follow-up, and ASD incidence in our series was 4.76% (one patient out of 21). We are aware that this is a small series, but our long-term follow-up may be sufficient to contribute to the expanding body of literature on the development of symptomatic ASD associated with dynamic or hybrid fixation. PMID:29713407

Signal Processing Methods for Liquid Rocket Engine Combustion Stability Assessments

NASA Technical Reports Server (NTRS)

Kenny, R. Jeremy; Lee, Erik; Hulka, James R.; Casiano, Matthew

2011-01-01

The J2X Gas Generator engine design specifications include dynamic, spontaneous, and broadband combustion stability requirements. These requirements are verified empirically based high frequency chamber pressure measurements and analyses. Dynamic stability is determined with the dynamic pressure response due to an artificial perturbation of the combustion chamber pressure (bomb testing), and spontaneous and broadband stability are determined from the dynamic pressure responses during steady operation starting at specified power levels. J2X Workhorse Gas Generator testing included bomb tests with multiple hardware configurations and operating conditions, including a configuration used explicitly for engine verification test series. This work covers signal processing techniques developed at Marshall Space Flight Center (MSFC) to help assess engine design stability requirements. Dynamic stability assessments were performed following both the CPIA 655 guidelines and a MSFC in-house developed statistical-based approach. The statistical approach was developed to better verify when the dynamic pressure amplitudes corresponding to a particular frequency returned back to pre-bomb characteristics. This was accomplished by first determining the statistical characteristics of the pre-bomb dynamic levels. The pre-bomb statistical characterization provided 95% coverage bounds; these bounds were used as a quantitative measure to determine when the post-bomb signal returned to pre-bomb conditions. The time for post-bomb levels to acceptably return to pre-bomb levels was compared to the dominant frequency-dependent time recommended by CPIA 655. Results for multiple test configurations, including stable and unstable configurations, were reviewed. Spontaneous stability was assessed using two processes: 1) characterization of the ratio of the peak response amplitudes to the excited chamber acoustic mode amplitudes and 2) characterization of the variability of the peak response's frequency over the test duration. This characterization process assists in evaluating the discreteness of a signal as well as the stability of the chamber response. Broadband stability was assessed using a running root-mean-square evaluation. These techniques were also employed, in a comparative analysis, on available Fastrac data, and these results are presented here.

Development of Quadratic Programming Algorithm Based on Interior Point Method with Estimation Mechanism of Active Constraints

NASA Astrophysics Data System (ADS)

Hashimoto, Hiroyuki; Takaguchi, Yusuke; Nakamura, Shizuka

Instability of calculation process and increase of calculation time caused by increasing size of continuous optimization problem remain the major issues to be solved to apply the technique to practical industrial systems. This paper proposes an enhanced quadratic programming algorithm based on interior point method mainly for improvement of calculation stability. The proposed method has dynamic estimation mechanism of active constraints on variables, which fixes the variables getting closer to the upper/lower limit on them and afterwards releases the fixed ones as needed during the optimization process. It is considered as algorithm-level integration of the solution strategy of active-set method into the interior point method framework. We describe some numerical results on commonly-used bench-mark problems called “CUTEr” to show the effectiveness of the proposed method. Furthermore, the test results on large-sized ELD problem (Economic Load Dispatching problems in electric power supply scheduling) are also described as a practical industrial application.

Artificial Neural Network Based Mission Planning Mechanism for Spacecraft

NASA Astrophysics Data System (ADS)

Li, Zhaoyu; Xu, Rui; Cui, Pingyuan; Zhu, Shengying

2018-04-01

The ability to plan and react fast in dynamic space environments is central to intelligent behavior of spacecraft. For space and robotic applications, many planners have been used. But it is difficult to encode the domain knowledge and directly use existing techniques such as heuristic to improve the performance of the application systems. Therefore, regarding planning as an advanced control problem, this paper first proposes an autonomous mission planning and action selection mechanism through a multiple layer perceptron neural network approach to select actions in planning process and improve efficiency. To prove the availability and effectiveness, we use autonomous mission planning problems of the spacecraft, which is a sophisticated system with complex subsystems and constraints as an example. Simulation results have shown that artificial neural networks (ANNs) are usable for planning problems. Compared with the existing planning method in EUROPA, the mechanism using ANNs is more efficient and can guarantee stable performance. Therefore, the mechanism proposed in this paper is more suitable for planning problems of spacecraft that require real time and stability.

Perspective: Memcomputing: Leveraging memory and physics to compute efficiently

NASA Astrophysics Data System (ADS)

Di Ventra, Massimiliano; Traversa, Fabio L.

2018-05-01

It is well known that physical phenomena may be of great help in computing some difficult problems efficiently. A typical example is prime factorization that may be solved in polynomial time by exploiting quantum entanglement on a quantum computer. There are, however, other types of (non-quantum) physical properties that one may leverage to compute efficiently a wide range of hard problems. In this perspective, we discuss how to employ one such property, memory (time non-locality), in a novel physics-based approach to computation: Memcomputing. In particular, we focus on digital memcomputing machines (DMMs) that are scalable. DMMs can be realized with non-linear dynamical systems with memory. The latter property allows the realization of a new type of Boolean logic, one that is self-organizing. Self-organizing logic gates are "terminal-agnostic," namely, they do not distinguish between the input and output terminals. When appropriately assembled to represent a given combinatorial/optimization problem, the corresponding self-organizing circuit converges to the equilibrium points that express the solutions of the problem at hand. In doing so, DMMs take advantage of the long-range order that develops during the transient dynamics. This collective dynamical behavior, reminiscent of a phase transition, or even the "edge of chaos," is mediated by families of classical trajectories (instantons) that connect critical points of increasing stability in the system's phase space. The topological character of the solution search renders DMMs robust against noise and structural disorder. Since DMMs are non-quantum systems described by ordinary differential equations, not only can they be built in hardware with the available technology, they can also be simulated efficiently on modern classical computers. As an example, we will show the polynomial-time solution of the subset-sum problem for the worst cases, and point to other types of hard problems where simulations of DMMs' equations of motion on classical computers have already demonstrated substantial advantages over traditional approaches. We conclude this article by outlining further directions of study.

Robust controller designs for second-order dynamic system: A virtual passive approach

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Phan, Minh

1990-01-01

A robust controller design is presented for second-order dynamic systems. The controller is model-independent and itself is a virtual second-order dynamic system. Conditions on actuator and sensor placements are identified for controller designs that guarantee overall closed-loop stability. The dynamic controller can be viewed as a virtual passive damping system that serves to stabilize the actual dynamic system. The control gains are interpreted as virtual mass, spring, and dashpot elements that play the same roles as actual physical elements in stability analysis. Position, velocity, and acceleration feedback are considered. Simple examples are provided to illustrate the physical meaning of this controller design.

Non-Newtonian Hele-Shaw Flow and the Saffman-Taylor Instability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kondic, L.; Shelley, M.J.; Palffy-Muhoray, P.

We explore the Saffman-Taylor instability of a gas bubble expanding into a shear thinning liquid in a radial Hele-Shaw cell. Using Darcy{close_quote}s law generalized for non-Newtonian fluids, we perform simulations of the full dynamical problem. The simulations show that shear thinning significantly influences the developing interfacial patterns. Shear thinning can suppress tip splitting, and produce fingers which oscillate during growth and shed side branches. Emergent length scales show reasonable agreement with a general linear stability analysis. {copyright} {ital 1998} {ital The American Physical Society}

Parallel aeroelastic computations for wing and wing-body configurations

NASA Technical Reports Server (NTRS)

Byun, Chansup

1994-01-01

The objective of this research is to develop computationally efficient methods for solving fluid-structural interaction problems by directly coupling finite difference Euler/Navier-Stokes equations for fluids and finite element dynamics equations for structures on parallel computers. This capability will significantly impact many aerospace projects of national importance such as Advanced Subsonic Civil Transport (ASCT), where the structural stability margin becomes very critical at the transonic region. This research effort will have direct impact on the High Performance Computing and Communication (HPCC) Program of NASA in the area of parallel computing.

Transverse and Quantum Effects in Light Control by Light; (A) Parallel Beams: Pump Dynamics for Three Level Superfluorescence; and (B) Counterflow Beams: An Algorithm for Transverse, Full Transient Effects in Optical Bi-Stability in a Fabryperot Cavity.

DTIC Science & Technology

1983-01-01

The resolution of the compu- and also leads to an expression for "dz,"*. tational grid is thereby defined according to e the actual requirements of...computational economy are achieved simultaneously by redistributing the computational grid points according to the physical requirements of the problem...computational Eulerian grid points according to implemented using a two-dimensionl time- the physical requirements of the nonlinear dependent finite

Stable adaptive neurocontrollers for spacecraft and space robots

NASA Technical Reports Server (NTRS)

Sanner, Robert M.

1995-01-01

This paper reviews recently developed techniques of adaptive nonlinear control using neural networks, and demonstrates their application to two important practical problems in orbital operations. An adaptive neurocontroller is first developed for spacecraft attitude control applications, and then the same design, slightly modified, is shown to be effective in the control of free-floating orbital manipulators. The algorithms discussed have guaranteed stability and convergence properties, and thus constitute viable alternatives to existing control methodologies. Simulation results are presented demonstrating the performance of each algorithm with representative dynamic models.

Enabling Microscopic Simulators to Perform System Level Tasks: A System-Identification Based, Closure-on-Demand Toolkit for Multiscale Simulation Stability/Bifurcation Analysis, Optimization and Control

DTIC Science & Technology

2006-10-01

The objective was to construct a bridge between existing and future microscopic simulation codes ( kMC , MD, MC, BD, LB etc.) and traditional, continuum...kinetic Monte Carlo, kMC , equilibrium MC, Lattice-Boltzmann, LB, Brownian Dynamics, BD, or general agent-based, AB) simulators. It also, fortuitously...cond-mat/0310460 at arXiv.org. 27. Coarse Projective kMC Integration: Forward/Reverse Initial and Boundary Value Problems", R. Rico-Martinez, C. W

End-State Relative Equilibria in the Sphere-Restricted Full Three-Body Problem

NASA Astrophysics Data System (ADS)

Gabriel, Travis; Scheeres, Daniel J.

2015-05-01

The Sphere-Restricted Full Three-Body Problem studies the motion of three finite density spheres as they interact under surface and gravitational forces. When accounting for the dissipation of energy, full-body systems may achieve minimum energy states that are unatainable in the classic treatment of the N-Body Problem. This serves as a simple model for the mechanics of rubble pile asteroids, interacting grains in a protoplanetary disk, and potentially the interactions of planetary ring particles. Previous studies of this problem have been performed in the case where the three spheres are of equal size and mass, with all possible relative equilibria and their stability having been identified as a function of the total angular momentum of the system. These studies uncovered that at certain levels of angular momentum there exists more than one stable relative equilibrium state. Thus a question of interest is which of these states a dissipative system would preferentially settle in provided some domain of initial conditions, and whether this would be a function of the dissipation parameters. Using perfectly-rigid dynamics, three-equal-sphere systems are simulated in a purpose-written C-based code to uncover these details. Results from this study are relevant to the mechanics and dynamics in small solar system bodies where relative forces are not great enough to compromise the rigidity of the constituents.

Intrarater test-retest reliability of static and dynamic stability indexes measurement using the Biodex Stability System during unilateral stance.

PubMed

Arifin, Nooranida; Abu Osman, Noor Azuan; Wan Abas, Wan Abu Bakar

2014-04-01

The measurements of postural balance often involve measurement error, which affects the analysis and interpretation of the outcomes. In most of the existing clinical rehabilitation research, the ability to produce reliable measures is a prerequisite for an accurate assessment of an intervention after a period of time. Although clinical balance assessment has been performed in previous study, none has determined the intrarater test-retest reliability of static and dynamic stability indexes during dominant single stance. In this study, one rater examined 20 healthy university students (female=12, male=8) in two sessions separated by 7 day intervals. Three stability indexes--the overall stability index (OSI), anterior/posterior stability index (APSI), and medial/ lateral stability index (MLSI) in static and dynamic conditions--were measured during single dominant stance. Intraclass correlation coefficient (ICC), standard error measurement (SEM) and 95% confidence interval (95% CI) were calculated. Test-retest ICCs for OSI, APSI, and MLSI were 0.85, 0.78, and 0.84 during static condition and were 0.77, 0.77, and 0.65 during dynamic condition, respectively. We concluded that the postural stability assessment using Biodex stability system demonstrates good-to-excellent test-retest reliability over a 1 week time interval.

Dynamic stability requirements during gait and standing exergames on the wii fit® system in the elderly

PubMed Central

2012-01-01

Background In rehabilitation, training intensity is usually adapted to optimize the trained system to attain better performance (overload principle). However, in balance rehabilitation, the level of intensity required during training exercises to optimize improvement in balance has rarely been studied, probably due to the difficulty in quantifying the stability level during these exercises. The goal of the present study was to test whether the stabilizing/destabilizing forces model could be used to analyze how stability is challenged during several exergames, that are more and more used in balance rehabilitation, and a dynamic functional task, such as gait. Methods Seven healthy older adults were evaluated with three-dimensional motion analysis during gait at natural and fast speed, and during three balance exergames (50/50 Challenge, Ski Slalom and Soccer). Mean and extreme values for stabilizing force, destabilizing force and the ratio of the two forces (stability index) were computed from kinematic and kinetic data to determine the mean and least level of dynamic, postural and overall balance stability, respectively. Results Mean postural stability was lower (lower mean destabilizing force) during the 50/50 Challenge game than during all the other tasks, but peak postural instability moments were less challenging during this game than during any of the other tasks, as shown by the minimum destabilizing force values. Dynamic stability was progressively more challenged (higher mean and maximum stabilizing force) from the 50/50 Challenge to the Soccer and Slalom games, to the natural gait speed task and to the fast gait speed task, increasing the overall stability difficulty (mean and minimum stability index) in the same manner. Conclusions The stabilizing/destabilizing forces model can be used to rate the level of balance requirements during different tasks such as gait or exergames. The results of our study showed that postural stability did not differ much between the evaluated tasks (except for the 50/50 Challenge), compared to dynamic stability, which was significantly less challenged during the games than during the functional tasks. Games with greater centre of mass displacements and changes in the base of support are likely to stimulate balance control enough to see improvements in balance during dynamic functional tasks, and could be tested in pathological populations with the approach used here. PMID:22607025

Does dynamic stability govern propulsive force generation in human walking?

PubMed Central

Browne, Michael G.

2017-01-01

Before succumbing to slower speeds, older adults may walk with a diminished push-off to prioritize stability over mobility. However, direct evidence for trade-offs between push-off intensity and balance control in human walking, independent of changes in speed, has remained elusive. As a critical first step, we conducted two experiments to investigate: (i) the independent effects of walking speed and propulsive force (FP) generation on dynamic stability in young adults, and (ii) the extent to which young adults prioritize dynamic stability in selecting their preferred combination of walking speed and FP generation. Subjects walked on a force-measuring treadmill across a range of speeds as well as at constant speeds while modulating their FP according to a visual biofeedback paradigm based on real-time force measurements. In contrast to improvements when walking slower, walking with a diminished push-off worsened dynamic stability by up to 32%. Rather, we find that young adults adopt an FP at their preferred walking speed that maximizes dynamic stability. One implication of these findings is that the onset of a diminished push-off in old age may independently contribute to poorer balance control and precipitate slower walking speeds. PMID:29291129

Does dynamic stability govern propulsive force generation in human walking?

PubMed

Browne, Michael G; Franz, Jason R

2017-11-01

Before succumbing to slower speeds, older adults may walk with a diminished push-off to prioritize stability over mobility. However, direct evidence for trade-offs between push-off intensity and balance control in human walking, independent of changes in speed, has remained elusive. As a critical first step, we conducted two experiments to investigate: (i) the independent effects of walking speed and propulsive force ( F P ) generation on dynamic stability in young adults, and (ii) the extent to which young adults prioritize dynamic stability in selecting their preferred combination of walking speed and F P generation. Subjects walked on a force-measuring treadmill across a range of speeds as well as at constant speeds while modulating their F P according to a visual biofeedback paradigm based on real-time force measurements. In contrast to improvements when walking slower, walking with a diminished push-off worsened dynamic stability by up to 32%. Rather, we find that young adults adopt an F P at their preferred walking speed that maximizes dynamic stability. One implication of these findings is that the onset of a diminished push-off in old age may independently contribute to poorer balance control and precipitate slower walking speeds.

Preliminary results of dancing exercise on postural stability in adolescent females.

PubMed

Cheng, Hsu-Sheng; Law, Cheung-Lun; Pan, Hui-Fang; Hsiao, Yueh-Ping; Hu, Jeng-Ho; Chuang, Fu-Kai; Huang, Mao-Hsiung

2011-12-01

Twenty-six female student dancers of Chung-hua school of Art (mean age 17.5 ± 0.5 years) and twenty-five healthy active female collegiate students (mean age 18.1 ± 1.0 years) participated in this study to investigate the effects of dancing exercise on postural stability of adolescent female through a comparison study of two cohorts. The groups were matched in height and weight. Participants were excluded for left-side dominance, sustained lower extremity injury, any known vestibular system dysfunction, uncorrected visual problems, and other neurological conditions. Static and dynamic standing balances were measured by means of Biodex Stability System in six conditions include bilateral, dominant, and nondominant single leg stances with eye-open and eye-closed conditions. To investigate the difference between static and dynamic stabilities, two protocols were performed: the first protocol consisted of four positions including static position, Level 8, Level 4, and Level 1, respectively. They were instructed to maintain a level platform as stably as possible for a period of 30 seconds for each test and given a 30-second rest between tests. The second protocol was descending stability level that was gradually changed from Level 12 to Level 1 for 60 seconds. Balance indices included overall stability index, anterior-posterior stability index (APSI), and medial-lateral stability index. The results of first protocol showed that there were significant differences in overall stability index score between study and control groups at Level 8 with dominant single leg standing in the eye-open condition and the APSI score at Level 8 and at Level 4 with dominant single-leg standing in the eye-closed condition. There was no significant difference in the second protocol. The possible explanation is loss of familiarization adaptation because of level change consequently in both the groups, not step-by-step as in the first protocol study. Furthermore, a positive correlation was found between the dancing experience and the APSI at Level 8 and Level 4 with dominant single-leg standing in the eye-closed condition. In conclusion the findings implied that dancing exercise results in better postural stability and less visual dependence on postural control in adolescent females. Copyright © 2011. Published by Elsevier B.V.

Walking in simulated Martian gravity: influence of the portable life support system's design on dynamic stability.

PubMed

Scott-Pandorf, Melissa M; O'Connor, Daniel P; Layne, Charles S; Josić, Kresimir; Kurz, Max J

2009-09-01

With human exploration of the moon and Mars on the horizon, research considerations for space suit redesign have surfaced. The portable life support system (PLSS) used in conjunction with the space suit during the Apollo missions may have influenced the dynamic balance of the gait pattern. This investigation explored potential issues with the PLSS design that may arise during the Mars exploration. A better understanding of how the location of the PLSS load influences the dynamic stability of the gait pattern may provide insight, such that space missions may have more productive missions with a smaller risk of injury and damaging equipment while falling. We explored the influence the PLSS load position had on the dynamic stability of the walking pattern. While walking, participants wore a device built to simulate possible PLSS load configurations. Floquet and Lyapunov analysis techniques were used to quantify the dynamic stability of the gait pattern. The dynamic stability of the gait pattern was influenced by the position of load. PLSS loads that are placed high and forward on the torso resulted in less dynamically stable walking patterns than loads placed evenly and low on the torso. Furthermore, the kinematic results demonstrated that all joints of the lower extremity may be important for adjusting to different load placements and maintaining dynamic stability. Space scientists and engineers may want to consider PLSS designs that distribute loads evenly and low, and space suit designs that will not limit the sagittal plane range of motion at the lower extremity joints.

Kinematic variability, fractal dynamics and local dynamic stability of treadmill walking

PubMed Central

2011-01-01

Background Motorized treadmills are widely used in research or in clinical therapy. Small kinematics, kinetics and energetics changes induced by Treadmill Walking (TW) as compared to Overground Walking (OW) have been reported in literature. The purpose of the present study was to characterize the differences between OW and TW in terms of stride-to-stride variability. Classical (Standard Deviation, SD) and non-linear (fractal dynamics, local dynamic stability) methods were used. In addition, the correlations between the different variability indexes were analyzed. Methods Twenty healthy subjects performed 10 min TW and OW in a random sequence. A triaxial accelerometer recorded trunk accelerations. Kinematic variability was computed as the average SD (MeanSD) of acceleration patterns among standardized strides. Fractal dynamics (scaling exponent α) was assessed by Detrended Fluctuation Analysis (DFA) of stride intervals. Short-term and long-term dynamic stability were estimated by computing the maximal Lyapunov exponents of acceleration signals. Results TW did not modify kinematic gait variability as compared to OW (multivariate T2, p = 0.87). Conversely, TW significantly modified fractal dynamics (t-test, p = 0.01), and both short and long term local dynamic stability (T2 p = 0.0002). No relationship was observed between variability indexes with the exception of significant negative correlation between MeanSD and dynamic stability in TW (3 × 6 canonical correlation, r = 0.94). Conclusions Treadmill induced a less correlated pattern in the stride intervals and increased gait stability, but did not modify kinematic variability in healthy subjects. This could be due to changes in perceptual information induced by treadmill walking that would affect locomotor control of the gait and hence specifically alter non-linear dependencies among consecutive strides. Consequently, the type of walking (i.e. treadmill or overground) is important to consider in each protocol design. PMID:21345241

Attention Problems and Stability of WISC-IV Scores Among Clinically Referred Children.

PubMed

Green Bartoi, Marla; Issner, Jaclyn Beth; Hetterscheidt, Lesley; January, Alicia M; Kuentzel, Jeffrey Garth; Barnett, Douglas

2015-01-01

We examined the stability of Wechsler Intelligence Scale for Children-Fourth Edition (WISC-IV) scores among 51 diverse, clinically referred 8- to 16-year-olds (M(age) = 11.24 years, SD = 2.36). Children were referred to and tested at an urban, university-based training clinic; 70% of eligible children completed follow-up testing 12 months to 40 months later (M = 22.05, SD = 5.94). Stability for index scores ranged from .58 (Processing Speed) to .81 (Verbal Comprehension), with a stability of .86 for Full-Scale IQ. Subtest score stability ranged from .35 (Letter-Number Sequencing) to .81 (Vocabulary). Indexes believed to be more susceptible to concentration (Processing Speed and Working Memory) had lower stability. We also examined attention problems as a potential moderating factor of WISC-IV index and subtest score stability. Children with attention problems had significantly lower stability for Digit Span and Matrix Reasoning subtests compared with children without attention problems. These results provide support for the temporal stability of the WISC-IV and also provide some support for the idea that attention problems contribute to children producing less stable IQ estimates when completing the WISC-IV. We hope our report encourages further examination of this hypothesis and its implications.

Interpretation of dynamic tensile behavior by austenite stability in ferrite-austenite duplex lightweight steels.

PubMed

Park, Jaeyeong; Jo, Min Cheol; Jeong, Hyeok Jae; Sohn, Seok Su; Kwak, Jai-Hyun; Kim, Hyoung Seop; Lee, Sunghak

2017-11-16

Phenomena occurring in duplex lightweight steels under dynamic loading are hardly investigated, although its understanding is essentially needed in applications of automotive steels. In this study, quasi-static and dynamic tensile properties of duplex lightweight steels were investigated by focusing on how TRIP and TWIP mechanisms were varied under the quasi-static and dynamic loading conditions. As the annealing temperature increased, the grain size and volume fraction of austenite increased, thereby gradually decreasing austenite stability. The strain-hardening rate curves displayed a multiple-stage strain-hardening behavior, which was closely related with deformation mechanisms. Under the dynamic loading, the temperature rise due to adiabatic heating raised the austenite stability, which resulted in the reduction in the TRIP amount. Though the 950 °C-annealed specimen having the lowest austenite stability showed the very low ductility and strength under the quasi-static loading, it exhibited the tensile elongation up to 54% as well as high strain-hardening rate and tensile strength (1038 MPa) due to appropriate austenite stability under dynamic loading. Since dynamic properties of the present duplex lightweight steels show the excellent strength-ductility combination as well as continuously high strain hardening, they can be sufficiently applied to automotive steel sheets demanded for stronger vehicle bodies and safety enhancement.

Response surface method in geotechnical/structural analysis, phase 1

NASA Astrophysics Data System (ADS)

Wong, F. S.

1981-02-01

In the response surface approach, an approximating function is fit to a long running computer code based on a limited number of code calculations. The approximating function, called the response surface, is then used to replace the code in subsequent repetitive computations required in a statistical analysis. The procedure of the response surface development and feasibility of the method are shown using a sample problem in slop stability which is based on data from centrifuge experiments of model soil slopes and involves five random soil parameters. It is shown that a response surface can be constructed based on as few as four code calculations and that the response surface is computationally extremely efficient compared to the code calculation. Potential applications of this research include probabilistic analysis of dynamic, complex, nonlinear soil/structure systems such as slope stability, liquefaction, and nuclear reactor safety.

Introduction to Focus Issue: Time-delay dynamics

NASA Astrophysics Data System (ADS)

Erneux, Thomas; Javaloyes, Julien; Wolfrum, Matthias; Yanchuk, Serhiy

2017-11-01

The field of dynamical systems with time delay is an active research area that connects practically all scientific disciplines including mathematics, physics, engineering, biology, neuroscience, physiology, economics, and many others. This Focus Issue brings together contributions from both experimental and theoretical groups and emphasizes a large variety of applications. In particular, lasers and optoelectronic oscillators subject to time-delayed feedbacks have been explored by several authors for their specific dynamical output, but also because they are ideal test-beds for experimental studies of delay induced phenomena. Topics include the control of cavity solitons, as light spots in spatially extended systems, new devices for chaos communication or random number generation, higher order locking phenomena between delay and laser oscillation period, and systematic bifurcation studies of mode-locked laser systems. Moreover, two original theoretical approaches are explored for the so-called Low Frequency Fluctuations, a particular chaotical regime in laser output which has attracted a lot of interest for more than 30 years. Current hot problems such as the synchronization properties of networks of delay-coupled units, novel stabilization techniques, and the large delay limit of a delay differential equation are also addressed in this special issue. In addition, analytical and numerical tools for bifurcation problems with or without noise and two reviews on concrete questions are proposed. The first review deals with the rich dynamics of simple delay climate models for El Nino Southern Oscillations, and the second review concentrates on neuromorphic photonic circuits where optical elements are used to emulate spiking neurons. Finally, two interesting biological problems are considered in this Focus Issue, namely, multi-strain epidemic models and the interaction of glucose and insulin for more effective treatment.

Energy management during the space shuttle transition

NASA Technical Reports Server (NTRS)

Stengel, R. F.

1972-01-01

An approach to calculating optimal, gliding flight paths of the type associated with the space shuttle's transition from entry to cruising flight is presented. Kinetic energy and total energy (per unit weight) replace velocity and time in the dynamic equations, reducing the dimension and complexity of the problem. The capability for treating integral and terminal penalties (as well as Mach number effects) is retained in the numerical optimization; hence, stability and control boundaries can be observed as trajectories to the desired final energy, flight path angle, and range are determined. Numerical results show that the jump to the front-side of the L/D curve need not be made until the end of the transition and that the dynamic model provides a conservative range estimate. Alternatives for real time trajectory control are discussed.

Extreme learning machine for reduced order modeling of turbulent geophysical flows.

PubMed

San, Omer; Maulik, Romit

2018-04-01

We investigate the application of artificial neural networks to stabilize proper orthogonal decomposition-based reduced order models for quasistationary geophysical turbulent flows. An extreme learning machine concept is introduced for computing an eddy-viscosity closure dynamically to incorporate the effects of the truncated modes. We consider a four-gyre wind-driven ocean circulation problem as our prototype setting to assess the performance of the proposed data-driven approach. Our framework provides a significant reduction in computational time and effectively retains the dynamics of the full-order model during the forward simulation period beyond the training data set. Furthermore, we show that the method is robust for larger choices of time steps and can be used as an efficient and reliable tool for long time integration of general circulation models.