Linear decentralized systems with special structure. [for twin lift helicopters

NASA Technical Reports Server (NTRS)

Martin, C. F.

1982-01-01

Certain fundamental structures associated with linear systems having internal symmetries are outlined. It is shown that the theory of finite-dimensional algebras and their representations are closely related to such systems. It is also demonstrated that certain problems in the decentralized control of symmetric systems are equivalent to long-standing problems of linear systems theory. Even though the structure imposed arose in considering the problems of twin-lift helicopters, any large system composed of several identical intercoupled control systems can be modeled by a linear system that satisfies the constraints imposed. Internal symmetry can be exploited to yield new system-theoretic invariants and a better understanding of the way in which the underlying structure affects overall system performance.

Linear control theory for gene network modeling.

PubMed

Shin, Yong-Jun; Bleris, Leonidas

2010-09-16

Systems biology is an interdisciplinary field that aims at understanding complex interactions in cells. Here we demonstrate that linear control theory can provide valuable insight and practical tools for the characterization of complex biological networks. We provide the foundation for such analyses through the study of several case studies including cascade and parallel forms, feedback and feedforward loops. We reproduce experimental results and provide rational analysis of the observed behavior. We demonstrate that methods such as the transfer function (frequency domain) and linear state-space (time domain) can be used to predict reliably the properties and transient behavior of complex network topologies and point to specific design strategies for synthetic networks.

Solving rational matrix equations in the state space with applications to computer-aided control-system design

NASA Technical Reports Server (NTRS)

Packard, A. K.; Sastry, S. S.

1986-01-01

A method of solving a class of linear matrix equations over various rings is proposed, using results from linear geometric control theory. An algorithm, successfully implemented, is presented, along with non-trivial numerical examples. Applications of the method to the algebraic control system design methodology are discussed.

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

NASA Technical Reports Server (NTRS)

Burns, John A.; Marrekchi, Hamadi

1993-01-01

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

New nonlinear control algorithms for multiple robot arms

NASA Technical Reports Server (NTRS)

Tarn, T. J.; Bejczy, A. K.; Yun, X.

1988-01-01

Multiple coordinated robot arms are modeled by considering the arms as closed kinematic chains and as a force-constrained mechanical system working on the same object simultaneously. In both formulations, a novel dynamic control method is discussed. It is based on feedback linearization and simultaneous output decoupling technique. By applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, it was found that by choosing a general output equation it became possible simultaneously to superimpose the position and velocity error feedback with the force-torque error feedback in the task space.

Reduced state feedback gain computation. [optimization and control theory for aircraft control

NASA Technical Reports Server (NTRS)

Kaufman, H.

1976-01-01

Because application of conventional optimal linear regulator theory to flight controller design requires the capability of measuring and/or estimating the entire state vector, it is of interest to consider procedures for computing controls which are restricted to be linear feedback functions of a lower dimensional output vector and which take into account the presence of measurement noise and process uncertainty. Therefore, a stochastic linear model that was developed is presented which accounts for aircraft parameter and initial uncertainty, measurement noise, turbulence, pilot command and a restricted number of measurable outputs. Optimization with respect to the corresponding output feedback gains was performed for both finite and infinite time performance indices without gradient computation by using Zangwill's modification of a procedure originally proposed by Powell. Results using a seventh order process show the proposed procedures to be very effective.

Digital signal processing and control and estimation theory -- Points of tangency, area of intersection, and parallel directions

NASA Technical Reports Server (NTRS)

Willsky, A. S.

1976-01-01

A number of current research directions in the fields of digital signal processing and modern control and estimation theory were studied. Topics such as stability theory, linear prediction and parameter identification, system analysis and implementation, two-dimensional filtering, decentralized control and estimation, image processing, and nonlinear system theory were examined in order to uncover some of the basic similarities and differences in the goals, techniques, and philosophy of the two disciplines. An extensive bibliography is included.

Algebraic methods for the solution of some linear matrix equations

NASA Technical Reports Server (NTRS)

Djaferis, T. E.; Mitter, S. K.

1979-01-01

The characterization of polynomials whose zeros lie in certain algebraic domains (and the unification of the ideas of Hermite and Lyapunov) is the basis for developing finite algorithms for the solution of linear matrix equations. Particular attention is given to equations PA + A'P = Q (the Lyapunov equation) and P - A'PA = Q the (discrete Lyapunov equation). The Lyapunov equation appears in several areas of control theory such as stability theory, optimal control (evaluation of quadratic integrals), stochastic control (evaluation of covariance matrices) and in the solution of the algebraic Riccati equation using Newton's method.

Lie theory and control systems defined on spheres

NASA Technical Reports Server (NTRS)

Brockett, R. W.

1972-01-01

It is shown that in constructing a theory for the most elementary class of control problems defined on spheres, some results from the Lie theory play a natural role. To understand controllability, optimal control, and certain properties of stochastic equations, Lie theoretic ideas are needed. The framework considered here is the most natural departure from the usual linear system/vector space problems which have dominated control systems literature. For this reason results are compared with those previously available for the finite dimensional vector space case.

Koopman operator theory: Past, present, and future

NASA Astrophysics Data System (ADS)

Brunton, Steven; Kaiser, Eurika; Kutz, Nathan

2017-11-01

Koopman operator theory has emerged as a dominant method to represent nonlinear dynamics in terms of an infinite-dimensional linear operator. The Koopman operator acts on the space of all possible measurement functions of the system state, advancing these measurements with the flow of the dynamics. A linear representation of nonlinear dynamics has tremendous potential to enable the prediction, estimation, and control of nonlinear systems with standard textbook methods developed for linear systems. Dynamic mode decomposition has become the leading data-driven method to approximate the Koopman operator, although there are still open questions and challenges around how to obtain accurate approximations for strongly nonlinear systems. This talk will provide an introductory overview of modern Koopman operator theory, reviewing the basics and describing recent theoretical and algorithmic developments. Particular emphasis will be placed on the use of data-driven Koopman theory to characterize and control high-dimensional fluid dynamic systems. This talk will also address key advances in the rapidly growing fields of machine learning and data science that are likely to drive future developments.

Linear dark field control: simulation for implementation and testing on the UA wavefront control testbed

NASA Astrophysics Data System (ADS)

Miller, Kelsey; Guyon, Olivier

2016-07-01

This paper presents the early-stage simulation results of linear dark field control (LDFC) as a new approach to maintaining a stable dark hole within a stellar post-coronagraphic PSF. In practice, conventional speckle nulling is used to create a dark hole in the PSF, and LDFC is then employed to maintain the dark field by using information from the bright speckle field. The concept exploits the linear response of the bright speckle intensity to wavefront variations in the pupil, and therefore has many advantages over conventional speckle nulling as a method for stabilizing the dark hole. In theory, LDFC is faster, more sensitive, and more robust than using conventional speckle nulling techniques, like electric field conjugation, to maintain the dark hole. In this paper, LDFC theory, linear bright speckle characterization, and first results in simulation are presented as an initial step toward the deployment of LDFC on the UA Wavefront Control testbed in the coming year.

Modal control of an unstable periodic orbit

NASA Astrophysics Data System (ADS)

Wiesel, W.; Shelton, W.

1983-03-01

Floquet theory is applied to the problem of designing a control system for a satellite in an unstable periodic orbit. Expansion about a periodic orbit produces a time-periodic linear system, which is augmented by a time-periodic control term. It is shown that this can be done such that (1) the application of control produces only inertial accelerations, (2) positive real Poincareexponents are shifted into the left half-plane, and (3) the shift of the exponent is linear with control gain. These developments are applied to an unstable orbit near the earth-moon L(3) point pertubed by the sun. Finally, it is shown that the control theory can be extended to include first order perturbations about the periodic orbit without increase in control cost.

Modal control of an unstable periodic orbit

NASA Technical Reports Server (NTRS)

Wiesel, W.; Shelton, W.

1983-01-01

Floquet theory is applied to the problem of designing a control system for a satellite in an unstable periodic orbit. Expansion about a periodic orbit produces a time-periodic linear system, which is augmented by a time-periodic control term. It is shown that this can be done such that (1) the application of control produces only inertial accelerations, (2) positive real Poincareexponents are shifted into the left half-plane, and (3) the shift of the exponent is linear with control gain. These developments are applied to an unstable orbit near the earth-moon L(3) point pertubed by the sun. Finally, it is shown that the control theory can be extended to include first order perturbations about the periodic orbit without increase in control cost.

A generalized Lyapunov theory for robust root clustering of linear state space models with real parameter uncertainty

NASA Technical Reports Server (NTRS)

Yedavalli, R. K.

1992-01-01

The problem of analyzing and designing controllers for linear systems subject to real parameter uncertainty is considered. An elegant, unified theory for robust eigenvalue placement is presented for a class of D-regions defined by algebraic inequalities by extending the nominal matrix root clustering theory of Gutman and Jury (1981) to linear uncertain time systems. The author presents explicit conditions for matrix root clustering for different D-regions and establishes the relationship between the eigenvalue migration range and the parameter range. The bounds are all obtained by one-shot computation in the matrix domain and do not need any frequency sweeping or parameter gridding. The method uses the generalized Lyapunov theory for getting the bounds.

Linearizing feedforward/feedback attitude control

NASA Technical Reports Server (NTRS)

Paielli, Russell A.; Bach, Ralph E.

1991-01-01

An approach to attitude control theory is introduced in which a linear form is postulated for the closed-loop rotation error dynamics, then the exact control law required to realize it is derived. The nonminimal (four-component) quaternion form is used to attitude because it is globally nonsingular, but the minimal (three-component) quaternion form is used for attitude error because it has no nonlinear constraints to prevent the rotational error dynamics from being linearized, and the definition of the attitude error is based on quaternion algebra. This approach produces an attitude control law that linearizes the closed-loop rotational error dynamics exactly, without any attitude singularities, even if the control errors become large.

Design Criteria for the Future of Flight Controls. Proceedings of the Flight Dynamics Laboratory Flying Qualities and Flight Control Symposium 2-5 March 1982.

DTIC Science & Technology

1982-07-01

robustness of the closed-loop system as compared to state feedback. The observer theory of Luenberger specifies the conditions that must be satisfied for...No. ID-17SI-F-l, October 1963. 8. Rynaski, E. G. and Whitbeck, R. F.: "The Theory and Application of Linear Optimal Control," Calspan Report No. IH...pilots tend to control them open-loop. Frequencies much beyond 10 rad/sec are generally beyond pilots’ control capability. Control theory indicates a need

Theory, Guidance, and Flight Control for High Maneuverability Projectiles

DTIC Science & Technology

2014-01-01

estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining...2.8 Linear System Modeling with Time Delay ...................................................................22 2.9 Linear System Modeling Without... Time Delay .............................................................23 3. Guidance and Flight Control 24 3.1 Proportional Navigation Guidance Law

Analysis and control of hourglass instabilities in underintegrated linear and nonlinear elasticity

NASA Technical Reports Server (NTRS)

Jacquotte, Olivier P.; Oden, J. Tinsley

1994-01-01

Methods are described to identify and correct a bad finite element approximation of the governing operator obtained when under-integration is used in numerical code for several model problems: the Poisson problem, the linear elasticity problem, and for problems in the nonlinear theory of elasticity. For each of these problems, the reason for the occurrence of instabilities is given, a way to control or eliminate them is presented, and theorems of existence, uniqueness, and convergence for the given methods are established. Finally, numerical results are included which illustrate the theory.

Minimal-Inversion Feedforward-And-Feedback Control System

NASA Technical Reports Server (NTRS)

Seraji, Homayoun

1990-01-01

Recent developments in theory of control systems support concept of minimal-inversion feedforward-and feedback control system consisting of three independently designable control subsystems. Applicable to the control of linear, time-invariant plant.

Toward Control of Universal Scaling in Critical Dynamics

DTIC Science & Technology

2016-01-27

program that aims to synergistically combine two powerful and very successful theories for non-linear stochastic dynamics of cooperative multi...RESPONSIBLE PERSON 19b. TELEPHONE NUMBER Uwe Tauber Uwe C. T? uber , Michel Pleimling, Daniel J. Stilwell 611102 c. THIS PAGE The public reporting burden...to synergistically combine two powerful and very successful theories for non-linear stochastic dynamics of cooperative multi-component systems, namely

A model for rotorcraft flying qualities studies

NASA Technical Reports Server (NTRS)

Mittal, Manoj; Costello, Mark F.

1993-01-01

This paper outlines the development of a mathematical model that is expected to be useful for rotorcraft flying qualities research. A computer model is presented that can be applied to a range of different rotorcraft configurations. The algorithm computes vehicle trim and a linear state-space model of the aircraft. The trim algorithm uses non linear optimization theory to solve the nonlinear algebraic trim equations. The linear aircraft equations consist of an airframe model and a flight control system dynamic model. The airframe model includes coupled rotor and fuselage rigid body dynamics and aerodynamics. The aerodynamic model for the rotors utilizes blade element theory and a three state dynamic inflow model. Aerodynamics of the fuselage and fuselage empennages are included. The linear state-space description for the flight control system is developed using standard block diagram data.

Linear Quantum Systems: Non-Classical States and Robust Stability

DTIC Science & Technology

2016-06-29

quantum linear systems subject to non-classical quantum fields. The major outcomes of this project are (i) derivation of quantum filtering equations for...derivation of quantum filtering equations for systems non-classical input states including single photon states, (ii) determination of how linear...history going back some 50 years, to the birth of modern control theory with Kalman’s foundational work on filtering and LQG optimal control

Rotorcraft control system design for uncertain vehicle dynamics using quantitative feedback theory

NASA Technical Reports Server (NTRS)

Hess, R. A.

1994-01-01

Quantitative Feedback Theory describes a frequency-domain technique for the design of multi-input, multi-output control systems which must meet time or frequency domain performance criteria when specified uncertainty exists in the linear description of the vehicle dynamics. This theory is applied to the design of the longitudinal flight control system for a linear model of the BO-105C rotorcraft. Uncertainty in the vehicle model is due to the variation in the vehicle dynamics over a range of airspeeds from 0-100 kts. For purposes of exposition, the vehicle description contains no rotor or actuator dynamics. The design example indicates the manner in which significant uncertainty exists in the vehicle model. The advantage of using a sequential loop closure technique to reduce the cost of feedback is demonstrated by example.

Time-Dependent Thermal Transport Theory.

PubMed

Biele, Robert; D'Agosta, Roberto; Rubio, Angel

2015-07-31

Understanding thermal transport in nanoscale systems presents important challenges to both theory and experiment. In particular, the concept of local temperature at the nanoscale appears difficult to justify. Here, we propose a theoretical approach where we replace the temperature gradient with controllable external blackbody radiations. The theory recovers known physical results, for example, the linear relation between the thermal current and the temperature difference of two blackbodies. Furthermore, our theory is not limited to the linear regime and goes beyond accounting for nonlinear effects and transient phenomena. Since the present theory is general and can be adapted to describe both electron and phonon dynamics, it provides a first step toward a unified formalism for investigating thermal and electronic transport.

Neighboring extremal optimal control design including model mismatch errors

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

Kim, T.J.; Hull, D.G.

1994-11-01

The mismatch control technique that is used to simplify model equations of motion in order to determine analytic optimal control laws is extended using neighboring extremal theory. The first variation optimal control equations are linearized about the extremal path to account for perturbations in the initial state and the final constraint manifold. A numerical example demonstrates that the tuning procedure inherent in the mismatch control method increases the performance of the controls to the level of a numerically-determined piecewise-linear controller.

Probability theory, not the very guide of life.

PubMed

Juslin, Peter; Nilsson, Håkan; Winman, Anders

2009-10-01

Probability theory has long been taken as the self-evident norm against which to evaluate inductive reasoning, and classical demonstrations of violations of this norm include the conjunction error and base-rate neglect. Many of these phenomena require multiplicative probability integration, whereas people seem more inclined to linear additive integration, in part, at least, because of well-known capacity constraints on controlled thought. In this article, the authors show with computer simulations that when based on approximate knowledge of probabilities, as is routinely the case in natural environments, linear additive integration can yield as accurate estimates, and as good average decision returns, as estimates based on probability theory. It is proposed that in natural environments people have little opportunity or incentive to induce the normative rules of probability theory and, given their cognitive constraints, linear additive integration may often offer superior bounded rationality.

Prediction and control of chaotic processes using nonlinear adaptive networks

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

Jones, R.D.; Barnes, C.W.; Flake, G.W.

1990-01-01

We present the theory of nonlinear adaptive networks and discuss a few applications. In particular, we review the theory of feedforward backpropagation networks. We then present the theory of the Connectionist Normalized Linear Spline network in both its feedforward and iterated modes. Also, we briefly discuss the theory of stochastic cellular automata. We then discuss applications to chaotic time series, tidal prediction in Venice lagoon, finite differencing, sonar transient detection, control of nonlinear processes, control of a negative ion source, balancing a double inverted pendulum and design advice for free electron lasers and laser fusion targets.

Linear Quantum Systems: Non-Classical States and Robust Stability

DTIC Science & Technology

2016-06-29

has a history going back some 50 years, to the birth of modern control theory with Kalman’s foundational work on filtering and LQG optimal control ...information   if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ORGANIZATION. 1. REPORT DATE (DD...analysis and control of quantum linear systems and their interactions with non-classical quantum fields by developing control theoretic concepts exploiting

A linear quadratic regulator approach to the stabilization of uncertain linear systems

NASA Technical Reports Server (NTRS)

Shieh, L. S.; Sunkel, J. W.; Wang, Y. J.

1990-01-01

This paper presents a linear quadratic regulator approach to the stabilization of uncertain linear systems. The uncertain systems under consideration are described by state equations with the presence of time-varying unknown-but-bounded uncertainty matrices. The method is based on linear quadratic regulator (LQR) theory and Liapunov stability theory. The robust stabilizing control law for a given uncertain system can be easily constructed from the symmetric positive-definite solution of the associated augmented Riccati equation. The proposed approach can be applied to matched and/or mismatched systems with uncertainty matrices in which only their matrix norms are bounded by some prescribed values and/or their entries are bounded by some prescribed constraint sets. Several numerical examples are presented to illustrate the results.

Robust nonlinear control of vectored thrust aircraft

NASA Technical Reports Server (NTRS)

Doyle, John C.; Murray, Richard; Morris, John

1993-01-01

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations.

A variable structure approach to robust control of VTOL aircraft

NASA Technical Reports Server (NTRS)

Calise, A. J.; Kramer, F.

1982-01-01

This paper examines the application of variable structure control theory to the design of a flight control system for the AV-8A Harrier in a hover mode. The objective in variable structure design is to confine the motion to a subspace of the total state space. The motion in this subspace is insensitive to system parameter variations and external disturbances that lie in the range space of the control. A switching type of control law results from the design procedure. The control system was designed to track a vector velocity command defined in the body frame. For comparison purposes, a proportional controller was designed using optimal linear regulator theory. Both control designs were first evaluated for transient response performance using a linearized model, then a nonlinear simulation study of a hovering approach to landing was conducted. Wind turbulence was modeled using a 1052 destroyer class air wake model.

A Simplified Theory of Coupled Oscillator Array Phase Control

NASA Technical Reports Server (NTRS)

Pogorzelski, R. J.; York, R. A.

1997-01-01

Linear and planar arrays of coupled oscillators have been proposed as means of achieving high power rf sources through coherent spatial power combining. In such - applications, a uniform phase distribution over the aperture is desired. However, it has been shown that by detuning some of the oscillators away from the oscillation frequency of the ensemble of oscillators, one may achieve other useful aperture phase distributions. Notable among these are linear phase distributions resulting in steering of the output rf beam away from the broadside direction. The theory describing the operation of such arrays of coupled oscillators is quite complicated since the phenomena involved are inherently nonlinear. This has made it difficult to develop an intuitive understanding of the impact of oscillator tuning on phase control and has thus impeded practical application. In this work a simpl!fied theory is developed which facilitates intuitive understanding by establishing an analog of the phase control problem in terms of electrostatics.

Linearization: Students Forget the Operating Point

ERIC Educational Resources Information Center

Roubal, J.; Husek, P.; Stecha, J.

2010-01-01

Linearization is a standard part of modeling and control design theory for a class of nonlinear dynamical systems taught in basic undergraduate courses. Although linearization is a straight-line methodology, it is not applied correctly by many students since they often forget to keep the operating point in mind. This paper explains the topic and…

Control design based on a linear state function observer

NASA Technical Reports Server (NTRS)

Su, Tzu-Jeng; Craig, Roy R., Jr.

1992-01-01

An approach to the design of low-order controllers for large scale systems is proposed. The method is derived from the theory of linear state function observers. First, the realization of a state feedback control law is interpreted as the observation of a linear function of the state vector. The linear state function to be reconstructed is the given control law. Then, based on the derivation for linear state function observers, the observer design is formulated as a parameter optimization problem. The optimization objective is to generate a matrix that is close to the given feedback gain matrix. Based on that matrix, the form of the observer and a new control law can be determined. A four-disk system and a lightly damped beam are presented as examples to demonstrate the applicability and efficacy of the proposed method.

The infinum principle

NASA Technical Reports Server (NTRS)

Geering, H. P.; Athans, M.

1973-01-01

A complete theory of necessary and sufficient conditions is discussed for a control to be superior with respect to a nonscalar-valued performance criterion. The latter maps into a finite dimensional, integrally closed directed, partially ordered linear space. The applicability of the theory to the analysis of dynamic vector estimation problems and to a class of uncertain optimal control problems is demonstrated.

Nonlinear gearshifts control of dual-clutch transmissions during inertia phase.

PubMed

Hu, Yunfeng; Tian, Lu; Gao, Bingzhao; Chen, Hong

2014-07-01

In this paper, a model-based nonlinear gearshift controller is designed by the backstepping method to improve the shift quality of vehicles with a dual-clutch transmission (DCT). Considering easy-implementation, the controller is rearranged into a concise structure which contains a feedforward control and a feedback control. Then, robustness of the closed-loop error system is discussed in the framework of the input to state stability (ISS) theory, where model uncertainties are considered as the additive disturbance inputs. Furthermore, due to the application of the backstepping method, the closed-loop error system is ordered as a linear system. Using the linear system theory, a guideline for selecting the controller parameters is deduced which could reduce the workload of parameters tuning. Finally, simulation results and Hardware in the Loop (HiL) simulation are presented to validate the effectiveness of the designed controller. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

VTOL controls for shipboard landing. M.S.Thesis

NASA Technical Reports Server (NTRS)

Mcmuldroch, C. G.

1979-01-01

The problem of landing a VTOL aircraft on a small ship in rough seas using an automatic controller is examined. The controller design uses the linear quadratic Gaussian results of modern control theory. Linear time invariant dynamic models are developed for the aircraft, ship, and wave motions. A hover controller commands the aircraft to track position and orientation of the ship deck using only low levels of control power. Commands for this task are generated by the solution of the steady state linear quadratic gaussian regulator problem. Analytical performance and control requirement tradeoffs are obtained. A landing controller commands the aircraft from stationary hover along a smooth, low control effort trajectory, to a touchdown on a predicted crest of ship motion. The design problem is formulated and solved as an approximate finite-time linear quadratic stochastic regulator. Performance and control results are found by Monte Carlo simulations.

Pressure fluctuations and time scales in turbulent channel flow

NASA Astrophysics Data System (ADS)

Septham, Kamthon; Morrison, Jonathan; Diwan, Sourabh

2015-11-01

Pressure fluctuations in turbulent channel flow subjected to globally stabilising linear feedback control are investigated at Reτ = 400 . The passivity-based control is adopted and explained by the conservative characteristics of the nonlinear terms contributing to the Reynolds-Orr equation (Sharma et al. Phys. Fluids 2011). The linear control operates via vU' ; the maximum forcing is located at y+ ~ 20 , corresponding to the location of the maximum in the mean-square pressure gradient. The responses of the rapid (linear) and slow (nonlinear) pressure fluctuations to the linear control are investigated using the Green's function representations. It demonstrates that the linear control operates via the linear source terms of the Poisson equation for pressure fluctuations. Landahl's timescales of the minimal flow unit (MFU) in turbulent channel flow are examined at y+ = 20 . It shows that the timescales of MFU agree well with the theoretical values proposed by Landahl (1993). Therefore, the effectiveness of the linear control to attenuate wall turbulence is explained by Landahl's theory for timescales, in that the control proceeds via the shear interaction timescale which is significantly shorter than both the nonlinear and viscous timescales.

Non-linear feedback control of the p53 protein-mdm2 inhibitor system using the derivative-free non-linear Kalman filter.

PubMed

Rigatos, Gerasimos G

2016-06-01

It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Adamian, A.

1988-01-01

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

A computational algorithm for spacecraft control and momentum management

NASA Technical Reports Server (NTRS)

Dzielski, John; Bergmann, Edward; Paradiso, Joseph

1990-01-01

Developments in the area of nonlinear control theory have shown how coordinate changes in the state and input spaces of a dynamical system can be used to transform certain nonlinear differential equations into equivalent linear equations. These techniques are applied to the control of a spacecraft equipped with momentum exchange devices. An optimal control problem is formulated that incorporates a nonlinear spacecraft model. An algorithm is developed for solving the optimization problem using feedback linearization to transform to an equivalent problem involving a linear dynamical constraint and a functional approximation technique to solve for the linear dynamics in terms of the control. The original problem is transformed into an unconstrained nonlinear quadratic program that yields an approximate solution to the original problem. Two examples are presented to illustrate the results.

A nonlinear Kalman filtering approach to embedded control of turbocharged diesel engines

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Siano, Pierluigi; Arsie, Ivan

2014-10-01

The development of efficient embedded control for turbocharged Diesel engines, requires the programming of elaborated nonlinear control and filtering methods. To this end, in this paper nonlinear control for turbocharged Diesel engines is developed with the use of Differential flatness theory and the Derivative-free nonlinear Kalman Filter. It is shown that the dynamic model of the turbocharged Diesel engine is differentially flat and admits dynamic feedback linearization. It is also shown that the dynamic model can be written in the linear Brunovsky canonical form for which a state feedback controller can be easily designed. To compensate for modeling errors and external disturbances the Derivative-free nonlinear Kalman Filter is used and redesigned as a disturbance observer. The filter consists of the Kalman Filter recursion on the linearized equivalent of the Diesel engine model and of an inverse transformation based on differential flatness theory which enables to obtain estimates for the state variables of the initial nonlinear model. Once the disturbances variables are identified it is possible to compensate them by including an additional control term in the feedback loop. The efficiency of the proposed control method is tested through simulation experiments.

Application of quadratic optimization to supersonic inlet control

NASA Technical Reports Server (NTRS)

Lehtinen, B.; Zeller, J. R.

1971-01-01

The application of linear stochastic optimal control theory to the design of the control system for the air intake (inlet) of a supersonic air-breathing propulsion system is discussed. The controls must maintain a stable inlet shock position in the presence of random airflow disturbances and prevent inlet unstart. Two different linear time invariant control systems are developed. One is designed to minimize a nonquadratic index, the expected frequency of inlet unstart, and the other is designed to minimize the mean square value of inlet shock motion. The quadratic equivalence principle is used to obtain the best linear controller that minimizes the nonquadratic performance index. The two systems are compared on the basis of unstart prevention, control effort requirements, and sensitivity to parameter variations.

New Steering Strategies for the USNO Master Clocks

DTIC Science & Technology

1999-12-01

1992. P. Koppang and R. Leland , “Linear quadratic stochastic control of atomic hydrogen masers,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr...vol. 46, pp. 517-522, May 1999. P. Koppang and R. Leland , “Steering of frequency standards by the use of linear quadratic gaussian control theory...3lst Annual Precise Time and Time Interval (PTTI) Meeting NEWSTEERINGSTRATEGIESFOR THEUSNOMASTERCLOCKS Paul A. Koppang Datum, Inc. Beverly, MA

Modern control techniques in active flutter suppression using a control moment gyro

NASA Technical Reports Server (NTRS)

Buchek, P. M.

1974-01-01

Development of organized synthesis techniques, using concepts of modern control theory was studied for the design of active flutter suppression systems for two and three-dimensional lifting surfaces, utilizing a control moment gyro (CMG) to generate the required control torques. Incompressible flow theory is assumed, with the unsteady aerodynamic forces and moments for arbitrary airfoil motion obtained by using the convolution integral based on Wagner's indicial lift function. Linear optimal control theory is applied to find particular optimal sets of gain values which minimize a quadratic performance function. The closed loop system's response to impulsive gust disturbances and the resulting control power requirements are investigated, and the system eigenvalues necessary to minimize the maximum value of control power are determined.

A new eddy current model for magnetic bearing control system design

NASA Technical Reports Server (NTRS)

Feeley, Joseph J.; Ahlstrom, Daniel J.

1992-01-01

This paper describes a new VLSI-based controller for the implementation of a Linear-Quadratic-Gaussian (LQG) theory-based control system. Use of the controller is demonstrated by design of a controller for a magnetic bearing and its performance is evaluated by computer simulation.

A methodology for designing robust multivariable nonlinear control systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Grunberg, D. B.

1986-01-01

A new methodology is described for the design of nonlinear dynamic controllers for nonlinear multivariable systems providing guarantees of closed-loop stability, performance, and robustness. The methodology is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate inverse operator for the plant. A major feature of the methodology is a unification of both the state-space and input-output formulations. In addition, new results on stability theory, nonlinear state estimation, and optimal nonlinear regulator theory are presented, including the guaranteed global properties of the extended Kalman filter and optimal nonlinear regulators.

Linear analysis near a steady-state of biochemical networks: control analysis, correlation metrics and circuit theory.

PubMed

Heuett, William J; Beard, Daniel A; Qian, Hong

2008-05-15

Several approaches, including metabolic control analysis (MCA), flux balance analysis (FBA), correlation metric construction (CMC), and biochemical circuit theory (BCT), have been developed for the quantitative analysis of complex biochemical networks. Here, we present a comprehensive theory of linear analysis for nonequilibrium steady-state (NESS) biochemical reaction networks that unites these disparate approaches in a common mathematical framework and thermodynamic basis. In this theory a number of relationships between key matrices are introduced: the matrix A obtained in the standard, linear-dynamic-stability analysis of the steady-state can be decomposed as A = SRT where R and S are directly related to the elasticity-coefficient matrix for the fluxes and chemical potentials in MCA, respectively; the control-coefficients for the fluxes and chemical potentials can be written in terms of RTBS and STBS respectively where matrix B is the inverse of A; the matrix S is precisely the stoichiometric matrix in FBA; and the matrix eAt plays a central role in CMC. One key finding that emerges from this analysis is that the well-known summation theorems in MCA take different forms depending on whether metabolic steady-state is maintained by flux injection or concentration clamping. We demonstrate that if rate-limiting steps exist in a biochemical pathway, they are the steps with smallest biochemical conductances and largest flux control-coefficients. We hypothesize that biochemical networks for cellular signaling have a different strategy for minimizing energy waste and being efficient than do biochemical networks for biosynthesis. We also discuss the intimate relationship between MCA and biochemical systems analysis (BSA).

ORACLS- OPTIMAL REGULATOR ALGORITHMS FOR THE CONTROL OF LINEAR SYSTEMS (CDC VERSION)

NASA Technical Reports Server (NTRS)

Armstrong, E. S.

1994-01-01

This control theory design package, called Optimal Regulator Algorithms for the Control of Linear Systems (ORACLS), was developed to aid in the design of controllers and optimal filters for systems which can be modeled by linear, time-invariant differential and difference equations. Optimal linear quadratic regulator theory, currently referred to as the Linear-Quadratic-Gaussian (LQG) problem, has become the most widely accepted method of determining optimal control policy. Within this theory, the infinite duration time-invariant problems, which lead to constant gain feedback control laws and constant Kalman-Bucy filter gains for reconstruction of the system state, exhibit high tractability and potential ease of implementation. A variety of new and efficient methods in the field of numerical linear algebra have been combined into the ORACLS program, which provides for the solution to time-invariant continuous or discrete LQG problems. The ORACLS package is particularly attractive to the control system designer because it provides a rigorous tool for dealing with multi-input and multi-output dynamic systems in both continuous and discrete form. The ORACLS programming system is a collection of subroutines which can be used to formulate, manipulate, and solve various LQG design problems. The ORACLS program is constructed in a manner which permits the user to maintain considerable flexibility at each operational state. This flexibility is accomplished by providing primary operations, analysis of linear time-invariant systems, and control synthesis based on LQG methodology. The input-output routines handle the reading and writing of numerical matrices, printing heading information, and accumulating output information. The basic vector-matrix operations include addition, subtraction, multiplication, equation, norm construction, tracing, transposition, scaling, juxtaposition, and construction of null and identity matrices. The analysis routines provide for the following computations: the eigenvalues and eigenvectors of real matrices; the relative stability of a given matrix; matrix factorization; the solution of linear constant coefficient vector-matrix algebraic equations; the controllability properties of a linear time-invariant system; the steady-state covariance matrix of an open-loop stable system forced by white noise; and the transient response of continuous linear time-invariant systems. The control law design routines of ORACLS implement some of the more common techniques of time-invariant LQG methodology. For the finite-duration optimal linear regulator problem with noise-free measurements, continuous dynamics, and integral performance index, a routine is provided which implements the negative exponential method for finding both the transient and steady-state solutions to the matrix Riccati equation. For the discrete version of this problem, the method of backwards differencing is applied to find the solutions to the discrete Riccati equation. A routine is also included to solve the steady-state Riccati equation by the Newton algorithms described by Klein, for continuous problems, and by Hewer, for discrete problems. Another routine calculates the prefilter gain to eliminate control state cross-product terms in the quadratic performance index and the weighting matrices for the sampled data optimal linear regulator problem. For cases with measurement noise, duality theory and optimal regulator algorithms are used to calculate solutions to the continuous and discrete Kalman-Bucy filter problems. Finally, routines are included to implement the continuous and discrete forms of the explicit (model-in-the-system) and implicit (model-in-the-performance-index) model following theory. These routines generate linear control laws which cause the output of a dynamic time-invariant system to track the output of a prescribed model. In order to apply ORACLS, the user must write an executive (driver) program which inputs the problem coefficients, formulates and selects the routines to be used to solve the problem, and specifies the desired output. There are three versions of ORACLS source code available for implementation: CDC, IBM, and DEC. The CDC version has been implemented on a CDC 6000 series computer with a central memory of approximately 13K (octal) of 60 bit words. The CDC version is written in FORTRAN IV, was developed in 1978, and last updated in 1989. The IBM version has been implemented on an IBM 370 series computer with a central memory requirement of approximately 300K of 8 bit bytes. The IBM version is written in FORTRAN IV and was generated in 1981. The DEC version has been implemented on a VAX series computer operating under VMS. The VAX version is written in FORTRAN 77 and was generated in 1986.

ORACLS- OPTIMAL REGULATOR ALGORITHMS FOR THE CONTROL OF LINEAR SYSTEMS (DEC VAX VERSION)

NASA Technical Reports Server (NTRS)

Frisch, H.

1994-01-01

This control theory design package, called Optimal Regulator Algorithms for the Control of Linear Systems (ORACLS), was developed to aid in the design of controllers and optimal filters for systems which can be modeled by linear, time-invariant differential and difference equations. Optimal linear quadratic regulator theory, currently referred to as the Linear-Quadratic-Gaussian (LQG) problem, has become the most widely accepted method of determining optimal control policy. Within this theory, the infinite duration time-invariant problems, which lead to constant gain feedback control laws and constant Kalman-Bucy filter gains for reconstruction of the system state, exhibit high tractability and potential ease of implementation. A variety of new and efficient methods in the field of numerical linear algebra have been combined into the ORACLS program, which provides for the solution to time-invariant continuous or discrete LQG problems. The ORACLS package is particularly attractive to the control system designer because it provides a rigorous tool for dealing with multi-input and multi-output dynamic systems in both continuous and discrete form. The ORACLS programming system is a collection of subroutines which can be used to formulate, manipulate, and solve various LQG design problems. The ORACLS program is constructed in a manner which permits the user to maintain considerable flexibility at each operational state. This flexibility is accomplished by providing primary operations, analysis of linear time-invariant systems, and control synthesis based on LQG methodology. The input-output routines handle the reading and writing of numerical matrices, printing heading information, and accumulating output information. The basic vector-matrix operations include addition, subtraction, multiplication, equation, norm construction, tracing, transposition, scaling, juxtaposition, and construction of null and identity matrices. The analysis routines provide for the following computations: the eigenvalues and eigenvectors of real matrices; the relative stability of a given matrix; matrix factorization; the solution of linear constant coefficient vector-matrix algebraic equations; the controllability properties of a linear time-invariant system; the steady-state covariance matrix of an open-loop stable system forced by white noise; and the transient response of continuous linear time-invariant systems. The control law design routines of ORACLS implement some of the more common techniques of time-invariant LQG methodology. For the finite-duration optimal linear regulator problem with noise-free measurements, continuous dynamics, and integral performance index, a routine is provided which implements the negative exponential method for finding both the transient and steady-state solutions to the matrix Riccati equation. For the discrete version of this problem, the method of backwards differencing is applied to find the solutions to the discrete Riccati equation. A routine is also included to solve the steady-state Riccati equation by the Newton algorithms described by Klein, for continuous problems, and by Hewer, for discrete problems. Another routine calculates the prefilter gain to eliminate control state cross-product terms in the quadratic performance index and the weighting matrices for the sampled data optimal linear regulator problem. For cases with measurement noise, duality theory and optimal regulator algorithms are used to calculate solutions to the continuous and discrete Kalman-Bucy filter problems. Finally, routines are included to implement the continuous and discrete forms of the explicit (model-in-the-system) and implicit (model-in-the-performance-index) model following theory. These routines generate linear control laws which cause the output of a dynamic time-invariant system to track the output of a prescribed model. In order to apply ORACLS, the user must write an executive (driver) program which inputs the problem coefficients, formulates and selects the routines to be used to solve the problem, and specifies the desired output. There are three versions of ORACLS source code available for implementation: CDC, IBM, and DEC. The CDC version has been implemented on a CDC 6000 series computer with a central memory of approximately 13K (octal) of 60 bit words. The CDC version is written in FORTRAN IV, was developed in 1978, and last updated in 1986. The IBM version has been implemented on an IBM 370 series computer with a central memory requirement of approximately 300K of 8 bit bytes. The IBM version is written in FORTRAN IV and was generated in 1981. The DEC version has been implemented on a VAX series computer operating under VMS. The VAX version is written in FORTRAN 77 and was generated in 1986.

Factorization and reduction methods for optimal control of distributed parameter systems

NASA Technical Reports Server (NTRS)

Burns, J. A.; Powers, R. K.

1985-01-01

A Chandrasekhar-type factorization method is applied to the linear-quadratic optimal control problem for distributed parameter systems. An aeroelastic control problem is used as a model example to demonstrate that if computationally efficient algorithms, such as those of Chandrasekhar-type, are combined with the special structure often available to a particular problem, then an abstract approximation theory developed for distributed parameter control theory becomes a viable method of solution. A numerical scheme based on averaging approximations is applied to hereditary control problems. Numerical examples are given.

Process Dynamics and Control, a Theory-Experiential Approach.

ERIC Educational Resources Information Center

Perna, A. J.; And Others

A required senior-level chemical engineering course at Colorado State University is described. The first nine weeks are devoted to the theory portion of the course, which includes the following topics: LaPlace transformations and time constants, block diagrams, inverse transformations, linearization, frequency response analysis, graphical…

Nonlinear robust control of hypersonic aircrafts with interactions between flight dynamics and propulsion systems.

PubMed

Li, Zhaoying; Zhou, Wenjie; Liu, Hao

2016-09-01

This paper addresses the nonlinear robust tracking controller design problem for hypersonic vehicles. This problem is challenging due to strong coupling between the aerodynamics and the propulsion system, and the uncertainties involved in the vehicle dynamics including parametric uncertainties, unmodeled model uncertainties, and external disturbances. By utilizing the feedback linearization technique, a linear tracking error system is established with prescribed references. For the linear model, a robust controller is proposed based on the signal compensation theory to guarantee that the tracking error dynamics is robustly stable. Numerical simulation results are given to show the advantages of the proposed nonlinear robust control method, compared to the robust loop-shaping control approach. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Angular scale expansion theory and the misperception of egocentric distance in locomotor space.

PubMed

Durgin, Frank H

Perception is crucial for the control of action, but perception need not be scaled accurately to produce accurate actions. This paper reviews evidence for an elegant new theory of locomotor space perception that is based on the dense coding of angular declination so that action control may be guided by richer feedback. The theory accounts for why so much direct-estimation data suggests that egocentric distance is underestimated despite the fact that action measures have been interpreted as indicating accurate perception. Actions are calibrated to the perceived scale of space and thus action measures are typically unable to distinguish systematic (e.g., linearly scaled) misperception from accurate perception. Whereas subjective reports of the scaling of linear extent are difficult to evaluate in absolute terms, study of the scaling of perceived angles (which exist in a known scale, delimited by vertical and horizontal) provides new evidence regarding the perceptual scaling of locomotor space.

An approximation theory for nonlinear partial differential equations with applications to identification and control

NASA Technical Reports Server (NTRS)

Banks, H. T.; Kunisch, K.

1982-01-01

Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

Adaptive Control Of Remote Manipulator

NASA Technical Reports Server (NTRS)

Seraji, Homayoun

1989-01-01

Robotic control system causes remote manipulator to follow closely reference trajectory in Cartesian reference frame in work space, without resort to computationally intensive mathematical model of robot dynamics and without knowledge of robot and load parameters. System, derived from linear multivariable theory, uses relatively simple feedforward and feedback controllers with model-reference adaptive control.

Linear dependence between the wavefront gradient and the masked intensity for the point source with a CCD sensor

NASA Astrophysics Data System (ADS)

Yang, Huizhen; Ma, Liang; Wang, Bin

2018-01-01

In contrast to the conventional adaptive optics (AO) system, the wavefront sensorless (WFSless) AO system doesn't need a WFS to measure the wavefront aberrations. It is simpler than the conventional AO in system architecture and can be applied to the complex conditions. The model-based WFSless system has a great potential in real-time correction applications because of its fast convergence. The control algorithm of the model-based WFSless system is based on an important theory result that is the linear relation between the Mean-Square Gradient (MSG) magnitude of the wavefront aberration and the second moment of the masked intensity distribution in the focal plane (also called as Masked Detector Signal-MDS). The linear dependence between MSG and MDS for the point source imaging with a CCD sensor will be discussed from theory and simulation in this paper. The theory relationship between MSG and MDS is given based on our previous work. To verify the linear relation for the point source, we set up an imaging model under atmospheric turbulence. Additionally, the value of MDS will be deviate from that of theory because of the noise of detector and further the deviation will affect the correction effect. The theory results under noise will be obtained through theoretical derivation and then the linear relation between MDS and MDS under noise will be discussed through the imaging model. Results show the linear relation between MDS and MDS under noise is also maintained well, which provides a theoretical support to applications of the model-based WFSless system.

Linear Mechanisms and Pressure Fluctuations in Wall Turbulence

NASA Astrophysics Data System (ADS)

Septham, Kamthon; Morrison, Jonathan

2014-11-01

Full-domain, linear feedback control of turbulent channel flow at Reτ <= 400 via vU' at low wavenumbers is an effective method to attenuate turbulent channel flow such that it is relaminarised. The passivity-based control approach is adopted and explained by the conservative characteristics of the nonlinear terms contributing to the Reynolds-Orr equation (Sharma et al .Phys .Fluids 2011). The linear forcing acts on the wall-normal velocity field and thus the pressure field via the linear (rapid) source term of the Poisson equation for pressure fluctuations, 2U'∂v/∂x . The minimum required spanwise wavelength resolution without losing control is constant at λz+ = 125, based on the wall friction velocity at t = 0 . The result shows that the maximum forcing is located at y+ ~ 20 , corresponding to the location of the maximum in the mean-square pressure gradient. The effectiveness of linear control is qualitatively explained by Landahl's theory for timescales, in that the control proceeds via the shear interaction timescale which is much shorter than both the nonlinear and viscous timescales. The response of the rapid (linear) and slow (nonlinear) pressure fluctuations to the linear control is examined and discussed.

Modeling and control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Mingori, D. L.

1988-01-01

This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory.

Unified control/structure design and modeling research

NASA Technical Reports Server (NTRS)

Mingori, D. L.; Gibson, J. S.; Blelloch, P. A.; Adamian, A.

1986-01-01

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed.

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.

Incompressible boundary-layer stability analysis of LFC experimental data for sub-critical Mach numbers. M.S. Thesis

NASA Technical Reports Server (NTRS)

Berry, S. A.

1986-01-01

An incompressible boundary-layer stability analysis of Laminar Flow Control (LFC) experimental data was completed and the results are presented. This analysis was undertaken for three reasons: to study laminar boundary-layer stability on a modern swept LFC airfoil; to calculate incompressible design limits of linear stability theory as applied to a modern airfoil at high subsonic speeds; and to verify the use of linear stability theory as a design tool. The experimental data were taken from the slotted LFC experiment recently completed in the NASA Langley 8-Foot Transonic Pressure Tunnel. Linear stability theory was applied and the results were compared with transition data to arrive at correlated n-factors. Results of the analysis showed that for the configuration and cases studied, Tollmien-Schlichting (TS) amplification was the dominating disturbance influencing transition. For these cases, incompressible linear stability theory correlated with an n-factor for TS waves of approximately 10 at transition. The n-factor method correlated rather consistently to this value despite a number of non-ideal conditions which indicates the method is useful as a design tool for advanced laminar flow airfoils.

Attitude and Configuration Control of Flexible Multi-Body Spacecraft

NASA Astrophysics Data System (ADS)

Cho, Sung-Ki; Cochran, John E., Jr.

2002-06-01

Multi-body spacecraft attitude and configuration control formulations based on the use of collaborative control theory are considered. The control formulations are based on two-player, nonzero-sum, differential game theory applied using a Nash strategy. It is desired that the control laws allow different components of the multi-body system to perform different tasks. For example, it may be desired that one body points toward a fixed star while another body in the system slews to track another satellite. Although similar to the linear quadratic regulator formulation, the collaborative control formulation contains a number of additional design parameters because the problem is formulated as two control problems coupled together. The use of the freedom of the partitioning of the total problem into two coupled control problems and the selection of the elements of the cross-coupling matrices are specific problems addressed in this paper. Examples are used to show that significant improvement in performance, as measured by realistic criteria, of collaborative control over conventional linear quadratic regulator control can be achieved by using proposed design guidelines.

Focal points and principal solutions of linear Hamiltonian systems revisited

NASA Astrophysics Data System (ADS)

Šepitka, Peter; Šimon Hilscher, Roman

2018-05-01

In this paper we present a novel view on the principal (and antiprincipal) solutions of linear Hamiltonian systems, as well as on the focal points of their conjoined bases. We present a new and unified theory of principal (and antiprincipal) solutions at a finite point and at infinity, and apply it to obtain new representation of the multiplicities of right and left proper focal points of conjoined bases. We show that these multiplicities can be characterized by the abnormality of the system in a neighborhood of the given point and by the rank of the associated T-matrix from the theory of principal (and antiprincipal) solutions. We also derive some additional important results concerning the representation of T-matrices and associated normalized conjoined bases. The results in this paper are new even for completely controllable linear Hamiltonian systems. We also discuss other potential applications of our main results, in particular in the singular Sturmian theory.

Control Variate Selection for Multiresponse Simulation.

DTIC Science & Technology

1987-05-01

M. H. Knuter, Applied Linear Regression Mfodels, Richard D. Erwin, Inc., Homewood, Illinois, 1983. Neuts, Marcel F., Probability, Allyn and Bacon...1982. Neter, J., V. Wasserman, and M. H. Knuter, Applied Linear Regression .fodels, Richard D. Erwin, Inc., Homewood, Illinois, 1983. Neuts, Marcel F...Aspects of J%,ultivariate Statistical Theory, John Wiley and Sons, New York, New York, 1982. dY Neter, J., W. Wasserman, and M. H. Knuter, Applied Linear Regression Mfodels

1985 Particle Accelerator Conference: Accelerator Engineering and Technology, 11th, Vancouver, Canada, May 13-16, 1985, Proceedings

NASA Astrophysics Data System (ADS)

Strathdee, A.

1985-10-01

The topics discussed are related to high-energy accelerators and colliders, particle sources and electrostatic accelerators, controls, instrumentation and feedback, beam dynamics, low- and intermediate-energy circular accelerators and rings, RF and other acceleration systems, beam injection, extraction and transport, operations and safety, linear accelerators, applications of accelerators, radiation sources, superconducting supercolliders, new acceleration techniques, superconducting components, cryogenics, and vacuum. Accelerator and storage ring control systems are considered along with linear and nonlinear orbit theory, transverse and longitudinal instabilities and cures, beam cooling, injection and extraction orbit theory, high current dynamics, general beam dynamics, and medical and radioisotope applications. Attention is given to superconducting RF structures, magnet technology, superconducting magnets, and physics opportunities with relativistic heavy ion accelerators.

Bisimulation equivalence of differential-algebraic systems

NASA Astrophysics Data System (ADS)

Megawati, Noorma Yulia; Schaft, Arjan van der

2018-01-01

In this paper, the notion of bisimulation relation for linear input-state-output systems is extended to general linear differential-algebraic (DAE) systems. Geometric control theory is used to derive a linear-algebraic characterisation of bisimulation relations, and an algorithm for computing the maximal bisimulation relation between two linear DAE systems. The general definition is specialised to the case where the matrix pencil sE - A is regular. Furthermore, by developing a one-sided version of bisimulation, characterisations of simulation and abstraction are obtained.

A Factorization Approach to the Linear Regulator Quadratic Cost Problem

NASA Technical Reports Server (NTRS)

Milman, M. H.

1985-01-01

A factorization approach to the linear regulator quadratic cost problem is developed. This approach makes some new connections between optimal control, factorization, Riccati equations and certain Wiener-Hopf operator equations. Applications of the theory to systems describable by evolution equations in Hilbert space and differential delay equations in Euclidean space are presented.

Structural Properties and Estimation of Delay Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kwong, R. H. S.

1975-01-01

Two areas in the theory of delay systems were studied: structural properties and their applications to feedback control, and optimal linear and nonlinear estimation. The concepts of controllability, stabilizability, observability, and detectability were investigated. The property of pointwise degeneracy of linear time-invariant delay systems is considered. Necessary and sufficient conditions for three dimensional linear systems to be made pointwise degenerate by delay feedback were obtained, while sufficient conditions for this to be possible are given for higher dimensional linear systems. These results were applied to obtain solvability conditions for the minimum time output zeroing control problem by delay feedback. A representation theorem is given for conditional moment functionals of general nonlinear stochastic delay systems, and stochastic differential equations are derived for conditional moment functionals satisfying certain smoothness properties.

Linear analysis near a steady-state of biochemical networks: Control analysis, correlation metrics and circuit theory

PubMed Central

Heuett, William J; Beard, Daniel A; Qian, Hong

2008-01-01

Background Several approaches, including metabolic control analysis (MCA), flux balance analysis (FBA), correlation metric construction (CMC), and biochemical circuit theory (BCT), have been developed for the quantitative analysis of complex biochemical networks. Here, we present a comprehensive theory of linear analysis for nonequilibrium steady-state (NESS) biochemical reaction networks that unites these disparate approaches in a common mathematical framework and thermodynamic basis. Results In this theory a number of relationships between key matrices are introduced: the matrix A obtained in the standard, linear-dynamic-stability analysis of the steady-state can be decomposed as A = SRT where R and S are directly related to the elasticity-coefficient matrix for the fluxes and chemical potentials in MCA, respectively; the control-coefficients for the fluxes and chemical potentials can be written in terms of RTBS and STBS respectively where matrix B is the inverse of A; the matrix S is precisely the stoichiometric matrix in FBA; and the matrix eAt plays a central role in CMC. Conclusion One key finding that emerges from this analysis is that the well-known summation theorems in MCA take different forms depending on whether metabolic steady-state is maintained by flux injection or concentration clamping. We demonstrate that if rate-limiting steps exist in a biochemical pathway, they are the steps with smallest biochemical conductances and largest flux control-coefficients. We hypothesize that biochemical networks for cellular signaling have a different strategy for minimizing energy waste and being efficient than do biochemical networks for biosynthesis. We also discuss the intimate relationship between MCA and biochemical systems analysis (BSA). PMID:18482450

Mathematical Techniques for Nonlinear System Theory.

DTIC Science & Technology

1981-09-01

This report deals with research results obtained in the following areas: (1) Finite-dimensional linear system theory by algebraic methods--linear...Infinite-dimensional linear systems--realization theory of infinite-dimensional linear systems; (3) Nonlinear system theory --basic properties of

Flight control application of new stability robustness bounds for linear uncertain systems

NASA Technical Reports Server (NTRS)

Yedavalli, Rama K.

1993-01-01

This paper addresses the issue of obtaining bounds on the real parameter perturbations of a linear state-space model for robust stability. Based on Kronecker algebra, new, easily computable sufficient bounds are derived that are much less conservative than the existing bounds since the technique is meant for only real parameter perturbations (in contrast to specializing complex variation case to real parameter case). The proposed theory is illustrated with application to several flight control examples.

Annual Review of Research Under the Joint Services Electronics Program.

DTIC Science & Technology

1983-12-01

Total Number of Professionals: PI 2 RA 2 (1/2 time ) 6. Sunmmary: Our research into the theory of nonlinear control systems and appli- * cations to...known that all linear time -invariant controllable systems can be transformed to Brunovsky canonical form by a transformation consist- ing only of...estimating the impulse response ( = transfer matrix) of a discrete- time linear system x(t+l) = Fx(t) + Gu(t) y(t) = Hx(t) from a finite set of finite

Application of a repetitive process setting to design of monotonically convergent iterative learning control

NASA Astrophysics Data System (ADS)

Boski, Marcin; Paszke, Wojciech

2015-11-01

This paper deals with the problem of designing an iterative learning control algorithm for discrete linear systems using repetitive process stability theory. The resulting design produces a stabilizing output feedback controller in the time domain and a feedforward controller that guarantees monotonic convergence in the trial-to-trial domain. The results are also extended to limited frequency range design specification. New design procedure is introduced in terms of linear matrix inequality (LMI) representations, which guarantee the prescribed performances of ILC scheme. A simulation example is given to illustrate the theoretical developments.

Nonlinear adaptive networks: A little theory, a few applications

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

Jones, R.D.; Qian, S.; Barnes, C.W.

1990-01-01

We present the theory of nonlinear adaptive networks and discuss a few applications. In particular, we review the theory of feedforward backpropagation networks. We than present the theory of the Connectionist Normalized Linear Spline network in both its feedforward and iterated modes. Also, we briefly discuss the theory of stochastic cellular automata. We then discuss applications to chaotic time series tidal prediction in Venice Lagoon, sonar transient detection, control of nonlinear processes, balancing a double inverted pendulum and design advice for free electron lasers. 26 refs., 23 figs.

Flatness-based embedded adaptive fuzzy control of turbocharged diesel engines

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Siano, Pierluigi; Arsie, Ivan

2014-10-01

In this paper nonlinear embedded control for turbocharged Diesel engines is developed with the use of Differential flatness theory and adaptive fuzzy control. It is shown that the dynamic model of the turbocharged Diesel engine is differentially flat and admits dynamic feedback linearization. It is also shown that the dynamic model can be written in the linear Brunovsky canonical form for which a state feedback controller can be easily designed. To compensate for modeling errors and external disturbances an adaptive fuzzy control scheme is implemanted making use of the transformed dynamical system of the diesel engine that is obtained through the application of differential flatness theory. Since only the system's output is measurable the complete state vector has to be reconstructed with the use of a state observer. It is shown that a suitable learning law can be defined for neuro-fuzzy approximators, which are part of the controller, so as to preserve the closed-loop system stability. With the use of Lyapunov stability analysis it is proven that the proposed observer-based adaptive fuzzy control scheme results in H∞ tracking performance.

Loop Shaping Control Design for a Supersonic Propulsion System Model Using Quantitative Feedback Theory (QFT) Specifications and Bounds

NASA Technical Reports Server (NTRS)

Connolly, Joseph W.; Kopasakis, George

2010-01-01

This paper covers the propulsion system component modeling and controls development of an integrated mixed compression inlet and turbojet engine that will be used for an overall vehicle Aero-Propulso-Servo-Elastic (APSE) model. Using previously created nonlinear component-level propulsion system models, a linear integrated propulsion system model and loop shaping control design have been developed. The design includes both inlet normal shock position control and jet engine rotor speed control for a potential supersonic commercial transport. A preliminary investigation of the impacts of the aero-elastic effects on the incoming flow field to the propulsion system are discussed, however, the focus here is on developing a methodology for the propulsion controls design that prevents unstart in the inlet and minimizes the thrust oscillation experienced by the vehicle. Quantitative Feedback Theory (QFT) specifications and bounds, and aspects of classical loop shaping are used in the control design process. Model uncertainty is incorporated in the design to address possible error in the system identification mapping of the nonlinear component models into the integrated linear model.

Self-optimizing Pitch Control for Large Scale Wind Turbine Based on ADRC

NASA Astrophysics Data System (ADS)

Xia, Anjun; Hu, Guoqing; Li, Zheng; Huang, Dongxiao; Wang, Fengxiang

2018-01-01

Since wind turbine is a complex nonlinear and strong coupling system, traditional PI control method can hardly achieve good control performance. A self-optimizing pitch control method based on the active-disturbance-rejection control theory is proposed in this paper. A linear model of the wind turbine is derived by linearizing the aerodynamic torque equation and the dynamic response of wind turbine is transformed into a first-order linear system. An expert system is designed to optimize the amplification coefficient according to the pitch rate and the speed deviation. The purpose of the proposed control method is to regulate the amplification coefficient automatically and keep the variations of pitch rate and rotor speed in proper ranges. Simulation results show that the proposed pitch control method has the ability to modify the amplification coefficient effectively, when it is not suitable, and keep the variations of pitch rate and rotor speed in proper ranges

Stimulation of a turbofan engine for evaluation of multivariable optimal control concepts. [(computerized simulation)

NASA Technical Reports Server (NTRS)

Seldner, K.

1976-01-01

The development of control systems for jet engines requires a real-time computer simulation. The simulation provides an effective tool for evaluating control concepts and problem areas prior to actual engine testing. The development and use of a real-time simulation of the Pratt and Whitney F100-PW100 turbofan engine is described. The simulation was used in a multi-variable optimal controls research program using linear quadratic regulator theory. The simulation is used to generate linear engine models at selected operating points and evaluate the control algorithm. To reduce the complexity of the design, it is desirable to reduce the order of the linear model. A technique to reduce the order of the model; is discussed. Selected results between high and low order models are compared. The LQR control algorithms can be programmed on digital computer. This computer will control the engine simulation over the desired flight envelope.

Loudspeakers: Modeling and control

NASA Astrophysics Data System (ADS)

Al-Ali, Khalid Mohammad

This thesis documented a comprehensive study of loudspeaker modeling and control. A lumped-parameter model for a voice-coil loudspeaker in a vented enclosure was presented that derived from a consideration of physical principles. In addition, a low-frequency (20 Hz to 100 Hz), feedback control method designed to improve the nonlinear performance of the loudspeaker and a suitable performance measure for use in design and evaluation were proposed. Data from experiments performed on a variety of actual loudspeakers confirmed the practicality of the theory developed in this work. The lumped-parameter loudspeaker model, although simple, captured much of the nonlinear behavior of the loudspeaker. In addition, the model formulation allowed a straightforward application of modern control system methods and lent itself well to modern parametric identification techniques. The nonlinear performance of the loudspeaker system was evaluated using a suitable distortion measure that was proposed and compared with other distortion measures currently used in practice. Furthermore, the linearizing effect of feedback using a linear controller (both static and dynamic) was studied on a class of nonlinear systems. The results illustrated that the distortion reduction was potentially significant and a useful upper bound on the closed-loop distortion was found based on the sensitivity function of the system's linearization. A feedback scheme based on robust control theory was chosen for application to the loudspeaker system. Using the pressure output of the loudspeaker system for feedback, the technique offered significant advantages over those previously attempted. Illustrative examples were presented that proved the applicability of the theory developed in this dissertation to a variety of loudspeaker systems. The examples included a vented loudspeaker model and actual loudspeakers enclosed in both vented and sealed configurations. In each example, predictable and measurable distortion reduction at the output of the closed-loop system was recorded.

Robustness in linear quadratic feedback design with application to an aircraft control problem

NASA Technical Reports Server (NTRS)

Patel, R. V.; Sridhar, B.; Toda, M.

1977-01-01

Some new results concerning robustness and asymptotic properties of error bounds of a linear quadratic feedback design are applied to an aircraft control problem. An autopilot for the flare control of the Augmentor Wing Jet STOL Research Aircraft (AWJSRA) is designed based on Linear Quadratic (LQ) theory and the results developed in this paper. The variation of the error bounds to changes in the weighting matrices in the LQ design is studied by computer simulations, and appropriate weighting matrices are chosen to obtain a reasonable error bound for variations in the system matrix and at the same time meet the practical constraints for the flare maneuver of the AWJSRA. Results from the computer simulation of a satisfactory autopilot design for the flare control of the AWJSRA are presented.

Attitude estimation of earth orbiting satellites by decomposed linear recursive filters

NASA Technical Reports Server (NTRS)

Kou, S. R.

1975-01-01

Attitude estimation of earth orbiting satellites (including Large Space Telescope) subjected to environmental disturbances and noises was investigated. Modern control and estimation theory is used as a tool to design an efficient estimator for attitude estimation. Decomposed linear recursive filters for both continuous-time systems and discrete-time systems are derived. By using this accurate estimation of the attitude of spacecrafts, state variable feedback controller may be designed to achieve (or satisfy) high requirements of system performance.

Optimal preview control for a linear continuous-time stochastic control system in finite-time horizon

NASA Astrophysics Data System (ADS)

Wu, Jiang; Liao, Fucheng; Tomizuka, Masayoshi

2017-01-01

This paper discusses the design of the optimal preview controller for a linear continuous-time stochastic control system in finite-time horizon, using the method of augmented error system. First, an assistant system is introduced for state shifting. Then, in order to overcome the difficulty of the state equation of the stochastic control system being unable to be differentiated because of Brownian motion, the integrator is introduced. Thus, the augmented error system which contains the integrator vector, control input, reference signal, error vector and state of the system is reconstructed. This leads to the tracking problem of the optimal preview control of the linear stochastic control system being transformed into the optimal output tracking problem of the augmented error system. With the method of dynamic programming in the theory of stochastic control, the optimal controller with previewable signals of the augmented error system being equal to the controller of the original system is obtained. Finally, numerical simulations show the effectiveness of the controller.

Quantitative Robust Control Engineering: Theory and Applications

DTIC Science & Technology

2006-09-01

30]. Gutman, PO., Baril , C. Neuman, L. (1994), An algorithm for computing value sets of uncertain transfer functions in factored real form...linear compensation design for saturating unstable uncertain plants. Int. J. Control, Vol. 44, pp. 1137-1146. [90]. Oldak S., Baril C. and Gutman

Application of modern control theory to the design of optimum aircraft controllers

NASA Technical Reports Server (NTRS)

Power, L. J.

1973-01-01

The synthesis procedure presented is based on the solution of the output regulator problem of linear optimal control theory for time-invariant systems. By this technique, solution of the matrix Riccati equation leads to a constant linear feedback control law for an output regulator which will maintain a plant in a particular equilibrium condition in the presence of impulse disturbances. Two simple algorithms are presented that can be used in an automatic synthesis procedure for the design of maneuverable output regulators requiring only selected state variables for feedback. The first algorithm is for the construction of optimal feedforward control laws that can be superimposed upon a Kalman output regulator and that will drive the output of a plant to a desired constant value on command. The second algorithm is for the construction of optimal Luenberger observers that can be used to obtain feedback control laws for the output regulator requiring measurement of only part of the state vector. This algorithm constructs observers which have minimum response time under the constraint that the magnitude of the gains in the observer filter be less than some arbitrary limit.

Computation of output feedback gains for linear stochastic systems using the Zangwill-Powell method

NASA Technical Reports Server (NTRS)

Kaufman, H.

1977-01-01

Because conventional optimal linear regulator theory results in a controller which requires the capability of measuring and/or estimating the entire state vector, it is of interest to consider procedures for computing controls which are restricted to be linear feedback functions of a lower dimensional output vector and which take into account the presence of measurement noise and process uncertainty. To this effect a stochastic linear model has been developed that accounts for process parameter and initial uncertainty, measurement noise, and a restricted number of measurable outputs. Optimization with respect to the corresponding output feedback gains was then performed for both finite and infinite time performance indices without gradient computation by using Zangwill's modification of a procedure originally proposed by Powell.

The Stability Region for Feedback Control of the Wake Behind Twin Oscillating Cylinders

NASA Astrophysics Data System (ADS)

Borggaard, Jeff; Gugercin, Serkan; Zietsman, Lizette

2016-11-01

Linear feedback control has the ability to stabilize vortex shedding behind twin cylinders where cylinder rotation is the actuation mechanism. Complete elimination of the wake is only possible for certain Reynolds numbers and cylinder spacing. This is related to the presence of asymmetric unstable modes in the linearized system. We investigate this region of parameter space using a number of closed-loop simulations that bound this region. We then consider the practical issue of designing feedback controls based on limited state measurements by building a nonlinear compensator using linear robust control theory with and incorporating the nonlinear terms in the compensator (e.g., using the extended Kalman filter). Interpolatory model reduction methods are applied to the large discretized, linearized Navier-Stokes system and used for computing the control laws and compensators. Preliminary closed-loop simulations of a three-dimensional version of this problem will also be presented. Supported in part by the National Science Foundation.

Flatness-based control and Kalman filtering for a continuous-time macroeconomic model

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Ghosh, T.; Busawon, K.; Binns, R.

2017-11-01

The article proposes flatness-based control for a nonlinear macro-economic model of the UK economy. The differential flatness properties of the model are proven. This enables to introduce a transformation (diffeomorphism) of the system's state variables and to express the state-space description of the model in the linear canonical (Brunowsky) form in which both the feedback control and the state estimation problem can be solved. For the linearized equivalent model of the macroeconomic system, stabilizing feedback control can be achieved using pole placement methods. Moreover, to implement stabilizing feedback control of the system by measuring only a subset of its state vector elements the Derivative-free nonlinear Kalman Filter is used. This consists of the Kalman Filter recursion applied on the linearized equivalent model of the financial system and of an inverse transformation that is based again on differential flatness theory. The asymptotic stability properties of the control scheme are confirmed.

Turbulence closure for mixing length theories

NASA Astrophysics Data System (ADS)

Jermyn, Adam S.; Lesaffre, Pierre; Tout, Christopher A.; Chitre, Shashikumar M.

2018-05-01

We present an approach to turbulence closure based on mixing length theory with three-dimensional fluctuations against a two-dimensional background. This model is intended to be rapidly computable for implementation in stellar evolution software and to capture a wide range of relevant phenomena with just a single free parameter, namely the mixing length. We incorporate magnetic, rotational, baroclinic, and buoyancy effects exactly within the formalism of linear growth theories with non-linear decay. We treat differential rotation effects perturbatively in the corotating frame using a novel controlled approximation, which matches the time evolution of the reference frame to arbitrary order. We then implement this model in an efficient open source code and discuss the resulting turbulent stresses and transport coefficients. We demonstrate that this model exhibits convective, baroclinic, and shear instabilities as well as the magnetorotational instability. It also exhibits non-linear saturation behaviour, and we use this to extract the asymptotic scaling of various transport coefficients in physically interesting limits.

Koopman Operator Framework for Time Series Modeling and Analysis

NASA Astrophysics Data System (ADS)

Surana, Amit

2018-01-01

We propose an interdisciplinary framework for time series classification, forecasting, and anomaly detection by combining concepts from Koopman operator theory, machine learning, and linear systems and control theory. At the core of this framework is nonlinear dynamic generative modeling of time series using the Koopman operator which is an infinite-dimensional but linear operator. Rather than working with the underlying nonlinear model, we propose two simpler linear representations or model forms based on Koopman spectral properties. We show that these model forms are invariants of the generative model and can be readily identified directly from data using techniques for computing Koopman spectral properties without requiring the explicit knowledge of the generative model. We also introduce different notions of distances on the space of such model forms which is essential for model comparison/clustering. We employ the space of Koopman model forms equipped with distance in conjunction with classical machine learning techniques to develop a framework for automatic feature generation for time series classification. The forecasting/anomaly detection framework is based on using Koopman model forms along with classical linear systems and control approaches. We demonstrate the proposed framework for human activity classification, and for time series forecasting/anomaly detection in power grid application.

Steering of Frequency Standards by the Use of Linear Quadratic Gaussian Control Theory

NASA Technical Reports Server (NTRS)

Koppang, Paul; Leland, Robert

1996-01-01

Linear quadratic Gaussian control is a technique that uses Kalman filtering to estimate a state vector used for input into a control calculation. A control correction is calculated by minimizing a quadratic cost function that is dependent on both the state vector and the control amount. Different penalties, chosen by the designer, are assessed by the controller as the state vector and control amount vary from given optimal values. With this feature controllers can be designed to force the phase and frequency differences between two standards to zero either more or less aggressively depending on the application. Data will be used to show how using different parameters in the cost function analysis affects the steering and the stability of the frequency standards.

Unsymmetric Lanczos model reduction and linear state function observer for flexible structures

NASA Technical Reports Server (NTRS)

Su, Tzu-Jeng; Craig, Roy R., Jr.

1991-01-01

This report summarizes part of the research work accomplished during the second year of a two-year grant. The research, entitled 'Application of Lanczos Vectors to Control Design of Flexible Structures' concerns various ways to use Lanczos vectors and Krylov vectors to obtain reduced-order mathematical models for use in the dynamic response analyses and in control design studies. This report presents a one-sided, unsymmetric block Lanczos algorithm for model reduction of structural dynamics systems with unsymmetric damping matrix, and a control design procedure based on the theory of linear state function observers to design low-order controllers for flexible structures.

Modern digital flight control system design for VTOL aircraft

NASA Technical Reports Server (NTRS)

Broussard, J. R.; Berry, P. W.; Stengel, R. F.

1979-01-01

Methods for and results from the design and evaluation of a digital flight control system (DFCS) for a CH-47B helicopter are presented. The DFCS employed proportional-integral control logic to provide rapid, precise response to automatic or manual guidance commands while following conventional or spiral-descent approach paths. It contained altitude- and velocity-command modes, and it adapted to varying flight conditions through gain scheduling. Extensive use was made of linear systems analysis techniques. The DFCS was designed, using linear-optimal estimation and control theory, and the effects of gain scheduling are assessed by examination of closed-loop eigenvalues and time responses.

On the Stability of Jump-Linear Systems Driven by Finite-State Machines with Markovian Inputs

NASA Technical Reports Server (NTRS)

Patilkulkarni, Sudarshan; Herencia-Zapana, Heber; Gray, W. Steven; Gonzalez, Oscar R.

2004-01-01

This paper presents two mean-square stability tests for a jump-linear system driven by a finite-state machine with a first-order Markovian input process. The first test is based on conventional Markov jump-linear theory and avoids the use of any higher-order statistics. The second test is developed directly using the higher-order statistics of the machine s output process. The two approaches are illustrated with a simple model for a recoverable computer control system.

Integrated control-system design via generalized LQG (GLQG) theory

NASA Technical Reports Server (NTRS)

Bernstein, Dennis S.; Hyland, David C.; Richter, Stephen; Haddad, Wassim M.

1989-01-01

Thirty years of control systems research has produced an enormous body of theoretical results in feedback synthesis. Yet such results see relatively little practical application, and there remains an unsettling gap between classical single-loop techniques (Nyquist, Bode, root locus, pole placement) and modern multivariable approaches (LQG and H infinity theory). Large scale, complex systems, such as high performance aircraft and flexible space structures, now demand efficient, reliable design of multivariable feedback controllers which optimally tradeoff performance against modeling accuracy, bandwidth, sensor noise, actuator power, and control law complexity. A methodology is described which encompasses numerous practical design constraints within a single unified formulation. The approach, which is based upon coupled systems or modified Riccati and Lyapunov equations, encompasses time-domain linear-quadratic-Gaussian theory and frequency-domain H theory, as well as classical objectives such as gain and phase margin via the Nyquist circle criterion. In addition, this approach encompasses the optimal projection approach to reduced-order controller design. The current status of the overall theory will be reviewed including both continuous-time and discrete-time (sampled-data) formulations.

Adaptive Importance Sampling for Control and Inference

NASA Astrophysics Data System (ADS)

Kappen, H. J.; Ruiz, H. C.

2016-03-01

Path integral (PI) control problems are a restricted class of non-linear control problems that can be solved formally as a Feynman-Kac PI and can be estimated using Monte Carlo sampling. In this contribution we review PI control theory in the finite horizon case. We subsequently focus on the problem how to compute and represent control solutions. We review the most commonly used methods in robotics and control. Within the PI theory, the question of how to compute becomes the question of importance sampling. Efficient importance samplers are state feedback controllers and the use of these requires an efficient representation. Learning and representing effective state-feedback controllers for non-linear stochastic control problems is a very challenging, and largely unsolved, problem. We show how to learn and represent such controllers using ideas from the cross entropy method. We derive a gradient descent method that allows to learn feed-back controllers using an arbitrary parametrisation. We refer to this method as the path integral cross entropy method or PICE. We illustrate this method for some simple examples. The PI control methods can be used to estimate the posterior distribution in latent state models. In neuroscience these problems arise when estimating connectivity from neural recording data using EM. We demonstrate the PI control method as an accurate alternative to particle filtering.

Supervisory control based on minimal cuts and Petri net sub-controllers coordination

NASA Astrophysics Data System (ADS)

Rezig, Sadok; Achour, Zied; Rezg, Nidhal; Kammoun, Mohamed-Ali

2016-10-01

This paper addresses the synthesis of Petri net (PN) controller for the forbidden state transition problem with a new utilisation of the theory of regions. Moreover, as any method of control synthesis based on a reachability graph, the theory of regions suffers from the combinatorial explosion problem. The proposed work minimises the number of equations in the linear system of theory of regions and therefore one can reduce the computation time. In this paper, two different approaches are proposed to select minimal cuts in the reachability graph in order to synthesise a PN controller. Thanks to a switch from one cut to another, one can activate and deactivate the corresponding PNcontroller. An application is implemented in a flexible manufacturing system to illustrate the present method. Finally, comparison with previous works with experimental results in obtaining a maximally permissive controller is presented.

Investigation, development, and application of optimal output feedback theory. Volume 3: The relationship between dynamic compensators and observers and Kalman filters

NASA Technical Reports Server (NTRS)

Broussard, John R.

1987-01-01

Relationships between observers, Kalman Filters and dynamic compensators using feedforward control theory are investigated. In particular, the relationship, if any, between the dynamic compensator state and linear functions of a discrete plane state are investigated. It is shown that, in steady state, a dynamic compensator driven by the plant output can be expressed as the sum of two terms. The first term is a linear combination of the plant state. The second term depends on plant and measurement noise, and the plant control. Thus, the state of the dynamic compensator can be expressed as an estimator of the first term with additive error given by the second term. Conditions under which a dynamic compensator is a Kalman filter are presented, and reduced-order optimal estimaters are investigated.

Cooperative global optimal preview tracking control of linear multi-agent systems: an internal model approach

NASA Astrophysics Data System (ADS)

Lu, Yanrong; Liao, Fucheng; Deng, Jiamei; Liu, Huiyang

2017-09-01

This paper investigates the cooperative global optimal preview tracking problem of linear multi-agent systems under the assumption that the output of a leader is a previewable periodic signal and the topology graph contains a directed spanning tree. First, a type of distributed internal model is introduced, and the cooperative preview tracking problem is converted to a global optimal regulation problem of an augmented system. Second, an optimal controller, which can guarantee the asymptotic stability of the augmented system, is obtained by means of the standard linear quadratic optimal preview control theory. Third, on the basis of proving the existence conditions of the controller, sufficient conditions are given for the original problem to be solvable, meanwhile a cooperative global optimal controller with error integral and preview compensation is derived. Finally, the validity of theoretical results is demonstrated by a numerical simulation.

Aircraft ride quality controller design using new robust root clustering theory for linear uncertain systems

NASA Technical Reports Server (NTRS)

Yedavalli, R. K.

1992-01-01

The aspect of controller design for improving the ride quality of aircraft in terms of damping ratio and natural frequency specifications on the short period dynamics is addressed. The controller is designed to be robust with respect to uncertainties in the real parameters of the control design model such as uncertainties in the dimensional stability derivatives, imperfections in actuator/sensor locations and possibly variations in flight conditions, etc. The design is based on a new robust root clustering theory developed by the author by extending the nominal root clustering theory of Gutman and Jury to perturbed matrices. The proposed methodology allows to get an explicit relationship between the parameters of the root clustering region and the uncertainty radius of the parameter space. The current literature available for robust stability becomes a special case of this unified theory. The bounds derived on the parameter perturbation for robust root clustering are then used in selecting the robust controller.

Optimal discrete-time LQR problems for parabolic systems with unbounded input: Approximation and convergence

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An abstract approximation and convergence theory for the closed-loop solution of discrete-time linear-quadratic regulator problems for parabolic systems with unbounded input is developed. Under relatively mild stabilizability and detectability assumptions, functional analytic, operator techniques are used to demonstrate the norm convergence of Galerkin-based approximations to the optimal feedback control gains. The application of the general theory to a class of abstract boundary control systems is considered. Two examples, one involving the Neumann boundary control of a one-dimensional heat equation, and the other, the vibration control of a cantilevered viscoelastic beam via shear input at the free end, are discussed.

A Nonlinear Physics-Based Optimal Control Method for Magnetostrictive Actuators

NASA Technical Reports Server (NTRS)

Smith, Ralph C.

1998-01-01

This paper addresses the development of a nonlinear optimal control methodology for magnetostrictive actuators. At moderate to high drive levels, the output from these actuators is highly nonlinear and contains significant magnetic and magnetomechanical hysteresis. These dynamics must be accommodated by models and control laws to utilize the full capabilities of the actuators. A characterization based upon ferromagnetic mean field theory provides a model which accurately quantifies both transient and steady state actuator dynamics under a variety of operating conditions. The control method consists of a linear perturbation feedback law used in combination with an optimal open loop nonlinear control. The nonlinear control incorporates the hysteresis and nonlinearities inherent to the transducer and can be computed offline. The feedback control is constructed through linearization of the perturbed system about the optimal system and is efficient for online implementation. As demonstrated through numerical examples, the combined hybrid control is robust and can be readily implemented in linear PDE-based structural models.

Combined linear theory/impact theory method for analysis and design of high speed configurations

NASA Technical Reports Server (NTRS)

Brooke, D.; Vondrasek, D. V.

1980-01-01

Pressure distributions on a wing body at Mach 4.63 are calculated. The combined theory is shown to give improved predictions over either linear theory or impact theory alone. The combined theory is also applied in the inverse design mode to calculate optimum camber slopes at Mach 4.63. Comparisons with optimum camber slopes obtained from unmodified linear theory show large differences. Analysis of the results indicate that the combined theory correctly predicts the effect of thickness on the loading distributions at high Mach numbers, and that finite thickness wings optimized at high Mach numbers using unmodified linear theory will not achieve the minimum drag characteristics for which they are designed.

Linearization instability for generic gravity in AdS spacetime

NASA Astrophysics Data System (ADS)

Altas, Emel; Tekin, Bayram

2018-01-01

In general relativity, perturbation theory about a background solution fails if the background spacetime has a Killing symmetry and a compact spacelike Cauchy surface. This failure, dubbed as linearization instability, shows itself as non-integrability of the perturbative infinitesimal deformation to a finite deformation of the background. Namely, the linearized field equations have spurious solutions which cannot be obtained from the linearization of exact solutions. In practice, one can show the failure of the linear perturbation theory by showing that a certain quadratic (integral) constraint on the linearized solutions is not satisfied. For non-compact Cauchy surfaces, the situation is different and for example, Minkowski space having a non-compact Cauchy surface, is linearization stable. Here we study, the linearization instability in generic metric theories of gravity where Einstein's theory is modified with additional curvature terms. We show that, unlike the case of general relativity, for modified theories even in the non-compact Cauchy surface cases, there are some theories which show linearization instability about their anti-de Sitter backgrounds. Recent D dimensional critical and three dimensional chiral gravity theories are two such examples. This observation sheds light on the paradoxical behavior of vanishing conserved charges (mass, angular momenta) for non-vacuum solutions, such as black holes, in these theories.

Tackling non-linearities with the effective field theory of dark energy and modified gravity

NASA Astrophysics Data System (ADS)

Frusciante, Noemi; Papadomanolakis, Georgios

2017-12-01

We present the extension of the effective field theory framework to the mildly non-linear scales. The effective field theory approach has been successfully applied to the late time cosmic acceleration phenomenon and it has been shown to be a powerful method to obtain predictions about cosmological observables on linear scales. However, mildly non-linear scales need to be consistently considered when testing gravity theories because a large part of the data comes from those scales. Thus, non-linear corrections to predictions on observables coming from the linear analysis can help in discriminating among different gravity theories. We proceed firstly by identifying the necessary operators which need to be included in the effective field theory Lagrangian in order to go beyond the linear order in perturbations and then we construct the corresponding non-linear action. Moreover, we present the complete recipe to map any single field dark energy and modified gravity models into the non-linear effective field theory framework by considering a general action in the Arnowitt-Deser-Misner formalism. In order to illustrate this recipe we proceed to map the beyond-Horndeski theory and low-energy Hořava gravity into the effective field theory formalism. As a final step we derived the 4th order action in term of the curvature perturbation. This allowed us to identify the non-linear contributions coming from the linear order perturbations which at the next order act like source terms. Moreover, we confirm that the stability requirements, ensuring the positivity of the kinetic term and the speed of propagation for scalar mode, are automatically satisfied once the viability of the theory is demanded at linear level. The approach we present here will allow to construct, in a model independent way, all the relevant predictions on observables at mildly non-linear scales.

Program LRCDM2: Improved aerodynamic prediction program for supersonic canard-tail missiles with axisymmetric bodies

NASA Technical Reports Server (NTRS)

Dillenius, Marnix F. E.

1985-01-01

Program LRCDM2 was developed for supersonic missiles with axisymmetric bodies and up to two finned sections. Predicted are pressure distributions and loads acting on a complete configuration including effects of body separated flow vorticity and fin-edge vortices. The computer program is based on supersonic panelling and line singularity methods coupled with vortex tracking theory. Effects of afterbody shed vorticity on the afterbody and tail-fin pressure distributions can be optionally treated by companion program BDYSHD. Preliminary versions of combined shock expansion/linear theory and Newtonian/linear theory have been implemented as optional pressure calculation methods to extend the Mach number and angle-of-attack ranges of applicability into the nonlinear supersonic flow regime. Comparisons between program results and experimental data are given for a triform tail-finned configuration and for a canard controlled configuration with a long afterbody for Mach numbers up to 2.5. Initial tests of the nonlinear/linear theory approaches show good agreement for pressures acting on a rectangular wing and a delta wing with attached shocks for Mach numbers up to 4.6 and angles of attack up to 20 degrees.

Control of AUVs using differential flatness theory and the derivative-free nonlinear Kalman Filter

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Raffo, Guilerme

2015-12-01

The paper proposes nonlinear control and filtering for Autonomous Underwater Vessels (AUVs) based on differential flatness theory and on the use of the Derivative-free nonlinear Kalman Filter. First, it is shown that the 6-DOF dynamic model of the AUV is a differentially flat one. This enables its transformation into the linear canonical (Brunovsky) form and facilitates the design of a state feedback controller. A problem that has to be dealt with is the uncertainty about the parameters of the AUV's dynamic model, as well the external perturbations which affect its motion. To cope with this, it is proposed to use a disturbance observer which is based on the Derivative-free nonlinear Kalman Filter. The considered filtering method consists of the standard Kalman Filter recursion applied on the linearized model of the vessel and of an inverse transformation based on differential flatness theory, which enables to obtain estimates of the state variables of the initial nonlinear model of the vessel. The Kalman Filter-based disturbance observer performs simultaneous estimation of the non-measurable state variables of the AUV and of the perturbation terms that affect its dynamics. By estimating such disturbances, their compensation is also succeeded through suitable modification of the feedback control input. The efficiency of the proposed AUV control and estimation scheme is confirmed through simulation experiments.

Recent Developments In Theory Of Balanced Linear Systems

NASA Technical Reports Server (NTRS)

Gawronski, Wodek

1994-01-01

Report presents theoretical study of some issues of controllability and observability of system represented by linear, time-invariant mathematical model of the form. x = Ax + Bu, y = Cx + Du, x(0) = xo where x is n-dimensional vector representing state of system; u is p-dimensional vector representing control input to system; y is q-dimensional vector representing output of system; n,p, and q are integers; x(0) is intial (zero-time) state vector; and set of matrices (A,B,C,D) said to constitute state-space representation of system.

Controlling Flexible Manipulators, an Experimental Investigation. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Hastings, Gordon Greene

1986-01-01

Lightweight, slender manipulators offer faster response and/or greater workspace range for the same size actuators than tradional manipulators. Lightweight construction of manipulator links results in increased structural flexibility. The increase flexibility must be considered in the design of control systems to properly account for the dynamic flexible vibrations and static deflections. Real time control of the flexible manipulator vibrations are experimentally investigated. Models intended for real-time control of distributed parameter system such as flexible manipulators rely on model approximation schemes. An linear model based on the application of Lagrangian dynamics to a rigid body mode and a series of separable flexible modes is examined with respect to model order requirements, and modal candidate selection. Balanced realizations are applied to the linear flexible model to obtain an estimate of appropriate order for a selected model. Describing the flexible deflections as a linear combination of modes results in measurements of beam state, which yield information about several modes. To realize the potential of linear systems theory, knowledge of each state must be available. State estimation is also accomplished by implementation of a Kalman Filter. State feedback control laws are implemented based upon linear quadratic regulator design.

Nonlinear compensation techniques for magnetic suspension systems. Ph.D. Thesis - MIT

NASA Technical Reports Server (NTRS)

Trumper, David L.

1991-01-01

In aerospace applications, magnetic suspension systems may be required to operate over large variations in air-gap. Thus the nonlinearities inherent in most types of suspensions have a significant effect. Specifically, large variations in operating point may make it difficult to design a linear controller which gives satisfactory stability and performance over a large range of operating points. One way to address this problem is through the use of nonlinear compensation techniques such as feedback linearization. Nonlinear compensators have received limited attention in the magnetic suspension literature. In recent years, progress has been made in the theory of nonlinear control systems, and in the sub-area of feedback linearization. The idea is demonstrated of feedback linearization using a second order suspension system. In the context of the second order suspension, sampling rate issues in the implementation of feedback linearization are examined through simulation.

An adaptive Cartesian control scheme for manipulators

NASA Technical Reports Server (NTRS)

Seraji, H.

1987-01-01

A adaptive control scheme for direct control of manipulator end-effectors to achieve trajectory tracking in Cartesian space is developed. The control structure is obtained from linear multivariable theory and is composed of simple feedforward and feedback controllers and an auxiliary input. The direct adaptation laws are derived from model reference adaptive control theory and are not based on parameter estimation of the robot model. The utilization of feedforward control and the inclusion of auxiliary input are novel features of the present scheme and result in improved dynamic performance over existing adaptive control schemes. The adaptive controller does not require the complex mathematical model of the robot dynamics or any knowledge of the robot parameters or the payload, and is computationally fast for online implementation with high sampling rates.

An application of modern control theory to jet propulsion systems. [considering onboard computer

NASA Technical Reports Server (NTRS)

Merrill, W. C.

1975-01-01

The control of an airbreathing turbojet engine by an onboard digital computer is studied. The approach taken is to model the turbojet engine as a linear, multivariable system whose parameters vary with engine operating environment. From this model adaptive closed-loop or feedback control laws are designed and applied to the acceleration of the turbojet engine.

Aerospace plane guidance using geometric control theory

NASA Technical Reports Server (NTRS)

Van Buren, Mark A.; Mease, Kenneth D.

1990-01-01

A reduced-order method employing decomposition, based on time-scale separation, of the 4-D state space in a 2-D slow manifold and a family of 2-D fast manifolds is shown to provide an excellent approximation to the full-order minimum-fuel ascent trajectory. Near-optimal guidance is obtained by tracking the reduced-order trajectory. The tracking problem is solved as regulation problems on the family of fast manifolds, using the exact linearization methodology from nonlinear geometric control theory. The validity of the overall guidance approach is indicated by simulation.

Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

Complementary Roles of Care and Behavioral Control in Classroom Management: The Self-Determination Theory Perspective

ERIC Educational Resources Information Center

Nie, Youyan; Lau, Shun

2009-01-01

This study examined how classroom management practices--care and behavioral control--were differentially associated with students' engagement, misbehavior, and satisfaction with school, using a large representative sample of 3196 Grade 9 students from 117 classes in Singapore. Results of hierarchical linear modeling showed differential relations.…

Theory, simulation and experiments for precise deflection control of radiotherapy electron beams.

PubMed

Figueroa, R; Leiva, J; Moncada, R; Rojas, L; Santibáñez, M; Valente, M; Velásquez, J; Young, H; Zelada, G; Yáñez, R; Guillen, Y

2018-03-08

Conventional radiotherapy is mainly applied by linear accelerators. Although linear accelerators provide dual (electron/photon) radiation beam modalities, both of them are intrinsically produced by a megavoltage electron current. Modern radiotherapy treatment techniques are based on suitable devices inserted or attached to conventional linear accelerators. Thus, precise control of delivered beam becomes a main key issue. This work presents an integral description of electron beam deflection control as required for novel radiotherapy technique based on convergent photon beam production. Theoretical and Monte Carlo approaches were initially used for designing and optimizing device´s components. Then, dedicated instrumentation was developed for experimental verification of electron beam deflection due to the designed magnets. Both Monte Carlo simulations and experimental results support the reliability of electrodynamics models used to predict megavoltage electron beam control. Copyright © 2018 Elsevier Ltd. All rights reserved.

Simple robust control laws for robot manipulators. Part 2: Adaptive case

NASA Technical Reports Server (NTRS)

Bayard, D. S.; Wen, J. T.

1987-01-01

A new class of asymptotically stable adaptive control laws is introduced for application to the robotic manipulator. Unlike most applications of adaptive control theory to robotic manipulators, this analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and utilizes a parameterization based on physical (time-invariant) quantities. This approach is made possible by using energy-like Lyapunov functions which retain the nonlinear character and structure of the dynamics, rather than simple quadratic forms which are ubiquitous to the adaptive control literature, and which have bound the theory tightly to linear systems with unknown parameters. It is a unique feature of these results that the adaptive forms arise by straightforward certainty equivalence adaptation of their nonadaptive counterparts found in the companion to this paper (i.e., by replacing unknown quantities by their estimates) and that this simple approach leads to asymptotically stable closed-loop adaptive systems. Furthermore, it is emphasized that this approach does not require convergence of the parameter estimates (i.e., via persistent excitation), invertibility of the mass matrix estimate, or measurement of the joint accelerations.

A mathematical theory of learning control for linear discrete multivariable systems

NASA Technical Reports Server (NTRS)

Phan, Minh; Longman, Richard W.

1988-01-01

When tracking control systems are used in repetitive operations such as robots in various manufacturing processes, the controller will make the same errors repeatedly. Here consideration is given to learning controllers that look at the tracking errors in each repetition of the process and adjust the control to decrease these errors in the next repetition. A general formalism is developed for learning control of discrete-time (time-varying or time-invariant) linear multivariable systems. Methods of specifying a desired trajectory (such that the trajectory can actually be performed by the discrete system) are discussed, and learning controllers are developed. Stability criteria are obtained which are relatively easy to use to insure convergence of the learning process, and proper gain settings are discussed in light of measurement noise and system uncertainties.

Particle trapping: A key requisite of structure formation and stability of Vlasov–Poisson plasmas

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

Schamel, Hans, E-mail: hans.schamel@uni-bayreuth.de

2015-04-15

Particle trapping is shown to control the existence of undamped coherent structures in Vlasov–Poisson plasmas and thereby affects the onset of plasma instability beyond the realm of linear Landau theory.

Feasibility of Decentralized Linear-Quadratic-Gaussian Control of Autonomous Distributed Spacecraft

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

1999-01-01

A distributed satellite formation, modeled as an arbitrary number of fully connected nodes in a network, could be controlled using a decentralized controller framework that distributes operations in parallel over the network. For such problems, a solution that minimizes data transmission requirements, in the context of linear-quadratic-Gaussian (LQG) control theory, was given by Speyer. This approach is advantageous because it is non-hierarchical, detected failures gracefully degrade system performance, fewer local computations are required than for a centralized controller, and it is optimal with respect to the standard LQG cost function. Disadvantages of the approach are the need for a fully connected communications network, the total operations performed over all the nodes are greater than for a centralized controller, and the approach is formulated for linear time-invariant systems. To investigate the feasibility of the decentralized approach to satellite formation flying, a simple centralized LQG design for a spacecraft orbit control problem is adapted to the decentralized framework. The simple design uses a fixed reference trajectory (an equatorial, Keplerian, circular orbit), and by appropriate choice of coordinates and measurements is formulated as a linear time-invariant system.

Substructural controller synthesis

NASA Technical Reports Server (NTRS)

Su, Tzu-Jeng; Craig, Roy R., Jr.

1989-01-01

A decentralized design procedure which combines substructural synthesis, model reduction, decentralized controller design, subcontroller synthesis, and controller reduction is proposed for the control design of flexible structures. The structure to be controlled is decomposed into several substructures, which are modeled by component mode synthesis methods. For each substructure, a subcontroller is designed by using the linear quadratic optimal control theory. Then, a controller synthesis scheme called Substructural Controller Synthesis (SCS) is used to assemble the subcontrollers into a system controller, which is to be used to control the whole structure.

Numerical Evaluation of the "Dual-Kernel Counter-flow" Matric Convolution Integral that Arises in Discrete/Continuous (D/C) Control Theory

NASA Technical Reports Server (NTRS)

Nixon, Douglas D.

2009-01-01

Discrete/Continuous (D/C) control theory is a new generalized theory of discrete-time control that expands the concept of conventional (exact) discrete-time control to create a framework for design and implementation of discretetime control systems that include a continuous-time command function generator so that actuator commands need not be constant between control decisions, but can be more generally defined and implemented as functions that vary with time across sample period. Because the plant/control system construct contains two linear subsystems arranged in tandem, a novel dual-kernel counter-flow convolution integral appears in the formulation. As part of the D/C system design and implementation process, numerical evaluation of that integral over the sample period is required. Three fundamentally different evaluation methods and associated algorithms are derived for the constant-coefficient case. Numerical results are matched against three available examples that have closed-form solutions.

Feedback Control Systems Loop Shaping Design with Practical Considerations

NASA Technical Reports Server (NTRS)

Kopsakis, George

2007-01-01

This paper describes loop shaping control design in feedback control systems, primarily from a practical stand point that considers design specifications. Classical feedback control design theory, for linear systems where the plant transfer function is known, has been around for a long time. But it s still a challenge of how to translate the theory into practical and methodical design techniques that simultaneously satisfy a variety of performance requirements such as transient response, stability, and disturbance attenuation while taking into account the capabilities of the plant and its actuation system. This paper briefly addresses some relevant theory, first in layman s terms, so that it becomes easily understood and then it embarks into a practical and systematic design approach incorporating loop shaping design coupled with lead-lag control compensation design. The emphasis is in generating simple but rather powerful design techniques that will allow even designers with a layman s knowledge in controls to develop effective feedback control designs.

Computation of output feedback gains for linear stochastic systems using the Zangnill-Powell Method

NASA Technical Reports Server (NTRS)

Kaufman, H.

1975-01-01

Because conventional optimal linear regulator theory results in a controller which requires the capability of measuring and/or estimating the entire state vector, it is of interest to consider procedures for computing controls which are restricted to be linear feedback functions of a lower dimensional output vector and which take into account the presence of measurement noise and process uncertainty. To this effect a stochastic linear model has been developed that accounts for process parameter and initial uncertainty, measurement noise, and a restricted number of measurable outputs. Optimization with respect to the corresponding output feedback gains was then performed for both finite and infinite time performance indices without gradient computation by using Zangwill's modification of a procedure originally proposed by Powell. Results using a seventh order process show the proposed procedures to be very effective.

Dark energy and modified gravity in the Effective Field Theory of Large-Scale Structure

NASA Astrophysics Data System (ADS)

Cusin, Giulia; Lewandowski, Matthew; Vernizzi, Filippo

2018-04-01

We develop an approach to compute observables beyond the linear regime of dark matter perturbations for general dark energy and modified gravity models. We do so by combining the Effective Field Theory of Dark Energy and Effective Field Theory of Large-Scale Structure approaches. In particular, we parametrize the linear and nonlinear effects of dark energy on dark matter clustering in terms of the Lagrangian terms introduced in a companion paper [1], focusing on Horndeski theories and assuming the quasi-static approximation. The Euler equation for dark matter is sourced, via the Newtonian potential, by new nonlinear vertices due to modified gravity and, as in the pure dark matter case, by the effects of short-scale physics in the form of the divergence of an effective stress tensor. The effective fluid introduces a counterterm in the solution to the matter continuity and Euler equations, which allows a controlled expansion of clustering statistics on mildly nonlinear scales. We use this setup to compute the one-loop dark-matter power spectrum.

Experimental verification of rank 1 chaos in switch-controlled Chua circuit.

PubMed

Oksasoglu, Ali; Ozoguz, Serdar; Demirkol, Ahmet S; Akgul, Tayfun; Wang, Qiudong

2009-03-01

In this paper, we provide the first experimental proof for the existence of rank 1 chaos in the switch-controlled Chua circuit by following a step-by-step procedure given by the theory of rank 1 maps. At the center of this procedure is a periodically kicked limit cycle obtained from the unforced system. Then, this limit cycle is subjected to periodic kicks by adding externally controlled switches to the original circuit. Both the smooth nonlinearity and the piecewise linear cases are considered in this experimental investigation. Experimental results are found to be in concordance with the conclusions of the theory.

Approximations of thermoelastic and viscoelastic control systems

NASA Technical Reports Server (NTRS)

Burns, J. A.; Liu, Z. Y.; Miller, R. E.

1990-01-01

Well-posed models and computational algorithms are developed and analyzed for control of a class of partial differential equations that describe the motions of thermo-viscoelastic structures. An abstract (state space) framework and a general well-posedness result are presented that can be applied to a large class of thermo-elastic and thermo-viscoelastic models. This state space framework is used in the development of a computational scheme to be used in the solution of a linear quadratic regulator (LQR) control problem. A detailed convergence proof is provided for the viscoelastic model and several numerical results are presented to illustrate the theory and to analyze problems for which the theory is incomplete.

A feedback linearization approach to spacecraft control using momentum exchange devices. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Dzielski, John Edward

1988-01-01

Recent developments in the area of nonlinear control theory have shown how coordiante changes in the state and input spaces can be used with nonlinear feedback to transform certain nonlinear ordinary differential equations into equivalent linear equations. These feedback linearization techniques are applied to resolve two problems arising in the control of spacecraft equipped with control moment gyroscopes (CMGs). The first application involves the computation of rate commands for the gimbals that rotate the individual gyroscopes to produce commanded torques on the spacecraft. The second application is to the long-term management of stored momentum in the system of control moment gyroscopes using environmental torques acting on the vehicle. An approach to distributing control effort among a group of redundant actuators is described that uses feedback linearization techniques to parameterize sets of controls which influence a specified subsystem in a desired way. The approach is adapted for use in spacecraft control with double-gimballed gyroscopes to produce an algorithm that avoids problematic gimbal configurations by approximating sets of gimbal rates that drive CMG rotors into desirable configurations. The momentum management problem is stated as a trajectory optimization problem with a nonlinear dynamical constraint. Feedback linearization and collocation are used to transform this problem into an unconstrainted nonlinear program. The approach to trajectory optimization is fast and robust. A number of examples are presented showing applications to the proposed NASA space station.

Anatomy of an experimental two-link flexible manipulator under end-point control

NASA Technical Reports Server (NTRS)

Oakley, Celia M.; Cannon, Robert H., Jr.

1990-01-01

The design and experimental implementation of an end-point controller for two-link flexible manipulators are presented. The end-point controller is based on linear quadratic Gaussian (LQG) theory and is shown to exhibit significant improvements in trajectory tracking over a conventional controller design. To understand the behavior of the manipulator structure under end-point control, a strobe sequence illustrating the link deflections during a typical slew maneuver is included.

Model based control of dynamic atomic force microscope.

PubMed

Lee, Chibum; Salapaka, Srinivasa M

2015-04-01

A model-based robust control approach is proposed that significantly improves imaging bandwidth for the dynamic mode atomic force microscopy. A model for cantilever oscillation amplitude and phase dynamics is derived and used for the control design. In particular, the control design is based on a linearized model and robust H(∞) control theory. This design yields a significant improvement when compared to the conventional proportional-integral designs and verified by experiments.

Non-linear interaction of a detonation/vorticity wave

NASA Technical Reports Server (NTRS)

Lasseigne, D. G.; Jackson, T. L.; Hussaini, M. Y.

1991-01-01

The interaction of an oblique, overdriven detonation wave with a vorticity disturbance is investigated by a direct two-dimensional numerical simulation using a multi-domain, finite-difference solution of the compressible Euler equations. The results are compared to those of linear theory, which predict that the effect of exothermicity on the interaction is relatively small except possibly near a critical angle where linear theory no longer holds. It is found that the steady-state computational results agree with the results of linear theory. However, for cases with incident angle near the critical angle, moderate disturbance amplitudes, and/or sudden transient encounter with a disturbance, the effects of exothermicity are more pronounced than predicted by linear theory. Finally, it is found that linear theory correctly determines the critical angle.

Application of quadratic optimization to supersonic inlet control.

NASA Technical Reports Server (NTRS)

Lehtinen, B.; Zeller, J. R.

1972-01-01

This paper describes the application of linear stochastic optimal control theory to the design of the control system for the air intake, the inlet, of a supersonic air-breathing propulsion system. The controls must maintain a stable inlet shock position in the presence of random airflow disturbances and prevent inlet unstart. Two different linear time invariant controllers are developed. One is designed to minimize a nonquadratic index, the expected frequency of inlet unstart, and the other is designed to minimize the mean square value of inlet shock motion. The quadratic equivalence principle is used to obtain a linear controller that minimizes the nonquadratic index. The two controllers are compared on the basis of unstart prevention, control effort requirements, and frequency response. It is concluded that while controls designed to minimize unstarts are desirable in that the index minimized is physically meaningful, computation time required is longer than for the minimum mean square shock position approach. The simpler minimum mean square shock position solution produced expected unstart frequency values which were not significantly larger than those of the nonquadratic solution.

Controlling the wave propagation through the medium designed by linear coordinate transformation

NASA Astrophysics Data System (ADS)

Wu, Yicheng; He, Chengdong; Wang, Yuzhuo; Liu, Xuan; Zhou, Jing

2015-01-01

Based on the principle of transformation optics, we propose to control the wave propagating direction through the homogenous anisotropic medium designed by linear coordinate transformation. The material parameters of the medium are derived from the linear coordinate transformation applied. Keeping the space area unchanged during the linear transformation, the polarization-dependent wave control through a non-magnetic homogeneous medium can be realized. Beam benders, polarization splitter, and object illusion devices are designed, which have application prospects in micro-optics and nano-optics. The simulation results demonstrate the feasibilities and the flexibilities of the method and the properties of these devices. Design details and full-wave simulation results are provided. The work in this paper comprehensively applies the fundamental theories of electromagnetism and mathematics. The method of obtaining a new solution of the Maxwell equations in a medium from a vacuum plane wave solution and a linear coordinate transformation is introduced. These have a pedagogical value and are methodologically and motivationally appropriate for physics students and teachers at the undergraduate and graduate levels.

The Linear Quadratic Gaussian Multistage Game with Nonclassical Information Pattern Using a Direct Solution Method

NASA Astrophysics Data System (ADS)

Clemens, Joshua William

Game theory has application across multiple fields, spanning from economic strategy to optimal control of an aircraft and missile on an intercept trajectory. The idea of game theory is fascinating in that we can actually mathematically model real-world scenarios and determine optimal decision making. It may not always be easy to mathematically model certain real-world scenarios, nonetheless, game theory gives us an appreciation for the complexity involved in decision making. This complexity is especially apparent when the players involved have access to different information upon which to base their decision making (a nonclassical information pattern). Here we will focus on the class of adversarial two-player games (sometimes referred to as pursuit-evasion games) with nonclassical information pattern. We present a two-sided (simultaneous) optimization solution method for the two-player linear quadratic Gaussian (LQG) multistage game. This direct solution method allows for further interpretation of each player's decision making (strategy) as compared to previously used formal solution methods. In addition to the optimal control strategies, we present a saddle point proof and we derive an expression for the optimal performance index value. We provide some numerical results in order to further interpret the optimal control strategies and to highlight real-world application of this game-theoretic optimal solution.

Linear, multivariable robust control with a mu perspective

NASA Technical Reports Server (NTRS)

Packard, Andy; Doyle, John; Balas, Gary

1993-01-01

The structured singular value is a linear algebra tool developed to study a particular class of matrix perturbation problems arising in robust feedback control of multivariable systems. These perturbations are called linear fractional, and are a natural way to model many types of uncertainty in linear systems, including state-space parameter uncertainty, multiplicative and additive unmodeled dynamics uncertainty, and coprime factor and gap metric uncertainty. The structured singular value theory provides a natural extension of classical SISO robustness measures and concepts to MIMO systems. The structured singular value analysis, coupled with approximate synthesis methods, make it possible to study the tradeoff between performance and uncertainty that occurs in all feedback systems. In MIMO systems, the complexity of the spatial interactions in the loop gains make it difficult to heuristically quantify the tradeoffs that must occur. This paper examines the role played by the structured singular value (and its computable bounds) in answering these questions, as well as its role in the general robust, multivariable control analysis and design problem.

Quantum corrections to the generalized Proca theory via a matter field

NASA Astrophysics Data System (ADS)

Amado, André; Haghani, Zahra; Mohammadi, Azadeh; Shahidi, Shahab

2017-09-01

We study the quantum corrections to the generalized Proca theory via matter loops. We consider two types of interactions, linear and nonlinear in the vector field. Calculating the one-loop correction to the vector field propagator, three- and four-point functions, we show that the non-linear interactions are harmless, although they renormalize the theory. The linear matter-vector field interactions introduce ghost degrees of freedom to the generalized Proca theory. Treating the theory as an effective theory, we calculate the energy scale up to which the theory remains healthy.

Applications of nonlinear systems theory to control design

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1988-01-01

For most applications in the control area, the standard practice is to approximate a nonlinear mathematical model by a linear system. Since the feedback linearizable systems contain linear systems as a subclass, the procedure of approximating a nonlinear system by a feedback linearizable one is examined. Because many physical plants (e.g., aircraft at the NASA Ames Research Center) have mathematical models which are close to feedback linearizable systems, such approximations are certainly justified. Results and techniques are introduced for measuring the gap between the model and its truncated linearizable part. The topic of pure feedback systems is important to the study.

Some optimal considerations in attitude control systems. [evaluation of value of relative weighting between time and fuel for relay control law

NASA Technical Reports Server (NTRS)

Boland, J. S., III

1973-01-01

The conventional six-engine reaction control jet relay attitude control law with deadband is shown to be a good linear approximation to a weighted time-fuel optimal control law. Techniques for evaluating the value of the relative weighting between time and fuel for a particular relay control law is studied along with techniques to interrelate other parameters for the two control laws. Vehicle attitude control laws employing control moment gyros are then investigated. Steering laws obtained from the expression for the reaction torque of the gyro configuration are compared to a total optimal attitude control law that is derived from optimal linear regulator theory. This total optimal attitude control law has computational disadvantages in the solving of the matrix Riccati equation. Several computational algorithms for solving the matrix Riccati equation are investigated with respect to accuracy, computational storage requirements, and computational speed.

Stabilization of Inviscid Vortex Sheets

NASA Astrophysics Data System (ADS)

Protas, Bartosz; Sakajo, Takashi

2017-11-01

In this study we investigate the problem of stabilizing inviscid vortex sheets via feedback control. Such models, expressed in terms of the Birkhoff-Rott equation, are often used to describe the Kevin-Helmholtz instability of shear layers and are known to be strongly unstable to small-scale perturbations. First, we consider the linear stability of a straight vortex sheet in the periodic setting with actuation in the form of an array of point vortices or sources located a certain distance away from the sheet. We establish conditions under which this system is controllable and observable. Next, using methods of the linear control theory, we synthesize a feedback control strategy which stabilizes a straight vortex sheet in the linear regime. Given the poor conditioning of the discretized problem, reliable solution of the resulting algebraic Riccati equation requires the use of high-precision arithmetic. Finally, we demonstrate that this control approach also succeeds in the nonlinear regime, provided the magnitude of the initial perturbation is sufficiently small.

Movement Precision and Amplitude as Separate Factors in the Control of Movement.

ERIC Educational Resources Information Center

Kerr, Robert

The purpose of this study was to assess Welford's dual controlling factor interpretation of Fitts' Law--describing movement time as being a linear function of movement distance (or amplitude) and the required precision of the movement (or target width). Welford's amplification of the theory postulates that two separate processes ought to be…

Information distribution in distributed microprocessor based flight control systems

NASA Technical Reports Server (NTRS)

Montgomery, R. C.; Lee, P. S.

1977-01-01

This paper presents an optimal control theory that accounts for variable time intervals in the information distribution to control effectors in a distributed microprocessor based flight control system. The theory is developed using a linear process model for the aircraft dynamics and the information distribution process is modeled as a variable time increment process where, at the time that information is supplied to the control effectors, the control effectors know the time of the next information update only in a stochastic sense. An optimal control problem is formulated and solved that provides the control law that minimizes the expected value of a quadratic cost function. An example is presented where the theory is applied to the control of the longitudinal motions of the F8-DFBW aircraft. Theoretical and simulation results indicate that, for the example problem, the optimal cost obtained using a variable time increment Markov information update process where the control effectors know only the past information update intervals and the Markov transition mechanism is almost identical to that obtained using a known uniform information update interval.

A Resume of Stochastic, Time-Varying, Linear System Theory with Application to Active-Sonar Signal-Processing Problems

DTIC Science & Technology

1981-06-15

relationships 5 3. Normalized energy in ambiguity function for i = 0 14 k ilI SACLANTCEN SR-50 A RESUME OF STOCHASTIC, TIME-VARYING, LINEAR SYSTEM THEORY WITH...the order in which systems are concatenated is unimportant. These results are exactly analogous to the results of time-invariant linear system theory in...REFERENCES 1. MEIER, L. A rdsum6 of deterministic time-varying linear system theory with application to active sonar signal processing problems, SACLANTCEN

Suboptimal LQR-based spacecraft full motion control: Theory and experimentation

NASA Astrophysics Data System (ADS)

Guarnaccia, Leone; Bevilacqua, Riccardo; Pastorelli, Stefano P.

2016-05-01

This work introduces a real time suboptimal control algorithm for six-degree-of-freedom spacecraft maneuvering based on a State-Dependent-Algebraic-Riccati-Equation (SDARE) approach and real-time linearization of the equations of motion. The control strategy is sub-optimal since the gains of the linear quadratic regulator (LQR) are re-computed at each sample time. The cost function of the proposed controller has been compared with the one obtained via a general purpose optimal control software, showing, on average, an increase in control effort of approximately 15%, compensated by real-time implementability. Lastly, the paper presents experimental tests on a hardware-in-the-loop six-degree-of-freedom spacecraft simulator, designed for testing new guidance, navigation, and control algorithms for nano-satellites in a one-g laboratory environment. The tests show the real-time feasibility of the proposed approach.

Orbit control of a stratospheric satellite with parameter uncertainties

NASA Astrophysics Data System (ADS)

Xu, Ming; Huo, Wei

2016-12-01

When a stratospheric satellite travels by prevailing winds in the stratosphere, its cross-track displacement needs to be controlled to keep a constant latitude orbital flight. To design the orbit control system, a 6 degree-of-freedom (DOF) model of the satellite is established based on the second Lagrangian formulation, it is proven that the input/output feedback linearization theory cannot be directly implemented for the orbit control with this model, thus three subsystem models are deduced from the 6-DOF model to develop a sequential nonlinear control strategy. The control strategy includes an adaptive controller for the balloon-tether subsystem with uncertain balloon parameters, a PD controller based on feedback linearization for the tether-sail subsystem, and a sliding mode controller for the sail-rudder subsystem with uncertain sail parameters. Simulation studies demonstrate that the proposed control strategy is robust to uncertainties and satisfies high precision requirements for the orbit flight of the satellite.

The role of modern control theory in the design of controls for aircraft turbine engines

NASA Technical Reports Server (NTRS)

Zeller, J.; Lehtinen, B.; Merrill, W.

1982-01-01

The development, applications, and current research in modern control theory (MCT) are reviewed, noting the importance for fuel-efficient operation of turbines with variable inlet guide vanes, compressor stators, and exhaust nozzle area. The evolution of multivariable propulsion control design is examined, noting a basis in a matrix formulation of the differential equations defining the process, leading to state space formulations. Reports and papers which appeared from 1970-1982 which dealt with problems in MCT applications to turbine engine control design are outlined, including works on linear quadratic regulator methods, frequency domain methods, identification, estimation, and model reduction, detection, isolation, and accommodation, and state space control, adaptive control, and optimization approaches. Finally, NASA programs in frequency domain design, sensor failure detection, computer-aided control design, and plant modeling are explored

Linear and nonlinear 2D finite element analysis of sloshing modes and pressures in rectangular tanks subject to horizontal harmonic motions

NASA Astrophysics Data System (ADS)

Virella, Juan C.; Prato, Carlos A.; Godoy, Luis A.

2008-05-01

The influence of nonlinear wave theory on the sloshing natural periods and their modal pressure distributions are investigated for rectangular tanks under the assumption of two-dimensional behavior. Natural periods and mode shapes are computed and compared for both linear wave theory (LWT) and nonlinear wave theory (NLWT) models, using the finite element package ABAQUS. Linear wave theory is implemented in an acoustic model, whereas a plane strain problem with large displacements is used in NLWT. Pressure distributions acting on the tank walls are obtained for the first three sloshing modes using both linear and nonlinear wave theory. It is found that the nonlinearity does not have significant effects on the natural sloshing periods. For the sloshing pressures on the tank walls, different distributions were found using linear and nonlinear wave theory models. However, in all cases studied, the linear wave theory conservatively estimated the magnitude of the pressure distribution, whereas larger pressures resultant heights were obtained when using the nonlinear theory. It is concluded that the nonlinearity of the surface wave does not have major effects in the pressure distribution on the walls for rectangular tanks.

B-737 Linear Autoland Simulink Model

NASA Technical Reports Server (NTRS)

Belcastro, Celeste (Technical Monitor); Hogge, Edward F.

2004-01-01

The Linear Autoland Simulink model was created to be a modular test environment for testing of control system components in commercial aircraft. The input variables, physical laws, and referenced frames used are summarized. The state space theory underlying the model is surveyed and the location of the control actuators described. The equations used to realize the Dryden gust model to simulate winds and gusts are derived. A description of the pseudo-random number generation method used in the wind gust model is included. The longitudinal autopilot, lateral autopilot, automatic throttle autopilot, engine model and automatic trim devices are considered as subsystems. The experience in converting the Airlabs FORTRAN aircraft control system simulation to a graphical simulation tool (Matlab/Simulink) is described.

Lagrangian or Eulerian; real or Fourier? Not all approaches to large-scale structure are created equal

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

Tassev, Svetlin, E-mail: tassev@astro.princeton.edu

We present a pedagogical systematic investigation of the accuracy of Eulerian and Lagrangian perturbation theories of large-scale structure. We show that significant differences exist between them especially when trying to model the Baryon Acoustic Oscillations (BAO). We find that the best available model of the BAO in real space is the Zel'dovich Approximation (ZA), giving an accuracy of ∼<3% at redshift of z = 0 in modelling the matter 2-pt function around the acoustic peak. All corrections to the ZA around the BAO scale are perfectly perturbative in real space. Any attempt to achieve better precision requires calibrating the theorymore » to simulations because of the need to renormalize those corrections. In contrast, theories which do not fully preserve the ZA as their solution, receive O(1) corrections around the acoustic peak in real space at z = 0, and are thus of suspicious convergence at low redshift around the BAO. As an example, we find that a similar accuracy of 3% for the acoustic peak is achieved by Eulerian Standard Perturbation Theory (SPT) at linear order only at z ≈ 4. Thus even when SPT is perturbative, one needs to include loop corrections for z∼<4 in real space. In Fourier space, all models perform similarly, and are controlled by the overdensity amplitude, thus recovering standard results. However, that comes at a price. Real space cleanly separates the BAO signal from non-linear dynamics. In contrast, Fourier space mixes signal from short mildly non-linear scales with the linear signal from the BAO to the level that non-linear contributions from short scales dominate. Therefore, one has little hope in constructing a systematic theory for the BAO in Fourier space.« less

Geometry program for aerodynamic lifting surface theory

NASA Technical Reports Server (NTRS)

Medan, R. T.

1973-01-01

A computer program that provides the geometry and boundary conditions appropriate for an analysis of a lifting, thin wing with control surfaces in linearized, subsonic, steady flow is presented. The kernel function method lifting surface theory is applied. The data which is generated by the program is stored on disk files or tapes for later use by programs which calculate an influence matrix, plot the wing planform, and evaluate the loads on the wing. In addition to processing data for subsequent use in a lifting surface analysis, the program is useful for computing area and mean geometric chords of the wing and control surfaces.

Sliding Mode Thermal Control System for Space Station Furnace Facility

NASA Technical Reports Server (NTRS)

Jackson Mark E.; Shtessel, Yuri B.

1998-01-01

The decoupled control of the nonlinear, multiinput-multioutput, and highly coupled space station furnace facility (SSFF) thermal control system is addressed. Sliding mode control theory, a subset of variable-structure control theory, is employed to increase the performance, robustness, and reliability of the SSFF's currently designed control system. This paper presents the nonlinear thermal control system description and develops the sliding mode controllers that cause the interconnected subsystems to operate in their local sliding modes, resulting in control system invariance to plant uncertainties and external and interaction disturbances. The desired decoupled flow-rate tracking is achieved by optimization of the local linear sliding mode equations. The controllers are implemented digitally and extensive simulation results are presented to show the flow-rate tracking robustness and invariance to plant uncertainties, nonlinearities, external disturbances, and variations of the system pressure supplied to the controlled subsystems.

Trajectory tracking control for underactuated stratospheric airship

NASA Astrophysics Data System (ADS)

Zheng, Zewei; Huo, Wei; Wu, Zhe

2012-10-01

Stratospheric airship is a new kind of aerospace system which has attracted worldwide developing interests for its broad application prospects. Based on the trajectory linearization control (TLC) theory, a novel trajectory tracking control method for an underactuated stratospheric airship is presented in this paper. Firstly, the TLC theory is described sketchily, and the dynamic model of the stratospheric airship is introduced with kinematics and dynamics equations. Then, the trajectory tracking control strategy is deduced in detail. The designed control system possesses a cascaded structure which consists of desired attitude calculation, position control loop and attitude control loop. Two sub-loops are designed for the position and attitude control loops, respectively, including the kinematics control loop and dynamics control loop. Stability analysis shows that the controlled closed-loop system is exponentially stable. Finally, simulation results for the stratospheric airship to track typical trajectories are illustrated to verify effectiveness of the proposed approach.

Learning-based position control of a closed-kinematic chain robot end-effector

NASA Technical Reports Server (NTRS)

Nguyen, Charles C.; Zhou, Zhen-Lei

1990-01-01

A trajectory control scheme whose design is based on learning theory, for a six-degree-of-freedom (DOF) robot end-effector built to study robotic assembly of NASA hardwares in space is presented. The control scheme consists of two control systems: the feedback control system and the learning control system. The feedback control system is designed using the concept of linearization about a selected operating point, and the method of pole placement so that the closed-loop linearized system is stabilized. The learning control scheme consisting of PD-type learning controllers, provides additional inputs to improve the end-effector performance after each trial. Experimental studies performed on a 2 DOF end-effector built at CUA, for three tracking cases show that actual trajectories approach desired trajectories as the number of trials increases. The tracking errors are substantially reduced after only five trials.

Optimal control theory investigation of proprotor/wing response to vertical gust

NASA Technical Reports Server (NTRS)

Frick, J. K. D.; Johnson, W.

1974-01-01

Optimal control theory is used to design linear state variable feedback to improve the dynamic characteristics of a rotor and cantilever wing representing the tilting proprotor aircraft in cruise flight. The response to a vertical gust and system damping are used as criteria for the open and closed loop performance. The improvement in the dynamic characteristics achievable is examined for a gimballed rotor and for a hingeless rotor design. Several features of the design process are examined, including: (1) using only the wing or only the rotor dynamics in the control system design; (2) the use of a wing flap as well as the rotor controls for inputs; (3) and the performance of the system designed for one velocity at other forward speeds.

A manual control theory analysis of vertical situation displays for STOL aircraft

NASA Technical Reports Server (NTRS)

Baron, S.; Levison, W. H.

1973-01-01

Pilot-vehicle-display systems theory is applied to the analysis of proposed vertical situation displays for manual control in approach-to-landing of a STOL aircraft. The effects of display variables on pilot workload and on total closed-loop system performance was calculated using an optimal-control model for the human operator. The steep approach of an augmentor wing jet STOL aircraft was analyzed. Both random turbulence and mean-wind shears were considered. Linearized perturbation equations were used to describe longitudinal and lateral dynamics of the aircraft. The basic display configuration was one that abstracted the essential status information (including glide-slope and localizer errors) of an EADI display. Proposed flight director displays for both longitudinal and lateral control were also investigated.

Optimal regulation in systems with stochastic time sampling

NASA Technical Reports Server (NTRS)

Montgomery, R. C.; Lee, P. S.

1980-01-01

An optimal control theory that accounts for stochastic variable time sampling in a distributed microprocessor based flight control system is presented. The theory is developed by using a linear process model for the airplane dynamics and the information distribution process is modeled as a variable time increment process where, at the time that information is supplied to the control effectors, the control effectors know the time of the next information update only in a stochastic sense. An optimal control problem is formulated and solved for the control law that minimizes the expected value of a quadratic cost function. The optimal cost obtained with a variable time increment Markov information update process where the control effectors know only the past information update intervals and the Markov transition mechanism is almost identical to that obtained with a known and uniform information update interval.

Direct adaptive control of manipulators in Cartesian space

NASA Technical Reports Server (NTRS)

Seraji, H.

1987-01-01

A new adaptive-control scheme for direct control of manipulator end effector to achieve trajectory tracking in Cartesian space is developed in this article. The control structure is obtained from linear multivariable theory and is composed of simple feedforward and feedback controllers and an auxiliary input. The direct adaptation laws are derived from model reference adaptive control theory and are not based on parameter estimation of the robot model. The utilization of adaptive feedforward control and the inclusion of auxiliary input are novel features of the present scheme and result in improved dynamic performance over existing adaptive control schemes. The adaptive controller does not require the complex mathematical model of the robot dynamics or any knowledge of the robot parameters or the payload, and is computationally fast for on-line implementation with high sampling rates. The control scheme is applied to a two-link manipulator for illustration.

Adaptive Control of Linear Modal Systems Using Residual Mode Filters and a Simple Disturbance Estimator

NASA Technical Reports Server (NTRS)

Balas, Mark; Frost, Susan

2012-01-01

Flexible structures containing a large number of modes can benefit from adaptive control techniques which are well suited to applications that have unknown modeling parameters and poorly known operating conditions. In this paper, we focus on a direct adaptive control approach that has been extended to handle adaptive rejection of persistent disturbances. We extend our adaptive control theory to accommodate troublesome modal subsystems of a plant that might inhibit the adaptive controller. In some cases the plant does not satisfy the requirements of Almost Strict Positive Realness. Instead, there maybe be a modal subsystem that inhibits this property. This section will present new results for our adaptive control theory. We will modify the adaptive controller with a Residual Mode Filter (RMF) to compensate for the troublesome modal subsystem, or the Q modes. Here we present the theory for adaptive controllers modified by RMFs, with attention to the issue of disturbances propagating through the Q modes. We apply the theoretical results to a flexible structure example to illustrate the behavior with and without the residual mode filter.

The response of multidegree-of-freedom systems with quadratic non-linearities to a harmonic parametric resonance

NASA Astrophysics Data System (ADS)

Nayfeh, A. H.

1983-09-01

An analysis is presented of the response of multidegree-of-freedom systems with quadratic non-linearities to a harmonic parametric excitation in the presence of an internal resonance of the combination type ω3 ≈ ω2 + ω1, where the ωn are the linear natural frequencies of the systems. In the case of a fundamental resonance of the third mode (i.e., Ω ≈ω 3, where Ω is the frequency of the excitation), one can identify two critical values ζ 1 and ζ 2, where ζ 2 ⩾ ζ 1, of the amplitude F of the excitation. The value F = ζ2 corresponds to the transition from stable to unstable solutions. When F < ζ1, the motion decays to zero according to both linear and non-linear theories. When F > ζ2, the motion grows exponentially with time according to the linear theory but the non-linearity limits the motion to a finite amplitude steady state. The amplitude of the third mode, which is directly excited, is independent of F, whereas the amplitudes of the first and second modes, which are indirectly excited through the internal resonance, are functions of F. When ζ1 ⩽ F ⩽ ζ2, the motion decays or achieves a finite amplitude steady state depending on the initial conditions according to the non-linear theory, whereas it decays to zero according to the linear theory. This is an example of subcritical instability. In the case of a fundamental resonance of either the first or second mode, the trivial response is the only possible steady state. When F ⩽ ζ2, the motion decays to zero according to both linear and non-linear theories. When F > ζ2, the motion grows exponentially with time according to the linear theory but it is aperiodic according to the non-linear theory. Experiments are being planned to check these theoretical results.

Control by model error estimation

NASA Technical Reports Server (NTRS)

Likins, P. W.; Skelton, R. E.

1976-01-01

Modern control theory relies upon the fidelity of the mathematical model of the system. Truncated modes, external disturbances, and parameter errors in linear system models are corrected by augmenting to the original system of equations an 'error system' which is designed to approximate the effects of such model errors. A Chebyshev error system is developed for application to the Large Space Telescope (LST).

Control of the maneuvering SCOLE structure

NASA Technical Reports Server (NTRS)

Lim, S.; Meirovitch, L.

1992-01-01

This paper is concerned with the vibration control of the SCOLE structure while it undergoes a slewing maneuver. The control law is designed according to the linear quadratic regulator theory. In view of saturation limits on the actuators, the actual implementation is modified so as to observe these limits, resulting in suboptimal control. State estimation is carried out by means of a Kalman filter. The control and state estimation are carried out in discrete time. Numerical simulations for several cases of interest are presented.

Do deterrence and social-control theories predict driving after drinking 15 years after a DWI conviction?

PubMed

Lapham, Sandra C; Todd, Michael

2012-03-01

This study investigates the utility of deterrence and social-control theories for prospective prediction of driving-while-impaired (DWI) outcomes of first-time DWI offenders. The sample consisted of a subset of 544 convicted first-time DWI offenders (N=337 females) who were interviewed 5 and 15 years after referral to a Screening Program in Bernalillo County, New Mexico. Variables collected at the 5-year (initial) interview were used in structural equation models to predict past 3-months, self-reported DWI at the 15-year follow-up (follow-up) interview. These variables represented domains defined by deterrence and social-control theories of DWI behavior, with one model corresponding to deterrence theory and one to social-control theory. Both models fit the data. DWI jail time was positively related to perceived enforcement, which was negatively but not significantly related to self-reported DWI. Neither jail time for DWI nor perceived likelihood of arrest was linearly related to self-reported DWI at follow-up. Interactions between jail time and prior DWI behavior indicated relatively weaker associations between initial and 15-year DWI for those reporting more jail time. Our prospective study demonstrated that for this convicted DWI offender cohort, classic formulations of deterrence and social-control theories did not account for DWI. However, results suggest that punishment may decrease the likelihood of DWI recidivism. Copyright © 2012 Elsevier Ltd. All rights reserved.

Theory of an airfoil equipped with a jet flap under low-speed flight conditions

NASA Technical Reports Server (NTRS)

Addessio, F. L.; Skifstad, J. G.

1975-01-01

A theory is developed, for the inviscid, incompressible flow past a thin airfoil equipped with a thin, part-span jet flap, by treating the induced flowfields of the jet and the wing separately and by obtaining the fully coupled solution in an iterative manner. Spanwise variation of the jet vortex strength is assumed to be elliptical in the analysis. Since the method considers the vorticity associated with the jet to be positioned on the computed locus of the jet, the downwash aft of the wing is evaluated as well as forces and moments on the wing. A lifting-surface theory is incorporated for the aerodynamics of the wing. Computational results are presented for a rectangular wing at momentum coefficients above 2.0 and compared with existing linear theories and experimental data. Good agreement is found for small angles of attack, jet-deflection angles, and jet-momentum coefficients where the linear theories and experimental data are applicable. Downwash data at a point in the vicinity of a control surface, the load distribution on the airfoil, and the jet, and the jet location are also presented for representative flight conditons.

Feasibility of combining linear theory and impact theory methods for the analysis and design of high speed configurations

NASA Technical Reports Server (NTRS)

Brooke, D.; Vondrasek, D. V.

1978-01-01

The aerodynamic influence coefficients calculated using an existing linear theory program were used to modify the pressures calculated using impact theory. Application of the combined approach to several wing-alone configurations shows that the combined approach gives improved predictions of the local pressure and loadings over either linear theory alone or impact theory alone. The approach not only removes most of the short-comings of the individual methods, as applied in the Mach 4 to 8 range, but also provides the basis for an inverse design procedure applicable to high speed configurations.

Employing Theories Far beyond Their Limits - Linear Dichroism Theory.

PubMed

Mayerhöfer, Thomas G

2018-05-15

Using linear polarized light, it is possible in case of ordered structures, such as stretched polymers or single crystals, to determine the orientation of the transition moments of electronic and vibrational transitions. This not only helps to resolve overlapping bands, but also assigning the symmetry species of the transitions and to elucidate the structure. To perform spectral evaluation quantitatively, a sometimes "Linear Dichroism Theory" called approach is very often used. This approach links the relative orientation of the transition moment and polarization direction to the quantity absorbance. This linkage is highly questionable for several reasons. First of all, absorbance is a quantity that is by its definition not compatible with Maxwell's equations. Furthermore, absorbance seems not to be the quantity which is generally compatible with linear dichroism theory. In addition, linear dichroism theory disregards that it is not only the angle between transition moment and polarization direction, but also the angle between sample surface and transition moment, that influences band shape and intensity. Accordingly, the often invoked "magic angle" has never existed and the orientation distribution influences spectra to a much higher degree than if linear dichroism theory would hold strictly. A last point that is completely ignored by linear dichroism theory is the fact that partially oriented or randomly-oriented samples usually consist of ordered domains. It is their size relative to the wavelength of light that can also greatly influence a spectrum. All these findings can help to elucidate orientation to a much higher degree by optical methods than currently thought possible by the users of linear dichroism theory. Hence, it is the goal of this contribution to point out these shortcomings of linear dichroism theory to its users to stimulate efforts to overcome the long-lasting stagnation of this important field. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Data-driven discovery of Koopman eigenfunctions using deep learning

NASA Astrophysics Data System (ADS)

Lusch, Bethany; Brunton, Steven L.; Kutz, J. Nathan

2017-11-01

Koopman operator theory transforms any autonomous non-linear dynamical system into an infinite-dimensional linear system. Since linear systems are well-understood, a mapping of non-linear dynamics to linear dynamics provides a powerful approach to understanding and controlling fluid flows. However, finding the correct change of variables remains an open challenge. We present a strategy to discover an approximate mapping using deep learning. Our neural networks find this change of variables, its inverse, and a finite-dimensional linear dynamical system defined on the new variables. Our method is completely data-driven and only requires measurements of the system, i.e. it does not require derivatives or knowledge of the governing equations. We find a minimal set of approximate Koopman eigenfunctions that are sufficient to reconstruct and advance the system to future states. We demonstrate the method on several dynamical systems.

From linear to nonlinear control means: a practical progression.

PubMed

Gao, Zhiqiang

2002-04-01

With the rapid advance of digital control hardware, it is time to take the simple but effective proportional-integral-derivative (PID) control technology to the next level of performance and robustness. For this purpose, a nonlinear PID and active disturbance rejection framework are introduced in this paper. It complements the existing theory in that (1) it actively and systematically explores the use of nonlinear control mechanisms for better performance, even for linear plants; (2) it represents a control strategy that is rather independent of mathematical models of the plants, thus achieving inherent robustness and reducing design complexity. Stability analysis, as well as software/hardware test results, are presented. It is evident that the proposed framework lends itself well in seeking innovative solutions to practical problems while maintaining the simplicity and the intuitiveness of the existing technology.

Application of nonlinear transformations to automatic flight control

NASA Technical Reports Server (NTRS)

Meyer, G.; Su, R.; Hunt, L. R.

1984-01-01

The theory of transformations of nonlinear systems to linear ones is applied to the design of an automatic flight controller for the UH-1H helicopter. The helicopter mathematical model is described and it is shown to satisfy the necessary and sufficient conditions for transformability. The mapping is constructed, taking the nonlinear model to canonical form. The performance of the automatic control system in a detailed simulation on the flight computer is summarized.

Alterations in theory of mind in patients with schizophrenia and non-psychotic relatives.

PubMed

Janssen, I; Krabbendam, L; Jolles, J; van Os, Jim

2003-08-01

It has been proposed that alterations in theory of mind underlie specific symptoms of psychosis. The present study examined whether alterations in theory of mind reflect a trait that can be detected in non-psychotic relatives of patients with schizophrenia. Participants were 43 patients with schizophrenia or schizoaffective disorder, 41 first-degree non-psychotic relatives and 43 controls from the general population. Theory of mind was assessed using a hinting task and a false-belief task. There was a significant association between schizophrenia risk and failure on the hinting task (OR linear trend = 2.01, 95% CI: 1.22-3.31), with relatives having intermediate values between patients and controls. Adjustment for IQ and neuropsychological factors reduced the association by small amounts. The association between schizophrenia risk and failure on the false-belief tasks was not significant. Changes in theory of mind are associated with schizophrenia liability. General cognitive ability and neuropsychological measures seem to mediate only part of this association.

Massively parallel and linear-scaling algorithm for second-order Møller-Plesset perturbation theory applied to the study of supramolecular wires

NASA Astrophysics Data System (ADS)

Kjærgaard, Thomas; Baudin, Pablo; Bykov, Dmytro; Eriksen, Janus Juul; Ettenhuber, Patrick; Kristensen, Kasper; Larkin, Jeff; Liakh, Dmitry; Pawłowski, Filip; Vose, Aaron; Wang, Yang Min; Jørgensen, Poul

2017-03-01

We present a scalable cross-platform hybrid MPI/OpenMP/OpenACC implementation of the Divide-Expand-Consolidate (DEC) formalism with portable performance on heterogeneous HPC architectures. The Divide-Expand-Consolidate formalism is designed to reduce the steep computational scaling of conventional many-body methods employed in electronic structure theory to linear scaling, while providing a simple mechanism for controlling the error introduced by this approximation. Our massively parallel implementation of this general scheme has three levels of parallelism, being a hybrid of the loosely coupled task-based parallelization approach and the conventional MPI +X programming model, where X is either OpenMP or OpenACC. We demonstrate strong and weak scalability of this implementation on heterogeneous HPC systems, namely on the GPU-based Cray XK7 Titan supercomputer at the Oak Ridge National Laboratory. Using the "resolution of the identity second-order Møller-Plesset perturbation theory" (RI-MP2) as the physical model for simulating correlated electron motion, the linear-scaling DEC implementation is applied to 1-aza-adamantane-trione (AAT) supramolecular wires containing up to 40 monomers (2440 atoms, 6800 correlated electrons, 24 440 basis functions and 91 280 auxiliary functions). This represents the largest molecular system treated at the MP2 level of theory, demonstrating an efficient removal of the scaling wall pertinent to conventional quantum many-body methods.

Robust design of feedback feed-forward iterative learning control based on 2D system theory for linear uncertain systems

NASA Astrophysics Data System (ADS)

Li, Zhifu; Hu, Yueming; Li, Di

2016-08-01

For a class of linear discrete-time uncertain systems, a feedback feed-forward iterative learning control (ILC) scheme is proposed, which is comprised of an iterative learning controller and two current iteration feedback controllers. The iterative learning controller is used to improve the performance along the iteration direction and the feedback controllers are used to improve the performance along the time direction. First of all, the uncertain feedback feed-forward ILC system is presented by an uncertain two-dimensional Roesser model system. Then, two robust control schemes are proposed. One can ensure that the feedback feed-forward ILC system is bounded-input bounded-output stable along time direction, and the other can ensure that the feedback feed-forward ILC system is asymptotically stable along time direction. Both schemes can guarantee the system is robust monotonically convergent along the iteration direction. Third, the robust convergent sufficient conditions are given, which contains a linear matrix inequality (LMI). Moreover, the LMI can be used to determine the gain matrix of the feedback feed-forward iterative learning controller. Finally, the simulation results are presented to demonstrate the effectiveness of the proposed schemes.

Loop shaping design for tracking performance in machine axes.

PubMed

Schinstock, Dale E; Wei, Zhouhong; Yang, Tao

2006-01-01

A modern interpretation of classical loop shaping control design methods is presented in the context of tracking control for linear motor stages. Target applications include noncontacting machines such as laser cutters and markers, water jet cutters, and adhesive applicators. The methods are directly applicable to the common PID controller and are pertinent to many electromechanical servo actuators other than linear motors. In addition to explicit design techniques a PID tuning algorithm stressing the importance of tracking is described. While the theory behind these techniques is not new, the analysis of their application to modern systems is unique in the research literature. The techniques and results should be important to control practitioners optimizing PID controller designs for tracking and in comparing results from classical designs to modern techniques. The methods stress high-gain controller design and interpret what this means for PID. Nothing in the methods presented precludes the addition of feedforward control methods for added improvements in tracking. Laboratory results from a linear motor stage demonstrate that with large open-loop gain very good tracking performance can be achieved. The resultant tracking errors compare very favorably to results from similar motions on similar systems that utilize much more complicated controllers.

A Linear Theory for Inflatable Plates of Arbitrary Shape

NASA Technical Reports Server (NTRS)

McComb, Harvey G., Jr.

1961-01-01

A linear small-deflection theory is developed for the elastic behavior of inflatable plates of which Airmat is an example. Included in the theory are the effects of a small linear taper in the depth of the plate. Solutions are presented for some simple problems in the lateral deflection and vibration of constant-depth rectangular inflatable plates.

Zonal flow dynamics and control of turbulent transport in stellarators.

PubMed

Xanthopoulos, P; Mischchenko, A; Helander, P; Sugama, H; Watanabe, T-H

2011-12-09

The relation between magnetic geometry and the level of ion-temperature-gradient (ITG) driven turbulence in stellarators is explored through gyrokinetic theory and direct linear and nonlinear simulations. It is found that the ITG radial heat flux is sensitive to details of the magnetic configuration that can be understood in terms of the linear behavior of zonal flows. The results throw light on the question of how the optimization of neoclassical confinement is related to the reduction of turbulence.

Experimental and Theoretical Results in Output Trajectory Redesign for Flexible Structures

NASA Technical Reports Server (NTRS)

Dewey, J. S.; Leang, K.; Devasia, S.

1998-01-01

In this paper we study the optimal redesign of output trajectories for linear invertible systems. This is particularly important for tracking control of flexible structures because the input-state trajectores, that achieve tracking of the required output may cause excessive vibrations in the structure. We pose and solve this problem, in the context of linear systems, as the minimization of a quadratic cost function. The theory is developed and applied to the output tracking of a flexible structure and experimental results are presented.

Development of a two-dimensional skin friction balance nulling circuit using multivariable control theory

NASA Technical Reports Server (NTRS)

Tripp, John S.; Patek, Stephen D.

1988-01-01

Measurement of planar skin friction forces in aerodynamic testing currently requires installation of two perpendicularly mounted, single-axis balances; consequently, force components must be sensed at two distinct locations. A two-axis instrument developed at the Langley Research Center to overcome this disadvantage allows measurement of a two-dimensional force at one location. This paper describes a feedback-controlled nulling circuit developed for the NASA two-axis balance which, without external compensation, is inherently unstable because of its low friction mechanical design. Linear multivariable control theory is applied to an experimentally validated mathematical model of the balance to synthesize a state-variable feedback control law. Pole placement techniques and computer simulation studies are employed to select eigenvalues which provide ideal transient response with decoupled sensing dynamics.

Stochastic control of inertial sea wave energy converter.

PubMed

Raffero, Mattia; Martini, Michele; Passione, Biagio; Mattiazzo, Giuliana; Giorcelli, Ermanno; Bracco, Giovanni

2015-01-01

The ISWEC (inertial sea wave energy converter) is presented, its control problems are stated, and an optimal control strategy is introduced. As the aim of the device is energy conversion, the mean absorbed power by ISWEC is calculated for a plane 2D irregular sea state. The response of the WEC (wave energy converter) is driven by the sea-surface elevation, which is modeled by a stationary and homogeneous zero mean Gaussian stochastic process. System equations are linearized thus simplifying the numerical model of the device. The resulting response is obtained as the output of the coupled mechanic-hydrodynamic model of the device. A stochastic suboptimal controller, derived from optimal control theory, is defined and applied to ISWEC. Results of this approach have been compared with the ones obtained with a linear spring-damper controller, highlighting the capability to obtain a higher value of mean extracted power despite higher power peaks.

Stochastic Control of Inertial Sea Wave Energy Converter

PubMed Central

Mattiazzo, Giuliana; Giorcelli, Ermanno

2015-01-01

The ISWEC (inertial sea wave energy converter) is presented, its control problems are stated, and an optimal control strategy is introduced. As the aim of the device is energy conversion, the mean absorbed power by ISWEC is calculated for a plane 2D irregular sea state. The response of the WEC (wave energy converter) is driven by the sea-surface elevation, which is modeled by a stationary and homogeneous zero mean Gaussian stochastic process. System equations are linearized thus simplifying the numerical model of the device. The resulting response is obtained as the output of the coupled mechanic-hydrodynamic model of the device. A stochastic suboptimal controller, derived from optimal control theory, is defined and applied to ISWEC. Results of this approach have been compared with the ones obtained with a linear spring-damper controller, highlighting the capability to obtain a higher value of mean extracted power despite higher power peaks. PMID:25874267

Nonlinear SVM-DTC for induction motor drive using input-output feedback linearization and high order sliding mode control.

PubMed

Ammar, Abdelkarim; Bourek, Amor; Benakcha, Abdelhamid

2017-03-01

This paper presents a nonlinear Direct Torque Control (DTC) strategy with Space Vector Modulation (SVM) for an induction motor. A nonlinear input-output feedback linearization (IOFL) is implemented to achieve a decoupled torque and flux control and the SVM is employed to reduce high torque and flux ripples. Furthermore, the control scheme performance is improved by inserting a super twisting speed controller in the outer loop and a load torque observer to enhance the speed regulation. The combining of dual nonlinear strategies ensures a good dynamic and robustness against parameters variation and disturbance. The system stability has been analyzed using Lyapunov stability theory. The effectiveness of the control algorithm is investigated by simulation and experimental validation using Matlab/Simulink software with real-time interface based on dSpace 1104. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Neural-Based Compensation of Nonlinearities in an Airplane Longitudinal Model with Dynamic-Inversion Control

PubMed Central

Li, YuHui; Jin, FeiTeng

2017-01-01

The inversion design approach is a very useful tool for the complex multiple-input-multiple-output nonlinear systems to implement the decoupling control goal, such as the airplane model and spacecraft model. In this work, the flight control law is proposed using the neural-based inversion design method associated with the nonlinear compensation for a general longitudinal model of the airplane. First, the nonlinear mathematic model is converted to the equivalent linear model based on the feedback linearization theory. Then, the flight control law integrated with this inversion model is developed to stabilize the nonlinear system and relieve the coupling effect. Afterwards, the inversion control combined with the neural network and nonlinear portion is presented to improve the transient performance and attenuate the uncertain effects on both external disturbances and model errors. Finally, the simulation results demonstrate the effectiveness of this controller. PMID:29410680

Simulation Research on Vehicle Active Suspension Controller Based on G1 Method

NASA Astrophysics Data System (ADS)

Li, Gen; Li, Hang; Zhang, Shuaiyang; Luo, Qiuhui

2017-09-01

Based on the order relation analysis method (G1 method), the optimal linear controller of vehicle active suspension is designed. The system of the main and passive suspension of the single wheel vehicle is modeled and the system input signal model is determined. Secondly, the system motion state space equation is established by the kinetic knowledge and the optimal linear controller design is completed with the optimal control theory. The weighting coefficient of the performance index coefficients of the main passive suspension is determined by the relational analysis method. Finally, the model is simulated in Simulink. The simulation results show that: the optimal weight value is determined by using the sequence relation analysis method under the condition of given road conditions, and the vehicle acceleration, suspension stroke and tire motion displacement are optimized to improve the comprehensive performance of the vehicle, and the active control is controlled within the requirements.

An LQR controller design approach for a Large Gap Magnetic Suspension System (LGMSS)

NASA Technical Reports Server (NTRS)

Groom, Nelson J.; Schaffner, Philip R.

1990-01-01

Two control approaches for a Large Gap Magnetic Suspension System (LGMSS) are investigated and numerical results are presented. The approaches are based on Linear Quadratic Regulator (LQR) control theory and include a nonzero set point regulator with constant disturbance input and an integral feedback regulator. The LGMSS provides five degree of freedom control of a cylindrical suspended element which is composed of permanent magnet material. The magnetic actuators are air core electromagnets mounted in a planar way.

Robust high-precision attitude control for flexible spacecraft with improved mixed H2/H∞ control strategy under poles assignment constraint

NASA Astrophysics Data System (ADS)

Liu, Chuang; Ye, Dong; Shi, Keke; Sun, Zhaowei

2017-07-01

A novel improved mixed H2/H∞ control technique combined with poles assignment theory is presented to achieve attitude stabilization and vibration suppression simultaneously for flexible spacecraft in this paper. The flexible spacecraft dynamics system is described and transformed into corresponding state space form. Based on linear matrix inequalities (LMIs) scheme and poles assignment theory, the improved mixed H2/H∞ controller does not restrict the equivalence of the two Lyapunov variables involved in H2 and H∞ performance, which can reduce conservatives compared with traditional mixed H2/H∞ controller. Moreover, it can eliminate the coupling of Lyapunov matrix variables and system matrices by introducing slack variable that provides additional degree of freedom. Several simulations are performed to demonstrate the effectiveness and feasibility of the proposed method in this paper.

Graph theory analysis of cortical thickness networks in adolescents with d-transposition of the great arteries.

PubMed

Watson, Christopher G; Stopp, Christian; Newburger, Jane W; Rivkin, Michael J

2018-02-01

Adolescents with d-transposition of the great arteries (d-TGA) who had the arterial switch operation in infancy have been found to have structural brain differences compared to healthy controls. We used cortical thickness measurements obtained from structural brain MRI to determine group differences in global brain organization using a graph theoretical approach. Ninety-two d-TGA subjects and 49 controls were scanned using one of two identical 1.5-Tesla MRI systems. Mean cortical thickness was obtained from 34 regions per hemisphere using Freesurfer. A linear model was used for each brain region to adjust for subject age, sex, and scanning location. Structural connectivity for each group was inferred based on the presence of high inter-regional correlations of the linear model residuals, and binary connectivity matrices were created by thresholding over a range of correlation values for each group. Graph theory analysis was performed using packages in R. Permutation tests were performed to determine significance of between-group differences in global network measures. Within-group connectivity patterns were qualitatively different between groups. At lower network densities, controls had significantly more long-range connections. The location and number of hub regions differed between groups: controls had a greater number of hubs at most network densities. The control network had a significant rightward asymmetry compared to the d-TGA group at all network densities. Using graph theory analysis of cortical thickness correlations, we found differences in brain structural network organization among d-TGA adolescents compared to controls. These may be related to the white matter and gray matter differences previously found in this cohort, and in turn may be related to the cognitive deficits this cohort presents.

Kullback-Leibler information function and the sequential selection of experiments to discriminate among several linear models. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Sidik, S. M.

1972-01-01

A sequential adaptive experimental design procedure for a related problem is studied. It is assumed that a finite set of potential linear models relating certain controlled variables to an observed variable is postulated, and that exactly one of these models is correct. The problem is to sequentially design most informative experiments so that the correct model equation can be determined with as little experimentation as possible. Discussion includes: structure of the linear models; prerequisite distribution theory; entropy functions and the Kullback-Leibler information function; the sequential decision procedure; and computer simulation results. An example of application is given.

Boundary-Layer Linear Stability Theory

DTIC Science & Technology

1984-06-01

give aa aapllfieatloa rate that Is 151 too high. This ia an iaproveaeat over the 2D results, but »till net as good as the result obtsleed whoa only th...useful to say about the origin of turbulence, whi ch is inherently nonlinear. A good idea of the low repute of the theory can be gained by reading the...engineering studies of laminar flow control [see, e.g., Hefner and Bushnell ( 1979) ]. A good introduction to the complexities of transition and the

Further studies using matched filter theory and stochastic simulation for gust loads prediction

NASA Technical Reports Server (NTRS)

Scott, Robert C.; Pototzky, Anthony S.; Perry, Boyd Iii

1993-01-01

This paper describes two analysis methods -- one deterministic, the other stochastic -- for computing maximized and time-correlated gust loads for aircraft with nonlinear control systems. The first method is based on matched filter theory; the second is based on stochastic simulation. The paper summarizes the methods, discusses the selection of gust intensity for each method and presents numerical results. A strong similarity between the results from the two methods is seen to exist for both linear and nonlinear configurations.

The dynamics and control of large-flexible space structures, part 10

NASA Technical Reports Server (NTRS)

Bainum, Peter M.; Reddy, A. S. S. R.

1988-01-01

A mathematical model is developed to predict the dynamics of the proposed orbiting Spacecraft Control Laboratory Experiment (SCOLE) during the station keeping phase. The equations of motion are derived using a Newton-Euler formulation. The model includes the effects of gravity, flexibility, and orbital dynamics. The control is assumed to be provided to the system through the Shuttle's three torquers, and through six actuators located by pairs at two points on the mast and at the mass center of the reflector. The modal shape functions are derived using the fourth order beam equation. The generic mode equations are derived to account for the effects of the control forces on the modal shape and frequencies. The equations are linearized about a nominal equilibrium position. The linear regulator theory is used to derive control laws for both the linear model of the rigidized SCOLE as well as that of the actual SCOLE including the first four flexible modes. The control strategy previously derived for the linear model of the rigidized SCOLE is applied to the nonlinear model of the same configuration of the system and preliminary single axis slewing maneuvers conducted. The results obtained confirm the applicability of the intuitive and appealing two-stage control strategy which would slew the SCOLE system, as if rigid to its desired position and then concentrate on damping out the residual flexible motions.

Quasi-linear theory via the cumulant expansion approach

NASA Technical Reports Server (NTRS)

Jones, F. C.; Birmingham, T. J.

1974-01-01

The cumulant expansion technique of Kubo was used to derive an intergro-differential equation for f , the average one particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the f equation degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory for this limited class of fluctuations. For more physically realistic fluctuations, however, quasi-linear theory is at best approximate.

LPV Controller Interpolation for Improved Gain-Scheduling Control Performance

NASA Technical Reports Server (NTRS)

Wu, Fen; Kim, SungWan

2002-01-01

In this paper, a new gain-scheduling control design approach is proposed by combining LPV (linear parameter-varying) control theory with interpolation techniques. The improvement of gain-scheduled controllers can be achieved from local synthesis of Lyapunov functions and continuous construction of a global Lyapunov function by interpolation. It has been shown that this combined LPV control design scheme is capable of improving closed-loop performance derived from local performance improvement. The gain of the LPV controller will also change continuously across parameter space. The advantages of the newly proposed LPV control is demonstrated through a detailed AMB controller design example.

Nonlinear Large Deflection Theory with Modified Aeroelastic Lifting Line Aerodynamics for a High Aspect Ratio Flexible Wing

NASA Technical Reports Server (NTRS)

Nguyen, Nhan; Ting, Eric; Chaparro, Daniel

2017-01-01

This paper investigates the effect of nonlinear large deflection bending on the aerodynamic performance of a high aspect ratio flexible wing. A set of nonlinear static aeroelastic equations are derived for the large bending deflection of a high aspect ratio wing structure. An analysis is conducted to compare the nonlinear bending theory with the linear bending theory. The results show that the nonlinear bending theory is length-preserving whereas the linear bending theory causes a non-physical effect of lengthening the wing structure under the no axial load condition. A modified lifting line theory is developed to compute the lift and drag coefficients of a wing structure undergoing a large bending deflection. The lift and drag coefficients are more accurately estimated by the nonlinear bending theory due to its length-preserving property. The nonlinear bending theory yields lower lift and span efficiency than the linear bending theory. A coupled aerodynamic-nonlinear finite element model is developed to implement the nonlinear bending theory for a Common Research Model (CRM) flexible wing wind tunnel model to be tested in the University of Washington Aeronautical Laboratory (UWAL). The structural stiffness of the model is designed to give about 10% wing tip deflection which is large enough that could cause the nonlinear deflection effect to become significant. The computational results show that the nonlinear bending theory yields slightly less lift than the linear bending theory for this wind tunnel model. As a result, the linear bending theory is deemed adequate for the CRM wind tunnel model.

Ion radial diffusion in an electrostatic impulse model for stormtime ring current formation

NASA Technical Reports Server (NTRS)

Chen, Margaret W.; Schulz, Michael; Lyons, Larry R.; Gorney, David J.

1992-01-01

Two refinements to the quasi-linear theory of ion radial diffusion are proposed and examined analytically with simulations of particle trajectories. The resonance-broadening correction by Dungey (1965) is applied to the quasi-linear diffusion theory by Faelthammar (1965) for an individual model storm. Quasi-linear theory is then applied to the mean diffusion coefficients resulting from simulations of particle trajectories in 20 model storms. The correction for drift-resonance broadening results in quasi-linear diffusion coefficients with discrepancies from the corresponding simulated values that are reduced by a factor of about 3. Further reductions in the discrepancies are noted following the averaging of the quasi-linear diffusion coefficients, the simulated coefficients, and the resonance-broadened coefficients for the 20 storms. Quasi-linear theory provides good descriptions of particle transport for a single storm but performs even better in conjunction with the present ensemble-averaging.

Newton's method: A link between continuous and discrete solutions of nonlinear problems

NASA Technical Reports Server (NTRS)

Thurston, G. A.

1980-01-01

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

Robust control design with real parameter uncertainty using absolute stability theory. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

How, Jonathan P.; Hall, Steven R.

1993-01-01

The purpose of this thesis is to investigate an extension of mu theory for robust control design by considering systems with linear and nonlinear real parameter uncertainties. In the process, explicit connections are made between mixed mu and absolute stability theory. In particular, it is shown that the upper bounds for mixed mu are a generalization of results from absolute stability theory. Both state space and frequency domain criteria are developed for several nonlinearities and stability multipliers using the wealth of literature on absolute stability theory and the concepts of supply rates and storage functions. The state space conditions are expressed in terms of Riccati equations and parameter-dependent Lyapunov functions. For controller synthesis, these stability conditions are used to form an overbound of the H2 performance objective. A geometric interpretation of the equivalent frequency domain criteria in terms of off-axis circles clarifies the important role of the multiplier and shows that both the magnitude and phase of the uncertainty are considered. A numerical algorithm is developed to design robust controllers that minimize the bound on an H2 cost functional and satisfy an analysis test based on the Popov stability multiplier. The controller and multiplier coefficients are optimized simultaneously, which avoids the iteration and curve-fitting procedures required by the D-K procedure of mu synthesis. Several benchmark problems and experiments on the Middeck Active Control Experiment at M.I.T. demonstrate that these controllers achieve good robust performance and guaranteed stability bounds.

Dynamics of Permanent-Magnet Biased Active Magnetic Bearings

NASA Technical Reports Server (NTRS)

Fukata, Satoru; Yutani, Kazuyuki

1996-01-01

Active magnetic radial bearings are constructed with a combination of permanent magnets to provide bias forces and electromagnets to generate control forces for the reduction of cost and the operating energy consumption. Ring-shaped permanent magnets with axial magnetization are attached to a shaft and share their magnet stators with the electromagnets. The magnet cores are made of solid iron for simplicity. A simplified magnetic circuit of the combined magnet system is analyzed with linear circuit theory by approximating the characteristics of permanent magnets with a linear relation. A linearized dynamical model of the control force is presented with the first-order approximation of the effects of eddy currents. Frequency responses of the rotor motion to disturbance inputs and the motion for impulsive forces are tested in the non-rotating state. The frequency responses are compared with numerical results. The decay of rotor speed due to magnetic braking is examined. The experimental results and the presented linearized model are similar to those of the all-electromagnetic design.

Multivariable control of a rolling spider drone

NASA Astrophysics Data System (ADS)

Lyu, Haifeng

The research and application of Unmanned Aerial Vehicles (UAVs) has been a hot topic recently. A UAV is dened as an aircraft which is designed not to carry a human pilot or operated with remote electronic input by the flight controller. In this thesis, the design of a control system for a quadcopter named Rolling Spider Drone is conducted. The thesis work presents the design of two kinds of controllers that can control the Drone to keep it balanced and track different kinds of input trajectories. The nonlinear mathematical model for the Drone is derived by the Newton-Euler method. The rotational subsystem and translational system are derived to describe the attitude and position motion of Drone. Techniques from linear control theory are employed to linearize the highly coupled and nonlinear quadcopter plant around equilibrium points and apply the linear feedback controller to stabilize the system. The controller is a digital tracking system that deploys LQR for system stability design. Fixed gain and adaptive gain scheduled controllers are developed and compared with different LQR weights. Step references and reference trajectories involving signicant variation for the yaw angle in the xy-plane and three-dimensional spaces are tracked in the simulation. The physical implementation and an output feedback controller are considered for future work.

On the Control of Consensus Networks: Theory and Applications

NASA Astrophysics Data System (ADS)

Hudoba de Badyn, Mathias

Signed networks allow the study of positive and negative interactions between agents. In this thesis, three papers are presented that address controllability of networked dynamics. First, controllability of signed consensus networks is approached from a symmetry perspective, for both linear and nonlinear consensus protocols. It is shown that the graph-theoretic property of signed networks known as structural balance renders the consensus protocol uncontrollable when coupled with a certain type of symmetry. Stabilizability and output controllability of signed linear consensus is also examined, as well as a data-driven approach to finding bipartite consensus stemming from structural balance for signed nonlinear consensus. Second, an algorithm is constructed that allows one to grow a network while preserving controllability, and some generalizations of this algorithm are presented. Submodular optimization is used to analyze a second algorithm that adds nodes to a network to maximize the network connectivity.

A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories

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

Lagos, Macarena; Baker, Tessa; Ferreira, Pedro G.

We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and ''Beyond Horndeski'' theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbationsmore » that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (à la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic actions for perturbations, and the number of free parameters that need to be defined, to cosmologically characterize these two broad classes of theories.« less

On estimation of linear transformation models with nested case–control sampling

PubMed Central

Liu, Mengling

2011-01-01

Nested case–control (NCC) sampling is widely used in large epidemiological cohort studies for its cost effectiveness, but its data analysis primarily relies on the Cox proportional hazards model. In this paper, we consider a family of linear transformation models for analyzing NCC data and propose an inverse selection probability weighted estimating equation method for inference. Consistency and asymptotic normality of our estimators for regression coefficients are established. We show that the asymptotic variance has a closed analytic form and can be easily estimated. Numerical studies are conducted to support the theory and an application to the Wilms’ Tumor Study is also given to illustrate the methodology. PMID:21912975

Application of Control Theory in the Formation of a Timescale

DTIC Science & Technology

2004-09-01

York). [3] P. Koppang and R. Leland , 1999, “Linear quadratic stochastic control of atomic hydrogen masers,” IEEE Transactions on Ultrasonics... Koppang , D. Johns, and J. Skinner U.S. Naval Observatory Abstract We have created a timescale that joins the short-term stability of...comparison. REFERENCES [1] D. Matsakis, M. Miranian, and P. Koppang , 1999, “Steering the U.S. Naval Observatory (USNO) Master Clock,” in

Finite-time robust passive control for a class of switched reaction-diffusion stochastic complex dynamical networks with coupling delays and impulsive control

NASA Astrophysics Data System (ADS)

Syed Ali, M.; Yogambigai, J.; Kwon, O. M.

2018-03-01

Finite-time boundedness and finite-time passivity for a class of switched stochastic complex dynamical networks (CDNs) with coupling delays, parameter uncertainties, reaction-diffusion term and impulsive control are studied. Novel finite-time synchronisation criteria are derived based on passivity theory. This paper proposes a CDN consisting of N linearly and diffusively coupled identical reaction- diffusion neural networks. By constructing of a suitable Lyapunov-Krasovskii's functional and utilisation of Jensen's inequality and Wirtinger's inequality, new finite-time passivity criteria for the networks are established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, two interesting numerical examples are given to show the effectiveness of the theoretical results.

Novel associative-memory-based self-learning neurocontrol model

NASA Astrophysics Data System (ADS)

Chen, Ke

1992-09-01

Intelligent control is an important field of AI application, which is closely related to machine learning, and the neurocontrol is a kind of intelligent control that controls actions of a physical system or a plant. Linear associative memory model is a good analytic tool for artificial neural networks. In this paper, we present a novel self-learning neurocontrol on the basis of the linear associative memory model to support intelligent control. Using our self-learning neurocontrol model, the learning process is viewed as an extension of one of J. Piaget's developmental stages. After a particular linear associative model developed by us is presented, a brief introduction to J. Piaget's cognitive theory is described as the basis of our self-learning style control. It follows that the neurocontrol model is presented, which usually includes two learning stages, viz. primary learning and high-level learning. As a demonstration of our neurocontrol model, an example is also presented with simulation techniques, called that `bird' catches an aim. The tentative experimental results show that the learning and controlling performance of this approach is surprisingly good. In conclusion, future research is pointed out to improve our self-learning neurocontrol model and explore other areas of application.

An enstrophy-based linear and nonlinear receptivity theory

NASA Astrophysics Data System (ADS)

Sengupta, Aditi; Suman, V. K.; Sengupta, Tapan K.; Bhaumik, Swagata

2018-05-01

In the present research, a new theory of instability based on enstrophy is presented for incompressible flows. Explaining instability through enstrophy is counter-intuitive, as it has been usually associated with dissipation for the Navier-Stokes equation (NSE). This developed theory is valid for both linear and nonlinear stages of disturbance growth. A previously developed nonlinear theory of incompressible flow instability based on total mechanical energy described in the work of Sengupta et al. ["Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003)] is used to compare with the present enstrophy based theory. The developed equations for disturbance enstrophy and disturbance mechanical energy are derived from NSE without any simplifying assumptions, as compared to other classical linear/nonlinear theories. The theory is tested for bypass transition caused by free stream convecting vortex over a zero pressure gradient boundary layer. We explain the creation of smaller scales in the flow by a cascade of enstrophy, which creates rotationality, in general inhomogeneous flows. Linear and nonlinear versions of the theory help explain the vortex-induced instability problem under consideration.

Active control of panel vibrations induced by boundary-layer flow

NASA Technical Reports Server (NTRS)

Chow, Pao-Liu

1991-01-01

Some problems in active control of panel vibration excited by a boundary layer flow over a flat plate are studied. In the first phase of the study, the optimal control problem of vibrating elastic panel induced by a fluid dynamical loading was studied. For a simply supported rectangular plate, the vibration control problem can be analyzed by a modal analysis. The control objective is to minimize the total cost functional, which is the sum of a vibrational energy and the control cost. By means of the modal expansion, the dynamical equation for the plate and the cost functional are reduced to a system of ordinary differential equations and the cost functions for the modes. For the linear elastic plate, the modes become uncoupled. The control of each modal amplitude reduces to the so-called linear regulator problem in control theory. Such problems can then be solved by the method of adjoint state. The optimality system of equations was solved numerically by a shooting method. The results are summarized.

Comparison of Linear Induction Motor Theories for the LIMRV and TLRV Motors

DOT National Transportation Integrated Search

1978-01-01

The Oberretl, Yamamura, and Mosebach theories of the linear induction motor are described and also applied to predict performance characteristics of the TLRV & LIMRV linear induction motors. The effect of finite motor width and length on performance ...

Control of discrete time systems based on recurrent Super-Twisting-like algorithm.

PubMed

Salgado, I; Kamal, S; Bandyopadhyay, B; Chairez, I; Fridman, L

2016-09-01

Most of the research in sliding mode theory has been carried out to in continuous time to solve the estimation and control problems. However, in discrete time, the results in high order sliding modes have been less developed. In this paper, a discrete time super-twisting-like algorithm (DSTA) was proposed to solve the problems of control and state estimation. The stability proof was developed in terms of the discrete time Lyapunov approach and the linear matrix inequalities theory. The system trajectories were ultimately bounded inside a small region dependent on the sampling period. Simulation results tested the DSTA. The DSTA was applied as a controller for a Furuta pendulum and for a DC motor supplied by a DSTA signal differentiator. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Self-Consistent Field Theories for the Role of Large Length-Scale Architecture in Polymers

NASA Astrophysics Data System (ADS)

Wu, David

At large length-scales, the architecture of polymers can be described by a coarse-grained specification of the distribution of branch points and monomer types within a molecule. This includes molecular topology (e.g., cyclic or branched) as well as distances between branch points or chain ends. Design of large length-scale molecular architecture is appealing because it offers a universal strategy, independent of monomer chemistry, to tune properties. Non-linear analogs of linear chains differ in molecular-scale properties, such as mobility, entanglements, and surface segregation in blends that are well-known to impact rheological, dynamical, thermodynamic and surface properties including adhesion and wetting. We have used Self-Consistent Field (SCF) theories to describe a number of phenomena associated with large length-scale polymer architecture. We have predicted the surface composition profiles of non-linear chains in blends with linear chains. These predictions are in good agreement with experimental results, including from neutron scattering, on a range of well-controlled branched (star, pom-pom and end-branched) and cyclic polymer architectures. Moreover, the theory allows explanation of the segregation and conformations of branched polymers in terms of effective surface potentials acting on the end and branch groups. However, for cyclic chains, which have no end or junction points, a qualitatively different topological mechanism based on conformational entropy drives cyclic chains to a surface, consistent with recent neutron reflectivity experiments. We have also used SCF theory to calculate intramolecular and intermolecular correlations for polymer chains in the bulk, dilute solution, and trapped at a liquid-liquid interface. Predictions of chain swelling in dilute star polymer solutions compare favorably with existing PRISM theory and swelling at an interface helps explain recent measurements of chain mobility at an oil-water interface. In collaboration with: Renfeng Hu, Colorado School of Mines, and Mark Foster, University of Akron. This work was supported by NSF Grants No. CBET- 0730692 and No. CBET-0731319.

Reduced-order model based active disturbance rejection control of hydraulic servo system with singular value perturbation theory.

PubMed

Wang, Chengwen; Quan, Long; Zhang, Shijie; Meng, Hongjun; Lan, Yuan

2017-03-01

Hydraulic servomechanism is the typical mechanical/hydraulic double-dynamics coupling system with the high stiffness control and mismatched uncertainties input problems, which hinder direct applications of many advanced control approaches in the hydraulic servo fields. In this paper, by introducing the singular value perturbation theory, the original double-dynamics coupling model of the hydraulic servomechanism was reduced to a integral chain system. So that, the popular ADRC (active disturbance rejection control) technology could be directly applied to the reduced system. In addition, the high stiffness control and mismatched uncertainties input problems are avoided. The validity of the simplified model is analyzed and proven theoretically. The standard linear ADRC algorithm is then developed based on the obtained reduced-order model. Extensive comparative co-simulations and experiments are carried out to illustrate the effectiveness of the proposed method. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Multi-objective optimal control of vibratory energy harvesting systems

NASA Astrophysics Data System (ADS)

Scruggs, J. T.

2008-03-01

This paper presents a new approach, based on H II optimal control theory, for the maximization of power generation in energy harvesting systems. The theory determines the optimal harvested power attainable through the use of power electronics to effect linear feedback control of transducer current. In contrast to most of the prior work in this area, which has assumed harmonic response, the theory proposed here applies to stochastically-excited systems in broadband response, and can be used to harvest power simultaneously from multiple significant vibratory modes. It is also applicable to coupled networks of many transducers. The theory accounts for the impact of energy harvesting on the dynamics of the vibrating system in which the transducers are embedded. It also accounts for resistive and semiconductor dissipation in the power-electronic network interfacing the transducers with energy storage. Thus, losses in the electronics are addressed in the formulation of the optimal control law. Finally, the H II-optimal control formulation of the problem naturally allows for harvested power to be systematically balanced against other response objectives. Here, this is illustrated by showing how the harvesting objective can be maximized, subject to the constraint that the transducer voltages be maintained below that of the power-electronic bus; a condition which is required for the power-electronic control system to be fully operational. Although the theory is applicable across a broad range of applications, it is presented in the context of a piezoelectric bimorph example.

Controlled Quantum Packets

NASA Technical Reports Server (NTRS)

DeMartino, Salvatore; DeSiena, Silvio

1996-01-01

We look at time evolution of a physical system from the point of view of dynamical control theory. Normally we solve motion equation with a given external potential and we obtain time evolution. Standard examples are the trajectories in classical mechanics or the wave functions in Quantum Mechanics. In the control theory, we have the configurational variables of a physical system, we choose a velocity field and with a suited strategy we force the physical system to have a well defined evolution. The evolution of the system is the 'premium' that the controller receives if he has adopted the right strategy. The strategy is given by well suited laboratory devices. The control mechanisms are in many cases non linear; it is necessary, namely, a feedback mechanism to retain in time the selected evolution. Our aim is to introduce a scheme to obtain Quantum wave packets by control theory. The program is to choose the characteristics of a packet, that is, the equation of evolution for its centre and a controlled dispersion, and to give a building scheme from some initial state (for example a solution of stationary Schroedinger equation). It seems natural in this view to use stochastic approach to Quantum Mechanics, that is, Stochastic Mechanics [S.M.]. It is a quantization scheme different from ordinary ones only formally. This approach introduces in quantum theory the whole mathematical apparatus of stochastic control theory. Stochastic Mechanics, in our view, is more intuitive when we want to study all the classical-like problems. We apply our scheme to build two classes of quantum packets both derived generalizing some properties of coherent states.

Time-sliced perturbation theory for large scale structure I: general formalism

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

Blas, Diego; Garny, Mathias; Sibiryakov, Sergey

2016-07-01

We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein-de Sitter universe, the time evolution ofmore » the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This paves the way towards the systematic resummation of infrared effects in large scale structure formation. We also argue that the approach proposed here provides a natural framework to account for the influence of short-scale dynamics on larger scales along the lines of effective field theory.« less

How does non-linear dynamics affect the baryon acoustic oscillation?

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

Sugiyama, Naonori S.; Spergel, David N., E-mail: nao.s.sugiyama@gmail.com, E-mail: dns@astro.princeton.edu

2014-02-01

We study the non-linear behavior of the baryon acoustic oscillation in the power spectrum and the correlation function by decomposing the dark matter perturbations into the short- and long-wavelength modes. The evolution of the dark matter fluctuations can be described as a global coordinate transformation caused by the long-wavelength displacement vector acting on short-wavelength matter perturbation undergoing non-linear growth. Using this feature, we investigate the well known cancellation of the high-k solutions in the standard perturbation theory. While the standard perturbation theory naturally satisfies the cancellation of the high-k solutions, some of the recently proposed improved perturbation theories do notmore » guarantee the cancellation. We show that this cancellation clarifies the success of the standard perturbation theory at the 2-loop order in describing the amplitude of the non-linear power spectrum even at high-k regions. We propose an extension of the standard 2-loop level perturbation theory model of the non-linear power spectrum that more accurately models the non-linear evolution of the baryon acoustic oscillation than the standard perturbation theory. The model consists of simple and intuitive parts: the non-linear evolution of the smoothed power spectrum without the baryon acoustic oscillations and the non-linear evolution of the baryon acoustic oscillations due to the large-scale velocity of dark matter and due to the gravitational attraction between dark matter particles. Our extended model predicts the smoothing parameter of the baryon acoustic oscillation peak at z = 0.35 as ∼ 7.7Mpc/h and describes the small non-linear shift in the peak position due to the galaxy random motions.« less

Hierarchical Control and Trajectory Planning

NASA Technical Reports Server (NTRS)

Martin, Clyde F.; Horn, P. W.

1994-01-01

Most of the time on this project was spent on the trajectory planning problem. The construction is equivalent to the classical spline construction in the case that the system matrix is nilpotent. If the dimension of the system is n then the spline of degree 2n-1 is constructed. This gives a new approach to the construction of splines that is more efficient than the usual construction and at the same time allows the construction of a much larger class of splines. All known classes of splines are reconstructed using the approach of linear control theory. As a numerical analysis tool control theory gives a very good tool for constructing splines. However, for the purposes of trajectory planning it is quite another story. Enclosed in this document are four reports done under this grant.

The semiotics of control and modeling relations in complex systems.

PubMed

Joslyn, C

2001-01-01

We provide a conceptual analysis of ideas and principles from the systems theory discourse which underlie Pattee's semantic or semiotic closure, which is itself foundational for a school of theoretical biology derived from systems theory and cybernetics, and is now being related to biological semiotics and explicated in the relational biological school of Rashevsky and Rosen. Atomic control systems and models are described as the canonical forms of semiotic organization, sharing measurement relations, but differing topologically in that control systems are circularly and models linearly related to their environments. Computation in control systems is introduced, motivating hierarchical decomposition, hybrid modeling and control systems, and anticipatory or model-based control. The semiotic relations in complex control systems are described in terms of relational constraints, and rules and laws are distinguished as contingent and necessary functional entailments, respectively. Finally, selection as a meta-level of constraint is introduced as the necessary condition for semantic relations in control systems and models.

Centralized, decentralized, and independent control of a flexible manipulator on a flexible base

NASA Technical Reports Server (NTRS)

Li, Feiyue; Bainum, Peter M.; Xu, Jianke

1991-01-01

The dynamics and control of a flexible manipulator arm with payload mass on a flexible base in space are considered. The controllers are provided by one torquer at the center of the base and one torquer at the connection joint of the robot and the base. The nonlinear dynamics of the system is modeled by applying the finite element method and Lagrangian formula. Three control strategies are considered and compared, i.e., centralized control, decentralized control, and independent control. All these control designs are based on the linear quadratic regulator theory. A mathematical decomposition is used in the decentralization process so that the coupling between the subsystems is weak, while a physical decomposition is used in the independent control design process. For both the decentralized and the independent controls, the stability of the overall linear system is checked before a numerical simulations is initiated. Two numerical examples show that the response of the independent control system are close to those of the centralized control system, while the responses of the decentralized control system are not.

Recent developments in learning control and system identification for robots and structures

NASA Technical Reports Server (NTRS)

Phan, M.; Juang, J.-N.; Longman, R. W.

1990-01-01

This paper reviews recent results in learning control and learning system identification, with particular emphasis on discrete-time formulation, and their relation to adaptive theory. Related continuous-time results are also discussed. Among the topics presented are proportional, derivative, and integral learning controllers, time-domain formulation of discrete learning algorithms. Newly developed techniques are described including the concept of the repetition domain, and the repetition domain formulation of learning control by linear feedback, model reference learning control, indirect learning control with parameter estimation, as well as related basic concepts, recursive and non-recursive methods for learning identification.

Periodic Methods for Controlling a Satellite in Formation

DTIC Science & Technology

2002-03-01

5 5. Clohessy - Wiltshire Reference Frame................................................................... 10 6...techniques to study relative position errors within a satellite cluster [19, 24]. The dynamics were based on Clohessy - Wiltshire equations with near...dynamics model by solving the time periodic, linearized system using Floquet Theory. More accurate than the Clohessy - Wiltshire solutions used in previous

Theory of mind and executive function: working-memory capacity and inhibitory control as predictors of false-belief task performance.

PubMed

Mutter, Brigitte; Alcorn, Mark B; Welsh, Marilyn

2006-06-01

This study of the relationship between theory of mind and executive function examined whether on the false-belief task age differences between 3 and 5 ears of age are related to development of working-memory capacity and inhibitory processes. 72 children completed tasks measuring false belief, working memory, and inhibition. Significant age effects were observed for false-belief and working-memory performance, as well as for the false-alarm and perseveration measures of inhibition. A simultaneous multiple linear regression specified the contribution of age, inhibition, and working memory to the prediction of false-belief performance. This model was significant, explaining a total of 36% of the variance. To examine the independent contributions of the working-memory and inhibition variables, after controlling for age, two hierarchical multiple linear regressions were conducted. These multiple regression analyses indicate that working memory and inhibition make small, overlapping contributions to false-belief performance after accounting for age, but that working memory, as measured in this study, is a somewhat better predictor of false-belief understanding than is inhibition.

Research in Applied Mathematics Related to Mathematical System Theory.

DTIC Science & Technology

1977-06-01

This report deals with research results obtained in the field of mathematical system theory . Special emphasis was given to the following areas: (1...Linear system theory over a field: parametrization of multi-input, multi-output systems and the geometric structure of classes of systems of...constant dimension. (2) Linear systems over a ring: development of the theory for very general classes of rings. (3) Nonlinear system theory : basic

Large-Scale Linear Optimization through Machine Learning: From Theory to Practical System Design and Implementation

DTIC Science & Technology

2016-08-10

AFRL-AFOSR-JP-TR-2016-0073 Large-scale Linear Optimization through Machine Learning: From Theory to Practical System Design and Implementation ...2016 4.  TITLE AND SUBTITLE Large-scale Linear Optimization through Machine Learning: From Theory to Practical System Design and Implementation 5a...performances on various machine learning tasks and it naturally lends itself to fast parallel implementations . Despite this, very little work has been

A reciprocal theorem for a mixture theory. [development of linearized theory of interacting media

NASA Technical Reports Server (NTRS)

Martin, C. J.; Lee, Y. M.

1972-01-01

A dynamic reciprocal theorem for a linearized theory of interacting media is developed. The constituents of the mixture are a linear elastic solid and a linearly viscous fluid. In addition to Steel's field equations, boundary conditions and inequalities on the material constants that have been shown by Atkin, Chadwick and Steel to be sufficient to guarantee uniqueness of solution to initial-boundary value problems are used. The elements of the theory are given and two different boundary value problems are considered. The reciprocal theorem is derived with the aid of the Laplace transform and the divergence theorem and this section is concluded with a discussion of the special cases which arise when one of the constituents of the mixture is absent.

Study on longitudinal dispersion relation in one-dimensional relativistic plasma: Linear theory and Vlasov simulation

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

Zhang, H.; Wu, S. Z.; Zhou, C. T.

2013-09-15

The dispersion relation of one-dimensional longitudinal plasma waves in relativistic homogeneous plasmas is investigated with both linear theory and Vlasov simulation in this paper. From the Vlasov-Poisson equations, the linear dispersion relation is derived for the proper one-dimensional Jüttner distribution. Numerically obtained linear dispersion relation as well as an approximate formula for plasma wave frequency in the long wavelength limit is given. The dispersion of longitudinal wave is also simulated with a relativistic Vlasov code. The real and imaginary parts of dispersion relation are well studied by varying wave number and plasma temperature. Simulation results are in agreement with establishedmore » linear theory.« less

Distributed fault-tolerant time-varying formation control for high-order linear multi-agent systems with actuator failures.

PubMed

Hua, Yongzhao; Dong, Xiwang; Li, Qingdong; Ren, Zhang

2017-11-01

This paper investigates the fault-tolerant time-varying formation control problems for high-order linear multi-agent systems in the presence of actuator failures. Firstly, a fully distributed formation control protocol is presented to compensate for the influences of both bias fault and loss of effectiveness fault. Using the adaptive online updating strategies, no global knowledge about the communication topology is required and the bounds of actuator failures can be unknown. Then an algorithm is proposed to determine the control parameters of the fault-tolerant formation protocol, where the time-varying formation feasible conditions and an approach to expand the feasible formation set are given. Furthermore, the stability of the proposed algorithm is proven based on the Lyapunov-like theory. Finally, two simulation examples are given to demonstrate the effectiveness of the theoretical results. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Design of an optimal preview controller for linear discrete-time descriptor systems with state delay

NASA Astrophysics Data System (ADS)

Cao, Mengjuan; Liao, Fucheng

2015-04-01

In this paper, the linear discrete-time descriptor system with state delay is studied, and a design method for an optimal preview controller is proposed. First, by using the discrete lifting technique, the original system is transformed into a general descriptor system without state delay in form. Then, taking advantage of the first-order forward difference operator, we construct a descriptor augmented error system, including the state vectors of the lifted system, error vectors, and desired target signals. Rigorous mathematical proofs are given for the regularity, stabilisability, causal controllability, and causal observability of the descriptor augmented error system. Based on these, the optimal preview controller with preview feedforward compensation for the original system is obtained by using the standard optimal regulator theory of the descriptor system. The effectiveness of the proposed method is shown by numerical simulation.

Bioinspired Concepts: Unified Theory for Complex Biological and Engineering Systems

DTIC Science & Technology

2006-01-01

i.e., data flows of finite size arrive at the system randomly. For such a system , we propose a modified dual scheduling algorithm that stabilizes ...demon. We compute the efficiency of the controller over finite and infinite time intervals, and since the controller is optimal, this yields hard limits...and highly optimized tolerance. PNAS, 102, 2005. 51. G. N. Nair and R. J. Evans. Stabilizability of stochastic linear systems with finite feedback

Fuzzy distributed cooperative tracking for a swarm of unmanned aerial vehicles with heterogeneous goals

NASA Astrophysics Data System (ADS)

Kladis, Georgios P.; Menon, Prathyush P.; Edwards, Christopher

2016-12-01

This article proposes a systematic analysis for a tracking problem which ensures cooperation amongst a swarm of unmanned aerial vehicles (UAVs), modelled as nonlinear systems with linear and angular velocity constraints, in order to achieve different goals. A distributed Takagi-Sugeno (TS) framework design is adopted for the representation of the nonlinear model of the dynamics of the UAVs. The distributed control law which is introduced is composed of both node and network level information. Firstly, feedback gains are synthesised using a parallel distributed compensation (PDC) control law structure, for a collection of isolated UAVs; ignoring communications among the swarm. Then secondly, based on an alternation-like procedure, the resulting feedback gains are used to determine Lyapunov matrices which are utilised at network level to incorporate into the control law, the relative differences in the states of the vehicles, and to induce cooperative behaviour. Eventually stability is guaranteed for the entire swarm. The control synthesis is performed using tools from linear control theory: in particular the design criteria are posed as linear matrix inequalities (LMIs). An example based on a UAV tracking scenario is included to outline the efficacy of the approach.

Lie algebras and linear differential equations.

NASA Technical Reports Server (NTRS)

Brockett, R. W.; Rahimi, A.

1972-01-01

Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.

General theory of conical flows and its application to supersonic aerodynamics

NASA Technical Reports Server (NTRS)

Germain, Paul

1955-01-01

Points treated in this report are: homogeneous flows, the general study of conical flows with infinitesimal cone angles, the numerical or analogous methods for the study of flows flattened in one direction, and a certain number of results. A thorough consideration of the applications on conical flows and demonstration of how one may solve within the scope of linear theory, by combinations of conical flows, the general problems of the supersonic wing, taking into account dihedral and sweepback, and also fuselage and control surface effects.

The Linear Quadratic Optimal Control Problem for Infinite Dimensional Systems with Unbounded Input and Output Operators.

DTIC Science & Technology

1984-01-01

5.5) respectively (5.3) and (5.8) which means that u(t) - 0 respectively v(t) - 0 for t > o. The evolution of the systems (5.1) and (5.3) in terms ...input/output delays; and b) the general theory is presented in such a way that it applies to both . . ... ..- Lr parabolic and hyperbolic I P9es as...particular emphasis is placed on the development of the duality theory by means of two different state concepts. The resulting evolution equations

On the linear relation between the mean and the standard deviation of a response time distribution.

PubMed

Wagenmakers, Eric-Jan; Brown, Scott

2007-07-01

Although it is generally accepted that the spread of a response time (RT) distribution increases with the mean, the precise nature of this relation remains relatively unexplored. The authors show that in several descriptive RT distributions, the standard deviation increases linearly with the mean. Results from a wide range of tasks from different experimental paradigms support a linear relation between RT mean and RT standard deviation. Both R. Ratcliff's (1978) diffusion model and G. D. Logan's (1988) instance theory of automatization provide explanations for this linear relation. The authors identify and discuss 3 specific boundary conditions for the linear law to hold. The law constrains RT models and supports the use of the coefficient of variation to (a) compare variability while controlling for differences in baseline speed of processing and (b) assess whether changes in performance with practice are due to quantitative speedup or qualitative reorganization. Copyright 2007 APA.

Theory of unidirectional magnetoresistance in magnetic heterostructures

NASA Astrophysics Data System (ADS)

Zhang, Steven S.-L.; Vignale, Giovanni

2017-09-01

We present a general drift-diffusion theory beyond linear response to explain the unidirectional magnetoresistance (UMR) observed in recent experiments in various magnetic heterostructures. In general, such nonlinear magnetoresistance may originate from the concerted action of current-induced spin accumulation and spin asymmetry in electron mobility. As a case study, we calculate the UMR in a bilayer system consisting of a heavy-metal (HM) and a ferromagnetic metal (FM), where the spin accumulation is induced via the spin Hall effect in the bulk of the HM layer. Our previous formulation [cf. PRB 94, 140411(R) (2016)] is generalized to include the interface resistance and spin memory loss, which allows us to analyze in details their effects on the UMR. We found that the UMR turns out to be independent of the spin asymmetry of the interfacial resistance, at variance with the linear giant-magnetoresistance (GMR) effect. A linear relation between the UMR and the conductivity-spin asymmetry is revealed, which provides an alternative way to control the sign and magnitude of the UMR and hence may serve as an experimental signature of our proposed mechanism.

Users of withdrawal method in the Islamic Republic of Iran: are they intending to use oral contraceptives? Applying the theory of planned behaviour.

PubMed

Rahnama, P; Hidarnia, A; Shokravi, F A; Kazemnejad, A; Montazeri, A; Najorkolaei, F R; Saburi, A

2013-09-01

Many couples in the Islamic Republic of Iran rely on coital withdrawal for contraception. The purpose of this cross-sectional study was to use the theory of planned behaviour to explore factors that influence withdrawal users' intent to switch to oral contraception (OC). Participants were 336 sexually active, married women, who were current users of withdrawal and were recruited from 5 public family planning clinics in Tehran. A questionnair included measures of the theory of planned behaviour: attitude (behavioural beliefs, outcome evaluations), subjective norms (normative beliefs, motivation to comply), perceived behaviour control, past behaviour and behavioural intention. Linear regression analyses showed that past behaviour, perceived behaviour control, attitude and subjective norms accounted for the highest percentage of total variance observed for intention to use OC (36%). Beliefs-based family planning education and counsellingshould to be designed for users of the withdrawal method.

Robust reinforcement learning.

PubMed

Morimoto, Jun; Doya, Kenji

2005-02-01

This letter proposes a new reinforcement learning (RL) paradigm that explicitly takes into account input disturbance as well as modeling errors. The use of environmental models in RL is quite popular for both offline learning using simulations and for online action planning. However, the difference between the model and the real environment can lead to unpredictable, and often unwanted, results. Based on the theory of H(infinity) control, we consider a differential game in which a "disturbing" agent tries to make the worst possible disturbance while a "control" agent tries to make the best control input. The problem is formulated as finding a min-max solution of a value function that takes into account the amount of the reward and the norm of the disturbance. We derive online learning algorithms for estimating the value function and for calculating the worst disturbance and the best control in reference to the value function. We tested the paradigm, which we call robust reinforcement learning (RRL), on the control task of an inverted pendulum. In the linear domain, the policy and the value function learned by online algorithms coincided with those derived analytically by the linear H(infinity) control theory. For a fully nonlinear swing-up task, RRL achieved robust performance with changes in the pendulum weight and friction, while a standard reinforcement learning algorithm could not deal with these changes. We also applied RRL to the cart-pole swing-up task, and a robust swing-up policy was acquired.

Synchronization control in multiplex networks of nonlinear multi-agent systems

NASA Astrophysics Data System (ADS)

He, Wangli; Xu, Zhiwei; Du, Wenli; Chen, Guanrong; Kubota, Naoyuki; Qian, Feng

2017-12-01

This paper is concerned with synchronization control of a multiplex network, in which two different kinds of relationships among agents coexist. Hybrid coupling, including continuous linear coupling and impulsive coupling, is proposed to model the coexisting distinguishable interactions. First, by adding impulsive controllers on a small portion of agents, local synchronization is analyzed by linearizing the error system at the desired trajectory. Then, global synchronization is studied based on the Lyapunov stability theory, where a time-varying coupling strength is involved. To further deal with the time-varying coupling strength, an adaptive updating law is introduced and a corresponding sufficient condition is obtained to ensure synchronization of the multiplex network towards the desired trajectory. Networks of Chua's circuits and other chaotic systems with double layers of interactions are simulated to verify the proposed method.

Chaos control in delayed phase space constructed by the Takens embedding theory

NASA Astrophysics Data System (ADS)

Hajiloo, R.; Salarieh, H.; Alasty, A.

2018-01-01

In this paper, the problem of chaos control in discrete-time chaotic systems with unknown governing equations and limited measurable states is investigated. Using the time-series of only one measurable state, an algorithm is proposed to stabilize unstable fixed points. The approach consists of three steps: first, using Takens embedding theory, a delayed phase space preserving the topological characteristics of the unknown system is reconstructed. Second, a dynamic model is identified by recursive least squares method to estimate the time-series data in the delayed phase space. Finally, based on the reconstructed model, an appropriate linear delayed feedback controller is obtained for stabilizing unstable fixed points of the system. Controller gains are computed using a systematic approach. The effectiveness of the proposed algorithm is examined by applying it to the generalized hyperchaotic Henon system, prey-predator population map, and the discrete-time Lorenz system.

Blind Deconvolution for Distributed Parameter Systems with Unbounded Input and Output and Determining Blood Alcohol Concentration from Transdermal Biosensor Data.

PubMed

Rosen, I G; Luczak, Susan E; Weiss, Jordan

2014-03-15

We develop a blind deconvolution scheme for input-output systems described by distributed parameter systems with boundary input and output. An abstract functional analytic theory based on results for the linear quadratic control of infinite dimensional systems with unbounded input and output operators is presented. The blind deconvolution problem is then reformulated as a series of constrained linear and nonlinear optimization problems involving infinite dimensional dynamical systems. A finite dimensional approximation and convergence theory is developed. The theory is applied to the problem of estimating blood or breath alcohol concentration (respectively, BAC or BrAC) from biosensor-measured transdermal alcohol concentration (TAC) in the field. A distributed parameter model with boundary input and output is proposed for the transdermal transport of ethanol from the blood through the skin to the sensor. The problem of estimating BAC or BrAC from the TAC data is formulated as a blind deconvolution problem. A scheme to identify distinct drinking episodes in TAC data based on a Hodrick Prescott filter is discussed. Numerical results involving actual patient data are presented.

First-principles simulations of doping-dependent mesoscale screening of adatoms in graphene

NASA Astrophysics Data System (ADS)

Mostofi, Arash; Corsetti, Fabiano; Wong, Dillon; Crommie, Michael; Lischner, Johannes

Adsorbed atoms and molecules play an important role in controlling and tuning the functional properties of 2D materials. Understanding and predicting this phenomenon from theory is challenging because of the need to capture both the local chemistry of the adsorbate-substrate interaction and its complex interplay with the long-range screening response of the substrate. To address this challenge, we have developed a first-principles multi-scale approach that combines linear-scaling density-functional theory, continuum screening theory and large-scale tight-binding simulations. Focussing on the case of a calcium adatom on graphene, we draw comparison between the effect of (i) non-linearity, (ii) intraband and interband transitions, and (iii) the exchange-correlation potential, thus providing insight into the relative importance of these different factors on the screening response. We also determine the charge transfer from the adatom to the graphene substrate (the key parameter used in continuum screening models), showing it to be significantly larger than previous estimates. AM and FC acknowledge support of the EPSRC under Grant EP/J015059/1, and JL under Grant EP/N005244/1.

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.

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

Mooij, E.

Application of simple adaptive control (SAC) theory to the design of guidance and control systems for winged re-entry vehicles has been proven successful. To apply SAC to these non-linear and non-stationary systems, it needs to be Almost Strictly Passive (ASP), which is an extension of the Almost Strictly Positive Real (ASPR) condition for linear, time-invariant systems. To fulfill the ASP condition, the controlled, non-linear system has to be minimum-phase (i.e., the zero dynamics is stable), and there is a specific condition for the product of output and input matrix. Earlier studies indicate that even the linearised system is not ASPR.more » The two problems at hand are: 1) the system is non-minimum phase when flying with zero bank angle, and 2) whenever there is hybrid control, e.g., yaw control is established by combined reaction and aerodynamic control for the major part of flight, the second ASPR condition cannot be met. In this paper we look at both issues, the former related to the guidance system and the latter to the attitude-control system. It is concluded that whenever the nominal bank angle is zero, the passivity conditions can never be met, and guidance should be based on nominal commands and a redefinition of those whenever the error becomes too large. For the remaining part of the trajectory, the passivity conditions are marginally met, but it is proposed to add feedforward compensators to alleviate these conditions. The issue of hybrid control is avoided by redefining the controls with total control moments and adding a so-called control allocator. Deriving the passivity conditions for rotational motion, and evaluating these conditions along the trajectory shows that the (non-linear) winged entry vehicle is ASP. The sufficient conditions to apply SAC for attitude control are thus met.« less

Vehicle dynamics control of four in-wheel motor drive electric vehicle using gain scheduling based on tyre cornering stiffness estimation

NASA Astrophysics Data System (ADS)

Xiong, Lu; Yu, Zhuoping; Wang, Yang; Yang, Chen; Meng, Yufeng

2012-06-01

This paper focuses on the vehicle dynamic control system for a four in-wheel motor drive electric vehicle, aiming at improving vehicle stability under critical driving conditions. The vehicle dynamics controller is composed of three modules, i.e. motion following control, control allocation and vehicle state estimation. Considering the strong nonlinearity of the tyres under critical driving conditions, the yaw motion of the vehicle is regulated by gain scheduling control based on the linear quadratic regulator theory. The feed-forward and feedback gains of the controller are updated in real-time by online estimation of the tyre cornering stiffness, so as to ensure the control robustness against environmental disturbances as well as parameter uncertainty. The control allocation module allocates the calculated generalised force requirements to each in-wheel motor based on quadratic programming theory while taking the tyre longitudinal/lateral force coupling characteristic into consideration. Simulations under a variety of driving conditions are carried out to verify the control algorithm. Simulation results indicate that the proposed vehicle stability controller can effectively stabilise the vehicle motion under critical driving conditions.

Methods of Investigation of Equations that Describe Waves in Tubes with Elastic Walls and Application of the Theory of Reversible and Weak Dissipative Shocks

NASA Astrophysics Data System (ADS)

Bakholdin, Igor

2018-02-01

Various models of a tube with elastic walls are investigated: with controlled pressure, filled with incompressible fluid, filled with compressible gas. The non-linear theory of hyperelasticity is applied. The walls of a tube are described with complete membrane model. It is proposed to use linear model of plate in order to take the bending resistance of walls into account. The walls of the tube were treated previously as inviscid and incompressible. Compressibility of material of walls and viscosity of material, either gas or liquid are considered. Equations are solved numerically. Three-layer time and space centered reversible numerical scheme and similar two-layer space reversible numerical scheme with approximation of time derivatives by Runge-Kutta method are used. A method of correction of numerical schemes by inclusion of terms with highorder derivatives is developed. Simplified hyperbolic equations are derived.

Optimal control theory (OWEM) applied to a helicopter in the hover and approach phase

NASA Technical Reports Server (NTRS)

Born, G. J.; Kai, T.

1975-01-01

A major difficulty in the practical application of linear-quadratic regulator theory is how to choose the weighting matrices in quadratic cost functions. The control system design with optimal weighting matrices was applied to a helicopter in the hover and approach phase. The weighting matrices were calculated to extremize the closed loop total system damping subject to constraints on the determinants. The extremization is really a minimization of the effects of disturbances, and interpreted as a compromise between the generalized system accuracy and the generalized system response speed. The trade-off between the accuracy and the response speed is adjusted by a single parameter, the ratio of determinants. By this approach an objective measure can be obtained for the design of a control system. The measure is to be determined by the system requirements.

Spacecraft stability and control using new techniques for periodic and time-delayed systems

NASA Astrophysics Data System (ADS)

NAzari, Morad

This dissertation addresses various problems in spacecraft stability and control using specialized theoretical and numerical techniques for time-periodic and time-delayed systems. First, the effects of energy dissipation are considered in the dual-spin spacecraft, where the damper masses in the platform (?) and the rotor (?) cause energy loss in the system. Floquet theory is employed to obtain stability charts for different relative spin rates of the subsystem [special characters omitted] with respect to the subsystem [special characters omitted]. Further, the stability and bifurcation of delayed feedback spin stabilization of a rigid spacecraft is investigated. The spin is stabilized about the principal axis of the intermediate moment of inertia using a simple delayed feedback control law. In particular, linear stability is analyzed via the exponential-polynomial characteristic equations and then the method of multiple scales is used to obtain the normal form of the Hopf bifurcation. Next, the dynamics of a rigid spacecraft with nonlinear delayed multi-actuator feedback control are studied, where a nonlinear feedback controller using an inverse dynamics approach is sought for the controlled system to have the desired linear delayed closed-loop dynamics (CLD). Later, three linear state feedback control strategies based on Chebyshev spectral collocation and the Lyapunov Floquet transformation (LFT) are explored for regulation control of linear periodic time delayed systems. First , a delayed feedback control law with discrete delay is implemented and the stability of the closed-loop response is investigated in the parameter space of available control gains using infinite-dimensional Floquet theory. Second, the delay differential equation (DDE) is discretized into a large set of ordinary differential equations (ODEs) using the Chebyshev spectral continuous time approximation (CSCTA) and delayed feedback with distributed delay is applied. The third strategy involves use of both CSCTA and the reduced Lyapunov Floquet transformation (RLFT) in order to design a non-delayed feedback control law. The delayed Mathieu equation is used as an illustrative example in which the closed-loop response and control effort are compared for all three control strategies. Finally, three example applications of control of time-periodic astrodynamic systems, i.e. formation flying control for an elliptic Keplerian chief orbit, body-fixed hovering control over a tumbling asteroid, and stationkeeping in Earth-Moon L1 halo orbits, are shown using versions of the control strategies introduced above. These applications employ a mixture of feedforward and non-delayed periodic-gain state feedback for tracking control of natural and non-natural motions in these systems. A major conclusion is that control effort is minimized by employing periodic-gain (rather than constant-gain) feedback control in such systems.

Extensions of the Ferry shear wave model for active linear and nonlinear microrheology

PubMed Central

Mitran, Sorin M.; Forest, M. Gregory; Yao, Lingxing; Lindley, Brandon; Hill, David B.

2009-01-01

The classical oscillatory shear wave model of Ferry et al. [J. Polym. Sci. 2:593-611, (1947)] is extended for active linear and nonlinear microrheology. In the Ferry protocol, oscillation and attenuation lengths of the shear wave measured from strobe photographs determine storage and loss moduli at each frequency of plate oscillation. The microliter volumes typical in biology require modifications of experimental method and theory. Microbead tracking replaces strobe photographs. Reflection from the top boundary yields counterpropagating modes which are modeled here for linear and nonlinear viscoelastic constitutive laws. Furthermore, bulk imposed strain is easily controlled, and we explore the onset of normal stress generation and shear thinning using nonlinear viscoelastic models. For this paper, we present the theory, exact linear and nonlinear solutions where possible, and simulation tools more generally. We then illustrate errors in inverse characterization by application of the Ferry formulas, due to both suppression of wave reflection and nonlinearity, even if there were no experimental error. This shear wave method presents an active and nonlinear analog of the two-point microrheology of Crocker et al. [Phys. Rev. Lett. 85: 888 - 891 (2000)]. Nonlocal (spatially extended) deformations and stresses are propagated through a small volume sample, on wavelengths long relative to bead size. The setup is ideal for exploration of nonlinear threshold behavior. PMID:20011614

F100 Multivariable Control Synthesis Program. Computer Implementation of the F100 Multivariable Control Algorithm

NASA Technical Reports Server (NTRS)

Soeder, J. F.

1983-01-01

As turbofan engines become more complex, the development of controls necessitate the use of multivariable control techniques. A control developed for the F100-PW-100(3) turbofan engine by using linear quadratic regulator theory and other modern multivariable control synthesis techniques is described. The assembly language implementation of this control on an SEL 810B minicomputer is described. This implementation was then evaluated by using a real-time hybrid simulation of the engine. The control software was modified to run with a real engine. These modifications, in the form of sensor and actuator failure checks and control executive sequencing, are discussed. Finally recommendations for control software implementations are presented.

An Introduction to Multilinear Formula Score Theory. Measurement Series 84-4.

ERIC Educational Resources Information Center

Levine, Michael V.

Formula score theory (FST) associates each multiple choice test with a linear operator and expresses all of the real functions of item response theory as linear combinations of the operator's eigenfunctions. Hard measurement problems can then often be reformulated as easier, standard mathematical problems. For example, the problem of estimating…

Lack of Set Theory Relevant Prerequisite Knowledge

ERIC Educational Resources Information Center

Dogan-Dunlap, Hamide

2006-01-01

Many students struggle with college mathematics topics due to a lack of mastery of prerequisite knowledge. Set theory language is one such prerequisite for linear algebra courses. Many students' mistakes on linear algebra questions reveal a lack of mastery of set theory knowledge. This paper reports the findings of a qualitative analysis of a…

Computational Study of Laminar Flow Control on a Subsonic Swept Wing Using Discrete Roughness Elements

NASA Technical Reports Server (NTRS)

Li, Fei; Choudhari, Meelan M.; Chang, Chau-Lyan; Streett, Craig L.; Carpenter, Mark H.

2011-01-01

A combination of parabolized stability equations and secondary instability theory has been applied to a low-speed swept airfoil model with a chord Reynolds number of 7.15 million, with the goals of (i) evaluating this methodology in the context of transition prediction for a known configuration for which roughness based crossflow transition control has been demonstrated under flight conditions and (ii) of analyzing the mechanism of transition delay via the introduction of discrete roughness elements (DRE). Roughness based transition control involves controlled seeding of suitable, subdominant crossflow modes, so as to weaken the growth of naturally occurring, linearly more unstable crossflow modes. Therefore, a synthesis of receptivity, linear and nonlinear growth of stationary crossflow disturbances, and the ensuing development of high frequency secondary instabilities is desirable to understand the experimentally observed transition behavior. With further validation, such higher fidelity prediction methodology could be utilized to assess the potential for crossflow transition control at even higher Reynolds numbers, where experimental data is currently unavailable.

SPHERES tethered formation flight testbed: application to NASA's SPECS mission

NASA Astrophysics Data System (ADS)

Chung, Soon-Jo; Kong, Edmund M.; Miller, David W.

2005-08-01

This paper elaborates on theory and experiment of the formation flight control for the future space-borne tethered interferometers. The nonlinear equations of multi-vehicle tethered spacecraft system are derived by Lagrange equations and decoupling method. The preliminary analysis predicts unstable dynamics depending on the direction of the tether motor. The controllability analysis indicates that both array resizing and spin-up are fully controllable only by the reaction wheels and the tether motor, thereby eliminating the need for thrusters. Linear and nonlinear decentralized control techniques have been implemented into the tethered SPHERES testbed, and tested at the NASA MSFC's flat floor facility using two and three SPHERES configurations. The nonlinear control using feedback linearization technique performed successfully in both two SPHERES in-line configuration and three triangular configuration while varying the tether length. The relative metrology system, using the ultra sound metrology system and the inertial sensors as well as the decentralized nonlinear estimator, is developed to provide necessary state information.

Sensitivity method for integrated structure/active control law design

NASA Technical Reports Server (NTRS)

Gilbert, Michael G.

1987-01-01

The development is described of an integrated structure/active control law design methodology for aeroelastic aircraft applications. A short motivating introduction to aeroservoelasticity is given along with the need for integrated structures/controls design algorithms. Three alternative approaches to development of an integrated design method are briefly discussed with regards to complexity, coordination and tradeoff strategies, and the nature of the resulting solutions. This leads to the formulation of the proposed approach which is based on the concepts of sensitivity of optimum solutions and multi-level decompositions. The concept of sensitivity of optimum is explained in more detail and compared with traditional sensitivity concepts of classical control theory. The analytical sensitivity expressions for the solution of the linear, quadratic cost, Gaussian (LQG) control problem are summarized in terms of the linear regulator solution and the Kalman Filter solution. Numerical results for a state space aeroelastic model of the DAST ARW-II vehicle are given, showing the changes in aircraft responses to variations of a structural parameter, in this case first wing bending natural frequency.

Roughness Based Crossflow Transition Control: A Computational Assessment

NASA Technical Reports Server (NTRS)

Li, Fei; Choudhari, Meelan M.; Chang, Chau-Lyan; Streett, Craig L.; Carpenter, Mark H.

2009-01-01

A combination of parabolized stability equations and secondary instability theory has been applied to a low-speed swept airfoil model with a chord Reynolds number of 7.15 million, with the goals of (i) evaluating this methodology in the context of transition prediction for a known configuration for which roughness based crossflow transition control has been demonstrated under flight conditions and (ii) of analyzing the mechanism of transition delay via the introduction of discrete roughness elements (DRE). Roughness based transition control involves controlled seeding of suitable, subdominant crossflow modes, so as to weaken the growth of naturally occurring, linearly more unstable crossflow modes. Therefore, a synthesis of receptivity, linear and nonlinear growth of stationary crossflow disturbances, and the ensuing development of high frequency secondary instabilities is desirable to understand the experimentally observed transition behavior. With further validation, such higher fidelity prediction methodology could be utilized to assess the potential for crossflow transition control at even higher Reynolds numbers, where experimental data is currently unavailable.

Model-Based Battery Management Systems: From Theory to Practice

NASA Astrophysics Data System (ADS)

Pathak, Manan

Lithium-ion batteries are now extensively being used as the primary storage source. Capacity and power fade, and slow recharging times are key issues that restrict its use in many applications. Battery management systems are critical to address these issues, along with ensuring its safety. This dissertation focuses on exploring various control strategies using detailed physics-based electrochemical models developed previously for lithium-ion batteries, which could be used in advanced battery management systems. Optimal charging profiles for minimizing capacity fade based on SEI-layer formation are derived and the benefits of using such control strategies are shown by experimentally testing them on a 16 Ah NMC-based pouch cell. This dissertation also explores different time-discretization strategies for non-linear models, which gives an improved order of convergence for optimal control problems. Lastly, this dissertation also explores a physics-based model for predicting the linear impedance of a battery, and develops a freeware that is extremely robust and computationally fast. Such a code could be used for estimating transport, kinetic and material properties of the battery based on the linear impedance spectra.

Vibration control of large linear quadratic symmetric systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Jeon, G. J.

1983-01-01

Some unique properties on a class of the second order lambda matrices were found and applied to determine a damping matrix of the decoupled subsystem in such a way that the damped system would have preassigned eigenvalues without disturbing the stiffness matrix. The resulting system was realized as a time invariant velocity only feedback control system with desired poles. Another approach using optimal control theory was also applied to the decoupled system in such a way that the mode spillover problem could be eliminated. The procedures were tested successfully by numerical examples.

Active control of helicopter air resonance in hover and forward flight

NASA Technical Reports Server (NTRS)

Takahashi, M. D.; Friedman, P. P.

1988-01-01

A coupled rotor/fuselage helicopter analysis is presented. The accuracy of the model is illustrated by comparing it with experimental data. The sensitivity of the open loop damping of the unstable resonance mode to such modeling effects as blade torsional flexibility, unsteady aerodynamics, forward flight, periodic terms, and trim solution is illustrated by numerous examples. Subsequently, the model is used in conjunction with linear optimal control theory to stabilize the air resonance mode. The influence of the modeling effects mentioned before on active resonance control is then investigated.

Transient response of multidegree-of-freedom linear systems to forcing functions with inequality constraints

NASA Technical Reports Server (NTRS)

Michalopoulos, C. D.

1974-01-01

Optimal control theory is applied to analyze the transient response of discrete linear systems to forcing functions with unknown time dependence but having known bounds. Particular attention is given to forcing functions which include: (1) maximum displacement of any given mass element, (2) maximum relative displacement of any two adjacent masses, and (3) maximum acceleration of a given mass. Linear mechanical systems with an arbitrary number of degrees of freedom and only one forcing function acting are considered. In the general case, the desired forcing function is found to be a function that switches from the upper-to-lower bound and vice-versa at certain moments of time. A general procedure for finding such switching times is set forth.

Consensus for linear multi-agent system with intermittent information transmissions using the time-scale theory

NASA Astrophysics Data System (ADS)

Taousser, Fatima; Defoort, Michael; Djemai, Mohamed

2016-01-01

This paper investigates the consensus problem for linear multi-agent system with fixed communication topology in the presence of intermittent communication using the time-scale theory. Since each agent can only obtain relative local information intermittently, the proposed consensus algorithm is based on a discontinuous local interaction rule. The interaction among agents happens at a disjoint set of continuous-time intervals. The closed-loop multi-agent system can be represented using mixed linear continuous-time and linear discrete-time models due to intermittent information transmissions. The time-scale theory provides a powerful tool to combine continuous-time and discrete-time cases and study the consensus protocol under a unified framework. Using this theory, some conditions are derived to achieve exponential consensus under intermittent information transmissions. Simulations are performed to validate the theoretical results.

A study of the limitations of linear theory methods as applied to sonic boom calculations

NASA Technical Reports Server (NTRS)

Darden, Christine M.

1990-01-01

Current sonic boom minimization theories have been reviewed to emphasize the capabilities and flexibilities of the methods. Flexibility is important because it is necessary for the designer to meet optimized area constraints while reducing the impact on vehicle aerodynamic performance. Preliminary comparisons of sonic booms predicted for two Mach 3 concepts illustrate the benefits of shaping. Finally, for very simple bodies of revolution, sonic boom predictions were made using two methods - a modified linear theory method and a nonlinear method - for signature shapes which were both farfield N-waves and midfield waves. Preliminary analysis on these simple bodies verified that current modified linear theory prediction methods become inadequate for predicting midfield signatures for Mach numbers above 3. The importance of impulse is sonic boom disturbance and the importance of three-dimensional effects which could not be simulated with the bodies of revolution will determine the validity of current modified linear theory methods in predicting midfield signatures at lower Mach numbers.

Minimal complexity control law synthesis

NASA Technical Reports Server (NTRS)

Bernstein, Dennis S.; Haddad, Wassim M.; Nett, Carl N.

1989-01-01

A paradigm for control law design for modern engineering systems is proposed: Minimize control law complexity subject to the achievement of a specified accuracy in the face of a specified level of uncertainty. Correspondingly, the overall goal is to make progress towards the development of a control law design methodology which supports this paradigm. Researchers achieve this goal by developing a general theory of optimal constrained-structure dynamic output feedback compensation, where here constrained-structure means that the dynamic-structure (e.g., dynamic order, pole locations, zero locations, etc.) of the output feedback compensation is constrained in some way. By applying this theory in an innovative fashion, where here the indicated iteration occurs over the choice of the compensator dynamic-structure, the paradigm stated above can, in principle, be realized. The optimal constrained-structure dynamic output feedback problem is formulated in general terms. An elegant method for reducing optimal constrained-structure dynamic output feedback problems to optimal static output feedback problems is then developed. This reduction procedure makes use of star products, linear fractional transformations, and linear fractional decompositions, and yields as a byproduct a complete characterization of the class of optimal constrained-structure dynamic output feedback problems which can be reduced to optimal static output feedback problems. Issues such as operational/physical constraints, operating-point variations, and processor throughput/memory limitations are considered, and it is shown how anti-windup/bumpless transfer, gain-scheduling, and digital processor implementation can be facilitated by constraining the controller dynamic-structure in an appropriate fashion.

Chaos, complexity and complicatedness: lessons from rocket science.

PubMed

Norman, Geoff

2011-06-01

Recently several authors have drawn parallels between educational research and some theories of natural science, in particular complexity theory and chaos theory. The central claim is that both the natural science theories are useful metaphors for education research in that they deal with phenomena that involve many variables interacting in complex, non-linear and unstable ways, and leading to effects that are neither reproducible nor comprehensible. This paper presents a counter-argument. I begin by carefully examining the concepts of uncertainty, complexity and chaos, as described in physical science. I distinguish carefully between systems that are, respectively, complex, chaotic and complicated. I demonstrate that complex and chaotic systems have highly specific characteristics that are unlikely to be present in education systems. I then suggest that, in fact, there is ample evidence that human learning can be understood adequately with conventional linear models. The implications of these opposing world views are substantial. If education science has the properties of complex or chaotic systems, we should abandon any attempt at control or understanding. However, as I point out, to do so would ignore a number of recent developments in our understanding of learning that hold promise to yield substantial improvements in effectiveness and efficiency of learning. © Blackwell Publishing Ltd 2011.

Categorization and identification of simultaneous targets.

PubMed

Theeuwes, J

1991-02-01

Early and late selection theories of visual attention disagree about whether identification occurs before or after selection. Studies showing the category effect, i.e., the time to detect a letter is hardly affected by the number of digits present in the display, are taken as evidence for late selection theories since these studies suggest parallel identification of all items in the display. As an extension of previous studies, in the present study two categorically different targets were presented simultaneously among a variable number of nontargets. Subjects were shown brief displays of two target letters among either 2, 4 or 6 nontarget digits. Subjects responded 'same' when the two letters were identical and 'different' otherwise. Since the 'same-different' response reflects the combined outcome of the simultaneous targets, late-selection theory predicts that the time to match the target letters is independent of the number of nontarget digits. Alternatively, early-selection theory predicts a linear increase of reaction time with display size since the presence of more than one target disrupts parallel preattentive processing, leading to a serial search through all items in the display. The results provide evidence for the early-selection view since reaction time increased linearly with the number of categorically different nontargets. A control experiment revealed that none of the alternative explanations could account for the display size effect.

Einstein’s quadrupole formula from the kinetic-conformal Hořava theory

NASA Astrophysics Data System (ADS)

Bellorín, Jorge; Restuccia, Alvaro

We analyze the radiative and nonradiative linearized variables in a gravity theory within the family of the nonprojectable Hořava theories, the Hořava theory at the kinetic-conformal point. There is no extra mode in this formulation, the theory shares the same number of degrees of freedom with general relativity. The large-distance effective action, which is the one we consider, can be given in a generally-covariant form under asymptotically flat boundary conditions, the Einstein-aether theory under the condition of hypersurface orthogonality on the aether vector. In the linearized theory, we find that only the transverse-traceless tensorial modes obey a sourced wave equation, as in general relativity. The rest of variables are nonradiative. The result is gauge-independent at the level of the linearized theory. For the case of a weak source, we find that the leading mode in the far zone is exactly Einstein’s quadrupole formula of general relativity, if some coupling constants are properly identified. There are no monopoles nor dipoles in this formulation, in distinction to the nonprojectable Horava theory outside the kinetic-conformal point. We also discuss some constraints on the theory arising from the observational bounds on Lorentz-violating theories.

Optimal control and Galois theory

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

Zelikin, M I; Kiselev, D D; Lokutsievskiy, L V

2013-11-30

An important role is played in the solution of a class of optimal control problems by a certain special polynomial of degree 2(n−1) with integer coefficients. The linear independence of a family of k roots of this polynomial over the field Q implies the existence of a solution of the original problem with optimal control in the form of an irrational winding of a k-dimensional Clifford torus, which is passed in finite time. In the paper, we prove that for n≤15 one can take an arbitrary positive integer not exceeding [n/2] for k. The apparatus developed in the paper is applied to the systems ofmore » Chebyshev-Hermite polynomials and generalized Chebyshev-Laguerre polynomials. It is proved that for such polynomials of degree 2m every subsystem of [(m+1)/2] roots with pairwise distinct squares is linearly independent over the field Q. Bibliography: 11 titles.« less

Finite-time mixed outer synchronization of complex networks with coupling time-varying delay.

PubMed

He, Ping; Ma, Shu-Hua; Fan, Tao

2012-12-01

This article is concerned with the problem of finite-time mixed outer synchronization (FMOS) of complex networks with coupling time-varying delay. FMOS is a recently developed generalized synchronization concept, i.e., in which different state variables of the corresponding nodes can evolve into finite-time complete synchronization, finite-time anti-synchronization, and even amplitude finite-time death simultaneously for an appropriate choice of the controller gain matrix. Some novel stability criteria for the synchronization between drive and response complex networks with coupling time-varying delay are derived using the Lyapunov stability theory and linear matrix inequalities. And a simple linear state feedback synchronization controller is designed as a result. Numerical simulations for two coupled networks of modified Chua's circuits are then provided to demonstrate the effectiveness and feasibility of the proposed complex networks control and synchronization schemes and then compared with the proposed results and the previous schemes for accuracy.

Attitude and vibration control of a large flexible space-based antenna

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1982-01-01

Control systems synthesis is considered for controlling the rigid body attitude and elastic motion of a large deployable space-based antenna. Two methods for control systems synthesis are considered. The first method utilizes the stability and robustness properties of the controller consisting of torque actuators and collocated attitude and rate sensors. The second method is based on the linear-quadratic-Gaussian control theory. A combination of the two methods, which results in a two level hierarchical control system, is also briefly discussed. The performance of the controllers is analyzed by computing the variances of pointing errors, feed misalignment errors and surface contour errors in the presence of sensor and actuator noise.

Scalar-tensor linear inflation

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

Artymowski, Michał; Racioppi, Antonio, E-mail: Michal.Artymowski@uj.edu.pl, E-mail: Antonio.Racioppi@kbfi.ee

2017-04-01

We investigate two approaches to non-minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for a non-minimal coupling to gravity of the form of f (φ) R /2; b) the particle physics approach, where we motivate the form of the Jordan frame potential by loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced gravity inflationary scenario, but instead of the Starobinsky attractor they lead tomore » linear inflation in the strong coupling limit.« less

An outflow boundary condition for aeroacoustic computations

NASA Technical Reports Server (NTRS)

Hayder, M. Ehtesham; Hagstrom, Thomas

1995-01-01

A formulation of boundary condition for flows with small disturbances is presented. The authors test their methodology in an axisymmetric jet flow calculation, using both the Navier-Stokes and Euler equations. Solutions in the far field are assumed to be oscillatory. If the oscillatory disturbances are small, the growth of the solution variables can be predicted by linear theory. Eigenfunctions of the linear theory are used explicitly in the formulation of the boundary conditions. This guarantees correct solutions at the boundary in the limit where the predictions of linear theory are valid.

Modeling and Analysis of Micro-Spacecraft Attitude Sensing with Gyrowheel.

PubMed

Liu, Xiaokun; Zhao, Hui; Yao, Yu; He, Fenghua

2016-08-19

This paper proposes two kinds of approaches of angular rate sensing for micro-spacecraft with a gyrowheel (GW), which can combine attitude sensing with attitude control into one single device to achieve a compact micro-spacecraft design. In this implementation, during the three-dimensional attitude control torques being produced, two-dimensional spacecraft angular rates can be sensed from the signals of the GW sensors, such as the currents of the torque coils, the tilt angles of the rotor, the motor rotation, etc. This paper focuses on the problems of the angular rate sensing with the GW at large tilt angles of the rotor. For this purpose, a novel real-time linearization approach based on Lyapunov's linearization theory is proposed, and a GW linearized measurement model at arbitrary tilt angles of the rotor is derived. Furthermore, by representing the two-dimensional rotor tilt angles and tilt control torques as complex quantities and separating the twice periodic terms about the motor spin speed, the linearized measurement model at smaller tilt angles of the rotor is given and simplified. According to the respective characteristics, the application schemes of the two measurement models are analyzed from the engineering perspective. Finally, the simulation results are presented to demonstrate the effectiveness of the proposed strategy.

Modeling and Analysis of Micro-Spacecraft Attitude Sensing with Gyrowheel

PubMed Central

Liu, Xiaokun; Zhao, Hui; Yao, Yu; He, Fenghua

2016-01-01

This paper proposes two kinds of approaches of angular rate sensing for micro-spacecraft with a gyrowheel (GW), which can combine attitude sensing with attitude control into one single device to achieve a compact micro-spacecraft design. In this implementation, during the three-dimensional attitude control torques being produced, two-dimensional spacecraft angular rates can be sensed from the signals of the GW sensors, such as the currents of the torque coils, the tilt angles of the rotor, the motor rotation, etc. This paper focuses on the problems of the angular rate sensing with the GW at large tilt angles of the rotor. For this purpose, a novel real-time linearization approach based on Lyapunov’s linearization theory is proposed, and a GW linearized measurement model at arbitrary tilt angles of the rotor is derived. Furthermore, by representing the two-dimensional rotor tilt angles and tilt control torques as complex quantities and separating the twice periodic terms about the motor spin speed, the linearized measurement model at smaller tilt angles of the rotor is given and simplified. According to the respective characteristics, the application schemes of the two measurement models are analyzed from the engineering perspective. Finally, the simulation results are presented to demonstrate the effectiveness of the proposed strategy. PMID:27548178

Realizing Broadband and Invertible Linear-to-circular Polarization Converter with Ultrathin Single-layer Metasurface

PubMed Central

Li, Zhancheng; Liu, Wenwei; Cheng, Hua; Chen, Shuqi; Tian, Jianguo

2015-01-01

The arbitrary control of the polarization states of light has attracted the interest of the scientific community because of the wide range of modern optical applications that such control can afford. However, conventional polarization control setups are bulky and very often operate only within a narrow wavelength range, thereby resisting optical system miniaturization and integration. Here, we present the basic theory, simulated demonstration, and in-depth analysis of a high-performance broadband and invertible linear-to-circular (LTC) polarization converter composed of a single-layer gold nanorod array with a total thickness of ~λ/70 for the near-infrared regime. This setup can transform a circularly polarized wave into a linearly polarized one or a linearly polarized wave with a wavelength-dependent electric field polarization angle into a circularly polarized one in the transmission mode. The broadband and invertible LTC polarization conversion can be attributed to the tailoring of the light interference at the subwavelength scale via the induction of the anisotropic optical resonance mode. This ultrathin single-layer metasurface relaxes the high-precision requirements of the structure parameters in general metasurfaces while retaining the polarization conversion performance. Our findings open up intriguing possibilities towards the realization of novel integrated metasurface-based photonics devices for polarization manipulation, modulation, and phase retardation. PMID:26667360

The dynamics and control of large flexible space structures, 3. Part A: Shape and orientation control of a platform in orbit using point actuators

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Reddy, A. S. S. R.; Krishna, R.; James, P. K.

1980-01-01

The dynamics, attitude, and shape control of a large thin flexible square platform in orbit are studied. Attitude and shape control are assumed to result from actuators placed perpendicular to the main surface and one edge and their effect on the rigid body and elastic modes is modelled to first order. The equations of motion are linearized about three different nominal orientations: (1) the platform following the local vertical with its major surface perpendicular to the orbital plane; (2) the platform following the local horizontal with its major surface normal to the local vertical; and (3) the platform following the local vertical with its major surface perpendicular to the orbit normal. The stability of the uncontrolled system is investigated analytically. Once controllability is established for a set of actuator locations, control law development is based on decoupling, pole placement, and linear optimal control theory. Frequencies and elastic modal shape functions are obtained using a finite element computer algorithm, two different approximate analytical methods, and the results of the three methods compared.

Linear quadratic stochastic control of atomic hydrogen masers.

PubMed

Koppang, P; Leland, R

1999-01-01

Data are given showing the results of using the linear quadratic Gaussian (LQG) technique to steer remote hydrogen masers to Coordinated Universal Time (UTC) as given by the United States Naval Observatory (USNO) via two-way satellite time transfer and the Global Positioning System (GPS). Data also are shown from the results of steering a hydrogen maser to the real-time USNO mean. A general overview of the theory behind the LQG technique also is given. The LQG control is a technique that uses Kalman filtering to estimate time and frequency errors used as input into a control calculation. A discrete frequency steer is calculated by minimizing a quadratic cost function that is dependent on both the time and frequency errors and the control effort. Different penalties, chosen by the designer, are assessed by the controller as the time and frequency errors and control effort vary from zero. With this feature, controllers can be designed to force the time and frequency differences between two standards to zero, either more or less aggressively depending on the application.

A Novel Approach to Anharmonicity for a Wealth of Applications in Nonlinear Science Technologies

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

Hanusse, Patrick

2011-04-19

We present a new theory of the anharmonicity of nonlinear oscillations that are exhibited by many physical systems. New physical quantities are introduced that describe the departure from linear or harmonic behavior and as far as extremely anharmonic situations. In order to solve the nonlinear phase equation, the key notion of our theory, which controls the anharmonic behavior, a new and fascinating nonlinear trigonometry is designed. These results provide a general and accurate yet compact description of such signals, by far better than the Fourier description, both quantitatively and qualitatively and will benefit many application fields.

Economic policy optimization based on both one stochastic model and the parametric control theory

NASA Astrophysics Data System (ADS)

Ashimov, Abdykappar; Borovskiy, Yuriy; Onalbekov, Mukhit

2016-06-01

A nonlinear dynamic stochastic general equilibrium model with financial frictions is developed to describe two interacting national economies in the environment of the rest of the world. Parameters of nonlinear model are estimated based on its log-linearization by the Bayesian approach. The nonlinear model is verified by retroprognosis, estimation of stability indicators of mappings specified by the model, and estimation the degree of coincidence for results of internal and external shocks' effects on macroeconomic indicators on the basis of the estimated nonlinear model and its log-linearization. On the base of the nonlinear model, the parametric control problems of economic growth and volatility of macroeconomic indicators of Kazakhstan are formulated and solved for two exchange rate regimes (free floating and managed floating exchange rates)

Language Measure for Robust Optimal Control

DTIC Science & Technology

2006-01-01

ROBUST OPTIMAL CONTROL 6. AUTHOR(S) Asok Ray , Travis Ortogero 5. FUNDING NUMBERS C - F30602-01-2-0575 PE - 62301E PR - M414...element of Π is non-negative, so each element of kΠ is also. Thus, 0][ 1 ≥Π− −I elementwise. ■ Wang and Ray [WR02] and Ray and Phoha [RP02] have...Sell, Linear Operator Theory in Science and Engineering, Springer-Verlag, New York, 1982. [RP02] A. Ray and S. Phoha, “A language measure for

A synthesis theory for self-oscillating adaptive systems /SOAS/

NASA Technical Reports Server (NTRS)

Horowitz, I.; Smay, J.; Shapiro, A.

1974-01-01

A quantitative synthesis theory is presented for the Self-Oscillating Adaptive System (SOAS), whose nonlinear element has a static, odd character with hard saturation. The synthesis theory is based upon the quasilinear properties of the SOAS to forced inputs, which permits the extension of quantitative linear feedback theory to the SOAS. A reasonable definition of optimum design is shown to be the minimization of the limit cycle frequency. The great advantages of the SOAS is its zero sensitivity to pure gain changes. However, quasilinearity and control of the limit cycle amplitude at the system output, impose additional constraints which partially or completely cancel this advantage, depending on the numerical values of the design parameters. By means of narrow-band filtering, an additional factor is introduced which permits trade-off between filter complexity and limit cycle frequency minimization.

Towards a non-linear theory for fluid pressure and osmosis in shales

NASA Astrophysics Data System (ADS)

Droghei, Riccardo; Salusti, Ettore

2015-04-01

In exploiting deep hydrocarbon reservoirs, often injections of fluid and/or solute are used. To control and avoid troubles as fluid and gas unexpected diffusions, a reservoir characterization can be obtained also from observations of space and time evolution of micro-earthquake clouds resulting from such injections. This is important since several among the processes caused by fluid injections can modify the deep matrix. Information about the evolution of such micro-seismicity clouds therefore plays a realistic role in the reservoir analyses. To reach a better insight about such processes, and obtain a better system control, we here analyze the initial stress necessary to originate strong non linear transients of combined fluid pressure and solute density (osmosis) in a porous matrix. All this can indeed perturb in a mild (i.e. a linear diffusion) or dramatic non linear way the rock structure, till inducing rock deformations, micro-earthquakes or fractures. I more detail we here assume first a linear Hooke law relating strain, stress, solute density and fluid pressure, and analyze their effect in the porous rock dynamics. Then we analyze its generalization, i.e. the further non linear effect of a stronger external pressure, also in presence of a trend of pressure or solute in the whole region. We moreover characterize the zones where a sudden arrival of such a front can cause micro-earthquakes or fractures. All this allows to reach a novel, more realistic insight about the control of rock evolution in presence of strong pressure fronts. We thus obtain a more efficient reservoir control to avoid large geological perturbations. It is of interest that our results are very similar to those found by Shapiro et al.(2013) with a different approach.

Flight test trajectory control analysis

NASA Technical Reports Server (NTRS)

Walker, R.; Gupta, N.

1983-01-01

Recent extensions to optimal control theory applied to meaningful linear models with sufficiently flexible software tools provide powerful techniques for designing flight test trajectory controllers (FTTCs). This report describes the principal steps for systematic development of flight trajectory controllers, which can be summarized as planning, modeling, designing, and validating a trajectory controller. The techniques have been kept as general as possible and should apply to a wide range of problems where quantities must be computed and displayed to a pilot to improve pilot effectiveness and to reduce workload and fatigue. To illustrate the approach, a detailed trajectory guidance law is developed and demonstrated for the F-15 aircraft flying the zoom-and-pushover maneuver.

A slewing control experiment for flexible structures

NASA Technical Reports Server (NTRS)

Juang, J.-N.; Horta, L. G.; Robertshaw, H. H.

1985-01-01

A hardware set-up has been developed to study slewing control for flexible structures including a steel beam and a solar panel. The linear optimal terminal control law is used to design active controllers which are implemented in an analog computer. The objective of this experiment is to demonstrate and verify the dynamics and optimal terminal control laws as applied to flexible structures for large angle maneuver. Actuation is provided by an electric motor while sensing is given by strain gages and angle potentiometer. Experimental measurements are compared with analytical predictions in terms of modal parameters of the system stability matrix and sufficient agreement is achieved to validate the theory.

Development of helicopter attitude axes controlled hover flight without pilot assistance and vehicle crashes

NASA Astrophysics Data System (ADS)

Simon, Miguel

In this work, we show how to computerize a helicopter to fly attitude axes controlled hover flight without the assistance of a pilot and without ever crashing. We start by developing a helicopter research test bed system including all hardware, software, and means for testing and training the helicopter to fly by computer. We select a Remote Controlled helicopter with a 5 ft. diameter rotor and 2.2 hp engine. We equip the helicopter with a payload of sensors, computers, navigation and telemetry equipment, and batteries. We develop a differential GPS system with cm accuracy and a ground computerized navigation system for six degrees of freedom (6-DoF) free flight while tracking navigation commands. We design feedback control loops with yet-to-be-determined gains for the five control "knobs" available to a flying radio-controlled (RC) miniature helicopter: engine throttle, main rotor collective pitch, longitudinal cyclic pitch, lateral cyclic pitch, and tail rotor collective pitch. We develop helicopter flight equations using fundamental dynamics, helicopter momentum theory and blade element theory. The helicopter flight equations include helicopter rotor equations of motions, helicopter rotor forces and moments, helicopter trim equations, helicopter stability derivatives, and a coupled fuselage-rotor helicopter 6-DoF model. The helicopter simulation also includes helicopter engine control equations, a helicopter aerodynamic model, and finally helicopter stability and control equations. The derivation of a set of non-linear equations of motion for the main rotor is a contribution of this thesis work. We design and build two special test stands for training and testing the helicopter to fly attitude axes controlled hover flight, starting with one axis at a time and progressing to multiple axes. The first test stand is built for teaching and testing controlled flight of elevation and yaw (i.e., directional control). The second test stand is built for teaching and testing any one or combination of the following attitude axes controlled flight: (1) pitch, (2) roll and (3) yaw. The subsequent development of a novel method to decouple, stabilize and teach the helicopter hover flight is a primary contribution of this thesis. The novel method included the development of a non-linear modeling technique for linearizing the RPM state equation dynamics so that a simple but accurate transfer function is derivable between the "available torque of the engine" and RPM. Specifically, the main rotor and tail rotor torques are modeled accurately with a bias term plus a nonlinear term involving the product of RPM squared times the main rotor blade pitch angle raised to the three-halves power. Application of this non-linear modeling technique resulted in a simple, representative and accurate transfer function model of the open-loop plant for the entire helicopter system so that all the feedback control laws for autonomous flight purposes could be derived easily using classical control theory. This is one of the contributions of this dissertation work. After discussing the integration of hardware and software elements of our helicopter research test bed system, we perform a number of experiments and tests using the two specially built test stands. Feedback gains are derived for controlling the following: (1) engine throttle to maintain prescribed main rotor angular speed, (2) main rotor collective pitch to maintain constant elevation, (3) longitudinal cyclic pitch to maintain prescribed pitch angle, (4) lateral cyclic pitch to maintain prescribed roll angle, and (5) yaw axis to maintain prescribed compass direction. (Abstract shortened by UMI.)

Quantum Linear Systems Theory

DTIC Science & Technology

2013-02-15

Matthew James, Andre Carvalho and Michael Hush completed some work analyzing cross-phase modulation using single photon quantum filtering techniques...ANU Michael Hush January – June, 2012, Postdoc, ANU Matthew R. James Professor, Australian National University Ian R. Petersen Professor...appear, IEEE Trans. Aut. Control., 2013. A. R. R. Carvalho, M. R. Hush , and M. R. James, “Cavity driven by a single photon: Conditional dynamics and

Chandrasekhar equations and computational algorithms for distributed parameter systems

NASA Technical Reports Server (NTRS)

Burns, J. A.; Ito, K.; Powers, R. K.

1984-01-01

The Chandrasekhar equations arising in optimal control problems for linear distributed parameter systems are considered. The equations are derived via approximation theory. This approach is used to obtain existence, uniqueness, and strong differentiability of the solutions and provides the basis for a convergent computation scheme for approximating feedback gain operators. A numerical example is presented to illustrate these ideas.

Design of Distributed Engine Control Systems with Uncertain Delay.

PubMed

Liu, Xiaofeng; Li, Yanxi; Sun, Xu

Future gas turbine engine control systems will be based on distributed architecture, in which, the sensors and actuators will be connected to the controllers via a communication network. The performance of the distributed engine control (DEC) is dependent on the network performance. This study introduces a distributed control system architecture based on a networked cascade control system (NCCS). Typical turboshaft engine-distributed controllers are designed based on the NCCS framework with a H∞ output feedback under network-induced time delays and uncertain disturbances. The sufficient conditions for robust stability are derived via the Lyapunov stability theory and linear matrix inequality approach. Both numerical and hardware-in-loop simulations illustrate the effectiveness of the presented method.

Design of Distributed Engine Control Systems with Uncertain Delay

PubMed Central

Li, Yanxi; Sun, Xu

2016-01-01

Future gas turbine engine control systems will be based on distributed architecture, in which, the sensors and actuators will be connected to the controllers via a communication network. The performance of the distributed engine control (DEC) is dependent on the network performance. This study introduces a distributed control system architecture based on a networked cascade control system (NCCS). Typical turboshaft engine-distributed controllers are designed based on the NCCS framework with a H∞ output feedback under network-induced time delays and uncertain disturbances. The sufficient conditions for robust stability are derived via the Lyapunov stability theory and linear matrix inequality approach. Both numerical and hardware-in-loop simulations illustrate the effectiveness of the presented method. PMID:27669005

Practical synchronization on complex dynamical networks via optimal pinning control

NASA Astrophysics Data System (ADS)

Li, Kezan; Sun, Weigang; Small, Michael; Fu, Xinchu

2015-07-01

We consider practical synchronization on complex dynamical networks under linear feedback control designed by optimal control theory. The control goal is to minimize global synchronization error and control strength over a given finite time interval, and synchronization error at terminal time. By utilizing the Pontryagin's minimum principle, and based on a general complex dynamical network, we obtain an optimal system to achieve the control goal. The result is verified by performing some numerical simulations on Star networks, Watts-Strogatz networks, and Barabási-Albert networks. Moreover, by combining optimal control and traditional pinning control, we propose an optimal pinning control strategy which depends on the network's topological structure. Obtained results show that optimal pinning control is very effective for synchronization control in real applications.

A general theory of linear cosmological perturbations: bimetric theories

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

Lagos, Macarena; Ferreira, Pedro G., E-mail: m.lagos13@imperial.ac.uk, E-mail: p.ferreira1@physics.ox.ac.uk

2017-01-01

We implement the method developed in [1] to construct the most general parametrised action for linear cosmological perturbations of bimetric theories of gravity. Specifically, we consider perturbations around a homogeneous and isotropic background, and identify the complete form of the action invariant under diffeomorphism transformations, as well as the number of free parameters characterising this cosmological class of theories. We discuss, in detail, the case without derivative interactions, and compare our results with those found in massive bigravity.

Fourier transform and particle swarm optimization based modified LQR algorithm for mitigation of vibrations using magnetorheological dampers

NASA Astrophysics Data System (ADS)

Kumar, Gaurav; Kumar, Ashok

2017-11-01

Structural control has gained significant attention in recent times. The standalone issue of power requirement during an earthquake has already been solved up to a large extent by designing semi-active control systems using conventional linear quadratic control theory, and many other intelligent control algorithms such as fuzzy controllers, artificial neural networks, etc. In conventional linear-quadratic regulator (LQR) theory, it is customary to note that the values of the design parameters are decided at the time of designing the controller and cannot be subsequently altered. During an earthquake event, the response of the structure may increase or decrease, depending the quasi-resonance occurring between the structure and the earthquake. In this case, it is essential to modify the value of the design parameters of the conventional LQR controller to obtain optimum control force to mitigate the vibrations due to the earthquake. A few studies have been done to sort out this issue but in all these studies it was necessary to maintain a database of the earthquake. To solve this problem and to find the optimized design parameters of the LQR controller in real time, a fast Fourier transform and particle swarm optimization based modified linear quadratic regulator method is presented here. This method comprises four different algorithms: particle swarm optimization (PSO), the fast Fourier transform (FFT), clipped control algorithm and the LQR. The FFT helps to obtain the dominant frequency for every time window. PSO finds the optimum gain matrix through the real-time update of the weighting matrix R, thereby, dispensing with the experimentation. The clipped control law is employed to match the magnetorheological (MR) damper force with the desired force given by the controller. The modified Bouc-Wen phenomenological model is taken to recognize the nonlinearities in the MR damper. The assessment of the advised method is done by simulation of a three-story structure having an MR damper at the ground floor level subjected to three different near-fault historical earthquake time histories, and the outcomes are equated with those of simple conventional LQR. The results establish that the advised methodology is more effective than conventional LQR controllers in reducing inter-storey drift, relative displacement, and acceleration response.

Robust and real-time control of magnetic bearings for space engines

NASA Technical Reports Server (NTRS)

Sinha, Alok; Wang, Kon-Well; Mease, K.; Lewis, S.

1991-01-01

Currently, NASA Lewis Research Center is developing magnetic bearings for Space Shuttle Main Engine (SSME) turbopumps. The control algorithms which have been used are based on either the proportional-intergral-derivative control (PID) approach or the linear quadratic (LQ) state space approach. These approaches lead to an acceptable performance only when the system model is accurately known, which is seldom true in practice. For example, the rotor eccentricity, which is a major source of vibration at high speeds, cannot be predicted accurately. Furthermore, the dynamics of a rotor shaft, which must be treated as a flexible system to model the elastic rotor shaft, is infinite dimensional in theory and the controller can only be developed on the basis of a finite number of modes. Therefore, the development of the control system is further complicated by the possibility of closed loop system instability because of residual or uncontrolled modes, the so called spillover problem. Consequently, novel control algorithms for magnetic bearings are being developed to be robust to inevitable parametric uncertainties, external disturbances, spillover phenomenon and noise. Also, as pointed out earlier, magnetic bearings must exhibit good performance at a speed over 30,000 rpm. This implies that the sampling period available for the design of a digital control system has to be of the order of 0.5 milli-seconds. Therefore, feedback coefficients and other required controller parameters have to be computed off-line so that the on-line computational burden is extremely small. The development of the robust and real-time control algorithms is based on the sliding mode control theory. In this method, a dynamic system is made to move along a manifold of sliding hyperplanes to the origin of the state space. The number of sliding hyperplanes equals that of actuators. The sliding mode controller has two parts; linear state feedback and nonlinear terms. The nonlinear terms guarantee that the systems would reach the intersection of all sliding hyperplanes and remain on it when bounds on the errors in the system parameters and external disturbances are known. The linear part of the control drives the system to the origin of state space. Another important feature is that the controller parameter can be computed off-line. Consequently, on-line computational burden is small.

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

NASA Technical Reports Server (NTRS)

Lisano, Michael E.

2007-01-01

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to nonlinear sequential consider covariance analysis, i.e. in the presence of nonlinear dynamics and nonlinear measurements. A simple SPCF for orbit determination, exemplifying an algorithm hosted in the guidance, navigation and control (GN&C) computer processor of a hypothetical robotic spacecraft, was implemented, and compared with an identically-parameterized (standard) extended, consider-parameterized Kalman filter. The onboard filtering scenario examined is a hypothetical spacecraft orbit about a small natural body with imperfectly-known mass. The formulations, relative complexities, and performances of the filters are compared and discussed.

Modern control concepts in hydrology. [parameter identification in adaptive stochastic control approach

NASA Technical Reports Server (NTRS)

Duong, N.; Winn, C. B.; Johnson, G. R.

1975-01-01

Two approaches to an identification problem in hydrology are presented, based upon concepts from modern control and estimation theory. The first approach treats the identification of unknown parameters in a hydrologic system subject to noisy inputs as an adaptive linear stochastic control problem; the second approach alters the model equation to account for the random part in the inputs, and then uses a nonlinear estimation scheme to estimate the unknown parameters. Both approaches use state-space concepts. The identification schemes are sequential and adaptive and can handle either time-invariant or time-dependent parameters. They are used to identify parameters in the Prasad model of rainfall-runoff. The results obtained are encouraging and confirm the results from two previous studies; the first using numerical integration of the model equation along with a trial-and-error procedure, and the second using a quasi-linearization technique. The proposed approaches offer a systematic way of analyzing the rainfall-runoff process when the input data are imbedded in noise.

Fault-tolerant optimised tracking control for unknown discrete-time linear systems using a combined reinforcement learning and residual compensation methodology

NASA Astrophysics Data System (ADS)

Han, Ke-Zhen; Feng, Jian; Cui, Xiaohong

2017-10-01

This paper considers the fault-tolerant optimised tracking control (FTOTC) problem for unknown discrete-time linear system. A research scheme is proposed on the basis of data-based parity space identification, reinforcement learning and residual compensation techniques. The main characteristic of this research scheme lies in the parity-space-identification-based simultaneous tracking control and residual compensation. The specific technical line consists of four main contents: apply subspace aided method to design observer-based residual generator; use reinforcement Q-learning approach to solve optimised tracking control policy; rely on robust H∞ theory to achieve noise attenuation; adopt fault estimation triggered by residual generator to perform fault compensation. To clarify the design and implementation procedures, an integrated algorithm is further constructed to link up these four functional units. The detailed analysis and proof are subsequently given to explain the guaranteed FTOTC performance of the proposed conclusions. Finally, a case simulation is provided to verify its effectiveness.

Stability and Control of Human Trunk Movement During Walking.

PubMed

Wu, Q.; Sepehri, N.; Thornton-Trump, A. B.; Alexander, M.

1998-01-01

A mathematical model has been developed to study the control mechanisms of human trunk movement during walking. The trunk is modeled as a base-excited inverted pendulum with two-degrees of rotational freedom. The base point, corresponding to the bony landmark of the sacrum, can move in three-dimensional space in a general way. Since the stability of upright posture is essential for human walking, a controller has been designed such that the stability of the pendulum about the upright position is guaranteed. The control laws are developed based on Lyapunov's stability theory and include feedforward and linear feedback components. It is found that the feedforward component plays a critical role in keeping postural stability, and the linear feedback component, (resulting from viscoelastic function of the musculoskeletal system) can effectively duplicate the pattern of trunk movement. The mathematical model is validated by comparing the simulation results with those based on gait measurements performed in the Biomechanics Laboratory at the University of Manitoba.

Graph theory applied to noise and vibration control in statistical energy analysis models.

PubMed

Guasch, Oriol; Cortés, Lluís

2009-06-01

A fundamental aspect of noise and vibration control in statistical energy analysis (SEA) models consists in first identifying and then reducing the energy flow paths between subsystems. In this work, it is proposed to make use of some results from graph theory to address both issues. On the one hand, linear and path algebras applied to adjacency matrices of SEA graphs are used to determine the existence of any order paths between subsystems, counting and labeling them, finding extremal paths, or determining the power flow contributions from groups of paths. On the other hand, a strategy is presented that makes use of graph cut algorithms to reduce the energy flow from a source subsystem to a receiver one, modifying as few internal and coupling loss factors as possible.

Use of digital control theory state space formalism for feedback at SLC

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

Himel, T.; Hendrickson, L.; Rouse, F.

The algorithms used in the database-driven SLC fast-feedback system are based on the state space formalism of digital control theory. These are implemented as a set of matrix equations which use a Kalman filter to estimate a vector of states from a vector of measurements, and then apply a gain matrix to determine the actuator settings from the state vector. The matrices used in the calculation are derived offline using Linear Quadratic Gaussian minimization. For a given noise spectrum, this procedure minimizes the rms of the states (e.g., the position or energy of the beam). The offline program also allowsmore » simulation of the loop's response to arbitrary inputs, and calculates its frequency response. 3 refs., 3 figs.« less

Reducing the pressure drag of a D-shaped bluff body using linear feedback control

NASA Astrophysics Data System (ADS)

Dalla Longa, L.; Morgans, A. S.; Dahan, J. A.

2017-12-01

The pressure drag of blunt bluff bodies is highly relevant in many practical applications, including to the aerodynamic drag of road vehicles. This paper presents theory revealing that a mean drag reduction can be achieved by manipulating wake flow fluctuations. A linear feedback control strategy then exploits this idea, targeting attenuation of the spatially integrated base (back face) pressure fluctuations. Large-eddy simulations of the flow over a D-shaped blunt bluff body are used as a test-bed for this control strategy. The flow response to synthetic jet actuation is characterised using system identification, and controller design is via shaping of the frequency response to achieve fluctuation attenuation. The designed controller successfully attenuates integrated base pressure fluctuations, increasing the time-averaged pressure on the body base by 38%. The effect on the flow field is to push the roll-up of vortices further downstream and increase the extent of the recirculation bubble. This control approach uses only body-mounted sensing/actuation and input-output model identification, meaning that it could be applied experimentally.

Colombeau algebra as a mathematical tool for investigating step load and step deformation of systems of nonlinear springs and dashpots

NASA Astrophysics Data System (ADS)

Průša, Vít; Řehoř, Martin; Tůma, Karel

2017-02-01

The response of mechanical systems composed of springs and dashpots to a step input is of eminent interest in the applications. If the system is formed by linear elements, then its response is governed by a system of linear ordinary differential equations. In the linear case, the mathematical method of choice for the analysis of the response is the classical theory of distributions. However, if the system contains nonlinear elements, then the classical theory of distributions is of no use, since it is strictly limited to the linear setting. Consequently, a question arises whether it is even possible or reasonable to study the response of nonlinear systems to step inputs. The answer is positive. A mathematical theory that can handle the challenge is the so-called Colombeau algebra. Building on the abstract result by Průša and Rajagopal (Int J Non-Linear Mech 81:207-221, 2016), we show how to use the theory in the analysis of response of nonlinear spring-dashpot and spring-dashpot-mass systems.

Linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization

NASA Astrophysics Data System (ADS)

Camporesi, Roberto

2011-06-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and the variation of constants method. The approach presented here can be used in a first course on differential equations for science and engineering majors.

Predictive Feedback and Feedforward Control for Systems with Unknown Disturbances

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Eure, Kenneth W.

1998-01-01

Predictive feedback control has been successfully used in the regulation of plate vibrations when no reference signal is available for feedforward control. However, if a reference signal is available it may be used to enhance regulation by incorporating a feedforward path in the feedback controller. Such a controller is known as a hybrid controller. This paper presents the theory and implementation of the hybrid controller for general linear systems, in particular for structural vibration induced by acoustic noise. The generalized predictive control is extended to include a feedforward path in the multi-input multi-output case and implemented on a single-input single-output test plant to achieve plate vibration regulation. There are cases in acoustic-induce vibration where the disturbance signal is not available to be used by the hybrid controller, but a disturbance model is available. In this case the disturbance model may be used in the feedback controller to enhance performance. In practice, however, neither the disturbance signal nor the disturbance model is available. This paper presents the theory of identifying and incorporating the noise model into the feedback controller. Implementations are performed on a test plant and regulation improvements over the case where no noise model is used are demonstrated.

Gravitons as Embroidery on the Weave

NASA Astrophysics Data System (ADS)

Iwasaki, Junichi; Rovelli, Carlo

We investigate the physical interpretation of the loop states that appear in the loop representation of quantum gravity. By utilizing the “weave” state, which has been recently introduced as a quantum description of the microstructure of flat space, we analyze the relation between loop states and graviton states. This relation determines a linear map M from the state-space of the nonperturbative theory (loop space) into the state-space of the linearized theory (Fock space). We present an explicit form of this map, and a preliminary investigation of its properties. The existence of such a map indicates that the full nonperturbative quantum theory includes a sector that describes the same physics as (the low energy regimes of) the linearized theory, namely gravitons on flat space.

Difference equation state approximations for nonlinear hereditary control problems

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1982-01-01

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.

Experiments on stress dependent borehole acoustic waves.

PubMed

Hsu, Chaur-Jian; Kane, Michael R; Winkler, Kenneth; Wang, Canyun; Johnson, David Linton

2011-10-01

In the laboratory setup, a borehole traverses a dry sandstone formation, which is subjected to a controlled uniaxial stress in the direction perpendicular to the borehole axis. Measurements are made in a single loading-unloading stress cycle from zero to 10 MPa and then back down to zero stress. The applied stress and the presence of the borehole induce anisotropy in the bulk of the material and stress concentration around the borehole, both azimuthally and radially. Acoustic waves are generated and detected in the water-filled borehole, including compressional and shear headwaves, as well as modes of monopole, dipole, quadrupole, and higher order azimuthal symmetries. The linear and non-linear elastic parameters of the formation material are independently quantified, and utilized in conjunction with elastic theories to predict the characteristics of various borehole waves at zero and finite stress conditions. For example, an analytic theory is developed which is successfully used to estimate the changes of monopole tube mode at low frequency resulted from uniaxial stress, utilizing the measured material third order elasticity parameters. Comparisons between various measurements as well as that between experiments and theories are also presented. © 2011 Acoustical Society of America

Linear instability of plane Couette and Poiseuille flows

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

Chefranov, S. G., E-mail: schefranov@mail.ru; Chefranov, A. G., E-mail: Alexander.chefranov@emu.edu.tr

2016-05-15

It is shown that linear instability of plane Couette flow can take place even at finite Reynolds numbers Re > Re{sub th} ≈ 139, which agrees with the experimental value of Re{sub th} ≈ 150 ± 5 [16, 17]. This new result of the linear theory of hydrodynamic stability is obtained by abandoning traditional assumption of the longitudinal periodicity of disturbances in the flow direction. It is established that previous notions about linear stability of this flow at arbitrarily large Reynolds numbers relied directly upon the assumed separation of spatial variables of the field of disturbances and their longitudinal periodicitymore » in the linear theory. By also abandoning these assumptions for plane Poiseuille flow, a new threshold Reynolds number Re{sub th} ≈ 1035 is obtained, which agrees to within 4% with experiment—in contrast to 500% discrepancy for the previous estimate of Re{sub th} ≈ 5772 obtained in the framework of the linear theory under assumption of the “normal” shape of disturbances [2].« less

Variational Theory of Motion of Curved, Twisted and Extensible Elastic Rods

DTIC Science & Technology

1993-01-18

nonlinear theory such as questions of existence of solutions and global behavior have been carried out by Antman (1976). His basic work entitled "The...Aerosp. Ens. Q017/018 16 REFERENCES Antman , S.S., "Ordinary Differential Equations of Non-Linear ElastIcity 1: Foundatious of the Theories of Non-Linearly...Elutic rods and Shells," A.R.M.A. 61 (1976), 307-351. Antman , S.S., "The Theory of Rods", Handbuch der Physik, Vol. Vla/2, Springer-Verlq, Berlin

The gravitational wave stress–energy (pseudo)-tensor in modified gravity

NASA Astrophysics Data System (ADS)

Saffer, Alexander; Yunes, Nicolás; Yagi, Kent

2018-03-01

The recent detections of gravitational waves by the advanced LIGO and Virgo detectors open up new tests of modified gravity theories in the strong-field and dynamical, extreme gravity regime. Such tests rely sensitively on the phase evolution of the gravitational waves, which is controlled by the energy–momentum carried by such waves out of the system. We here study four different methods for finding the gravitational wave stress–energy pseudo-tensor in gravity theories with any combination of scalar, vector, or tensor degrees of freedom. These methods rely on the second variation of the action under short-wavelength averaging, the second perturbation of the field equations in the short-wavelength approximation, the construction of an energy complex leading to a Landau–Lifshitz tensor, and the use of Noether’s theorem in field theories about a flat background. We apply these methods in general relativity, Jordan–Fierz–Brans–Dicky theoy, and Einstein-Æther theory to find the gravitational wave stress–energy pseudo-tensor and calculate the rate at which energy and linear momentum is carried away from the system. The stress–energy tensor and the rate of linear momentum loss in Einstein-Æther theory are presented here for the first time. We find that all methods yield the same rate of energy loss, although the stress–energy pseudo-tensor can be functionally different. We also find that the Noether method yields a stress–energy tensor that is not symmetric or gauge-invariant, and symmetrization via the Belinfante procedure does not fix these problems because this procedure relies on Lorentz invariance, which is spontaneously broken in Einstein-Æther theory. The methods and results found here will be useful for the calculation of predictions in modified gravity theories that can then be contrasted with observations.

A non-axisymmetric linearized supersonic wave drag analysis: Mathematical theory

NASA Technical Reports Server (NTRS)

Barnhart, Paul J.

1996-01-01

A Mathematical theory is developed to perform the calculations necessary to determine the wave drag for slender bodies of non-circular cross section. The derivations presented in this report are based on extensions to supersonic linearized small perturbation theory. A numerical scheme is presented utilizing Fourier decomposition to compute the pressure coefficient on and about a slender body of arbitrary cross section.

Massively parallel and linear-scaling algorithm for second-order Moller–Plesset perturbation theory applied to the study of supramolecular wires

DOE PAGES

Kjaergaard, Thomas; Baudin, Pablo; Bykov, Dmytro; ...

2016-11-16

Here, we present a scalable cross-platform hybrid MPI/OpenMP/OpenACC implementation of the Divide–Expand–Consolidate (DEC) formalism with portable performance on heterogeneous HPC architectures. The Divide–Expand–Consolidate formalism is designed to reduce the steep computational scaling of conventional many-body methods employed in electronic structure theory to linear scaling, while providing a simple mechanism for controlling the error introduced by this approximation. Our massively parallel implementation of this general scheme has three levels of parallelism, being a hybrid of the loosely coupled task-based parallelization approach and the conventional MPI +X programming model, where X is either OpenMP or OpenACC. We demonstrate strong and weak scalabilitymore » of this implementation on heterogeneous HPC systems, namely on the GPU-based Cray XK7 Titan supercomputer at the Oak Ridge National Laboratory. Using the “resolution of the identity second-order Moller–Plesset perturbation theory” (RI-MP2) as the physical model for simulating correlated electron motion, the linear-scaling DEC implementation is applied to 1-aza-adamantane-trione (AAT) supramolecular wires containing up to 40 monomers (2440 atoms, 6800 correlated electrons, 24 440 basis functions and 91 280 auxiliary functions). This represents the largest molecular system treated at the MP2 level of theory, demonstrating an efficient removal of the scaling wall pertinent to conventional quantum many-body methods.« less

LQR Control of Shell Vibrations Via Piezoceramic Actuators

NASA Technical Reports Server (NTRS)

delRosario, R. C. H.; Smith, R. C.

1997-01-01

A model-based Linear Quadratic Regulator (LQR) method for controlling vibrations in cylindrical shells is presented. Surface-mounted piezo-ceramic patches are employed as actuators which leads to unbounded control input operators. Modified Donnell-Mushtari shell equations incorporating strong or Kelvin-Voigt damping are used to model the system. The model is then abstractly formulated in terms of sesquilinear forms. This provides a framework amenable for proving model well-posedness and convergence of LQR gains using analytic semigroup results combined with LQR theory for unbounded input operators. Finally, numerical examples demonstrating the effectiveness of the method are presented.

A model for active control of helicopter air resonance in hover and forward flight

NASA Technical Reports Server (NTRS)

Takahashi, M. D.; Friedmann, P. P.

1988-01-01

A coupled rotor/fuselage helicopter analysis is presented. The accuracy of the model is verified by comparing it with the experimental data. The sensitivity of the open loop damping of the unstable air resonance mode to such modeling effects as blade torsional flexibility, unsteady aerodynamics, forward flight, periodic terms, and trim solution is illustrated by numerous examples. Subsequently, the model is used in conjunction with linear optimal control theory to stabilize the air resonance mode. The influence of the modeling effects mentioned before on active air resonance control is then investigated.

Flutter suppression digital control law design and testing for the AFW wind tunnel model

NASA Technical Reports Server (NTRS)

Mukhopadhyay, Vivek

1994-01-01

The design of a control law for simultaneously suppressing the symmetric and antisymmetric flutter modes of a sting mounted fixed-in-roll aeroelastic wind-tunnel model is described. The flutter suppression control law was designed using linear quadratic Gaussian theory, and it also involved control law order reduction, a gain root-locus study, and use of previous experimental results. A 23 percent increase in the open-loop flutter dynamic pressure was demonstrated during the wind-tunnel test. Rapid roll maneuvers at 11 percent above the symmetric flutter boundary were also performed when the model was in a free-to-roll configuration.

Flutter suppression digital control law design and testing for the AFW wind tunnel model

NASA Technical Reports Server (NTRS)

Mukhopadhyay, Vivek

1992-01-01

Design of a control law for simultaneously suppressing the symmetric and antisymmetric flutter modes of a sting mounted fixed-in-roll aeroelastic wind tunnel model is described. The flutter suppression control law was designed using linear quadratic Gaussian theory, and involved control law order reduction, a gain root-locus study and use of previous experimental results. A 23 percent increase in the open-loop flutter dynamic pressure was demonstrated during the wind tunnel test. Rapid roll maneuvers at 11 percent above the symmetric flutter boundary were also performed when the model was in a free-to-roll configuration.

Flutter suppression digital control law design and testing for the AFW wind-tunnel model

NASA Technical Reports Server (NTRS)

Mukhopadhyay, Vivek

1992-01-01

Design of a control law for simultaneously suppressing the symmetric and antisymmetric flutter modes of a string mounted fixed-in-roll aeroelastic wind tunnel model is described. The flutter suppression control law was designed using linear quadratic Gaussian theory and involved control law order reduction, a gain root-locus study, and the use of previous experimental results. A 23 percent increase in open-loop flutter dynamic pressure was demonstrated during the wind tunnel test. Rapid roll maneuvers at 11 percent above the symmetric flutter boundary were also performed when the model was in a free-to-roll configuration.

On the Validity of the Streaming Model for the Redshift-Space Correlation Function in the Linear Regime

NASA Astrophysics Data System (ADS)

Fisher, Karl B.

1995-08-01

The relation between the galaxy correlation functions in real-space and redshift-space is derived in the linear regime by an appropriate averaging of the joint probability distribution of density and velocity. The derivation recovers the familiar linear theory result on large scales but has the advantage of clearly revealing the dependence of the redshift distortions on the underlying peculiar velocity field; streaming motions give rise to distortions of θ(Ω0.6/b) while variations in the anisotropic velocity dispersion yield terms of order θ(Ω1.2/b2). This probabilistic derivation of the redshift-space correlation function is similar in spirit to the derivation of the commonly used "streaming" model, in which the distortions are given by a convolution of the real-space correlation function with a velocity distribution function. The streaming model is often used to model the redshift-space correlation function on small, highly nonlinear, scales. There have been claims in the literature, however, that the streaming model is not valid in the linear regime. Our analysis confirms this claim, but we show that the streaming model can be made consistent with linear theory provided that the model for the streaming has the functional form predicted by linear theory and that the velocity distribution is chosen to be a Gaussian with the correct linear theory dispersion.

Multivariable control theory applied to hierarchial attitude control for planetary spacecraft

NASA Technical Reports Server (NTRS)

Boland, J. S., III; Russell, D. W.

1972-01-01

Multivariable control theory is applied to the design of a hierarchial attitude control system for the CARD space vehicle. The system selected uses reaction control jets (RCJ) and control moment gyros (CMG). The RCJ system uses linear signal mixing and a no-fire region similar to that used on the Skylab program; the y-axis and z-axis systems which are coupled use a sum and difference feedback scheme. The CMG system uses the optimum steering law and the same feedback signals as the RCJ system. When both systems are active the design is such that the torques from each system are never in opposition. A state-space analysis was made of the CMG system to determine the general structure of the input matrices (steering law) and feedback matrices that will decouple the axes. It is shown that the optimum steering law and proportional-plus-rate feedback are special cases. A derivation of the disturbing torques on the space vehicle due to the motion of the on-board television camera is presented. A procedure for computing an upper bound on these torques (given the system parameters) is included.

Estimating cosmic velocity fields from density fields and tidal tensors

NASA Astrophysics Data System (ADS)

Kitaura, Francisco-Shu; Angulo, Raul E.; Hoffman, Yehuda; Gottlöber, Stefan

2012-10-01

In this work we investigate the non-linear and non-local relation between cosmological density and peculiar velocity fields. Our goal is to provide an algorithm for the reconstruction of the non-linear velocity field from the fully non-linear density. We find that including the gravitational tidal field tensor using second-order Lagrangian perturbation theory based upon an estimate of the linear component of the non-linear density field significantly improves the estimate of the cosmic flow in comparison to linear theory not only in the low density, but also and more dramatically in the high-density regions. In particular we test two estimates of the linear component: the lognormal model and the iterative Lagrangian linearization. The present approach relies on a rigorous higher order Lagrangian perturbation theory analysis which incorporates a non-local relation. It does not require additional fitting from simulations being in this sense parameter free, it is independent of statistical-geometrical optimization and it is straightforward and efficient to compute. The method is demonstrated to yield an unbiased estimator of the velocity field on scales ≳5 h-1 Mpc with closely Gaussian distributed errors. Moreover, the statistics of the divergence of the peculiar velocity field is extremely well recovered showing a good agreement with the true one from N-body simulations. The typical errors of about 10 km s-1 (1σ confidence intervals) are reduced by more than 80 per cent with respect to linear theory in the scale range between 5 and 10 h-1 Mpc in high-density regions (δ > 2). We also find that iterative Lagrangian linearization is significantly superior in the low-density regime with respect to the lognormal model.

A User’s Manual for Linear Control Programs on IBM/360.

DTIC Science & Technology

1979-12-01

problems is presented in the following paragraphs. However, the theory on which the subprogram is based is not given. The user who wishes to learn more...21-22, of the system (N < 10), 23-24, 25-26 dimension of the Fandom input vector (L < 10), number of measurements (M < 10) 2 t (NxN) matrix (one row

Optimal and robust control of transition

NASA Technical Reports Server (NTRS)

Bewley, T. R.; Agarwal, R.

1996-01-01

Optimal and robust control theories are used to determine feedback control rules that effectively stabilize a linearly unstable flow in a plane channel. Wall transpiration (unsteady blowing/suction) with zero net mass flux is used as the control. Control algorithms are considered that depend both on full flowfield information and on estimates of that flowfield based on wall skin-friction measurements only. The development of these control algorithms accounts for modeling errors and measurement noise in a rigorous fashion; these disturbances are considered in both a structured (Gaussian) and unstructured ('worst case') sense. The performance of these algorithms is analyzed in terms of the eigenmodes of the resulting controlled systems, and the sensitivity of individual eigenmodes to both control and observation is quantified.

A parametric model for the changes in the complex valued conductivity of a lung during tidal breathing

NASA Astrophysics Data System (ADS)

Nordebo, Sven; Dalarsson, Mariana; Khodadad, Davood; Müller, Beat; Waldmann, Andreas D.; Becher, Tobias; Frerichs, Inez; Sophocleous, Louiza; Sjöberg, Daniel; Seifnaraghi, Nima; Bayford, Richard

2018-05-01

Classical homogenization theory based on the Hashin–Shtrikman coated ellipsoids is used to model the changes in the complex valued conductivity (or admittivity) of a lung during tidal breathing. Here, the lung is modeled as a two-phase composite material where the alveolar air-filling corresponds to the inclusion phase. The theory predicts a linear relationship between the real and the imaginary parts of the change in the complex valued conductivity of a lung during tidal breathing, and where the loss cotangent of the change is approximately the same as of the effective background conductivity and hence easy to estimate. The theory is illustrated with numerical examples based on realistic parameter values and frequency ranges used with electrical impedance tomography (EIT). The theory may be potentially useful for imaging and clinical evaluations in connection with lung EIT for respiratory management and control.

Index of NACA Technical Publications, 1915 - 1949

DTIC Science & Technology

1950-03-31

in Linearized Supersonic Swanson, Robert S. and Gillis, Clarence Wing Theory. TN 1767, April 1949. L.: ’Vind-Tunnel Calibration and Cor- rection...Symmetrical Joukowski Profiles.Heaslet, Max, A.; Lomax, Harvard and Rept. 621, 1938. Spreiter, John R.: Linearized Com- pressible-Flow Theory for Sonic Flight...Rept. 624, 1938. TheApplication of Green’s Theoremto the Solution of Boundary-Value Stack, John; Lindsey, W. F. and-Littell, Problems in Linearized

Robust outer synchronization between two nonlinear complex networks with parametric disturbances and mixed time-varying delays

NASA Astrophysics Data System (ADS)

Zhang, Chuan; Wang, Xingyuan; Luo, Chao; Li, Junqiu; Wang, Chunpeng

2018-03-01

In this paper, we focus on the robust outer synchronization problem between two nonlinear complex networks with parametric disturbances and mixed time-varying delays. Firstly, a general complex network model is proposed. Besides the nonlinear couplings, the network model in this paper can possess parametric disturbances, internal time-varying delay, discrete time-varying delay and distributed time-varying delay. Then, according to the robust control strategy, linear matrix inequality and Lyapunov stability theory, several outer synchronization protocols are strictly derived. Simple linear matrix controllers are designed to driver the response network synchronize to the drive network. Additionally, our results can be applied on the complex networks without parametric disturbances. Finally, by utilizing the delayed Lorenz chaotic system as the dynamics of all nodes, simulation examples are given to demonstrate the effectiveness of our theoretical results.

? PID output-feedback control under event-triggered protocol

NASA Astrophysics Data System (ADS)

Zhao, Di; Wang, Zidong; Ding, Derui; Wei, Guoliang; Alsaadi, Fuad E.

2018-07-01

This paper is concerned with the ? proportional-integral-derivative (PID) output-feedback control problem for a class of linear discrete-time systems under event-triggered protocols. The controller and the actuators are connected through a communication network of limited bandwidth, and an event-triggered communication mechanism is adopted to decide when a certain control signal should be transmitted to the respective actuator. Furthermore, a novel PID output-feedback controller is designed where the accumulative sum-loop (the counterpart to the integral-loop in the continues-time setting) operates on a limited time-window with hope to mitigate the effect from the past measurement data. The main objective of the problem under consideration is to design a desired PID controller such that the closed-loop system is exponentially stable and the prescribed ? disturbance rejection attenuation level is guaranteed under event-triggered protocols. By means of the Lyapunov stability theory combined with the orthogonal decomposition, sufficient conditions are established under which the addressed PID controller design problem is recast into a linear convex optimization one that can be easily solved via available software packages. Finally, a simulation example is exploited to illustrate the usefulness and effectiveness of the established control scheme.

Sliding mode based trajectory linearization control for hypersonic reentry vehicle via extended disturbance observer.

PubMed

Xingling, Shao; Honglun, Wang

2014-11-01

This paper proposes a novel hybrid control framework by combing observer-based sliding mode control (SMC) with trajectory linearization control (TLC) for hypersonic reentry vehicle (HRV) attitude tracking problem. First, fewer control consumption is achieved using nonlinear tracking differentiator (TD) in the attitude loop. Second, a novel SMC that employs extended disturbance observer (EDO) to counteract the effect of uncertainties using a new sliding surface which includes the estimation error is integrated to address the tracking error stabilization issues in the attitude and angular rate loop, respectively. In addition, new results associated with EDO are examined in terms of dynamic response and noise-tolerant performance, as well as estimation accuracy. The key feature of the proposed compound control approach is that chattering free tracking performance with high accuracy can be ensured for HRV in the presence of multiple uncertainties under control constraints. Based on finite time convergence stability theory, the stability of the resulting closed-loop system is well established. Also, comparisons and extensive simulation results are presented to demonstrate the effectiveness of the control strategy. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

You don't always get what you want, and you don't always want what you get: An examination of control-desire for control congruence in transactional relationships.

PubMed

Mullins, Ryan R; Bachrach, Daniel G; Rapp, Adam A; Grewal, Dhruv; Beitelspacher, Lauren Skinner

2015-07-01

In this research we develop a framework to examine the drivers of customers' desire for control over the sales relationship, and consequences of fit between perceived and desired control. Data collected in a lagged field study of 144 retailer manager (customer)-salesperson dyads were modeled using hierarchical linear modeling and response surface modeling techniques. Results from our analysis reveal that salesperson expertise drives retailers' desire for control in these relationships. In addition, while incongruence in perceived-desired control was negatively associated with both satisfaction and objective sales, retailer satisfaction was higher when both desired and perceived control were high. Further, as desired and perceived control over the sales relationship both increase, product sales initially decrease, and then increase, exhibiting a "U-shaped" effect. Implications for both theory and practice are discussed. These include adaptive sales training to identify misalignment between desired and perceived control, optimization of cocreation strategies, incorporation of interorganizational relational constructs, exploration of triadic social network configurations, examination of unmet expectations, and the implications of assimilation-contrast theory. (c) 2015 APA, all rights reserved).

The spectral applications of Beer-Lambert law for some biological and dosimetric materials

NASA Astrophysics Data System (ADS)

Içelli, Orhan; Yalçin, Zeynel; Karakaya, Vatan; Ilgaz, Işıl P.

2014-08-01

The aim of this study is to conduct quantitative and qualitative analysis of biological and dosimetric materials which contain organic and inorganic materials and to make the determination by using the spectral theorem Beer-Lambert law. Beer-Lambert law is a system of linear equations for the spectral theory. It is possible to solve linear equations with a non-zero coefficient matrix determinant forming linear equations. Characteristic matrix of the linear equation with zero determinant is called point spectrum at the spectral theory.

Applicability of linearized-theory attached-flow methods to design and analysis of flap systems at low speeds for thin swept wings with sharp leading edges

NASA Technical Reports Server (NTRS)

Carlson, Harry W.; Darden, Christine M.

1987-01-01

Low-speed experimental force and data on a series of thin swept wings with sharp leading edges and leading and trailing-edge flaps are compared with predictions made using a linearized-theory method which includes estimates of vortex forces. These comparisons were made to assess the effectiveness of linearized-theory methods for use in the design and analysis of flap systems in subsonic flow. Results demonstrate that linearized-theory, attached-flow methods (with approximate representation of vortex forces) can form the basis of a rational system for flap design and analysis. Even attached-flow methods that do not take vortex forces into account can be used for the selection of optimized flap-system geometry, but design-point performance levels tend to be underestimated unless vortex forces are included. Illustrative examples of the use of these methods in the design of efficient low-speed flap systems are included.

Waves and instabilities in plasmas

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

Chen, L.

1987-01-01

The contents of this book are: Plasma as a Dielectric Medium; Nyquist Technique; Absolute and Convective Instabilities; Landau Damping and Phase Mixing; Particle Trapping and Breakdown of Linear Theory; Solution of Viasov Equation via Guilding-Center Transformation; Kinetic Theory of Magnetohydrodynamic Waves; Geometric Optics; Wave-Kinetic Equation; Cutoff and Resonance; Resonant Absorption; Mode Conversion; Gyrokinetic Equation; Drift Waves; Quasi-Linear Theory; Ponderomotive Force; Parametric Instabilities; Problem Sets for Homework, Midterm and Final Examinations.

The Importance of Why: An Intelligence Approach for a Multi-Polar World

DTIC Science & Technology

2016-04-04

December 27, 2015). 12. 2 Jupiter Scientific, “Definitions of Important Terms in Chaos Theory ,” Jupiter Scientific website, http...Important Terms in Chaos Theory .” Linearizing a system is approximating a nonlinear system through the application of linear system model. 25...Complexity Theory to Anticipate Strategic Surprise,” 24. 16 M. Mitchell Waldrop, Complexity: The Emerging Science at the Edge of Order and Chaos (New

Robust global identifiability theory using potentials--Application to compartmental models.

PubMed

Wongvanich, N; Hann, C E; Sirisena, H R

2015-04-01

This paper presents a global practical identifiability theory for analyzing and identifying linear and nonlinear compartmental models. The compartmental system is prolonged onto the potential jet space to formulate a set of input-output equations that are integrals in terms of the measured data, which allows for robust identification of parameters without requiring any simulation of the model differential equations. Two classes of linear and non-linear compartmental models are considered. The theory is first applied to analyze the linear nitrous oxide (N2O) uptake model. The fitting accuracy of the identified models from differential jet space and potential jet space identifiability theories is compared with a realistic noise level of 3% which is derived from sensor noise data in the literature. The potential jet space approach gave a match that was well within the coefficient of variation. The differential jet space formulation was unstable and not suitable for parameter identification. The proposed theory is then applied to a nonlinear immunological model for mastitis in cows. In addition, the model formulation is extended to include an iterative method which allows initial conditions to be accurately identified. With up to 10% noise, the potential jet space theory predicts the normalized population concentration infected with pathogens, to within 9% of the true curve. Copyright © 2015 Elsevier Inc. All rights reserved.

Numerical Test of Analytical Theories for Perpendicular Diffusion in Small Kubo Number Turbulence

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

Heusen, M.; Shalchi, A., E-mail: husseinm@myumanitoba.ca, E-mail: andreasm4@yahoo.com

In the literature, one can find various analytical theories for perpendicular diffusion of energetic particles interacting with magnetic turbulence. Besides quasi-linear theory, there are different versions of the nonlinear guiding center (NLGC) theory and the unified nonlinear transport (UNLT) theory. For turbulence with high Kubo numbers, such as two-dimensional turbulence or noisy reduced magnetohydrodynamic turbulence, the aforementioned nonlinear theories provide similar results. For slab and small Kubo number turbulence, however, this is not the case. In the current paper, we compare different linear and nonlinear theories with each other and test-particle simulations for a noisy slab model corresponding to smallmore » Kubo number turbulence. We show that UNLT theory agrees very well with all performed test-particle simulations. In the limit of long parallel mean free paths, the perpendicular mean free path approaches asymptotically the quasi-linear limit as predicted by the UNLT theory. For short parallel mean free paths we find a Rechester and Rosenbluth type of scaling as predicted by UNLT theory as well. The original NLGC theory disagrees with all performed simulations regardless what the parallel mean free path is. The random ballistic interpretation of the NLGC theory agrees much better with the simulations, but compared to UNLT theory the agreement is inferior. We conclude that for this type of small Kubo number turbulence, only the latter theory allows for an accurate description of perpendicular diffusion.« less

Tunable polarization plasma channel undulator for narrow bandwidth photon emission

DOE PAGES

Rykovanov, S. G.; Wang, J. W.; Kharin, V. Yu.; ...

2016-09-09

The theory of a plasma undulator excited by a short intense laser pulse in a parabolic plasma channel is presented. The undulator fields are generated either by the laser pulse incident off-axis and/or under the angle with respect to the channel axis. Linear plasma theory is used to derive the wakefield structure. It is shown that the electrons injected into the plasma wakefields experience betatron motion and undulator oscillations. Optimal electron beam injection conditions are derived for minimizing the amplitude of the betatron motion, producing narrow-bandwidth undulator radiation. Polarization control is readily achieved by varying the laser pulse injection conditions.

A fresh look at linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization

NASA Astrophysics Data System (ADS)

Camporesi, Roberto

2016-01-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The approach presented here can be used in a first course on differential equations for science and engineering majors.

The Growing Importance of Linear Algebra in Undergraduate Mathematics.

ERIC Educational Resources Information Center

Tucker, Alan

1993-01-01

Discusses the theoretical and practical importance of linear algebra. Presents a brief history of linear algebra and matrix theory and describes the place of linear algebra in the undergraduate curriculum. (MDH)

Fractional Order PIλDμ Control for Maglev Guiding System

NASA Astrophysics Data System (ADS)

Hu, Qing; Hu, Yuwei

To effectively suppress the external disturbances and parameter perturbation problem of the maglev guiding system, and improve speed and robustness, the electromagnetic guiding system is exactly linearized using state feedback method, Fractional calculus theory is introduced, the order of integer order PID control was extended to the field of fractional, then fractional order PIλDμ Controller was presented, Due to the extra two adjustable parameters compared with traditional PID controller, fractional order PIλDμ controllers were expected to show better control performance. The results of the computer simulation show that the proposed controller suppresses the external disturbances and parameter perturbation of the system effectively; the system response speed was increased; at the same time, it had flexible structure and stronger robustness.

Final Report: CNC Micromachines LDRD No.10793

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

JOKIEL JR., BERNHARD; BENAVIDES, GILBERT L.; BIEG, LOTHAR F.

2003-04-01

The three-year LDRD ''CNC Micromachines'' was successfully completed at the end of FY02. The project had four major breakthroughs in spatial motion control in MEMS: (1) A unified method for designing scalable planar and spatial on-chip motion control systems was developed. The method relies on the use of parallel kinematic mechanisms (PKMs) that when properly designed provide different types of motion on-chip without the need for post-fabrication assembly, (2) A new type of actuator was developed--the linear stepping track drive (LSTD) that provides open loop linear position control that is scalable in displacement, output force and step size. Several versionsmore » of this actuator were designed, fabricated and successfully tested. (3) Different versions of XYZ translation only and PTT motion stages were designed, successfully fabricated and successfully tested demonstrating absolutely that on-chip spatial motion control systems are not only possible, but are a reality. (4) Control algorithms, software and infrastructure based on MATLAB were created and successfully implemented to drive the XYZ and PTT motion platforms in a controlled manner. The control software is capable of reading an M/G code machine tool language file, decode the instructions and correctly calculate and apply position and velocity trajectories to the motion devices linear drive inputs to position the device platform along the trajectory as specified by the input file. A full and detailed account of design methodology, theory and experimental results (failures and successes) is provided.« less

The Use of a Microcomputer System as an Aid to Classical and Digital Control System Design and Analysis,

DTIC Science & Technology

1983-06-01

the study of linear control theory may be adapted to run on an inex- pensive home/microcomputer. To demonstrate this, five programs were chosen from...COMMON LOG OF FREQUENCY ORDINATE -> PHASE (DEGREES) TIC MARKS SHOW MULTIPLES OF 98 DEGREES MINIMUM FREQUENCY SHOI ON ABSCISSA = .1 RADIANS/SEC...stability. The phase margin is 64.5 degrees which is also lower than the previous case but only by one tenth of a degree. d. w’-Plane with a Period of .1

Modules as Learning Tools in Linear Algebra

ERIC Educational Resources Information Center

Cooley, Laurel; Vidakovic, Draga; Martin, William O.; Dexter, Scott; Suzuki, Jeff; Loch, Sergio

2014-01-01

This paper reports on the experience of STEM and mathematics faculty at four different institutions working collaboratively to integrate learning theory with curriculum development in a core undergraduate linear algebra context. The faculty formed a Professional Learning Community (PLC) with a focus on learning theories in mathematics and…

Investigating multiphoton phenomena using nonlinear dynamics

NASA Astrophysics Data System (ADS)

Huang, Shu

Many seemingly simple systems can display extraordinarily complex dynamics which has been studied and uncovered through nonlinear dynamical theory. The leitmotif of this thesis is changing phase-space structures and their (linear or non-linear) stabilities by adding control functions (which act on the system as external perturbations) to the relevant Hamiltonians. These phase-space structures may be periodic orbits, invariant tori or their stable and unstable manifolds. One-electron systems and diatomic molecules are fundamental and important staging ground for new discoveries in nonlinear dynamics. In past years, increasing emphasis and effort has been put on the control or manipulation of these systems. Recent developments of nonlinear dynamical tools can provide efficient ways of doing so. In the first subtopic of the thesis, we are adding a control function to restore tori at prescribed locations in phase space. In the remainder of the thesis, a control function with parameters is used to change the linear stability of the periodic orbits which govern the processes in question. In this thesis, we report our theoretical analyses on multiphoton ionization of Rydberg atoms exposed to strong microwave fields and the dissociation of diatomic molecules exposed to bichromatic lasers using nonlinear dynamical tools. This thesis is composed of three subtopics. In the first subtopic, we employ local control theory to reduce the stochastic ionization of hydrogen atom in a strong microwave field by adding a relatively small control term to the original Hamiltonian. In the second subtopic, we perform periodic orbit analysis to investigate multiphoton ionization driven by a bichromatic microwave field. Our results show quantitative and qualitative agreement with previous studies, and hence identify the mechanism through which short periodic orbits organize the dynamics in multiphoton ionization. In addition, we achieve substantial time savings with this approach. In the third subtopic we extend our periodic orbit analysis to the dissociation of diatomic molecules driven by a bichromatic laser. In this problem, our results based on periodic orbit analysis again show good agreement with previous work, and hence promise more potential applications of this approach in molecular physics.

Calculation of the distributed loads on the blades of individual multiblade propellers in axial flow using linear and nonlinear lifting surface theories

NASA Technical Reports Server (NTRS)

Pesetskaya, N. N.; Timofeev, I. YA.; Shipilov, S. D.

1988-01-01

In recent years much attention has been given to the development of methods and programs for the calculation of the aerodynamic characteristics of multiblade, saber-shaped air propellers. Most existing methods are based on the theory of lifting lines. Elsewhere, the theory of a lifting surface is used to calculate screw and lifting propellers. In this work, methods of discrete eddies are described for the calculation of the aerodynamic characteristics of propellers using the linear and nonlinear theories of lifting surfaces.

Distributed Cooperative Optimal Control for Multiagent Systems on Directed Graphs: An Inverse Optimal Approach.

PubMed

Zhang, Huaguang; Feng, Tao; Yang, Guang-Hong; Liang, Hongjing

2015-07-01

In this paper, the inverse optimal approach is employed to design distributed consensus protocols that guarantee consensus and global optimality with respect to some quadratic performance indexes for identical linear systems on a directed graph. The inverse optimal theory is developed by introducing the notion of partial stability. As a result, the necessary and sufficient conditions for inverse optimality are proposed. By means of the developed inverse optimal theory, the necessary and sufficient conditions are established for globally optimal cooperative control problems on directed graphs. Basic optimal cooperative design procedures are given based on asymptotic properties of the resulting optimal distributed consensus protocols, and the multiagent systems can reach desired consensus performance (convergence rate and damping rate) asymptotically. Finally, two examples are given to illustrate the effectiveness of the proposed methods.

Molecular Interaction Control in Diblock Copolymer Blends and Multiblock Copolymers with Opposite Phase Behaviors

NASA Astrophysics Data System (ADS)

Cho, Junhan

2014-03-01

Here we show how to control molecular interactions via mixing AB and AC diblock copolymers, where one copolymer exhibits upper order-disorder transition and the other does lower disorder-order transition. Linear ABC triblock copolymers possessing both barotropic and baroplastic pairs are also taken into account. A recently developed random-phase approximation (RPA) theory and the self-consistent field theory (SCFT) for general compressible mixtures are used to analyze stability criteria and morphologies for the given systems. It is demonstrated that the copolymer systems can yield a variety of phase behaviors in their temperature and pressure dependence upon proper mixing conditions and compositions, which is caused by the delicate force fields generated in the systems. We acknowledge the financial support from National Research Foundation of Korea and Center for Photofunctional Energy Materials.

A quantum description of linear, and non-linear optical interactions in arrays of plasmonic nanoparticles

NASA Astrophysics Data System (ADS)

Arabahmadi, Ehsan; Ahmadi, Zabihollah; Rashidian, Bizhan

2018-06-01

A quantum theory for describing the interaction of photons and plasmons, in one- and two-dimensional arrays is presented. Ohmic losses and inter-band transitions are not considered. We use macroscopic approach, and quantum field theory methods including S-matrix expansion, and Feynman diagrams for this purpose. Non-linear interactions are also studied, and increasing the probability of such interactions, and its application are also discussed.

Features of control systems analysis with discrete control devices using mathematical packages

NASA Astrophysics Data System (ADS)

Yakovleva, E. M.; Faerman, V. A.

2017-02-01

The article contains presentation of basic provisions of the theory of automatic pulse control systems as well as methods of analysis of such systems using the mathematical software widespread in the academic environment. The pulse systems under research are considered as analogues systems interacting among themselves, including sensors, amplifiers, controlled objects, and discrete parts. To describe such systems, one uses a mathematical apparatus of difference equations as well as discrete transfer functions. To obtain a transfer function of the open-loop system, being important from the point of view of the analysis of control systems, one uses mathematical packages Mathcad and Matlab. Despite identity of the obtained result, the way of its achievement from the point of view of user’s action is various for the specified means. In particular, Matlab uses a structural model of the control system while Mathcad allows only execution of a chain of operator transforms. It is worth noting that distinctions taking place allow considering transformation of signals during interaction of the linear and continuous parts of the control system from different sides. The latter can be used in an educational process for the best assimilation of the course of the control system theory by students.

Reentry Vehicle Flight Controls Design Guidelines: Dynamic Inversion

NASA Technical Reports Server (NTRS)

Ito, Daigoro; Georgie, Jennifer; Valasek, John; Ward, Donald T.

2002-01-01

This report addresses issues in developing a flight control design for vehicles operating across a broad flight regime and with highly nonlinear physical descriptions of motion. Specifically it addresses the need for reentry vehicles that could operate through reentry from space to controlled touchdown on Earth. The latter part of controlled descent is achieved by parachute or paraglider - or by all automatic or a human-controlled landing similar to that of the Orbiter. Since this report addresses the specific needs of human-carrying (not necessarily piloted) reentry vehicles, it deals with highly nonlinear equations of motion, and then-generated control systems must be robust across a very wide range of physics. Thus, this report deals almost exclusively with some form of dynamic inversion (DI). Two vital aspects of control theory - noninteracting control laws and the transformation of nonlinear systems into equivalent linear systems - are embodied in DI. Though there is no doubt that the mathematical tools and underlying theory are widely available, there are open issues as to the practicality of using DI as the only or primary design approach for reentry articles. This report provides a set of guidelines that can be used to determine the practical usefulness of the technique.

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.

Enabling Controlling Complex Networks with Local Topological Information.

PubMed

Li, Guoqi; Deng, Lei; Xiao, Gaoxi; Tang, Pei; Wen, Changyun; Hu, Wuhua; Pei, Jing; Shi, Luping; Stanley, H Eugene

2018-03-15

Complex networks characterize the nature of internal/external interactions in real-world systems including social, economic, biological, ecological, and technological networks. Two issues keep as obstacles to fulfilling control of large-scale networks: structural controllability which describes the ability to guide a dynamical system from any initial state to any desired final state in finite time, with a suitable choice of inputs; and optimal control, which is a typical control approach to minimize the cost for driving the network to a predefined state with a given number of control inputs. For large complex networks without global information of network topology, both problems remain essentially open. Here we combine graph theory and control theory for tackling the two problems in one go, using only local network topology information. For the structural controllability problem, a distributed local-game matching method is proposed, where every node plays a simple Bayesian game with local information and local interactions with adjacent nodes, ensuring a suboptimal solution at a linear complexity. Starring from any structural controllability solution, a minimizing longest control path method can efficiently reach a good solution for the optimal control in large networks. Our results provide solutions for distributed complex network control and demonstrate a way to link the structural controllability and optimal control together.

Correlation, evaluation, and extension of linearized theories for tire motion and wheel shimmy

NASA Technical Reports Server (NTRS)

Smiley, Robert F

1957-01-01

An evaluation is made of the existing theories of a linearized tire motion and wheel shimmy. It is demonstrated that most of the previously published theories represent varying degrees of approximation to a summary theory developed in this report which is a minor modification of the basic theory of Von Schlippe and Dietrich. In most cases where strong differences exist between the previously published theories and summary theory, the previously published theories are shown to possess certain deficiencies. A series of systematic approximations to the summary theory is developed for the treatment of problems too simple to merit the use of the complete summary theory, and procedures are discussed for applying the summary theory and its systematic approximations to the shimmy of more complex landing-gear structures than have previously been considered. Comparisons of the existing experimental data with the predictions of the summary theory and the systematic approximations provide a fair substantiation of the more detailed approximate theories.

Statistical Ring Catenation under Thermodynamic Control: Should the Jacobson-Stockmayer Cyclization Theory Take into Account Catenane Formation?

PubMed

Di Stefano, Stefano; Ercolani, Gianfranco

2017-01-26

An extension of the Jacobson-Stockmayer theory is presented to include the reversible formation of [2]catenanes in a ring-chain system under thermodynamic control. The extended theory is based on the molar catenation constant, measuring the ease of catenation of two ring oligomers, whose expression was obtained in a previous work. Two scenarios have been considered: that of "thick" (hydrocarbon-like) chains and that of "thin" (DNA-like) chains. In the case of "thick" chains, the formation of catenanes can be neglected, unless in the unlikely case of a very large value of the equilibrium constant for linear propagation (K ≈ 10 8 mol -1 L, or larger). For K tending to infinity, the system becomes a chain-free system where only ring-catenane equilibria occur. Under this condition, there is a critical concentration below which only rings are present at equilibrium and above which the ring fraction remains constant, and the excess monomer is converted only into catenanes. In the case of "thin" chains, the formation of catenanes cannot be neglected even for values of K as low as 10 2 mol -1 L, thus justifying the use of the extended theory.

When is quasi-linear theory exact. [particle acceleration

NASA Technical Reports Server (NTRS)

Jones, F. C.; Birmingham, T. J.

1975-01-01

We use the cumulant expansion technique of Kubo (1962, 1963) to derive an integrodifferential equation for the average one-particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the equation for this function degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory only for this limited class of fluctuations.

A Thermodynamic Theory Of Solid Viscoelasticity. Part 1: Linear Viscoelasticity.

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Leonov, Arkady I.

2002-01-01

The present series of three consecutive papers develops a general theory for linear and finite solid viscoelasticity. Because the most important object for nonlinear studies are rubber-like materials, the general approach is specified in a form convenient for solving problems important for many industries that involve rubber-like materials. General linear and nonlinear theories for non-isothermal deformations of viscoelastic solids are developed based on the quasi-linear approach of non-equilibrium thermodynamics. In this, the first paper of the series, we analyze non-isothermal linear viscoelasticity, which is applicable in a range of small strains not only to all synthetic polymers and bio-polymers but also to some non-polymeric materials. Although the linear case seems to be well developed, there still are some reasons to implement a thermodynamic derivation of constitutive equations for solid-like, non-isothermal, linear viscoelasticity. The most important is the thermodynamic modeling of thermo-rheological complexity , i.e. different temperature dependences of relaxation parameters in various parts of relaxation spectrum. A special structure of interaction matrices is established for different physical mechanisms contributed to the normal relaxation modes. This structure seems to be in accord with observations, and creates a simple mathematical framework for both continuum and molecular theories of the thermo-rheological complex relaxation phenomena. Finally, a unified approach is briefly discussed that, in principle, allows combining both the long time (discrete) and short time (continuous) descriptions of relaxation behaviors for polymers in the rubbery and glassy regions.

The "Chaos" Pattern in Piaget's Theory of Cognitive Development.

ERIC Educational Resources Information Center

Lindsay, Jean S.

Piaget's theory of the cognitive development of the child is related to the recently developed non-linear "chaos" model. The term "chaos" refers to the tendency of dynamical, non-linear systems toward irregular, sometimes unpredictable, deterministic behavior. Piaget identified this same pattern in his model of cognitive…

Are All Non-Linear Systems (Approx.) Bilinear,

DTIC Science & Technology

1977-06-01

There is a rumor going around in mathematical system theory circles that all non-linear systems are bilinear or nearly so. This note examines the...case for such an assertion and finds it wanting and en passant, offers some comments on the current proliferation of mathematical literature on system theory .

Linear kinetic theory and particle transport in stochastic mixtures

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

Pomraning, G.C.

We consider the formulation of linear transport and kinetic theory describing energy and particle flow in a random mixture of two or more immiscible materials. Following an introduction, we summarize early and fundamental work in this area, and we conclude with a brief discussion of recent results.

Difference equation state approximations for nonlinear hereditary control problems

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1984-01-01

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589

Stochastic Control of Multi-Scale Networks: Modeling, Analysis and Algorithms

DTIC Science & Technology

2014-10-20

Theory, (02 2012): 0. doi: B. T. Swapna, Atilla Eryilmaz, Ness B. Shroff. Throughput-Delay Analysis of Random Linear Network Coding for Wireless ... Wireless Sensor Networks and Effects of Long-Range Dependent Data, Sequential Analysis , (10 2012): 0. doi: 10.1080/07474946.2012.719435 Stefano...Sequential Analysis , (10 2012): 0. doi: John S. Baras, Shanshan Zheng. Sequential Anomaly Detection in Wireless Sensor Networks andEffects of Long

A Mathematical Theory of Command and Control Structures.

DTIC Science & Technology

1984-08-30

minimize the functional J over the space of all linear maps,then (a) 6J ( HKL l 0)n 0 0 6JKi+Li (HK’L K i +Li) =0 .61H (H,K,L, )= 0 13 for all i=l,...N, and...Castanon, G. C. Verghese, A. S. Willsky, "A Scaterring Framework for Decentralized Estimation Problems," MIT/LIDS paper 1075 , March 1981, Submitted to

Tracking performance under time sharing conditions with a digit processing task: A feedback control theory analysis. [attention sharing effect on operator performance

NASA Technical Reports Server (NTRS)

Gopher, D.; Wickens, C. D.

1975-01-01

A one dimensional compensatory tracking task and a digit processing reaction time task were combined in a three phase experiment designed to investigate tracking performance in time sharing. Adaptive techniques, elaborate feedback devices, and on line standardization procedures were used to adjust task difficulty to the ability of each individual subject and manipulate time sharing demands. Feedback control analysis techniques were employed in the description of tracking performance. The experimental results show that when the dynamics of a system are constrained, in such a manner that man machine system stability is no longer a major concern of the operator, he tends to adopt a first order control describing function, even with tracking systems of higher order. Attention diversion to a concurrent task leads to an increase in remnant level, or nonlinear power. This decrease in linearity is reflected both in the output magnitude spectra of the subjects, and in the linear fit of the amplitude ratio functions.

Adaptive tracking control of leader-following linear multi-agent systems with external disturbances

NASA Astrophysics Data System (ADS)

Lin, Hanquan; Wei, Qinglai; Liu, Derong; Ma, Hongwen

2016-10-01

In this paper, the consensus problem for leader-following linear multi-agent systems with external disturbances is investigated. Brownian motions are used to describe exogenous disturbances. A distributed tracking controller based on Riccati inequalities with an adaptive law for adjusting coupling weights between neighbouring agents is designed for leader-following multi-agent systems under fixed and switching topologies. In traditional distributed static controllers, the coupling weights depend on the communication graph. However, coupling weights associated with the feedback gain matrix in our method are updated by state errors between neighbouring agents. We further present the stability analysis of leader-following multi-agent systems with stochastic disturbances under switching topology. Most traditional literature requires the graph to be connected all the time, while the communication graph is only assumed to be jointly connected in this paper. The design technique is based on Riccati inequalities and algebraic graph theory. Finally, simulations are given to show the validity of our method.

A study of attitude control concepts for precision-pointing non-rigid spacecraft

NASA Technical Reports Server (NTRS)

Likins, P. W.

1975-01-01

Attitude control concepts for use onboard structurally nonrigid spacecraft that must be pointed with great precision are examined. The task of determining the eigenproperties of a system of linear time-invariant equations (in terms of hybrid coordinates) representing the attitude motion of a flexible spacecraft is discussed. Literal characteristics are developed for the associated eigenvalues and eigenvectors of the system. A method is presented for determining the poles and zeros of the transfer function describing the attitude dynamics of a flexible spacecraft characterized by hybrid coordinate equations. Alterations are made to linear regulator and observer theory to accommodate modeling errors. The results show that a model error vector, which evolves from an error system, can be added to a reduced system model, estimated by an observer, and used by the control law to render the system less sensitive to uncertain magnitudes and phase relations of truncated modes and external disturbance effects. A hybrid coordinate formulation using the provided assumed mode shapes, rather than incorporating the usual finite element approach is provided.

Modern control concepts in hydrology

NASA Technical Reports Server (NTRS)

Duong, N.; Johnson, G. R.; Winn, C. B.

1974-01-01

Two approaches to an identification problem in hydrology are presented based upon concepts from modern control and estimation theory. The first approach treats the identification of unknown parameters in a hydrologic system subject to noisy inputs as an adaptive linear stochastic control problem; the second approach alters the model equation to account for the random part in the inputs, and then uses a nonlinear estimation scheme to estimate the unknown parameters. Both approaches use state-space concepts. The identification schemes are sequential and adaptive and can handle either time invariant or time dependent parameters. They are used to identify parameters in the Prasad model of rainfall-runoff. The results obtained are encouraging and conform with results from two previous studies; the first using numerical integration of the model equation along with a trial-and-error procedure, and the second, by using a quasi-linearization technique. The proposed approaches offer a systematic way of analyzing the rainfall-runoff process when the input data are imbedded in noise.

Optimal exponential synchronization of general chaotic delayed neural networks: an LMI approach.

PubMed

Liu, Meiqin

2009-09-01

This paper investigates the optimal exponential synchronization problem of general chaotic neural networks with or without time delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. This general model, which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator, covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks (CNNs), bidirectional associative memory (BAM) networks, and recurrent multilayer perceptrons (RMLPs) with or without delays. Using the drive-response concept, time-delay feedback controllers are designed to synchronize two identical chaotic neural networks as quickly as possible. The control design equations are shown to be a generalized eigenvalue problem (GEVP) which can be easily solved by various convex optimization algorithms to determine the optimal control law and the optimal exponential synchronization rate. Detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.

Resource Theory of Superposition

NASA Astrophysics Data System (ADS)

Theurer, T.; Killoran, N.; Egloff, D.; Plenio, M. B.

2017-12-01

The superposition principle lies at the heart of many nonclassical properties of quantum mechanics. Motivated by this, we introduce a rigorous resource theory framework for the quantification of superposition of a finite number of linear independent states. This theory is a generalization of resource theories of coherence. We determine the general structure of operations which do not create superposition, find a fundamental connection to unambiguous state discrimination, and propose several quantitative superposition measures. Using this theory, we show that trace decreasing operations can be completed for free which, when specialized to the theory of coherence, resolves an outstanding open question and is used to address the free probabilistic transformation between pure states. Finally, we prove that linearly independent superposition is a necessary and sufficient condition for the faithful creation of entanglement in discrete settings, establishing a strong structural connection between our theory of superposition and entanglement theory.

Linear network representation of multistate models of transport.

PubMed Central

Sandblom, J; Ring, A; Eisenman, G

1982-01-01

By introducing external driving forces in rate-theory models of transport we show how the Eyring rate equations can be transformed into Ohm's law with potentials that obey Kirchhoff's second law. From such a formalism the state diagram of a multioccupancy multicomponent system can be directly converted into linear network with resistors connecting nodal (branch) points and with capacitances connecting each nodal point with a reference point. The external forces appear as emf or current generators in the network. This theory allows the algebraic methods of linear network theory to be used in solving the flux equations for multistate models and is particularly useful for making proper simplifying approximation in models of complex membrane structure. Some general properties of linear network representation are also deduced. It is shown, for instance, that Maxwell's reciprocity relationships of linear networks lead directly to Onsager's relationships in the near equilibrium region. Finally, as an example of the procedure, the equivalent circuit method is used to solve the equations for a few transport models. PMID:7093425

On some problems in a theory of thermally and mechanically interacting continuous media. Ph.D. Thesis; [linearized theory of interacting mixture of elastic solid and viscous fluid

NASA Technical Reports Server (NTRS)

Lee, Y. M.

1971-01-01

Using a linearized theory of thermally and mechanically interacting mixture of linear elastic solid and viscous fluid, we derive a fundamental relation in an integral form called a reciprocity relation. This reciprocity relation relates the solution of one initial-boundary value problem with a given set of initial and boundary data to the solution of a second initial-boundary value problem corresponding to a different initial and boundary data for a given interacting mixture. From this general integral relation, reciprocity relations are derived for a heat-conducting linear elastic solid, and for a heat-conducting viscous fluid. An initial-boundary value problem is posed and solved for the mixture of linear elastic solid and viscous fluid. With the aid of the Laplace transform and the contour integration, a real integral representation for the displacement of the solid constituent is obtained as one of the principal results of the analysis.

Linear-response time-dependent density-functional theory with pairing fields.

PubMed

Peng, Degao; van Aggelen, Helen; Yang, Yang; Yang, Weitao

2014-05-14

Recent development in particle-particle random phase approximation (pp-RPA) broadens the perspective on ground state correlation energies [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013), Y. Yang, H. van Aggelen, S. N. Steinmann, D. Peng, and W. Yang, J. Chem. Phys. 139, 174110 (2013); D. Peng, S. N. Steinmann, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 104112 (2013)] and N ± 2 excitation energies [Y. Yang, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 224105 (2013)]. So far Hartree-Fock and approximated density-functional orbitals have been utilized to evaluate the pp-RPA equation. In this paper, to further explore the fundamentals and the potential use of pairing matrix dependent functionals, we present the linear-response time-dependent density-functional theory with pairing fields with both adiabatic and frequency-dependent kernels. This theory is related to the density-functional theory and time-dependent density-functional theory for superconductors, but is applied to normal non-superconducting systems for our purpose. Due to the lack of the proof of the one-to-one mapping between the pairing matrix and the pairing field for time-dependent systems, the linear-response theory is established based on the representability assumption of the pairing matrix. The linear response theory justifies the use of approximated density-functionals in the pp-RPA equation. This work sets the fundamentals for future density-functional development to enhance the description of ground state correlation energies and N ± 2 excitation energies.

Theory of "laser distillation" of enantiomers: purification of a racemic mixture of randomly oriented dimethylallene in a collisional environment.

PubMed

Gerbasi, David; Shapiro, Moshe; Brumer, Paul

2006-02-21

Enantiomeric control of 1,3 dimethylallene in a collisional environment is examined. Specifically, our previous "laser distillation" scenario wherein three perpendicular linearly polarized light fields are applied to excite a set of vib-rotational eigenstates of a randomly oriented sample is considered. The addition of internal conversion, dissociation, decoherence, and collisional relaxation mimics experimental conditions and molecular decay processes. Of greatest relevance is internal conversion which, in the case of dimethylallene, is followed by molecular dissociation. For various rates of internal conversion, enantiomeric control is maintained in this scenario by a delicate balance between collisional relaxation of excited dimethylallene that enhances control and collisional dephasing, which diminishes control.

Magnetothermal Convection in Nonconducting Diamagnetic and Paramagnetic Fluids

NASA Technical Reports Server (NTRS)

Edwards, Boyd F.; Gray, Donald D.; Huang, Jie

1996-01-01

Nonuniform magnetic fields exert a magnetic body force on electrically nonconducting classical fluids. These include paramagnetic fluids such as gaseous and liquid oxygen and diamagnetic fluids such as helium. Recent experiments show that this force can overwhelm the force of gravity even at the surface of the earth; it can levitate liquids and gases, quench candle flames, block gas flows, and suppress heat transport. Thermal gradients render the magnetic force nonuniform through the temperature-dependent magnetic susceptibility. These thermal gradients can therefore drive magnetic convection analogous to buoyancy-driven convection. This magnetothermal convection can overwhelm convection driven by gravitational buoyancy in terrestrial experiments. The objectives of the proposed ground-based theoretical study are (a) to supply the magnetothermohydrodynamic theory necessary to understand these recent experiments and (b) to explore the consequences of nonuniform magnetic fields in microgravity. Even the linear theory for the onset of magnetothermal convection is lacking in the literature. We intend to supply the linear and nonlinear theory based on the thermohydrodynamic equations supplemented by the magnetic body force. We intend to investigate the effect of magnetic fields on gas blockage and heat transport in microgravity. Since magnetic fields provide a means of creating arbitrary, controllable body force distributions, we intend to investigate the possibility of using magnetic fields to position and control fluids in microgravity. We also intend to investigate the possibility of creating stationary terrestrial microgravity environments by using the magnetic force to effectively cancel gravity. These investigations may aid in the design of space-based heat-transfer, combustion, and human-life-support equipment.

Stochastic optimal control of non-stationary response of a single-degree-of-freedom vehicle model

NASA Astrophysics Data System (ADS)

Narayanan, S.; Raju, G. V.

1990-09-01

An active suspension system to control the non-stationary response of a single-degree-of-freedom (sdf) vehicle model with variable velocity traverse over a rough road is investigated. The suspension is optimized with respect to ride comfort and road holding, using stochastic optimal control theory. The ground excitation is modelled as a spatial homogeneous random process, being the output of a linear shaping filter to white noise. The effect of the rolling contact of the tyre is considered by an additional filter in cascade. The non-stationary response with active suspension is compared with that of a passive system.

Research on Snake-Like Robot with Controllable Scales

NASA Astrophysics Data System (ADS)

Chen, Kailin; Zhao, Yuting; Chen, Shuping

The purpose of this paper is to propose a new structure for a snake-like robot. This type of snake-like robot is different from the normal snake-like robot because it has lots of controllable scales which have a large role in helping moving. Besides, a new form of robot gait named as linear motion mode is developed based on theoretical analysis for the new mechanical structure. Through simulation and analysis in simmechanics of matlab, we proved the validity of theories about the motion mode of snake-like robot. The proposed machine construction and control method for the designed motion is verified experimentally by the independent developed snake robot.

Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

Integral force feedback control with input shaping: Application to piezo-based scanning systems in ECDLs.

PubMed

Zhang, Meng; Liu, Zhigang; Zhu, Yu; Bu, Mingfan; Hong, Jun

2017-07-01

In this paper, a hybrid control system is developed by integrating the closed-loop force feedback and input shaping method to overcome the problem of the hysteresis and dynamic behavior in piezo-based scanning systems and increase the scanning speed of tunable external cavity diode lasers. The flexible hinge and piezoelectric actuators are analyzed, and a dynamic model of the scanning systems is established. A force sensor and an integral controller are utilized in integral force feedback (IFF) to directly augment the damping of the piezoelectric scanning systems. Hysteresis has been effectively eliminated, but the mechanical resonance is still evident. Noticeable residual vibration occurred after the inflection points and then gradually disappeared. For the further control of mechanical resonance, based on the theory of minimum-acceleration trajectory planning, the time-domain input shaping method was developed. The turning sections of a scanning trajectory are replaced by smooth curves, while the linear sections are retained. The IFF method is combined with the input shaping method to control the non-linearity and mechanical resonance in high-speed piezo-based scanning systems. Experiments are conducted, and the results demonstrate the effectiveness of the proposed control approach.

Integral force feedback control with input shaping: Application to piezo-based scanning systems in ECDLs

NASA Astrophysics Data System (ADS)

Zhang, Meng; Liu, Zhigang; Zhu, Yu; Bu, Mingfan; Hong, Jun

2017-07-01

In this paper, a hybrid control system is developed by integrating the closed-loop force feedback and input shaping method to overcome the problem of the hysteresis and dynamic behavior in piezo-based scanning systems and increase the scanning speed of tunable external cavity diode lasers. The flexible hinge and piezoelectric actuators are analyzed, and a dynamic model of the scanning systems is established. A force sensor and an integral controller are utilized in integral force feedback (IFF) to directly augment the damping of the piezoelectric scanning systems. Hysteresis has been effectively eliminated, but the mechanical resonance is still evident. Noticeable residual vibration occurred after the inflection points and then gradually disappeared. For the further control of mechanical resonance, based on the theory of minimum-acceleration trajectory planning, the time-domain input shaping method was developed. The turning sections of a scanning trajectory are replaced by smooth curves, while the linear sections are retained. The IFF method is combined with the input shaping method to control the non-linearity and mechanical resonance in high-speed piezo-based scanning systems. Experiments are conducted, and the results demonstrate the effectiveness of the proposed control approach.

Resistive wall modes in the EXTRAP T2R reversed-field pinch

NASA Astrophysics Data System (ADS)

Brunsell, P. R.; Malmberg, J.-A.; Yadikin, D.; Cecconello, M.

2003-10-01

Resistive wall modes (RWM) in the reversed field pinch are studied and a detailed comparison of experimental growth rates and linear magnetohydrodynamic (MHD) theory is made. RWM growth rates are experimentally measured in the thin shell device EXTRAP T2R [P. R. Brunsell et al., Plasma Phys. Controlled Fusion 43, 1 (2001)]. Linear MHD calculations of RWM growth rates are based on experimental equilibria. Experimental and linear MHD RWM growth rate dependency on the equilibrium profiles is investigated experimentally by varying the pinch parameter Θ=Bθ(a)/ in the range Θ=1.5-1.8. Quantitative agreement between experimental and linear MHD growth rates is seen. The dominating RWMs are the internal on-axis modes (having the same helicity as the central equilibrium field). At high Θ, external nonresonant modes are also observed. For internal modes experimental growth rates decrease with Θ while for external modes, growth rates increase with Θ. The effect of RWMs on the reversed-field pinch plasma performance is discussed.

Developing ultrasensitive pressure sensor based on graphene nanoribbon: Molecular dynamics simulation

NASA Astrophysics Data System (ADS)

Kwon, Oh Kuen; Lee, Jun Ha; Kim, Ki-Sub; Kang, Jeong Won

2013-01-01

We propose schematics for an ultra-sensitive pressure sensor based on graphene-nanoribbon (GNR) and investigate its electromechanical properties using classical molecular dynamics simulations and piezo-electricity theory. Since the top plate applied to the actual pressure is large whereas the contact area on the GNR is very small, both the sensitivity and the sensing range can be adjusted by controlling the aspect ratio between the top plate and the contact point areas. Our calculation shows that the electrical conductivity of GNRs can be tuned by the applied pressure and the electric conductance of the deflected GNR linearly increases with increasing applied pressure for the linear elastic region in low pressure below the cut-off point. In the curves for both the deflection and potential energy, the linear elastic regime in low pressure was explicitly separated with the non-linear elastic regime in high pressure. The proposed GNR-based nanoelectromechanical devices have great potential for application as electromechanical memory, relay or switching devices.

Non-linear temperature-dependent curvature of a phase change composite bimorph beam

NASA Astrophysics Data System (ADS)

Blonder, Greg

2017-06-01

Bimorph films curl in response to temperature. The degree of curvature typically varies in proportion to the difference in thermal expansion of the individual layers, and linearly with temperature. In many applications, such as controlling a thermostat, this gentle linear behavior is acceptable. In other cases, such as opening or closing a valve or latching a deployable column into place, an abrupt motion at a fixed temperature is preferred. To achieve this non-linear motion, we describe the fabrication and performance of a new bilayer structure we call a ‘phase change composite bimorph (PCBM)’. In a PCBM, one layer in the bimorph is a composite containing small inclusions of phase change materials. When the inclusions melt, their large (generally positive and  >1%) expansion coefficient induces a strong, reversible step function jump in bimorph curvature. The measured jump amplitude and thermal response is consistent with theory, and can be harnessed by a new class of actuators and sensors.

Direct perturbation theory for the dark soliton solution to the nonlinear Schroedinger equation with normal dispersion

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

Yu Jialu; Yang Chunnuan; Cai Hao

2007-04-15

After finding the basic solutions of the linearized nonlinear Schroedinger equation by the method of separation of variables, the perturbation theory for the dark soliton solution is constructed by linear Green's function theory. In application to the self-induced Raman scattering, the adiabatic corrections to the soliton's parameters are obtained and the remaining correction term is given as a pure integral with respect to the continuous spectral parameter.

Control of electronic transport in graphene by electromagnetic dressing

PubMed Central

Kristinsson, K.; Kibis, O. V.; Morina, S.; Shelykh, I. A.

2016-01-01

We demonstrated theoretically that the renormalization of the electron energy spectrum near the Dirac point of graphene by a strong high-frequency electromagnetic field (dressing field) drastically depends on polarization of the field. Namely, linear polarization results in an anisotropic gapless energy spectrum, whereas circular polarization leads to an isotropic gapped one. As a consequence, the stationary (dc) electronic transport in graphene strongly depends on parameters of the dressing field: A circularly polarized field monotonically decreases the isotropic conductivity of graphene, whereas a linearly polarized one results in both giant anisotropy of conductivity (which can reach thousands of percents) and the oscillating behavior of the conductivity as a function of the field intensity. Since the predicted phenomena can be observed in a graphene layer irradiated by a monochromatic electromagnetic wave, the elaborated theory opens a substantially new way to control electronic properties of graphene with light. PMID:26838371

A linear triple quantum dot system in isolated configuration

NASA Astrophysics Data System (ADS)

Flentje, Hanno; Bertrand, Benoit; Mortemousque, Pierre-André; Thiney, Vivien; Ludwig, Arne; Wieck, Andreas D.; Bäuerle, Christopher; Meunier, Tristan

2017-06-01

The scaling up of electron spin qubit based nanocircuits has remained challenging up till date and involves the development of efficient charge control strategies. Here, we report on the experimental realization of a linear triple quantum dot in a regime isolated from the reservoir. We show how this regime can be reached with a fixed number of electrons. Charge stability diagrams of the one, two, and three electron configurations where only electron exchange between the dots is allowed are observed. They are modeled with the established theory based on a capacitive model of the dot systems. The advantages of the isolated regime with respect to experimental realizations of quantum simulators and qubits are discussed. We envision that the results presented here will make more manipulation schemes for existing qubit implementations possible and will ultimately allow to increase the number of tunnel coupled quantum dots which can be simultaneously controlled.

Control of electronic transport in graphene by electromagnetic dressing.

PubMed

Kristinsson, K; Kibis, O V; Morina, S; Shelykh, I A

2016-02-03

We demonstrated theoretically that the renormalization of the electron energy spectrum near the Dirac point of graphene by a strong high-frequency electromagnetic field (dressing field) drastically depends on polarization of the field. Namely, linear polarization results in an anisotropic gapless energy spectrum, whereas circular polarization leads to an isotropic gapped one. As a consequence, the stationary (dc) electronic transport in graphene strongly depends on parameters of the dressing field: A circularly polarized field monotonically decreases the isotropic conductivity of graphene, whereas a linearly polarized one results in both giant anisotropy of conductivity (which can reach thousands of percents) and the oscillating behavior of the conductivity as a function of the field intensity. Since the predicted phenomena can be observed in a graphene layer irradiated by a monochromatic electromagnetic wave, the elaborated theory opens a substantially new way to control electronic properties of graphene with light.

Wing box transonic-flutter suppression using piezoelectric self-sensing actuators attached to skin

NASA Astrophysics Data System (ADS)

Otiefy, R. A. H.; Negm, H. M.

2010-12-01

The main objective of this research is to study the capability of piezoelectric (PZT) self-sensing actuators to suppress the transonic wing box flutter, which is a flow-structure interaction phenomenon. The unsteady general frequency modified transonic small disturbance (TSD) equation is used to model the transonic flow about the wing. The wing box structure and piezoelectric actuators are modeled using the equivalent plate method, which is based on the first order shear deformation plate theory (FSDPT). The piezoelectric actuators are bonded to the skin. The optimal electromechanical coupling conditions between the piezoelectric actuators and the wing are collected from previous work. Three main different control strategies, a linear quadratic Gaussian (LQG) which combines the linear quadratic regulator (LQR) with the Kalman filter estimator (KFE), an optimal static output feedback (SOF), and a classic feedback controller (CFC), are studied and compared. The optimum actuator and sensor locations are determined using the norm of feedback control gains (NFCG) and norm of Kalman filter estimator gains (NKFEG) respectively. A genetic algorithm (GA) optimization technique is used to calculate the controller and estimator parameters to achieve a target response.

Linear stability theory and three-dimensional boundary layer transition

NASA Technical Reports Server (NTRS)

Spall, Robert E.; Malik, Mujeeb R.

1992-01-01

The viewgraphs and discussion of linear stability theory and three dimensional boundary layer transition are provided. The ability to predict, using analytical tools, the location of boundary layer transition over aircraft-type configurations is of great importance to designers interested in laminar flow control (LFC). The e(sup N) method has proven to be fairly effective in predicting, in a consistent manner, the location of the onset of transition for simple geometries in low disturbance environments. This method provides a correlation between the most amplified single normal mode and the experimental location of the onset of transition. Studies indicate that values of N between 8 and 10 correlate well with the onset of transition. For most previous calculations, the mean flows were restricted to two-dimensional or axisymmetric cases, or have employed simple three-dimensional mean flows (e.g., rotating disk, infinite swept wing, or tapered swept wing with straight isobars). Unfortunately, for flows over general wing configurations, and for nearly all flows over fuselage-type bodies at incidence, the analysis of fully three-dimensional flow fields is required. Results obtained for the linear stability of fully three-dimensional boundary layers formed over both wing and fuselage-type geometries, and for both high and low speed flows are discussed. When possible, transition estimates form the e(sup N) method are compared to experimentally determined locations. The stability calculations are made using a modified version of the linear stability code COSAL. Mean flows were computed using both Navier Stokes and boundary-layer codes.

Tilt-rotor flutter control in cruise flight

NASA Technical Reports Server (NTRS)

Nasu, Ken-Ichi

1986-01-01

Tilt-rotor flutter control under cruising operation is analyzed. The rotor model consists of a straight fixed wing, a pylon attached to the wingtip, and a three-blade rotor. The wing is cantilevered to the fuselage and is allowed to bend forward and upward. It also has a torsional degree of freedom about the elastic axis. Each rotor blade has two bending degrees of freedom. Feedback of wingtip velocity and acceleration to cyclic pitch is investigated for flutter control, using strip theory and linearized equations of motion. To determine the feedback gain, an eigenvalue analysis is performed. A second, independent, timewise calculation is conducted to evaluate the control law while employing more sophisticated aerodynamics. The effectiveness of flutter control by cyclic pitch change was confirmed.

A control-theory model for human decision-making

NASA Technical Reports Server (NTRS)

Levison, W. H.; Tanner, R. B.

1971-01-01

A model for human decision making is an adaptation of an optimal control model for pilot/vehicle systems. The models for decision and control both contain concepts of time delay, observation noise, optimal prediction, and optimal estimation. The decision making model was intended for situations in which the human bases his decision on his estimate of the state of a linear plant. Experiments are described for the following task situations: (a) single decision tasks, (b) two-decision tasks, and (c) simultaneous manual control and decision making. Using fixed values for model parameters, single-task and two-task decision performance can be predicted to within an accuracy of 10 percent. Agreement is less good for the simultaneous decision and control situation.

An approximation theory for the identification of linear thermoelastic systems

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Su, Chien-Hua Frank

1990-01-01

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

Diffusion by one wave and by many waves

NASA Astrophysics Data System (ADS)

Albert, J. M.

2010-03-01

Radiation belt electrons and chorus waves are an outstanding instance of the important role cyclotron resonant wave-particle interactions play in the magnetosphere. Chorus waves are particularly complex, often occurring with large amplitude, narrowband but drifting frequency and fine structure. Nevertheless, modeling their effect on radiation belt electrons with bounce-averaged broadband quasi-linear theory seems to yield reasonable results. It is known that coherent interactions with monochromatic waves can cause particle diffusion, as well as radically different phase bunching and phase trapping behavior. Here the two formulations of diffusion, while conceptually different, are shown to give identical diffusion coefficients, in the narrowband limit of quasi-linear theory. It is further shown that suitably averaging the monochromatic diffusion coefficients over frequency and wave normal angle parameters reproduces the full broadband quasi-linear results. This may account for the rather surprising success of quasi-linear theory in modeling radiation belt electrons undergoing diffusion by chorus waves.

Density-dependent host choice by disease vectors: epidemiological implications of the ideal free distribution.

PubMed

Basáñez, María-Gloria; Razali, Karina; Renz, Alfons; Kelly, David

2007-03-01

The proportion of vector blood meals taken on humans (the human blood index, h) appears as a squared term in classical expressions of the basic reproduction ratio (R(0)) for vector-borne infections. Consequently, R(0) varies non-linearly with h. Estimates of h, however, constitute mere snapshots of a parameter that is predicted, from evolutionary theory, to vary with vector and host abundance. We test this prediction using a population dynamics model of river blindness assuming that, before initiation of vector control or chemotherapy, recorded measures of vector density and human infection accurately represent endemic equilibrium. We obtain values of h that satisfy the condition that the effective reproduction ratio (R(e)) must equal 1 at equilibrium. Values of h thus obtained decrease with vector density, decrease with the vector:human ratio and make R(0) respond non-linearly rather than increase linearly with vector density. We conclude that if vectors are less able to obtain human blood meals as their density increases, antivectorial measures may not lead to proportional reductions in R(0) until very low vector levels are achieved. Density dependence in the contact rate of infectious diseases transmitted by insects may be an important non-linear process with implications for their epidemiology and control.

Reducing bias and analyzing variability in the time-left procedure.

PubMed

Trujano, R Emmanuel; Orduña, Vladimir

2015-04-01

The time-left procedure was designed to evaluate the psychophysical function for time. Although previous results indicated a linear relationship, it is not clear what role the observed bias toward the time-left option plays in this procedure and there are no reports of how variability changes with predicted indifference. The purposes of this experiment were to reduce bias experimentally, and to contrast the difference limen (a measure of variability around indifference) with predictions from scalar expectancy theory (linear timing) and behavioral economic model (logarithmic timing). A control group of 6 rats performed the original time-left procedure with C=60 s and S=5, 10,…, 50, 55 s, whereas a no-bias group of 6 rats performed the same conditions in a modified time-left procedure in which only a single response per choice trial was allowed. Results showed that bias was reduced for the no-bias group, observed indifference grew linearly with predicted indifference for both groups, and difference limen and Weber ratios decreased as expected indifference increased for the control group, which is consistent with linear timing, whereas for the no-bias group they remained constant, consistent with logarithmic timing. Therefore, the time-left procedure generates results consistent with logarithmic perceived time once bias is experimentally reduced. Copyright © 2015 Elsevier B.V. All rights reserved.

Classification of sodium MRI data of cartilage using machine learning.

PubMed

Madelin, Guillaume; Poidevin, Frederick; Makrymallis, Antonios; Regatte, Ravinder R

2015-11-01

To assess the possible utility of machine learning for classifying subjects with and subjects without osteoarthritis using sodium magnetic resonance imaging data. Theory: Support vector machine, k-nearest neighbors, naïve Bayes, discriminant analysis, linear regression, logistic regression, neural networks, decision tree, and tree bagging were tested. Sodium magnetic resonance imaging with and without fluid suppression by inversion recovery was acquired on the knee cartilage of 19 controls and 28 osteoarthritis patients. Sodium concentrations were measured in regions of interests in the knee for both acquisitions. Mean (MEAN) and standard deviation (STD) of these concentrations were measured in each regions of interest, and the minimum, maximum, and mean of these two measurements were calculated over all regions of interests for each subject. The resulting 12 variables per subject were used as predictors for classification. Either Min [STD] alone, or in combination with Mean [MEAN] or Min [MEAN], all from fluid suppressed data, were the best predictors with an accuracy >74%, mainly with linear logistic regression and linear support vector machine. Other good classifiers include discriminant analysis, linear regression, and naïve Bayes. Machine learning is a promising technique for classifying osteoarthritis patients and controls from sodium magnetic resonance imaging data. © 2014 Wiley Periodicals, Inc.

Shape of Strained Solid He-4 at Low Temperatures

NASA Technical Reports Server (NTRS)

Kojima, Harry

2004-01-01

(1) Interferometer apparatus for measuring surface profile (2) For small strains, the expected linear decrease in height is not seen. (3) For large strains, undulation and irreversible deformations begin to set in, but we cannot yet make clear connection with stress-driven instability theory. Torii and Balibar have observed appearances of deformations beyond threshold stress on He-4 solid surface. The difference of our results from theory real? We are not ready to claim in affirmative. To be able to answer: 1) improve crystal growth techniques; (orientation, annealing, better pressure control) 2) improve homogeneity of stress; (better alignment with vertical, better understanding of interaction between solid He-4 and walls) 4) improve optics.

Controllability Analysis for Multirotor Helicopter Rotor Degradation and Failure

NASA Astrophysics Data System (ADS)

Du, Guang-Xun; Quan, Quan; Yang, Binxian; Cai, Kai-Yuan

2015-05-01

This paper considers the controllability analysis problem for a class of multirotor systems subject to rotor failure/wear. It is shown that classical controllability theories of linear systems are not sufficient to test the controllability of the considered multirotors. Owing to this, an easy-to-use measurement index is introduced to assess the available control authority. Based on it, a new necessary and sufficient condition for the controllability of multirotors is derived. Furthermore, a controllability test procedure is approached. The proposed controllability test method is applied to a class of hexacopters with different rotor configurations and different rotor efficiency parameters to show its effectiveness. The analysis results show that hexacopters with different rotor configurations have different fault-tolerant capabilities. It is therefore necessary to test the controllability of the multirotors before any fault-tolerant control strategies are employed.

Effect of motor dynamics on nonlinear feedback robot arm control

NASA Technical Reports Server (NTRS)

Tarn, Tzyh-Jong; Li, Zuofeng; Bejczy, Antal K.; Yun, Xiaoping

1991-01-01

A nonlinear feedback robot controller that incorporates the robot manipulator dynamics and the robot joint motor dynamics is proposed. The manipulator dynamics and the motor dynamics are coupled to obtain a third-order-dynamic model, and differential geometric control theory is applied to produce a linearized and decoupled robot controller. The derived robot controller operates in the robot task space, thus eliminating the need for decomposition of motion commands into robot joint space commands. Computer simulations are performed to verify the feasibility of the proposed robot controller. The controller is further experimentally evaluated on the PUMA 560 robot arm. The experiments show that the proposed controller produces good trajectory tracking performances and is robust in the presence of model inaccuracies. Compared with a nonlinear feedback robot controller based on the manipulator dynamics only, the proposed robot controller yields conspicuously improved performance.

Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

NASA Technical Reports Server (NTRS)

Buchert, T.; Melott, A. L.; Weiss, A. G.

1993-01-01

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the onset of hierarchical clustering. This success is found at a considerable higher non-linearity than is usual for perturbation theory. Whether a truncation of the initial power-spectrum in hierarchical models retains this improvement will be analyzed in a forthcoming work.

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

Bose, Benjamin; Koyama, Kazuya, E-mail: benjamin.bose@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk

We develop a code to produce the power spectrum in redshift space based on standard perturbation theory (SPT) at 1-loop order. The code can be applied to a wide range of modified gravity and dark energy models using a recently proposed numerical method by A.Taruya to find the SPT kernels. This includes Horndeski's theory with a general potential, which accommodates both chameleon and Vainshtein screening mechanisms and provides a non-linear extension of the effective theory of dark energy up to the third order. Focus is on a recent non-linear model of the redshift space power spectrum which has been shownmore » to model the anisotropy very well at relevant scales for the SPT framework, as well as capturing relevant non-linear effects typical of modified gravity theories. We provide consistency checks of the code against established results and elucidate its application within the light of upcoming high precision RSD data.« less

On the interaction of small-scale linear waves with nonlinear solitary waves

NASA Astrophysics Data System (ADS)

Xu, Chengzhu; Stastna, Marek

2017-04-01

In the study of environmental and geophysical fluid flows, linear wave theory is well developed and its application has been considered for phenomena of various length and time scales. However, due to the nonlinear nature of fluid flows, in many cases results predicted by linear theory do not agree with observations. One of such cases is internal wave dynamics. While small-amplitude wave motion may be approximated by linear theory, large amplitude waves tend to be solitary-like. In some cases, when the wave is highly nonlinear, even weakly nonlinear theories fail to predict the wave properties correctly. We study the interaction of small-scale linear waves with nonlinear solitary waves using highly accurate pseudo spectral simulations that begin with a fully nonlinear solitary wave and a train of small-amplitude waves initialized from linear waves. The solitary wave then interacts with the linear waves through either an overtaking collision or a head-on collision. During the collision, there is a net energy transfer from the linear wave train to the solitary wave, resulting in an increase in the kinetic energy carried by the solitary wave and a phase shift of the solitary wave with respect to a freely propagating solitary wave. At the same time the linear waves are greatly reduced in amplitude. The percentage of energy transferred depends primarily on the wavelength of the linear waves. We found that after one full collision cycle, the longest waves may retain as much as 90% of the kinetic energy they had initially, while the shortest waves lose almost all of their initial energy. We also found that a head-on collision is more efficient in destroying the linear waves than an overtaking collision. On the other hand, the initial amplitude of the linear waves has very little impact on the percentage of energy that can be transferred to the solitary wave. Because of the nonlinearity of the solitary wave, these results provide us some insight into wave-mean flow interaction in a fully nonlinear framework.

A cognitive movement scientist's view on the link between thought and action: insights from the "Badische Zimmer" metaphor.

PubMed

Hossner, Ernst-Joachim

2009-01-01

The problem of a bidirectional link between thought and action is approached from the perspective of cognitive movement science. The metaphor of the "Badische Zimmer" - an adaptation of Searle's Chinese room metaphor - is used to illustrate shortcomings in the classical conception of linear information processing and to introduce some features which current theories of movement control and learning should embrace. On this basis, the case is made for a return to an ideomotor view of motor control and learning based on effect prediction (E') as a function of the situational context (S') and one's own motor responses (R'). The relevance of the derived concept of sensorimotor chains linking elementary S'R'E' units in the course of motor learning is finally discussed with respect to potential implications for an integrative theory of perception, action, and decision making.

Stability theory applications to laminar-flow control

NASA Technical Reports Server (NTRS)

Malik, Mujeeb R.

1987-01-01

In order to design Laminar Flow Control (LFC) configurations, reliable methods are needed for boundary-layer transition predictions. Among the available methods, there are correlations based upon R sub e, shape factors, Goertler number and crossflow Reynolds number. The most advanced transition prediction method is based upon linear stability theory in the form of the e sup N method which has proven to be successful in predicting transition in two- and three-dimensional boundary layers. When transition occurs in a low disturbance environment, the e sup N method provides a viable design tool for transition prediction and LFC in both 2-D and 3-D subsonic/supersonic flows. This is true for transition dominated by either TS, crossflow, or Goertler instability. If Goertler/TS or crossflow/TS interaction is present, the e sup N will fail to predict transition. However, there is no evidence of such interaction at low amplitudes of Goertler and crossflow vortices.

Direct perturbation theory for the dark soliton solution to the nonlinear Schrödinger equation with normal dispersion.

PubMed

Yu, Jia-Lu; Yang, Chun-Nuan; Cai, Hao; Huang, Nian-Ning

2007-04-01

After finding the basic solutions of the linearized nonlinear Schrödinger equation by the method of separation of variables, the perturbation theory for the dark soliton solution is constructed by linear Green's function theory. In application to the self-induced Raman scattering, the adiabatic corrections to the soliton's parameters are obtained and the remaining correction term is given as a pure integral with respect to the continuous spectral parameter.

Excited states with internally contracted multireference coupled-cluster linear response theory.

PubMed

Samanta, Pradipta Kumar; Mukherjee, Debashis; Hanauer, Matthias; Köhn, Andreas

2014-04-07

In this paper, the linear response (LR) theory for the variant of internally contracted multireference coupled cluster (ic-MRCC) theory described by Hanauer and Köhn [J. Chem. Phys. 134, 204211 (2011)] has been formulated and implemented for the computation of the excitation energies relative to a ground state of pronounced multireference character. We find that straightforward application of the linear-response formalism to the time-averaged ic-MRCC Lagrangian leads to unphysical second-order poles. However, the coupling matrix elements that cause this behavior are shown to be negligible whenever the internally contracted approximation as such is justified. Hence, for the numerical implementation of the method, we adopt a Tamm-Dancoff-type approximation and neglect these couplings. This approximation is also consistent with an equation-of-motion based derivation, which neglects these couplings right from the start. We have implemented the linear-response approach in the ic-MRCC singles-and-doubles framework and applied our method to calculate excitation energies for a number of molecules ranging from CH2 to p-benzyne and conjugated polyenes (up to octatetraene). The computed excitation energies are found to be very accurate, even for the notoriously difficult case of doubly excited states. The ic-MRCC-LR theory is also applicable to systems with open-shell ground-state wavefunctions and is by construction not biased towards a particular reference determinant. We have also compared the linear-response approach to the computation of energy differences by direct state-specific ic-MRCC calculations. We finally compare to Mk-MRCC-LR theory for which spurious roots have been reported [T.-C. Jagau and J. Gauss, J. Chem. Phys. 137, 044116 (2012)], being due to the use of sufficiency conditions to solve the Mk-MRCC equations. No such problem is present in ic-MRCC-LR theory.

Vibration suppression of a piezo-equipped cylindrical shell in a broad-band frequency domain

NASA Astrophysics Data System (ADS)

Loghmani, Ali; Danesh, Mohammad; Kwak, Moon K.; Keshmiri, Mehdi

2017-12-01

This paper focuses on the dynamic modeling of a cylindrical shell equipped with piezoceramic sensors and actuators, as well as the design of a broad band multi-input and multi-output linear quadratic Gaussian controller for the suppression of vibrations. The optimal locations of actuators are derived by Genetic Algorithm (GA) to effectively control the specific structural modes of the cylinder. The dynamic model is derived based on the Sanders shell theory and the energy approach for both the cylinder and the piezoelectric transducers, all of which reflect the piezoelectric effect. The natural vibration characteristics of the cylindrical shell are investigated both theoretically and experimentally. The theoretical predictions are in good agreement with the experimental results. Then, the broad band multi-input and multi-output linear quadratic Gaussian controller was designed and applied to the test article. An active vibration control experiment is carried out on the cylindrical shell and the digital control system is used to implement the proposed control algorithm. The experimental results show that vibrations of the cylindrical shell can be suppressed by the piezoceramic sensors and actuators along with the proposed controller. The optimal location of the actuators makes the proposed control system more efficient than other configurations.

Applications of Cosmological Perturbation Theory

NASA Astrophysics Data System (ADS)

Christopherson, Adam J.

2011-06-01

Cosmological perturbation theory is crucial for our understanding of the universe. The linear theory has been well understood for some time, however developing and applying the theory beyond linear order is currently at the forefront of research in theoretical cosmology. This thesis studies the applications of perturbation theory to cosmology and, specifically, to the early universe. Starting with some background material introducing the well-tested 'standard model' of cosmology, we move on to develop the formalism for perturbation theory up to second order giving evolution equations for all types of scalar, vector and tensor perturbations, both in gauge dependent and gauge invariant form. We then move on to the main result of the thesis, showing that, at second order in perturbation theory, vorticity is sourced by a coupling term quadratic in energy density and entropy perturbations. This source term implies a qualitative difference to linear order. Thus, while at linear order vorticity decays with the expansion of the universe, the same is not true at higher orders. This will have important implications on future measurements of the polarisation of the Cosmic Microwave Background, and could give rise to the generation of a primordial seed magnetic field. Having derived this qualitative result, we then estimate the scale dependence and magnitude of the vorticity power spectrum, finding, for simple power law inputs a small, blue spectrum. The final part of this thesis concerns higher order perturbation theory, deriving, for the first time, the metric tensor, gauge transformation rules and governing equations for fully general third order perturbations. We close with a discussion of natural extensions to this work and other possible ideas for off-shooting projects in this continually growing field.

Fleet Assignment Using Collective Intelligence

NASA Technical Reports Server (NTRS)

Antoine, Nicolas E.; Bieniawski, Stefan R.; Kroo, Ilan M.; Wolpert, David H.

2004-01-01

Product distribution theory is a new collective intelligence-based framework for analyzing and controlling distributed systems. Its usefulness in distributed stochastic optimization is illustrated here through an airline fleet assignment problem. This problem involves the allocation of aircraft to a set of flights legs in order to meet passenger demand, while satisfying a variety of linear and non-linear constraints. Over the course of the day, the routing of each aircraft is determined in order to minimize the number of required flights for a given fleet. The associated flow continuity and aircraft count constraints have led researchers to focus on obtaining quasi-optimal solutions, especially at larger scales. In this paper, the authors propose the application of this new stochastic optimization algorithm to a non-linear objective cold start fleet assignment problem. Results show that the optimizer can successfully solve such highly-constrained problems (130 variables, 184 constraints).

Aspect ratio effects on limited scrape-off layer plasma turbulence

NASA Astrophysics Data System (ADS)

Jolliet, Sébastien; Halpern, Federico D.; Loizu, Joaquim; Mosetto, Annamaria; Ricci, Paolo

2014-02-01

The drift-reduced Braginskii model describing turbulence in the tokamak scrape-off layer is written for a general magnetic configuration with a limiter. The equilibrium is then specified for a circular concentric magnetic geometry retaining aspect ratio effects. Simulations are then carried out with the help of the global, flux-driven fluid three-dimensional code GBS [Ricci et al., Plasma Phys. Controlled Fusion 54, 124047 (2012)]. Linearly, both simulations and simplified analytical models reveal a stabilization of ballooning modes. Nonlinearly, flux-driven nonlinear simulations give a pressure characteristic length whose trends are correctly captured by the gradient removal theory [Ricci and Rogers, Phys. Plasmas 20, 010702 (2013)], that assumes the profile flattening from the linear modes as the saturation mechanism. More specifically, the linear stabilization of ballooning modes is reflected by a 15% increase in the steady-state pressure gradient obtained from GBS nonlinear simulations when going from an infinite to a realistic aspect ratio.

Robust Control Design for Uncertain Nonlinear Dynamic Systems

NASA Technical Reports Server (NTRS)

Kenny, Sean P.; Crespo, Luis G.; Andrews, Lindsey; Giesy, Daniel P.

2012-01-01

Robustness to parametric uncertainty is fundamental to successful control system design and as such it has been at the core of many design methods developed over the decades. Despite its prominence, most of the work on robust control design has focused on linear models and uncertainties that are non-probabilistic in nature. Recently, researchers have acknowledged this disparity and have been developing theory to address a broader class of uncertainties. This paper presents an experimental application of robust control design for a hybrid class of probabilistic and non-probabilistic parametric uncertainties. The experimental apparatus is based upon the classic inverted pendulum on a cart. The physical uncertainty is realized by a known additional lumped mass at an unknown location on the pendulum. This unknown location has the effect of substantially altering the nominal frequency and controllability of the nonlinear system, and in the limit has the capability to make the system neutrally stable and uncontrollable. Another uncertainty to be considered is a direct current motor parameter. The control design objective is to design a controller that satisfies stability, tracking error, control power, and transient behavior requirements for the largest range of parametric uncertainties. This paper presents an overview of the theory behind the robust control design methodology and the experimental results.

The Hagen-Poiseuille, Plane Couette and Poiseuille Flows Linear Instability and Rogue Waves Excitation Mechanism

NASA Astrophysics Data System (ADS)

Chefranov, Sergey; Chefranov, Alexander

2016-04-01

Linear hydrodynamic stability theory for the Hagen-Poiseuille (HP) flow yields a conclusion of infinitely large threshold Reynolds number, Re, value. This contradiction to the observation data is bypassed using assumption of the HP flow instability having hard type and possible for sufficiently high-amplitude disturbances. HP flow disturbance evolution is considered by nonlinear hydrodynamic stability theory. Similar is the case of the plane Couette (PC) flow. For the plane Poiseuille (PP) flow, linear theory just quantitatively does not agree with experimental data defining the threshold Reynolds number Re= 5772 ( S. A. Orszag, 1971), more than five-fold exceeding however the value observed, Re=1080 (S. J. Davies, C. M. White, 1928). In the present work, we show that the linear stability theory conclusions for the HP and PC on stability for any Reynolds number and evidently too high threshold Reynolds number estimate for the PP flow are related with the traditional use of the disturbance representation assuming the possibility of separation of the longitudinal (along the flow direction) variable from the other spatial variables. We show that if to refuse from this traditional form, conclusions on the linear instability for the HP and PC flows may be obtained for finite Reynolds numbers (for the HP flow, for Re>704, and for the PC flow, for Re>139). Also, we fit the linear stability theory conclusion on the PP flow to the experimental data by getting an estimate of the minimal threshold Reynolds number as Re=1040. We also get agreement of the minimal threshold Reynolds number estimate for PC with the experimental data of S. Bottin, et.al., 1997, where the laminar PC flow stability threshold is Re = 150. Rogue waves excitation mechanism in oppositely directed currents due to the PC flow linear instability is discussed. Results of the new linear hydrodynamic stability theory for the HP, PP, and PC flows are published in the following papers: 1. S.G. Chefranov, A.G. Chefranov, JETP, v.119, No.2, 331, 2014 2. S.G. Chefranov, A.G. Chefranov, Doklady Physics, vol.60, No.7, 327-332, 2015 3. S.G. Chefranov, A. G. Chefranov, arXiv: 1509.08910v1 [physics.flu-dyn] 29 Sep 2015 (accepted to JETP)

A Comparison of Measurement Equivalence Methods Based on Confirmatory Factor Analysis and Item Response Theory.

ERIC Educational Resources Information Center

Flowers, Claudia P.; Raju, Nambury S.; Oshima, T. C.

Current interest in the assessment of measurement equivalence emphasizes two methods of analysis, linear, and nonlinear procedures. This study simulated data using the graded response model to examine the performance of linear (confirmatory factor analysis or CFA) and nonlinear (item-response-theory-based differential item function or IRT-Based…

Constructive Processes in Linear Order Problems Revealed by Sentence Study Times

ERIC Educational Resources Information Center

Mynatt, Barbee T.; Smith, Kirk H.

1977-01-01

This research was a further test of the theory of constructive processes proposed by Foos, Smith, Sabol, and Mynatt (1976) to account for differences among presentation orders in the construction of linear orders. This theory is composed of different series of mental operations that must be performed when an order relationship is integrated with…

The application of Green's theorem to the solution of boundary-value problems in linearized supersonic wing theory

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Lomax, Harvard

1950-01-01

Following the introduction of the linearized partial differential equation for nonsteady three-dimensional compressible flow, general methods of solution are given for the two and three-dimensional steady-state and two-dimensional unsteady-state equations. It is also pointed out that, in the absence of thickness effects, linear theory yields solutions consistent with the assumptions made when applied to lifting-surface problems for swept-back plan forms at sonic speeds. The solutions of the particular equations are determined in all cases by means of Green's theorem, and thus depend on the use of Green's equivalent layer of sources, sinks, and doublets. Improper integrals in the supersonic theory are treated by means of Hadamard's "finite part" technique.

Non-linear Frequency Shifts, Mode Couplings, and Decay Instability of Plasma Waves

NASA Astrophysics Data System (ADS)

Affolter, Mathew; Anderegg, F.; Driscoll, C. F.; Valentini, F.

2015-11-01

We present experiments and theory for non-linear plasma wave decay to longer wavelengths, in both the oscillatory coupling and exponential decay regimes. The experiments are conducted on non-neutral plasmas in cylindrical Penning-Malmberg traps, θ-symmetric standing plasma waves have near acoustic dispersion ω (kz) ~kz - αkz2 , discretized by kz =mz (π /Lp) . Large amplitude waves exhibit non-linear frequency shifts δf / f ~A2 and Fourier harmonic content, both of which are increased as the plasma dispersion is reduced. Non-linear coupling rates are measured between large amplitude mz = 2 waves and small amplitude mz = 1 waves, which have a small detuning Δω = 2ω1 -ω2 . At small excitation amplitudes, this detuning causes the mz = 1 mode amplitude to ``bounce'' at rate Δω , with amplitude excursions ΔA1 ~ δn2 /n0 consistent with cold fluid theory and Vlasov simulations. At larger excitation amplitudes, where the non-linear coupling exceeds the dispersion, phase-locked exponential growth of the mz = 1 mode is observed, in qualitative agreement with simple 3-wave instability theory. However, significant variations are observed experimentally, and N-wave theory gives stunningly divergent predictions that depend sensitively on the dispersion-moderated harmonic content. Measurements on higher temperature Langmuir waves and the unusual ``EAW'' (KEEN) waves are being conducted to investigate the effects of wave-particle kinetics on the non-linear coupling rates. Department of Energy Grants DE-SC0002451and DE-SC0008693.

A new lattice hydrodynamic model based on control method considering the flux change rate and delay feedback signal

NASA Astrophysics Data System (ADS)

Qin, Shunda; Ge, Hongxia; Cheng, Rongjun

2018-02-01

In this paper, a new lattice hydrodynamic model is proposed by taking delay feedback and flux change rate effect into account in a single lane. The linear stability condition of the new model is derived by control theory. By using the nonlinear analysis method, the mKDV equation near the critical point is deduced to describe the traffic congestion. Numerical simulations are carried out to demonstrate the advantage of the new model in suppressing traffic jam with the consideration of flux change rate effect in delay feedback model.

Theoretical characteristics in supersonic flow of two types of control surfaces on triangular wings

NASA Technical Reports Server (NTRS)

Tucker, Warren A; Nelson, Robert L

1949-01-01

Methods based on the linearized theory for supersonic flow were used to find the characteristics of two types of control surfaces on thin triangular wings. The first type, the constant-chord partial-span flap, was considered to extend either outboard from the center of the wing or inboard from the wing tip. The second type, the full-triangular-tip flap, was treated only for the case in which the Mach number component normal to the leading edge is supersonic. For each type, expressions were found for the lift, rolling-moment, pitching-moment, and hinge-moment characteristics.

Research on the unsteady hydrodynamic characteristics of vertical axis tidal turbine

NASA Astrophysics Data System (ADS)

Zhang, Xue-wei; Zhang, Liang; Wang, Feng; Zhao, Dong-ya; Pang, Cheng-yan

2014-03-01

The unsteady hydrodynamic characteristics of vertical axis tidal turbine are investigated by numerical simulation based on viscous CFD method. The starting mechanism of the turbine is revealed through analyzing the interaction of its motion and dynamics during starting process. The operating hydrodynamic characteristics of the turbine in wave-current condition are also explored by combining with the linear wave theory. According to possible magnification of the cyclic loads in the maximum power tracking control of vertical axis turbine, a novel torque control strategy is put forward, which can improve the structural characteristics significantly without effecting energy efficiency.

Unified Theory for Aircraft Handling Qualities and Adverse Aircraft-Pilot Coupling

NASA Technical Reports Server (NTRS)

Hess, R. A.

1997-01-01

A unified theory for aircraft handling qualities and adverse aircraft-pilot coupling or pilot-induced oscillations is introduced. The theory is based on a structural model of the human pilot. A methodology is presented for the prediction of (1) handling qualities levels; (2) pilot-induced oscillation rating levels; and (3) a frequency range in which pilot-induced oscillations are likely to occur. Although the dynamics of the force-feel system of the cockpit inceptor is included, the methodology will not account for effects attributable to control sensitivity and is limited to single-axis tasks and, at present, to linear vehicle models. The theory is derived from the feedback topology of the structural model and an examination of flight test results for 32 aircraft configurations simulated by the U.S. Air Force/CALSPAN NT-33A and Total In-Flight Simulator variable stability aircraft. An extension to nonlinear vehicle dynamics such as that encountered with actuator saturation is discussed.

A survey of wheel-rail contact models for rail vehicles

NASA Astrophysics Data System (ADS)

Meymand, Sajjad Z.; Keylin, Alexander; Ahmadian, Mehdi

2016-03-01

Accurate and efficient contact models for wheel-rail interaction are essential for the study of the dynamic behaviour of a railway vehicle. Assessment of the contact forces and moments, as well as contact geometry provide a fundamental foundation for such tasks as design of braking and traction control systems, prediction of wheel and rail wear, and evaluation of ride safety and comfort. This paper discusses the evolution and the current state of the theories for solving the wheel-rail contact problem for rolling stock. The well-known theories for modelling both normal contact (Hertzian and non-Hertzian) and tangential contact (Kalker's linear theory, FASTSIM, CONTACT, Polach's theory, etc.) are reviewed. The paper discusses the simplifying assumptions for developing these models and compares their functionality. The experimental studies for evaluation of contact models are also reviewed. This paper concludes with discussing open areas in contact mechanics that require further research for developing better models to represent the wheel-rail interaction.

Trajectory control method of stratospheric airship based on the sliding mode control and prediction in wind field

NASA Astrophysics Data System (ADS)

Zhang, Jia-shi; Yang, Xi-xiang

2017-11-01

The stratospheric airship has the characteristics of large inertia, long time delay and large disturbance of wind field , so the trajectory control is very difficult .Build the lateral three degrees of freedom dynamic model which consider the wind interference , the dynamics equation is linearized by the small perturbation theory, propose a trajectory control method Combine with the sliding mode control and prediction, design the trajectory controller , takes the HAA airship as the reference to carry out simulation analysis. Results show that the improved sliding mode control with front-feedback method not only can solve well control problems of airship trajectory in wind field, but also can effectively improve the control accuracy of the traditional sliding mode control method, solved problems that using the traditional sliding mode control to control. It provides a useful reference for dynamic modeling and trajectory control of stratospheric airship.

Linear-scaling method for calculating nuclear magnetic resonance chemical shifts using gauge-including atomic orbitals within Hartree-Fock and density-functional theory.

PubMed

Kussmann, Jörg; Ochsenfeld, Christian

2007-08-07

Details of a new density matrix-based formulation for calculating nuclear magnetic resonance chemical shifts at both Hartree-Fock and density functional theory levels are presented. For systems with a nonvanishing highest occupied molecular orbital-lowest unoccupied molecular orbital gap, the method allows us to reduce the asymptotic scaling order of the computational effort from cubic to linear, so that molecular systems with 1000 and more atoms can be tackled with today's computers. The key feature is a reformulation of the coupled-perturbed self-consistent field (CPSCF) theory in terms of the one-particle density matrix (D-CPSCF), which avoids entirely the use of canonical MOs. By means of a direct solution for the required perturbed density matrices and the adaptation of linear-scaling integral contraction schemes, the overall scaling of the computational effort is reduced to linear. A particular focus of our formulation is to ensure numerical stability when sparse-algebra routines are used to obtain an overall linear-scaling behavior.

Linear {GLP}-algebras and their elementary theories

NASA Astrophysics Data System (ADS)

Pakhomov, F. N.

2016-12-01

The polymodal provability logic {GLP} was introduced by Japaridze in 1986. It is the provability logic of certain chains of provability predicates of increasing strength. Every polymodal logic corresponds to a variety of polymodal algebras. Beklemishev and Visser asked whether the elementary theory of the free {GLP}-algebra generated by the constants \\mathbf{0}, \\mathbf{1} is decidable [1]. For every positive integer n we solve the corresponding question for the logics {GLP}_n that are the fragments of {GLP} with n modalities. We prove that the elementary theory of the free {GLP}_n-algebra generated by the constants \\mathbf{0}, \\mathbf{1} is decidable for all n. We introduce the notion of a linear {GLP}_n-algebra and prove that all free {GLP}_n-algebras generated by the constants \\mathbf{0}, \\mathbf{1} are linear. We also consider the more general case of the logics {GLP}_α whose modalities are indexed by the elements of a linearly ordered set α: we define the notion of a linear algebra and prove the latter result in this case.

Linearized-moment analysis of the temperature jump and temperature defect in the Knudsen layer of a rarefied gas.

PubMed

Gu, Xiao-Jun; Emerson, David R

2014-06-01

Understanding the thermal behavior of a rarefied gas remains a fundamental problem. In the present study, we investigate the predictive capabilities of the regularized 13 and 26 moment equations. In this paper, we consider low-speed problems with small gradients, and to simplify the analysis, a linearized set of moment equations is derived to explore a classic temperature problem. Analytical solutions obtained for the linearized 26 moment equations are compared with available kinetic models and can reliably capture all qualitative trends for the temperature-jump coefficient and the associated temperature defect in the thermal Knudsen layer. In contrast, the linearized 13 moment equations lack the necessary physics to capture these effects and consistently underpredict kinetic theory. The deviation from kinetic theory for the 13 moment equations increases significantly for specular reflection of gas molecules, whereas the 26 moment equations compare well with results from kinetic theory. To improve engineering analyses, expressions for the effective thermal conductivity and Prandtl number in the Knudsen layer are derived with the linearized 26 moment equations.

Daubechies wavelets for linear scaling density functional theory.

PubMed

Mohr, Stephan; Ratcliff, Laura E; Boulanger, Paul; Genovese, Luigi; Caliste, Damien; Deutsch, Thierry; Goedecker, Stefan

2014-05-28

We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10,000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.

Long-wave theory for a new convective instability with exponential growth normal to the wall.

PubMed

Healey, J J

2005-05-15

A linear stability theory is presented for the boundary-layer flow produced by an infinite disc rotating at constant angular velocity in otherwise undisturbed fluid. The theory is developed in the limit of long waves and when the effects of viscosity on the waves can be neglected. This is the parameter regime recently identified by the author in a numerical stability investigation where a curious new type of instability was found in which disturbances propagate and grow exponentially in the direction normal to the disc, (i.e. the growth takes place in a region of zero mean shear). The theory describes the mechanisms controlling the instability, the role and location of critical points, and presents a saddle-point analysis describing the large-time evolution of a wave packet in frames of reference moving normal to the disc. The theory also shows that the previously obtained numerical solutions for numerically large wavelengths do indeed lie in the asymptotic long-wave regime, and so the behaviour and mechanisms described here may apply to a number of cross-flow instability problems.

Cosmic-ray streaming perpendicular to the mean magnetic field. II - The gyrophase distribution function

NASA Technical Reports Server (NTRS)

Forman, M. A.; Jokipii, J. R.

1978-01-01

The distribution function of cosmic rays streaming perpendicular to the mean magnetic field in a turbulent medium is reexamined. Urch's (1977) discovery that in quasi-linear theory, the flux is due to particles at 90 deg pitch angle is discussed and shown to be consistent with previous formulations of the theory. It is pointed out that this flux of particles at 90 deg cannot be arbitrarily set equal to zero, and hence the alternative theory which proceeds from this premise is dismissed. A further, basic inconsistency in Urch's transport equation is demonstrated, and the connection between quasi-linear theory and compound diffusion is discussed.

Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory.

PubMed

Coriani, Sonia; Høst, Stinne; Jansík, Branislav; Thøgersen, Lea; Olsen, Jeppe; Jørgensen, Poul; Reine, Simen; Pawłowski, Filip; Helgaker, Trygve; Sałek, Paweł

2007-04-21

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories for the calculation of frequency-dependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution). As a result, the performance of the iterative method is the same as in canonical molecular-orbital theory, with five to ten iterations needed for convergence. As in traditional direct Hartree-Fock and Kohn-Sham theories, the calculations are dominated by the construction of the effective Fock/Kohn-Sham matrix, once in each iteration. Linear complexity is achieved by using sparse-matrix algebra, as illustrated in calculations of excitation energies and frequency-dependent polarizabilities of polyalanine peptides containing up to 1400 atoms.

Mittag-Leffler synchronization of fractional neural networks with time-varying delays and reaction-diffusion terms using impulsive and linear controllers.

PubMed

Stamova, Ivanka; Stamov, Gani

2017-12-01

In this paper, we propose a fractional-order neural network system with time-varying delays and reaction-diffusion terms. We first develop a new Mittag-Leffler synchronization strategy for the controlled nodes via impulsive controllers. Using the fractional Lyapunov method sufficient conditions are given. We also study the global Mittag-Leffler synchronization of two identical fractional impulsive reaction-diffusion neural networks using linear controllers, which was an open problem even for integer-order models. Since the Mittag-Leffler stability notion is a generalization of the exponential stability concept for fractional-order systems, our results extend and improve the exponential impulsive control theory of neural network system with time-varying delays and reaction-diffusion terms to the fractional-order case. The fractional-order derivatives allow us to model the long-term memory in the neural networks, and thus the present research provides with a conceptually straightforward mathematical representation of rather complex processes. Illustrative examples are presented to show the validity of the obtained results. We show that by means of appropriate impulsive controllers we can realize the stability goal and to control the qualitative behavior of the states. An image encryption scheme is extended using fractional derivatives. Copyright © 2017 Elsevier Ltd. All rights reserved.

Computer aided design of digital controller for radial active magnetic bearings

NASA Technical Reports Server (NTRS)

Cai, Zhong; Shen, Zupei; Zhang, Zuming; Zhao, Hongbin

1992-01-01

A five degree of freedom Active Magnetic Bearing (AMB) system is developed which is controlled by digital controllers. The model of the radial AMB system is linearized and the state equation is derived. Based on the state variables feedback theory, digital controllers are designed. The performance of the controllers are evaluated according to experimental results. The Computer Aided Design (CAD) method is used to design controllers for magnetic bearings. The controllers are implemented with a digital signal processing (DSP) system. The control algorithms are realized with real-time programs. It is very easy to change the controller by changing or modifying the programs. In order to identify the dynamic parameters of the controlled magnetic system, a special experiment was carried out. Also, the online Recursive Least Squares (RLS) parameter identification method is studied. It can be realized with the digital controllers. Online parameter identification is essential for the realization of an adaptive controller.

Couple stress theory of curved rods. 2-D, high order, Timoshenko's and Euler-Bernoulli models

NASA Astrophysics Data System (ADS)

Zozulya, V. V.

2017-01-01

New models for plane curved rods based on linear couple stress theory of elasticity have been developed.2-D theory is developed from general 2-D equations of linear couple stress elasticity using a special curvilinear system of coordinates related to the middle line of the rod as well as special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and rotation along with body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby, all equations of elasticity including Hooke's law have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of elasticity, a system of differential equations in terms of displacements and boundary conditions for Fourier coefficients have been obtained. Timoshenko's and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear couple stress theory of elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scales when taking into account couple stress and rotation effects.

Chaos in World Politics: A Reflection

NASA Astrophysics Data System (ADS)

Ferreira, Manuel Alberto Martins; Filipe, José António Candeias Bonito; Coelho, Manuel F. P.; Pedro, Isabel C.

Chaos theory results from natural scientists' findings in the area of non-linear dynamics. The importance of related models has increased in the last decades, by studying the temporal evolution of non-linear systems. In consequence, chaos is one of the concepts that most rapidly have been expanded in what research topics respects. Considering that relationships in non-linear systems are unstable, chaos theory aims to understand and to explain this kind of unpredictable aspects of nature, social life, the uncertainties, the nonlinearities, the disorders and confusion, scientifically it represents a disarray connection, but basically it involves much more than that. The existing close relationship between change and time seems essential to understand what happens in the basics of chaos theory. In fact, this theory got a crucial role in the explanation of many phenomena. The relevance of this kind of theories has been well recognized to explain social phenomena and has permitted new advances in the study of social systems. Chaos theory has also been applied, particularly in the context of politics, in this area. The goal of this chapter is to make a reflection on chaos theory - and dynamical systems such as the theories of complexity - in terms of the interpretation of political issues, considering some kind of events in the political context and also considering the macro-strategic ideas of states positioning in the international stage.

Vibration Control in Turbomachinery Using Active Magnetic Journal Bearings

NASA Technical Reports Server (NTRS)

Knight, Josiah D.

1996-01-01

The effective use of active magnetic bearings for vibration control in turbomachinery depends on an understanding of the forces available from a magnetic bearing actuator. The purpose of this project was to characterize the forces as functions shaft position. Both numerical and experimental studies were done to determine the characteristics of the forces exerted on a stationary shaft by a magnetic bearing actuator. The numerical studies were based on finite element computations and included both linear and nonlinear magnetization functions. Measurements of the force versus position of a nonrotating shaft were made using two separate measurement rigs, one based on strain gage measurement of forces, the other based on deflections of a calibrated beam. The general trends of the measured principal forces agree with the predictions of the theory while the magnitudes of forces are somewhat smaller than those predicted. Other aspects of theory are not confirmed by the measurements. The measured forces in the normal direction are larger than those predicted by theory when the rotor has a normal eccentricity. Over the ranges of position examined, the data indicate an approximately linear relationship between the normal eccentricity of the shaft and the ratio of normal to principal force. The constant of proportionality seems to be larger at lower currents, but for all cases examined its value is between 0.14 and 0.17. The nonlinear theory predicts the existence of normal forces, but has not predicted such a large constant of proportionality for the ratio. The type of coupling illustrated by these measurements would not tend to cause whirl, because the coupling coefficients have the same sign, unlike the case of a fluid film bearing, where the normal stiffness coefficients often have opposite signs. They might, however, tend to cause other self-excited behavior. This possibility must be considered when designing magnetic bearings for flexible rotor applications, such as gas turbines and other turbomachinery.

Precision comparison of the power spectrum in the EFTofLSS with simulations

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

Foreman, Simon; Senatore, Leonardo; Perrier, Hideki, E-mail: sfore@stanford.edu, E-mail: senatore@stanford.edu, E-mail: hideki.perrier@unige.ch

2016-05-01

We study the prediction of the dark matter power spectrum at two-loop order in the Effective Field Theory of Large Scale Structures (EFTofLSS) using high precision numerical simulations. In our universe, short distance non-linear fluctuations, not under perturbative control, affect long distance fluctuations through an effective stress tensor that needs to be parametrized in terms of counterterms that are functions of the long distance fluctuating fields. We find that at two-loop order it is necessary to include three counterterms: a linear term in the overdensity, δ, a quadratic term, δ{sup 2}, and a higher derivative term, ∂{sup 2}δ. After themore » inclusion of these three terms, the EFTofLSS at two-loop order matches simulation data up to k ≅ 0.34 h Mpc{sup −1} at redshift z = 0, up to k ≅ 0.55 h Mpc{sup −1} at z = 1, and up to k ≅ 1.1 h Mpc{sup −1} at z = 2. At these wavenumbers, the cosmic variance of the simulation is at least as small as 10{sup −3}, providing for the first time a high precision comparison between theory and data. The actual reach of the theory is affected by theoretical uncertainties associated to not having included higher order terms in perturbation theory, for which we provide an estimate, and by potentially overfitting the data, which we also try to address. Since in the EFTofLSS the coupling constants associated with the counterterms are unknown functions of time, we show how a simple parametrization gives a sensible description of their time-dependence. Overall, the k -reach of the EFTofLSS is much larger than previous analytical techniques, showing that the amount of cosmological information amenable to high-precision analytical control might be much larger than previously believed.« less

A non-linear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma

NASA Astrophysics Data System (ADS)

Rosin, M. S.; Schekochihin, A. A.; Rincon, F.; Cowley, S. C.

2011-05-01

Weakly collisional magnetized cosmic plasmas have a dynamical tendency to develop pressure anisotropies with respect to the local direction of the magnetic field. These anisotropies trigger plasma instabilities at scales just above the ion Larmor radius ρi and much below the mean free path λmfp. They have growth rates of a fraction of the ion cyclotron frequency, which is much faster than either the global dynamics or even local turbulence. Despite their microscopic nature, these instabilities dramatically modify the transport properties and, therefore, the macroscopic dynamics of the plasma. The non-linear evolution of these instabilities is expected to drive pressure anisotropies towards marginal stability values, controlled by the plasma beta βi. Here this non-linear evolution is worked out in an ab initio kinetic calculation for the simplest analytically tractable example - the parallel (k⊥= 0) firehose instability in a high-beta plasma. An asymptotic theory is constructed, based on a particular physical ordering and leading to a closed non-linear equation for the firehose turbulence. In the non-linear regime, both the analytical theory and the numerical solution predict secular (∝t) growth of magnetic fluctuations. The fluctuations develop a k-3∥ spectrum, extending from scales somewhat larger than ρi to the maximum scale that grows secularly with time (∝t1/2); the relative pressure anisotropy (p⊥-p∥)/p∥ tends to the marginal value -2/βi. The marginal state is achieved via changes in the magnetic field, not particle scattering. When a parallel ion heat flux is present, the parallel firehose mutates into the new gyrothermal instability (GTI), which continues to exist up to firehose-stable values of pressure anisotropy, which can be positive and are limited by the magnitude of the ion heat flux. The non-linear evolution of the GTI also features secular growth of magnetic fluctuations, but the fluctuation spectrum is eventually dominated by modes around a maximal scale ˜ρilT/λmfp, where lT is the scale of the parallel temperature variation. Implications for momentum and heat transport are speculated about. This study is motivated by our interest in the dynamics of galaxy cluster plasmas (which are used as the main astrophysical example), but its relevance to solar wind and accretion flow plasmas is also briefly discussed.

A Lagrangian effective field theory

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

Vlah, Zvonimir; White, Martin; Aviles, Alejandro

We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.« less

A Lagrangian effective field theory

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

Vlah, Zvonimir; White, Martin; Aviles, Alejandro, E-mail: zvlah@stanford.edu, E-mail: mwhite@berkeley.edu, E-mail: aviles@berkeley.edu

We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The 'new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. All the perturbative models fare better than linear theory.« less

A Lagrangian effective field theory

DOE PAGES

Vlah, Zvonimir; White, Martin; Aviles, Alejandro

2015-09-02

We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.« less

Protection motivation theory and cigarette smoking among vocational high school students in China: a cusp catastrophe modeling analysis.

PubMed

Xu, Yunan; Chen, Xinguang

2016-01-01

Tobacco use is one of the greatest public health problems worldwide and the hazards of cigarette smoking to public health call for better recognition of cigarette smoking behaviors to guide evidence-based policy. Protection motivation theory (PMT) provides a conceptual framework to investigate tobacco use. Evidence from diverse sources implies that the dynamics of smoking behavior may be quantum in nature, consisting of an intuition and an analytical process, challenging the traditional linear continuous analytical approach. In this study, we used cusp catastrophe, a nonlinear analytical approach to test the dual-process hypothesis of cigarette smoking. Data were collected from a random sample of vocational high school students in China ( n = 528). The multivariate stochastic cusp modeling was used and executed with the Cusp Package in R. The PMT-based Threat Appraisal and Coping Appraisal were used as the two control variables and the frequency of cigarette smoking (daily, weekly, occasional, and never) in the past month was used as the outcome variable. Consistent with PMT, the Threat Appraisal (asymmetry, α 1 = 0.1987, p < 0.001) and Coping Appraisal (bifurcation, β 2 = 0.1760, p < 0.05) significantly predicted the smoking behavior after controlling for covariates. Furthermore, the cusp model performed better than the alternative linear and logistic regression models with regard to higher R 2 (0.82 for cusp, but 0.21 for linear and 0.25 for logistic) and smaller AIC and BIC. Study findings support the conclusion that cigarette smoking in adolescents is a quantum process and PMT is relevant to guide studies to understand smoking behavior for smoking prevention and cessation.

Semigroup theory and numerical approximation for equations in linear viscoelasticity

NASA Technical Reports Server (NTRS)

Fabiano, R. H.; Ito, K.

1990-01-01

A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.

Development as a Complex Process of Change: Conception and Analysis of Projects, Programs and Policies

ERIC Educational Resources Information Center

Nordtveit, Bjorn Harald

2010-01-01

Development is often understood as a linear process of change towards Western modernity, a vision that is challenged by this paper, arguing that development efforts should rather be connected to the local stakeholders' sense of their own development. Further, the paper contends that Complexity Theory is more effective than a linear theory of…

The generic world-sheet action of irrational conformal field theory

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

Clubok, K.; Halpern, M.B.

1995-05-01

We review developments in the world-sheet action formulation of the generic irrational conformal field theory, including the non-linear and the linearized forms of the action. These systems form a large class of spin-two gauged WZW actions which exhibit exotic gravitational couplings. Integrating out the gravitational field, we also speculate on a connection with sigma models.

Linear dispersion relation for the mirror instability in context of the gyrokinetic theory

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

Porazik, Peter; Johnson, Jay R.

2013-10-15

The linear dispersion relation for the mirror instability is discussed in context of the gyrokinetic theory. The objective is to provide a coherent view of different kinetic approaches used to derive the dispersion relation. The method based on gyrocenter phase space transformations is adopted in order to display the origin and ordering of various terms.

A minimal approach to the scattering of physical massless bosons

NASA Astrophysics Data System (ADS)

Boels, Rutger H.; Luo, Hui

2018-05-01

Tree and loop level scattering amplitudes which involve physical massless bosons are derived directly from physical constraints such as locality, symmetry and unitarity, bypassing path integral constructions. Amplitudes can be projected onto a minimal basis of kinematic factors through linear algebra, by employing four dimensional spinor helicity methods or at its most general using projection techniques. The linear algebra analysis is closely related to amplitude relations, especially the Bern-Carrasco-Johansson relations for gluon amplitudes and the Kawai-Lewellen-Tye relations between gluons and graviton amplitudes. Projection techniques are known to reduce the computation of loop amplitudes with spinning particles to scalar integrals. Unitarity, locality and integration-by-parts identities can then be used to fix complete tree and loop amplitudes efficiently. The loop amplitudes follow algorithmically from the trees. A number of proof-of-concept examples are presented. These include the planar four point two-loop amplitude in pure Yang-Mills theory as well as a range of one loop amplitudes with internal and external scalars, gluons and gravitons. Several interesting features of the results are highlighted, such as the vanishing of certain basis coefficients for gluon and graviton amplitudes. Effective field theories are naturally and efficiently included into the framework. Dimensional regularisation is employed throughout; different regularisation schemes are worked out explicitly. The presented methods appear most powerful in non-supersymmetric theories in cases with relatively few legs, but with potentially many loops. For instance, in the introduced approach iterated unitarity cuts of four point amplitudes for non-supersymmetric gauge and gravity theories can be computed by matrix multiplication, generalising the so-called rung-rule of maximally supersymmetric theories. The philosophy of the approach to kinematics also leads to a technique to control colour quantum numbers of scattering amplitudes with matter, especially efficient in the adjoint and fundamental representations.

Computation of Nonlinear Hydrodynamic Loads on Floating Wind Turbines Using Fluid-Impulse Theory: Preprint

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

Kok Yan Chan, G.; Sclavounos, P. D.; Jonkman, J.

2015-04-02

A hydrodynamics computer module was developed for the evaluation of the linear and nonlinear loads on floating wind turbines using a new fluid-impulse formulation for coupling with the FAST program. The recently developed formulation allows the computation of linear and nonlinear loads on floating bodies in the time domain and avoids the computationally intensive evaluation of temporal and nonlinear free-surface problems and efficient methods are derived for its computation. The body instantaneous wetted surface is approximated by a panel mesh and the discretization of the free surface is circumvented by using the Green function. The evaluation of the nonlinear loadsmore » is based on explicit expressions derived by the fluid-impulse theory, which can be computed efficiently. Computations are presented of the linear and nonlinear loads on the MIT/NREL tension-leg platform. Comparisons were carried out with frequency-domain linear and second-order methods. Emphasis was placed on modeling accuracy of the magnitude of nonlinear low- and high-frequency wave loads in a sea state. Although fluid-impulse theory is applied to floating wind turbines in this paper, the theory is applicable to other offshore platforms as well.« less

An algorithm for the numerical solution of linear differential games

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

Polovinkin, E S; Ivanov, G E; Balashov, M V

2001-10-31

A numerical algorithm for the construction of stable Krasovskii bridges, Pontryagin alternating sets, and also of piecewise program strategies solving two-person linear differential (pursuit or evasion) games on a fixed time interval is developed on the basis of a general theory. The aim of the first player (the pursuer) is to hit a prescribed target (terminal) set by the phase vector of the control system at the prescribed time. The aim of the second player (the evader) is the opposite. A description of numerical algorithms used in the solution of differential games of the type under consideration is presented andmore » estimates of the errors resulting from the approximation of the game sets by polyhedra are presented.« less

Limited variance control in statistical low thrust guidance analysis. [stochastic algorithm for SEP comet Encke flyby mission

NASA Technical Reports Server (NTRS)

Jacobson, R. A.

1975-01-01

Difficulties arise in guiding a solar electric propulsion spacecraft due to nongravitational accelerations caused by random fluctuations in the magnitude and direction of the thrust vector. These difficulties may be handled by using a low thrust guidance law based on the linear-quadratic-Gaussian problem of stochastic control theory with a minimum terminal miss performance criterion. Explicit constraints are imposed on the variances of the control parameters, and an algorithm based on the Hilbert space extension of a parameter optimization method is presented for calculation of gains in the guidance law. The terminal navigation of a 1980 flyby mission to the comet Encke is used as an example.

Global exponential synchronization of inertial memristive neural networks with time-varying delay via nonlinear controller.

PubMed

Gong, Shuqing; Yang, Shaofu; Guo, Zhenyuan; Huang, Tingwen

2018-06-01

The paper is concerned with the synchronization problem of inertial memristive neural networks with time-varying delay. First, by choosing a proper variable substitution, inertial memristive neural networks described by second-order differential equations can be transformed into first-order differential equations. Then, a novel controller with a linear diffusive term and discontinuous sign term is designed. By using the controller, the sufficient conditions for assuring the global exponential synchronization of the derive and response neural networks are derived based on Lyapunov stability theory and some inequality techniques. Finally, several numerical simulations are provided to substantiate the effectiveness of the theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

Function projective synchronization of memristor-based Cohen-Grossberg neural networks with time-varying delays.

PubMed

Abdurahman, Abdujelil; Jiang, Haijun; Rahman, Kaysar

2015-12-01

This paper deals with the problem of function projective synchronization for a class of memristor-based Cohen-Grossberg neural networks with time-varying delays. Based on the theory of differential equations with discontinuous right-hand side, some novel criteria are obtained to realize the function projective synchronization of addressed networks by combining open loop control and linear feedback control. As some special cases, several control strategies are given to ensure the realization of complete synchronization, anti-synchronization and the stabilization of the considered memristor-based Cohen-Grossberg neural network. Finally, a numerical example and its simulations are provided to demonstrate the effectiveness of the obtained results.

Compensator improvement for multivariable control systems

NASA Technical Reports Server (NTRS)

Mitchell, J. R.; Mcdaniel, W. L., Jr.; Gresham, L. L.

1977-01-01

A theory and the associated numerical technique are developed for an iterative design improvement of the compensation for linear, time-invariant control systems with multiple inputs and multiple outputs. A strict constraint algorithm is used in obtaining a solution of the specified constraints of the control design. The result of the research effort is the multiple input, multiple output Compensator Improvement Program (CIP). The objective of the Compensator Improvement Program is to modify in an iterative manner the free parameters of the dynamic compensation matrix so that the system satisfies frequency domain specifications. In this exposition, the underlying principles of the multivariable CIP algorithm are presented and the practical utility of the program is illustrated with space vehicle related examples.

Quantum learning of classical stochastic processes: The completely positive realization problem

NASA Astrophysics Data System (ADS)

Monràs, Alex; Winter, Andreas

2016-01-01

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651-664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [M. Guţă, Phys. Rev. A 83(6), 062324 (2011); M. Guţă and N. Yamamoto, e-print arXiv:1303.3771(2013)].

Robust root clustering for linear uncertain systems using generalized Lyapunov theory

NASA Technical Reports Server (NTRS)

Yedavalli, R. K.

1993-01-01

Consideration is given to the problem of matrix root clustering in subregions of a complex plane for linear state space models with real parameter uncertainty. The nominal matrix root clustering theory of Gutman & Jury (1981) using the generalized Liapunov equation is extended to the perturbed matrix case, and bounds are derived on the perturbation to maintain root clustering inside a given region. The theory makes it possible to obtain an explicit relationship between the parameters of the root clustering region and the uncertainty range of the parameter space.

On the Stationarity of Multiple Autoregressive Approximants: Theory and Algorithms

DTIC Science & Technology

1976-08-01

a I (3.4) Hannan and Terrell (1972) consider problems of a similar nature. Efficient estimates A(1),... , A(p) , and i of A(1)... ,A(p) and...34Autoregressive model fitting for control, Ann . Inst. Statist. Math., 23, 163-180. Hannan, E. J. (1970), Multiple Time Series, New York, John Wiley...Hannan, E. J. and Terrell , R. D. (1972), "Time series regression with linear constraints, " International Economic Review, 13, 189-200. Masani, P

Reachability Analysis Applied to Space Situational Awareness

NASA Astrophysics Data System (ADS)

Holzinger, M.; Scheeres, D.

Several existing and emerging applications of Space Situational Awareness (SSA) relate directly to spacecraft Rendezvous, Proximity Operations, and Docking (RPOD) and Formation / Cluster Flight (FCF). When multiple Resident Space Ob jects (RSOs) are in vicinity of one another with appreciable periods between observations, correlating new RSO tracks to previously known objects becomes a non-trivial problem. A particularly difficult sub-problem is seen when long breaks in observations are coupled with continuous, low- thrust maneuvers. Reachability theory, directly related to optimal control theory, can compute contiguous reachability sets for known or estimated control authority and can support such RSO search and correlation efforts in both ground and on-board settings. Reachability analysis can also directly estimate the minimum control authority of a given RSO. For RPOD and FCF applications, emerging mission concepts such as fractionation drastically increase system complexity of on-board autonomous fault management systems. Reachability theory, as applied to SSA in RPOD and FCF applications, can involve correlation of nearby RSO observations, control authority estimation, and sensor track re-acquisition. Additional uses of reachability analysis are formation reconfiguration, worst-case passive safety, and propulsion failure modes such as a "stuck" thruster. Existing reachability theory is applied to RPOD and FCF regimes. An optimal control policy is developed to maximize the reachability set and optimal control law discontinuities (switching) are examined. The Clohessy-Wiltshire linearized equations of motion are normalized to accentuate relative control authority for spacecraft propulsion systems at both Low Earth Orbit (LEO) and Geostationary Earth Orbit (GEO). Several examples with traditional and low thrust propulsion systems in LEO and GEO are explored to illustrate the effects of relative control authority on the time-varying reachability set surface. Both monopropellant spacecraft at LEO and Hall thruster spacecraft at GEO are shown to be strongly actuated while Hall thruster spacecraft at LEO are found to be weakly actuated. Weaknesses with the current implementation are discussed and future numerical improvements and analytical efforts are discussed.

Realizable optimal control for a remotely piloted research vehicle. [stability augmentation

NASA Technical Reports Server (NTRS)

Dunn, H. J.

1980-01-01

The design of a control system using the linear-quadratic regulator (LQR) control law theory for time invariant systems in conjunction with an incremental gradient procedure is presented. The incremental gradient technique reduces the full-state feedback controller design, generated by the LQR algorithm, to a realizable design. With a realizable controller, the feedback gains are based only on the available system outputs instead of being based on the full-state outputs. The design is for a remotely piloted research vehicle (RPRV) stability augmentation system. The design includes methods for accounting for noisy measurements, discrete controls with zero-order-hold outputs, and computational delay errors. Results from simulation studies of the response of the RPRV to a step in the elevator and frequency analysis techniques are included to illustrate these abnormalities and their influence on the controller design.

Reconstruction of real-space linear matter power spectrum from multipoles of BOSS DR12 results

NASA Astrophysics Data System (ADS)

Lee, Seokcheon

2018-02-01

Recently, the power spectrum (PS) multipoles using the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12 (DR12) sample are analyzed [1]. The based model for the analysis is the so-called TNS quasi-linear model and the analysis provides the multipoles up to the hexadecapole [2]. Thus, one might be able to recover the real-space linear matter PS by using the combinations of multipoles to investigate the cosmology [3]. We provide the analytic form of the ratio of quadrupole (hexadecapole) to monopole moments of the quasi-linear PS including the Fingers-of-God (FoG) effect to recover the real-space PS in the linear regime. One expects that observed values of the ratios of multipoles should be consistent with those of the linear theory at large scales. Thus, we compare the ratios of multipoles of the linear theory, including the FoG effect with the measured values. From these, we recover the linear matter power spectra in real-space. These recovered power spectra are consistent with the linear matter power spectra.

Simple estimation of linear 1+1 D tsunami run-up

NASA Astrophysics Data System (ADS)

Fuentes, M.; Campos, J. A.; Riquelme, S.

2016-12-01

An analytical expression is derived concerning the linear run-up for any given initial wave generated over a sloping bathymetry. Due to the simplicity of the linear formulation, complex transformations are unnecessay, because the shoreline motion is directly obtained in terms of the initial wave. This analytical result not only supports maximum run-up invariance between linear and non-linear theories, but also the time evolution of shoreline motion and velocity. The results exhibit good agreement with the non-linear theory. The present formulation also allows computing the shoreline motion numerically from a customised initial waveform, including non-smooth functions. This is useful for numerical tests, laboratory experiments or realistic cases in which the initial disturbance might be retrieved from seismic data rather than using a theoretical model. It is also shown that the real case studied is consistent with the field observations.

Embeddings of the "New Massive Gravity"

NASA Astrophysics Data System (ADS)

Dalmazi, D.; Mendonça, E. L.

2016-07-01

Here we apply different types of embeddings of the equations of motion of the linearized "New Massive Gravity" in order to generate alternative and even higher-order (in derivatives) massive gravity theories in D=2+1. In the first part of the work we use the Weyl symmetry as a guiding principle for the embeddings. First we show that a Noether gauge embedding of the Weyl symmetry leads to a sixth-order model in derivatives with either a massive or a massless ghost, according to the chosen overall sign of the theory. On the other hand, if the Weyl symmetry is implemented by means of a Stueckelberg field we obtain a new scalar-tensor model for massive gravitons. It is ghost-free and Weyl invariant at the linearized level around Minkowski space. The model can be nonlinearly completed into a scalar field coupled to the NMG theory. The elimination of the scalar field leads to a nonlocal modification of the NMG. In the second part of the work we prove to all orders in derivatives that there is no local, ghost-free embedding of the linearized NMG equations of motion around Minkowski space when written in terms of one symmetric tensor. Regarding that point, NMG differs from the Fierz-Pauli theory, since in the latter case we can replace the Einstein-Hilbert action by specific f(R,Box R) generalizations and still keep the theory ghost-free at the linearized level.

Linear spin-2 fields in most general backgrounds

NASA Astrophysics Data System (ADS)

Bernard, Laura; Deffayet, Cédric; Schmidt-May, Angnis; von Strauss, Mikael

2016-04-01

We derive the full perturbative equations of motion for the most general background solutions in ghost-free bimetric theory in its metric formulation. Clever field redefinitions at the level of fluctuations enable us to circumvent the problem of varying a square-root matrix appearing in the theory. This greatly simplifies the expressions for the linear variation of the bimetric interaction terms. We show that these field redefinitions exist and are uniquely invertible if and only if the variation of the square-root matrix itself has a unique solution, which is a requirement for the linearized theory to be well defined. As an application of our results we examine the constraint structure of ghost-free bimetric theory at the level of linear equations of motion for the first time. We identify a scalar combination of equations which is responsible for the absence of the Boulware-Deser ghost mode in the theory. The bimetric scalar constraint is in general not manifestly covariant in its nature. However, in the massive gravity limit the constraint assumes a covariant form when one of the interaction parameters is set to zero. For that case our analysis provides an alternative and almost trivial proof of the absence of the Boulware-Deser ghost. Our findings generalize previous results in the metric formulation of massive gravity and also agree with studies of its vielbein version.

Magnetic Actuators and Suspension for Space Vibration Control

NASA Technical Reports Server (NTRS)

Knospe, Carl R.; Allaire, Paul E.; Lewis, David W.

1993-01-01

The research on microgravity vibration isolation performed at the University of Virginia is summarized. This research on microgravity vibration isolation was focused in three areas: (1) the development of new actuators for use in microgravity isolation; (2) the design of controllers for multiple-degree-of-freedom active isolation; and (3) the construction of a single-degree-of-freedom test rig with umbilicals. Described are the design and testing of a large stroke linear actuator; the conceptual design and analysis of a redundant coarse-fine six-degree-of-freedom actuator; an investigation of the control issues of active microgravity isolation; a methodology for the design of multiple-degree-of-freedom isolation control systems using modern control theory; and the design and testing of a single-degree-of-freedom test rig with umbilicals.

Cooperative path following control of multiple nonholonomic mobile robots.

PubMed

Cao, Ke-Cai; Jiang, Bin; Yue, Dong

2017-11-01

Cooperative path following control problem of multiple nonholonomic mobile robots has been considered in this paper. Based on the framework of decomposition, the cooperative path following problem has been transformed into path following problem and cooperative control problem; Then cascaded theory of non-autonomous system has been employed in the design of controllers without resorting to feedback linearization. One time-varying coordinate transformation based on dilation has been introduced to solve the uncontrollable problem of nonholonomic robots when the whole group's reference converges to stationary point. Cooperative path following controllers for nonholonomic robots have been proposed under persistent reference or reference target that converges to stationary point respectively. Simulation results using Matlab have illustrated the effectiveness of the obtained theoretical results. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

A comparison of Theory of Planned Behavior beliefs and healthy eating between couples without children and first-time parents.

PubMed

Bassett-Gunter, Rebecca L; Levy-Milne, Ryna; Naylor, Patti Jean; Symons Downs, Danielle; Benoit, Cecilia; Warburton, Darren E R; Blanchard, Chris M; Rhodes, Ryan E

2015-01-01

To examine the relationship between Theory of Planned Behavior (TPB) beliefs and eating behavior, explore which beliefs have the greatest association with eating behavior, and explore differences between adults without children and first-time parents. Longitudinal evaluation via questionnaires and food records at baseline and 6 and 12 months. Couples without children (n = 72) and first-time parents (n = 100). fruit and vegetable consumption and fat consumption. TPB beliefs. Pearson correlations between TPB beliefs and eating behavior; exploratory data reduction via linear regression. Control beliefs were associated with eating behavior (r = .26-.46; P < .05). After controlling for past behavior, control beliefs were associated with eating behavior for first-time parents only. Control beliefs regarding preparation and time had the strongest associations with fruit and vegetable consumption for mothers (β = .26; P < .05) and fathers (β = .38; P < .01). The absence of a ceiling effect for control beliefs suggests room for improvement via intervention. Interventions guided by TPB should target control beliefs to enhance healthy eating among new parents. Strategies (eg, individual, environmental, policy) to enhance control beliefs regarding healthy eating despite limited time and opportunity for preparation may be particularly valuable. Copyright © 2015 Society for Nutrition Education and Behavior. Published by Elsevier Inc. All rights reserved.

Robust synergetic control design under inputs and states constraints

NASA Astrophysics Data System (ADS)

Rastegar, Saeid; Araújo, Rui; Sadati, Jalil

2018-03-01

In this paper, a novel robust-constrained control methodology for discrete-time linear parameter-varying (DT-LPV) systems is proposed based on a synergetic control theory (SCT) approach. It is shown that in DT-LPV systems without uncertainty, and for any unmeasured bounded additive disturbance, the proposed controller accomplishes the goal of stabilising the system by asymptotically driving the error of the controlled variable to a bounded set containing the origin and then maintaining it there. Moreover, given an uncertain DT-LPV system jointly subject to unmeasured and constrained additive disturbances, and constraints in states, input commands and reference signals (set points), then invariant set theory is used to find an appropriate polyhedral robust invariant region in which the proposed control framework is guaranteed to robustly stabilise the closed-loop system. Furthermore, this is achieved even for the case of varying non-zero control set points in such uncertain DT-LPV systems. The controller is characterised to have a simple structure leading to an easy implementation, and a non-complex design process. The effectiveness of the proposed method and the implications of the controller design on feasibility and closed-loop performance are demonstrated through application examples on the temperature control on a continuous-stirred tank reactor plant, on the control of a real-coupled DC motor plant, and on an open-loop unstable system example.

An improved understanding of the natural resonances of moonpools contained within floating rigid-bodies: Theory and application to oscillating water column devices

DOE PAGES

Bull, Diana L.

2015-09-23

The fundamental interactions between waves, a floating rigid-body, and a moonpool that is selectively open to atmosphere or enclosed to purposefully induce pressure fluctuations are investigated. The moonpool hydrodynamic characteristics and the hydrodynamic coupling to the rigid-body are derived implicitly through reciprocity relations on an array of field points. By modeling the free surface of the moonpool in this manner, an explicit hydrodynamic coupling term is included in the equations of motion. This coupling results in the migration of the moonpool's natural resonance frequency from the piston frequency to a new frequency when enclosed in a floating rigid-body. Two geometriesmore » that highlight distinct aspects of marine vessels and oscillating water column (OWC) renewable energy devices are analyzed to reveal the coupled natural resonance migration. The power performance of these two OWCs in regular waves is also investigated. The air chamber is enclosed and a three-dimensional, linear, frequency domain performance model that links the rigid-body to the moonpool through a linear resistive control strategy is detailed. Furthermore, an analytic expression for the optimal linear resistive control values in regular waves is presented.« less

An improved understanding of the natural resonances of moonpools contained within floating rigid-bodies: Theory and application to oscillating water column devices

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

Bull, Diana L.

The fundamental interactions between waves, a floating rigid-body, and a moonpool that is selectively open to atmosphere or enclosed to purposefully induce pressure fluctuations are investigated. The moonpool hydrodynamic characteristics and the hydrodynamic coupling to the rigid-body are derived implicitly through reciprocity relations on an array of field points. By modeling the free surface of the moonpool in this manner, an explicit hydrodynamic coupling term is included in the equations of motion. This coupling results in the migration of the moonpool's natural resonance frequency from the piston frequency to a new frequency when enclosed in a floating rigid-body. Two geometriesmore » that highlight distinct aspects of marine vessels and oscillating water column (OWC) renewable energy devices are analyzed to reveal the coupled natural resonance migration. The power performance of these two OWCs in regular waves is also investigated. The air chamber is enclosed and a three-dimensional, linear, frequency domain performance model that links the rigid-body to the moonpool through a linear resistive control strategy is detailed. Furthermore, an analytic expression for the optimal linear resistive control values in regular waves is presented.« less

Predictors of Nurses’ Intention and Behavior in Using Health Literacy Strategies in Patient Education Based on the Theory of Planned Behavior

PubMed Central

Sharifirad, Gholamreza; Mostafavi, Firoozeh; Reisi, Mahnouush; Mahaki, Behzad; Javadzade, Homamodin; Heydarabadi, Akbar Babaei; Esfahani, Mahmoud Nasr

2015-01-01

Background: Health literacy is one of the most important priorities for improving health care quality through enhancing patient-provider communication. Implementing health literacy strategies enable nurses to provide information and instructions for patients in a manner that is more commensurate and understandable. The purpose of this study was to investigate the factors affecting nurses’ intention to implement health literacy strategies in patient education based on theory of planned behavior. Methods: A cross-sectional study was done on 148 nurse practitioners of AL-Zahra educational hospital in Isfahan, Iran, using a descriptive-analytic method. Data collected via a standardized questionnaire based on theory of planned behavior constructed and analyzed by SPSS v.17 using ANOVA, Independent T-test, Pearson correlation and linear regression. Results: There was statistically significant correlation between using health literacy strategies and marriage status, attending in retraining courses, employment type, job history, and job status. Perceived behavioral control was the most powerful predictor of intention (β=0.417) and use health literacy strategies in patient education and behavior of nurses (β=0.33). Conclusion: According to the findings of this study, perceived behavioral control is a powerful determinant of nurses’ intention and behavior of using health literacy strategies in patient education. Hence we recommend nurse educators to pay special attention to the constructs of this theory mainly perceived behavioral control in retrain courses about patient education and health literacy strategies. PMID:25945078

An analysis of hypercritical states in elastic and inelastic systems

NASA Astrophysics Data System (ADS)

Kowalczk, Maciej

The author raises a wide range of problems whose common characteristic is an analysis of hypercritical states in elastic and inelastic systems. the article consists of two basic parts. The first part primarily discusses problems of modelling hypercritical states, while the second analyzes numerical methods (so-called continuation methods) used to solve non-linear problems. The original approaches for modelling hypercritical states found in this article include the combination of plasticity theory and an energy condition for cracking, accounting for the variability and cyclical nature of the forms of fracture of a brittle material under a die, and the combination of plasticity theory and a simplified description of the phenomenon of localization along a discontinuity line. The author presents analytical solutions of three non-linear problems for systems made of elastic/brittle/plastic and elastic/ideally plastic materials. The author proceeds to discuss the analytical basics of continuation methods and analyzes the significance of the parameterization of non-linear problems, provides a method for selecting control parameters based on an analysis of the rank of a rectangular matrix of a uniform system of increment equations, and also provides a new method for selecting an equilibrium path originating from a bifurcation point. The author provides a general outline of continuation methods based on an analysis of the rank of a matrix of a corrective system of equations. The author supplements his theoretical solutions with numerical solutions of non-linear problems for rod systems and problems of the plastic disintegration of a notched rectangular plastic plate.

Frequency domain system identification of helicopter rotor dynamics incorporating models with time periodic coefficients

NASA Astrophysics Data System (ADS)

Hwang, Sunghwan

1997-08-01

One of the most prominent features of helicopter rotor dynamics in forward flight is the periodic coefficients in the equations of motion introduced by the rotor rotation. The frequency response characteristics of such a linear time periodic system exhibits sideband behavior, which is not the case for linear time invariant systems. Therefore, a frequency domain identification methodology for linear systems with time periodic coefficients was developed, because the linear time invariant theory cannot account for sideband behavior. The modulated complex Fourier series was introduced to eliminate the smearing effect of Fourier series expansions of exponentially modulated periodic signals. A system identification theory was then developed using modulated complex Fourier series expansion. Correlation and spectral density functions were derived using the modulated complex Fourier series expansion for linear time periodic systems. Expressions of the identified harmonic transfer function were then formulated using the spectral density functions both with and without additive noise processes at input and/or output. A procedure was developed to identify parameters of a model to match the frequency response characteristics between measured and estimated harmonic transfer functions by minimizing an objective function defined in terms of the trace of the squared frequency response error matrix. Feasibility was demonstrated by the identification of the harmonic transfer function and parameters for helicopter rigid blade flapping dynamics in forward flight. This technique is envisioned to satisfy the needs of system identification in the rotating frame, especially in the context of individual blade control. The technique was applied to the coupled flap-lag-inflow dynamics of a rigid blade excited by an active pitch link. The linear time periodic technique results were compared with the linear time invariant technique results. Also, the effect of noise processes and initial parameter guess on the identification procedure were investigated. To study the effect of elastic modes, a rigid blade with a trailing edge flap excited by a smart actuator was selected and system parameters were successfully identified, but with some expense of computational storage and time. Conclusively, the linear time periodic technique substantially improved the identified parameter accuracy compared to the linear time invariant technique. Also, the linear time periodic technique was robust to noises and initial guess of parameters. However, an elastic mode of higher frequency relative to the system pumping frequency tends to increase the computer storage requirement and computing time.

Active control of acoustic pressure fields using smart material technologies

NASA Technical Reports Server (NTRS)

Banks, H. T.; Smith, R. C.

1993-01-01

An overview describing the use of piezoceramic patches in reducing noise in a structural acoustics setting is presented. The passive and active contributions due to patches which are bonded to an Euler-Bernoulli beam or thin shell are briefly discussed and the results are incorporated into a 2-D structural acoustics model. In this model, an exterior noise source causes structural vibrations which in turn lead to interior noise as a result of nonlinear fluid/structure coupling mechanism. Interior sound pressure levels are reduced via patches bonded to the flexible boundary (a beam in this case) which generate pure bending moments when an out-of-phase voltage is applied. Well-posedness results for the infinite dimensional system are discussed and a Galerkin scheme for approximating the system dynamics is outlined. Control is implemented by using linear quadratic regulator (LQR) optimal control theory to calculate gains for the linearized system and then feeding these gains back into the nonlinear system of interest. The effectiveness of this strategy for this problem is illustrated in an example.

Closed-form solutions for linear regulator design of mechanical systems including optimal weighting matrix selection

NASA Technical Reports Server (NTRS)

Hanks, Brantley R.; Skelton, Robert E.

1991-01-01

Vibration in modern structural and mechanical systems can be reduced in amplitude by increasing stiffness, redistributing stiffness and mass, and/or adding damping if design techniques are available to do so. Linear Quadratic Regulator (LQR) theory in modern multivariable control design, attacks the general dissipative elastic system design problem in a global formulation. The optimal design, however, allows electronic connections and phase relations which are not physically practical or possible in passive structural-mechanical devices. The restriction of LQR solutions (to the Algebraic Riccati Equation) to design spaces which can be implemented as passive structural members and/or dampers is addressed. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical system. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist.

State and actuator fault estimation observer design integrated in a riderless bicycle stabilization system.

PubMed

Brizuela Mendoza, Jorge Aurelio; Astorga Zaragoza, Carlos Manuel; Zavala Río, Arturo; Pattalochi, Leo; Canales Abarca, Francisco

2016-03-01

This paper deals with an observer design for Linear Parameter Varying (LPV) systems with high-order time-varying parameter dependency. The proposed design, considered as the main contribution of this paper, corresponds to an observer for the estimation of the actuator fault and the system state, considering measurement noise at the system outputs. The observer gains are computed by considering the extension of linear systems theory to polynomial LPV systems, in such a way that the observer reaches the characteristics of LPV systems. As a result, the actuator fault estimation is ready to be used in a Fault Tolerant Control scheme, where the estimated state with reduced noise should be used to generate the control law. The effectiveness of the proposed methodology has been tested using a riderless bicycle model with dependency on the translational velocity v, where the control objective corresponds to the system stabilization towards the upright position despite the variation of v along the closed-loop system trajectories. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.

PubMed

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.

Investigating parameters participating in the infant respiratory control system attractor.

PubMed

Terrill, Philip I; Wilson, Stephen J; Suresh, Sadasivam; Cooper, David M; Dakin, Carolyn

2008-01-01

Theoretically, any participating parameter in a non-linear system represents the dynamics of the whole system. Taken's time delay embedding theory provides the fundamental basis for allowing non-linear analysis to be performed on physiological, time-series data. In practice, only one measurable parameter is required to be measured to convey an accurate representation of the system dynamics. In this paper, the infant respiratory control system is represented using three variables-a digitally sampled respiratory inductive plethysmography waveform, and the derived parameters tidal volume and inter-breath interval time series data. For 14 healthy infants, these data streams were analysed using recurrence plot analysis across one night of sleep. The measured attractor size of these variables followed the same qualitative trends across the nights study. Results suggest that the attractor size measures of the derived IBI and tidal volume are representative surrogates for the raw respiratory waveform. The extent to which the relative attractor sizes of IBI and tidal volume remain constant through changing sleep state could potentially be used to quantify pathology, or maturation of breathing control.

Guidance and Control strategies for aerospace vehicles

NASA Technical Reports Server (NTRS)

Hibey, J. L.; Naidu, D. S.; Charalambous, C. D.

1989-01-01

A neighboring optimal guidance scheme was devised for a nonlinear dynamic system with stochastic inputs and perfect measurements as applicable to fuel optimal control of an aeroassisted orbital transfer vehicle. For the deterministic nonlinear dynamic system describing the atmospheric maneuver, a nominal trajectory was determined. Then, a neighboring, optimal guidance scheme was obtained for open loop and closed loop control configurations. Taking modelling uncertainties into account, a linear, stochastic, neighboring optimal guidance scheme was devised. Finally, the optimal trajectory was approximated as the sum of the deterministic nominal trajectory and the stochastic neighboring optimal solution. Numerical results are presented for a typical vehicle. A fuel-optimal control problem in aeroassisted noncoplanar orbital transfer is also addressed. The equations of motion for the atmospheric maneuver are nonlinear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighboring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in reference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditions.

Survey and analysis of research on supersonic drag-due-to-lift minimization with recommendations for wing design

NASA Technical Reports Server (NTRS)

Carlson, Harry W.; Mann, Michael J.

1992-01-01

A survey of research on drag-due-to-lift minimization at supersonic speeds, including a study of the effectiveness of current design and analysis methods was conducted. The results show that a linearized theory analysis with estimated attainable thrust and vortex force effects can predict with reasonable accuracy the lifting efficiency of flat wings. Significantly better wing performance can be achieved through the use of twist and camber. Although linearized theory methods tend to overestimate the amount of twist and camber required for a given application and provide an overly optimistic performance prediction, these deficiencies can be overcome by implementation of recently developed empirical corrections. Numerous examples of the correlation of experiment and theory are presented to demonstrate the applicability and limitations of linearized theory methods with and without empirical corrections. The use of an Euler code for the estimation of aerodynamic characteristics of a twisted and cambered wing and its application to design by iteration are discussed.

Magnetic field power density spectra during 'scatter-free' solar particle events

NASA Technical Reports Server (NTRS)

Tan, L. C.; Mason, G. M.

1993-01-01

We have examined interplanetary magnetic field power spectral density during four previously identified 3He-rich flare periods when the about 1 MeV nucleon-1 particles exhibited nearly scatter-free transport from the sun to 1 AU. Since the scattering mean free path A was large, it might be expected that interplanetary turbulence was low, yet the spectral density value was low only for one of the four periods. For the other three, however, the spectral index q of the power density spectrum was near 2.0, a value at which quasi-linear theories predict an increase in the scattering mean free path. Comparing the lambda values from the energetic particles with that computed from a recent quasi-linear theory which includes helicity and the propagation direction of waves, we find lambda(QLT)/lambda(SEP) = 0.08 +/- 0.03 for the four events. Thus, the theory fits the q-dependence of lambda; however, as found for previous quasi-linear theories, the absolute value is low.

Quantum corrections for the cubic Galileon in the covariant language

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

Saltas, Ippocratis D.; Vitagliano, Vincenzo, E-mail: isaltas@fc.ul.pt, E-mail: vincenzo.vitagliano@ist.utl.pt

We present for the first time an explicit exposition of quantum corrections within the cubic Galileon theory including the effect of quantum gravity, in a background- and gauge-invariant manner, employing the field-reparametrisation approach of the covariant effective action at 1-loop. We show that the consideration of gravitational effects in combination with the non-linear derivative structure of the theory reveals new interactions at the perturbative level, which manifest themselves as higher-operators in the associated effective action, which' relevance is controlled by appropriate ratios of the cosmological vacuum and the Galileon mass scale. The significance and concept of the covariant approach inmore » this context is discussed, while all calculations are explicitly presented.« less

Finite state modeling of aeroelastic systems

NASA Technical Reports Server (NTRS)

Vepa, R.

1977-01-01

A general theory of finite state modeling of aerodynamic loads on thin airfoils and lifting surfaces performing completely arbitrary, small, time-dependent motions in an airstream is developed and presented. The nature of the behavior of the unsteady airloads in the frequency domain is explained, using as raw materials any of the unsteady linearized theories that have been mechanized for simple harmonic oscillations. Each desired aerodynamic transfer function is approximated by means of an appropriate Pade approximant, that is, a rational function of finite degree polynomials in the Laplace transform variable. The modeling technique is applied to several two dimensional and three dimensional airfoils. Circular, elliptic, rectangular and tapered planforms are considered as examples. Identical functions are also obtained for control surfaces for two and three dimensional airfoils.

A formation control strategy with coupling weights for the multi-robot system

NASA Astrophysics Data System (ADS)

Liang, Xudong; Wang, Siming; Li, Weijie

2017-12-01

The distributed formation problem of the multi-robot system with general linear dynamic characteristics and directed communication topology is discussed. In order to avoid that the multi-robot system can not maintain the desired formation in the complex communication environment, the distributed cooperative algorithm with coupling weights based on zipf distribution is designed. The asymptotic stability condition for the formation of the multi-robot system is given, and the theory of the graph and the Lyapunov theory are used to prove that the formation can converge to the desired geometry formation and the desired motion rules of the virtual leader under this condition. Nontrivial simulations are performed to validate the effectiveness of the distributed cooperative algorithm with coupling weights.

Enhancing vehicle cornering limit through sideslip and yaw rate control

NASA Astrophysics Data System (ADS)

Lu, Qian; Gentile, Pierangelo; Tota, Antonio; Sorniotti, Aldo; Gruber, Patrick; Costamagna, Fabio; De Smet, Jasper

2016-06-01

Fully electric vehicles with individually controlled drivetrains can provide a high degree of drivability and vehicle safety, all while increasing the cornering limit and the 'fun-to-drive' aspect. This paper investigates a new approach on how sideslip control can be integrated into a continuously active yaw rate controller to extend the limit of stable vehicle cornering and to allow sustained high values of sideslip angle. The controllability-related limitations of integrated yaw rate and sideslip control, together with its potential benefits, are discussed through the tools of multi-variable feedback control theory and non-linear phase-plane analysis. Two examples of integrated yaw rate and sideslip control systems are presented and their effectiveness is experimentally evaluated and demonstrated on a four-wheel-drive fully electric vehicle prototype. Results show that the integrated control system allows safe operation at the vehicle cornering limit at a specified sideslip angle independent of the tire-road friction conditions.

The elastic theory of shells using geometric algebra

PubMed Central

Lasenby, J.; Agarwal, A.

2017-01-01

We present a novel derivation of the elastic theory of shells. We use the language of geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools to express equations in an arbitrary coordinate system, which enhances their usefulness. The role of moments and angular velocity, and the apparent use by previous authors of an unphysical angular velocity, has been clarified through the use of a bivector representation. In the linearized theory, clarification of previous coordinate conventions which have been the cause of confusion is provided, and the introduction of prior strain into the linearized theory of shells is made possible. PMID:28405404

New infinite-dimensional hidden symmetries for heterotic string theory

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

Gao Yajun

The symmetry structures of two-dimensional heterotic string theory are studied further. A (2d+n)x(2d+n) matrix complex H-potential is constructed and the field equations are extended into a complex matrix formulation. A pair of Hauser-Ernst-type linear systems are established. Based on these linear systems, explicit formulations of new hidden symmetry transformations for the considered theory are given and then these symmetry transformations are verified to constitute infinite-dimensional Lie algebras: the semidirect product of the Kac-Moody o(d,d+n-circumflex) and Virasoro algebras (without center charges). These results demonstrate that the heterotic string theory under consideration possesses more and richer symmetry structures than previously expected.

The elastic theory of shells using geometric algebra.

PubMed

Gregory, A L; Lasenby, J; Agarwal, A

2017-03-01

We present a novel derivation of the elastic theory of shells. We use the language of geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools to express equations in an arbitrary coordinate system, which enhances their usefulness. The role of moments and angular velocity, and the apparent use by previous authors of an unphysical angular velocity, has been clarified through the use of a bivector representation. In the linearized theory, clarification of previous coordinate conventions which have been the cause of confusion is provided, and the introduction of prior strain into the linearized theory of shells is made possible.

Lyapunov stability and its application to systems of ordinary differential equations

NASA Technical Reports Server (NTRS)

Kennedy, E. W.

1979-01-01

An outline and a brief introduction to some of the concepts and implications of Lyapunov stability theory are presented. Various aspects of the theory are illustrated by the inclusion of eight examples, including the Cartesian coordinate equations of the two-body problem, linear and nonlinear (Van der Pol's equation) oscillatory systems, and the linearized Kustaanheimo-Stiefel element equations for the unperturbed two-body problem.

Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem

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

Pribram-Jones, Aurora; Grabowski, Paul E.; Burke, Kieron

We present that the van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. Finally, this produces a natural method for generating new thermal exchange-correlation approximations.

Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem

DOE PAGES

Pribram-Jones, Aurora; Grabowski, Paul E.; Burke, Kieron

2016-06-08

We present that the van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. Finally, this produces a natural method for generating new thermal exchange-correlation approximations.

A system for aerodynamic design and analysis of supersonic aircraft. Part 4: Test cases

NASA Technical Reports Server (NTRS)

Middleton, W. D.; Lundry, J. L.

1980-01-01

An integrated system of computer programs was developed for the design and analysis of supersonic configurations. The system uses linearized theory methods for the calculation of surface pressures and supersonic area rule concepts in combination with linearized theory for calculation of aerodynamic force coefficients. Interactive graphics are optional at the user's request. Representative test cases and associated program output are presented.

Cosmic ray diffusion: Report of the Workshop in Cosmic Ray Diffusion Theory

NASA Technical Reports Server (NTRS)

Birmingham, T. J.; Jones, F. C.

1975-01-01

A workshop in cosmic ray diffusion theory was held at Goddard Space Flight Center on May 16-17, 1974. Topics discussed and summarized are: (1) cosmic ray measurements as related to diffusion theory; (2) quasi-linear theory, nonlinear theory, and computer simulation of cosmic ray pitch-angle diffusion; and (3) magnetic field fluctuation measurements as related to diffusion theory.

Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows

NASA Astrophysics Data System (ADS)

Schmidt, Patrick; Ó Náraigh, Lennon; Lucquiaud, Mathieu; Valluri, Prashant

2016-04-01

We consider the genesis and dynamics of interfacial instability in vertical gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream. To make contact with existing studies in the literature, the effect of various density contrasts is also examined. Energy budget analyses based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low density contrast. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. Direct numerical simulations of the same system (low density contrast) show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts, corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. The same linear stability theory predicts when the direction of travel of the waves changes — from downwards to upwards. We outline the practical implications of this change in terms of loading and flooding. The change in direction of the wave propagation is represented graphically in terms of a flow map based on the liquid and gas flow rates and the prediction carries over to the nonlinear regime with only a small deviation.

Universal Linear Scaling of Permeability and Time for Heterogeneous Fracture Dissolution

NASA Astrophysics Data System (ADS)

Wang, L.; Cardenas, M. B.

2017-12-01

Fractures are dynamically changing over geological time scale due to mechanical deformation and chemical reactions. However, the latter mechanism remains poorly understood with respect to the expanding fracture, which leads to a positively coupled flow and reactive transport processes, i.e., as a fracture expands, so does its permeability (k) and thus flow and reactive transport processes. To unravel this coupling, we consider a self-enhancing process that leads to fracture expansion caused by acidic fluid, i.e., CO2-saturated brine dissolving calcite fracture. We rigorously derive a theory, for the first time, showing that fracture permeability increases linearly with time [Wang and Cardenas, 2017]. To validate this theory, we resort to the direct simulation that solves the Navier-Stokes and Advection-Diffusion equations with a moving mesh according to the dynamic dissolution process in two-dimensional (2D) fractures. We find that k slowly increases first until the dissolution front breakthrough the outbound when we observe a rapid k increase, i.e., the linear time-dependence of k occurs. The theory agrees well with numerical observations across a broad range of Peclet and Damkohler numbers through homogeneous and heterogeneous 2D fractures. Moreover, the theory of linear scaling relationship between k and time matches well with experimental observations of three-dimensional (3D) fractures' dissolution. To further attest to our theory's universality for 3D heterogeneous fractures across a broad range of roughness and correlation length of aperture field, we develop a depth-averaged model that simulates the process-based reactive transport. The simulation results show that, regardless of a wide variety of dissolution patterns such as the presence of dissolution fingers and preferential dissolution paths, the linear scaling relationship between k and time holds. Our theory sheds light on predicting permeability evolution in many geological settings when the self-enhancing process is relevant. References: Wang, L., and M. B. Cardenas (2017), Linear permeability evolution of expanding conduits due to feedback between flow and fast phase change, Geophys. Res. Lett., 44(9), 4116-4123, doi: 10.1002/2017gl073161.

Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows

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

Schmidt, Patrick; Lucquiaud, Mathieu; Valluri, Prashant, E-mail: prashant.valluri@ed.ac.uk

We consider the genesis and dynamics of interfacial instability in vertical gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream. To make contact with existing studies in the literature, the effect of various density contrasts is also examined. Energy budget analysesmore » based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low density contrast. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. Direct numerical simulations of the same system (low density contrast) show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts, corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. The same linear stability theory predicts when the direction of travel of the waves changes — from downwards to upwards. We outline the practical implications of this change in terms of loading and flooding. The change in direction of the wave propagation is represented graphically in terms of a flow map based on the liquid and gas flow rates and the prediction carries over to the nonlinear regime with only a small deviation.« less