Stability with large step sizes for multistep discretizations of stiff ordinary differential equations

NASA Technical Reports Server (NTRS)

Majda, George

1986-01-01

One-leg and multistep discretizations of variable-coefficient linear systems of ODEs having both slow and fast time scales are investigated analytically. The stability properties of these discretizations are obtained independent of ODE stiffness and compared. The results of numerical computations are presented in tables, and it is shown that for large step sizes the stability of one-leg methods is better than that of the corresponding linear multistep methods.

Theoretical considerations of some nonlinear aspects of hypersonic panel flutter

NASA Technical Reports Server (NTRS)

Mcintosh, S. C., Jr.

1974-01-01

A research project to analyze the effects of hypersonic nonlinear aerodynamic loading on panel flutter is reported. The test equipment and procedures for conducting the tests are explained. The effects of aerodynamic linearities on stability were evaluated by determining constant-initial-energy amplitude-sensitive stability boundaries and comparing them with the corresponding linear stability boundaries. An attempt to develop an alternative method of analysis for systems where amplitude-sensitive instability is possible is presented.

Control method for physical systems and devices

DOEpatents

Guckenheimer, John

1997-01-01

A control method for stabilizing systems or devices that are outside the control domain of a linear controller is provided. When applied to nonlinear systems, the effectiveness of this method depends upon the size of the domain of stability that is produced for the stabilized equilibrium. If this domain is small compared to the accuracy of measurements or the size of disturbances within the system, then the linear controller is likely to fail within a short period. Failure of the system or device can be catastrophic: the system or device can wander far from the desired equilibrium. The method of the invention presents a general procedure to recapture the stability of a linear controller, when the trajectory of a system or device leaves its region of stability. By using a hybrid strategy based upon discrete switching events within the state space of the system or device, the system or device will return from a much larger domain to the region of stability utilized by the linear controller. The control procedure is robust and remains effective under large classes of perturbations of a given underlying system or device.

Multiple origins of linear dunes on Earth and Titan

USGS Publications Warehouse

Rubin, David M.; Hesp, Patrick A.

2009-01-01

Dunes with relatively long and parallel crests are classified as linear dunes. On Earth, they form in at least two environmental settings: where winds of bimodal direction blow across loose sand, and also where single-direction winds blow over sediment that is locally stabilized, be it through vegetation, sediment cohesion or topographic shelter from the winds. Linear dunes have also been identified on Titan, where they are thought to form in loose sand. Here we present evidence that in the Qaidam Basin, China, linear dunes are found downwind of transverse dunes owing to higher cohesiveness in the downwind sediments, which contain larger amounts of salt and mud. We also present a compilation of other settings where sediment stabilization has been reported to produce linear dunes. We suggest that in this dune-forming process, loose sediment accumulates on the dunes and is stabilized; the stable dune then functions as a topographic shelter, which induces the deposition of sediments downwind. We conclude that a model in which Titan's dunes formed similarly in cohesive sediments cannot be ruled out by the existing data.

Stability margin of linear systems with parameters described by fuzzy numbers.

PubMed

Husek, Petr

2011-10-01

This paper deals with the linear systems with uncertain parameters described by fuzzy numbers. The problem of determining the stability margin of those systems with linear affine dependence of the coefficients of a characteristic polynomial on system parameters is studied. Fuzzy numbers describing the system parameters are allowed to be characterized by arbitrary nonsymmetric membership functions. An elegant solution, graphical in nature, based on generalization of the Tsypkin-Polyak plot is presented. The advantage of the presented approach over the classical robust concept is demonstrated on a control of the Fiat Dedra engine model and a control of the quarter car suspension model.

Robust Stabilization of Uncertain Systems Based on Energy Dissipation Concepts

NASA Technical Reports Server (NTRS)

Gupta, Sandeep

1996-01-01

Robust stability conditions obtained through generalization of the notion of energy dissipation in physical systems are discussed in this report. Linear time-invariant (LTI) systems which dissipate energy corresponding to quadratic power functions are characterized in the time-domain and the frequency-domain, in terms of linear matrix inequalities (LMls) and algebraic Riccati equations (ARE's). A novel characterization of strictly dissipative LTI systems is introduced in this report. Sufficient conditions in terms of dissipativity and strict dissipativity are presented for (1) stability of the feedback interconnection of dissipative LTI systems, (2) stability of dissipative LTI systems with memoryless feedback nonlinearities, and (3) quadratic stability of uncertain linear systems. It is demonstrated that the framework of dissipative LTI systems investigated in this report unifies and extends small gain, passivity, and sector conditions for stability. Techniques for selecting power functions for characterization of uncertain plants and robust controller synthesis based on these stability results are introduced. A spring-mass-damper example is used to illustrate the application of these methods for robust controller synthesis.

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.

Local projection stabilization for linearized Brinkman-Forchheimer-Darcy equation

NASA Astrophysics Data System (ADS)

Skrzypacz, Piotr

2017-09-01

The Local Projection Stabilization (LPS) is presented for the linearized Brinkman-Forchheimer-Darcy equation with high Reynolds numbers. The considered equation can be used to model porous medium flows in chemical reactors of packed bed type. The detailed finite element analysis is presented for the case of nonconstant porosity. The enriched variant of LPS is based on the equal order interpolation for the velocity and pressure. The optimal error bounds for the velocity and pressure errors are justified numerically.

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.

Analytic theory for the determination of velocity and stability of bubbles in a Hele-Shaw cell. I - Velocity selection. II - Stability

NASA Technical Reports Server (NTRS)

Tanveer, S.

1989-01-01

An asymptotic theory is presented for the determination of velocity and linear stability of a steady symmetric bubble in a Hele-Shaw cell for small surface tension. First the bubble velocity relative to the fluid velocity at infinity is determined for small surface tension by means of a transcendentally small correction to the asymptotic series solution. In addition, a linear stability analysis shows that only the solution branch corresponding to the largest possible bubble velocity for given surface tension is stable, while all the others are unstable.

Some Properties and Stability Results for Sector-Bounded LTI Systems

NASA Technical Reports Server (NTRS)

Gupta, Sandeep; Joshi, Suresh M.

1994-01-01

This paper presents necessary and sufficient conditions for a linear, time-invariant (LTI) system to be inside sector (n, b) in terms of linear matrix inequalities in its state-space realization matrices, which represents a generalization of similar conditions for bounded H(sub infinity)-norm systems. Further, a weaker definition of LTI systems strictly inside closed sector (a, b) is proposed, and state-space characterization of such systems is presented. Sector conditions for stability of the negative feedback interconnection of two LTI systems and for stability of LTI systems with feedback nonlinearities are investigated using the Lyapunov function approach. It is shown that the proposed weaker conditions for an LTI system to be strictly inside a sector are sufficient to establish closed-loop stability of these systems.

Prediction of trivalent actinide amino(poly)carboxylate complex stability constants using linear free energy relationships with the lanthanide series

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

Uhnak, Nic E.

Prediction of Trivalent Actinide Amino(poly)carboxylate Complex Stability Constants Using Linear Free Energy Relationships with the Lanthanide Series Alternative title: LFER Based Prediction of An(III) APC Stability Constants There is a gap in the literature regarding the complexation of amino(poly)carboxylate (APC) ligands with trivalent actinides (An(III))). The chemistry of the An(III) is nearly identical to that of the trivalent lanthanides Lns, but the An(III) express a slight enhancement when binding APC ligands. Presented in this report is a simple method of predicting the stability constants of the An(III), Pu, Am, Cm, Bk and Cf by using linear free energy relationships (LFER)more » of the An and the lanthanide (Ln) series for 91 APCs. This method produced An stability constants within uncertainty to available literature values for most ligands.« less

Squeeze-film dampers for turbomachinery stabilization

NASA Technical Reports Server (NTRS)

Mclean, L. J.; Hahn, E. J.

1984-01-01

A technique for investigating the stability and damping present in centrally preloaded radially symmetric multi-mass flexible rotor bearing systems is presented. In general, one needs to find the eigenvalues of the linearized perturbation equations, though zero frequency stability maps may be found by solving as many simultaneous non-linear equations as there are dampers; and in the case of a single damper, such maps may be found directly, regardless of the number of degrees of freedom. The technique is illustrated for a simple symmetric four degree of freedom flexible rotor with an unpressurized damper. This example shows that whereas zero frequency stability maps are likely to prove to be a simple way to delineate multiple solution possibilities, they do not provide full stability information. Further, particularly for low bearing parameters, the introduction of an unpressurized squeeze film damper may promote instability in an otherwise stable system.

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.

Nonlinearity measure and internal model control based linearization in anti-windup design

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

Perev, Kamen

2013-12-18

This paper considers the problem of internal model control based linearization in anti-windup design. The nonlinearity measure concept is used for quantifying the control system degree of nonlinearity. The linearizing effect of a modified internal model control structure is presented by comparing the nonlinearity measures of the open-loop and closed-loop systems. It is shown that the linearization properties are improved by increasing the control system local feedback gain. However, it is emphasized that at the same time the stability of the system deteriorates. The conflicting goals of stability and linearization are resolved by solving the design problem in different frequencymore » ranges.« less

Flight Stability and Control and Performance Results from the Linear Aerospike SR-71 Experiment (LASRE)

NASA Technical Reports Server (NTRS)

Moes, Timothy R.; Cobleigh, Brent R.; Cox, Timothy H.; Conners, Timothy R.; Iliff, Kenneth W.; Powers, Bruce G.

1998-01-01

The Linear Aerospike SR-71 Experiment (LASRE) is presently being conducted to test a 20-percent-scale version of the Linear Aerospike rocket engine. This rocket engine has been chosen to power the X-33 Single Stage to Orbit Technology Demonstrator Vehicle. The rocket engine was integrated into a lifting body configuration and mounted to the upper surface of an SR-71 aircraft. This paper presents stability and control results and performance results from the envelope expansion flight tests of the LASRE configuration up to Mach 1.8 and compares the results with wind tunnel predictions. Longitudinal stability and elevator control effectiveness were well-predicted from wind tunnel tests. Zero-lift pitching moment was mispredicted transonically. Directional stability, dihedral stability, and rudder effectiveness were overpredicted. The SR-71 handling qualities were never significantly impacted as a result of the missed predictions. Performance results confirmed the large amount of wind-tunnel-predicted transonic drag for the LASRE configuration. This drag increase made the performance of the vehicle so poor that acceleration through transonic Mach numbers could not be achieved on a hot day without depleting the available fuel.

Nonlinear Stability and Saturation of Ballooning Modes in Tokamaks*

NASA Astrophysics Data System (ADS)

Ham, C. J.; Cowley, S. C.; Brochard, G.; Wilson, H. R.

2016-06-01

The theory of tokamak stability to nonlinear "ballooning" displacements of elliptical magnetic flux tubes is presented. Above a critical pressure profile the energy stored in the plasma may be lowered by finite (but not infinitesimal) displacements of such tubes (metastability). Above a higher pressure profile, the linear stability boundary, such tubes are linearly and nonlinearly unstable. The predicted saturated flux tube displacement can be of the order of the pressure gradient scale length. Plasma transport from these displaced flux tubes may explain the rapid loss of confinement in some experiments.

Elastic robot control - Nonlinear inversion and linear stabilization

NASA Technical Reports Server (NTRS)

Singh, S. N.; Schy, A. A.

1986-01-01

An approach to the control of elastic robot systems for space applications using inversion, servocompensation, and feedback stabilization is presented. For simplicity, a robot arm (PUMA type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a nonlinear decoupling control law u(d) is derived such that in the closed-loop system independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law u(s) is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u = u(d) + u(s).

Stability of soliton families in nonlinear Schrödinger equations with non-parity-time-symmetric complex potentials

NASA Astrophysics Data System (ADS)

Yang, Jianke; Nixon, Sean

2016-11-01

Stability of soliton families in one-dimensional nonlinear Schrödinger equations with non-parity-time (PT)-symmetric complex potentials is investigated numerically. It is shown that these solitons can be linearly stable in a wide range of parameter values both below and above phase transition. In addition, a pseudo-Hamiltonian-Hopf bifurcation is revealed, where pairs of purely-imaginary eigenvalues in the linear-stability spectra of solitons collide and bifurcate off the imaginary axis, creating oscillatory instability, which resembles Hamiltonian-Hopf bifurcations of solitons in Hamiltonian systems even though the present system is dissipative and non-Hamiltonian. The most important numerical finding is that, eigenvalues of linear-stability operators of these solitons appear in quartets (λ , - λ ,λ* , -λ*), similar to conservative systems and PT-symmetric systems. This quartet eigenvalue symmetry is very surprising for non- PT-symmetric systems, and it has far-reaching consequences on the stability behaviors of solitons.

Fractional representation theory - Robustness results with applications to finite dimensional control of a class of linear distributed systems

NASA Technical Reports Server (NTRS)

Nett, C. N.; Jacobson, C. A.; Balas, M. J.

1983-01-01

This paper reviews and extends the fractional representation theory. In particular, new and powerful robustness results are presented. This new theory is utilized to develop a preliminary design methodology for finite dimensional control of a class of linear evolution equations on a Banach space. The design is for stability in an input-output sense, but particular attention is paid to internal stability as well.

A new theory for multistep discretizations of stiff ordinary differential equations: Stability with large step sizes

NASA Technical Reports Server (NTRS)

Majda, G.

1985-01-01

A large set of variable coefficient linear systems of ordinary differential equations which possess two different time scales, a slow one and a fast one is considered. A small parameter epsilon characterizes the stiffness of these systems. A system of o.d.e.s. in this set is approximated by a general class of multistep discretizations which includes both one-leg and linear multistep methods. Sufficient conditions are determined under which each solution of a multistep method is uniformly bounded, with a bound which is independent of the stiffness of the system of o.d.e.s., when the step size resolves the slow time scale, but not the fast one. This property is called stability with large step sizes. The theory presented lets one compare properties of one-leg methods and linear multistep methods when they approximate variable coefficient systems of stiff o.d.e.s. In particular, it is shown that one-leg methods have better stability properties with large step sizes than their linear multistep counter parts. The theory also allows one to relate the concept of D-stability to the usual notions of stability and stability domains and to the propagation of errors for multistep methods which use large step sizes.

A pseudospectra-based approach to non-normal stability of embedded boundary methods

NASA Astrophysics Data System (ADS)

Rapaka, Narsimha; Samtaney, Ravi

2017-11-01

We present non-normal linear stability of embedded boundary (EB) methods employing pseudospectra and resolvent norms. Stability of the discrete linear wave equation is characterized in terms of the normalized distance of the EB to the nearest ghost node (α) in one and two dimensions. An important objective is that the CFL condition based on the Cartesian grid spacing remains unaffected by the EB. We consider various discretization methods including both central and upwind-biased schemes. Stability is guaranteed when α <=αmax ranges between 0.5 and 0.77 depending on the discretization scheme. Also, the stability characteristics remain the same in both one and two dimensions. Sharper limits on the sufficient conditions for stability are obtained based on the pseudospectral radius (the Kreiss constant) than the restrictive limits based on the usual singular value decomposition analysis. We present a simple and robust reclassification scheme for the ghost cells (``hybrid ghost cells'') to ensure Lax stability of the discrete systems. This has been tested successfully for both low and high order discretization schemes with transient growth of at most O (1). Moreover, we present a stable, fourth order EB reconstruction scheme. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1394-01.

Stability and error estimation for Component Adaptive Grid methods

NASA Technical Reports Server (NTRS)

Oliger, Joseph; Zhu, Xiaolei

1994-01-01

Component adaptive grid (CAG) methods for solving hyperbolic partial differential equations (PDE's) are discussed in this paper. Applying recent stability results for a class of numerical methods on uniform grids. The convergence of these methods for linear problems on component adaptive grids is established here. Furthermore, the computational error can be estimated on CAG's using the stability results. Using these estimates, the error can be controlled on CAG's. Thus, the solution can be computed efficiently on CAG's within a given error tolerance. Computational results for time dependent linear problems in one and two space dimensions are presented.

A Lie algebraic condition for exponential stability of discrete hybrid systems and application to hybrid synchronization.

PubMed

Zhao, Shouwei

2011-06-01

A Lie algebraic condition for global exponential stability of linear discrete switched impulsive systems is presented in this paper. By considering a Lie algebra generated by all subsystem matrices and impulsive matrices, when not all of these matrices are Schur stable, we derive new criteria for global exponential stability of linear discrete switched impulsive systems. Moreover, simple sufficient conditions in terms of Lie algebra are established for the synchronization of nonlinear discrete systems using a hybrid switching and impulsive control. As an application, discrete chaotic system's synchronization is investigated by the proposed method.

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.

Attitude Determination Error Analysis System (ADEAS) mathematical specifications document

NASA Technical Reports Server (NTRS)

Nicholson, Mark; Markley, F.; Seidewitz, E.

1988-01-01

The mathematical specifications of Release 4.0 of the Attitude Determination Error Analysis System (ADEAS), which provides a general-purpose linear error analysis capability for various spacecraft attitude geometries and determination processes, are presented. The analytical basis of the system is presented. The analytical basis of the system is presented, and detailed equations are provided for both three-axis-stabilized and spin-stabilized attitude sensor models.

Linear stability analysis of a levitated nanomagnet in a static magnetic field: Quantum spin stabilized magnetic levitation

NASA Astrophysics Data System (ADS)

Rusconi, C. C.; Pöchhacker, V.; Cirac, J. I.; Romero-Isart, O.

2017-10-01

We theoretically study the levitation of a single magnetic domain nanosphere in an external static magnetic field. We show that, apart from the stability provided by the mechanical rotation of the nanomagnet (as in the classical Levitron), the quantum spin origin of its magnetization provides two additional mechanisms to stably levitate the system. Despite the Earnshaw theorem, such stable phases are present even in the absence of mechanical rotation. For large magnetic fields, the Larmor precession of the quantum magnetic moment stabilizes the system in full analogy with magnetic trapping of a neutral atom. For low magnetic fields, the magnetic anisotropy stabilizes the system via the Einstein-de Haas effect. These results are obtained with a linear stability analysis of a single magnetic domain rigid nanosphere with uniaxial anisotropy in a Ioffe-Pritchard magnetic field.

Stability and stabilisation of a class of networked dynamic systems

NASA Astrophysics Data System (ADS)

Liu, H. B.; Wang, D. Q.

2018-04-01

We investigate the stability and stabilisation of a linear time invariant networked heterogeneous system with arbitrarily connected subsystems. A new linear matrix inequality based sufficient and necessary condition for the stability is derived, based on which the stabilisation is provided. The obtained conditions efficiently utilise the block-diagonal characteristic of system parameter matrices and the sparseness of subsystem connection matrix. Moreover, a sufficient condition only dependent on each individual subsystem is also presented for the stabilisation of the networked systems with a large scale. Numerical simulations show that these conditions are computationally valid in the analysis and synthesis of a large-scale networked system.

Stability, performance and sensitivity analysis of I.I.D. jump linear systems

NASA Astrophysics Data System (ADS)

Chávez Fuentes, Jorge R.; González, Oscar R.; Gray, W. Steven

2018-06-01

This paper presents a symmetric Kronecker product analysis of independent and identically distributed jump linear systems to develop new, lower dimensional equations for the stability and performance analysis of this type of systems than what is currently available. In addition, new closed form expressions characterising multi-parameter relative sensitivity functions for performance metrics are introduced. The analysis technique is illustrated with a distributed fault-tolerant flight control example where the communication links are allowed to fail randomly.

Linear morphological stability analysis of the solid-liquid interface in rapidsolidification of a binary system

NASA Astrophysics Data System (ADS)

Galenko, P. K.; Danilov, D. A.

2004-05-01

The interface stability against small perturbations of the planar solid-liquid interface is considered analytically in linear approximation. Following the analytical procedure of Trivedi and Kurz [

An extended continuum model accounting for the driver's timid and aggressive attributions

NASA Astrophysics Data System (ADS)

Cheng, Rongjun; Ge, Hongxia; Wang, Jufeng

2017-04-01

Considering the driver's timid and aggressive behaviors simultaneously, a new continuum model is put forwarded in this paper. By applying the linear stability theory, we presented the analysis of new model's linear stability. Through nonlinear analysis, the KdV-Burgers equation is derived to describe density wave near the neutral stability line. Numerical results verify that aggressive driving is better than timid act because the aggressive driver will adjust his speed timely according to the leading car's speed. The key improvement of this new model is that the timid driving deteriorates traffic stability while the aggressive driving will enhance traffic stability. The relationship of energy consumption between the aggressive and timid driving is also studied. Numerical results show that aggressive driver behavior can not only suppress the traffic congestion but also reduce the energy consumption.

Linear time-invariant controller design for two-channel decentralized control systems

NASA Technical Reports Server (NTRS)

Desoer, Charles A.; Gundes, A. Nazli

1987-01-01

This paper analyzes a linear time-invariant two-channel decentralized control system with a 2 x 2 strictly proper plant. It presents an algorithm for the algebraic design of a class of decentralized compensators which stabilize the given plant.

Stabilizing skateboard speed-wobble with reflex delay.

PubMed

Varszegi, Balazs; Takacs, Denes; Stepan, Gabor; Hogan, S John

2016-08-01

A simple mechanical model of the skateboard-skater system is analysed, in which the effect of human control is considered by means of a linear proportional-derivative (PD) controller with delay. The equations of motion of this non-holonomic system are neutral delay-differential equations. A linear stability analysis of the rectilinear motion is carried out analytically. It is shown how to vary the control gains with respect to the speed of the skateboard to stabilize the uniform motion. The critical reflex delay of the skater is determined as the function of the speed. Based on this analysis, we present an explanation for the linear instability of the skateboard-skater system at high speed. Moreover, the advantages of standing ahead of the centre of the board are demonstrated from the viewpoint of reflex delay and control gain sensitivity. © 2016 The Author(s).

Simulation of Nonlinear Instabilities in an Attachment-Line Boundary Layer

NASA Technical Reports Server (NTRS)

Joslin, Ronald D.

1996-01-01

The linear and the nonlinear stability of disturbances that propagate along the attachment line of a three-dimensional boundary layer is considered. The spatially evolving disturbances in the boundary layer are computed by direct numerical simulation (DNS) of the unsteady, incompressible Navier-Stokes equations. Disturbances are introduced either by forcing at the in ow or by applying suction and blowing at the wall. Quasi-parallel linear stability theory and a nonparallel theory yield notably different stability characteristics for disturbances near the critical Reynolds number; the DNS results con rm the latter theory. Previously, a weakly nonlinear theory and computations revealed a high wave-number region of subcritical disturbance growth. More recent computations have failed to achieve this subcritical growth. The present computational results indicate the presence of subcritically growing disturbances; the results support the weakly nonlinear theory. Furthermore, an explanation is provided for the previous theoretical and computational discrepancy. In addition, the present results demonstrate that steady suction can be used to stabilize disturbances that otherwise grow subcritically along the attachment line.

Linear Approximation to Optimal Control Allocation for Rocket Nozzles with Elliptical Constraints

NASA Technical Reports Server (NTRS)

Orr, Jeb S.; Wall, Johnm W.

2011-01-01

In this paper we present a straightforward technique for assessing and realizing the maximum control moment effectiveness for a launch vehicle with multiple constrained rocket nozzles, where elliptical deflection limits in gimbal axes are expressed as an ensemble of independent quadratic constraints. A direct method of determining an approximating ellipsoid that inscribes the set of attainable angular accelerations is derived. In the case of a parameterized linear generalized inverse, the geometry of the attainable set is computationally expensive to obtain but can be approximated to a high degree of accuracy with the proposed method. A linear inverse can then be optimized to maximize the volume of the true attainable set by maximizing the volume of the approximating ellipsoid. The use of a linear inverse does not preclude the use of linear methods for stability analysis and control design, preferred in practice for assessing the stability characteristics of the inertial and servoelastic coupling appearing in large boosters. The present techniques are demonstrated via application to the control allocation scheme for a concept heavy-lift launch vehicle.

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

PubMed

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

2015-04-01

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

Study report on guidelines and test procedures for investigating stability of nonlinear cardiovascular control system models

NASA Technical Reports Server (NTRS)

Fitzjerrell, D. G.

1974-01-01

A general study of the stability of nonlinear as compared to linear control systems is presented. The analysis is general and, therefore, applies to other types of nonlinear biological control systems as well as the cardiovascular control system models. Both inherent and numerical stability are discussed for corresponding analytical and graphic methods and numerical methods.

Development of Resistive Micromegas for Sampling Calorimetry

NASA Astrophysics Data System (ADS)

Geralis, T.; Fanourakis, G.; Kalamaris, A.; Nikas, D.; Psallidas, A.; Chefdeville, M.; Karyotakis, I.; Koletsou, I.; Titov, M.

2018-02-01

Resistive micromegas is proposed as an active element for sampling calorimetry. Future linear collider experiments or the HL-LHC experiments can profit from those developments for Particle Flow Calorimetry. Micromegas possesses remarkable properties concerning gain stability, reduced ion feedback, response linearity, adaptable sensitive element granularity, fast response and high rate capability. Recent developments on Micromegas with a protective resistive layer present excellent results, resolving the problem of discharges caused by local high charge deposition, thanks to its RC-slowed charge evacuation. Higher resistivity though, may cause loss of the response linearity at high rates. We have scanned a wide range of resistivities and performed laboratory tests with X-rays that demonstrate excellent response linearity up to rates of (a few) times 10MHz/cm2, with simultaneous mitigation of discharges. Beam test studies at SPS/CERN with hadrons have also shown a remarkable stability of the resistive Micromegas and low currents for rates up to 15MHz/cm2. We present results from the aforementioned studies confronted with MC simulation

Exponential stability of impulsive stochastic genetic regulatory networks with time-varying delays and reaction-diffusion

DOE PAGES

Cao, Boqiang; Zhang, Qimin; Ye, Ming

2016-11-29

We present a mean-square exponential stability analysis for impulsive stochastic genetic regulatory networks (GRNs) with time-varying delays and reaction-diffusion driven by fractional Brownian motion (fBm). By constructing a Lyapunov functional and using linear matrix inequality for stochastic analysis we derive sufficient conditions to guarantee the exponential stability of the stochastic model of impulsive GRNs in the mean-square sense. Meanwhile, the corresponding results are obtained for the GRNs with constant time delays and standard Brownian motion. Finally, an example is presented to illustrate our results of the mean-square exponential stability analysis.

Analyses of a heterogeneous lattice hydrodynamic model with low and high-sensitivity vehicles

NASA Astrophysics Data System (ADS)

Kaur, Ramanpreet; Sharma, Sapna

2018-06-01

Basic lattice model is extended to study the heterogeneous traffic by considering the optimal current difference effect on a unidirectional single lane highway. Heterogeneous traffic consisting of low- and high-sensitivity vehicles is modeled and their impact on stability of mixed traffic flow has been examined through linear stability analysis. The stability of flow is investigated in five distinct regions of the neutral stability diagram corresponding to the amount of higher sensitivity vehicles present on road. In order to investigate the propagating behavior of density waves non linear analysis is performed and near the critical point, the kink antikink soliton is obtained by driving mKdV equation. The effect of fraction parameter corresponding to high sensitivity vehicles is investigated and the results indicates that the stability rise up due to the fraction parameter. The theoretical findings are verified via direct numerical simulation.

Global stability and periodic solution of the viral dynamics

NASA Astrophysics Data System (ADS)

Song, Xinyu; Neumann, Avidan U.

2007-05-01

It is well known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV). However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T cells and the viral particles. In this paper, we consider the classical mathematical model with saturation response of the infection rate. By stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection-free steady state. We also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution. Numerical simulations are presented to illustrate the results.

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

NASA Technical Reports Server (NTRS)

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

2014-01-01

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

A simplified computer program for the prediction of the linear stability behavior of liquid propellant combustors

NASA Technical Reports Server (NTRS)

Mitchell, C. E.; Eckert, K.

1979-01-01

A program for predicting the linear stability of liquid propellant rocket engines is presented. The underlying model assumptions and analytical steps necessary for understanding the program and its input and output are also given. The rocket engine is modeled as a right circular cylinder with an injector with a concentrated combustion zone, a nozzle, finite mean flow, and an acoustic admittance, or the sensitive time lag theory. The resulting partial differential equations are combined into two governing integral equations by the use of the Green's function method. These equations are solved using a successive approximation technique for the small amplitude (linear) case. The computational method used as well as the various user options available are discussed. Finally, a flow diagram, sample input and output for a typical application and a complete program listing for program MODULE are presented.

On the linear stability of blood flow through model capillary networks.

PubMed

Davis, Jeffrey M

2014-12-01

Under the approximation that blood behaves as a continuum, a numerical implementation is presented to analyze the linear stability of capillary blood flow through model tree and honeycomb networks that are based on the microvascular structures of biological tissues. The tree network is comprised of a cascade of diverging bifurcations, in which a parent vessel bifurcates into two descendent vessels, while the honeycomb network also contains converging bifurcations, in which two parent vessels merge into one descendent vessel. At diverging bifurcations, a cell partitioning law is required to account for the nonuniform distribution of red blood cells as a function of the flow rate of blood into each descendent vessel. A linearization of the governing equations produces a system of delay differential equations involving the discharge hematocrit entering each network vessel and leads to a nonlinear eigenvalue problem. All eigenvalues in a specified region of the complex plane are captured using a transformation based on contour integrals to construct a linear eigenvalue problem with identical eigenvalues, which are then determined using a standard QR algorithm. The predicted value of the dimensionless exponent in the cell partitioning law at the instability threshold corresponds to a supercritical Hopf bifurcation in numerical simulations of the equations governing unsteady blood flow. Excellent agreement is found between the predictions of the linear stability analysis and nonlinear simulations. The relaxation of the assumption of plug flow made in previous stability analyses typically has a small, quantitative effect on the stability results that depends on the specific network structure. This implementation of the stability analysis can be applied to large networks with arbitrary structure provided only that the connectivity among the network segments is known.

Routh's algorithm - A centennial survey

NASA Technical Reports Server (NTRS)

Barnett, S.; Siljak, D. D.

1977-01-01

One hundred years have passed since the publication of Routh's fundamental work on determining the stability of constant linear systems. The paper presents an outline of the algorithm and considers such aspects of it as the distribution of zeros and applications of it that relate to the greatest common divisor, the abscissa of stability, continued fractions, canonical forms, the nonnegativity of polynomials and polynomial matrices, the absolute stability, optimality and passivity of dynamic systems, and the stability of two-dimensional circuits.

USING LINEAR AND POLYNOMIAL MODELS TO EXAMINE THE ENVIRONMENTAL STABILITY OF VIRUSES

EPA Science Inventory

The article presents the development of model equations for describing the fate of viral infectivity in environmental samples. Most of the models were based upon the use of a two-step linear regression approach. The first step employs regression of log base 10 transformed viral t...

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

Kelvin-Helmholtz instability for flow in porous media under the influence of oblique magnetic fields: A viscous potential flow analysis

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

Moatimid, Galal M.; Obied Allah, M. H.; Hassan, Mohamed A.

2013-10-15

In this paper, the Kelvin-Helmholtz instability of viscous incompressible magnetic fluid fully saturated porous media is achieved through the viscous potential theory. The flow is considered to be through semi-permeable boundaries above and below the fluids through which the fluid may either be blown in or sucked out, in a direction normal to the main streaming direction of the fluid flow. An oblique magnetic field, mass, heat transfer, and surface tension are present across the interface. Through the linear stability analysis, a general dispersion relation is derived and the natural curves are plotted. Therefore, the linear stability condition is discussedmore » in some depth. In view of the multiple time scale technique, the Ginzburg–Landau equation, which describes the behavior of the system in the nonlinear approach, is obtained. The effects of the orientation of the magnetic fields on the stability configuration in linear, as well as nonlinear approaches, are discussed. It is found that the Darcy's coefficient for the porous layers plays a stabilizing role. The injection of the fluids at both boundaries has a stabilizing effect, in contrast with the suction at both boundaries.« less

A class of stabilizing controllers for flexible multibody systems

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

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)

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

NASA Astrophysics Data System (ADS)

Nathan, Terrence

1991-09-01

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

Direct use of linear time-domain aerodynamics in aeroservoelastic analysis: Aerodynamic model

NASA Technical Reports Server (NTRS)

Woods, J. A.; Gilbert, Michael G.

1990-01-01

The work presented here is the first part of a continuing effort to expand existing capabilities in aeroelasticity by developing the methodology which is necessary to utilize unsteady time-domain aerodynamics directly in aeroservoelastic design and analysis. The ultimate objective is to define a fully integrated state-space model of an aeroelastic vehicle's aerodynamics, structure and controls which may be used to efficiently determine the vehicle's aeroservoelastic stability. Here, the current status of developing a state-space model for linear or near-linear time-domain indicial aerodynamic forces is presented.

Passivity-Based Control for Two-Wheeled Robot Stabilization

NASA Astrophysics Data System (ADS)

Uddin, Nur; Aryo Nugroho, Teguh; Agung Pramudito, Wahyu

2018-04-01

A passivity-based control system design for two-wheeled robot (TWR) stabilization is presented. A TWR is a statically-unstable non-linear system. A control system is applied to actively stabilize the TWR. Passivity-based control method is applied to design the control system. The design results in a state feedback control law that makes the TWR closed loop system globally asymptotically stable (GAS). The GAS is proven mathematically. The TWR stabilization is demonstrated through computer simulation. The simulation results show that the designed control system is able to stabilize the TWR.

Decentralization, stabilization, and estimation of large-scale linear systems

NASA Technical Reports Server (NTRS)

Siljak, D. D.; Vukcevic, M. B.

1976-01-01

In this short paper we consider three closely related aspects of large-scale systems: decentralization, stabilization, and estimation. A method is proposed to decompose a large linear system into a number of interconnected subsystems with decentralized (scalar) inputs or outputs. The procedure is preliminary to the hierarchic stabilization and estimation of linear systems and is performed on the subsystem level. A multilevel control scheme based upon the decomposition-aggregation method is developed for stabilization of input-decentralized linear systems Local linear feedback controllers are used to stabilize each decoupled subsystem, while global linear feedback controllers are utilized to minimize the coupling effect among the subsystems. Systems stabilized by the method have a tolerance to a wide class of nonlinearities in subsystem coupling and high reliability with respect to structural perturbations. The proposed output-decentralization and stabilization schemes can be used directly to construct asymptotic state estimators for large linear systems on the subsystem level. The problem of dimensionality is resolved by constructing a number of low-order estimators, thus avoiding a design of a single estimator for the overall system.

Delay-Dependent Stability Criterion for Bidirectional Associative Memory Neural Networks with Interval Time-Varying Delays

NASA Astrophysics Data System (ADS)

Park, Ju H.; Kwon, O. M.

In the letter, the global asymptotic stability of bidirectional associative memory (BAM) neural networks with delays is investigated. The delay is assumed to be time-varying and belongs to a given interval. A novel stability criterion for the stability is presented based on the Lyapunov method. The criterion is represented in terms of linear matrix inequality (LMI), which can be solved easily by various optimization algorithms. Two numerical examples are illustrated to show the effectiveness of our new result.

Stabilization of the Rayleigh-Taylor instability in quantum magnetized plasmas

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

Wang, L. F.; Ye, W. H.; He, X. T.

2012-07-15

In this research, stabilization of the Rayleigh-Taylor instability (RTI) due to density gradients, magnetic fields, and quantum effects, in an ideal incompressible plasma, is studied analytically and numerically. A second-order ordinary differential equation (ODE) for the RTI including quantum corrections, with a continuous density profile, in a uniform external magnetic field, is obtained. Analytic expressions of the linear growth rate of the RTI, considering modifications of density gradients, magnetic fields, and quantum effects, are presented. Numerical approaches are performed to solve the second-order ODE. The analytical model proposed here agrees with the numerical calculation. It is found that the densitymore » gradients, the magnetic fields, and the quantum effects, respectively, have a stabilizing effect on the RTI (reduce the linear growth of the RTI). The RTI can be completely quenched by the magnetic field stabilization and/or the quantum effect stabilization in proper circumstances leading to a cutoff wavelength. The quantum effect stabilization plays a central role in systems with large Atwood number and small normalized density gradient scale length. The presence of external transverse magnetic fields beside the quantum effects will bring about more stability on the RTI. The stabilization of the linear growth of the RTI, for parameters closely related to inertial confinement fusion and white dwarfs, is discussed. Results could potentially be valuable for the RTI treatment to analyze the mixing in supernovas and other RTI-driven objects.« less

The initial instability and finite-amplitude stability of alternate bars in straight channels

USGS Publications Warehouse

Nelson, J.M.

1990-01-01

The initial instability and fully developed stability of alternate bars in straight channels are investigated using linearized and nonlinear analyses. The fundamental instability leading to these features is identified through a linear stability analysis of the equations governing the flow and sediment transport fields. This instability is explained in terms of topographically induced steering of the flow and the associated pattern of erosion and deposition on the bed. While the linear theory is useful for examining the instability mechanism, this approach is shown to yield relatively little information about well-developed alternate bars and, specifically, the linear analysis is shown to yield poor predictions of the fully developed bar wavelength. A fully nonlinear approach is presented that permits computation of the evolution of these bed features from an initial perturbation to their fully developed morphology. This analysis indicates that there is typically substantial elongation of the bar wavelength during the evolution process, a result that is consistent with observations of bar development in flumes and natural channels. The nonlinear approach demonstrates that the eventual stability of these features is a result of the interplay between topographic steering effects, secondary flow production as a result of streamline curvature, and gravitationally induced modifications of sediment fluxes over a sloping bed. ?? 1990.

Global exponential stability of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays.

PubMed

Huang, Haiying; Du, Qiaosheng; Kang, Xibing

2013-11-01

In this paper, a class of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays is investigated. The jumping parameters are modeled as a continuous-time finite-state Markov chain. At first, the existence of equilibrium point for the addressed neural networks is studied. By utilizing the Lyapunov stability theory, stochastic analysis theory and linear matrix inequality (LMI) technique, new delay-dependent stability criteria are presented in terms of linear matrix inequalities to guarantee the neural networks to be globally exponentially stable in the mean square. Numerical simulations are carried out to illustrate the main results. © 2013 ISA. Published by ISA. All rights reserved.

Implementation of model predictive control for resistive wall mode stabilization on EXTRAP T2R

NASA Astrophysics Data System (ADS)

Setiadi, A. C.; Brunsell, P. R.; Frassinetti, L.

2015-10-01

A model predictive control (MPC) method for stabilization of the resistive wall mode (RWM) in the EXTRAP T2R reversed-field pinch is presented. The system identification technique is used to obtain a linearized empirical model of EXTRAP T2R. MPC employs the model for prediction and computes optimal control inputs that satisfy performance criterion. The use of a linearized form of the model allows for compact formulation of MPC, implemented on a millisecond timescale, that can be used for real-time control. The design allows the user to arbitrarily suppress any selected Fourier mode. The experimental results from EXTRAP T2R show that the designed and implemented MPC successfully stabilizes the RWM.

H∞ control problem of linear periodic piecewise time-delay systems

NASA Astrophysics Data System (ADS)

Xie, Xiaochen; Lam, James; Li, Panshuo

2018-04-01

This paper investigates the H∞ control problem based on exponential stability and weighted L2-gain analyses for a class of continuous-time linear periodic piecewise systems with time delay. A periodic piecewise Lyapunov-Krasovskii functional is developed by integrating a discontinuous time-varying matrix function with two global terms. By applying the improved constraints to the stability and L2-gain analyses, sufficient delay-dependent exponential stability and weighted L2-gain criteria are proposed for the periodic piecewise time-delay system. Based on these analyses, an H∞ control scheme is designed under the considerations of periodic state feedback control input and iterative optimisation. Finally, numerical examples are presented to illustrate the effectiveness of our proposed conditions.

A Coupled Aeroelastic Model for Launch Vehicle Stability Analysis

NASA Technical Reports Server (NTRS)

Orr, Jeb S.

2010-01-01

A technique for incorporating distributed aerodynamic normal forces and aeroelastic coupling effects into a stability analysis model of a launch vehicle is presented. The formulation augments the linear state-space launch vehicle plant dynamics that are compactly derived as a system of coupled linear differential equations representing small angular and translational perturbations of the rigid body, nozzle, and sloshing propellant coupled with normal vibration of a set of orthogonal modes. The interaction of generalized forces due to aeroelastic coupling and thrust can be expressed as a set of augmenting non-diagonal stiffness and damping matrices in modal coordinates with no penalty on system order. While the eigenvalues of the structural response in the presence of thrust and aeroelastic forcing can be predicted at a given flight condition independent of the remaining degrees of freedom, the coupled model provides confidence in closed-loop stability in the presence of rigid-body, slosh, and actuator dynamics. Simulation results are presented that characterize the coupled dynamic response of the Ares I launch vehicle and the impact of aeroelasticity on control system stability margins.

Characterisation of acoustic energy content in an experimental combustion chamber with and without external forcing

NASA Astrophysics Data System (ADS)

Webster, S.; Hardi, J.; Oschwald, M.

2015-03-01

The influence of injection conditions on rocket engine combustion stability is investigated for a sub-scale combustion chamber with shear coaxial injection elements and the propellant combination hydrogen-oxygen. The experimental results presented are from a series of tests conducted at subcritical and supercritical pressures for oxygen and for both ambient and cryogenic temperature hydrogen. The stability of the system is characterised by the root mean squared amplitude of dynamic combustion chamber pressure in the upper part of the acoustic spectrum relevant for high frequency combustion instabilities. Results are presented for both unforced and externally forced combustion chamber configurations. It was found that, for both the unforced and externally forced configurations, the injection velocity had the strongest influence on combustion chamber stability. Through the use of multivariate linear regression the influence of hydrogen injection temperature and hydrogen injection mass flow rate were best able to explain the variance in stability for dependence on injection velocity ratio. For unforced tests turbulent jet noise from injection was found to dominate the energy content of the signal. For the externally forced configuration a non-linear regression model was better able to predict the variance, suggesting the influence of non-linear behaviour. The response of the system to variation of injection conditions was found to be small; suggesting that the combustion chamber investigated in the experiment is highly stable.

Hydrostatic calculations of axisymmetric flow and its stability for the AGCE model

NASA Technical Reports Server (NTRS)

Miller, T. L.; Gall, R. L.

1981-01-01

Baroclinic waves in the atmospherics general circulation experiment (AGCE) apparatus by the use of numerical hydrostatic primitive equation models were determined. The calculation is accomplished by using an axisymmetric primitive equation model to compute, for a given set of experimental parameters, a steady state axisymmetric flow and then testing this axisymmetric flow for stability using a linear primitive equation model. Some axisymmetric flows are presented together with preliminary stability calculations.

Automated design and optimization of flexible booster autopilots via linear programming. Volume 2: User's manual

NASA Technical Reports Server (NTRS)

Hauser, F. D.; Szollosi, G. D.; Lakin, W. S.

1972-01-01

COEBRA, the Computerized Optimization of Elastic Booster Autopilots, is an autopilot design program. The bulk of the design criteria is presented in the form of minimum allowed gain/phase stability margins. COEBRA has two optimization phases: (1) a phase to maximize stability margins; and (2) a phase to optimize structural bending moment load relief capability in the presence of minimum requirements on gain/phase stability margins.

An experimental and analytical investigation of stall effects on flap-lag stability in forward flight

NASA Technical Reports Server (NTRS)

Nagabhushanam, J.; Gaonkar, Gopal H.; Mcnulty, Michael J.

1987-01-01

Experiments have been performed with a 1.62 m diameter hingeless rotor in a wind tunnel to investigate flap-lag stability of isolated rotors in forward flight. The three-bladed rotor model closely approaches the simple theoretical concept of a hingeless rotor as a set of rigid, articulated flap-lag blades with offset and spring restrained flap and lag hinges. Lag regressing mode stability data was obtained for advance ratios as high as 0.55 for various combinations of collective pitch and shaft angle. The prediction includes quasi-steady stall effects on rotor trim and Floquet stability analyses. Correlation between data and prediction is presented and is compared with that of an earlier study based on a linear theory without stall effects. While the results with stall effects show marked differences from the linear theory results, the stall theory still falls short of adequate agreement with the experimental data.

Onset of density-driven instabilities in fractured aquifers

NASA Astrophysics Data System (ADS)

Jafari Raad, Seyed Mostafa; Hassanzadeh, Hassan

2018-04-01

Linear stability analysis is conducted to study the onset of density-driven convection involved in solubility trapping of C O2 in fractured aquifers. The effect of physical properties of a fracture network on the stability of a diffusive boundary layer in a saturated fractured porous media is investigated using the dual porosity concept. Linear stability analysis results show that both fracture interporosity flow and fracture storativity play an important role in the stability behavior of the system. It is shown that a diffusive boundary layer under the gravity field in fractured porous media with lower fracture storativity and/or higher fracture interporosity flow coefficient is more stable. We present scaling relations for the onset of convective instability in fractured aquifers with single and variable matrix block size distribution. These findings improve our understanding of density-driven flow in fractured aquifers and are important in the estimation of potential storage capacity, risk assessment, and storage site characterization and screening.

A solid criterion based on strict LMI without invoking equality constraint for stabilization of continuous singular systems.

PubMed

Zhang, Xuefeng; Chen, YangQuan

2017-11-01

The paper considers the stabilization issue of linear continuous singular systems by dealing with strict linear matrix inequalities (LMIs) without invoking equality constraint and proposes a complete and effective solved LMIs formulation. The criterion is necessary and sufficient condition and can be directly solved the feasible solutions with LMI toolbox and is much more tractable and reliable in numerical simulation than existing results, which involve positive semi-definite LMIs with equality constraints. The most important property of the criterion proposed in the paper is that it can overcome the drawbacks of the invalidity caused by the singularity of Ω=PE T +SQ for stabilization of singular systems. Two counterexamples are presented to avoid the disadvantages of the existing condition of stabilization of continuous singular systems. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Coexistence and local μ-stability of multiple equilibrium points for memristive neural networks with nonmonotonic piecewise linear activation functions and unbounded time-varying delays.

PubMed

Nie, Xiaobing; Zheng, Wei Xing; Cao, Jinde

2016-12-01

In this paper, the coexistence and dynamical behaviors of multiple equilibrium points are discussed for a class of memristive neural networks (MNNs) with unbounded time-varying delays and nonmonotonic piecewise linear activation functions. By means of the fixed point theorem, nonsmooth analysis theory and rigorous mathematical analysis, it is proven that under some conditions, such n-neuron MNNs can have 5 n equilibrium points located in ℜ n , and 3 n of them are locally μ-stable. As a direct application, some criteria are also obtained on the multiple exponential stability, multiple power stability, multiple log-stability and multiple log-log-stability. All these results reveal that the addressed neural networks with activation functions introduced in this paper can generate greater storage capacity than the ones with Mexican-hat-type activation function. Numerical simulations are presented to substantiate the theoretical results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Aeroelastic Stability of Idling Wind Turbines

NASA Astrophysics Data System (ADS)

Wang, Kai; Riziotis, Vasilis A.; Voutsinas, Spyros G.

2016-09-01

Wind turbine rotors in idling operation mode can experience high angles of attack, within the post stall region that are capable of triggering stall-induced vibrations. In the present paper rotor stability in slow idling operation is assessed on the basis of non-linear time domain and linear eigenvalue analysis. Analysis is performed for a 10 MW conceptual wind turbine designed by DTU. First the flow conditions that are likely to favour stall induced instabilities are identified through non-linear time domain aeroelastic analysis. Next, for the above specified conditions, eigenvalue stability simulations are performed aiming at identifying the low damped modes of the turbine. Finally the results of the eigenvalue analysis are evaluated through computations of the work of the aerodynamic forces by imposing harmonic vibrations following the shape and frequency of the various modes. Eigenvalue analysis indicates that the asymmetric and symmetric out-of-plane modes have the lowest damping. The results of the eigenvalue analysis agree well with those of the time domain analysis.

Development of Curved-Plate Elements for the Exact Buckling Analysis of Composite Plate Assemblies Including Transverse-Shear Effects

NASA Technical Reports Server (NTRS)

McGowan, David M.

1999-01-01

The analytical formulation of curved-plate non-linear equilibrium equations including transverse-shear-deformation effects is presented. A unified set of non-linear strains that contains terms from both physical and tensorial strain measures is used. Linearized, perturbed equilibrium equations (stability equations) that describe the response of the plate just after buckling occurs are derived. These equations are then modified to allow the plate reference surface to be located a distance z(sub c) from the centroidal surface. The implementation of the new theory into the VICONOPT exact buckling and vibration analysis and optimum design computer program is described. The terms of the plate stiffness matrix using both classical plate theory (CPT) and first-order shear-deformation plate theory (SDPT) are presented. The effects of in-plane transverse and in-plane shear loads are included in the in-plane stability equations. Numerical results for several example problems with different loading states are presented. Comparisons of analyses using both physical and tensorial strain measures as well as CPT and SDPT are made. The computational effort required by the new analysis is compared to that of the analysis currently in the VICONOPT program. The effects of including terms related to in-plane transverse and in-plane shear loadings in the in-plane stability equations are also examined. Finally, results of a design-optimization study of two different cylindrical shells subject to uniform axial compression are presented.

Feedback control of combustion instabilities from within limit cycle oscillations using H∞ loop-shaping and the ν-gap metric

PubMed Central

Morgans, Aimee S.

2016-01-01

Combustion instabilities arise owing to a two-way coupling between acoustic waves and unsteady heat release. Oscillation amplitudes successively grow, until nonlinear effects cause saturation into limit cycle oscillations. Feedback control, in which an actuator modifies some combustor input in response to a sensor measurement, can suppress combustion instabilities. Linear feedback controllers are typically designed, using linear combustor models. However, when activated from within limit cycle, the linear model is invalid, and such controllers are not guaranteed to stabilize. This work develops a feedback control strategy guaranteed to stabilize from within limit cycle oscillations. A low-order model of a simple combustor, exhibiting the essential features of more complex systems, is presented. Linear plane acoustic wave modelling is combined with a weakly nonlinear describing function for the flame. The latter is determined numerically using a level set approach. Its implication is that the open-loop transfer function (OLTF) needed for controller design varies with oscillation level. The difference between the mean and the rest of the OLTFs is characterized using the ν-gap metric, providing the minimum required ‘robustness margin’ for an H∞ loop-shaping controller. Such controllers are designed and achieve stability both for linear fluctuations and from within limit cycle oscillations. PMID:27493558

On Time Delay Margin Estimation for Adaptive Control and Optimal Control Modification

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.

2011-01-01

This paper presents methods for estimating time delay margin for adaptive control of input delay systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent an adaptive law by a locally bounded linear approximation within a small time window. The time delay margin of this input delay system represents a local stability measure and is computed analytically by three methods: Pade approximation, Lyapunov-Krasovskii method, and the matrix measure method. These methods are applied to the standard model-reference adaptive control, s-modification adaptive law, and optimal control modification adaptive law. The windowing analysis results in non-unique estimates of the time delay margin since it is dependent on the length of a time window and parameters which vary from one time window to the next. The optimal control modification adaptive law overcomes this limitation in that, as the adaptive gain tends to infinity and if the matched uncertainty is linear, then the closed-loop input delay system tends to a LTI system. A lower bound of the time delay margin of this system can then be estimated uniquely without the need for the windowing analysis. Simulation results demonstrates the feasibility of the bounded linear stability method for time delay margin estimation.

Experimental and analytical determination of stability parameters for a balloon tethered in a wind

NASA Technical Reports Server (NTRS)

Redd, L. T.; Bennett, R. M.; Bland, S. R.

1973-01-01

Experimental and analytical techniques for determining stability parameters for a balloon tethered in a steady wind are described. These techniques are applied to a particular 7.64-meter-long balloon, and the results are presented. The stability parameters of interest appear as coefficients in linearized stability equations and are derived from the various forces and moments acting on the balloon. In several cases the results from the experimental and analytical techniques are compared and suggestions are given as to which techniques are the most practical means of determining values for the stability parameters.

Comments on the "Byzantine Self-Stabilizing Pulse Synchronization" Protocol: Counter-examples

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R.; Siminiceanu, Radu

2006-01-01

Embedded distributed systems have become an integral part of many safety-critical applications. There have been many attempts to solve the self-stabilization problem of clocks across a distributed system. An analysis of one such protocol called the Byzantine Self-Stabilizing Pulse Synchronization (BSS-Pulse-Synch) protocol from a paper entitled "Linear Time Byzantine Self-Stabilizing Clock Synchronization" by Daliot, et al., is presented in this report. This report also includes a discussion of the complexity and pitfalls of designing self-stabilizing protocols and provides counter-examples for the claims of the above protocol.

Influence of fracture network physical properties on stability criteria of density-driven flow in a dual-porosity system

NASA Astrophysics Data System (ADS)

Hassanzadeh, H.; Jafari Raad, S. M.

2017-12-01

Linear stability analysis is conducted to study the onset of buoyancy-driven convection involved in solubility trapping of CO2 into deep fractured aquifers. In this study, the effect of fracture network physical properties on the stability criteria in a brine-rich fractured porous layer is investigated using dual porosity concept for both single and variable matrix block size distributions. Linear stability analysis results show that both fracture interporosity flow and fracture storativity factors play an important role in the stability behavior of the system. It is shown that a diffusive boundary layer under the gravity field in a fractured rock with lower fracture storativity and/or higher fracture interporosity flow coefficient is more stable. We present scaling relations that relate the onset of convective instability in fractured aquifers. These findings improve our understanding of buoyancy driven flow in fractured aquifers and are particularly important in estimation of potential storage capacity, risk assessment, and storage sites characterization and screening.Keywords: CO2 sequestration; fractured rock; buoyancy-driven convection; stability analysis

Linear stability analysis of particle-laden hypopycnal plumes

NASA Astrophysics Data System (ADS)

Farenzena, Bruno Avila; Silvestrini, Jorge Hugo

2017-12-01

Gravity-driven riverine outflows are responsible for carrying sediments to the coastal waters. The turbulent mixing in these flows is associated with shear and gravitational instabilities such as Kelvin-Helmholtz, Holmboe, and Rayleigh-Taylor. Results from temporal linear stability analysis of a two-layer stratified flow are presented, investigating the behavior of settling particles and mixing region thickness on the flow stability in the presence of ambient shear. The particles are considered suspended in the transport fluid, and its sedimentation is modeled with a constant valued settling velocity. Three scenarios, regarding the mixing region thickness, were identified: the poorly mixed environment, the strong mixed environment, and intermediate scenario. It was observed that Kelvin-Helmholtz and settling convection modes are the two fastest growing modes depending on the particles settling velocity and the total Richardson number. The second scenario presents a modified Rayleigh-Taylor instability, which is the dominant mode. The third case can have Kelvin-Helmholtz, settling convection, and modified Rayleigh-Taylor modes as the fastest growing mode depending on the combination of parameters.

Design and Stability of an On-Orbit Attitude Control System Using Reaction Control Thrusters

NASA Technical Reports Server (NTRS)

Hall, Robert A.; Hough, Steven; Orphee, Carolina; Clements, Keith

2016-01-01

Basic principles for the design and stability of a spacecraft on-orbit attitude control system employing on-off Reaction Control System (RCS) thrusters are presented. Both vehicle dynamics and the control system actuators are inherently nonlinear, hence traditional linear control system design approaches are not directly applicable. This paper has two main aspects: It summarizes key RCS design principles from earlier NASA vehicles, notably the Space Shuttle and Space Station programs, and introduces advances in the linear modelling and analyses of a phase plane control system derived in the initial development of the NASA's next upper stage vehicle, the Exploration Upper Stage (EUS). Topics include thruster hardware specifications, phase plane design and stability, jet selection approaches, filter design metrics, and RCS rotational maneuver logic.

Design and Stability of an On-Orbit Attitude Control System Using Reaction Control Thrusters

NASA Technical Reports Server (NTRS)

Hall, Robert A.; Hough, Steven; Orphee, Carolina; Clements, Keith

2015-01-01

Principles for the design and stability of a spacecraft on-orbit attitude control system employing on-off Reaction Control System (RCS) thrusters is presented. Both the vehicle dynamics and the control system actuators are inherently nonlinear, hence traditional linear control system design approaches are not directly applicable. This paper has three main aspects: It summarizes key RCS control System design principles from the Space Shuttle and Space Station programs, it demonstrates a new approach to develop a linear model of a phase plane control system using describing functions, and applies each of these to the initial development of the NASA's next generation of upper stage vehicles. Topics addressed include thruster hardware specifications, phase plane design and stability, jet selection approaches, filter design metrics, and automaneuver logic.

Verifiable Adaptive Control with Analytical Stability Margins by Optimal Control Modification

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.

2010-01-01

This paper presents a verifiable model-reference adaptive control method based on an optimal control formulation for linear uncertain systems. A predictor model is formulated to enable a parameter estimation of the system parametric uncertainty. The adaptation is based on both the tracking error and predictor error. Using a singular perturbation argument, it can be shown that the closed-loop system tends to a linear time invariant model asymptotically under an assumption of fast adaptation. A stability margin analysis is given to estimate a lower bound of the time delay margin using a matrix measure method. Using this analytical method, the free design parameter n of the optimal control modification adaptive law can be determined to meet a specification of stability margin for verification purposes.

Reduced conservatism in stability robustness bounds by state transformation

NASA Technical Reports Server (NTRS)

Yedavalli, R. K.; Liang, Z.

1986-01-01

This note addresses the issue of 'conservatism' in the time domain stability robustness bounds obtained by the Liapunov approach. A state transformation is employed to improve the upper bounds on the linear time-varying perturbation of an asymptotically stable linear time-invariant system for robust stability. This improvement is due to the variance of the conservatism of the Liapunov approach with respect to the basis of the vector space in which the Liapunov function is constructed. Improved bounds are obtained, using a transformation, on elemental and vector norms of perturbations (i.e., structured perturbations) as well as on a matrix norm of perturbations (i.e., unstructured perturbations). For the case of a diagonal transformation, an algorithm is proposed to find the 'optimal' transformation. Several examples are presented to illustrate the proposed analysis.

Stability Metrics for Simulation and Flight-Software Assessment and Monitoring of Adaptive Control Assist Compensators

NASA Technical Reports Server (NTRS)

Hodel, A. S.; Whorton, Mark; Zhu, J. Jim

2008-01-01

Due to a need for improved reliability and performance in aerospace systems, there is increased interest in the use of adaptive control or other nonlinear, time-varying control designs in aerospace vehicles. While such techniques are built on Lyapunov stability theory, they lack an accompanying set of metrics for the assessment of stability margins such as the classical gain and phase margins used in linear time-invariant systems. Such metrics must both be physically meaningful and permit the user to draw conclusions in a straightforward fashion. We present in this paper a roadmap to the development of metrics appropriate to nonlinear, time-varying systems. We also present two case studies in which frozen-time gain and phase margins incorrectly predict stability or instability. We then present a multi-resolution analysis approach that permits on-line real-time stability assessment of nonlinear systems.

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

NASA Technical Reports Server (NTRS)

Wen, John T.

1990-01-01

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

Robust Stability and Control of Multi-Body Ground Vehicles with Uncertain Dynamics and Failures

DTIC Science & Technology

2010-01-01

and N. Zhang, 2008. “Robust stability control of vehicle rollover subject to actuator time delay”. Proc. IMechE Part I: J. of systems and control ...Dynamic Systems and Control Conference, Boston, MA, Sept 2010 R.K. Yedavalli,”Robust Stability of Linear Interval Parameter Matrix Family Problem...for control coupled output regulation for a class of systems is presented. In section 2.1.7, the control design algorithm developed in section

Experimental evaluation of HJB optimal controllers for the attitude dynamics of a multirotor aerial vehicle.

PubMed

Prado, Igor Afonso Acampora; Pereira, Mateus de Freitas Virgílio; de Castro, Davi Ferreira; Dos Santos, Davi Antônio; Balthazar, Jose Manoel

2018-06-01

The present paper is concerned with the design and experimental evaluation of optimal control laws for the nonlinear attitude dynamics of a multirotor aerial vehicle. Three design methods based on Hamilton-Jacobi-Bellman equation are taken into account. The first one is a linear control with guarantee of stability for nonlinear systems. The second and third are a nonlinear suboptimal control techniques. These techniques are based on an optimal control design approach that takes into account the nonlinearities present in the vehicle dynamics. The stability Proof of the closed-loop system is presented. The performance of the control system designed is evaluated via simulations and also via an experimental scheme using the Quanser 3-DOF Hover. The experiments show the effectiveness of the linear control method over the nonlinear strategy. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

String Stability of a Linear Formation Flight Control System

NASA Technical Reports Server (NTRS)

Allen, Michael J.; Ryan, Jack; Hanson, Curtis E.; Parle, James F.

2002-01-01

String stability analysis of an autonomous formation flight system was performed using linear and nonlinear simulations. String stability is a measure of how position errors propagate from one vehicle to another in a cascaded system. In the formation flight system considered here, each i(sup th) aircraft uses information from itself and the preceding ((i-1)(sup th)) aircraft to track a commanded relative position. A possible solution for meeting performance requirements with such a system is to allow string instability. This paper explores two results of string instability and outlines analysis techniques for string unstable systems. The three analysis techniques presented here are: linear, nonlinear formation performance, and ride quality. The linear technique was developed from a worst-case scenario and could be applied to the design of a string unstable controller. The nonlinear formation performance and ride quality analysis techniques both use nonlinear formation simulation. Three of the four formation-controller gain-sets analyzed in this paper were limited more by ride quality than by performance. Formations of up to seven aircraft in a cascaded formation could be used in the presence of light gusts with this string unstable system.

Nonlinear stability analysis of Darcy’s flow with viscous heating

PubMed Central

Alves, Leonardo S. de B.; Barletta, Antonio

2016-01-01

The nonlinear stability of a rectangular porous channel saturated by a fluid is here investigated. The aspect ratio of the channel is assumed to be variable. The channel walls are considered impermeable and adiabatic except for the horizontal top which is assumed to be isothermal. The viscous dissipation is acting inside the channel as internal heat generator. A basic throughflow is imposed, and the nonlinear convective stability is investigated by means of the generalized integral transform technique. The neutral stability curve is compared with the one obtained by the linear stability analysis already present in the literature. The growth rate analysis of different unstable modes is performed. The Nusselt number is investigated for several supercritical configurations in order to better understand how the system behaves when conditions far away from neutral stability are considered. The patterns of the neutrally stable convective cells are also reported. Nonlinear simulations support the results obtained by means of the linear stability analysis, confirming that viscous dissipation alone is indeed capable of inducing mixed convection. Low Gebhart or high Péclet numbers lead to a transient overheating of the originally motionless fluid before it settles in its convective steady state. PMID:27279772

LONG TERM STABILITY STUDY AT FNAL AND SLAC USING BINP DEVELOPED HYDROSTATIC LEVEL SYSTEM

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

Seryi, Andrei

2003-05-28

Long term ground stability is essential for achieving the performance goals of the Next Linear Collider. To characterize ground motion on relevant time scales, measurements have been performed at three geologically different locations using a hydrostatic level system developed specifically for these studies. Comparative results from the different sites are presented in this paper.

An iterative technique to stabilize a linear time invariant multivariable system with output feedback

NASA Technical Reports Server (NTRS)

Sankaran, V.

1974-01-01

An iterative procedure for determining the constant gain matrix that will stabilize a linear constant multivariable system using output feedback is described. The use of this procedure avoids the transformation of variables which is required in other procedures. For the case in which the product of the output and input vector dimensions is greater than the number of states of the plant, general solution is given. In the case in which the states exceed the product of input and output vector dimensions, a least square solution which may not be stable in all cases is presented. The results are illustrated with examples.

Energy-balance climate models

NASA Technical Reports Server (NTRS)

North, G. R.; Cahalan, R. F.; Coakley, J. A., Jr.

1980-01-01

An introductory survey of the global energy balance climate models is presented with an emphasis on analytical results. A sequence of increasingly complicated models involving ice cap and radiative feedback processes are solved and the solutions and parameter sensitivities are studied. The model parameterizations are examined critically in light of many current uncertainties. A simple seasonal model is used to study the effects of changes in orbital elements on the temperature field. A linear stability theorem and a complete nonlinear stability analysis for the models are developed. Analytical solutions are also obtained for the linearized models driven by stochastic forcing elements. In this context the relation between natural fluctuation statistics and climate sensitivity is stressed.

Energy balance climate models

NASA Technical Reports Server (NTRS)

North, G. R.; Cahalan, R. F.; Coakley, J. A., Jr.

1981-01-01

An introductory survey of the global energy balance climate models is presented with an emphasis on analytical results. A sequence of increasingly complicated models involving ice cap and radiative feedback processes are solved, and the solutions and parameter sensitivities are studied. The model parameterizations are examined critically in light of many current uncertainties. A simple seasonal model is used to study the effects of changes in orbital elements on the temperature field. A linear stability theorem and a complete nonlinear stability analysis for the models are developed. Analytical solutions are also obtained for the linearized models driven by stochastic forcing elements. In this context the relation between natural fluctuation statistics and climate sensitivity is stressed.

Linear-stability theory of thermocapillary convection in a model of float-zone crystal growth

NASA Technical Reports Server (NTRS)

Neitzel, G. P.; Chang, K.-T.; Jankowski, D. F.; Mittelmann, H. D.

1992-01-01

Linear-stability theory has been applied to a basic state of thermocapillary convection in a model half-zone to determine values of the Marangoni number above which instability is guaranteed. The basic state must be determined numerically since the half-zone is of finite, O(1) aspect ratio with two-dimensional flow and temperature fields. This, in turn, means that the governing equations for disturbance quantities will remain partial differential equations. The disturbance equations are treated by a staggered-grid discretization scheme. Results are presented for a variety of parameters of interest in the problem, including both terrestrial and microgravity cases.

21-nm-range wavelength-tunable L-band Er-doped fiber linear-cavity laser

NASA Astrophysics Data System (ADS)

Yang, Shiquan; Zhao, Chunliu; Li, Zhaohui; Ding, Lei; Yuan, Shuzhong; Dong, Xiaoyi

2001-10-01

A novel method, which utilizes amplified spontaneous emission (ASE) as a secondary pump source, is presented for implanting a linear cavity erbium-doped fiber laser operating in L-Band. The output wavelength tuned from 1566 nm to 1587 nm, about 21 nm tuning range, was obtained in the experiment and the stability of the laser is very good.

Linearization of digital derived rate algorithm for use in linear stability analysis

NASA Technical Reports Server (NTRS)

Graham, R. E.; Porada, T. W.

1985-01-01

The digital derived rate (DDR) algorithm is used to calculate the rate of rotation of the Centaur upper-stage rocket. The DDR is highly nonlinear algorithm, and classical linear stability analysis of the spacecraft cannot be performed without linearization. The performance of this rate algorithm is characterized by a gain and phase curve that drop off at the same frequency. This characteristic is desirable for many applications. A linearization technique for the DDR algorithm is investigated. The linearization method is described. Examples of the results of the linearization technique are illustrated, and the effects of linearization are described. A linear digital filter may be used as a substitute for performing classical linear stability analyses, while the DDR itself may be used in time response analysis.

Robust stability bounds for multi-delay networked control systems

NASA Astrophysics Data System (ADS)

Seitz, Timothy; Yedavalli, Rama K.; Behbahani, Alireza

2018-04-01

In this paper, the robust stability of a perturbed linear continuous-time system is examined when controlled using a sampled-data networked control system (NCS) framework. Three new robust stability bounds on the time-invariant perturbations to the original continuous-time plant matrix are presented guaranteeing stability for the corresponding discrete closed-loop augmented delay-free system (ADFS) with multiple time-varying sensor and actuator delays. The bounds are differentiated from previous work by accounting for the sampled-data nature of the NCS and for separate communication delays for each sensor and actuator, not a single delay. Therefore, this paper expands the knowledge base in multiple inputs multiple outputs (MIMO) sampled-data time delay systems. Bounds are presented for unstructured, semi-structured, and structured perturbations.

Non Lyapunov stability of a constant spatially developing 2-D gas flow

NASA Astrophysics Data System (ADS)

Balint, Agneta M.; Balint, Stefan; Tanasie, Loredana

2017-01-01

Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 2-D gas flow are analyzed in a particular phase space of continuously differentiable functions, endowed with the usual algebraic operations and the topology generated by the uniform convergence on the plane. For this purpose the Euler equations linearized at the constant flow are used. The Lyapunov stability analysis was presented in [1] and this paper is a continuation of [1].

Nonparallel stability of three-dimensional compressible boundary layers. Part 1: Stability analysis

NASA Technical Reports Server (NTRS)

El-Hady, N. M.

1980-01-01

A compressible linear stability theory is presented for nonparallel three-dimensional boundary-layer flows, taking into account the normal velocity component as well as the streamwise and spanwise variations of the basic flow. The method of multiple scales is used to account for the nonparallelism of the basic flow, and equations are derived for the spatial evolution of the disturbance amplitude and wavenumber. The numerical procedure for obtaining the solution of the nonparallel problem is outlined.

Applying the methodology of Design of Experiments to stability studies: a Partial Least Squares approach for evaluation of drug stability.

PubMed

Jordan, Nika; Zakrajšek, Jure; Bohanec, Simona; Roškar, Robert; Grabnar, Iztok

2018-05-01

The aim of the present research is to show that the methodology of Design of Experiments can be applied to stability data evaluation, as they can be seen as multi-factor and multi-level experimental designs. Linear regression analysis is usually an approach for analyzing stability data, but multivariate statistical methods could also be used to assess drug stability during the development phase. Data from a stability study for a pharmaceutical product with hydrochlorothiazide (HCTZ) as an unstable drug substance was used as a case example in this paper. The design space of the stability study was modeled using Umetrics MODDE 10.1 software. We showed that a Partial Least Squares model could be used for a multi-dimensional presentation of all data generated in a stability study and for determination of the relationship among factors that influence drug stability. It might also be used for stability predictions and potentially for the optimization of the extent of stability testing needed to determine shelf life and storage conditions, which would be time and cost-effective for the pharmaceutical industry.

Lyapunov Stability of Fuzzy Discrete Event Systems

NASA Astrophysics Data System (ADS)

Liu, Fuchun; Qiu, Daowen

Fuzzy discrete event systems (FDESs) as a generalization of (crisp) discrete event systems (DESs) may better deal with the problems of fuzziness, impreciseness, and subjectivity. Qiu, Cao and Ying, Liu and Qiu interestingly developed the theory of FDESs. As a continuation of Qiu's work, this paper is to deal with the Lyapunov stability of FDESs, some main results of crisp DESs are generalized. We formalize the notions of the reachability of fuzzy states defined on a metric space. A linear algorithm of computing the r-reachable fuzzy state set is presented. Then we introduce the definitions of stability and asymptotical stability in the sense of Lyapunov to guarantee the convergence of the behaviors of fuzzy automaton to the desired fuzzy states when system engages in some illegal behaviors which can be tolerated. In particular, we present a necessary and sufficient condition for stability and another for asymptotical stability of FDESs.

The inviscid stability of supersonic flow past axisymmetric bodies

NASA Technical Reports Server (NTRS)

Duck, Peter W.

1990-01-01

The supersonic flow past a sharp cone is studied. The associated boundary layer flow (i.e., the velocity and temperature field) is computed. The inviscid linear temporal stability of axisymmetric boundary layers in general is considered, and in particular, a so-called 'triply generalized' inflection condition for 'subsonic' nonaxisymmetric neutral modes is presented. Preliminary numerical results for the stability of the cone boundary layer are presented for a freestream Mach number of 3.8. In particular, a new inviscid mode of instability is seen to occur in certain regimes, and this is shown to be related to a viscous mode found by Duck and Hall (1988).

Cross Flow Effects on Glaze Ice Roughness Formation

NASA Technical Reports Server (NTRS)

Tsao, Jen-Ching

2004-01-01

The present study examines the impact of large-scale cross flow on the creation of ice roughness elements on the leading edge of a swept wing under glaze icing conditions. A three-dimensional triple-deck structure is developed to describe the local interaction of a 3 D air boundary layer with ice sheets and liquid films. A linear stability analysis is presented here. It is found that, as the sweep angle increases, the local icing instabilities enhance and the most linearly unstable modes are strictly three dimensional.

Stability of Nonlinear Systems with Unknown Time-varying Feedback Delay

NASA Astrophysics Data System (ADS)

Chunodkar, Apurva A.; Akella, Maruthi R.

2013-12-01

This paper considers the problem of stabilizing a class of nonlinear systems with unknown bounded delayed feedback wherein the time-varying delay is 1) piecewise constant 2) continuous with a bounded rate. We also consider application of these results to the stabilization of rigid-body attitude dynamics. In the first case, the time-delay in feedback is modeled specifically as a switch among an arbitrarily large set of unknown constant values with a known strict upper bound. The feedback is a linear function of the delayed states. In the case of linear systems with switched delay feedback, a new sufficiency condition for average dwell time result is presented using a complete type Lyapunov-Krasovskii (L-K) functional approach. Further, the corresponding switched system with nonlinear perturbations is proven to be exponentially stable inside a well characterized region of attraction for an appropriately chosen average dwell time. In the second case, the concept of the complete type L-K functional is extended to a class of nonlinear time-delay systems with unknown time-varying time-delay. This extension ensures stability robustness to time-delay in the control design for all values of time-delay less than the known upper bound. Model-transformation is used in order to partition the nonlinear system into a nominal linear part that is exponentially stable with a bounded perturbation. We obtain sufficient conditions which ensure exponential stability inside a region of attraction estimate. A constructive method to evaluate the sufficient conditions is presented together with comparison with the corresponding constant and piecewise constant delay. Numerical simulations are performed to illustrate the theoretical results of this paper.

Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks

NASA Astrophysics Data System (ADS)

Faria, Teresa; Oliveira, José J.

This paper addresses the local and global stability of n-dimensional Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks. Necessary and sufficient conditions for local stability independent of the choice of the delay functions are given, by imposing a weak nondelayed diagonal dominance which cancels the delayed competition effect. The global asymptotic stability of positive equilibria is established under conditions slightly stronger than the ones required for the linear stability. For the case of monotone interactions, however, sharper conditions are presented. This paper generalizes known results for discrete delays to systems with distributed delays. Several applications illustrate the results.

Stability analysis and stabilization strategies for linear supply chains

NASA Astrophysics Data System (ADS)

Nagatani, Takashi; Helbing, Dirk

2004-04-01

Due to delays in the adaptation of production or delivery rates, supply chains can be dynamically unstable with respect to perturbations in the consumption rate, which is known as “bull-whip effect”. Here, we study several conceivable production strategies to stabilize supply chains, which is expressed by different specifications of the management function controlling the production speed in dependence of the stock levels. In particular, we will investigate, whether the reaction to stock levels of other producers or suppliers has a stabilizing effect. We will also demonstrate that the anticipation of future stock levels can stabilize the supply system, given the forecast horizon τ is long enough. To show this, we derive linear stability conditions and carry out simulations for different control strategies. The results indicate that the linear stability analysis is a helpful tool for the judgement of the stabilization effect, although unexpected deviations can occur in the non-linear regime. There are also signs of phase transitions and chaotic behavior, but this remains to be investigated more thoroughly in the future.

On entanglement-assisted quantum codes achieving the entanglement-assisted Griesmer bound

NASA Astrophysics Data System (ADS)

Li, Ruihu; Li, Xueliang; Guo, Luobin

2015-12-01

The theory of entanglement-assisted quantum error-correcting codes (EAQECCs) is a generalization of the standard stabilizer formalism. Any quaternary (or binary) linear code can be used to construct EAQECCs under the entanglement-assisted (EA) formalism. We derive an EA-Griesmer bound for linear EAQECCs, which is a quantum analog of the Griesmer bound for classical codes. This EA-Griesmer bound is tighter than known bounds for EAQECCs in the literature. For a given quaternary linear code {C}, we show that the parameters of the EAQECC that EA-stabilized by the dual of {C} can be determined by a zero radical quaternary code induced from {C}, and a necessary condition under which a linear EAQECC may achieve the EA-Griesmer bound is also presented. We construct four families of optimal EAQECCs and then show the necessary condition for existence of EAQECCs is also sufficient for some low-dimensional linear EAQECCs. The four families of optimal EAQECCs are degenerate codes and go beyond earlier constructions. What is more, except four codes, our [[n,k,d_{ea};c

Scientific Activities Pursuant to the Provisions of AFOSR Grant 79-0018.

DTIC Science & Technology

1984-01-01

controllability implies stabilizability n the case of autono- mous finite dimensional linear systems , we are not surprised to find control ...Current Status of the Control Theory of Single Space Dim- ension Hyperbolicr Systems " was presented at the NASA JPL Symposium on Cbntrol and Stabilization ...theory of hyperbolic systems , including controllability , stabilization , control canonical form theory, etc. To allow a unified and not

Development of Curved-Plate Elements for the Exact Buckling Analysis of Composite Plate Assemblies Including Transverse-Shear Effects

NASA Technical Reports Server (NTRS)

McGowan, David Michael

1997-01-01

The analytical formulation of curved-plate non-linear equilibrium equations including transverse-shear-deformation effects is presented. The formulation uses the principle of virtual work. A unified set of non-linear strains that contains terms from both physical and tensorial strain measures is used. Linearized, perturbed equilibrium equations (stability equations) that describe the response of the plate just after buckling occurs are then derived after the application of several simplifying assumptions. These equations are then modified to allow the reference surface of the plate to be located at a distance z(sub c) from the centroidal surface. The implementation of the new theory into the VICONOPT exact buckling and vibration analysis and optimum design computer program is described as well. The terms of the plate stiffness matrix using both Classical Plate Theory (CPT) and first-order Shear-Deformation Plate Theory (SDPT) are presented. The necessary steps to include the effects of in-plane transverse and in-plane shear loads in the in-plane stability equations are also outlined. Numerical results are presented using the newly implemented capability. Comparisons of results for several example problems with different loading states are made. Comparisons of analyses using both physical and tensorial strain measures as well as CPT and SDPF are also made. Results comparing the computational effort required by the new analysis to that of the analysis currently in the VICONOPT program are presented. The effects of including terms related to in-plane transverse and in-plane shear loadings in the in-plane stability equations are also examined. Finally, results of a design-optimization study of two different cylindrical shells subject to uniform axial compression are presented.

Control logic to track the outputs of a command generator or randomly forced target

NASA Technical Reports Server (NTRS)

Trankle, T. L.; Bryson, A. E., Jr.

1977-01-01

A procedure is presented for synthesizing time-invariant control logic to cause the outputs of a linear plant to track the outputs of an unforced (or randomly forced) linear dynamic system. The control logic uses feed-forward of the reference system state variables and feedback of the plant state variables. The feed-forward gains are obtained from the solution of a linear algebraic matrix equation of the Liapunov type. The feedback gains are the usual regulator gains, determined to stabilize (or augment the stability of) the plant, possibly including integral control. The method is applied here to the design of control logic for a second-order servomechanism to follow a linearly increasing (ramp) signal, an unstable third-order system with two controls to track two separate ramp signals, and a sixth-order system with two controls to track a constant signal and an exponentially decreasing signal (aircraft landing-flare or glide-slope-capture with constant velocity).

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.

Computerized dynamic posturography: the influence of platform stability on postural control.

PubMed

Palm, Hans-Georg; Lang, Patricia; Strobel, Johannes; Riesner, Hans-Joachim; Friemert, Benedikt

2014-01-01

Postural stability can be quantified using posturography systems, which allow different foot platform stability settings to be selected. It is unclear, however, how platform stability and postural control are mathematically correlated. Twenty subjects performed tests on the Biodex Stability System at all 13 stability levels. Overall stability index, medial-lateral stability index, and anterior-posterior stability index scores were calculated, and data were analyzed using analysis of variance and linear regression analysis. A decrease in platform stability from the static level to the second least stable level was associated with a linear decrease in postural control. The overall stability index scores were 1.5 ± 0.8 degrees (static), 2.2 ± 0.9 degrees (level 8), and 3.6 ± 1.7 degrees (level 2). The slope of the regression lines was 0.17 for the men and 0.10 for the women. A linear correlation was demonstrated between platform stability and postural control. The influence of stability levels seems to be almost twice as high in men as in women.

Dc microgrid stabilization through fuzzy control of interleaved, heterogeneous storage elements

NASA Astrophysics Data System (ADS)

Smith, Robert David

As microgrid power systems gain prevalence and renewable energy comprises greater and greater portions of distributed generation, energy storage becomes important to offset the higher variance of renewable energy sources and maximize their usefulness. One of the emerging techniques is to utilize a combination of lead-acid batteries and ultracapacitors to provide both short and long-term stabilization to microgrid systems. The different energy and power characteristics of batteries and ultracapacitors imply that they ought to be utilized in different ways. Traditional linear controls can use these energy storage systems to stabilize a power grid, but cannot effect more complex interactions. This research explores a fuzzy logic approach to microgrid stabilization. The ability of a fuzzy logic controller to regulate a dc bus in the presence of source and load fluctuations, in a manner comparable to traditional linear control systems, is explored and demonstrated. Furthermore, the expanded capabilities (such as storage balancing, self-protection, and battery optimization) of a fuzzy logic system over a traditional linear control system are shown. System simulation results are presented and validated through hardware-based experiments. These experiments confirm the capabilities of the fuzzy logic control system to regulate bus voltage, balance storage elements, optimize battery usage, and effect self-protection.

Stabilization of business cycles of finance agents using nonlinear optimal control

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Ghosh, T.; Sarno, D.

2017-11-01

Stabilization of the business cycles of interconnected finance agents is performed with the use of a new nonlinear optimal control method. First, the dynamics of the interacting finance agents and of the associated business cycles is described by a modeled of coupled nonlinear oscillators. Next, this dynamic model undergoes approximate linearization round a temporary operating point which is defined by the present value of the system's state vector and the last value of the control inputs vector that was exerted on it. The linearization procedure is based on Taylor series expansion of the dynamic model and on the computation of Jacobian matrices. The modelling error, which is due to the truncation of higher-order terms in the Taylor series expansion is considered as a disturbance which is compensated by the robustness of the control loop. Next, for the linearized model of the interacting finance agents, an H-infinity feedback controller is designed. The computation of the feedback control gain requires the solution of an algebraic Riccati equation at each iteration of the control algorithm. Through Lyapunov stability analysis it is proven that the control scheme satisfies an H-infinity tracking performance criterion, which signifies elevated robustness against modelling uncertainty and external perturbations. Moreover, under moderate conditions the global asymptotic stability features of the control loop are proven.

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.

Linearized aerodynamic and control law models of the X-29A airplane and comparison with flight data

NASA Technical Reports Server (NTRS)

Bosworth, John T.

1992-01-01

Flight control system design and analysis for aircraft rely on mathematical models of the vehicle dynamics. In addition to a six degree of freedom nonlinear simulation, the X-29A flight controls group developed a set of programs that calculate linear perturbation models throughout the X-29A flight envelope. The models include the aerodynamics as well as flight control system dynamics and were used for stability, controllability, and handling qualities analysis. These linear models were compared to flight test results to help provide a safe flight envelope expansion. A description is given of the linear models at three flight conditions and two flight control system modes. The models are presented with a level of detail that would allow the reader to reproduce the linear results if desired. Comparison between the response of the linear model and flight measured responses are presented to demonstrate the strengths and weaknesses of the linear models' ability to predict flight dynamics.

Improved Stability and Stabilization Results for Stochastic Synchronization of Continuous-Time Semi-Markovian Jump Neural Networks With Time-Varying Delay.

PubMed

Wei, Yanling; Park, Ju H; Karimi, Hamid Reza; Tian, Yu-Chu; Jung, Hoyoul; Yanling Wei; Park, Ju H; Karimi, Hamid Reza; Yu-Chu Tian; Hoyoul Jung; Tian, Yu-Chu; Wei, Yanling; Jung, Hoyoul; Karimi, Hamid Reza; Park, Ju H

2018-06-01

Continuous-time semi-Markovian jump neural networks (semi-MJNNs) are those MJNNs whose transition rates are not constant but depend on the random sojourn time. Addressing stochastic synchronization of semi-MJNNs with time-varying delay, an improved stochastic stability criterion is derived in this paper to guarantee stochastic synchronization of the response systems with the drive systems. This is achieved through constructing a semi-Markovian Lyapunov-Krasovskii functional together as well as making use of a novel integral inequality and the characteristics of cumulative distribution functions. Then, with a linearization procedure, controller synthesis is carried out for stochastic synchronization of the drive-response systems. The desired state-feedback controller gains can be determined by solving a linear matrix inequality-based optimization problem. Simulation studies are carried out to demonstrate the effectiveness and less conservatism of the presented approach.

Computer Programs for Calculating and Plotting the Stability Characteristics of a Balloon Tethered in a Wind

NASA Technical Reports Server (NTRS)

Bennett, R. M.; Bland, S. R.; Redd, L. T.

1973-01-01

Computer programs for calculating the stability characteristics of a balloon tethered in a steady wind are presented. Equilibrium conditions, characteristic roots, and modal ratios are calculated for a range of discrete values of velocity for a fixed tether-line length. Separate programs are used: (1) to calculate longitudinal stability characteristics, (2) to calculate lateral stability characteristics, (3) to plot the characteristic roots versus velocity, (4) to plot the characteristic roots in root-locus form, (5) to plot the longitudinal modes of motion, and (6) to plot the lateral modes for motion. The basic equations, program listings, and the input and output data for sample cases are presented, with a brief discussion of the overall operation and limitations. The programs are based on a linearized, stability-derivative type of analysis, including balloon aerodynamics, apparent mass, buoyancy effects, and static forces which result from the tether line.

Some problems of nonlinear waves in solid propellant rocket motors

NASA Technical Reports Server (NTRS)

Culick, F. E. C.

1979-01-01

An approximate technique for analyzing nonlinear waves in solid propellant rocket motors is presented which inexpensively provides accurate results up to amplitudes of ten percent. The connection with linear stability analysis is shown. The method is extended to third order in the amplitude of wave motion in order to study nonlinear stability, or triggering. Application of the approximate method to the behavior of pulses is described.

Discrete-time bidirectional associative memory neural networks with variable delays

NASA Astrophysics Data System (ADS)

Liang, variable delays [rapid communication] J.; Cao, J.; Ho, D. W. C.

2005-02-01

Based on the linear matrix inequality (LMI), some sufficient conditions are presented in this Letter for the existence, uniqueness and global exponential stability of the equilibrium point of discrete-time bidirectional associative memory (BAM) neural networks with variable delays. Some of the stability criteria obtained in this Letter are delay-dependent, and some of them are delay-independent, they are less conservative than the ones reported so far in the literature. Furthermore, the results provide one more set of easily verified criteria for determining the exponential stability of discrete-time BAM neural networks.

Non Lyapunov stability of the constant spatially developing 1-D gas flow in presence of solutions having strictly positive exponential growth rate

NASA Astrophysics Data System (ADS)

Balint, Stefan; Balint, Agneta M.

2017-01-01

Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 1-D gas flow are analyzed in the phase space of continuously differentiable functions, endowed with the usual algebraic operations and the topology generated by the uniform convergence on the real axis. For this purpose the Euler equations linearized at the constant flow are used. The Lyapunov stability analysis was presented in [1] and this paper is a continuation of [1].

Integrability and Linear Stability of Nonlinear Waves

NASA Astrophysics Data System (ADS)

Degasperis, Antonio; Lombardo, Sara; Sommacal, Matteo

2018-03-01

It is well known that the linear stability of solutions of 1+1 partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the linearized equation which makes use only of the associated Lax pair with no reference to spectral data and boundary conditions. This local construction is given in the general N× N matrix scheme so as to be applicable to a large class of integrable equations, including the multicomponent nonlinear Schrödinger system and the multiwave resonant interaction system. The analytical and numerical computations involved in this general approach are detailed as an example for N=3 for the particular system of two coupled nonlinear Schrödinger equations in the defocusing, focusing and mixed regimes. The instabilities of the continuous wave solutions are fully discussed in the entire parameter space of their amplitudes and wave numbers. By defining and computing the spectrum in the complex plane of the spectral variable, the eigenfrequencies are explicitly expressed. According to their topological properties, the complete classification of these spectra in the parameter space is presented and graphically displayed. The continuous wave solutions are linearly unstable for a generic choice of the coupling constants.

Stability of multiloop LQ regulators with nonlinearities. I - Regions of attraction. II - Regions of ultimate boundedness

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1986-01-01

An investigation is conducted for the closed loop stability of linear time-invariant systems controlled by linear quadratic (LQ) regulators, in cases where nonlinearities exist in the control channels lying outside the stability sector in regions away from the origin. The estimate of the region of attraction thus obtained furnishes methods for the selection of performance function weights for more robust LQ designs. Attention is then given to the closed loop stability of linear time-invariant systems controlled by the LQ regulators when the nonlinearities in the loops escape the stability sector in a bounded region containing the origin.

Applied Time Domain Stability Margin Assessment for Nonlinear Time-Varying Systems

NASA Technical Reports Server (NTRS)

Kiefer, J. M.; Johnson, M. D.; Wall, J. H.; Dominguez, A.

2016-01-01

The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation. This technique was implemented by using the Stability Aerospace Vehicle Analysis Tool (SAVANT) computer simulation to evaluate the stability of the SLS system with the Adaptive Augmenting Control (AAC) active and inactive along its ascent trajectory. The gains for which the vehicle maintains apparent time-domain stability defines the gain margins, and the time delay similarly defines the phase margin. This method of extracting the control stability margins from the time-domain simulation is relatively straightforward and the resultant margins can be compared to the linearized system results. The sections herein describe the techniques employed to extract the time-domain margins, compare the results between these nonlinear and the linear methods, and provide explanations for observed discrepancies. The SLS ascent trajectory was simulated with SAVANT and the classical linear stability margins were evaluated at one second intervals. The linear analysis was performed with the AAC algorithm disabled to attain baseline stability margins. At each time point, the system was linearized about the current operating point using Simulink's built-in solver. Each linearized system in time was evaluated for its rigid-body gain margin (high frequency gain margin), rigid-body phase margin, and aero gain margin (low frequency gain margin) for each control axis. Using the stability margins derived from the baseline linearization approach, the time domain derived stability margins were determined by executing time domain simulations in which axis-specific incremental gain and phase adjustments were made to the nominal system about the expected neutral stability point at specific flight times. The baseline stability margin time histories were used to shift the system gain to various values around the zero margin point such that a precise amount of expected gain margin was maintained throughout flight. When assessing the gain margins, the gain was applied starting at the time point under consideration, thereafter following the variation in the margin found in the linear analysis. When assessing the rigid-body phase margin, a constant time delay was applied to the system starting at the time point under consideration. If the baseline stability margins were correctly determined via the linear analysis, the time domain simulation results should contain unstable behavior at certain gain and phase values. Examples will be shown from repeated simulations with variable added gain and phase lag. Faithfulness of margins calculated from the linear analysis to the nonlinear system will be demonstrated.

Microsegregation during directional solidification

NASA Technical Reports Server (NTRS)

Coriell, S. R.; Mcfadden, G. B.

1984-01-01

During the directional solidification of alloys, solute inhomogeneities transverse to the growth direction arise due to morphological instabilities (leading to cellular or dendritic growth) and/or due to convection in the melt. In the absence of convection, the conditions for the onset of morphological instability are given by the linear stability analysis of Mullins and Sekerka. For ordinary solidification rates, the predictions of linear stability analysis are similar to the constitutional supercooling criterion. However, at very rapid solidification rates, linear stability analysis predicts a vast increase in stabilization in comparison to constitutional supercooling.

Stability of a diffuse linear pinch with axial boundaries

NASA Technical Reports Server (NTRS)

Einaudi, G.; Van Hoven, G.

1981-01-01

A formulation of the stability behavior of a finite-length pinch is presented. A general initial perturbation is expressed as a uniformly convergent sum over a complete discrete k set. A variational calculation is then performed, based on the energy principle, in which the end-boundary conditions appear as constraints. The requisite Lagrange multipliers mutually couple the elemental periodic excitations. The resulting extended form of delta-W still admits a proper second-variation treatment so that the minimization and stability considerations of Newcomb remain applicable. Comparison theorems are discussed as is the relevance of this end-effect model to the stability of solar coronal loops.

Robust stability of bidirectional associative memory neural networks with time delays

NASA Astrophysics Data System (ADS)

Park, Ju H.

2006-01-01

Based on the Lyapunov Krasovskii functionals combined with linear matrix inequality approach, a novel stability criterion is proposed for asymptotic stability of bidirectional associative memory neural networks with time delays. A novel delay-dependent stability criterion is given in terms of linear matrix inequalities, which can be solved easily by various optimization algorithms.

Development of fault tolerant adaptive control laws for aerospace systems

NASA Astrophysics Data System (ADS)

Perez Rocha, Andres E.

The main topic of this dissertation is the design, development and implementation of intelligent adaptive control techniques designed to maintain healthy performance of aerospace systems subjected to malfunctions, external parameter changes and/or unmodeled dynamics. The dissertation is focused on the development of novel adaptive control configurations that rely on non-linear functions that appear in the immune system of living organisms as main source of adaptation. One of the main goals of this dissertation is to demonstrate that these novel adaptive control architectures are able to improve overall performance and protect the system while reducing control effort and maintaining adequate operation outside bounds of nominal design. This research effort explores several phases, ranging from theoretical stability analysis, simulation and hardware implementation on different types of aerospace systems including spacecraft, aircraft and quadrotor vehicles. The results presented in this dissertation are focused on two main adaptivity approaches, the first one is intended for aerospace systems that do not attain large angles and use exact feedback linearization of Euler angle kinematics. A proof of stability is presented by means of the circle Criterion and Lyapunov's direct method. The second approach is intended for aerospace systems that can attain large attitude angles (e.g. space systems in gravity-less environments), the adaptation is incorporated on a baseline architecture that uses partial feedback linearization of quaternions kinematics. In this case, the closed loop stability was analyzed using Lyapunov's direct method and Barbalat's Lemma. It is expected that some results presented in this dissertation can contribute towards the validation and certification of direct adaptive controllers.

Stability investigations of relaxing molecular gas flows. Results and perspectives

NASA Astrophysics Data System (ADS)

Grigor'ev, Yurii N.; Ershov, Igor V.

2017-10-01

This article presents results of systematic investigations of a dissipative effect which manifests itself as the growth of hydrodynamic stability and suppression of turbulence in relaxing molecular gas flows. The effect can be a new way for control stability and laminar turbulent transition in aerodynamic flows. The consideration of suppression of inviscid acoustic waves in 2D shear flows is presented. Nonlinear evolution of large-scale vortices and Kelvin — Helmholtz waves in relaxing shear flows are studied. Critical Reynolds numbers in supersonic Couette flows are calculated analytically and numerically within the framework of both classical linear and nonlinear energy hydrodynamic stability theories. The calculations clearly show that the relaxation process can appreciably delay the laminar-turbulent transition. The aim of this article is to show the new dissipative effect, which can be used for flow control and laminarization.

Implant stability during initiation and resolution of experimental periimplantitis: an experimental study in the dog.

PubMed

Sennerby, Lars; Persson, Leif G; Berglundh, Tord; Wennerberg, Ann; Lindhe, Jan

2005-01-01

Histologic studies have demonstrated the possibility to reestablish direct bone-implant contacts after ligature-induced periimplantitis. The influence of the reosseointegration on the stability of implants is not known. The aim of the present investigation was to study bone tissue and associated implant stability alterations that occurred during induction and resolution of periimplantitis using resonance frequency analysis (RFA), radiography, and histology. Three implants with smooth (turned) or roughened (SLA) surfaces were placed in each side of the edentulous mandible of four dogs. Experimental periimplantitis was induced for 3 months. Five weeks later, the animals were treated with antibiotics and surgical therapy and were followed for another 6 months. Periapical radiographs and RFA were used to evaluate marginal bone levels and implant stability throughout the study period. After termination, the tissue-implant interface was evaluated by light microscopy in ground sections. There was a linear relationship between radiographic and RFA findings because continuous loss of marginal bone and a decrease in implant stability were observed for both implant surfaces during the periimplantitis period. Antibiotic treatment and surgical therapy resulted in some reosseointegration, which was more marked for the SLA surface. The resonance frequency values corresponded well to the histometric measurements because reosseointegration resulted in an increase in implant stability. The findings from the present study indicate a linear relationship between marginal bone level and resonance frequency value. It is suggested that the RFA technique is sensitive and may be used to detect even a minor change in the level of bone-implant contact.

Numerical analysis of stiffened shells of revolution. Volume 1: Theory manual for STARS-2S, 2B, 2V digital computer programs

NASA Technical Reports Server (NTRS)

Svalbonas, V.

1973-01-01

The theoretical analysis background for the STARS-2 (shell theory automated for rotational structures) program is presented. The theory involved in the axisymmetric nonlinear and unsymmetric linear static analyses, and the stability and vibrations (including critical rotation speed) analyses involving axisymmetric prestress are discussed. The theory for nonlinear static, stability, and vibrations analyses, involving shells with unsymmetric loadings are included.

Linearized Poststall Aerodynamic and Control Law Models of the X-31A Aircraft and Comparison with Flight Data

NASA Technical Reports Server (NTRS)

Stoliker, Patrick C.; Bosworth, John T.; Georgie, Jennifer

1997-01-01

The X-31A aircraft has a unique configuration that uses thrust-vector vanes and aerodynamic control effectors to provide an operating envelope to a maximum 70 deg angle of attack, an inherently nonlinear portion of the flight envelope. This report presents linearized versions of the X-31A longitudinal and lateral-directional control systems, with aerodynamic models sufficient to evaluate characteristics in the poststall envelope at 30 deg, 45 deg, and 60 deg angle of attack. The models are presented with detail sufficient to allow the reader to reproduce the linear results or perform independent control studies. Comparisons between the responses of the linear models and flight data are presented in the time and frequency domains to demonstrate the strengths and weaknesses of the ability to predict high-angle-of-attack flight dynamics using linear models. The X-31A six-degree-of-freedom simulation contains a program that calculates linear perturbation models throughout the X-31A flight envelope. The models include aerodynamics and flight control system dynamics that are used for stability, controllability, and handling qualities analysis. The models presented in this report demonstrate the ability to provide reasonable linear representations in the poststall flight regime.

Linear Augmentation for Stabilizing Stationary Solutions: Potential Pitfalls and Their Application

PubMed Central

Karnatak, Rajat

2015-01-01

Linear augmentation has recently been shown to be effective in targeting desired stationary solutions, suppressing bistablity, in regulating the dynamics of drive response systems and in controlling the dynamics of hidden attractors. The simplicity of the procedure is the main highlight of this scheme but questions related to its general applicability still need to be addressed. Focusing on the issue of targeting stationary solutions, this work demonstrates instances where the scheme fails to stabilize the required solutions and leads to other complicated dynamical scenarios. Examples from conservative as well as dissipative systems are presented in this regard and important applications in dissipative predator—prey systems are discussed, which include preventative measures to avoid potentially catastrophic dynamical transitions in these systems. PMID:26544879

Stability analysis and trend study of a balloon tethered in a wind, with experimental comparisons

NASA Technical Reports Server (NTRS)

Redd, L. T.; Bland, S. R.; Bennett, R. M.

1973-01-01

A stability analysis and trend study for a balloon tethered in a steady wind are presented. The linearized, stability-derivative type analysis includes balloon aerodynamics, buoyancy, mass (including apparent mass), and static forces resulting from the tether cable. The analysis has been applied to a balloon 7.64 m in length, and the results are compared with those from tow tests of this balloon. This comparison shows that the analysis gives reasonable predictions for the damping, frequencies, modes of motion, and stability boundaries exhibited by the balloon. A trend study for the 7.64-m balloon was made to illustrate how the stability boundaries are affected by changes in individual stability parameters. The trends indicated in this study may also be applicable to many other tethered-balloon systems.

Miscible gravitational instability of initially stable horizontal interface in a porous medium: Non-monotonic density profiles

NASA Astrophysics Data System (ADS)

Kim, Min Chan

2014-11-01

To simulate a CO2 sequestration process, some researchers employed a water/propylene glycol (PPG) system which shows a non-monotonic density profile. Motivated by this fact, the stability of the diffusion layer of two miscible fluids saturated in a porous medium is analyzed. For a non-monotonic density profile system, linear stability equations are derived in a global domain, and then transformed into a system of ordinary differential equations in an infinite domain. Initial growth rate analysis is conducted without the quasi-steady state approximation (QSSA) and shows that initially the system is unconditionally stable for the least stable disturbance. For the time evolving case, the ordinary differential equations are solved applying the eigen-analysis and numerical shooting scheme with and without the QSSA. To support these theoretical results, direct numerical simulations are conducted using the Fourier spectral method. The results of theoretical linear stability analyses and numerical simulations validate one another. The present linear and nonlinear analyses show that the water/PPG system is more unstable than the CO2/brine one, and the flow characteristics of these two systems are quite different from each other.

Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

NASA Astrophysics Data System (ADS)

Densmore, Jeffery D.; Warsa, James S.; Lowrie, Robert B.; Morel, Jim E.

2009-09-01

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

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

NASA Technical Reports Server (NTRS)

Chu, K. C.

1975-01-01

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

Immittance Data Validation by Kramers‐Kronig Relations – Derivation and Implications

PubMed Central

2017-01-01

Abstract Explicitly based on causality, linearity (superposition) and stability (time invariance) and implicit on continuity (consistency), finiteness (convergence) and uniqueness (single valuedness) in the time domain, Kramers‐Kronig (KK) integral transform (KKT) relations for immittances are derived as pure mathematical constructs in the complex frequency domain using the two‐sided (bilateral) Laplace integral transform (LT) reduced to the Fourier domain for sufficiently rapid exponential decaying, bounded immittances. Novel anti KK relations are also derived to distinguish LTI (linear, time invariant) systems from non‐linear, unstable and acausal systems. All relations can be used to test KK transformability on the LTI principles of linearity, stability and causality of measured and model data by Fourier transform (FT) in immittance spectroscopy (IS). Also, integral transform relations are provided to estimate (conjugate) immittances at zero and infinite frequency particularly useful to normalise data and compare data. Also, important implications for IS are presented and suggestions for consistent data analysis are made which generally apply likewise to complex valued quantities in many fields of engineering and natural sciences. PMID:29577007

A linear stability analysis for nonlinear, grey, thermal radiative transfer problems

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

Wollaber, Allan B., E-mail: wollaber@lanl.go; Larsen, Edward W., E-mail: edlarsen@umich.ed

2011-02-20

We present a new linear stability analysis of three time discretizations and Monte Carlo interpretations of the nonlinear, grey thermal radiative transfer (TRT) equations: the widely used 'Implicit Monte Carlo' (IMC) equations, the Carter Forest (CF) equations, and the Ahrens-Larsen or 'Semi-Analog Monte Carlo' (SMC) equations. Using a spatial Fourier analysis of the 1-D Implicit Monte Carlo (IMC) equations that are linearized about an equilibrium solution, we show that the IMC equations are unconditionally stable (undamped perturbations do not exist) if {alpha}, the IMC time-discretization parameter, satisfies 0.5 < {alpha} {<=} 1. This is consistent with conventional wisdom. However, wemore » also show that for sufficiently large time steps, unphysical damped oscillations can exist that correspond to the lowest-frequency Fourier modes. After numerically confirming this result, we develop a method to assess the stability of any time discretization of the 0-D, nonlinear, grey, thermal radiative transfer problem. Subsequent analyses of the CF and SMC methods then demonstrate that the CF method is unconditionally stable and monotonic, but the SMC method is conditionally stable and permits unphysical oscillatory solutions that can prevent it from reaching equilibrium. This stability theory provides new conditions on the time step to guarantee monotonicity of the IMC solution, although they are likely too conservative to be used in practice. Theoretical predictions are tested and confirmed with numerical experiments.« less

A linear stability analysis for nonlinear, grey, thermal radiative transfer problems

NASA Astrophysics Data System (ADS)

Wollaber, Allan B.; Larsen, Edward W.

2011-02-01

We present a new linear stability analysis of three time discretizations and Monte Carlo interpretations of the nonlinear, grey thermal radiative transfer (TRT) equations: the widely used “Implicit Monte Carlo” (IMC) equations, the Carter Forest (CF) equations, and the Ahrens-Larsen or “Semi-Analog Monte Carlo” (SMC) equations. Using a spatial Fourier analysis of the 1-D Implicit Monte Carlo (IMC) equations that are linearized about an equilibrium solution, we show that the IMC equations are unconditionally stable (undamped perturbations do not exist) if α, the IMC time-discretization parameter, satisfies 0.5 < α ⩽ 1. This is consistent with conventional wisdom. However, we also show that for sufficiently large time steps, unphysical damped oscillations can exist that correspond to the lowest-frequency Fourier modes. After numerically confirming this result, we develop a method to assess the stability of any time discretization of the 0-D, nonlinear, grey, thermal radiative transfer problem. Subsequent analyses of the CF and SMC methods then demonstrate that the CF method is unconditionally stable and monotonic, but the SMC method is conditionally stable and permits unphysical oscillatory solutions that can prevent it from reaching equilibrium. This stability theory provides new conditions on the time step to guarantee monotonicity of the IMC solution, although they are likely too conservative to be used in practice. Theoretical predictions are tested and confirmed with numerical experiments.

Multi-flexible-body analysis for application to wind turbine control design

NASA Astrophysics Data System (ADS)

Lee, Donghoon

The objective of the present research is to build a theoretical and computational framework for the aeroelastic analysis of flexible rotating systems, more specifically with special application to a wind turbine control design. The methodology is based on the integration of Kane's approach for the analysis of the multi-rigid-body subsystem and a mixed finite element method for the analysis of the flexible-body subsystem. The combined analysis is then strongly coupled with an aerodynamic model based on Blade Element Momentum theory for inflow model. The unified framework from the analysis of subsystems is represented as, in a symbolic manner, a set of nonlinear ordinary differential equations with time-variant, periodic coefficients, which describe the aeroelastic behavior of whole system. The framework can be directly applied to control design due to its symbolic characteristics. The solution procedures for the equations are presented for the study of nonlinear simulation, periodic steady-state solution, and Floquet stability of the linearized system about the steady-state solution. Finally the linear periodic system equation can be obtained with both system and control matrices as explicit functions of time, which can be directly applicable to control design. The structural model is validated by comparison of its results with those from software, some of which is commercial. The stability of the linearized system about periodic steady-state solution is different from that obtained about a constant steady-state solution, which have been conventional in the field of wind turbine dynamics. Parametric studies are performed on a wind turbine model with various pitch angles, precone angles, and rotor speeds. Combined with composite material, their effects on wind turbine aeroelastic stability are investigated. Finally it is suggested that the aeroelastic stability analysis and control design for the whole system is crucial for the design of wind turbines, and the present research breaks new ground in the ability to treat the issue.

On-orbit frequency stability analysis of the GPS NAVSTAR-1 quartz clock and the NAVSTARs-6 and -8 rubidium clocks

NASA Technical Reports Server (NTRS)

Mccaskill, T. B.; Buisson, J. A.; Reid, W. G.

1984-01-01

An on-orbit frequency stability performance analysis of the GPS NAVSTAR-1 quartz clock and the NAVSTARs-6 and -8 rubidium clocks is presented. The clock offsets were obtained from measurements taken at the GPS monitor stations which use high performance cesium standards as a reference. Clock performance is characterized through the use of the Allan variance, which is evaluated for sample times of 15 minutes to two hours, and from one day to 10 days. The quartz and rubidium clocks' offsets were corrected for aging rate before computing the frequency stability. The effect of small errors in aging rate is presented for the NAVSTAR-8 rubidium clock's stability analysis. The analysis includes presentation of time and frequency residuals with respect to linear and quadratic models, which aid in obtaining aging rate values and identifying systematic and random effects. The frequency stability values were further processed with a time domain noise process analysis, which is used to classify random noise process and modulation type.

The influence of dynamic inflow and torsional flexibility on rotor damping in forward flight from symbolically generated equations

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Warmbrodt, W.

1985-01-01

The combined effects of blade torsion and dynamic inflow on the aeroelastic stability of an elastic rotor blade in forward flight are studied. The governing sets of equations of motion (fully nonlinear, linearized, and multiblade equations) used in this study are derived symbolically using a program written in FORTRAN. Stability results are presented for different structural models with and without dynamic inflow. A combination of symbolic and numerical programs at the proper stage in the derivation process makes the obtainment of final stability results an efficient and straightforward procedure.

Stabilization and control of distributed systems with time-dependent spatial domains

NASA Technical Reports Server (NTRS)

Wang, P. K. C.

1990-01-01

This paper considers the problem of the stabilization and control of distributed systems with time-dependent spatial domains. The evolution of the spatial domains with time is described by a finite-dimensional system of ordinary differential equations, while the distributed systems are described by first-order or second-order linear evolution equations defined on appropriate Hilbert spaces. First, results pertaining to the existence and uniqueness of solutions of the system equations are presented. Then, various optimal control and stabilization problems are considered. The paper concludes with some examples which illustrate the application of the main results.

LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays

NASA Astrophysics Data System (ADS)

Zhang, Hai; Ye, Renyu; Liu, Song; Cao, Jinde; Alsaedi, Ahmad; Li, Xiaodi

2018-02-01

This paper is concerned with the asymptotic stability of the Riemann-Liouville fractional-order neural networks with discrete and distributed delays. By constructing a suitable Lyapunov functional, two sufficient conditions are derived to ensure that the addressed neural network is asymptotically stable. The presented stability criteria are described in terms of the linear matrix inequalities. The advantage of the proposed method is that one may avoid calculating the fractional-order derivative of the Lyapunov functional. Finally, a numerical example is given to show the validity and feasibility of the theoretical results.

Guidelines for Computing Longitudinal Dynamic Stability Characteristics of a Subsonic Transport

NASA Technical Reports Server (NTRS)

Thompson, Joseph R.; Frank, Neal T.; Murphy, Patrick C.

2010-01-01

A systematic study is presented to guide the selection of a numerical solution strategy for URANS computation of a subsonic transport configuration undergoing simulated forced oscillation about its pitch axis. Forced oscillation is central to the prevalent wind tunnel methodology for quantifying aircraft dynamic stability derivatives from force and moment coefficients, which is the ultimate goal for the computational simulations. Extensive computations are performed that lead in key insights of the critical numerical parameters affecting solution convergence. A preliminary linear harmonic analysis is included to demonstrate the potential of extracting dynamic stability derivatives from computational solutions.

Riding and handling qualities of light aircraft: A review and analysis

NASA Technical Reports Server (NTRS)

Smetana, F. O.; Summery, D. C.; Johnson, W. D.

1972-01-01

Design procedures and supporting data necessary for configuring light aircraft to obtain desired responses to pilot commands and gusts are presented. The procedures employ specializations of modern military and jet transport practice where these provide an improvement over earlier practice. General criteria for riding and handling qualities are discussed in terms of the airframe dynamics. Methods available in the literature for calculating the coefficients required for a linearized analysis of the airframe dynamics are reviewed in detail. The review also treats the relation of spin and stall to airframe geometry. Root locus analysis is used to indicate the sensitivity of airframe dynamics to variations in individual stability derivatives and to variations in geometric parameters. Computer programs are given for finding the frequencies, damping ratios, and time constants of all rigid body modes and for generating time histories of aircraft motions in response to control inputs. Appendices are included presenting the derivation of the linearized equations of motion; the stability derivatives; the transfer functions; approximate solutions for the frequency, damping ratio, and time constants; an indication of methods to be used when linear analysis is inadequate; sample calculations; and an explanation of the use of root locus diagrams and Bode plots.

Quasi-Static Analysis of Round LaRC THUNDER Actuators

NASA Technical Reports Server (NTRS)

Campbell, Joel F.

2007-01-01

An analytic approach is developed to predict the shape and displacement with voltage in the quasi-static limit of round LaRC Thunder Actuators. The problem is treated with classical lamination theory and Von Karman non-linear analysis. In the case of classical lamination theory exact analytic solutions are found. It is shown that classical lamination theory is insufficient to describe the physical situation for large actuators but is sufficient for very small actuators. Numerical results are presented for the non-linear analysis and compared with experimental measurements. Snap-through behavior, bifurcation, and stability are presented and discussed.

Quasi-Static Analysis of LaRC THUNDER Actuators

NASA Technical Reports Server (NTRS)

Campbell, Joel F.

2007-01-01

An analytic approach is developed to predict the shape and displacement with voltage in the quasi-static limit of LaRC Thunder Actuators. The problem is treated with classical lamination theory and Von Karman non-linear analysis. In the case of classical lamination theory exact analytic solutions are found. It is shown that classical lamination theory is insufficient to describe the physical situation for large actuators but is sufficient for very small actuators. Numerical results are presented for the non-linear analysis and compared with experimental measurements. Snap-through behavior, bifurcation, and stability are presented and discussed.

Robust shrinking ellipsoid model predictive control for linear parameter varying system

PubMed Central

Yan, Yan

2017-01-01

In this paper, a new off-line model predictive control strategy is presented for a kind of linear parameter varying system with polytopic uncertainty. A nest of shrinking ellipsoids is constructed by solving linear matrix inequality. By splitting the objective function into two parts, the proposed strategy moves most computations off-line. The on-line computation is only calculating the current control to assure the system shrinking into the smaller ellipsoid. With the proposed formulation, the stability of the closed system is proved, followed with two numerical examples to demonstrate the proposed method’s effectiveness in the end. PMID:28575028

YADCLAN: yet another digitally-controlled linear artificial neuron.

PubMed

Frenger, Paul

2003-01-01

This paper updates the author's 1999 RMBS presentation on digitally controlled linear artificial neuron design. Each neuron is based on a standard operational amplifier having excitatory and inhibitory inputs, variable gain, an amplified linear analog output and an adjustable threshold comparator for digital output. This design employs a 1-wire serial network of digitally controlled potentiometers and resistors whose resistance values are set and read back under microprocessor supervision. This system embodies several unique and useful features, including: enhanced neuronal stability, dynamic reconfigurability and network extensibility. This artificial neuronal is being employed for feature extraction and pattern recognition in an advanced robotic application.

A note on the effects of viscosity on the stability of a trailing-line vortex

NASA Technical Reports Server (NTRS)

Duck, Peter W.; Khorrami, Mehdi R.

1992-01-01

The linear stability of the Batchelor (1964) vortex is examined with emphasis on new viscous modes recently found numerically by Khorrami (1991). Unlike the previously reported inviscid modes of instability, these modes are destabilized by viscosity and exhibit small growth rates at large Reynolds numbers. The analysis presented here uses a combination of asymptotic and numerical techniques. The results confirm the existence of the additional modes of instability due to viscosity.

Byzantine-fault tolerant self-stabilizing protocol for distributed clock synchronization systems

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R. (Inventor)

2010-01-01

A rapid Byzantine self-stabilizing clock synchronization protocol that self-stabilizes from any state, tolerates bursts of transient failures, and deterministically converges within a linear convergence time with respect to the self-stabilization period. Upon self-stabilization, all good clocks proceed synchronously. The Byzantine self-stabilizing clock synchronization protocol does not rely on any assumptions about the initial state of the clocks. Furthermore, there is neither a central clock nor an externally generated pulse system. The protocol converges deterministically, is scalable, and self-stabilizes in a short amount of time. The convergence time is linear with respect to the self-stabilization period.

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

PubMed

Hamed, Kaveh Akbari; Gregg, Robert D

2016-07-01

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

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

PubMed

Hamed, Kaveh Akbari; Gregg, Robert D

2017-07-01

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

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

PubMed Central

Hamed, Kaveh Akbari; Gregg, Robert D.

2016-01-01

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

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

PubMed Central

Hamed, Kaveh Akbari; Gregg, Robert D.

2016-01-01

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

Dwell time-based stabilisation of switched delay systems using free-weighting matrices

NASA Astrophysics Data System (ADS)

Koru, Ahmet Taha; Delibaşı, Akın; Özbay, Hitay

2018-01-01

In this paper, we present a quasi-convex optimisation method to minimise an upper bound of the dwell time for stability of switched delay systems. Piecewise Lyapunov-Krasovskii functionals are introduced and the upper bound for the derivative of Lyapunov functionals is estimated by free-weighting matrices method to investigate non-switching stability of each candidate subsystems. Then, a sufficient condition for the dwell time is derived to guarantee the asymptotic stability of the switched delay system. Once these conditions are represented by a set of linear matrix inequalities , dwell time optimisation problem can be formulated as a standard quasi-convex optimisation problem. Numerical examples are given to illustrate the improvements over previously obtained dwell time bounds. Using the results obtained in the stability case, we present a nonlinear minimisation algorithm to synthesise the dwell time minimiser controllers. The algorithm solves the problem with successive linearisation of nonlinear conditions.

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.

Stabilization of nucleic acids by unusual polyamines produced by an extreme thermophile, Thermus thermophilus

PubMed Central

2005-01-01

Extreme thermophiles produce two types of unusual polyamine: long linear polyamines such as caldopentamine and caldohexamine, and branched polyamines such as quaternary ammonium compounds [e.g. tetrakis(3-aminopropyl)ammonium]. To clarify the physiological roles of long linear and branched polyamines in thermophiles, we synthesized them chemically and tested their effects on the stability of ds (double-stranded) and ss (single-stranded) DNAs and tRNA in response to thermal denaturation, as measured by differential scanning calorimetry. Linear polyamines stabilized dsDNA in proportion to the number of amino nitrogen atoms within their molecular structure. We used the empirical results to derive formulae that estimate the melting temperature of dsDNA in the presence of polyamines of a particular molecular composition. ssDNA and tRNA were stabilized more effectively by tetrakis(3-aminopropyl)ammonium than any of the other polyamines tested. We propose that long linear polyamines are effective to stabilize DNA, and tetrakis(3-aminopropyl)ammonium plays important roles in stabilizing RNAs in thermophile cells. PMID:15673283

Stability Analysis of Finite Difference Schemes for Hyperbolic Systems, and Problems in Applied and Computational Linear Algebra.

DTIC Science & Technology

FINITE DIFFERENCE THEORY, * LINEAR ALGEBRA , APPLIED MATHEMATICS, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, COMPUTATIONS, HYPERBOLAS, MATHEMATICAL MODELS, NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, STABILITY.

Length-dependent structural stability of linear monatomic Cu wires

NASA Astrophysics Data System (ADS)

Singh, Gurvinder; Kumar, Krishan; Singh, Baljinder; Moudgil, R. K.

2018-05-01

We present first-principle calculations based on density functional theory for the finite-length monatomic Cu atom linear wires. The structure and its stability with increasing wire length in terms of number of atoms (N) is determined. Interestingly, the bond length is found to exhibit an oscillatory structure (the so-called magic length phenomenon), with a qualitative change in oscillatory behavior as one moves from even N wire to odd N wire. The even N wires follow simple even-odd oscillations whereas odd N wires show a phase change at the half length of the wires. The stability of the wire structure, determined in terms of the wire formation energy, also contains even-odd oscillation as a function of wire length. However, the oscillations in formation energy reverse its phase after the wire length is increased beyond N=12. Our findings are seen to be qualitatively consistent with recent simulations for a similar class finite-length metal atom wires.

Practical robustness measures in multivariable control system analysis. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Lehtomaki, N. A.

1981-01-01

The robustness of the stability of multivariable linear time invariant feedback control systems with respect to model uncertainty is considered using frequency domain criteria. Available robustness tests are unified under a common framework based on the nature and structure of model errors. These results are derived using a multivariable version of Nyquist's stability theorem in which the minimum singular value of the return difference transfer matrix is shown to be the multivariable generalization of the distance to the critical point on a single input, single output Nyquist diagram. Using the return difference transfer matrix, a very general robustness theorem is presented from which all of the robustness tests dealing with specific model errors may be derived. The robustness tests that explicitly utilized model error structure are able to guarantee feedback system stability in the face of model errors of larger magnitude than those robustness tests that do not. The robustness of linear quadratic Gaussian control systems are analyzed.

Space Flyable Hg(sup +) Frequency Standards

NASA Technical Reports Server (NTRS)

Prestage, John D.; Maleki, Lute

1994-01-01

We discuss a design for a space based atomic frequency standard (AFS) based on Hg(sup +) ions confined in a linear ion trap. This newly developed AFS should be well suited for space borne applications because it can supply the ultra-high stability of a H-maser but its total mass is comparable to that of a NAVSTAR/GPS cesium clock, i.e., about 11kg. This paper will compare the proposed Hg(sup +) AFS to the present day GPS cesium standards to arrive at the 11 kg mass estimate. The proposed space borne Hg(sup +) standard is based upon the recently developed extended linear ion trap architecture which has reduced the size of existing trapped Hg(sup +) standards to a physics package which is comparable in size to a cesium beam tube. The demonstrated frequency stability to below 10(sup -15) of existing Hg(sup +) standards should be maintained or even improved upon in this new architecture. This clock would deliver far more frequency stability per kilogram than any current day space qualified standard.

Protein linear indices of the 'macromolecular pseudograph alpha-carbon atom adjacency matrix' in bioinformatics. Part 1: prediction of protein stability effects of a complete set of alanine substitutions in Arc repressor.

PubMed

Marrero-Ponce, Yovani; Medina-Marrero, Ricardo; Castillo-Garit, Juan A; Romero-Zaldivar, Vicente; Torrens, Francisco; Castro, Eduardo A

2005-04-15

A novel approach to bio-macromolecular design from a linear algebra point of view is introduced. A protein's total (whole protein) and local (one or more amino acid) linear indices are a new set of bio-macromolecular descriptors of relevance to protein QSAR/QSPR studies. These amino-acid level biochemical descriptors are based on the calculation of linear maps on Rn[f k(xmi):Rn-->Rn] in canonical basis. These bio-macromolecular indices are calculated from the kth power of the macromolecular pseudograph alpha-carbon atom adjacency matrix. Total linear indices are linear functional on Rn. That is, the kth total linear indices are linear maps from Rn to the scalar R[f k(xm):Rn-->R]. Thus, the kth total linear indices are calculated by summing the amino-acid linear indices of all amino acids in the protein molecule. A study of the protein stability effects for a complete set of alanine substitutions in the Arc repressor illustrates this approach. A quantitative model that discriminates near wild-type stability alanine mutants from the reduced-stability ones in a training series was obtained. This model permitted the correct classification of 97.56% (40/41) and 91.67% (11/12) of proteins in the training and test set, respectively. It shows a high Matthews correlation coefficient (MCC=0.952) for the training set and an MCC=0.837 for the external prediction set. Additionally, canonical regression analysis corroborated the statistical quality of the classification model (Rcanc=0.824). This analysis was also used to compute biological stability canonical scores for each Arc alanine mutant. On the other hand, the linear piecewise regression model compared favorably with respect to the linear regression one on predicting the melting temperature (tm) of the Arc alanine mutants. The linear model explains almost 81% of the variance of the experimental tm (R=0.90 and s=4.29) and the LOO press statistics evidenced its predictive ability (q2=0.72 and scv=4.79). Moreover, the TOMOCOMD-CAMPS method produced a linear piecewise regression (R=0.97) between protein backbone descriptors and tm values for alanine mutants of the Arc repressor. A break-point value of 51.87 degrees C characterized two mutant clusters and coincided perfectly with the experimental scale. For this reason, we can use the linear discriminant analysis and piecewise models in combination to classify and predict the stability of the mutant Arc homodimers. These models also permitted the interpretation of the driving forces of such folding process, indicating that topologic/topographic protein backbone interactions control the stability profile of wild-type Arc and its alanine mutants.

Fuzzy attitude control of solar sail via linear matrix inequalities

NASA Astrophysics Data System (ADS)

Baculi, Joshua; Ayoubi, Mohammad A.

2017-09-01

This study presents a fuzzy tracking controller based on the Takagi-Sugeno (T-S) fuzzy model of the solar sail. First, the T-S fuzzy model is constructed by linearizing the existing nonlinear equations of motion of the solar sail. Then, the T-S fuzzy model is used to derive the state feedback controller gains for the Twin Parallel Distributed Compensation (TPDC) technique. The TPDC tracks and stabilizes the attitude of the solar sail to any desired state in the presence of parameter uncertainties and external disturbances while satisfying actuator constraints. The performance of the TPDC is compared to a PID controller that is tuned using the Ziegler-Nichols method. Numerical simulation shows the TPDC outperforms the PID controller when stabilizing the solar sail to a desired state.

Switching State-Feedback LPV Control with Uncertain Scheduling Parameters

NASA Technical Reports Server (NTRS)

He, Tianyi; Al-Jiboory, Ali Khudhair; Swei, Sean Shan-Min; Zhu, Guoming G.

2017-01-01

This paper presents a new method to design Robust Switching State-Feedback Gain-Scheduling (RSSFGS) controllers for Linear Parameter Varying (LPV) systems with uncertain scheduling parameters. The domain of scheduling parameters are divided into several overlapped subregions to undergo hysteresis switching among a family of simultaneously designed LPV controllers over the corresponding subregion with the guaranteed H-infinity performance. The synthesis conditions are given in terms of Parameterized Linear Matrix Inequalities that guarantee both stability and performance at each subregion and associated switching surfaces. The switching stability is ensured by descent parameter-dependent Lyapunov function on switching surfaces. By solving the optimization problem, RSSFGS controller can be obtained for each subregion. A numerical example is given to illustrate the effectiveness of the proposed approach over the non-switching controllers.

Stability analysis of ELMs in long-pulse discharges with ELITE code on EAST tokamak

NASA Astrophysics Data System (ADS)

Wang, Y. F.; Xu, G. S.; Wan, B. N.; Li, G. Q.; Yan, N.; Li, Y. L.; Wang, H. Q.; Peng, Y.-K. Martin; Xia, T. Y.; Ding, S. Y.; Chen, R.; Yang, Q. Q.; Liu, H. Q.; Zang, Q.; Zhang, T.; Lyu, B.; Xu, J. C.; Feng, W.; Wang, L.; Chen, Y. J.; Luo, Z. P.; Hu, G. H.; Zhang, W.; Shao, L. M.; Ye, Y.; Lan, H.; Chen, L.; Li, J.; Zhao, N.; Wang, Q.; Snyder, P. B.; Liang, Y.; Qian, J. P.; Gong, X. Z.; EAST team

2018-05-01

One challenge in long-pulse and high performance tokamak operation is to control the edge localized modes (ELMs) to reduce the transient heat load on plasma facing components. Minute-scale discharges in H-mode have been achieved repeatedly on Experimental Advanced Superconducting Tokamak (EAST) since the 2016 campaign and understanding the characteristics of the ELMs in these discharges can be helpful for effective ELM control in long-pulse discharges. The kinetic profile diagnostics recently developed on EAST make it possible to perform the pedestal stability analysis quantitatively. Pedestal stability calculation of a typical long-pulse discharge with ELITE code is presented. The ideal linear stability results show that the ELM is dominated by toroidal mode number n around 10–15 and the most unstable mode structure is mainly localized in the steep pressure gradient region, which is consistent with experimental results. Compared with a typical type-I ELM discharge with larger total plasma current (I p = 600 kA), pedestal in the long-pulse H-mode discharge (I p = 450 kA) is more stable in peeling-ballooning instability and its critical peak pressure gradient is evaluated to be 65% of the former. Two important features of EAST tokamak in the long-pulse discharge are presented by comparison with other tokamaks, including a wider pedestal correlated with the poloidal pedestal beta and a smaller inverse aspect ratio and their effects on the pedestal stability are discussed. The effects of uncertainties in measurements on the linear stability results are also analyzed, including the edge electron density profile position, the separatrix position and the line-averaged effective ion charge {Z}{{e}{{f}}{{f}}} value.

Stability and performance tradeoffs in bi-lateral telemanipulation

NASA Technical Reports Server (NTRS)

Hannaford, Blake

1989-01-01

Kinesthetic force feedback provides measurable increase in remote manipulation system performance. Intensive computation time requirements or operation under conditions of time delay can cause serious stability problems in control-system design. Here, a simplified linear analysis of this stability problem is presented for the forward-flow generalized architecture, applying the hybrid two-port representation to express the loop gain of the traditional master-slave architecture, which can be subjected to similar analysis. The hybrid two-port representation is also used to express the effects on the fidelity of manipulation or feel of one design approach used to stabilize the forward-flow architecture. The results suggest that, when local force feedback at the slave side is used to reduce manipulator stability problems, a price is paid in terms of telemanipulation fidelity.

Xcas as a Programming Environment for Stability Conditions for a Class of Differential Equation Models in Economics

NASA Astrophysics Data System (ADS)

Halkos, George E.; Tsilika, Kyriaki D.

2011-09-01

In this paper we examine the property of asymptotic stability in several dynamic economic systems, modeled in ordinary differential equation formulations of time parameter t. Asymptotic stability ensures intertemporal equilibrium for the economic quantity the solution stands for, regardless of what the initial conditions happen to be. Existence of economic equilibrium in continuous time models is checked via a Symbolic language, the Xcas program editor. Using stability theorems of differential equations as background a brief overview of symbolic capabilities of free software Xcas is given. We present computational experience with a programming style for stability results of ordinary linear and nonlinear differential equations. Numerical experiments on traditional applications of economic dynamics exhibit the simplicity clarity and brevity of input and output of our computer codes.

On the Stability of Periodic Mercury-type Rotations

NASA Astrophysics Data System (ADS)

Churkina, Tatyana E.; Stepanov, Sergey Y.

2017-12-01

We consider the stability of planar periodic Mercury-type rotations of a rigid body around its center of mass in an elliptical orbit in a central Newtonian field of forces. Mercurytype rotations mean that the body makes 3 turns around its center of mass during 2 revolutions of the center of mass in its orbit (resonance 3:2). These rotations can be 1) symmetrical 2π- periodic, 2) symmetrical 4π-periodic and 3) asymmetrical 4π-periodic. The stability of rotations of type 1) was investigated by A.P.Markeev. In our paper we present a nonlinear stability analysis for some rotations of types 2) and 3) in 3rd- and 4th-order resonant cases, in the nonresonant case and at the boundaries of regions of linear stability.

Three-dimensional instabilities of natural convection between two differentially heated vertical plates: Linear and nonlinear complementary approaches

NASA Astrophysics Data System (ADS)

Gao, Zhenlan; Podvin, Berengere; Sergent, Anne; Xin, Shihe; Chergui, Jalel

2018-05-01

The transition to the chaos of the air flow between two vertical plates maintained at different temperatures is studied in the Boussinesq approximation. After the first bifurcation at critical Rayleigh number Rac, the flow consists of two-dimensional (2D) corotating rolls. The stability of the 2D rolls is examined, confronting linear predictions with nonlinear integration. In all cases the 2D rolls are destabilized in the spanwise direction. Efficient linear stability analysis based on an Arnoldi method shows competition between two eigenmodes, corresponding to different spanwise wavelengths and different types of roll distortion. Nonlinear integration shows that the lower-wave-number mode is always dominant. A partial route to chaos is established through the nonlinear simulations. The flow becomes temporally chaotic for Ra =1.05 Rac , but remains characterized by the spatial patterns identified by linear stability analysis. This highlights the complementary role of linear stability analysis and nonlinear simulation.

Stochastic Stability of Nonlinear Sampled Data Systems with a Jump Linear Controller

NASA Technical Reports Server (NTRS)

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

2004-01-01

This paper analyzes the stability of a sampled- data system consisting of a deterministic, nonlinear, time- invariant, continuous-time plant and a stochastic, discrete- time, jump linear controller. The jump linear controller mod- els, for example, computer systems and communication net- works that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. To analyze stability, appropriate topologies are introduced for the signal spaces of the sampled- data system. With these topologies, the ideal sampling and zero-order-hold operators are shown to be measurable maps. This paper shows that the known equivalence between the stability of a deterministic, linear sampled-data system and its associated discrete-time representation as well as between a nonlinear sampled-data system and a linearized representation holds even in a stochastic framework.

A fast efficient implicit scheme for the gasdynamic equations using a matrix reduction technique

NASA Technical Reports Server (NTRS)

Barth, T. J.; Steger, J. L.

1985-01-01

An efficient implicit finite-difference algorithm for the gasdynamic equations utilizing matrix reduction techniques is presented. A significant reduction in arithmetic operations is achieved without loss of the stability characteristics generality found in the Beam and Warming approximate factorization algorithm. Steady-state solutions to the conservative Euler equations in generalized coordinates are obtained for transonic flows and used to show that the method offers computational advantages over the conventional Beam and Warming scheme. Existing Beam and Warming codes can be retrofit with minimal effort. The theoretical extension of the matrix reduction technique to the full Navier-Stokes equations in Cartesian coordinates is presented in detail. Linear stability, using a Fourier stability analysis, is demonstrated and discussed for the one-dimensional Euler equations.

Stochastic Stability of Sampled Data Systems with a Jump Linear Controller

NASA Technical Reports Server (NTRS)

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

2004-01-01

In this paper an equivalence between the stochastic stability of a sampled-data system and its associated discrete-time representation is established. The sampled-data system consists of a deterministic, linear, time-invariant, continuous-time plant and a stochastic, linear, time-invariant, discrete-time, jump linear controller. The jump linear controller models computer systems and communication networks that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. This paper shows that the known equivalence between the stability of a deterministic sampled-data system and the associated discrete-time representation holds even in a stochastic framework.

Switched periodic systems in discrete time: stability and input-output norms

NASA Astrophysics Data System (ADS)

Bolzern, Paolo; Colaneri, Patrizio

2013-07-01

This paper deals with the analysis of stability and the characterisation of input-output norms for discrete-time periodic switched linear systems. Such systems consist of a network of time-periodic linear subsystems sharing the same state vector and an exogenous switching signal that triggers the jumps between the subsystems. The overall system exhibits a complex dynamic behaviour due to the interplay between the time periodicity of the subsystem parameters and the switching signal. Both arbitrary switching signals and signals satisfying a dwell-time constraint are considered. Linear matrix inequality conditions for stability and guaranteed H2 and H∞ performances are provided. The results heavily rely on the merge of the theory of linear periodic systems and recent developments on switched linear time-invariant systems.

Explicit asymmetric bounds for robust stability of continuous and discrete-time systems

NASA Technical Reports Server (NTRS)

Gao, Zhiqiang; Antsaklis, Panos J.

1993-01-01

The problem of robust stability in linear systems with parametric uncertainties is considered. Explicit stability bounds on uncertain parameters are derived and expressed in terms of linear inequalities for continuous systems, and inequalities with quadratic terms for discrete-times systems. Cases where system parameters are nonlinear functions of an uncertainty are also examined.

A Crank–Nicolson Leapfrog stabilization: Unconditional stability and two applications

DOE PAGES

Jiang, Nan; Kubacki, Michaela; Layton, William; ...

2014-12-09

We propose and analyze a linear stabilization of the Crank-Nicolson Leapfrog (CNLF) method that removes all time step/CFL conditions for stability and controls the unstable mode. It also increases the SPD part of the linear system to be solved at each time step while increasing solution accuracy. We give a proof of unconditional stability of the method as well as a proof of unconditional, asymptotic stability of both the stable and unstable modes. As a result, we illustrate two applications of the method: uncoupling groundwater-surface water flows and Stokes flow plus a Coriolis term.

Piecewise linear approximation for hereditary control problems

NASA Technical Reports Server (NTRS)

Propst, Georg

1987-01-01

Finite dimensional approximations are presented for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in case the cost integral ranges over a finite time interval as well as in the case it ranges over an infinite time interval. The arguments in the latter case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space R(n) x L(2) and the favorable eigenvalue behavior of the piecewise linear approximations.

Projection Operator: A Step Towards Certification of Adaptive Controllers

NASA Technical Reports Server (NTRS)

Larchev, Gregory V.; Campbell, Stefan F.; Kaneshige, John T.

2010-01-01

One of the major barriers to wider use of adaptive controllers in commercial aviation is the lack of appropriate certification procedures. In order to be certified by the Federal Aviation Administration (FAA), an aircraft controller is expected to meet a set of guidelines on functionality and reliability while not negatively impacting other systems or safety of aircraft operations. Due to their inherent time-variant and non-linear behavior, adaptive controllers cannot be certified via the metrics used for linear conventional controllers, such as gain and phase margin. Projection Operator is a robustness augmentation technique that bounds the output of a non-linear adaptive controller while conforming to the Lyapunov stability rules. It can also be used to limit the control authority of the adaptive component so that the said control authority can be arbitrarily close to that of a linear controller. In this paper we will present the results of applying the Projection Operator to a Model-Reference Adaptive Controller (MRAC), varying the amount of control authority, and comparing controller s performance and stability characteristics with those of a linear controller. We will also show how adjusting Projection Operator parameters can make it easier for the controller to satisfy the certification guidelines by enabling a tradeoff between controller s performance and robustness.

Relevance of Linear Stability Results to Enhanced Oil Recovery

NASA Astrophysics Data System (ADS)

Ding, Xueru; Daripa, Prabir

2012-11-01

How relevant can the results based on linear stability theory for any problem for that matter be to full scale simulation results? Put it differently, is the optimal design of a system based on linear stability results is optimal or even near optimal for the complex nonlinear system with certain objectives of interest in mind? We will address these issues in the context of enhanced oil recovery by chemical flooding. This will be based on an ongoing work. Supported by Qatar National Research Fund (a member of the Qatar Foundation).

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

NASA Technical Reports Server (NTRS)

Luquette,Richard J.; Sanner, Robert M.

2004-01-01

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

Stability Results for Idealized Shear Flows on a Rectangular Periodic Domain

NASA Astrophysics Data System (ADS)

Dullin, Holger R.; Worthington, Joachim

2018-06-01

We present a new linearly stable solution of the Euler fluid flow on a torus. On a two-dimensional rectangular periodic domain [0,2π )× [0,2π / κ ) for κ \\in R^+, the Euler equations admit a family of stationary solutions given by the vorticity profiles Ω ^*(x)= Γ cos (p_1x_1+ κ p_2x_2). We show linear stability for such flows when p_2=0 and κ ≥ |p_1| (equivalently p_1=0 and κ {|p_2|}≤ {1}). The classical result due to Arnold is that for p_1 = 1, p_2 = 0 and κ ≥ 1 the stationary flow is nonlinearly stable via the energy-Casimir method. We show that for κ ≥ |p_1| ≥ 2, p_2 = 0 the flow is linearly stable, but one cannot expect a similar nonlinear stability result. Finally we prove nonlinear instability for all steady states satisfying p_1^2+κ ^2{p_2^2}>{3(κ ^2+1)}/4(7-4√{3)}. The modification and application of a structure-preserving Hamiltonian truncation is discussed for the anisotropic case κ ≠ 1. This leads to an explicit Lie-Poisson integrator for the approximate system, which is used to illustrate our analytical results.

Continuous control of chaos based on the stability criterion.

PubMed

Yu, Hong Jie; Liu, Yan Zhu; Peng, Jian Hua

2004-06-01

A method of chaos control based on stability criterion is proposed in the present paper. This method can stabilize chaotic systems onto a desired periodic orbit by a small time-continuous perturbation nonlinear feedback. This method does not require linearization of the system around the stabilized orbit and only an approximate location of the desired periodic orbit is required which can be automatically detected in the control process. The control can be started at any moment by choosing appropriate perturbation restriction condition. It seems that more flexibility and convenience are the main advantages of this method. The discussions on control of attitude motion of a spacecraft, Rössler system, and two coupled Duffing oscillators are given as numerical examples.

Dynamic stability analysis of torsional vibrations of a shaft system connected by a Hooke's joint through a continuous system model

NASA Astrophysics Data System (ADS)

Bulut, Gökhan

2014-08-01

Stability of parametrically excited torsional vibrations of a shaft system composed of two torsionally elastic shafts interconnected through a Hooke's joint is studied. The shafts are considered to be continuous (distributed-parameter) systems and an approximate discrete model for the torsional vibrations of the shaft system is derived via a finite element scheme. The stability of the solutions of the linearized equations of motion, consisting of a set of Mathieu-Hill type equations, is examined by means of a monodromy matrix method and the results are presented in the form of a Strutt-Ince diagram visualizing the effects of the system parameters on the stability of the shaft system.

Design and fabrication of a hybrid maglev model employing PML and SML

NASA Astrophysics Data System (ADS)

Sun, R. X.; Zheng, J.; Zhan, L. J.; Huang, S. Y.; Li, H. T.; Deng, Z. G.

2017-10-01

A hybrid maglev model combining permanent magnet levitation (PML) and superconducting magnetic levitation (SML) was designed and fabricated to explore a heavy-load levitation system advancing in passive stability and simple structure. In this system, the PML was designed to levitate the load, and the SML was introduced to guarantee the stability. In order to realize different working gaps of the two maglev components, linear bearings were applied to connect the PML layer (for load) and the SML layer (for stability) of the hybrid maglev model. Experimental results indicate that the hybrid maglev model possesses excellent advantages of heavy-load ability and passive stability at the same time. This work presents a possible way to realize a heavy-load passive maglev concept.

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme

NASA Astrophysics Data System (ADS)

Rõõm, Rein; Männik, Aarne; Luhamaa, Andres

2007-10-01

Two-time-level, semi-implicit, semi-Lagrangian (SISL) scheme is applied to the non-hydrostatic pressure coordinate equations, constituting a modified Miller-Pearce-White model, in hybrid-coordinate framework. Neutral background is subtracted in the initial continuous dynamics, yielding modified equations for geopotential, temperature and logarithmic surface pressure fluctuation. Implicit Lagrangian marching formulae for single time-step are derived. A disclosure scheme is presented, which results in an uncoupled diagnostic system, consisting of 3-D Poisson equation for omega velocity and 2-D Helmholtz equation for logarithmic pressure fluctuation. The model is discretized to create a non-hydrostatic extension to numerical weather prediction model HIRLAM. The discretization schemes, trajectory computation algorithms and interpolation routines, as well as the physical parametrization package are maintained from parent hydrostatic HIRLAM. For stability investigation, the derived SISL model is linearized with respect to the initial, thermally non-equilibrium resting state. Explicit residuals of the linear model prove to be sensitive to the relative departures of temperature and static stability from the reference state. Relayed on the stability study, the semi-implicit term in the vertical momentum equation is replaced to the implicit term, which results in stability increase of the model.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Boundary-layer stability and airfoil design

NASA Technical Reports Server (NTRS)

Viken, Jeffrey K.

1986-01-01

Several different natural laminar flow (NLF) airfoils have been analyzed for stability of the laminar boundary layer using linear stability codes. The NLF airfoils analyzed come from three different design conditions: incompressible; compressible with no sweep; and compressible with sweep. Some of the design problems are discussed, concentrating on those problems associated with keeping the boundary layer laminar. Also, there is a discussion on how a linear stability analysis was effectively used to improve the design for some of the airfoils.

Hydrodynamic Stability Analysis on Sheared Stratified Flow in a Convective Flow Environment

NASA Astrophysics Data System (ADS)

Xiao, Yuan; Lin, Wenxian; Armfiled, Steven; Kirkpatrick, Michael; He, Yinghe; Fluid Dynamics Research Group, James Cook University Team; Fluid Dynamics Research Group, University of Sydney Team

2014-11-01

A hydrodynamic stability analysis on the convective sheared boundary layer (SCBL) flow, where a sheared stratified flow and a thermally convective flow coexist, is carried out in this study. The linear unstable stratifications representing the convective flow are included in the TaylorGoldstein equations as an unstable factor Jb. A new unstable region corresponding to the convective instability, which is not present in pure sheared stratified flows, is found with the analysis. It is also found that the boundaries of the convective instability regions expand with increasing Jb and interact with the sheared stratified instability region. More results will be presented at the conference

Comparison of stability and control parameters for a light, single-engine, high-winged aircraft using different flight test and parameter estimation techniques

NASA Technical Reports Server (NTRS)

Suit, W. T.; Cannaday, R. L.

1979-01-01

The longitudinal and lateral stability and control parameters for a high wing, general aviation, airplane are examined. Estimations using flight data obtained at various flight conditions within the normal range of the aircraft are presented. The estimations techniques, an output error technique (maximum likelihood) and an equation error technique (linear regression), are presented. The longitudinal static parameters are estimated from climbing, descending, and quasi steady state flight data. The lateral excitations involve a combination of rudder and ailerons. The sensitivity of the aircraft modes of motion to variations in the parameter estimates are discussed.

Periodic orbits around areostationary points in the Martian gravity field

NASA Astrophysics Data System (ADS)

Liu, Xiao-Dong; Baoyin, Hexi; Ma, Xing-Rui

2012-05-01

This study investigates the problem of areostationary orbits around Mars in three-dimensional space. Areostationary orbits are expected to be used to establish a future telecommunication network for the exploration of Mars. However, no artificial satellites have been placed in these orbits thus far. The characteristics of the Martian gravity field are presented, and areostationary points and their linear stability are calculated. By taking linearized solutions in the planar case as the initial guesses and utilizing the Levenberg-Marquardt method, families of periodic orbits around areostationary points are shown to exist. Short-period orbits and long-period orbits are found around linearly stable areostationary points, but only short-period orbits are found around unstable areostationary points. Vertical periodic orbits around both linearly stable and unstable areostationary points are also examined. Satellites in these periodic orbits could depart from areostationary points by a few degrees in longitude, which would facilitate observation of the Martian topography. Based on the eigenvalues of the monodromy matrix, the evolution of the stability index of periodic orbits is determined. Finally, heteroclinic orbits connecting the two unstable areostationary points are found, providing the possibility for orbital transfer with minimal energy consumption.

Decomposition-aggregation stability analysis. [for large scale dynamic systems with application to spinning Skylab control system

NASA Technical Reports Server (NTRS)

Siljak, D. D.; Weissenberger, S.; Cuk, S. M.

1973-01-01

This report presents the development and description of the decomposition aggregation approach to stability investigations of high dimension mathematical models of dynamic systems. The high dimension vector differential equation describing a large dynamic system is decomposed into a number of lower dimension vector differential equations which represent interconnected subsystems. Then a method is described by which the stability properties of each subsystem are aggregated into a single vector Liapunov function, representing the aggregate system model, consisting of subsystem Liapunov functions as components. A linear vector differential inequality is then formed in terms of the vector Liapunov function. The matrix of the model, which reflects the stability properties of the subsystems and the nature of their interconnections, is analyzed to conclude over-all system stability characteristics. The technique is applied in detail to investigate the stability characteristics of a dynamic model of a hypothetical spinning Skylab.

Linear laser diode arrays for improvement in optical disk recording for space stations

NASA Technical Reports Server (NTRS)

Alphonse, G. A.; Carlin, D. B.; Connolly, J. C.

1990-01-01

The design and fabrication of individually addressable laser diode arrays for high performance magneto-optic recording systems are presented. Ten diode arrays with 30 mW cW light output, linear light vs. current characteristics and single longitudinal mode spectrum were fabricated using channel substrate planar (CSP) structures. Preliminary results on the inverse CSP structure, whose fabrication is less critically dependent on device parameters than the CSP, are also presented. The impact of systems parameters and requirements, in particular, the effect of feedback on laser design is assessed, and techniques to reduce feedback or minimize its effect on systems performance, including mode-stabilized structures, are evaluated.

Feasibility study of basic characterization of MAGAT polymer gel using CBCT attached in linear accelerator: Preliminary study

NASA Astrophysics Data System (ADS)

Sathiyaraj, P.; Samuel, E. James jebaseelan

2018-01-01

The aim of this study is to evaluate the methacrylic acid, gelatin and tetrakis (hydroxymethyl) phosphonium chloride gel (MAGAT) by cone beam computed tomography (CBCT) attached with modern linear accelerator. To compare the results of standard diagnostic computed tomography (CT) with CBCT, different parameters such as linearity, sensitivity and temporal stability were checked. MAGAT gel showed good linearity for both diagnostic CT and CBCT measurements. Sensitivity and temporal stability were also comparable with diagnostic CT measurements. In both the modalities, the sensitivity of the MAGAT increased to 4 days and decreased till the 10th day of post irradiation. Since all measurements (linearity, sensitivity and temporal stability) from diagnostic CT and CBCT were comparable, CBCT could be a potential tool for dose analysis study for polymer gel dosimeter.

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.

Stability and Optimal Harvesting of Modified Leslie-Gower Predator-Prey Model

NASA Astrophysics Data System (ADS)

Toaha, S.; Azis, M. I.

2018-03-01

This paper studies a modified of dynamics of Leslie-Gower predator-prey population model. The model is stated as a system of first order differential equations. The model consists of one predator and one prey. The Holling type II as a predation function is considered in this model. The predator and prey populations are assumed to be beneficial and then the two populations are harvested with constant efforts. Existence and stability of the interior equilibrium point are analysed. Linearization method is used to get the linearized model and the eigenvalue is used to justify the stability of the interior equilibrium point. From the analyses, we show that under a certain condition the interior equilibrium point exists and is locally asymptotically stable. For the model with constant efforts of harvesting, cost function, revenue function, and profit function are considered. The stable interior equilibrium point is then related to the maximum profit problem as well as net present value of revenues problem. We show that there exists a certain value of the efforts that maximizes the profit function and net present value of revenues while the interior equilibrium point remains stable. This means that the populations can live in coexistence for a long time and also maximize the benefit even though the populations are harvested with constant efforts.

Influence of unbalance on the nonlinear dynamical response and stability of flexible rotor-bearing systems

NASA Technical Reports Server (NTRS)

Gunter, E. J.; Humphris, R. R.; Springer, H.

1983-01-01

In this paper, some of the effects of unbalance on the nonlinear response and stability of flexible rotor-bearing systems is presented from both a theoretical and experimental standpoint. In a linear system, operating above its stability threshold, the amplitude of motion grows exponentially with time and the orbits become unbounded. In an actual system, this is not necessarily the case. The actual amplitudes of motion may be bounded due to various nonlinear effects in the system. These nonlinear effects cause limit cycles of motion. Nonlinear effects are inherent in fluid film bearings and seals. Other contributors to nonlinear effects are shafts, couplings and foundations. In addition to affecting the threshold of stability, the nonlinear effects can cause jump phenomena to occur at not only the critical speeds, but also at stability onset or restabilization speeds.

Effect of gravitational and aerodynamic torques on a rigid Skylab-type satellite

NASA Technical Reports Server (NTRS)

Sperling, H. J.

1974-01-01

A theoretical investigation of the influence of the aerodynamic torque on a Skylab-type satellite is presented. Only the case of free flow of uniform velocity and completely diffuse reflection is considered. It is found by linear stability analysis that the satellite has no stable equilibrium.

Mathematical model of unmanned aerial vehicle used for endurance autonomous monitoring

NASA Astrophysics Data System (ADS)

Chelaru, Teodor-Viorel; Chelaru, Adrian

2014-12-01

The paper purpose is to present some aspects regarding the control system of unmanned aerial vehicle - UAV, used to local observations, surveillance and monitoring interest area. The calculus methodology allows a numerical simulation of UAV evolution in bad atmospheric conditions by using nonlinear model, as well as a linear one for obtaining guidance command. The UAV model which will be presented has six DOF (degrees of freedom), and autonomous control system. This theoretical development allows us to build stability matrix, command matrix and control matrix and finally to analyse the stability of autonomous UAV flight. A robust guidance system, based on uncoupled state will be evaluated for different fly conditions and the results will be presented. The flight parameters and guidance will be analysed.

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

Chelaru, Teodor-Viorel, E-mail: teodor.chelaru@upb.ro; Chelaru, Adrian, E-mail: achelaru@incas.ro

The paper purpose is to present some aspects regarding the control system of unmanned aerial vehicle - UAV, used to local observations, surveillance and monitoring interest area. The calculus methodology allows a numerical simulation of UAV evolution in bad atmospheric conditions by using nonlinear model, as well as a linear one for obtaining guidance command. The UAV model which will be presented has six DOF (degrees of freedom), and autonomous control system. This theoretical development allows us to build stability matrix, command matrix and control matrix and finally to analyse the stability of autonomous UAV flight. A robust guidance system,more » based on uncoupled state will be evaluated for different fly conditions and the results will be presented. The flight parameters and guidance will be analysed.« less

Performance limitations of bilateral force reflection imposed by operator dynamic characteristics

NASA Technical Reports Server (NTRS)

Chapel, Jim D.

1989-01-01

A linearized, single-axis model is presented for bilateral force reflection which facilitates investigation into the effects of manipulator, operator, and task dynamics, as well as time delay and gain scaling. Structural similarities are noted between this model and impedance control. Stability results based upon this model impose requirements upon operator dynamic characteristics as functions of system time delay and environmental stiffness. An experimental characterization reveals the limited capabilities of the human operator to meet these requirements. A procedure is presented for determining the force reflection gain scaling required to provide stability and acceptable operator workload. This procedure is applied to a system with dynamics typical of a space manipulator, and the required gain scaling is presented as a function of environmental stiffness.

Investigation of ODE integrators using interactive graphics. [Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Brown, R. L.

1978-01-01

Two FORTRAN programs using an interactive graphic terminal to generate accuracy and stability plots for given multistep ordinary differential equation (ODE) integrators are described. The first treats the fixed stepsize linear case with complex variable solutions, and generates plots to show accuracy and error response to step driving function of a numerical solution, as well as the linear stability region. The second generates an analog to the stability region for classes of non-linear ODE's as well as accuracy plots. Both systems can compute method coefficients from a simple specification of the method. Example plots are given.

Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

NASA Astrophysics Data System (ADS)

Kabanov, Dmitry I.; Kasimov, Aslan R.

2018-03-01

We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The new approach is shown to be a viable alternative to the traditional normal-mode analysis used in detonation theory.

Large-Signal Lyapunov-Based Stability Analysis of DC/AC Inverters and Inverter-Based Microgrids

NASA Astrophysics Data System (ADS)

Kabalan, Mahmoud

Microgrid stability studies have been largely based on small-signal linearization techniques. However, the validity and magnitude of the linearization domain is limited to small perturbations. Thus, there is a need to examine microgrids with large-signal nonlinear techniques to fully understand and examine their stability. Large-signal stability analysis can be accomplished by Lyapunov-based mathematical methods. These Lyapunov methods estimate the domain of asymptotic stability of the studied system. A survey of Lyapunov-based large-signal stability studies showed that few large-signal studies have been completed on either individual systems (dc/ac inverters, dc/dc rectifiers, etc.) or microgrids. The research presented in this thesis addresses the large-signal stability of droop-controlled dc/ac inverters and inverter-based microgrids. Dc/ac power electronic inverters allow microgrids to be technically feasible. Thus, as a prelude to examining the stability of microgrids, the research presented in Chapter 3 analyzes the stability of inverters. First, the 13 th order large-signal nonlinear model of a droop-controlled dc/ac inverter connected to an infinite bus is presented. The singular perturbation method is used to decompose the nonlinear model into 11th, 9th, 7th, 5th, 3rd and 1st order models. Each model ignores certain control or structural components of the full order model. The aim of the study is to understand the accuracy and validity of the reduced order models in replicating the performance of the full order nonlinear model. The performance of each model is studied in three different areas: time domain simulations, Lyapunov's indirect method and domain of attraction estimation. The work aims to present the best model to use in each of the three domains of study. Results show that certain reduced order models are capable of accurately reproducing the performance of the full order model while others can be used to gain insights into those three areas of study. This will enable future studies to save computational effort and produce the most accurate results according to the needs of the study being performed. Moreover, the effect of grid (line) impedance on the accuracy of droop control is explored using the 5th order model. Simulation results show that traditional droop control is valid up to R/X line impedance value of 2. Furthermore, the 3rd order nonlinear model improves the currently available inverter-infinite bus models by accounting for grid impedance, active power-frequency droop and reactive power-voltage droop. Results show the 3rd order model's ability to account for voltage and reactive power changes during a transient event. Finally, the large-signal Lyapunov-based stability analysis is completed for a 3 bus microgrid system (made up of 2 inverters and 1 linear load). The thesis provides a systematic state space large-signal nonlinear mathematical modeling method of inverter-based microgrids. The inverters include the dc-side dynamics associated with dc sources. The mathematical model is then used to estimate the domain of asymptotic stability of the 3 bus microgrid. The three bus microgrid system was used as a case study to highlight the design and optimization capability of a large-signal-based approach. The study explores the effect of system component sizing, load transient and generation variations on the asymptotic stability of the microgrid. Essentially, this advancement gives microgrid designers and engineers the ability to manipulate the domain of asymptotic stability depending on performance requirements. Especially important, this research was able to couple the domain of asymptotic stability of the ac microgrid with that of the dc side voltage source. Time domain simulations were used to demonstrate the mathematical nonlinear analysis results.

Mode instability in one-dimensional anharmonic lattices: Variational equation approach

NASA Astrophysics Data System (ADS)

Yoshimura, K.

1999-03-01

The stability of normal mode oscillations has been studied in detail under the single-mode excitation condition for the Fermi-Pasta-Ulam-β lattice. Numerical experiments indicate that the mode stability depends strongly on k/N, where k is the wave number of the initially excited mode and N is the number of degrees of freedom in the system. It has been found that this feature does not change when N increases. We propose an average variational equation - approximate version of the variational equation - as a theoretical tool to facilitate a linear stability analysis. It is shown that this strong k/N dependence of the mode stability can be explained from the view point of the linear stability of the relevant orbits. We introduce a low-dimensional approximation of the average variational equation, which approximately describes the time evolution of variations in four normal mode amplitudes. The linear stability analysis based on this four-mode approximation demonstrates that the parametric instability mechanism plays a crucial role in the strong k/N dependence of the mode stability.

Stability analysis of the Peregrine solution via squared eigenfunctions

NASA Astrophysics Data System (ADS)

Schober, C. M.; Strawn, M.

2017-10-01

A preliminary numerical investigation involving ensembles of perturbed initial data for the Peregrine soliton (the lowest order rational solution of the nonlinear Schrödinger equation) indicates that it is unstable [16]. In this paper we analytically investigate the linear stability of the Peregrine soliton, appealing to the fact that the Peregrine solution can be viewed as the singular limit of a single mode spatially periodic breathers (SPB). The "squared eigenfunction" connection between the Zakharov-Shabat (Z-S) system and the linearized NLS equation is employed in the stability analysis. Specifically, we determine the eigenfunctions of the Z-S system associated with the Peregrine soliton and construct a family of solutions of the associated linearized NLS (about the Peregrine) in terms of quadratic products of components of the eigenfunctions (i.e., the squared eigenfunction). We find there exist solutions of the linearization that grow exponentially in time, thus showing the Peregrine soliton is linearly unstable.

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

DOE PAGES

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; ...

2015-11-12

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

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

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

The Absolute Stability Analysis in Fuzzy Control Systems with Parametric Uncertainties and Reference Inputs

NASA Astrophysics Data System (ADS)

Wu, Bing-Fei; Ma, Li-Shan; Perng, Jau-Woei

This study analyzes the absolute stability in P and PD type fuzzy logic control systems with both certain and uncertain linear plants. Stability analysis includes the reference input, actuator gain and interval plant parameters. For certain linear plants, the stability (i.e. the stable equilibriums of error) in P and PD types is analyzed with the Popov or linearization methods under various reference inputs and actuator gains. The steady state errors of fuzzy control systems are also addressed in the parameter plane. The parametric robust Popov criterion for parametric absolute stability based on Lur'e systems is also applied to the stability analysis of P type fuzzy control systems with uncertain plants. The PD type fuzzy logic controller in our approach is a single-input fuzzy logic controller and is transformed into the P type for analysis. In our work, the absolute stability analysis of fuzzy control systems is given with respect to a non-zero reference input and an uncertain linear plant with the parametric robust Popov criterion unlike previous works. Moreover, a fuzzy current controlled RC circuit is designed with PSPICE models. Both numerical and PSPICE simulations are provided to verify the analytical results. Furthermore, the oscillation mechanism in fuzzy control systems is specified with various equilibrium points of view in the simulation example. Finally, the comparisons are also given to show the effectiveness of the analysis method.

Film stability in a vertical rotating tube with a core-gas flow.

NASA Technical Reports Server (NTRS)

Sarma, G. S. R.; Lu, P. C.; Ostrach, S.

1971-01-01

The linear hydrodynamic stability of a thin-liquid layer flowing along the inside wall of a vertical tube rotating about its axis in the presence of a core-gas flow is examined. The stability problem is formulated under the conditions that the liquid film is thin, the density and viscosity ratios of gas to liquid are small and the relative (axial) pressure gradient in the gas is of the same order as gravity. The resulting eigenvalue problem is first solved by a perturbation method appropriate to axisymmetric long-wave disturbances. The damped nature (to within the thin-film and other approximations made) of the nonaxisymmetric and short-wave disturbances is noted. In view of the limitations on a truncated perturbation solution when the disturbance wavenumber is not small, an initial value method using digital computer is presented. Stability characteristics of neutral, growing, and damped modes are presented showing the influences of rotation, surface tension, and the core-gas flow. Energy balance in a neutral mode is also illustrated.

Linear stability of compressible Taylor-Couette flow

NASA Technical Reports Server (NTRS)

Kao, Kai-Hsiung; Chow, Chuen-Yen

1992-01-01

A temporal stability analysis of compressible Taylor-Couette flow is presented. The viscous flow studied in this paper is contained between two concentric cylinders of infinite length, which are rotating with different angular velocities and are kept at different surface temperatures. The effects of differential rotation and temperature difference on the stability of Taylor-Couette flow are contrasted for a range of Mach numbers ranging from incompressible to Mach 3.0. The relative motion of the cylinders dramatically affects the characteristics of the Couette flow at the onset of instability. The flow is stabilized or destabilized depending upon the temperature ratio and speeds of the two cylinders. Independent of Mach number and temperature ratio, increasing Reynolds number generally promotes a destabilizing effect, indicating the inviscid nature of the Taylor-Couette flow.

Dependency of Tearing Mode Stability on Current and Pressure Profiles in DIII-D Hybrid Discharges

NASA Astrophysics Data System (ADS)

Kim, K.; Park, J. M.; Murakami, M.; La Haye, R. J.; Na, Y.-S.; SNU/ORAU; ORNL; Atomics, General; SNU; DIII-D Team

2016-10-01

Understanding the physics of the onset and evolution of tearing modes (TMs) in tokamak plasmas is important for high- β steady-state operation. Based on DIII-D steady-state hybrid experiments with accurate equilibrium reconstruction and well-measured plasma profiles, the 2/1 tearing mode can be more stable with increasing local current and pressure gradient at rational surface and with lower pressure peaking and plasma inductance. The tearing stability index Δ', estimated by the Rutherford equation with experimental mode growth rate was validated against Δ' calculated by linear eigenvalue solver (PEST3); preliminary comprehensive MHD modeling by NIMROD reproduced the TM onset reasonably well. We present a novel integrated modeling for the purpose of predicting TM onset in experiment by combining a model equilibrium reconstruction using IPS/FASTRAN, linear stability Δ' calculation using PEST3, and fitting formula for critical Δ' from NIMROD. Work supported in part by the US DoE under DE-AC05-06OR23100, DE-AC05-00OR22725, and DEFC02-04ER54698.

Attitude stability of spinning satellites

NASA Technical Reports Server (NTRS)

Caughey, T. K.

1980-01-01

Some problems of attitude stability of spinning satellites are treated in a rigorous manner. With certain restrictions, linearized stability analysis correctly predicts the attitude stability of spinning satellites, even in the critical cases of the Liapunov-Poincare stability theory.

Stability of elastic bending and torsion of uniform cantilever rotor blades in hover with variable structural coupling

NASA Technical Reports Server (NTRS)

Hodges, D. H., Roberta.

1976-01-01

The stability of elastic flap bending, lead-lag bending, and torsion of uniform, untwisted, cantilever rotor blades without chordwise offsets between the elastic, mass, tension, and areodynamic center axes is investigated for the hovering flight condition. The equations of motion are obtained by simplifying the general, nonlinear, partial differential equations of motion of an elastic rotating cantilever blade. The equations are adapted for a linearized stability analysis in the hovering flight condition by prescribing aerodynamic forces, applying Galerkin's method, and linearizing the resulting ordinary differential equations about the equilibrium operating condition. The aerodynamic forces are obtained from strip theory based on a quasi-steady approximation of two-dimensional unsteady airfoil theory. Six coupled mode shapes, calculated from free vibration about the equilibrium operating condition, are used in the linearized stability analysis. The study emphasizes the effects of two types of structural coupling that strongly influence the stability of hingeless rotor blades. The first structural coupling is the linear coupling between flap and lead-lag bending of the rotor blade. The second structural coupling is a nonlinear coupling between flap bending, lead-lag bending, and torsion deflections. Results are obtained for a wide variety of hingeless rotor configurations and operating conditions in order to provide a reasonably complete picture of hingeless rotor blade stability characteristics.

Linearized blade row compression component model. Stability and frequency response analysis of a J85-3 compressor

NASA Technical Reports Server (NTRS)

Tesch, W. A.; Moszee, R. H.; Steenken, W. G.

1976-01-01

NASA developed stability and frequency response analysis techniques were applied to a dynamic blade row compression component stability model to provide a more economic approach to surge line and frequency response determination than that provided by time-dependent methods. This blade row model was linearized and the Jacobian matrix was formed. The clean-inlet-flow stability characteristics of the compressors of two J85-13 engines were predicted by applying the alternate Routh-Hurwitz stability criterion to the Jacobian matrix. The predicted surge line agreed with the clean-inlet-flow surge line predicted by the time-dependent method to a high degree except for one engine at 94% corrected speed. No satisfactory explanation of this discrepancy was found. The frequency response of the linearized system was determined by evaluating its Laplace transfer function. The results of the linearized-frequency-response analysis agree with the time-dependent results when the time-dependent inlet total-pressure and exit-flow function amplitude boundary conditions are less than 1 percent and 3 percent, respectively. The stability analysis technique was extended to a two-sector parallel compressor model with and without interstage crossflow and predictions were carried out for total-pressure distortion extents of 180 deg, 90 deg, 60 deg, and 30 deg.

Compatible diagonal-norm staggered and upwind SBP operators

NASA Astrophysics Data System (ADS)

Mattsson, Ken; O'Reilly, Ossian

2018-01-01

The main motivation with the present study is to achieve a provably stable high-order accurate finite difference discretisation of linear first-order hyperbolic problems on a staggered grid. The use of a staggered grid makes it non-trivial to discretise advective terms. To overcome this difficulty we discretise the advective terms using upwind Summation-By-Parts (SBP) operators, while the remaining terms are discretised using staggered SBP operators. The upwind and staggered SBP operators (for each order of accuracy) are compatible, here meaning that they are based on the same diagonal norms, allowing for energy estimates to be formulated. The boundary conditions are imposed using a penalty (SAT) technique, to guarantee linear stability. The resulting SBP-SAT approximations lead to fully explicit ODE systems. The accuracy and stability properties are demonstrated for linear hyperbolic problems in 1D, and for the 2D linearised Euler equations with constant background flow. The newly derived upwind and staggered SBP operators lead to significantly more accurate numerical approximations, compared with the exclusive usage of (previously derived) central-difference first derivative SBP operators.

Nonlinear evolution of the first mode supersonic oblique waves in compressible boundary layers. Part 1: Heated/cooled walls

NASA Technical Reports Server (NTRS)

Gajjar, J. S. B.

1993-01-01

The nonlinear stability of an oblique mode propagating in a two-dimensional compressible boundary layer is considered under the long wave-length approximation. The growth rate of the wave is assumed to be small so that the concept of unsteady nonlinear critical layers can be used. It is shown that the spatial/temporal evolution of the mode is governed by a pair of coupled unsteady nonlinear equations for the disturbance vorticity and density. Expressions for the linear growth rate show clearly the effects of wall heating and cooling and in particular how heating destabilizes the boundary layer for these long wavelength inviscid modes at O(1) Mach numbers. A generalized expression for the linear growth rate is obtained and is shown to compare very well for a range of frequencies and wave-angles at moderate Mach numbers with full numerical solutions of the linear stability problem. The numerical solution of the nonlinear unsteady critical layer problem using a novel method based on Fourier decomposition and Chebychev collocation is discussed and some results are presented.

General methods for determining the linear stability of coronal magnetic fields

NASA Technical Reports Server (NTRS)

Craig, I. J. D.; Sneyd, A. D.; Mcclymont, A. N.

1988-01-01

A time integration of a linearized plasma equation of motion has been performed to calculate the ideal linear stability of arbitrary three-dimensional magnetic fields. The convergence rates of the explicit and implicit power methods employed are speeded up by using sequences of cyclic shifts. Growth rates are obtained for Gold-Hoyle force-free equilibria, and the corkscrew-kink instability is found to be very weak.

General methods for determining the linear stability of coronal magnetic fields

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

Craig, I.J.D.; Sneyd, A.D.; McClymont, A.N.

1988-12-01

A time integration of a linearized plasma equation of motion has been performed to calculate the ideal linear stability of arbitrary three-dimensional magnetic fields. The convergence rates of the explicit and implicit power methods employed are speeded up by using sequences of cyclic shifts. Growth rates are obtained for Gold-Hoyle force-free equilibria, and the corkscrew-kink instability is found to be very weak. 19 references.

Stability of Capillary Surfaces in Rectangular Containers: The Right Square Cylinder

NASA Technical Reports Server (NTRS)

Weislogel, M. M.; Hsieh, K. C.

1998-01-01

The linearized governing equations for an ideal fluid are presented for numerical analysis for the stability of free capillary surfaces in rectangular containers against unfavorable disturbances (accelerations,i.e. Rayleigh-Taylor instability). The equations are solved for the case of the right square cylinder. The results are expressed graphically in term of a critical Bond number as a function of system contact angle. A critical wetting phenomena in the corners is shown to significantly alter the region of stability for such containers in contrast to simpler geometries such as the right circular cylinder or the infinite rectangular slot. Such computational results provide additional constraints for the design of fluids systems for space-based applications.

A Review of Hypersonic Boundary Layer Stability Experiments in a Quiet Mach 6 Wind Tunnel

NASA Technical Reports Server (NTRS)

Wilkinson, Stephen P.

1997-01-01

Three recent experimental studies of transition on cones with adverse pressure gradient produced by a flared afterbody and with the additive stability modifiers of wall cooling, angle of attack and bluntness are reviewed. All tests were conducted in a quiet Mach 6 wind tunnel. The dominant instability was found to be the second mode. For the cases examined with linear stability theory, the N factors at mode saturation were in the range of 8.5 to 11. Evidence of a combined second-mode/Gortler transition process was found. Mean, rms and spectral freestream data for the quiet facility is presented and the role of low frequency freestream noise is discussed.

Modeling and Analysis of Large Amplitude Flight Maneuvers

NASA Technical Reports Server (NTRS)

Anderson, Mark R.

2004-01-01

Analytical methods for stability analysis of large amplitude aircraft motion have been slow to develop because many nonlinear system stability assessment methods are restricted to a state-space dimension of less than three. The proffered approach is to create regional cell-to-cell maps for strategically located two-dimensional subspaces within the higher-dimensional model statespace. These regional solutions capture nonlinear behavior better than linearized point solutions. They also avoid the computational difficulties that emerge when attempting to create a cell map for the entire state-space. Example stability results are presented for a general aviation aircraft and a micro-aerial vehicle configuration. The analytical results are consistent with characteristics that were discovered during previous flight-testing.

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.

A Piloted Evaluation of Damage Accommodating Flight Control Using a Remotely Piloted Vehicle

NASA Technical Reports Server (NTRS)

Cunningham, Kevin; Cox, David E.; Murri, Daniel G.; Riddick, Stephen E.

2011-01-01

Toward the goal of reducing the fatal accident rate of large transport airplanes due to loss of control, the NASA Aviation Safety Program has conducted research into flight control technologies that can provide resilient control of airplanes under adverse flight conditions, including damage and failure. As part of the safety program s Integrated Resilient Aircraft Control Project, the NASA Airborne Subscale Transport Aircraft Research system was designed to address the challenges associated with the safe and efficient subscale flight testing of research control laws under adverse flight conditions. This paper presents the results of a series of pilot evaluations of several flight control algorithms used during an offset-to-landing task conducted at altitude. The purpose of this investigation was to assess the ability of various flight control technologies to prevent loss of control as stability and control characteristics were degraded. During the course of 8 research flights, data were recorded while one task was repeatedly executed by a single evaluation pilot. Two generic failures, which degraded stability and control characteristics, were simulated inflight for each of the 9 different flight control laws that were tested. The flight control laws included three different adaptive control methodologies, several linear multivariable designs, a linear robust design, a linear stability augmentation system, and a direct open-loop control mode. Based on pilot Cooper-Harper Ratings obtained for this test, the adaptive flight control laws provided the greatest overall benefit for the stability and control degradation scenarios that were considered. Also, all controllers tested provided a significant improvement in handling qualities over the direct open-loop control mode.

The linear stability of vertical mixture seepage into the close porous filter with clogging

NASA Astrophysics Data System (ADS)

Maryshev, Boris S.

2017-02-01

In the present paper, filtration of a mixture through a close porous filter is considered. A heavy solute penetrates from the upper side of the filter into the filter body due to seepage flow and diffusion. In the presence of heavy solute a domain with a heavy fluid is formed near the upper boundary of the filter. The stratification, at which the heavy fluid is located above the light, is unstable. When the mass of the heavy solute exceeds the critical value, one can observe the onset of instability. As a result, two regimes of vertical filtration can occur: (1) homogeneous seepage and (2) convective filtration. Filtration of a mixture in porous media is a complex process. It is necessary to take into account the solute immobilization (or sorption) and clogging of porous medium. We consider the case of low solute concentrations, in which the immobilization is described by the linear MIM (mobile/immobile media) model. The clogging is described by the dependence of permeability on porosity in terms of the Carman-Kozeny formula. The presence of immobile (or adsorbed) particles of the solute decreases the porosity of media and porous media becomes less permeable. The purpose of the paper is to find the stability conditions for the homogeneous vertical seepage of the mixture into the close porous filter. The linear stability problem is solved using the quasi-static approach. The critical times of instability are estimated. The stability maps have been plotted in the space of system parameters. The applicability of quasi-static approach is substantiated by direct numerical simulation.

Asymptotic Stability of Interconnected Passive Non-Linear Systems

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

The Langley Stability and Transition Analysis Code (LASTRAC) : LST, Linear and Nonlinear PSE for 2-D, Axisymmetric, and Infinite Swept Wing Boundary Layers

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan

2003-01-01

During the past two decades, our understanding of laminar-turbulent transition flow physics has advanced significantly owing to, in a large part, the NASA program support such as the National Aerospace Plane (NASP), High-speed Civil Transport (HSCT), and Advanced Subsonic Technology (AST). Experimental, theoretical, as well as computational efforts on various issues such as receptivity and linear and nonlinear evolution of instability waves take part in broadening our knowledge base for this intricate flow phenomenon. Despite all these advances, transition prediction remains a nontrivial task for engineers due to the lack of a widely available, robust, and efficient prediction tool. The design and development of the LASTRAC code is aimed at providing one such engineering tool that is easy to use and yet capable of dealing with a broad range of transition related issues. LASTRAC was written from scratch based on the state-of-the-art numerical methods for stability analysis and modem software technologies. At low fidelity, it allows users to perform linear stability analysis and N-factor transition correlation for a broad range of flow regimes and configurations by using either the linear stability theory (LST) or linear parabolized stability equations (LPSE) method. At high fidelity, users may use nonlinear PSE to track finite-amplitude disturbances until the skin friction rise. Coupled with the built-in receptivity model that is currently under development, the nonlinear PSE method offers a synergistic approach to predict transition onset for a given disturbance environment based on first principles. This paper describes the governing equations, numerical methods, code development, and case studies for the current release of LASTRAC. Practical applications of LASTRAC are demonstrated for linear stability calculations, N-factor transition correlation, non-linear breakdown simulations, and controls of stationary crossflow instability in supersonic swept wing boundary layers.

Elastic stability of biaxially loaded longitudinally stiffened composite structures.

NASA Technical Reports Server (NTRS)

Viswanathan, A. V.; Tamekuni, M.; Tripp, L. L.

1973-01-01

A linear analysis method is presented for the elastic stability of structures of uniform cross section, that may be idealized as an assemblage of laminated plate-strips, flat and curved, and beams. Each plate-strip and beam covers the entire length of the structure and is simply supported on the edges normal to the longitudinal axis. Arbitrary boundary conditions may be specified on any external longitudinal side of plate-strips. The structure or selected plate-strips may be loaded in any desired combination of inplane biaxial loads. The analysis simultaneously considers all modes of instability and is applicable for the buckling of laminated composite structures. Some numerical results are presented to indicate possible applications.

Attitude stability of a spinning spacecraft during appendage deployment/retraction

NASA Technical Reports Server (NTRS)

Fitz-Coy, Norman; Fullerton, Wayne

1994-01-01

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

Influence of heating rate on the condensational instability. [in outer layers of solar atmosphere

NASA Technical Reports Server (NTRS)

Dahlburg, R. B.; Mariska, J. T.

1988-01-01

Analysis and numerical simulation are used to determine the effect that various heating rates have on the linear and nonlinear evolution of a typical plasma within a solar magnetic flux tube subject to the condensational instability. It is found that linear stability depends strongly on the heating rate. The results of numerical simulations of the nonlinear evolution of the condensational instability in a solar magnetic flux tube are presented. Different heating rates lead to quite different nonlinear evolutions, as evidenced by the behavior of the global internal energy.

The Stability and Interfacial Motion of Multi-layer Radial Porous Media and Hele-Shaw Flows

NASA Astrophysics Data System (ADS)

Gin, Craig; Daripa, Prabir

2017-11-01

In this talk, we will discuss viscous fingering instabilities of multi-layer immiscible porous media flows within the Hele-Shaw model in a radial flow geometry. We study the motion of the interfaces for flows with both constant and variable viscosity fluids. We consider the effects of using a variable injection rate on multi-layer flows. We also present a numerical approach to simulating the interface motion within linear theory using the method of eigenfunction expansion. We compare these results with fully non-linear simulations.

Dynamics of thin-shell wormholes with different cosmological models

NASA Astrophysics Data System (ADS)

Sharif, Muhammad; Mumtaz, Saadia

This work is devoted to investigate the stability of thin-shell wormholes in Einstein-Hoffmann-Born-Infeld electrodynamics. We also study the attractive and repulsive characteristics of these configurations. A general equation-of-state is considered in the form of linear perturbation which explores the stability of the respective wormhole solutions. We assume Chaplygin, linear and logarithmic gas models to study exotic matter at thin-shell and evaluate stability regions for different values of the involved parameters. It is concluded that the Hoffmann-Born-Infeld parameter and electric charge enhance the stability regions.

Optimal model of PDIG based microgrid and design of complementary stabilizer using ICA.

PubMed

Amini, R Mohammad; Safari, A; Ravadanegh, S Najafi

2016-09-01

The generalized Heffron-Phillips model (GHPM) for a microgrid containing a photovoltaic (PV)-diesel machine (DM)-induction motor (IM)-governor (GV) (PDIG) has been developed at the low voltage level. A GHPM is calculated by linearization method about a loading condition. An effective Maximum Power Point Tracking (MPPT) approach for PV network has been done using sliding mode control (SMC) to maximize output power. Additionally, to improve stability of microgrid for more penetration of renewable energy resources with nonlinear load, a complementary stabilizer has been presented. Imperialist competitive algorithm (ICA) is utilized to design of gains for the complementary stabilizer with the multiobjective function. The stability analysis of the PDIG system has been completed with eigenvalues analysis and nonlinear simulations. Robustness and validity of the proposed controllers on damping of electromechanical modes examine through time domain simulation under input mechanical torque disturbances. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

A non-linear model of economic production processes

NASA Astrophysics Data System (ADS)

Ponzi, A.; Yasutomi, A.; Kaneko, K.

2003-06-01

We present a new two phase model of economic production processes which is a non-linear dynamical version of von Neumann's neoclassical model of production, including a market price-setting phase as well as a production phase. The rate of an economic production process is observed, for the first time, to depend on the minimum of its input supplies. This creates highly non-linear supply and demand dynamics. By numerical simulation, production networks are shown to become unstable when the ratio of different products to total processes increases. This provides some insight into observed stability of competitive capitalist economies in comparison to monopolistic economies. Capitalist economies are also shown to have low unemployment.

Nonlinear stability and control study of highly maneuverable high performance aircraft, phase 2

NASA Technical Reports Server (NTRS)

Mohler, R. R.

1992-01-01

Research leading to the development of new nonlinear methodologies for the adaptive control and stability analysis of high angle of attack aircraft such as the F-18 is discussed. The emphasis has been on nonlinear adaptive control, but associated model development, system identification, stability analysis, and simulation were studied in some detail as well. Studies indicated that nonlinear adaptive control can outperform linear adaptive control for rapid maneuvers with large changes in angle of attack. Included here are studies on nonlinear model algorithmic controller design and an analysis of nonlinear system stability using robust stability analysis for linear systems.

H-mode pedestal stability and ELMs in Alcator C-Mod

NASA Astrophysics Data System (ADS)

Mossessian, Dmitri

2002-11-01

For steady state H-mode operation, a relaxation mechanism is required to limit build-up of the edge gradient and impurity accumulation. The major relaxation mechanism seen on most of the existing tokamaks - large type I ELMs - drive high particle and energy fluxes that present a significant power load on the divertor plates. On Alcator C-Mod, however, type I ELMs are not observed. Instead, more benign mechanisms - EDA and small grassy ELMs - appear to drive enhanced particle transport at the edge of H-mode plasmas. Both have good energy confinement, no impurity accumulation, and are steady state. In EDA the edge relaxation mechanism is provided by a quasicoherent electromagnetic mode localized in the outer part of the pedestal. Non-linear gyrofluid and linear gyrokinetic simulations, as well as real geometry fluctuation modeling based on fluid equations show the presence of a coherent mode. Based on those results the observed mode is tentatively identified as resistive ballooning. At higher edge pressure gradient the mode is replaced by broadband fluctuations and small irregular ELMs are observed. Based on ideal MHD calculations that include effects of bootstrap current, these ELMs are identified as medium n coupled ideal peeling/ballooning modes. The stability threshold and modes structure of these modes are studied with recently developed linear MHD stability code ELITE and the results are compared with the observed dependence of the ELMs' character on pedestal parameters and plasma shape.

An aeroelastic analysis of the Darrieus wind turbine

NASA Astrophysics Data System (ADS)

Meyer, E. E.; Smith, C. E.

1983-12-01

The stability of a single Darrieus wind turbine blade spinning in still air is investigated using linearized equations of motion. The three most dangerous flutter modes are characterized for a one-parameter family of blades. In addition, the influence of blade density, mass and aerodynamic center offsets, and structural damping is presented.

Multivariable control of a twin lift helicopter system using the LQG/LTR design methodology

NASA Technical Reports Server (NTRS)

Rodriguez, A. A.; Athans, M.

1986-01-01

Guidelines for developing a multivariable centralized automatic flight control system (AFCS) for a twin lift helicopter system (TLHS) are presented. Singular value ideas are used to formulate performance and stability robustness specifications. A linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) design is obtained and evaluated.

Time-stable overset grid method for hyperbolic problems using summation-by-parts operators

NASA Astrophysics Data System (ADS)

Sharan, Nek; Pantano, Carlos; Bodony, Daniel J.

2018-05-01

A provably time-stable method for solving hyperbolic partial differential equations arising in fluid dynamics on overset grids is presented in this paper. The method uses interface treatments based on the simultaneous approximation term (SAT) penalty method and derivative approximations that satisfy the summation-by-parts (SBP) property. Time-stability is proven using energy arguments in a norm that naturally relaxes to the standard diagonal norm when the overlap reduces to a traditional multiblock arrangement. The proposed overset interface closures are time-stable for arbitrary overlap arrangements. The information between grids is transferred using Lagrangian interpolation applied to the incoming characteristics, although other interpolation schemes could also be used. The conservation properties of the method are analyzed. Several one-, two-, and three-dimensional, linear and non-linear numerical examples are presented to confirm the stability and accuracy of the method. A performance comparison between the proposed SAT-based interface treatment and the commonly-used approach of injecting the interpolated data onto each grid is performed to highlight the efficacy of the SAT method.

Thermal effects in rapid directional solidification - Linear theory

NASA Technical Reports Server (NTRS)

Huntley, D. A.; Davis, S. H.

1993-01-01

We study the morphological instability of the planar solid/liquid interface for a unidirectionally-solidified dilute binary mixture. We use a model developed by Boettinger et al. (1985, 1986), Aziz (1982), and Jackson et al. (1980), which allows for nonequilibrium effects on the interface through velocity-dependent segregation and attachment kinetics. Two types of instabilities are found in the linear stability analysis: (1) a cellular instability, and (2) an oscillatory instability driven by disequilibrium effects. Merchant and Davis (1990) characterized these instabilities subject to the frozen-temperature approximation (FTA). The present work relaxes the FTA by including the effects of latent heat and the full temperature distribution. Thermal effects slightly postpone the onset of the cellular instability but dramatically postpone the onset of the oscillatory instability; however, the absolute-stability conditions, at which at high speed the cellular and oscillatory instabilities are suppressed, remain unchanged from the FTA.

Influence of the local-spin-density correlation functional on the stability of bcc ferromagnetic iron

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

Singh, D.; Clougherty, D.P.; MacLaren, J.M.

1991-10-01

The influence of local-spin-dependent correlation effects on the predicted stable ground-state phase of iron is reexamined with use of general-potential linearized augmented-plane-wave calculations. Differences in the form of the Vosko-Wilk-Nusair (VWN) local-spin-density functional used in previous studies are noted, since in previous studies significant additional approximations were made with respect to those of Vosko, Wilk, and Nusan (Can. J. Phys. 58, 1200 (1980)) and of MacLaren, Clougherty, and Albers (Phys. Rev. B 42, 3205 (1990)). While the results of previous linear muffin-tin orbital calculations using the VWN functional predict a bcc ferromagnetic ground state, the present calculations show that themore » VWN spin-correlation effects fail to stabilize a bcc ground state. Considerable sensitivity to the form of the spin interpolation is found.« less

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.

Model Checking A Self-Stabilizing Synchronization Protocol for Arbitrary Digraphs

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R.

2012-01-01

This report presents the mechanical verification of a self-stabilizing distributed clock synchronization protocol for arbitrary digraphs in the absence of faults. This protocol does not rely on assumptions about the initial state of the system, other than the presence of at least one node, and no central clock or a centrally generated signal, pulse, or message is used. The system under study is an arbitrary, non-partitioned digraph ranging from fully connected to 1-connected networks of nodes while allowing for differences in the network elements. Nodes are anonymous, i.e., they do not have unique identities. There is no theoretical limit on the maximum number of participating nodes. The only constraint on the behavior of the node is that the interactions with other nodes are restricted to defined links and interfaces. This protocol deterministically converges within a time bound that is a linear function of the self-stabilization period. A bounded model of the protocol is verified using the Symbolic Model Verifier (SMV) for a subset of digraphs. Modeling challenges of the protocol and the system are addressed. The model checking effort is focused on verifying correctness of the bounded model of the protocol as well as confirmation of claims of determinism and linear convergence with respect to the self-stabilization period.

Verification of a Byzantine-Fault-Tolerant Self-stabilizing Protocol for Clock Synchronization

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R.

2008-01-01

This paper presents the mechanical verification of a simplified model of a rapid Byzantine-fault-tolerant self-stabilizing protocol for distributed clock synchronization systems. This protocol does not rely on any assumptions about the initial state of the system except for the presence of sufficient good nodes, thus making the weakest possible assumptions and producing the strongest results. This protocol tolerates bursts of transient failures, and deterministically converges within a time bound that is a linear function of the self-stabilization period. A simplified model of the protocol is verified using the Symbolic Model Verifier (SMV). The system under study consists of 4 nodes, where at most one of the nodes is assumed to be Byzantine faulty. The model checking effort is focused on verifying correctness of the simplified model of the protocol in the presence of a permanent Byzantine fault as well as confirmation of claims of determinism and linear convergence with respect to the self-stabilization period. Although model checking results of the simplified model of the protocol confirm the theoretical predictions, these results do not necessarily confirm that the protocol solves the general case of this problem. Modeling challenges of the protocol and the system are addressed. A number of abstractions are utilized in order to reduce the state space.

Implications for the dynamic health of a glacier from comparison of conventional and reference-surface balances

USGS Publications Warehouse

Harrison, W.D.; Cox, L.H.; Hock, R.; March, R.S.; Pettit, E.C.

2009-01-01

Conventional and reference-surface mass-balance data from Gulkana and Wolverine Glaciers, Alaska, USA, are used to address the questions of how rapidly these glaciers are adjusting (or 'responding') to climate, whether their responses are stable, and whether the glaciers are likely to survive in today's climate. Instability means that a glacier will eventually vanish, or at least become greatly reduced in volume, if the climate stabilizes at its present state. A simple non-linear theory of response is presented for the analysis. The response of Gulkana Glacier is characterized by a timescale of several decades, but its stability and therefore its survival in today's climate are uncertain. Wolverine seems to be responding to climate more slowly, on the timescale of one to several centuries. Its stability is also uncertain, but a slower response time would make it more susceptible to climate changes.

On the Stability of Collocated Controllers in the Presence or Uncertain Nonlinearities and Other Perils

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1985-01-01

Robustness properties are investigated for two types of controllers for large flexible space structures, which use collocated sensors and actuators. The first type is an attitude controller which uses negative definite feedback of measured attitude and rate, while the second type is a damping enhancement controller which uses only velocity (rate) feedback. It is proved that collocated attitude controllers preserve closed loop global asymptotic stability when linear actuator/sensor dynamics satisfying certain phase conditions are present, or monotonic increasing nonlinearities are present. For velocity feedback controllers, the global asymptotic stability is proved under much weaker conditions. In particular, they have 90 phase margin and can tolerate nonlinearities belonging to the (0,infinity) sector in the actuator/sensor characteristics. The results significantly enhance the viability of both types of collocated controllers, especially when the available information about the large space structure (LSS) parameters is inadequate or inaccurate.

Robust Stabilization of T-S Fuzzy Stochastic Descriptor Systems via Integral Sliding Modes.

PubMed

Li, Jinghao; Zhang, Qingling; Yan, Xing-Gang; Spurgeon, Sarah K

2017-09-19

This paper addresses the robust stabilization problem for T-S fuzzy stochastic descriptor systems using an integral sliding mode control paradigm. A classical integral sliding mode control scheme and a nonparallel distributed compensation (Non-PDC) integral sliding mode control scheme are presented. It is shown that two restrictive assumptions previously adopted developing sliding mode controllers for Takagi-Sugeno (T-S) fuzzy stochastic systems are not required with the proposed framework. A unified framework for sliding mode control of T-S fuzzy systems is formulated. The proposed Non-PDC integral sliding mode control scheme encompasses existing schemes when the previously imposed assumptions hold. Stability of the sliding motion is analyzed and the sliding mode controller is parameterized in terms of the solutions of a set of linear matrix inequalities which facilitates design. The methodology is applied to an inverted pendulum model to validate the effectiveness of the results presented.

An H-infinity approach to optimal control of oxygen and carbon dioxide contents in blood

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Siano, Pierluigi; Selisteanu, Dan; Precup, Radu

2016-12-01

Nonlinear H-infinity control is proposed for the regulation of the levels of oxygen and carbon dioxide in the blood of patients undergoing heart surgery and extracorporeal blood circulation. The levels of blood gases are administered through a membrane oxygenator and the control inputs are the externally supplied oxygen, the aggregate gas supply (oxygen plus nitrogen), and the blood flow which is regulated by a blood pump. The proposed control method is based on linearization of the oxygenator's dynamical model through Taylor series expansion and the computation of Jacobian matrices. The local linearization points are defined by the present value of the oxygenator's state vector and the last value of the control input that was exerted on this system. The modelling errors due to linearization are considered as disturbances which are compensated by the robustness of the control loop. Next, for the linearized model of the oxygenator an H-infinity control input is computed at each iteration of the control algorithm through the solution of an algebraic Riccati equation. With the use of Lyapunov stability analysis it is demonstrated that the control scheme satisfies the H-infinity tracking performance criterion, which signifies improved robustness against modelling uncertainty and external disturbances. Moreover, under moderate conditions the asymptotic stability of the control loop is also proven.

Conditions for Stabilizability of Linear Switched Systems

NASA Astrophysics Data System (ADS)

Minh, Vu Trieu

2011-06-01

This paper investigates some conditions that can provide stabilizability for linear switched systems with polytopic uncertainties via their closed loop linear quadratic state feedback regulator. The closed loop switched systems can stabilize unstable open loop systems or stable open loop systems but in which there is no solution for a common Lyapunov matrix. For continuous time switched linear systems, we show that if there exists solution in an associated Riccati equation for the closed loop systems sharing one common Lyapunov matrix, the switched linear systems are stable. For the discrete time switched systems, we derive a Linear Matrix Inequality (LMI) to calculate a common Lyapunov matrix and solution for the stable closed loop feedback systems. These closed loop linear quadratic state feedback regulators guarantee the global asymptotical stability for any switched linear systems with any switching signal sequence.

Reaction-Infiltration Instabilities in Fractured and Porous Rocks

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

Ladd, Anthony

In this project we are developing a multiscale analysis of the evolution of fracture permeability, using numerical simulations and linear stability analysis. Our simulations include fully three-dimensional simulations of the fracture topography, fluid flow, and reactant transport, two-dimensional simulations based on aperture models, and linear stability analysis.

Influence of foam on the stability characteristics of immiscible flow in porous media

NASA Astrophysics Data System (ADS)

van der Meer, J. M.; Farajzadeh, R.; Rossen, W. R.; Jansen, J. D.

2018-01-01

Accurate field-scale simulations of foam enhanced oil recovery are challenging, due to the sharp transition between gas and foam. Hence, unpredictable numerical and physical behavior is often observed, casting doubt on the validity of the simulation results. In this paper, a thorough stability analysis of the foam model is presented to validate the simulation results. We study the effect of a strongly non-monotonous total mobility function arising from foam models on the stability characteristics of the flow. To this end, we apply the linear stability analysis to nearly discontinuous relative permeability functions and compare the results with those of highly accurate numerical simulations. In addition, we present a qualitative analysis of the effect of different reservoir and fluid properties on the foam fingering behavior. In particular, we consider the effect of heterogeneity of the reservoir, injection rates, and foam quality. Relative permeability functions play an important role in the onset of fingering behavior of the injected fluid. Hence, we can deduce that stability properties are highly dependent on the non-linearity of the foam transition. The foam-water interface is governed by a very small total mobility ratio, implying a stable front. The transition between gas and foam, however, exhibits a huge total mobility ratio, leading to instabilities in the form of viscous fingering. This implies that there is an unstable pattern behind the front. We deduce that instabilities are able to grow behind the front but are later absorbed by the expanding wave. Moreover, the stability analysis, validated by numerical simulations, provides valuable insights about the important scales and wavelengths of the foam model. In this way, we remove the ambiguity regarding the effect of grid resolution on the convergence of the solutions. This insight forms an essential step toward the design of a suitable computational solver that captures all the appropriate scales, while retaining computational efficiency.

An extended car-following model to describe connected traffic dynamics under cyberattacks

NASA Astrophysics Data System (ADS)

Wang, Pengcheng; Yu, Guizhen; Wu, Xinkai; Qin, Hongmao; Wang, Yunpeng

2018-04-01

In this paper, the impacts of the potential cyberattacks on vehicles are modeled through an extended car-following model. To better understand the mechanism of traffic disturbance under cyberattacks, the linear and nonlinear stability analysis are conducted respectively. Particularly, linear stability analysis is performed to obtain different neutral stability conditions with various parameters; and nonlinear stability analysis is carried out by using reductive perturbation method to derive the soliton solution of the modified Korteweg de Vries equation (mKdV) near the critical point, which is used to draw coexisting stability lines. Furthermore, by applying linear and nonlinear stability analysis, traffic flow state can be divided into three states, i.e., stable, metastable and unstable states which are useful to describe shockwave dynamics and driving behaviors under cyberattacks. The theoretical results show that the proposed car-following model is capable of successfully describing the car-following behavior of connected vehicles with cyberattacks. Finally, numerical simulation using real values has confirmed the validity of theoretical analysis. The results further demonstrate our model can be used to help avoid collisions and relieve traffic congestion with cybersecurity threats.

Langley Stability and Transition Analysis Code (LASTRAC) Version 1.2 User Manual

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan

2004-01-01

LASTRAC is a general-purposed, physics-based transition prediction code released by NASA for Laminar Flow Control studies and transition research. The design and development of the LASTRAC code is aimed at providing an engineering tool that is easy to use and yet capable of dealing with a broad range of transition related issues. It was written from scratch based on the state-of-the-art numerical methods for stability analysis and modern software technologies. At low fidelity, it allows users to perform linear stability analysis and N-factor transition correlation for a broad range of flow regimes and configurations by using either the linear stability theory or linear parabolized stability equations method. At high fidelity, users may use nonlinear PSE to track finite-amplitude disturbances until the skin friction rise. This document describes the governing equations, numerical methods, code development, detailed description of input/output parameters, and case studies for the current release of LASTRAC.

Neurosurgery simulation using non-linear finite element modeling and haptic interaction

NASA Astrophysics Data System (ADS)

Lee, Huai-Ping; Audette, Michel; Joldes, Grand R.; Enquobahrie, Andinet

2012-02-01

Real-time surgical simulation is becoming an important component of surgical training. To meet the realtime requirement, however, the accuracy of the biomechancial modeling of soft tissue is often compromised due to computing resource constraints. Furthermore, haptic integration presents an additional challenge with its requirement for a high update rate. As a result, most real-time surgical simulation systems employ a linear elasticity model, simplified numerical methods such as the boundary element method or spring-particle systems, and coarse volumetric meshes. However, these systems are not clinically realistic. We present here an ongoing work aimed at developing an efficient and physically realistic neurosurgery simulator using a non-linear finite element method (FEM) with haptic interaction. Real-time finite element analysis is achieved by utilizing the total Lagrangian explicit dynamic (TLED) formulation and GPU acceleration of per-node and per-element operations. We employ a virtual coupling method for separating deformable body simulation and collision detection from haptic rendering, which needs to be updated at a much higher rate than the visual simulation. The system provides accurate biomechancial modeling of soft tissue while retaining a real-time performance with haptic interaction. However, our experiments showed that the stability of the simulator depends heavily on the material property of the tissue and the speed of colliding objects. Hence, additional efforts including dynamic relaxation are required to improve the stability of the system.

Le Chatelier Principle for Out-of-Equilibrium and Boundary-Driven Systems: Application to Dynamical Phase Transitions.

PubMed

Shpielberg, O; Akkermans, E

2016-06-17

A stability analysis is presented for boundary-driven and out-of-equilibrium systems in the framework of the hydrodynamic macroscopic fluctuation theory. A Hamiltonian description is proposed which allows us to thermodynamically interpret the additivity principle. A necessary and sufficient condition for the validity of the additivity principle is obtained as an extension of the Le Chatelier principle. These stability conditions result from a diagonal quadratic form obtained using the cumulant generating function. This approach allows us to provide a proof for the stability of the weakly asymmetric exclusion process and to reduce the search for stability to the solution of two coupled linear ordinary differential equations instead of nonlinear partial differential equations. Additional potential applications of these results are discussed in the realm of classical and quantum systems.

Le Chatelier Principle for Out-of-Equilibrium and Boundary-Driven Systems: Application to Dynamical Phase Transitions

NASA Astrophysics Data System (ADS)

Shpielberg, O.; Akkermans, E.

2016-06-01

A stability analysis is presented for boundary-driven and out-of-equilibrium systems in the framework of the hydrodynamic macroscopic fluctuation theory. A Hamiltonian description is proposed which allows us to thermodynamically interpret the additivity principle. A necessary and sufficient condition for the validity of the additivity principle is obtained as an extension of the Le Chatelier principle. These stability conditions result from a diagonal quadratic form obtained using the cumulant generating function. This approach allows us to provide a proof for the stability of the weakly asymmetric exclusion process and to reduce the search for stability to the solution of two coupled linear ordinary differential equations instead of nonlinear partial differential equations. Additional potential applications of these results are discussed in the realm of classical and quantum systems.

Stability properties of solitary waves for fractional KdV and BBM equations

NASA Astrophysics Data System (ADS)

Angulo Pava, Jaime

2018-03-01

This paper sheds new light on the stability properties of solitary wave solutions associated with Korteweg-de Vries-type models when the dispersion is very low. Using a compact, analytic approach and asymptotic perturbation theory, we establish sufficient conditions for the existence of exponentially growing solutions to the linearized problem and so a criterium of spectral instability of solitary waves is obtained for both models. Moreover, the nonlinear stability and spectral instability of the ground state solutions for both models is obtained for some specific regimen of parameters. Via a Lyapunov strategy and a variational analysis, we obtain the stability of the blow-up of solitary waves for the critical fractional KdV equation. The arguments presented in this investigation show promise for use in the study of the instability of traveling wave solutions of other nonlinear evolution equations.

The inviscid stability of supersonic flow past heated or cooled axisymmetric bodies

NASA Technical Reports Server (NTRS)

Shaw, Stephen J.; Duck, Peter W.

1992-01-01

The inviscid, linear, nonaxisymmetric, temporal stability of the boundary layer associated with the supersonic flow past axisymmetric bodies (with particular emphasis on long thin, straight circular cylinders), subject to heated or cooled wall conditions is investigated. The eigenvalue problem is computed in some detail for a particular Mach number or 3.8, revealing that the effect of curvature and the choice of wall conditions both have a significant effect on the stability of the flow. Both the asymptotic, large azimuthal wavenumber solution and the asymptotic, far downstream solution are obtained for the stability analysis and compared with numerical results. Additionally, asymptotic analyses valid for large radii of curvature with cooled/heated wall conditions are presented. In general, important differences were found to exist between the wall temperature conditions imposed and the adiabatic wall conditions considered previously.

The inviscid stability of supersonic flow past heated or cooled axisymmetric bodies

NASA Technical Reports Server (NTRS)

Shaw, Stephen J.; Duck, Peter W.

1990-01-01

The inviscid, linear, nonaxisymmetric, temporal stability of the boundary layer associated with the supersonic flow past axisymmetric bodies (with particular emphasis on long thin, straight circular cylinders), subject to heated or cooled wall conditions is investigated. The eigenvalue problem is computed in some detail for a particular Mach number or 3.8, revealing that the effect of curvature and the choice of wall conditions both have a significant effect on the stability of the flow. Both the asymptotic, large azimuthal wavenumber solution and the asymptotic, far downstream solution are obtained for the stability analysis and compared with numerical results. Additionally, asymptotic analyses valid for large radii of curvature with cooled/heated wall conditions, are presented. In general, important differences were found to exist between the wall temperature conditions imposed and the adiabatic wall conditions considered previously.

Orbital stability of periodic traveling-wave solutions for the log-KdV equation

NASA Astrophysics Data System (ADS)

Natali, Fábio; Pastor, Ademir; Cristófani, Fabrício

2017-09-01

In this paper we establish the orbital stability of periodic waves related to the logarithmic Korteweg-de Vries equation. Our motivation is inspired in the recent work [3], in which the authors established the well-posedness and the linear stability of Gaussian solitary waves. By using the approach put forward recently in [20] to construct a smooth branch of periodic waves as well as to get the spectral properties of the associated linearized operator, we apply the abstract theories in [13] and [25] to deduce the orbital stability of the periodic traveling waves in the energy space.

R-parametrization and its role in classification of linear multivariable feedback systems

NASA Technical Reports Server (NTRS)

Chen, Robert T. N.

1988-01-01

A classification of all the compensators that stabilize a given general plant in a linear, time-invariant multi-input, multi-output feedback system is developed. This classification, along with the associated necessary and sufficient conditions for stability of the feedback system, is achieved through the introduction of a new parameterization, referred to as R-Parameterization, which is a dual of the familiar Q-Parameterization. The classification is made to the stability conditions of the compensators and the plant by themselves; and necessary and sufficient conditions are based on the stability of Q and R themselves.

Stability of linear systems in second-order form based on structure preserving similarity transformations

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

Stoustrup, Jakob; Pommer, Christian; Kliem, Wolfhard

2015-10-31

This paper deals with two stability aspects of linear systems of the form I ¨ x +B˙ x +Cx = 0 given by the triple (I;B;C). A general transformation scheme is given for a structure and Jordan form preserving transformation of the triple. We investigate how a system can be transformed by suitable choices of the transformation parameters into a new system (I;B1;C1) with a symmetrizable matrix C1. This procedure facilitates stability investigations. We also consider systems with a Hamiltonian spectrum which discloses marginal stability after a Jordan form preserving transformation.

A conformal approach for the analysis of the non-linear stability of radiation cosmologies

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

Luebbe, Christian, E-mail: c.luebbe@ucl.ac.uk; Department of Mathematics, University of Leicester, University Road, LE1 8RH; Valiente Kroon, Juan Antonio, E-mail: j.a.valiente-kroon@qmul.ac.uk

2013-01-15

The conformal Einstein equations for a trace-free (radiation) perfect fluid are derived in terms of the Levi-Civita connection of a conformally rescaled metric. These equations are used to provide a non-linear stability result for de Sitter-like trace-free (radiation) perfect fluid Friedman-Lemaitre-Robertson-Walker cosmological models. The solutions thus obtained exist globally towards the future and are future geodesically complete. - Highlights: Black-Right-Pointing-Pointer We study the Einstein-Euler system in General Relativity using conformal methods. Black-Right-Pointing-Pointer We analyze the structural properties of the associated evolution equations. Black-Right-Pointing-Pointer We establish the non-linear stability of pure radiation cosmological models.

Stability and dynamic analysis of a slender column with curved longitudinal stiffeners

NASA Technical Reports Server (NTRS)

Lake, Mark S.

1989-01-01

The results of a stability design study are presented for a slender column with curved longitudinal stiffeners for large space structure applications. Linear stability analyses are performed using a link-plate representation of the stiffeners to determine stiffener local buckling stresses. Results from a set of parametric analyses are used to determine an approximate explicit expression for stiffener local buckling in terms of its geometric parameters. This expression along with other equations governing column stability and mass are assembled into a determinate system describing minimum mass stiffened column design. An iterative solution is determined to solve this system and a computer program incorporating this routine is presented. Example design problems are presented which verify the solution accuracy and illustrate the implementation of the solution routine. Also, observations are made which lead to a greatly simplified first iteration design equation relating the percent increase in column mass to the percent increase in column buckling load. From this, generalizations are drawn as to the mass savings offered by the stiffened column concept. Finally, the percent increase in fundamental column vibration frequency due to the addition of deployable stiffeners is studied.

Stability of Nonlinear Principal Components Analysis: An Empirical Study Using the Balanced Bootstrap

ERIC Educational Resources Information Center

Linting, Marielle; Meulman, Jacqueline J.; Groenen, Patrick J. F.; van der Kooij, Anita J.

2007-01-01

Principal components analysis (PCA) is used to explore the structure of data sets containing linearly related numeric variables. Alternatively, nonlinear PCA can handle possibly nonlinearly related numeric as well as nonnumeric variables. For linear PCA, the stability of its solution can be established under the assumption of multivariate…

Emergent kink stability of a magnetized plasma jet injected into a transverse background magnetic field

NASA Astrophysics Data System (ADS)

Zhang, Yue; Gilmore, Mark; Hsu, Scott C.; Fisher, Dustin M.; Lynn, Alan G.

2017-11-01

We report experimental results on the injection of a magnetized plasma jet into a transverse background magnetic field in the HelCat linear plasma device at the University of New Mexico [M. Gilmore et al., J. Plasma Phys. 81(1), 345810104 (2015)]. After the plasma jet leaves the plasma-gun muzzle, a tension force arising from an increasing curvature of the background magnetic field induces in the jet a sheared axial-flow gradient above the theoretical kink-stabilization threshold. We observe that this emergent sheared axial flow stabilizes the n = 1 kink mode in the jet, whereas a kink instability is observed in the jet when there is no background magnetic field present.

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

NASA Astrophysics Data System (ADS)

Du, Wei

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

An implicit adaptation algorithm for a linear model reference control system

NASA Technical Reports Server (NTRS)

Mabius, L.; Kaufman, H.

1975-01-01

This paper presents a stable implicit adaptation algorithm for model reference control. The constraints for stability are found using Lyapunov's second method and do not depend on perfect model following between the system and the reference model. Methods are proposed for satisfying these constraints without estimating the parameters on which the constraints depend.

MHD Simulations of Plasma Dynamics with Non-Axisymmetric Boundaries

NASA Astrophysics Data System (ADS)

Hansen, Chris; Levesque, Jeffrey; Morgan, Kyle; Jarboe, Thomas

2015-11-01

The arbitrary geometry, 3D extended MHD code PSI-TET is applied to linear and non-linear simulations of MCF plasmas with non-axisymmetric boundaries. Progress and results from simulations on two experiments will be presented: 1) Detailed validation studies of the HIT-SI experiment with self-consistent modeling of plasma dynamics in the helicity injectors. Results will be compared to experimental data and NIMROD simulations that model the effect of the helicity injectors through boundary conditions on an axisymmetric domain. 2) Linear studies of HBT-EP with different wall configurations focusing on toroidal asymmetries in the adjustable conducting wall. HBT-EP studies the effect of active/passive stabilization with an adjustable ferritic wall. Results from linear verification and benchmark studies of ideal mode growth with and without toroidal asymmetries will be presented and compared to DCON predictions. Simulations of detailed experimental geometries are enabled by use of the PSI-TET code, which employs a high order finite element method on unstructured tetrahedral grids that are generated directly from CAD models. Further development of PSI-TET will also be presented including work to support resistive wall regions within extended MHD simulations. Work supported by DoE.

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

DOE PAGES

Steyer, Andrew J.; Van Vleck, Erik S.

2018-04-13

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

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

Steyer, Andrew J.; Van Vleck, Erik S.

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

Geometry of thin liquid sheet flows

NASA Technical Reports Server (NTRS)

Chubb, Donald L.; Calfo, Frederick D.; Mcconley, Marc W.; Mcmaster, Matthew S.; Afjeh, Abdollah A.

1994-01-01

Incompresible, thin sheet flows have been of research interest for many years. Those studies were mainly concerned with the stability of the flow in a surrounding gas. Squire was the first to carry out a linear, invicid stability analysis of sheet flow in air and compare the results with experiment. Dombrowski and Fraser did an experimental study of the disintegration of sheet flows using several viscous liquids. They also detected the formulation of holes in their sheet flows. Hagerty and Shea carried out an inviscid stability analysis and calculated growth rates with experimental values. They compared their calculated growth rates with experimental values. Taylor studied extensively the stability of thin liquid sheets both theoretically and experimentally. He showed that thin sheets in a vacuum are stable. Brown experimentally investigated thin liquid sheet flows as a method of application of thin films. Clark and Dumbrowski carried out second-order stability analysis for invicid sheet flows. Lin introduced viscosity into the linear stability analysis of thin sheet flows in a vacuum. Mansour and Chigier conducted an experimental study of the breakup of a sheet flow surrounded by high-speed air. Lin et al. did a linear stability analysis that included viscosity and a surrounding gas. Rangel and Sirignano carried out both a linear and nonlinear invisid stability analysis that applies for any density ratio between the sheet liquid and the surrounding gas. Now there is renewed interest in sheet flows because of their possible application as low mass radiating surfaces. The objective of this study is to investigate the fluid dynamics of sheet flows that are of interest for a space radiator system. Analytical expressions that govern the sheet geometry are compared with experimental results. Since a space radiator will operate in a vacuum, the analysis does not include any drag force on the sheet flow.

PI Passivity-Based Control for Maximum Power Extraction of a Wind Energy System with Guaranteed Stability Properties

NASA Astrophysics Data System (ADS)

Cisneros, Rafael; Gao, Rui; Ortega, Romeo; Husain, Iqbal

2016-10-01

The present paper proposes a maximum power extraction control for a wind system consisting of a turbine, a permanent magnet synchronous generator, a rectifier, a load and one constant voltage source, which is used to form the DC bus. We propose a linear PI controller, based on passivity, whose stability is guaranteed under practically reasonable assumptions. PI structures are widely accepted in practice as they are easier to tune and simpler than other existing model-based methods. Real switching based simulations have been performed to assess the performance of the proposed controller.

Acceleration and stability of a high-current ion beam in induction fields

NASA Astrophysics Data System (ADS)

Karas', V. I.; Manuilenko, O. V.; Tarakanov, V. P.; Federovskaya, O. V.

2013-03-01

A one-dimensional nonlinear analytic theory of the filamentation instability of a high-current ion beam is formulated. The results of 2.5-dimensional numerical particle-in-cell simulations of acceleration and stability of an annular compensated ion beam (CIB) in a linear induction particle accelerator are presented. It is shown that additional transverse injection of electron beams in magnetically insulated gaps (cusps) improves the quality of the ion-beam distribution function and provides uniform beam acceleration along the accelerator. The CIB filamentation instability in both the presence and the absence of an external magnetic field is considered.

LMI-Based Fuzzy Optimal Variance Control of Airfoil Model Subject to Input Constraints

NASA Technical Reports Server (NTRS)

Swei, Sean S.M.; Ayoubi, Mohammad A.

2017-01-01

This paper presents a study of fuzzy optimal variance control problem for dynamical systems subject to actuator amplitude and rate constraints. Using Takagi-Sugeno fuzzy modeling and dynamic Parallel Distributed Compensation technique, the stability and the constraints can be cast as a multi-objective optimization problem in the form of Linear Matrix Inequalities. By utilizing the formulations and solutions for the input and output variance constraint problems, we develop a fuzzy full-state feedback controller. The stability and performance of the proposed controller is demonstrated through its application to the airfoil flutter suppression.

Estimation of regions of attraction and ultimate boundedness for multiloop LQ regulators. [Linear Quadratic

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1984-01-01

Closed-loop stability is investigated for multivariable linear time-invariant systems controlled by optimal full state feedback linear quadratic (LQ) regulators, with nonlinear gains present in the feedback channels. Estimates are obtained for the region of attraction when the nonlinearities escape the (0.5, infinity) sector in regions away from the origin and for the region of ultimate boundedness when the nonlinearities escape the sector near the origin. The expressions for these regions also provide methods for selecting the performance function parameters in order to obtain LQ designs with better tolerance for nonlinearities. The analytical results are illustrated by applying them to the problem of controlling the rigid-body pitch angle and elastic motion of a large, flexible space antenna.

Regional robust stabilisation and domain-of-attraction estimation for MIMO uncertain nonlinear systems with input saturation

NASA Astrophysics Data System (ADS)

Azizi, S.; Torres, L. A. B.; Palhares, R. M.

2018-01-01

The regional robust stabilisation by means of linear time-invariant state feedback control for a class of uncertain MIMO nonlinear systems with parametric uncertainties and control input saturation is investigated. The nonlinear systems are described in a differential algebraic representation and the regional stability is handled considering the largest ellipsoidal domain-of-attraction (DOA) inside a given polytopic region in the state space. A novel set of sufficient Linear Matrix Inequality (LMI) conditions with new auxiliary decision variables are developed aiming to design less conservative linear state feedback controllers with corresponding larger DOAs, by considering the polytopic description of the saturated inputs. A few examples are presented showing favourable comparisons with recently published similar control design methodologies.

Asymptotic Linearity of Optimal Control Modification Adaptive Law with Analytical Stability Margins

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.

2010-01-01

Optimal control modification has been developed to improve robustness to model-reference adaptive control. For systems with linear matched uncertainty, optimal control modification adaptive law can be shown by a singular perturbation argument to possess an outer solution that exhibits a linear asymptotic property. Analytical expressions of phase and time delay margins for the outer solution can be obtained. Using the gradient projection operator, a free design parameter of the adaptive law can be selected to satisfy stability margins.

Stability of the Baseline Holder in Readout Circuits For Radiation Detectors

PubMed Central

Chen, Y.; Cui, Y.; O’Connor, P.; Seo, Y.; Camarda, G. S.; Hossain, A.; Roy, U.; Yang, G.; James, R. B.

2016-01-01

Baseline holder (BLH) circuits are used widely to stabilize the analog output of application-specific integrated circuits (ASICs) for high-count-rate applications. The careful design of BLH circuits is vital to the overall stability of the analog-signal-processing chain in ASICs. Recently, we observed self-triggered fluctuations in an ASIC in which the shaping circuits have a BLH circuit in the feedback loop. In fact, further investigations showed that methods of enhancing small-signal stabilities cause an even worse situation. To resolve this problem, we used large-signal analyses to study the circuit’s stability. We found that a relatively small gain for the error amplifier and a small current in the non-linear stage of the BLH are required to enhance stability in large-signal analysis, which will compromise the properties of the BLH. These findings were verified by SPICE simulations. In this paper, we present our detailed analysis of the BLH circuits, and propose an improved version of them that have only minimal self-triggered fluctuations. We summarize the design considerations both for the stability and the properties of the BLH circuits. PMID:27182081

A Flight Dynamics Model for a Multi-Actuated Flexible Rocket Vehicle

NASA Technical Reports Server (NTRS)

Orr, Jeb S.

2011-01-01

A comprehensive set of motion equations for a multi-actuated flight vehicle is presented. The dynamics are derived from a vector approach that generalizes the classical linear perturbation equations for flexible launch vehicles into a coupled three-dimensional model. The effects of nozzle and aerosurface inertial coupling, sloshing propellant, and elasticity are incorporated without restrictions on the position, orientation, or number of model elements. The present formulation is well suited to matrix implementation for large-scale linear stability and sensitivity analysis and is also shown to be extensible to nonlinear time-domain simulation through the application of a special form of Lagrange s equations in quasi-coordinates. The model is validated through frequency-domain response comparison with a high-fidelity planar implementation.

Template-directed synthesis of linear porphyrin oligomers: classical, Vernier and mutual Vernier† †Electronic supplementary information (ESI) available: Synthesis and characterization of new compounds, ladder complexes, UV-vis-NIR titrations and binding data for reference compounds and for the formation of linear oligomer complexes, calculation of effective molarities, analytical GPC calibration and molar absorption coefficients. See DOI: 10.1039/c6sc05355f Click here for additional data file.

PubMed Central

Kamonsutthipaijit, Nuntaporn

2017-01-01

Three different types of template-directed syntheses of linear porphyrin oligomers are presented. In the classical approach the product has the same number of binding sites as the template, whereas in Vernier reactions the product has the lowest common multiple of the numbers of binding sites in the template and the building block. Mutual Vernier templating is like Vernier templating except that both strands of the Vernier complex undergo coupling simultaneously, so that it becomes impossible to say which is the ‘template’ and which is the ‘building block’. The template-directed synthesis of monodisperse linear oligomers is more difficult than that of cyclic oligomers, because the products of linear templating have reactive ends. All three types of templating are demonstrated here, and used to prepare a nickel(ii) porphyrin dodecamer with 4-pyridyl substituents on all twelve porphyrin units. The stabilities and cooperativities of the double-strand complexes involved in these reactions were investigated by UV-vis-NIR titration. The four-rung ladder duplex has a stability constant of about 2 × 1018 M–1 in dichloromethane at 298 K. PMID:28553508

A Self-Stabilizing Synchronization Protocol for Arbitrary Digraphs

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R.

2011-01-01

This paper presents a self-stabilizing distributed clock synchronization protocol in the absence of faults in the system. It is focused on the distributed clock synchronization of an arbitrary, non-partitioned digraph ranging from fully connected to 1-connected networks of nodes while allowing for differences in the network elements. This protocol does not rely on assumptions about the initial state of the system, other than the presence of at least one node, and no central clock or a centrally generated signal, pulse, or message is used. Nodes are anonymous, i.e., they do not have unique identities. There is no theoretical limit on the maximum number of participating nodes. The only constraint on the behavior of the node is that the interactions with other nodes are restricted to defined links and interfaces. This protocol deterministically converges within a time bound that is a linear function of the self-stabilization period. We present an outline of a deductive proof of the correctness of the protocol. A bounded model of the protocol was mechanically verified for a variety of topologies. Results of the mechanical proof of the correctness of the protocol are provided. The model checking results have verified the correctness of the protocol as they apply to the networks with unidirectional and bidirectional links. In addition, the results confirm the claims of determinism and linear convergence. As a result, we conjecture that the protocol solves the general case of this problem. We also present several variations of the protocol and discuss that this synchronization protocol is indeed an emergent system.

Carrier-envelope phase control using linear electro-optic effect.

PubMed

Gobert, O; Paul, P M; Hergott, J F; Tcherbakoff, O; Lepetit, F; 'Oliveira, P D; Viala, F; Comte, M

2011-03-14

We present a new method to control the Carrier-Envelope Phase of ultra-short laser pulses by using the linear Electro-Optic Effect. Experimental demonstration is carried out on a Chirped Pulse Amplification based laser. Phase shifts greater than π radian can be obtained by applying moderate voltage on a LiNbO3 crystal with practically no changes to all other parameters of the pulse with the exception of its group delay. Time response of the Electro-Optic effect makes possible shaping at a high repetition rate or stabilization of the CEP of ultra short CPA laser systems.

Nonlinear discrete-time multirate adaptive control of non-linear vibrations of smart beams

NASA Astrophysics Data System (ADS)

Georgiou, Georgios; Foutsitzi, Georgia A.; Stavroulakis, Georgios E.

2018-06-01

The nonlinear adaptive digital control of a smart piezoelectric beam is considered. It is shown that in the case of a sampled-data context, a multirate control strategy provides an appropriate framework in order to achieve vibration regulation, ensuring the stability of the whole control system. Under parametric uncertainties in the model parameters (damping ratios, frequencies, levels of non linearities and cross coupling, control input parameters), the scheme is completed with an adaptation law deduced from hyperstability concepts. This results in the asymptotic satisfaction of the control objectives at the sampling instants. Simulation results are presented.

An extended heterogeneous car-following model accounting for anticipation driving behavior and mixed maximum speeds

NASA Astrophysics Data System (ADS)

Sun, Fengxin; Wang, Jufeng; Cheng, Rongjun; Ge, Hongxia

2018-02-01

The optimal driving speeds of the different vehicles may be different for the same headway. In the optimal velocity function of the optimal velocity (OV) model, the maximum speed vmax is an important parameter determining the optimal driving speed. A vehicle with higher maximum speed is more willing to drive faster than that with lower maximum speed in similar situation. By incorporating the anticipation driving behavior of relative velocity and mixed maximum speeds of different percentages into optimal velocity function, an extended heterogeneous car-following model is presented in this paper. The analytical linear stable condition for this extended heterogeneous traffic model is obtained by using linear stability theory. Numerical simulations are carried out to explore the complex phenomenon resulted from the cooperation between anticipation driving behavior and heterogeneous maximum speeds in the optimal velocity function. The analytical and numerical results all demonstrate that strengthening driver's anticipation effect can improve the stability of heterogeneous traffic flow, and increasing the lowest value in the mixed maximum speeds will result in more instability, but increasing the value or proportion of the part already having higher maximum speed will cause different stabilities at high or low traffic densities.

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.

High-Alpha Research Vehicle Lateral-Directional Control Law Description, Analyses, and Simulation Results

NASA Technical Reports Server (NTRS)

Davidson, John B.; Murphy, Patrick C.; Lallman, Frederick J.; Hoffler, Keith D.; Bacon, Barton J.

1998-01-01

This report contains a description of a lateral-directional control law designed for the NASA High-Alpha Research Vehicle (HARV). The HARV is a F/A-18 aircraft modified to include a research flight computer, spin chute, and thrust-vectoring in the pitch and yaw axes. Two separate design tools, CRAFT and Pseudo Controls, were integrated to synthesize the lateral-directional control law. This report contains a description of the lateral-directional control law, analyses, and nonlinear simulation (batch and piloted) results. Linear analysis results include closed-loop eigenvalues, stability margins, robustness to changes in various plant parameters, and servo-elastic frequency responses. Step time responses from nonlinear batch simulation are presented and compared to design guidelines. Piloted simulation task scenarios, task guidelines, and pilot subjective ratings for the various maneuvers are discussed. Linear analysis shows that the control law meets the stability margin guidelines and is robust to stability and control parameter changes. Nonlinear batch simulation analysis shows the control law exhibits good performance and meets most of the design guidelines over the entire range of angle-of-attack. This control law (designated NASA-1A) was flight tested during the Summer of 1994 at NASA Dryden Flight Research Center.

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.

Does competition improve financial stability of the banking sector in ASEAN countries? An empirical analysis.

PubMed

Noman, Abu Hanifa Md; Gee, Chan Sok; Isa, Che Ruhana

2017-01-01

This study examines the influence of competition on the financial stability of the commercial banks of Association of Southeast Asian Nation (ASEAN) over the 1990 to 2014 period. Panzar-Rosse H-statistic, Lerner index and Herfindahl-Hirschman Index (HHI) are used as measures of competition, while Z-score, non-performing loan (NPL) ratio and equity ratio are used as measures of financial stability. Two-step system Generalized Method of Moments (GMM) estimates demonstrate that competition measured by H-statistic is positively related to Z-score and equity ratio, and negatively related to non-performing loan ratio. Conversely, market power measured by Lerner index is negatively related to Z-score and equity ratio and positively related to NPL ratio. These results strongly support the competition-stability view for ASEAN banks. We also capture the non-linear relationship between competition and financial stability by incorporating a quadratic term of competition in our models. The results show that the coefficient of the quadratic term of H-statistic is negative for the Z-score model given a positive coefficient of the linear term in the same model. These results support the non-linear relationship between competition and financial stability of the banking sector. The study contains significant policy implications for improving the financial stability of the commercial banks.

Does competition improve financial stability of the banking sector in ASEAN countries? An empirical analysis

PubMed Central

Gee, Chan Sok; Isa, Che Ruhana

2017-01-01

This study examines the influence of competition on the financial stability of the commercial banks of Association of Southeast Asian Nation (ASEAN) over the 1990 to 2014 period. Panzar-Rosse H-statistic, Lerner index and Herfindahl-Hirschman Index (HHI) are used as measures of competition, while Z-score, non-performing loan (NPL) ratio and equity ratio are used as measures of financial stability. Two-step system Generalized Method of Moments (GMM) estimates demonstrate that competition measured by H-statistic is positively related to Z-score and equity ratio, and negatively related to non-performing loan ratio. Conversely, market power measured by Lerner index is negatively related to Z-score and equity ratio and positively related to NPL ratio. These results strongly support the competition-stability view for ASEAN banks. We also capture the non-linear relationship between competition and financial stability by incorporating a quadratic term of competition in our models. The results show that the coefficient of the quadratic term of H-statistic is negative for the Z-score model given a positive coefficient of the linear term in the same model. These results support the non-linear relationship between competition and financial stability of the banking sector. The study contains significant policy implications for improving the financial stability of the commercial banks. PMID:28486548

Evans function computation for the stability of travelling waves

NASA Astrophysics Data System (ADS)

Barker, B.; Humpherys, J.; Lyng, G.; Lytle, J.

2018-04-01

In recent years, the Evans function has become an important tool for the determination of stability of travelling waves. This function, a Wronskian of decaying solutions of the eigenvalue equation, is useful both analytically and computationally for the spectral analysis of the linearized operator about the wave. In particular, Evans-function computation allows one to locate any unstable eigenvalues of the linear operator (if they exist); this allows one to establish spectral stability of a given wave and identify bifurcation points (loss of stability) as model parameters vary. In this paper, we review computational aspects of the Evans function and apply it to multidimensional detonation waves. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Linear Stability Analysis of an Acoustically Vaporized Droplet

NASA Astrophysics Data System (ADS)

Siddiqui, Junaid; Qamar, Adnan; Samtaney, Ravi

2015-11-01

Acoustic droplet vaporization (ADV) is a phase transition phenomena of a superheat liquid (Dodecafluoropentane, C5F12) droplet to a gaseous bubble, instigated by a high-intensity acoustic pulse. This approach was first studied in imaging applications, and applicable in several therapeutic areas such as gas embolotherapy, thrombus dissolution, and drug delivery. High-speed imaging and theoretical modeling of ADV has elucidated several physical aspects, ranging from bubble nucleation to its subsequent growth. Surface instabilities are known to exist and considered responsible for evolving bubble shapes (non-spherical growth, bubble splitting and bubble droplet encapsulation). We present a linear stability analysis of the dynamically evolving interfaces of an acoustically vaporized micro-droplet (liquid A) in an infinite pool of a second liquid (liquid B). We propose a thermal ADV model for the base state. The linear analysis utilizes spherical harmonics (Ynm, of degree m and order n) and under various physical assumptions results in a time-dependent ODE of the perturbed interface amplitudes (one at the vapor/liquid A interface and the other at the liquid A/liquid B interface). The perturbation amplitudes are found to grow exponentially and do not depend on m. Supported by KAUST Baseline Research Funds.

Sum-of-Squares-Based Region of Attraction Analysis for Gain-Scheduled Three-Loop Autopilot

NASA Astrophysics Data System (ADS)

Seo, Min-Won; Kwon, Hyuck-Hoon; Choi, Han-Lim

2018-04-01

A conventional method of designing a missile autopilot is to linearize the original nonlinear dynamics at several trim points, then to determine linear controllers for each linearized model, and finally implement gain-scheduling technique. The validation of such a controller is often based on linear system analysis for the linear closed-loop system at the trim conditions. Although this type of gain-scheduled linear autopilot works well in practice, validation based solely on linear analysis may not be sufficient to fully characterize the closed-loop system especially when the aerodynamic coefficients exhibit substantial nonlinearity with respect to the flight condition. The purpose of this paper is to present a methodology for analyzing the stability of a gain-scheduled controller in a setting close to the original nonlinear setting. The method is based on sum-of-squares (SOS) optimization that can be used to characterize the region of attraction of a polynomial system by solving convex optimization problems. The applicability of the proposed SOS-based methodology is verified on a short-period autopilot of a skid-to-turn missile.

Synchronization of cyclic power grids: Equilibria and stability of the synchronous state

NASA Astrophysics Data System (ADS)

Xi, Kaihua; Dubbeldam, Johan L. A.; Lin, Hai Xiang

2017-01-01

Synchronization is essential for the proper functioning of power grids; we investigate the synchronous states and their stability for cyclic power grids. We calculate the number of stable equilibria and investigate both the linear and nonlinear stabilities of the synchronous state. The linear stability analysis shows that the stability of the state, determined by the smallest nonzero eigenvalue, is inversely proportional to the size of the network. We use the energy barrier to measure the nonlinear stability and calculate it by comparing the potential energy of the type-1 saddles with that of the stable synchronous state. We find that the energy barrier depends on the network size (N) in a more complicated fashion compared to the linear stability. In particular, when the generators and consumers are evenly distributed in an alternating way, the energy barrier decreases to a constant when N approaches infinity. For a heterogeneous distribution of generators and consumers, the energy barrier decreases with N. The more heterogeneous the distribution is, the stronger the energy barrier depends on N. Finally, we find that by comparing situations with equal line loads in cyclic and tree networks, tree networks exhibit reduced stability. This difference disappears in the limit of N →∞ . This finding corroborates previous results reported in the literature and suggests that cyclic (sub)networks may be applied to enhance power transfer while maintaining stable synchronous operation.

Stability and synchronization analysis of inertial memristive neural networks with time delays.

PubMed

Rakkiyappan, R; Premalatha, S; Chandrasekar, A; Cao, Jinde

2016-10-01

This paper is concerned with the problem of stability and pinning synchronization of a class of inertial memristive neural networks with time delay. In contrast to general inertial neural networks, inertial memristive neural networks is applied to exhibit the synchronization and stability behaviors due to the physical properties of memristors and the differential inclusion theory. By choosing an appropriate variable transmission, the original system can be transformed into first order differential equations. Then, several sufficient conditions for the stability of inertial memristive neural networks by using matrix measure and Halanay inequality are derived. These obtained criteria are capable of reducing computational burden in the theoretical part. In addition, the evaluation is done on pinning synchronization for an array of linearly coupled inertial memristive neural networks, to derive the condition using matrix measure strategy. Finally, the two numerical simulations are presented to show the effectiveness of acquired theoretical results.

Cilazapril stability in the presence of hydrochlorothiazide in model mixtures and fixed dose combination.

PubMed

Paszun, Sylwia K; Stanisz, Beata J; Gradowska, Agnieszka

2013-01-01

The presented study aimed at the evaluation of hydrochlorothiazide influence on cilazapril stability in model mixture and fixed dose tablet formulation. The degradation of cilazapril in the presence of hydrochlorothiazide took place according to autocatalytic reaction kinetic mechanism, described mathematically by Prout-Tompkins equation. Hydrochlorothiazide coexistence with cilazapril in model mixture and fixed dose tablet without blister package accelerated cilazapril degradation in comparison with degradation of cilazapril substance. Values of reaction induction time shortened, while those of observed reaction rate constant increased. Increasing values of relative humidity and temperature have negative impact on cilazapril stability. Determined semi-logarithmic relationships: In k = f(RH) and Arrhenius ln k = f(1/T) are linear and are cilazapril stability predictive. The blister (OPA/Alu/PVC//Alu) package of fixed dose tablets, constitutes absolute moisture protection and prevent cilazapril--hydrochlorothiazide interaction occurrence.

Effects of viscosity and conductivity stratification on the linear stability and transient growth within compressible Couette flow

NASA Astrophysics Data System (ADS)

Saikia, Bijaylakshmi; Ramachandran, Ashwin; Sinha, Krishnendu; Govindarajan, Rama

2017-02-01

Accurate prediction of laminar to turbulent transition in compressible flows is a challenging task, as it can be affected by a combination of factors. Compressibility causes large variations in thermodynamic as well as transport properties of a gas, which in turn are known to affect flow stability. We study the stratification of individual transport properties and their combined behavior. We also examine the effect of a change in the magnitude of viscosity and conductivity on flow stability. The Couette flow of a perfect gas is our model problem and both modal and non-modal analyses are carried out. We notice a large destabilizing role of the increase in the conductivity value and a dramatic stabilizing effect of mean viscosity stratification, over a range of free-stream Mach number, Reynolds number, Prandtl number, and disturbance wavenumber. In the combined case, viscosity stratification plays a dominant role. We find this to be the case for finite-time transient growth in the parameter regime below linear instability as well as asymptotically at large time. A budget of the transient growth energy amplification is also shown to identify the effects of transport properties on the constituents of perturbation energy. The extensive results presented in this paper, we believe should motivate those studying more realistic flows to examine how these contrasting effects of stratification come together.

CS-AMPPred: An Updated SVM Model for Antimicrobial Activity Prediction in Cysteine-Stabilized Peptides

PubMed Central

Porto, William F.; Pires, Állan S.; Franco, Octavio L.

2012-01-01

The antimicrobial peptides (AMP) have been proposed as an alternative to control resistant pathogens. However, due to multifunctional properties of several AMP classes, until now there has been no way to perform efficient AMP identification, except through in vitro and in vivo tests. Nevertheless, an indication of activity can be provided by prediction methods. In order to contribute to the AMP prediction field, the CS-AMPPred (Cysteine-Stabilized Antimicrobial Peptides Predictor) is presented here, consisting of an updated version of the Support Vector Machine (SVM) model for antimicrobial activity prediction in cysteine-stabilized peptides. The CS-AMPPred is based on five sequence descriptors: indexes of (i) α-helix and (ii) loop formation; and averages of (iii) net charge, (iv) hydrophobicity and (v) flexibility. CS-AMPPred was based on 310 cysteine-stabilized AMPs and 310 sequences extracted from PDB. The polynomial kernel achieves the best accuracy on 5-fold cross validation (85.81%), while the radial and linear kernels achieve 84.19%. Testing in a blind data set, the polynomial and radial kernels achieve an accuracy of 90.00%, while the linear model achieves 89.33%. The three models reach higher accuracies than previously described methods. A standalone version of CS-AMPPred is available for download at and runs on any Linux machine. PMID:23240023

Model Checking a Byzantine-Fault-Tolerant Self-Stabilizing Protocol for Distributed Clock Synchronization Systems

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R.

2007-01-01

This report presents the mechanical verification of a simplified model of a rapid Byzantine-fault-tolerant self-stabilizing protocol for distributed clock synchronization systems. This protocol does not rely on any assumptions about the initial state of the system. This protocol tolerates bursts of transient failures, and deterministically converges within a time bound that is a linear function of the self-stabilization period. A simplified model of the protocol is verified using the Symbolic Model Verifier (SMV) [SMV]. The system under study consists of 4 nodes, where at most one of the nodes is assumed to be Byzantine faulty. The model checking effort is focused on verifying correctness of the simplified model of the protocol in the presence of a permanent Byzantine fault as well as confirmation of claims of determinism and linear convergence with respect to the self-stabilization period. Although model checking results of the simplified model of the protocol confirm the theoretical predictions, these results do not necessarily confirm that the protocol solves the general case of this problem. Modeling challenges of the protocol and the system are addressed. A number of abstractions are utilized in order to reduce the state space. Also, additional innovative state space reduction techniques are introduced that can be used in future verification efforts applied to this and other protocols.

Unifying dynamical and structural stability of equilibria

NASA Astrophysics Data System (ADS)

Arnoldi, Jean-François; Haegeman, Bart

2016-09-01

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

Unifying dynamical and structural stability of equilibria.

PubMed

Arnoldi, Jean-François; Haegeman, Bart

2016-09-01

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

CSI, optimal control, and accelerometers: Trials and tribulations

NASA Technical Reports Server (NTRS)

Benjamin, Brian J.; Sesak, John R.

1994-01-01

New results concerning optimal design with accelerometers are presented. These results show that the designer must be concerned with the stability properties of two Linear Quadratic Gaussian (LQG) compensators, one of which does not explicitly appear in the closed-loop system dynamics. The new concepts of virtual and implemented compensators are introduced to cope with these subtleties. The virtual compensator appears in the closed-loop system dynamics and the implemented compensator appears in control electronics. The stability of one compensator does not guarantee the stability of the other. For strongly stable (robust) systems, both compensators should be stable. The presence of controlled and uncontrolled modes in the system results in two additional forms of the compensator with corresponding terms that are of like form, but opposite sign, making simultaneous stabilization of both the virtual and implemented compensator difficult. A new design algorithm termed sensor augmentation is developed that aids stabilization of these compensator forms by incorporating a static augmentation term associated with the uncontrolled modes in the design process.

Long life lithium batteries with stabilized electrodes

DOEpatents

Amine, Khalil; Liu, Jun; Vissers, Donald R; Lu, Wenquan

2015-04-21

The present invention relates to non-aqueous electrolytes having electrode stabilizing additives, stabilized electrodes, and electrochemical devices containing the same. Thus the present invention provides electrolytes containing an alkali metal salt, a polar aprotic solvent, and an electrode stabilizing additive. In certain electrolytes, the alkali metal salt is a bis(chelato)borate and the additives include substituted or unsubstituted linear, branched or cyclic hydrocarbons comprising at least one oxygen atom and at least one aryl, alkenyl or alkynyl group. In other electrolytes, the additives include a substituted aryl compound or a substituted or unsubstituted heteroaryl compound wherein the additive comprises at least one oxygen atom. There are also provided methods of making the electrolytes and batteries employing the electrolytes. The invention also provides for electrode materials. Cathodes of the present invention may be further stabilized by surface coating the particles of the spinel or olivine with a material that can neutralize acid or otherwise lessen or prevent leaching of the manganese or iron ions. In some embodiments the coating is polymeric and in other embodiments the coating is a metal oxide such as ZrO.sub.2, TiO.sub.2, ZnO, WO.sub.3, Al.sub.2O.sub.3, MgO, SiO.sub.2, SnO.sub.2 AlPO.sub.4, Al(OH).sub.3, a mixture of any two or more thereof.

Beam Dynamics for ARIA

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

Ekdahl, Carl August Jr.

2014-10-14

Beam dynamics issues are assessed for a new linear induction electron accelerator being designed for flash radiography of large explosively driven hydrodynamic experiments. Special attention is paid to equilibrium beam transport, possible emittance growth, and beam stability. It is concluded that a radiographic quality beam will be produced possible if engineering standards and construction details are equivalent to those on the present radiography accelerators at Los Alamos.

Stability analysis on the flow and heat transfer of nanofluid past a stretching/shrinking cylinder with suction effect

NASA Astrophysics Data System (ADS)

Bakar, Nor Ashikin Abu; Bachok, Norfifah; Arifin, Norihan Md.; Pop, Ioan

2018-06-01

The steady boundary layer flow over a stretching/shrinking cylinder with suction effect is numerically studied. Using a similarity transformations, the governing partial differential equations are transformed into a set of nonlinear differential equations and have been solved numerically using a bvp4c code in Matlab software. The nanofluid model used is taking into account the effects of Brownian motion and thermophoresis. The influences of the governing parameters namely the curvature parameter γ, mass suction parameter S, Brownian motion parameter Nb and thermophoresis parameter Nt on the flow, heat and mass transfers characteristics are presented graphically. The numerical results obtained for the skin friction coefficient, local Nusselt number and local Sherwood number are thoroughly determined and presented graphically for several values of the governing parameters. From our investigation, it is found that the non-unique (dual) solutions exist for a certain range of mass suction parameter. It is observed that as curvature parameter increases, the skin friction coefficient and heat transfer rate decrease, meanwhile the mass transfer rates increase. Moreover, the stability analysis showed that the first solution is linearly stable, while the second solution is linearly unstable.

Ab initio calculations of the elastic and thermodynamic properties of gold under pressure

NASA Astrophysics Data System (ADS)

Smirnov, N. A.

2017-03-01

The paper presents first-principles FP-LMTO calculations on the relative stability of fcc, bcc, hcp and dhcp gold under pressure. They were done in local density approximation (LDA), as well as in generalized gradient approximation (GGA) with and without spin-orbit interaction. Phonon spectra for the considered gold structures were obtained from LDA calculations within linear response theory and the contribution of lattice vibrations to the free energy of the system was determined in quasiharmonic approximation. Our thorough adjustment of FP-LMTO internal parameters (linearization and tail energies, the MT-sphere radius) helped us to obtain results that agree well with the available experimental phase relation Dubrovinsky et al (2007 Phys. Rev. Lett. 98 045503) between fcc and hcp structures of gold under pressure. The calculations suggest that gold compressed at room temperature successively undergoes the following structural changes: fcc\\to hcp\\to bcc . The paper also presents the calculated elastic constants of fcc, bcc and hcp Au, the principal Hugoniot and the melting curve. Calculated results were used to construct the PT-diagram which describes the relative stability of the gold structures under study up to 500 GPa.

Ab initio calculations of the elastic and thermodynamic properties of gold under pressure.

PubMed

Smirnov, N A

2017-03-15

The paper presents first-principles FP-LMTO calculations on the relative stability of fcc, bcc, hcp and dhcp gold under pressure. They were done in local density approximation (LDA), as well as in generalized gradient approximation (GGA) with and without spin-orbit interaction. Phonon spectra for the considered gold structures were obtained from LDA calculations within linear response theory and the contribution of lattice vibrations to the free energy of the system was determined in quasiharmonic approximation. Our thorough adjustment of FP-LMTO internal parameters (linearization and tail energies, the MT-sphere radius) helped us to obtain results that agree well with the available experimental phase relation Dubrovinsky et al (2007 Phys. Rev. Lett. 98 045503) between fcc and hcp structures of gold under pressure. The calculations suggest that gold compressed at room temperature successively undergoes the following structural changes: [Formula: see text]. The paper also presents the calculated elastic constants of fcc, bcc and hcp Au, the principal Hugoniot and the melting curve. Calculated results were used to construct the PT-diagram which describes the relative stability of the gold structures under study up to 500 GPa.

The inviscid stability of supersonic flow past a sharp cone

NASA Technical Reports Server (NTRS)

Duck, Peter W.; Shaw, Stephen J.

1990-01-01

The laminar boundary layer which forms on a sharp cone in a supersonic freestream, where lateral curvature plays a key role in the physics of the problem is considered. This flow is then analyzed from the point of view of linear, temporal, inviscid stability. The basic, non-axisymmetric disturbance equations are derived for general flows of this class, and a so called triply generalized inflexion condition is found for the existence of subsonic neutral modes of instability. This condition is analogous to the well-known generalized inflexion condition found in planar flows, although in the present case the condition depends on both axial and aximuthal wavenumbers. Extensive numerical results are presented for the stability problem at a freestream Mach number of 3.8, for a range of streamwise locations. These results reveal that a new mode of instability may occur, peculiar to flows of this type involving curvature. Additionally, asymptotic analyses valid close to the tip of the cone, far downstream of the cone are presented, and these give a partial (asymptotic) description of this additional mode of instability.

Perturbations of linear delay differential equations at the verge of instability.

PubMed

Lingala, N; Namachchivaya, N Sri

2016-06-01

The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e., a pair of roots of the characteristic equation lies on the imaginary axis of the complex plane and all other roots have negative real parts. It is shown that when small noise perturbations are present, the probability distribution of the dynamics can be approximated by the probability distribution of a certain one-dimensional stochastic differential equation (SDE) without delay. This is advantageous because equations without delay are easier to simulate and one-dimensional SDEs are analytically tractable. When the perturbations are also linear, it is shown that the stability depends on a specific complex number. The theory is applied to study oscillators with delayed feedback. Some errors in other articles that use multiscale approach are pointed out.

Combined analytical and numerical approaches in Dynamic Stability analyses of engineering systems

NASA Astrophysics Data System (ADS)

Náprstek, Jiří

2015-03-01

Dynamic Stability is a widely studied area that has attracted many researchers from various disciplines. Although Dynamic Stability is usually associated with mechanics, theoretical physics or other natural and technical disciplines, it is also relevant to social, economic, and philosophical areas of our lives. Therefore, it is useful to occasionally highlight the general aspects of this amazing area, to present some relevant examples and to evaluate its position among the various branches of Rational Mechanics. From this perspective, the aim of this study is to present a brief review concerning the Dynamic Stability problem, its basic definitions and principles, important phenomena, research motivations and applications in engineering. The relationships with relevant systems that are prone to stability loss (encountered in other areas such as physics, other natural sciences and engineering) are also noted. The theoretical background, which is applicable to many disciplines, is presented. In this paper, the most frequently used Dynamic Stability analysis methods are presented in relation to individual dynamic systems that are widely discussed in various engineering branches. In particular, the Lyapunov function and exponent procedures, Routh-Hurwitz, Liénard, and other theorems are outlined together with demonstrations. The possibilities for analytical and numerical procedures are mentioned together with possible feedback from experimental research and testing. The strengths and shortcomings of these approaches are evaluated together with examples of their effective complementing of each other. The systems that are widely encountered in engineering are presented in the form of mathematical models. The analyses of their Dynamic Stability and post-critical behaviour are also presented. The stability limits, bifurcation points, quasi-periodic response processes and chaotic regimes are discussed. The limit cycle existence and stability are examined together with their separating roles as attractors and repulsers. Two levels of stability loss (recovery of the system is possible or final collapse is inevitable) as can be observed in softening systems are noted. Time-limited excitation and relevant transition effects (e.g., seismic excitation) are also discussed, together with the evaluation of possible system reliability improvement. The Dynamic Stability investigation of two degrees-of-freedom aero-elastic systems in a linear formulation using several approaches is briefly highlighted. Further systems modelling problems that arise in transport engineering are also outlined. A few hints for applications are given. Some open problems and possible future research strategies are outlined.

Stability analysis of gyroscopic systems with delay via decomposition

NASA Astrophysics Data System (ADS)

Aleksandrov, A. Yu.; Zhabko, A. P.; Chen, Y.

2018-05-01

A mechanical system describing by the second order linear differential equations with a positive parameter at the velocity forces and with time delay in the positional forces is studied. Using the decomposition method and Lyapunov-Krasovskii functionals, conditions are obtained under which from the asymptotic stability of two auxiliary first order subsystems it follows that, for sufficiently large values of the parameter, the original system is also asymptotically stable. Moreover, it is shown that the proposed approach can be applied to the stability investigation of linear gyroscopic systems with switched positional forces.

On exponential stability of linear Levin-Nohel integro-differential equations

NASA Astrophysics Data System (ADS)

Tien Dung, Nguyen

2015-02-01

The aim of this paper is to investigate the exponential stability for linear Levin-Nohel integro-differential equations with time-varying delays. To the best of our knowledge, the exponential stability for such equations has not yet been discussed. In addition, since we do not require that the kernel and delay are continuous, our results improve those obtained in Becker and Burton [Proc. R. Soc. Edinburgh, Sect. A: Math. 136, 245-275 (2006)]; Dung [J. Math. Phys. 54, 082705 (2013)]; and Jin and Luo [Comput. Math. Appl. 57(7), 1080-1088 (2009)].

Optimization-Based Robust Nonlinear Control

DTIC Science & Technology

2006-08-01

ABSTRACT New control algorithms were developed for robust stabilization of nonlinear dynamical systems . Novel, linear matrix inequality-based synthesis...was to further advance optimization-based robust nonlinear control design, for general nonlinear systems (especially in discrete time ), for linear...Teel, IEEE Transactions on Control Systems Technology, vol. 14, no. 3, p. 398-407, May 2006. 3. "A unified framework for input-to-state stability in

How can we make stable linear monoatomic chains? Gold-cesium binary subnanowires as an example of a charge-transfer-driven approach to alloying.

PubMed

Choi, Young Cheol; Lee, Han Myoung; Kim, Woo Youn; Kwon, S K; Nautiyal, Tashi; Cheng, Da-Yong; Vishwanathan, K; Kim, Kwang S

2007-02-16

On the basis of first-principles calculations of clusters and one dimensional infinitely long subnanowires of the binary systems, we find that alkali-noble metal alloy wires show better linearity and stability than either pure alkali metal or noble metal wires. The enhanced alternating charge buildup on atoms by charge transfer helps the atoms line up straight. The cesium doped gold wires showing significant charge transfer from cesium to gold can be stabilized as linear or circular monoatomic chains.

Kinematic variability, fractal dynamics and local dynamic stability of treadmill walking

PubMed Central

2011-01-01

Background Motorized treadmills are widely used in research or in clinical therapy. Small kinematics, kinetics and energetics changes induced by Treadmill Walking (TW) as compared to Overground Walking (OW) have been reported in literature. The purpose of the present study was to characterize the differences between OW and TW in terms of stride-to-stride variability. Classical (Standard Deviation, SD) and non-linear (fractal dynamics, local dynamic stability) methods were used. In addition, the correlations between the different variability indexes were analyzed. Methods Twenty healthy subjects performed 10 min TW and OW in a random sequence. A triaxial accelerometer recorded trunk accelerations. Kinematic variability was computed as the average SD (MeanSD) of acceleration patterns among standardized strides. Fractal dynamics (scaling exponent α) was assessed by Detrended Fluctuation Analysis (DFA) of stride intervals. Short-term and long-term dynamic stability were estimated by computing the maximal Lyapunov exponents of acceleration signals. Results TW did not modify kinematic gait variability as compared to OW (multivariate T2, p = 0.87). Conversely, TW significantly modified fractal dynamics (t-test, p = 0.01), and both short and long term local dynamic stability (T2 p = 0.0002). No relationship was observed between variability indexes with the exception of significant negative correlation between MeanSD and dynamic stability in TW (3 × 6 canonical correlation, r = 0.94). Conclusions Treadmill induced a less correlated pattern in the stride intervals and increased gait stability, but did not modify kinematic variability in healthy subjects. This could be due to changes in perceptual information induced by treadmill walking that would affect locomotor control of the gait and hence specifically alter non-linear dependencies among consecutive strides. Consequently, the type of walking (i.e. treadmill or overground) is important to consider in each protocol design. PMID:21345241

A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow

NASA Astrophysics Data System (ADS)

Krank, Benjamin; Fehn, Niklas; Wall, Wolfgang A.; Kronbichler, Martin

2017-11-01

We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration as well as nodal equal-order discretizations for velocity and pressure. The non-linear convective term is treated explicitly while a linear system is solved for the pressure Poisson equation and the viscous term. The key feature of our solver is a consistent penalty term reducing the local divergence error in order to overcome recently reported instabilities in spatially under-resolved high-Reynolds-number flows as well as small time steps. This penalty method is similar to the grad-div stabilization widely used in continuous finite elements. We further review and compare our method to several other techniques recently proposed in literature to stabilize the method for such flow configurations. The solver is specifically designed for large-scale computations through matrix-free linear solvers including efficient preconditioning strategies and tensor-product elements, which have allowed us to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores. We validate our code and demonstrate optimal convergence rates with laminar flows present in a vortex problem and flow past a cylinder and show applicability of our solver to direct numerical simulation as well as implicit large-eddy simulation of turbulent channel flow at Reτ = 180 as well as 590.

Bifurcations and Chaos of AN Immersed Cantilever Beam in a Fluid and Carrying AN Intermediate Mass

NASA Astrophysics Data System (ADS)

AL-QAISIA, A. A.; HAMDAN, M. N.

2002-06-01

The concern of this work is the local stability and period-doubling bifurcations of the response to a transverse harmonic excitation of a slender cantilever beam partially immersed in a fluid and carrying an intermediate lumped mass. The unimodal form of the non-linear dynamic model describing the beam-mass in-plane large-amplitude flexural vibration, which accounts for axial inertia, non-linear curvature and inextensibility condition, developed in Al-Qaisia et al. (2000Shock and Vibration7 , 179-194), is analyzed and studied for the resonance responses of the first three modes of vibration, using two-term harmonic balance method. Then a consistent second order stability analysis of the associated linearized variational equation is carried out using approximate methods to predict the zones of symmetry breaking leading to period-doubling bifurcation and chaos on the resonance response curves. The results of the present work are verified for selected physical system parameters by numerical simulations using methods of the qualitative theory, and good agreement was obtained between the analytical and numerical results. Also, analytical prediction of the period-doubling bifurcation and chaos boundaries obtained using a period-doubling bifurcation criterion proposed in Al-Qaisia and Hamdan (2001 Journal of Sound and Vibration244, 453-479) are compared with those of computer simulations. In addition, results of the effect of fluid density, fluid depth, mass ratio, mass position and damping on the period-doubling bifurcation diagrams are studies and presented.

The influence of continuous historical velocity difference information on micro-cooperative driving stability

NASA Astrophysics Data System (ADS)

Yang, Liang-Yi; Sun, Di-Hua; Zhao, Min; Cheng, Sen-Lin; Zhang, Geng; Liu, Hui

2018-03-01

In this paper, a new micro-cooperative driving car-following model is proposed to investigate the effect of continuous historical velocity difference information on traffic stability. The linear stability criterion of the new model is derived with linear stability theory and the results show that the unstable region in the headway-sensitivity space will be shrunk by taking the continuous historical velocity difference information into account. Through nonlinear analysis, the mKdV equation is derived to describe the traffic evolution behavior of the new model near the critical point. Via numerical simulations, the theoretical analysis results are verified and the results indicate that the continuous historical velocity difference information can enhance the stability of traffic flow in the micro-cooperative driving process.

Linear feedback stabilization of a dispersively monitored qubit

NASA Astrophysics Data System (ADS)

Patti, Taylor Lee; Chantasri, Areeya; García-Pintos, Luis Pedro; Jordan, Andrew N.; Dressel, Justin

2017-08-01

The state of a continuously monitored qubit evolves stochastically, exhibiting competition between coherent Hamiltonian dynamics and diffusive partial collapse dynamics that follow the measurement record. We couple these distinct types of dynamics together by linearly feeding the collected record for dispersive energy measurements directly back into a coherent Rabi drive amplitude. Such feedback turns the competition cooperative and effectively stabilizes the qubit state near a target state. We derive the conditions for obtaining such dispersive state stabilization and verify the stabilization conditions numerically. We include common experimental nonidealities, such as energy decay, environmental dephasing, detector efficiency, and feedback delay, and show that the feedback delay has the most significant negative effect on the feedback protocol. Setting the measurement collapse time scale to be long compared to the feedback delay yields the best stabilization.

Status of linear boundary-layer stability and the e to the nth method, with emphasis on swept-wing applications

NASA Technical Reports Server (NTRS)

Hefner, J. N.; Bushnell, D. M.

1980-01-01

The-state-of-the-art for the application of linear stability theory and the e to the nth power method for transition prediction and laminar flow control design are summarized, with analyses of previously published low disturbance, swept wing data presented. For any set of transition data with similar stream distrubance levels and spectra, the e to the nth power method for estimating the beginning of transition works reasonably well; however, the value of n can vary significantly, depending upon variations in disturbance field or receptivity. Where disturbance levels are high, the values of n are appreciably below the usual average value of 9 to 10 obtained for relatively low disturbance levels. It is recommended that the design of laminar flow control systems be based on conservative estimates of n and that, in considering the values of n obtained from different analytical approaches or investigations, the designer explore the various assumptions which entered into the analyses.

The Analysis and Construction of Perfectly Matched Layers for the Linearized Euler Equations

NASA Technical Reports Server (NTRS)

Hesthaven, J. S.

1997-01-01

We present a detailed analysis of a recently proposed perfectly matched layer (PML) method for the absorption of acoustic waves. The split set of equations is shown to be only weakly well-posed, and ill-posed under small low order perturbations. This analysis provides the explanation for the stability problems associated with the split field formulation and illustrates why applying a filter has a stabilizing effect. Utilizing recent results obtained within the context of electromagnetics, we develop strongly well-posed absorbing layers for the linearized Euler equations. The schemes are shown to be perfectly absorbing independent of frequency and angle of incidence of the wave in the case of a non-convecting mean flow. In the general case of a convecting mean flow, a number of techniques is combined to obtain a absorbing layers exhibiting PML-like behavior. The efficacy of the proposed absorbing layers is illustrated though computation of benchmark problems in aero-acoustics.

A Byzantine-Fault Tolerant Self-Stabilizing Protocol for Distributed Clock Synchronization Systems

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R.

2006-01-01

Embedded distributed systems have become an integral part of safety-critical computing applications, necessitating system designs that incorporate fault tolerant clock synchronization in order to achieve ultra-reliable assurance levels. Many efficient clock synchronization protocols do not, however, address Byzantine failures, and most protocols that do tolerate Byzantine failures do not self-stabilize. Of the Byzantine self-stabilizing clock synchronization algorithms that exist in the literature, they are based on either unjustifiably strong assumptions about initial synchrony of the nodes or on the existence of a common pulse at the nodes. The Byzantine self-stabilizing clock synchronization protocol presented here does not rely on any assumptions about the initial state of the clocks. Furthermore, there is neither a central clock nor an externally generated pulse system. The proposed protocol converges deterministically, is scalable, and self-stabilizes in a short amount of time. The convergence time is linear with respect to the self-stabilization period. Proofs of the correctness of the protocol as well as the results of formal verification efforts are reported.

Stabilization of Taylor-Couette flow due to time-periodic outer cylinder oscillation

NASA Technical Reports Server (NTRS)

Murray, B. T.; Mcfadden, G. B.; Coriell, S. R.

1990-01-01

The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case when the inner cylinder is rotated at a constant angular velocity and the outer cylinder is driven sinusoidally in time with zero mean rotation. This configuration was studied experimentally by Walsh and Donnelly. The critical Reynolds numbers calculated from linear stability theory agree well with the experimental values, except at large modulation amplitudes and small frequencies. The theoretical values are obtained using Floquet theory implemented in two distinct approaches: a truncated Fourier series representation in time, and a fundamental solution matrix based on a Chebyshev pseudospectral representation in space. For large amplitude, low frequency modulation, the linear eigenfunctions are temporally complex, consisting of a quiescent region followed by rapid change in the perturbed flow velocities.

Controller Synthesis for Periodically Forced Chaotic Systems

NASA Astrophysics Data System (ADS)

Basso, Michele; Genesio, Roberto; Giovanardi, Lorenzo

Delayed feedback controllers are an appealing tool for stabilization of periodic orbits in chaotic systems. Despite their conceptual simplicity, specific and reliable design procedures are difficult to obtain, partly also because of their inherent infinite-dimensional structure. This chapter considers the use of finite dimensional linear time invariant controllers for stabilization of periodic solutions in a general class of sinusoidally forced nonlinear systems. For such controllers — which can be interpreted as rational approximations of the delayed ones — we provide a computationally attractive synthesis technique based on Linear Matrix Inequalities (LMIs), by mixing results concerning absolute stability of nonlinear systems and robustness of uncertain linear systems. The resulting controllers prove to be effective for chaos suppression in electronic circuits and systems, as shown by two different application examples.

Mixed H2/Hinfinity output-feedback control of second-order neutral systems with time-varying state and input delays.

PubMed

Karimi, Hamid Reza; Gao, Huijun

2008-07-01

A mixed H2/Hinfinity output-feedback control design methodology is presented in this paper for second-order neutral linear systems with time-varying state and input delays. Delay-dependent sufficient conditions for the design of a desired control are given in terms of linear matrix inequalities (LMIs). A controller, which guarantees asymptotic stability and a mixed H2/Hinfinity performance for the closed-loop system of the second-order neutral linear system, is then developed directly instead of coupling the model to a first-order neutral system. A Lyapunov-Krasovskii method underlies the LMI-based mixed H2/Hinfinity output-feedback control design using some free weighting matrices. The simulation results illustrate the effectiveness of the proposed methodology.

Robust distributed model predictive control of linear systems with structured time-varying uncertainties

NASA Astrophysics Data System (ADS)

Zhang, Langwen; Xie, Wei; Wang, Jingcheng

2017-11-01

In this work, synthesis of robust distributed model predictive control (MPC) is presented for a class of linear systems subject to structured time-varying uncertainties. By decomposing a global system into smaller dimensional subsystems, a set of distributed MPC controllers, instead of a centralised controller, are designed. To ensure the robust stability of the closed-loop system with respect to model uncertainties, distributed state feedback laws are obtained by solving a min-max optimisation problem. The design of robust distributed MPC is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints. An iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance. The simulation results show the effectiveness of the proposed robust distributed MPC algorithm.

On the persistence of unstable bump-on-tail electron velocity distributions in the earth's foreshock

NASA Technical Reports Server (NTRS)

Klimas, Alexander J.; Fitzenreiter, Richard J.

1988-01-01

This paper presents further evidence for the persistence of bump-on-tail unstable reduced velocity distributions in the earth's electron foreshock, which contradicts the understanding of quasi-linear saturation of the bump-on-tail instability. A modified theory for the saturation of the bump-on-tail instability in the earth's foreshock is proposed to explain the mechanism of this persistence, and the predictions are compared to the results of a numerical simulation of the electron plasma in the foreshock. The results support the thesis that quasi-linear saturation of the bump-on-tail instability is modified in the foreshock, due to the driven nature of the region, so that at saturation the stabilized velocity distribution still appears bump-on-tail unstable to linear plasma analysis.

Electronic circuit delivers pulse of high interval stability

NASA Technical Reports Server (NTRS)

Fisher, B.

1966-01-01

Circuit generates a pulse of high interval stability with a complexity level considerably below systems of comparable stability. This circuit is being used as a linear frequency discriminator in the signal conditioner of the Apollo command module.

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.

Synthesis of linear and cyclic peptide-PEG-lipids for stabilization and targeting of cationic liposome-DNA complexes.

PubMed

Ewert, Kai K; Kotamraju, Venkata Ramana; Majzoub, Ramsey N; Steffes, Victoria M; Wonder, Emily A; Teesalu, Tambet; Ruoslahti, Erkki; Safinya, Cyrus R

2016-03-15

Because nucleic acids (NAs) have immense potential value as therapeutics, the development of safe and effective synthetic NA vectors continues to attract much attention. In vivo applications of NA vectors require stabilized, nanometer-scale particles, but the commonly used approaches of steric stabilization with a polymer coat (e.g., PEGylation; PEG=poly(ethylene glycol)) interfere with attachment to cells, uptake, and endosomal escape. Conjugation of peptides to PEG-lipids can improve cell attachment and uptake for cationic liposome-DNA (CL-DNA) complexes. We present several synthetic approaches to peptide-PEG-lipids and discuss their merits and drawbacks. A lipid-PEG-amine building block served as the common key intermediate in all synthetic routes. Assembling the entire peptide-PEG-lipid by manual solid phase peptide synthesis (employing a lipid-PEG-carboxylic acid) allowed gram-scale synthesis but is mostly applicable to linear peptides connected via their N-terminus. Conjugation via thiol-maleimide or strain-promoted (copper-free) azide-alkyne cycloaddition chemistry is highly amenable to on-demand preparation of peptide-PEG-lipids, and the appropriate PEG-lipid precursors are available in a single chemical step from the lipid-PEG-amine building block. Azide-alkyne cycloaddition is especially suitable for disulfide-bridged peptides such as iRGD (cyclic CRGDKGPDC). Added at 10 mol% of a cationic/neutral lipid mixture, the peptide-PEG-lipids stabilize the size of CL-DNA complexes. They also affect cell attachment and uptake of nanoparticles in a peptide-dependent manner, thereby providing a platform for preparing stabilized, affinity-targeted CL-DNA nanoparticles. Copyright © 2016 Elsevier Ltd. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Ni, Ming; Tao, Fei; Yang, Jiandong

2018-01-01

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

Bio-inspired sensing and control for disturbance rejection and stabilization

NASA Astrophysics Data System (ADS)

Gremillion, Gregory; Humbert, James S.

2015-05-01

The successful operation of small unmanned aircraft systems (sUAS) in dynamic environments demands robust stability in the presence of exogenous disturbances. Flying insects are sensor-rich platforms, with highly redundant arrays of sensors distributed across the insect body that are integrated to extract rich information with diminished noise. This work presents a novel sensing framework in which measurements from an array of accelerometers distributed across a simulated flight vehicle are linearly combined to directly estimate the applied forces and torques with improvements in SNR. In simulation, the estimation performance is quantified as a function of sensor noise level, position estimate error, and sensor quantity.

Parametric Excitation of Marangoni Instability in a Heated Thin Layer Covered by Insoluble Surfactant

NASA Astrophysics Data System (ADS)

Mikishev, Alexander B.; Nepomnyashchy, Alexander A.

2018-05-01

The paper presents the analysis of the impact of vertical periodic vibrations on the long-wavelength Marangoni instability in a liquid layer with poorly conducting boundaries in the presence of insoluble surfactant on the deformable gas-liquid interface. The layer is subject to a uniform transverse temperature gradient. Linear stability analysis is performed in order to find critical values of Marangoni numbers for both monotonic and oscillatory instability modes. Longwave asymptotic expansions are used. At the leading order, the critical values are independent on vibration parameters; at the next order of approximation we obtained the rise of stability thresholds due to vibration.

Real-Time Exponential Curve Fits Using Discrete Calculus

NASA Technical Reports Server (NTRS)

Rowe, Geoffrey

2010-01-01

An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.

Transition Studies on a Swept-Wing Model

NASA Technical Reports Server (NTRS)

Saric, William S.

1996-01-01

The present investigation contributes to the understanding of boundary-layer stability and transition by providing detailed measurements of carefully-produced stationary crossflow vortices. It is clear that a successful prediction of transition in swept-wing flows must include an understanding of the detailed physics involved. Receptivity and nonlinear effects must not be ignored. Linear stability theory correctly predicts the expected wavelengths and mode shapes for stationary crossflow, but fails to predict the growth rates, even for low amplitudes. As new computational and analytical methods are developed to deal with three-dimensional boundary layers, the data provided by this experiment will serve as a useful benchmark for comparison.

Nonlinear Viscoelastic Mechanics of Cross-linked Rubbers

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Leonov, Arkady I.; Gray, Hugh R. (Technical Monitor)

2002-01-01

The paper develops a general theory for finite rubber viscoelasticity, and specifies it in the form, convenient for solving problems important for rubber, tire and space industries. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory has been developed for arbitrary nonisothermal deformations of viscoelastic solids. In this theory, the constitutive equations are presented as the sum of known equilibrium (rubber elastic) and non-equilibrium (liquid polymer viscoelastic) terms. These equations are then simplified using several modeling arguments. Stability constraints for the proposed constitutive equations are also discussed. It is shown that only strong ellipticity criteria are applicable for assessing stability of the equations governing viscoelastic solids.

Spacecraft nonlinear control

NASA Technical Reports Server (NTRS)

Sheen, Jyh-Jong; Bishop, Robert H.

1992-01-01

The feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs). The feedback linearization consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model. Pole placement techniques are then used to place the closed-loop poles. The coordinate transformation proposed here evolves from three output functions of relative degree four, three, and two, respectively. The nonlinear feedback control law is presented. Stability in a neighborhood of a controllable torque equilibrium attitude (TEA) is guaranteed and this fact is demonstrated by the simulation results. An investigation of the nonlinear control law shows that singularities exist in the state space outside the neighborhood of the controllable TEA. The nonlinear control law is simplified by a standard linearization technique and it is shown that the linearized nonlinear controller provides a natural way to select control gains for the multiple-input, multiple-output system. Simulation results using the linearized nonlinear controller show good performance relative to the nonlinear controller in the neighborhood of the TEA.

Linear modal stability analysis of bowed-strings.

PubMed

Debut, V; Antunes, J; Inácio, O

2017-03-01

Linearised models are often invoked as a starting point to study complex dynamical systems. Besides their attractive mathematical simplicity, they have a central role for determining the stability properties of static or dynamical states, and can often shed light on the influence of the control parameters on the system dynamical behaviour. While the bowed string dynamics has been thoroughly studied from a number of points of view, mainly by time-domain computer simulations, this paper proposes to explore its dynamical behaviour adopting a linear framework, linearising the friction force near an equilibrium state in steady sliding conditions, and using a modal representation of the string dynamics. Starting from the simplest idealisation of the friction force given by Coulomb's law with a velocity-dependent friction coefficient, the linearised modal equations of the bowed string are presented, and the dynamical changes of the system as a function of the bowing parameters are studied using linear stability analysis. From the computed complex eigenvalues and eigenvectors, several plots of the evolution of the modal frequencies, damping values, and modeshapes with the bowing parameters are produced, as well as stability charts for each system mode. By systematically exploring the influence of the parameters, this approach appears as a preliminary numerical characterisation of the bifurcations of the bowed string dynamics, with the advantage of being very simple compared to sophisticated numerical approaches which demand the regularisation of the nonlinear interaction force. To fix the idea about the potential of the proposed approach, the classic one-degree-of-freedom friction-excited oscillator is first considered, and then the case of the bowed string. Even if the actual stick-slip behaviour is rather far from the linear description adopted here, the results show that essential musical features of bowed string vibrations can be interpreted from this simple approach, at least qualitatively. Notably, the technique provides an instructive and original picture of bowed motions, in terms of groups of well-defined unstable modes, which is physically intuitive to discuss tonal changes observed in real bowed string.

Mode switching and linear stability analysis of resonant acoustic flows

NASA Astrophysics Data System (ADS)

Panickar, Praveen

Resonant acoustic flows occur in a wide variety of practical, aerospace-related applications and are a rich source of complex flow-physics. The primary concern associated with these types of flows is the high-amplitude fluctuating pressures associated with the resonant tones that could lead to sonic fatigue failure of sensitive components in the vicinity of such flows. However, before attempting to devise methods to suppress the resonant tones, it is imperative to understand the physics governing these flows in the hope that such an understanding will lead to more robust and effective suppression techniques. To this end, an in-depth study of various resonant acoustic flows was undertaken in this thesis, the main aim being to bring about a better understanding of such flows by revealing physically relevant information. Starting with the resonant acoustic mechanism in underexpanded jets from two-dimensional nozzles, it was shown that, for a variety of flow situations (geometries, shock-cell structures and orientations) in such jets, the nonlinear interaction density acted as a faithful precursor to a, hitherto unpredictable, spanwise instability mode switch. Following this, a study of the occurrence of, previously undocumented and theoretically unexpected, helical instabilities in subsonic impinging jets was undertaken. Using metrics from linear stability analysis, it was shown that the presence of the helical modes was justified. The results from this study on impinging jets are directly applicable to modern Stationary Take-Off and Vertical Landing (STOVL) aircraft that have twin, closely spaced exhausts. Finally, a novel technique that yielded dramatic suppression of resonant acoustic tones using high frequency excitation, in subsonic flows over open cavities, was investigated. Linear stability calculations of the experimentally measured baseline and excited velocity profiles showed that the instability of the high frequency excitation corresponded to a spatially decaying mode, which in turn lead to the resonance suppression associated with this mechanism. The experimental results showed good agreement with linear stability calculations for the measured mean velocity profiles. It is hoped that the work presented in this thesis will further the understanding of resonant acoustic flows and provide insights that can lead to better control techniques in the future.

Stable Spheromaks Sustained by Neutral Beam Injection

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

Fowler, T K; Jayakumar, R; McLean, H S

It is shown that spheromak equilibria, stable at zero-beta but departing from the Taylor state, could be sustained by non-inductive current drive at acceptable power levels. Stability to both ideal MHD and tearing modes is verified using the NIMROD code for linear stability analysis. Non-linear NIMROD calculations with non-inductive current drive and pressure effects could point the way to improved fusion reactors.

An improved linear ion trap physics package

NASA Technical Reports Server (NTRS)

Prestage, J. D.

1993-01-01

This article describes an improvement in the architecture of the physics package used in the Linear Ion Trap (LIT)-based frequency standard recently developed at JPL. This new design is based on the observation that ions can be moved along the axis of an LIT by applied dc voltages. The state selection and interrogation region can be separated from the more critical microwave resonance region where the multiplied local oscillator signal is compared with the stable atomic transition. This separation relaxes many of the design constraints of the present units. Improvements include increased frequency stability and a substantial reduction in size, mass, and cost of the final frequency standard.

Strange mode instabilities and mass loss in evolved massive primordial stars

NASA Astrophysics Data System (ADS)

Yadav, Abhay Pratap; Kühnrich Biavatti, Stefan Henrique; Glatzel, Wolfgang

2018-04-01

A linear stability analysis of models for evolved primordial stars with masses between 150 and 250 M⊙ is presented. Strange mode instabilities with growth rates in the dynamical range are identified for stellar models with effective temperatures below log Teff = 4.5. For selected models, the final fate of the instabilities is determined by numerical simulation of their evolution into the non-linear regime. As a result, the instabilities lead to finite amplitude pulsations. Associated with them are acoustic energy fluxes capable of driving stellar winds with mass-loss rates in the range between 7.7 × 10-7 and 3.5 × 10-4 M⊙ yr-1.

Dual solutions of three-dimensional flow and heat transfer over a non-linearly stretching/shrinking sheet

NASA Astrophysics Data System (ADS)

Naganthran, Kohilavani; Nazar, Roslinda; Pop, Ioan

2018-05-01

This study investigated the influence of the non-linearly stretching/shrinking sheet on the boundary layer flow and heat transfer. A proper similarity transformation simplified the system of partial differential equations into a system of ordinary differential equations. This system of similarity equations is then solved numerically by using the bvp4c function in the MATLAB software. The generated numerical results presented graphically and discussed in the relevance of the governing parameters. Dual solutions found as the sheet stretched and shrunk in the horizontal direction. Stability analysis showed that the first solution is physically realizable whereas the second solution is not practicable.

Shear-flexible finite-element models of laminated composite plates and shells

NASA Technical Reports Server (NTRS)

Noor, A. K.; Mathers, M. D.

1975-01-01

Several finite-element models are applied to the linear static, stability, and vibration analysis of laminated composite plates and shells. The study is based on linear shallow-shell theory, with the effects of shear deformation, anisotropic material behavior, and bending-extensional coupling included. Both stiffness (displacement) and mixed finite-element models are considered. Discussion is focused on the effects of shear deformation and anisotropic material behavior on the accuracy and convergence of different finite-element models. Numerical studies are presented which show the effects of increasing the order of the approximating polynomials, adding internal degrees of freedom, and using derivatives of generalized displacements as nodal parameters.

Oxidatively-Stable Linear Poly(propylenimine)-Containing Adsorbents for CO2 Capture from Ultra-Dilute Streams.

PubMed

Pang, Simon H; Lively, Ryan P; Jones, Christopher W

2018-05-29

Aminopolymer-based solid sorbents have been widely investigated for CO2 capture from dilute streams such as flue gas or ambient air. However, the oxidative stability of the most well-studied aminopolymer, poly(ethylenimine) (PEI), is limited, causing it to lose its CO2 capture capacity after exposure to oxygen at elevated temperatures. Here we demonstrate the use of linear poly(propylenimine) (PPI), synthesized via a simple cationic ring-opening polymerization, as a more oxidatively-stable alternative to PEI with high CO2 capacity and amine efficiency. The performance of linear PPI/SBA-15 composites is investigated over a range of CO2 capture conditions (CO2 partial pressure, adsorption temperature) to examine the trade-off between adsorption capacity and sorption site accessibility, which may be expected to be more limited in linear polymers relative to the prototypical hyperbranched PEI. Linear PPI/SBA-15 composites are more efficient at CO2 capture and retain 65-83% of their CO2 capacity after exposure to a harsh oxidative treatment, compared to 20-40% retention for linear PEI. Additionally, we demonstrate long-term stability of linear PPI sorbents over 50 adsorption/desorption cycles with no loss in performance. Combined with other strategies for improving oxidative stability and adsorption kinetics, linear PPI may play a role as a component of stable, solid adsorbents in commercial applications for CO2 capture. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Nonlinear transient analysis of multi-mass flexible rotors - theory and applications

NASA Technical Reports Server (NTRS)

Kirk, R. G.; Gunter, E. J.

1973-01-01

The equations of motion necessary to compute the transient response of multi-mass flexible rotors are formulated to include unbalance, rotor acceleration, and flexible damped nonlinear bearing stations. A method of calculating the unbalance response of flexible rotors from a modified Myklestad-Prohl technique is discussed in connection with the method of solution for the transient response. Several special cases of simplified rotor-bearing systems are presented and analyzed for steady-state response, stability, and transient behavior. These simplified rotor models produce extensive design information necessary to insure stable performance to elastic mounted rotor-bearing systems under varying levels and forms of excitation. The nonlinear journal bearing force expressions derived from the short bearing approximation are utilized in the study of the stability and transient response of the floating bush squeeze damper support system. Both rigid and flexible rotor models are studied, and results indicate that the stability of flexible rotors supported by journal bearings can be greatly improved by the use of squeeze damper supports. Results from linearized stability studies of flexible rotors indicate that a tuned support system can greatly improve the performance of the units from the standpoint of unbalanced response and impact loading. Extensive stability and design charts may be readily produced for given rotor specifications by the computer codes presented in this analysis.

Destabilizing effect of time-dependent oblique magnetic field on magnetic fluids streaming in porous media.

PubMed

El-Dib, Yusry O; Ghaly, Ahmed Y

2004-01-01

The present work studies Kelvin-Helmholtz waves propagating between two magnetic fluids. The system is composed of two semi-infinite magnetic fluids streaming throughout porous media. The system is influenced by an oblique magnetic field. The solution of the linearized equations of motion under the boundary conditions leads to deriving the Mathieu equation governing the interfacial displacement and having complex coefficients. The stability criteria are discussed theoretically and numerically, from which stability diagrams are obtained. Regions of stability and instability are identified for the magnetic fields versus the wavenumber. It is found that the increase of the fluid density ratio, the fluid velocity ratio, the upper viscosity, and the lower porous permeability play a stabilizing role in the stability behavior in the presence of an oscillating vertical magnetic field or in the presence of an oscillating tangential magnetic field. The increase of the fluid viscosity plays a stabilizing role and can be used to retard the destabilizing influence for the vertical magnetic field. Dual roles are observed for the fluid velocity in the stability criteria. It is found that the field frequency plays against the constant part for the magnetic field.

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

NASA Technical Reports Server (NTRS)

Gunderson, R. W.

1975-01-01

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

A Spectral Lyapunov Function for Exponentially Stable LTV Systems

NASA Technical Reports Server (NTRS)

Zhu, J. Jim; Liu, Yong; Hang, Rui

2010-01-01

This paper presents the formulation of a Lyapunov function for an exponentially stable linear timevarying (LTV) system using a well-defined PD-spectrum and the associated PD-eigenvectors. It provides a bridge between the first and second methods of Lyapunov for stability assessment, and will find significant applications in the analysis and control law design for LTV systems and linearizable nonlinear time-varying systems.

Contributions of Mirror and Ion Bernstein Instabilities to the Scattering of Pickup Ions in the Outer Heliosheath

NASA Astrophysics Data System (ADS)

Min, Kyungguk; Liu, Kaijun

2018-01-01

Maintaining the stability of pickup ions in the outer heliosheath is a critical element for the secondary energetic neutral atom (ENA) mechanism, a theory put forth to explain the nearly annular band of ENA emission observed by the Interstellar Boundary EXplorer. A recent study showed that a pickup ion ring can remain stable to the Alfvén/ion cyclotron (AC) instability at propagation parallel to the background magnetic field when the parallel thermal spread of the ring is comparable to that of a background population. This study investigates the potential role that the mirror or ion Bernstein (IB) instabilities can play in the stability of pickup ions when conditions are such that the AC instability is suppressed. Linear Vlasov theory predicts relatively fast mirror and IB instability growth even though AC instability growth is suppressed. For a few such cases, two-dimensional hybrid and macroscopic quasi-linear simulations are carried out to examine how the unstable mirror and IB modes evolve and affect the pickup ion ring beyond the linear theory picture. For the parameters used, the mirror mode dominates initially and leads to a rapid parallel heating of the pickup ions in excess of the parallel temperature of the background protons. The heated pickup ions subsequently trigger onset of the AC mode, which grows sufficiently large to be the dominant pitch angle scattering agent after the mirror mode has decayed away. The present results indicate that the pickup ion stability needed may not be guaranteed once the mirror and IB instabilities are taken into account.

A nonlinear optimal control approach to stabilization of a macroeconomic development model

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Ghosh, T.; Sarno, D.

2017-11-01

A nonlinear optimal (H-infinity) control approach is proposed for the problem of stabilization of the dynamics of a macroeconomic development model that is known as the Grossman-Helpman model of endogenous product cycles. The dynamics of the macroeconomic development model is divided in two parts. The first one describes economic activities in a developed country and the second part describes variation of economic activities in a country under development which tries to modify its production so as to serve the needs of the developed country. The article shows that through control of the macroeconomic model of the developed country, one can finally control the dynamics of the economy in the country under development. The control method through which this is achieved is the nonlinear H-infinity control. The macroeconomic model for the country under development undergoes approximate linearization round a temporary operating point. This is defined at each time instant by the present value of the system's state vector and the last value of the control input vector that was exerted on it. The linearization is based on Taylor series expansion and the computation of the associated Jacobian matrices. For the linearized model an H-infinity feedback controller is computed. The controller's gain is calculated by solving an algebraic Riccati equation at each iteration of the control method. The asymptotic stability of the control approach is proven through Lyapunov analysis. This assures that the state variables of the macroeconomic model of the country under development will finally converge to the designated reference values.

Marginal Stability of Sweet–Parker Type Current Sheets at Low Lundquist Numbers

NASA Astrophysics Data System (ADS)

Shi, Chen; Velli, Marco; Tenerani, Anna

2018-06-01

Magnetohydrodynamic simulations have shown that a nonunique critical Lundquist number S c exists, hovering around S c ∼ 104, above which threshold Sweet–Parker type stationary reconnecting configurations become unstable to a fast tearing mode dominated by plasmoid generation. It is known that the flow along the sheet plays a stabilizing role, though a satisfactory explanation of the nonuniversality and variable critical Lundquist numbers observed is still lacking. Here we discuss this question using 2D linear MHD simulations and linear stability analyses of Sweet–Parker type current sheets in the presence of background stationary inflows and outflows at low Lundquist numbers (S ≤ 104). Simulations show that the inhomogeneous outflow stabilizes the current sheet by stretching the growing magnetic islands and at the same time evacuating the magnetic islands out of the current sheet. This limits the time during which fluctuations that begin at any given wavelength can remain unstable, rendering the instability nonexponential. We find that the linear theory based on the expanding-wavelength assumption works well for S larger than ∼1000. However, we also find that the inflow and location of the initial perturbation also affect the stability threshold.

Classical linear-control analysis applied to business-cycle dynamics and stability

NASA Technical Reports Server (NTRS)

Wingrove, R. C.

1983-01-01

Linear control analysis is applied as an aid in understanding the fluctuations of business cycles in the past, and to examine monetary policies that might improve stabilization. The analysis shows how different policies change the frequency and damping of the economic system dynamics, and how they modify the amplitude of the fluctuations that are caused by random disturbances. Examples are used to show how policy feedbacks and policy lags can be incorporated, and how different monetary strategies for stabilization can be analytically compared. Representative numerical results are used to illustrate the main points.

On the monoaxial stabilization of a rigid body under vanishing restoring torque

NASA Astrophysics Data System (ADS)

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

2018-05-01

The problem of monoaxial stabilization of a rigid body is studied. It is assumed that a linear time-invariant dissipative torque and a time-varying restoring torque vanishing as time increases act on the body. Both the case of linear restoring torque and that of essentially nonlinear one are considered. With the aid of the decomposition method, conditions are obtained under which we can guarantee the asymptotic stability of an equilibrium position of the body despite the vanishing of the restoring torque. A numerical simulation is provided to demonstrate the effectiveness of our theoretical results.

Parameterized Linear Longitudinal Airship Model

NASA Technical Reports Server (NTRS)

Kulczycki, Eric; Elfes, Alberto; Bayard, David; Quadrelli, Marco; Johnson, Joseph

2010-01-01

A parameterized linear mathematical model of the longitudinal dynamics of an airship is undergoing development. This model is intended to be used in designing control systems for future airships that would operate in the atmospheres of Earth and remote planets. Heretofore, the development of linearized models of the longitudinal dynamics of airships has been costly in that it has been necessary to perform extensive flight testing and to use system-identification techniques to construct models that fit the flight-test data. The present model is a generic one that can be relatively easily specialized to approximate the dynamics of specific airships at specific operating points, without need for further system identification, and with significantly less flight testing. The approach taken in the present development is to merge the linearized dynamical equations of an airship with techniques for estimation of aircraft stability derivatives, and to thereby make it possible to construct a linearized dynamical model of the longitudinal dynamics of a specific airship from geometric and aerodynamic data pertaining to that airship. (It is also planned to develop a model of the lateral dynamics by use of the same methods.) All of the aerodynamic data needed to construct the model of a specific airship can be obtained from wind-tunnel testing and computational fluid dynamics

Analysis on nonlinear optical properties of Cd (Zn) Se quantum dots synthesized using three different stabilizing agents

NASA Astrophysics Data System (ADS)

J, Joy Sebastian Prakash; G, Vinitha; Ramachandran, Murugesan; Rajamanickam, Karunanithi

2017-10-01

Three different stabilizing agents, namely, L-cysteine, Thioglycolic acid and cysteamine hydrochloride were used to synthesize Cd(Zn)Se quantum dots (QDs). It was characterized using UV-vis spectroscopy, x-ray diffraction (XRD) and transmission electron microscopy (TEM). The non-linear optical properties (non-linear absorption and non-linear refraction) of synthesized Cd(Zn)Se quantum dots were studied with z-scan technique using diode pumped continuous wavelaser system at a wavelength of 532 nm. Our (organic) synthesized quantum dots showed optical properties similar to the inorganic materials reported elsewhere.

Estimating conformation content of a protein using citrate-stabilized Au nanoparticles

NASA Astrophysics Data System (ADS)

Deka, Jashmini; Paul, Anumita; Chattopadhyay, Arun

2010-08-01

Herein we report the use of the optical properties of citrate-stabilized gold nanoparticles (Au NPs) for estimation of native or denatured conformation content in a mixture of a protein in solution. The UV-vis extinction spectrum of citrate-stabilized Au NPs is known to broaden differently in the presence of native and denatured states of α-amylase, bovine serum albumin (BSA) or amyloglucosidase (AMG). On the other hand, herein we show that when a mixture of native and denatured protein was present in the medium, the broadening of the spectrum differed for different fractional content of the conformations. Also, the total area under the extinction spectrum varied linearly with the change in the mole fraction content of a state and for a constant total protein concentration. Transmission electron microscopy (TEM) measurements revealed different levels of agglomeration for different fractional contents of the native or denatured state of a protein. In addition, time-dependent denaturation of a protein could be followed using the present method. The rate constants calculated for denaturation indicated a possible fast change in conformation of a protein before complete thermal denaturation. The observations have been explained based on the changes in extinction coefficient (thereby oscillator strength) upon interaction of citrate-stabilized NPs with proteins being in different states and levels of agglomeration.Herein we report the use of the optical properties of citrate-stabilized gold nanoparticles (Au NPs) for estimation of native or denatured conformation content in a mixture of a protein in solution. The UV-vis extinction spectrum of citrate-stabilized Au NPs is known to broaden differently in the presence of native and denatured states of α-amylase, bovine serum albumin (BSA) or amyloglucosidase (AMG). On the other hand, herein we show that when a mixture of native and denatured protein was present in the medium, the broadening of the spectrum differed for different fractional content of the conformations. Also, the total area under the extinction spectrum varied linearly with the change in the mole fraction content of a state and for a constant total protein concentration. Transmission electron microscopy (TEM) measurements revealed different levels of agglomeration for different fractional contents of the native or denatured state of a protein. In addition, time-dependent denaturation of a protein could be followed using the present method. The rate constants calculated for denaturation indicated a possible fast change in conformation of a protein before complete thermal denaturation. The observations have been explained based on the changes in extinction coefficient (thereby oscillator strength) upon interaction of citrate-stabilized NPs with proteins being in different states and levels of agglomeration. Electronic supplementary information (ESI) available: Additional UV-vis and fluorescence spectra and graphs based on UV-vis studies. See DOI: 10.1039/c0nr00154f

Stability of Electrons in the Virtual Cathode Region of an IEC

NASA Astrophysics Data System (ADS)

Kim, Hyng-Jin; Miley, George; Momota, Hiromu

2003-04-01

In the Inertial Electrostatic Confinement (IEC) device, electrons are confined inside a virtual anode that in turn confines ions. Prior stability studies [1, 2] have considered systems in which one species is electrostatically confined by the other, and either or both species are out of local thermal equilibrium. In the present research, electron stability in the virtual cathode region of an ion injected IEC is being studied. The ion density in an IEC is non-uniform due to the radial electrostatic potential, and increases toward the center region. The potential near the virtual cathode is assumed to have a parabolic shape and is determined assuming that the net space charge density is constant in that region. The corresponding ion distribution function is assumed to have the form f = C [sigma] (H W) /L^0.5 and the electron response is taken to be diabatic. Then using a variational principle after linearizing the hydrodynamic equations, stability properties of the electron layer are determined. Results will be presented as a function of injected ion/electron current ratios. 1. L. Chacon and D. C. Barnes, Phys. Plasma 7, 4774 (2000). 2. D. C. Barnes, L. Chacon, and J. M. Finn, Phys. Plasmas 9, 4448 (2002).

Stability Analysis of an Encapsulated Microbubble against Gas Diffusion

PubMed Central

Katiyar, Amit; Sarkar, Kausik

2009-01-01

Linear stability analysis is performed for a mathematical model of diffusion of gases from an encapsulated microbubble. It is an Epstein-Plesset model modified to account for encapsulation elasticity and finite gas permeability. Although, bubbles, containing gases other than air is considered, the final stable bubble, if any, contains only air, and stability is achieved only when the surrounding medium is saturated or oversaturated with air. In absence of encapsulation elasticity, only a neutral stability is achieved for zero surface tension, the other solution being unstable. For an elastic encapsulation, different equilibrium solutions are obtained depending on the saturation level and whether the surface tension is smaller or higher than the elasticity. For an elastic encapsulation, elasticity can stabilize the bubble. However, imposing a non-negativity condition on the effective surface tension (consisting of reference surface tension and the elastic stress) leads to an equilibrium radius which is only neutrally stable. If the encapsulation can support net compressive stress, it achieves actual stability. The linear stability results are consistent with our recent numerical findings. Physical mechanisms for the stability or instability of various equilibriums are provided. PMID:20005522

The linear tearing instability in three dimensional, toroidal gyro-kinetic simulations

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

Hornsby, W. A., E-mail: william.hornsby@ipp.mpg.de; Migliano, P.; Buchholz, R.

2015-02-15

Linear gyro-kinetic simulations of the classical tearing mode in three-dimensional toroidal geometry were performed using the global gyro-kinetic turbulence code, GKW. The results were benchmarked against a cylindrical ideal MHD and analytical theory calculations. The stability, growth rate, and frequency of the mode were investigated by varying the current profile, collisionality, and the pressure gradients. Both collisionless and semi-collisional tearing modes were found with a smooth transition between the two. A residual, finite, rotation frequency of the mode even in the absence of a pressure gradient is observed, which is attributed to toroidal finite Larmor-radius effects. When a pressure gradientmore » is present at low collisionality, the mode rotates at the expected electron diamagnetic frequency. However, the island rotation reverses direction at high collisionality. The growth rate is found to follow a η{sup 1∕7} scaling with collisional resistivity in the semi-collisional regime, closely following the semi-collisional scaling found by Fitzpatrick. The stability of the mode closely follows the stability analysis as performed by Hastie et al. using the same current and safety factor profiles but for cylindrical geometry, however, here a modification due to toroidal coupling and pressure effects is seen.« less

Control designs and stability analyses for Helly’s car-following model

NASA Astrophysics Data System (ADS)

Rosas-Jaimes, Oscar A.; Quezada-Téllez, Luis A.; Fernández-Anaya, Guillermo

Car-following is an approach to understand traffic behavior restricted to pairs of cars, identifying a “leader” moving in front of a “follower”, which at the same time, it is assumed that it does not surpass to the first one. From the first attempts to formulate the way in which individual cars are affected in a road through these models, linear differential equations were suggested by author like Pipes or Helly. These expressions represent such phenomena quite well, even though they have been overcome by other more recent and accurate models. However, in this paper, we show that those early formulations have some properties that are not fully reported, presenting the different ways in which they can be expressed, and analyzing them in their stability behaviors. Pipes’ model can be extended to what it is known as Helly’s model, which is viewed as a more precise model to emulate this microscopic approach to traffic. Once established some convenient forms of expression, two control designs are suggested herein. These regulation schemes are also complemented with their respective stability analyses, which reflect some important properties with implications in real driving. It is significant that these linear designs can be very easy to understand and to implement, including those important features related to safety and comfort.

A nonlinear optimal control approach for chaotic finance dynamics

NASA Astrophysics Data System (ADS)

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

2017-11-01

A new nonlinear optimal control approach is proposed for stabilization of the dynamics of a chaotic finance model. The dynamic model of the financial system, which expresses interaction between the interest rate, the investment demand, the price exponent and the profit margin, undergoes approximate linearization round local operating points. These local equilibria are defined at each iteration of the control algorithm and consist of the present value of the systems state vector and the last value of the control inputs vector that was exerted on it. The approximate linearization makes use of Taylor series expansion and of the computation of the associated Jacobian matrices. The truncation of higher order terms in the Taylor series expansion is considered to be a modelling error that is compensated by the robustness of the control loop. As the control algorithm runs, the temporary equilibrium is shifted towards the reference trajectory and finally converges to it. The control method needs to compute an H-infinity feedback control law at each iteration, and requires the repetitive solution of an algebraic Riccati equation. Through Lyapunov stability analysis it is shown that an H-infinity tracking performance criterion holds for the control loop. This implies elevated robustness against model approximations and external perturbations. Moreover, under moderate conditions the global asymptotic stability of the control loop is proven.

Enhancing the stabilization of aircraft pitch motion control via intelligent and classical method

NASA Astrophysics Data System (ADS)

Lukman, H.; Munawwarah, S.; Azizan, A.; Yakub, F.; Zaki, S. A.; Rasid, Z. A.

2017-12-01

The pitching movement of an aircraft is very important to ensure passengers are intrinsically safe and the aircraft achieve its maximum stability. The equations governing the motion of an aircraft are a complex set of six nonlinear coupled differential equations. Under certain assumptions, it can be decoupled and linearized into longitudinal and lateral equations. Pitch control is a longitudinal problem and thus, only the longitudinal dynamics equations are involved in this system. It is a third order nonlinear system, which is linearized about the operating point. The system is also inherently unstable due to the presence of a free integrator. Because of this, a feedback controller is added in order to solve this problem and enhance the system performance. This study uses two approaches in designing controller: a conventional controller and an intelligent controller. The pitch control scheme consists of proportional, integral and derivatives (PID) for conventional controller and fuzzy logic control (FLC) for intelligent controller. Throughout the paper, the performance of the presented controllers are investigated and compared based on the common criteria of step response. Simulation results have been obtained and analysed by using Matlab and Simulink software. The study shows that FLC controller has higher ability to control and stabilize the aircraft's pitch angle as compared to PID controller.

Stability of a family of uniform vortices related to vortex configurations before merging

NASA Astrophysics Data System (ADS)

Luzzatto-Fegiz, P.; Williamson, C. H. K.

2006-11-01

Motivated by the merger of two corotating vortices, Cerretelli & Williamson (JFM 2003) discovered a family of uniform vorticity patches representing the continuation of two corotating vortices into a single ``dumbbell'' shape. This branch of solutions passes through a bifurcation from the Kirchhoff ellipses (discovered by Kamm 1987 and Saffman 1988) and ends into a cat's eye shape. By using a more accurate method for equilibrium shape calculation, we find some differences in the equilibrium shapes to those discovered by Cerretelli & Williamson, particularly near the topological change (from a two-vortex to a single vortex shape). We implement the approach of Dritschel (1985), and show that all the simply connected shapes are unstable to a three-fold perturbation, while a regime of the two-vortex shapes nearing the topological change is unstable to a two-fold antisymmetric perturbation. The stability of two patches has been source of debate in the literature. Saffman & Szeto (1980) predicted exchange of stability at an extremum in energy and angular momentum; on the other hand, Dritschel (1985) found that conditions for instability from linear analysis did not match those coming from the energy criterion. In the present work, we find precise agreement between results from linear analysis and energy criterion, in accordance with the more recent work of Kamm (1987) and Dritschel (1995).

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.

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.

Intrinsic energy localization through discrete gap breathers in one-dimensional diatomic granular crystals.

PubMed

Theocharis, G; Boechler, N; Kevrekidis, P G; Job, S; Porter, Mason A; Daraio, C

2010-11-01

We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic, consisting of a periodic arrangement of heavy and light spherical particles. We examine two families of discrete gap breathers: (1) an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and (2) a potentially stable discrete gap breather that is centered on a light particle and is characterized by an asymmetric spatial energy profile. We investigate their existence, structure, and stability throughout the band gap of the linear spectrum and classify them into four regimes: a regime near the lower optical band edge of the linear spectrum, a moderately discrete regime, a strongly discrete regime that lies deep within the band gap of the linearized version of the system, and a regime near the upper acoustic band edge. We contrast discrete breathers in anharmonic Fermi-Pasta-Ulam (FPU)-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and note that the asymmetric nature of the tensionless interaction potential can lead to hybrid bulk-surface localized solutions.

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

PubMed

Chan, Pak Yuen; Goldenfeld, Nigel

2007-10-01

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

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

NASA Astrophysics Data System (ADS)

Chan, Pak Yuen; Goldenfeld, Nigel

2007-10-01

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

Intrinsic energy localization through discrete gap breathers in one-dimensional diatomic granular crystals

NASA Astrophysics Data System (ADS)

Theocharis, G.; Boechler, N.; Kevrekidis, P. G.; Job, S.; Porter, Mason A.; Daraio, C.

2010-11-01

We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic, consisting of a periodic arrangement of heavy and light spherical particles. We examine two families of discrete gap breathers: (1) an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and (2) a potentially stable discrete gap breather that is centered on a light particle and is characterized by an asymmetric spatial energy profile. We investigate their existence, structure, and stability throughout the band gap of the linear spectrum and classify them into four regimes: a regime near the lower optical band edge of the linear spectrum, a moderately discrete regime, a strongly discrete regime that lies deep within the band gap of the linearized version of the system, and a regime near the upper acoustic band edge. We contrast discrete breathers in anharmonic Fermi-Pasta-Ulam (FPU)-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and note that the asymmetric nature of the tensionless interaction potential can lead to hybrid bulk-surface localized solutions.

Theoretical analyses of Baroclinic flows

NASA Technical Reports Server (NTRS)

Antar, B.

1982-01-01

A stability analysis of a thin horizontal rotating fluid layer which is subjected to arbitrary horizontal and vertical temperature gradients is presented. The basic state is a nonlinear Hadley cell which contains both Ekman and thermal boundary layers; it is given in closed form. The stability analysis is based on the linearized Navier-Stokes equations, and zonally symmetric perturbations in the form of waves propagating in the meridional direction are considered. Numerical methods were used for the stability problem. It was found that the instability sets in when the Richardson number is close to unity and that the critical Richardson number is a non-monotonic function of the Prandtl number. Further, it was found that the critical Richardson number decreases with increasing Ekman number until a critical value of the Ekman number is reached beyond which the fluid is stable.

Universality Results for Multi-phase Hele-Shaw Flows

NASA Astrophysics Data System (ADS)

Daripa, Prabir

2013-03-01

Saffman-Taylor instability is a well known viscosity driven instability of an interface separating two immiscible fluids. We study linear stability of displacement processes in a Hele-Shaw cell involving an arbitrary number of immiscible fluid phases. This is a problem involving many interfaces. Universal stability results have been obtained for this multi-phase immiscible flow in the sense that the results hold for arbitrary number of interfaces. These stability results have been applied to design displacement processes that are considerably less unstable than the pure Saffman-Taylor case. In particular, we derive universal formula which gives specific values of the viscosities of the fluid layers corresponding to smallest unstable band. Other similar universal results will also be presented. The talk is based on the following paper. This work was supported by the Qatar National Research Fund (a member of The Qatar Foundation).

Studies of beam position monitor stability

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

Tenenbaum, P.

1998-05-01

The authors present the results from two studies of the time stability between the mechanical center of a beam position monitor and its electrical/electronic center. In the first study, a group of 93 BPM processors was calibrated via Test Pulse Generator once per hour in order to measure the contribution of the readout electronics to offset drifts. In the second study, a triplet of stripline BPMs in the Final Focus Test Beam, separated only by drift spaces, was read out every 6 minutes during 1 week of beam operation. In both cases offset stability was observed to be on themore » order of microns over time spans ranging from hours to days, although during the beam study much worse performance was also observed. Implications for the beam position monitor system of future linear collider systems are discussed.« less

Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton–Krylov-AMG

DOE PAGES

Shadid, J. N.; Pawlowski, R. P.; Cyr, E. C.; ...

2016-02-10

Here, we discuss that the computational solution of the governing balance equations for mass, momentum, heat transfer and magnetic induction for resistive magnetohydrodynamics (MHD) systems can be extremely challenging. These difficulties arise from both the strong nonlinear, nonsymmetric coupling of fluid and electromagnetic phenomena, as well as the significant range of time- and length-scales that the interactions of these physical mechanisms produce. This paper explores the development of a scalable, fully-implicit stabilized unstructured finite element (FE) capability for 3D incompressible resistive MHD. The discussion considers the development of a stabilized FE formulation in context of the variational multiscale (VMS) method,more » and describes the scalable implicit time integration and direct-to-steady-state solution capability. The nonlinear solver strategy employs Newton–Krylov methods, which are preconditioned using fully-coupled algebraic multilevel preconditioners. These preconditioners are shown to enable a robust, scalable and efficient solution approach for the large-scale sparse linear systems generated by the Newton linearization. Verification results demonstrate the expected order-of-accuracy for the stabilized FE discretization. The approach is tested on a variety of prototype problems, that include MHD duct flows, an unstable hydromagnetic Kelvin–Helmholtz shear layer, and a 3D island coalescence problem used to model magnetic reconnection. Initial results that explore the scaling of the solution methods are also presented on up to 128K processors for problems with up to 1.8B unknowns on a CrayXK7.« less

Field stabilization studies for a radio frequency quadrupole accelerator

NASA Astrophysics Data System (ADS)

Gaur, R.; Kumar, V.

2014-07-01

The Radio Frequency Quadrupole (RFQ) linear accelerator is an accelerator that efficiently focuses, bunches and accelerates a high intensity DC beam from an ion source, for various applications. Unlike other conventional RF linear accelerators, the electromagnetic mode used for its operation is not the lowest frequency mode supported by the structure. In a four vane type RFQ, there are several undesired electromagnetic modes having frequency close to that of the operating mode. While designing an RFQ accelerator, care must be taken to ensure that the frequencies of these nearby modes are sufficiently separated from the operating mode. If the undesired nearby modes have frequencies close to the operating mode, the electromagnetic field pattern in the presence of geometrical errors will not be stabilized to the desired field profile, and will be perturbed by the nearby modes. This will affect the beam dynamics and reduce the beam transmission. In this paper, we present a detailed study of the electromagnetic modes supported, which is followed by calculations for implementation of suitable techniques to make the desired operating mode stable against mixing with unwanted modes for an RFQ being designed for the proposed Indian Spallation Neutron Source (ISNS) project at Raja Ramanna Centre for Advanced Technology, Indore. Resonant coupling scheme, along with dipole stabilization rods has been proposed to increase the mode separation. The paper discusses the details of a generalized optimization procedure that has been used for the design of mode stabilization scheme.

Stability of Linear Equations--Algebraic Approach

ERIC Educational Resources Information Center

Cherif, Chokri; Goldstein, Avraham; Prado, Lucio M. G.

2012-01-01

This article could be of interest to teachers of applied mathematics as well as to people who are interested in applications of linear algebra. We give a comprehensive study of linear systems from an application point of view. Specifically, we give an overview of linear systems and problems that can occur with the computed solution when the…

Kinematic measures for assessing gait stability in elderly individuals: a systematic review

PubMed Central

Hamacher, D.; Singh, N.B.; Van Dieën, J.H.; Heller, M.O.; Taylor, W.R.

2011-01-01

Falls not only present a considerable health threat, but the resulting treatment and loss of working days also place a heavy economic burden on society. Gait instability is a major fall risk factor, particularly in geriatric patients, and walking is one of the most frequent dynamic activities of daily living. To allow preventive strategies to become effective, it is therefore imperative to identify individuals with an unstable gait. Assessment of dynamic stability and gait variability via biomechanical measures of foot kinematics provides a viable option for quantitative evaluation of gait stability, but the ability of these methods to predict falls has generally not been assessed. Although various methods for assessing gait stability exist, their sensitivity and applicability in a clinical setting, as well as their cost-effectiveness, need verification. The objective of this systematic review was therefore to evaluate the sensitivity of biomechanical measures that quantify gait stability among elderly individuals and to evaluate the cost of measurement instrumentation required for application in a clinical setting. To assess gait stability, a comparative effect size (Cohen's d) analysis of variability and dynamic stability of foot trajectories during level walking was performed on 29 of an initial yield of 9889 articles from four electronic databases. The results of this survey demonstrate that linear variability of temporal measures of swing and stance was most capable of distinguishing between fallers and non-fallers, whereas step width and stride velocity prove more capable of discriminating between old versus young (OY) adults. In addition, while orbital stability measures (Floquet multipliers) applied to gait have been shown to distinguish between both elderly fallers and non-fallers as well as between young and old adults, local stability measures (λs) have been able to distinguish between young and old adults. Both linear and nonlinear measures of foot time series during gait seem to hold predictive ability in distinguishing healthy from fall-prone elderly adults. In conclusion, biomechanical measurements offer promise for identifying individuals at risk of falling and can be obtained with relatively low-cost tools. Incorporation of the most promising measures in combined retrospective and prospective studies for understanding fall risk and designing preventive strategies is warranted. PMID:21880615

Kinematic measures for assessing gait stability in elderly individuals: a systematic review.

PubMed

Hamacher, D; Singh, N B; Van Dieën, J H; Heller, M O; Taylor, W R

2011-12-07

Falls not only present a considerable health threat, but the resulting treatment and loss of working days also place a heavy economic burden on society. Gait instability is a major fall risk factor, particularly in geriatric patients, and walking is one of the most frequent dynamic activities of daily living. To allow preventive strategies to become effective, it is therefore imperative to identify individuals with an unstable gait. Assessment of dynamic stability and gait variability via biomechanical measures of foot kinematics provides a viable option for quantitative evaluation of gait stability, but the ability of these methods to predict falls has generally not been assessed. Although various methods for assessing gait stability exist, their sensitivity and applicability in a clinical setting, as well as their cost-effectiveness, need verification. The objective of this systematic review was therefore to evaluate the sensitivity of biomechanical measures that quantify gait stability among elderly individuals and to evaluate the cost of measurement instrumentation required for application in a clinical setting. To assess gait stability, a comparative effect size (Cohen's d) analysis of variability and dynamic stability of foot trajectories during level walking was performed on 29 of an initial yield of 9889 articles from four electronic databases. The results of this survey demonstrate that linear variability of temporal measures of swing and stance was most capable of distinguishing between fallers and non-fallers, whereas step width and stride velocity prove more capable of discriminating between old versus young (OY) adults. In addition, while orbital stability measures (Floquet multipliers) applied to gait have been shown to distinguish between both elderly fallers and non-fallers as well as between young and old adults, local stability measures (λs) have been able to distinguish between young and old adults. Both linear and nonlinear measures of foot time series during gait seem to hold predictive ability in distinguishing healthy from fall-prone elderly adults. In conclusion, biomechanical measurements offer promise for identifying individuals at risk of falling and can be obtained with relatively low-cost tools. Incorporation of the most promising measures in combined retrospective and prospective studies for understanding fall risk and designing preventive strategies is warranted.

Role of zonal flows in trapped electron mode turbulence through nonlinear gyrokinetic particle and continuum simulationa)

NASA Astrophysics Data System (ADS)

Ernst, D. R.; Lang, J.; Nevins, W. M.; Hoffman, M.; Chen, Y.; Dorland, W.; Parker, S.

2009-05-01

Trapped electron mode (TEM) turbulence exhibits a rich variety of collisional and zonal flow physics. This work explores the parametric variation of zonal flows and underlying mechanisms through a series of linear and nonlinear gyrokinetic simulations, using both particle-in-cell and continuum methods. A new stability diagram for electron modes is presented, identifying a critical boundary at ηe=1, separating long and short wavelength TEMs. A novel parity test is used to separate TEMs from electron temperature gradient driven modes. A nonlinear scan of ηe reveals fine scale structure for ηe≳1, consistent with linear expectation. For ηe<1, zonal flows are the dominant saturation mechanism, and TEM transport is insensitive to ηe. For ηe>1, zonal flows are weak, and TEM transport falls inversely with a power law in ηe. The role of zonal flows appears to be connected to linear stability properties. Particle and continuum methods are compared in detail over a range of ηe=d ln Te/d ln ne values from zero to five. Linear growth rate spectra, transport fluxes, fluctuation wavelength spectra, zonal flow shearing spectra, and correlation lengths and times are in close agreement. In addition to identifying the critical parameter ηe for TEM zonal flows, this paper takes a challenging step in code verification, directly comparing very different methods of simulating simultaneous kinetic electron and ion dynamics in TEM turbulence.

The lateral/directional stability characteristics of a four-propeller tilt-wing V/STOL model in low-speed steep descent. M.S. Thesis - Princeton Univ., N.J.

NASA Technical Reports Server (NTRS)

Dicarlo, D. J.

1971-01-01

Lateral-directional dynamic stability derivatives are presented for a O.1-scale model of the XC-142A tilt-wing transport. The tests involved various descending flight conditions achieved at constant speed and wing incidence by varying the vehicle angle of attack. The propeller blade angle and the speed were also changed in the steepest descent case. The experimental data were analyzed assuming that the dynamic motions of the vehicle may be described by linearized equations, with the lateral-directional characteristics of the full-scale aircraft also presented and discussed. Results from this experimental investigation indicated that the full-scale aircraft would have a stable lateral-directional motion in level flight, with the dynamic motion becoming less stable as the descent angle was increased.

Sliding mode control-based linear functional observers for discrete-time stochastic systems

NASA Astrophysics Data System (ADS)

Singh, Satnesh; Janardhanan, Sivaramakrishnan

2017-11-01

Sliding mode control (SMC) is one of the most popular techniques to stabilise linear discrete-time stochastic systems. However, application of SMC becomes difficult when the system states are not available for feedback. This paper presents a new approach to design a SMC-based functional observer for discrete-time stochastic systems. The functional observer is based on the Kronecker product approach. Existence conditions and stability analysis of the proposed observer are given. The control input is estimated by a novel linear functional observer. This approach leads to a non-switching type of control, thereby eliminating the fundamental cause of chatter. Furthermore, the functional observer is designed in such a way that the effect of process and measurement noise is minimised. Simulation example is given to illustrate and validate the proposed design method.

Deletion of internal structured repeats increases the stability of a leucine-rich repeat protein, YopM

PubMed Central

Barrick, Doug

2011-01-01

Mapping the stability distributions of proteins in their native folded states provides a critical link between structure, thermodynamics, and function. Linear repeat proteins have proven more amenable to this kind of mapping than globular proteins. C-terminal deletion studies of YopM, a large, linear leucine-rich repeat (LRR) protein, show that stability is distributed quite heterogeneously, yet a high level of cooperativity is maintained [1]. Key components of this distribution are three interfaces that strongly stabilize adjacent sequences, thereby maintaining structural integrity and promoting cooperativity. To better understand the distribution of interaction energy around these critical interfaces, we studied internal (rather than terminal) deletions of three LRRs in this region, including one of these stabilizing interfaces. Contrary to our expectation that deletion of structured repeats should be destabilizing, we find that internal deletion of folded repeats can actually stabilize the native state, suggesting that these repeats are destabilizing, although paradoxically, they are folded in the native state. We identified two residues within this destabilizing segment that deviate from the consensus sequence at a position that normally forms a stacked leucine ladder in the hydrophobic core. Replacement of these nonconsensus residues with leucine is stabilizing. This stability enhancement can be reproduced in the context of nonnative interfaces, but it requires an extended hydrophobic core. Our results demonstrate that different LRRs vary widely in their contribution to stability, and that this variation is context-dependent. These two factors are likely to determine the types of rearrangements that lead to folded, functional proteins, and in turn, are likely to restrict the pathways available for the evolution of linear repeat proteins. PMID:21764506

Linear signal noise summer accurately determines and controls S/N ratio

NASA Technical Reports Server (NTRS)

Sundry, J. L.

1966-01-01

Linear signal noise summer precisely controls the relative power levels of signal and noise, and mixes them linearly in accurately known ratios. The S/N ratio accuracy and stability are greatly improved by this technique and are attained simultaneously.

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

DOE PAGES

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

2014-10-22

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

Flame analysis using image processing techniques

NASA Astrophysics Data System (ADS)

Her Jie, Albert Chang; Zamli, Ahmad Faizal Ahmad; Zulazlan Shah Zulkifli, Ahmad; Yee, Joanne Lim Mun; Lim, Mooktzeng

2018-04-01

This paper presents image processing techniques with the use of fuzzy logic and neural network approach to perform flame analysis. Flame diagnostic is important in the industry to extract relevant information from flame images. Experiment test is carried out in a model industrial burner with different flow rates. Flame features such as luminous and spectral parameters are extracted using image processing and Fast Fourier Transform (FFT). Flame images are acquired using FLIR infrared camera. Non-linearities such as thermal acoustic oscillations and background noise affect the stability of flame. Flame velocity is one of the important characteristics that determines stability of flame. In this paper, an image processing method is proposed to determine flame velocity. Power spectral density (PSD) graph is a good tool for vibration analysis where flame stability can be approximated. However, a more intelligent diagnostic system is needed to automatically determine flame stability. In this paper, flame features of different flow rates are compared and analyzed. The selected flame features are used as inputs to the proposed fuzzy inference system to determine flame stability. Neural network is used to test the performance of the fuzzy inference system.

Clusters in nonsmooth oscillator networks

NASA Astrophysics Data System (ADS)

Nicks, Rachel; Chambon, Lucie; Coombes, Stephen

2018-03-01

For coupled oscillator networks with Laplacian coupling, the master stability function (MSF) has proven a particularly powerful tool for assessing the stability of the synchronous state. Using tools from group theory, this approach has recently been extended to treat more general cluster states. However, the MSF and its generalizations require the determination of a set of Floquet multipliers from variational equations obtained by linearization around a periodic orbit. Since closed form solutions for periodic orbits are invariably hard to come by, the framework is often explored using numerical techniques. Here, we show that further insight into network dynamics can be obtained by focusing on piecewise linear (PWL) oscillator models. Not only do these allow for the explicit construction of periodic orbits, their variational analysis can also be explicitly performed. The price for adopting such nonsmooth systems is that many of the notions from smooth dynamical systems, and in particular linear stability, need to be modified to take into account possible jumps in the components of Jacobians. This is naturally accommodated with the use of saltation matrices. By augmenting the variational approach for studying smooth dynamical systems with such matrices we show that, for a wide variety of networks that have been used as models of biological systems, cluster states can be explicitly investigated. By way of illustration, we analyze an integrate-and-fire network model with event-driven synaptic coupling as well as a diffusively coupled network built from planar PWL nodes, including a reduction of the popular Morris-Lecar neuron model. We use these examples to emphasize that the stability of network cluster states can depend as much on the choice of single node dynamics as it does on the form of network structural connectivity. Importantly, the procedure that we present here, for understanding cluster synchronization in networks, is valid for a wide variety of systems in biology, physics, and engineering that can be described by PWL oscillators.

Analytic theory for the determination of velocity and stability of bubbles in a Hele-Shaw cell. Part 1: Velocity selection

NASA Technical Reports Server (NTRS)

Tanveer, Saleh

1989-01-01

An asymptotic theory is presented for the determination of velocity and linear stability of a steady symmetric bubble in a Hele-Shaw cell for small surface tension. In the first part, the bubble velocity U relative to the fluid velocity at infinity is determined for small surface tension T by determining transcendentally small correction to the asymptotic series solution. It is found that for any relative bubble velocity U in the interval (U(c),2), solutions exist at a countably infinite set of values of T (which has zero as its limit point) corresponding to the different branches of bubble solutions. U(c) decreases monotonically from 2 to 1 as the bubble area increases from 0 to infinity. However, for a bubble of arbitrarily given size, as T approaches 0, solution exists on any given branch with relative bubble velocity U satisfying the relation 2-U = cT to the 2/3 power, where c depends on the branch but is independent of the bubble area. The analytical evidence further suggests that there are no solutions for U greater than 2. These results are in agreement with earlier analytical results for a finger. In Part 2, an analytic theory is presented for the determination of the linear stability of the bubble in the limit of zero surface tension. Only the solution branch corresponding to the largest possible U for given surface tension is found to be stable, while all the others are unstable, in accordance with earlier numerical results.

Techniques for the Enhancement of Linear Predictive Speech Coding in Adverse Conditions

NASA Astrophysics Data System (ADS)

Wrench, Alan A.

Available from UMI in association with The British Library. Requires signed TDF. The Linear Prediction model was first applied to speech two and a half decades ago. Since then it has been the subject of intense research and continues to be one of the principal tools in the analysis of speech. Its mathematical tractability makes it a suitable subject for study and its proven success in practical applications makes the study worthwhile. The model is known to be unsuited to speech corrupted by background noise. This has led many researchers to investigate ways of enhancing the speech signal prior to Linear Predictive analysis. In this thesis this body of work is extended. The chosen application is low bit-rate (2.4 kbits/sec) speech coding. For this task the performance of the Linear Prediction algorithm is crucial because there is insufficient bandwidth to encode the error between the modelled speech and the original input. A review of the fundamentals of Linear Prediction and an independent assessment of the relative performance of methods of Linear Prediction modelling are presented. A new method is proposed which is fast and facilitates stability checking, however, its stability is shown to be unacceptably poorer than existing methods. A novel supposition governing the positioning of the analysis frame relative to a voiced speech signal is proposed and supported by observation. The problem of coding noisy speech is examined. Four frequency domain speech processing techniques are developed and tested. These are: (i) Combined Order Linear Prediction Spectral Estimation; (ii) Frequency Scaling According to an Aural Model; (iii) Amplitude Weighting Based on Perceived Loudness; (iv) Power Spectrum Squaring. These methods are compared with the Recursive Linearised Maximum a Posteriori method. Following on from work done in the frequency domain, a time domain implementation of spectrum squaring is developed. In addition, a new method of power spectrum estimation is developed based on the Minimum Variance approach. This new algorithm is shown to be closely related to Linear Prediction but produces slightly broader spectral peaks. Spectrum squaring is applied to both the new algorithm and standard Linear Prediction and their relative performance is assessed. (Abstract shortened by UMI.).

Propagation and stability characteristics of a 500-m-long laser-based fiducial line for high-precision alignment of long-distance linear accelerators.

PubMed

Suwada, Tsuyoshi; Satoh, Masanori; Telada, Souichi; Minoshima, Kaoru

2013-09-01

A laser-based alignment system with a He-Ne laser has been newly developed in order to precisely align accelerator units at the KEKB injector linac. The laser beam was first implemented as a 500-m-long fiducial straight line for alignment measurements. We experimentally investigated the propagation and stability characteristics of the laser beam passing through laser pipes in vacuum. The pointing stability at the last fiducial point was successfully obtained with the transverse displacements of ±40 μm level in one standard deviation by applying a feedback control. This pointing stability corresponds to an angle of ±0.08 μrad. This report contains a detailed description of the experimental investigation for the propagation and stability characteristics of the laser beam in the laser-based alignment system for long-distance linear accelerators.

Tuneable enhancement of the salt and thermal stability of polymeric micelles by cyclized amphiphiles

PubMed Central

Honda, Satoshi; Yamamoto, Takuya; Tezuka, Yasuyuki

2013-01-01

Cyclic molecules provide better stability for their aggregates. Typically in nature, the unique cyclic cell membrane lipids allow thermophilic archaea to inhabit extreme conditions. By mimicking the biological design, the robustness of self-assembled synthetic nanostructures is expected to be improved. Here we report topology effects by cyclized polymeric amphiphiles against their linear counterparts, demonstrating a drastic enhancement in the thermal, as well as salt stability of self-assembled micelles. Furthermore, through coassembly of the linear and cyclic amphiphiles, the stability was successfully tuned for a wide range of temperatures and salt concentrations. The enhanced thermal/salt stability was exploited in a halogen exchange reaction to stimulate the catalytic activity. The mechanism for the enhancement was also investigated. These topology effects by the cyclic amphiphiles offer unprecedented opportunities in polymer materials design unattainable by traditional means. PMID:23481382

Propagation and stability characteristics of a 500-m-long laser-based fiducial line for high-precision alignment of long-distance linear accelerators

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

Suwada, Tsuyoshi; Satoh, Masanori; Telada, Souichi

2013-09-15

A laser-based alignment system with a He-Ne laser has been newly developed in order to precisely align accelerator units at the KEKB injector linac. The laser beam was first implemented as a 500-m-long fiducial straight line for alignment measurements. We experimentally investigated the propagation and stability characteristics of the laser beam passing through laser pipes in vacuum. The pointing stability at the last fiducial point was successfully obtained with the transverse displacements of ±40 μm level in one standard deviation by applying a feedback control. This pointing stability corresponds to an angle of ±0.08 μrad. This report contains a detailedmore » description of the experimental investigation for the propagation and stability characteristics of the laser beam in the laser-based alignment system for long-distance linear accelerators.« less

Development of a High-Stability Microstrip-based L-band Radiometer for Ocean Salinity Measurements

NASA Technical Reports Server (NTRS)

Pellerano, Fernando A.; Horgan, Kevin A.; Wilson, William J.; Tanner, Alan B.

2004-01-01

The development of a microstrip-based L-band Dicke radiometer with the long-term stability required for future ocean salinity measurements to an accuracy of 0.1 psu is presented. This measurement requires the L-band radiometers to have calibration stabilities of less than or equal to 0.05 K over 2 days. This research has focused on determining the optimum radiometer requirements and configuration to achieve this objective. System configuration and component performance have been evaluated with radiometer test beds at both JPL and GSFC. The GSFC testbed uses a cryogenic chamber that allows long-term characterization at radiometric temperatures in the range of 70 - 120 K. The research has addressed several areas including component characterization as a function of temperature and DC bias, system linearity, optimum noise diode injection calibration, and precision temperature control of components. A breadboard radiometer, utilizing microstrip-based technologies, has been built to demonstrate this long-term stability.

Numerical proof of stability of roll waves in the small-amplitude limit for inclined thin film flow

NASA Astrophysics Data System (ADS)

Barker, Blake

2014-10-01

We present a rigorous numerical proof based on interval arithmetic computations categorizing the linearized and nonlinear stability of periodic viscous roll waves of the KdV-KS equation modeling weakly unstable flow of a thin fluid film on an incline in the small-amplitude KdV limit. The argument proceeds by verification of a stability condition derived by Bar-Nepomnyashchy and Johnson-Noble-Rodrigues-Zumbrun involving inner products of various elliptic functions arising through the KdV equation. One key point in the analysis is a bootstrap argument balancing the extremely poor sup norm bounds for these functions against the extremely good convergence properties for analytic interpolation in order to obtain a feasible computation time. Another is the way of handling analytic interpolation in several variables by a two-step process carving up the parameter space into manageable pieces for rigorous evaluation. These and other general aspects of the analysis should serve as blueprints for more general analyses of spectral stability.

The influence of adhesive on fiber Bragg grating strain sensor

NASA Astrophysics Data System (ADS)

Chen, Jixuan; Gong, Huaping; Jin, Shangzhong; Li, Shuhua

2009-08-01

A fiber Bragg grating (FBG) sensor was fixed on the uniform strength beam with three adhesives, which were modified acrylate, glass glue and epoxy resin. The influence of adhesive on FBG strain sensor was investigated. The strain of FBG sensor was varied by loading weight to the uniform strength beam. The wavelength shift of the FBG sensor fixed by the three kinds of adhesive were measured with different weight at the temperatures 0°C, 10°C, 20°C, 30°C, 40°C. The linearity, sensitivity and their stability at different temperature of FBG sensor which fixed by every kind of adhesives were analyzed. The results show that, the FBG sensor fixed by the modified acrylate has a high linearity, and the linear correlation coefficient is 0.9996. It also has a high sensitivity which is 0.251nm/kg. The linearity and the sensitivity of the FBG sensor have a high stability at different temperatures. The FBG sensor fixed by the glass glue also has a high linearity, and the linear correlation coefficient is 0.9986, but it has a low sensitivity which is only 0.041nm/kg. The linearity and the sensitivity of the FBG sensor fixed by the glass glue have a high stability at different temperatures. When the FBG sensor is fixed by epoxy resin, the sensitivity and linearity is affected significantly by the temperature. When the temperature changes from 0°C to 40°C, the sensitivity decreases from 0.302nm/kg to 0.058nm/kg, and the linear correlation coefficient decreases from 0.9999 to 0.9961.

On the nonlinear trapping nature of undamped, coherent structures in collisionless plasmas and its impact on stability

NASA Astrophysics Data System (ADS)

Schamel, Hans; Mandal, Debraj; Sharma, Devendra

2017-03-01

An outstanding notion for collisionless plasmas is the essential nonlinear character of their coherent structures, which in the stationary, weak amplitude limit are described by a continuum of cnoidal electron and ion hole modes governed by a multiparametric nonlinear dispersion relation. The well-known discrete structure of undamped linear plasma modes is seamlessly embedded in this nonlinear continuum as the microscopic texture of plasma begins to reveal itself in the high temperature collisionless plasma limit. This transforms the linear-threshold-based operating mechanism of plasma turbulence into a fundamental nonlinear, multifaceted one. Based on a comprehensive three-level description of increasing profundity, a proof of this novel dictum is presented, which makes use of the joint properties of such structures, their coherency and stationarity, and uses in succession a fluid, linear Vlasov and a full Vlasov description. It unifies discrete and continuum limits by resolving the inevitable resonant region and shows that coherent electrostatic equilibria are generally controlled by kinetic particle trapping and are hence fundamentally nonlinear. By forging a link between damped and growing wave solutions, these modes render plasma stability complex and difficult to evaluate due to the entangled pattern of the stability boundary in function and parameter space, respectively. A direct consequence is the existence of negative energy modes of arbitrarily small amplitudes in the subcritical region of the two-stream instability as well as the failure of linear Landau (Vlasov, van Kampen) theory, whenever resonant particles are involved, in addressing the onset of instability in a current-carrying plasma. Responsible for this subtle phase space behavior is hence the thresholdless omnipresence of the trapping nonlinearity originating from coherency. A high resolution, exact-mass-ratio, multispecies, and collisionless plasma simulation is employed to illustrate exemplarily how tiny seed fluctuations in phase-space can act as a triggering agent for a subcritical plasma excitation verifying an access to these modes in the noisy, collisionless plasma limit.

COED Transactions, Vol. IX, No. 1, January 1977. Rapid Production of System Phase-Plane Portraits on the EAI 380 Hybrid/Analog Computer.

ERIC Educational Resources Information Center

Marcovitz, Alan B., Ed.

The method of phase-plane presentation as an educational tool in the study of the dynamic behavior of systems is discussed. In the treatment of nonlinear or piecewise-linear systems, the phase-plane portrait is used to exhibit the nature of singular points, regions of stability, and switching lines to aid comprehension. A technique is described by…

Stabilization Approaches for Linear and Nonlinear Reduced Order Models

NASA Astrophysics Data System (ADS)

Rezaian, Elnaz; Wei, Mingjun

2017-11-01

It has been a major concern to establish reduced order models (ROMs) as reliable representatives of the dynamics inherent in high fidelity simulations, while fast computation is achieved. In practice it comes to stability and accuracy of ROMs. Given the inviscid nature of Euler equations it becomes more challenging to achieve stability, especially where moving discontinuities exist. Originally unstable linear and nonlinear ROMs are stabilized here by two approaches. First, a hybrid method is developed by integrating two different stabilization algorithms. At the same time, symmetry inner product is introduced in the generation of ROMs for its known robust behavior for compressible flows. Results have shown a notable improvement in computational efficiency and robustness compared to similar approaches. Second, a new stabilization algorithm is developed specifically for nonlinear ROMs. This method adopts Particle Swarm Optimization to enforce a bounded ROM response for minimum discrepancy between the high fidelity simulation and the ROM outputs. Promising results are obtained in its application on the nonlinear ROM of an inviscid fluid flow with discontinuities. Supported by ARL.

Influence of age on the correlations of hematological and biochemical variables with the stability of erythrocyte membrane in relation to sodium dodecyl sulfate.

PubMed

de Freitas, Mariana V; Marquez-Bernardes, Liandra F; de Arvelos, Letícia R; Paraíso, Lara F; Gonçalves E Oliveira, Ana Flávia M; Mascarenhas Netto, Rita de C; Neto, Morun Bernardino; Garrote-Filho, Mario S; de Souza, Paulo César A; Penha-Silva, Nilson

2014-10-01

To evaluate the influence of age on the relationships between biochemical and hematological variables and stability of erythrocyte membrane in relation to the sodium dodecyl sulfate (SDS) in population of 105 female volunteers between 20 and 90 years. The stability of RBC membrane was determined by non-linear regression of the dependency of the absorbance of hemoglobin released as a function of SDS concentration, represented by the half-transition point of the curve (D50) and the variation in the concentration of the detergent to promote lysis (dD). There was an age-dependent increase in the membrane stability in relation to SDS. Analyses by multiple linear regression showed that this stability increase is significantly related to the hematological variable red cell distribution width (RDW) and the biochemical variables blood albumin and cholesterol. The positive association between erythrocyte stability and RDW may reflect one possible mechanism involved in the clinical meaning of this hematological index.

Stability analysis of an equilibrium position in the photogravitational Sitnikov problem

NASA Astrophysics Data System (ADS)

Bardin, B. S.; Avdushkin, A. N.

2018-05-01

We deal with the so-called photogravitational Sitnikov problem, that is we consider rectilinear motion of a body of infinitesimal mass in a field of two graviting and radiating primaries, which have equal masses and act on the body with equal repulsive forces of radiation pressure. The body has equilibrium position in the barycenter of the system. In this paper the stability of the equilibrium position is investigated in detail. In particular, by the study of the linearized system we have found in the plane of parameter values the regions of instability. It appears that the instability regions alternate with stability regions and become very narrower when the eccentricity of the primaries orbits approaches to 1. Outside the instability regions we have performed non-linear stability analysis and shown that the stability of the equilibrium position in the sense of Lyapunov takes place both in resonant and non-resonant cases. The results of the study are represented in a form of stability diagram.

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

NASA Technical Reports Server (NTRS)

Wauer, J.

1977-01-01

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

Inviscid linear stability analysis of two vertical columns of different densities in a gravitational acceleration field

DOE PAGES

Prathama, Aditya Heru; Pantano, Carlos

2017-08-09

Here, we study the inviscid linear stability of a vertical interface separating two fluids of different densities and subject to a gravitational acceleration field parallel to the interface. In this arrangement, the two free streams are constantly accelerated, which means that the linear stability analysis is not amenable to Fourier or Laplace solution in time. Instead, we derive the equations analytically by the initial-value problem method and express the solution in terms of the well-known parabolic cylinder function. The results, which can be classified as an accelerating Kelvin–Helmholtz configuration, show that even in the presence of surface tension, the interfacemore » is unconditionally unstable at all wavemodes. This is a consequence of the ever increasing momentum of the free streams, as gravity accelerates them indefinitely. The instability can be shown to grow as the exponential of a quadratic function of time.« less

Experimental and numerical investigation of development of disturbances in the boundary layer on sharp and blunted cone

NASA Astrophysics Data System (ADS)

Borisov, S. P.; Bountin, D. A.; Gromyko, Yu. V.; Khotyanovsky, D. V.; Kudryavtsev, A. N.

2016-10-01

Development of disturbances in the supersonic boundary layer on sharp and blunted cones is studied both experimentally and theoretically. The experiments were conducted at the Transit-M hypersonic wind tunnel of the Institute of Theoretical and Applied Mechanics. Linear stability calculations use the basic flow profiles provided by the numerical simulations performed by solving the Navier-Stokes equations with the ANSYS Fluent and the in-house CFS3D code. Both the global pseudospectral Chebyshev method and the local iteration procedure are employed to solve the eigenvalue problem and determine linear stability characteristics. The calculated amplification factors for disturbances of various frequencies are compared with the experimentally measured pressure fluctuation spectra at different streamwise positions. It is shown that the linear stability calculations predict quite accurately the frequency of the most amplified disturbances and enable us to estimate reasonably well their relative amplitudes.

Linear Stability of Binary Alloy Solidification for Unsteady Growth Rates

NASA Technical Reports Server (NTRS)

Mazuruk, K.; Volz, M. P.

2010-01-01

An extension of the Mullins and Sekerka (MS) linear stability analysis to the unsteady growth rate case is considered for dilute binary alloys. In particular, the stability of the planar interface during the initial solidification transient is studied in detail numerically. The rapid solidification case, when the system is traversing through the unstable region defined by the MS criterion, has also been treated. It has been observed that the onset of instability is quite accurately defined by the "quasi-stationary MS criterion", when the growth rate and other process parameters are taken as constants at a particular time of the growth process. A singular behavior of the governing equations for the perturbed quantities at the constitutional supercooling demarcation line has been observed. However, when the solidification process, during its transient, crosses this demarcation line, a planar interface is stable according to the linear analysis performed.

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.

Unconditionally marginal stability of harmonic electron hole equilibria in current-driven plasmas

NASA Astrophysics Data System (ADS)

Schamel, Hans

2018-06-01

Two forms of the linearized eigenvalue problem with respect to linear perturbations of a privileged cnoidal electron hole as a structural nonlinear equilibrium element are established. Whereas its integral form involves integrations along the characteristics or unperturbed particle orbits, the differential form has to cope with a differential operator of infinite order. Both are hence faced with difficulties to obtain a solution. A first successful attempt is, however, made by addressing a single harmonic wave as a nonlinear equilibrium structure. By this microscopic nonlinear approach, its marginal stability against linear perturbations in both linear stability regimes, the sub- and super-critical one, is shown independent of the mobility of ions and in favor with recent observations. Responsible for vanishing damping (growth) is the microscopic distortion of the resonant distribution function. The macroscopic form of the trapping nonlinearity—the 3/2 power term of the electrostatic potential in the density—which disappears in the monochromatic harmonic wave limit is consequently necessary for the occurrence of a nonlinear plasma instability in the sub-critical regime.

Stability of viscosity stratified flows down an incline: Role of miscibility and wall slip

NASA Astrophysics Data System (ADS)

Ghosh, Sukhendu; Usha, R.

2016-10-01

The effects of wall velocity slip on the linear stability of a gravity-driven miscible two-fluid flow down an incline are examined. The fluids have the matched density but different viscosity. A smooth viscosity stratification is achieved due to the presence of a thin mixed layer between the fluids. The results show that the presence of slip exhibits a promise for stabilizing the miscible flow system by raising the critical Reynolds number at the onset and decreasing the bandwidth of unstable wave numbers beyond the threshold of the dominant instability. This is different from its role in the case of a single fluid down a slippery substrate where slip destabilizes the flow system at the onset. Though the stability properties are analogous to the same flow system down a rigid substrate, slip is shown to delay the surface mode instability for any viscosity contrast. It has a damping/promoting effect on the overlap modes (which exist due to the overlap of critical layer of dominant disturbance with the mixed layer) when the mixed layer is away/close from/to the slippery inclined wall. The trend of slip effect is influenced by the location of the mixed layer, the location of more viscous fluid, and the mass diffusivity of the two fluids. The stabilizing characteristics of slip can be favourably used to suppress the non-linear breakdown which may happen due to the coexistence of the unstable modes in a flow over a substrate with no slip. The results of the present study suggest that it is desirable to design a slippery surface with appropriate slip sensitivity in order to meet a particular need for a specific application.

Genetic analyses using GGE model and a mixed linear model approach, and stability analyses using AMMI bi-plot for late-maturity alpha-amylase activity in bread wheat genotypes.

PubMed

Rasul, Golam; Glover, Karl D; Krishnan, Padmanaban G; Wu, Jixiang; Berzonsky, William A; Fofana, Bourlaye

2017-06-01

Low falling number and discounting grain when it is downgraded in class are the consequences of excessive late-maturity α-amylase activity (LMAA) in bread wheat (Triticum aestivum L.). Grain expressing high LMAA produces poorer quality bread products. To effectively breed for low LMAA, it is necessary to understand what genes control it and how they are expressed, particularly when genotypes are grown in different environments. In this study, an International Collection (IC) of 18 spring wheat genotypes and another set of 15 spring wheat cultivars adapted to South Dakota (SD), USA were assessed to characterize the genetic component of LMAA over 5 and 13 environments, respectively. The data were analysed using a GGE model with a mixed linear model approach and stability analysis was presented using an AMMI bi-plot on R software. All estimated variance components and their proportions to the total phenotypic variance were highly significant for both sets of genotypes, which were validated by the AMMI model analysis. Broad-sense heritability for LMAA was higher in SD adapted cultivars (53%) compared to that in IC (49%). Significant genetic effects and stability analyses showed some genotypes, e.g. 'Lancer', 'Chester' and 'LoSprout' from IC, and 'Alsen', 'Traverse' and 'Forefront' from SD cultivars could be used as parents to develop new cultivars expressing low levels of LMAA. Stability analysis using an AMMI bi-plot revealed that 'Chester', 'Lancer' and 'Advance' were the most stable across environments, while in contrast, 'Kinsman', 'Lerma52' and 'Traverse' exhibited the lowest stability for LMAA across environments.

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.

A semi-implicit level set method for multiphase flows and fluid-structure interaction problems

NASA Astrophysics Data System (ADS)

Cottet, Georges-Henri; Maitre, Emmanuel

2016-06-01

In this paper we present a novel semi-implicit time-discretization of the level set method introduced in [8] for fluid-structure interaction problems. The idea stems from a linear stability analysis derived on a simplified one-dimensional problem. The semi-implicit scheme relies on a simple filter operating as a pre-processing on the level set function. It applies to multiphase flows driven by surface tension as well as to fluid-structure interaction problems. The semi-implicit scheme avoids the stability constraints that explicit scheme need to satisfy and reduces significantly the computational cost. It is validated through comparisons with the original explicit scheme and refinement studies on two-dimensional benchmarks.

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

Asymptotic aspect of derivations in Banach algebras.

PubMed

Roh, Jaiok; Chang, Ick-Soon

2017-01-01

We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.

Mixed linear-non-linear inversion of crustal deformation data: Bayesian inference of model, weighting and regularization parameters

NASA Astrophysics Data System (ADS)

Fukuda, Jun'ichi; Johnson, Kaj M.

2010-06-01

We present a unified theoretical framework and solution method for probabilistic, Bayesian inversions of crustal deformation data. The inversions involve multiple data sets with unknown relative weights, model parameters that are related linearly or non-linearly through theoretic models to observations, prior information on model parameters and regularization priors to stabilize underdetermined problems. To efficiently handle non-linear inversions in which some of the model parameters are linearly related to the observations, this method combines both analytical least-squares solutions and a Monte Carlo sampling technique. In this method, model parameters that are linearly and non-linearly related to observations, relative weights of multiple data sets and relative weights of prior information and regularization priors are determined in a unified Bayesian framework. In this paper, we define the mixed linear-non-linear inverse problem, outline the theoretical basis for the method, provide a step-by-step algorithm for the inversion, validate the inversion method using synthetic data and apply the method to two real data sets. We apply the method to inversions of multiple geodetic data sets with unknown relative data weights for interseismic fault slip and locking depth. We also apply the method to the problem of estimating the spatial distribution of coseismic slip on faults with unknown fault geometry, relative data weights and smoothing regularization weight.

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

Theoretical study of structure and stability of small gadolinium carboxylate complexes in liquid scintillator solvents.

PubMed

Huang, Pin-Wen

2014-09-01

The structural properties of three small gadolinium carboxylate complexes in three liquid scintillator solvents (pseudocumene, linear alkylbenzene, and phenyl xylylethane) were theoretically investigated using density functional theory (B3LYP/LC-RECP) and polarizable continuum model (PCM). The average interaction energy between gadolinium atom and carboxylate ligand (E(int)) and the energy difference of the highest singly occupied molecular orbital and lowest unoccupied molecular orbital (Δ(SL)) were calculated to evaluate and compare the relative stability of these complexes in solvents. The calculation results show that the larger (with a longer alkyl chain) gadolinium carboxylate complex has greater stability than the smaller one, while these gadolinium carboxylates in linear alkylbenzene were found to have greater stability than those in the other two solvents.

Linear stability analysis of the three-dimensional thermally-driven ocean circulation: application to interdecadal oscillations

NASA Astrophysics Data System (ADS)

Huck, Thierry; Vallis, Geoffrey K.

2001-08-01

What can we learn from performing a linear stability analysis of the large-scale ocean circulation? Can we predict from the basic state the occurrence of interdecadal oscillations, such as might be found in a forward integration of the full equations of motion? If so, do the structure and period of the linearly unstable modes resemble those found in a forward integration? We pursue here a preliminary study of these questions for a case in idealized geometry, in which the full nonlinear behavior can also be explored through forward integrations. Specifically, we perform a three-dimensional linear stability analysis of the thermally-driven circulation of the planetary geostrophic equations. We examine the resulting eigenvalues and eigenfunctions, comparing them with the structure of the interdecadal oscillations found in the fully nonlinear model in various parameter regimes. We obtain a steady state by running the time-dependent, nonlinear model to equilibrium using restoring boundary conditions on surface temperature. If the surface heat fluxes are then diagnosed, and these values applied as constant flux boundary conditions, the nonlinear model switches into a state of perpetual, finite amplitude, interdecadal oscillations. We construct a linearized version of the model by empirically evaluating the tangent linear matrix at the steady state, under both restoring and constant-flux boundary conditions. An eigen-analysis shows there are no unstable eigenmodes of the linearized model with restoring conditions. In contrast, under constant flux conditions, we find a single unstable eigenmode that shows a striking resemblance to the fully-developed oscillations in terms of three-dimensional structure, period and growth rate. The mode may be damped through either surface restoring boundary conditions or sufficiently large horizontal tracer diffusion. The success of this simple numerical method in idealized geometry suggests applications in the study of the stability of the ocean circulation in more realistic configurations, and the possibility of predicting potential oceanic modes, even weakly damped, that might be excited by stochastic atmospheric forcing or mesoscale ocean eddies.

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.

Chemical networks with inflows and outflows: a positive linear differential inclusions approach.

PubMed

Angeli, David; De Leenheer, Patrick; Sontag, Eduardo D

2009-01-01

Certain mass-action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state-dependent linear time-varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to a ubiquitous biochemical reaction network with inflows and outflows, known as the futile cycle. We also provide a characterization of exponential stability of general homogeneous switched systems which is not only of interest in itself, but also plays a role in the analysis of the futile cycle. 2009 American Institute of Chemical Engineers

3-D MHD modeling and stability analysis of jet and spheromak plasmas launched into a magnetized plasma

NASA Astrophysics Data System (ADS)

Fisher, Dustin; Zhang, Yue; Wallace, Ben; Gilmore, Mark; Manchester, Ward; Arge, C. Nick

2016-10-01

The Plasma Bubble Expansion Experiment (PBEX) at the University of New Mexico uses a coaxial plasma gun to launch jet and spheromak magnetic plasma configurations into the Helicon-Cathode (HelCat) plasma device. Plasma structures launched from the gun drag frozen-in magnetic flux into the background magnetic field of the chamber providing a rich set of dynamics to study magnetic turbulence, force-free magnetic spheromaks, and shocks. Preliminary modeling is presented using the highly-developed 3-D, MHD, BATS-R-US code developed at the University of Michigan. BATS-R-US employs an adaptive mesh refinement grid that enables the capture and resolution of shock structures and current sheets, and is particularly suited to model the parameter regime under investigation. CCD images and magnetic field data from the experiment suggest the stabilization of an m =1 kink mode trailing a plasma jet launched into a background magnetic field. Results from a linear stability code investigating the effect of shear-flow as a cause of this stabilization from magnetic tension forces on the jet will be presented. Initial analyses of a possible magnetic Rayleigh Taylor instability seen at the interface between launched spheromaks and their entraining background magnetic field will also be presented. Work supported by the Army Research Office Award No. W911NF1510480.

Nonlinear bending-torsional vibration and stability of rotating, pretwisted, preconed blades including Coriolis effects

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.; Brown, G. V.; Lawrence, C.

1986-01-01

The coupled bending-bending-torsional equations of dynamic motion of rotating, linearly pretwisted blades are derived including large precone, second degree geometric nonlinearities and Coriolis effects. The equations are solved by the Galerkin method and a linear perturbation technique. Accuracy of the present method is verified by comparisons of predicted frequencies and steady state deflections with those from MSC/NASTRAN and from experiments. Parametric results are generated to establish where inclusion of only the second degree geometric nonlinearities is adequate. The nonlinear terms causing torsional divergence in thin blades are identified. The effects of Coriolis terms and several other structurally nonlinear terms are studied, and their relative importance is examined.

Nonlinear vibration and stability of rotating, pretwisted, preconed blades including Coriolis effects

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.; Brown, G. V.; Lawrence, C.

1987-01-01

The coupled bending-bending-torsional equations of dynamic motion of rotating, linearly pretwisted blades are derived including large precone, second degree geometric nonlinearities and Coriolis effects. The equations are solved by the Galerkin method and a linear perturbation technique. Accuracy of the present method is verified by conparisons of predicted frequencies and steady state deflections with those from MSC/NASTRAN and from experiments. Parametric results are generated to establish where inclusion of only the second degree geometric nonlinearities is adequate. The nonlinear terms causing torsional divergence in thin blades are identified. The effects of Coriolis terms and several other structurally nonlinear terms are studied, and their relative importance is examined.

Molecular basis of branched peptides resistance to enzyme proteolysis.

PubMed

Falciani, Chiara; Lozzi, Luisa; Pini, Alessandro; Corti, Federico; Fabbrini, Monica; Bernini, Andrea; Lelli, Barbara; Niccolai, Neri; Bracci, Luisa

2007-03-01

We found that synthetic peptides in the form of dendrimers become resistant to proteolysis. To determine the molecular basis of this resistance, different bioactive peptides were synthesized in monomeric, two-branched and tetra-branched form and incubated with human plasma and serum. Proteolytic resistance of branched multimeric sequences was compared to that of the same peptides synthesized as multimeric linear molecules. Unmodified peptides and cleaved sequences were detected by high pressure liquid chromatography and mass spectrometry. An increase in peptide copies did not increase peptide resistance in linear multimeric sequences, whereas multimericity progressively enhanced proteolytic stability of branched multimeric peptides. A structure-based hypothesis of branched peptide resistance to proteolysis by metallopeptidases is presented.

Observation of Rayleigh-Taylor-instability evolution in a plasma with magnetic and viscous effects

DOE PAGES

Adams, Colin S.; Moser, Auna L.; Hsu, Scott C.

2015-11-06

We present time-resolved observations of Rayleigh-Taylor-instability (RTI) evolution at the interface between an unmagnetized plasma jet colliding with a stagnated, magnetized plasma. The observed instability growth time (~10μs) is consistent with the estimated linear RTI growth rate calculated using experimentally inferred values of density (~10 14cm–3) and deceleration (~10 9 m/s 2). The observed mode wavelength (≳1 cm) nearly doubles within a linear growth time. Furthermore, theoretical estimates of magnetic and viscous stabilization and idealized magnetohydrodynamic simulations including a physical viscosity model both suggest that the observed instability evolution is subject to magnetic and/or viscous effects.

Optimal Recursive Digital Filters for Active Bending Stabilization

NASA Technical Reports Server (NTRS)

Orr, Jeb S.

2013-01-01

In the design of flight control systems for large flexible boosters, it is common practice to utilize active feedback control of the first lateral structural bending mode so as to suppress transients and reduce gust loading. Typically, active stabilization or phase stabilization is achieved by carefully shaping the loop transfer function in the frequency domain via the use of compensating filters combined with the frequency response characteristics of the nozzle/actuator system. In this paper we present a new approach for parameterizing and determining optimal low-order recursive linear digital filters so as to satisfy phase shaping constraints for bending and sloshing dynamics while simultaneously maximizing attenuation in other frequency bands of interest, e.g. near higher frequency parasitic structural modes. By parameterizing the filter directly in the z-plane with certain restrictions, the search space of candidate filter designs that satisfy the constraints is restricted to stable, minimum phase recursive low-pass filters with well-conditioned coefficients. Combined with optimal output feedback blending from multiple rate gyros, the present approach enables rapid and robust parametrization of autopilot bending filters to attain flight control performance objectives. Numerical results are presented that illustrate the application of the present technique to the development of rate gyro filters for an exploration-class multi-engined space launch vehicle.

Evaluation of energy consumption during aerobic sewage sludge treatment in dairy wastewater treatment plant.

PubMed

Dąbrowski, Wojciech; Żyłka, Radosław; Malinowski, Paweł

2017-02-01

The subject of the research conducted in an operating dairy wastewater treatment plant (WWTP) was to examine electric energy consumption during sewage sludge treatment. The excess sewage sludge was aerobically stabilized and dewatered with a screw press. Organic matter varied from 48% to 56% in sludge after stabilization and dewatering. It proves that sludge was properly stabilized and it was possible to apply it as a fertilizer. Measurement factors for electric energy consumption for mechanically dewatered sewage sludge were determined, which ranged between 0.94 and 1.5 kWhm -3 with the average value at 1.17 kWhm -3 . The shares of devices used for sludge dewatering and aerobic stabilization in the total energy consumption of the plant were also established, which were 3% and 25% respectively. A model of energy consumption during sewage sludge treatment was estimated according to experimental data. Two models were applied: linear regression for dewatering process and segmented linear regression for aerobic stabilization. The segmented linear regression model was also applied to total energy consumption during sewage sludge treatment in the examined dairy WWTP. The research constitutes an introduction for further studies on defining a mathematical model used to optimize electric energy consumption by dairy WWTPs. Copyright © 2016 Elsevier Inc. All rights reserved.

Linear Dimensional Stability of Irreversible Hydrocolloid Materials Over Time.

PubMed

Garrofé, Analía B; Ferrari, Beatriz A; Picca, Mariana; Kaplan, Andrea E

2015-12-01

The aim of this study was to evaluate the linear dimensional stability of different irreversible hydrocolloid materials over time. A metal mold was designed with custom trays made of thermoplastic sheets (Sabilex, sheets 0.125 mm thick). Perforations were made in order to improve retention of the material. Five impressions were taken with each of the following: Kromopan 100 (LASCOD) [AlKr], which has dimensional stability of 100 hours, and Phase Plus (ZHERMACK) [AlPh], which has dimensional stability of 48 hours. Standardized digital photographs were taken at different time intervals (0, 15, 30, 45, 60, 120 minutes; 12, 24 and 96 hours), using an "ad-hoc" device. The images were analyzed with software (UTHSCSA Image Tool) by measuring the distance between intersection of the lines previously made at the top of the mold. The results were analyzed by ANOVA for repeated measures. Initial and final values were (mean and standard deviation): AlKr: 16.44 (0.22) and 16.34 (0.11), AlPh: 16.40 (0.06) and 16.18 (0.06). Statistical evaluation showed significant effect of material and time factors. Under the conditions in this study, time significantly affects the linear dimensional stability of irreversible hydrocolloid materials. Sociedad Argentina de Investigación Odontológica.

Influence of sodium metabisulfite and glutathione on the stability of vitamin C in O/W emulsion and extemporaneous aqueous gel.

PubMed

Maia, Adriana M; Baby, André Rolim; Pinto, Claudinéia A S O; Yasaka, Wilson J; Suenaga, Eunice; Kaneko, Telma M; Velasco, Maria Valéria Robles

2006-09-28

Vitamin C exerts several functions on skin as collagen synthesis, depigmentant and antioxidant activity. Vitamin C is unstable in the presence of oxygen, luminosity, humidity, high temperatures and heavy metals, which presents a significant challenge to the development of cosmetic formulations. Therefore, the utilization of an effective antioxidant system is required to maintain the vitamin C stability. The purpose of this research work was to develop prototypes of cosmetic formulations, as O/W emulsion and extemporaneous aqueous gel, containing vitamin C and to evaluate the influence of sodium metabisulfite (SMB) and glutathione (GLT), as antioxidants, on the stability of the active substance. A HPLC stability-indicating method was developed and validated for this study and stability assays were performed in 90 and 26 days and storage conditions were 5.0+/-0.5, 24+/-2 and 40.0+/-0.5 degrees C. The HPLC stability-indicating method showed linearity (r(2)>0.99), specificity, R.S.D.<1.22% and accuracy/recovery ranging from 95.46 to 101.54%. Preparations with SMB or GLT and the antioxidant-free presented results statistically distinct, demonstrating the necessity of the antioxidant system addition. O/W emulsions with SMB or GLT retained the vitamin C content >90.38% stored at 5.0+/-0.5 and 24+/-2 degrees C. For the aqueous gel with SMB or GLT, the active substance concentration was maintained >94.03%. Considering the vitamin C stability, the SMB and the GLT showed to be statistically adequate, as antioxidants, for the cosmetic formulations.

Stability of nonuniform rotor blades in hover using a mixed formulation

NASA Technical Reports Server (NTRS)

Stephens, W. B.; Hodges, D. H.; Avila, J. H.; Kung, R. M.

1980-01-01

A mixed formulation for calculating static equilibrium and stability eigenvalues of nonuniform rotor blades in hover is presented. The static equilibrium equations are nonlinear and are solved by an accurate and efficient collocation method. The linearized perturbation equations are solved by a one step, second order integration scheme. The numerical results correlate very well with published results from a nearly identical stability analysis based on a displacement formulation. Slight differences in the results are traced to terms in the equations that relate moments to derivatives of rotations. With the present ordering scheme, in which terms of the order of squares of rotations are neglected with respect to unity, it is not possible to achieve completely equivalent models based on mixed and displacement formulations. The one step methods reveal that a second order Taylor expansion is necessary to achieve good convergence for nonuniform rotating blades. Numerical results for a hypothetical nonuniform blade, including the nonlinear static equilibrium solution, were obtained with no more effort or computer time than that required for a uniform blade.

New Evidence That Nonlinear Source-Filter Coupling Affects Harmonic Intensity and fo Stability During Instances of Harmonics Crossing Formants.

PubMed

Maxfield, Lynn; Palaparthi, Anil; Titze, Ingo

2017-03-01

The traditional source-filter theory of voice production describes a linear relationship between the source (glottal flow pulse) and the filter (vocal tract). Such a linear relationship does not allow for nor explain how changes in the filter may impact the stability and regularity of the source. The objective of this experiment was to examine what effect unpredictable changes to vocal tract dimensions could have on fo stability and individual harmonic intensities in situations in which low frequency harmonics cross formants in a fundamental frequency glide. To determine these effects, eight human subjects (five male, three female) were recorded producing fo glides while their vocal tracts were artificially lengthened by a section of vinyl tubing inserted into the mouth. It was hypothesized that if the source and filter operated as a purely linear system, harmonic intensities would increase and decrease at nearly the same rates as they passed through a formant bandwidth, resulting in a relatively symmetric peak on an intensity-time contour. Additionally, fo stability should not be predictably perturbed by formant/harmonic crossings in a linear system. Acoustic analysis of these recordings, however, revealed that harmonic intensity peaks were asymmetric in 76% of cases, and that 85% of fo instabilities aligned with a crossing of one of the first four harmonics with the first three formants. These results provide further evidence that nonlinear dynamics in the source-filter relationship can impact fo stability as well as harmonic intensities as harmonics cross through formant bandwidths. Copyright © 2017 The Voice Foundation. Published by Elsevier Inc. All rights reserved.

Stability and Interaction of Coherent Structure in Supersonic Reactive Wakes

NASA Technical Reports Server (NTRS)

Menon, Suresh

1983-01-01

A theoretical formulation and analysis is presented for a study of the stability and interaction of coherent structure in reacting free shear layers. The physical problem under investigation is a premixed hydrogen-oxygen reacting shear layer in the wake of a thin flat plate. The coherent structure is modeled as a periodic disturbance and its stability is determined by the application of linearized hydrodynamic stability theory which results in a generalized eigenvalue problem for reactive flows. Detailed stability analysis of the reactive wake for neutral, symmetrical and antisymmetrical disturbance is presented. Reactive stability criteria is shown to be quite different from classical non-reactive stability. The interaction between the mean flow, coherent structure and fine-scale turbulence is theoretically formulated using the von-Kaman integral technique. Both time-averaging and conditional phase averaging are necessary to separate the three types of motion. The resulting integro-differential equations can then be solved subject to initial conditions with appropriate shape functions. In the laminar flow transition region of interest, the spatial interaction between the mean motion and coherent structure is calculated for both non-reactive and reactive conditions and compared with experimental data wherever available. The fine-scale turbulent motion determined by the application of integral analysis to the fluctuation equations. Since at present this turbulence model is still untested, turbulence is modeled in the interaction problem by a simple algebraic eddy viscosity model. The applicability of the integral turbulence model formulated here is studied parametrically by integrating these equations for the simple case of self-similar mean motion with assumed shape functions. The effect of the motion of the coherent structure is studied and very good agreement is obtained with previous experimental and theoretical works for non-reactive flow. For the reactive case, lack of experimental data made direct comparison difficult. It was determined that the growth rate of the disturbance amplitude is lower for reactive case. The results indicate that the reactive flow stability is in qualitative agreement with experimental observation.

Coherent structures in interacting vortex rings

NASA Astrophysics Data System (ADS)

Deng, Jian; Xue, Jingyu; Mao, Xuerui; Caulfield, C. P.

2017-02-01

We investigate experimentally the nonlinear structures that develop from interacting vortex rings induced by a sinusoidally oscillating ellipsoidal disk in fluid at rest. We vary the scaled amplitude or Keulegan-Carpenter number 0.3

The role of turbulent suppression in the triggering ITBs on C-Mod

NASA Astrophysics Data System (ADS)

Zhurovich, K.; Fiore, C. L.; Ernst, D. R.; Bonoli, P. T.; Greenwald, M. J.; Hubbard, A. E.; Hughes, J. W.; Marmar, E. S.; Mikkelsen, D. R.; Phillips, P.; Rice, J. E.

2007-11-01

Internal transport barriers can be routinely produced in C-Mod steady EDA H-mode plasmas by applying ICRF at |r/a|>= 0.5. Access to the off-axis ICRF heated ITBs may be understood within the paradigm of marginal stability. Analysis of the Te profiles shows a decrease of R/LTe in the ITB region as the RF resonance is moved off axis. Ti profiles broaden as the ICRF power deposition changes from on-axis to off-axis. TRANSP calculations of the Ti profiles support this trend. Linear GS2 calculations do not reveal any difference in ETG growth rate profiles for ITB vs. non-ITB discharges. However, they do show that the region of stability to ITG modes widens as the ICRF resonance is moved outward. Non-linear simulations show that the outward turbulent particle flux exceeds the Ware pinch by factor of 2 in the outer plasma region. Reducing the temperature gradient significantly decreases the diffusive flux and allows the Ware pinch to peak the density profile. Details of these experiments and simulations will be presented.

Stability and Performance Metrics for Adaptive Flight Control

NASA Technical Reports Server (NTRS)

Stepanyan, Vahram; Krishnakumar, Kalmanje; Nguyen, Nhan; VanEykeren, Luarens

2009-01-01

This paper addresses the problem of verifying adaptive control techniques for enabling safe flight in the presence of adverse conditions. Since the adaptive systems are non-linear by design, the existing control verification metrics are not applicable to adaptive controllers. Moreover, these systems are in general highly uncertain. Hence, the system's characteristics cannot be evaluated by relying on the available dynamical models. This necessitates the development of control verification metrics based on the system's input-output information. For this point of view, a set of metrics is introduced that compares the uncertain aircraft's input-output behavior under the action of an adaptive controller to that of a closed-loop linear reference model to be followed by the aircraft. This reference model is constructed for each specific maneuver using the exact aerodynamic and mass properties of the aircraft to meet the stability and performance requirements commonly accepted in flight control. The proposed metrics are unified in the sense that they are model independent and not restricted to any specific adaptive control methods. As an example, we present simulation results for a wing damaged generic transport aircraft with several existing adaptive controllers.

Neoclassical tearing mode seeding by coupling with infernal modes in low-shear tokamaks

NASA Astrophysics Data System (ADS)

Kleiner, A.; Graves, J. P.; Brunetti, D.; Cooper, W. A.; Halpern, F. D.; Luciani, J.-F.; Lütjens, H.

2016-09-01

A numerical and an analytical study of the triggering of resistive MHD modes in tokamak plasmas with low magnetic shear core is presented. Flat q profiles give rise to fast growing pressure driven MHD modes, such as infernal modes. It has been shown that infernal modes drive fast growing islands on neighbouring rational surfaces. Numerical simulations of such instabilities in a MAST-like configuration are performed with the initial value stability code XTOR-2F in the resistive frame. The evolution of magnetic islands are computed from XTOR-2F simulations and an analytical model is developed based on Rutherford’s theory in combination with a model of resistive infernal modes. The parameter {{Δ }\\prime} is extended from the linear phase to the non-linear phase. Additionally, the destabilising contribution due to a helically perturbed bootstrap current is considered. Comparing the numerical XTOR-2F simulations to the model, we find that coupling has a strong destabilising effect on (neoclassical) tearing modes and is able to seed 2/1 magnetic islands in situations when the standard NTM theory predicts stability.

A Study of Electron Modes in Off-axis Heated Alcator C-Mod Plasmas

NASA Astrophysics Data System (ADS)

Fiore, C. L.; Ernst, D. R.; Mikkelsen, D.; Ennever, P. C.; Howard, N. T.; Gao, C.; Reinke, M. L.; Rice, J. E.; Hughes, J. W.; Walk, J. R.

2013-10-01

Understanding the underlying physics and stability of the peaked density internal transport barriers (ITB) that have been observed during off-axis ICRF heating of Alcator C-Mod plasmas is the goal of recent gyro-kinetic simulations. Two scenarios are examined: an ITB plasma formed with maximal (4.5 MW) off-axis heating power; also the use of off-axis heating in an I-mode plasma as a target in the hopes of establishing an ITB. In the former, it is expected that evidence of trapped electron mode instabilities could be found if a sufficiently high electron temperature is achieved in the core. Linear simulations show unstable modes are present across the plasma core from r/a = 0.2 and greater. In the latter case, despite establishing similar conditions to those in which ITBS were formed, none developed in the I-mode plasmas. Linear gyrokinetic analyses show no unstable ion modes at r/a < 0.55 in these I-mode plasmas, with both ITG and ETG modes present beyond r/a = 0.65. The details of the experimental results will be presented. Linear and non-linear simulations of both of these cases will attempt to explore the underlying role of electron and ion gradient driven instabilities to explain the observations. This work was supported by US-DoE DE-FC02-99ER54512 and DE-AC02-09CH11466.

An h-p Taylor-Galerkin finite element method for compressible Euler equations

NASA Technical Reports Server (NTRS)

Demkowicz, L.; Oden, J. T.; Rachowicz, W.; Hardy, O.

1991-01-01

An extension of the familiar Taylor-Galerkin method to arbitrary h-p spatial approximations is proposed. Boundary conditions are analyzed, and a linear stability result for arbitrary meshes is given, showing the unconditional stability for the parameter of implicitness alpha not less than 0.5. The wedge and blunt body problems are solved with both linear, quadratic, and cubic elements and h-adaptivity, showing the feasibility of higher orders of approximation for problems with shocks.

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.

Dewetting Kinetics in Polymer Grafted Nanoparticle Thin Films: Impact of Architecture and Viscosity on Thermal Stability

NASA Astrophysics Data System (ADS)

Che, Justin; Jawaid, Ali; Grabowski, Christopher; Yi, Yoon-Jae; Vaia, Richard; AFRL Collaboration

Rapid formation of ordered monolayers of polymer grafted nanoparticles (PGN) directly onto solid surfaces has spurred interest in using these materials for additive manufacturing of optical devices and energy storage. Herein, we discuss dewetting of polystyrene grafted Au nanoparticles (PS@Au) with an increased thermal (10-25oC) and energetic (5-15 mN/m) stability relative to linear polymer films of comparable thickness. Analogous to star macromolecules, the enhanced stability is related to the conformations of chains in the grafted canopy. Mechanistically, dewetting of PS@Au is similar to linear PS, however, the thickness transition from spinodal to heterogeneous nucleation is at least 5-6x larger. Time resolved optical microscopy during dewetting at 160oC revealed that the zero shear viscosity for linear PS scaled as η0 Mn3. 3 , consistent with reptation of entangled polymers. In contrast, PS@Au showed η0 Mn2. 2 where Mn reflects the molecular weight of the grafted chains. Overall, PS@Au exhibited significantly slower dewetting rates, consistent with a 100x increase in viscosity relative to the linear chain analogues. Quantification of the relationship between PGN architecture (e.g. nanoparticle size, graft density, polymer molecular weight) and dewetting processes is crucial to optimize the order of these assemblies via post-processing, as well as design the PGN canopy to maximize stability for devices.

The Lyapunov-Krasovskii theorem and a sufficient criterion for local stability of isochronal synchronization in networks of delay-coupled oscillators

NASA Astrophysics Data System (ADS)

Grzybowski, J. M. V.; Macau, E. E. N.; Yoneyama, T.

2017-05-01

This paper presents a self-contained framework for the stability assessment of isochronal synchronization in networks of chaotic and limit-cycle oscillators. The results were based on the Lyapunov-Krasovskii theorem and they establish a sufficient condition for local synchronization stability of as a function of the system and network parameters. With this in mind, a network of mutually delay-coupled oscillators subject to direct self-coupling is considered and then the resulting error equations are block-diagonalized for the purpose of studying their stability. These error equations are evaluated by means of analytical stability results derived from the Lyapunov-Krasovskii theorem. The proposed approach is shown to be a feasible option for the investigation of local stability of isochronal synchronization for a variety of oscillators coupled through linear functions of the state variables under a given undirected graph structure. This ultimately permits the systematic identification of stability regions within the high-dimensionality of the network parameter space. Examples of applications of the results to a number of networks of delay-coupled chaotic and limit-cycle oscillators are provided, such as Lorenz, Rössler, Cubic Chua's circuit, Van der Pol oscillator and the Hindmarsh-Rose neuron.

New insights into transcription fidelity: thermal stability of non-canonical structures in template DNA regulates transcriptional arrest, pause, and slippage.

PubMed

Tateishi-Karimata, Hisae; Isono, Noburu; Sugimoto, Naoki

2014-01-01

The thermal stability and topology of non-canonical structures of G-quadruplexes and hairpins in template DNA were investigated, and the effect of non-canonical structures on transcription fidelity was evaluated quantitatively. We designed ten template DNAs: A linear sequence that does not have significant higher-order structure, three sequences that form hairpin structures, and six sequences that form G-quadruplex structures with different stabilities. Templates with non-canonical structures induced the production of an arrested, a slipped, and a full-length transcript, whereas the linear sequence produced only a full-length transcript. The efficiency of production for run-off transcripts (full-length and slipped transcripts) from templates that formed the non-canonical structures was lower than that from the linear. G-quadruplex structures were more effective inhibitors of full-length product formation than were hairpin structure even when the stability of the G-quadruplex in an aqueous solution was the same as that of the hairpin. We considered that intra-polymerase conditions may differentially affect the stability of non-canonical structures. The values of transcription efficiencies of run-off or arrest transcripts were correlated with stabilities of non-canonical structures in the intra-polymerase condition mimicked by 20 wt% polyethylene glycol (PEG). Transcriptional arrest was induced when the stability of the G-quadruplex structure (-ΔG°37) in the presence of 20 wt% PEG was more than 8.2 kcal mol(-1). Thus, values of stability in the presence of 20 wt% PEG are an important indicator of transcription perturbation. Our results further our understanding of the impact of template structure on the transcription process and may guide logical design of transcription-regulating drugs.

New Insights into Transcription Fidelity: Thermal Stability of Non-Canonical Structures in Template DNA Regulates Transcriptional Arrest, Pause, and Slippage

PubMed Central

Tateishi-Karimata, Hisae; Isono, Noburu; Sugimoto, Naoki

2014-01-01

The thermal stability and topology of non-canonical structures of G-quadruplexes and hairpins in template DNA were investigated, and the effect of non-canonical structures on transcription fidelity was evaluated quantitatively. We designed ten template DNAs: A linear sequence that does not have significant higher-order structure, three sequences that form hairpin structures, and six sequences that form G-quadruplex structures with different stabilities. Templates with non-canonical structures induced the production of an arrested, a slipped, and a full-length transcript, whereas the linear sequence produced only a full-length transcript. The efficiency of production for run-off transcripts (full-length and slipped transcripts) from templates that formed the non-canonical structures was lower than that from the linear. G-quadruplex structures were more effective inhibitors of full-length product formation than were hairpin structure even when the stability of the G-quadruplex in an aqueous solution was the same as that of the hairpin. We considered that intra-polymerase conditions may differentially affect the stability of non-canonical structures. The values of transcription efficiencies of run-off or arrest transcripts were correlated with stabilities of non-canonical structures in the intra-polymerase condition mimicked by 20 wt% polyethylene glycol (PEG). Transcriptional arrest was induced when the stability of the G-quadruplex structure (−ΔGo 37) in the presence of 20 wt% PEG was more than 8.2 kcal mol−1. Thus, values of stability in the presence of 20 wt% PEG are an important indicator of transcription perturbation. Our results further our understanding of the impact of template structure on the transcription process and may guide logical design of transcription-regulating drugs. PMID:24594642

Drive beam stabilisation in the CLIC Test Facility 3

NASA Astrophysics Data System (ADS)

Malina, L.; Corsini, R.; Persson, T.; Skowroński, P. K.; Adli, E.

2018-06-01

The proposed Compact Linear Collider (CLIC) uses a high intensity, low energy drive beam to produce the RF power needed to accelerate a lower intensity main beam with 100 MV/m gradient. This scheme puts stringent requirements on drive beam stability in terms of phase, energy and current. The consequent experimental work was carried out in CLIC Test Facility CTF3. In this paper, we present a novel analysis technique in accelerator physics to find beam drifts and their sources in the vast amount of the continuously gathered signals. The instability sources are identified and adequately mitigated either by hardware improvements or by implementation and commissioning of various feedbacks, mostly beam-based. The resulting drive beam stability is of 0.2°@ 3 GHz in phase, 0.08% in relative beam energy and about 0.2% beam current. Finally, we propose a stabilisation concept for CLIC to guarantee the main beam stability.

Delay-dependent dynamical analysis of complex-valued memristive neural networks: Continuous-time and discrete-time cases.

PubMed

Wang, Jinling; Jiang, Haijun; Ma, Tianlong; Hu, Cheng

2018-05-01

This paper considers the delay-dependent stability of memristive complex-valued neural networks (MCVNNs). A novel linear mapping function is presented to transform the complex-valued system into the real-valued system. Under such mapping function, both continuous-time and discrete-time MCVNNs are analyzed in this paper. Firstly, when activation functions are continuous but not Lipschitz continuous, an extended matrix inequality is proved to ensure the stability of continuous-time MCVNNs. Furthermore, if activation functions are discontinuous, a discontinuous adaptive controller is designed to acquire its stability by applying Lyapunov-Krasovskii functionals. Secondly, compared with techniques in continuous-time MCVNNs, the Halanay-type inequality and comparison principle are firstly used to exploit the dynamical behaviors of discrete-time MCVNNs. Finally, the effectiveness of theoretical results is illustrated through numerical examples. Copyright © 2018 Elsevier Ltd. All rights reserved.

Model Checking a Self-Stabilizing Distributed Clock Synchronization Protocol for Arbitrary Digraphs

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R.

2011-01-01

This report presents the mechanical verification of a self-stabilizing distributed clock synchronization protocol for arbitrary digraphs in the absence of faults. This protocol does not rely on assumptions about the initial state of the system, other than the presence of at least one node, and no central clock or a centrally generated signal, pulse, or message is used. The system under study is an arbitrary, non-partitioned digraph ranging from fully connected to 1-connected networks of nodes while allowing for differences in the network elements. Nodes are anonymous, i.e., they do not have unique identities. There is no theoretical limit on the maximum number of participating nodes. The only constraint on the behavior of the node is that the interactions with other nodes are restricted to defined links and interfaces. This protocol deterministically converges within a time bound that is a linear function of the self-stabilization period.

Qualitative fusion technique based on information poor system and its application to factor analysis for vibration of rolling bearings

NASA Astrophysics Data System (ADS)

Xia, Xintao; Wang, Zhongyu

2008-10-01

For some methods of stability analysis of a system using statistics, it is difficult to resolve the problems of unknown probability distribution and small sample. Therefore, a novel method is proposed in this paper to resolve these problems. This method is independent of probability distribution, and is useful for small sample systems. After rearrangement of the original data series, the order difference and two polynomial membership functions are introduced to estimate the true value, the lower bound and the supper bound of the system using fuzzy-set theory. Then empirical distribution function is investigated to ensure confidence level above 95%, and the degree of similarity is presented to evaluate stability of the system. Cases of computer simulation investigate stable systems with various probability distribution, unstable systems with linear systematic errors and periodic systematic errors and some mixed systems. The method of analysis for systematic stability is approved.

A dynamic analysis of the motion of a low-wing general aviation aircraft about its calculated equilibrium flat spin mode

NASA Technical Reports Server (NTRS)

Tischler, M. B.; Barlow, J. B.

1980-01-01

The properties of the flat spin mode of a general aviation configuration have been studied through analysis of rotary balance data, numerical simulation, and analytical study of the equilibrium state. The equilibrium state is predicted well from rotary balance data. The variations of yawing moment and pitching moment as functions of sideslip have been shown to be of great importance in obtaining accurate modeling. These dependencies are not presently available with sufficient accuracy from previous tests or theories. The stability of the flat spin mode has been examined extensively using numerical linearization, classical perturbation methods, and reduced order modeling. The stability exhibited by the time histories and the eigenvalue analyses is shown to be strongly dependent on certain static cross derivatives and more so on the dynamic derivatives. Explicit stability criteria are obtained from the reduced order models.

Waves on radial film flows

NASA Astrophysics Data System (ADS)

Cholemari, Murali R.; Arakeri, Jaywant H.

2005-08-01

We study the stability of surface waves on the radial film flow created by a vertical cylindrical water jet striking a horizontal plate. In such flows, surface waves have been found to be unstable and can cause transition to turbulence. This surface-wave-induced transition is different from the well-known Tollmien-Schlichting wave-induced transition. The present study aims at understanding the instability and the transition process. We do a temporal stability analysis by assuming the flow to be locally two-dimensional but including spatial variations to first order in the basic flow. The waves are found to be dispersive, mostly unstable, and faster than the mean flow. Spatial variation is the major destabilizing factor. Experiments are done to test the results of the linear stability analysis and to document the wave breakup and transition. Comparison between theory and experiments is fairly good and indicates the adequacy of the model.

Conformational stability and thermodynamic characterization of the lipoic acid bearing domain of human mitochondrial branched chain α-ketoacid dehydrogenase

PubMed Central

Naik, Mandar T.; Huang, Tai-Huang

2004-01-01

The lipoic acid bearing domain (hbLBD) of human mitochondrial branched chain α-ketoacid dehydrogenase (BCKD) plays important role of substrate channeling in oxidative decarboxylation of the branched chain α-ketoacids. Recently hbLBD has been found to follow two-step folding mechanism without detectable presence of stable or kinetic intermediates. The present study describes the conformational stability underlying the folding of this small β-barrel domain. Thermal denaturation in presence of urea and isothermal urea denaturation titrations are used to evaluate various thermodynamic parameters defining the equilibrium unfolding. The linear extrapolation model successfully describes the two-step; native state ↔denatured state unfolding transition of hbLBD. The average temperature of maximum stability of hbLBD is estimated as 295.6 ± 0.9 K. Cold denaturation of hbLBD is also predicted and discussed. PMID:15322287

Bright discrete solitons in spatially modulated DNLS systems

DOE PAGES

Kevrekidis, P. G.; Horne, R. L.; Whitaker, N.; ...

2015-08-04

In the present work, we revisit the highly active research area of inhomogeneously nonlinear defocusing media and consider the existence, spectral stability and nonlinear dynamics of bright solitary waves in them. We use the anti-continuum limit of vanishing coupling as the starting point of our analysis, enabling in this way a systematic characterization of the branches of solutions. Our stability findings and bifurcation characteristics reveal the enhanced robustness and wider existence intervals of solutions with a broader support, culminating in the 'extended' solution in which all sites are excited. Our eigenvalue predictions are corroborated by numerical linear stability analysis. Inmore » conclusion, the dynamics also reveal a tendency of the solution profiles to broaden, in line with the above findings. These results pave the way for further explorations of such states in discrete systems, including in higher dimensional settings.« less

Development and validation of a stability indicating HPLC method for determination of lisinopril, lisinopril degradation product and parabens in the lisinopril extemporaneous formulation.

PubMed

Beasley, Christopher A; Shaw, Jessica; Zhao, Zack; Reed, Robert A

2005-03-09

The purpose of the research described herein was to develop and validate a stability-indicating HPLC method for lisinopril, lisinopril degradation product (DKP), methyl paraben and propyl paraben in a lisinopril extemporaneous formulation. The method developed in this report is selective for the components listed above, in the presence of the complex and chromatographically rich matrix presented by the Bicitra and Ora-Sweet SF formulation diluents. The method was also shown to have adequate sensitivity with a detection limit of 0.0075 microg/mL (0.03% of lisinopril method concentration). The validation elements investigated showed that the method has acceptable specificity, recovery, linearity, solution stability, and method precision. Acceptable robustness indicates that the assay method remains unaffected by small but deliberate variations, which are described in ICH Q2A and Q2B guidelines.

Exploiting structure: Introduction and motivation

NASA Technical Reports Server (NTRS)

Xu, Zhong Ling

1994-01-01

This annual report summarizes the research activities that were performed from 26 Jun. 1993 to 28 Feb. 1994. We continued to investigate the Robust Stability of Systems where transfer functions or characteristic polynomials are affine multilinear functions of parameters. An approach that differs from 'Stability by Linear Process' and that reduces the computational burden of checking the robust stability of the system with multilinear uncertainty was found for low order, 2-order, and 3-order cases. We proved a crucial theorem, the so-called Face Theorem. Previously, we have proven Kharitonov's Vertex Theorem and the Edge Theorem by Bartlett. The detail of this proof is contained in the Appendix. This Theorem provides a tool to describe the boundary of the image of the affine multilinear function. For SPR design, we have developed some new results. The third objective for this period is to design a controller for IHM by the H-infinity optimization technique. The details are presented in the Appendix.

Robust Takagi-Sugeno fuzzy control for fractional order hydro-turbine governing system.

PubMed

Wang, Bin; Xue, Jianyi; Wu, Fengjiao; Zhu, Delan

2016-11-01

A robust fuzzy control method for fractional order hydro-turbine governing system (FOHGS) in the presence of random disturbances is investigated in this paper. Firstly, the mathematical model of FOHGS is introduced, and based on Takagi-Sugeno (T-S) fuzzy rules, the generalized T-S fuzzy model of FOHGS is presented. Secondly, based on fractional order Lyapunov stability theory, a novel T-S fuzzy control method is designed for the stability control of FOHGS. Thirdly, the relatively loose sufficient stability condition is acquired, which could be transformed into a group of linear matrix inequalities (LMIs) via Schur complement as well as the strict mathematical derivation is given. Furthermore, the control method could resist random disturbances, which shows the good robustness. Simulation results indicate the designed fractional order T-S fuzzy control scheme works well compared with the existing method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Magnetotail dynamics under isobaric constraints

NASA Technical Reports Server (NTRS)

Birn, Joachim; Schindler, Karl; Janicke, Lutz; Hesse, Michael

1994-01-01

Using linear theory and nonlinear MHD simulations, we investigate the resistive and ideal MHD stability of two-dimensional plasma configurations under the isobaric constraint dP/dt = 0, which in ideal MHD is equivalent to conserving the pressure function P = P(A), where A denotes the magnetic flux. This constraint is satisfied for incompressible modes, such as Alfven waves, and for systems undergoing energy losses. The linear stability analysis leads to a Schroedinger equation, which can be investigated by standard quantum mechanics procedures. We present an application to a typical stretched magnetotail configuration. For a one-dimensional sheet equilibrium characteristic properties of tearing instability are rediscovered. However, the maximum growth rate scales with the 1/7 power of the resistivity, which implies much faster growth than for the standard tearing mode (assuming that the resistivity is small). The same basic eigen-mode is found also for weakly two-dimensional equilibria, even in the ideal MHD limit. In this case the growth rate scales with the 1/4 power of the normal magnetic field. The results of the linear stability analysis are confirmed qualitatively by nonlinear dynamic MHD simulations. These results suggest the interesting possibility that substorm onset, or the thinning in the late growth phase, is caused by the release of a thermodynamic constraint without the (immediate) necessity of releasing the ideal MHD constraint. In the nonlinear regime the resistive and ideal developments differ in that the ideal mode does not lead to neutral line formation without the further release of the ideal MHD constraint; instead a thin current sheet forms. The isobaric constraint is critically discussed. Under perhaps more realistic adiabatic conditions the ideal mode appears to be stable but could be driven by external perturbations and thus generate the thin current sheet in the late growth phase, before a nonideal instability sets in.

Findings from the experience with the punch technique for auditory osseointegrated implants: A retrospective single center comparative study.

PubMed

Bonilla, Alfonso; Magri, Carlos; Juan, Eulalia

To compare the punch technique and linear incision with soft tissue reduction for the placement of auditory osseointegrated implants (AOI) and analyze results of osseointegration obtained with the punch technique as measured with the Implant Stability Quotient (ISQ). Case review of 34 patients who received auditory osseointegrated implants between January 2010 and July 2015 and were divided into two groups according to the surgical technique: 18 with the punch technique (PT) and 16 with the linear incision technique (LI). Minimum follow-up was four months (mean: 24 months; range 4-64 months). Included in the analysis were patient profiles and records of the demographic data, surgical indications, surgical technique, implant placement, surgical time, intraoperative complications, as well as postsurgical complications (Holgers classification) and implant stability quotients (ISQ). Use of larger abutments was significantly greater in the PT group (PT, 10mm; LI, 6mm, p<0.001). The PT technique resulted in a shorter procedure than the LI (PT, 20min; LI, 45min, p<0.001). Holgers classification scores identified significantly fewer skin complications one week after surgery for the PT group; however, only small differences were seen between the two groups at the one- and three-month control visits. As shown for our cohort, the punch technique for surgical placement of AOI is faster and presents fewer immediate postoperative complications when compared to the linear incision technique. The clinical application of the ISQ is a useful, easy method to demonstrate the status of osseointegration and, thus, the stability of the device. Copyright © 2017 Elsevier España, S.L.U. and Sociedad Española de Otorrinolaringología y Cirugía de Cabeza y Cuello. All rights reserved.

A new method for the prediction of combustion instability

NASA Astrophysics Data System (ADS)

Flanagan, Steven Meville

This dissertation presents a new approach to the prediction of combustion instability in solid rocket motors. Previous attempts at developing computational tools to solve this problem have been largely unsuccessful, showing very poor agreement with experimental results and having little or no predictive capability. This is due primarily to deficiencies in the linear stability theory upon which these efforts have been based. Recent advances in linear instability theory by Flandro have demonstrated the importance of including unsteady rotational effects, previously considered negligible. Previous versions of the theory also neglected corrections to the unsteady flow field of the first order in the mean flow Mach number. This research explores the stability implications of extending the solution to include these corrections. Also, the corrected linear stability theory based upon a rotational unsteady flow field extended to first order in mean flow Mach number has been implemented in two computer programs developed for the Macintosh platform. A quasi one-dimensional version of the program has been developed which is based upon an approximate solution to the cavity acoustics problem. The three-dimensional program applies Greens's Function Discretization (GFD) to the solution for the acoustic mode shapes and frequency. GFD is a recently developed numerical method for finding fully three dimensional solutions for this class of problems. The analysis of complex motor geometries, previously a tedious and time consuming task, has also been greatly simplified through the development of a drawing package designed specifically to facilitate the specification of typical motor geometries. The combination of the drawing package, improved acoustic solutions, and new analysis, results in a tool which is capable of producing more accurate and meaningful predictions than have been possible in the past.

Development of Curved-Plate Elements for the Exact Buckling Analysis of Composite Plate Assemblies Including Transverse Shear Effects

NASA Technical Reports Server (NTRS)

McGowan, David M.; Anderson, Melvin S.

1998-01-01

The analytical formulation of curved-plate non-linear equilibrium equations that include transverse-shear-deformation effects is presented. A unified set of non-linear strains that contains terms from both physical and tensorial strain measures is used. Using several simplifying assumptions, linearized, stability equations are derived that describe the response of the plate just after bifurcation buckling occurs. These equations are then modified to allow the plate reference surface to be located a distance z(c), from the centroid surface which is convenient for modeling stiffened-plate assemblies. The implementation of the new theory into the VICONOPT buckling and vibration analysis and optimum design program code is described. Either classical plate theory (CPT) or first-order shear-deformation plate theory (SDPT) may be selected in VICONOPT. Comparisons of numerical results for several example problems with different loading states are made. Results from the new curved-plate analysis compare well with closed-form solution results and with results from known example problems in the literature. Finally, a design-optimization study of two different cylindrical shells subject to uniform axial compression is presented.

Quasi-laminar stability and sensitivity analyses for turbulent flows: Prediction of low-frequency unsteadiness and passive control

NASA Astrophysics Data System (ADS)

Mettot, Clément; Sipp, Denis; Bézard, Hervé

2014-04-01

This article presents a quasi-laminar stability approach to identify in high-Reynolds number flows the dominant low-frequencies and to design passive control means to shift these frequencies. The approach is based on a global linear stability analysis of mean-flows, which correspond to the time-average of the unsteady flows. Contrary to the previous work by Meliga et al. ["Sensitivity of 2-D turbulent flow past a D-shaped cylinder using global stability," Phys. Fluids 24, 061701 (2012)], we use the linearized Navier-Stokes equations based solely on the molecular viscosity (leaving aside any turbulence model and any eddy viscosity) to extract the least stable direct and adjoint global modes of the flow. Then, we compute the frequency sensitivity maps of these modes, so as to predict before hand where a small control cylinder optimally shifts the frequency of the flow. In the case of the D-shaped cylinder studied by Parezanović and Cadot [J. Fluid Mech. 693, 115 (2012)], we show that the present approach well captures the frequency of the flow and recovers accurately the frequency control maps obtained experimentally. The results are close to those already obtained by Meliga et al., who used a more complex approach in which turbulence models played a central role. The present approach is simpler and may be applied to a broader range of flows since it is tractable as soon as mean-flows — which can be obtained either numerically from simulations (Direct Numerical Simulation (DNS), Large Eddy Simulation (LES), unsteady Reynolds-Averaged-Navier-Stokes (RANS), steady RANS) or from experimental measurements (Particle Image Velocimetry - PIV) — are available. We also discuss how the influence of the control cylinder on the mean-flow may be more accurately predicted by determining an eddy-viscosity from numerical simulations or experimental measurements. From a technical point of view, we finally show how an existing compressible numerical simulation code may be used in a black-box manner to extract the global modes and sensitivity maps.

Mover Position Detection for PMTLM Based on Linear Hall Sensors through EKF Processing

PubMed Central

Yan, Leyang; Zhang, Hui; Ye, Peiqing

2017-01-01

Accurate mover position is vital for a permanent magnet tubular linear motor (PMTLM) control system. In this paper, two linear Hall sensors are utilized to detect the mover position. However, Hall sensor signals contain third-order harmonics, creating errors in mover position detection. To filter out the third-order harmonics, a signal processing method based on the extended Kalman filter (EKF) is presented. The limitation of conventional processing method is first analyzed, and then EKF is adopted to detect the mover position. In the EKF model, the amplitude of the fundamental component and the percentage of the harmonic component are taken as state variables, and they can be estimated based solely on the measured sensor signals. Then, the harmonic component can be calculated and eliminated. The proposed method has the advantages of faster convergence, better stability and higher accuracy. Finally, experimental results validate the effectiveness and superiority of the proposed method. PMID:28383505

Linear and nonlinear stability of the Blasius boundary layer

NASA Technical Reports Server (NTRS)

Bertolotti, F. P.; Herbert, TH.; Spalart, P. R.

1992-01-01

Two new techniques for the study of the linear and nonlinear instability in growing boundary layers are presented. The first technique employs partial differential equations of parabolic type exploiting the slow change of the mean flow, disturbance velocity profiles, wavelengths, and growth rates in the streamwise direction. The second technique solves the Navier-Stokes equation for spatially evolving disturbances using buffer zones adjacent to the inflow and outflow boundaries. Results of both techniques are in excellent agreement. The linear and nonlinear development of Tollmien-Schlichting (TS) waves in the Blasius boundary layer is investigated with both techniques and with a local procedure based on a system of ordinary differential equations. The results are compared with previous work and the effects of non-parallelism and nonlinearity are clarified. The effect of nonparallelism is confirmed to be weak and, consequently, not responsible for the discrepancies between measurements and theoretical results for parallel flow.

A globally convergent LCL method for nonlinear optimization.

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

Friedlander, M. P.; Saunders, M. A.; Mathematics and Computer Science

2005-01-01

For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods solve a sequence of subproblems of the form 'minimize an augmented Lagrangian function subject to linearized constraints.' Such methods converge rapidly near a solution but may not be reliable from arbitrary starting points. Nevertheless, the well-known software package MINOS has proved effective on many large problems. Its success motivates us to derive a related LCL algorithm that possesses three important properties: it is globally convergent, the subproblem constraints are always feasible, and the subproblems may be solved inexactly. The new algorithm has been implemented in Matlab, with an optionmore » to use either MINOS or SNOPT (Fortran codes) to solve the linearly constrained subproblems. Only first derivatives are required. We present numerical results on a subset of the COPS, HS, and CUTE test problems, which include many large examples. The results demonstrate the robustness and efficiency of the stabilized LCL procedure.« less

A Monolithic CMOS Magnetic Hall Sensor with High Sensitivity and Linearity Characteristics

PubMed Central

Huang, Haiyun; Wang, Dejun; Xu, Yue

2015-01-01

This paper presents a fully integrated linear Hall sensor by means of 0.8 μm high voltage complementary metal-oxide semiconductor (CMOS) technology. This monolithic Hall sensor chip features a highly sensitive horizontal switched Hall plate and an efficient signal conditioner using dynamic offset cancellation technique. An improved cross-like Hall plate achieves high magnetic sensitivity and low offset. A new spinning current modulator stabilizes the quiescent output voltage and improves the reliability of the signal conditioner. The tested results show that at the 5 V supply voltage, the maximum Hall output voltage of the monolithic Hall sensor microsystem, is up to ±2.1 V and the linearity of Hall output voltage is higher than 99% in the magnetic flux density range from ±5 mT to ±175 mT. The output equivalent residual offset is 0.48 mT and the static power consumption is 20 mW. PMID:26516864

A Monolithic CMOS Magnetic Hall Sensor with High Sensitivity and Linearity Characteristics.

PubMed

Huang, Haiyun; Wang, Dejun; Xu, Yue

2015-10-27

This paper presents a fully integrated linear Hall sensor by means of 0.8 μm high voltage complementary metal-oxide semiconductor (CMOS) technology. This monolithic Hall sensor chip features a highly sensitive horizontal switched Hall plate and an efficient signal conditioner using dynamic offset cancellation technique. An improved cross-like Hall plate achieves high magnetic sensitivity and low offset. A new spinning current modulator stabilizes the quiescent output voltage and improves the reliability of the signal conditioner. The tested results show that at the 5 V supply voltage, the maximum Hall output voltage of the monolithic Hall sensor microsystem, is up to ±2.1 V and the linearity of Hall output voltage is higher than 99% in the magnetic flux density range from ±5 mT to ±175 mT. The output equivalent residual offset is 0.48 mT and the static power consumption is 20 mW.

Instability, finite amplitude pulsation and mass-loss in models of massive OB-type stars

NASA Astrophysics Data System (ADS)

Yadav, Abhay Pratap; Glatzel, Wolfgang

2017-11-01

Variability and mass-loss are common phenomena in massive OB-type stars. It is argued that they are caused by violent strange mode instabilities identified in corresponding stellar models. We present a systematic linear stability analysis with respect to radial perturbations of massive OB-type stars with solar chemical composition and masses between 23 and 100 M⊙. For selected unstable stellar models, we perform non-linear simulations of the evolution of the instabilities into the non-linear regime. Finite amplitude pulsations with periods in the range between hours and 100 d are found to be the final result of the instabilities. The pulsations are associated with a mean acoustic luminosity which can be the origin of a pulsationally driven wind. Corresponding mass-loss rates lie in the range between 10-9 and 10-4 M⊙ yr-1 and may thus affect the evolution of massive stars.

Correctness Proof of a Self-Stabilizing Distributed Clock Synchronization Protocol for Arbitrary Digraphs

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R.

2011-01-01

This report presents a deductive proof of a self-stabilizing distributed clock synchronization protocol. It is focused on the distributed clock synchronization of an arbitrary, non-partitioned digraph ranging from fully connected to 1-connected networks of nodes while allowing for differences in the network elements. This protocol does not rely on assumptions about the initial state of the system, and no central clock or a centrally generated signal, pulse, or message is used. Nodes are anonymous, i.e., they do not have unique identities. There is no theoretical limit on the maximum number of participating nodes. The only constraint on the behavior of the node is that the interactions with other nodes are restricted to defined links and interfaces. We present a deductive proof of the correctness of the protocol as it applies to the networks with unidirectional and bidirectional links. We also confirm the claims of determinism and linear convergence.

Control of mechanical systems with rolling constraints: Application to dynamic control of mobile robots

NASA Technical Reports Server (NTRS)

Sarkar, Nilanjan; Yun, Xiaoping; Kumar, Vijay

1994-01-01

There are many examples of mechanical systems that require rolling contacts between two or more rigid bodies. Rolling contacts engender nonholonomic constraints in an otherwise holonomic system. In this article, we develop a unified approach to the control of mechanical systems subject to both holonomic and nonholonomic constraints. We first present a state space realization of a constrained system. We then discuss the input-output linearization and zero dynamics of the system. This approach is applied to the dynamic control of mobile robots. Two types of control algorithms for mobile robots are investigated: trajectory tracking and path following. In each case, a smooth nonlinear feedback is obtained to achieve asymptotic input-output stability and Lagrange stability of the overall system. Simulation results are presented to demonstrate the effectiveness of the control algorithms and to compare the performane of trajectory-tracking and path-following algorithms.

Design and fabrication of absorber coupled TES microbolometers on continuous silicon-nitride windows.

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

Chang, C. L.; Carlstrom, J. E.; Datesman, A.

2008-04-01

The implementation of TES based microbolometer arrays will achieve unprecedented sensitivities for mm and sub-mm astronomy through fabrication of large format arrays and improved linearity and stability arising from strong electro-thermal feedback. We report on progress in developing TES microbolometers using Mo/Au thin films and Au absorbing structures. We present measurements of suppressing the thermal conductance through the etching of features on a continuous Silicon-Nitride window.

Parametrically excited multidegree-of-freedom systems with repeated frequencies

NASA Astrophysics Data System (ADS)

Nayfeh, A. H.

1983-05-01

An analysis is presented of the linear response of multidegree-of-freedom systems with a repeated frequency of order three to a harmonic parametric excitation. The method of multiple scales is used to determine the modulation of the amplitudes and phases for two cases: fundamental resonance of the modes with the repeated frequency and combination resonance involving these modes and another mode. Conditions are then derived for determining the stability of the motion.

Linear Stability of Relativistic Space-Charge Flow in a Magnetically Insulated Transmission Line Oscillator

DTIC Science & Technology

1989-04-01

MILO Magnetica fy insulated transmission line Slow-wave structure Relativistic Brillouin flow Space-charge waves Slow electromagnetic waves (over) 19... resonant layer always see a decelerating axial electric field. Consequently, field energy increases at the expense of particle energy. 17 AFWL-TR-88-103...Ve). If ve is greater than the structure coupling velocity, a resonant layer of electrons will always be present, and oscillations will occur at any

Study of three-dimensional effects on vortex breakdown

NASA Technical Reports Server (NTRS)

Salas, M. D.; Kuruvila, G.

1988-01-01

The incompressible axisymmetric steady Navier-Stokes equations in primitive variables are used to simulate vortex breakdown. The equations, discretized using a second-order, central-difference scheme, are linearized and then solved using an exact LU decomposition, Gaussian elimination, and Newton iteration. Solutions are presented for Reynolds numbers, based on vortex-core radius, as high as 1500. An attempt to study the stability of the axisymmetric solutions against three-dimensional perturbations is discussed.

Impact self-excited vibrations of linear motor

NASA Astrophysics Data System (ADS)

Zhuravlev, V. Ph.

2010-08-01

Impact self-exciting vibration modes in a linear motor of a monorail car are studied. Existence and stability conditions of self-exciting vibrations are found. Ways of avoiding the vibrations are discussed.

Study of Piezoelectric Vibration Energy Harvester with non-linear conditioning circuit using an integrated model

NASA Astrophysics Data System (ADS)

Manzoor, Ali; Rafique, Sajid; Usman Iftikhar, Muhammad; Mahmood Ul Hassan, Khalid; Nasir, Ali

2017-08-01

Piezoelectric vibration energy harvester (PVEH) consists of a cantilever bimorph with piezoelectric layers pasted on its top and bottom, which can harvest power from vibrations and feed to low power wireless sensor nodes through some power conditioning circuit. In this paper, a non-linear conditioning circuit, consisting of a full-bridge rectifier followed by a buck-boost converter, is employed to investigate the issues of electrical side of the energy harvesting system. An integrated mathematical model of complete electromechanical system has been developed. Previously, researchers have studied PVEH with sophisticated piezo-beam models but employed simplistic linear circuits, such as resistor, as electrical load. In contrast, other researchers have worked on more complex non-linear circuits but with over-simplified piezo-beam models. Such models neglect different aspects of the system which result from complex interactions of its electrical and mechanical subsystems. In this work, authors have integrated the distributed parameter-based model of piezo-beam presented in literature with a real world non-linear electrical load. Then, the developed integrated model is employed to analyse the stability of complete energy harvesting system. This work provides a more realistic and useful electromechanical model having realistic non-linear electrical load unlike the simplistic linear circuit elements employed by many researchers.

Protein substitution affects glass transition temperature and thermal stability.

PubMed

Budhavaram, Naresh K; Miller, Jonathan A; Shen, Ying; Barone, Justin R

2010-09-08

When proteins are removed from their native state they suffer from two deficiencies: (1) glassy behavior with glass transition temperatures (Tg) well above room temperature and (2) thermal instability. The glassy behavior originates in multiple hydrogen bonds between amino acids on adjacent protein molecules. Proteins, like most biopolymers, are thermally unstable. Substituting ovalbumin with linear and cyclic substituents using a facile nucleophilic addition reaction can affect Tg and thermal stability. More hydrophobic linear substituents lowered Tg by interrupting intermolecular interactions and increasing free volume. More hydrophilic and cyclic substituents increased thermal stability by increasing intermolecular interactions. In some cases, substituents instituted cross-linking between protein chains that enhanced thermal stability. Internal plasticization using covalent substitution and external plasticization using low molecular weight polar liquids show the same protein structural changes and a signature of plasticization is identified.

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

PubMed

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

2018-07-01

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

First-principles study of structural stability, electronic, optical and elastic properties of binary intermetallic: PtZr

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

Pagare, Gitanjali, E-mail: gita-pagare@yahoo.co.in; Jain, Ekta, E-mail: jainekta05@gmail.com; Sanyal, S. P., E-mail: sps.physicsbu@gmail.com

2016-05-06

Structural, electronic, optical and elastic properties of PtZr have been studied using the full-potential linearized augmented plane wave (FP-LAPW) method within density functional theory (DFT). The energy against volume and enthalpy vs. pressure variation in three different structures i.e. B{sub 1}, B{sub 2} and B{sub 3} for PtZr has been presented. The equilibrium lattice parameter, bulk modulus and its pressure derivative have been obtained using optimization method for all the three phases. Furthermore, electronic structure was discussed to reveal the metallic character of the present compound. The linear optical properties are also studied under zero pressure for the first time.more » Results on elastic properties are obtained using generalized gradient approximation (GGA) for exchange correlation potentials. Ductile nature of PtZr compound is predicted in accordance with Pugh’s criteria.« less

The effects of the Asselin time filter on numerical solutions to the linearized shallow-water wave equations

NASA Technical Reports Server (NTRS)

Schlesinger, R. E.; Johnson, D. R.; Uccellini, L. W.

1983-01-01

In the present investigation, a one-dimensional linearized analysis is used to determine the effect of Asselin's (1972) time filter on both the computational stability and phase error of numerical solutions for the shallow water wave equations, in cases with diffusion but without rotation. An attempt has been made to establish the approximate optimal values of the filtering parameter nu for each of the 'lagged', Dufort-Frankel, and Crank-Nicholson diffusion schemes, suppressing the computational wave mode without materially altering the physical wave mode. It is determined that in the presence of diffusion, the optimum filter length depends on whether waves are undergoing significant propagation. When moderate propagation is present, with or without diffusion, the Asselin filter has little effect on the spatial phase lag of the physical mode for the leapfrog advection scheme of the three diffusion schemes considered.

On solving three-dimensional open-dimension rectangular packing problems

NASA Astrophysics Data System (ADS)

Junqueira, Leonardo; Morabito, Reinaldo

2017-05-01

In this article, a recently proposed three-dimensional open-dimension rectangular packing problem is considered, in which the objective is to find a minimal volume rectangular container that packs a set of rectangular boxes. The literature has tackled small-sized instances of this problem by means of optimization solvers, position-free mixed-integer programming (MIP) formulations and piecewise linearization approaches. In this study, the problem is alternatively addressed by means of grid-based position MIP formulations, whereas still considering optimization solvers and the same piecewise linearization techniques. A comparison of the computational performance of both models is then presented, when tested with benchmark problem instances and with new instances, and it is shown that the grid-based position MIP formulation can be competitive, depending on the characteristics of the instances. The grid-based position MIP formulation is also embedded with real-world practical constraints, such as cargo stability, and results are additionally presented.

Pole-placement Predictive Functional Control for under-damped systems with real numbers algebra.

PubMed

Zabet, K; Rossiter, J A; Haber, R; Abdullah, M

2017-11-01

This paper presents the new algorithm of PP-PFC (Pole-placement Predictive Functional Control) for stable, linear under-damped higher-order processes. It is shown that while conventional PFC aims to get first-order exponential behavior, this is not always straightforward with significant under-damped modes and hence a pole-placement PFC algorithm is proposed which can be tuned more precisely to achieve the desired dynamics, but exploits complex number algebra and linear combinations in order to deliver guarantees of stability and performance. Nevertheless, practical implementation is easier by avoiding complex number algebra and hence a modified formulation of the PP-PFC algorithm is also presented which utilises just real numbers while retaining the key attributes of simple algebra, coding and tuning. The potential advantages are demonstrated with numerical examples and real-time control of a laboratory plant. Copyright © 2017 ISA. All rights reserved.

LMI-based stability and performance conditions for continuous-time nonlinear systems in Takagi-Sugeno's form.

PubMed

Lam, H K; Leung, Frank H F

2007-10-01

This correspondence presents the stability analysis and performance design of the continuous-time fuzzy-model-based control systems. The idea of the nonparallel-distributed-compensation (non-PDC) control laws is extended to the continuous-time fuzzy-model-based control systems. A nonlinear controller with non-PDC control laws is proposed to stabilize the continuous-time nonlinear systems in Takagi-Sugeno's form. To produce the stability-analysis result, a parameter-dependent Lyapunov function (PDLF) is employed. However, two difficulties are usually encountered: 1) the time-derivative terms produced by the PDLF will complicate the stability analysis and 2) the stability conditions are not in the form of linear-matrix inequalities (LMIs) that aid the design of feedback gains. To tackle the first difficulty, the time-derivative terms are represented by some weighted-sum terms in some existing approaches, which will increase the number of stability conditions significantly. In view of the second difficulty, some positive-definitive terms are added in order to cast the stability conditions into LMIs. In this correspondence, the favorable properties of the membership functions and nonlinear control laws, which allow the introduction of some free matrices, are employed to alleviate the two difficulties while retaining the favorable properties of PDLF-based approach. LMI-based stability conditions are derived to ensure the system stability. Furthermore, based on a common scalar performance index, LMI-based performance conditions are derived to guarantee the system performance. Simulation examples are given to illustrate the effectiveness of the proposed approach.

Nonlinear resonances in linear segmented Paul trap of short central segment.

PubMed

Kłosowski, Łukasz; Piwiński, Mariusz; Pleskacz, Katarzyna; Wójtewicz, Szymon; Lisak, Daniel

2018-03-23

Linear segmented Paul trap system has been prepared for ion mass spectroscopy experiments. A non-standard approach to stability of trapped ions is applied to explain some effects observed with ensembles of calcium ions. Trap's stability diagram is extended to 3-dimensional one using additional ∆a besides standard q and a stability parameters. Nonlinear resonances in (q,∆a) diagrams are observed and described with a proposed model. The resonance lines have been identified using simple simulations and comparing the numerical and experimental results. The phenomenon can be applied in electron-impact ionization experiments for mass-identification of obtained ions or purification of their ensembles. This article is protected by copyright. All rights reserved.

Applicational possibilities of linear and non-linear (polynomial) regression and analysis of variance. III. Stability determination of pharmaceutical preparations: stability of diclofenac-sodium in Diclofen injections.

PubMed

Arambasić, M B; Jatić-Slavković, D

2004-05-01

This paper presents the application of the regression analysis program and the program for comparing linear regressions (modified method for one-way, analysis of variance), writtens in BASIC program language, for instance, determination of content of Diclofenac-Sodium (active ingredient in DIKLOFEN injections, ampules á 75 mg/3 ml). Stability testing of Diclofenac-Sodium was done by isothermic method of accelerated aging at 4 different temperatures (30 degrees, 40 degrees, 50 degrees and 60 degrees C) as a function of time (4 different duration of treatment: (0-155, 0-145, 0-74 and 0-44 days). The decrease in stability (decrease in the mean value of the content of Diclofenac-Sodium (in %), at different temperatures as a function of time, is possible to describe by, linear dependance. According to the value for regression equation values, the times are assessed in which the content of Diclofenac-Sodium (in %) will decrease by 10%, of the initial value. The times are follows at 30 degrees C 761.02 days, at 40 degrees C 397.26 days, at 50 degrees C 201.96 days and at 60 degrees C 58.85 days. The estimated times (in days) in which the mean value for Diclofenac-Sodium content (in %) will by 10% of the initial values, as a junction of time, are most suitably described by 3rd order parabola. Based on the parameter values which describe the 3rd order parabola, the time was estimated in which Diclofenac-Sodium content mean value (in %) will fall by 10% of the initial one at average ambient temperatures of 20 degrees C and 25 degrees C. The times are: 1409.47 days (20 degrees C) and 1042.39 days (25 degrees C). Based on the value for Fischer's coefficien (F), the comparison of trenf of Diclofenac-Sodium content (in %) shows that, under the influence of different temperatures as a function of time, among them, depending on temperature value, there is: statistically very significant difference (P < .05) at 50 degrees C and lower toward 60 degrees C, i.e. statistically probably significant difference (P > 0.01) at 40 degrees C and lower towards 50 degrees C and there is no statistically significance difference (P > 0.05) at 30 degrees C towards 40 degrees C.

Poster - Thur Eve - 10: Long term stability of VMAT quality assurance parameters using an EPID.

PubMed

Pekar, J; Diamond, K R

2012-07-01

The rapidly growing use of volumetric modulated arc therapy (VMAT) treatments in radiation therapy calls for a quantitative, automated, and reliable quality assurance (QA) procedure that can be used routinely in the clinical setting. In this work, we present a series VMAT QA procedures used to assess dynamic multi-leaf collimator (MLC) positional accuracy, variable dose-rate accuracy, and MLC leaf speed accuracy. The QA procedures were performed using amorphous silicon electronic portal imaging devices (EPID) to determine the long term stability of the measured parameters on two Varian linear accelerators. The measurements were repeated weekly on both linear accelerators for a period of three months and the EPID images were analyzed using custom Matlab software. The results of the picket fence tests indicate that MLC leaf positions can be identified to within 0.11 mm and 0.15 mm for static gantry delivery and VMAT delivery respectively. In addition, the dose-rate, gantry speed and MLC leaf speed tests both show very good stability over the measurement period. The measurements thus far, suggest that a number of the dosimetry tests may be suitable for quarterly QA for Varian iX and Trilogy linacs. However, additional measurements are required to confirm the frequency with which each test is required for safe and reliable VMAT delivery at our centre. © 2012 American Association of Physicists in Medicine.

Charge-transfer complexes of 2,3-dichloro-5,6-dicyano-1,4-benzoquinone with amino molecules in polar solvents

NASA Astrophysics Data System (ADS)

Berto, Silvia; Chiavazza, Enrico; Ribotta, Valentina; Daniele, Pier Giuseppe; Barolo, Claudia; Giacomino, Agnese; Vione, Davide; Malandrino, Mery

2015-10-01

The charge-transfer complexes have scientific relevance because this type of molecular interaction is at the basis of the activity of pharmacological compounds and because the absorption bands of the complexes can be used for the quantification of electron donor molecules. This work aims to assess the stability of the charge-transfer complexes between the electron acceptor 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ) and two drugs, procaine and atenolol, in acetonitrile and ethanol. The stability of DDQ in solution and the time required to obtain the maximum complex formation were evaluated. The stoichiometry and the stability of the complexes were determined, respectively, by Job's plot method and by the elaboration of UV-vis titrations data. The latter task was carried out by using the non-linear global analysis approach to determine the equilibrium constants. This approach to data elaboration allowed us to overcome the disadvantages of the classical linear-regression method, to obtain reliable values of the association constants and to calculate the entire spectra of the complexes. NMR spectra were recorded to identify the portion of the donor molecule that was involved in the interaction. The data support the participation of the aliphatic amino groups in complex formation and exclude the involvement of the aromatic amine present in the procaine molecule.