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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Equicontrollability and the model following problem

Equicontrollability and its application to the linear time-invariant model-following problem are discussed. The problem is presented in the form of two systems, the plant and the model. The requirement is to find a controller to apply to the plant so that the resultant compensated plant behaves, in an input-output sense, the same as the model. All systems are assumed to be linear and time-invariant. The basic approach is to find suitable equicontrollable realizations of the plant and model and to utilize feedback so as to produce a controller of minimal state dimension. The concept of equicontrollability is a generalization of control canonical (phase variable) form applied to multivariable systems. It allows one to visualize clearly the effects of feedback and to pinpoint the parameters of a multivariable system which are invariant under feedback. The basic contributions are the development of equicontrollable form; solution of the model-following problem in an entirely algorithmic way, suitable for computer programming; and resolution of questions on system decoupling.

Curran, R. T.↗
NASA NTRS1986

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

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.

Joshi, S. M.↗
NASA NTRS1978

ORACLS: A system for linear-quadratic-Gaussian control law design

A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

Armstrong, E. S.↗
NASA NTRS1999

Asymptotic Stability of Interconnected Passive Non-Linear Systems

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.

Isidori, A.↗
NASA NTRS1980

Modal methods in optimal control synthesis

Efficient algorithms for solving linear smoother-follower problems with quadratic criteria are presented. For time-invariant systems, the algorithm consists of one backward integration of a linear vector equation and one forward integration of another linear vector equation. Furthermore, the backward and forward Riccati matrices can be expressed in terms of the eigenvalues and eigenvectors of the Euler-Lagrange equations. Hence, the gains of the forward and backward Kalman-Bucy filters and of the optimal state-feedback regulator can be determined without integration of matrix Riccati equations. A computer program has been developed, based on this method of determining the gains, to synthesize the optimal time-invariant compensator in the presence of random disturbance inputs and random measurement errors. The program also computes the rms state and control variables of the optimal closed-loop system.

Bryson, A. E., Jr.↗
NASA NTRS1994

Achieving unequal error protection with convolutional codes

This paper examines the unequal error protection capabilities of convolutional codes. Both time-invariant and periodically time-varying convolutional encoders are examined. The effective free distance vector is defined and is shown to be useful in determining the unequal error protection (UEP) capabilities of convolutional codes. A modified transfer function is used to determine an upper bound on the bit error probabilities for individual input bit positions in a convolutional encoder. The bound is heavily dependent on the individual effective free distance of the input bit position. A bound relating two individual effective free distances is presented. The bound is a useful tool in determining the maximum possible disparity in individual effective free distances of encoders of specified rate and memory distribution. The unequal error protection capabilities of convolutional encoders of several rates and memory distributions are determined and discussed.

Mills, D. G.↗
NASA NTRS1974

Optimal output feedback control of linear systems in presence of forcing and measurement noise

The problem of obtaining an optimal control law, which is constrained to be a linear feedback of the available measurements, for both continuous and discrete time linear systems subjected to additive white process noise and measurement noise was Necessary conditions are obtained for minimizing a quadratic performance function for both finite and infinite terminal time cases. The feedback gains are constrained to be time invariant for the infinite terminal time cases. For all the cases considered, algorithms are derived for generating sequences of feedback gain matrices which successively improve the performance function. A continuous time numerical example is included for the purpose of demonstration.

Joshi, S. M.↗
NASA NTRS1977

Gain and phase margin for multiloop LQG regulators

Multiloop linear-quadratic state-feedback (LQSF) regulators are shown to be robust against a variety of large dynamical linear time-invariant and memoryless nonlinear time-varying variations in open-loop dynamics. The results are interpreted in terms of the classical concepts of gain and phase margin, thus strengthening the link between classical and modern feedback theory.

Safonov, M. G.↗
NASA NTRS1977

Linear tracking systems with applications to aircraft control system design

A class of optimal linear time invariant tracking systems, both in continuous time and discrete time, of which the number of inputs (which are restricted to be step functions) is equal to the number of system outputs, is studied. Along with derivation of equations and design procedures, two discretization schemes are presented, constraining either the control or its time derivative, to be a constant over each sampling period. Descriptions are given for the linearized model of the F-8C aircraft longitudinal dynamics, and the C* handling qualities criterion, which then serve as an illustration of the applications of these linear tracking designs. A suboptimal reduced state design is also presented. Numerical results are given for both the continuous time and discrete time designs.

Lee, W. H.↗
NASA NTRS1987

Estimability and regulability of linear systems

A linear state-space system will be said to be estimable if in estimating its state from its output the posterior error covariance matrix is strictly smaller than the prior covariance matrix. It will be said to be regulable if the quadratic cost of state feedback control is strictly smaller than the cost when no feedback is used. These properties, which are shown to be dual, are different from the well known observability and controllability properties of linear systems. Necessary and sufficient conditions for estimability and regulability are derived for time variant and time invariant systems, in discrete and continuous time.

Baram, Yoram↗
NASA NTRS1987

Estimability and regulability of linear systems

A linear state-space system will be said to be estimable if in estimating its state from its output the posterior error covariance matrix is strictly smaller than the prior covariance matrix. It will be said to be regulable if the quadratic cost of state feedback control is strictly smaller than the cost when no feedback is used. These properties, which are are shown to be dual, are different from the well known observability and controllability properties of linear systems. Necessary and sufficient conditions for estimability and regulability are derived for time variant and time invariant systems, in discrete and continuous time.

Baram, Yoram↗
NASA NTRS1992

On an origin of numerical diffusion: Violation of invariance under space-time inversion

The invariant properties of the convection equation du/dt + adu/dx = 0 (where d is the partial differential operator) with respect to spatial reflection, time reversal, and space-time inversion are studied. Generally, a finite-difference analog of this equation may possess some or none of these properties. It is shown that, under certain conditions, the von Neumann amplification factor of an analog satisfies a special relation for each invariant property this analog possesses. Particularly, an analog is neutrally stable and thus free of numerical diffusion if it possesses the invariant property related to space-time inversion. It is also explained why generally (1) an upwind scheme possesses neither the invariant property related to spatial reflection nor that related to space-time inversion, and (2) an explicit scheme possesses neither the invariant property related to time reversal nor that related to space-time inversion. Extension to the viscous case and a remarkable connection between the current work and a new numerical framework for solving conservation laws are also discussed.

Chang, Sin-Chung↗
NASA NTRS1983

Model reference adaptive control for systems with time varying model commands

Model reference adaptive control is applied to linear time invariant systems for the case of arbitrary time varying model commands. Asymptotic stability is guaranteed, provided that the output stabilized transfer matrix is strictly positive real. Only output measurements are needed. Neither perfect model following nor explicit parameter identification is required. Simulations show the scheme to be capable of guaranteeing stability when the model inputs are time varying.

Abida, L.↗
NASA NTRS1989

Passivity In Analysis Of Robustness Of A Control System

Robustness margin (measure of degree of passivity) defined. Paper presents new approach to analysis of stability of multivariable feedforward-and-feedback control system consisting of exponentially stable linear time-invariant (LTI) feedforward subsystem and nonlinear time-varying (NTV) or dynamic feedback subsystem. New method based on notion of passivity, quantified by robustness margin. Margin provides bound on magnitudes of perturbations, below which perturbations will not make system unstable.

Wen, John Ting-Yung↗
NASA NTRS1996

LTI Representations of Adaptive Systems with Tap Delay-Line Regressors under Sinusoidal Excitation

It is shown that and adaptive system whose regressor is formed by tap delay-line (TDL) filtering of a multitone sinusoidal signal is representable as a parallel connection of a linear time-invariant (LTI) block and a linear time-varying (LTV) block. Furthermore, a norm-bound (induced 2-norm) is computed explicity on the LTV block and is shown to decrease as N -1 where N is the number of taps.

adaptive↗
NASA NTRS1985

Robustness of velocity feedback controllers for flexible spacecraft

The robustness properties of collocated velocity feedback controllers used for damping enhancement in large, flexible space structures are investigated. It is proved that the closed-loop system using such controllers is asymptotically stable in the large when: (1) unmodeled linear time-invariant dynamics (such as sensors/actuators) are present, provided that the phase angle of such dynamics is between -90 deg and 90 deg; (2) time-varying or invariant nonlinearities lying in the first and the third quadrant (i.e., belonging to the /0, infinity/ sector) are present; or (3) sector-type nonlinearities following first-order stable dynamics are present in the feedback loop.

Joshi, S. M.↗
NASA NTRS1990

Analytical study of the origin and behavior of asymmetric vortices

An hypothesis advanced originally to explain computational observations is supported by theoretical considerations: The asymmetric mean flow observed on bodies of revolution at moderate to high angles of attack is the result of a convective instability of an originally symmetric flow to a time-invariant space-fixed disturbance. Additionally, the time-dependent fluctuations characteristic of the flow at higher angles of attack (up to 90 deg) are the result of an absolute instability of an originally steady flow to a small temporal disturbance of finite duration. Within a common domain, the instability mechanisms may coexist. The experimentally confirmed existence of bistable states, wherein the side-force variation with nose roll angle approaches a square-wave distribution, is attributed to the dominant influence of a pair of trailing vortices from the ogival forebody. Their existence is made possible by the appearance of foci of separation in the skin-friction line pattern beyond a critical angle of attack. The extreme sensitivity of the asymmetric flow orientation to nose geometry, demonstrated experimentally, is attributed to the presence of an indeterminate phase in the family of possible solutions for the three-dimensional wave system.

Tobak, Murray↗