Simple methods for identifying linear systems from frequency or time response data
Decomposing method for linear transfer functions identification from frequency or time response, using Cauer form continued fraction expansion
Chen, C. F.↗
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A first-order Lyapunov robustness method for linear systems with uncertain parameters
A method for stability-robustness analysis based on a quadratic Liapunov function that varies linearly with uncertainty parameters is derived. Linear time-invariant systems with structured uncertainties are discussed. The Liapunov function is optimized numerically to maximize the robustness region in parameter space. Numerical results are given for four examples in which the first-order method is compared to previous Liapunov methods. While the zero-order method is slightly better than the first-order method for one example, the first-order method is clearly superior in the other three (more realistic) examples. The first-order method is especially superior for the active control of flexible structures, where robustness with respect to (1) unmodeled coupling between modeled modes and (2) unmodeled modes is important. For such applications, the first-order method is much better at detecting the increased robustness associated with increased separation between frequencies.
Leal, M. A.↗
On the adaptive control of linear systems using the open-loop-feedback-optimal approach.
This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with unknown or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal (O.L.F.O.) method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first order systems are presented.
Ku, R.↗
On the adaptive control of linear systems using the open-loop-feedback-optimal approach.
This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with uncertain or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal (OLFO) method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first-order systems are presented.
Ku, R.↗
Identification of linear system models and state estimators for controls
The following paper is presented in viewgraph format and covers topics including: (1) linear state feedback control system; (2) Kalman filter state estimation; (3) relation between residual and stochastic part of output; (4) obtaining Kalman filter gain; (5) state estimation under unknown system model and unknown noises; and (6) relationship between filter Markov parameters and system Markov parameters.
Chen, Chung-Wen↗
Average correlation functions in on-line testing of linear systems
This paper is a report on new methods for on-line testing of single-input/single-output linear and time-invariant systems. No interruption of system operation is necessary, since the signals used in this test procedure are the normal operating signals. Test results indicate that detectable system errors using finite amounts of data are well within tolerance for normal operation in all but the most stringent applications.
Mix, D. F.↗
Controllability of higher order linear systems.
Dynamical system with time evolution described by second order linear differential equation in complex Banach space, discussing controllability
Fattorini, H. O.↗
Symmetric linear systems - An application of algebraic systems theory
Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.
Hazewinkel, M.↗
A computational method for the determination of the response of a linear system
A number of issues are discussed relating to the analysis of a linear damped oscillator equation with a forcing term where the right side of the equation, g(t), is known only at fixed, equal time intervals. (A particular class of such equations has application to civil earthquake engineering.) It is noted that the equation is not a differential equation because the condition of uniqueness does not obtain. A general computational method is presented for calculating x(t), based on an unconditionally stable finite difference technique. The work generalizes the results given in the recent paper of Ly (1984).
Mickens, R. E.↗
Forced periodic vibration of unsymmetric piecewise-linear systems
The forced steady response of a single degree of freedom system involving a large nonlinearity, represented by unsymmetric piecewise-linear stiffness, is determined by a harmonic balance Newton-Raphson method with the application of the fast Fourier transformation (FFT) algorithm. All possible subharmonic, harmonic, and superharmonic responses are sought. The responses of two systems involving subharmonic and superharmonic dominant motions are calculated by the newly developed method and compared with previously published findings. The results obtained by using this method reveal the details of the response of the systems more efficiently than previous methods.
Choi, Y. S.↗
Partitioned Matrices for Combined Linear Systems
Multiple-input, multiple-output mathematical models combined. Report presents mathematical background for combination of linear multiple-input, multiple-output equations of subsystems into overall matrix equations for whole system. Development of such system mathematical models essential for design of complicated control systems.
Duke, Eugene L.↗
A geometric approach to failure detection and identification in linear systems
Using concepts of (C,A)-invariant and unobservability (complementary observability) subspaces, a geometric formulation of the failure detection and identification filter problem is stated. Using these geometric concepts, it is shown that it is possible to design a causal linear time-invariant processor that can be used to detect and uniquely identify a component failure in a linear time-invariant system, assuming: (1) The components can fail simultaneously, and (2) The components can fail only one at a time. In addition, a geometric formulation of Beard's failure detection filter problem is stated. This new formulation completely clarifies of output separability and mutual detectability introduced by Beard and also exploits the dual relationship between a restricted version of the failure detection and identification problem and the control decoupling problem. Moreover, the frequency domain interpretation of the results is used to relate the concepts of failure sensitive observers with the generalized parity relations introduced by Chow. This interpretation unifies the various failure detection and identification concepts and design procedures.
Massoumnia, M. A.↗
Optimal Regulator Algorithms For The Control Of Linear Systems (ORACLS)
Control theory design package offers engineer full range of subroutines to manipulate and solve Linear-Quadratic-Gaussian types of problems. ORACLS is rigorous tool, intended for multi-input and multi-output dynamic systems in both continuous and discrete form. Written in FORTRAN.
Frisch, Harold P.↗
A block iterative LU solver for weakly coupled linear systems
A hybrid technique, called the block iterative LU solver, is proposed for solving the linear equations resulting from a finite element numerical analysis of certain fluid dynamics problems where the equations are weakly coupled between distinct sets of variables. Either the block Jacobi iterative method or the block Gauss-Seidel iterative solver is combined with LU decomposition.
Cooke, C. H.↗
Upper bounds for convergence rates of vector extrapolation methods on linear systems with initial iterations
The application of the minimal polynomial extrapolation (MPE) and the reduced rank extrapolation (RRE) to a vector sequence obtained by the linear iterative technique x(sub j) + 1 = Ax(sub j) = b,j = 1,2,..., is considered. Both methods produce a two dimensional array of approximations s(sub n,k) to the solution of the system (I - A)x = b. Here, s(sub n,k) is obtained from the vectors x(sub j), n is less than or equal to j is less than or equal to n + k + 1. It was observed in an earlier publication by the first author that the sequence s(sub n,k), k = 1,2,..., for n greater than 0, but fixed, possesses better convergence properties than the sequence s(sub 0,k), k = 1,2,.... A detailed theoretical explanation for this phenomenon is provided in the present work. This explanation is heavily based on approximations by incomplete polynomials. It is demonstrated by numerical examples when the matrix A is sparse that cycling with s(sub n,k) for n greater than 0, but fixed, produces better convergence rates and costs less computationally than cycling with s(sub 0,k). It is also illustrated numerically with a convection-diffusion problem that the former may produce excellent results where the latter may fail completely. As has been shown in an earlier publication, the results produced by s(sub 0,k) are identical to the corresponding results obtained by applying the Arnoldi method or generalized minimal residual scheme (GMRES) to the system (I - A)x = b.
Sidi, Avram↗
Analysis and application of minimum variance discrete linear system identification
An on-line minimum variance (MV) parameter identifier is developed which embodies both accuracy and computational efficiency. The formulation results in a linear estimation problem with both additive and multiplicative noise (AMN). The resulting filter which utilizes both the covariance of the parameter vector itself and the covariance of the error in identification is proven to be mean-square convergent and mean-square consistent. The MV parameter identification scheme is then used to construct a stable state and parameter estimation algorithm.
Kotob, S.↗
Some estimation formulae for continuous time-invariant linear systems
In this brief paper we examine a Riccati equation decomposition due to Reid and Lainiotis and apply the result to the continuous time-invariant linear filtering problem. Exploitation of the time-invariant structure leads to integration-free covariance recursions which are of use in covariance analyses and in filter implementations. A super-linearly convergent iterative solution to the algebraic Riccati equation (ARE) is developed. The resulting algorithm, arranged in a square-root form, is thought to be numerically stable and competitive with other ARE solution methods. Certain covariance relations that are relevant to the fixed-point and fixed-lag smoothing problems are also discussed.
Bierman, G. J.↗
Stability of dithered non-linear systems with backlash or hysteresis
A study is conducted of the effect of dither on the nonlinear element of a single-input single-outout feedback system. Nonlinearities are considered with memory (backlash, hysteresis), in the feedforward loop; a dither of a given amplitude is injected at the input of the nonlinearity. The nonlinearity is followed by a linear element with low-pass characteristic. The stability of the dithered system and an approximate equivalent system (in which the nonlinearity is a smooth function) are compared. Conditions on the input and on the dither frequency are obtained so that the approximate-system stability guarantees that of the given hysteretic system.
Desoer, C. A.↗