B. Porter

Singular perturbation analysis of the transfer function matrices of a class of multivariable linear systems

Singular perturbation methods are used to demonstrate that the transfer function matrices of multivariable linear systems containing small ‘parasitic’ elements have a distinctive structure which can be exploited in the design of controllers fur systems of this class by the application of frequency-domain methods.

Closed-loop eigenstructure assignment by state feedback in multivariable linear systems

In this paper, results are presented which facilitate the complete exploitation of state feedback in the assignment of the entire closed-loop eigenstructure of multivariable linear systems. These results provide a method for the direct computation of the state-feedback matrix which assigns prescribed Jordan canonical forms, eigenvectors, and generalized eigenvectors to the plant matrices of closed-loop systems. This method is illustrated by assigning the entire closed-loop eigenstructure of a third-order two-input discrete-time system in such a way that the resulting closed-loop system exhibits finite settling time behaviour.

Eigenvalue and eigenvector sensitivities in linear systems theory

Simplo and explicit derivations arc given of expressions for the eigenvalue and eigenvector sensitivity coefficients for the fundamental eigenproblem associated with tho behaviour of linear systems governed by equations of the form xxa0=xa0Ax. Such expressions relating changes in the eigenvalues and eigenvectors of tho matrix A to changes in A have been given by numerous authors since tho early work of Jaeobi (1846). These expressions have been given in various forms and from different points of view, and have also heen derived by a number of different methods. Thus, the sensitivity cigenproblem has been viewed as a problem in numerical analysis (Faddeev and Faddecva 1963, Wilkinson 1965), as a problem in perturbation theory (Bellman 1960, Wilkinson 1965), and as a problem in linear systems theory (Laughton HI64, Mann and Marshall 1965, Mann et al. 1965, Van Ness et al. 1965, Rosenbrock 1965, Morgan 1966 a, b, Nicholson 1967 a, b). It is hoped that this paper may help to clarify n.ny obscurities which may hav...

Design of dead-beat controllers and full-order observers for linear multivariable discrete-time plants

Abstract In this paper a method based upon the use of the Brunovsky canonical form (Brunovsky 1966) is presented for the design of controllers and full-order observers for a class of linear multivariable discrete-time plants with inaccessible state vectors

Algorithm for closed-loop eigenstructure assignment by state feedback in multivariable linear systems

Abstract In this paper an algorithm is presented which greatly facilitates the complete exploitation of state feedback in the assignment of the entire closed-loop eigenstructure of controllable multi-input systems. This algorithm is a generalization of the algorithm of MacLane and Birkhoff (1968) for the computation of a basis for the null space of a matrix and is ideally suited to digital computer implementation. The algorithm readily yields the vectors which are required (Porter and DAzzo 1978) for the simultaneous assignment of Jordan canonical forms, eigenvectors, and generalized eigenvectors to the plant matrices of closed-loop controllable multivariable linear systems. The effectiveness of the algorithm is illustrated by assigning the entire closed-loop eigenstructure of a third-order two-input discrete-time system in such a way that the resulting closed-loop system exhibits time-optimal behaviour.

Design of tunable set-point tracking controllers for linear multivariable plants

It is shown that, for a large class of multivariable plants, the design of both analogue and digital set-point tracking controllers can be readily effected on the basis only of structural plant properties which are directly derivable from the plant transfer function matrices. This general design methodology is illustrated by designing both an analogue and a digital set-point tracking controller for a boiler furnace

Singular perturbation methods in the design of stabilizing feedback controllers for multivariable linear systems

Abstract Singular perturbation methods are used to reduce the design of stabilizing feedback controllers for a class of (n + m)th order multivariable linear systems to the design of stabilizing feedback controllers for an associated class of nth order systems obtained by ignoring ‘ parasitic ’ elements which correspond to the presence of a small parameter in the state equations of the (n + m)th order systems.

Eigenvalue assignment in linear multivariable systems by output feedback

The assignment of arbitrary cloacd-loop eigenvalue spectra by output feedback is investigated in the special ease of systems for which the set of state-feedback matrices P which yield a desired closed-loop eigenvalue spectrum is finite and can be readily generated. In particular, a simple necessary and sufficient condition for the existence of an output-feedback matrix K corresponding to a prescribed state-feedback matrix P is established which also leads directly to the matrix K in cases when the condition is satisfied. The condition derived in this paper requires neither the computation of generalized inverse matrices (Munro and Vardulakis 1973), nor the transformation of state vectors (Patel 1974), nor the determination of Luenberger canonical forms (Vardulakis 1976), and indicates very clearly that an output-feedback matrix K corresponding to a prescribed state-feedback matrix P exists only in very special circumstances.

Performance characteristics of multi-variable model-reference adaptive systems synthesized by Liapunov's direct method†

The performance characteristics of multi-variable model-reference adaptive systems synthesized by Liapunovs direct method are investigated. Computer results obtained by simulating the behaviour of several such systems subjected to both constant and time-varying inputs are presented and discussed in some detail. In each case the time variations of the state variables, the error variables, the adaptive parameters, the Liapunov function and the time-derivative of the Liapunov function are given.

Multivariable time-invariant linear systems with input-derivative control: state controllability and eigenvalue assignability†

Abstract Necessary and sufficient conditions for the state controllability of multivariable time-invariant linear systems with input-derivative control are derived. The conditions ore expressed explicitly in terms of the plant and input matrices associated with systems of this class. The relationship between state controllability and eigenvalue assignability for such systems is also discussed