Showing papers by "Edward J. Davison published in 1986"

New perturbation bounds for the robust stability of linear state space models

Abstract: In this paper, the problem of robust stability of linear time-invariant systems in state space models is considered. Explicit bounds on linear time-invariant perturbations which do not destabilize the system are given for both unstructured and structured perturbations. These bounds are superior to those reported in the recent literature in two senses: i) they are less conservative and ii) they can be applied to a more general class of systems and perturbations. The bounds are easy to compute numerically. Several simple examples are given to demonstrate the new bounds and compare them with results previously reported.

Decentralized control for descriptor type systems

Abstract: The decentralized robust servomechanism problem [1] for a linear time-invariant system described by: Tx = Ax + Bu + Ew y = Cx + Du + Fw e = y - yref where E may be singular, is considered in this paper, where u, y, e, w denotes the input, output, error and disturbance respectively for the system. In particular, necessary and sufficient conditions to solve the robust decentralized control problem are obtained and a constructive controller synthesis procedure is given for this class of systems. Some simple examples are given to illustrate the result obtained.

Robust control for industrial systems

Abstract: An overview of some problem associated with the robust control of industrial systems, together with some notions/design techniques which are potentially useful, are given in this paper. The paper begins by describing some representative "real system" examples (a large flexible space structure, a nuclear reactor control problem), and examines the type of problems which arise in attempting to control these systems. In this case, it is concluded that an input/output description of a plant does not by itself necessarily provide sufficient information to be able to guarantee robustness properties of a controller. The application of "gain margin" as a measure of robustness, and the parameter structural perturbation problem (which arises from "low frequency" uncertainty) are shown to be important for these classes of problems. Given that it is difficult to obtain even crude models for industrial systems, it is then suggested that a possible effective control design procedure is to use a "tuning regulator for unknown systems" approach, which does not require that a mathematical model of the system be available.

Minimal controller structure realization in decentralized control of unknown systems

Abstract: The following type of problem is considered. Given a linear time-invariant system, assume that there exists a solution to the robust servomechanism problem for the system, for the case of a given class of disturbance/reference input signals. Then it is desired to implement a controller for the system, which solves the robust servomechanism problem, and such that the resulting controller has the property that the number of input/output interconnections required to implement the controller is minimized. Such a controller is said to have a "minimal controller structure realization". The motivation for studying this problem arises in large scale systems, e.g. chemical process control, where, in general, one would like to find the "simplest possible controller", i.e. one which has a minimal controller structure realization, which satisfactorily regulates the system.

Control of Unknown Nonlinear System using Gain-Scheduling Tuning Regulators

Abstract: This paper considers an extension of the tuning regulator design method of [1]-[3] to include a large class of nonlinear multivariable systems. In particular, it is desired to solve the servomechanism problem for an unknown nonlinear plant, which is assumed to be open loop asymptotically stable, for the class of constant set-points and disturbances. In this case, three classes of nonlinear controllers, which are gain-scheduling controllers, are described: (i) error attenuation, (ii) feedforward and (iii) robust controllers, and sufficient conditions by which the resultant closed loop system gives global asymptotic stability and regulation are obtained. The sufficient conditions obtained simplify to the necessary and sufficient conditions [1] associated with the case when the plant is assumed to be described by a linear time-invariant model.

Steady-state interaction indices for decentralized unknown

Abstract: A set of steady-state interaction indices is defined and analyzed in this paper. These indices are found to play a very important role in characterizing solvability conditions of decentralized feedback control problems, and general interaction analysis of multi-loop systems. Furthermore, these interaction indices may be determined experimentally for stable plants, and therefore, no a priori knowledge of the plant model is necessary. Comparison with the relative gain array method shows that the indices are more complete and accurate to apply.

The Decentralized Control Expanding System Problem

Abstract: Suppose a controlled system denoted by S old exists with the property that robust tracking and regulation occurs in each of the system's local control agents. We wish to examine the conditions under which a new subsystem and a new set of local control agents denoted by S new can be connected to S old' so that the new outputs and previous outputs are regulated, without the need for retuning the original control agents. This problem is a generalizaiton of the results obtained in [3] which deals with the case when the control agents of S new are centralized.