A versatile controller design software for unstable systems

Abstract

A new software utility for use with linear unstable plants is developed. The software is in the Matlab environment, and it is based on Youla parameterization. The software optimizes the location of all coprime factors. A two-layer optimization approach is used to arrive at the desired controller. At the inner layer, an exact model-matching optimization procedure is utilized, and a stable design is obtained. This optimization process is then placed inside a nonlinear optimization routine to optimize the assumed locations of the poles of the coprime factors. The software is applied to an unstable plant, and the results are compared with two other techniques.

Introduction

Methods for design of stable linear plants are well established [1]. It is of no surprise that such approaches have also helped advancing the design of stable nonlinear systems [2]. However, there are many good practical problems that are inherently unstable. For example, the attitude control of a space craft is such a problem [3]. There are a number of techniques for control system design of unstable systems [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20]. The most attractive approaches (such as H_∞ approach) are based on one form of factorization [21]; however, still research is in progress to systematize those approaches [22], [23]. One other approach that has received considerable attention is based on the Youla parameterization; however, systematic controller design procedures for model-matching in unstable plants using this approach have received limited attention [4]. The primary contribution of this paper is the developed software that accomplishes the controller design for unstable linear SISO plants. A demonstration example problem is presented, and the results are compared with other works reported in the open literature [4], [24]. The prior related software assumes that plants are stable [25]; and hence coprime factors are selected trivially as noted in the following section. However, if the plant is unstable, then a stable factorization involves selecting nontrivial stable factors; the corresponding optimum location of these factors must be determined. In this work, the prior software [25] is extended to allow determination of optimum pole locations of stable factors.