Multivariable Nyquist self-tuning: a general approach

Abstract

An earlier paper showed that the generalised Nyquist approach, although intrinsically a frequency-response approach, can be deployed to produce an effective multivariable self-tuning methodology. The results, however, were confined to the case of plants with open-loop stable poles and characteristic transfer functions whose branch points are all stable. The purpose of the present paper is to develop the framework that applies to the general case. In particular, consideration is given to fractional representations for the branches of the characteristic transfer functions, and algorithms are developed for both the computation of these representations and their implementation within a self-tuning configuration. Consideration is also given to issues of stability. The results of the paper are illustrated by means of numerical examples and the paper is concluded by a design study based on the open-loop unstable chemical reactor.