Representations of Uncertainty and Robustness Tests for Multivariable Feedback Systems

Abstract

In this essay we examine several different ways in which uncertainty can be represented in a control system. In general, not all of the commonly used representations can adequately represent all possible perturbations in the plant model. Given adequate representations of uncertainty we present three kinds of robustness test. The first kind is derived from Nyquist’s stability criterion, and can be used providing the plant and perturbed plant models have the same number of unstable poles. The second is derived from an inverse Nyquist stability criterion, and can be used providing the plant and perturbed plant models have the same number of non-minimum phase zeros. The third is a combination of the other two tests, but does not require the plant and perturbed plant models to have either the same number of poles or the same number of zeros in the right-half complex plane.