Robustness properties of feedback systems with multiple sources of modelling uncertainty.

Abstract

This thesis addresses problems in robustness analysis and design of linear multivariable feedback systems with several sources of modelling uncertainty. The problem of maintaining stability and performance robustness in the presence of plant uncertainty is of fundamental importance and has received considerable attention. A useful tool for such problems is furnished by structured singular value analysis. However, because the structured singular value is a complicated function of the system data and can only be calculated via a numerical optimization procedure, it is often difficult to obtain insights useful in design. The objective of this work is to develop such important insights. We first present a general analysis approach for robustness problems that may be studied using the structured singular value analysis. The first step of this approach is to identify certain important parameters which characterize how several sources of uncertainty may interact to cause robustness difficulties. The second step involves deriving bounds upon the structured singular value that explicitly display its dependence upon the plant, compensator, design specification and uncertainty description. Once these tasks are accomplished, we utilize the bounds and insights to study a class of typical multivariable design problems that are inherently difficult. We specifically investigate potential design difficulties that often arise due to the plant ill-conditioning. A robustness indicator is developed to quantify the degree of such difficulty, which is shown to depend upon the size of the plant condition number as well as its directionality properties. We further propose a loop-shaping design strategy that is useful in resolving this difficulty.