Worst Case Analysis of a MIMO Mass Spring Damper System Using the Skew Structured Singular Value

Authors:	Hayes Martin, University of Limerick, Ireland Halton Mark K., University of Limerick, Ireland Iordanov Petar I., National University of Ireland, Maynooth, Ireland
Topic:	2.5 Robust Control
Session:	Parametric Robustness
Keywords:	Robust Analysis; Real Parametric Uncertainty; Skew Structured Singular Value; Control Education

Abstract

This paper considers the application of the structured singular value, mu, and the skew structured singular value, abbreviated skew mu, to the worst case analysis of a (deceptively) simple MIMO double mass-spring-damper system subject to parametric uncertainty. This example highlights some pertinent outstanding mu analysis questions, namely the effect of strictly real, possibly repeated parameters and the limitations of classical grid based methods. It is shown that by suitable transformation of the original mu problem, and the use of skew mu to calculate the worst case, that more reliable and certifiably safe answers to the analysis question are determined. A comparison with conventional mu analysis methods is presented.