An interactive parameter space method for robust performance in mixed sensitivity problems

This paper presents an interactive graphical method to determine the set of fixed-order stabilizing controllers achieving robust performance, in the mixed sensitivity framework. The method is limited to single-input/single-output (SISO) systems but offers significant advantages over traditional loop gain shaping methods such as H^∞ and μ-synthesis. It can handle pure time delays in an exact manner and the weighting functions need not be rational. The technique translates frequency-domain weighting functions and stability constraints into the parameter space and thus gives the user more insights into the design than conventional methods. By virtue of producing the required parameter space region for the frequency response criteria, subsequent optimization of secondary objectives is possible. The controllers obtained are of lower order for comparable performance than those produced by current H^∞ and μ-synthesis techniques. The method is particularly well-suited to robust control problems where frequency-domain constraints emerge from the analysis of nonparametric uncertainties in the system and also to control problems where the frequency domain loop shaping is used to achieve time-domain specifications