Interactive control system design by a mixed H∞-parameter space method

This paper presents an interactive graphical method to determine sets of stabilizing controllers satisfying any combination of constraints on the sensitivity, complementary sensitivity, and input sensitivity transfer functions. The method is limited to single-input/single-output systems but offers significant advantages over current H^∞ methods. It can handle pure time delays in an exact manner. The weighting functions need not be rational. By virtue of producing the required parameter space region for the frequency response criteria, subsequent direct time-domain optimization is possible. The controllers obtained are of lower order for comparable performance than those produced by current H^∞ techniques. The method is particularly well suited to robust control problems, where frequency domain constraints emerge from the analysis of uncertainties in the system, and also to suboptimal problems, where the frequency-domain loop shaping is used to achieve time-domain specifications