After the introduction by George Zames in the late 1970’s, H_{∞} control has become an active research, with tons of articles published each year. Despite that academic growth, Its usage in practical industry remains minimal. While most control design software has toolbox functions for H_{∞} synthesis and beyond, the user-unfriendliness of these functions are well-known. It’s fair to say, if you don’t know much about robust control theory, leave them alone. Anyway, in this article we discuss introductory H_{∞} synthesis in a nutshell, and provide examples using functions and features available in Scilab/Xcos, an open-source alternative to MATLAB/Simulink.

To narrow down the scope, we focus on a particular H_{∞} scheme called “mixed-sensitivity approach” in [1]. Controller synthesis is formulated as closed-loop transfer function shaping problems, mostly the sensitivity S, complementary sensitivity T, or some combination like KS, where K is the resulting stabilizing controller, hence the name “mixed-sensitivity.” The discussion is restricted to SISO (single-input/single-output) systems. Moreover, we only show the how-to’s and omit the underlying math/theory to save space. Please consult robust control texts xuch as [1], my all-time favorite on the subject.

Continue reading “H-infinity synthesis with Scilab Part I : Problem Setup” →