Advances in robust control design [extended abstract]

Summary form only given, as follows. The author overviews the exciting developments in the field of Robust Multivariable Feedback Control System Design. The philosophy behind these design methodologies is that in addition to a nominal model of the plant, the designer must have quantitative information about the inevitable modeling errors. Two classes of modeling errors occur simultaneously: (a) parameter errors in the state differential equations, with typical upper and lower bounds on the value of each parameter, and (b) unstructured model errors reflecting neglected dynamics in the sensor, actuator and plant subsystems, for which an upper bound on their worst possible size vs. frequency is available. By stability-robustness synthesis he derives a dynamic multivariable compensator that guarantees closed-loop stability for all "legal" parametric and dynamic modeling errors. By robust-performance synthesis we mean to derive a dynamic multivariable compensator that guarantees not only stability-robustness, but guaranteed command-following and disturbance-rejection performance (this is typically quantified by requiring that the maximum singular value of the sensitivity transfer function matrix of the closed-loop system is below a prespecified fequency-depended performance boundary in the frequency domain, from which one can infer RMS errors and response to worst-case sinusoidal disturbances). He overviews the modern H2 and H-infinity design methodologies, with fiequency-dependent weights, for designing the nominal compensators. We then show how one utilizes the structured singular value framework (mu-synthesis and mixed-mu synthesis) together with the H-infinity design methodology to design robustly stable compensators with robust performance guarantees for all "legal" parametric and dynamic model errors. Open questions and future research directions will also be briefly addressed.