Parameter-robust control design using a minimax method

A controller design method is presented that gives the best linear-quadratic-Gaussian closed-loop performance over a set of worst plant parameter changes. The design algorithm combines a multiplant optimal design code, SANDY, with a new worst parameter algorithm that uses a quadratic norm on parameter changes. The minimax algorithm is unique in the way it weights worst plants to expand the stable region in the parameter space. The method is applied to a two-mass/spring American Control Conference "benchmark" problem. A minimax controller is first designed for the case where the spring constant alone is uncertain. Next, several minimax controllers, including a reduced-order design, are synthesized for the benchmark problem where both masses and the spring constant are uncertain. The results show that minimax control provides near-optimal nominal performance with significant robustness and parameter margin improvements.