A frequency domain optimisation algorithm for simultaneous design of performance weights and controllers in μ-synthesis

A novel iterative procedure is proposed in this paper as a valuable alternative/complement to D-K iterations frequently used in μ-synthesis. This new procedure gives both a robustly stabilising controller and performance weights which together achieve a closed-loop μ-value which is slightly less than unity, thereby immediately guaranteeing robust performance. The performance weights given by this algorithm maximise the achieved performance for the particular plant set considered according to some sensible cost function. The designer is only required to specify the desired directionality of the optimisation according to his engineering insight. Of course, a sensible plant set and a sensible directionality for the optimisation are still required for a sensible control problem. The algorithm proposed here thus eliminates the trial and error process usually adopted by designers in selecting such performance weights