Compensator Realizations that Minimize the Closed Loop Pole Sensitivity

Abstract

We investigate optimal realizations of systems and compensators in terms of minimizing a weighted pole sensitivity measure. Our main new result is to derive expressions for the pole sensitivity functions of a closed-loop system with respect to the parameters of the compensator realization and to give the necessary and sufficient condition that must be satisfied by all compensator realizations that minimize a weighted pole sensitivity measure of the closed-loop system. An algorithm is given to solve this optimization problem. Our weighted pole sensitivity minimization scheme is a contribution to the Stability Robustness theory: the optimal realizations have a maximal pole location robustness with respect to numerical errors.