Optimal Tuning of a Fuzzy Controller Using Boxs“Complex”Algorithm

A fuzzy control system typically requires“tuning,”or adjuctment of the parameters defining its linguistic variables. Automating this process amounts to applying a second“metacontrol”layer to drive the controller and plant to desired performance levels. Current methods of automated tuning rely on a single crisp numeric functional to evaluate control system performance. A generalization of Box's complex algorithm allows more realistic tuning based on lexicographic aggregation of multiple ordinal scales of performance, such as effectiveness and efficiency. The method is presented and illustrated using a simple inverted pendulum control system.