Auto-Tuning Fuzzy PID Control of a Pendubot System

The goal of this paper is to design a fuzzy proportional-integral-derivative (PID) controller to swing up the pendubot and maintain it in an unstable inverted equilibrium position. Different from PID controllers with fixed gains, the fuzzy PID controller is expressed in terms of fuzzy rules such that the PID gains are adaptive and the fuzzy PID controller has more flexibility and capability than the conventional ones. When tuning the fuzzy PID controller, a genetic algorithm (GA) method is proposed, in which the centers and the widths of the Gaussian membership functions, the number of fuzzy control rules, and the PID gains are chosen as parameters to be determined. When defining the fitness function of the genetic algorithm, the concept of multiobjective optimization is used such that the fitness function can be defined in a systematic way. To show the performance and robustness of the fuzzy PID controller, simulation results are presented.