An optimal fuzzy PID controller design based on conventional PID control and nonlinear factors

Abstract

This paper proposes an optimal fuzzy proportional-integral-derivative (PID) controller design based on conventional PID control and nonlinear factors. With the equivalence between fuzzy logic controllers (FLCs) and conventional PID controllers, a conventional PID controller design can be rapidly transformed into an equivalent FLC by defining the operating ranges of the input/output of the controller. The proposed nonlinear factors can further tune the nonlinearity of the membership functions (MFs) distributed in the operating ranges. In this manner, a fuzzy PID controller can be developed with less parameters and optimized by using the genetic algorithm (GA). In addition, the aforementioned equivalent FLC can act as one individual in the initial population of GA, and significantly enhances the GA efficiency. Simulation results demonstrate the feasibility of this technique. This resulted in an optimal fuzzy PID controller design with only eight parameters with a concise controller structure, and most importantly, the optimal fuzzy PID controller design is now more systematic.