Design and analysis of a fuzzy proportional-integral-derivative controller

This paper describes the desi,on principle, tracking performance and stability analysis of a fuzzy proportional-integral (PI) plus a derivative (D) controller. First, the fuzzy PI+D controller is derived from the conventional continuous-time linear PI+D controller. Then, the fuzzification, control-rule base, and defuzzification in the design of the fuzzy controller are discussed in detail. The resulting controller is a discrete-time fuzzy version of the conventional PI+D controller, which has the same linear structure in the proportional, integral and derivative parts but has nonconstant gains: the proportional, integral and derivative gains are nonlinear functions of the input signals. The new fuzzy PI+D controller thus preserves the simple linear structure of its conventional counterpart yet enhances the self-tuning control capability. Computer simulation results have demonstrated the advantages of the fuzzy controller, particularly when the process to be controlled is nonlinear. After a brief stability analysis, where a simple and realistic sufficient condition for the bounded-input/bounded-output stability of the overall feedback control system was derived, several computer simulation results are shown to compare with the conventional PI+D controller. Computer simulation results have shown the new fuzzy controller indeed has satisfactory tracking performance.