Design of Fuzzy PI+D and Fuzzy PID Controllers Using Gaussian Input Fuzzy Sets

This paper presents the design of fuzzy PI+D controller and fuzzy PID controller for nonlinear systems using 'Gaussian' membership functions. The fuzzy controllers are derived from their conventional continuous time domain controllers. The controllers are developed by first discretizing the controllers' laws and then progressively deriving the steps necessary to incorporate a fuzzy logic control mechanism into the modifications of the controllers' structure. The resulting controller is a discrete-time fuzzy version of the conventional controller, which has the same linear structure in proportional, integral and derivative parts but has non constant gains. Analytical structures for the fuzzy controllers using 'Gaussian' membership functions are derived. The final version of this fuzzy controller is a computationally efficient over its conventional counter part. Computer simulations are included to demonstrate the effectiveness of the fuzzy controller over its counterpart conventional PID controller.