New methodology for analytical and optimal design of fuzzy PID controllers

This paper describes a new methodology for the systematic design of fuzzy PID controllers based on theoretical fuzzy analysis and genetic-based optimization. An important feature of the proposed controller is its simple structure. It uses a one-input fuzzy inference with three rules and at most six tuning parameters. A closed-form solution for the control action is defined in terms of the nonlinear tuning parameters. The nonlinear proportional gain is explicitly derived in the error domain. A conservative design strategy is proposed for realizing a guaranteed-PID-performance (GPP) fuzzy controller. This strategy suggests that a fuzzy PID controller should be able to produce a linear function from its nonlinearity tuning of the system. The proposed PID system is able to produce a close approximation of a linear function for approximating the GPP system. This GPP system, incorporating with a genetic solver for the optimization, will provide the performance no worse than the corresponding linear controller with respect to the specific performance criteria (i.e., response error, stability, or robustness). Two indexes, linearity approximation index (LAI) and nonlinearity variation index (NVI), are suggested for evaluating the nonlinear design of fuzzy controllers. The proposed control system has been applied to several first-order, secondorder, and fifth-order processes. Simulation results show that the proposed fuzzy PID controller produces superior control performance than the conventional PID controllers, particularly in handling nonlinearities due to time delay and saturation.