Theoretic and genetic design of a three-rule fuzzy PI controller

This paper describes the optimal design of a fuzzy PI controller based on theoretical fuzzy analysis and genetic-based optimizations. The most important feature of the proposed controller is its simple structure, consisting of a single input variable, three rules, and four design parameters. The four parameters are a fuzzy integral gain, a scalar factor for crisp output, and two parameters for the allocation of the membership functions of the fuzzy sets. A closed-form solution for the proportional control action is defined in terms of the design parameters. The nonlinear proportional gain is explicitly presented in the error domain. Through genetic algorithms, the optimal design of the system is achieved. This new method has been applied for two problems, a first-order process with/without a time delay, and an overdamped second-order process. A practical limitation on actuator saturation is considered in the simulation. Good simulation results were obtained using the present method, which produced superior control performance in handling nonlinearities due to time delay and saturation