Evolutionary optimization-based tuning of low-cost fuzzy controllers for servo systems

This paper suggests the optimal tuning of low-cost fuzzy controllers dedicated to a class of servo systems by means of three new evolutionary optimization algorithms: Gravitational Search Algorithm (GSA), Particle Swarm Optimization (PSO) algorithm and Simulated Annealing (SA) algorithm. The processes in these servo systems are characterized by second-order models with an integral component and variable parameters; therefore the objective functions in the optimization problems include the output sensitivity functions of the sensitivity models defined with respect to the parametric variations of the processes. The servo systems are controlled by Takagi-Sugeno proportional-integral-fuzzy controllers (T-S PI-FCs) that consist of two inputs, triangular input membership functions, nine rules in the rule base, the SUM and PROD operators in the inference engine, and the weighted average method in the defuzzification module. The T-S PI-FCs are implemented as low-cost fuzzy controllers because of their simple structure and of the only three tuning parameters because of mapping the parameters of the linear proportional-integral (PI) controllers onto the parameters of the fuzzy ones in terms of the modal equivalence principle and of the Extended Symmetrical Optimum method. The optimization problems are solved by GSA, PSO and SA resulting in fuzzy controllers with a reduced parametric sensitivity. The comparison of the three evolutionary algorithms is carried out in the framework of a case study focused on the optimal tuning of T-S PI-FCs meant for the position control system of a servo system laboratory equipment. Reduced process gain sensitivity is ensured.