Application of grey wolf optimization in fuzzy controller tuning for servo systems

This chapter presents aspects concerning the tuning of fuzzy controllers (FCs) by grey wolf optimization (GWO) algorithms with focus on cost-effective Takagi-Sugeno proportional-integral fuzzy controllers (T-S PI-FCs). GWO is one of the latest swarm intelligence algorithms, which has been developed by mimicking grey wolf social hierarchy and hunting habits. T-S PI-FCs are applied to servo systems, represented as non-linear processes characterized by second-order dynamics with an integral component, variable parameters, a saturation and dead-zone static non-linearity. The variable parameters of the processjustify the need to design fuzzy control systems with a reduced process parametric sensitivity. Four optimization problems are defined with this regard, with the tuning parameters ofT-S PI-FCs considered as vector variables and with objective functions that include the weighted output sensitivity function of the state sensitivity model with respect to process parametric variations. GWO is next employed in the minimization of these objective functions. Simulation and experimental results are given for a case study that deals with the optimal tuning of T-S PI-FCs for the angular position control of a laboratory non-linear servo system. The process gain is variable, and fuzzy control systems with a reduced process gain sensitivity are offered.