An Easily Understandable Grey Wolf Optimizer and Its Application to Fuzzy Controller Tuning

Abstract

This paper proposes an easily understandable Grey Wolf Optimizer (GWO) applied to the optimal tuning of the parameters of Takagi-Sugeno proportional-integral fuzzy controllers (T-S PI-FCs). GWO is employed for solving optimization problems focused on the minimization of discrete-time objective functions defined as the weighted sum of the absolute value of the control error and of the squared output sensitivity function, and the vector variable consists of the tuning parameters of the T-S PI-FCs. Since the sensitivity functions are introduced with respect to the parametric variations of the process, solving these optimization problems is important as it leads to fuzzy control systems with a reduced process parametric sensitivity obtained by a GWO-based fuzzy controller tuning approach. GWO algorithms applied with this regard are formulated in easily understandable terms for both vector and scalar operations, and discussions on stability, convergence, and parameter settings are offered. The controlled processes referred to in the course of this paper belong to a family of nonlinear servo systems, which are modeled by second order dynamics plus a saturation and dead zone static nonlinearity. Experimental results concerning the angular position control of a laboratory servo system are included for validating the proposed method.

Keywords

• Grey Wolf Optimizer
• Takagi-Sugeno proportional-integral fuzzy controllers
• process parametric sensitivity
• stability
• convergence
• parameter settings
• angular position