Repetitive Control Based on Multi-Stage PSO Algorithm with Variable Intervals for T–S Fuzzy Systems

Abstract

This study presents a repetitive control method based on a multi-stage particle swarm optimization (PSO) algorithm with variable intervals to enhance the tracking performance of Takagi–Sugeno (T–S) fuzzy systems. First, a T–S fuzzy model is used to describe a nonlinear system. A modified repetitive control structure with two repetitive loops guarantees the tracking accuracy of periodic signals. Taking advantage of the two-dimensional (2D) property with continuous control and discrete learning, a continuous-discrete 2D model is presented to describe the nonlinear repetitive control system. Next, a multi-stage PSO algorithm with variable intervals searches for the best parameter combination in the linear matrix inequality-based stability condition to regulate the control and learning actions, which avoids a suboptimal solution and guarantees high control accuracy. Finally, an application to control the speed of synchronous motor with a permanent magnet demonstrates the validity of the method, and comparisons with related methods show its superiority.