Deep optimization design of 2D repetitive control systems with saturating actuators: An adaptive multi-population PSO algorithm

This paper presents an optimization design method for a two-dimensional (2D) modified repetitive control system (MRCS) with an anti-windup compensator. Using lifting technology, a 2D hybrid model of the MRCS considering actuator saturation is established to describe the control and learning of the repetitive control. A linear-matrix-inequality (LMI)-based sufficient condition is derived to ensure the stability of the MRCS. Two tuning parameters, the selection of which is critical to the system design, are used in the LMI to adjust the control and learning, and hence the reference-tracking performance. A new cost function, developed through time domain analysis, directly evaluates the control performance of the system without calculating control errors, thus reducing the optimization time. Based on this cost function, an adaptive multi-population particle swarm optimization algorithm is presented to select an optimal pair of tuning parameters in which multiple populations cooperatively search in non-intersecting search intervals. An anti-windup term is added between the low-pass filter and the time delay in the modified repetitive controller to mitigate the undesirable effect of actuator saturation on system performance and stability. Simulations and experiments on the speed control of a rotation control system demonstrate the validity of the approach.