Robust PD-type iterative learning control in a finite-frequency range for nonlinear systems based on T–S fuzzy models

Abstract

Considering the complexity and universality of nonlinearity in control systems, it is of great significance to investigate the robust proportional-derivative type (PD-type) iterative learning control (ILC) design for repetitive nonlinear systems in the Takagi–Sugeno (T–S) forms, Different from existing ILC laws, the proposed ones are designed in the finite-frequency domain. The nonlinear systems are described by Roesser-type two-dimensional (2D) uncertain T–S fuzzy models with non-repetitive disturbances. The main contribution of this article is that the novel fuzzy ILC method is proposed by exploiting the 2D linear systems theory. Further to this, the proposed design guarantees the robust asymptotic stability and finite-frequency 2D H _∞ performance of the resulting fuzzy systems, and the controller gains are obtained by solving a set of linear matrix inequality (LMI) constraints. Through the simulation of a nonlinear single-link rigid robot system, our major findings are that the proposed fuzzy control algorithm can lead to steady-state tracking performance and good robustness against non-repetitive disturbances and uncertainties, and the PD-type ILC performs significantly better than the P-type ILC, the former can efficiently improve the control effect.