Estimation and rejection of periodic disturbance in a preview repetitive control system

This paper deals with the problem of two‐dimensional (2D) system‐based preview repetitive control (PRC) with external periodic disturbance for a class of continuous‐time linear systems. First, a repetitive learning‐based estimator (RLE) is incorporated into the controller block to compensate for the periodic disturbance. Next, the PRC law with repetitive learning compensation disturbance is obtained by combining the observer and RLE. Then, we combine the 2D system theory with the linear matrix inequality (LMI) method to derive sufficient conditions to ensure the robustness and stability of the closed‐loop system. Finally, numerical simulations verify the superiority of the proposed method.