A robust disturbance rejection method for repetitive control systems with uncertainties

This paper deals with the disturbance rejection problem in a repetitive control system (RCS) with time-varying uncertainties. The RCS is first described in the two-dimensional (2D) form. Next, an equivalent-input-disturbance (EID)-based estimator is incorporated into the 2D RCS to solve the problem of aperiodic disturbance rejection. Under this configuration of the system, while a periodic reference input is tracked by the repetitive controller, both unknown periodic and aperiodic disturbances are compensated for by the EID estimator. A robust stability condition of the RCS is presented in the form of a linear matrix inequality, and the condition is further employed to design the parameters in the RCS. This design method enables preferential adjustment of control and learning actions. Simulations are illustrated to demonstrate the validity of this method.