Robust disturbance rejection in repetitive-control system based on improved equivalent-input-disturbance approach

This paper concerns disturbance rejection for a repetitive-control system (RCS) with unknown time-varying uncertainties and nonlinearity. The design of the RCS is based on the concept of equivalent input disturbance (EID). First, an EID estimator is constructed through a state observer with dynamic coefficient matrix that effectively estimates the total effect of the uncertainties and nonlinearity on the output of the plant. Next, a robust globally uniformly ultimately bounded stability condition for the EID-based RCS is derived in the form of a linear matrix inequality. Then, the methods of designing a modified repetitive controller, a state-feedback controller, and an EID estimator are explained. Finally, simulation results demonstrate the validity of the method.