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Repetitive control method is well known for its high performances in feedback systems that are subject to periodic exogenous inputs. This paper reviews the theory and applications of repetitive control based on both the internal model and external model, together with some repetitive control methods for nonlinear plants.

A new finite-dimensional repetitive controller of plug-in type is proposed for high precision velocity control of servomechanisms subject to significant nonlinear disturbance torque. The disturbance torque dealt with depends on system states, i.e. velocity and position, and is assumed to be continuously periodic in position and locally Lipschitzian in velocity, which can address most cases in practice. A sufficient condition for the effectiveness of the proposed method is derived by the application of fix point theorem. It should be noted that this condition is necessary for learning the algorithms utilizing the period-invariance property of the system. With the proposed finite-dimensional repetitive controller, the steady-state velocity error can be reduced to a very low degree. The effectiveness of the proposed method is confirmed by simulation results.