Application of repetitive controllers to nonlinear plants

Repetitive controllers are generally applied to reject periodic disturbances and track periodic reference signals with a known period. Their design is based on 'the internal model principle' proposed by Francis and Wonham (1975). The work described applies a finite-dimensional repetitive controller to two different classes of nonlinear plants. Simulation results show asymptotic tracking of the periodic reference signal by the proposed repetitive controller in closed loop up to the Nth harmonic frequency. A proof of robustness of the repetitive control system to small nonlinearities, like actuator nonlinearities is provided. Further an industrial application of the proposed controller to the optical turning process is discussed. For this application a modified repetitive controller is also presented which can track a quasi-periodic reference signal with a slowly changing amplitude.