Nonlinear Repetitive Control for Mitigating Noise Amplification

Repetitive control can lead to high performance by attenuating periodic disturbances completely, yet it may amplify non-periodic disturbances. The aim of this paper is to achieve both fast learning and low errors in repetitive control. To this end, a nonlinear learning filter is introduced that distinguishes between periodic and non-periodic errors based on their typical amplitude characteristics to adapt the extent to which they are included in the repetitive controller. Convergence conditions for the nonlinear repetitive control system are derived by casting the resulting closed-loop as a discrete-time convergent system. Simulation results of the proposed approach demonstrate fast learning and small errors.