Adaptive Repetitive Control for Periodic Disturbance Rejection with Unknown Period

In this paper, an adaptive repetitive controller (ARC) is proposed to reject periodic disturbance with an unknown period. First, a repetitive controller is designed when the disturbance period is known. In this case, the RC time delay is equal to the period of disturbance. Then, the closed-loop system with the RC controller is analyzed and the effect of RC gain, k, is studied analytically. It is shown that by increasing k, the steady-state error is reduced. It is dependent on the speed of the response convergence. Secondly, an adaptive fast Fourier transform (AFFT) algorithm is proposed to extract the accurate period of disturbance adaptively. Simulation results show that the period is converged to its true value even though varying the period. Also, simulation results about the effect of controller gain are in good agreement with analytical results. Finally, it is shown that the proposed method can decrease the amplitude and energy of output signal significantly.