Repetitive control for asymptotic tracking of periodic signals with an unknown period

Repetitive control schemes for asymptotic tracking and disturbance rejection of periodic signals with an unknown period are presented. A sampled data recursive scheme for identifying the period of a periodic signal with a resolution finer than the sampling interval is presented. Discrete-time self-tuning repetitive controllers, which adapt both the periodic signal period and sampling interval, are proposed based on the period identification scheme. The fine adaptation of the controller sampling interval makes the identified signal period an exact integer multiples of the controller sampling interval and renders a superior tracking performance than that of the conventional fixed sampling interval repetitive controllers. Experimental results on a linear motion system are presented to demonstrate the effectiveness of the proposed control schemes.