Disturbance rejection in repetitive controllers

The p-integrator is a digital controller that learns from previous experience executing a repetitive command in order to improve its performance in future repetitions. This class of repetitive controller is an analog of the integral controller of classical control theory. This paper addresses several issues related to the performance of the p-integrator. This is followed by a derivation that will demonstrate the repetitive disturbance rejection capabilities of the controller. The effect of the tracking performance in practical implementations with prefiltering and postfiltering devices are studied - using an exact and approximate formulation. Relations showing the actual system response during steady state operation with these filters are derived. The results are then extended to include the tracking error performance of systems subjected to repetitive disturbances. Finally, the system response between sample times is developed.