The importance of smooth updates in producing good error levels in repetitive control

Repetitive control iteratively adjusts the command to a feedback controller in order to eliminate periodic tracking errors. It is seen that repetitive control laws typically produce step or slope discontinuities in the command, and these can produce transient effects that slow the learning process, or influence the steady state error levels. Here we develop methods of causing repetitive control actions to have greater continuity and smoothness, and show that there is significant improvement in performance. Methods include turning on the repetitive control at an appropriate time, waiting for transients to decay and for a zero error crossing before starting the next repetition updates, phasing in the learning, and phasing in each repetition