A novel second order repetitive control that facilitates stability analysis and its application to magnetically suspended rotors

Repetitive control is an effective method to eliminate the effects of a periodic disturbance on a control system. In some applications the period is not known with sufficient accuracy, or the period may fluctuate sufficiently to seriously compromise performance. Second order repetitive control has been developed in response to this issue. Existing methods of analyzing stability for such systems are either very difficult to use, or excessively conservative sufficient conditions. A novel second order repetitive control is proposed here which achieves the behavior of second order but uses data from only one period in the past. This better meets the requirements for real time storage, but more importantly, it allows us to develop a stability criterion that is much less conservative. The experimental results demonstrate that the suppression effect can achieve a high level under frequency fluctuation with the proposed control method.