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.

Introduction

A novel form of second order repetitive control (RC) is proposed in this paper, which can greatly facilitate the stability analysis. The motivation of the study originates from the urgent requirements of micro-vibration spacecraft. Spacecraft often suffer from vibrations produced by the rotating wheels used as attitude control actuators, i.e., reaction wheels or control moment gyros [1]. This degrades the performance of fine pointing equipment on board. Passive vibration isolation methods have limited performance, hence active vibration cancellation strategies are considered [2]. Laser communications between spacecrafts or with ground offer a different option of canceling the influence of spacecraft jitter by control methods applied to pan and tilt of the outgoing mirror [3] that cancels vibrations in the beam. The hardware demonstration of the proposed second order repetitive control approach, considers magnetically suspended rotor (MSR) performance, which can have disturbances of rotor mass imbalance and sensor runout. The objective is to reduce the vibrations at their source in the spacecraft, instead of at the sensor location of fine pointing equipment by vibration isolation.