Robust repetitive controller design and its application on the track-following control system in optical disk drives

A repetitive controller has been applied owing to its prominent capability for attenuating periodic disturbances and/or tracking periodic reference commands. A repetitive controller is generally added on the existing feedback control system to improve the tracking performance. However, the repetitive controller has been designed without utilizing the effective information such as the performance weighting function used in the design of the feedback controller. In this paper, we deal with the problem of a robust repetitive controller design for an uncertain feedback control system using its explicit performance information. We first show that a robust stability condition of repetitive control systems is closely related with the well-known robust performance condition of general feedback control systems. It is also shown that the steady-state tracking error of the repetitive control system is described in a simple form without time-delay element. From this result, we explain how different loop properties of the repetitive control system are from those of the feedback control system. Moreover, sufficient conditions are provided, which ensure that the power of the steady-state tracking error generated by the repetitive control system is less than or equal to that only by the feedback control system. Based on the obtained results, we present repetitive controller design criteria. Finally, to show the validity of the proposed method, application studies on the track-following control system of optical disk drives are performed.