Robust approach to repetitive controller design for uncertain feedback control systems

In many applications, add-on type repetitive controllers have been reported to have prominent capability of attenuating periodic disturbances and/or tracking periodic reference commands. However, the effective information such as performance weighting functions for the design of feedback controllers has not been considered sufficiently on the design of repetitive controllers. In this study, we deal with a 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 has a similar form with the well-known robust performance condition of general feedback control systems. The repetitive controller is designed using the performance weighting function for the design of the robust feedback controller. It is also shown that a steady-state tracking error of the repetitive control system is described in a simple form without time-delay term. This result yields that the repetitive control system has a much larger loop gain in the steady state than the feedback control system. Moreover, this paper provides sufficient conditions ensuring that the power of the steady-state tracking error in the repetitive control system is less than or equal to that of the feedback control system. Based on the obtained results, we present repetitive controller design method using the design information of the feedback control system. Finally, application studies on the track-following control system of optical disk drives are performed to show the validity of the proposed method.