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Add-on type repetitive controller design for the feedback control system satisfying the robust performance condition

Given a periodic reference signal or disturbance, repetitive control is a special control scheme to reduce a tracking error effectively by the periodic signal generator in the repetitive controller. In general, a repetitive controller is added on the existing feedback control system to improve the tracking performance. However, the repetitive controller has been designed without utilizing the information used in the design of the feedback controller. In this paper, we present a method to design an add-on type repetitive controller using the information on the performance of the existing feedback control system. We first show that a robust stability condition of repetitive control systems is obtained using the well-known robust performance condition of general feedback control systems. It is also shown that we can obtain a steady-state tracking error described in a simple form without time-delay element if the robust stability condition is satisfied for the repetitive control system. From the obtained results, several design criterions for repetitive controller are provided. Finally, to show the validity of the proposed method, simulation studies on the track-following control system of optical disk drives are performed.