In an optical disk drive servo system, disturbances with significant periodic components cause tracking errors of a periodic nature. As an effective control scheme for improving periodic disturbance attenuation performance, repetitive control has been applied successfully to the trackfollowing servo system of optical disk drives. The increase in disk rotational speed to achieve a better data throughput leads to the increase in the frequency of periodic disturbance, which needs a high loop gain in a wider control bandwidth. However, this requirement is not easily accomplished because plant uncertainty hinders selecting the bandwidth of a filter in the repetitive controller. The problem of add-on type repetitive controller design for a track-following servo with norm-bounded uncertainties in optical disk drives with high rotational speed is examined. Using the Lyapunov functional for time-delay systems, a sufficient condition for robust stability of the repetitive control system is derived in terms of an algebraic Ricatti inequality or a linear matrix inequality (LMI). On the basis of the derived condition, it is shown that the repetitive controller design problem can be reformulated as an optimisation problem with an LMI constraint on the free parameter. The validity of the proposed method is verified through experiments using a DVD-ROM drive.

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The design of a repetitive control system for linear systems with time-varying normbounded uncertainties is presented. Using a Lyapunov functional for the time-delay systems, a sufficient condition is derived in terms of either an algebraic Ricatti inequality or a linear matrix inequality (LMI), which ensures robust stability of the repetitive control system. Based on the derived condition, we show that the repetitive controller design problem can be reformulated as an optimisation problem with an LMI constraint of the free parameter.

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