A modified equivalent-input-disturbance compensation method is investigated for repetitive control systems with state time delays, which achieve effective rejection of unknown disturbance and effective tracking control of periodic reference input. By incorporating the sliding mode observer into the equivalent-input-disturbance theory, the equivalent-input-disturbance estimator structure is determined. The structure presented in this work can effectively estimate the unknown disturbance without making use of the inverse model of the system. Moreover, an asymptotic stability condition is devised to ensure that the repetitive control systems are stable, as well as the corresponding controller gains are designed with the aim to guarantee the performance of the system to suppress unknown disturbances. Numerical example simulations demonstrate the effectiveness and advantages of the devise scheme.
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