Adaptive Output Regulation for the Rejection of a Periodic Disturbance With an Unknown Frequency

This brief presents an adaptive output regulator, an add-on type output regulator with a frequency adaptation algorithm. The frequency adaptation algorithm, based on an internal model principle, is used to identify the frequency of a sinusoidal disturbance. By adding the modified adaptive algorithm to the add-on output regulator, the adaptive output regulator can reject a biased sinusoidal disturbance with unknown bias, magnitude, phase, and frequency, while preserving the merits of the output regulator and the performance of the pre-existing controller. It is shown that the proposed method is stable for frequencies within a connected compact set. The stability of the closed-loop system is analyzed by the singular perturbation method and averaging theorem. The proposed controller is applied to an optical disk drive for verifying the performance of the controller. The performance of the proposed method is validated by both simulation and experimental results.