Systematic Control Design for Adaptive Rejection of Narrow-Band Disturbances Based on a Novel Resonant Generalized Extended State Observer

Abstract

In this paper, the adaptive rejection of multiple narrow-band disturbances with time-varying frequencies is investigated. A systematic control approach based on a resonant generalized extended state observer (RGESO) is proposed. The frequency response of the RGESO is shaped into a desired form to reject the total disturbance, including the wide-band uncertainties and the narrow-band disturbances. The state-space realization of the RGESO is also provided to estimate both the states and the total disturbance. To handle the time-varying frequencies of the narrow-band disturbances, a direct frequency estimation approach based on the Levenberg–Marquardt method and an online supervision strategy is presented to improve convergence and reliability, and the estimations are then used to adapt the RGESO parameters. Parameter tuning and stability robustness analysis methods are also developed for the proposed scheme to facilitate its application. Finally, extensive simulations are conducted to demonstrate the effectiveness of our method.