Output-Feedback Adaptive Periodic Disturbances Attenuation for Linear MIMO Systems Subject to Input Delay

This paper presents a novel output-feedback direct adaptive controller with a decoupling design to completely attenuate periodic disturbances in the linear multi-input multi-output (MIMO) system subject to input delay. First, the family of strictly causal stabilizing controllers for this system is derived by using the Youla parameterization method. The stabilizing controller consists of a fixed base controller J and an adjustable block Q. Periodic disturbances can be completely attenuated by adjusting the block Q. Then, to improve the attenuation rate of the periodic disturbance, a diagonal decoupling strategy is proposed. Based on the internal model principle (IMP), the interpolation condition for the complete attenuation of periodic disturbance is established. Next, to attenuate unknown time-varying periodic disturbances, a parameter adaptive algorithm is designed to update online the Q parameters. Finally, the effectiveness of the proposed controller is validated by simulation results. Note to Practitioners—The simultaneous presence of input delays and periodic disturbances in real systems not only limits control effectiveness but also leads to instability in the closed-loop system. Therefore, it is crucial to attenuate the periodic disturbances in input delay systems. However, existing adaptive controllers cannot completely attenuate unknown time-varying periodic disturbances if the system state is unavailable. Moreover, the multi-channel cross-coupling inherent in MIMO systems further constrains the controller performance. Motivated by this challenge, this paper proposes an output-feedback direct adaptive controller with decoupling design to completely attenuate periodic disturbances in linear MIMO input delay systems. It is hoped that the proposed method can provide valuable theoretical and technical guidance for the design of controllers aimed at compensating for periodic disturbances in linear MIMO systems subject to input delay.