Adaptive Spatial Repetitive-control for Time-varying Periodic Signals in a Rotational System

This paper presents a new disturbance-observer-based adaptive spatial repetitive control scheme that enhances tracking performance for a time-varying periodic reference signal in a rotational system with parametric and nonparametric uncertainties. First, operator theory is used to establish a spatial modified repetitive controller (SMRC) that incorporates the position-domain internal model of the time-varying periodic reference signal. Second, a full-order state observer is designed to estimate the system state and a disturbance observer is constructed to estimate the nonparametric uncertainties, while a derivative-free weight update law is derived to estimate the parametric uncertainties. This ensures direct adaptive control even in the presence of rapid or sudden changes in the uncertain system dynamics. Third, a digital implementation approach for the SMRC is developed that guarantees the synchronization of the spatial repetitive control and the temporal disturbance-observer-based adaptive control for fixed time sampling rates. Stability criteria and an optimization algorithm for the controller parameters are provided. Finally, an application to the speed control of a variable-speed rotational brushless DC motor servo system demonstrates the efficacy of the method, which outperforms conventional adaptive control and other spatial repetitive control methods.