Spatially Periodic Disturbance Rejection for Uncertain Rotational Motion Systems Using Spatial Domain Adaptive Backstepping Repetitive Control

In this paper, we propose a new design of spatial-based repetitive control system for rotational motion systems required to operate at various speeds, and subject to structured parameter uncertainty and spatially periodic disturbances. To synthesize a repetitive controller in spatial domain, a linear time-invariant system is reformulated with respect to a spatial coordinate (e.g., angular displacement), which results in a nonlinear system. Adaptive backstepping is applied to stabilize the system while adapting the parameters at the same time. Then, a spatial-based reduced-order repetitive controller along with a stabilizing controller is designed and operates in parallel with the adaptive backstepping system. The overall spatial-based adaptive backstepping repetitive control system is thus robust to structured parameter uncertainty. Also its capability of rejecting spatially periodic disturbances is invariant to process speed. Feasibility and effectiveness of the proposed scheme is verified by simulation.