Spatial domain adaptive repetitive controller design for uncertain variable-speed rotational motion systems

In this paper, we propose a repetitive control design 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 feedback linearization is applied to linearize the system while seeking the correct system parameters online. Then, a spatial-based reduced-order repetitive controller along with a stabilizing controller is designed and operates in parallel with the adaptively feedback linearized system. The overall adaptive repetitive control system is thus robust to structured parameter uncertainty and spatially periodic disturbances under variable process speed. Feasibility and effectiveness of the proposed scheme is verified by simulation.