Spatially periodic disturbance rejection using spatial-based output feedback adaptive backstepping repetitive control

In this paper, we propose a new design of spatial-based repetitive control for rotational motion systems required to operate at varying speeds and subject to spatially periodic disturbances. The system has known model structure with uncertain parameters. 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. A nonlinear state observer is then established for the system. Adaptive backstepping is applied to the system with the state observer so as to stabilize the system and reduce the tacking error. Moreover, a spatial-based repetitive controller is added and operates in parallel with the adaptively backstepped system, which further reduces the tracking error. The overall output feedback adaptive backstepping repetitive control system is robust to structured parameter uncertainty, capable of rejecting spatially periodic disturbances under varying process speeds, and can be shown to be stable and produce bounded state estimated error and bounded tracking error under sensible assumptions. Finally, feasibility and effectiveness of the proposed scheme is verified by simulation.