Spatially Periodic Disturbance Rejection With Spatially Sampled Robust Repetitive Control

Repetitive controllers have been shown to be effective for tracking periodic reference commands or for rejecting periodic disturbances. Typical repetitive controllers are synthesized in temporal domain where the periods of the reference or disturbance signals are assumed to be known and stationary. For periodic references and disturbances with varying periods, researchers usually resort to adaptive and robust control approaches. For rotational motion systems where the disturbances or reference signals are spatially periodic (i.e., periodic with respect to angular displacement), the temporal period of the disturbance and reference signals will be inversely proportional to the rotational speed and vary accordingly. Motivating by reducing halftone banding for laser printers, we propose a design framework for synthesizing spatially sampled repetitive controller by reformulating a linear time-invariant system subject to spatially periodic disturbances using angular displacement as the independent variable. The resulting nonlinear system can be represented as a quasi-linear parameter-varying (quasi-LPV) system with the angular velocity as one of the varying state-dependent parameters. An LPV self-gain–scheduling controller that includes a spatially sampled repetitive control can be designed to take into consideration bounded model uncertainty and input nonlinearity, such as actuator saturation. Using the signal from an optical encoder pulse as a triggering interrupt, experimental results verified the effectiveness of the proposed approach in rejecting spatially periodic disturbances that cannot be compensated with fixed period temporal repetitive controllers.