Compensating for spatially repetitive disturbance with linear parameter varying repetitive control

Repetitive controllers have been shown to work well for tracking periodic reference commands or for rejecting periodic disturbances in regulation applications. Typical repetitive controllers are synthesized in a temporal domain. For motor/gear transmission systems, disturbances due to gear eccentricity or tooth profile error are spatially periodic. This implies that the temporal frequency values for these two types of disturbances are proportional to the nominal angular velocity and vary accordingly. A repetitive controller designed based on the temporal information of disturbances cannot perform well as the spatially periodic disturbances also affect the nominal angular velocity. We reformulate the temporal domain system with respect to a spatial coordinate, which resulted in a nonlinear position invariant (NPI) system. By treating the angular velocity as varying but measurable parameters, the nonlinear NPI system can be treated as a linear parameter varying (LPV) system, for which an LPV gain-scheduling repetitive controller (LPVRC) with anti-windup can be designed. Experimental results on the velocity regulation of the photosensitive drum in a laser printer verified the effectiveness of the proposed LPVRC design.