Repetitive controller for periodic disturbance rejection in motor-gear transmission system

In control systems, disturbance or reference inputs invariably include a significant periodic component with a known period. Repetitive controllers are those control elements that strategically reduce or nullify the effect of these repeating signals. In motor gear transmission system, the tooth-to-tooth error manifests as periodic disturbance. Repetitive control has by now proved as an effective control scheme for improving periodic disturbance attenuation performance. This paper aims to formulate the repetitive controller design for the Motor-Gear system as an optimization problem with an LMI (Linear Matrix Inequality) constraint on the free parameter of the bandwidth of the filter and demonstrate the effect of such a controller through MATLAB simulation. The filter is used to cater to the stability requirements of the system with the repetitive controller incorporated with it. The form of the repetitive controller is based on a single parameter determined by the fundamental period of the disturbance. It is demonstrated through the results that the repetitive controller indeed reduces the periodic disturbances. Also as the bandwidth is increased, stability is found to be at stake whereas the disturbance rejection is affected if the bandwidth is reduced.