A new Robust Delay-Variable Repetitive Controller with application to media transport in a printer

Repetitive Control (RC) is an effective tool to reject the repetitive disturbances and their harmonics. However, the effectiveness of RC decays when the time period of the RC does not exactly match with the period of the repetitive disturbance. RC also leads to reduced performance in between harmonics in terms of degraded sensitivity (more noise sensitive). High Order Repetitive Control (HORC) is an RC structure, which allows to shape the sensitivity function to make it either more robust for time period of the repetitive disturbances, or more noise robust. In addition, standard RC will also fail in systems with spatial repetitive disturbances, since the time period of this kind of repetitive disturbances may vary. Delay-Varying Repetitive Control (DVRC) can cope with spatial disturbances, however, it lacks the robustness attained by HORC. By combining these two RC structures, HORC and DVRC, a new Robust Delay-Variable Repetitive Controller (RDVRC) is obtained. The RDVRC is successfully applied to measurement data from a media transport system of an industrial printer. Robust DVRC will be useful for many motion control systems with repetitive tasks, as disturbances often repeat along the motion path.