Repetitive control applied to a walking piezo actuator

The performance of systems that exhibit repetitive disturbances can be significantly improved using repetitive control (RC). If the period-time of the repetitive disturbance is exactly known and constant in time, perfect asymptotic disturbance rejection can be achieved. In this paper, we apply RC to a high-precision stage driven by a walking piezo actuator with four bimorph piezoelectric legs. The repetitive nature of the walking movement introduces repetitive disturbances in the system, which are periodic with respect to the angular orientation of the legs, but not with respect to time. Therefore, an adjusted RC scheme is introduced, which incorporates a time-varying delay that is dependent on the momentary orientation of the legs during the walking movement. Experiments show that the tracking error can be significantly reduced by the adjusted RC method compared to standard RC. Furthermore, the adjusted RC scheme can also suppress repetitive disturbances for varying setpoint velocities.