Compensator design for hysteresis of a stacked PZT actuator using a congruency-based hysteresis model

This paper proposes a rate-independent hysteresis compensator for a stacked PZT (lead zirconate titanate) actuator. From a congruency-based hysteresis (CBH) model which is derived from the inherent properties of this actuator, especially the congruency, a feedforward compensator associated with it is developed. The formulation of the proposed compensator is based on an assumption that the inverse operator also possesses the same properties as the CBH model does. This implies that the compensator also possesses properties such as the wiped-out loop closing between the consecutive control points and congruency. Consequently, the expressions for the compensator can be conducted by exploiting the equations for the CBH model in two cases of monotonic increase and monotonic decrease of input excitation. In order to assess the performance of the compensator, several experiments in both open-loop and closed-loop controls are undertaken. In the open-loop control experiment, the performance of the feedforward compensator using the CBH model is compared with the classical Preisach model-based one in three cases of reference waveforms. In the closed-loop control experiment, the proposed compensator is incorporated into a PID (proportional-integral-derivative) control system and the performance of this integrated system is then evaluated and compared to that of the PID with and without compensator.