9. Compensation of Rate-Dependent Hysteresis in a Piezomicropositioning Actuator

Piezomicropositioning actuators exhibit strong rate-dependent hysteresis nonlinearities that affect the accuracy of these micropositioning systems in open-loop system and may even lead to system instability of the closed-loop control system. Compensation of rate-dependent hysteresis effects using inverse rate-independent hysteresis models may yield high compensation error at high-excitation frequencies since these hysteresis effects increase as the excitation frequency of the input voltage increases. The inverse rate-dependent Prandtl–Ishlinskii model is utilized for compensation of the rate-dependent hysteresis nonlinearities in a piezomicropositioning stage. The exact inversion of the rate-dependent model is on hold under the condition that the distances between the thresholds do not decrease in time. The inverse of the rate-dependent model is applied as a feedforward compensator to compensate for the rate-dependent hysteresis nonlinearities of a piezomicropositioning actuator at different excitation frequencies between 0.1 and 50 Hz. The results show that the inverse compensator suppresses the hysteresis percent and the maximum positioning error in the output displacement of the piezomicropositioning actuator at different excitation frequencies, respectively.