Modeling and control of rate-dependent hysteresis in piezoelectric actuators

Piezoelectric actuators show dependency of the output displacement on the rate of change of the applied input voltage. In this paper, a rate-dependent Prandtl-Ishlinskii model is developed to characterize the time-dependent hysteresis in the piezoelectric actuators. This model employs the dynamic threshold and weighting values formulated on the speed of the input voltage. The validation of the rate-dependent Prandtl-Ishlinskii model is demonstrated by comparing its out responses with the measured responses obtained for a piezoelectric actuator under different input frequencies. Finally, a feedforward controller with an inverse rate-dependent Prandtl-Ishlinskii model is designed to account for the dynamic hysteresis. The results show that the hysteresis nonlinearities are significantly reduced at both the lower and higher frequencies.