Modeling piezoelectric actuator hysteresis with a family of ellipses

In this paper, a new mathematic model is developed to describe the frequency-dependent and amplitude-dependent hysteresis in a piezoelectric actuator. The developed hysteresis model consists of a family of ellipses with arbitrary major and minor axes and orientation in the 2D plane, relating with frequencies and amplitudes of the control input. To describe the hysteresis characteristics, experiments are performed with designed harmonic excitations under different frequencies in the range 0.5 Hz to 300 Hz. Both the input voltage and the feedback displacement are analyzed through the direct least square method to identify the elliptic models. In the developed model, the length of the minor radius describes the hysteresis height varying with the input frequencies and amplitudes, while the length of major radius and the orientation of the ellipses describe peak-to-peak output amplitudes. The simulation results are compared with the measured data from the actuator to demonstrate the validity of the proposed model. The results show that the elliptic model can completely match the rate-dependent hysteresis of the piezoelectric actuator at both the lower and higher frequencies.