Hybrid hysteresis modeling and inverse model compensation of piezoelectric actuators

Piezoelectric actuators have shown great application potential in active vibration suppression and noise reduction. However, the nonlinear hysteresis effect in piezoelectric materials often compromises the control efficiency in practical application. This paper aims at presenting an innovative hybrid hysteresis model combining an original static operator and the frequency-dependent dynamic module. The static hysteresis operator is obtained through a system-level approach, using a butterfly-shape function which is inspired from the shape analysis of hysteresis loops. For the dynamic component, the classical Bouc-Wen model and the transfer function is introduced to predict the initial loop and frequency-dependent response, respectively. The comparison between the hybrid hysteresis model and experimental result performed on a unipolar piezoelectric actuator shows a good agreement with respect to the voltage range and the frequency bandwidth of interest. Meanwhile, it is able to track the transient initial loading loop and the major-minor loops switching phenomenon. Based on the identified hybrid hysteresis model, an inverse model compensation scheme is developed to linearize the relationship between the desired output and the practical output of the piezoelectric actuators. The mechanism of the inverse model compensator is theoretically investigated and experimentally verified. Therefore, it is a quite simple yet efficient compensation approach due to the accuracy and adaptability of the proposed hybrid hysteresis model.