System-level modeling of nonlinear hysteretic piezoelectric actuators in quasi-static operations

This paper aims at providing a simple yet efficient model for predicting the strain-voltage relationship in piezoelectric actuators subjected to high driving conditions, and featuring hysteretic response under such excitation. The originality of the model lies in proposing a high-level, system approach for modeling hysterestic response, using a butterfly-shaped electromechanical coupling term between the voltage and strain derivatives. The model is based on function reversal, and can be applied to many hysteresis types as the function can be properly chosen. Furthermore, the model requires few parameters and works both in unipolar and symmetric cycles, while being able to handle minor loops as well. Experimental results made on an unipolar piezoelectric actuator show good agreement with theoretical predictions. As a general hysteresis model, the proposed model can besides be applied to other domains, such as in magnetism, magnetic actuation or hydraulics.