Thanks to their integrability and good electromechanical conversion abilities, piezoelectric actuators are a good choice for many actuation applications. However, these elements feature a frequency-dependent hysteresis response that may yield complex control implementation. The purpose of this paper is to provide the extension of a simple hysteresis model based on a system-level approach linking the strain derivative to the driving voltage derivative and taking into account the dynamic behavior of the hysteretic response of the actuator. The proposed enhancement consists of transient and harmonic regimes, allowing to extend the quasi-static model to dynamic behavior with any frequency. In particular, initial strain shift arising from stabilization and accommodation effects as well as frequency-dependent hysteresis shape are considered. The inclusion of the system dynamics in the model is obtained thanks to fractional derivatives and associated fractional transfer functions, allowing the consideration of the full actuator history as well as a fine tuning of the system dynamics over a wide frequency band. Finally, a numerical example of linearized control through compensation loop is provided, demonstrating the interest in the proposed approach for providing a computationally-efficient, simple yet efficient way for finely predicting the actuator response and thus designing appropriate controllers.
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