An integrated physical model that characterizes creep and hysteresis in piezoelectric actuators

In this paper, a model that can precisely portray hysteresis and creep in piezoelectric actuators is proposed. The model, which is originally constructed using bond-graph representation, describes the actuator’s various physical effects and energy interaction between physical domains. Specifically, the model utilizes a parallel connection of Maxwell-slip elements and a nonlinear spring to describe hysteresis, and a series connection of Kelvin–Voigt units to describe creep. Using the experimental data, the constitutive relation of the nonlinear spring and the parameters of linear, physical elements in the model can be systematically identified via the linear programming method. To further account for the frequency-dependent hysteresis behavior, a dynamic damper is incorporated. By analyzing the model, the influence of initial strain/charges on the creep response is revealed and an initialization procedure is devised to eliminate such an influence. An inverse model control, in the sense of feedback linearization, is constructed based on the identified model to make the actuator track reference trajectories. Experiments show that both creep and hysteresis are effectively cancelled and accurate tracking of selected reference trajectories is achieved.