On hysteresis modeling of a piezoelectric precise positioning system under variable temperature

Abstract We propose the modeling of hysteresis nonlinearities in a piezoelectric material-based tube actuator classically employed in precise positioning applications under different surrounding temperatures. Beyond the voltage-to-displacement hysteresis nonlinearities they exhibit, these actuators are sensitive to the surrounding temperature. Therefore, contrary to the existing works in the literature where the two phenomena were treated individually, this paper suggests to model the hysteresis nonlinearities and the temperature effects simultaneously. First an experimental study was performed to investigate the effects of the surrounding temperature on the voltage-to-displacement hysteresis loops of the piezoelectric tube actuators. The experimental results show that increasing the input surrounding temperature contributes an increase in the voltage-to-displacement sensitivity of the piezoelectric tube actuator under the input voltage range considered in the experimental tests. Then, two different nonlinear temperature-dependent hysteresis models a temperature-dependent (TD) electromechanical model and a temperature-dependent Prandtl-Ishlinskii model (TD-PI) were proposed to account the temperature effects on the hysteresis nonlinearity. In First, the mathematical formulation of TD-electromechanical model was presented to describe the electrical and mechanical properties of piezoelectric tube actuator. This model integrates the temperature dependent electromechanical coupling factor to model the temperature effects, the Simscape library in MATLAB-Simulink software was used to develop a physical simulation for the TD-electromechanical model. In a second time, a TD-PI model was proposed to describe the voltage-to-displacement characteristic of piezoelectric tube actuator using a proposed temperature shape function. The parameters of the two proposed models were estimated using proposed optimization algorithms based on Grey Wolf Optimizer (GWO). The modeling results demonstrate that the two proposed models can account for the hysteresis nonlinearities of the piezoelectric tube actuators under different levels of the surrounding temperatures. Finally, the analytical inverse of TD-PI model was derived and applied in feed forward manner to compensate the hysteresis nonlinearities under different levels of the surrounding temperatures.