串联死区算子的压电微夹钳PI迟滞模型

Research on PI Hysteresis Model with Dead-zero Operator of Piezoelectric Micro-gripper

针对Prandtl-Ishlinskii（PI）模型要求被描述对象的初载曲线为凸函数,且模型与其逆模型都应关于算子中心对称的不足,通过引入死区算子对PI模型进行改进,以使其更好地描述具有非凸、非奇对称的压电陶瓷材料的迟滞特性。基于实测的压电微夹钳初载曲线,采用等分阈值方式,并通过使改进PI模型与实测初载曲线间的误差函数为最小,辨识出改进PI模型的参数,建立了压电微夹钳的迟滞模型。实验结果表明,在微夹钳15.2μm的最大位移范围内,模型误差的变化范围为-0.310～0.156μm,所建模型能很好地描述压电微夹钳的迟滞特性。

Prandtl-Ishlinskii（PI） model requires that an initial loading curve of described object is convex func- tion. At the same time,the requirements of PI model and its inverse model are symmetric about operator center. To overcome this shortage, PI model is improved by connecting dead-zero operator. The proposed model can well de- scribe the piezoelectric ceramic material hysteresis curve with non-convex, non odd symmetric characteristic. Based on the measured initial loading curve of the piezoelectric micro-gripper, using a method of equal division threshold and minimizing the error function between improved PI model and the initial loading curve, the parameters of the pro- posed PI model are identified. Then the hysteresis model of the micro-gripper is established. Experimental results in- dicate that in the maximum displacement range of 15.2 μm,the error range of the model is --0. 310～0. 156 μm. The proposed model can well deserihe the hysteresis characteristic of the micro-gripper.