压电陶瓷驱动器迟滞非线性误差的建模与分析
2023,31(2):196-203
摘要：压电陶瓷驱动器的最大迟滞非线性误差可以超过输出行程的15%，而快刀伺服系统(FTS，Fast Tool Servo)要求重复定位精度优于10nm，相对线性度误差优于0.5%，压电陶瓷驱动器的误差无法满足该精度要求。首先对压电陶瓷迟滞非线性误差进行实验分析，将迟滞非线性误差分为频率无关迟滞现象和频率相关迟滞现象。接着对Bouc-Wen（BW）和Prandtl-Ishlinskii（PI）的频率无关迟滞模型进行修正和对比，确定了采用PI模型描述本文的频率无关迟滞现象，PI模型对频率无关迟滞曲线的辨识精度为0.392%。然后设计基于Hammerstein模型的频率相关迟滞模型，Hammerstein模型对频率相关迟滞曲线的辨识误差相比PI模型时，其均方根值降低了88.068%。提出了压电陶瓷驱动器迟滞非线性误差的建模方法，并分析了其有效性和准确性，给FTS伺服控制提供了一种实用的前馈控制器。
关键词：压电陶瓷;迟滞非线性;Bouc-Wen模型;Prandtl-Ishlinskii模型;Hammerstein模型
Modeling and Analysis of Hysteresis Nonlinear Error of Piezoelectric Ceramic Actuator
Abstract：The maximum hysteresis nonlinear error of the Piezoelectric ceramic actuator can exceed 15% of the output displacement. For the fast-tool-servo (FTS) system, the repeated positioning accuracy is better than 10nm and the relative linearity error is better than 0.5%, the above errors bring great challenges. In this paper, the hysteresis nonlinear error of piezoelectric ceramics is experimentally analyzed, and the hysteresis nonlinear error is divided into frequency-independent hysteresis phenomenon and frequency-dependent hysteresis phenomenon. Then, the frequency-independent hysteresis models of Bouc-Wen (BW) and Prandtl-Ishlinskii (PI) are revised and compared, and it is determined that the PI model is used to describe the frequency-independent hysteresis phenomenon in this paper. The identification accuracy of the PI model for the frequency-independent hysteresis curve is 0.392 %. Then a frequency-dependent hysteresis model based on the Hammerstein model is designed. Compared with the PI model, the root-mean-square value of the Hammerstein model's identification error for the frequency-dependent hysteresis curve is reduced by 88.068%. In this paper, a modeling method of hysteresis nonlinear error of piezoelectric ceramic actuator is proposed, and its validity and accuracy are analyzed, which provides a practical feedforward controller for FTS servo control.
Key words：Piezoelectric ceramic; Hysteresis nonlinear; Bouc-Wen model; Prandtl-Ishlinskii model; Hammerstein model
收稿日期：2022-09-28
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