压电驱动器迟滞非线性的分数阶建模及实验验证

李致富; 黄楠; 钟云; 曾俊海; 马鸽

doi:10.3788/OPE.20202805.1124

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压电驱动器迟滞非线性的分数阶建模及实验验证

微纳技术与精密机械 | 更新时间：2020-07-09

- 压电驱动器迟滞非线性的分数阶建模及实验验证
- Fractional order modeling and experimental verification of hysteresis nonlinearities in piezoelectric actuators
- 光学精密工程 2020年28卷第5期页码：1124-1131
- 作者机构：
  
  1.广州大学机械与电气工程学院, 广东广州 510006
  2.广州大学智能装备与网联系统研究中心, 广东广州 510006
- 作者简介：
  
  [ "李致富(1981-), 男, 湖南郴州人, 博士, 副研究员, 硕士生导师, 2003年, 2006年于中南大学分别获得学士、硕士学位, 2012年于华南理工大学获得博士学位, 主要从事非线性控制理论与应用、分数阶建模与控制、智能优化算法、机器人技术等方面的研究。E-mail: lizhifu8@163.com" ]
  马鸽(1988-), 女, 山东济宁人, 博士, 讲师。2010年于山东建筑大学获得学士学位, 2016年于华南理工大学获得博士学位, 主要从事图像处理、机器视觉、控制理论与应用等方面的研究。E-mail:m_ge@gzhu.edu.cn MA Ge, E-mail:m_ge@gzhu.edu.cn
- 基金信息：
  
  广州市属高校科研项目资助(1201610154);国家自然科学基金资助项目(61603105)
- DOI：10.3788/OPE.20202805.1124
  中图分类号： TP273.1;TN384
- 收稿日期：2019-10-30，
  
  修回日期：2019-12-19，
  
  录用日期：2019-12-19，
  
  纸质出版日期：2020-05-15
- 稿件说明：
移动端阅览
李致富, 黄楠, 钟云, 等. 压电驱动器迟滞非线性的分数阶建模及实验验证[J]. 光学精密工程, 2020,28(5):1124-1131.

Zhi-fu LI, Nan HUANG, Yun ZHONG, et al. Fractional order modeling and experimental verification of hysteresis nonlinearities in piezoelectric actuators[J]. Optics and precision engineering, 2020, 28(5): 1124-1131.
李致富, 黄楠, 钟云, 等. 压电驱动器迟滞非线性的分数阶建模及实验验证[J]. 光学精密工程, 2020,28(5):1124-1131. DOI： 10.3788/OPE.20202805.1124.

Zhi-fu LI, Nan HUANG, Yun ZHONG, et al. Fractional order modeling and experimental verification of hysteresis nonlinearities in piezoelectric actuators[J]. Optics and precision engineering, 2020, 28(5): 1124-1131. DOI： 10.3788/OPE.20202805.1124.

摘要

存在于压电陶瓷全工作范围内的迟滞非线性特性

往往会导致压电陶瓷执行器的系统精度下降、振荡

甚至造成系统的不稳定。针对周期性的正弦输入信号

提出一种基于分数阶算子的迟滞建模方法。首先

在分析压电特性和分数阶算子特性的基础上

采用结构简单参数少的分数阶算子来描述压电陶瓷的迟滞特性; 然后

搭建了基于dSpace的压电驱动微位移定位实验平台; 最后

将基于分数阶算子的迟滞建模方法应用于压电驱动微位移定位平台中

对压电陶瓷的迟滞非线性特性进行辨识。实验结果表明：采用基于分数阶的迟滞模型(FOM)比传统的Prandtl-Ishlinskii模型(PIM)及其改进的增强型Prandtl-Ishlinskii模型(EPIM)更有优势; 在低频段

FOM模型比PIM模型和EPIM模型精度略有提高

但是在高频段

FOM模型比PIM模型和EPIM模型精度则提高显著。在输入频率为100HZ的情况下

所提出的FOM模型较PIM模型的均方根误差(RMSE)值精度提高69.84%

较EPIM模型的RMSE值精度提高68.88%。

Abstract

Hysteresis nonlinearities in the entire working range of piezoelectric ceramic actuators often result in reduced system accuracy

oscillations

and system instability. For a periodic sinusoidal input signal

a hysteresis modeling method based on a fractional-order operator was proposed herein. First

based on the analysis of piezoelectric and fractional-order operator characteristics

a fractional-order operator involving a simple structure and few parameters was used to describe the hysteresis characteristics of piezoelectric ceramics. Subsequently

a piezoelectric actuated micro-displacement positioning experimental platform based on dSpace was built. Finally

a fractional-order-operator-based hysteresis modeling method was applied to the piezoelectric actuated micro-displacement positioning platform to identify the hysteretic nonlinear characteristics of piezoelectric ceramics. The experimental results show that the Fractional-Order hysteresis Model (FOM) is superior to the traditional Prandtl-Ishlinskii Model (PIM) and the Enhanced Prandtl-Ishlinskii model (EPIM). In the low-frequency range

the precision of the FOM is slightly higher than that of the PIM and EPIM models; however

in the high-frequency range

the precision of the FOM model is significantly higher than that of the PIM and EPIM models. When the input frequency is 100 Hz

the accuracy of the proposed FOM is 69.84% and 68.88% higher than that of the PIM and EPIM models on the root mean square error

respectively.

关键词

Keywords

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