压电陶瓷驱动器迟滞非线性建模及逆补偿控制

刘鑫, 李新阳, 杜睿. 压电陶瓷驱动器迟滞非线性建模及逆补偿控制[J]. 光电工程, 2019, 46(8): 180328. doi: 10.12086/oee.2019.180328
引用本文: 刘鑫, 李新阳, 杜睿. 压电陶瓷驱动器迟滞非线性建模及逆补偿控制[J]. 光电工程, 2019, 46(8): 180328. doi: 10.12086/oee.2019.180328
Liu Xin, Li Xinyang, Du Rui. Hysteresis nonlinear modeling and inverse compensation of piezoelectric actuators[J]. Opto-Electronic Engineering, 2019, 46(8): 180328. doi: 10.12086/oee.2019.180328
Citation: Liu Xin, Li Xinyang, Du Rui. Hysteresis nonlinear modeling and inverse compensation of piezoelectric actuators[J]. Opto-Electronic Engineering, 2019, 46(8): 180328. doi: 10.12086/oee.2019.180328

压电陶瓷驱动器迟滞非线性建模及逆补偿控制

  • 基金项目:
    国家重点研发计划项目(2017YFB0405100)
详细信息
    作者简介:
    通讯作者: 李新阳(1971-),男,博士,研究员,主要从事自适应光学相关技术方面的研究。E-mail:xyli@ioe.ac.cn
  • 中图分类号: TP29; TH703

Hysteresis nonlinear modeling and inverse compensation of piezoelectric actuators

  • Fund Project: Supported by National Key Research and Development Program (2017YFB0405100)
More Information
  • 自适应光学系统中的倾斜镜、变形镜通常是应用压电陶瓷驱动器来进行精密位移控制,但压电陶瓷驱动器都有较大的非线性迟滞效应,对系统定位性能造成了一定的影响。为了补偿迟滞现象,需要对迟滞效应进行建模。本文通过引入迟滞算子,使用贝叶斯正则化训练算法训练BP神经网络来构建压电陶瓷驱动器迟滞模型,以中国科学院光电技术研究所自主研制的压电陶瓷驱动器为对象开展了实验研究。实验结果表明,通过BP神经网络构建的压电陶瓷驱动器迟滞模型具有较准确的辨识能力,其中正模型的相对误差为0.0127,逆模型的相对误差为0.014。利用所建立的模型,压电陶瓷驱动器的非线性度从14.6%降低到了1.43%。

  • Overview: Adaptive optics is used to correct the wavefront distortion caused by atmospheric turbulence in real time. The tilt mirrors and deformable mirrors in adaptive optics system usually use piezoelectric ceramic actuators for precise displacement, however, piezoelectric ceramic actuators own obviously nonlinear hysteresis effect which affects the positioning performance of the system. In order to compensate the hysteresis, there is a need to model hysteresis effects. Due to the limitation of computation quantity and dimension of traditional hysteresis model, it is difficult to find the analytic inverse model, which is not conducive to the application of engineering practice. Neural network can approximate any nonlinear curve and owns the adaptive learning ability, strong fault tolerance and the very high ability of system identification, data processing ability and the ability of fast parallel computing, which makes the neural network widely used in nonlinear system modeling. It can be inferred from incomplete or noisy data in the training process and can be easily combined with the controller design. In the application of neural network, the input and output relationship of mapping is one-to-one or many-to-one mapping relationship, but the relationship between voltage and displacement of piezoelectric ceramic actuator is one-to-many mapping relations, neural network cannot deal directly with this nonlinear mapping. In this paper, by introducing a hysteresis operators to expand the input voltage of piezoelectric ceramic actuator in neural network input space, the multimapping of hysteresis is transformed into one-to-one mapping in 3D space. In the transformed space, the neural network is used to approximate the one-to-one mapping and a hysteresis non-linearity based on the neural network is established, the one-dimensional feature is introduced for the input of neural network by constructing the hysteresis operator. In this paper, the Powell-Beale algorithm, Levenberg-Marquardt algorithm and Bayesian regularization algorithm are compared, and the Bayesian regularization training algorithm was used to train BP neural network to construct the positive hysteresis model and inverse model of piezoelectric ceramic actuators, and an experimental study was conducted on a piezoelectric actuator developed by Institute of Optics and Electronics, Chinese Academy of Sciences. According to the established model, the hysteresis positive model, inverse model and hysteresis compensation experiment of piezoelectric ceramic actuator are carried out. The final experimental results show that the hysteresis model of piezoelectric ceramic actuators constructed by BP neural network has more accurate identification capability. The relative error of the positive model is 0.0127 and the relative error of the inverse model is 0.014. The nonlinearity of the piezoelectric actuators has been reduced from 14.6% to 1.43%.

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  • 图 1  实验平台实物图

    Figure 1.  Experiment platform

    图 2  压电陶瓷驱动器迟滞现象

    Figure 2.  The hysteresis phenomenon of piezoelectric actuator

    图 3  引入的迟滞算子示意图。(a)正迟滞算子示意图;(b)逆迟滞算子示意图

    Figure 3.  Hysteresis operator. (a) Positive hysteresis operator; (b) Inverse hysteresis operator

    图 4  压电陶瓷驱动器迟滞正模型神经网络训练结构

    Figure 4.  Neural network training structure of hysteresis positive model

    图 5  验证正模型。(a)正模型辨识结果图;(b)正模型误差示意图

    Figure 5.  Verify the positive model. (a) Positive model identification results; (b) Positive model error

    图 6  验证逆模型。(a)逆模型辨识结果图;(b)逆模型误差示意图

    Figure 6.  Verify the inverse model. (a) Inverse model identification results; (b) Inverse model error

    图 7  压电陶瓷驱动器迟滞模型跟踪示意图。(a)位移跟踪示意图;(b)误差示意图

    Figure 7.  Hysteresis model tracking for piezoelectric actuators. (a) Displacement tracking; (b) Error diagram

    图 8  压电陶瓷驱动器迟滞补偿示意图

    Figure 8.  Hysteresis compensation

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收稿日期:  2018-09-05
修回日期:  2018-11-06
刊出日期:  2019-08-01

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