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

Hysteresis nonlinear modeling and inverse compensation of piezoelectric actuators

    Fund Project: Supported by National Key Research and Development Program (2017YFB0405100)
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  • The tilt mirrors and deformable mirrors in adaptive optics system are usually using 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. In this paper, hysteresis operator is introduced and using Bayesian regularization training algorithm to train BP neural network to construct hysteresis model of piezoelectric ceramic actuator, an experimental study was conducted on a piezoelectric actuator developed by Institute of Optics and Electronics, Chinese Academy of Sciences. 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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  • [1] Jiang W, Li H, Liu C, et al. A 37-element adaptive optics system with H-S wavefront sensor[C]//Proceedings of the 16th Congress of the International Commission for Optics, 1993: 127-134.

    Google Scholar

    [2] Parenti R R, Sasiela R J. Laser-guide-star systems for astronomical applications[J]. Journal of the Optical Society of America A, 1994, 11(1): 288-309. doi: 10.1364/JOSAA.11.000288

    CrossRef Google Scholar

    [3] 姜文汉.自适应光学发展综述[J].光电工程, 2018, 45(3): 170489. doi: 10.12086/oee.2018.170489

    CrossRef Google Scholar

    Jiang W H. Overview of adaptive optics development[J]. Opto-Electronic Engineering, 2018, 45(3): 170489. doi: 10.12086/oee.2018.170489

    CrossRef Google Scholar

    [4] Tyson R K. Principles of Adaptive Optics[M]. Boston: Academic Press, 1991.

    Google Scholar

    [5] 黄林海, 凡木文, 周睿, 等.大口径压电倾斜镜模型辨识与控制[J].光电工程, 2018, 45(3): 170704. doi: 10.12086/oee.2018.170704

    CrossRef Google Scholar

    Huang L H, Fan M W, Zhou R, et al. System identification and control for large aperture fast-steering mirror driven by PZT[J]. Opto-Electronic Engineering, 2018, 45(3): 170704. doi: 10.12086/oee.2018.170704

    CrossRef Google Scholar

    [6] 汪为民, 王强. 140单元MEMS变形镜研制及测试分析[J].光电工程, 2018, 45(3): 170698. doi: 10.12086/oee.2018.170698

    CrossRef Google Scholar

    Wang W M, Wang Q. Development and characterization of a 140-element MEMS deformable mirror[J]. Opto-Electronic Engineering, 2018, 45(3): 170698. doi: 10.12086/oee.2018.170698

    CrossRef Google Scholar

    [7] 颜召军, 李新阳.基于神经网络的自适应光学系统变形镜控制电压预测方法[J].光学学报, 2010, 30(4): 911-916. doi: 10.3788/m0000620103004.0911

    CrossRef Google Scholar

    Yan Z J, Li X Y. Neural network prediction algorithm for control voltage of deformable mirror in adaptive optical system[J]. Acta Optica Sinica, 2010, 30(4): 911-916. doi: 10.3788/m0000620103004.0911

    CrossRef Google Scholar

    [8] 王冲冲, 胡立发, 何斌, 等.基于神经网络的压电倾斜镜磁滞补偿方法研究[J].中国激光, 2013, 40(11): 1113001. doi: 10.3788/CJL201340.1113001

    CrossRef Google Scholar

    Wang C C, Hu L F, He B, et al. Hysteresis compensation method of piezoelectric steering mirror based on neural network[J]. Chinese Journal of Lasers, 2013, 40(11): 1113001. doi: 10.3788/CJL201340.1113001

    CrossRef Google Scholar

    [9] Moheimani S O R. Accurate and fast nanopositioning with piezoelectric tube scanners: Emerging trends and future challenges[J]. Review of Scientific Instruments, 2008, 79(5): 1-11. doi: 10.1063/1.2957649

    CrossRef Google Scholar

    [10] Mayergoyz I D. Mathematical Models of Hysteresis[M]. New York: Springer-Verlag, 1991.

    Google Scholar

    [11] Hu H, Mrad R B. On the classical Preisach model for hysteresis in piezoceramic actuators[J]. Mechatronics, 2003, 13(2): 85-94. doi: 10.1016/S0957-4158(01)00043-5

    CrossRef Google Scholar

    [12] Banks H T, Kurdila A J. Hysteretic control influence operators representing smart material actuators: identification and approximation[C]//Proceedings of the 35th IEEE Conference on Decision and Control, 1996: 3711-3716.

    Google Scholar

    [13] Su C Y, Wang Q Q, Chen X K, et al. Adaptive variable structure control of a class of nonlinear systems with unknown Prandtl-Ishlinskii hysteresis[J]. IEEE Transactions on Automatic Control, 2005, 50(12): 2069-2074. doi: 10.1109/TAC.2005.860260

    CrossRef Google Scholar

    [14] 刘向东, 修春波, 李黎, 等.迟滞非线性系统的神经网络建模[J].压电与声光, 2007, 29(1): 106-108. doi: 10.3969/j.issn.1004-2474.2007.01.035

    CrossRef Google Scholar

    Liu X D, Xiu C B, Li L, et al. Hysteresis modeling using neural networks[J]. Piezoelectrics & Acoustooptics, 2007, 29(1): 106-108. doi: 10.3969/j.issn.1004-2474.2007.01.035

    CrossRef Google Scholar

    [15] 钱飞, 许素安, 刘亚睿, 等.基于多项式拟合的压电陶瓷迟滞神经网络建模[J].计算机仿真, 2015, 32(1): 361-366. doi: 10.3969/j.issn.1006-9348.2015.01.077

    CrossRef Google Scholar

    Qian F, Xu S A, Liu Y R, et al. Neural network modeling based on polynomial fitting for hysteresis behavior of piezoelectric actuator[J]. Computer Simulation, 2015, 32(1): 361-366. doi: 10.3969/j.issn.1006-9348.2015.01.077

    CrossRef Google Scholar

    [16] 赵新龙.基于迟滞算子的迟滞非线性系统建模与控制研究[D].上海: 上海交通大学, 2006.

    Google Scholar

    Zhao X L. Modeling and control for hysteresis systems based on hysteretic operator[D]. Shanghai: Shanghai Jiao Tong University, 2006.http://www.wanfangdata.com.cn/details/detail.do?_type=degree&id=Y1812272

    Google Scholar

    [17] 马连伟, 谭永红, 邹涛.采用拓展空间法建立迟滞模型[J].系统仿真学报, 2008, 20(20): 5635-5637, 5641.

    Google Scholar

    Ma L W, Tan Y H, Zou T. Modeling hysteresis using expanding-space method[J]. Journal of System Simulation, 2008, 20(20): 5635-5637, 5641.

    Google Scholar

    [18] 罗烨, 柳益君, 朱广萍, 等.基于贝叶斯正则化神经网络的企业资信评估[J].计算机仿真, 2010, 27(11): 303-306. doi: 10.3969/j.issn.1006-9348.2010.11.077

    CrossRef Google Scholar

    Luo Y, Liu Y J, Zhu G P, et al. Bayesian-regularization neural network for corporation credit rating[J]. Computer Simulation, 2010, 27(11): 303-306. doi: 10.3969/j.issn.1006-9348.2010.11.077

    CrossRef Google Scholar

    [19] 王耿.压电驱动器非线性校正技术研究[D].成都: 中国科学院研究生院(光电技术研究所), 2013.

    Google Scholar

    Wang G. Study on correction of nonlinearity of piezoelectric actuator[D]. Chengdu: Institute of Optics and Electronics, Chinese Academy of Sciences, 2013.http://www.wanfangdata.com.cn/details/detail.do?_type=degree&id=Y2368543

    Google Scholar

  • 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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