压电陶瓷驱动器迟滞非线性建模及逆补偿控制
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摘要
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%。
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%.
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%.
引文
[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.
[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.
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[4] Tyson R K. Principles of Adaptive Optics[M]. Boston:Academic Press, 1991.
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[6] Wang W M, Wang Q. Development and characterization of a140-element MEMS deformable mirror[J]. Opto-Electronic Engineering, 2018, 45(3):170698.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.
[7] 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.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.
[8] 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.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.
[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.
[10] Mayergoyz I D. Mathematical Models of Hysteresis[M]. New York:Springer-Verlag, 1991.
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[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.
[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.
[14] Liu X D, Xiu C B, Li L, et al. Hysteresis modeling using neural networks[J]. Piezoelectrics&Acoustooptics, 2007, 29(1):106–108.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.
[15] 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.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.
[16] Zhao X L. Modeling and control for hysteresis systems based on hysteretic operator[D]. Shanghai:Shanghai Jiao Tong University, 2006.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.
[17] 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.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.
[18] 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.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.
[19] Wang G. Study on correction of nonlinearity of piezoelectric actuator[D]. Chengdu:Institute of Optics and Electronics, Chinese Academy of Sciences, 2013.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.
[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.
[3] Jiang W H. Overview of adaptive optics development[J]. Opto-Electronic Engineering, 2018, 45(3):170489.姜文汉.自适应光学发展综述[J].光电工程, 2018, 45(3):170489.
[4] Tyson R K. Principles of Adaptive Optics[M]. Boston:Academic Press, 1991.
[5] 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.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.
[6] Wang W M, Wang Q. Development and characterization of a140-element MEMS deformable mirror[J]. Opto-Electronic Engineering, 2018, 45(3):170698.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.
[7] 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.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.
[8] 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.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.
[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.
[10] Mayergoyz I D. Mathematical Models of Hysteresis[M]. New York:Springer-Verlag, 1991.
[11] Hu H, Mrad R B. On the classical Preisach model for hysteresis in piezoceramic actuators[J]. Mechatronics, 2003, 13(2):85–94.
[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.
[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.
[14] Liu X D, Xiu C B, Li L, et al. Hysteresis modeling using neural networks[J]. Piezoelectrics&Acoustooptics, 2007, 29(1):106–108.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.
[15] 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.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.
[16] Zhao X L. Modeling and control for hysteresis systems based on hysteretic operator[D]. Shanghai:Shanghai Jiao Tong University, 2006.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.
[17] 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.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.
[18] 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.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.
[19] Wang G. Study on correction of nonlinearity of piezoelectric actuator[D]. Chengdu:Institute of Optics and Electronics, Chinese Academy of Sciences, 2013.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.
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