广东工业大学学报 ›› 2024, Vol. 41 ›› Issue (04): 14-25.doi: 10.12052/gdutxb.230134

• 特约综述 • 上一篇    

压电致动器非线性特征的控制策略研究进展

施建昌1,2, 肖晓兰1,2, 李昊1, 冯发辉1, 陈志健1, 区森荣1, 陈可3   

  1. 1. 广东工业大学 机电工程学院, 广东 广州 510006;
    2. 广东工业大学 高性能工具全国重点实验室, 广东 广州 510006;
    3. 利物浦大学 电气与电子工程学院, 利物浦 L69 3GJ
  • 收稿日期:2023-08-30 发布日期:2024-08-13
  • 通信作者: 肖晓兰(1979–) ，女，高级实验师，工学博士，主要研究方向为机电一体化创新设计、超精密加工技术与装备，E-mail：xxlan@gdut.edu.cn
  • 作者简介:施建昌(1996–) ，男，硕士研究生，主要研究方向为压电驱动及先进运动控制，E-mail：1714361760@qq.com
  • 基金资助:
    国家重点研发计划项目(2023YFE0204400)；国家重点实验室开放课题项目(JMDZ2021009)

Research Progress on Control Strategies for Nonlinear Characteristics of Piezoelectric Actuators

Shi Jian-chang1,2, Xiao Xiao-lan1,2, Li Hao1, Feng Fa-hui1, Chen Zhi-jian1, Ou Sen-rong1, Chen Ke3   

  1. 1. School of Electromechanical Engineering, Guangdong University of Technology, Guangzhou 510006, China;
    2. National Key Laboratory of High Performance Tools, Guangdong University of Technology, Guangzhou 510006, China;
    3. Department of Electrical Engineering & Electronics, University of Liverpool, Liverpool L69 3GJ, The United Kingdom of Great Britain and Northern Ireland
  • Received:2023-08-30 Published:2024-08-13

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摘要： 压电致动器具有位移分辨率高、体积小、响应快、驱动负载能力强、可多自由度输出以及不受电磁干扰等优点，被广泛应用在微纳加工、微机电系统封装、生物医学以及航空航天等领域。然而，由于压电致动器自身存在的迟滞、蠕变等非线性特征，使得输出的稳定性以及精确度受到一定的影响，需采取恰当的控制策略解决上述问题。本文首先对压电致动器的非线性特征进行概述；其次，重点回顾了迟滞模型和蠕变模型的发展历程；然后，介绍了压电致动器的控制补偿策略及研究进展；最后对压电致动器控制技术的未来发展方向进行了讨论与展望。

关键词: 压电致动器, 非线性特征, 迟滞模型, 蠕变模型, 控制策略

Abstract: Piezoelectric actuators have the advantages of high displacement resolution, compact size, rapid response, strong load-driving capability, the ability to provide multi-degree of freedom outputs, and immunity to electromagnetic interference etc, which are widely used in micro-nano processing, micro-electromechanical system packaging, bio-medicine, aerospace engineering and other fields. However, the nonlinear characteristics of piezoelectric actuators, such as hysteresis and creep, make affection for the stability and can cause unstable and inaccurate outputs, which requires certain appropriate control strategies to overcome the above problems. In this research, the nonlinear characteristics of piezoelectric actuators are firstly summarized.Secondly, research progress of hysteresis model and creep model is reviewed. Then, the compensation of control strategy and research progress of piezoelectric actuators are introduced. Finally, the trend of piezoelectric actuator future development in control technology is discussed and prospected.

Key words: piezoelectric actuators, nonlinear characteristics, hysteresis model, creep model, control strategies

中图分类号: 

  • O482.41
[1] 谭久彬. 超精密测量是支撑光刻机技术发展的基石[J]. 仪器仪表学报, 2023, 44(3): 1-7.
TAN J B. Ultra-precision measurement: the cornerstone of the lithography development [J]. Chinese Journal of Scientific Instrument, 2023, 44(3): 1-7.
[2] 张威, 肖渊, 张津瑞, 等. 压电式微滴喷头电源驱动系统设计与实现[J]. 西安工程大学学报, 2019, 33(3): 326-331.
ZHANG W, XIAO Y, ZHANG J R, et al. Design and imple- mentation of driven system for piezoelectric droplet sprinkler [J]. Journal of Xi'an Polytechnic University, 2019, 33(3): 326-331.
[3] DENG J, LIU S H, LIU Y X, et al. A 2-DOF needle insertion device using inertial piezoelectric actuator [J]. IEEE Transactions on Industrial Electronics, 2022, 69(4): 3918-3927.
[4] 刘军. 用于航天控制力矩陀螺的行波型超声电机技术研究[D]. 南京: 南京航空航天大学, 2020.
[5] HANGYEOL B, ABDUL M K, YOUNGSHIK K. A bidirectional rotating actuator by using a single shape memory alloy wire in adouble bend shape [J]. Sensors and Actuators: A. Physical, 2023, 360: 114526.
[6] AI K E, RAZZAGHI P, HURMUZLU Y. Feedback control of millimeter scale pivot walkers using magnetic actuation [J]. Robotics and Autonomous System, 2023, 168: 104496.
[7] 李锐. 基于迟滞环对称性的压电陶瓷迟滞补偿算法研究[D]. 哈尔滨: 哈尔滨工业大学, 2018.
[8] 彭国祥. 压电驱动器输出力迟滞效应的建模与控制方法研究[D]. 哈尔滨: 哈尔滨工业大学, 2021.
[9] GAN J Q, ZHANG X M. A review of nonlinear hysteresis modeling and control of piezoelectric actuators [J]. AIP Advances, 2019, 9: 040702.
[10] 李泽琨. 压电陶瓷作动器迟滞非线性建模与补偿控制研究[D]. 哈尔滨: 哈尔滨工业大学, 2022.
[11] 于志亮. 压电陶瓷执行器迟滞补偿与控制方法研究[D]. 哈尔滨: 哈尔滨工业大学, 2019.
[12] 徐瑞瑞. 基于Bouc-Wen模型的压电陶瓷驱动的运动平台迟滞建模与控制研究[D]. 武汉: 武汉工程大学, 2022.
[13] 甘金强. 微位移平台压电陶瓷驱动系统非线性建模与控制方法研究[D]. 广州: 华南理工大学, 2017.
[14] LIU Y F, DU D S, QI N M, et al. A distributed parameter Maxwell-slip model for the hysteresis in piezoelectric actuators [J]. IEEE Transactions on Industrial Electronics, 2018, 66(9): 7150-7158.
[15] XIE S B, NI C R, DUAN H Y, et al. Hybrid model based on the Maxwell-Slip model and a support vector machine for hysteresis in piezoelectric actuators[C] //2020 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM) . Boston: IEEE, 2020: 36-41.
[16] 段建东, 雷阳, 李浩, 等. 铁磁元件J-A模型的研究进展与趋势[J]. 高压电器, 2020, 56(12): 16-23.
DUAN J D, LEI Y, LI H, et al. Review of ferromagnetic components J-A models [J]. High Voltage Apparatus, 2020, 56(12): 16-23.
[17] SAVOIE M, SHAN J J. Monte carlo study of Jiles-Atherton parameters on hysteresis area and remnant displacement[C]//2022 IEEE 31st International Symposium on Industrial Electronics (ISI E) . Anchorage: IEEE, 2022: 1017-1022.
[18] ZHANG B, GUPTA B, DUCHARNE B, et al. Dynamic magneticscalar hysteresis lump model based on Jiles-Atherton quasistatichysteresis model extended with dynamic fractional derivativecontribution [J]. IEEE Transactions on Magnetics, 2018, 54(11): 1-5.
[19] 明敏. 压电微动平台迟滞补偿与运动控制研究[D]. 武汉: 武汉大学, 2021.
[20] 严秀权, 吴洪涛, 李耀, 等. 压电作动器的支持向量机迟滞模型[J]. 仪器仪表学报, 2018, 39(9): 228-235.
YAN X Q, WU H T, LI Y, et al. Support vector machine-based hystersis model of piezoelectric actuator [J]. Chinese Journal of Scientific Instrument, 2018, 39(9): 228-235.
[21] IKHOUANE F. A survey of the hysteretic Duhem model [J]. Archives of Computational Methods in Engineering, 2018, 25(4): 965-1002.
[22] 孙涛, 李国平, 孙浩益. 基于Duhem模型和逆模型的压电执行器精密定位及控制[J]. 宁波大学学报(理工版), 2017, 30(1): 13-17.
SUN T, LI G P, SUN H Y. Accurate positioning and control of piezoelectric actuator based on Duhem model and inverse model [J]. Journal of Ningbo University (NSEE), 2017, 30(1): 13-17.
[23] 贺一丹, 王贞艳, 何延超, 等. 压电陶瓷作动器的改进Duhem迟滞模型[J]. 压电与声光, 2021, 43(3): 431-434.
HE Y D, WANG Z Y, HE Y C, et al. Improved Duhem hysteresis modeling of piezoelctric actuators [J]. Piezoelectrics & Acoustooptics, 2021, 43(3): 431-434.
[24] 高源蓬, 张泉, 李清灵, 等. 压电陶瓷执行器迟滞非线性补偿与最优控制[J]. 仪器仪表学报, 2022, 43(8): 163-172.
GAO Y P, ZHANG Q, LI Q L, et al. Hysteresis nonlinear compensation and optimal control of piezoelectric actuators [J]. Chinese Journal of Science Instrument, 2022, 43(8): 163-172.
[25] SU C Y, STEPANENKO Y, SVONODA J, et al. Robust adaptive control of a class of nonlinear systems with unknown backlash-like hysteresis [J]. IEEE Transactions on Automatic Control, 2000, 45(12): 2427-2432.
[26] ZHOU J, WEN C Y, ZHANG Y. Adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash-like hysteresis [J]. IEEE Transactions on Automatic Control, 2004, 49(10): 1751-1759.
[27] 杨晓京, 胡俊文, 李庭树. 压电微定位台的率相关动态迟滞建模及参数辨识[J]. 光学精密工程, 2019, 27(3): 610-618.
YANG X J, HU J W, LI T S. Rate-dependent dynamic hysteresismodeling of piezoelectric micro platform and its parameter identification [J]. Optics and Precision Engineering, 2019, 27(3): 610-618.
[28] CHEN Y Y, WANG Y , DONG Q, et al. Robust adaptive back-stepping control for nonlinear systems with unknown backlash-like hysteresis[C] //2021 IEEE International Conference on Mechatronics and Automation (ICMA) . Takamatsu: IEEE, 2021: 554-559.
[29] LI Z, LI Z K, XU H Z, et al. Development of a butterfly fractional-order backlash-like hysteresis model for dielectric elastomer actuators [J]. IEEE Transactions on Industrial Electronics, 2022, 70(2): 1794-1801.
[30] WEN Y K. Method for random vibration of hysteretic system [J]. Journal of the Engineering Mechanics Division, 1976, 102(2): 249-263.
[31] WANG D H, ZHU W. A phenomenological model for pre- stressed piezoelectric ceramic stack actuators [J]. Smart Materials & Structures, 2011, 20(3): 35018.
[32] RAKOTONDRABE M. Bouc-Wen modeling and inverse multiplicative structure to compensate hysteresis nonlinearity in piezoelectric actuators [J]. IEEE Transactions on Automation Science & Engineering, 2010, 8(2): 428-431.
[33] ZABLOTSKAYA T Y. Analyzing the classical and extended Bouc-Wen model parameters[C] //2020 2nd International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA) . Lipetsk: IEEE, 2020: 576-581.
[34] ABOURA F. Modeling and analyzing Bouc-Wen hysteresis model[C] //2019 19th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering (ISEF) . Nancy: IEEE, 2019: 1-2.
[35] HU J Y, DONG R L, TAN Y H. A new improved Bouc-Wen model of piezoelectric ceramics actuators[C] //2021 40th Chinese Control Conference (CCC) . Shanghai: IEEE, 2021: 1-5.
[36] SALEEM A, AL-RATROUT S, MESBAH M. A fitness function for parameters identification of Bouc-Wen hysteresis model for piezoelectric actuators[C] //2018 5th International Conference on Electrical and Electronic Engineering (ICEEE) . Istanbul: IEEE, 2018: 119-123.
[37] MINH T V, TUNG T T, CHEN X K. Precision control of piezoelectric actuator using modified Bouc-Wen model[C] //2020 International Conference on Advanced Mechatronic Systems (ICAMS) . Hanoi: IEEE, 2020: 162-167.
[38] 赵博文. 压电陶瓷驱动平台的迟滞补偿控制方法研究[D]. 盐城: 盐城工学院, 2023.
[39] PREISACH F. Über die magnetische Nachwirkung [J]. Zeitschrift Für Physik, 1935, 94(5): 277-302.
[40] MGOLDFARB M, CELANOVIC N. Modeling piezoelectric stack actuators for control of micromanipulation [J]. IEEE Control Systems Magazine, 1997, 17(3): 69-79.
[41] 范青武, 张恒, 刘旭东, 等. 基于三线性插值法的Preisach模型及数值实现[J]. 压电与声光, 2018, 40(5): 811-814.
FAN Q W, ZHANG H, LIU X D, et al. The Preisach model based on trilinear interpolation method and its numerical implementation [J]. Piezoelectrics & Acoustooptics, 2018, 40(5): 811-814.
[42] 武毅男, 方勇纯. 基于Preisach模型的深度学习网络迟滞建模[J]. 控制理论与应用, 2018, 35(6): 723-731.
WU Y N, FANG Y C. Hysteresis modeling with deep leaning network based on Preisach model [J]. Control Theory & Application, 2018, 35(6): 723-731.
[43] 陈彬, 王斐然, 陈睿, 等. 基于R-L型分数阶导数的动态解析逆Preisach模型[J]. 高压电技术, 2023, 49(9): 3918-3926.
CHEN B, WANG F R, CHEN R, et al. Dynamic analytical inverse Preisach model based on R-L fractional derivative [J]. High Voltage Engineering, 2023, 49(9): 3918-3926.
[44] MACKI J W, NISTRI P, ZECCA P. Mathematical models for hysteresis [J]. SIAM Review, 1993, 35(1): 94-123.
[45] GU G Y, YANG M J, ZHU L M. Real-time inverse hysteresis compensation of piezoelectric actuators with a modified Prandtl-Ishlinskii mode [J]. Review of Scientific Instruments, 2012, 83(6): 065106.
[46] XIE S, REN G, WANG B. A modified asymmetric generalized Prandtl-Ishlinskii model for characterizing the irregular asymmetrichysteresis of self-made pneumatic muscle actuators [J]. Mechanism and Machine Theory, 2020, 149: 103836.
[47] KO Y R, CHUN S, KIM T H. Identification of inverse gen- eralized asymmetric Prandtl-Ishlinskii model for compensation of hysteresis nonlinearities[C] //2017 IEEE Conference on Control Technology and Applications (CCTA) . Maui: IEEE, 2017: 1183- 1188.
[48] 钟云, 黄楠, 曾俊海. 压电驱动器迟滞非线性的增强型Prandtl-Ishlinskii模型建模及实验验证[J]. 机电工程技术, 2020, 49(10): 33-35.
ZHONG Y, HUANG N, ZENG J H. Enhanced Prandtl-Ishlinskii modeling and experimental verification of hysteresis nonlinearities in piezoelectric actuators [J]. Mechanical & Electrical Engineering Technology, 2020, 49(10): 33-35.
[49] 张金, 张健滔, 宁艺文, 等. 基于神经网络的压电能量收集器性能预估模型[J]. 振动, 测试与诊断, 2023, 49(1): 172-178.
ZHANG J, ZHANG J T, NING Y W, et al. Performance prediction model of piezoelectric energy harvester based on artificial neural network [J]. Journal of Vibration, Measurement & Diagnosis, 2023, 49(1): 172-178.
[50] 熊永程, 贾文红, 张丽敏, 等. 基于深度神经网络(DNN) 的压电陶瓷前馈补偿研究[J]. 压电与声光, 2022, 44(1): 35-41.
XIONG Y C, JIA W H, ZHANG L M, et al. Research on feedforward compensation of piezoelectric ceramics based on deep neural network [J]. Piezoelectrics & Acoustooptics, 2022, 44(1): 35-41.
[51] WANG G, YAO X M, CUI J J, et al. A novel piezoelectric hysteresis modeling method combining LSTM and NARX neural network [J]. Modern Physics Letters B, 2020, 34(28): 1-14.
[52] CHENG L, LIU W C, HOU Z G, et al. Neural-network based nonlinear model predictive control for piezoelectric actuators [J]. IEEE Transactions on Industrial Electronics, 2015, 62(12): 7717-7727.
[53] ZADEH L A. Fuzzy sets [J]. Information and Control, 1965, 8(3): 338-353.
[54] 毛剑琴, 丁海山. 率相关迟滞非线性系统的智能化建模与控制[J]. 中国科学, 2009, 39(3): 289-304.
[55] 陈圣鑫. 基于T-S模糊系统的压电执行器建模与控制[D]. 杭州: 浙江理工大学, 2021.
[56] 张伟, 毛剑琴. 基于模糊树模型的非线性系统内模控制[J]. 控制理论与应用, 2013(4): 463-468.
ZHANG W, MAO J Q. Internal model control for nonlinear system based on fuzzy-tree method [J]. Control Theory & Application, 2013(4): 463-468.
[57] LI P Z, ZHANG D F, HU J Y, et al. Hysteresis modelling and feedforward control of piezoelectric actuator based on simplified interval type-2 fuzzy system [J]. Sensor, 2020, 20(9): 2587.
[58] YANG L, WANG Q T, XIAO Y Q, et al. Hysteresis modeling of piezoelectric actuators based on a T-S fuzzy model [J]. Electronics, 2022, 11(17): 2786.
[59] LIU G W, ÖZER A Ö, WANG M G. Longtime dynamics for a novel piezoelectric beam model with creep and thermo-viscoelasticeffects [J]. Nonlinear Analysis: Real World Application, 2022, 68: 103666.
[60] 范伟, 林瑜阳, 李钟慎. 基于BP神经网络的压电陶瓷蠕变预测[J]. 计量学报, 2017, 38(4): 429-434.
FAN W, LIN Y Y, LI Z S. Prediction of the creep of piezoelectric ceramic based on BP neural network optimized by genetic algorithm [J]. Acta Metrologica Sinica, 2017, 38(4): 429-434.
[61] 温盛军, 李亮, 喻俊, 等. 迟滞与蠕变耦合压电系统的建模及补偿方法[J]. 振动与冲击, 2023, 42(7): 25-37.
WEN S J, LI L, YU J, et al. Modeling and compensation method of hysteresis-creep coupled piezoelectric system [J]. Journal of Vibration and Shock, 2023, 42(7): 25-37.
[62] 赵学良. 低速大范围下压电执行器动态蠕变特性分析与控制方法研究[D]. 济南: 山东大学, 2016.
[63] ZHONG J P, NISHIDA R, SHINSHI T. A digital charge control strategy for reducing the hysteresis in piezoelectric actuators: analysis, design and implementation [J]. Precision Engineering, 2021, 67: 370-382.
[64] GAN J Q, ZHANG X M. A review of nonlinear hysteresis modeling and control of piezoelectric actuators [J]. AIP Advance, 2019, 9(4): 1-10.
[65] COMSTOCK R H. Charge control of piezoelectric actuators to reduce hysteresis effects: US4263527A[P]. 1981-4-21.
[66] 余婷婷. 基于电荷控制法的压电惯性摩擦驱动器的设计及控制研究[D]. 上海: 华东理工大学, 2023.
[67] 喻奇志. 基于电荷驱动的压电变形镜控制方法研究[D]. 宁波: 宁波大学, 2019.
[68] 王博文, 崔玉国, 谢启芳, 等. 基于率相关迟滞模型的压电微动平台前馈控制[J]. 压电与声光, 2022, 44(6): 898-900.
WANG B W, CUI Y G, XIE Q F, et al. Feedforward control of piezoelectric micro-positioning stage based on rate-dependent hysteresis model [J]. Piezoelectric & Acoustooptics, 2022, 44(6): 898-900.
[69] 赵建杰. 基于前馈控制算法的快速响应压电陶瓷模型设计[D]. 哈尔滨: 哈尔滨工业大学, 2020.
[70] 陈辉. 多维超精密定位系统建模与控制关键技术研究[D]. 南京: 东南大学, 2015.
[71] 韩少鹏. 压电陶瓷驱动器多段改进动态PI模型研究与精度控制[D]. 杭州: 杭州电子科技大学, 2019.
[72] 郭兴旺. 纳米定位与扫描平台模型辨识与控制算法研究[D]. 沈阳: 沈阳建筑大学, 2016.
[73] 于文慧. 二维压电平台迟滞动力学复合建模及其运动特性研究[D]. 哈尔滨: 哈尔滨工业大学, 2022.
[74] LI W G, YANG Z C, LI K, et al. Hybrid feedback PID-FxLMSalgorithm for active vibration control of cantilever beam with piezoelectric stack actuator [J]. Journal of Sound and Vibration, 2021, 509: 116243.
[75] WANG L, ZHAO Y Y, LIU J X, et al. Uncertainty-oriented optimal PID control design framework for piezoelectric structures based on subinterval dimension-wise method (SDWM) and non-probabilistic time-dependent reliability (NTDR) analysis [J]. Journal of Sound and Vibration, 2023, 549: 117588.
[76] 杜建周, 陈远晟, 刘绍娜, 等. 基于自适应逆控制的压电驱动电源[J]. 压电与声光, 2022, 44(6): 901-906.
DU J Z, CHEN Y S, LIU S N, et al. Research on piezoelectric drive power with adaptive inverse control [J]. Piezoelectric & Acoustooptics, 2022, 44(6): 901-906.
[77] 陆奇涛. 自驱动自适应压电步进驱动器的研究[D]. 杭州: 浙江师范大学, 2022.
[78] SUN J F, CHEN W K, CHEN X S. Model reference adaptive control with adjustable gain for piezoelectric actuator [J]. European Journal of control, 2022, 67: 100712.
[79] SHI B C, SHI R, WANG F J. Design of an adaptive feedfor- ward feedback combined control for piezoelectric actuated micro positioning stage[J]. Precision Engineering, 2022, 78: 199-205.
[80] 张毅. 压电作动器的非线性建模及控制方法研究[D]. 哈尔滨: 哈尔滨理工大学, 2022.
[81] DING Z A, YANG Z J, CHEN C H, et al. Improved sliding mode dynamic matrix control strategy: application on spindle loading and precision measuring device based on piezoelectric actuator [J]. Mechanical Systems and Signal Processing, 2022, 167: 108543.
[82] SHIEH H J, CHIU Y J, CHEN Y T. Optimal PID control system of a piezoelectric micropositioner[C] //2008 IEEE/SCIE International Symposium on System Integration, Nagoya: IEEE, 2008: 1-5.
[83] XU R, WANG Z S, ZHOU M L, et al. A robust fractional-order sliding mode control technique for piezoelectric nanopositioning stage in Trajectory-tracking application [J]. Sensors and Actuators: A. Physical, 2023, 363: 114711.
[84] CHANG K M, CHEN J M, LIU Y T. Nonlinear sliding mode control for piezoelectric tool holder with bellow-type hydraulic displacement amplification mechanism [J]. Sensors and Actuators: A. Physical, 2023, 361: 114543.
[85] ZHANG C, YU Y W, ZHANG X Y, et al. Predefined-time adaptive control of a piezoelectric-driven motion system with time-varying output constraint [J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2023, 70(7): 2605-2609.
[86] WU Y N, CHEN H, SUN N, et al. Neural network based adaptive control for a piezoelectric actuator with model uncertainty and unknown external disturbance [J]. International Journal of Robust and Nonlinear Control, 2023, 33(3): 2251-227.
[87] ZHANG Z G, DONG Y K, YU S, et al. Model-free adaptive positioning control of the bidirectional stick-slip piezoelectric actuator with coupled asymmetric flexure-hinge mechanisms [J]. Sensors, 2023, 23(18): 7795.
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