压电驱动器非线性校正技术研究
|
摘要
随着各行各业对高精度定位的需求的增加，压电精密定位技术得到了越来越广泛的应用，随之也出现了许许多多要解决的问题。其中，压电驱动定位系统的非线性特性对定位精度的影响最为显著，直接影响着系统的性能。论文针对在低频领域使用压电驱动器进行跟踪定位和控制进行了详细的分析和研究，设计出了一种应变反馈式压电驱动器，并提出了新的控制算法对其进行控制，最后在一个光学偏转镜上进行了验证，实验效果较好。论文的主要研究内容有：
首先，全面细致地调研了现有的压电陶瓷驱动器的迟滞和蠕变等非线性特性，并进行了定性和定量的实验测定，找出了其规律和特征。这些特性也是本论文研究的前提和出发点，既是研究对象也是研究基础。
其次，提出并研制了一种驱动与传感一体化的微型精密应变反馈式压电驱动器。该结构克服了压电陶瓷应变量小无法测定的缺陷，采用电容传感器对应变信号调理电路进行了标定，通过最终的实验结果能够得出其定位性能在准静态范围内是有效的，这同时证明了该结构设计是成功的。
再次，研究了前人提出的经典的PI模型，并采用经典的PI模型对我们使用的压电陶瓷驱动器进行建模，从实验结果发现经典的PI模型存在较大的系统误差，并不适合于我室所使用的驱动器。为此，对该经典的PI模型进行了改进，提出了一种新的改进的PI模型，它可以弥补经典PI模型的不足，通过实验证实了该模型的精确性。然后，研究了基于该改进的PI模型的多种控制算法，对各种算法的跟踪定位效果进行了对比，最终得出基于改进的PI逆模型的前馈控制加模糊PID反馈控制的复合控制算法的效果最好，可以有效的抑制迟滞非线性作用。而对于蠕变非线性，通过实验证实了只要存在反馈通道形成小闭环，蠕变效应就可以消除，可以在较长的时间内精确定位而不产生漂移。
最后，设计了一个光学偏转镜并对其偏转角进行了跟踪和定位控制研究。在设计了光学偏转镜结构的基础上，测试了光学偏转镜在没有内部小闭环条件下的跟踪定位性能，证实了迟滞、蠕变效应的存在。然后，使用了内部小闭环对光学偏转镜进行转角控制，内部小闭环中采用了前文提出的基于改进的PI逆模型的前馈控制加模糊PID反馈控制的复合控制算法，通过实验证实了该算法对迟滞、蠕变等非线性的校正作用。该部分工作内容，既验证了迟滞理论模型的正确性，又验证了控制方法的可行性。
本论文的研究工作成功地利用压电驱动器实现了精确定位，消除了迟滞蠕变等非线性效应的影响。用理论和实验证明了，在低频实时定位领域，提出的控制模型和算法能够有效的消除驱动器的非线性效应，为其精确定位应用扫清了障碍。
With the increase in demand for high-precision positioning， piezoelectricprecision positioning technology has been more and more widely used. Meanwhile,many problems appeared. Wherein, the nonlinear characteristic of the piezoelectricactuator has the most significant impact on the positioning accuracy. This has a directimpact on the performance of many systems with piezoelectric actuators. This thesiscarried out a detailed analysis and research for the control of tracking and positioningof piezoelectric actuators in the field of low-frequency field. A strain feedbackpiezoelectric actuator has successfully designed, and a new control algorithm has beenproposed to control the piezoelectric actuator. Ultimately, an optical deflector isdesigned, with which an experiment was carried out to verify the effectiveness of thestrain feedback piezoelectric actuator and its control algorithm. The main researchcontents include the following:
Firstly, we have a comprehensive and detailed investigation of the nonlinearcharacteristics of the piezoelectric ceramic actuator. With the qualitative andquantitative experiments, the rules and characters was found out. These features arethe prerequisite and starting point of this thesis, and they are also the study object anda research base.
Secondly, a strain feedback piezoelectric actuator was designed, which integratedthe driving and sensing functions. With this structure of actuator, the slight strain ofthe piezoelectric actuator can be measured. Then, the output of strain signalconditioning circuit was calibrated with a capacitance sensor. From the experimentalresults, we can see that the positioning performance of piezoelectric actuator is validwithin the quasi-static application. It also shows that the designed structure ofpiezoelectric actuator is successful.
Thirdly, the classic PI model was studied, and with it we modeled thepiezoelectric actuator in our lab. However, we find a larger system error with theclassic PI model. That is to say, the classic model is not suitable for modeling ourpiezoelectric actuator. So, we improved the classic PI model, and got a new modifiedPI model. Finally, the accuracy of the model is confirmed by experiment. A variety ofcontrol algorithms based on this modified PI model were investigated, and thetracking and positioning effects were compared. The experimental results show thatthe complex control algorithms based on the improved PI inverse model feed-forward control plus fuzzy PID feedback control can get a better experimental result, and canhave an effective suppression of nonlinear effects. As for creep nonlinearity, fromexperiment we can conclude that as long as there is a feedback channel, precisepositioning in a longer period of time can be reached without causing drift.
Finally, an optical deflector was designed and some tracking and positioningcontrol experiments for the deflection angle was carried out. When the internalclosed-loop does not work, the tracking and positioning performances of the opticaldeflector were tested. From the test results, we can see the existence of hysteresis andcreep effects in the optical deflector. When the internal closed-loop works, thetracking and positioning performances of the optical deflector were improved greatly.These results confirmed the effectiveness of the complex control algorithms based onthe improved PI inverse model feed-forward control plus fuzzy PID feedback control.The control algorithm can effectively correct the nonlinear characteristics ofhysteresis and creep. This part of the work not only confirmed the correctness of thetheoretical hysteresis model, but also confirmed the feasibility of the control method.
With the work of this thesis, we can see the successful realization of the precisepositioning of the piezoelectric actuator effectively eliminates hysteresis and creepnonlinear effect. Theory and experiments have proved that the proposed controlmodels and algorithms are effective in the low frequency and real-time application.All this cleared the way for its precise positioning applications.
首先，全面细致地调研了现有的压电陶瓷驱动器的迟滞和蠕变等非线性特性，并进行了定性和定量的实验测定，找出了其规律和特征。这些特性也是本论文研究的前提和出发点，既是研究对象也是研究基础。
其次，提出并研制了一种驱动与传感一体化的微型精密应变反馈式压电驱动器。该结构克服了压电陶瓷应变量小无法测定的缺陷，采用电容传感器对应变信号调理电路进行了标定，通过最终的实验结果能够得出其定位性能在准静态范围内是有效的，这同时证明了该结构设计是成功的。
再次，研究了前人提出的经典的PI模型，并采用经典的PI模型对我们使用的压电陶瓷驱动器进行建模，从实验结果发现经典的PI模型存在较大的系统误差，并不适合于我室所使用的驱动器。为此，对该经典的PI模型进行了改进，提出了一种新的改进的PI模型，它可以弥补经典PI模型的不足，通过实验证实了该模型的精确性。然后，研究了基于该改进的PI模型的多种控制算法，对各种算法的跟踪定位效果进行了对比，最终得出基于改进的PI逆模型的前馈控制加模糊PID反馈控制的复合控制算法的效果最好，可以有效的抑制迟滞非线性作用。而对于蠕变非线性，通过实验证实了只要存在反馈通道形成小闭环，蠕变效应就可以消除，可以在较长的时间内精确定位而不产生漂移。
最后，设计了一个光学偏转镜并对其偏转角进行了跟踪和定位控制研究。在设计了光学偏转镜结构的基础上，测试了光学偏转镜在没有内部小闭环条件下的跟踪定位性能，证实了迟滞、蠕变效应的存在。然后，使用了内部小闭环对光学偏转镜进行转角控制，内部小闭环中采用了前文提出的基于改进的PI逆模型的前馈控制加模糊PID反馈控制的复合控制算法，通过实验证实了该算法对迟滞、蠕变等非线性的校正作用。该部分工作内容，既验证了迟滞理论模型的正确性，又验证了控制方法的可行性。
本论文的研究工作成功地利用压电驱动器实现了精确定位，消除了迟滞蠕变等非线性效应的影响。用理论和实验证明了，在低频实时定位领域，提出的控制模型和算法能够有效的消除驱动器的非线性效应，为其精确定位应用扫清了障碍。
With the increase in demand for high-precision positioning， piezoelectricprecision positioning technology has been more and more widely used. Meanwhile,many problems appeared. Wherein, the nonlinear characteristic of the piezoelectricactuator has the most significant impact on the positioning accuracy. This has a directimpact on the performance of many systems with piezoelectric actuators. This thesiscarried out a detailed analysis and research for the control of tracking and positioningof piezoelectric actuators in the field of low-frequency field. A strain feedbackpiezoelectric actuator has successfully designed, and a new control algorithm has beenproposed to control the piezoelectric actuator. Ultimately, an optical deflector isdesigned, with which an experiment was carried out to verify the effectiveness of thestrain feedback piezoelectric actuator and its control algorithm. The main researchcontents include the following:
Firstly, we have a comprehensive and detailed investigation of the nonlinearcharacteristics of the piezoelectric ceramic actuator. With the qualitative andquantitative experiments, the rules and characters was found out. These features arethe prerequisite and starting point of this thesis, and they are also the study object anda research base.
Secondly, a strain feedback piezoelectric actuator was designed, which integratedthe driving and sensing functions. With this structure of actuator, the slight strain ofthe piezoelectric actuator can be measured. Then, the output of strain signalconditioning circuit was calibrated with a capacitance sensor. From the experimentalresults, we can see that the positioning performance of piezoelectric actuator is validwithin the quasi-static application. It also shows that the designed structure ofpiezoelectric actuator is successful.
Thirdly, the classic PI model was studied, and with it we modeled thepiezoelectric actuator in our lab. However, we find a larger system error with theclassic PI model. That is to say, the classic model is not suitable for modeling ourpiezoelectric actuator. So, we improved the classic PI model, and got a new modifiedPI model. Finally, the accuracy of the model is confirmed by experiment. A variety ofcontrol algorithms based on this modified PI model were investigated, and thetracking and positioning effects were compared. The experimental results show thatthe complex control algorithms based on the improved PI inverse model feed-forward control plus fuzzy PID feedback control can get a better experimental result, and canhave an effective suppression of nonlinear effects. As for creep nonlinearity, fromexperiment we can conclude that as long as there is a feedback channel, precisepositioning in a longer period of time can be reached without causing drift.
Finally, an optical deflector was designed and some tracking and positioningcontrol experiments for the deflection angle was carried out. When the internalclosed-loop does not work, the tracking and positioning performances of the opticaldeflector were tested. From the test results, we can see the existence of hysteresis andcreep effects in the optical deflector. When the internal closed-loop works, thetracking and positioning performances of the optical deflector were improved greatly.These results confirmed the effectiveness of the complex control algorithms based onthe improved PI inverse model feed-forward control plus fuzzy PID feedback control.The control algorithm can effectively correct the nonlinear characteristics ofhysteresis and creep. This part of the work not only confirmed the correctness of thetheoretical hysteresis model, but also confirmed the feasibility of the control method.
With the work of this thesis, we can see the successful realization of the precisepositioning of the piezoelectric actuator effectively eliminates hysteresis and creepnonlinear effect. Theory and experiments have proved that the proposed controlmodels and algorithms are effective in the low frequency and real-time application.All this cleared the way for its precise positioning applications.
引文
[1] Sitti M. NSF workshop on future directions in nano-scale systems，dynamics and control [J]
[2] Shapiro B. Workshop on control of micro-and nano-scale systems [J]. IEEE Control SystemsMagazine，April2005:82-88
[3]白春礼.扫描隧道显微术及其应用[M].上海:上海科学技术出版社，1992
[4]彭昌盛，宋少先，谷庆宝.扫描探针显微术理论与应用[M].北京:化学工业出版社，2007
[5] J.L. Jang, Y.S. Tarng. A study of the active vibration control of a cutting tool [J] Journal ofMaterials Processing Technology,1999, vol.95, pp.78-82.
[6] S.O.R. Moheimani, G. C. Goodwin. Introduction to the special issue on dynamics and controlof smart structures[J] IEEE Trans. Control Syst. Technol,2001,vol.9, pp.3-4.
[7] ZHANG D, CHANG C, ONO T, etal. A piezodriven XY-microstage for multiprobenanorecording[J]．Sensors and Actuators,2003,108(1-3)：230—233．
[8]Curie P，Curie J. Development by Pressure of Polar eleetrieity in hemihedral crystals withinclined faees[J]. Bull.soc.min.de France，1880，3，90-93
[9]Jaffe B，Roth R S. Marzullo S.Piezoelectric Properties of Lead Zirconate-Lead TitanateSolid-Solution Ceramies[J]. Journal of Applied Physics.1954.25(6).809-810.
[10]唐凤，黄尚廉.PZT非线性特性的研究[J].压电与声光，1997，19(3):180-183
[11]张涛，孙立宁，蔡鹤皋.压电陶瓷基本特性研究[J].光学精密工程,1998，6(5):26-32
[12] GUYOMAR D. Piezoelectric ceramics nonlinear behavior: application to langevintransducer[J]. Journal de Physique,1997,7(6):1197-1208.
[13]崔玉国,孙宝元等.压电陶瓷执行器迟滞与非线性成因分析[J].光学精密工程,2003，11(3):270-275
[14] H. T. Banks and R. C. Smith,“Hysteresis modeling in smart material systems,” J. Appl. Mech.Eng., vol.5, no.1, pp.31–45,2000.
[15] Ge P, Jouaneh M. Tracking control of a piezoceramic actuator[J]. IEEE Transactions onControl System Technology,1996,4(3):209-216.
[16] Kam K. Leang, Santosh Devasia. Design of hysteresis-compensating iterative learningcontrol for piezo-positioners: Application to atomic force microscopes[J] Mechatronics16(2006)141–158
[17] B. Mokaberi and A. A. G. Requicha,“Drift compensation for automatic nanomanipulationwith scanning probe microscopes,” IEEE Trans. Autom. Sci. Eng., vol.3, no.3, pp.199–207,Jul.2006.
[18] D. Croft, G. Shed, and S. Devasia,“Creep, hysteresis, and vibration compensation forpiezoactuators: Atomic force microscopy application,” J. Dynamic Syst., Measure., Control,vol.123, pp.35–43, Mar.2001.
[19] Aoshima S., Yoshizawa N., and Yabuta T.,“Compact mass axis alignment device withpiezoelements for optial fibers,” IEEE Photonics Technology Letters,4, pp.462-464,1992.
[20] Hocken R J. Nanotechnology and its impact on manufacturing [A].Tokyo:Japan\USASymposium on Flexible Auto-oration [C],1993:7-15.
[21] Uchino K. Piezoelectric actuator and ultrasonic motors. Norwell, MA: Kluwer AcademicPublishers;1997.
[22]孙立宁，孙绍云，曲东升，等.基于PZT的微驱动定位系统及控制方法的研究[J].光学精密工程，2004，12(1)：55~59.
[23]田延岭，张大卫，闫兵.二自由度微定位平台的研制[J].光学精密工程，2006，14(1)：94-99.
[24]范伟，余晓芬，奚琳.压电陶瓷驱动系统及控制方法研究[J].光学精密工程，2007，15(3)：368-371
[25]杨志刚，刘登云，吴丽萍，等.应用于压电叠堆泵的微位移放大机构[J].光学精密工程，2007，15(6)：884-888.
[26] Kim, J.D., Nam, S.R.: A piezoelectrically driven micro-positioning system for theductilemode griding of brittle materials. Journal of Materials Processing Technology61,309–319(1999)
[27].孔祥东，张玉林，尹明.电子束三维光刻技术的研究[J].微细加工技术，2003，(4):9-13.
[28].孔祥东，孙晓军，张玉林等.电子束真空辐射固化技术基础研究[J].微细加工技术，2004，(3):10-13
[29] P. Ge and M. Jouaneh,“Tracking Control of a Piezoceramic Actuator”, IEEE Trans. Controland System Tech., Vol.4, No.3, pp.209-216, May1996.
[30] W. S. Galinaitis,“Two Methods for Modeling Scalar Hysteresis and their use in ControllingActuators with Hysteresis”, Ph.D. Thesis,1999.
[31]陈辉，谭永红，周杏鹏等.压电陶瓷执行器的动态模型辨识与控制[J].光学精密工程,2012，20(1):88-95
[32] Jean-Jacques E.Slotine Weiping Li.应用非线性控制（程代展译）.北京：机械工业出版社.2006.4
[33] Changhai Ru, Liguo Chen, Bing Shao,“A hysteresis compensation method of piezoelectricactuator: Model, Identification and Control”, Control Engineering Practice,2009
[34] H.C.Liaw, D.Oetomo,B.Shirinzadeh, and G. Alici,“Robust motion tracking control ofpiezoelectric actuator systems,” IEEE Int,Conf. On Robotics and Automation, Orlando,Florida,15-19May2006.
[35] Sun Lining, Ru Changhai,et al. Tracking control of piezoelectric actuator based on a newmathematical model[J] OURNAL OF MICROMECHANICS AND MICROENGINEERING14(2004)1439–1444
[36] Jonq-Jer Tzen, Shyr-Long Jeng, et al. Modeling of piezoelectric actuator for compensationand controller design[J] Precision Engineering27(2003)70–86
[37] Saeid Bashash, Nader Jalili， Underlying memory-dominant nature of hysteresis inpiezoelectric materials,JOURNAL OF APPLIED PHYSICS,0141032006：161-166P
[38] Saeid Bashash,Nader Jalili,Feedforward hysteresis compensation in trajectory control ofpiezoelectrically-driven nanostagers,Smart Structures and Materials,2006：106-111P
[39] Saeid Bashash and Nader Jalili，Intelligence rules of hysteresis in the feedforward trajectorycontrol of piezoelectrically-driven nanostagers，JOURNAL OF MICROMECHANICS ANDMICROENGINEERING，J.Micromech Microeng.17(2007)342–349P
[40] GuoYing Gu, LiMin Zhu. Modeling of rate-dependent hysteresis in piezoelectric actuatorsusing a family of ellipses[J] Sensors and Actuators A165(2011)303–309
[41]孙增坼等.智能控制理论与技术.清华大学出版社，1992
[42] K. Furutani, M. Urushibata, and N. Mohri,“Improvement of Control Method forPiezoelectric Actuator by Combing Induced Charge Feedback with Inverse Transfer FunctionCompensation,” IEEE Int. Conf. on Robotics&Automation, Leuven, Belgium, May1998.
[43] Comstock，R.H.，Charge control of piezoelectric actuators to reduce hysteresis，1981，U.S.Patent42653527
[44] J. M. Cruz-Hernandez and V. Hayward,“Phase Control Approach to Hysteresis Reduction”IEEE Trans. Control Systems Technology, vol.9,2001
[45] Luigi Bruno. Carmine Maletta. Real-time calibration of open-loop piezoelectric actuators forinterferometric applications[J] Int J Mech Mater Des (2008)4:97–103
[46] Omatu, S., Yoshioka, M.: Self-Tuning Neuro-PID Control and Applications. In: IEEEInternational Conference on System, Man, and Cybernetics, vol.3, pp.1985–1989(1997)
[47] Yamamoto, T., Kaneda, M., Oki, T., Watanabe, E., Tanaka, K.: Intelligent tuning PIDcontrollers. In: IEEE International on Systems, Man and Cybernetics, Intelligent Systems forthe21st Century, vol.3, pp.2610–2615(1995)
[48] Van-tsai Liu, Ming-jen Chen, et al. Modeling of Micro-Piezoelectric Motion Platform forCompensation and Neuro-PID Contriller Design[J] LNCS5754, pp.784–793,2009.
[49] J. Minase, T.-F. Lu, et al. Adaptive identification of hysteresis and creep in piezoelectric stackactuators[J] Int J Adv Manuf Technol (2010)46:913–921
[50] Chun-Yi Su, Yury Stepanenko, et al. Robust Adaptive Control of a Class of NonlinearSystems with Unknown Backlash-like Hysteresis[J] IEEE TRANSACTIONS ONAUTOMATIC CONTROL, VOL.45, NO.12, DECEMBER2000
[51] Hung-Yi Chen, Jin-Wei Liang. Model-Free Adaptive Sensing and Control for aPiezoelectrically Actuated System[J] Sensor2010,10,10545-10559
[52] S.S.Ku, U. Pinsopon, S.Cetinkunt, and S.Nakjima,”Design, fabrication, and real-time neuralnetwork of a three-degree-of-freedom nanopositioner,” IEEE/ASME Trans. Mechatron., vol.5,n0.3,pp.273-280,Sep.2000.
[53] C.L.Hwang and C.Jan,”A reinforcement discrete neuron-adaptive control for unknownpiezoelectric actuator system with dominant hysteresis,”IEEE Trans.Neural Netw., vol.14,no.1, pp.66-78,.Jan,2003.
[54] DONG R, TAN Y, CHEN H, et al..A neural networks based model for rate-dependenthysteresis for piezoceramic actuators[J]. Sensors and Actuators A:Physical,2008,143(2):370-376
[55] Xinliang Zhang, YonghongTan. Neural networks based identification and compensation ofrate-dependent hysteresis in piezoelectric actuators[J] Physica B405(2010)2687–2693
[56] Chih-Hsiang Yang, Kuo-Ming Chang, et al. Adaptive Neutal Network Control forPiezoelectric Hysteresis Compensation in A Positioning System[J] IEEE lSlE2006, July9-12,2006, Montreal, Quebec, Canada
[57] S.Bashash and N.Jalili,“Trajectory control of piezoelectric actuators using nonlinear variablestructure control,” presented at the Int. Symp. Collaborat. Res. Appl.Sci., Vancouver,BC,Canada,2005
[58] S.Bashash and N.Jalili,“A new hysteresis mode for piezoelectric actuator with application toprecision trajectory control,”presented at the ASME Int.Mechan. Eng.Congr.Expo., Orlando,FL,2005
[59] K.Abidi, A. Sabanovic, and S.Yesilyurt,“Sliding Model Control Based Disturbancecompensation and External Force Estimation for a Piezoelectric Actuator,” IEEE Int.Workshop on Advance Motion Control, pp.529-534, March2004.
[60] Alberto Isidori.非线性控制系统（第三版）(王奔庄圣贤译).北京：电子工业出版社，2005.6
[61] Khalid Abidi, Asif Sabanovic. Sliding-Mode Control for High-Precision Motion of aPiezo-stage[J] IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL.54, NO.1, FEBRUARY2007
[62] C. J. Chien, C. T. Hsu, and C. Y. Yao,“Fuzzy system-based adaptive iterative learning controlfor nonlinear plants with initial state errors,” IEEE Trans. Fuzzy Syst., vol.12, no.5, pp.724–732, Oct.2004.
[63] JIUM-MING LIN, PO-KUANG CHANG. Applying Intelligent Fuzzy Control to ReduceHysteresis Effect of Force Actuator in a SPM[J] WSEAS TRANSACTIONS on SYSTEMSand CONTROL
[64] Basem M. Badr, Wahied. G. Ali. Nanopositioning Fuzzy Control for Piezoelectric Actuators[J]International Journal of Engineering&Technology IJET-IJENS Vol:10No:01
[65] B. Dijkstra,“Iterative learning control with applications to a waferstage,” Ph.D. dissertation,Mech. Eng. Dept., TU Eindhoven, Eindhoven, The Netherlands,2004.
[66] Ying Wu, Qingze Zou. Iterative Control Approach to Compensate for Both the Hysteresisand the Dynamics Effects of Piezo Actuators[J]. IEEE TRANSACTIONS ON CONTROLSYSTEMS TECHNOLOGY, VOL.15, NO.5, SEPTEMBER2007
[67] B.M.Chen, T.H.Lee, C.C.Hang,Y.Guo,and S.Weerasmriya,”An H-infinite Almost DisturbanceDecoupling Robust Controller Design for a Piezoelectric Bimorph Actuator with Hysteresis,”IEEE Tran. Automation and Control, Vol.7, No.2, pp.160-174, Mar1999.
[68] Brian E. Helfrich, Chibum Lee. Combined H-inf-Feedback Control and Iterative LearningControl Design With Application to Nanopositioning Systems[J] IEEE TRANSACTIONSON CONTROL SYSTEMS TECHNOLOGY, VOL.18, NO.2, MARCH2010
[69] Mayergoyz ID. Mathematical Models of Hysteresis. New York: Springer-Verlag;1991.
[70] A. J. Fleming and S. O. R. Moheimani,“Sensorless vibration suppression and scancompensation for piezoelectric tube nanopositioners,” IEEE Trans. Control Syst. Technol.,vol.14, no.1, pp.33–44, Jan.2007.
[71] H Hu and R.. Ben Mrad,"On the classical Preisach model for hysteresis in piezoelectricactuators," Mechatronics, vol.13, no.2, pp.85-94,2002.
[72] G. Tao and P. Kokotovic,"Adaptive Control of Plants with Unknown Hysteresis," IEEETransactions On Automatic Control, vol.40, no.2, pp.200-212,1995.
[73] TANIGUCHI Motoya. Ultra precision wafer positioning by six-axis micro-motionmechanism[J]. Int.J.Japan Soc.Prec.Eng.1992,26(1):582-58
[74] H. Jung, D.G. Gweon, Creep characteristics of piezoelectric actuators, Review of ScientificInstruments71(4)(2000)1896–1900.
[75]周晓峰基于PZT微定位系统控制研究：[硕士学位论文]，浙江：浙江大学，2004年.
[76]王耿、官春林等.应变式微型精密压电驱动器的一体化设计及其PID控制.光学精密工程.2013年第3期
[77] ASTM E251-92,“Standard Test Methods for Performance Characteristics of Metallic BondedResistance Strain Gages,” ASTM International,2003.
[78]博弈创作室编著. APDL参数化有限元分析技术及其应用实例，北京：中国水利水电出版社，2004.3
[79]龚曙光、谢桂兰、黄云清.ANSYS参数化编程与命令手册，北京：机械工业出版社，2009.8
[80] Murray, W. M. and W.R. Miller,“The Bonded Electrical Resistance Strain Gage,” OxfordUniversity Press,2002.
[81] Tech Note TN-504-1,“Strain Gage Thermal Output and Gage Factor Variation withTemperature”, Vishay Micro-Measurements, January2005.
[82] Parker, Jr., Allen R.,“Simultaneous Measurement of Temperature and Strain Using FourConnecting Wires,” NASA TM-104271, November1993.
[83] Ang, W.T., Khosla, P.K., Riviere, C.N.: Feedforward controller with inverse ratedependentmodel for piezoelectric actuators in trajectory-tracking applications. IEEE/ASME Trans.Mechatron.12(2),134–142(2007)
[84] P. Krejci and K. Kuhnen2001Inverse control of systems with hysteresis and creep”, IEEProc. Control Theory Appl., vol.148, no.3
[85] K. Ikuta, M. Tsukamoto, and S. Hirose1991Mathematical model and experimentalverification of shape memory alloy for designing micro actuator,” in Proc. IEEE Int. Conf.Micro Electro Mech. Syst., pp.103–111.
[86] K. Kuhnen,”Inverse feedforward controller for complex hysteretic nonlinearities insmart-material systems,” Control Intell. Syst., vol.29, no.3, pp.74-83,2001.
[87] Hao Jiang, Hongli Ji, Jinhao Qiu, and Yuansheng Chen,“A Modified Prandtl-Ishlinskii Modelfor Modeling Asymmetric Hysteresis of Piezoelectric Actuators.”, IEEE TRANSACTIONSON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL.57,MAY2010
[88] Kuhnen “modeling, identification and compensation of complex hysteretic nonlinearities amodified Prandtl-Ishlinskii approach”2003
[89] W T A, A F G, modeling rate-dependent hysteresis in piezoelectric actuator, proc.IEEE2003
[90] DONG R, TAN Y. Modeling hysteresis in piezoceramic actuators using modifiedPrandtl-Ishlinskii model[J]. Physica B,2009,404(8-11):1336-1342.
[91]王岳宇，赵学增.补偿压电陶瓷迟滞与蠕变的逆控制算法[J].光学精密工程，2006，14(6):1032-1040.
[92] P. Krejci and K. Kuhnen,“Inverse control of systems with hysteresis and creep,” Proc. Inst.Elect. Eng. Control Theory Appl., vol.148, no.3, pp.185–192, May2001.
[93] Yun Li, Kiam Heong Ang, Chong G. C. Y. PID Control System Analysis and Design[J]. IEEEControl Systems Magazine,2006,26:32-41
[94]刘金琨.先进PID控制MATLAB仿真.电子工业出版社，2007年。
[95]曾光奇等.模糊控制理论及工程应用.华中科技大学出版社.2000年。
[96]尤昌德.现代控制理论基础.电子工业出版社.1996
[97] Gustavo Luiz C.M. de Abreu and José F. Ribeiro,“A self-organizing fuzzy logic controllerfor the active control of flexible structures using piezoelectric actuators”, Applied SoftComputing, pp271–283,2002.
[98] L. X. Wang, A course in fuzzy systems and control. Prentice Hall PTR,1997.
[99] Hao Jiang, Hongli Ji, et al. A modified Prandtl-Ishlinskii Model for Modeling AsymmetricHysteresis of Piezoelectric Actuators. IEEE TRANSACTIONS ON ULTRASONICS,FERROELECTRICS, AND FREQUENCY CONTROL, VOL.57, NO.5,MAY2010.
[100] Jianghua Zhong, Bin Yao. Adaptive Robust Precision Motion Control of a PiezoelectricPositioning Stage, IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY,VOL.16,NO.5,SEPTEMBER2008
[2] Shapiro B. Workshop on control of micro-and nano-scale systems [J]. IEEE Control SystemsMagazine，April2005:82-88
[3]白春礼.扫描隧道显微术及其应用[M].上海:上海科学技术出版社，1992
[4]彭昌盛，宋少先，谷庆宝.扫描探针显微术理论与应用[M].北京:化学工业出版社，2007
[5] J.L. Jang, Y.S. Tarng. A study of the active vibration control of a cutting tool [J] Journal ofMaterials Processing Technology,1999, vol.95, pp.78-82.
[6] S.O.R. Moheimani, G. C. Goodwin. Introduction to the special issue on dynamics and controlof smart structures[J] IEEE Trans. Control Syst. Technol,2001,vol.9, pp.3-4.
[7] ZHANG D, CHANG C, ONO T, etal. A piezodriven XY-microstage for multiprobenanorecording[J]．Sensors and Actuators,2003,108(1-3)：230—233．
[8]Curie P，Curie J. Development by Pressure of Polar eleetrieity in hemihedral crystals withinclined faees[J]. Bull.soc.min.de France，1880，3，90-93
[9]Jaffe B，Roth R S. Marzullo S.Piezoelectric Properties of Lead Zirconate-Lead TitanateSolid-Solution Ceramies[J]. Journal of Applied Physics.1954.25(6).809-810.
[10]唐凤，黄尚廉.PZT非线性特性的研究[J].压电与声光，1997，19(3):180-183
[11]张涛，孙立宁，蔡鹤皋.压电陶瓷基本特性研究[J].光学精密工程,1998，6(5):26-32
[12] GUYOMAR D. Piezoelectric ceramics nonlinear behavior: application to langevintransducer[J]. Journal de Physique,1997,7(6):1197-1208.
[13]崔玉国,孙宝元等.压电陶瓷执行器迟滞与非线性成因分析[J].光学精密工程,2003，11(3):270-275
[14] H. T. Banks and R. C. Smith,“Hysteresis modeling in smart material systems,” J. Appl. Mech.Eng., vol.5, no.1, pp.31–45,2000.
[15] Ge P, Jouaneh M. Tracking control of a piezoceramic actuator[J]. IEEE Transactions onControl System Technology,1996,4(3):209-216.
[16] Kam K. Leang, Santosh Devasia. Design of hysteresis-compensating iterative learningcontrol for piezo-positioners: Application to atomic force microscopes[J] Mechatronics16(2006)141–158
[17] B. Mokaberi and A. A. G. Requicha,“Drift compensation for automatic nanomanipulationwith scanning probe microscopes,” IEEE Trans. Autom. Sci. Eng., vol.3, no.3, pp.199–207,Jul.2006.
[18] D. Croft, G. Shed, and S. Devasia,“Creep, hysteresis, and vibration compensation forpiezoactuators: Atomic force microscopy application,” J. Dynamic Syst., Measure., Control,vol.123, pp.35–43, Mar.2001.
[19] Aoshima S., Yoshizawa N., and Yabuta T.,“Compact mass axis alignment device withpiezoelements for optial fibers,” IEEE Photonics Technology Letters,4, pp.462-464,1992.
[20] Hocken R J. Nanotechnology and its impact on manufacturing [A].Tokyo:Japan\USASymposium on Flexible Auto-oration [C],1993:7-15.
[21] Uchino K. Piezoelectric actuator and ultrasonic motors. Norwell, MA: Kluwer AcademicPublishers;1997.
[22]孙立宁，孙绍云，曲东升，等.基于PZT的微驱动定位系统及控制方法的研究[J].光学精密工程，2004，12(1)：55~59.
[23]田延岭，张大卫，闫兵.二自由度微定位平台的研制[J].光学精密工程，2006，14(1)：94-99.
[24]范伟，余晓芬，奚琳.压电陶瓷驱动系统及控制方法研究[J].光学精密工程，2007，15(3)：368-371
[25]杨志刚，刘登云，吴丽萍，等.应用于压电叠堆泵的微位移放大机构[J].光学精密工程，2007，15(6)：884-888.
[26] Kim, J.D., Nam, S.R.: A piezoelectrically driven micro-positioning system for theductilemode griding of brittle materials. Journal of Materials Processing Technology61,309–319(1999)
[27].孔祥东，张玉林，尹明.电子束三维光刻技术的研究[J].微细加工技术，2003，(4):9-13.
[28].孔祥东，孙晓军，张玉林等.电子束真空辐射固化技术基础研究[J].微细加工技术，2004，(3):10-13
[29] P. Ge and M. Jouaneh,“Tracking Control of a Piezoceramic Actuator”, IEEE Trans. Controland System Tech., Vol.4, No.3, pp.209-216, May1996.
[30] W. S. Galinaitis,“Two Methods for Modeling Scalar Hysteresis and their use in ControllingActuators with Hysteresis”, Ph.D. Thesis,1999.
[31]陈辉，谭永红，周杏鹏等.压电陶瓷执行器的动态模型辨识与控制[J].光学精密工程,2012，20(1):88-95
[32] Jean-Jacques E.Slotine Weiping Li.应用非线性控制（程代展译）.北京：机械工业出版社.2006.4
[33] Changhai Ru, Liguo Chen, Bing Shao,“A hysteresis compensation method of piezoelectricactuator: Model, Identification and Control”, Control Engineering Practice,2009
[34] H.C.Liaw, D.Oetomo,B.Shirinzadeh, and G. Alici,“Robust motion tracking control ofpiezoelectric actuator systems,” IEEE Int,Conf. On Robotics and Automation, Orlando,Florida,15-19May2006.
[35] Sun Lining, Ru Changhai,et al. Tracking control of piezoelectric actuator based on a newmathematical model[J] OURNAL OF MICROMECHANICS AND MICROENGINEERING14(2004)1439–1444
[36] Jonq-Jer Tzen, Shyr-Long Jeng, et al. Modeling of piezoelectric actuator for compensationand controller design[J] Precision Engineering27(2003)70–86
[37] Saeid Bashash, Nader Jalili， Underlying memory-dominant nature of hysteresis inpiezoelectric materials,JOURNAL OF APPLIED PHYSICS,0141032006：161-166P
[38] Saeid Bashash,Nader Jalili,Feedforward hysteresis compensation in trajectory control ofpiezoelectrically-driven nanostagers,Smart Structures and Materials,2006：106-111P
[39] Saeid Bashash and Nader Jalili，Intelligence rules of hysteresis in the feedforward trajectorycontrol of piezoelectrically-driven nanostagers，JOURNAL OF MICROMECHANICS ANDMICROENGINEERING，J.Micromech Microeng.17(2007)342–349P
[40] GuoYing Gu, LiMin Zhu. Modeling of rate-dependent hysteresis in piezoelectric actuatorsusing a family of ellipses[J] Sensors and Actuators A165(2011)303–309
[41]孙增坼等.智能控制理论与技术.清华大学出版社，1992
[42] K. Furutani, M. Urushibata, and N. Mohri,“Improvement of Control Method forPiezoelectric Actuator by Combing Induced Charge Feedback with Inverse Transfer FunctionCompensation,” IEEE Int. Conf. on Robotics&Automation, Leuven, Belgium, May1998.
[43] Comstock，R.H.，Charge control of piezoelectric actuators to reduce hysteresis，1981，U.S.Patent42653527
[44] J. M. Cruz-Hernandez and V. Hayward,“Phase Control Approach to Hysteresis Reduction”IEEE Trans. Control Systems Technology, vol.9,2001
[45] Luigi Bruno. Carmine Maletta. Real-time calibration of open-loop piezoelectric actuators forinterferometric applications[J] Int J Mech Mater Des (2008)4:97–103
[46] Omatu, S., Yoshioka, M.: Self-Tuning Neuro-PID Control and Applications. In: IEEEInternational Conference on System, Man, and Cybernetics, vol.3, pp.1985–1989(1997)
[47] Yamamoto, T., Kaneda, M., Oki, T., Watanabe, E., Tanaka, K.: Intelligent tuning PIDcontrollers. In: IEEE International on Systems, Man and Cybernetics, Intelligent Systems forthe21st Century, vol.3, pp.2610–2615(1995)
[48] Van-tsai Liu, Ming-jen Chen, et al. Modeling of Micro-Piezoelectric Motion Platform forCompensation and Neuro-PID Contriller Design[J] LNCS5754, pp.784–793,2009.
[49] J. Minase, T.-F. Lu, et al. Adaptive identification of hysteresis and creep in piezoelectric stackactuators[J] Int J Adv Manuf Technol (2010)46:913–921
[50] Chun-Yi Su, Yury Stepanenko, et al. Robust Adaptive Control of a Class of NonlinearSystems with Unknown Backlash-like Hysteresis[J] IEEE TRANSACTIONS ONAUTOMATIC CONTROL, VOL.45, NO.12, DECEMBER2000
[51] Hung-Yi Chen, Jin-Wei Liang. Model-Free Adaptive Sensing and Control for aPiezoelectrically Actuated System[J] Sensor2010,10,10545-10559
[52] S.S.Ku, U. Pinsopon, S.Cetinkunt, and S.Nakjima,”Design, fabrication, and real-time neuralnetwork of a three-degree-of-freedom nanopositioner,” IEEE/ASME Trans. Mechatron., vol.5,n0.3,pp.273-280,Sep.2000.
[53] C.L.Hwang and C.Jan,”A reinforcement discrete neuron-adaptive control for unknownpiezoelectric actuator system with dominant hysteresis,”IEEE Trans.Neural Netw., vol.14,no.1, pp.66-78,.Jan,2003.
[54] DONG R, TAN Y, CHEN H, et al..A neural networks based model for rate-dependenthysteresis for piezoceramic actuators[J]. Sensors and Actuators A:Physical,2008,143(2):370-376
[55] Xinliang Zhang, YonghongTan. Neural networks based identification and compensation ofrate-dependent hysteresis in piezoelectric actuators[J] Physica B405(2010)2687–2693
[56] Chih-Hsiang Yang, Kuo-Ming Chang, et al. Adaptive Neutal Network Control forPiezoelectric Hysteresis Compensation in A Positioning System[J] IEEE lSlE2006, July9-12,2006, Montreal, Quebec, Canada
[57] S.Bashash and N.Jalili,“Trajectory control of piezoelectric actuators using nonlinear variablestructure control,” presented at the Int. Symp. Collaborat. Res. Appl.Sci., Vancouver,BC,Canada,2005
[58] S.Bashash and N.Jalili,“A new hysteresis mode for piezoelectric actuator with application toprecision trajectory control,”presented at the ASME Int.Mechan. Eng.Congr.Expo., Orlando,FL,2005
[59] K.Abidi, A. Sabanovic, and S.Yesilyurt,“Sliding Model Control Based Disturbancecompensation and External Force Estimation for a Piezoelectric Actuator,” IEEE Int.Workshop on Advance Motion Control, pp.529-534, March2004.
[60] Alberto Isidori.非线性控制系统（第三版）(王奔庄圣贤译).北京：电子工业出版社，2005.6
[61] Khalid Abidi, Asif Sabanovic. Sliding-Mode Control for High-Precision Motion of aPiezo-stage[J] IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL.54, NO.1, FEBRUARY2007
[62] C. J. Chien, C. T. Hsu, and C. Y. Yao,“Fuzzy system-based adaptive iterative learning controlfor nonlinear plants with initial state errors,” IEEE Trans. Fuzzy Syst., vol.12, no.5, pp.724–732, Oct.2004.
[63] JIUM-MING LIN, PO-KUANG CHANG. Applying Intelligent Fuzzy Control to ReduceHysteresis Effect of Force Actuator in a SPM[J] WSEAS TRANSACTIONS on SYSTEMSand CONTROL
[64] Basem M. Badr, Wahied. G. Ali. Nanopositioning Fuzzy Control for Piezoelectric Actuators[J]International Journal of Engineering&Technology IJET-IJENS Vol:10No:01
[65] B. Dijkstra,“Iterative learning control with applications to a waferstage,” Ph.D. dissertation,Mech. Eng. Dept., TU Eindhoven, Eindhoven, The Netherlands,2004.
[66] Ying Wu, Qingze Zou. Iterative Control Approach to Compensate for Both the Hysteresisand the Dynamics Effects of Piezo Actuators[J]. IEEE TRANSACTIONS ON CONTROLSYSTEMS TECHNOLOGY, VOL.15, NO.5, SEPTEMBER2007
[67] B.M.Chen, T.H.Lee, C.C.Hang,Y.Guo,and S.Weerasmriya,”An H-infinite Almost DisturbanceDecoupling Robust Controller Design for a Piezoelectric Bimorph Actuator with Hysteresis,”IEEE Tran. Automation and Control, Vol.7, No.2, pp.160-174, Mar1999.
[68] Brian E. Helfrich, Chibum Lee. Combined H-inf-Feedback Control and Iterative LearningControl Design With Application to Nanopositioning Systems[J] IEEE TRANSACTIONSON CONTROL SYSTEMS TECHNOLOGY, VOL.18, NO.2, MARCH2010
[69] Mayergoyz ID. Mathematical Models of Hysteresis. New York: Springer-Verlag;1991.
[70] A. J. Fleming and S. O. R. Moheimani,“Sensorless vibration suppression and scancompensation for piezoelectric tube nanopositioners,” IEEE Trans. Control Syst. Technol.,vol.14, no.1, pp.33–44, Jan.2007.
[71] H Hu and R.. Ben Mrad,"On the classical Preisach model for hysteresis in piezoelectricactuators," Mechatronics, vol.13, no.2, pp.85-94,2002.
[72] G. Tao and P. Kokotovic,"Adaptive Control of Plants with Unknown Hysteresis," IEEETransactions On Automatic Control, vol.40, no.2, pp.200-212,1995.
[73] TANIGUCHI Motoya. Ultra precision wafer positioning by six-axis micro-motionmechanism[J]. Int.J.Japan Soc.Prec.Eng.1992,26(1):582-58
[74] H. Jung, D.G. Gweon, Creep characteristics of piezoelectric actuators, Review of ScientificInstruments71(4)(2000)1896–1900.
[75]周晓峰基于PZT微定位系统控制研究：[硕士学位论文]，浙江：浙江大学，2004年.
[76]王耿、官春林等.应变式微型精密压电驱动器的一体化设计及其PID控制.光学精密工程.2013年第3期
[77] ASTM E251-92,“Standard Test Methods for Performance Characteristics of Metallic BondedResistance Strain Gages,” ASTM International,2003.
[78]博弈创作室编著. APDL参数化有限元分析技术及其应用实例，北京：中国水利水电出版社，2004.3
[79]龚曙光、谢桂兰、黄云清.ANSYS参数化编程与命令手册，北京：机械工业出版社，2009.8
[80] Murray, W. M. and W.R. Miller,“The Bonded Electrical Resistance Strain Gage,” OxfordUniversity Press,2002.
[81] Tech Note TN-504-1,“Strain Gage Thermal Output and Gage Factor Variation withTemperature”, Vishay Micro-Measurements, January2005.
[82] Parker, Jr., Allen R.,“Simultaneous Measurement of Temperature and Strain Using FourConnecting Wires,” NASA TM-104271, November1993.
[83] Ang, W.T., Khosla, P.K., Riviere, C.N.: Feedforward controller with inverse ratedependentmodel for piezoelectric actuators in trajectory-tracking applications. IEEE/ASME Trans.Mechatron.12(2),134–142(2007)
[84] P. Krejci and K. Kuhnen2001Inverse control of systems with hysteresis and creep”, IEEProc. Control Theory Appl., vol.148, no.3
[85] K. Ikuta, M. Tsukamoto, and S. Hirose1991Mathematical model and experimentalverification of shape memory alloy for designing micro actuator,” in Proc. IEEE Int. Conf.Micro Electro Mech. Syst., pp.103–111.
[86] K. Kuhnen,”Inverse feedforward controller for complex hysteretic nonlinearities insmart-material systems,” Control Intell. Syst., vol.29, no.3, pp.74-83,2001.
[87] Hao Jiang, Hongli Ji, Jinhao Qiu, and Yuansheng Chen,“A Modified Prandtl-Ishlinskii Modelfor Modeling Asymmetric Hysteresis of Piezoelectric Actuators.”, IEEE TRANSACTIONSON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL.57,MAY2010
[88] Kuhnen “modeling, identification and compensation of complex hysteretic nonlinearities amodified Prandtl-Ishlinskii approach”2003
[89] W T A, A F G, modeling rate-dependent hysteresis in piezoelectric actuator, proc.IEEE2003
[90] DONG R, TAN Y. Modeling hysteresis in piezoceramic actuators using modifiedPrandtl-Ishlinskii model[J]. Physica B,2009,404(8-11):1336-1342.
[91]王岳宇，赵学增.补偿压电陶瓷迟滞与蠕变的逆控制算法[J].光学精密工程，2006，14(6):1032-1040.
[92] P. Krejci and K. Kuhnen,“Inverse control of systems with hysteresis and creep,” Proc. Inst.Elect. Eng. Control Theory Appl., vol.148, no.3, pp.185–192, May2001.
[93] Yun Li, Kiam Heong Ang, Chong G. C. Y. PID Control System Analysis and Design[J]. IEEEControl Systems Magazine,2006,26:32-41
[94]刘金琨.先进PID控制MATLAB仿真.电子工业出版社，2007年。
[95]曾光奇等.模糊控制理论及工程应用.华中科技大学出版社.2000年。
[96]尤昌德.现代控制理论基础.电子工业出版社.1996
[97] Gustavo Luiz C.M. de Abreu and José F. Ribeiro,“A self-organizing fuzzy logic controllerfor the active control of flexible structures using piezoelectric actuators”, Applied SoftComputing, pp271–283,2002.
[98] L. X. Wang, A course in fuzzy systems and control. Prentice Hall PTR,1997.
[99] Hao Jiang, Hongli Ji, et al. A modified Prandtl-Ishlinskii Model for Modeling AsymmetricHysteresis of Piezoelectric Actuators. IEEE TRANSACTIONS ON ULTRASONICS,FERROELECTRICS, AND FREQUENCY CONTROL, VOL.57, NO.5,MAY2010.
[100] Jianghua Zhong, Bin Yao. Adaptive Robust Precision Motion Control of a PiezoelectricPositioning Stage, IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY,VOL.16,NO.5,SEPTEMBER2008