超声电机驱动的大行程、高精度二维运动平台关键技术的研究
|
摘要
精密运动平台在显微外科手术设备、电子隧道扫描显微镜、三坐标测量机等很多精密设备上都有着广泛的应用需求。利用压电陶瓷的逆压电效应工作的超声电机以其响应快、分辨率高等独特的性能愈来愈得到精密驱动领域专家学者的重视和认可。目前，利用压电陶瓷的静变形来实现纳米级定位精度的运动平台，其行程往往只有几十到几百微米，而利用电磁电机和压电作动器组合而成的宏微结合运动平台又有着机械结构和控制系统复杂的缺点，因此，由具有纳米级位移分辨率的超声电机构建大行程、高精度运动平台成为前沿技术之一。
本文的主要工作围绕着超声电机驱动的大行程、高精度运动平台的关键技术，进行了深入的研究，并取得以下成果：
（1）研究了行波型旋转超声电机的单周速度波动率、步距一致性的问题，提出了一种提高单周速度稳定性的结构改进方案。理论分析认为加工和装配误差引起的定/转子接触界面上沿圆周方向的压力不均衡是影响行波型旋转超声电机单周速度稳定性、步距均匀性的主要原因之一。为此，提出一种单轴承支撑附加调心结构的方案，可以使接触界面实现压力自平衡，改善接触界面的压力分布。实验结果表明，空载单周相对速度波动率降低了约40.0%，波动小于2.0%；这有利于提高运动平台开环步进运动时步距的一致性。
（2）研究了行波型旋转超声电机的最小响应脉冲宽度和电机关断时过冲量的大小。旋转超声电机的启动/停止瞬态特性决定了其角度分辨率，进而影响丝杠平台的位移分辨率（最小步距），影响运动平台的定位精度。结合丝杠导程（4mm），研究结果可以预测出超声电机驱动的丝杠平台理论上所能达到的定位精度（0.6μm）。
（3）开发了行波型旋转超声电机驱动的二维平台。利用直线光栅尺和编码器两种不同的位置反馈单元的信号作比对，分别测试了平台的螺距不均匀误差、回程误差，并在搭建的基于GT-400运动控制卡的控制系统中对其进行了补偿，将丝杠平台的定位精度由丝杠的标称定位精度±5μm提高至±2.5μm。
（4）直线超声电机驱动的运动平台的性能很大程度上取决于直线超声电机的性能，而直线超声电机的性能很大程度上取决于其定子与动子（平台）的接触状态，而为了减小接触变形对定位精度的影响，本文采用高硬度摩擦材料（ZrO、AL2O3）作为摩擦副。因此，作者研究了高硬度材料摩擦副直线超声电机定子与动子之间的接触匹配问题，提出了“接触频率”的概念。通过建立高硬度摩擦副直线超声电机的定子/动子在接触面法向上的接触模型并进行理论和实验研究，得出了定子支撑弹簧刚度、预压力、定子质心和驱动足的振幅等对接触频率的影响规律，探讨了相关改善方法。
（5）为了提高运动平台的驱动单元的性能，研究了提高直线超声电机驱动单元的推力、效率及稳定性的途径。提出采用多个超声电机协同工作的“异步并联”的方法。通过设定每个超声电机的驱动信号之间的相位，使得不同的超声电机定子依次交替作用于动子，以避免多个定子间相互干扰、磨损加剧和内耗增加的问题，提高了驱动单元的驱动效率，并进行了实验验证。
（6）直线电机驱动的运动平台的位移分辨率、瞬态特性决定了直线平台的定位精度；作者研究了单足V形、双足碟形直线超声电机的瞬态特性及双足蝶形直线超声电机驱动的运动平台的位移分辨率，分析了各种参数对位移分辨率的影响。实验结果表明：定子从开始振动至达到稳定振幅仅需1.7ms，关断时间小于1ms；本文双足直线超声电机驱动的精密运动平台的分辨率达到25nm。
（7）建立了直线超声电机驱动的运动平台的等效电路模型，得到了其传递函数。分析比较了基于MSP430单片机、DSP以及GT-400运动控制卡的各种控制器的特点，并在基于GT-400运动控制卡的控制系统上实验了模糊与PID双模控制算法，使运动平台的精度在60mm行程范围内达到了±0.5μm。
There are broad needs for the precision motion stage in various fields, such as micro surgeryequipment, the electron scanning tunneling microscope, the three coordinate measuring machines, etc.Ultrasonic motor (USM) which utilizes the inverse piezoelectric effect of the piezoelectric material,has got more and more attention from the experts and scholars working in the precision driving fieldsfor its advantages like fast response, high resolution, etc. The travel range of piezoelectric stage usedthe static deformation of piezoelectric ceramics always be only get to a few hundred microns. On theother hand, the actual applications of macro/micro combined stage have been restricted in thecomplex structure and controller. As a result, the research of the large travel precision motion stagedriven by USM is becomeing one of the frontier technologies.
The main work in this paper focus on some key aspects of the precision motion stage driven byUSM with a large travel:
（1） In this paper, the author studied the velocity fluctuation ratio in each cycle and the steppitch consistency of traveling wave type rotary ultrasonic motors (TRUM) and proposed a structuralimprovement scheme. The analysis results show that one of the main reasons for velocity fluctuationof TRUM is pressure imbalance along the circumference on the contact interface because ofmachining or assembling error in the present case of duplex bearing structure. Theoretical analysisshows that the scheme can realize pressure auto-balance with single bearing and self-aligningstructure. It also can make the pressure distribution on contact interface more uniform. Experimentalresults show that the no-load velocity fluctuation ratio decreased40.0%, and velocity fluctuationrange less than2.0%. This will help improve the consistency of the step pitch when the stage isworking in the open loop stepping mode.
（2）The minimum pulse width which can drive TRUM and the amount of overshoot pulseswhen the TRUM is power off were studied in this paper. They are closely related to the TRUM’stransient characteristics. The angular resolution of TRUM is determined by its transient characteristics.Meanwhile, the displacement resolution of the stage driven by TRUM is determined by the angular resolution of TRUM. This research can forecast the positioning accuracy of the ball-screw-drivenstage if the screw lead was given.
（3）One2-DOF stage driven by TRUM was developed in this paper. The lead-screw pitch errorand the return error were studied through setup two sets of position feedback systems with linearencoders and rotary encoders. Finally, the verification experiment has been accomplished on the stage.Experimental results show that the positioning accuracy of the stage has been improved to2.5μm bythe control system based on GT-400motion control card with error compensation.
（4）The performance of the stage driven by linear ultrasonic motors (LUSM) is determined bythe performance of LUSM. The performance of LUSM depends on the contact state on the contactinterface. Therefore, the contact problem of linear ultrasonic motor was studied in this paper. Hardcontact materials, such as ZrO or AL2O3, have been used to reduce the impact of contact deformationand surface roughness. However, experimental results show that, in this kind of hard contact materialslinear ultrasonic motors (HLUSM), there exists a phenomenon that the contact frequency betweenthe stator and the mover (slider) is far less than the frequency of the driving signal, which prevents thevibration energy of the stator from being utilized fully. In order to solve this problem, we have madethe model of the high frequency micro-amplitude contact behavior in normal direction of HLUSM.Then, theoretical analysis and experimental investigation on micro-impact processes of HLUSM havebeen finished. The impact laws of parameters on the contact frequency have been derived, includingthe stiffness of the stator supporting spring, preload and the high frequency vibration amplitude of thedriving tip and the low-frequency vibration amplitude of stator. Finally, the related improvementmeasures have been discussed.
（5）Aim at improving the performance of driving units of motion stage, the asynchronousbundle of linear ultrasonic motor (ABLUSM) which can build the high thrust, high efficiency, stableand reliable driving unit with LUSM has been discussed. The concept of ABLUSM is proposed. Thebasic principle is that numbers of stators (vibrators) alternately drive a mover (rotor) in a drivingsignal cycle, so that, it can avoid the problem of mutual interference of different stators, wear andinternal power dissipation increased. Therefore, the efficiency of the driving unit can be improvedsignificantly. Finally, the verification experiment was conducted.
（6）The positioning accuracy of the stage driven by LUSM is largely depends on thedisplacement resolution and the transient characteristics of the LUSM. So, the transient characteristicsof two kinds of USMs have been studied in this paper. Furthermore, theoretical analysis andexperimental investigation on the resolution of the stage driven by the HLUSM with two driving tips have been completed. The impact of various parameters on the displacement resolution of the stagewas also discussed. Experimental results show that, the displacement resolution of the precision stagedriven by HLUSM with two driving tips reached25nm.
（7） The equivalent circuit model of motion stage driven by HLUSM was established, and thetransfer function of this model was derived. The characteristics of controllers which based on MCU,DSP and GT-400motion control card have been compared with, respectively. One experiment usedfuzzy and PID dual-mode control algorithm has been finished on the control system based on GT-400motion control card. Experimental results show that the positioning accuracy of the stage has beenimproved to0.5μm with the travel of60mm.
本文的主要工作围绕着超声电机驱动的大行程、高精度运动平台的关键技术，进行了深入的研究，并取得以下成果：
（1）研究了行波型旋转超声电机的单周速度波动率、步距一致性的问题，提出了一种提高单周速度稳定性的结构改进方案。理论分析认为加工和装配误差引起的定/转子接触界面上沿圆周方向的压力不均衡是影响行波型旋转超声电机单周速度稳定性、步距均匀性的主要原因之一。为此，提出一种单轴承支撑附加调心结构的方案，可以使接触界面实现压力自平衡，改善接触界面的压力分布。实验结果表明，空载单周相对速度波动率降低了约40.0%，波动小于2.0%；这有利于提高运动平台开环步进运动时步距的一致性。
（2）研究了行波型旋转超声电机的最小响应脉冲宽度和电机关断时过冲量的大小。旋转超声电机的启动/停止瞬态特性决定了其角度分辨率，进而影响丝杠平台的位移分辨率（最小步距），影响运动平台的定位精度。结合丝杠导程（4mm），研究结果可以预测出超声电机驱动的丝杠平台理论上所能达到的定位精度（0.6μm）。
（3）开发了行波型旋转超声电机驱动的二维平台。利用直线光栅尺和编码器两种不同的位置反馈单元的信号作比对，分别测试了平台的螺距不均匀误差、回程误差，并在搭建的基于GT-400运动控制卡的控制系统中对其进行了补偿，将丝杠平台的定位精度由丝杠的标称定位精度±5μm提高至±2.5μm。
（4）直线超声电机驱动的运动平台的性能很大程度上取决于直线超声电机的性能，而直线超声电机的性能很大程度上取决于其定子与动子（平台）的接触状态，而为了减小接触变形对定位精度的影响，本文采用高硬度摩擦材料（ZrO、AL2O3）作为摩擦副。因此，作者研究了高硬度材料摩擦副直线超声电机定子与动子之间的接触匹配问题，提出了“接触频率”的概念。通过建立高硬度摩擦副直线超声电机的定子/动子在接触面法向上的接触模型并进行理论和实验研究，得出了定子支撑弹簧刚度、预压力、定子质心和驱动足的振幅等对接触频率的影响规律，探讨了相关改善方法。
（5）为了提高运动平台的驱动单元的性能，研究了提高直线超声电机驱动单元的推力、效率及稳定性的途径。提出采用多个超声电机协同工作的“异步并联”的方法。通过设定每个超声电机的驱动信号之间的相位，使得不同的超声电机定子依次交替作用于动子，以避免多个定子间相互干扰、磨损加剧和内耗增加的问题，提高了驱动单元的驱动效率，并进行了实验验证。
（6）直线电机驱动的运动平台的位移分辨率、瞬态特性决定了直线平台的定位精度；作者研究了单足V形、双足碟形直线超声电机的瞬态特性及双足蝶形直线超声电机驱动的运动平台的位移分辨率，分析了各种参数对位移分辨率的影响。实验结果表明：定子从开始振动至达到稳定振幅仅需1.7ms，关断时间小于1ms；本文双足直线超声电机驱动的精密运动平台的分辨率达到25nm。
（7）建立了直线超声电机驱动的运动平台的等效电路模型，得到了其传递函数。分析比较了基于MSP430单片机、DSP以及GT-400运动控制卡的各种控制器的特点，并在基于GT-400运动控制卡的控制系统上实验了模糊与PID双模控制算法，使运动平台的精度在60mm行程范围内达到了±0.5μm。
There are broad needs for the precision motion stage in various fields, such as micro surgeryequipment, the electron scanning tunneling microscope, the three coordinate measuring machines, etc.Ultrasonic motor (USM) which utilizes the inverse piezoelectric effect of the piezoelectric material,has got more and more attention from the experts and scholars working in the precision driving fieldsfor its advantages like fast response, high resolution, etc. The travel range of piezoelectric stage usedthe static deformation of piezoelectric ceramics always be only get to a few hundred microns. On theother hand, the actual applications of macro/micro combined stage have been restricted in thecomplex structure and controller. As a result, the research of the large travel precision motion stagedriven by USM is becomeing one of the frontier technologies.
The main work in this paper focus on some key aspects of the precision motion stage driven byUSM with a large travel:
（1） In this paper, the author studied the velocity fluctuation ratio in each cycle and the steppitch consistency of traveling wave type rotary ultrasonic motors (TRUM) and proposed a structuralimprovement scheme. The analysis results show that one of the main reasons for velocity fluctuationof TRUM is pressure imbalance along the circumference on the contact interface because ofmachining or assembling error in the present case of duplex bearing structure. Theoretical analysisshows that the scheme can realize pressure auto-balance with single bearing and self-aligningstructure. It also can make the pressure distribution on contact interface more uniform. Experimentalresults show that the no-load velocity fluctuation ratio decreased40.0%, and velocity fluctuationrange less than2.0%. This will help improve the consistency of the step pitch when the stage isworking in the open loop stepping mode.
（2）The minimum pulse width which can drive TRUM and the amount of overshoot pulseswhen the TRUM is power off were studied in this paper. They are closely related to the TRUM’stransient characteristics. The angular resolution of TRUM is determined by its transient characteristics.Meanwhile, the displacement resolution of the stage driven by TRUM is determined by the angular resolution of TRUM. This research can forecast the positioning accuracy of the ball-screw-drivenstage if the screw lead was given.
（3）One2-DOF stage driven by TRUM was developed in this paper. The lead-screw pitch errorand the return error were studied through setup two sets of position feedback systems with linearencoders and rotary encoders. Finally, the verification experiment has been accomplished on the stage.Experimental results show that the positioning accuracy of the stage has been improved to2.5μm bythe control system based on GT-400motion control card with error compensation.
（4）The performance of the stage driven by linear ultrasonic motors (LUSM) is determined bythe performance of LUSM. The performance of LUSM depends on the contact state on the contactinterface. Therefore, the contact problem of linear ultrasonic motor was studied in this paper. Hardcontact materials, such as ZrO or AL2O3, have been used to reduce the impact of contact deformationand surface roughness. However, experimental results show that, in this kind of hard contact materialslinear ultrasonic motors (HLUSM), there exists a phenomenon that the contact frequency betweenthe stator and the mover (slider) is far less than the frequency of the driving signal, which prevents thevibration energy of the stator from being utilized fully. In order to solve this problem, we have madethe model of the high frequency micro-amplitude contact behavior in normal direction of HLUSM.Then, theoretical analysis and experimental investigation on micro-impact processes of HLUSM havebeen finished. The impact laws of parameters on the contact frequency have been derived, includingthe stiffness of the stator supporting spring, preload and the high frequency vibration amplitude of thedriving tip and the low-frequency vibration amplitude of stator. Finally, the related improvementmeasures have been discussed.
（5）Aim at improving the performance of driving units of motion stage, the asynchronousbundle of linear ultrasonic motor (ABLUSM) which can build the high thrust, high efficiency, stableand reliable driving unit with LUSM has been discussed. The concept of ABLUSM is proposed. Thebasic principle is that numbers of stators (vibrators) alternately drive a mover (rotor) in a drivingsignal cycle, so that, it can avoid the problem of mutual interference of different stators, wear andinternal power dissipation increased. Therefore, the efficiency of the driving unit can be improvedsignificantly. Finally, the verification experiment was conducted.
（6）The positioning accuracy of the stage driven by LUSM is largely depends on thedisplacement resolution and the transient characteristics of the LUSM. So, the transient characteristicsof two kinds of USMs have been studied in this paper. Furthermore, theoretical analysis andexperimental investigation on the resolution of the stage driven by the HLUSM with two driving tips have been completed. The impact of various parameters on the displacement resolution of the stagewas also discussed. Experimental results show that, the displacement resolution of the precision stagedriven by HLUSM with two driving tips reached25nm.
（7） The equivalent circuit model of motion stage driven by HLUSM was established, and thetransfer function of this model was derived. The characteristics of controllers which based on MCU,DSP and GT-400motion control card have been compared with, respectively. One experiment usedfuzzy and PID dual-mode control algorithm has been finished on the control system based on GT-400motion control card. Experimental results show that the positioning accuracy of the stage has beenimproved to0.5μm with the travel of60mm.
引文
[1]王立鼎，褚金奎，刘冲，等.中国微纳制造研究进展.机械工程学报,2008(11):2-12.
[2]刘俊标，薛虹.微纳加工中的精密工件台技术.北京:北京工业大学出版社,2004.
[3]赵淳生.超声电机技术与应用.北京:科学出版社,2007.
[4]刘建芳，杨志刚，程光明，等.压电驱动精密直线步进电机研究.中国电机工程学报,2004,24(4):102-107.
[5] Zhao C S. Ultrasonic motors technologies and applications. China: Science Press Springer,2010.
[6]赵淳生.对发展我国超声电机技术的若干建议:全国第三届超声波电机理论和应用技术研讨会.杭州:2005.
[7]时运来.新型直线超声电机的研究及其在运动平台中的应用,博士.南京:南京航空航天大学,2011.
[8] Hatsuzawa T, Toyoda K, Tanimura Y. Speed control characteristics and digital servo-system for acircular travelling wave motor: Rev.Sci. Instrum.1986:57,2886-2890.
[9] Kusakabe C, Takano T, Tomikawa Y. Driving and controlling of a watch device ultrasonic motor bytwo phase pulse signals.1990,30(206-208).
[10] Okamura I, Mukohjima H. Optimized Ultrasonic Motor Achieves36%Efficiency Driving Camera’sAutococul Lens.1987:67-71.
[11] Nakaoka M, Izuno I. High-performance sensorless load-adaptive speed control of two-phaseinverter-fed ultrasonic motor.1990,37:137-149.
[12] Narendra K S, Parthasarathy K. dentification and control of dynamical systems using neuralnetworks.1990,1(1):4-27.
[13] Izuno Y. New fuzzy reasoning-based high-performance speed/position control schemes for ultrasonicmotor driven by two phase resonant inverter: Conf. IEEE Indus. Appli. Society Annual Meeting.1990325-330.
[14] Izuno Y, Nakaoka M. Adaptive control-based high-performance drive system implementation oftraveling-wave type ultrasonic motor.1990,110(11):1147-1154.
[15] Sashida T, Kenjo T. An Introduction to Ultrasonic Motors. Oxford. Clarendon Press,1993.
[16] Ueha S, Tomikawa Y. Ultrasonic Motors Theory and Applications. Oxford Science Publications,1993.
[17] Izuno Y, Nakaoka M. High performance and high precision ultrasonic motor-actuated positioningservo drive system using improved fuzzy-reasoning controlle: Proc. IEEE Power ElectronicsSpecialists Conf.19941269-1274.
[18] Furuya S I, Maruhashi T, Izuno Y, et al. Load Adaptive Frequency Tracking ControlImplementation of Two-Phase Resonant Inverter for Ultrasonic Motor: IEEE Transactions on PowerElectronics.1992542-550.
[19] Senjyu T, Miyazato H, Yokoda S, et al. Speed control of ultrasonic motors using neural network.Power Electronics, IEEE Transactions on,1998,13(3):381-387.
[20] Senjyu T, Uezato K. Adjustable speed control of ultrasonic motors by adaptive control: PowerElectronics Specialists Conference, PESC '94Record.,25th Annual IEEE.19941237-1242.
[21] Senjyu T, Yoshida T, Uezato K, et al. Position control of ultrasonic motors using adaptivebackstepping control and dead-zone compensation with fuzzy inference: Industrial Technology,2002.IEEE ICIT '02.2002IEEE International Conference on.2002560-565.
[22] Suzuki T, Fukumi J, Harada H. Self-tuning fuzzy feedforward controller for positioning system withprogressive wave type ultrasonic motor: Proc. Int. Power Electronics Conf.19951766-1771.
[23] Lin F J, Wai R J, Lee C C. Fuzzy neural network position controller for ultrasonic motor drive usingpush-pull DC-DC converter. Control Theory and Applications, IEE Proceedings-,1999,146(1):99-107.
[24] Faa-Jeng L, Rong-Jong W, Rou-Yong D. Neural-network controller for parallel-resonant ultrasonicmotor drive. Control Systems Technology, IEEE Transactions on,1999,7(4):494-501.
[25] Faa-Jeng L, Rong-Jong W, Hsin-Hai L. An adaptive fuzzy-neural-network controller for ultrasonicmotor drive using the LLCC resonant technique. Ultrasonics, Ferroelectrics and Frequency Control,IEEE Transactions on,1999,46(3):715-727.
[26] Ozawa S, Yuasa T, Yoshida R, et al. Development of an ultra-compact zoom lens unit for cameraphones. KONICA MINOLTA TECHNOLOGY REPORT,2007,478:81.
[27] Wohlleber C, Schlaak H F. Position Control of Piezoelectric Motors for a Dexterous LaparoscopicInstrument[M].4th European Conference of the International Federation for Medical and BiologicalEngineering, Sloten J, Verdonck P, Nyssen M, et al, Springer Berlin Heidelberg,2009:22,1668.
[28] Faa-Jeng L, Po-Huang S, Po-Huan C. Robust Adaptive Backstepping Motion Control of LinearUltrasonic Motors Using Fuzzy Neural Network. Fuzzy Systems, IEEE Transactions on,2008,16(3):676-692.
[29] Chen T, Yu C, Chen C, et al. Neuro-fuzzy speed control of traveling-wave type ultrasonic motordrive using frequency and phase modulation. ISA Transactions,2008,47(3):325-338.
[30] Jahani M, Mojallali H. GA-neural network based position control of Traveling Wave UltrasonicMotor: Computer Engineering and Technology (ICCET),20102nd International Conference on.2010V6-V369.
[31] Bal G, Bekiroglu E. A highly effective load adaptive servo drive system for speed control oftravelling-wave ultrasonic motor. Power Electronics, IEEE Transactions on,2005,20(5):1143-1149.
[32] Bal G, Bekiroglu E, Demirbas S, et al. A fuzzy logic based DSP controlled servo position control forultrasonic motor. Energy Conversion and Management,2004,45(20):3139-3153.
[33]张新星.基于ARM的超声波电机速度位置控制系统研究,硕士.扬州：扬州大学,2009.
[34]王敏才.基于DSP的超声波电机转速控制特性的研究,硕士.南京：东南大学,2006.
[35]史婷娜，徐绍辉，夏长亮，等.超声波电机模糊-PI双模自适应速度控制.电工技术学报,2003(3):1-4.
[36]杨忠，金龙.用人工神经网络对压电行波超声马达进行速度控制(英文). Journal of SoutheastUniversity(English Edition),1999(2):63-68.
[37]王龙帅.基于DDS的超声波电机驱动控制研究,硕士.洛阳:河南科技大学,2009.
[38]郝铭，陈维山，刘军考，等.基于DDS技术的行波超声电机电源.机械与电子,2007(9):29-31.
[39]许海，赵淳生.基于DDS技术驱动的精密直线超声电机.中国机械工程,2007,18(13):1595-1597.
[40]周斌，李志钧，Others.基于DDS的超声电机驱动电源.压电与声光,2002,24(3):202-204.
[41]俞浦，李杰，陈曦，等.基于PSoC的超声电机小型驱动器.微电机,2011,44(10):51-54.
[42]王红占.基于PSoC的超声电机驱动器的研究,南京航空航天大学,2009.
[43]俞浦，李华峰，李杰.基于MSP430的超声电机小型驱动器.微型机与应用,2011,30(18):26-28.
[44]王文琦.基于DSP数据采集的超声波电机测试.中国科技财富,2009(6).
[45]金龙.一种基于DSP的超声波电动机控制器.第十届中国小电机技术研讨会.上海.2005.
[46]张新星，莫岳平，段小汇，等.基于ARM和DDS的行波型超声波电机驱动技术.扬州大学学报(自然科学版),2009,12(4).
[47]段小汇，莫岳平，张新星，等.基于ARM的行波超声波电机驱动控制系统研究与实验.微电机,2008,41(5):53-55.
[48]李恒，朱煜，贾松涛，等.电磁式超精密微动工作台研究现状与方向.现代机械,2007(2):1-3.
[49] Physikinstrument. P-611.3NanoCube XYZ Piezo Stage.2012Compact Multi-Axis Piezo Systemfor Nanopositioning and Fiber Alignment.
[50] Npoint. Piezo Stages and Nanopositioning Systems NPX25A.2012:2012, http://www.npoint.com.
[51]哈尔滨工业大学博实精密测控有限责任公司.纳米级精密定位工作台.2012:2012,http://www.bsjm.com.
[52]张江波，朱涛，王越超，等.一种具有纳米定位精度的四自由度微动平台的研制.2003,25(3):213-216.
[53] Tung-Li W, Jia-Hao C, Shuo-Hung C. A six-DOF prismatic-spherical-spherical parallel compliantnanopositioner. Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on,2008,55(12):2544-2551.
[54] Dong W, Sun L N, Du Z J. Design of a precision compliant parallel positioner driven by dualpiezoelectric actuators. Sensors and Actuators A: Physical,2007,135(1):250-256.
[55]张建军，高峰，金振林，等.结构解耦6-PSS并联微操作平台的研究与开发.中国机械工程,2004(1):3-6.
[56]魏强.纳米定位微位移工作台的控制技术研究,博士.济南:山东大学,2006.
[57]纪华伟.压电陶瓷驱动的微位移工作台建模与控制技术研究,博士.杭州:浙江大学,2006.
[58]魏燕定.压电驱动器的非线性模型及其精密定位控制研究.中国机械工程,2004(7):3-6.
[59]姜文锐.大行程高精度微进给系统的研究,博士.哈尔滨:哈尔滨工业大学,2009.
[60] Gyorki J R, Tal J. Servomotors Take Piezoceramic Transducers for a Ride. Machine design,1999,71(23):92-94.
[61] Elfizy A T, Bone G M, Elbestawi M A. Design and control of a dual-stage feed drive.Journal of Machine Tools&Manufacture,2005,45(2):153-160.
[62]朱煜.光刻机超精密工件台研究.电子工业专用设备,2004(02).
[63]王强.纳米工作台运动控制技术的研究,硕士.上海:上海大学,2007.
[64]陈亚英，朱煜，段广洪.基于电流变阻尼超精密气浮工作台建模及控制研究.润滑与密封,2007(8):24-27.
[65]贾松涛，朱煜，杨开明，等.双边驱动精密运动台振动特性研究.机械科学与技术,2009(5):582-586.
[66]贾松涛，朱煜，尹文生，等.超精密工作台运动轨迹规划.组合机床与自动化加工技术,2007(10):14-16.
[67]王建林，周秀珍.压电驱动三维纳米定位系统的研究.压电与声光,2001(6):439-442.
[68]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.光学精密工程,2004(1):55-59.
[69]节德刚，刘延杰，孙立宁，等.一种宏微双重驱动精密定位机构的建模与控制.光学精密工程,2005(2):171-178.
[70]徐从裕.大行程纳米定位驱动控制方法与系统研究,博士.合肥:合肥工业大学,2008.
[71] Mao J, Tachikawa H, Shimokohbe A. precision positionning of a DC-motor-driven aerostatic slidesystem. Precision Engineering,2003(27):32-41.
[72] International D T. NTS NanoDirect series.2012:2012.
[73] Borodin S, Kim J, Kim H, et al. Nano-Positioning System Using Linear Ultrasonic Motor with“Shaking Beam”. Journal of Electroceramics,2004,12(3):169.
[74] Shutov M V, Howard D L, Sandoza E E, et al. Electrostatic inchworm microsystem with long rangetranslatio. Sensors and Actuators,2004,114(2-3):379-386.
[75]李玉宝.新型直线型超声电机及其应用的研究,博士.南京:南京航空航天大学,2009.
[76] Hagood Iv N W, Mcfarland A J. Modeling of a piezoelectric rotary ultrasonic motor. Ultrasonics,Ferroelectrics and Frequency Control, IEEE Transactions on,1995,42(2):210-224.
[77] Pons J L, Rodriguez H, Ceres R, et al. Novel modeling technique for the stator of traveling waveultrasonic motors: IEEE trans. Ultrasonic Ferroelectric Frequency Control.2003:50,1429-1435.
[78]陈超.旋转型行波超声电机理论模型的研究,博士.南京:南京航空航天大学,2005.
[79]陈超，赵淳生.柔性转子对行波超声波电动机性能的影响.机械工程学报,2008,44(3):152-159.
[80] Maeno T, Tsukimoto T, Miyake A. Finite-element analysis of the rotor/stator contact in a ring-typeultrasonic motor. Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on,1992,39(6):668-674.
[81] Norddin E, G. Hybrid modeling of a traveling wave piezoelectric motor, Denmark: AalborgUniversity,2000.
[82] Pons J L, Rodriguez H, Fernandez J F. Modelling of piezoelectric transducers applied to piezoelectricmotors_a comparative study and new perspective. Sensors and Actuators A: Physical,2003,107(2):169-182.
[83] Wallaschek J. Contact mechanics of piezoelectric ultrasonic motors. Smart material and Structures,1999,7(3):369.
[84]夏长亮，郑尧，史婷娜，等.行波接触型超声波电机定子振动有限元分析.中国电机工程学报,2001,21(2):25-28.
[85] Storck H, Wallaschek J. The effect of tangential elasticity of the contact layer between stator androtor in travelling wave ultrasonic motors. International journal of non-linear mechanics,2003,38(2):143-159.
[86]曲建俊，孙凤艳，田秀.粘弹性接触层在定子表面的行波超声电动机接触模型.机械工程学报,2006(12):175-179.
[87]陈超，赵淳生.旋转型行波超声电机中三维接触机理的研究.中国电机工程学报,2006(21):149-155.
[88] Duan W H, Quek S T, Lim S P. Finite element solution for intermittent-contact problem withpiezoelectric actuation in ring type USM[. Finite Elements in Analysis and Design,2007,43(3):193-205.
[89]周盛强，赵淳生.超声电机接触界面的两种简化有限元模型.振动、测试与诊断,2009(3):251-255.
[90]周盛强，赵淳生，黄卫清.旋转型行波超声电机接触界面的空间域分析.中国电机工程学报,2010(12):63-68.
[91] Radi B, El Hami A. The study of the dynamic contact in ultrasonic motor. Applied MathematicalModelling,2010,34(12):3767-3777.
[92]于建国，赵志刚，夏元地.电动机气隙尺寸链的分析计算.防爆电机,1999(1):41-42.
[93]机械科学研究院.尺寸链计算方法.北京,中国国家标准化管理委员会,2004.
[94]卜炎.实用轴承技术手册.北京:机械工业出版社,2003.
[95]王光庆，沈润杰，郭吉丰.预压力对超声波电机特性的影响研究.浙江大学学报,2007,41(3):436-440.
[96]赵向东.旋转型行波超声电机动力学模型及性能仿真的研究,博士.南京:南京航空航天大学,2000.
[97]南京工艺装备制造有限公司.滚珠丝杠副http://www.njyigong.cn/products.asp?parentid=1.2012.
[98]固高科技深圳有限公司. GT系列运动控制器用户手册[DB/CD].2006.
[99] Jin J M, Zhao C S. Characteristic matching between stator and rotor in standing-wave-type ultrasonicmotors. Journal of Electroceramics,2008,20(3):197-202.
[100] Houben M, Van de Vijver W, Al-Bender F, et al. A generic modelling approach for studying thecontact mechanism and dynamic behavior of bimodal standing wave piezomotors.2008:227-231.
[101] Ho S T. Modelling of the Linear Ultrasonic Motor using an Elliptical Shape Stator.2006:82-87.
[102] Shi Y L, Zhao C S, Zhang J. Contact analysis and modeling of standing wave linear ultrasonicmotor. Journal of Wuhan University of Technology--Materials Science Edition,2011,26(6):1235-1242.
[103] Twiefel J, Potthast C, Mracek M, et al. Fundamental experiments as benchmark problems formodeling ultrasonic micro-impact processes. Journal of Electroceramics,2008,20(3):209-214.
[104] Wurpts W, Twiefel J. An ultrasonic motor with intermittent contact modeled as a two degree offreedom oscillator in time domain. PAMM,2009,9(1):287-288.
[105]郭翠娟.超高加速度精密运动平台研制,硕士.哈尔滨：哈尔滨工业大学,2011.
[106] Kuribayashi Kurosawa M, Kodaira O, Tsuchitoi Y, et al. Transducer for high speed and large thrustultrasonic linear motor using two sandwich-type vibrators. Ultrasonics, Ferroelectrics and FrequencyControl, IEEE Transactions on,1998,45(5):1188-1195.
[107]时运来，李玉宝，赵淳生. V型大推力直线超声电机的运动机理分析.压电与声光,2008,30(6):772-775.
[108] Li Y B, Shi Y L, Zhao C S. Design and experiment of butterfly linear ultrasonic motor with twodriving tips. Optics and Precision Engineering,2008,16(12):2327-2333.
[109]金家楣.若干新型超声电机的研究,博士.南京:南京航空航天大学,2007.
[110] Yang M, Richardson R C, Levesley M C, et al. Performance improvement of rectangular-platelinear ultrasonic motors using dual-frequency drive. Ultrasonics, Ferroelectrics and FrequencyControl, IEEE Transactions on,2004,51(12):1600-1606.
[111] Jin J M, Zhao C S. Linear ultrasonic motor using quadrate plate transducer. Frontiers of MechanicalEngineering in China,2009,4(1):88-91.
[112] Wakai T, Kurosawa M K, Higuchi T. Transducer for an ultrasonic linear motor with flexible drivingpart.1998:683-686.
[113]李亭，张铁民，刘潇建.超声电机多定子同步驱动技术的研究.振动、测试与诊断,2008(4):343-346.
[114] Hemsel T, Mracek M, Wallaschek J, et al. A novel approach for high power ultrasonic linearmotors.2004:1161-1164.
[115] Mracek M, Hemsel T. Synergetic driving concepts for bundled miniature ultrasonic linear motors.Ultrasonics,2006,44: e597-e602.
[116] Mracek M, Hemsel T, Sattel T, et al. Driving concepts for bundled ultrasonic linear motors. Journalof Electroceramics,2008,20(3):153-158.
[117]李欣欣.宏/微两级驱动的大行程高精度二维定位平台基础技术研究,博士.杭州:浙江大学,2008.
[118]严天宏，许畅，李青，等.高速超精运动台的离散滑模控制研究.控制工程,2010(004).
[119]赵增辉.超声电机压电振子的动力学特性研究,硕士.青岛:山东科技大学,2006.
[120]张晓峰.大行程超精密工作台关键技术研究,博士.天津:天津大学,2008.
[121]薛雯玉.基于直线超声电机仿三维运动平台驱动控制系统的研究,硕士.南京:南京航空航天大学,2012.
[122] Texasinstruments. TMS320F28235, TMS320F28234, TMS320F28232Digital Signal Controllers(DSCs) Data Manual.2009.
[123] Motorola. AM26LS32datasheet.1995. http://www.alldatasheet.com
[124]蒋嗣荣，洪振华.计算机控制技术.西北电讯工程学院,1985.
[125]高金源.计算机控制技术.北京:中央广播电视大学出版社,2002.
[126]贺红林.超声电机及其在机器人上的应用研究,博士.南京:南京航空航天大学,2006.
[127]李华峰，辜承林.使用PI控制的超声波电机精密位置控制.微电机(伺服技术),2002(2):23-26.
[128]应浩.关于模糊控制理论与应用的若干问题.自动化学报,2001(4):591-592.
[129]胡守仁，胡德文，时春.神经网络应用技术.长沙:国防科技大学出版社,1993.
[130]陶永华，尹怡欣，葛芦生.新型PID控制及其应用.北京:机械工业出版社,1998.
[131]张德丰. MATLAB神经网络应用设计.2.北京:机械工业出版社,2012.
[132]王旭东，邵惠鹤. RBF神经网络理论及其在控制中的应用.信息与控制,1997(4):32-44.
[133] Moody J, Darken C. Learning with localized receptive fields. Yale Univ., Department of ComputerScience,1988.
[134] Moody J, Darken C J. Fast learning in networks of locally-tuned processing units. Neuralcomputation,1989,1(2):281-294.
[135] Chen S, Grant P M, Cowan C F N. Orthogonal least-squares algorithm for training multioutputradial basis function networks. Radar and Signal Processing, IEE Proceedings F,1992,139(6):378-384.
[136]夏长亮，祁温雅，杨荣，等.基于RBF神经网络的超声波电机参数辨识与模型参考自适应控制.中国电机工程学报,2004(7):121-125.
[137] Jahani M, Mojallali H. Neural network based modeling of traveling wave ultrasonic motor usinggenetic algorithm.2010:486-490.
[138]孙志峻，帅双辉，金家楣，等.基于径向基神经网络的直线超声电机位置控制.振动.测试与诊断,2010(6):650-653.
[139] Lin F J, Shieh P H. Recurrent RBFN-based fuzzy neural network control for XY-/spl Theta/motioncontrol stage using linear ultrasonic motors. Ultrasonics, Ferroelectrics and Frequency Control, IEEETransactions on,2006,53(12):2450-2464.
[140]张德丰. MATLAB/Simulink建模与仿真实例精讲.1.北京:机械工业出版社,2011.
[141]王心坚，胡敏强，金龙，等.基于单神经元PID-PI的行波超声波电机速度复合控制研究.微电机,2008(3):19-22.
[142]王心坚，胡敏强，金龙，等.行波超声波电机多调节量协调控制方法.中国电机工程学报,2009(6):73-79.
[143]张炎，宋爱国，王心坚，等.一种行波超声波电机低速控制的方法.东南大学学报(自然科学版),2008(3):429-433.
[144]邢仁涛.超声电机驱动的多关节机器人,硕士.南京:南京航空航天大学,2007.
[2]刘俊标，薛虹.微纳加工中的精密工件台技术.北京:北京工业大学出版社,2004.
[3]赵淳生.超声电机技术与应用.北京:科学出版社,2007.
[4]刘建芳，杨志刚，程光明，等.压电驱动精密直线步进电机研究.中国电机工程学报,2004,24(4):102-107.
[5] Zhao C S. Ultrasonic motors technologies and applications. China: Science Press Springer,2010.
[6]赵淳生.对发展我国超声电机技术的若干建议:全国第三届超声波电机理论和应用技术研讨会.杭州:2005.
[7]时运来.新型直线超声电机的研究及其在运动平台中的应用,博士.南京:南京航空航天大学,2011.
[8] Hatsuzawa T, Toyoda K, Tanimura Y. Speed control characteristics and digital servo-system for acircular travelling wave motor: Rev.Sci. Instrum.1986:57,2886-2890.
[9] Kusakabe C, Takano T, Tomikawa Y. Driving and controlling of a watch device ultrasonic motor bytwo phase pulse signals.1990,30(206-208).
[10] Okamura I, Mukohjima H. Optimized Ultrasonic Motor Achieves36%Efficiency Driving Camera’sAutococul Lens.1987:67-71.
[11] Nakaoka M, Izuno I. High-performance sensorless load-adaptive speed control of two-phaseinverter-fed ultrasonic motor.1990,37:137-149.
[12] Narendra K S, Parthasarathy K. dentification and control of dynamical systems using neuralnetworks.1990,1(1):4-27.
[13] Izuno Y. New fuzzy reasoning-based high-performance speed/position control schemes for ultrasonicmotor driven by two phase resonant inverter: Conf. IEEE Indus. Appli. Society Annual Meeting.1990325-330.
[14] Izuno Y, Nakaoka M. Adaptive control-based high-performance drive system implementation oftraveling-wave type ultrasonic motor.1990,110(11):1147-1154.
[15] Sashida T, Kenjo T. An Introduction to Ultrasonic Motors. Oxford. Clarendon Press,1993.
[16] Ueha S, Tomikawa Y. Ultrasonic Motors Theory and Applications. Oxford Science Publications,1993.
[17] Izuno Y, Nakaoka M. High performance and high precision ultrasonic motor-actuated positioningservo drive system using improved fuzzy-reasoning controlle: Proc. IEEE Power ElectronicsSpecialists Conf.19941269-1274.
[18] Furuya S I, Maruhashi T, Izuno Y, et al. Load Adaptive Frequency Tracking ControlImplementation of Two-Phase Resonant Inverter for Ultrasonic Motor: IEEE Transactions on PowerElectronics.1992542-550.
[19] Senjyu T, Miyazato H, Yokoda S, et al. Speed control of ultrasonic motors using neural network.Power Electronics, IEEE Transactions on,1998,13(3):381-387.
[20] Senjyu T, Uezato K. Adjustable speed control of ultrasonic motors by adaptive control: PowerElectronics Specialists Conference, PESC '94Record.,25th Annual IEEE.19941237-1242.
[21] Senjyu T, Yoshida T, Uezato K, et al. Position control of ultrasonic motors using adaptivebackstepping control and dead-zone compensation with fuzzy inference: Industrial Technology,2002.IEEE ICIT '02.2002IEEE International Conference on.2002560-565.
[22] Suzuki T, Fukumi J, Harada H. Self-tuning fuzzy feedforward controller for positioning system withprogressive wave type ultrasonic motor: Proc. Int. Power Electronics Conf.19951766-1771.
[23] Lin F J, Wai R J, Lee C C. Fuzzy neural network position controller for ultrasonic motor drive usingpush-pull DC-DC converter. Control Theory and Applications, IEE Proceedings-,1999,146(1):99-107.
[24] Faa-Jeng L, Rong-Jong W, Rou-Yong D. Neural-network controller for parallel-resonant ultrasonicmotor drive. Control Systems Technology, IEEE Transactions on,1999,7(4):494-501.
[25] Faa-Jeng L, Rong-Jong W, Hsin-Hai L. An adaptive fuzzy-neural-network controller for ultrasonicmotor drive using the LLCC resonant technique. Ultrasonics, Ferroelectrics and Frequency Control,IEEE Transactions on,1999,46(3):715-727.
[26] Ozawa S, Yuasa T, Yoshida R, et al. Development of an ultra-compact zoom lens unit for cameraphones. KONICA MINOLTA TECHNOLOGY REPORT,2007,478:81.
[27] Wohlleber C, Schlaak H F. Position Control of Piezoelectric Motors for a Dexterous LaparoscopicInstrument[M].4th European Conference of the International Federation for Medical and BiologicalEngineering, Sloten J, Verdonck P, Nyssen M, et al, Springer Berlin Heidelberg,2009:22,1668.
[28] Faa-Jeng L, Po-Huang S, Po-Huan C. Robust Adaptive Backstepping Motion Control of LinearUltrasonic Motors Using Fuzzy Neural Network. Fuzzy Systems, IEEE Transactions on,2008,16(3):676-692.
[29] Chen T, Yu C, Chen C, et al. Neuro-fuzzy speed control of traveling-wave type ultrasonic motordrive using frequency and phase modulation. ISA Transactions,2008,47(3):325-338.
[30] Jahani M, Mojallali H. GA-neural network based position control of Traveling Wave UltrasonicMotor: Computer Engineering and Technology (ICCET),20102nd International Conference on.2010V6-V369.
[31] Bal G, Bekiroglu E. A highly effective load adaptive servo drive system for speed control oftravelling-wave ultrasonic motor. Power Electronics, IEEE Transactions on,2005,20(5):1143-1149.
[32] Bal G, Bekiroglu E, Demirbas S, et al. A fuzzy logic based DSP controlled servo position control forultrasonic motor. Energy Conversion and Management,2004,45(20):3139-3153.
[33]张新星.基于ARM的超声波电机速度位置控制系统研究,硕士.扬州：扬州大学,2009.
[34]王敏才.基于DSP的超声波电机转速控制特性的研究,硕士.南京：东南大学,2006.
[35]史婷娜，徐绍辉，夏长亮，等.超声波电机模糊-PI双模自适应速度控制.电工技术学报,2003(3):1-4.
[36]杨忠，金龙.用人工神经网络对压电行波超声马达进行速度控制(英文). Journal of SoutheastUniversity(English Edition),1999(2):63-68.
[37]王龙帅.基于DDS的超声波电机驱动控制研究,硕士.洛阳:河南科技大学,2009.
[38]郝铭，陈维山，刘军考，等.基于DDS技术的行波超声电机电源.机械与电子,2007(9):29-31.
[39]许海，赵淳生.基于DDS技术驱动的精密直线超声电机.中国机械工程,2007,18(13):1595-1597.
[40]周斌，李志钧，Others.基于DDS的超声电机驱动电源.压电与声光,2002,24(3):202-204.
[41]俞浦，李杰，陈曦，等.基于PSoC的超声电机小型驱动器.微电机,2011,44(10):51-54.
[42]王红占.基于PSoC的超声电机驱动器的研究,南京航空航天大学,2009.
[43]俞浦，李华峰，李杰.基于MSP430的超声电机小型驱动器.微型机与应用,2011,30(18):26-28.
[44]王文琦.基于DSP数据采集的超声波电机测试.中国科技财富,2009(6).
[45]金龙.一种基于DSP的超声波电动机控制器.第十届中国小电机技术研讨会.上海.2005.
[46]张新星，莫岳平，段小汇，等.基于ARM和DDS的行波型超声波电机驱动技术.扬州大学学报(自然科学版),2009,12(4).
[47]段小汇，莫岳平，张新星，等.基于ARM的行波超声波电机驱动控制系统研究与实验.微电机,2008,41(5):53-55.
[48]李恒，朱煜，贾松涛，等.电磁式超精密微动工作台研究现状与方向.现代机械,2007(2):1-3.
[49] Physikinstrument. P-611.3NanoCube XYZ Piezo Stage.2012Compact Multi-Axis Piezo Systemfor Nanopositioning and Fiber Alignment.
[50] Npoint. Piezo Stages and Nanopositioning Systems NPX25A.2012:2012, http://www.npoint.com.
[51]哈尔滨工业大学博实精密测控有限责任公司.纳米级精密定位工作台.2012:2012,http://www.bsjm.com.
[52]张江波，朱涛，王越超，等.一种具有纳米定位精度的四自由度微动平台的研制.2003,25(3):213-216.
[53] Tung-Li W, Jia-Hao C, Shuo-Hung C. A six-DOF prismatic-spherical-spherical parallel compliantnanopositioner. Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on,2008,55(12):2544-2551.
[54] Dong W, Sun L N, Du Z J. Design of a precision compliant parallel positioner driven by dualpiezoelectric actuators. Sensors and Actuators A: Physical,2007,135(1):250-256.
[55]张建军，高峰，金振林，等.结构解耦6-PSS并联微操作平台的研究与开发.中国机械工程,2004(1):3-6.
[56]魏强.纳米定位微位移工作台的控制技术研究,博士.济南:山东大学,2006.
[57]纪华伟.压电陶瓷驱动的微位移工作台建模与控制技术研究,博士.杭州:浙江大学,2006.
[58]魏燕定.压电驱动器的非线性模型及其精密定位控制研究.中国机械工程,2004(7):3-6.
[59]姜文锐.大行程高精度微进给系统的研究,博士.哈尔滨:哈尔滨工业大学,2009.
[60] Gyorki J R, Tal J. Servomotors Take Piezoceramic Transducers for a Ride. Machine design,1999,71(23):92-94.
[61] Elfizy A T, Bone G M, Elbestawi M A. Design and control of a dual-stage feed drive.Journal of Machine Tools&Manufacture,2005,45(2):153-160.
[62]朱煜.光刻机超精密工件台研究.电子工业专用设备,2004(02).
[63]王强.纳米工作台运动控制技术的研究,硕士.上海:上海大学,2007.
[64]陈亚英，朱煜，段广洪.基于电流变阻尼超精密气浮工作台建模及控制研究.润滑与密封,2007(8):24-27.
[65]贾松涛，朱煜，杨开明，等.双边驱动精密运动台振动特性研究.机械科学与技术,2009(5):582-586.
[66]贾松涛，朱煜，尹文生，等.超精密工作台运动轨迹规划.组合机床与自动化加工技术,2007(10):14-16.
[67]王建林，周秀珍.压电驱动三维纳米定位系统的研究.压电与声光,2001(6):439-442.
[68]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.光学精密工程,2004(1):55-59.
[69]节德刚，刘延杰，孙立宁，等.一种宏微双重驱动精密定位机构的建模与控制.光学精密工程,2005(2):171-178.
[70]徐从裕.大行程纳米定位驱动控制方法与系统研究,博士.合肥:合肥工业大学,2008.
[71] Mao J, Tachikawa H, Shimokohbe A. precision positionning of a DC-motor-driven aerostatic slidesystem. Precision Engineering,2003(27):32-41.
[72] International D T. NTS NanoDirect series.2012:2012.
[73] Borodin S, Kim J, Kim H, et al. Nano-Positioning System Using Linear Ultrasonic Motor with“Shaking Beam”. Journal of Electroceramics,2004,12(3):169.
[74] Shutov M V, Howard D L, Sandoza E E, et al. Electrostatic inchworm microsystem with long rangetranslatio. Sensors and Actuators,2004,114(2-3):379-386.
[75]李玉宝.新型直线型超声电机及其应用的研究,博士.南京:南京航空航天大学,2009.
[76] Hagood Iv N W, Mcfarland A J. Modeling of a piezoelectric rotary ultrasonic motor. Ultrasonics,Ferroelectrics and Frequency Control, IEEE Transactions on,1995,42(2):210-224.
[77] Pons J L, Rodriguez H, Ceres R, et al. Novel modeling technique for the stator of traveling waveultrasonic motors: IEEE trans. Ultrasonic Ferroelectric Frequency Control.2003:50,1429-1435.
[78]陈超.旋转型行波超声电机理论模型的研究,博士.南京:南京航空航天大学,2005.
[79]陈超，赵淳生.柔性转子对行波超声波电动机性能的影响.机械工程学报,2008,44(3):152-159.
[80] Maeno T, Tsukimoto T, Miyake A. Finite-element analysis of the rotor/stator contact in a ring-typeultrasonic motor. Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on,1992,39(6):668-674.
[81] Norddin E, G. Hybrid modeling of a traveling wave piezoelectric motor, Denmark: AalborgUniversity,2000.
[82] Pons J L, Rodriguez H, Fernandez J F. Modelling of piezoelectric transducers applied to piezoelectricmotors_a comparative study and new perspective. Sensors and Actuators A: Physical,2003,107(2):169-182.
[83] Wallaschek J. Contact mechanics of piezoelectric ultrasonic motors. Smart material and Structures,1999,7(3):369.
[84]夏长亮，郑尧，史婷娜，等.行波接触型超声波电机定子振动有限元分析.中国电机工程学报,2001,21(2):25-28.
[85] Storck H, Wallaschek J. The effect of tangential elasticity of the contact layer between stator androtor in travelling wave ultrasonic motors. International journal of non-linear mechanics,2003,38(2):143-159.
[86]曲建俊，孙凤艳，田秀.粘弹性接触层在定子表面的行波超声电动机接触模型.机械工程学报,2006(12):175-179.
[87]陈超，赵淳生.旋转型行波超声电机中三维接触机理的研究.中国电机工程学报,2006(21):149-155.
[88] Duan W H, Quek S T, Lim S P. Finite element solution for intermittent-contact problem withpiezoelectric actuation in ring type USM[. Finite Elements in Analysis and Design,2007,43(3):193-205.
[89]周盛强，赵淳生.超声电机接触界面的两种简化有限元模型.振动、测试与诊断,2009(3):251-255.
[90]周盛强，赵淳生，黄卫清.旋转型行波超声电机接触界面的空间域分析.中国电机工程学报,2010(12):63-68.
[91] Radi B, El Hami A. The study of the dynamic contact in ultrasonic motor. Applied MathematicalModelling,2010,34(12):3767-3777.
[92]于建国，赵志刚，夏元地.电动机气隙尺寸链的分析计算.防爆电机,1999(1):41-42.
[93]机械科学研究院.尺寸链计算方法.北京,中国国家标准化管理委员会,2004.
[94]卜炎.实用轴承技术手册.北京:机械工业出版社,2003.
[95]王光庆，沈润杰，郭吉丰.预压力对超声波电机特性的影响研究.浙江大学学报,2007,41(3):436-440.
[96]赵向东.旋转型行波超声电机动力学模型及性能仿真的研究,博士.南京:南京航空航天大学,2000.
[97]南京工艺装备制造有限公司.滚珠丝杠副http://www.njyigong.cn/products.asp?parentid=1.2012.
[98]固高科技深圳有限公司. GT系列运动控制器用户手册[DB/CD].2006.
[99] Jin J M, Zhao C S. Characteristic matching between stator and rotor in standing-wave-type ultrasonicmotors. Journal of Electroceramics,2008,20(3):197-202.
[100] Houben M, Van de Vijver W, Al-Bender F, et al. A generic modelling approach for studying thecontact mechanism and dynamic behavior of bimodal standing wave piezomotors.2008:227-231.
[101] Ho S T. Modelling of the Linear Ultrasonic Motor using an Elliptical Shape Stator.2006:82-87.
[102] Shi Y L, Zhao C S, Zhang J. Contact analysis and modeling of standing wave linear ultrasonicmotor. Journal of Wuhan University of Technology--Materials Science Edition,2011,26(6):1235-1242.
[103] Twiefel J, Potthast C, Mracek M, et al. Fundamental experiments as benchmark problems formodeling ultrasonic micro-impact processes. Journal of Electroceramics,2008,20(3):209-214.
[104] Wurpts W, Twiefel J. An ultrasonic motor with intermittent contact modeled as a two degree offreedom oscillator in time domain. PAMM,2009,9(1):287-288.
[105]郭翠娟.超高加速度精密运动平台研制,硕士.哈尔滨：哈尔滨工业大学,2011.
[106] Kuribayashi Kurosawa M, Kodaira O, Tsuchitoi Y, et al. Transducer for high speed and large thrustultrasonic linear motor using two sandwich-type vibrators. Ultrasonics, Ferroelectrics and FrequencyControl, IEEE Transactions on,1998,45(5):1188-1195.
[107]时运来，李玉宝，赵淳生. V型大推力直线超声电机的运动机理分析.压电与声光,2008,30(6):772-775.
[108] Li Y B, Shi Y L, Zhao C S. Design and experiment of butterfly linear ultrasonic motor with twodriving tips. Optics and Precision Engineering,2008,16(12):2327-2333.
[109]金家楣.若干新型超声电机的研究,博士.南京:南京航空航天大学,2007.
[110] Yang M, Richardson R C, Levesley M C, et al. Performance improvement of rectangular-platelinear ultrasonic motors using dual-frequency drive. Ultrasonics, Ferroelectrics and FrequencyControl, IEEE Transactions on,2004,51(12):1600-1606.
[111] Jin J M, Zhao C S. Linear ultrasonic motor using quadrate plate transducer. Frontiers of MechanicalEngineering in China,2009,4(1):88-91.
[112] Wakai T, Kurosawa M K, Higuchi T. Transducer for an ultrasonic linear motor with flexible drivingpart.1998:683-686.
[113]李亭，张铁民，刘潇建.超声电机多定子同步驱动技术的研究.振动、测试与诊断,2008(4):343-346.
[114] Hemsel T, Mracek M, Wallaschek J, et al. A novel approach for high power ultrasonic linearmotors.2004:1161-1164.
[115] Mracek M, Hemsel T. Synergetic driving concepts for bundled miniature ultrasonic linear motors.Ultrasonics,2006,44: e597-e602.
[116] Mracek M, Hemsel T, Sattel T, et al. Driving concepts for bundled ultrasonic linear motors. Journalof Electroceramics,2008,20(3):153-158.
[117]李欣欣.宏/微两级驱动的大行程高精度二维定位平台基础技术研究,博士.杭州:浙江大学,2008.
[118]严天宏，许畅，李青，等.高速超精运动台的离散滑模控制研究.控制工程,2010(004).
[119]赵增辉.超声电机压电振子的动力学特性研究,硕士.青岛:山东科技大学,2006.
[120]张晓峰.大行程超精密工作台关键技术研究,博士.天津:天津大学,2008.
[121]薛雯玉.基于直线超声电机仿三维运动平台驱动控制系统的研究,硕士.南京:南京航空航天大学,2012.
[122] Texasinstruments. TMS320F28235, TMS320F28234, TMS320F28232Digital Signal Controllers(DSCs) Data Manual.2009.
[123] Motorola. AM26LS32datasheet.1995. http://www.alldatasheet.com
[124]蒋嗣荣，洪振华.计算机控制技术.西北电讯工程学院,1985.
[125]高金源.计算机控制技术.北京:中央广播电视大学出版社,2002.
[126]贺红林.超声电机及其在机器人上的应用研究,博士.南京:南京航空航天大学,2006.
[127]李华峰，辜承林.使用PI控制的超声波电机精密位置控制.微电机(伺服技术),2002(2):23-26.
[128]应浩.关于模糊控制理论与应用的若干问题.自动化学报,2001(4):591-592.
[129]胡守仁，胡德文，时春.神经网络应用技术.长沙:国防科技大学出版社,1993.
[130]陶永华，尹怡欣，葛芦生.新型PID控制及其应用.北京:机械工业出版社,1998.
[131]张德丰. MATLAB神经网络应用设计.2.北京:机械工业出版社,2012.
[132]王旭东，邵惠鹤. RBF神经网络理论及其在控制中的应用.信息与控制,1997(4):32-44.
[133] Moody J, Darken C. Learning with localized receptive fields. Yale Univ., Department of ComputerScience,1988.
[134] Moody J, Darken C J. Fast learning in networks of locally-tuned processing units. Neuralcomputation,1989,1(2):281-294.
[135] Chen S, Grant P M, Cowan C F N. Orthogonal least-squares algorithm for training multioutputradial basis function networks. Radar and Signal Processing, IEE Proceedings F,1992,139(6):378-384.
[136]夏长亮，祁温雅，杨荣，等.基于RBF神经网络的超声波电机参数辨识与模型参考自适应控制.中国电机工程学报,2004(7):121-125.
[137] Jahani M, Mojallali H. Neural network based modeling of traveling wave ultrasonic motor usinggenetic algorithm.2010:486-490.
[138]孙志峻，帅双辉，金家楣，等.基于径向基神经网络的直线超声电机位置控制.振动.测试与诊断,2010(6):650-653.
[139] Lin F J, Shieh P H. Recurrent RBFN-based fuzzy neural network control for XY-/spl Theta/motioncontrol stage using linear ultrasonic motors. Ultrasonics, Ferroelectrics and Frequency Control, IEEETransactions on,2006,53(12):2450-2464.
[140]张德丰. MATLAB/Simulink建模与仿真实例精讲.1.北京:机械工业出版社,2011.
[141]王心坚，胡敏强，金龙，等.基于单神经元PID-PI的行波超声波电机速度复合控制研究.微电机,2008(3):19-22.
[142]王心坚，胡敏强，金龙，等.行波超声波电机多调节量协调控制方法.中国电机工程学报,2009(6):73-79.
[143]张炎，宋爱国，王心坚，等.一种行波超声波电机低速控制的方法.东南大学学报(自然科学版),2008(3):429-433.
[144]邢仁涛.超声电机驱动的多关节机器人,硕士.南京:南京航空航天大学,2007.