压电驱动器磁滞补偿的模糊控制方法及应用
|
摘要
压电驱动超精密微位移平台作为各种现代微电子制造装备的核心部件,其研发水平直接影响国家电子信息产业的技术进步。但是,压电驱动器固有的磁滞特性,会使系统精度严重下降,甚至导致系统闭环的不稳定。因此为了进一步提高超精密机电系统快速运动精度,满足纳米级加工和操作的要求,急需研究磁滞补偿控制的理论与方法。
本文主要研究了压电驱动器磁滞补偿的模糊控制方法,设计了二维并联微动平台,采用了多输入单输出的模糊系统对压电驱动器的磁滞特性建模,构造了xPC Target实时仿真系统,在此基础上,实现了磁滞补偿的模糊确定等效控制实验。
首先,采用复合双平行直板型柔性铰链机构,设计了具有极低运动耦合度的二维并联微动平台,对其进行了结构优化计算和有限元分析,使用电火花线切割加工完成后,实现了相关的测试及实验验证。
其次,针对压电驱动器的磁滞特性,提出了一种基于MISO模糊系统的磁滞建模方法,将一维输入空间中的多值函数映射为多维输入空间的单值函数,有效地解决了磁滞曲线多值映射的问题。基于Matlab7.9软件,该方法根据磁滞系统的输入输出数据,在最大隶属度、最近邻居和超半径概念的基础上,基于1阶T-S型模糊推理对模糊系统进行训练和参数优化,从而精确的建立了压电驱动器的磁滞特性模型。
然后,应用xPC Target系统构成硬件在回路仿真实时试验系统,它可以完成压电驱动器磁滞补偿控制系统的快速原形化、硬件在回路中测试等工作。
最后,使用模糊确定等效控制器补偿压电驱动器的磁滞特性,对微动台进行了高频正弦轨迹及圆轨迹快速跟踪控制实验。实验结果表明,该控制方法具有较高的跟踪精度,简单易行,具有良好的经济效用。
Piezoelectric actuated stage for ultra-precision micro-displacement of modern microelectronics manufacturing equipment as the core components, its R&D level directly affects the level of national electronic information industry and technological progress. However, the inherent hysteresis property of piezoelectric actuator will make a serious decline in system accuracy, and even cause the system closed-loop instability. Therefore, to further improve the motion precision of ultra-precise electromechanical systems, and meet the requirements of nano-processing and operations, it is urgent to study the hysteresis compensation control theory and method.
This paper studies the piezoelectric actuator hysteresis compensation fuzzy control method, designs two-dimensional parallel micro-stage, uses a multi-input single-output fuzzy system to model the hysteresis of piezoelectric actuator, constructs the xPC Target real-time simulation system, and based on all these above, realizes the hysteresis compensation fuzzy equivalent control experiments.
First, two parallel straight type of composite hinge body are adopted to design a low degree of coupled two-dimensional motion parallel micro-stage, then implement its structural optimization and finite element analysis, the use of EDWM is completed, to achieve the related testing and experiments.
Second, an approach of modeling hysteresis based on MISO fuzzy system is presented with respect to the hysteresis of piezoelectric actuators. The proposed model can sufficiently solve the problem of multi-value hysteresis via an expanded input space. On the basis of concepts such as maximum membership, nearest neighbor and super radius, through training fuzzy system and parameter optimization with one order T-S fuzzy implication, the model of hysteresis can be precisely established using input and output data with the software Matlab7.9.
Then, xPC Target system is used to construct real-time hardware-in -the-loop simulation test system. It can complete the piezoelectric actuator hysteresis compensation control system, rapid prototyping, hardware-in -the-loop testing and so on.
Finally, use the fuzzy equivalent controller to perform compensation of hysteresis characteristics of piezoelectric actuators for micro-stage high-frequency sinusoidal trajectory and circular trajectory fast tracking control experiments. Experimental results show that the control method has a high tracking accuracy, simple and of good economic effect.
本文主要研究了压电驱动器磁滞补偿的模糊控制方法,设计了二维并联微动平台,采用了多输入单输出的模糊系统对压电驱动器的磁滞特性建模,构造了xPC Target实时仿真系统,在此基础上,实现了磁滞补偿的模糊确定等效控制实验。
首先,采用复合双平行直板型柔性铰链机构,设计了具有极低运动耦合度的二维并联微动平台,对其进行了结构优化计算和有限元分析,使用电火花线切割加工完成后,实现了相关的测试及实验验证。
其次,针对压电驱动器的磁滞特性,提出了一种基于MISO模糊系统的磁滞建模方法,将一维输入空间中的多值函数映射为多维输入空间的单值函数,有效地解决了磁滞曲线多值映射的问题。基于Matlab7.9软件,该方法根据磁滞系统的输入输出数据,在最大隶属度、最近邻居和超半径概念的基础上,基于1阶T-S型模糊推理对模糊系统进行训练和参数优化,从而精确的建立了压电驱动器的磁滞特性模型。
然后,应用xPC Target系统构成硬件在回路仿真实时试验系统,它可以完成压电驱动器磁滞补偿控制系统的快速原形化、硬件在回路中测试等工作。
最后,使用模糊确定等效控制器补偿压电驱动器的磁滞特性,对微动台进行了高频正弦轨迹及圆轨迹快速跟踪控制实验。实验结果表明,该控制方法具有较高的跟踪精度,简单易行,具有良好的经济效用。
Piezoelectric actuated stage for ultra-precision micro-displacement of modern microelectronics manufacturing equipment as the core components, its R&D level directly affects the level of national electronic information industry and technological progress. However, the inherent hysteresis property of piezoelectric actuator will make a serious decline in system accuracy, and even cause the system closed-loop instability. Therefore, to further improve the motion precision of ultra-precise electromechanical systems, and meet the requirements of nano-processing and operations, it is urgent to study the hysteresis compensation control theory and method.
This paper studies the piezoelectric actuator hysteresis compensation fuzzy control method, designs two-dimensional parallel micro-stage, uses a multi-input single-output fuzzy system to model the hysteresis of piezoelectric actuator, constructs the xPC Target real-time simulation system, and based on all these above, realizes the hysteresis compensation fuzzy equivalent control experiments.
First, two parallel straight type of composite hinge body are adopted to design a low degree of coupled two-dimensional motion parallel micro-stage, then implement its structural optimization and finite element analysis, the use of EDWM is completed, to achieve the related testing and experiments.
Second, an approach of modeling hysteresis based on MISO fuzzy system is presented with respect to the hysteresis of piezoelectric actuators. The proposed model can sufficiently solve the problem of multi-value hysteresis via an expanded input space. On the basis of concepts such as maximum membership, nearest neighbor and super radius, through training fuzzy system and parameter optimization with one order T-S fuzzy implication, the model of hysteresis can be precisely established using input and output data with the software Matlab7.9.
Then, xPC Target system is used to construct real-time hardware-in -the-loop simulation test system. It can complete the piezoelectric actuator hysteresis compensation control system, rapid prototyping, hardware-in -the-loop testing and so on.
Finally, use the fuzzy equivalent controller to perform compensation of hysteresis characteristics of piezoelectric actuators for micro-stage high-frequency sinusoidal trajectory and circular trajectory fast tracking control experiments. Experimental results show that the control method has a high tracking accuracy, simple and of good economic effect.
引文
[1] D.M. Kim, D.W. Kang, J.Y. Shim, I.C. Song, D. G.Gweon. Optimal design of a flexure hinge-based XYZ atomic force microscopy scanner for minimizing Abbe errors. Review of Scientific Instruments. 2005, 76(7):0737061-0737067.
[2] K. Sugihara, I. Mori, T. Tojo, C. Ito, C. Tabata, T. Shinozaki. Piezoelectrically driven XYθtable for submicron lithography systems. Review of Scientific Instruments. 1989, 60(9):3024-3029.
[3] B.H. Kang, J.T. Wen, N.G. Dagalakis, J.J. Gorman. Analysis and design of parallel mechanisms with flexure joints. Proc. 2004 IEEE Int. Conf. on Robot. Autom.. New Orleans, L.A. 2004, 4097-4102.
[4] I.M. Pham, H.H. Chen. Stiffness modeling of flexure parallel mechanism. Precision Engineering. 2005, 29(4):467-478.
[5] K.X. Hu, J.H. Kim, J. Schmiedeler, C.H. Menq. Design, implementation, and control of a six-axis compliant stage. Review of Scientific Instruments. 2008, 79(2): 0251051-02510511.
[6] Q.S. Xu, Y.M. Li. Mechanical Design of Compliant Parallel Micromanipulators for Nano Scale Manipulation. Proceedings of the 1st IEEE International Conference on Nano/Micro Engineered and Molecular Systems. 2006, 653-657.
[7]吴鹰飞,周兆英.柔性铰链的计算与分析.机械设计与研究. 2002(3):29-30.
[8] J.M. Paros, L. Weisboro.How to Design Flexure Hinges.Machine Design.1965, 37(27):151-157.
[9] S. Awtar, A.H. Slocum. Constraint-based design of parallel kinematic XY flexuremechanisms. Journal of Mechanical Design. 2007, 129:814-830.
[10] Y.K. Yong, S. Aphale, S.O.R. Moheimani. Design, Identification, and Control of a Flexure-Based XY Stage for Fast Nanoscale Positioning. IEEE Transactions on Nanotechnology. 2009, 8(1):46-54.
[11] K.B. Choi, D.H Kim. Monolithic parallel linear compliant mechanism for two axes ultraprecision linear motion. Review of Scientific Instruments. 2006, 77: 0651061-0651067.
[12] Y.M. Li, Q.S. Xu. Development and Assessment of a Novel Decoupled XY Parallel Micropositioning Platform. IEEE/ASME Transactions on Mechatronics. 2010, 15(1):125-135.
[13]刘品宽,曲东升,王莉,孙立宁.新型二维压电驱动微动工作台的设计分析.压电与声光. 2002, 24(1):31-34.
[14]刘品宽,孙立宁,曲东升,荣伟彬.新型二维纳米级微动工作台的动力学分析.光学精密工程. 2002, 10(2):143-147.
[15]马立,荣伟彬,孙立宁.三维纳米级微动工作台的设计与分析.光学精密工程. 2006, 14(6):1017-1024.
[16]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[博士论文].浙江:浙江大学. 2006.
[17]陶惠峰.超精密微位移系统研究[硕士论文].浙江:浙江大学. 2003.
[18]桑武斌.二维超精工件台及其控制系统的研究[硕士论文].浙江:浙江大学. 2008.
[19]魏强.纳米定位微位移工作台的控制技术研究[博士论文].山东:山东大学. 2006.
[20] M.J. Dapino, R.C. Smith, A.B. Flatau. Structural magnetic strain model for magnetostrictive transducers. IEEE Transactions on Magnetics. 2000, 36(3):545-55.
[21] D.C. Jiles, J.B.Thoelke. Theory of ferromagnetic hysteresis determination ofmodel parameters from experimental hysteresis loops. IEEE Transactions on Magnetics. 1989, 25(5):3928-3930.
[22]李欣欣,王文,陈戬恒,陈子辰. Jiles-Atherton模型的超磁致伸缩驱动器磁滞补偿控制.光学精密工程. 2007, 15(10):1558-1563.
[23] R. Bouc. Forced vibration of mechanical systems with hysteresis. Proceedings of the 4th Conference on Nonlinear Oscilations. Prague, Czechoslovakia. 1967, 315.
[24] Y.K. Wen. Method for random vibration of hysteretic systems. ASCE Journal of Engineering Mechanics. 1976, 102(2):249-263.
[25]王代华,朱炜. WTYD型压电陶瓷微位移器的迟滞特性建模与实验验证.光学精密工程. 2010, 18(1):205-211.
[26] S. Devasia, E. ElEftheriou, S.O.R. Moheimani. A survey of control issues in nanopositioning. IEEE Transactions on Control Systems Technolog. 2007, 15 (5):802-823.
[27] K. Kuhnen, H. Janocha. Inverse feedforward controller for complex hysteretic nonlinearities in smart material systems. Control and Intelligent Systems. 2001, 29:74-83.
[28]张栋,张承进,魏强.压电微动工作台的动态迟滞模型.光学精密工程. 2009, 17(3):549-556.
[29]赵新龙,谭永红,董建萍.基于神经网络的迟滞非线性逆模型.上海交通大学学报. 2007, 41(1):104-107.
[30]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.中国科学F辑:信息科学. 2009, 39(3):289-304.
[31] S. Bashash, N. Jalili. Robust multiple frequency trajectory tracking control of piezoelectrically driven micro/nanopositioning systems. IEEE Transactions on Control Systems. 2007, 15:867-878.
[32] J.H. Zhong, B.Yao. Adaptive Robust Precision Motion Control of aPiezoelectric Positioning Stage. IEEE Transactions on Control Systems Technology. 2008, 16:1039-1046.
[33] Q.Q. Wang, C.Y. Su. Robust adaptive control of a class of nonlinear systems including actuator hysteresis with Prandtl–Ishlinskii presentations. Automatica. 2006, 42: 859-867.
[34]节德刚,孙立宁,曲东升,王力,蔡鹤皋.压电陶瓷微位移系统的模糊PID控制方法.哈尔滨工业大学学报. 2005, 37(2):145-147.
[35] L.J. Lai, G.Y. Gu, P.Z. Li, L.M. Zhu. Design of a decoupled 2-DOF translational parallel micro-positioning stage. IEEE International Conference on Robotics and Automation. 2011(accepted).
[36]朱利民,赖磊捷,谷国迎,李朋志.二自由度平动并联解耦微动平台.中国:发明专利. 201010216326.X. 2010(已公开).
[37] Q. Yao, J. Dong, P.M. Ferreira. Design, analysis, fabrication and testing of a parallel-kinematic micropositioning XY stage. International Journal of Machine Tools & Manufacture. 2007, 47(6):946-961.
[38] L.C. Hale, A.H. Slocum. Optimal design techniques for kinematic couplings. Precision Engineering. 2001, 25(2):114-127.
[39] Y.M. Li, Q.S. Xu. Design and Analysis of a Totally Decoupled Flexure-Based XY Parallel Micromanipulator. IEEE Transactions on Robotics. 2009, 25(3):645-657.
[40]周宁. ANSYS机械工程应用实例.北京:中国水利水电出版社. 2006:8-300.
[41]扎德.模糊集合、语言变量及模糊逻辑.陈国权,译.北京:科学出版社. 1982:6-80.
[42]石辛民,郝整清.模糊控制及其matlab仿真.北京:清华大学出版社. 2008:11-170.
[43] M. Sugeno, T. Yasukawa. A fuzzy-logic-based approach to qualitative modeling. IEEE Transactions on Fuzzy Systems. 1993, 1(1):7-31.
[44] L.X. Wang. Adaptive fuzzy systems and control. Englewood Cliffs, NJ: Prentice-Hall. 1994:60-200.
[45] J. Nie. Fuzzy control of multivariable nonlinear servomechanisms with explicit decoupling scheme. IEEE Transactions on Fuzzy Systems. 1997, 5(2):304-311.
[46] L.X. Wang, J.M. Mendel. Generating fuzzy rules from numerical data with applications. IEEE Transactions on System, Man and Cybernetics. 1992, 22(6):1414-1427.
[47] T. George, S. Haralambos, B. George. A simple algorithm for training fuzzy systems using input–output data. Advances in Engineering Software. 2003, 34:247-259.
[48] J. An, Q. Yang, Z. Ma. Study on method of modeling and controlling of magnetostrictive material. 17th International Zurich Symposium on Electromagnetic Compatibility. Piscataway, NJ. 2006:387-390.
[49]王晓煜.超磁致伸缩微位移执行器的系统建模与控制方法研究[博士论文].大连:大连理工大学. 2007.
[50]杨涤,李立涛.系统实时仿真开发环境与应用.北京:清华大学出版社. 2002:22-312.
[51] The Mathworks Inc. Real-Time Windows Target User's Guide. The Mathworks Inc, 2002.
[52]苗立东. xPC目标机的启动方法研究.计算机应用与软件. 2009, 26(6):83-85.
[53]张宏立.基于Stateflow和xPC的监控系统实现.计算机应用与软件. 2005, 22(12):72-75.
[54]毕效辉,王书,张琦.基于MATLAB /xPC的快速原型技术的应用.微计算机信息. 2007, 23(1-1):55-57.
[55]谢晗,吴光强,邱绪云.基于xPC目标的实时仿真技术及实现.微计算机信息. 2006, 22(12-1):200-202.
[56] The Mathworks Inc. Simulink 7 Developing S-Functions. The Mathworks Inc, 2002.
[57] J.E. Slotine, W. Li.应用非线性控制.程代展等,译.北京:机械工业出版社. 2009:138-185.
[58] R. Marino, P. Tomei.非线性系统设计-微分几何、自适应及鲁棒控制.姚郁,贺风华,译.北京:电子工业出版社. 2006:28-74.
[59]王立新.模糊系统与模糊控制教程.王迎军,译.北京:清华大学出版社. 2003:13-271.
[60] The Mathworks Inc. Simulink 7 user guide. The Mathworks Inc, 2002.
[2] K. Sugihara, I. Mori, T. Tojo, C. Ito, C. Tabata, T. Shinozaki. Piezoelectrically driven XYθtable for submicron lithography systems. Review of Scientific Instruments. 1989, 60(9):3024-3029.
[3] B.H. Kang, J.T. Wen, N.G. Dagalakis, J.J. Gorman. Analysis and design of parallel mechanisms with flexure joints. Proc. 2004 IEEE Int. Conf. on Robot. Autom.. New Orleans, L.A. 2004, 4097-4102.
[4] I.M. Pham, H.H. Chen. Stiffness modeling of flexure parallel mechanism. Precision Engineering. 2005, 29(4):467-478.
[5] K.X. Hu, J.H. Kim, J. Schmiedeler, C.H. Menq. Design, implementation, and control of a six-axis compliant stage. Review of Scientific Instruments. 2008, 79(2): 0251051-02510511.
[6] Q.S. Xu, Y.M. Li. Mechanical Design of Compliant Parallel Micromanipulators for Nano Scale Manipulation. Proceedings of the 1st IEEE International Conference on Nano/Micro Engineered and Molecular Systems. 2006, 653-657.
[7]吴鹰飞,周兆英.柔性铰链的计算与分析.机械设计与研究. 2002(3):29-30.
[8] J.M. Paros, L. Weisboro.How to Design Flexure Hinges.Machine Design.1965, 37(27):151-157.
[9] S. Awtar, A.H. Slocum. Constraint-based design of parallel kinematic XY flexuremechanisms. Journal of Mechanical Design. 2007, 129:814-830.
[10] Y.K. Yong, S. Aphale, S.O.R. Moheimani. Design, Identification, and Control of a Flexure-Based XY Stage for Fast Nanoscale Positioning. IEEE Transactions on Nanotechnology. 2009, 8(1):46-54.
[11] K.B. Choi, D.H Kim. Monolithic parallel linear compliant mechanism for two axes ultraprecision linear motion. Review of Scientific Instruments. 2006, 77: 0651061-0651067.
[12] Y.M. Li, Q.S. Xu. Development and Assessment of a Novel Decoupled XY Parallel Micropositioning Platform. IEEE/ASME Transactions on Mechatronics. 2010, 15(1):125-135.
[13]刘品宽,曲东升,王莉,孙立宁.新型二维压电驱动微动工作台的设计分析.压电与声光. 2002, 24(1):31-34.
[14]刘品宽,孙立宁,曲东升,荣伟彬.新型二维纳米级微动工作台的动力学分析.光学精密工程. 2002, 10(2):143-147.
[15]马立,荣伟彬,孙立宁.三维纳米级微动工作台的设计与分析.光学精密工程. 2006, 14(6):1017-1024.
[16]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[博士论文].浙江:浙江大学. 2006.
[17]陶惠峰.超精密微位移系统研究[硕士论文].浙江:浙江大学. 2003.
[18]桑武斌.二维超精工件台及其控制系统的研究[硕士论文].浙江:浙江大学. 2008.
[19]魏强.纳米定位微位移工作台的控制技术研究[博士论文].山东:山东大学. 2006.
[20] M.J. Dapino, R.C. Smith, A.B. Flatau. Structural magnetic strain model for magnetostrictive transducers. IEEE Transactions on Magnetics. 2000, 36(3):545-55.
[21] D.C. Jiles, J.B.Thoelke. Theory of ferromagnetic hysteresis determination ofmodel parameters from experimental hysteresis loops. IEEE Transactions on Magnetics. 1989, 25(5):3928-3930.
[22]李欣欣,王文,陈戬恒,陈子辰. Jiles-Atherton模型的超磁致伸缩驱动器磁滞补偿控制.光学精密工程. 2007, 15(10):1558-1563.
[23] R. Bouc. Forced vibration of mechanical systems with hysteresis. Proceedings of the 4th Conference on Nonlinear Oscilations. Prague, Czechoslovakia. 1967, 315.
[24] Y.K. Wen. Method for random vibration of hysteretic systems. ASCE Journal of Engineering Mechanics. 1976, 102(2):249-263.
[25]王代华,朱炜. WTYD型压电陶瓷微位移器的迟滞特性建模与实验验证.光学精密工程. 2010, 18(1):205-211.
[26] S. Devasia, E. ElEftheriou, S.O.R. Moheimani. A survey of control issues in nanopositioning. IEEE Transactions on Control Systems Technolog. 2007, 15 (5):802-823.
[27] K. Kuhnen, H. Janocha. Inverse feedforward controller for complex hysteretic nonlinearities in smart material systems. Control and Intelligent Systems. 2001, 29:74-83.
[28]张栋,张承进,魏强.压电微动工作台的动态迟滞模型.光学精密工程. 2009, 17(3):549-556.
[29]赵新龙,谭永红,董建萍.基于神经网络的迟滞非线性逆模型.上海交通大学学报. 2007, 41(1):104-107.
[30]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.中国科学F辑:信息科学. 2009, 39(3):289-304.
[31] S. Bashash, N. Jalili. Robust multiple frequency trajectory tracking control of piezoelectrically driven micro/nanopositioning systems. IEEE Transactions on Control Systems. 2007, 15:867-878.
[32] J.H. Zhong, B.Yao. Adaptive Robust Precision Motion Control of aPiezoelectric Positioning Stage. IEEE Transactions on Control Systems Technology. 2008, 16:1039-1046.
[33] Q.Q. Wang, C.Y. Su. Robust adaptive control of a class of nonlinear systems including actuator hysteresis with Prandtl–Ishlinskii presentations. Automatica. 2006, 42: 859-867.
[34]节德刚,孙立宁,曲东升,王力,蔡鹤皋.压电陶瓷微位移系统的模糊PID控制方法.哈尔滨工业大学学报. 2005, 37(2):145-147.
[35] L.J. Lai, G.Y. Gu, P.Z. Li, L.M. Zhu. Design of a decoupled 2-DOF translational parallel micro-positioning stage. IEEE International Conference on Robotics and Automation. 2011(accepted).
[36]朱利民,赖磊捷,谷国迎,李朋志.二自由度平动并联解耦微动平台.中国:发明专利. 201010216326.X. 2010(已公开).
[37] Q. Yao, J. Dong, P.M. Ferreira. Design, analysis, fabrication and testing of a parallel-kinematic micropositioning XY stage. International Journal of Machine Tools & Manufacture. 2007, 47(6):946-961.
[38] L.C. Hale, A.H. Slocum. Optimal design techniques for kinematic couplings. Precision Engineering. 2001, 25(2):114-127.
[39] Y.M. Li, Q.S. Xu. Design and Analysis of a Totally Decoupled Flexure-Based XY Parallel Micromanipulator. IEEE Transactions on Robotics. 2009, 25(3):645-657.
[40]周宁. ANSYS机械工程应用实例.北京:中国水利水电出版社. 2006:8-300.
[41]扎德.模糊集合、语言变量及模糊逻辑.陈国权,译.北京:科学出版社. 1982:6-80.
[42]石辛民,郝整清.模糊控制及其matlab仿真.北京:清华大学出版社. 2008:11-170.
[43] M. Sugeno, T. Yasukawa. A fuzzy-logic-based approach to qualitative modeling. IEEE Transactions on Fuzzy Systems. 1993, 1(1):7-31.
[44] L.X. Wang. Adaptive fuzzy systems and control. Englewood Cliffs, NJ: Prentice-Hall. 1994:60-200.
[45] J. Nie. Fuzzy control of multivariable nonlinear servomechanisms with explicit decoupling scheme. IEEE Transactions on Fuzzy Systems. 1997, 5(2):304-311.
[46] L.X. Wang, J.M. Mendel. Generating fuzzy rules from numerical data with applications. IEEE Transactions on System, Man and Cybernetics. 1992, 22(6):1414-1427.
[47] T. George, S. Haralambos, B. George. A simple algorithm for training fuzzy systems using input–output data. Advances in Engineering Software. 2003, 34:247-259.
[48] J. An, Q. Yang, Z. Ma. Study on method of modeling and controlling of magnetostrictive material. 17th International Zurich Symposium on Electromagnetic Compatibility. Piscataway, NJ. 2006:387-390.
[49]王晓煜.超磁致伸缩微位移执行器的系统建模与控制方法研究[博士论文].大连:大连理工大学. 2007.
[50]杨涤,李立涛.系统实时仿真开发环境与应用.北京:清华大学出版社. 2002:22-312.
[51] The Mathworks Inc. Real-Time Windows Target User's Guide. The Mathworks Inc, 2002.
[52]苗立东. xPC目标机的启动方法研究.计算机应用与软件. 2009, 26(6):83-85.
[53]张宏立.基于Stateflow和xPC的监控系统实现.计算机应用与软件. 2005, 22(12):72-75.
[54]毕效辉,王书,张琦.基于MATLAB /xPC的快速原型技术的应用.微计算机信息. 2007, 23(1-1):55-57.
[55]谢晗,吴光强,邱绪云.基于xPC目标的实时仿真技术及实现.微计算机信息. 2006, 22(12-1):200-202.
[56] The Mathworks Inc. Simulink 7 Developing S-Functions. The Mathworks Inc, 2002.
[57] J.E. Slotine, W. Li.应用非线性控制.程代展等,译.北京:机械工业出版社. 2009:138-185.
[58] R. Marino, P. Tomei.非线性系统设计-微分几何、自适应及鲁棒控制.姚郁,贺风华,译.北京:电子工业出版社. 2006:28-74.
[59]王立新.模糊系统与模糊控制教程.王迎军,译.北京:清华大学出版社. 2003:13-271.
[60] The Mathworks Inc. Simulink 7 user guide. The Mathworks Inc, 2002.