基于遗传算法的摩擦模型参数辨识研究
|
摘要
摩擦是制约伺服系统控制精度提高的一个重要因素，要想实现伺服系统的低速高精度控制，就须对系统存在的摩擦进行补偿。基于摩擦模型的补偿方法更加具有针对性，如果能得到系统的比较准确的摩擦模型，一般都能得到很好的控制效果。摩擦模型参数辨识是本文讨论的主要问题。
综述了国内外在摩擦模型参数辨识方面的研究进展情况，通过分析比较，提出了一种基于遗传算法进行摩擦模型参数辨识的方法。
详细分析了摩擦力的产生机理、摩擦的动态现象、伺服系统中的摩擦现象以及几种常用的静态、动态摩擦模型。通过分析、比较，从而选择“库仑+粘性”摩擦模型和Tustin摩擦模型作为辨识对象进行辨识仿真。然后选择一个二阶系统为被控对象，在被控系统上加一个随机干扰信号来模拟系统中的摩擦现象，设计了一种遗传辨识方法，来辨识系统的摩擦模型参数，并通过设计Matlab程序实现这个辨识仿真，得到摩擦模型参数。
最后利用“PID+前馈”摩擦补偿方法，通过设计Matlab／Simulink程序实现了基于摩擦模型的伺服系统摩擦补偿仿真，验证了辨识结果的有效性，也说明基于遗传算法的摩擦模型参数辨识方法是可行的。
Friction is an impediment to improve the control accuracy of servo systems,before to achieve low-velocity and high precision control, we must compensate thefriction exist in the system. Model-based friction compensation is more pertinency.Generally, this method can achieve good control effect if we can gain an exactfriction model of the system. Parameters identification of friction model is the mainissue of this dissertation.
The present research work of parameters identification of friction model athome and abroad is summarized firstly. After analyze and compare these methods, Aparameter identification method of friction model with Generic Algorithms is putforward.
Then this dissertation analyzed the creation theory of friction, the dynamicphenomenon of friction, the friction phenomenon in servo sysytems and somestatic/dynamic friction models which are commonly used. Via analyze and compareof the characteristics of these models, I choose the "Coulomb&Viscous model" and"Tustin model" as the identification objects. I choose a two rank system as thecontrol system, a random distubance was plus to this system to simulate the frictionphenomenon in servo system, and use the Generitc Algorithms to identify theparameters of the "Coulomb&Viscous model" and "Tustin model". These are carriedout by some Maflab programs.
Finally, using the Matlab/Simulink, a model-based "PID+feedforward" frictioncompensation method is carried out, and proved this parameter identificationmethod based on the Genetic Algorithms is effective.
综述了国内外在摩擦模型参数辨识方面的研究进展情况，通过分析比较，提出了一种基于遗传算法进行摩擦模型参数辨识的方法。
详细分析了摩擦力的产生机理、摩擦的动态现象、伺服系统中的摩擦现象以及几种常用的静态、动态摩擦模型。通过分析、比较，从而选择“库仑+粘性”摩擦模型和Tustin摩擦模型作为辨识对象进行辨识仿真。然后选择一个二阶系统为被控对象，在被控系统上加一个随机干扰信号来模拟系统中的摩擦现象，设计了一种遗传辨识方法，来辨识系统的摩擦模型参数，并通过设计Matlab程序实现这个辨识仿真，得到摩擦模型参数。
最后利用“PID+前馈”摩擦补偿方法，通过设计Matlab／Simulink程序实现了基于摩擦模型的伺服系统摩擦补偿仿真，验证了辨识结果的有效性，也说明基于遗传算法的摩擦模型参数辨识方法是可行的。
Friction is an impediment to improve the control accuracy of servo systems,before to achieve low-velocity and high precision control, we must compensate thefriction exist in the system. Model-based friction compensation is more pertinency.Generally, this method can achieve good control effect if we can gain an exactfriction model of the system. Parameters identification of friction model is the mainissue of this dissertation.
The present research work of parameters identification of friction model athome and abroad is summarized firstly. After analyze and compare these methods, Aparameter identification method of friction model with Generic Algorithms is putforward.
Then this dissertation analyzed the creation theory of friction, the dynamicphenomenon of friction, the friction phenomenon in servo sysytems and somestatic/dynamic friction models which are commonly used. Via analyze and compareof the characteristics of these models, I choose the "Coulomb&Viscous model" and"Tustin model" as the identification objects. I choose a two rank system as thecontrol system, a random distubance was plus to this system to simulate the frictionphenomenon in servo system, and use the Generitc Algorithms to identify theparameters of the "Coulomb&Viscous model" and "Tustin model". These are carriedout by some Maflab programs.
Finally, using the Matlab/Simulink, a model-based "PID+feedforward" frictioncompensation method is carried out, and proved this parameter identificationmethod based on the Genetic Algorithms is effective.
引文
[1] 周擎坤，范大鹏，张智永．摩擦对稳定跟踪平台低速性能影响的研究[J]．机械与电子，2005(12)：21-23
[2] 吴盛林，刘春芳．超低速高精度转台中摩擦力矩的动态补偿[J]．南京理工大学学报，2002(26)：393-402
[3] 马建设，李尚义，怯军，赵克定。仿真转台用连续回转电液伺服马达低速摩擦特性研究[J]．航空学报，2000(21)：361-363
[4] 刘强，尔联洁，刘金琨．摩擦非线性环节的特性、建模与控制补偿[J]．系统工程与电子技术，2002，24(11)：45-52
[5] 陈娟，乔彦峰．伺服系统低速摩擦力矩特性及补偿研究概况[J]．光机电信息，2002(11)：30-34
[6] 曾庆双，秦嘉川．转台伺服系统低速性能分析[J]．中国惯性技术学报，2001(9)：64-69
[7] 张锦江，吴宏鑫，李季苏，邹广瑞．高精度伺服系统低速问题研究[J]．自动化学报，2002(28)：431-434
[8] 袭著燕，张涛，路长厚．数控伺服进给系统中摩擦补偿控制研究进展[J]．现代制造工程，2006(1)：21-26
[9] H. Olson, K. J. Astrom, C. Canudas de Wit, M. Gafvert, and P. Lischinsky. Friction models and friction compensation[J]. European Journal of Control, 1998(4): 76-114
[10] 李书训，姚郁，马杰．基于观测器的伺服系统低速摩擦补偿分析[J]．电机与控制学报，2000(4)：27-30
[11] John Adams, Shahram Payandeh. On Methods for Low Velocity Friction Compensation: Theory and Experimental Study[J]. Journal of Robotic Systems, 1996, 13(6): 391-404
[12] Armstrong B, Neevel D, Kusik T. New Result in NPID Control: Tracking, Integral Control, Friction compensation and Experimental Results[J]. In Proceedings of the 1999 IEEE International Conference on Robotics & Automation，1999：837-842
[13] 李书训，姚郁．无刷直流电动机系统的一种摩擦补偿方法研究[J]．哈尔滨工业大学学报，2001(33)：55-59
[14] 杨元恺，郎需英．精密转台中摩擦力矩的动态补偿[J]．自动化学报，1983(9)：248-252
[15] Jayesh Amin, Bernard Friedland, and Avraham Harnoy. Implementation of a Friction Estimation and Compensation Technique[J]. IEEE Control Systems, 1997:71-76
[16] B. Friedland, Y. J. Park. On adaptive friction compensation[J]. IEEE, Trans. Auto. contr. 37, 1992 (10): 1609-1612
[17] C. Cadunas, K. J. Astrom, K. Braun. Adaptive friction compensation in DC-motor drives[J]. IEEE J. Robot. Automat RA, 1987, 3 (6), 681-685
[18] S. S. Ge, T. H. Lee, and S. X. Ren. Adaptive friction compensation of servo mechanisms[J]. International Journal of Systems Science, 2001, volume 32,number 4, pages 523-532
[19] 王琳，马平．系统辨识方法综述[J]．电力情报，2001(4)：63-66
[20] 李言俊，张科．系统辨识理论及应用．北京：国防工业出版社，2003
[2l] 方崇智，箫德云．过程辨识．北京：清华大学出版社，1988
[22] 李秀英，韩志刚．非线性系统辨识方法的新进展[J]．自动化技术与应用，2004(10)：5-7
[23] 万峰，孙优贤．非线性系统辨识中模糊模型参数收敛问题的进一步研究[J]．自动化学报，2007(33)：109-112
[24] 张广莹，邓正隆．小波分析在系统辨识中的应用[J]．电机与控制学报，2002(6)：64-67
[25] 李涌，韩崇昭，吴艳萍．一类非线性系统辨识的参数空间优化遗传算法[J]．控制与决策，2001(16)：965-967
[26] 张绍德．一类基于模糊辨识器的非线性动态系统辨识[J]．电子科技大学学报，2000(29)：170-173
[27] 郭会军，刘君华．基于GA-Fuzzy的混沌系统辨识研究[J]．系统仿真学报，2004(16)：1323-1326
[28] 杨德．简论非线性系统的神经网络辨识[J]．运城学院学报，2005(23)：48-49
[29] 从爽，高雪鹏，魏衡华．非线性直流电机仿真模型系统的建立[J]．系统仿真学报，200l(13)：25-28
[30] U. Parlitz, A. Homstein, and D. Engster, F. Al-Bender, V. Lampaert, T. Tjahjowidodo, S. D. Fassois, D. Rizos, C. X. Wong, K. Worden, G. Manson. Identification of pre-sliding friction dynamics[J]. American Institute of Physics, VOLUME 14, NUMBER 2, JUNE 2004:420-430
[31] 曹健，李尚义，赵克定．仿真转台用新型连续回转液压伺服马达摩擦特性研究[J]．宇航学报，2003(24)：374-378
[32] 王中华，王兴松，王群．新型摩擦模型的参数辨识及补偿实验研究[J]．制造业自动化，2001，23(6)：30-32
[33] 王英，熊振华，丁汉．基于状态观测的自适应摩擦力补偿的高精度控制[J]．自然科学进展，2005(15)：1100-1105
[34] 张涛，路长厚，李泉．基于扭矩测量的交流伺服工作台摩擦建模与仿真研究[J]．润滑与密封，2006(4)：32-36
[35] 吴子英，刘宏昭，刘丽兰，李鹏飞，原大宁．运动副摩擦参数的识别方法研究[J]．应用力学学报，2007(24)：115-120
[36] Francisco J. T. Vargas, Edson R. De Pied, Eugenio B. Castelan. identification and friction compensation for an industrial robot using two degree of freedom controllers[J]. IEEE, 8th International Conference on Control, Automation, Robotics and Vision Kunming, China, 6-9th December 2004:1146-1153
[37] Jan Swevers, Farid Al-Bender, Chris G. Ganseman, and Tutuko Prajogo. An Integrated Friction Model Structure with improved presliding behavior for accurate frciton compensation[J]. IEEE Transactions on Automatic Control, Vol. 45, No. 4, April 2000:675-686
[38] 刘强，扈宏杰，刘金琨，尔联洁．基于遗传算法的伺服系统摩擦参数辨识研究[J]．系统工程与电子技术，2003(25)：77-80
[39] De-peng Liu. Research on Parameter Identification of Friction Modeling for Servo Systems based on Genetic Alogrithms[J]. IEEE, Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou, 18-21 August 2005:1116-1120
[40] K. S. Low, M. T. Keck, K. J. Tseng. Parameter Identification and Controller Optimization using GA for a Precision Stage[J]. IEEE, 2001:694-698
[41] Jong-Hwan Kim, Hng-Kook Chae, Jeong-Yul Jeon, Sepm-Woo Lee. Identification and Control of Systems with Friction Using Accelerated Evolutionary Programming[J]. IEEE Control Systems, August 1996:38-47
[42] K. Worden, C. X. Wong, U. Parlitz, A. Homstein, D. Engster, T. Tjahjowidodo, F. Al-Bender, D. D. Rizos, S. D. Fassois. Identification of Pre-sliding and Sliding Friction Dynamics Grey Box and Black Box Models[J]. Mechanical Systems and Signal Processing, 2005:1-19
[43] Jeong-Yul Jeon, Seon-Woo Lee, Hong-Kook Chae, Jong-Hwan Kim. Low Velocity Friction Identification and Compensation Using Accelerated Evolutionary Programming[J]. IEEE, 1996:372-377
[44] Hongliu Du, Satish S. Modeling and Compensation of Low-Velocity Friction with Bounds[J]. IEEE Transactions on Control Systems Technology, Vol.7, No.1, January 1999:110-121
[45] Demosthenis D. Rizos, Spilios D. Fassois. Maxwell Slip Model Based Identification and Control of Systems with Friction[J]. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005 Seville, Spain, December 12-15, 2005:4578-4583
[46] Lampaert. V, F. Al-Bender and J. Swevers. Experimental chacterization of dry friction at low velocities on a developed tribometer setup for macroscopic measurements[J]. Tribol. Lett. 2004(16): 95-105
[47] M. S. Madi, K. Khayati, P. Bigras. Parameter Estimation for the LuGre Friction Model using Interval Analysis and Set Inversion[J]. IEEE International Conference on Systems, Man and Cybernetics, 2004:428-433
[48] 段海滨，王道波，朱家强，黄向华．基于ACA的飞行仿真伺服系统LuGre摩擦参数辨识[J]．南京航空航天大学学报，2004(21)：179-184
[49] 郑言海，王洪祥，庄显义．基于匹配追随算法的摩擦力自适应辨识与补偿研 究[J]．高技术通讯，2001：77-80
[50] S. Hashimotol, K. Ohishi, T. Ishikawa, K. Kosaka, H. Kubota, T. Ohmi. On-Line Identification Method of Static Friction for Ultra-Precision Positioning[J]. SICE, Annual Conference in Sapporo, Japan, August 4-6, 2004: 137-142
[51] Carlos Canudas de Wit, H. Olsson, K. J. Astrom, P. Lischinsky. A new model for control of systems with friction[J]. IEEE Transactions on Automatic Control, Vol.40, No.3, 1995:419-425
[52] Carlos Canudas de Wit. Comments on "A new model for control of systems with friction"[J]. IEEE Transations on Automatic Control, Vol.43, No.8, August, 1998:1189-1190
[53] C. Makkar, W. E. Dixon, W. G. Sawyer, G. Hu. A New Continuously Differentiable Friction Model for control systems design[J]. Proceedings of the 2005 IEEE/ASME International Conference on Advanced Intelligent Mechatronics Monterey, California, USA, 24-28 July, 2005
[54] JinHyoung Oh, Ashwani K. Padthe, Dennis S. Bemstein, Demosthenis D. Rizos, and Spilios D. Fassois. Duhem Models for Hysteresis in Sliding and Presliding Friction[J]. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005 Seville, Spain, December 12-15, 2005
[55] Farid Al-Bender, Vincent Lampaert, and Jan Swevers. The Generalized Maxwell-Slip Model: A Novel Model for Friction Simulation and Compensation[J]. IEEE Transactions on Automatic Control, Vol.50, No.11, Novemeber 2005:1883-1887
[56] 王欣峰．基于BP神经网络摩擦力补偿算法的研究．[中国科学院工学硕士学位论文]．2006
[57] 魏立新．X_Y数控平台运动摩擦补偿及边缘跟踪力控制研究．[燕山大学工学博士学位论文]．2005：27-28
[58] 黄进．含摩擦环节伺服系统的分析及控制补偿研究．[西安电子科技大学工 学博士学位论文]．2000：1-3
[59] Magnus Gafvert. Comparisons of Two Dynamic Friction Models[J]. IEEE International Conference on Control Applications Harford, CT, October 5-7, 1997:386-391
[60] R. Kelly. Enhancement to the LuGre Model for Global Description of Friction Phenomena[J]. Latin American Applied Research, 2004(34): 173-77
[61] Ryo Kikuuwe, Naoyuki Takesue, Akihito Sano, Hiromi Mochiyama, Hideo Fujimoto. Fixed-Step Friction Simulation: From Classical Coulomb Model To Modem Continuous Models[J]. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2005:3910-3917
[62] LBrinc MArton. Friction Model for Low Velocities. Proprieties and Applications[J]. Fourth International Workshop on Robot Motion and Control, June 17-20, 2004:333-338
[63] Martin Aberger, Martin Otter. Modeling Friction in Modelica with the Lund-Grenoble Friction Model[J]. International Modelica Conference, Proceedings, March 18-19, 2002:285-294
[64] 陈根社，陈新海．遗传算法的研究与进展[J]．信息与控制，1994(23)：215-222
[65] 席裕庚，柴天佑，恽为民．遗传算法综述[J]．控制理论与应用，1996(13)：697-708
[66] 戴晓晖，李敏强，寇纪淞．遗传算法理论研究综述[J]．控制与决策，2000(15)：263-269
[67] 吉根林．遗传算法研究综述[J]．计算机应用与软件，2004(21)：69-73
[68] 王耀南．智能控制系统-模糊逻辑、专家系统、神经网络控制．长沙：湖南大学出版社，1996：282-302
[69] 周明，孙树栋．遗传算法原理及应用．北京：国防工业出版社，2005
[70] 黄永安，马路，刘慧敏．MATLAB7.0／Simulink6.0建模仿真开发与高级工程应用．北京：清华大学出版社，2005
[71] 薛定宇．控制系统计算机辅助设计——MATLAB语言与应用(第2版)．北京：清华大学出版社，2006
[72] 刘金琨．先进PID控制MATLAB仿真(第2版)．北京：电子工业出版社，2006
[73] Gianni Ferretti, Gianantonio Magnani, Paolo Rocco. Model-Based Friction Compensation[J]. Advances in Control of Articulated and Mobile Robots, STAR 10, 2004:87-100
[74] 徐丽娜，李琳琳．遗传算法在非线性系统辨识中的应用研究[J]．哈尔滨工业大学学报，1999(31)：39-42
[2] 吴盛林，刘春芳．超低速高精度转台中摩擦力矩的动态补偿[J]．南京理工大学学报，2002(26)：393-402
[3] 马建设，李尚义，怯军，赵克定。仿真转台用连续回转电液伺服马达低速摩擦特性研究[J]．航空学报，2000(21)：361-363
[4] 刘强，尔联洁，刘金琨．摩擦非线性环节的特性、建模与控制补偿[J]．系统工程与电子技术，2002，24(11)：45-52
[5] 陈娟，乔彦峰．伺服系统低速摩擦力矩特性及补偿研究概况[J]．光机电信息，2002(11)：30-34
[6] 曾庆双，秦嘉川．转台伺服系统低速性能分析[J]．中国惯性技术学报，2001(9)：64-69
[7] 张锦江，吴宏鑫，李季苏，邹广瑞．高精度伺服系统低速问题研究[J]．自动化学报，2002(28)：431-434
[8] 袭著燕，张涛，路长厚．数控伺服进给系统中摩擦补偿控制研究进展[J]．现代制造工程，2006(1)：21-26
[9] H. Olson, K. J. Astrom, C. Canudas de Wit, M. Gafvert, and P. Lischinsky. Friction models and friction compensation[J]. European Journal of Control, 1998(4): 76-114
[10] 李书训，姚郁，马杰．基于观测器的伺服系统低速摩擦补偿分析[J]．电机与控制学报，2000(4)：27-30
[11] John Adams, Shahram Payandeh. On Methods for Low Velocity Friction Compensation: Theory and Experimental Study[J]. Journal of Robotic Systems, 1996, 13(6): 391-404
[12] Armstrong B, Neevel D, Kusik T. New Result in NPID Control: Tracking, Integral Control, Friction compensation and Experimental Results[J]. In Proceedings of the 1999 IEEE International Conference on Robotics & Automation，1999：837-842
[13] 李书训，姚郁．无刷直流电动机系统的一种摩擦补偿方法研究[J]．哈尔滨工业大学学报，2001(33)：55-59
[14] 杨元恺，郎需英．精密转台中摩擦力矩的动态补偿[J]．自动化学报，1983(9)：248-252
[15] Jayesh Amin, Bernard Friedland, and Avraham Harnoy. Implementation of a Friction Estimation and Compensation Technique[J]. IEEE Control Systems, 1997:71-76
[16] B. Friedland, Y. J. Park. On adaptive friction compensation[J]. IEEE, Trans. Auto. contr. 37, 1992 (10): 1609-1612
[17] C. Cadunas, K. J. Astrom, K. Braun. Adaptive friction compensation in DC-motor drives[J]. IEEE J. Robot. Automat RA, 1987, 3 (6), 681-685
[18] S. S. Ge, T. H. Lee, and S. X. Ren. Adaptive friction compensation of servo mechanisms[J]. International Journal of Systems Science, 2001, volume 32,number 4, pages 523-532
[19] 王琳，马平．系统辨识方法综述[J]．电力情报，2001(4)：63-66
[20] 李言俊，张科．系统辨识理论及应用．北京：国防工业出版社，2003
[2l] 方崇智，箫德云．过程辨识．北京：清华大学出版社，1988
[22] 李秀英，韩志刚．非线性系统辨识方法的新进展[J]．自动化技术与应用，2004(10)：5-7
[23] 万峰，孙优贤．非线性系统辨识中模糊模型参数收敛问题的进一步研究[J]．自动化学报，2007(33)：109-112
[24] 张广莹，邓正隆．小波分析在系统辨识中的应用[J]．电机与控制学报，2002(6)：64-67
[25] 李涌，韩崇昭，吴艳萍．一类非线性系统辨识的参数空间优化遗传算法[J]．控制与决策，2001(16)：965-967
[26] 张绍德．一类基于模糊辨识器的非线性动态系统辨识[J]．电子科技大学学报，2000(29)：170-173
[27] 郭会军，刘君华．基于GA-Fuzzy的混沌系统辨识研究[J]．系统仿真学报，2004(16)：1323-1326
[28] 杨德．简论非线性系统的神经网络辨识[J]．运城学院学报，2005(23)：48-49
[29] 从爽，高雪鹏，魏衡华．非线性直流电机仿真模型系统的建立[J]．系统仿真学报，200l(13)：25-28
[30] U. Parlitz, A. Homstein, and D. Engster, F. Al-Bender, V. Lampaert, T. Tjahjowidodo, S. D. Fassois, D. Rizos, C. X. Wong, K. Worden, G. Manson. Identification of pre-sliding friction dynamics[J]. American Institute of Physics, VOLUME 14, NUMBER 2, JUNE 2004:420-430
[31] 曹健，李尚义，赵克定．仿真转台用新型连续回转液压伺服马达摩擦特性研究[J]．宇航学报，2003(24)：374-378
[32] 王中华，王兴松，王群．新型摩擦模型的参数辨识及补偿实验研究[J]．制造业自动化，2001，23(6)：30-32
[33] 王英，熊振华，丁汉．基于状态观测的自适应摩擦力补偿的高精度控制[J]．自然科学进展，2005(15)：1100-1105
[34] 张涛，路长厚，李泉．基于扭矩测量的交流伺服工作台摩擦建模与仿真研究[J]．润滑与密封，2006(4)：32-36
[35] 吴子英，刘宏昭，刘丽兰，李鹏飞，原大宁．运动副摩擦参数的识别方法研究[J]．应用力学学报，2007(24)：115-120
[36] Francisco J. T. Vargas, Edson R. De Pied, Eugenio B. Castelan. identification and friction compensation for an industrial robot using two degree of freedom controllers[J]. IEEE, 8th International Conference on Control, Automation, Robotics and Vision Kunming, China, 6-9th December 2004:1146-1153
[37] Jan Swevers, Farid Al-Bender, Chris G. Ganseman, and Tutuko Prajogo. An Integrated Friction Model Structure with improved presliding behavior for accurate frciton compensation[J]. IEEE Transactions on Automatic Control, Vol. 45, No. 4, April 2000:675-686
[38] 刘强，扈宏杰，刘金琨，尔联洁．基于遗传算法的伺服系统摩擦参数辨识研究[J]．系统工程与电子技术，2003(25)：77-80
[39] De-peng Liu. Research on Parameter Identification of Friction Modeling for Servo Systems based on Genetic Alogrithms[J]. IEEE, Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou, 18-21 August 2005:1116-1120
[40] K. S. Low, M. T. Keck, K. J. Tseng. Parameter Identification and Controller Optimization using GA for a Precision Stage[J]. IEEE, 2001:694-698
[41] Jong-Hwan Kim, Hng-Kook Chae, Jeong-Yul Jeon, Sepm-Woo Lee. Identification and Control of Systems with Friction Using Accelerated Evolutionary Programming[J]. IEEE Control Systems, August 1996:38-47
[42] K. Worden, C. X. Wong, U. Parlitz, A. Homstein, D. Engster, T. Tjahjowidodo, F. Al-Bender, D. D. Rizos, S. D. Fassois. Identification of Pre-sliding and Sliding Friction Dynamics Grey Box and Black Box Models[J]. Mechanical Systems and Signal Processing, 2005:1-19
[43] Jeong-Yul Jeon, Seon-Woo Lee, Hong-Kook Chae, Jong-Hwan Kim. Low Velocity Friction Identification and Compensation Using Accelerated Evolutionary Programming[J]. IEEE, 1996:372-377
[44] Hongliu Du, Satish S. Modeling and Compensation of Low-Velocity Friction with Bounds[J]. IEEE Transactions on Control Systems Technology, Vol.7, No.1, January 1999:110-121
[45] Demosthenis D. Rizos, Spilios D. Fassois. Maxwell Slip Model Based Identification and Control of Systems with Friction[J]. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005 Seville, Spain, December 12-15, 2005:4578-4583
[46] Lampaert. V, F. Al-Bender and J. Swevers. Experimental chacterization of dry friction at low velocities on a developed tribometer setup for macroscopic measurements[J]. Tribol. Lett. 2004(16): 95-105
[47] M. S. Madi, K. Khayati, P. Bigras. Parameter Estimation for the LuGre Friction Model using Interval Analysis and Set Inversion[J]. IEEE International Conference on Systems, Man and Cybernetics, 2004:428-433
[48] 段海滨，王道波，朱家强，黄向华．基于ACA的飞行仿真伺服系统LuGre摩擦参数辨识[J]．南京航空航天大学学报，2004(21)：179-184
[49] 郑言海，王洪祥，庄显义．基于匹配追随算法的摩擦力自适应辨识与补偿研 究[J]．高技术通讯，2001：77-80
[50] S. Hashimotol, K. Ohishi, T. Ishikawa, K. Kosaka, H. Kubota, T. Ohmi. On-Line Identification Method of Static Friction for Ultra-Precision Positioning[J]. SICE, Annual Conference in Sapporo, Japan, August 4-6, 2004: 137-142
[51] Carlos Canudas de Wit, H. Olsson, K. J. Astrom, P. Lischinsky. A new model for control of systems with friction[J]. IEEE Transactions on Automatic Control, Vol.40, No.3, 1995:419-425
[52] Carlos Canudas de Wit. Comments on "A new model for control of systems with friction"[J]. IEEE Transations on Automatic Control, Vol.43, No.8, August, 1998:1189-1190
[53] C. Makkar, W. E. Dixon, W. G. Sawyer, G. Hu. A New Continuously Differentiable Friction Model for control systems design[J]. Proceedings of the 2005 IEEE/ASME International Conference on Advanced Intelligent Mechatronics Monterey, California, USA, 24-28 July, 2005
[54] JinHyoung Oh, Ashwani K. Padthe, Dennis S. Bemstein, Demosthenis D. Rizos, and Spilios D. Fassois. Duhem Models for Hysteresis in Sliding and Presliding Friction[J]. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005 Seville, Spain, December 12-15, 2005
[55] Farid Al-Bender, Vincent Lampaert, and Jan Swevers. The Generalized Maxwell-Slip Model: A Novel Model for Friction Simulation and Compensation[J]. IEEE Transactions on Automatic Control, Vol.50, No.11, Novemeber 2005:1883-1887
[56] 王欣峰．基于BP神经网络摩擦力补偿算法的研究．[中国科学院工学硕士学位论文]．2006
[57] 魏立新．X_Y数控平台运动摩擦补偿及边缘跟踪力控制研究．[燕山大学工学博士学位论文]．2005：27-28
[58] 黄进．含摩擦环节伺服系统的分析及控制补偿研究．[西安电子科技大学工 学博士学位论文]．2000：1-3
[59] Magnus Gafvert. Comparisons of Two Dynamic Friction Models[J]. IEEE International Conference on Control Applications Harford, CT, October 5-7, 1997:386-391
[60] R. Kelly. Enhancement to the LuGre Model for Global Description of Friction Phenomena[J]. Latin American Applied Research, 2004(34): 173-77
[61] Ryo Kikuuwe, Naoyuki Takesue, Akihito Sano, Hiromi Mochiyama, Hideo Fujimoto. Fixed-Step Friction Simulation: From Classical Coulomb Model To Modem Continuous Models[J]. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2005:3910-3917
[62] LBrinc MArton. Friction Model for Low Velocities. Proprieties and Applications[J]. Fourth International Workshop on Robot Motion and Control, June 17-20, 2004:333-338
[63] Martin Aberger, Martin Otter. Modeling Friction in Modelica with the Lund-Grenoble Friction Model[J]. International Modelica Conference, Proceedings, March 18-19, 2002:285-294
[64] 陈根社，陈新海．遗传算法的研究与进展[J]．信息与控制，1994(23)：215-222
[65] 席裕庚，柴天佑，恽为民．遗传算法综述[J]．控制理论与应用，1996(13)：697-708
[66] 戴晓晖，李敏强，寇纪淞．遗传算法理论研究综述[J]．控制与决策，2000(15)：263-269
[67] 吉根林．遗传算法研究综述[J]．计算机应用与软件，2004(21)：69-73
[68] 王耀南．智能控制系统-模糊逻辑、专家系统、神经网络控制．长沙：湖南大学出版社，1996：282-302
[69] 周明，孙树栋．遗传算法原理及应用．北京：国防工业出版社，2005
[70] 黄永安，马路，刘慧敏．MATLAB7.0／Simulink6.0建模仿真开发与高级工程应用．北京：清华大学出版社，2005
[71] 薛定宇．控制系统计算机辅助设计——MATLAB语言与应用(第2版)．北京：清华大学出版社，2006
[72] 刘金琨．先进PID控制MATLAB仿真(第2版)．北京：电子工业出版社，2006
[73] Gianni Ferretti, Gianantonio Magnani, Paolo Rocco. Model-Based Friction Compensation[J]. Advances in Control of Articulated and Mobile Robots, STAR 10, 2004:87-100
[74] 徐丽娜，李琳琳．遗传算法在非线性系统辨识中的应用研究[J]．哈尔滨工业大学学报，1999(31)：39-42