含摩擦环节伺服系统的补偿控制
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摘要
摩擦普遍存在于机电伺服系统中,它不但与接触表面间的正压力、相对速度相关,而且还与停滞时间相关,表现出摩擦记忆、变静摩擦等特性,从而导致了低速爬行,增大了稳态误差,降低了稳定性。为了消除或减小摩擦给系统带来的危害,提高伺服跟踪性能,本文研究了其控制补偿问题,主要内容如下:
首先,以X-Y平台为研究对象,建立了基于动态LuGre摩擦模型的机电伺服系统模型,设计了非线性观测器,用于在线估计系统未知参数和受到的扰动;基于Lyapunov稳定性理论,应用反步积分方法,设计了反步控制器,保证了参数估值的收敛性和系统的全局稳定性。仿真结果表明,与传统的PID控制相比,反步积分自适应控制方法能够有效地对摩擦和其他干扰进行补偿,从而显著地减小了跟踪误差,增强了系统的鲁棒性。
其次,针对LuGre摩擦模型,提出基于遗传算法的模型参数一步辨识方法,一次性辨识出摩擦模型中的静态参数和动态参数,克服了已有的两步辨识方法过程复杂、实验耗时等缺陷。
Friction is widely present in servo systems. It depends not only on the normal forces in contact and relative velocity, but also on the lag time, leading to the friction memory and rising static friction, which may result in stick-slip in low speed, increasing steady-state errors and reducing stability of system. In order to eliminate or reduce the effect of friction, and increase the system performance, appropriate methods must be carried out. This dissertation focuses on the following work:
Firstly, a mathematic model for X-Y table with dynamic LuGre friction model is established. And an nonlinear observer is designed to estimate the unknown friction parameters and other disturbances for adaptive friction compensation and disturbances rejection. A backstepping control law is derived with Lyapunov stability theory to ensure astringency of parameter estimation and global stability of servo systems with friction. Simulation results show that system robustness and tacking accuracy are improved with proposed method than that with traditional PID control.
Finally, a one-step method for LuGre friction model parameter identification is presented. With the proper selected objective function, four static parameters and two dynamic parameters are obtained at one time. Thus, the complex and time-consuming constant velocity experiments, which are necessary for the two-step method, is avoided that makes the proposed method more practical.
首先,以X-Y平台为研究对象,建立了基于动态LuGre摩擦模型的机电伺服系统模型,设计了非线性观测器,用于在线估计系统未知参数和受到的扰动;基于Lyapunov稳定性理论,应用反步积分方法,设计了反步控制器,保证了参数估值的收敛性和系统的全局稳定性。仿真结果表明,与传统的PID控制相比,反步积分自适应控制方法能够有效地对摩擦和其他干扰进行补偿,从而显著地减小了跟踪误差,增强了系统的鲁棒性。
其次,针对LuGre摩擦模型,提出基于遗传算法的模型参数一步辨识方法,一次性辨识出摩擦模型中的静态参数和动态参数,克服了已有的两步辨识方法过程复杂、实验耗时等缺陷。
Friction is widely present in servo systems. It depends not only on the normal forces in contact and relative velocity, but also on the lag time, leading to the friction memory and rising static friction, which may result in stick-slip in low speed, increasing steady-state errors and reducing stability of system. In order to eliminate or reduce the effect of friction, and increase the system performance, appropriate methods must be carried out. This dissertation focuses on the following work:
Firstly, a mathematic model for X-Y table with dynamic LuGre friction model is established. And an nonlinear observer is designed to estimate the unknown friction parameters and other disturbances for adaptive friction compensation and disturbances rejection. A backstepping control law is derived with Lyapunov stability theory to ensure astringency of parameter estimation and global stability of servo systems with friction. Simulation results show that system robustness and tacking accuracy are improved with proposed method than that with traditional PID control.
Finally, a one-step method for LuGre friction model parameter identification is presented. With the proper selected objective function, four static parameters and two dynamic parameters are obtained at one time. Thus, the complex and time-consuming constant velocity experiments, which are necessary for the two-step method, is avoided that makes the proposed method more practical.
引文
[1]周立峰,巢来春.伺服机械结构(第一分册),伺服系统基本原理.北京:国防工业出版社.1979.
[2]刘强,尔联洁,刘金琨.摩擦非线性环节的特性,建模与控制补偿综述.系统工程与电子技术.2002,24(11):45-52.
[3] B.A rmatrong-Helouvry,P .Dupont,C .Canudas de Wit.A Survey of Analysis Tools and Compensation Methods for the Control of Machines with Friction.Automatic.1994,30(7): 1083-1138.
[4]陈兴林,张福恩.仿真转台的低速性能研究.宇航学报.1995, 14 (4):65-69.
[5] P.E .Dupont,S .Kasturi Prakash.Experimental investigation of friction Dynamics associated with normal load.A SME.15th Biennial Conference on Mechanical Vibration and Noise.Vibration of Nonlinear Random and Time-Varying Systems.1995:1109-1115.
[6] B. Armstrong. Stick-slip and Control in low-speed Motion. IEEE Transactions on Automatic Control.1993, 38(10):1483-1496.
[7] P. E. Dupont, E. P. Dunlap. Friction Modeling and PD Compensation at very Low Velocities. Journal of Dynamic System.Measurement and Control. 1998, 117(1):8-14.
[8] C.Canudas de Wit, P. Noel, A. Aubin, B. Brogliato. Adaptive Friction Compensation in Robot Manipulators: Low velocities. International Journal of Robotics Research.1991, 10 (3):189-199.
[9] N. E. Leonard, P .S. Krishnaprasad. Adaptive Friction Compensation for Bi-Directional Low Velocity Position Tracking. 31st Conference on Decision and Control.1992:267-273.
[10] Dahl P. A Solid Friction Model. Aerospace Corp. .1968.
[11] R.S.H.Richardson, H.Nolle. Surface Friction under Time-Dependent Loads. Wear.1976, 37(1):87-101.
[12] D .Karnopp.Computer simulation of stick-slip frictionin mechanical dynamic systems.ASME J.Dyn. Sys .Meas Contr.1985, 107(1):100-103.
[13] Bliman P A, Sorine M. Easy-to-Use Realistic Dry Friction Models for Automatic Control. In Proceedings of 3th European Control Conference.1995: 3788-3794.
[14] Canudas De Wit C. A New Model for Control of Systems with Friction. IEEETran. on Automatic Control .1995 , 40(3) : 419-425.
[15] D. A. Haessing and B. Friedland. On the Modeling and Simulation of Friction. Trans. ASME: J.of dynamic Systems, Measurement, and Control.1991, 113(3): 354-362.
[16] Friedland B, Park YJ. On Adaptive Friction Compensation. IEEE Trans on Automatic Control.1992, 37 (10): 1609-1612.
[17] Phillips S M, Ballou K R, Friction Modeling and Compensation for an Industrial Robot. Journal of Robotic Systems.1993, 10 (7): 947-971.
[18] Yang Y P, Chu J S. Adaptive Velocity Control of DC Motors with Coulomb Friction Identification. ASME Journal of Dynamic Systems, Measurement and Control.1993, 115: 95-102.
[19] Canudas De Wit C. Robust Control for Servo-Mechanisms under Inexact Friction Compensation. Automatica.1993, 29 (30): 757-761.
[20] Deur, Josko.Asgari, Jahan.Hrovat, Davor. Modeling of an automotive planetary gear set based on Karnopp model for clutch friction. Proceedings of the ASME Dynamic Systems and Control Division. 2003, 2: 903-910.
[21] Cheok KC, Hu H, Loh N K. Modeling and Identification of a Class of Servomechanism Systems with Stick-Slip Friction. ASME Journal of Dynamic Systems, Measurement, and Control .1988, 110 : 324-328.
[22] Walrath C D. Adaptive Bearing Friction Compensation Based on Recent Knowledge of Dynamic Friction. Automatica.1984, 20(6): 717-727.
[23] Ashwani K. Padthe, JinHyoung Oh, Dennis S. Bernstein. On the LuGre Model and Friction Induced Hysteresis. Proceedings of the 2006 American Control Conference. 2006: 3247-3252.
[24] Emmanuel C. Dean-Leon, Vicente Parra-Vega, Arturo Espinosa-Romero. Visual Servoing for Constrained Planar Robots Subject to Complex Friction. IEEE Transactions on Mechatronics.2006, 11(4): 389-400.
[25] Basilio Bona, Marina Indri, Nicola Smaldone. Rapid Prototyping of a Model-Based Control with Friction Compensation for a Direct-Drive Robot. IEEE/ASME Transactions on Mechatronics. 2006, 11(5): 576-584.
[26] J. Lin, C.H. Chen. A Novel Fuzzy Friction Compensation Approach for Tracking of a Linear Motion Stage. Proceedings of the 2006 American ControlConference. 2006: 3188-3198.
[27] Yaolong Tan, Jie Chang, Hualin Tan. Adaptive Backstepping Control and Friction Compensation for AC Servo with Inertia and Load Uncertainties. IEEETransactions on Industrial Electronics.2003, 50(5): 944-952.
[28] Nitin Patel, Christopher Edwards, Sarah K Spurgeon. A Sliding Mode Observer for Tyre Friction Estimation during Braking. Proceedings of the 2006 American Control Conference. 2006: 5867-5872.
[29] Andres Guesalaga. Modelling End-of-roll Dynamics in Positioning Servos. Control Engineering Practice.2004, 12(2): 217-224.
[30] Armstrong B, Neevel D , Kusik T. New Result in NPID Control: Tracking, Integral Control, Friction Compensation and Experimental Result. In Proceedings of the 1999 IEEE International Conference on Robotics &Automation.1999: 837-842.
[31] Armstrong B. Control of Machines with Friction. Norwell , Kluwer Academic Publishers , 1991.
[32] Morel G, Iagnemma K. The Precise Control of Manipulators with High Joint Friction Using Base Force/ Torque Sensing. Automatica .2000, 36 : 931-941.
[33] Seungrohk O, Hassan K K. Nolinear Output-Feedback Tracking Using High-Gain Observer and Variable Structure Control. Automatica.1999, 33 (10) :1845-1856.
[34] Parra-vega,V.Chattering-free dynamical TBG adaptive sliding mode control of robot arms with dynamic friction for tracking in finite-time. Proceedings IEEE International Conference on Robotics and Automation. 2001,4:21-26.
[35] Kovacic Z, Bogdan S, Balenovic M. A Model Reference &Sensitivity Model-Based Self-Learning Fuzzy Logic Controller as a Solution for Control of Nonlinear Servo Systems. IEEE Trans. on Energy Conversion.1999, 14(4): 1479-1484.
[36] Mitsunaga,Kouichli,Matsuo. Adaptive estimation of friction forces with fuzzy basis function expansion. TAKAMI 2006SICE-ICASE International Joint Conference. 2006:4481-4486.
[37] Selmic R, Lewis F L. Neural Network Approximation of Piecewise Continuous Functions: Application to Friction Compensation. In Proceedings of the12th IEEE International Symposium on Intelligent Control. 1997: 227-232.
[38]刘媛,王卫红.基于CMAC的伺服系统控制研究.航空学报.2006,27(13):515-519.
[39]王洪瑞,吴丽燕,温淑焕.基于神经网络的鲁棒自适应控制.控制工程.2002, 9(2):66-68.
[40] Kanellakopoulos I, P Koko tovic, A S Morse Systematic design of adaptive controllers for feedback linearizable systems. IEEE Trans on AC, 1991, 36(11): 1241-1253.
[41]陈卫田,施颂椒,张钟俊.不确定非线性系统的鲁棒自适应控制.上海交通大学学报, 1998, 32 (6) : 88-93.
[42] Yazdizadeh A, Khorasani K. Adaptive Friction Compensation Based on the Lyapunov Scheme. In Proceedings of the 1996 IEEE International Conference on Control Applications.1996: 1060-1065.
[43] Feemster M, Vedagarbha P, Dawson D M, Haste D. Adaptive Control Techniques for Friction Compensation. Mechatronics.1999, 9: 125-145.
[44]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年.
[45] Liu Jinkun, Sun Fuchun.Fuzzy Global Sliding Mode Control for a Servo System with LuGre Friction Model.Proceedings of the 6th World Congress on Intelligent Control and Automation. 2006,6:1933-1936.
[46]刘强,扈宏杰,刘金琨.基于遗传算法的伺服系统摩擦参数辨识研究.系统工程与电子技术,2003,1,77-79.
[47] Han Jiapeng, Sun Yongli, Wang Yanyang. Parameter Identification of LuGre Tire Model for the Simplified Motion Dynamics of a Quarter-vehicle Model Based on Ant Colony Algorithm. Proceedings of the IEEE International Conference on Automation and Logistics. 2007, 8: 18– 21.
[48] Zhang Wenjing. Parameter Identification of LuGre Friction Model in Servo System Based on Improved Particle Swarm Optimization Algorithm.Proceedings of the 26th Chinese Control Conference.2007, 7:135-139.
[49] C. Canudas de Wit and P. Lischinsky. Adaptive friction compensation with partially known dynamic friction model. Int. J. Adapt. Control Signal Process.1997, 11:65–80.
[50] Ron H. A. Hensen, Marinus (René) J. G. van de Molengraft, and Maarten Steinbuch.Frequency Domain Identification of Dynamic Friction Model Parameters.IEEE Transactions on Control systems Technology. 2002,10(2):191-196.
[51]姜波,汪秉文.基于遗传算法的非线性系统模型参数估计.控制理论与应用,2000,2(17):150-152.
[52]雷英杰,张善文.MATLAB遗传算法工具箱及应用.西安:西安电子科技大学出版社, 2005.
[2]刘强,尔联洁,刘金琨.摩擦非线性环节的特性,建模与控制补偿综述.系统工程与电子技术.2002,24(11):45-52.
[3] B.A rmatrong-Helouvry,P .Dupont,C .Canudas de Wit.A Survey of Analysis Tools and Compensation Methods for the Control of Machines with Friction.Automatic.1994,30(7): 1083-1138.
[4]陈兴林,张福恩.仿真转台的低速性能研究.宇航学报.1995, 14 (4):65-69.
[5] P.E .Dupont,S .Kasturi Prakash.Experimental investigation of friction Dynamics associated with normal load.A SME.15th Biennial Conference on Mechanical Vibration and Noise.Vibration of Nonlinear Random and Time-Varying Systems.1995:1109-1115.
[6] B. Armstrong. Stick-slip and Control in low-speed Motion. IEEE Transactions on Automatic Control.1993, 38(10):1483-1496.
[7] P. E. Dupont, E. P. Dunlap. Friction Modeling and PD Compensation at very Low Velocities. Journal of Dynamic System.Measurement and Control. 1998, 117(1):8-14.
[8] C.Canudas de Wit, P. Noel, A. Aubin, B. Brogliato. Adaptive Friction Compensation in Robot Manipulators: Low velocities. International Journal of Robotics Research.1991, 10 (3):189-199.
[9] N. E. Leonard, P .S. Krishnaprasad. Adaptive Friction Compensation for Bi-Directional Low Velocity Position Tracking. 31st Conference on Decision and Control.1992:267-273.
[10] Dahl P. A Solid Friction Model. Aerospace Corp. .1968.
[11] R.S.H.Richardson, H.Nolle. Surface Friction under Time-Dependent Loads. Wear.1976, 37(1):87-101.
[12] D .Karnopp.Computer simulation of stick-slip frictionin mechanical dynamic systems.ASME J.Dyn. Sys .Meas Contr.1985, 107(1):100-103.
[13] Bliman P A, Sorine M. Easy-to-Use Realistic Dry Friction Models for Automatic Control. In Proceedings of 3th European Control Conference.1995: 3788-3794.
[14] Canudas De Wit C. A New Model for Control of Systems with Friction. IEEETran. on Automatic Control .1995 , 40(3) : 419-425.
[15] D. A. Haessing and B. Friedland. On the Modeling and Simulation of Friction. Trans. ASME: J.of dynamic Systems, Measurement, and Control.1991, 113(3): 354-362.
[16] Friedland B, Park YJ. On Adaptive Friction Compensation. IEEE Trans on Automatic Control.1992, 37 (10): 1609-1612.
[17] Phillips S M, Ballou K R, Friction Modeling and Compensation for an Industrial Robot. Journal of Robotic Systems.1993, 10 (7): 947-971.
[18] Yang Y P, Chu J S. Adaptive Velocity Control of DC Motors with Coulomb Friction Identification. ASME Journal of Dynamic Systems, Measurement and Control.1993, 115: 95-102.
[19] Canudas De Wit C. Robust Control for Servo-Mechanisms under Inexact Friction Compensation. Automatica.1993, 29 (30): 757-761.
[20] Deur, Josko.Asgari, Jahan.Hrovat, Davor. Modeling of an automotive planetary gear set based on Karnopp model for clutch friction. Proceedings of the ASME Dynamic Systems and Control Division. 2003, 2: 903-910.
[21] Cheok KC, Hu H, Loh N K. Modeling and Identification of a Class of Servomechanism Systems with Stick-Slip Friction. ASME Journal of Dynamic Systems, Measurement, and Control .1988, 110 : 324-328.
[22] Walrath C D. Adaptive Bearing Friction Compensation Based on Recent Knowledge of Dynamic Friction. Automatica.1984, 20(6): 717-727.
[23] Ashwani K. Padthe, JinHyoung Oh, Dennis S. Bernstein. On the LuGre Model and Friction Induced Hysteresis. Proceedings of the 2006 American Control Conference. 2006: 3247-3252.
[24] Emmanuel C. Dean-Leon, Vicente Parra-Vega, Arturo Espinosa-Romero. Visual Servoing for Constrained Planar Robots Subject to Complex Friction. IEEE Transactions on Mechatronics.2006, 11(4): 389-400.
[25] Basilio Bona, Marina Indri, Nicola Smaldone. Rapid Prototyping of a Model-Based Control with Friction Compensation for a Direct-Drive Robot. IEEE/ASME Transactions on Mechatronics. 2006, 11(5): 576-584.
[26] J. Lin, C.H. Chen. A Novel Fuzzy Friction Compensation Approach for Tracking of a Linear Motion Stage. Proceedings of the 2006 American ControlConference. 2006: 3188-3198.
[27] Yaolong Tan, Jie Chang, Hualin Tan. Adaptive Backstepping Control and Friction Compensation for AC Servo with Inertia and Load Uncertainties. IEEETransactions on Industrial Electronics.2003, 50(5): 944-952.
[28] Nitin Patel, Christopher Edwards, Sarah K Spurgeon. A Sliding Mode Observer for Tyre Friction Estimation during Braking. Proceedings of the 2006 American Control Conference. 2006: 5867-5872.
[29] Andres Guesalaga. Modelling End-of-roll Dynamics in Positioning Servos. Control Engineering Practice.2004, 12(2): 217-224.
[30] Armstrong B, Neevel D , Kusik T. New Result in NPID Control: Tracking, Integral Control, Friction Compensation and Experimental Result. In Proceedings of the 1999 IEEE International Conference on Robotics &Automation.1999: 837-842.
[31] Armstrong B. Control of Machines with Friction. Norwell , Kluwer Academic Publishers , 1991.
[32] Morel G, Iagnemma K. The Precise Control of Manipulators with High Joint Friction Using Base Force/ Torque Sensing. Automatica .2000, 36 : 931-941.
[33] Seungrohk O, Hassan K K. Nolinear Output-Feedback Tracking Using High-Gain Observer and Variable Structure Control. Automatica.1999, 33 (10) :1845-1856.
[34] Parra-vega,V.Chattering-free dynamical TBG adaptive sliding mode control of robot arms with dynamic friction for tracking in finite-time. Proceedings IEEE International Conference on Robotics and Automation. 2001,4:21-26.
[35] Kovacic Z, Bogdan S, Balenovic M. A Model Reference &Sensitivity Model-Based Self-Learning Fuzzy Logic Controller as a Solution for Control of Nonlinear Servo Systems. IEEE Trans. on Energy Conversion.1999, 14(4): 1479-1484.
[36] Mitsunaga,Kouichli,Matsuo. Adaptive estimation of friction forces with fuzzy basis function expansion. TAKAMI 2006SICE-ICASE International Joint Conference. 2006:4481-4486.
[37] Selmic R, Lewis F L. Neural Network Approximation of Piecewise Continuous Functions: Application to Friction Compensation. In Proceedings of the12th IEEE International Symposium on Intelligent Control. 1997: 227-232.
[38]刘媛,王卫红.基于CMAC的伺服系统控制研究.航空学报.2006,27(13):515-519.
[39]王洪瑞,吴丽燕,温淑焕.基于神经网络的鲁棒自适应控制.控制工程.2002, 9(2):66-68.
[40] Kanellakopoulos I, P Koko tovic, A S Morse Systematic design of adaptive controllers for feedback linearizable systems. IEEE Trans on AC, 1991, 36(11): 1241-1253.
[41]陈卫田,施颂椒,张钟俊.不确定非线性系统的鲁棒自适应控制.上海交通大学学报, 1998, 32 (6) : 88-93.
[42] Yazdizadeh A, Khorasani K. Adaptive Friction Compensation Based on the Lyapunov Scheme. In Proceedings of the 1996 IEEE International Conference on Control Applications.1996: 1060-1065.
[43] Feemster M, Vedagarbha P, Dawson D M, Haste D. Adaptive Control Techniques for Friction Compensation. Mechatronics.1999, 9: 125-145.
[44]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年.
[45] Liu Jinkun, Sun Fuchun.Fuzzy Global Sliding Mode Control for a Servo System with LuGre Friction Model.Proceedings of the 6th World Congress on Intelligent Control and Automation. 2006,6:1933-1936.
[46]刘强,扈宏杰,刘金琨.基于遗传算法的伺服系统摩擦参数辨识研究.系统工程与电子技术,2003,1,77-79.
[47] Han Jiapeng, Sun Yongli, Wang Yanyang. Parameter Identification of LuGre Tire Model for the Simplified Motion Dynamics of a Quarter-vehicle Model Based on Ant Colony Algorithm. Proceedings of the IEEE International Conference on Automation and Logistics. 2007, 8: 18– 21.
[48] Zhang Wenjing. Parameter Identification of LuGre Friction Model in Servo System Based on Improved Particle Swarm Optimization Algorithm.Proceedings of the 26th Chinese Control Conference.2007, 7:135-139.
[49] C. Canudas de Wit and P. Lischinsky. Adaptive friction compensation with partially known dynamic friction model. Int. J. Adapt. Control Signal Process.1997, 11:65–80.
[50] Ron H. A. Hensen, Marinus (René) J. G. van de Molengraft, and Maarten Steinbuch.Frequency Domain Identification of Dynamic Friction Model Parameters.IEEE Transactions on Control systems Technology. 2002,10(2):191-196.
[51]姜波,汪秉文.基于遗传算法的非线性系统模型参数估计.控制理论与应用,2000,2(17):150-152.
[52]雷英杰,张善文.MATLAB遗传算法工具箱及应用.西安:西安电子科技大学出版社, 2005.