柔性臂的动力学及其轨迹控制
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摘要
随着科技的发展,轻质和柔性构件在工程中的应用越来越多,另外机构的运行速度加快,运行精度的要求越来越高。如何消除因为柔性而产生的弹性振动成为一个急需解决的问题。本文基于此背景研究柔性臂的动力学及其轨迹控制问题。
首先,采用虚拟钢性臂假定和模态截断方法,运用Lagrange方程,建立了平面双连杆柔性臂的动力学模型和奇异摄动模型并对模型进行分析,找出引起振动的主要因素。其次,针对动力学模型的非线性特性,深入研究了柔性臂的非线性鲁棒控制方法,设计了模糊PD控制器,该控制器由PD控制和模糊控制构成,避免了单纯线性PD控制鲁棒性不强的问题,控制器结构简单、容易实现,对不同期望轨迹的跟踪上具有很好的鲁棒性;针对奇异摄动模型设计了自适应滑模PD控制器,该方法的特点是对系统中各个等效的摄动参数分别进行自适应估计和补偿,因而控制算法简单,易于工程实现,解决了传统PID控制初始力矩过大的问题,并对柔性臂结构参数的变化有一定的自适应能力。最后在对算法进行理论推导的基础上,应用Matlab/simulink,对各个算法和系统进行了仿真,检验了算法和控制方案的可行性。
With the development of technology, the light and flexible structure is widely used in the aerospace and aviation with the requirements of faster and more accurate, how to resolve the vibration problem of works in aether is a very important topic. The dynamics and trajectory control of the flexible manipulators is studied in this thesis.
Firstly, the dynamics model and singular perturbation model is examined by means of Lagrange equation, assumed rigid arms and the finite modal exapansion, and then finding out the main facts which cause the vibration. Secondly, based on the studying of the nonlinear robust control methods of the flexible manipulators, a fuzzy-PD controller and an adaptive sliding PD controller are designed which has good robust performance both on the torque control and adaption of the parameters change when the trajectory changed. The fuzzy-PD controller avoids the signal PD controller's ill-robust and it is a simple, easy to realize. The adaptive sliding PD controller can estimate and compensate the perturbed parameters and reduce the peak levels of servo initial output of the PD control. Lastly based on the Matlab/Simulink, the simulation models of the system are developed, and the simulation results shown that the above scheme is feasible.
首先,采用虚拟钢性臂假定和模态截断方法,运用Lagrange方程,建立了平面双连杆柔性臂的动力学模型和奇异摄动模型并对模型进行分析,找出引起振动的主要因素。其次,针对动力学模型的非线性特性,深入研究了柔性臂的非线性鲁棒控制方法,设计了模糊PD控制器,该控制器由PD控制和模糊控制构成,避免了单纯线性PD控制鲁棒性不强的问题,控制器结构简单、容易实现,对不同期望轨迹的跟踪上具有很好的鲁棒性;针对奇异摄动模型设计了自适应滑模PD控制器,该方法的特点是对系统中各个等效的摄动参数分别进行自适应估计和补偿,因而控制算法简单,易于工程实现,解决了传统PID控制初始力矩过大的问题,并对柔性臂结构参数的变化有一定的自适应能力。最后在对算法进行理论推导的基础上,应用Matlab/simulink,对各个算法和系统进行了仿真,检验了算法和控制方案的可行性。
With the development of technology, the light and flexible structure is widely used in the aerospace and aviation with the requirements of faster and more accurate, how to resolve the vibration problem of works in aether is a very important topic. The dynamics and trajectory control of the flexible manipulators is studied in this thesis.
Firstly, the dynamics model and singular perturbation model is examined by means of Lagrange equation, assumed rigid arms and the finite modal exapansion, and then finding out the main facts which cause the vibration. Secondly, based on the studying of the nonlinear robust control methods of the flexible manipulators, a fuzzy-PD controller and an adaptive sliding PD controller are designed which has good robust performance both on the torque control and adaption of the parameters change when the trajectory changed. The fuzzy-PD controller avoids the signal PD controller's ill-robust and it is a simple, easy to realize. The adaptive sliding PD controller can estimate and compensate the perturbed parameters and reduce the peak levels of servo initial output of the PD control. Lastly based on the Matlab/Simulink, the simulation models of the system are developed, and the simulation results shown that the above scheme is feasible.
引文
[1]Book W J,Maizza-Neto,Whitney D E.Feedback Control of Two Beam,Two Joint Systems with Distributed Flexibility.ASME J.Dynamic Systems,Measurement and Control,1975,97(4):424-431.
[2]Yoshiyuki Sakawa and Zheng Hua Luo.Modeling and Control of Coupled Bending and Torsional Vibration of Flexible Beams.IEEE Transactions on Automatic Control,1989.9,34(9):970-977.
[3]Fumitoshi Matsuno and Kazutaka Murate.Passivity and PDS Control of Flexible Mechanical Systems on the Basic of Distributed Parameter System,1999,5:51-56.
[4]Fumitoshi Matsuno,Toshio Asano and Yoshiyuki Sakawa.Modeling and Quasi-static Hybrid Position/Force Control of Constrained Planar Two-link Flexible Manipulato -rs.IEEE Transactions on Robotics and Automation,1994.6,10(3):287-297.
[5]王彬,冯冠民,张京军,空间柔性机械臂的真-伪混合坐标形式的运动方程,机器人,1993,15(4):19.
[6]Usoro.P.B.,Nadira.R.,Mihil.S.S.A Finite Element/Lagrange Approach to Modeling Lightweight Flexible Manipulator,Journal of Dynamic Systems.Measurement and Control,1986.9,108:198-205.
[7]Bruno Siciliano.elosed-Loop Inverse Kinematics Algorithm for Constrained Flexible Manipulators Under Gravity.Journal of Robotic System,1999,16(6):353-362.
[8]赵平,薛克宗,柔性多体动力学的建模与计算,华北水利水电学院学报,1994.3,1:52-61.
[9]Lucibello P.Output Tracking for a Nonlinear Flexible Arm.ASME.Journal of Dynamic Systems,Measurement and Control,1993,115:75-85.
[10]Xia,Jack Zhijie,Menq,Chia-Hsiang.Real Time Estimation of Elastic Deformation for End-point Tracking Control of Flexible Two-link Manipulators,Journal of Dynamic Systems,Measurement and Control,1993,115(3):385-393.
[11]洪在地,负超,陈力,柔性臂漂浮基空间机器人建模与轨迹跟踪控制,机器人,2007.1,29(1):92-96.
[12]张承龙,王从庆,空间柔性双臂机器人的动力学建模及控制,南京理工大学学报,2005.10,29(增刊):70-72.
[13]曾克俭,李光,液压柔性机械臂奇异摄动法控制,中国机械工程,2006.6,17(11):1128-1131.
[14]Song Z S,Yi J Q,Zhao D B and Li X C.A Computed Torque Controller for Uncertain Robotic Manipulator System:Fuzzy Approach[J].Fuzzy Sets and Systems,2005,154:208-226.
[15]Bai RRobust Neural-network Compensating Control for Robot Manipulator Based on Computed Torque Control[J].Control Theory and Applications,2001,18(6):897-901.
[16]Fumitoshi Matsuno,and Takashi Ohoo,Distributed Parameter Control of a Large Spa -ce Structure with Lumped and Distributed Flexibility,Proceedings of the 36th Conferen -ce on Decision&Control,1997,269-274.
[17]Kino Masaru,Goden Tatsuhito,Reaction Torque Feedback Based Vibration Control in Multi-degrees of Freedom Motion System.IECON Proceedings,1998.3,1807-1811.
[18]Figen Ozen,An Optimal Switched Compensation Controller for Flexible-link Man -ipulators,Proceedings of the American Control Conference Philadelphia,Pennsylvan -ia,1998.6,1804-1809.
[19]范猛,李丹,刘克平,基于奇异摄动法的受约束双连杆柔性机械臂组合控制,吉林工学院学报,2002.12,23(4):16-18.
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[22]李元春,唐保健等,双连杆柔性臂轨迹跟踪的鲁棒控制,自动化学报,1999,25:330-336.
[23]Leu Y G,Wang W Y and Lee T T.Robust Adaptive Fuzzy-neural Controllers for Unc -ertain Nonlinear Systems[J].IEEE Transactions on Robotics and Automation,1999,5(4):805-817.
[24]Gao Y,Er M J,Leithead W E and Leith D J.On-line Adaptive Aontrol of Robot Manipulators Using Dynamic Fuzzy Neural Networks[C].Proceedings of the American Control Conference,2001,4828-4833.
[25]王文琰,王晓兰,柔性机械臂运动控制策略的研究,电气传动自动化,2006,28(5):6-9.
[26]孙富春,孙增圻,柔性连杆机器人的多速率神经网络混和控制器设计,控制与决策,1996,(增刊)425-429.
[27]黄季妮,黄金泉,基于奇异摄动与神经网络的柔性臂控制,南京航空航天大学学报,2003.8,35(4):420-423.
[28]Talebi.H.A,Patel.R.V,Asmer.H.Neural Network Based Dynamic Modeling of Flexib -le-link Manipulators with Application to the SSRMS.Journal of Robotic System,2000,17(7):385-401.
[29]张雪莲,潘铁强,唐可洪,马晓丽,柔性机械臂T_S模糊模型的辨识及其分析,机电工程,2006.11,23(11):36-38.
[30]J.X.Lee,G.Vukovich.Fuzzy Logic Control of Flexible Link Manipulators-controller Design and Experimental Demonstrations,Proceedings of the IEEE International Confer -ence on Systems,Man and Cybernetics 2,1998,2002-2007.
[31]樊晓平,徐建闽,毛宗源,受限柔性机器人基于遗传算法的自适应模糊控制,自动化学报,2000.1,26(1):61-67.
[32]樊晓平,徐建闽,毛宗源,周其节,平面双连杆受限柔性机器人臂的自适应模糊力/位置控制,机器人,1999.11,21(6):455-465.
[33]李大艽,诸静,田彦涛.一类弹性机械臂的模糊控制,机器人,2000.1,22(1):55-59
[34]Nanayakkara T,Watanabe K,Kiguchi K and Izumi K.Controlling Multi-link Manip -ulators by Fuzzy Selection of Dynamic Models[C].Industrial Electronics Society,26th Annual Conference of the IEEE,2000,1:638-643.
[35]Kim Y T.Independent Joint Adaptive Fuzzy Control of Robot Manipulator[C].Proc -eedings of the 5th Biannual,World Automation Congress,2002,14:645-652.
[36]J.Lin and F.L.Lewis,Two-link Scale Fuzzy Logic Controller of Flexible Link Robot Arm,Fuzzy Set and Systems,2003,139:125-149.
[37]邱志成,柔性机械臂的变结构振动控制研究,动力学与控制学报,2007,3,5(1):62-67.
[38]张袅娜,冯勇,孙黎霞,双臂柔性机械手的终端滑模控制,控制与决策,2004.10,19(10):1142-1146.
[39]刘才山,王建明,刘又午,柔性机械臂运动轨迹变结构双模控制,非线性动力学报,1997,4(1):19.
[40]Ingole.A.R.Bandyopadhyay B,Variable Structure Control Application for Flexible Manipulators.Proceedings of the IEEE Conference on Control Applications.1994,2:1311-1316.
[41]Sundareshan M.K,Askew C,Neural Network-assisted Variable Structure Control Scheme for Control of a Flexible Manipulator Arm,J.of Automatica,1997,33:1699-1710.
[42]Elangovan S and Woo P Y.Adaptive Fuzzy Sliding Control for a Three-link Passive Robotic Manipulator[C].Proceedings of the 2004 American Control Conference,2004,6:5274-5279.
[43]Purewar S,Kar I N,Jha A N.Nero sliding mode control of robotic manipulators[C].Proceedings of the 2004 IEEE Conference on Robotics,Automation and Mechatronics.2004:595-600.
[44]樊晓平,徐建闽,毛宗源,周其节,受限柔性机器人臂的鲁棒变结构混合位置/力控制,自动化学报,2000,26(2):176-183.
[45]李善姬,金在权,刘龙哲,双连杆柔性机械臂的轨迹控制,延边大学学报,2000,26(1):44-47.
[46]Yim W,Singh S N.Predictive End-point Trajectory Control of Elastic Manipulators -[J],Journal of Robotic System,1996,13(9):561-569.
[47]ClarkeDW,MohtadiC,TuffsPS,Generalized Predictive Control:Partl and Part2,Auto -matica,1987,23(1):137-160.
[48]孙奇志,孙增圻,孙富春,基于奇异摄动的柔性机械手预测控制,机械科学与技术,2001,20(2):172-173.
[49]Yoshiyuki Sakawa,Fumitoshi Matsuno and Shigenobu Fukushima,Modeling and Feedback Control of A Flexible Arm.Journal of Robotic Systems,1985,2(4):453-472.
[50]王从庆,张承龙,自由浮动柔性双臂空间机器人系统动力学建模与抑振控制,机械科学与技术,2007.2,26(2):192-196.
[51]蔡国平,洪嘉振,柔性机械臂的位置主动控制,机械科学与技术,2005,24(10):1178-1180.
[52]王敏,杜克林,黄心汉,机器人滑模轨迹跟踪控制研究[J].机器人,2001,23(3):217-221.
[53]冯勇,鲍晟,余星火,用于刚性机械手的无抖振快速终端滑模控制[J].控制与策,2002,17(3):381-384.
[54]晁红敏,胡跃明,吴忻生.高阶滑模控制在非完整移动机器人鲁棒输出跟踪中的应用[J].控制理论与应用,2002,19(2):253-257.
[2]Yoshiyuki Sakawa and Zheng Hua Luo.Modeling and Control of Coupled Bending and Torsional Vibration of Flexible Beams.IEEE Transactions on Automatic Control,1989.9,34(9):970-977.
[3]Fumitoshi Matsuno and Kazutaka Murate.Passivity and PDS Control of Flexible Mechanical Systems on the Basic of Distributed Parameter System,1999,5:51-56.
[4]Fumitoshi Matsuno,Toshio Asano and Yoshiyuki Sakawa.Modeling and Quasi-static Hybrid Position/Force Control of Constrained Planar Two-link Flexible Manipulato -rs.IEEE Transactions on Robotics and Automation,1994.6,10(3):287-297.
[5]王彬,冯冠民,张京军,空间柔性机械臂的真-伪混合坐标形式的运动方程,机器人,1993,15(4):19.
[6]Usoro.P.B.,Nadira.R.,Mihil.S.S.A Finite Element/Lagrange Approach to Modeling Lightweight Flexible Manipulator,Journal of Dynamic Systems.Measurement and Control,1986.9,108:198-205.
[7]Bruno Siciliano.elosed-Loop Inverse Kinematics Algorithm for Constrained Flexible Manipulators Under Gravity.Journal of Robotic System,1999,16(6):353-362.
[8]赵平,薛克宗,柔性多体动力学的建模与计算,华北水利水电学院学报,1994.3,1:52-61.
[9]Lucibello P.Output Tracking for a Nonlinear Flexible Arm.ASME.Journal of Dynamic Systems,Measurement and Control,1993,115:75-85.
[10]Xia,Jack Zhijie,Menq,Chia-Hsiang.Real Time Estimation of Elastic Deformation for End-point Tracking Control of Flexible Two-link Manipulators,Journal of Dynamic Systems,Measurement and Control,1993,115(3):385-393.
[11]洪在地,负超,陈力,柔性臂漂浮基空间机器人建模与轨迹跟踪控制,机器人,2007.1,29(1):92-96.
[12]张承龙,王从庆,空间柔性双臂机器人的动力学建模及控制,南京理工大学学报,2005.10,29(增刊):70-72.
[13]曾克俭,李光,液压柔性机械臂奇异摄动法控制,中国机械工程,2006.6,17(11):1128-1131.
[14]Song Z S,Yi J Q,Zhao D B and Li X C.A Computed Torque Controller for Uncertain Robotic Manipulator System:Fuzzy Approach[J].Fuzzy Sets and Systems,2005,154:208-226.
[15]Bai RRobust Neural-network Compensating Control for Robot Manipulator Based on Computed Torque Control[J].Control Theory and Applications,2001,18(6):897-901.
[16]Fumitoshi Matsuno,and Takashi Ohoo,Distributed Parameter Control of a Large Spa -ce Structure with Lumped and Distributed Flexibility,Proceedings of the 36th Conferen -ce on Decision&Control,1997,269-274.
[17]Kino Masaru,Goden Tatsuhito,Reaction Torque Feedback Based Vibration Control in Multi-degrees of Freedom Motion System.IECON Proceedings,1998.3,1807-1811.
[18]Figen Ozen,An Optimal Switched Compensation Controller for Flexible-link Man -ipulators,Proceedings of the American Control Conference Philadelphia,Pennsylvan -ia,1998.6,1804-1809.
[19]范猛,李丹,刘克平,基于奇异摄动法的受约束双连杆柔性机械臂组合控制,吉林工学院学报,2002.12,23(4):16-18.
[20]张友安,糜玉林,吕凤琳,孙富春,双连杆柔性臂自适应模糊滑模控制,吉林 大学学报(工学版),2005.9,35(5):520-525.
[21]申铁龙,∞H控制理论及应用,北京:清华大学出版社.
[22]李元春,唐保健等,双连杆柔性臂轨迹跟踪的鲁棒控制,自动化学报,1999,25:330-336.
[23]Leu Y G,Wang W Y and Lee T T.Robust Adaptive Fuzzy-neural Controllers for Unc -ertain Nonlinear Systems[J].IEEE Transactions on Robotics and Automation,1999,5(4):805-817.
[24]Gao Y,Er M J,Leithead W E and Leith D J.On-line Adaptive Aontrol of Robot Manipulators Using Dynamic Fuzzy Neural Networks[C].Proceedings of the American Control Conference,2001,4828-4833.
[25]王文琰,王晓兰,柔性机械臂运动控制策略的研究,电气传动自动化,2006,28(5):6-9.
[26]孙富春,孙增圻,柔性连杆机器人的多速率神经网络混和控制器设计,控制与决策,1996,(增刊)425-429.
[27]黄季妮,黄金泉,基于奇异摄动与神经网络的柔性臂控制,南京航空航天大学学报,2003.8,35(4):420-423.
[28]Talebi.H.A,Patel.R.V,Asmer.H.Neural Network Based Dynamic Modeling of Flexib -le-link Manipulators with Application to the SSRMS.Journal of Robotic System,2000,17(7):385-401.
[29]张雪莲,潘铁强,唐可洪,马晓丽,柔性机械臂T_S模糊模型的辨识及其分析,机电工程,2006.11,23(11):36-38.
[30]J.X.Lee,G.Vukovich.Fuzzy Logic Control of Flexible Link Manipulators-controller Design and Experimental Demonstrations,Proceedings of the IEEE International Confer -ence on Systems,Man and Cybernetics 2,1998,2002-2007.
[31]樊晓平,徐建闽,毛宗源,受限柔性机器人基于遗传算法的自适应模糊控制,自动化学报,2000.1,26(1):61-67.
[32]樊晓平,徐建闽,毛宗源,周其节,平面双连杆受限柔性机器人臂的自适应模糊力/位置控制,机器人,1999.11,21(6):455-465.
[33]李大艽,诸静,田彦涛.一类弹性机械臂的模糊控制,机器人,2000.1,22(1):55-59
[34]Nanayakkara T,Watanabe K,Kiguchi K and Izumi K.Controlling Multi-link Manip -ulators by Fuzzy Selection of Dynamic Models[C].Industrial Electronics Society,26th Annual Conference of the IEEE,2000,1:638-643.
[35]Kim Y T.Independent Joint Adaptive Fuzzy Control of Robot Manipulator[C].Proc -eedings of the 5th Biannual,World Automation Congress,2002,14:645-652.
[36]J.Lin and F.L.Lewis,Two-link Scale Fuzzy Logic Controller of Flexible Link Robot Arm,Fuzzy Set and Systems,2003,139:125-149.
[37]邱志成,柔性机械臂的变结构振动控制研究,动力学与控制学报,2007,3,5(1):62-67.
[38]张袅娜,冯勇,孙黎霞,双臂柔性机械手的终端滑模控制,控制与决策,2004.10,19(10):1142-1146.
[39]刘才山,王建明,刘又午,柔性机械臂运动轨迹变结构双模控制,非线性动力学报,1997,4(1):19.
[40]Ingole.A.R.Bandyopadhyay B,Variable Structure Control Application for Flexible Manipulators.Proceedings of the IEEE Conference on Control Applications.1994,2:1311-1316.
[41]Sundareshan M.K,Askew C,Neural Network-assisted Variable Structure Control Scheme for Control of a Flexible Manipulator Arm,J.of Automatica,1997,33:1699-1710.
[42]Elangovan S and Woo P Y.Adaptive Fuzzy Sliding Control for a Three-link Passive Robotic Manipulator[C].Proceedings of the 2004 American Control Conference,2004,6:5274-5279.
[43]Purewar S,Kar I N,Jha A N.Nero sliding mode control of robotic manipulators[C].Proceedings of the 2004 IEEE Conference on Robotics,Automation and Mechatronics.2004:595-600.
[44]樊晓平,徐建闽,毛宗源,周其节,受限柔性机器人臂的鲁棒变结构混合位置/力控制,自动化学报,2000,26(2):176-183.
[45]李善姬,金在权,刘龙哲,双连杆柔性机械臂的轨迹控制,延边大学学报,2000,26(1):44-47.
[46]Yim W,Singh S N.Predictive End-point Trajectory Control of Elastic Manipulators -[J],Journal of Robotic System,1996,13(9):561-569.
[47]ClarkeDW,MohtadiC,TuffsPS,Generalized Predictive Control:Partl and Part2,Auto -matica,1987,23(1):137-160.
[48]孙奇志,孙增圻,孙富春,基于奇异摄动的柔性机械手预测控制,机械科学与技术,2001,20(2):172-173.
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