基于分布参数模型机械臂操作柔性负载系统控制方法研究
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摘要
随着科技的进步，机器人技术已经在工业、军事、制造业以及医疗等领域得到了广泛应用。在航空航天、汽车造船等对精确性和安全性要求极高的工业军事领域中，经常需要利用机械臂对大型轻薄金属板或者细长柔性梁进行搬运或者加工。比如，在汽车工业中，为了将汽车上的柔性金属板装配成工件，需要设计复杂的夹具，当汽车体发生微小改变时，就要重新对夹具进行设计，而夹具的设计通常要耗费巨大的人力和物力。这就需要用机械臂代替夹具，对于形状改变时不必对硬件进行重新设计，只需修改程序中的任务目标即可。在航天领域中，需要依靠空间机器人对飞行器进行维护和更换失效的电池，并且电池板大都由柔性材料做成的，操作过程中避免不了振动，因此对机器人的控制必须考虑振动的耦合特性。此外，在其他工业领域，许多部件都具有柔性，利用机械臂完成这项工作可以使效率和安全性得到很大的提高，因此对机械臂操作柔性负载进行研究具有重要的理论意义和工程应用价值。
机械臂操作柔性负载是非线性、刚柔耦合、无穷维的复杂动力学系统。不仅包含大范围的刚性运动，又含有局部弹性变形。相比于操作刚性负载，机械臂操作柔性负载的研究成果还较少，还有很多有待解决的问题。比如机械臂在完成搬运、装配等操作任务时的位置控制问题，以及在位置控制同时还面临着振动抑制的难题；在实际操作中，系统存在的不确定因素和外部干扰，以及机械臂与柔性负载接触时彼此之间产生的作用力问题，这些都增加了系统的动力学分析和控制的复杂性。从国内外的研究现状来看，对于含有柔性结构的系统，很多学者基于其简化的集中参数模型来进行系统分析和控制器设计，然而由于模型的简化会给系统带来控制/观测溢出问题，因此对于机械臂操作柔性负载的分布参数模型的研究是十分重要和有意义的。
本文以机械臂操作柔性负载为研究对象，基于分布参数模型，不进行有限维近似，避免了由集中参数模型而导致的溢出问题。研究了机械臂操作柔性负载系统的位置控制问题、无穷维观测器设计问题、基于系统存在不确定性和外部干扰时的鲁棒控制策略问题，以及双机械臂协调操作柔性负载的力/位置控制问题。全文的主要内容和研究工作如下：
针对机械臂操作柔性负载系统，研究基于分布参数模型的位置控制方法，利用系统的总能量，由Lyapunov函数构造了静态反馈位置控制器，证明了闭环系统的主算子可以生成一个C0半群，从而由LaSalle不变集原理证明了系统在期望位置邻域内的渐近稳定性。使得系统的关节角达到期望位置的同时抑制柔性负载的振动。由于在负载上安装传感器不现实，设计了非线性无穷维观测器来估计负载的振动信息，并且在所提出观测器的基础上设计了控制器，分析了观测器的渐近稳定性。仿真结果验证了所设计控制方法的有效性。
考虑系统存在不确定性以及外部干扰时的位置控制问题。基于对柔性负载的能量分析，设计了滑模控制方法，其中滑模面是由关节角误差、角速度误差和负载的振动信息耦合组成。当系统的不确定参数上界未知时，设计了自适应滑模控制方法，估计其未知的上界。利用正实引理将动态反馈控制方法引入机械臂操作柔性负载系统中，使得系统在设计时具有更多的自由度。由半群理论以及LaSalle不变集原理，证明了系统的渐近稳定性。
针对双机械臂协调操作柔性负载系统，研究基于分布参数模型的力/位置控制方法。根据对系统的静态分析，利用Lyapunov函数提出了力/位置控制器，使得系统的关节角和力达到期望值，并抑制柔性负载的振动。考虑当系统存在参数不确定性时，设计了滑模力/位置控制方法，证明了闭环系统是Lyapunov稳定的。
最后，总结本文的工作，结合本人在分布参数系统、柔性体系统、以及机械臂操作系统的研究心得，做出对未来的展望和下一步的研究计划。
With the improvement of science and technology, robot technology has been widelyused in the fields such as industry、military affairs、manufacturing and medical scienceand service. In aerospace, automobile, shipbuilding and other fields, the accuracy andsafety requirements are very high, and the elastic sheets and flexible slightness beams arealways need to be moved and assembled. For example, in the automotive industry, weneed design the complex fixture since the sheet flexible metal must be held while robotsspot weld them together. When the auto body places a small change in space, the fixtureneed be redesigned. However, the design for fixture always spent a great number oflabour power and material resources. This will require the manipulators instead of fixtureto modify task goals of the program without redesigning the hardware for the shapechange. In space field, it requires space robot to maintain and replace the failing batteriesfor the aircraft. These panels are mostly made from flexible materials and their operationsoften bring vibration, so the robot control must consider the coupled vibrationcharacteristics. Besides, in other industry areas, many parts are made of flexible material,these operations all involve the issue of flexible payload，so efficiency and safety can begreatly improved while the manipulators are used. Thus, the study on manipulatorhandling flexible payload is of great significance in theory and practical value inengineering.
Manipulator handling a flexible payload is a nonlinear, rigid-flexible coupled andinfinite dimensional complex dynamic system，which including not only the rigid motionof large range, but also the local elastic deformation. Compared with the researchachievement about rigid payload, the research achievement about flexible payload arerelatively few, which exists many problems to be solved. When manipulator moved andassembled, the position control and the vibration suppression should be considered. Inpractice, the uncertain parameters and external disturbance of the system, and the contactforce between flexible payload and manipulator, all the above problems increase thecomplexity of the system kinetic analysis and control. From the current situation ofresearch at home and abroad for the system with flexible structure, many researches studythe system analysis and control design based on the simplified lumped parameter model,however, the simplified model may bring control/observer overflow problem. Thus, theresearch on manipulator handling a flexible payload based on distributed parameter modelis of importance and significance.
In this paper, manipulator handling a flexible payload is researched based ondistributed parameter model, and the finite dimensional approximation model is not used.So the overflow problem of the lumped parameter model is avoided. The position controlproblem and the infinite dimensional observer are researched, the robust control isresolved based on the system with uncertainties and external disturbance, and theforce/position control problem of the two manipulators handling a flexible payload isresearched. The main content and innovation are a follows.
The position control for manipulator handling a flexible payload based on distributedparameter model is researched. By using the system total energy, the static feedbackcontroller is constructed by applying the Lyapunov method, and the operator of theclosed-loop system generate aC0semigroup. The asymptotic stability in theneighbor-hood of the desired states of the closed-loop system is proved by LaSalleinvariance principle. The angle can arrived at the desired position, as well as the elasticvibration of flexible payload is suppressed. Considering that it is impractical for flexiblepayload to be equipped with sensors, this paper proposed infinite dimensional nonlinearobserver to estimate the vibration information of flexible payload, and designed theposition controller based on the observer. The asymptotic stability of the closed-loopsystem is analysis, and the effectiveness of the control strategy is supported by somesimulations.
The position control of manipulator handling a flexible payload is researched underthe parameter uncertain. Based on the energy dynamic of payload, a sliding modecontroller is proposed by designing a coupled sliding surface, and then extended to anadaptive scheme to cope with the upper bounds of the uncertainties were unknown. Thesliding surface is designed as the joint angle error and angular velocity error with thevibration information of the payload. By using the positive real lemma, the dynamicfeedback control was used in the system of manipulator handling a flexible payload, it canintroduces extra degrees of freedom in designing controllers. The asymptotic stability ofthe closed-loop system is proved by semigroup theory and LaSalle invariance principle.
The force/position control for manipulator handling a flexible payload wasresearched. Based on the analysis of static states, the force/position controller wasproposed by using Lyapunov method, the angle and the force can arrived at the desiredstate, as well as the elastic vibration of flexible payload is suppressed. Considering thesystem with uncertainties, the sliding-mode force/position controller was proposed, thesystem was proved to be Lyapunov stable.
Based on the research on distributed parameter system, flexible multi-body system and the manipulating system, the conclusion and the perspective of future research aregiven at the end of the paper.
机械臂操作柔性负载是非线性、刚柔耦合、无穷维的复杂动力学系统。不仅包含大范围的刚性运动，又含有局部弹性变形。相比于操作刚性负载，机械臂操作柔性负载的研究成果还较少，还有很多有待解决的问题。比如机械臂在完成搬运、装配等操作任务时的位置控制问题，以及在位置控制同时还面临着振动抑制的难题；在实际操作中，系统存在的不确定因素和外部干扰，以及机械臂与柔性负载接触时彼此之间产生的作用力问题，这些都增加了系统的动力学分析和控制的复杂性。从国内外的研究现状来看，对于含有柔性结构的系统，很多学者基于其简化的集中参数模型来进行系统分析和控制器设计，然而由于模型的简化会给系统带来控制/观测溢出问题，因此对于机械臂操作柔性负载的分布参数模型的研究是十分重要和有意义的。
本文以机械臂操作柔性负载为研究对象，基于分布参数模型，不进行有限维近似，避免了由集中参数模型而导致的溢出问题。研究了机械臂操作柔性负载系统的位置控制问题、无穷维观测器设计问题、基于系统存在不确定性和外部干扰时的鲁棒控制策略问题，以及双机械臂协调操作柔性负载的力/位置控制问题。全文的主要内容和研究工作如下：
针对机械臂操作柔性负载系统，研究基于分布参数模型的位置控制方法，利用系统的总能量，由Lyapunov函数构造了静态反馈位置控制器，证明了闭环系统的主算子可以生成一个C0半群，从而由LaSalle不变集原理证明了系统在期望位置邻域内的渐近稳定性。使得系统的关节角达到期望位置的同时抑制柔性负载的振动。由于在负载上安装传感器不现实，设计了非线性无穷维观测器来估计负载的振动信息，并且在所提出观测器的基础上设计了控制器，分析了观测器的渐近稳定性。仿真结果验证了所设计控制方法的有效性。
考虑系统存在不确定性以及外部干扰时的位置控制问题。基于对柔性负载的能量分析，设计了滑模控制方法，其中滑模面是由关节角误差、角速度误差和负载的振动信息耦合组成。当系统的不确定参数上界未知时，设计了自适应滑模控制方法，估计其未知的上界。利用正实引理将动态反馈控制方法引入机械臂操作柔性负载系统中，使得系统在设计时具有更多的自由度。由半群理论以及LaSalle不变集原理，证明了系统的渐近稳定性。
针对双机械臂协调操作柔性负载系统，研究基于分布参数模型的力/位置控制方法。根据对系统的静态分析，利用Lyapunov函数提出了力/位置控制器，使得系统的关节角和力达到期望值，并抑制柔性负载的振动。考虑当系统存在参数不确定性时，设计了滑模力/位置控制方法，证明了闭环系统是Lyapunov稳定的。
最后，总结本文的工作，结合本人在分布参数系统、柔性体系统、以及机械臂操作系统的研究心得，做出对未来的展望和下一步的研究计划。
With the improvement of science and technology, robot technology has been widelyused in the fields such as industry、military affairs、manufacturing and medical scienceand service. In aerospace, automobile, shipbuilding and other fields, the accuracy andsafety requirements are very high, and the elastic sheets and flexible slightness beams arealways need to be moved and assembled. For example, in the automotive industry, weneed design the complex fixture since the sheet flexible metal must be held while robotsspot weld them together. When the auto body places a small change in space, the fixtureneed be redesigned. However, the design for fixture always spent a great number oflabour power and material resources. This will require the manipulators instead of fixtureto modify task goals of the program without redesigning the hardware for the shapechange. In space field, it requires space robot to maintain and replace the failing batteriesfor the aircraft. These panels are mostly made from flexible materials and their operationsoften bring vibration, so the robot control must consider the coupled vibrationcharacteristics. Besides, in other industry areas, many parts are made of flexible material,these operations all involve the issue of flexible payload，so efficiency and safety can begreatly improved while the manipulators are used. Thus, the study on manipulatorhandling flexible payload is of great significance in theory and practical value inengineering.
Manipulator handling a flexible payload is a nonlinear, rigid-flexible coupled andinfinite dimensional complex dynamic system，which including not only the rigid motionof large range, but also the local elastic deformation. Compared with the researchachievement about rigid payload, the research achievement about flexible payload arerelatively few, which exists many problems to be solved. When manipulator moved andassembled, the position control and the vibration suppression should be considered. Inpractice, the uncertain parameters and external disturbance of the system, and the contactforce between flexible payload and manipulator, all the above problems increase thecomplexity of the system kinetic analysis and control. From the current situation ofresearch at home and abroad for the system with flexible structure, many researches studythe system analysis and control design based on the simplified lumped parameter model,however, the simplified model may bring control/observer overflow problem. Thus, theresearch on manipulator handling a flexible payload based on distributed parameter modelis of importance and significance.
In this paper, manipulator handling a flexible payload is researched based ondistributed parameter model, and the finite dimensional approximation model is not used.So the overflow problem of the lumped parameter model is avoided. The position controlproblem and the infinite dimensional observer are researched, the robust control isresolved based on the system with uncertainties and external disturbance, and theforce/position control problem of the two manipulators handling a flexible payload isresearched. The main content and innovation are a follows.
The position control for manipulator handling a flexible payload based on distributedparameter model is researched. By using the system total energy, the static feedbackcontroller is constructed by applying the Lyapunov method, and the operator of theclosed-loop system generate aC0semigroup. The asymptotic stability in theneighbor-hood of the desired states of the closed-loop system is proved by LaSalleinvariance principle. The angle can arrived at the desired position, as well as the elasticvibration of flexible payload is suppressed. Considering that it is impractical for flexiblepayload to be equipped with sensors, this paper proposed infinite dimensional nonlinearobserver to estimate the vibration information of flexible payload, and designed theposition controller based on the observer. The asymptotic stability of the closed-loopsystem is analysis, and the effectiveness of the control strategy is supported by somesimulations.
The position control of manipulator handling a flexible payload is researched underthe parameter uncertain. Based on the energy dynamic of payload, a sliding modecontroller is proposed by designing a coupled sliding surface, and then extended to anadaptive scheme to cope with the upper bounds of the uncertainties were unknown. Thesliding surface is designed as the joint angle error and angular velocity error with thevibration information of the payload. By using the positive real lemma, the dynamicfeedback control was used in the system of manipulator handling a flexible payload, it canintroduces extra degrees of freedom in designing controllers. The asymptotic stability ofthe closed-loop system is proved by semigroup theory and LaSalle invariance principle.
The force/position control for manipulator handling a flexible payload wasresearched. Based on the analysis of static states, the force/position controller wasproposed by using Lyapunov method, the angle and the force can arrived at the desiredstate, as well as the elastic vibration of flexible payload is suppressed. Considering thesystem with uncertainties, the sliding-mode force/position controller was proposed, thesystem was proved to be Lyapunov stable.
Based on the research on distributed parameter system, flexible multi-body system and the manipulating system, the conclusion and the perspective of future research aregiven at the end of the paper.
引文
[1] T Yukawa, M Uchiyama, H Inook. Handling of a Constrained Flexible Object by aRobot[C]. IEEE International Conference on Robotics and Automation,1995, v1:324-329.
[2] R Lai, F Ohkawa. Digital Control of A Manipulator Handling Flexible Objects[C].Proceedings of the5th World Congress on Intelligent Control and Automation,2004,4595-4597.
[3] J Q Wu, Z W Luo, Koji Ito. Gain Scheduled Control for Robot Manipulator'sContact Tasks on Flexible Environments[C]. International Workshop on AdvancedMotion Control,1996, v2：512-517.
[4] W K Jr, Brenan J. McCarragher. Force Fields in the Manipulation of FlexibleMaterials[C]. Proceedings of the1996IEEE International Conference on Roboticsand Automation,1996, v3,2352-2357.
[5] F Arai, L L Rong, T Fukuda. Trajectory Control of Flexible Plate Using NeuralNetwork[C].IEEE International Conference on Robotics an Automation,1993,v1,155-159.
[6] H Nakagaki, K Kit agaki, H Tsukune. Study of Insertion Task of a Flexible Beaminto a Hole[C]. IEEE International Conference on Robotics and Automation.1995,v1,330-335.
[7] C Joseph Lee, C Mavroidis. Discrete-Time LQR and H2Damping Control ofFlexible Payloads Using a Robot Manipulator with a Wrist-Mounted Force TorqueSensor[C]. ASME Int.Mechanical Engineering Congress.Exposition DynamicSystems and Control Division,2000,62(2):997-1004.
[8] F E Pacheco, A P Tzes. On-Line Fkequency Domain Information for Control of aFlexible-Link Robot with Varying Payload[J]. IEEE Transactions On AutomaticControl,1989,34(12):1300-1304.
[9] K M Yuen, G M Bone. Robotic Assembly of Flexible Sheet Metal Parts[C].IEEEInternational Conference on Robotics and Automation,1996,1511-1516.
[10] J K Mills, J G-L Ing. Robotic Fixtureless Assembly of Sheet Metal Parts UsingDynamic Finite Element Models: Modelling and Simulation[C].IEEE InternationalConference on Robotics and Automation,1995, v3,2350-2357.
[11] D Sun, Y H Liu. Modeling and Impedance Control of a Two-Manipulator SystemHandling a Flexible Beam, IEEE International Conference on Robotics andAutomation,1997, v2,1787-1792.
[12] D Sun, Y H Liu. Position and Force Tracking of a Two-Manipulator SystemManipulating a Flexible Beam[J].Journal of Robotic Systems,2001,18(4):197-212.
[13] H Bai, J T Wen. Motion Coordination Through Cooperative Payload Transport[C].American Control Conference,2009, v5,978-1-424.
[14] K Kosuge, H Yoshida. Manipulation of a Flexible Object by Dual Manipulators[C].IEEE International Conference on Robotics and Automation. New York: IEEE Press,1995,318-323.
[15]张鹏,李元春,姜日花.一种基于观测器的机械臂协调操作柔性负载的控制方法[J].吉林大学学报(工学版)，2009,39(5):1240-1244.
[16] Z G Tang, Y C Li. Modeling and Control of Two Manipulators Handling a FlexiblePayload Based on Singular Perturbation[C].International Conference on AdvancedComputer Control,2010,558-562.
[17] J L Lions. Optimal Control of Systems Governed by Partial Differential Equations
[M], Sringer-Verlag,Berlin,1971.
[18]王康宁,关肇直.弹性振动的镇定问题[J].中国科学,1976，2134-148.
[19]宋健,于景元,胡顺菊,肖永震.具有结构阻尼的自由弹性梁的解的渐近性质[J].中国科学,1984，v8:759-765.
[20]于景元，朱广田.细长飞行器飞行姿态的渐近性质[J].中国科学,1984,v5：474-482.
[21]李胜家,朱广田.具结构阻尼细长体飞行器系统相应发展方程主算子生成的半群性质[J].系统科学与数学，1988，8(3)：219-225.
[22]侯学章.具结构阻尼非线性细长体飞行器系统的能量指数衰减[J].东北师大学报自然科学版,1994,v3,6-12.
[23]宋健,于景元,王彦祖,胡顺菊,赵忠信,刘嘉荃,冯德兴,朱广田.人口算子的谱特性与人口半群的渐近性质[J].数学物理学报,1982，l2(2):138-144.
[24]宋健,于景元,刘长凯,张连平,朱广田.人口发展算子的谱性质及人口系统的能控性[J].中国种学A辑,1986,2,114-123.
[25] S Yoshiyuki，Z H Luo. Modeling and Control of Coupled Bending and TorsionalVibrations of Flexible Beams[J]. IEEE Transaxrions on Automic Control,1989,34(9),970-977.
[26] X P Zhang, W W Xu, S S Nair. PDE Modeling and Control of a Flexible Two-LinkManipulator[J]. IEEE Transactions On control Systems Technology,2005,13(2):301-312.
[27] M Dogan, O Morgol. Nonlinear PDE Control of Two-Link Flexible Arm withNonuniform Cross Section[C]. Proceedings of the2006American ControlConference,2006,401-405.
[28] M Dogan, O Morgül. On the Control of Two-link Flexible Robot Arm withNonuniform Cross Section, Journal of Vibration and Control[J].201016(5):619-646.
[29] M Kimata, Y Morita, H Ukai, H Kando. PDS Control of Macro-Micro Arm[C].Proceedings of the2004American Control Conference,2006,123-128.
[30] F Matsuno, T Ohno, V. Orlov Yuri. Proportional Derivative and Strain (PDS)Boundary feedback Control of a Flexible Space Structure with a Closed-loop ChainMechanism[J]. Automatica,2002,38(7):1201-1211.
[31] F Matsuno, A Hayashi. PDS Cooperative Control of Two One-link Flexible Arms[C].Proceedings of the IEEE International Conference on Robotics and Automation,2000,1490-1495.
[32] F Matsuno, K Murata. Passivity and PDS Control of Flexible Mechanical Systemson the Basis of Distributed Parameter System[C]. IEEE International Conference onstems, Man, and Cybernetics,1999, v5,51-56.
[33] R F Fung, H C Chang. Dynamic Modelling of A Non-linearly Constrained flexibleManipulator with a Tip Mass by Hamiltion’s Principle[J]. Journal of Sound andVibration,1998,216(5):751-769.
[34] F Matsuno, T Ohno. Distributed Parameter Control of a Large Space Structure withLumped and Distributed Flexibility[C]. Proceedings of the36th Conference onDecision and Control,1997,269-274.
[35] T Endo, F Matsuno. Dynamics Based Force Control of One-link Flexible Arm[C].SICE Annual Conference in Sapporo,2004,2736-2741.
[36] K Krishnamurthy, L Yang. Dynamic Modeling and Simulation of Two CooperatingStructurally-Flexible Robotic Manipulators[J]. Robotica,199513(4):375-384.
[37] F Matsuno, M Hatayama. Robust Cooperative Control of Two Two-Link FlexibleManipulators on the Basis of Quasi-Static Equations[J]. The International Journal ofRobotics Research,1999,18(4):414-428.
[38] F Matsuno, M Hatayama. Quasi-Static Cooperative Control of Two Two-LinkFlexible Manipulators[C]. IEEE lnternatlonal Conference on Robotlcs andAutomatlon,1995,615-620.
[39] F Matsuno, K Yamamoto. Dynamic Hybrid Position/Force Control of a Two Degreeof Freedom Flexible Manipulator[J]. Journal of Robotic Systems,1994,11(5):355-366.
[40]李冬宁,赵雁,沈铖武,刘畅.一种双连杆柔性臂动力学模型的研究[J].测控技术,2009,28(12):40-43.
[41] E H K Fung, Z X Shi. Multivariable Feedforward-feedback Motion Control of aConstrained Two-link Manipulator with a Flexible Forearm[C]. Proceedings of the37th IEEE Conference on Decision and Control,1998,949-954.
[42] F Matsuno, S Kasai. Modeling and Robust Force Control of Constrained One-LinkFlexible Arms[J]. Journal of Robotic Systems,1998,15(8):447-464.
[43]李元春,刘姝阳,唐志国.基于分布参数机械臂协调操作柔性负载双时标控制,控制与决策[J].2012，27(5):686-690.
[44] E Balasubramanian, S Abilash, S Riyazahammed. Collaborative ManipulatorsHandling Flexible Object in Joint Space Modeling, Control and Analysis[J].International Journal of Mechanical Production Engineering Research andDevelopment,2013,3(1):163-180.
[45] A Lotfazar, M Eghtesad, A Najafi. Vibration Control and Trajectory Tracking forGeneral In-Plane Motion of an Euler–Bernoulli Beam Via Two-Time Scale andBoundary Control Methods[J]. Journal of Vibration and Acoustics,2008,130(5):1-11.
[46] H A Malki, D Misit, D Feigenspan, G Chen. Fuzzy PID Control of a Flexible-JointRobot Arm with Uncertainties from Time-varying Loads[J].IEEE Transactions oncontrol Systems Technology,1997,5(3):371-378.
[47] R Kelly, R Ortega, A Ailton. Global Regulation of Flexible Joint Robots UsingApproximate Differentiation[J].IEEE Transactions on Automatic Control,1994,36(6):1222-1224.
[48] S S Ge, T H Lee, G Zhu. Improving Joint PD Control of Single-Link FlexibleRobots by Strain/Tip Feedback[C]. Proceedings of IEEE International Conferenceon Control Applications,1996:965-969.
[49] M Moallem, R V Patel, K Khorasani. Nonlinear Tip-Position Tracking Control of aFlexible-Link Manipulator: Theory and Experiments[C]. Automatica,2001,37:1825-1834.
[50] S S Ge, T H Lee. Nonlinear Feedback Controller for a Single-Link FlexibleManipulators Based Finite Element Model[C]. Journal of Robotic Systems,1997,14(3):165-178.
[51] Z D Wang, H Q Zeng, D W C Ho, H Unbehauen. Multiobjective Control of aFour-Link Flexible Manipulator: a Robust H∞Approach[J]. IEEE Transactions onControl System Technology,2002,10(6):866-875.
[52] Y C Li, B J Tang, Z X Shi, Y F Lu. Experimental Study for Trajectory of aTwo-Link Flexible Manipulator[J]. International Journal of Systems Science,2000,31(1):1-9.
[53]张袅娜,冯勇,王冬梅,于兰.柔性机械手的鲁棒控制器设计[J].控制与决策,2006,21(7):750-754.
[54] M Sasaki, H Asai. Self-Tuning Control of a Translational Flexible Arm UsingNeural Networks[C]. IEEE International Conference on Systems, Man, andCybernetics,2000,3259-3264.
[55] L.B.Gutierrez, F.L.Lewis, J.A. Lowe. Imlementation of a Neural Network TrackingController for a Single Flexible Link: Comparison with PD and PIDControllers[J].IEEE Transactions on Industrial Electronics,1998,45(2):307-318.
[56] A Chatterjee, R Chatterjee. Augmented Stable Fuzzzy Control for Flexible RoboticArm Using LMI Approach and Neuro-Fuzzy State Space Modeling[J]. IEEETransactions on Industrial Electronics,2008,55(3):1256-1270.
[57] Y Tang, F Sun, Z Sun. Neural Network Control of Flexible-Link ManipulatorsUsing Sliding Mode[J]. Neurocomputing,2006,70:288-295.
[58] Y Sakawa, F Matsuno, S Fukushima. Modeling and feedback control of a flexiblearm[J]. Journal of Robotic Systems,1985,2(4):453–472.
[59] E Bayo. A Finite-Element Approach to Control the End-Point Motion of aSingle-Link Flexible Robot[J]. Journal of Robotic Systems,1987,4(1):63-75.
[60] A J Pritchard, J Zabczyk. Stability and Stabilizability of Infinite DimensionalSystems[J].SIAM Review,1981,23(1):25–52.
[61] J S Gibson. Approximation theory for Linear-Quadratic-Gaussian optimal control offlexible structures[J]. SIAM Journal on control and optimization,1991,29(1):1–37.
[62] M Xiao, T Basar. Finite-Dimensional Compensators for the H∞optimal Control ofInfinite Dimensional Systems via a Galerkin-Type Approximation[J]. SIAM Journalon Control and Optimization,1999,37(5):1614–1647.
[63] M J Balas.Active control of flexible systems.Journal of Optimazation Theory andApplications,25,415-436
[64] F Matsuno, T Ohno, Y V Orlov. PDS (Proportional Derivative and Strain) FeedbackControl of a Flexible Structure with Closed-loop Mechanism[C]. Proceedings of the38th Conference on Decision and Control,1999, v5,4331-4336.
[65] F Matsuno, T Endo. Dynamics based control of two-link flexible arm[C].The8thIEEE International Workshop on Advanced Motion Control,2004,135-140.
[66] Y Moritat, M Kimatat, H Ukait, H Kandot, F Matsunot. Lyapunov-Based Control ofMacro-Micro Manipulator Considering Bending and Torsional Vibrations[C]. FifthInternational Workshop on Robot Motion and Control,2005,325-330.
[67] Z H Luo. Direct Strain Feedback Control of Flexible Robot Arms: New Theoreticaland Experimental Results[J].IEEE Transactions on automatic Control,1993,38(11):1611-1622.
[68] Z H Luo. Exponential Stability of Some Differential Equations Arising from Controlof Flexible Arms[C]. The33rd Conference on Decision and Control,1994,757-762.
[69]陈涛,胡超,黄文虎.分布参数柔性航天器的变结构控制[J].工程力学,2008,25(5):222-226.
[70]陈涛,胡超,黄文虎.航天器姿态调整时的变结构控制与振动抑制方法[J].宇航学报,2007,28(5):1200-1204.
[71] S S Ge, T H Lee, G Zhu, F Hong. Variable Structure Control of a Distributed-Parameter Flexible Beam[J]. Journal of Robotic Systems,2001,18(1):17-27.
[72] S S Ge, T H Lee, F Hong. Variable Structure Maneuvering Control of a FlexibleSpacecraft[C]. Proceedings of the American Control Conference,2001,1599-1604.
[73] G Zhu, S S Ge, T H Lee. Variable Structure Regulation of a Flexible Arm with aTranslational Base[J]. The36th Conference on Decision and Control,1997,1361-1366.
[74] H H Lee, J Prevost. A Coupled Sliding-Surface Approach for the Trajectory Controlof a Flexible-Link Robot based on a Distributed Dynamic Model[J]. InternationalJournal of Control,2005,78(9):629–637.
[75] H H Lee, Y Liang. A Coupled-Sliding-Surface Approach for the Robust TrajectoryControl of a Horizontal two-Link Rigid/Flexible Robot[J]. International Journal ofControl,2007,80(12):1880–1892.
[76] M S de Queiroz, D M Dawson, M Agarwal, F Zhang. Adaptive Nonlinear BoundaryControl of a Flexible Link Robot Arm[J]. IEEE Transactions on Robotics andAutomation,1999,15(4):779-787.
[77] V Erfanian, M Kabganian. Adaptive Trajectory Control and Dynamic FrictionCompensation for a Flexible-Link Robot[J]. Journal of Mechanics,2010,26(2):205-217.
[78] H Canbolat, D Dawson, C Rahn, P Vedagarbha. Boundary Control of a CantileveredFlexible Beam with Point-mass Dynamics at the Free End[J], Mechatronics,1998,8(2),163-186.
[79] L J Zhang, J K Liu. Adaptive Boundary Control for Flexible Two-Link ManipulatorBased on Partial Differential Equation Dynamic Model[J]. IET Control Theory&Applications,2013,7(3):43-5.
[80] T Endo, F Matsuno, H Kawasaki. Simple Boundary Control of Two One-LinkFlexible Arms for grasping[C], The16th IEEE International Conference on ControlApplications part of IEEE Multi-conference on Systems and Control,2007,244-249.
[81] T Endo, F Matsuno, H Kawasaki. Simple Boundary Cooperative Control of TwoOne-Link Flexible Arms for Grasping[J].IEEE Transactions on Automatic Control,2009,54(10):2470-2476.
[82] T Endo, F Matsuno. Force Control and Exponential Stability for One-Link FlexibleArm[C]. Proceedings of the16th IFAC World Congress,2005,16(1):1312-1312.
[83] S Kasai, F Matsuno. Force Control of One-Link Flexible Arms mounted on a LinearMotor with PD and Shear Force (PDSF) Feedback[C].The26th Annual Conferenceof the Industrial Electronics Society,2000, v1,195-200.
[84] Y Morita, F Matsuno, Y Kobayashi, M Ikeda, H Ukai, H Kando. Lyapunov-basedForce Control of a Flexible Arm Considering Bending and TorsionalDeformationl.The15th Triennial World Congress[C].2002, Session slot T-Tu-M04,v1.
[85] F Matsuno, A Hayashi. PDS Cooperative Control of Two One-link FlexibleArms[C]. Proceedings of the2000IEEE International Conference on Robotics andAutomation,2000,1490-1495.
[86] Y Moritat, R Matsunot, M I Hiroyuki Ukait, H Kandot. Experimental Study on PDSForce Control of a Flexible Arm Considering Bending and Torsional Deformation
[C]. American Control Conference,2002,408-413.
[87] Y T Shen, N Xi, U C Wejinya, Wen J Li, J Z Xiao. Infinite Dimension SystemApproach for Hybrid ForcePosition Control in Micromanipulation[C]. Proceedingsof IEEE International Conference on Robtics,2004,2912-2917.
[88] W He, S S Ge, B V E How, Y S Choo, K-S Hong. Robust Adaptive BoundaryControl of a Flexible Marine Riser with Vessel Dynamics[J]. Automatica,2011,47(4):722–732.
[89] W He, S S Ge. Robust Adaptive Boundary Control of a Vibrating String UnderUnknown Time-Varying Disturbance[J].IEEE Transactions on Control SystemsTechnology,2012,20(1):48-58.
[90] S S Ge, S Zhang, W He. Modeling and Control of an Euler-Bernoulli Beam underUnknown Spatiotemporally Varying Disturbance[C].2011American ControlConference,2011,2988-2993.
[91]王耀庭,王光,李胜家. Euler—Bernoulli梁边界反馈控制系统的Riesz基生成问题[J].数学学报,2000,43(6):1089-1098.
[92] B Lazzari, R Nibbi. On the exponential decay of the Euler-Bernoulli beam withboundary energy dissipation[J]. Journal of Mathematical Analysis and Applications,2012,389(2):1078–1085.
[93]杜燕,许跟起.具有边界控制的线性Timoshenko型系统的指数稳定性[J].控制理论与应用,2008, l25(1):34-39.
[94] B Z Guo, J M Wang, K Y Yang. Dynamic Stabilization of an Euler-Bernoulli Beamunder Boundary Control and Non-collocated Observation[J]. Systems&ControlLetters,2008,57(9):740-749.
[95] Y L Chen, Z J Han, G Q Xu, D Liu. Exponential Stability Of String System withVariable Coefficients Under Non-collocated Feedback Controls[J]. Asian Journal ofControl,2011,13(1):148-163.
[96] Y L Chen, G Q Xu. Stability Analysis of Cooperation System of Two RobotArms[C]. Proceedings of the29th Chinese Control Conference,2010,819-824.
[97] M Krstic, A Smyshlyaev. Boundary Control of PDEs: a Course on BacksteppingDesigns[M]. Philadelphia: Society for Industrial&Applied Mathematics,2008.
[98] M Krstic, A Siranosian, A Smyshlyaev. Backstepping Boundary Controllers andObservers for the Slender Timoshenko Beam: Part I–Design[C] Proceedings of theAmerican Control Conference,2006,2412-2417.
[99] M Krstic, B Z Guo, B A ALOGH. Control of a Tip-Force Destabilized Shear Beamby Observer-Based Boundary Feedback[J]. SIAM Journal of Control Optimization,2008,47(2):553-574.
[100] A Smyshlyaev, B Z Guo, M Krstic. Arbitrary decay rate for Euler-Bernoulli beamby backstepping boundary feedback[J].IEEE Transactions on Automatic Control,2009,54(5):1134-1140.
[101] B Z Guo, F F Jin. Backstepping Approach to the Arbitrary Decay Rate forEuler-Bernoulli Beam Under Boundary Feedback[J]. International Journal ofControl,2010,83(10):2098-2106.
[102]杨坤一,姚翠珍.树状结构的弹性振动弦的节点反馈镇定[J].应用泛函分析学,2005,7(4):324-330.
[103] Q X Yan, Y Xie, D X Feng. Nonlinear DissiPasive Boundary feedbacksabilization of Euler-Bernouli Beam[J]，Acta Automatica Sinica，2003,29(1):1-7.
[104] G Q Xu, B Z Guo. Riesz Basis Property of Evolution Equations in Hilbert Spacesand Application to a Coupled String Equation[C], SIAM Journal on ControlOptimization,2003,42(3):966–984.
[105] G Q Xu, Z J Han, S P Yunga. Riesz basis property of serially connectedTimoshenko beams[J]. International Journal of Control,2007,80(3):470–485.
[106] B Z Guo, Y Xie, X Z Hou. On Spectrum Of A General Petrovsky Type Equationand Riesz Basis of N-Connected Beams with Lineaer feedback at Joints[J].Journal of Dynamical and Control Systems,2004,10(2):187-211.
[107] B Z Guo. Riesz Basis Approach to the Stabilization of A Flexible Beam with ATip Mass[J].SIAM Journal on Control Optimization,2001,39(6):1736-1747.
[108] B Z Guo. Riesz Basis Property and Exponential Stability of ControlledEuler-Bernoulli Beam Equations with Variable Coeffcients[J], SIAM Journal onControl Optimization,2002,40(6):1905–1923.
[109] T D Nguyen, O Egeland. Observer Design for A Flexible Robot Arm with A TipLoad[C]. American Control Conference,2005,1389-1394.
[110] T D Nguyen, O Egeland. Infinite Dimensional Observer for A Flexible Robot Armwith A Tip Load[J]. Asian Journal of Control,200810(4):456461.
[111] T D Nguyen, Olav Egeland. Tracking and Observer Design for a MotorizedEuler-Bernoulli Beam[C]. Proceedings of the42nd IEEE Conference on Decisionand Control,2003,3325-3330.
[112] T D Nguyen, OEgeland. Observer Design for a Towed Seismic Cable[C].Proceeding of the2004American Control Conference,2004,2233-2238.
[113]王康宁.分布参数控制系统的镇定问题[J].控制理论与应用，1984,v2,11-21.
[114] M Krstic, B Z Guo, A Smyshlyaev. Boundary Controllers and Observers forSchrodinger Equation. Proceedings of the46th IEEE Conference on Decision andControl,2007,12-14.
[115] W Guo, B Z Guo, Z C Shao. Parameter Estimation and Stabilization for a WaveEquation with Boundary Output Harmonic Disturbance and Non-CollocatedControl[J].Internationl Journal Of Robust And Nonlinear Control,2011,21(11):1297–1321.
[116] X D Li, C Z Xu. Infinite-dimensional Luenberger-like Observers for a RotatingBody-beam System[J]. Systems&Control Letters,2011,60(2):138–145.
[117] L J Zhang, J K Lin. Nonlinear PDE Observer Design for a Flexible Two-linkManipulator[C]. American Control Conference,2012:5336-5341.
[118] L J Zhang, J K Liu. Observer-based Partial Differential Equation BoundaryControl for a Flexible Two-link Manipulator in Task Space[J]. IET Control Theoryand Applications,2012,6(13):2120–2133.
[119] D Sun, M K James, Y H Liu. Hybrid Position and Force Control of Two IndustrialRobots Manipulating a Flexible Sheet: Theory and Experiment[C]. IEEEInternational Conference on Robotics and Automation,1998, v2,1835-1840.
[120]郭宝珠,柴树根.无穷维线性系统控制理论[M].科学出版社,2012.
[121] A Pazy. Semigroups of Linear Operators and Applications to Partial DifferentialEquations[M]. New York: Springer-Verlag,1983.
[122] O Morgul. Stabilization and Distrubance Rejection for the Wave Equation[J].IEEETransactions on Qutomatic Control,1998,43(1):89-95.
[123] Z H Luo, B Z Guo, Morgul O. Stability and Stabilization of Infinite dimensionalSystems with Applications[M].Springer, London,1999.
[124] M Krstic, A Smyshlyaev. Boundary Control of PDEs-A Course on BacksteppingDesign[M]. Philadelphia: Society for Industrial and Applied Mathematics,20008,23-27.
[125] M Omer. Dynamic Boundary Control of Euler-Bernoulli Beam[J]. IEEETransactions on Automatic control,1992,37(5):639-642.
[126] J J E Slotine, W P Li. Applied Nonlinear Control[M]. Englewood Cliffs: PrenticeHall,1991.
[2] R Lai, F Ohkawa. Digital Control of A Manipulator Handling Flexible Objects[C].Proceedings of the5th World Congress on Intelligent Control and Automation,2004,4595-4597.
[3] J Q Wu, Z W Luo, Koji Ito. Gain Scheduled Control for Robot Manipulator'sContact Tasks on Flexible Environments[C]. International Workshop on AdvancedMotion Control,1996, v2：512-517.
[4] W K Jr, Brenan J. McCarragher. Force Fields in the Manipulation of FlexibleMaterials[C]. Proceedings of the1996IEEE International Conference on Roboticsand Automation,1996, v3,2352-2357.
[5] F Arai, L L Rong, T Fukuda. Trajectory Control of Flexible Plate Using NeuralNetwork[C].IEEE International Conference on Robotics an Automation,1993,v1,155-159.
[6] H Nakagaki, K Kit agaki, H Tsukune. Study of Insertion Task of a Flexible Beaminto a Hole[C]. IEEE International Conference on Robotics and Automation.1995,v1,330-335.
[7] C Joseph Lee, C Mavroidis. Discrete-Time LQR and H2Damping Control ofFlexible Payloads Using a Robot Manipulator with a Wrist-Mounted Force TorqueSensor[C]. ASME Int.Mechanical Engineering Congress.Exposition DynamicSystems and Control Division,2000,62(2):997-1004.
[8] F E Pacheco, A P Tzes. On-Line Fkequency Domain Information for Control of aFlexible-Link Robot with Varying Payload[J]. IEEE Transactions On AutomaticControl,1989,34(12):1300-1304.
[9] K M Yuen, G M Bone. Robotic Assembly of Flexible Sheet Metal Parts[C].IEEEInternational Conference on Robotics and Automation,1996,1511-1516.
[10] J K Mills, J G-L Ing. Robotic Fixtureless Assembly of Sheet Metal Parts UsingDynamic Finite Element Models: Modelling and Simulation[C].IEEE InternationalConference on Robotics and Automation,1995, v3,2350-2357.
[11] D Sun, Y H Liu. Modeling and Impedance Control of a Two-Manipulator SystemHandling a Flexible Beam, IEEE International Conference on Robotics andAutomation,1997, v2,1787-1792.
[12] D Sun, Y H Liu. Position and Force Tracking of a Two-Manipulator SystemManipulating a Flexible Beam[J].Journal of Robotic Systems,2001,18(4):197-212.
[13] H Bai, J T Wen. Motion Coordination Through Cooperative Payload Transport[C].American Control Conference,2009, v5,978-1-424.
[14] K Kosuge, H Yoshida. Manipulation of a Flexible Object by Dual Manipulators[C].IEEE International Conference on Robotics and Automation. New York: IEEE Press,1995,318-323.
[15]张鹏,李元春,姜日花.一种基于观测器的机械臂协调操作柔性负载的控制方法[J].吉林大学学报(工学版)，2009,39(5):1240-1244.
[16] Z G Tang, Y C Li. Modeling and Control of Two Manipulators Handling a FlexiblePayload Based on Singular Perturbation[C].International Conference on AdvancedComputer Control,2010,558-562.
[17] J L Lions. Optimal Control of Systems Governed by Partial Differential Equations
[M], Sringer-Verlag,Berlin,1971.
[18]王康宁,关肇直.弹性振动的镇定问题[J].中国科学,1976，2134-148.
[19]宋健,于景元,胡顺菊,肖永震.具有结构阻尼的自由弹性梁的解的渐近性质[J].中国科学,1984，v8:759-765.
[20]于景元，朱广田.细长飞行器飞行姿态的渐近性质[J].中国科学,1984,v5：474-482.
[21]李胜家,朱广田.具结构阻尼细长体飞行器系统相应发展方程主算子生成的半群性质[J].系统科学与数学，1988，8(3)：219-225.
[22]侯学章.具结构阻尼非线性细长体飞行器系统的能量指数衰减[J].东北师大学报自然科学版,1994,v3,6-12.
[23]宋健,于景元,王彦祖,胡顺菊,赵忠信,刘嘉荃,冯德兴,朱广田.人口算子的谱特性与人口半群的渐近性质[J].数学物理学报,1982，l2(2):138-144.
[24]宋健,于景元,刘长凯,张连平,朱广田.人口发展算子的谱性质及人口系统的能控性[J].中国种学A辑,1986,2,114-123.
[25] S Yoshiyuki，Z H Luo. Modeling and Control of Coupled Bending and TorsionalVibrations of Flexible Beams[J]. IEEE Transaxrions on Automic Control,1989,34(9),970-977.
[26] X P Zhang, W W Xu, S S Nair. PDE Modeling and Control of a Flexible Two-LinkManipulator[J]. IEEE Transactions On control Systems Technology,2005,13(2):301-312.
[27] M Dogan, O Morgol. Nonlinear PDE Control of Two-Link Flexible Arm withNonuniform Cross Section[C]. Proceedings of the2006American ControlConference,2006,401-405.
[28] M Dogan, O Morgül. On the Control of Two-link Flexible Robot Arm withNonuniform Cross Section, Journal of Vibration and Control[J].201016(5):619-646.
[29] M Kimata, Y Morita, H Ukai, H Kando. PDS Control of Macro-Micro Arm[C].Proceedings of the2004American Control Conference,2006,123-128.
[30] F Matsuno, T Ohno, V. Orlov Yuri. Proportional Derivative and Strain (PDS)Boundary feedback Control of a Flexible Space Structure with a Closed-loop ChainMechanism[J]. Automatica,2002,38(7):1201-1211.
[31] F Matsuno, A Hayashi. PDS Cooperative Control of Two One-link Flexible Arms[C].Proceedings of the IEEE International Conference on Robotics and Automation,2000,1490-1495.
[32] F Matsuno, K Murata. Passivity and PDS Control of Flexible Mechanical Systemson the Basis of Distributed Parameter System[C]. IEEE International Conference onstems, Man, and Cybernetics,1999, v5,51-56.
[33] R F Fung, H C Chang. Dynamic Modelling of A Non-linearly Constrained flexibleManipulator with a Tip Mass by Hamiltion’s Principle[J]. Journal of Sound andVibration,1998,216(5):751-769.
[34] F Matsuno, T Ohno. Distributed Parameter Control of a Large Space Structure withLumped and Distributed Flexibility[C]. Proceedings of the36th Conference onDecision and Control,1997,269-274.
[35] T Endo, F Matsuno. Dynamics Based Force Control of One-link Flexible Arm[C].SICE Annual Conference in Sapporo,2004,2736-2741.
[36] K Krishnamurthy, L Yang. Dynamic Modeling and Simulation of Two CooperatingStructurally-Flexible Robotic Manipulators[J]. Robotica,199513(4):375-384.
[37] F Matsuno, M Hatayama. Robust Cooperative Control of Two Two-Link FlexibleManipulators on the Basis of Quasi-Static Equations[J]. The International Journal ofRobotics Research,1999,18(4):414-428.
[38] F Matsuno, M Hatayama. Quasi-Static Cooperative Control of Two Two-LinkFlexible Manipulators[C]. IEEE lnternatlonal Conference on Robotlcs andAutomatlon,1995,615-620.
[39] F Matsuno, K Yamamoto. Dynamic Hybrid Position/Force Control of a Two Degreeof Freedom Flexible Manipulator[J]. Journal of Robotic Systems,1994,11(5):355-366.
[40]李冬宁,赵雁,沈铖武,刘畅.一种双连杆柔性臂动力学模型的研究[J].测控技术,2009,28(12):40-43.
[41] E H K Fung, Z X Shi. Multivariable Feedforward-feedback Motion Control of aConstrained Two-link Manipulator with a Flexible Forearm[C]. Proceedings of the37th IEEE Conference on Decision and Control,1998,949-954.
[42] F Matsuno, S Kasai. Modeling and Robust Force Control of Constrained One-LinkFlexible Arms[J]. Journal of Robotic Systems,1998,15(8):447-464.
[43]李元春,刘姝阳,唐志国.基于分布参数机械臂协调操作柔性负载双时标控制,控制与决策[J].2012，27(5):686-690.
[44] E Balasubramanian, S Abilash, S Riyazahammed. Collaborative ManipulatorsHandling Flexible Object in Joint Space Modeling, Control and Analysis[J].International Journal of Mechanical Production Engineering Research andDevelopment,2013,3(1):163-180.
[45] A Lotfazar, M Eghtesad, A Najafi. Vibration Control and Trajectory Tracking forGeneral In-Plane Motion of an Euler–Bernoulli Beam Via Two-Time Scale andBoundary Control Methods[J]. Journal of Vibration and Acoustics,2008,130(5):1-11.
[46] H A Malki, D Misit, D Feigenspan, G Chen. Fuzzy PID Control of a Flexible-JointRobot Arm with Uncertainties from Time-varying Loads[J].IEEE Transactions oncontrol Systems Technology,1997,5(3):371-378.
[47] R Kelly, R Ortega, A Ailton. Global Regulation of Flexible Joint Robots UsingApproximate Differentiation[J].IEEE Transactions on Automatic Control,1994,36(6):1222-1224.
[48] S S Ge, T H Lee, G Zhu. Improving Joint PD Control of Single-Link FlexibleRobots by Strain/Tip Feedback[C]. Proceedings of IEEE International Conferenceon Control Applications,1996:965-969.
[49] M Moallem, R V Patel, K Khorasani. Nonlinear Tip-Position Tracking Control of aFlexible-Link Manipulator: Theory and Experiments[C]. Automatica,2001,37:1825-1834.
[50] S S Ge, T H Lee. Nonlinear Feedback Controller for a Single-Link FlexibleManipulators Based Finite Element Model[C]. Journal of Robotic Systems,1997,14(3):165-178.
[51] Z D Wang, H Q Zeng, D W C Ho, H Unbehauen. Multiobjective Control of aFour-Link Flexible Manipulator: a Robust H∞Approach[J]. IEEE Transactions onControl System Technology,2002,10(6):866-875.
[52] Y C Li, B J Tang, Z X Shi, Y F Lu. Experimental Study for Trajectory of aTwo-Link Flexible Manipulator[J]. International Journal of Systems Science,2000,31(1):1-9.
[53]张袅娜,冯勇,王冬梅,于兰.柔性机械手的鲁棒控制器设计[J].控制与决策,2006,21(7):750-754.
[54] M Sasaki, H Asai. Self-Tuning Control of a Translational Flexible Arm UsingNeural Networks[C]. IEEE International Conference on Systems, Man, andCybernetics,2000,3259-3264.
[55] L.B.Gutierrez, F.L.Lewis, J.A. Lowe. Imlementation of a Neural Network TrackingController for a Single Flexible Link: Comparison with PD and PIDControllers[J].IEEE Transactions on Industrial Electronics,1998,45(2):307-318.
[56] A Chatterjee, R Chatterjee. Augmented Stable Fuzzzy Control for Flexible RoboticArm Using LMI Approach and Neuro-Fuzzy State Space Modeling[J]. IEEETransactions on Industrial Electronics,2008,55(3):1256-1270.
[57] Y Tang, F Sun, Z Sun. Neural Network Control of Flexible-Link ManipulatorsUsing Sliding Mode[J]. Neurocomputing,2006,70:288-295.
[58] Y Sakawa, F Matsuno, S Fukushima. Modeling and feedback control of a flexiblearm[J]. Journal of Robotic Systems,1985,2(4):453–472.
[59] E Bayo. A Finite-Element Approach to Control the End-Point Motion of aSingle-Link Flexible Robot[J]. Journal of Robotic Systems,1987,4(1):63-75.
[60] A J Pritchard, J Zabczyk. Stability and Stabilizability of Infinite DimensionalSystems[J].SIAM Review,1981,23(1):25–52.
[61] J S Gibson. Approximation theory for Linear-Quadratic-Gaussian optimal control offlexible structures[J]. SIAM Journal on control and optimization,1991,29(1):1–37.
[62] M Xiao, T Basar. Finite-Dimensional Compensators for the H∞optimal Control ofInfinite Dimensional Systems via a Galerkin-Type Approximation[J]. SIAM Journalon Control and Optimization,1999,37(5):1614–1647.
[63] M J Balas.Active control of flexible systems.Journal of Optimazation Theory andApplications,25,415-436
[64] F Matsuno, T Ohno, Y V Orlov. PDS (Proportional Derivative and Strain) FeedbackControl of a Flexible Structure with Closed-loop Mechanism[C]. Proceedings of the38th Conference on Decision and Control,1999, v5,4331-4336.
[65] F Matsuno, T Endo. Dynamics based control of two-link flexible arm[C].The8thIEEE International Workshop on Advanced Motion Control,2004,135-140.
[66] Y Moritat, M Kimatat, H Ukait, H Kandot, F Matsunot. Lyapunov-Based Control ofMacro-Micro Manipulator Considering Bending and Torsional Vibrations[C]. FifthInternational Workshop on Robot Motion and Control,2005,325-330.
[67] Z H Luo. Direct Strain Feedback Control of Flexible Robot Arms: New Theoreticaland Experimental Results[J].IEEE Transactions on automatic Control,1993,38(11):1611-1622.
[68] Z H Luo. Exponential Stability of Some Differential Equations Arising from Controlof Flexible Arms[C]. The33rd Conference on Decision and Control,1994,757-762.
[69]陈涛,胡超,黄文虎.分布参数柔性航天器的变结构控制[J].工程力学,2008,25(5):222-226.
[70]陈涛,胡超,黄文虎.航天器姿态调整时的变结构控制与振动抑制方法[J].宇航学报,2007,28(5):1200-1204.
[71] S S Ge, T H Lee, G Zhu, F Hong. Variable Structure Control of a Distributed-Parameter Flexible Beam[J]. Journal of Robotic Systems,2001,18(1):17-27.
[72] S S Ge, T H Lee, F Hong. Variable Structure Maneuvering Control of a FlexibleSpacecraft[C]. Proceedings of the American Control Conference,2001,1599-1604.
[73] G Zhu, S S Ge, T H Lee. Variable Structure Regulation of a Flexible Arm with aTranslational Base[J]. The36th Conference on Decision and Control,1997,1361-1366.
[74] H H Lee, J Prevost. A Coupled Sliding-Surface Approach for the Trajectory Controlof a Flexible-Link Robot based on a Distributed Dynamic Model[J]. InternationalJournal of Control,2005,78(9):629–637.
[75] H H Lee, Y Liang. A Coupled-Sliding-Surface Approach for the Robust TrajectoryControl of a Horizontal two-Link Rigid/Flexible Robot[J]. International Journal ofControl,2007,80(12):1880–1892.
[76] M S de Queiroz, D M Dawson, M Agarwal, F Zhang. Adaptive Nonlinear BoundaryControl of a Flexible Link Robot Arm[J]. IEEE Transactions on Robotics andAutomation,1999,15(4):779-787.
[77] V Erfanian, M Kabganian. Adaptive Trajectory Control and Dynamic FrictionCompensation for a Flexible-Link Robot[J]. Journal of Mechanics,2010,26(2):205-217.
[78] H Canbolat, D Dawson, C Rahn, P Vedagarbha. Boundary Control of a CantileveredFlexible Beam with Point-mass Dynamics at the Free End[J], Mechatronics,1998,8(2),163-186.
[79] L J Zhang, J K Liu. Adaptive Boundary Control for Flexible Two-Link ManipulatorBased on Partial Differential Equation Dynamic Model[J]. IET Control Theory&Applications,2013,7(3):43-5.
[80] T Endo, F Matsuno, H Kawasaki. Simple Boundary Control of Two One-LinkFlexible Arms for grasping[C], The16th IEEE International Conference on ControlApplications part of IEEE Multi-conference on Systems and Control,2007,244-249.
[81] T Endo, F Matsuno, H Kawasaki. Simple Boundary Cooperative Control of TwoOne-Link Flexible Arms for Grasping[J].IEEE Transactions on Automatic Control,2009,54(10):2470-2476.
[82] T Endo, F Matsuno. Force Control and Exponential Stability for One-Link FlexibleArm[C]. Proceedings of the16th IFAC World Congress,2005,16(1):1312-1312.
[83] S Kasai, F Matsuno. Force Control of One-Link Flexible Arms mounted on a LinearMotor with PD and Shear Force (PDSF) Feedback[C].The26th Annual Conferenceof the Industrial Electronics Society,2000, v1,195-200.
[84] Y Morita, F Matsuno, Y Kobayashi, M Ikeda, H Ukai, H Kando. Lyapunov-basedForce Control of a Flexible Arm Considering Bending and TorsionalDeformationl.The15th Triennial World Congress[C].2002, Session slot T-Tu-M04,v1.
[85] F Matsuno, A Hayashi. PDS Cooperative Control of Two One-link FlexibleArms[C]. Proceedings of the2000IEEE International Conference on Robotics andAutomation,2000,1490-1495.
[86] Y Moritat, R Matsunot, M I Hiroyuki Ukait, H Kandot. Experimental Study on PDSForce Control of a Flexible Arm Considering Bending and Torsional Deformation
[C]. American Control Conference,2002,408-413.
[87] Y T Shen, N Xi, U C Wejinya, Wen J Li, J Z Xiao. Infinite Dimension SystemApproach for Hybrid ForcePosition Control in Micromanipulation[C]. Proceedingsof IEEE International Conference on Robtics,2004,2912-2917.
[88] W He, S S Ge, B V E How, Y S Choo, K-S Hong. Robust Adaptive BoundaryControl of a Flexible Marine Riser with Vessel Dynamics[J]. Automatica,2011,47(4):722–732.
[89] W He, S S Ge. Robust Adaptive Boundary Control of a Vibrating String UnderUnknown Time-Varying Disturbance[J].IEEE Transactions on Control SystemsTechnology,2012,20(1):48-58.
[90] S S Ge, S Zhang, W He. Modeling and Control of an Euler-Bernoulli Beam underUnknown Spatiotemporally Varying Disturbance[C].2011American ControlConference,2011,2988-2993.
[91]王耀庭,王光,李胜家. Euler—Bernoulli梁边界反馈控制系统的Riesz基生成问题[J].数学学报,2000,43(6):1089-1098.
[92] B Lazzari, R Nibbi. On the exponential decay of the Euler-Bernoulli beam withboundary energy dissipation[J]. Journal of Mathematical Analysis and Applications,2012,389(2):1078–1085.
[93]杜燕,许跟起.具有边界控制的线性Timoshenko型系统的指数稳定性[J].控制理论与应用,2008, l25(1):34-39.
[94] B Z Guo, J M Wang, K Y Yang. Dynamic Stabilization of an Euler-Bernoulli Beamunder Boundary Control and Non-collocated Observation[J]. Systems&ControlLetters,2008,57(9):740-749.
[95] Y L Chen, Z J Han, G Q Xu, D Liu. Exponential Stability Of String System withVariable Coefficients Under Non-collocated Feedback Controls[J]. Asian Journal ofControl,2011,13(1):148-163.
[96] Y L Chen, G Q Xu. Stability Analysis of Cooperation System of Two RobotArms[C]. Proceedings of the29th Chinese Control Conference,2010,819-824.
[97] M Krstic, A Smyshlyaev. Boundary Control of PDEs: a Course on BacksteppingDesigns[M]. Philadelphia: Society for Industrial&Applied Mathematics,2008.
[98] M Krstic, A Siranosian, A Smyshlyaev. Backstepping Boundary Controllers andObservers for the Slender Timoshenko Beam: Part I–Design[C] Proceedings of theAmerican Control Conference,2006,2412-2417.
[99] M Krstic, B Z Guo, B A ALOGH. Control of a Tip-Force Destabilized Shear Beamby Observer-Based Boundary Feedback[J]. SIAM Journal of Control Optimization,2008,47(2):553-574.
[100] A Smyshlyaev, B Z Guo, M Krstic. Arbitrary decay rate for Euler-Bernoulli beamby backstepping boundary feedback[J].IEEE Transactions on Automatic Control,2009,54(5):1134-1140.
[101] B Z Guo, F F Jin. Backstepping Approach to the Arbitrary Decay Rate forEuler-Bernoulli Beam Under Boundary Feedback[J]. International Journal ofControl,2010,83(10):2098-2106.
[102]杨坤一,姚翠珍.树状结构的弹性振动弦的节点反馈镇定[J].应用泛函分析学,2005,7(4):324-330.
[103] Q X Yan, Y Xie, D X Feng. Nonlinear DissiPasive Boundary feedbacksabilization of Euler-Bernouli Beam[J]，Acta Automatica Sinica，2003,29(1):1-7.
[104] G Q Xu, B Z Guo. Riesz Basis Property of Evolution Equations in Hilbert Spacesand Application to a Coupled String Equation[C], SIAM Journal on ControlOptimization,2003,42(3):966–984.
[105] G Q Xu, Z J Han, S P Yunga. Riesz basis property of serially connectedTimoshenko beams[J]. International Journal of Control,2007,80(3):470–485.
[106] B Z Guo, Y Xie, X Z Hou. On Spectrum Of A General Petrovsky Type Equationand Riesz Basis of N-Connected Beams with Lineaer feedback at Joints[J].Journal of Dynamical and Control Systems,2004,10(2):187-211.
[107] B Z Guo. Riesz Basis Approach to the Stabilization of A Flexible Beam with ATip Mass[J].SIAM Journal on Control Optimization,2001,39(6):1736-1747.
[108] B Z Guo. Riesz Basis Property and Exponential Stability of ControlledEuler-Bernoulli Beam Equations with Variable Coeffcients[J], SIAM Journal onControl Optimization,2002,40(6):1905–1923.
[109] T D Nguyen, O Egeland. Observer Design for A Flexible Robot Arm with A TipLoad[C]. American Control Conference,2005,1389-1394.
[110] T D Nguyen, O Egeland. Infinite Dimensional Observer for A Flexible Robot Armwith A Tip Load[J]. Asian Journal of Control,200810(4):456461.
[111] T D Nguyen, Olav Egeland. Tracking and Observer Design for a MotorizedEuler-Bernoulli Beam[C]. Proceedings of the42nd IEEE Conference on Decisionand Control,2003,3325-3330.
[112] T D Nguyen, OEgeland. Observer Design for a Towed Seismic Cable[C].Proceeding of the2004American Control Conference,2004,2233-2238.
[113]王康宁.分布参数控制系统的镇定问题[J].控制理论与应用，1984,v2,11-21.
[114] M Krstic, B Z Guo, A Smyshlyaev. Boundary Controllers and Observers forSchrodinger Equation. Proceedings of the46th IEEE Conference on Decision andControl,2007,12-14.
[115] W Guo, B Z Guo, Z C Shao. Parameter Estimation and Stabilization for a WaveEquation with Boundary Output Harmonic Disturbance and Non-CollocatedControl[J].Internationl Journal Of Robust And Nonlinear Control,2011,21(11):1297–1321.
[116] X D Li, C Z Xu. Infinite-dimensional Luenberger-like Observers for a RotatingBody-beam System[J]. Systems&Control Letters,2011,60(2):138–145.
[117] L J Zhang, J K Lin. Nonlinear PDE Observer Design for a Flexible Two-linkManipulator[C]. American Control Conference,2012:5336-5341.
[118] L J Zhang, J K Liu. Observer-based Partial Differential Equation BoundaryControl for a Flexible Two-link Manipulator in Task Space[J]. IET Control Theoryand Applications,2012,6(13):2120–2133.
[119] D Sun, M K James, Y H Liu. Hybrid Position and Force Control of Two IndustrialRobots Manipulating a Flexible Sheet: Theory and Experiment[C]. IEEEInternational Conference on Robotics and Automation,1998, v2,1835-1840.
[120]郭宝珠,柴树根.无穷维线性系统控制理论[M].科学出版社,2012.
[121] A Pazy. Semigroups of Linear Operators and Applications to Partial DifferentialEquations[M]. New York: Springer-Verlag,1983.
[122] O Morgul. Stabilization and Distrubance Rejection for the Wave Equation[J].IEEETransactions on Qutomatic Control,1998,43(1):89-95.
[123] Z H Luo, B Z Guo, Morgul O. Stability and Stabilization of Infinite dimensionalSystems with Applications[M].Springer, London,1999.
[124] M Krstic, A Smyshlyaev. Boundary Control of PDEs-A Course on BacksteppingDesign[M]. Philadelphia: Society for Industrial and Applied Mathematics,20008,23-27.
[125] M Omer. Dynamic Boundary Control of Euler-Bernoulli Beam[J]. IEEETransactions on Automatic control,1992,37(5):639-642.
[126] J J E Slotine, W P Li. Applied Nonlinear Control[M]. Englewood Cliffs: PrenticeHall,1991.
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