大射电望远镜馈源支撑系统定位与指向控制研究
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摘要
本文以国家天文台500米口径球面射电望远镜FAST项目为应用背景,针对其关键技术移动小车式无平台馈源支撑系统,进行动力学与反馈控制一体化仿真研究和测量控制方案研究。论文主要进行了如下三项研究工作:
针对移动小车式无平台馈源支撑系统中大尺度时变索系和Stewart平台机构耦合动力学仿真的需要,本文实现了一种大范围运动一阶连续长索单元,利用它模拟了卷扬钢索和钢索过定滑轮的动力学,并在多体动力学框架下实现了时变索系与多刚体组合系统的建模和数值求解。
为实现射电望远镜馈源在大范围运动中高精度定位和指向的目标,本文提出了直接测量受控平台位姿的末端反馈控制策略。在驱动索系定位控制的同时,耦合索系张力分配的非线性控制,有效地避免了钢索虚牵。通过模型实验和仿真实验,对大范围运动驱动索系、指向机构和Stewart平台三级耦合机械结构的测量控制方案进行了验证。针对测量数据的噪声问题,本文提出了一种基于频率分析的实时滤波器。该滤波器在传统多项式拟合滤波器的基础上,采用动态频率分析和预测技术,使得滤波时滞只有采样周期的三分之一左右,适合高实时性要求的应用。在柔性悬挂Stewart平台振动控制实验中,该滤波器的应用提高了控制效果。
本文构建了一套基于多体动力学的反馈控制仿真系统。对密云50米尺度时变索系驱动馈源小车运动控制实验,和柔性悬挂Stewart平台振动控制实验,进行动力学与反馈控制一体化仿真。仿真结果与物理实验相符合。利用基于多体动力学的反馈控制仿真系统,对500米尺度原型移动小车式无平台馈源支撑系统进行仿真研究。在大范围运动时变机械结构和测量控制耦合仿真模型上进行虚拟实验,优化机械结构、控制算法和控制参数,考察风荷载作用下馈源长时间跟踪观测的定位和指向控制效果。通过对大量的系统的虚拟反馈控制实验的结果进行对比和整理,本文工作为FAST馈源支撑系统的方案设计提供了建议和参考。
As part of the Five-hundred-meter Aperture Spherical Telescope (FAST) project from the National Astronomical Observatory, this work carries out dynamics and control all-in-one simulation research and feedback control scheme study on the moving-car platformless feed support system, which is one of the key technologies of FAST.
In order to simulate dynamics of the large-scale time varying cable network combined with a Stewart parallel mechanism, which arises from the moving-car platformless feed support system, this paper implements a large-displacement first order continuous long cable element, uses it as the base to simulate dynamics of winding cable and sliding cable through fixed pulley, and numerically solves the time varying cable network and rigid bodies combined system under the framework of flexible multibody dynamics.
To achieve high precision positioning and orientating control in large-range tracing of the radio telescope feed, this paper proposes a terminal feedback control scheme by directly measuring the position and orientation of the platform to be controlled. Nonlinear control for distributing tension among cable network is applied simultaneously with positioning control of the cable drive architecture and effectively avoids runtime cable over-sagging. Feedback control scheme for the feed support mechanism consisting of a large scale cable drive architecture, an orientating platform and a Stewart platform is verified through field and virtual control tests. For the measurement noise problem, this paper proposes a real time filter based on frequency analysis. Derived from traditional least square polynomial fit filter, the new filter employs dynamic frequency analysis and prediction technique, making the filter-introduced-delay only one third of the sampling period and particularly suits applications where real time is heavily demanded. Application of the proposed filter improves control effect remarkably in the flexible-supported Stewart platform vibration control experiments.
This paper constructs a set of feedback control simulation system based on flexible multibody dynamics. Dynamics and control all-in-one simulation is made on tracing control experiments of the 50-meter-scale cable driven trolley and vibration control experiments of the flexibly supported Stewart platform, results of which generally agree with the corresponding physical experiments. This paper then conducts simulation research on the 500-meter-scale moving-car platformless feed support system employing the feedback control simulation system based on multibody dynamics. Simulation experiments on the virtual digital model coupling large-displacement time varying mechanism and feedback control components are carried out on PC to optimize the mechanical structure,control algorithms and parameters and to investigate positioning and orientating precision of the feed in long term tracing under wind load. Quite a lot of result data from systematic virtual feedback control experiments are processed and provide design advices and reference for construction of the feed support system for FAST.
针对移动小车式无平台馈源支撑系统中大尺度时变索系和Stewart平台机构耦合动力学仿真的需要,本文实现了一种大范围运动一阶连续长索单元,利用它模拟了卷扬钢索和钢索过定滑轮的动力学,并在多体动力学框架下实现了时变索系与多刚体组合系统的建模和数值求解。
为实现射电望远镜馈源在大范围运动中高精度定位和指向的目标,本文提出了直接测量受控平台位姿的末端反馈控制策略。在驱动索系定位控制的同时,耦合索系张力分配的非线性控制,有效地避免了钢索虚牵。通过模型实验和仿真实验,对大范围运动驱动索系、指向机构和Stewart平台三级耦合机械结构的测量控制方案进行了验证。针对测量数据的噪声问题,本文提出了一种基于频率分析的实时滤波器。该滤波器在传统多项式拟合滤波器的基础上,采用动态频率分析和预测技术,使得滤波时滞只有采样周期的三分之一左右,适合高实时性要求的应用。在柔性悬挂Stewart平台振动控制实验中,该滤波器的应用提高了控制效果。
本文构建了一套基于多体动力学的反馈控制仿真系统。对密云50米尺度时变索系驱动馈源小车运动控制实验,和柔性悬挂Stewart平台振动控制实验,进行动力学与反馈控制一体化仿真。仿真结果与物理实验相符合。利用基于多体动力学的反馈控制仿真系统,对500米尺度原型移动小车式无平台馈源支撑系统进行仿真研究。在大范围运动时变机械结构和测量控制耦合仿真模型上进行虚拟实验,优化机械结构、控制算法和控制参数,考察风荷载作用下馈源长时间跟踪观测的定位和指向控制效果。通过对大量的系统的虚拟反馈控制实验的结果进行对比和整理,本文工作为FAST馈源支撑系统的方案设计提供了建议和参考。
As part of the Five-hundred-meter Aperture Spherical Telescope (FAST) project from the National Astronomical Observatory, this work carries out dynamics and control all-in-one simulation research and feedback control scheme study on the moving-car platformless feed support system, which is one of the key technologies of FAST.
In order to simulate dynamics of the large-scale time varying cable network combined with a Stewart parallel mechanism, which arises from the moving-car platformless feed support system, this paper implements a large-displacement first order continuous long cable element, uses it as the base to simulate dynamics of winding cable and sliding cable through fixed pulley, and numerically solves the time varying cable network and rigid bodies combined system under the framework of flexible multibody dynamics.
To achieve high precision positioning and orientating control in large-range tracing of the radio telescope feed, this paper proposes a terminal feedback control scheme by directly measuring the position and orientation of the platform to be controlled. Nonlinear control for distributing tension among cable network is applied simultaneously with positioning control of the cable drive architecture and effectively avoids runtime cable over-sagging. Feedback control scheme for the feed support mechanism consisting of a large scale cable drive architecture, an orientating platform and a Stewart platform is verified through field and virtual control tests. For the measurement noise problem, this paper proposes a real time filter based on frequency analysis. Derived from traditional least square polynomial fit filter, the new filter employs dynamic frequency analysis and prediction technique, making the filter-introduced-delay only one third of the sampling period and particularly suits applications where real time is heavily demanded. Application of the proposed filter improves control effect remarkably in the flexible-supported Stewart platform vibration control experiments.
This paper constructs a set of feedback control simulation system based on flexible multibody dynamics. Dynamics and control all-in-one simulation is made on tracing control experiments of the 50-meter-scale cable driven trolley and vibration control experiments of the flexibly supported Stewart platform, results of which generally agree with the corresponding physical experiments. This paper then conducts simulation research on the 500-meter-scale moving-car platformless feed support system employing the feedback control simulation system based on multibody dynamics. Simulation experiments on the virtual digital model coupling large-displacement time varying mechanism and feedback control components are carried out on PC to optimize the mechanical structure,control algorithms and parameters and to investigate positioning and orientating precision of the feed in long term tracing under wind load. Quite a lot of result data from systematic virtual feedback control experiments are processed and provide design advices and reference for construction of the feed support system for FAST.
引文
[1] R.D. Nan, B. Peng. A Chinese concept for the 1 km2 radio telescope. Acta Astronautica, 2000, 46 (12): 66.
[2] B.Y. Duan. The synthetical design of large spherical radio telescope by integrating the mechanical, electronic, optic and numerical control technologies. 25th General Assembly of the URSI (International Union of Radio Science), Lille, France, 1996.
[3]清华大学FAST研究组.大射电望远镜FAST移动小车—馈源稳定系统耦合研究.北京:清华大学工程力学系, 2003.
[4]路英杰.大射电望远镜馈源支撑缩尺模型试验控制系统研究[学士学位论文].北京:清华大学工程力学系, 2001.
[5]路英杰.大射电望远镜馈源支撑模型控制实验及索网反射面仿真研究[硕士学位论文].北京:清华大学工程力学系, 2004.
[6] Y.J. Lu, W.B. Zhu, G.X. Ren. Feedback Control of a Cable-driven Gough-Stewart Platform. IEEE Transactions on Robotics, 2006, 22(1): 198-202.
[7] W. Schiehlen. Multibody System Dynamics: Roots and Perspectives. Multibody System dynamics, 1997, 1: 149-188.
[8] E.J. Haug. Computer Aided Kinematics and Dynamics of Mechanical Systems [M]. Needham Heights, Massachusetts, U.S.: Allyn and Bacon, 1989, 305-335.
[9] A.A. Shabana. Dynamics of Multibody Systems [M]. U.S.: JOHN WILEY & SONS, 1989, 1-330.
[10] W. Schiehlen. Computational dynamics: theory and applications of multibody systems. European Journal of Mechanics A/Solids, 2006, 25: 566-594.
[11]刘又午.多体动力学的休斯敦方法及其发展.中国机械工程, 2000, 11(6): 601-607.
[12] A.A. Shabana. Flexible Multibody Dynamics: Review of Past and Recent Developments. Multibody System dynamics, 1997, 1: 189-222.
[13] P. Eberhard and W. Schiehlen. Computational Dynamics of Multibody Systems: History, Formalisms, and Applications. Journal of Computational and Nonlinear Dynamics, 2006, 1(1): 3-12.
[14]张其林.预应力结构非线性分析的索单元理论.工程力学, 1993, 10(4): 93-101.
[15] W.C. Knudson. Static and dynamic analysis of cable net structures [Doctoral dissertation]. U.S.: University of Califormia, Berkely, Califormia, 1971.
[16] V. Gattulli, L. Martinelli, F. Perotti, F. Vestroni. Nonlinear oscillations of cables under harmonic loading using analytical and finite element models. Comput. Methods Appl. Mech. Engrg., 2004, 193: 69-85.
[17]武建华,苏文章.四节点索单元的悬索结构非线性有限元分析.重庆建筑大学学报, 2005, 27(6): 55-58.
[18]唐建民,何署廷.悬索结构非线性有限元分析.河海大学学报, 1998, 26(6): 45-49.
[19]唐建民,董明,钱若军.张拉结构非线性分析的五节点等参单元.计算力学学报, 1997, 14(1): 108-113.
[20]张其林,张莉,周岱, Udo Peil.连续长索非线性静动力分析的样条单元.工程力学, 1999, 16(1):115-122.
[21]杨彦萍.柔索结构的样条元法和有限元法.昆明理工大学学报, 2000, 25(1): 54-67.
[22]杨彦萍.索结构样条元插值函数推导.昆明理工大学学报, 2000, 25(2): 72-74.
[23] J. Gerstmayr, J. Schoberl. A 3D finite element method for flexible multibody systems. Multibody Syst Dyn, 2006, 15: 309-324.
[24] J.L. Escalona. APPLICATION OF THE ABSOLUTE NODAL CO-ORDINATE FORMULATION TO MULTIBODY SYSTEM DYNAMICS. Journal of Sound and Vibration, 1998, 214(5): 833-851.
[25] A.A. Shabana. Computer Implementation of the Absolute Nodal Coordinate Formulation for Flexible Multibody Dynamics. Nonlinear Dynamics, 1998, 16: 293-306.
[26] D. GARCíA-VALLEJO, et al. Describing Rigid-Flexible Multibody Systems Using Absolute Coordinates. Nonlinear Dynamics, 2003, 34: 75-94.
[27] M. Berzeri, A.A. Shabana. DEVELOPMENT OF SIMPLE MODELS FOR THE ELASTIC FORCES IN THE ABSOLUTE NODAL CO-ORDINATE FORMULATION. Journal of Sound and vibration, 2000, 235(4): 539-565.
[28] L. KüBLER, et al. Flexible Multibody Systems with Large Deformations and Nonlinear Structural Damping Using Absolute Nodal Coordinates. Nonlinear Dynamics, 2003, 34: 31-52.
[29] R.Y. Yakoub, A.A. Shabana. Use of Cholesky Coordinates and the Absolute Nodal Coordinate Formulation in the Computer Simulation of Flexible Multibody Systems. Nonlinear Dynamics, 1999, 20: 267-282.
[30] S.V. Dombrowski. Analysis of Large Flexible Body Deformation in Multibody Systems Using Absolute Coordinates. Multibody System Dynamics, 2002, 8: 409–432.
[31] K.A.F. Moustafa and A.M. Ebied. Nonlinear modeling and control of overhead cranes load sway. Journal of Dynamic System Measurement and Control, 1988, 110: 266-271.
[32] M. Nalley and M. Trabia. Control of overhead cranes using fuzzy logic controllers. Journal of Intelligent & Fuzzy Systems, 2000, 8: 1-18.
[33] K.A.F. Moustafa et al. Modelling and control of overhead cranes with flexible variable-length cable by finite element method. Transactions of the Institute of Measurement and Control 2005, 27(1): 1-20.
[34] W.D. Zhu, G.Y. Xu. Vibration of elevator cables with small bending stiffness. Journal of Sound and Vibration, 2003, 263: 679-699.
[35] W.D. Zhu, J. Ni. Energetics and Stability of Translating Media with an Arbitrarily Varying Length. Journal of Vibration and Acoustics, 2000, 122: 295-304.
[36] P.H. Wang et al. FINITE ELEMENT ANALYSIS OF A THREE DIMENSIONAL UNDERWATER CABLE WITH TIME-DEPENDENT LENGTH. Journal of Sound and Vibration, 1998, 209(2): 223-249.
[37] M. Stylianou and B. Tabarrok. Finite element analysis of an axially moving beam, Part I: Time integration. Journal of Sound and Vibration, 1994, 178(4): 433-453.
[38]路英杰,任革学.刚体动力学方程的一个辛积分方法.应用数学与力学, 2006, 27(1): 47-52.
[39]殷翔,董正筑,王继燕. ADAMS和Matlab交互仿真的机械臂定位控制.长春工业大学学报, 2005, 26(4): 332-334.
[40]杨英,刘刚,赵广耀.基于ADAMS机械模型的车辆主动悬架控制策略与仿真.东北大学学报, 2006, 27(1): 72-75.
[41]王立权,王晓东,陈德望,魏洪兴,孟庆鑫.基于虚拟样机的控制系统仿真研究.哈尔滨工程大学学报, 2000, 21(6): 26-29
[42] E.F. Fichter. Stewart platform-based manipulator: general theory and practical construction. Int. J. Robot. Res., 1986, 5(2): 157-182.
[43] G. Lbret, K. Liu, F.L. Lewis. Dynamic analysis and control of a Stewart platform manipulator. J. Robot. Syst., 1993, 10(5): 629-655.
[44] D. Li, S.E. Salcudean. Modeling, simulation, and control of a hydraulic Stewart platform. Proc. 1997 IEEE Int. Conf. Robotics and Automation, 1997, 4: 3360-3366.
[45] Z. Geng, L.S. Haynes. Six degree-of-freedom active vibration isolation using Stewart platform manipulator. J. Robot. Syst., 1993, 10(5): 725-744.
[46] R. Graf, R. Dillmann. Active acceleration compensation using a Stewart platform on a mobile robot. Proc. Euromicro Workshop on Advanced Mobile Robots (EUROBOT), 1997: 59-64.
[47] S. Tadokoro, et al. A motion base with 6-DOF by parallel cable drive architecture. IEEE ASME Transactions on Mechatronics, 2002, 7(2):115-123.
[48] S. Tadokoro, et al. On Fundamental Design of Wire Configurations of Wire-Driven Parallel Manipulators with Redundancy. Proc. Japan-USA Symposium on Flexible Automation, 1996, 1: 151-158.
[49] A.B. Alp, S.K. Agrawal. Cable suspended robots: design, planning and control. Proceedings-IEEE International Conference on Robotics and Automation, 2002, 4: 4275-4280.
[50] N.G. Dagalakis, J.S. Albus, B.L. Wang, J. Unger, J.D. Lee. Stiffness Study of a Parallel Link Robot Crane for Shipbuilding Applications. ASME J. on Offshore Mechanics and Arctic Eng., 1991, 183-193.
[51] A. Ming, T. Higuchi. Study on Multiple Degree-of-freedom Positioning Mechanism Using Wires. Int. Journal of the Japanese Society for Precision Engineering, 1994, 28: 131-138, 235-242.
[52] G.X. Ren, et al. On vibration control with Stewart parallel mechanism. Mechatronics, 2004, 14: 1-13.
[53] Y. Cheng, G.X. Ren, S.L. Dai. Vibration Control of Gough-Stewart Platform on Flexible Suspension. IEEE transactions on robotics and automation, 2003, 19(3): 489-493.
[54] H.A. Buchholdt. Introduction to Cable Roof Structures. U.K.: Cambridge University Press, 1985.
[55]埃米尔.希缪.风对结构的作用——风工程导论.同济大学出版社, 1992.
[56]骆亚波,测量机器人在FAST馈源动态跟踪测量中的应用[硕士学位论文].解放军信息工程大学, 2003.
[57] R.A. Singer. Estimating optimal tracking filter performance for manned maneuvering targets. IEEE Trans. Aerospace and Electronic Systems, 1970, 6 (4): 473-483.
[58] J. Levine, R. Marino. Constant-Speed target tracking via bearings-only measurements. IEEE Trans. Aerospace and Electronic Systems, 1992, 28(1): 174-182.
[59] H.N. Li, Z.M. Zhu, J.S. Li. Tracking and navigating filter for maneuvering target. Chinese space science and technology, 2003, 3: 13-18.
[60] L.P. Xu. An adaptive filter algorithm for tracking the maneuvering target. Journal of Xidian university, 1998, 25(3): 314-317.
[61] R.X. Li, V.P. Jilkov. Survey of maneuvering target tracking. Part I : dynamic models. IEEE Trans. Aerospace and Electronic Systems, 2003, 39(4): 1333-1363.
[62]保宏,段宝岩,陈光达.具有慢速时滞机动目标三维跟踪.控制理论与应用, 2006, 23(4): 526-530
[2] B.Y. Duan. The synthetical design of large spherical radio telescope by integrating the mechanical, electronic, optic and numerical control technologies. 25th General Assembly of the URSI (International Union of Radio Science), Lille, France, 1996.
[3]清华大学FAST研究组.大射电望远镜FAST移动小车—馈源稳定系统耦合研究.北京:清华大学工程力学系, 2003.
[4]路英杰.大射电望远镜馈源支撑缩尺模型试验控制系统研究[学士学位论文].北京:清华大学工程力学系, 2001.
[5]路英杰.大射电望远镜馈源支撑模型控制实验及索网反射面仿真研究[硕士学位论文].北京:清华大学工程力学系, 2004.
[6] Y.J. Lu, W.B. Zhu, G.X. Ren. Feedback Control of a Cable-driven Gough-Stewart Platform. IEEE Transactions on Robotics, 2006, 22(1): 198-202.
[7] W. Schiehlen. Multibody System Dynamics: Roots and Perspectives. Multibody System dynamics, 1997, 1: 149-188.
[8] E.J. Haug. Computer Aided Kinematics and Dynamics of Mechanical Systems [M]. Needham Heights, Massachusetts, U.S.: Allyn and Bacon, 1989, 305-335.
[9] A.A. Shabana. Dynamics of Multibody Systems [M]. U.S.: JOHN WILEY & SONS, 1989, 1-330.
[10] W. Schiehlen. Computational dynamics: theory and applications of multibody systems. European Journal of Mechanics A/Solids, 2006, 25: 566-594.
[11]刘又午.多体动力学的休斯敦方法及其发展.中国机械工程, 2000, 11(6): 601-607.
[12] A.A. Shabana. Flexible Multibody Dynamics: Review of Past and Recent Developments. Multibody System dynamics, 1997, 1: 189-222.
[13] P. Eberhard and W. Schiehlen. Computational Dynamics of Multibody Systems: History, Formalisms, and Applications. Journal of Computational and Nonlinear Dynamics, 2006, 1(1): 3-12.
[14]张其林.预应力结构非线性分析的索单元理论.工程力学, 1993, 10(4): 93-101.
[15] W.C. Knudson. Static and dynamic analysis of cable net structures [Doctoral dissertation]. U.S.: University of Califormia, Berkely, Califormia, 1971.
[16] V. Gattulli, L. Martinelli, F. Perotti, F. Vestroni. Nonlinear oscillations of cables under harmonic loading using analytical and finite element models. Comput. Methods Appl. Mech. Engrg., 2004, 193: 69-85.
[17]武建华,苏文章.四节点索单元的悬索结构非线性有限元分析.重庆建筑大学学报, 2005, 27(6): 55-58.
[18]唐建民,何署廷.悬索结构非线性有限元分析.河海大学学报, 1998, 26(6): 45-49.
[19]唐建民,董明,钱若军.张拉结构非线性分析的五节点等参单元.计算力学学报, 1997, 14(1): 108-113.
[20]张其林,张莉,周岱, Udo Peil.连续长索非线性静动力分析的样条单元.工程力学, 1999, 16(1):115-122.
[21]杨彦萍.柔索结构的样条元法和有限元法.昆明理工大学学报, 2000, 25(1): 54-67.
[22]杨彦萍.索结构样条元插值函数推导.昆明理工大学学报, 2000, 25(2): 72-74.
[23] J. Gerstmayr, J. Schoberl. A 3D finite element method for flexible multibody systems. Multibody Syst Dyn, 2006, 15: 309-324.
[24] J.L. Escalona. APPLICATION OF THE ABSOLUTE NODAL CO-ORDINATE FORMULATION TO MULTIBODY SYSTEM DYNAMICS. Journal of Sound and Vibration, 1998, 214(5): 833-851.
[25] A.A. Shabana. Computer Implementation of the Absolute Nodal Coordinate Formulation for Flexible Multibody Dynamics. Nonlinear Dynamics, 1998, 16: 293-306.
[26] D. GARCíA-VALLEJO, et al. Describing Rigid-Flexible Multibody Systems Using Absolute Coordinates. Nonlinear Dynamics, 2003, 34: 75-94.
[27] M. Berzeri, A.A. Shabana. DEVELOPMENT OF SIMPLE MODELS FOR THE ELASTIC FORCES IN THE ABSOLUTE NODAL CO-ORDINATE FORMULATION. Journal of Sound and vibration, 2000, 235(4): 539-565.
[28] L. KüBLER, et al. Flexible Multibody Systems with Large Deformations and Nonlinear Structural Damping Using Absolute Nodal Coordinates. Nonlinear Dynamics, 2003, 34: 31-52.
[29] R.Y. Yakoub, A.A. Shabana. Use of Cholesky Coordinates and the Absolute Nodal Coordinate Formulation in the Computer Simulation of Flexible Multibody Systems. Nonlinear Dynamics, 1999, 20: 267-282.
[30] S.V. Dombrowski. Analysis of Large Flexible Body Deformation in Multibody Systems Using Absolute Coordinates. Multibody System Dynamics, 2002, 8: 409–432.
[31] K.A.F. Moustafa and A.M. Ebied. Nonlinear modeling and control of overhead cranes load sway. Journal of Dynamic System Measurement and Control, 1988, 110: 266-271.
[32] M. Nalley and M. Trabia. Control of overhead cranes using fuzzy logic controllers. Journal of Intelligent & Fuzzy Systems, 2000, 8: 1-18.
[33] K.A.F. Moustafa et al. Modelling and control of overhead cranes with flexible variable-length cable by finite element method. Transactions of the Institute of Measurement and Control 2005, 27(1): 1-20.
[34] W.D. Zhu, G.Y. Xu. Vibration of elevator cables with small bending stiffness. Journal of Sound and Vibration, 2003, 263: 679-699.
[35] W.D. Zhu, J. Ni. Energetics and Stability of Translating Media with an Arbitrarily Varying Length. Journal of Vibration and Acoustics, 2000, 122: 295-304.
[36] P.H. Wang et al. FINITE ELEMENT ANALYSIS OF A THREE DIMENSIONAL UNDERWATER CABLE WITH TIME-DEPENDENT LENGTH. Journal of Sound and Vibration, 1998, 209(2): 223-249.
[37] M. Stylianou and B. Tabarrok. Finite element analysis of an axially moving beam, Part I: Time integration. Journal of Sound and Vibration, 1994, 178(4): 433-453.
[38]路英杰,任革学.刚体动力学方程的一个辛积分方法.应用数学与力学, 2006, 27(1): 47-52.
[39]殷翔,董正筑,王继燕. ADAMS和Matlab交互仿真的机械臂定位控制.长春工业大学学报, 2005, 26(4): 332-334.
[40]杨英,刘刚,赵广耀.基于ADAMS机械模型的车辆主动悬架控制策略与仿真.东北大学学报, 2006, 27(1): 72-75.
[41]王立权,王晓东,陈德望,魏洪兴,孟庆鑫.基于虚拟样机的控制系统仿真研究.哈尔滨工程大学学报, 2000, 21(6): 26-29
[42] E.F. Fichter. Stewart platform-based manipulator: general theory and practical construction. Int. J. Robot. Res., 1986, 5(2): 157-182.
[43] G. Lbret, K. Liu, F.L. Lewis. Dynamic analysis and control of a Stewart platform manipulator. J. Robot. Syst., 1993, 10(5): 629-655.
[44] D. Li, S.E. Salcudean. Modeling, simulation, and control of a hydraulic Stewart platform. Proc. 1997 IEEE Int. Conf. Robotics and Automation, 1997, 4: 3360-3366.
[45] Z. Geng, L.S. Haynes. Six degree-of-freedom active vibration isolation using Stewart platform manipulator. J. Robot. Syst., 1993, 10(5): 725-744.
[46] R. Graf, R. Dillmann. Active acceleration compensation using a Stewart platform on a mobile robot. Proc. Euromicro Workshop on Advanced Mobile Robots (EUROBOT), 1997: 59-64.
[47] S. Tadokoro, et al. A motion base with 6-DOF by parallel cable drive architecture. IEEE ASME Transactions on Mechatronics, 2002, 7(2):115-123.
[48] S. Tadokoro, et al. On Fundamental Design of Wire Configurations of Wire-Driven Parallel Manipulators with Redundancy. Proc. Japan-USA Symposium on Flexible Automation, 1996, 1: 151-158.
[49] A.B. Alp, S.K. Agrawal. Cable suspended robots: design, planning and control. Proceedings-IEEE International Conference on Robotics and Automation, 2002, 4: 4275-4280.
[50] N.G. Dagalakis, J.S. Albus, B.L. Wang, J. Unger, J.D. Lee. Stiffness Study of a Parallel Link Robot Crane for Shipbuilding Applications. ASME J. on Offshore Mechanics and Arctic Eng., 1991, 183-193.
[51] A. Ming, T. Higuchi. Study on Multiple Degree-of-freedom Positioning Mechanism Using Wires. Int. Journal of the Japanese Society for Precision Engineering, 1994, 28: 131-138, 235-242.
[52] G.X. Ren, et al. On vibration control with Stewart parallel mechanism. Mechatronics, 2004, 14: 1-13.
[53] Y. Cheng, G.X. Ren, S.L. Dai. Vibration Control of Gough-Stewart Platform on Flexible Suspension. IEEE transactions on robotics and automation, 2003, 19(3): 489-493.
[54] H.A. Buchholdt. Introduction to Cable Roof Structures. U.K.: Cambridge University Press, 1985.
[55]埃米尔.希缪.风对结构的作用——风工程导论.同济大学出版社, 1992.
[56]骆亚波,测量机器人在FAST馈源动态跟踪测量中的应用[硕士学位论文].解放军信息工程大学, 2003.
[57] R.A. Singer. Estimating optimal tracking filter performance for manned maneuvering targets. IEEE Trans. Aerospace and Electronic Systems, 1970, 6 (4): 473-483.
[58] J. Levine, R. Marino. Constant-Speed target tracking via bearings-only measurements. IEEE Trans. Aerospace and Electronic Systems, 1992, 28(1): 174-182.
[59] H.N. Li, Z.M. Zhu, J.S. Li. Tracking and navigating filter for maneuvering target. Chinese space science and technology, 2003, 3: 13-18.
[60] L.P. Xu. An adaptive filter algorithm for tracking the maneuvering target. Journal of Xidian university, 1998, 25(3): 314-317.
[61] R.X. Li, V.P. Jilkov. Survey of maneuvering target tracking. Part I : dynamic models. IEEE Trans. Aerospace and Electronic Systems, 2003, 39(4): 1333-1363.
[62]保宏,段宝岩,陈光达.具有慢速时滞机动目标三维跟踪.控制理论与应用, 2006, 23(4): 526-530