基于定量反馈理论的飞行模拟器运动平台控制系统研究
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摘要
飞行模拟器是在地面上模拟飞机在空中飞行和在地面上运动的一种仿真设备。与用真实飞机训练驾驶员、进行飞行试验相比,这种设备具有安全性、经济性和无污染性等特点。在飞行模拟器各个组成部分中,六自由度运动系统占有极其重要的作用,它在计算机实时控制下可以提供六个自由度的瞬时过载动感。因此运动模拟系统性能优劣直接关系到飞行模拟逼真度,而飞行模拟系统控制策略的研究是提高飞行模拟器运动性能的关键技术之一。因此深入研究飞行模拟系统控制策略,设计出合理的控制器具有极其重要的意义。
在查阅国内外大量相关文献基础上,本文首先综述了国内外飞行模拟器的现状和发展趋势,总结了飞行模拟器六自由度运动系统特点和各项关键技术的研究现状。同时对六自由度运动平台在其他领域的应用做了简要介绍。
本文采用矩阵和向量分析方法,对六自由度运动平台运动学特性进行了研究。综合运用牛顿—欧拉方法、拉格朗日法对运动平台受力情况进行了详细分析。采用达郎贝尔原理和等效力法建立了运动系统上平台力平衡方程,采用凯恩方法建立了运动平台任务工作空间动力学方程。建立了运动平台关节工作空间动力学方程,对通道间交联耦合进行了分类。建立了通道间加速度交联耦合评价指标,对飞行模拟试验样机通道间加速度交联耦合进行了定量分析,为运动平台结构设计和通道间交联耦合评价提供了一种较好的借鉴依据。
建立了六自由度运动系统单通道数学模型,分析了模型参数对系统性能的影响。建立了单通道状态空间闭环数学模型和随机典范状态空间灰箱辨识模型,定义了模型参数辨识准则函数,建立了准则函数雅克比矩阵和梯度矩阵的数学模型。
本文设计了一种三维互不相关系统辨识激励信号发生器,对运动平台进行了闭环辨识试验。基于采集到的试验输入、输出数据对序列,采用基于LM准则函数寻优算法的预测误差法对各通道进行了模型参数辨识。在相同输入信号作用下,将状态空间辨识模型输出和实际系统输出进行了比较,比较结果说明两者的拟合率高达70%以上,从而证明了模型参数辨识值的合理性。
本文依据飞行模拟器对其运动模拟系统运动性能的要求,对飞行模拟试验样机电控部分进行了改造。同时采用VC++语言结合RTX实时扩展系统设计了飞行模拟控制软件。依据飞行模拟试验样机控制系统设计指标要求,结合单通道辨识模型,利用定量反馈理论设计了一种二自由度QFT鲁棒控制器。按照控制系统设计指标要求,对六自由度运动系统进行了仿真和试验研究。研究结果表明,二自由度QFT鲁棒控制器能够较好地补偿液压动力机构非对称性对系统性能的影响,具有很强的抑制通道间负载交联耦合的能力,对参数时变性和未建模动态特性具有强鲁棒性,满足了规定的设计指标要求。研究结果同时证明,本文设计的试验样机电控系统和控制软件是成功的,阐述的理论和观点是正确的,设计的模型辨识算法和控制器是合理可行的。
Flight simulator is a kind of emulation vehicle that can simulate aircraft flying in the sky and moving on the ground. Comparing with training driver by using real airplane and flying experiment, flight simulator has an advantage in security, indestructibility, and non-pollution. Six-freedom motion system plays an important role in all composing parts of flight simulator, and it is actually a six-freedom instantaneous overload-simulating vehicle which is controlled real time by computer. So the performances of motion simulating system directly relate with fidelity of flight simulating, and the research of flight simulating system about control strategy is one of the key technologies of improving motion performance of flying simulator. Therefore, research for control strategies of flying simulating system and designing reasonable controller have the very important meaning.
After synthesizing numerous related literatures and reference materials at home and abroad, the outline and current trend of domestic and oversea flight simulator is summarized in this paper, and characteristics, state-of-the-art of all kind of key issues of flying simulator 6-DOF moving simulation system is summarized. At the same time applications of six-freedom motion platform in other fields is introduced briefly.
In this paper, kinematics characteristics of 6-DOF motion platform are studied by using analysis method of matrix and vector. Detailed analysis of forces received by motion platform is done by using Newton-Euler and Lagrange methods synthetically. Force equilibrium equations of motion system upper platform are built based on d’Alembert Principle and reduction method, and a task-workspace dynamic equation of motion platform is established by using Kane method. A joint-workspace dynamic equation is established,and the coupling between channels is classified. The acceleration coupling between channels evaluating index are built, based on which the acceleration coupling between channels of flight simulation test prototype is analyzed quantitatively, and which provide with a better basis for design of motion platform structure and evaluation of coupling between channels.
In this paper, the mathematical model of single channel of 6-DOF motion system is established, and the influence of model parameters upon the system performance is analyzed. The single channel state space closed-loop mathematical model and general stochastic state space grey-box identification model are set up, and the criterion function for model parameters identification is defined, and the mathematical models for Jacobian matrix and gradient matrix of the criterion function are established.
A kind of three-dimensional mutually non-correlative exciting signals generator is designed, and the closed-loop identification experiment of motion platform is done. The model parameters are identified by using predicted-error method, which is based on the LM algorithm used for the criterion function optimization. The state space identification model outputs are compared with the real system outputs under the effect of the same input signal, and the comparison results show that the close ratio is over 70%, which proves that the model parameters identified in this paper are reasonable.
In accordance with flight simulator’s demand of motion simulation system motion performance, the electro-control part of flight simulation test prototype is reconstructed in this paper. At the same time the flight simulation control software is designed by using VC++ language and RTX real time extensive system. Based on the control system designing performance index demand of the flight simulation test prototype and the single channel identification model, a kind of 2-DOF QFT robust controller is designed by using quantitative feedback theory. Simulation and experiment researches on the 6-DOF motion system are performed based on the control system designing index demand. Research results show that the 2-DOF robust controller can compensate perfectly the influence on system performance caused by asymmetrical characteristic of power mechanism, and has the very strong ability of resisting the load coupling between channels and the strong robustness for parameters time-varying characteristics and non-modeled dynamic characteristics, which satisfies all designing performance index demand prescribed before. At the same time the research results prove that the electro-control system and control software of the test prototype designed in this paper are successful, and the theories and views set forth are right, and the model identification algorithm and the controller designed are reasonable and feasible.
在查阅国内外大量相关文献基础上,本文首先综述了国内外飞行模拟器的现状和发展趋势,总结了飞行模拟器六自由度运动系统特点和各项关键技术的研究现状。同时对六自由度运动平台在其他领域的应用做了简要介绍。
本文采用矩阵和向量分析方法,对六自由度运动平台运动学特性进行了研究。综合运用牛顿—欧拉方法、拉格朗日法对运动平台受力情况进行了详细分析。采用达郎贝尔原理和等效力法建立了运动系统上平台力平衡方程,采用凯恩方法建立了运动平台任务工作空间动力学方程。建立了运动平台关节工作空间动力学方程,对通道间交联耦合进行了分类。建立了通道间加速度交联耦合评价指标,对飞行模拟试验样机通道间加速度交联耦合进行了定量分析,为运动平台结构设计和通道间交联耦合评价提供了一种较好的借鉴依据。
建立了六自由度运动系统单通道数学模型,分析了模型参数对系统性能的影响。建立了单通道状态空间闭环数学模型和随机典范状态空间灰箱辨识模型,定义了模型参数辨识准则函数,建立了准则函数雅克比矩阵和梯度矩阵的数学模型。
本文设计了一种三维互不相关系统辨识激励信号发生器,对运动平台进行了闭环辨识试验。基于采集到的试验输入、输出数据对序列,采用基于LM准则函数寻优算法的预测误差法对各通道进行了模型参数辨识。在相同输入信号作用下,将状态空间辨识模型输出和实际系统输出进行了比较,比较结果说明两者的拟合率高达70%以上,从而证明了模型参数辨识值的合理性。
本文依据飞行模拟器对其运动模拟系统运动性能的要求,对飞行模拟试验样机电控部分进行了改造。同时采用VC++语言结合RTX实时扩展系统设计了飞行模拟控制软件。依据飞行模拟试验样机控制系统设计指标要求,结合单通道辨识模型,利用定量反馈理论设计了一种二自由度QFT鲁棒控制器。按照控制系统设计指标要求,对六自由度运动系统进行了仿真和试验研究。研究结果表明,二自由度QFT鲁棒控制器能够较好地补偿液压动力机构非对称性对系统性能的影响,具有很强的抑制通道间负载交联耦合的能力,对参数时变性和未建模动态特性具有强鲁棒性,满足了规定的设计指标要求。研究结果同时证明,本文设计的试验样机电控系统和控制软件是成功的,阐述的理论和观点是正确的,设计的模型辨识算法和控制器是合理可行的。
Flight simulator is a kind of emulation vehicle that can simulate aircraft flying in the sky and moving on the ground. Comparing with training driver by using real airplane and flying experiment, flight simulator has an advantage in security, indestructibility, and non-pollution. Six-freedom motion system plays an important role in all composing parts of flight simulator, and it is actually a six-freedom instantaneous overload-simulating vehicle which is controlled real time by computer. So the performances of motion simulating system directly relate with fidelity of flight simulating, and the research of flight simulating system about control strategy is one of the key technologies of improving motion performance of flying simulator. Therefore, research for control strategies of flying simulating system and designing reasonable controller have the very important meaning.
After synthesizing numerous related literatures and reference materials at home and abroad, the outline and current trend of domestic and oversea flight simulator is summarized in this paper, and characteristics, state-of-the-art of all kind of key issues of flying simulator 6-DOF moving simulation system is summarized. At the same time applications of six-freedom motion platform in other fields is introduced briefly.
In this paper, kinematics characteristics of 6-DOF motion platform are studied by using analysis method of matrix and vector. Detailed analysis of forces received by motion platform is done by using Newton-Euler and Lagrange methods synthetically. Force equilibrium equations of motion system upper platform are built based on d’Alembert Principle and reduction method, and a task-workspace dynamic equation of motion platform is established by using Kane method. A joint-workspace dynamic equation is established,and the coupling between channels is classified. The acceleration coupling between channels evaluating index are built, based on which the acceleration coupling between channels of flight simulation test prototype is analyzed quantitatively, and which provide with a better basis for design of motion platform structure and evaluation of coupling between channels.
In this paper, the mathematical model of single channel of 6-DOF motion system is established, and the influence of model parameters upon the system performance is analyzed. The single channel state space closed-loop mathematical model and general stochastic state space grey-box identification model are set up, and the criterion function for model parameters identification is defined, and the mathematical models for Jacobian matrix and gradient matrix of the criterion function are established.
A kind of three-dimensional mutually non-correlative exciting signals generator is designed, and the closed-loop identification experiment of motion platform is done. The model parameters are identified by using predicted-error method, which is based on the LM algorithm used for the criterion function optimization. The state space identification model outputs are compared with the real system outputs under the effect of the same input signal, and the comparison results show that the close ratio is over 70%, which proves that the model parameters identified in this paper are reasonable.
In accordance with flight simulator’s demand of motion simulation system motion performance, the electro-control part of flight simulation test prototype is reconstructed in this paper. At the same time the flight simulation control software is designed by using VC++ language and RTX real time extensive system. Based on the control system designing performance index demand of the flight simulation test prototype and the single channel identification model, a kind of 2-DOF QFT robust controller is designed by using quantitative feedback theory. Simulation and experiment researches on the 6-DOF motion system are performed based on the control system designing index demand. Research results show that the 2-DOF robust controller can compensate perfectly the influence on system performance caused by asymmetrical characteristic of power mechanism, and has the very strong ability of resisting the load coupling between channels and the strong robustness for parameters time-varying characteristics and non-modeled dynamic characteristics, which satisfies all designing performance index demand prescribed before. At the same time the research results prove that the electro-control system and control software of the test prototype designed in this paper are successful, and the theories and views set forth are right, and the model identification algorithm and the controller designed are reasonable and feasible.
引文
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68 S. H. Lee, J. B. Song, W. C. Choi and D. Hong. Controller Design for a Stewart Platform Using Small Workspace Characteristics. Proceedings of the 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. 2001:2184~2189
69 Jauasuriya S., Hwang C. N. Tracking controllers for robot manipulator: ahigh gain perspective. ASME Journal of Dynamics Systems, Measurement and Control. 1998,(110):39~45
70 高为炳. 变结构控制的理论及设计方法. 科学出版社. 1996:31~32
71 Ki Sung You and Min Cheol Lee. Sliding Mode Controller with Sliding Perturbation Observer Based on Gain Optimization Using Genetic Algorithm. Proceeding of the 2004 American Control Conference, Boston, Massachusetts, 2004:1958~1963
72 S. Iqbal and A. I. Bhatti. Direct Sliding-Mode Controller Design for a 6-DOF Stewart Manipulator. Multitopic Conference, 2006. INMIC’06.IEEE. Dec. 2006:421~426
73 N. Kim, and C. W. Lee. High speed tracking control of Stewart platform manipulator via enhanced sliding mode control. Proceeding of the IEEE International Conference on Robotics & Automation, 1998:2716~2721
74 C. I. Huang and L. C. Fu. Smooth Sliding Mode Tracking Control of the Stewart Platform. Proceeding of the 2005 IEEE Conference on Control Applications, Toronto, Canada, 2005:43~48
75 C. I. Huang, C. F. Chang, M. Y. Yu and L. C. Fu. Sliding-mode Tracking of the Stewart Platform. 5th Asian Control Conference. 2004:561~568
76 Denis Garagic and Krishnaswamy Srinivasan. Contouring Control of Stewart Platform Based Machine Tools. Proceeding of the 2004 American Control Conference, Boston, Massachusetts, 2004:3831~3838
77 Dong Hwan Kim, J. Y. Kang and K. l. Lee. Robust Tracking Control Design for a 6 DOF Parallel Manipulator. Journal of Robotics System. 2000,17(10) :527-547
78 王栋梁. 六自由度平台阀控缸驱动系统分析及控制策略研究. 哈尔滨工业大学博士学位论文. 2004: 22~39
79 M. A. Nahon , L. D. Reid. Simulator Motion-Drive Algorithms: A Designer’s Perspective. Journal of Guidance, Control and Dynamics. 1990, 13(2):356~362
80 Peter R. Grant,L. D. Reid. Motion Washout Fliter Tuning: Rules and Requirements. Journal of Aircraft. 1997, 34(2):145~151
81 张晋. 飞行模拟器的洗出算法研究. 哈尔滨工业大学硕士学位论文. 2005: 18~38
82 Dan Ariel, Rapheal Sivan. False Cue Reduction in Moving Flight Simulators. IEEE Transaction on System, Man and Cybernetics. 1984, 14(4): 665~671
83 Robert J.Telban. New Human-centered Linear and Nonlinear Motion Cueing Algorithms for Control of Simulator Motion Systems. PhD thesis, Binghamton University. 2003:1~95
84 Raphael Sivan, Jehuda I. S. An Optimal Control Approach to the Design of Moving Flight Simulators. IEEE Transaction on System, Man and Cybernetics. 1982, 12(6):818~827
85 郭政宏. 空间迷向机动感法则之设计与模拟验证. 台湾逢甲大学硕士学位论文. 1992:38~50
86 S. C. Wang, L. C. Fu. Predictive Washout Filter Design for VR-based Motion Simulator. 2004 IEEE International Conference on Systems, Man and Cybernetics. 2004:6291~6295
87 Robert J. Telban,Frank M. Cardullo. A Nonlinear, Human-Centered Approach to Motion Cueing with a Neurocomputing Solver. AIAA-2002-46922
88 陈安平. 三自由度运动平台系统建模与分析. 哈尔滨工业大学硕士学位论文. 2005: 6~7
89 Drosdol J and Panik F. The Daimler-Benz Driving Simulator, A Tool For Vehicle Development. SAE Technical Paper Series, 1985, No:850334
90 Hein Matzewitzki, Andreas Mühlenbruch. 奔驰汽车公司行驶模拟试验台-汽车发展的工具. 力士乐信息季刊, 1995(1):2~6
91 J. C. Shin and C. W. Lee. Rider’s Net Moment Estimation Using Control Force of Motion System for Bicycle Simulator. Journal of Robotic System. 2004, 21(11):597~607
92 K. Harib, K. Srinivasan. Kinematic and Dynamic Analysis of Stewart Platform –Based Machine Tool Structures. Journal of Robotica. 2003, 21(5):541~554
93 K. H. Harib, A. M. M. Sharif Ullah and A. Hammami. A Hexapod-based Machine Tool with Hybrid Structure: Kinematic Analysis and Trajectory Planning. International Journal of Machine Tools and Manufacture. 2007, 47(9):1426~1432
94 D. Hong, S. Kim and W. C. Choi, etc. Analysis of Machining Stability for a Parallel Machine Tool. Mechanics Based Design of Structures and Machines. 2003, 31(4):509~528
95 Anh X. H. Dang, Ebert Uphoff Imme. Active Acceleration Compensation for Transport Vehicles Carrying Delicate Objects. IEEE Transactions on Robotics. Piscataway, NJ 08855-1331, United States, Institute of Electrical and Electronics Engineers Inc., 2004, 20(5): 830~839
96 A. Preumont, M. Horodinca, I. Romanescu. A six-axis single-stage active vibration isolator based on Stewart Platform. Journal of Sound and Vibration. 2007, 300(3):644~661
97 Jin Zhenlin, Gao Feng, Zhang Xiaohui . Design and Analysis of a Novel Isotropic Six-Component Force/Torque Sensor. Sensors and Actuators A: Physical. 2003, 109(1):17~20
98 R. Ranganath, P. Nair, T. S. Mruthyunjaya, and A. Ghosal. A Force-Torque Sensor Based on a Stewart Platform in a Near-Singular Configuration. Mechanism and Machine Theory. 2004, 39(9):971~998
99 S. Koekebakker. Model Based Control of a Flight Simulator Motion System. PhD thesis, Delft University of Technology, 2001:3~34
100 袁立鹏. 并联运动模拟平台及其液压伺服系统的研究. 哈尔滨工业大学博士学位论文. 2005: 55~59
101 Lennart Ljung. System Identification Theory for the User. 清华大学出版社. 2002:434~440
102 吴庆宪,丁勇,胡寿松. 多维逆 M 序列及其在多变量系统辨识中的应用. 数据采集与处理. 2000, 15(2):200~203
103 吴广玉,范钦义,姜复兴,汪德辉. 系统辨识与自适应控制. 哈尔滨工业大学出版社. 1984:92~93, 288~289
104 Lennart Ljung. Theory and Practice of Recursive Identification. The MIT Press. 1983:122~125
105 O. Yaniv. Quantitative Feedback Design of Linear and Nonlinear Control System. Kluwer Academic Publisher. 1999:1~6
106 I. Horowitz. Survey of Quantitative Feedback Theory(QFT). International Journal of Control. 1991, 53(2):255~291
107 J. J. D’azzo, C. H. Houpis. Linear Control System Analysis and Design(Fourth Edition). McGraw-Hill. 2002:592~803
108 Y. Chait, O. Yaniv. Multi-input/single output Computer-aided Control Design using the Quantitative Feedback Theory. International Journal of Robust and Nonlinear Control. 1993, 3:47~54
109 Navid Niksefat. Design and Experimental Evaluation of Robust Controllers for Electro-hydraulic Actuator. A Dissertation for the Doctoral Degree of the University of Manitoba. Canada. 2002:22
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65 P. Begon, F. Pierrot and P. Dauchez. Fuzzy Sliding Mode Control of a Fast Parallel Robot. IEEE International Conference on Robotics and Automation. 1995:1178~1183
66 J. A. Ball and N. Cohen. The sensitivity minimization in an H∞ norm: parameterization of all optimal solutions. Int. J. Contr. 1987, 46:785~816
67 Abdallah D. Survey of Robust Control for Rigid Robots. IEEE control systems Magazine. 1991, 11(2):24~30
68 S. H. Lee, J. B. Song, W. C. Choi and D. Hong. Controller Design for a Stewart Platform Using Small Workspace Characteristics. Proceedings of the 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. 2001:2184~2189
69 Jauasuriya S., Hwang C. N. Tracking controllers for robot manipulator: ahigh gain perspective. ASME Journal of Dynamics Systems, Measurement and Control. 1998,(110):39~45
70 高为炳. 变结构控制的理论及设计方法. 科学出版社. 1996:31~32
71 Ki Sung You and Min Cheol Lee. Sliding Mode Controller with Sliding Perturbation Observer Based on Gain Optimization Using Genetic Algorithm. Proceeding of the 2004 American Control Conference, Boston, Massachusetts, 2004:1958~1963
72 S. Iqbal and A. I. Bhatti. Direct Sliding-Mode Controller Design for a 6-DOF Stewart Manipulator. Multitopic Conference, 2006. INMIC’06.IEEE. Dec. 2006:421~426
73 N. Kim, and C. W. Lee. High speed tracking control of Stewart platform manipulator via enhanced sliding mode control. Proceeding of the IEEE International Conference on Robotics & Automation, 1998:2716~2721
74 C. I. Huang and L. C. Fu. Smooth Sliding Mode Tracking Control of the Stewart Platform. Proceeding of the 2005 IEEE Conference on Control Applications, Toronto, Canada, 2005:43~48
75 C. I. Huang, C. F. Chang, M. Y. Yu and L. C. Fu. Sliding-mode Tracking of the Stewart Platform. 5th Asian Control Conference. 2004:561~568
76 Denis Garagic and Krishnaswamy Srinivasan. Contouring Control of Stewart Platform Based Machine Tools. Proceeding of the 2004 American Control Conference, Boston, Massachusetts, 2004:3831~3838
77 Dong Hwan Kim, J. Y. Kang and K. l. Lee. Robust Tracking Control Design for a 6 DOF Parallel Manipulator. Journal of Robotics System. 2000,17(10) :527-547
78 王栋梁. 六自由度平台阀控缸驱动系统分析及控制策略研究. 哈尔滨工业大学博士学位论文. 2004: 22~39
79 M. A. Nahon , L. D. Reid. Simulator Motion-Drive Algorithms: A Designer’s Perspective. Journal of Guidance, Control and Dynamics. 1990, 13(2):356~362
80 Peter R. Grant,L. D. Reid. Motion Washout Fliter Tuning: Rules and Requirements. Journal of Aircraft. 1997, 34(2):145~151
81 张晋. 飞行模拟器的洗出算法研究. 哈尔滨工业大学硕士学位论文. 2005: 18~38
82 Dan Ariel, Rapheal Sivan. False Cue Reduction in Moving Flight Simulators. IEEE Transaction on System, Man and Cybernetics. 1984, 14(4): 665~671
83 Robert J.Telban. New Human-centered Linear and Nonlinear Motion Cueing Algorithms for Control of Simulator Motion Systems. PhD thesis, Binghamton University. 2003:1~95
84 Raphael Sivan, Jehuda I. S. An Optimal Control Approach to the Design of Moving Flight Simulators. IEEE Transaction on System, Man and Cybernetics. 1982, 12(6):818~827
85 郭政宏. 空间迷向机动感法则之设计与模拟验证. 台湾逢甲大学硕士学位论文. 1992:38~50
86 S. C. Wang, L. C. Fu. Predictive Washout Filter Design for VR-based Motion Simulator. 2004 IEEE International Conference on Systems, Man and Cybernetics. 2004:6291~6295
87 Robert J. Telban,Frank M. Cardullo. A Nonlinear, Human-Centered Approach to Motion Cueing with a Neurocomputing Solver. AIAA-2002-46922
88 陈安平. 三自由度运动平台系统建模与分析. 哈尔滨工业大学硕士学位论文. 2005: 6~7
89 Drosdol J and Panik F. The Daimler-Benz Driving Simulator, A Tool For Vehicle Development. SAE Technical Paper Series, 1985, No:850334
90 Hein Matzewitzki, Andreas Mühlenbruch. 奔驰汽车公司行驶模拟试验台-汽车发展的工具. 力士乐信息季刊, 1995(1):2~6
91 J. C. Shin and C. W. Lee. Rider’s Net Moment Estimation Using Control Force of Motion System for Bicycle Simulator. Journal of Robotic System. 2004, 21(11):597~607
92 K. Harib, K. Srinivasan. Kinematic and Dynamic Analysis of Stewart Platform –Based Machine Tool Structures. Journal of Robotica. 2003, 21(5):541~554
93 K. H. Harib, A. M. M. Sharif Ullah and A. Hammami. A Hexapod-based Machine Tool with Hybrid Structure: Kinematic Analysis and Trajectory Planning. International Journal of Machine Tools and Manufacture. 2007, 47(9):1426~1432
94 D. Hong, S. Kim and W. C. Choi, etc. Analysis of Machining Stability for a Parallel Machine Tool. Mechanics Based Design of Structures and Machines. 2003, 31(4):509~528
95 Anh X. H. Dang, Ebert Uphoff Imme. Active Acceleration Compensation for Transport Vehicles Carrying Delicate Objects. IEEE Transactions on Robotics. Piscataway, NJ 08855-1331, United States, Institute of Electrical and Electronics Engineers Inc., 2004, 20(5): 830~839
96 A. Preumont, M. Horodinca, I. Romanescu. A six-axis single-stage active vibration isolator based on Stewart Platform. Journal of Sound and Vibration. 2007, 300(3):644~661
97 Jin Zhenlin, Gao Feng, Zhang Xiaohui . Design and Analysis of a Novel Isotropic Six-Component Force/Torque Sensor. Sensors and Actuators A: Physical. 2003, 109(1):17~20
98 R. Ranganath, P. Nair, T. S. Mruthyunjaya, and A. Ghosal. A Force-Torque Sensor Based on a Stewart Platform in a Near-Singular Configuration. Mechanism and Machine Theory. 2004, 39(9):971~998
99 S. Koekebakker. Model Based Control of a Flight Simulator Motion System. PhD thesis, Delft University of Technology, 2001:3~34
100 袁立鹏. 并联运动模拟平台及其液压伺服系统的研究. 哈尔滨工业大学博士学位论文. 2005: 55~59
101 Lennart Ljung. System Identification Theory for the User. 清华大学出版社. 2002:434~440
102 吴庆宪,丁勇,胡寿松. 多维逆 M 序列及其在多变量系统辨识中的应用. 数据采集与处理. 2000, 15(2):200~203
103 吴广玉,范钦义,姜复兴,汪德辉. 系统辨识与自适应控制. 哈尔滨工业大学出版社. 1984:92~93, 288~289
104 Lennart Ljung. Theory and Practice of Recursive Identification. The MIT Press. 1983:122~125
105 O. Yaniv. Quantitative Feedback Design of Linear and Nonlinear Control System. Kluwer Academic Publisher. 1999:1~6
106 I. Horowitz. Survey of Quantitative Feedback Theory(QFT). International Journal of Control. 1991, 53(2):255~291
107 J. J. D’azzo, C. H. Houpis. Linear Control System Analysis and Design(Fourth Edition). McGraw-Hill. 2002:592~803
108 Y. Chait, O. Yaniv. Multi-input/single output Computer-aided Control Design using the Quantitative Feedback Theory. International Journal of Robust and Nonlinear Control. 1993, 3:47~54
109 Navid Niksefat. Design and Experimental Evaluation of Robust Controllers for Electro-hydraulic Actuator. A Dissertation for the Doctoral Degree of the University of Manitoba. Canada. 2002:22