电液负载模拟器控制方法研究
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摘要
电液伺服系统是典型的机、电、液一体化耦合系统，具有非线性、参数不确定性、负载干扰等特性，与一般控制系统相比其控制器设计更为复杂。电液负载模拟器是被动式电液力矩伺服系统，其作用是在地面实验室条件下模拟飞行器舵面在飞行器飞行过程中所受的空气动力铰链力矩，以检测舵机技术性能指标。它不仅具有一般电液伺服系统的非线性等特性，还具有强运动干扰这一特性，因此其控制器设计难度更大。研究其先进控制方法不仅对于高精度电液负载模拟器的研制具有重要意义，而且对电液伺服系统控制方法的发展也具有指导意义，对控制理论的发展也起着推动作用。本文来源于多项工程项目，主要研究了电液负载模拟器的先进控制方法。
本文介绍了电液负载模拟器的基本结构和工作原理，建立了电液负载模拟器数学模型，分析了其静动态性能和多余力矩产生机理，揭示了系统的惯性负载、连接刚度等结构参数及被加载舵机动刚度对负载模拟器性能的影响，为负载模拟器及其控制器的设计提供了理论依据。
深入研究了实际工程中广泛应用的线性控制方案，重点分析了采用前馈补偿方法消除多余力矩的控制方法。将PID校正、串联校正、前馈补偿校正相结合，设计了负载模拟器的综合控制器。仿真和实验结果表明，本文提出的综合控制器有效提高了负载模拟器的动静态性能及载荷谱跟踪精度。
非线性、不确定性是影响系统性能进一步提高的关键因素，本文针对非匹配不确定系统，提出了两种非线性鲁棒自适应控制律。首先，将精确反馈线性化技术与GCMAC神经网络相结合，提出了一种鲁棒自适应控制律，Lyapunov稳定性分析表明闭环系统是稳定的，且具有输出渐近跟踪能力。其次，介绍了Backstepping方法的基本原理，将其与GCMAC神经网络相结合设计了自适应反演控制律，实现了对一类非匹配不确定非线性系统的渐近输出跟踪。将两种鲁棒控制方法应用于电液负载模拟器并进行了仿真研究，结果表明本文提出的两种鲁棒自适应控制律有效解决了其非线性、不确定性、强外干扰等问题。
采用LabWindows／CVI作为软件开发环境，设计了具有操作方便、界面友好、可扩展性、易维护性等优点的模块化、结构化负载模拟器通用测控软件。详细分析了负载模拟器软件的四个关键功能，给出了其设计方法和具体实现。本文设计的测控软件具有通用性，对一般计算机控制系统软件的设计具有指导作用。
Electro-hydraulic servo system is a typical couple system of mechanics and electro-hydraulic, which has the characteristic of nonlinearity, parameter uncertainties, loading disturbances and etc. Compared with generic control system, it's more complex to design the controller of electro-hydraulic servo system. Electro-hydraulic loading simulator is a passive electro-hydraulic torque servo system, which is used to simulate dynamic air power torque of the aircraft rudder under laboratory conditions, so as to detect technical performance index of the rudder driving system. It not only possesses the characteristic of the common electro-hydraulic servo system, but also has the characteristic of movement disturbance, so its controller design is more difficult. Studying its advanced control method not only is important for the development of higher performance electro-hydraulic loading simulator and electro-hydraulic servo system control method, but also promotes the development of control theory. This paper is originated from several practical projects, and mainly studies the advanced control method of electro-hydraulic loading simulator.
This paper first analyzes the basic structure and principle of the electro-hydraulic loading simulator, next establishes the linear mathematical model, then analyzes the system's static and dynamic performance, mechanism and characteristics of surplus torque, finally reveals the effect of system structure parameters (such as inertia, connect rigidity etc) and the impedance of rudder driving system for loading simulator performance. These analyses provide the theory reference for the design of loading simulator and its controller.
After deeply research on linear control strategy which widely applies in practical projects, the control method which uses feed-forward compensation to eliminate the surplus torque is analyzed detailed. Then, PID controller, cascade compensation and feed-forward compensation are combined together to design the synthetical controller of loading simulator. The simulation and experimentation results indicate that synthetical controller proposed in this paper effectively improved the static and dynamic performance of loading simulator.
Nonlinearity and uncertainties are the key factors that influence the further improvement of system performance. This paper proposes two nonlinear robust adaptive controllers for unmatched uncertainties system. Firstly, after comparison of exact feedback linearization technology with GCMAC neural network, a robust
本文介绍了电液负载模拟器的基本结构和工作原理，建立了电液负载模拟器数学模型，分析了其静动态性能和多余力矩产生机理，揭示了系统的惯性负载、连接刚度等结构参数及被加载舵机动刚度对负载模拟器性能的影响，为负载模拟器及其控制器的设计提供了理论依据。
深入研究了实际工程中广泛应用的线性控制方案，重点分析了采用前馈补偿方法消除多余力矩的控制方法。将PID校正、串联校正、前馈补偿校正相结合，设计了负载模拟器的综合控制器。仿真和实验结果表明，本文提出的综合控制器有效提高了负载模拟器的动静态性能及载荷谱跟踪精度。
非线性、不确定性是影响系统性能进一步提高的关键因素，本文针对非匹配不确定系统，提出了两种非线性鲁棒自适应控制律。首先，将精确反馈线性化技术与GCMAC神经网络相结合，提出了一种鲁棒自适应控制律，Lyapunov稳定性分析表明闭环系统是稳定的，且具有输出渐近跟踪能力。其次，介绍了Backstepping方法的基本原理，将其与GCMAC神经网络相结合设计了自适应反演控制律，实现了对一类非匹配不确定非线性系统的渐近输出跟踪。将两种鲁棒控制方法应用于电液负载模拟器并进行了仿真研究，结果表明本文提出的两种鲁棒自适应控制律有效解决了其非线性、不确定性、强外干扰等问题。
采用LabWindows／CVI作为软件开发环境，设计了具有操作方便、界面友好、可扩展性、易维护性等优点的模块化、结构化负载模拟器通用测控软件。详细分析了负载模拟器软件的四个关键功能，给出了其设计方法和具体实现。本文设计的测控软件具有通用性，对一般计算机控制系统软件的设计具有指导作用。
Electro-hydraulic servo system is a typical couple system of mechanics and electro-hydraulic, which has the characteristic of nonlinearity, parameter uncertainties, loading disturbances and etc. Compared with generic control system, it's more complex to design the controller of electro-hydraulic servo system. Electro-hydraulic loading simulator is a passive electro-hydraulic torque servo system, which is used to simulate dynamic air power torque of the aircraft rudder under laboratory conditions, so as to detect technical performance index of the rudder driving system. It not only possesses the characteristic of the common electro-hydraulic servo system, but also has the characteristic of movement disturbance, so its controller design is more difficult. Studying its advanced control method not only is important for the development of higher performance electro-hydraulic loading simulator and electro-hydraulic servo system control method, but also promotes the development of control theory. This paper is originated from several practical projects, and mainly studies the advanced control method of electro-hydraulic loading simulator.
This paper first analyzes the basic structure and principle of the electro-hydraulic loading simulator, next establishes the linear mathematical model, then analyzes the system's static and dynamic performance, mechanism and characteristics of surplus torque, finally reveals the effect of system structure parameters (such as inertia, connect rigidity etc) and the impedance of rudder driving system for loading simulator performance. These analyses provide the theory reference for the design of loading simulator and its controller.
After deeply research on linear control strategy which widely applies in practical projects, the control method which uses feed-forward compensation to eliminate the surplus torque is analyzed detailed. Then, PID controller, cascade compensation and feed-forward compensation are combined together to design the synthetical controller of loading simulator. The simulation and experimentation results indicate that synthetical controller proposed in this paper effectively improved the static and dynamic performance of loading simulator.
Nonlinearity and uncertainties are the key factors that influence the further improvement of system performance. This paper proposes two nonlinear robust adaptive controllers for unmatched uncertainties system. Firstly, after comparison of exact feedback linearization technology with GCMAC neural network, a robust
引文
[1] 王占林，近代电气液压伺服控制[M]，北京航空航天大学出版社，2005．2
[2] 华清，电液负载模拟器关键技术的研究[D]，北京航空航天大学博士论文，2001，9
[3] 常青等，电液伺服动态负载仿真系统中多余力矩的测量及抑制[J]，机床与液压，2001，(3)：16-17
[4] 焦宗夏，华清，王晓东，电液负载模拟器的复合控制[J]，机械工程学报，2002，38(12)：34-38
[5] 苏东海，刘庆和，吴盛林，电液负载仿真台多余力矩的理论分析及其克服方法的探讨[J]，机床与液压，1998，(1)：14-15
[6] 叶正茂，李洪仁，王经甫，基于CMAC的电液负载模拟器自学习控制[J]，控制与决策，2003，18(3)：343-347
[7] 王鑫，孙力，闫杰，应用复合前馈提高加载系统性能的实验研究[J]，系统仿真学报，2004，16(7)：1539-1541
[8] 于慈远，赵克定，耿春明等，飞行器负载仿真台速度反馈克服多余力矩的仿真研究[J]，哈尔滨工业大学学报，1997，29(6)：126-129
[9] 苏东海，刘庆和，吴盛林，提高电液负载仿真台控制性能的动态补偿及仿了分析[J]，中国机械工程，1999，10(1)：15-17
[10] 苏永清，岳继光，萧蕴诗，提高负载仿真台跟踪性能的方法[J]，同济大学学报，2003，31(1)：114-117
[11] 王晓东，华清，焦宗夏，负载模拟器中的摩擦力及其补偿控制[J]I中国机械工程，2003，14(6)：511-514
[12] 焦宗夏，华清，王晓东，负载模拟器的评价指标体系[J]，机械工程学报，2002，38(11)：26-29
[13] 袁朝辉，王磊，被动加载系统中的多余力矩复合补偿方法[J]，同济大学学报(自然科学版)，2004，32(5)：
[14] 李广兴，电液伺服负载模拟系统通用软件研究[D]，西北工业大学硕士学位论文，2004．3
[15] 西北工业大学508教研室，被动式加载四路的蓄压器校正方法[J]，科技资料，总第676期，1978，9：17-22
[16] 刘长年，跟踪型电液施力系统优化设计理论[J]，机床与液压，1979，(3)：24-40
[17] 刘长年，函数负载模拟器的设计与实验[J]，机床与液压，1979，(4)：11-32
[18] 王占林，近代液压控制[M]，机械工业出版社，1997．8
[19] 何长安，具有可测强外扰作用的伺服系统应用二次型最优控制和最优观测器的工程实践[J]，自动化学报，1987，11(5)：166-173
[20] 华清，焦宗夏，王晓东，电液负载模拟器的精确数学模型[J]，机械工程学报，2002， 38(11)：31-35
[21] 焦宗夏，华清，电液负载模拟器的RBF神经网络控制[J]，机械工程学报，2003，39(1)：10-14
[22] Li GQ, Cao J, Zhang B, Zhao Keding, Design of robust controller in electrohydraulic load simulator [C], 5th International Conference on Machine Learning and Cybernetics, 2006:779-784
[23] Yuan RB, Cao J, Li GQ, Zhao Keding, Torque control of electrohydraulic servo system based on mu-synthesis theory[C], 1st International Symposium on Systems and Conrol in Aerospace and Astronautics, 2006:1175-1179
[24] Yuan RB, Zhao Keding, Cao J, Torque control of electrohydraulic servo system based on robust control theory [C], 3rd International Symposium on Instrumentation Science and Technology, 2006:1027-1033
[25] 李运华，近代电液伺服系统中某些非线性控制问题的研究[D]，博士学位论文，西安交通大学，1994
[26] 何玉彬，李新忠等编著，神经网络控制技术及其应用[M]，科学出版社，2000．11
[27] 蒋志明，广义模糊CMAC神经网络控制理论及其在机电系统中的应用研究[D]，博士学位论文，西安交通大学，2000．10
[28] 沙道航，大型钢坯修磨机恒力加载系统跟随特性的研究[D]，博士学位论文，西安交通大学，1994
[29] 刘艳秋，参数自校正Fuzzy-PI控制器及其在电液伺服结构试验系统中的应用[D]，硕士学位论文，西安交通大学，1997
[30] 罗璟，赵克定，许宏光，基于H~∞鲁棒控制的电液负载模拟器的性能研究[J]，机床与液压，2006，(8)：113-116
[31] 韩俊伟，赵慧，马剑文等，具有时变柔性负载的电液力控制系统中Gain-Scheduled H~∞控制器的研究[J]，机械工程学报，2001，Vol．36，No．4，58-61
[32] Yoonsu Nam, Sung Kyung Hong, Force control system design for aerodynamic load simulator[J], Control Engineering Practice, 2002, 10:549-558
[33] 陈刚，不确定非线性系统的鲁棒自适应控制研究[D]，浙江大学博士学位论文，2006．1
[34] 李琳琳，赵光恒，赵长安，不确定非线性系统鲁棒控制研究[J]，宇航学报，2003，24(4)：331-336
[35] Wenjin Gu, Hongchao Zhao, Changpeng Pan, Sliding mode control for an aerodynamic missile based on backstepping design[J], Journal of Control Theory and AppliCations, 2005,1:71-75
[36] Freeman R A, Kokotovic P V, Backstepping Design of Robust Controllers for a Class of Nonlinear Systems[C], Proc of the IFAC Nonlinear Control Systems Design Symposium, Bordeaux: 1992, 307-312
[37] 李俊，徐德民，不确定非线性系统的多模反演滑模控制[J]，控制理论与应用，2001，18(5)：801-804
[38] J. X. Xu, J Donne, and U Ozguner, Synthesis of Feedback Linearization and Variable Structure Control with Neural Network Compensator[C], Poc. of IEEE Int. Symposium on Intelligent Contr., Arlington, VA, USA, 1991, 184-189
[39] Kanellakopoulos I, Kokotovic P, Morse A S. Systematic Design of Adaptive Controllers for Feedback Linearizable Systems[J]. IEEE Trans on AC, 1991, 36(11): 1241-1253
[40] Zhang T, Ge S, Hang C., Adaptive Neutral Network Control for Strict-feedback Nonlinear Systems Using Backstepping Design[J]. Automatica, 2000, 36(12): 1835-1846
[41] Nikifotov V O, Voronov K V., Adaptive Backstepping with a High-order Turner[J]. Automatica, 2001, 37(12): 1953-1960
[42] 张友安，胡云安，非线性系统的神经网络鲁棒自适应跟踪控制[J]，控制理论与应用，2001，18(8)：11-14
[43] 郝经佳，电液负载仿真台综合性能的研究[D]，哈尔滨工业大学博士学位论文，2001．9
[44] 王鑫，电液伺服加载台的设计与实验研究[D]，西北工业大学硕士学位论文，2003．3
[45] Jiao Zongxia, Gao Junxia, Hua Qing, The Velocity Synchronizing Control on the Electro-Hydraulic Load Simulator[J], Chinese Journal of Aeronautics, 2004, 17(1):39-46
[46] 黄琳，秦化椒，复杂控制系统理论：构想与前景[J]，自动化学报，1993，19(2)：129-137
[47] Chen Y H, Design of Robust Controllers for Uncertain Dynamical Systems[J], IEEE Trans on AC, 1988, 33(5):487-491
[48] Qu Z, A New Class of Robust Controllers for Nonlinear Uncertain Systems[C], Proc of the 31th Conference on Decision Control, Tucson, 1992:743-747
[49] Li Z H, Chai T Y, Wen C Y, Systematic Design of Robust Controllers For Nonlinear Uncertain Systems[J], Int J. Control, 1995, 62(4):871-892
[50] Tunay I, Kaynak O, A New Variable Structure Controller for A Nonlinear systems with Non-matching Uncertainties[J], Int J. Control, 1995, 62(4):917-939
[51] Liao T L, Adaptive Robust Neural Tracking Control of A Class of Unknown Nonlinear Systems[J], Int J. Systems Science, 1998, 29(7):731-741
[52] Jagannathan S, Commuri S, Lewis F L, Feedback Linearization Using CMAC Neural Networks[J], Automatica, 1998, 34(5):547-557
[53] Kanellakopoulos, L., Kokotovic, P. V., Mario R., Extended direct scheme for robust nonlinear control[J], Automatica, 1991, 27(2): 247-255
[54] Taylor, D. G., Kokotovic, P. V., Mario, R., Kanellakopoulos, I.,Adaptive regulation of nonlinear systems with unmodeled dynamics[J].IEEE Transactions on Automatic Control, 1989, 34(4):405-412
[55] Kanellakopoulos, L., Kokotovic, P. V., Mario R., Robustness of adaptive nonlinear control under an extended matching condition[C], Proceedings of the IFAC Symposium on Nonlinear Control System Design, Capri, Italy, 1989:192-197
[56] Nam, k., Arapostathis, A.A model-reference adaptive control scheme for pure-feedback nonlinear systems [J], IEEE Transactions on Automatic Control, 1988, 33:803-811
[57] Sastry, S. S., Isidori, A. Adaptive control of Linearizable systems [J].IEEE Transaction on Automatic Control, 1989, 34(11): 1123-1131
[58] Teel, A., Kadiyala, R., Kokotovic, P V, Sastry, S. S. Indirect techniques for adaptive input output linearization of nonlinear systems[J],International Journal of Control, 1991, 53(1):193-222
[59] Kanellakopoulos I, P Kokotivic, A S Morse, Systematic Design of Adaptive Controllers for Feedback Linearizable Systems[J], IEEE Trans onAC, 1991, 36(11): 1241-1253
[60] Krstic, M., Kanellakopoulos, L., Kokotovic, P. V., Adaptive nonlinear control without overpara-metrization[J], System & Control Letter, 1992, 19(2): 177-185
[61] Karsenti, L., Lamnabhi-Lagarrigue, F, Bastin, G. Backstepping technique extended to nonlinear parametrization[J], System & Control Letter, 1996, 27:87-97
[62] Hotel, R., Karsenti, L., Adaptive tracking strategy for a class of nonlinear systems [J]. IEEE Transactions on Automatic Control, 1998, 43(9): 1272-1279
[63] Kojic, A., Annaswamy, A. M., Loh, A. P,l.ozano, R Adaptive control of a class of nonlinear systems with convex/concave parameterization[J]. System & Control Letter, 1999, 37(5):267-274
[64] Kojic, A., Annaswamy, A. M. Adaptive control of nonlinearly parameterized systems with a triangular structure [J], Amomatica, 2002, 38(1): 115-123
[65] Lou Shuntian, Chen Xinhai, Zhang Xianda, Adaptive Backstepping Control Using Neural Networks[C], Proceedings of the 3rd World Congress on Intelligent Control and Automation, June 28-July2, 2000, Hefei, P.R.China
[66] Likui Yi, Jun Zhao, Adaptive Backstepping Sliding Mode Design for TCSC[C], Proceedings of the 6th World Congress on Intelligent Control and Automation, June 21-23, 2006, Dalian, China
[67] Chun-Fei Hsu, Chih-Min Lin, Tsu-Tian Lee, Wavelet Adaptive Backstepping Control for a Class of Nonlinear Systems[J], IEEE Transactions on Neural Networks, 2006, 17(5):1175-1183
[68] Yaolong Tan, Jie Chang, Hualin Tan, Adaptive Backstepping Control and Friction Compensation for AC Servo With Inertia and Load Uncertainties[J], IEEE Transactions on Industrial Electronics, 2003, 50(5):944-952
[69] 杨俊华，吴捷，胡跃明，反步方法原理及在非线性鲁棒控制中的应用[J]，控制与决策，2002，17(suppl)：64l-653
[70] Ioan Ursu, Felicia, Ursu, Florica Popescu, Backstepping design for controlling electrohydraulic servos[J], Journal of the Franklin Institute, 2005
[2] 华清，电液负载模拟器关键技术的研究[D]，北京航空航天大学博士论文，2001，9
[3] 常青等，电液伺服动态负载仿真系统中多余力矩的测量及抑制[J]，机床与液压，2001，(3)：16-17
[4] 焦宗夏，华清，王晓东，电液负载模拟器的复合控制[J]，机械工程学报，2002，38(12)：34-38
[5] 苏东海，刘庆和，吴盛林，电液负载仿真台多余力矩的理论分析及其克服方法的探讨[J]，机床与液压，1998，(1)：14-15
[6] 叶正茂，李洪仁，王经甫，基于CMAC的电液负载模拟器自学习控制[J]，控制与决策，2003，18(3)：343-347
[7] 王鑫，孙力，闫杰，应用复合前馈提高加载系统性能的实验研究[J]，系统仿真学报，2004，16(7)：1539-1541
[8] 于慈远，赵克定，耿春明等，飞行器负载仿真台速度反馈克服多余力矩的仿真研究[J]，哈尔滨工业大学学报，1997，29(6)：126-129
[9] 苏东海，刘庆和，吴盛林，提高电液负载仿真台控制性能的动态补偿及仿了分析[J]，中国机械工程，1999，10(1)：15-17
[10] 苏永清，岳继光，萧蕴诗，提高负载仿真台跟踪性能的方法[J]，同济大学学报，2003，31(1)：114-117
[11] 王晓东，华清，焦宗夏，负载模拟器中的摩擦力及其补偿控制[J]I中国机械工程，2003，14(6)：511-514
[12] 焦宗夏，华清，王晓东，负载模拟器的评价指标体系[J]，机械工程学报，2002，38(11)：26-29
[13] 袁朝辉，王磊，被动加载系统中的多余力矩复合补偿方法[J]，同济大学学报(自然科学版)，2004，32(5)：
[14] 李广兴，电液伺服负载模拟系统通用软件研究[D]，西北工业大学硕士学位论文，2004．3
[15] 西北工业大学508教研室，被动式加载四路的蓄压器校正方法[J]，科技资料，总第676期，1978，9：17-22
[16] 刘长年，跟踪型电液施力系统优化设计理论[J]，机床与液压，1979，(3)：24-40
[17] 刘长年，函数负载模拟器的设计与实验[J]，机床与液压，1979，(4)：11-32
[18] 王占林，近代液压控制[M]，机械工业出版社，1997．8
[19] 何长安，具有可测强外扰作用的伺服系统应用二次型最优控制和最优观测器的工程实践[J]，自动化学报，1987，11(5)：166-173
[20] 华清，焦宗夏，王晓东，电液负载模拟器的精确数学模型[J]，机械工程学报，2002， 38(11)：31-35
[21] 焦宗夏，华清，电液负载模拟器的RBF神经网络控制[J]，机械工程学报，2003，39(1)：10-14
[22] Li GQ, Cao J, Zhang B, Zhao Keding, Design of robust controller in electrohydraulic load simulator [C], 5th International Conference on Machine Learning and Cybernetics, 2006:779-784
[23] Yuan RB, Cao J, Li GQ, Zhao Keding, Torque control of electrohydraulic servo system based on mu-synthesis theory[C], 1st International Symposium on Systems and Conrol in Aerospace and Astronautics, 2006:1175-1179
[24] Yuan RB, Zhao Keding, Cao J, Torque control of electrohydraulic servo system based on robust control theory [C], 3rd International Symposium on Instrumentation Science and Technology, 2006:1027-1033
[25] 李运华，近代电液伺服系统中某些非线性控制问题的研究[D]，博士学位论文，西安交通大学，1994
[26] 何玉彬，李新忠等编著，神经网络控制技术及其应用[M]，科学出版社，2000．11
[27] 蒋志明，广义模糊CMAC神经网络控制理论及其在机电系统中的应用研究[D]，博士学位论文，西安交通大学，2000．10
[28] 沙道航，大型钢坯修磨机恒力加载系统跟随特性的研究[D]，博士学位论文，西安交通大学，1994
[29] 刘艳秋，参数自校正Fuzzy-PI控制器及其在电液伺服结构试验系统中的应用[D]，硕士学位论文，西安交通大学，1997
[30] 罗璟，赵克定，许宏光，基于H~∞鲁棒控制的电液负载模拟器的性能研究[J]，机床与液压，2006，(8)：113-116
[31] 韩俊伟，赵慧，马剑文等，具有时变柔性负载的电液力控制系统中Gain-Scheduled H~∞控制器的研究[J]，机械工程学报，2001，Vol．36，No．4，58-61
[32] Yoonsu Nam, Sung Kyung Hong, Force control system design for aerodynamic load simulator[J], Control Engineering Practice, 2002, 10:549-558
[33] 陈刚，不确定非线性系统的鲁棒自适应控制研究[D]，浙江大学博士学位论文，2006．1
[34] 李琳琳，赵光恒，赵长安，不确定非线性系统鲁棒控制研究[J]，宇航学报，2003，24(4)：331-336
[35] Wenjin Gu, Hongchao Zhao, Changpeng Pan, Sliding mode control for an aerodynamic missile based on backstepping design[J], Journal of Control Theory and AppliCations, 2005,1:71-75
[36] Freeman R A, Kokotovic P V, Backstepping Design of Robust Controllers for a Class of Nonlinear Systems[C], Proc of the IFAC Nonlinear Control Systems Design Symposium, Bordeaux: 1992, 307-312
[37] 李俊，徐德民，不确定非线性系统的多模反演滑模控制[J]，控制理论与应用，2001，18(5)：801-804
[38] J. X. Xu, J Donne, and U Ozguner, Synthesis of Feedback Linearization and Variable Structure Control with Neural Network Compensator[C], Poc. of IEEE Int. Symposium on Intelligent Contr., Arlington, VA, USA, 1991, 184-189
[39] Kanellakopoulos I, Kokotovic P, Morse A S. Systematic Design of Adaptive Controllers for Feedback Linearizable Systems[J]. IEEE Trans on AC, 1991, 36(11): 1241-1253
[40] Zhang T, Ge S, Hang C., Adaptive Neutral Network Control for Strict-feedback Nonlinear Systems Using Backstepping Design[J]. Automatica, 2000, 36(12): 1835-1846
[41] Nikifotov V O, Voronov K V., Adaptive Backstepping with a High-order Turner[J]. Automatica, 2001, 37(12): 1953-1960
[42] 张友安，胡云安，非线性系统的神经网络鲁棒自适应跟踪控制[J]，控制理论与应用，2001，18(8)：11-14
[43] 郝经佳，电液负载仿真台综合性能的研究[D]，哈尔滨工业大学博士学位论文，2001．9
[44] 王鑫，电液伺服加载台的设计与实验研究[D]，西北工业大学硕士学位论文，2003．3
[45] Jiao Zongxia, Gao Junxia, Hua Qing, The Velocity Synchronizing Control on the Electro-Hydraulic Load Simulator[J], Chinese Journal of Aeronautics, 2004, 17(1):39-46
[46] 黄琳，秦化椒，复杂控制系统理论：构想与前景[J]，自动化学报，1993，19(2)：129-137
[47] Chen Y H, Design of Robust Controllers for Uncertain Dynamical Systems[J], IEEE Trans on AC, 1988, 33(5):487-491
[48] Qu Z, A New Class of Robust Controllers for Nonlinear Uncertain Systems[C], Proc of the 31th Conference on Decision Control, Tucson, 1992:743-747
[49] Li Z H, Chai T Y, Wen C Y, Systematic Design of Robust Controllers For Nonlinear Uncertain Systems[J], Int J. Control, 1995, 62(4):871-892
[50] Tunay I, Kaynak O, A New Variable Structure Controller for A Nonlinear systems with Non-matching Uncertainties[J], Int J. Control, 1995, 62(4):917-939
[51] Liao T L, Adaptive Robust Neural Tracking Control of A Class of Unknown Nonlinear Systems[J], Int J. Systems Science, 1998, 29(7):731-741
[52] Jagannathan S, Commuri S, Lewis F L, Feedback Linearization Using CMAC Neural Networks[J], Automatica, 1998, 34(5):547-557
[53] Kanellakopoulos, L., Kokotovic, P. V., Mario R., Extended direct scheme for robust nonlinear control[J], Automatica, 1991, 27(2): 247-255
[54] Taylor, D. G., Kokotovic, P. V., Mario, R., Kanellakopoulos, I.,Adaptive regulation of nonlinear systems with unmodeled dynamics[J].IEEE Transactions on Automatic Control, 1989, 34(4):405-412
[55] Kanellakopoulos, L., Kokotovic, P. V., Mario R., Robustness of adaptive nonlinear control under an extended matching condition[C], Proceedings of the IFAC Symposium on Nonlinear Control System Design, Capri, Italy, 1989:192-197
[56] Nam, k., Arapostathis, A.A model-reference adaptive control scheme for pure-feedback nonlinear systems [J], IEEE Transactions on Automatic Control, 1988, 33:803-811
[57] Sastry, S. S., Isidori, A. Adaptive control of Linearizable systems [J].IEEE Transaction on Automatic Control, 1989, 34(11): 1123-1131
[58] Teel, A., Kadiyala, R., Kokotovic, P V, Sastry, S. S. Indirect techniques for adaptive input output linearization of nonlinear systems[J],International Journal of Control, 1991, 53(1):193-222
[59] Kanellakopoulos I, P Kokotivic, A S Morse, Systematic Design of Adaptive Controllers for Feedback Linearizable Systems[J], IEEE Trans onAC, 1991, 36(11): 1241-1253
[60] Krstic, M., Kanellakopoulos, L., Kokotovic, P. V., Adaptive nonlinear control without overpara-metrization[J], System & Control Letter, 1992, 19(2): 177-185
[61] Karsenti, L., Lamnabhi-Lagarrigue, F, Bastin, G. Backstepping technique extended to nonlinear parametrization[J], System & Control Letter, 1996, 27:87-97
[62] Hotel, R., Karsenti, L., Adaptive tracking strategy for a class of nonlinear systems [J]. IEEE Transactions on Automatic Control, 1998, 43(9): 1272-1279
[63] Kojic, A., Annaswamy, A. M., Loh, A. P,l.ozano, R Adaptive control of a class of nonlinear systems with convex/concave parameterization[J]. System & Control Letter, 1999, 37(5):267-274
[64] Kojic, A., Annaswamy, A. M. Adaptive control of nonlinearly parameterized systems with a triangular structure [J], Amomatica, 2002, 38(1): 115-123
[65] Lou Shuntian, Chen Xinhai, Zhang Xianda, Adaptive Backstepping Control Using Neural Networks[C], Proceedings of the 3rd World Congress on Intelligent Control and Automation, June 28-July2, 2000, Hefei, P.R.China
[66] Likui Yi, Jun Zhao, Adaptive Backstepping Sliding Mode Design for TCSC[C], Proceedings of the 6th World Congress on Intelligent Control and Automation, June 21-23, 2006, Dalian, China
[67] Chun-Fei Hsu, Chih-Min Lin, Tsu-Tian Lee, Wavelet Adaptive Backstepping Control for a Class of Nonlinear Systems[J], IEEE Transactions on Neural Networks, 2006, 17(5):1175-1183
[68] Yaolong Tan, Jie Chang, Hualin Tan, Adaptive Backstepping Control and Friction Compensation for AC Servo With Inertia and Load Uncertainties[J], IEEE Transactions on Industrial Electronics, 2003, 50(5):944-952
[69] 杨俊华，吴捷，胡跃明，反步方法原理及在非线性鲁棒控制中的应用[J]，控制与决策，2002，17(suppl)：64l-653
[70] Ioan Ursu, Felicia, Ursu, Florica Popescu, Backstepping design for controlling electrohydraulic servos[J], Journal of the Franklin Institute, 2005