刚体姿态控制驱动器失效补偿研究
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摘要
随着科学技术的发展,对刚体姿态控制问题的研究主要分为建模方法的研究以及各种控制策略的研究。目前国内外主要是在刚体三轴驱动的前提下对刚体姿态进行研究,其驱动器通常由分别控制三个主轴的喷气推力器或者动量飞轮装置组成。当刚体长时间在空间运行的时侯,由于燃料的消耗、润滑、元/器件的老化等原因,都有可能造成某一轴的驱动器卡死甚至完全的失效,这样就使得刚体的动力学性能发生改变。而这种驱动器失效有很大的不确定性,其失效方式及其哪一轴的驱动器失效都是不知道的。如果驱动器失效得不到有效的补偿,刚体的工作寿命可能终结,继而造成巨大损失。
刚体驱动器失效的补偿方法通常有两种:一种方法是从硬件设计上考虑,在每个主轴都配上冗余的备用驱动装置,这样一旦某一驱动器不能有效的工作,备用的马上投入工作。但是这种方法使得刚体的重量增大,从而会增加发射的成本。另一种方法则是用控制理论算法来进行补偿,在设计刚体的控制器时考虑到可能的某个控制器失效,采用三轴动力学耦合的特性,来达到在驱动器失效的状况下姿态控制的目的。后者无需额外进行投资,所以,研究刚体姿态驱动器失效补偿算法具有理论及其工程实践的重大意义。
本论文以非对称性刚体为控制对象,研究刚体姿态控制驱动器失效补偿策略,所完成的工作主要包括以下几个方面:
第一,通过阅读大量的文献,本文阐述了驱动器失效刚体控制系统在运动学和动力学及其系统的控制策略方面的主要研究成果及其尚未解决的问题。对刚体姿态控制系统的控制方式和控制规律进行了描述,并总结了驱动器失效刚体姿态控制的国内外研究现状,分析了现今刚体的姿态控制领域所存在的诸多问题,最后提出了本论文的研究目标。
第二,采用经典Newton-Euler方法建立了驱动器失效刚体姿态控制的动力学模型。并对描述刚体姿态的欧拉角参数法、四元数法、Rodrigues参数法及(w, z)参数化法进行了总结比较,分析其奇异性和数学特点,建立系统的数学模型。
第三,在刚体驱动器正常工作的条件下,提出了基于滑模控制方法的控制策略,给出了该控制策略的设计步骤,并应用李雅普诺夫理论进行了稳定性分析,仿真结果验证了所设计控制策略的有效性。
第四,对某一轴驱动器失效的刚体模型,采用滑模控制方法设计周期性连续时变反馈控制律,使欠驱动刚体的姿态和角速度都趋于平衡状态,进行仿真验证,结果表明所设计的控制策略满足预期要求。
第五,对某一轴驱动器失效的刚体模型,采用自适应与滑模相结合的方法,设计了滑模自适应控制律,并证明了系统的稳定性,仿真结果验证了所设计控制律的有效性。
在本文的最后,进行分析了文章中的控制方法,并进一步分析了各个控制方法的优缺点。并在此基础上,得出了本论文下一步的研究方向。
With the development of science, the research on attitude of rigid body can be divided into research on modeling and control methods. At present, study on the attitude of rigid body is mainly on three-axis drive. The actuators are made up of jet thrusters or momentum fly wheel devices. When spacecraft flying, its devices maybe braking- stuck, even failure completely due to fuel consumption or lubrication, thus make its dynamic performance change. The actuator failure has uncertainties, failure mode and which actuators are unknown. If the disabled actuator can not be compensated, the spacecraft maybe end, and case great loss.
Actuator failure compensation usually has two compensation methods. One method is hardware design, each axis is equipped with redundant backup device drivers, once a driver cannot work effectively, and the back-up immediately to work, but this method can increase the weight of the spacecraft and cost. Another method is adopted to control theory, when design controllers considering the possible actuator failure, using three axis dynamic coupling characteristics to achieve attitude control. The last method does not need additional investment. Therefore, research the actuator failure compensation algorithm has the significance on theory and engineering.
This paper uses the example of spacecraft systems to illustrate the control schemes of actuator failure systems. The content of the research includes the following:
Firstly, the main results on the kinematics, dynamic and control methods of the attitude systems were discussed on the basis of many references. Some development tendencies of control schemes were introduced. A detailed comment on the present development of the control systems is given, and the problems of the attitude control on a rigid body are analyzed.
Secondly, based on the Newton-Euler theorem, the mathematical model of rigid body is established. Four kinds of parameters for representing the attitude of a rigid body are studied. Formulas are given for changing for many kinds of parameters to the other three kinds of Parameters. The model for attitude stabilization is established.
Thirdly, in this section, we discuss an sliding control method for the attitude control of a rigid body. The control law is proposed and the convergence analysis is carried out based on Lyapunov stability theory. Simulation results are presented showing the performance of the systems.
Fourthly, when one actuator failure, designed the piecewise continuous variables and a continuous feedback control law with a periodic time-varying to achieve the attitude and angular velocity stabilization when the actuator failure. Finally, the numerical simulation results show that the method is effective.
Fifthly, with adaptive and sliding control designed the system control law, when the actuator failure. Simulation results demonstrate the practical applicability of the proposed approach.
Finally, the comparisons of several control methods are introduced which describes the advantages and deficiencies. In this paper, each control method is given stability provability and simulation example as well results respectively, the results illustrate the effectiveness of the control methods. At last, presents the main conclusions and possible avenues of further research. The advent of this paper is instrumentally and referentially significant for the attitude controller design of a rigid body.
刚体驱动器失效的补偿方法通常有两种:一种方法是从硬件设计上考虑,在每个主轴都配上冗余的备用驱动装置,这样一旦某一驱动器不能有效的工作,备用的马上投入工作。但是这种方法使得刚体的重量增大,从而会增加发射的成本。另一种方法则是用控制理论算法来进行补偿,在设计刚体的控制器时考虑到可能的某个控制器失效,采用三轴动力学耦合的特性,来达到在驱动器失效的状况下姿态控制的目的。后者无需额外进行投资,所以,研究刚体姿态驱动器失效补偿算法具有理论及其工程实践的重大意义。
本论文以非对称性刚体为控制对象,研究刚体姿态控制驱动器失效补偿策略,所完成的工作主要包括以下几个方面:
第一,通过阅读大量的文献,本文阐述了驱动器失效刚体控制系统在运动学和动力学及其系统的控制策略方面的主要研究成果及其尚未解决的问题。对刚体姿态控制系统的控制方式和控制规律进行了描述,并总结了驱动器失效刚体姿态控制的国内外研究现状,分析了现今刚体的姿态控制领域所存在的诸多问题,最后提出了本论文的研究目标。
第二,采用经典Newton-Euler方法建立了驱动器失效刚体姿态控制的动力学模型。并对描述刚体姿态的欧拉角参数法、四元数法、Rodrigues参数法及(w, z)参数化法进行了总结比较,分析其奇异性和数学特点,建立系统的数学模型。
第三,在刚体驱动器正常工作的条件下,提出了基于滑模控制方法的控制策略,给出了该控制策略的设计步骤,并应用李雅普诺夫理论进行了稳定性分析,仿真结果验证了所设计控制策略的有效性。
第四,对某一轴驱动器失效的刚体模型,采用滑模控制方法设计周期性连续时变反馈控制律,使欠驱动刚体的姿态和角速度都趋于平衡状态,进行仿真验证,结果表明所设计的控制策略满足预期要求。
第五,对某一轴驱动器失效的刚体模型,采用自适应与滑模相结合的方法,设计了滑模自适应控制律,并证明了系统的稳定性,仿真结果验证了所设计控制律的有效性。
在本文的最后,进行分析了文章中的控制方法,并进一步分析了各个控制方法的优缺点。并在此基础上,得出了本论文下一步的研究方向。
With the development of science, the research on attitude of rigid body can be divided into research on modeling and control methods. At present, study on the attitude of rigid body is mainly on three-axis drive. The actuators are made up of jet thrusters or momentum fly wheel devices. When spacecraft flying, its devices maybe braking- stuck, even failure completely due to fuel consumption or lubrication, thus make its dynamic performance change. The actuator failure has uncertainties, failure mode and which actuators are unknown. If the disabled actuator can not be compensated, the spacecraft maybe end, and case great loss.
Actuator failure compensation usually has two compensation methods. One method is hardware design, each axis is equipped with redundant backup device drivers, once a driver cannot work effectively, and the back-up immediately to work, but this method can increase the weight of the spacecraft and cost. Another method is adopted to control theory, when design controllers considering the possible actuator failure, using three axis dynamic coupling characteristics to achieve attitude control. The last method does not need additional investment. Therefore, research the actuator failure compensation algorithm has the significance on theory and engineering.
This paper uses the example of spacecraft systems to illustrate the control schemes of actuator failure systems. The content of the research includes the following:
Firstly, the main results on the kinematics, dynamic and control methods of the attitude systems were discussed on the basis of many references. Some development tendencies of control schemes were introduced. A detailed comment on the present development of the control systems is given, and the problems of the attitude control on a rigid body are analyzed.
Secondly, based on the Newton-Euler theorem, the mathematical model of rigid body is established. Four kinds of parameters for representing the attitude of a rigid body are studied. Formulas are given for changing for many kinds of parameters to the other three kinds of Parameters. The model for attitude stabilization is established.
Thirdly, in this section, we discuss an sliding control method for the attitude control of a rigid body. The control law is proposed and the convergence analysis is carried out based on Lyapunov stability theory. Simulation results are presented showing the performance of the systems.
Fourthly, when one actuator failure, designed the piecewise continuous variables and a continuous feedback control law with a periodic time-varying to achieve the attitude and angular velocity stabilization when the actuator failure. Finally, the numerical simulation results show that the method is effective.
Fifthly, with adaptive and sliding control designed the system control law, when the actuator failure. Simulation results demonstrate the practical applicability of the proposed approach.
Finally, the comparisons of several control methods are introduced which describes the advantages and deficiencies. In this paper, each control method is given stability provability and simulation example as well results respectively, the results illustrate the effectiveness of the control methods. At last, presents the main conclusions and possible avenues of further research. The advent of this paper is instrumentally and referentially significant for the attitude controller design of a rigid body.
引文
[1]Aeyels D. Stabilization by smooth feedback of the angular velocity of a rigid body[J], Systems&Control letters, 1985, 6(1):59-63.
[2]C.I.Byrnes and S.Isidori. On the attitude stabilization of a rigid spacecraft[J], 1991, 27(1): 87-95.
[3]Outbib R, and Sallet G. Stabilization of the angular velocity of a symmetric rigid body[J], Systems&Control letters, 1992, 18(2):93-98.
[4]Andriano V. Global feedback stabilization of the angular velicoty of a rigid body[J], Systems&Control letters, 1993, 20(5):361-364.
[5]Xidong Tang, Gang Tao, Suresh M. Joshi. Adaptive actuator failure compensation for nonlinear MIMO systems with anaircraft control application[J], Automatica, 2007, 43(11):1869-1883.
[6]O Egeland, JM Godhavn. Passivity based adaptive attitude control of a rigid spacecraft[J], IEEE Transactions on Automatic Control, 1994, 39(4):842-846.
[7]G. Tao, S. H. Chen, X. D. Tang, and S. M. Joshi. Adaptive control of systems with actuator failures[M], Springer, 2004.
[8]G. Tao, S. H. Chen, and S. M. Joshi. An adaptive actuator failure compensation controller using output feedback[J], IEEE Trans on Automatic Control, 2002, 47(3):506–511.
[9]G.Tao, X.D.Tang, and S.M. Joshi. Output tracking actuator failure compensation control[C], Proc of the 2001 American Control Conference, 2001,pp:1821–1826.
[10]Astolif A and Ortega R. Energy based stabilization of the angular veolcity of a rigid body operating in failure configuration[J], AIAA Journal of Guidance, Control and Dynamics, 2002, 25(1):184-187.
[11]G. Tao, S.M.Joshi and X.L.Ma. Adaptive state feedback and tracking control of systems with actuator failures[J], IEEE Transactions on Automatic Control, 2001, 46(1):78-95.
[12]Kjell. Attitude stabilization of an underactuated rigid spacecraft[D] .Siving Thesis, 2003.
[13]刘延柱,马晓敏.基于四元数的带飞轮航天器的自适应姿态控制[J].上海交通大学学报, 2003, 37(12):1957-1960.
[14]王景,刘良栋.小卫星的鲁棒自适应姿态控制[J].宇航学报, 2003, 24(3):235-239.
[15]Peter E.Crouch. Spacecraft attitude control and stabilization: applications of geometric control theory to rigid body models[J]. IEEE Transaction on automatic control, 1984, 29(4):321-331.
[16]C.I.Byrnes and S. Isidori. On the attitude stabilization of a rigid spacecraft[J]. 1991, 27(1):87-95.
[17]P.Tsiotras and V. Doumtchenko. Control of spacecraft subject to actuator failures: state of theart and open problems[J]. J.of the Astronautical Science, 2000, 48(2):337-358.
[18]G.Tao, S. H. Chen, and S. M. Joshi. An adaptive control scheme for systems with unknown actuator failures[J]. Automatica, 2002, 38(6):1027-1034.
[19]周祥龙,赵景波.欠驱动非线性控制方法综述[J].工业仪表与自动化装置, 2004, 5(1):10-13.
[20]高丙团,陈宏钧,张晓华.欠驱动机械系统控制设计综述[J].电机与控制学报, 2006, 10(5):541-546.
[21]Mcclamroch H, Kolmakosky I. A hybrid switched mode control for V/STOL flight control problems[J]. Decision and Control, 1996, 3(1):2648-2653.
[22]Huang C S, Yuan K. Output tracking of a nonlinear nonminimum phase PVTOL aircraft based on nonlinear state feedback[J]. International Journal of Control, 2002, 75(1):466-473.
[23]胡跃明.非线性控制系统理论与应用[M].北京:国防工业出版社, 2002.
[24]Olfati Saber R. Global configuration for the VTOL aircraft with strong input coupling[J]. IEEE Transactions on Automatic Control, 2002, 47(11):1949-1952.
[25]J.T.Y. Wen and K.D.Kenneth. The attitude control problem[J]. IEEE Trans. On Automatic Control, 1991, 36(10):1148-1162.
[26]J.C.Avila Vilchis, B.Brogliato, A.Dzul. Nonlinear modeling and control of helicopters[J]. Automatica, 2003, 39(1):1583-1596.
[27]Deng Mingcong, Inoue Akira, Kishida Takuya. Modeling and control of an underactuated helicopter experimental system[C]. Proceedings of the 26th Chinese Control Conference, 2007, pp:648-651.
[28]Luca A D, Sicil Iano B. Trajectory control of a nonlinear one-link flexible arm[J]. Journal of Control, 1989, 50(5):1699-1715.
[29]Olfati Saber. Trajectory tracking for a flexible one-link robot using a nonlinear noncollocated output[J]. Decision and Control, 2000, 4:4024-4029.
[30]张庆杰,朱华勇,沈林成.无人直升机欠驱动飞行控制系统设计与仿真[J].系统仿真学报, 2007, 19(18):4257-4262.
[31]Ranjan Mukherjee, Degang Chen. Control of free-flying underactuated space manipulators to equilibrium manifolds[J]. IEEE Transaction on Robotics and Automation, 1993, 9(5):561-570.
[32]Jean Michel Coron, El Yazid Kear I. Explicit feedbacks stabilizing the attitude of a rigid spacecraft with two control torques[J]. Automatica, 1996, 32(5):669-677.
[33]O.Egeland, J.M.Godhavn. Passivity based adaptive attitude control of a rigid spacecraft[J]. Automatic Control, 1994, 39(1):842-846.
[34]Panagiotis Tsiotras, Jihao Luo. Control of underactuated spacecraft with bounded inputs[J]. Automatica, 2000, 36(1):1153-1169.
[35]Bo Fang, Atul G.kelkar. On feedback linearization of underactuated nonlinear spacecraft dynamics[J]. Proceedings of the 40th IEEE Conference on Decision and Control, 2001, 4(1):3400-3405.
[36]A.Behal, D.Damon, E.Zergeroglu. Nonlinear tracking control of an underactuated spacecraft[C]. American Control Conference, 2002, 6(1):4684-4689.
[37]R.Q.Xie, Y.Yao, F.H.He. Simultaneous attitude stabilization and power tracking for a spacecraft with two VSCMGs[C]. 17th IEEE International Conference on Control Applications Part of 2008 IEEE, 2008:1121-1126.
[38]G.C.Walsh, R.Montgomery, S.S.Sastry. Orientation control of the dynamic satellite[C]. American Control Conference, 1994, 1:138-142.
[39]John-Morten Godhavn, Olav Egeland. Attitude control of an underactuated satellite[C]. Proceedings of the 34th Conference on Decision and Control, 1995:3986-3987.
[40]Nadjim Mehdi How, Stephen Hodgart. Attitude stabilization of an underactuated satellite using two wheels[C]. Aerospace Conference, 2003:2629-2635.
[41]Hashem Ashrafiuon, R.Scott Erwin. Shape change maneuvers for attitude control of underactuated satellites[J]. American Control Conference, 2005, 2:895-900.
[42]Congying Han, Alexandre N.Pechev. Underactuated satellite attitude control with two parallel CMGs [C]. 2007 IEEE International Conference on Control and Automation, 2007:666-671.
[43]Nikolaj Nordkvist, Francesco Bullo. Control algorithms along relative equilibria of underactuated lagrangian systems on Lie groups[C]. Proceedings of the 46th IEEE Conference on Decision and Control, 2007:6232-6237.
[44]刘海颖,王惠南,陈志明.基于(w,z)参数化的欠驱动微小卫星姿态再定位控制[J].动力学与控制学报, 2008, 6(1):506-511.
[45]J.T.Y.Wen and K.D.Kenneth. The attitude control problem[J]. IEEE Trans On Automatic Control, 1991, 36(10):1148-1162.
[46]李太玉.微小卫星姿态磁控制及三轴被动稳定研究[D].博士论文,国防科技大学, 2002.
[47]马骁敏,刘延柱.飞轮控制航天器的自适应姿态跟踪[J].力学季刊, 2003, 24(2):151-156.
[48]卜劭华,宋斌.航天器姿态跟踪系统的自适应滑模控制[J].控制工程, 2008, 15(1):38-41.
[49]王美仙,李明,张子军.飞行器控制规律设计方法发展综述[J].飞行力学, 2007,25(2):1906-1911.
[50]Altay.A, Tekinalp.O. Spacecraft energy storge and attitude control, Recent advances in space technologies[C], Proceedings of 2nd International Conference on. 2005, pp:201-206.
[51]Crassidis J L, Markley F L. Sliding mode control using modified rogdrigues parameters[J]. Journal of Guidance, 1996, 19(6):138-143.
[52]程代展,洪奕光,秦化淑.多输入非线性系统后推(Backstepping)[J].控制理论与应用, 1998, 15(6):824-830.
[53]P.Morin and C.Samson. Time-varying exponential stabilization of a rigid spacecraft with two control torques[J], IEEE transactions on automatic control, 1997, 42(4):528-534.
[54]Nikolaj Nordkvist, Francesco Bullo. Control algorithms along relative equilibria of underactuated Lagrangian systems on Lie groups[C]. Proceedings of the 46th IEEE Conference on Decision and Control, 2007:6232-6237.
[55]Maruthi R.Akella. Rigid body attitude tracking without angular velocity feedback[J]. Systems &Control Letters, 2000, 42(21):321-326.
[56]H Sira-Ramirez, Taw Dwyer. Variable stucture control of spacecraft reorientation maneuvers[C], Proceedings of Navigation and Control Conference. 1986.
[57]Hanspeter Schaub and John L.Junkins. Stereographic orientation parameters for attitude dynamics: a generalization of the rodrigues parameters[J]. Journal of the Astronautical Sciences, 1996, 44 (1):1-19.
[58]Maruthi R. Akella. Rigid body attitude tracking without angular velocity feedback[J]. Systems&Control Letters, 2000, 42(21): 321-326.
[59]C.A.Desor and M.Vidyasagar. Feedback systems: Input-output properties, Academic Press, New York, 1975.
[60]Wei Wang, Jianqiang Yi, Dongbin Zhao. Double layer sliding mode control for second-order underactuated mechanical systems[C]. Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Alberta, Canada, 2005, pp:3188-3193.
[61]Shuhao Chen, Gang Tao. Adaptive actuator failure compensation designs for linear systems[J], International Journal of Control, Automation and Systems, 2004, 2(1):1-14.
[62]P. Morin and C.Samson. Time-varying exponential stabilization of a rigid spacecraft with two control torques[J], IEEE transactions on automatic control, 1997, 42(4):528-534.
[63]L.Zhang. The H∞index of normal transfer function matrices[C]. Proceedings of the 1993 IEEE Region 10 Conference on Computer. 1993, pp:213-217.
[64]Gawav Bajpai, B.C. Chang, Harry.G.Kwatny. Design of fault-tolerant systems for actuator failures in nonlinear systems[C]. Proceedings of the American Control Conference, 2002,pp:3618-3623.
[65]H.Wong, M.S.Queiroz, and V. Kapila. Adaptive tracking control using synthesized velocity from attitude measurements[J]. Automatica, 2001, 37(6):947-953.
[66]Sira R H, Lanes.S.O. Adaptive dynamical sliding mode control via backstepping[C]. Proc of the 32nd IEEE Conf on Decision and Contro1, 1993, pp:1422-1427.
[67]Bolivar.M.R, Zionber.A, Sira.R.H. Dynamic adaptive sliding mode output tracking control of a class of nonlinera systems[J]. Int J of Robust and Nonlinear Control, 1997, 7(4):387-405.
[68]Lin.F.J, Chiu.S.L, Shyu.K. Novel sliding mode controller for synchronous motor drive[J]. IEEE Trans on Aerospace and Electronic Systems, 1998, 34(2):532-542.
[69]Wheeler.G, Stepanenko.Y.A. Sliding mode controller with improved adaptation laws for the upper bounds on the norm of uncertainties[J]. Automatica, 1998, 34(12):1657-1661.
[70]Bekiroglu.N, Bozma.H.I. Model reference adaptive approach to sliding mode control[C]. Proc of the 32nd IEEE Conf on Decision and Contro1, 1995, pp:1028-1032.
[71]Song.J.B, Ishida.Y.A. Robust sliding mode control for pneumatic servo systems[J]. Int J of Engineering Science, 1997, 35(8):711-723.
[2]C.I.Byrnes and S.Isidori. On the attitude stabilization of a rigid spacecraft[J], 1991, 27(1): 87-95.
[3]Outbib R, and Sallet G. Stabilization of the angular velocity of a symmetric rigid body[J], Systems&Control letters, 1992, 18(2):93-98.
[4]Andriano V. Global feedback stabilization of the angular velicoty of a rigid body[J], Systems&Control letters, 1993, 20(5):361-364.
[5]Xidong Tang, Gang Tao, Suresh M. Joshi. Adaptive actuator failure compensation for nonlinear MIMO systems with anaircraft control application[J], Automatica, 2007, 43(11):1869-1883.
[6]O Egeland, JM Godhavn. Passivity based adaptive attitude control of a rigid spacecraft[J], IEEE Transactions on Automatic Control, 1994, 39(4):842-846.
[7]G. Tao, S. H. Chen, X. D. Tang, and S. M. Joshi. Adaptive control of systems with actuator failures[M], Springer, 2004.
[8]G. Tao, S. H. Chen, and S. M. Joshi. An adaptive actuator failure compensation controller using output feedback[J], IEEE Trans on Automatic Control, 2002, 47(3):506–511.
[9]G.Tao, X.D.Tang, and S.M. Joshi. Output tracking actuator failure compensation control[C], Proc of the 2001 American Control Conference, 2001,pp:1821–1826.
[10]Astolif A and Ortega R. Energy based stabilization of the angular veolcity of a rigid body operating in failure configuration[J], AIAA Journal of Guidance, Control and Dynamics, 2002, 25(1):184-187.
[11]G. Tao, S.M.Joshi and X.L.Ma. Adaptive state feedback and tracking control of systems with actuator failures[J], IEEE Transactions on Automatic Control, 2001, 46(1):78-95.
[12]Kjell. Attitude stabilization of an underactuated rigid spacecraft[D] .Siving Thesis, 2003.
[13]刘延柱,马晓敏.基于四元数的带飞轮航天器的自适应姿态控制[J].上海交通大学学报, 2003, 37(12):1957-1960.
[14]王景,刘良栋.小卫星的鲁棒自适应姿态控制[J].宇航学报, 2003, 24(3):235-239.
[15]Peter E.Crouch. Spacecraft attitude control and stabilization: applications of geometric control theory to rigid body models[J]. IEEE Transaction on automatic control, 1984, 29(4):321-331.
[16]C.I.Byrnes and S. Isidori. On the attitude stabilization of a rigid spacecraft[J]. 1991, 27(1):87-95.
[17]P.Tsiotras and V. Doumtchenko. Control of spacecraft subject to actuator failures: state of theart and open problems[J]. J.of the Astronautical Science, 2000, 48(2):337-358.
[18]G.Tao, S. H. Chen, and S. M. Joshi. An adaptive control scheme for systems with unknown actuator failures[J]. Automatica, 2002, 38(6):1027-1034.
[19]周祥龙,赵景波.欠驱动非线性控制方法综述[J].工业仪表与自动化装置, 2004, 5(1):10-13.
[20]高丙团,陈宏钧,张晓华.欠驱动机械系统控制设计综述[J].电机与控制学报, 2006, 10(5):541-546.
[21]Mcclamroch H, Kolmakosky I. A hybrid switched mode control for V/STOL flight control problems[J]. Decision and Control, 1996, 3(1):2648-2653.
[22]Huang C S, Yuan K. Output tracking of a nonlinear nonminimum phase PVTOL aircraft based on nonlinear state feedback[J]. International Journal of Control, 2002, 75(1):466-473.
[23]胡跃明.非线性控制系统理论与应用[M].北京:国防工业出版社, 2002.
[24]Olfati Saber R. Global configuration for the VTOL aircraft with strong input coupling[J]. IEEE Transactions on Automatic Control, 2002, 47(11):1949-1952.
[25]J.T.Y. Wen and K.D.Kenneth. The attitude control problem[J]. IEEE Trans. On Automatic Control, 1991, 36(10):1148-1162.
[26]J.C.Avila Vilchis, B.Brogliato, A.Dzul. Nonlinear modeling and control of helicopters[J]. Automatica, 2003, 39(1):1583-1596.
[27]Deng Mingcong, Inoue Akira, Kishida Takuya. Modeling and control of an underactuated helicopter experimental system[C]. Proceedings of the 26th Chinese Control Conference, 2007, pp:648-651.
[28]Luca A D, Sicil Iano B. Trajectory control of a nonlinear one-link flexible arm[J]. Journal of Control, 1989, 50(5):1699-1715.
[29]Olfati Saber. Trajectory tracking for a flexible one-link robot using a nonlinear noncollocated output[J]. Decision and Control, 2000, 4:4024-4029.
[30]张庆杰,朱华勇,沈林成.无人直升机欠驱动飞行控制系统设计与仿真[J].系统仿真学报, 2007, 19(18):4257-4262.
[31]Ranjan Mukherjee, Degang Chen. Control of free-flying underactuated space manipulators to equilibrium manifolds[J]. IEEE Transaction on Robotics and Automation, 1993, 9(5):561-570.
[32]Jean Michel Coron, El Yazid Kear I. Explicit feedbacks stabilizing the attitude of a rigid spacecraft with two control torques[J]. Automatica, 1996, 32(5):669-677.
[33]O.Egeland, J.M.Godhavn. Passivity based adaptive attitude control of a rigid spacecraft[J]. Automatic Control, 1994, 39(1):842-846.
[34]Panagiotis Tsiotras, Jihao Luo. Control of underactuated spacecraft with bounded inputs[J]. Automatica, 2000, 36(1):1153-1169.
[35]Bo Fang, Atul G.kelkar. On feedback linearization of underactuated nonlinear spacecraft dynamics[J]. Proceedings of the 40th IEEE Conference on Decision and Control, 2001, 4(1):3400-3405.
[36]A.Behal, D.Damon, E.Zergeroglu. Nonlinear tracking control of an underactuated spacecraft[C]. American Control Conference, 2002, 6(1):4684-4689.
[37]R.Q.Xie, Y.Yao, F.H.He. Simultaneous attitude stabilization and power tracking for a spacecraft with two VSCMGs[C]. 17th IEEE International Conference on Control Applications Part of 2008 IEEE, 2008:1121-1126.
[38]G.C.Walsh, R.Montgomery, S.S.Sastry. Orientation control of the dynamic satellite[C]. American Control Conference, 1994, 1:138-142.
[39]John-Morten Godhavn, Olav Egeland. Attitude control of an underactuated satellite[C]. Proceedings of the 34th Conference on Decision and Control, 1995:3986-3987.
[40]Nadjim Mehdi How, Stephen Hodgart. Attitude stabilization of an underactuated satellite using two wheels[C]. Aerospace Conference, 2003:2629-2635.
[41]Hashem Ashrafiuon, R.Scott Erwin. Shape change maneuvers for attitude control of underactuated satellites[J]. American Control Conference, 2005, 2:895-900.
[42]Congying Han, Alexandre N.Pechev. Underactuated satellite attitude control with two parallel CMGs [C]. 2007 IEEE International Conference on Control and Automation, 2007:666-671.
[43]Nikolaj Nordkvist, Francesco Bullo. Control algorithms along relative equilibria of underactuated lagrangian systems on Lie groups[C]. Proceedings of the 46th IEEE Conference on Decision and Control, 2007:6232-6237.
[44]刘海颖,王惠南,陈志明.基于(w,z)参数化的欠驱动微小卫星姿态再定位控制[J].动力学与控制学报, 2008, 6(1):506-511.
[45]J.T.Y.Wen and K.D.Kenneth. The attitude control problem[J]. IEEE Trans On Automatic Control, 1991, 36(10):1148-1162.
[46]李太玉.微小卫星姿态磁控制及三轴被动稳定研究[D].博士论文,国防科技大学, 2002.
[47]马骁敏,刘延柱.飞轮控制航天器的自适应姿态跟踪[J].力学季刊, 2003, 24(2):151-156.
[48]卜劭华,宋斌.航天器姿态跟踪系统的自适应滑模控制[J].控制工程, 2008, 15(1):38-41.
[49]王美仙,李明,张子军.飞行器控制规律设计方法发展综述[J].飞行力学, 2007,25(2):1906-1911.
[50]Altay.A, Tekinalp.O. Spacecraft energy storge and attitude control, Recent advances in space technologies[C], Proceedings of 2nd International Conference on. 2005, pp:201-206.
[51]Crassidis J L, Markley F L. Sliding mode control using modified rogdrigues parameters[J]. Journal of Guidance, 1996, 19(6):138-143.
[52]程代展,洪奕光,秦化淑.多输入非线性系统后推(Backstepping)[J].控制理论与应用, 1998, 15(6):824-830.
[53]P.Morin and C.Samson. Time-varying exponential stabilization of a rigid spacecraft with two control torques[J], IEEE transactions on automatic control, 1997, 42(4):528-534.
[54]Nikolaj Nordkvist, Francesco Bullo. Control algorithms along relative equilibria of underactuated Lagrangian systems on Lie groups[C]. Proceedings of the 46th IEEE Conference on Decision and Control, 2007:6232-6237.
[55]Maruthi R.Akella. Rigid body attitude tracking without angular velocity feedback[J]. Systems &Control Letters, 2000, 42(21):321-326.
[56]H Sira-Ramirez, Taw Dwyer. Variable stucture control of spacecraft reorientation maneuvers[C], Proceedings of Navigation and Control Conference. 1986.
[57]Hanspeter Schaub and John L.Junkins. Stereographic orientation parameters for attitude dynamics: a generalization of the rodrigues parameters[J]. Journal of the Astronautical Sciences, 1996, 44 (1):1-19.
[58]Maruthi R. Akella. Rigid body attitude tracking without angular velocity feedback[J]. Systems&Control Letters, 2000, 42(21): 321-326.
[59]C.A.Desor and M.Vidyasagar. Feedback systems: Input-output properties, Academic Press, New York, 1975.
[60]Wei Wang, Jianqiang Yi, Dongbin Zhao. Double layer sliding mode control for second-order underactuated mechanical systems[C]. Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Alberta, Canada, 2005, pp:3188-3193.
[61]Shuhao Chen, Gang Tao. Adaptive actuator failure compensation designs for linear systems[J], International Journal of Control, Automation and Systems, 2004, 2(1):1-14.
[62]P. Morin and C.Samson. Time-varying exponential stabilization of a rigid spacecraft with two control torques[J], IEEE transactions on automatic control, 1997, 42(4):528-534.
[63]L.Zhang. The H∞index of normal transfer function matrices[C]. Proceedings of the 1993 IEEE Region 10 Conference on Computer. 1993, pp:213-217.
[64]Gawav Bajpai, B.C. Chang, Harry.G.Kwatny. Design of fault-tolerant systems for actuator failures in nonlinear systems[C]. Proceedings of the American Control Conference, 2002,pp:3618-3623.
[65]H.Wong, M.S.Queiroz, and V. Kapila. Adaptive tracking control using synthesized velocity from attitude measurements[J]. Automatica, 2001, 37(6):947-953.
[66]Sira R H, Lanes.S.O. Adaptive dynamical sliding mode control via backstepping[C]. Proc of the 32nd IEEE Conf on Decision and Contro1, 1993, pp:1422-1427.
[67]Bolivar.M.R, Zionber.A, Sira.R.H. Dynamic adaptive sliding mode output tracking control of a class of nonlinera systems[J]. Int J of Robust and Nonlinear Control, 1997, 7(4):387-405.
[68]Lin.F.J, Chiu.S.L, Shyu.K. Novel sliding mode controller for synchronous motor drive[J]. IEEE Trans on Aerospace and Electronic Systems, 1998, 34(2):532-542.
[69]Wheeler.G, Stepanenko.Y.A. Sliding mode controller with improved adaptation laws for the upper bounds on the norm of uncertainties[J]. Automatica, 1998, 34(12):1657-1661.
[70]Bekiroglu.N, Bozma.H.I. Model reference adaptive approach to sliding mode control[C]. Proc of the 32nd IEEE Conf on Decision and Contro1, 1995, pp:1028-1032.
[71]Song.J.B, Ishida.Y.A. Robust sliding mode control for pneumatic servo systems[J]. Int J of Engineering Science, 1997, 35(8):711-723.