用户名: 密码: 验证码:
欠驱动质量矩飞行器的控制设计方法研究
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
质量矩控制技术是近些年来提出的一种新型飞行器控制方式,它通过快速改变飞行器内部可移动质量块的位置来改变飞行器的质心,从而产生控制力矩以达到飞行器快速姿态响应和获得所需过载的目的。而欠驱动系统是指控制输入个数少于系统自由度个数的控制系统,它广泛存在于机器人、航空航天和交通运输等各个领域,由于控制输入的缺失使得欠驱动控制问题成为控制领域具有挑战性的研究热点之一。当质量矩飞行器内部可移动质量块的个数少于需要控制的姿态自由度个数时,该质量矩飞行器的姿态控制系统就是一种典型的欠驱动系统,研究其控制问题不但具有很强的实用价值,而且有助于促进欠驱动系统控制理论的发展。
     本文以欠驱动系统的能控度分析和控制设计作为理论研究基础,对大气层内欠驱动质量矩飞行器的特征参数优化设计方法和姿态控制设计方法进行了研究。
     对于大气层内工作的质量矩飞行器,考虑飞行器内部空间的限制,提出一种姿态控制的欠驱动配置方案,该方案采用两个沿直线导轨运动的质量块。通过推导两个质量块运动对转动惯量矩阵和气动力矩的影响,并基于拉格朗日方法建立欠驱动质量矩飞行器姿态控制系统的动力学模型。为了降低特征参数优化设计和姿态控制设计过程中的复杂性,对动力学模型进行简化处理,为后续研究奠定了基础。
     针对欠驱动系统的能控度分析问题,提出将欠驱动状态的恢复区域作为欠驱动系统能控度分析的度量指标。一方面,考虑了欠驱动系统的控制输入具有幅值限制的条件,通过研究欠驱动系统模型的级数展开形式,提出欠驱动系统时间最优能控度的分析方法。另一方面,考虑了欠驱动系统的控制输入具有能量限制的条件,通过求解欠驱动系统的能量最优控制问题,提出欠驱动系统能量最优能控度的分析方法。
     基于欠驱动系统的时间最优能控度分析及其指标,提出欠驱动质量矩飞行器特征参数的优化设计方法。将质量块位置输入有界情况下欠驱动自由度方向上姿态角的恢复区域定义为欠驱动质量矩飞行器的能控度指标,并将该能控度指标作为优化设计的目标函数,建立能控度指标与特征参数之间的函数关系。基于静稳定性分析、质量块功率限制和滚转角与俯仰角机动能力分析,提出欠驱动质量矩飞行器特征参数优化设计时需要满足的约束条件。在此基础上,提出欠驱动质量矩飞行器特征参数优化设计方法的具体步骤。仿真验证特征参数优化设计方法的有效性。
     基于欠驱动系统的无源化控制设计思想,提出欠驱动质量矩飞行器的姿态控制设计方法。通过研究欠驱动系统的无源化控制方法,设计得到在平衡点处的渐近稳定控制规律。为了保证欠驱动系统反馈控制规律的存在性,给出了选择Lyapunov函数时需要满足的匹配条件。由于该匹配条件是难于求解的非线性偏微分方程,进一步研究了匹配条件的简化和求解方法。基于无源化控制提出欠驱动质量矩飞行器姿态控制设计方法,为了满足求解匹配条件解析解过程中的假设条件,对姿态控制模型进行部分反馈线性化处理,并基于求解匹配条件得到姿态系统的无源化控制规律。仿真验证姿态控制设计方法的有效性。
     将特征参数优化方法和姿态控制设计方法应用到大气层内某型欠驱动质量矩飞行器的姿态控制设计中。通过分析欠驱动质量矩飞行器的机动方式,提出欠驱动质量矩飞行器姿态控制系统的性能指标要求,在此基础上,基于特征参数优化设计方法得到最优特征参数值。然后,基于以攻角、侧滑角和滚转角作为状态变量的数学模型,应用无源化控制方法设计姿态控制规律,使得攻角、滚转角跟踪期望的指令值,侧滑角保持在零值附近;最后,在闭环情况下仿真验证特征参数优化设计的有效性,并在考虑干扰力矩、质量块动态特性和气动参数摄动的情况下分别验证姿态控制设计的有效性。
The mass moment control technique is proposed as a new control method for space-craft in recent years, whose principle is to change the mass-center of the spacecraft bymoving the position of the masses inside the spacecraft with high-speed, so as to producemoment to obtain the fast attitude response and the required overload of the spacecraft.Underactuated systems are control systems with fewer control inputs than the numberof configuration variables, which are widely existed in robotics, aerospace vehicles, andtransportation vehicles. And the control of underactuated systems is becoming an activeand challenging field of research due to the lack of control inputs . Since the mass mo-ment spacecraft holds fewer actuators than the number of attitude freedom, the attitudecontrol systems of the mass moment spacecraft are typical underactuated systems.Thecontrol of underactuated attitude system is not only a practical but also a helpful work tothe development of control theory on underactuated systems.
     In the framework of control theory on underactuated systems , this dissertation isdevoted to special parameter optimal design and attitude control of underactuated massmoment spacecraft based on degree of controllability and control design.
     Firstly, due to the limitation of the internal space of the craft, an underactuatedconfiguration for attitude control, which holds two masses moving along linear lines, isproposed subjected to the mass moment spacecraft. The dynamical model of underac-tuated mass moment spacecraft is established by Lagrangian method, considering theimpacts to the inertia and aerodynamic torque caused by the moving of the masses. Fur-thermore, a simplified model of underactuated mass moment spacecraft is derived forreducing the complexity for design.
     Secondly, it is proposed that taking the recovery region of the underactuated statesas the index measurement, in terms of degree of controllability analysis. On one hand, atime optimal degree of controllability analysis method is derived by studying the seriesexpanding form of underactuated systems, considering the limitation of amplitude ofthe inputs. On the other, an energy optimal degree of controllability analysis method isderived by solving the energy optimal control problem due to the limitation of energyinputs.
     Thirdly, an optimization design method of special parameters is studied based on time optimal degree of controllability of the underactuated mass moment spacecraft. Thefunctional relation between the index of degree of controllability and the special param-eters is established based on the definition of index of degree of controllability for under-actuated systems, taking the recovery region of the attitude angle, which belongs to thedirection of degree of freedom that is underactuated when the position input is bounded,as the index measurement. An optimization design of special parameters is operated bytraversal in order to enhance the capability to change the attitude angel. The effectivenessof the design is proved by a simulation example.
     Furthermore, the attitude control method of underactuated spacecraft is studied, and an asymptotically stable control law is driven by passivity control method at equilibria.The matching condition is proposed to make sure that the control law is existed. Due tothe complexity of the nonlinear partial differential equations, the matching conditionis simplified and solved. The effectiveness of the control law is proved by simulationexamples.
     Lastly, on the basis of utilizing optimization and passivity method to implementthe underactuated system control design, the attitude control problem for a certain un-deractuated mass moment spacecraft in atmosphere is provided. Based on the analysisof the maneuver manner of the underactuated mass moment spacecraft, performance in-dex requirement of attitude control system is presented. The characteristic parametersoptimal design is implemented by considering restriction conditions of these parameters.The attitude controller law considering the Euler attitude angles as state variables is pre-sented to allow angles of attack and roll to track desired commands and angle of slide tostay close to zero, which satisfies the performance index requirement of attitude controlsystem. Finally, the close loop simulation shows the effectiveness of the characteristicparameters optimization and the attitude control method by considering disturbance mo-ment, the dynamics of mass displacement and atmospherical parameters perturbation,respectively.
引文
1唐伟,马强,张勇,等.带控制舵飞行器机动特性研究[J].空气动力学学报,2006, 24(1):80~84.
    2葛致磊,周军.远程地空导弹直接力/气动力复合控制技术研究[J].弹箭与制导学报, 2005, 25(2):42~44.
    3 P. K. Menon, G. D. Sweriduk, E. J. Ohlmeyer, et al. Integrated Guidance and Con-trol of Moving-mass Actuated Kinetic Warheads[J]. Journal of Guidance, Control,and Dynamics, 2004, 27(1):118~126.
    4郭庆,杨明,王松艳.三轴稳定质量矩拦截器的末制导律设计[J].系统仿真学报, 2007, 19(7):1531~1534.
    5和争春,何开锋,朱国林.机动弹头气动布局的一种新思路[J].空气动力学学报, 2008, 26(2):246~248.
    6 L. Brandies, J. Gill. Experiment Investigation of Supersonic and Hypersonic JetInteraction on Missle Configurations[J]. Journal of Spacecraft and Rockets, 1998,35(3):296~302.
    7 G. Oriolo, Y. Nakamura. Control of Mechanical Systems with Second-order Non-holonomicconstraints: Underactuated Manipulators[C]//In Proceedings of the 30thIEEE Conference on Decision and Control. Brighton: England, 1991:2398~2403.
    8 M. W. Spong. Underactuated Mechanical Systems[M]. Springer Berlin, 1998.
    9 I. Fantoni. Nonlinear Control for Underactuated Mechanical Systems[M].Springer, 2001.
    10高丙团.一类欠驱动机械系统的非线性控制研究[D].哈尔滨:哈尔滨工业大学, 2007.
    11 P. Tsiotras, J. Luo. Control of Underactuated Spacecraft with Bounded Inputs[J].Automatica, 2000, 36(8):1153~1169.
    12韩冰.欠驱动船舶非线性控制研究[D].哈尔滨:哈尔滨工程大学, 2004.
    13 M. W. Spong, P. Corke, R. Lozano. Nonlinear Control of the Reaction WheelPendulum[J]. Automatica, 2001, 37(11):1845~1851.
    14贺有智.非线性预测控制在质量矩导弹姿态控制系统设计上的应用[J].战术导弹技术, 2005, (1):47~51.
    15 T. Petsopoulos, F. J. Regan, J. Barlow. Moving Mass Roll Control Systemfor Fixed-trim Reentry Vehicle[J]. Journal of Spacecraft and Rockets, 1996,33(1):54~60.
    16 R. D. Robinett, B. Rainwater. Moving Mass Trim Control for Aeospace Vehicle[J].Journal of Guidance, Control and Dynamics, 1996, 19(5):1064~1079.
    17廖国宾,杨宇光,王丽丽.质量矩导弹的敏捷性分析[J].战术导弹技术, 2005,(1):41~46.
    18周凤岐,易彦,周军.克服旋转导弹螺旋运动的方法研究[J].战术导弹技术,2001, 22(5):77~81.
    19易彦,周凤岐.高超声速战术导弹的变质心矢量控制[J].中国科学(G辑),2003, 33(3):281~288.
    20廖国宾,万自明.两质量块质量矩控制导弹滚转速度的变化及对弹体姿态运动影响分析[J].航空兵器, 2005, (5):3~6.
    21廖国宾,于本水,杨宇光.质量矩控制技术的机理分析及方程简化研究[J].系统工程与电子技术, 2004, 26(11):1635~1639.
    22廖国宾,张晓宇,杨宇光.质量块控制自旋导弹的Lyapunov稳定性分析[J].现代防御技术, 2005, 33(3):34~38.
    23廖国宾,杨宇光,王丽丽.质量矩控制飞行器制导控制系统的仿真研究[J].战术导弹技术, 2004, (5):49~53.
    24廖国宾,罗宵.质量矩控制技术的控制力、控制力矩分析[C]//首届全国航空航天领域中力学问题学术研讨会. 2005:100~105.
    25 L. Guo-bin. Neural Networks and Adaptive Nonlinear Control of Mass MomentMissles[J]. Journal of Astronautics, 2004, 25(5):520~525.
    26毕开波,周军,周凤岐.变质心旋转弹头变结构控制研究[J].航天控制, 2006,24(3):17~20.
    27杨宇光,王丽丽,万自明,等.质量矩拦截器机动能力估算[J].现代防御技术,2004, 32(4):26~31.
    28秦莉,杨明,郭庆.基于RBF网络的质量矩导弹姿态控制[J].航空动力学报,2007, 22(7):1184~1189.
    29张晓宇,王子才.基于模糊神经网络的质量矩拦截弹动态逆控制[J].宇航学报, 2007, 28(3):551~556.
    30贺有智,李君龙.神经网络在质量矩导弹控制系统上的应用[J].系统工程与电子技术, 2005, 27(1):93~96.
    31秦莉,杨明,郭庆.遗传算法在质量矩导弹姿态控制中的应用[J].北京航空航天大学学报, 2007, 33(7):669~772.
    32郭庆,杨明,王子才.一种质量矩导弹模糊姿态控制规律的研究[J].航天控制, 2006, 24(3):7~12.
    33郭庆,杨明,王子才.质量矩导弹变质心姿态控制规律研究[J].控制与决策,2008, 23(1):19~24.
    34张晓宇,王子才.基于动态逆的质量矩拦截弹模糊滑模控制[J].哈尔滨工业大学学报, 2008, 40(5):673~677.
    35贺有智,张晓宇.模糊变结构在三滑块质量矩导弹系统上的应用[J].系统工程与电子技术, 2005, 27(2):292~294.
    36张晓宇,王子才.质量矩拦截弹的H∞鲁棒控制研究[J].哈尔滨工程大学学报, 2008, 29(1):50~55.
    37张晓宇,贺有智,王子才.基于H∞性能指标的质量矩拦截弹鲁棒控制[J].航空学报, 2007, 28(3):634~640.
    38张晓宇,王子才,高伟巍.基于ITAE准则的质量矩拦截弹鲁棒控制研究[J].系统工程与电子技术, 2007, 29(12):2101~2105.
    39 I. Kolmanovsky, N. H. McClamroch. Developments in Nonholonomic ControlProblems[J]. IEEE Control Systems Magazine, 1995, 15(6):20~36.
    40 I. Kolmanovsky, M. Reyhanoglu, N. H. McClamroch. Discontinuous FeedbackStabilization of Nonholonomic Systems in Extended Power Form[C]//In Proceed-ings of the 33th IEEE Conference on Decision and Control. Lake Buena Vista: FL,1994:3469~3474.
    41 R. M. Murray, S. Sastry. Nonholonomic Motion Planning Steering Using Sinu-soids[J]. IEEE Transactions on Automatic Control, 1993, 38(5):700~716.
    42 M. W. Spong. Partial Feedback Linearization of Underactuated Mechanical Sys-tems[C]//Proc. IEEE International Conference on Intelligent Robots and Systems.Munich: Germeny, 1994:314~321.
    43 R. Olfati-Saber. Cascade Normal Forms for Underactuated Mechanical Sys-tems[C]//In Proceedings of the 39th IEEE Conference on Decision and Control.Sydney: Australia, 2000:2162~2167.
    44 R. Olfati-Saber. Normal Forms for Underactuated Mechanical Systems with Sym-metry[J]. IEEE Transactions on Automatic Control, 2002, 47(2):305~308.
    45 H. Sussmann. A General Theorem on Local Controllability[J]. SIAM Journal oncontrol and optimization, 1987, 25(1):158~194.
    46 K. Y. Lian, L. S. Wang, L. C. Fu. Controllability of Spacecraft Systems in aCentral Gravitational Field[J]. IEEE Transactions on Automatic Control, 1994,39(12):2426~2441.
    47 V. Manikonda, P. S. Krishnaprasad. Controllability of a Class of UnderactuatedMechanical Systems with Symmetry[J]. Automatica, 2002, 38:1837~1850.
    48 K. A. Morgansen. Controllability and Trajectory Tracking for Classes of Cascade-form Second Order Nonholonomic Systems[C]//In Proceedings of the 40th IEEEConference on Decision and Control. Orlando: FL, 2001:3031~3036.
    49 H. J. Sussmann. Local Controllability and Motion Planning for some Classes ofSystems with Drift[C]//In Proceedings of the 30th IEEE Conference on Decisionand Control. Brighton: England, 1991:1110~1114.
    50 A. D. Lewis, R. M. Murray. Configuration Controllability of Simple Mechan-ical Control Systems[J]. SIAM Journal on control and optimization, 1997,35(3):766~790.
    51 J. P. Ostrowski, J. W. Burdick. Controllability Tests for Mechanical Systems withSymmetries and Constraints[J]. Journal Applied mathematics and computer sci-ence, 1997, 2(7):101~127.
    52 F. Bullo, N. E. Leonard, A. D. Lewis. Controllability and Motion Algorithmsfor Underactuated Lagrangian Systems on Lie Groups[J]. IEEE Transactionson Automatic control. Issue on mechanics nonlinear control systems, 2000,45(8):1437~1454.
    53 S. D. Kelly, R. M. Murray. Geometric Phases and Robotic Locomotion[J]. Journalof Robotic systems, 1995, 12(6):417~431.
    54 R. W. Brockett. Asymptotic Stability and Feedback Stabilization[J]. DifferentialGeomentric Control Theory, 1983:181~208.
    55 C. Samson. Control of Chained System: Application to Path Following and Time-varying Point-stabilization of Mobile Robots[J]. IEEE Transactions on AutomaticControl, 1995, 40(1):64~77.
    56 J. M. Coron. Global Asymptotic Stabilization for Controllable Systems withoutDrift[J]. Mathematics of Control, Signals and Systems, 1992, 5(3):295~312.
    57 J. B. Poment. Explicit Design of Time-varying Stabilizing Control Laws for aClass of Controllable Systems without Drift[J]. Systems and Control Letters, 1992,18(2):147~158.
    58 R. M. Murray. Control of Nonholonomic Systems Using Chained Form[J]. FieldsInstitue Communications, 1993, 1:219~245.
    59 R. T. Closkey, R. M. Murray. Exponential Stabilization of Driftless Nonlinear Con-trol Systems Using Homogeneous Feedback[J]. IEEE Transactions on Automaticcontrol, 1997, 42(5):614~628.
    60 M. Aicardi, G. Casalino, A. Balestrino, et al. Closed Loop Smooth Steering ofUnicycle-like Vehicles[C]//In Proceedings of the 33th IEEE Conference on Deci-sion and Control. Lake Buena Vista: FL, 1994:2455~2458.
    61 A. Astolfi. On the Stabilization of Nonlonomic Systems[C]//In Proceedings ofthe 33th IEEE Conference on Decision and Control. Lake Buena Vista: FL,1994:3481~3486.
    62 A. Astolfi. Exponential Stabilization of Nonlonomic Systems via DiscontinuousControl[C]//Nonlinear Control Systems Design Symposium. Tahoe City: IFACPreprints, 1995:741~746.
    63 E. Badreddin, M. Mansour. Fuzzy-tuned State-feedback Control of a Nonholo-nomic Mobile Robot[C]//In Proceedings of the 12th World Congress of the Inter-national Federation of Automatic Control. Sydney: Austalia, 1993:577~580.
    64 A. Bloch, M. Reyhanoglu, N. H. McClamroch. Control and Stabilization of Non-holonomic Dynamic Systems[J]. IEEE Transactions on Automatic Control, 1992,37(11):1746~1757.
    65刘殿通.一类欠驱动机械系统的智能控制研究[D].北京:中国科学院, 2004.
    66 K. Y. Pettersen, H. Nijmeijer. Underactuated Ship Tracking Control: Theory andExperiments[J]. International Journal of Control, 2001, 74(14):1435~1446.
    67 Z. P. Jiang, H. Nijmeijer. Tracking Control of Mobile Robots: A Case Study inBackstepping[J]. Automatica, 1997, 33(7):1393~1399.
    68 K. D. Do, Z. P. Jiang. Underactuated Ship Global Tracking under Relaxed Condi-tions[J]. IEEE Transactions on Automatic control, 2002, 47(9):1529~1536.
    69 P. Tsiotras. Feasible Trajectory Generation for Underactuated Spacecraft Us-ing Differential Flatness[C]//In AAS Astrodynamic Specialists Conference. Gird-wood: AL, 1999:99~323.
    70 C. O. Aguilar. Attitude Control of a Differentially Flat Underactuated Rigid Space-craft[D]. Edmonton:University of Alberta, 2005.
    71 E. Maalouf, M. Saad, H. Saliah. A Higher Level Path Tracking Controller for aFour-wheel Differentially Steered Mobile Robot[J]. Robotics and AutonomousSystems, 2006, 54(1):23~33.
    72 K. D. Do, Z. P. Jiang, J. Pan. A Global Output-feedback Controller for Simultane-ous Tracking and Stabilization of Unicycle-type Mobile Robots[J]. IEEE Transac-tions on Automatic control, 2004, 20(3):589~594.
    73 Z. R. Xi, G. Feng, Z. P. Jiang, et al. A Switching Algorithm for Global ExponentialStabilization of Uncertain Chained Systems[J]. IEEE Transactions on AutomaticControl, 2003, 48(10):1793~1798.
    74 R. W. Brockett. Lectures on Systems, Control and Information[M]. Beijing: Pro-ceedings of the American Mathematical Society, 2000.
    75周韬,黄运平,陈万春,等.导弹质量矩控制技术建模与静态性能分析[J].宇航学报, 2006, 27(5):801~807.
    76 A. M. Bloch, N. E. Leonard, J. E. Marsden. Controlled Lagrangians and the Sta-bilization of Mechanical Systems I: The First Matching Theorem[J]. IEEE Trans-actions on Automatic Control, 2000, 45(12):2253~2270.
    77 C. A. Woolsey. Reduced Hamiltonian Dynamics for a Rigid Body/mass ParticleSystem[J]. Journal of Guidance, Control and Dynamics, 2005, 28(1):131~138.
    78易彦,周凤岐,周军.基于变质心控制导弹的运动分析[J].航天控制, 2000,(3):1~5.
    79 C. A. Woolsey. Hamiltonian Attitude Dynamics for a Spacecraft with a Point MassOscillator[C]//In Proceedings of 15th International Symposium on MathematicalTheory of Networks and Systems. 2002:203~212.
    80 M. Reyhamoglu, A. van der Scbaft, N.H.McClamroch. Dynamics and Control of aClass of Underactuated Mechanical Systems[J]. IEEE Transactions on AutomaticControl, 1999, 44(9):1663~1671.
    81 H. Nijmeijer, A. J. van der Schaft. Nonlinear Dynamical Control Systems[M].New York: Springer-Verlag, 1990.
    82 O. Egeland. Modeling and Simulation for Automatic Control[M]. Marine Cyber-netics, 2002.
    83高长生,荆武兴,李瑞康.提高变质心飞行器可操纵性的方法研究[J].宇航学报, 2008, 29(6):1773~1777.
    84 P. E. Crouch, C. I. Byrnes. Local Accesibility, Local Reachability, and Represen-tations of Compact Groups[J]. Mathematical systems theory, 1986, 19:43~65.
    85 C. N. Viswanathan, R. W. Longman, P. W. Likins. A Definition of the Degreeof Controllability-a Criterion for Actuator Placement[C]//AIAA Symposium onDynamics and Control of Flexible Spacecraft. 1979:369~384.
    86程代展.非线性系统的分析与控制[M].北京:科学出版社, 2005.
    87 F. Bullo. A Series Describing the Evolution of Mechanical Control Systems[C]//InIFAC World Conference. Beijing: China, 1999:479~485.
    88 F. Bullo. Series Expansions for the Evolution of Mechanical Control Systems[J].SIAM Journal of Control and Optimization, 2001, 40(1):166~190.
    89高长生,荆武兴,李瑞康.质量矩再入飞行器的参数优化和性能分析[J].航空学报, 2008, 29(6):1419~1423.
    90 H. Khalil. Nonlinear Systems[M]. New Jersey: Prentice Hall, Upper Saddle River,1996.
    91 A. Isodori. Nonlinear Control Systems[M]. New York: Springer-Verlag, 1995.
    92 R. Ortega, M. W. Spong. Adaptive Motion Control of Rigid Robots: A Tutorial[J].Automatica, 1989, 25(6):877~888.
    93 A. M. Bloch, N. E. Leonard, J. E. Marsden. Stabilization of Mechanical SystemsUsing Controlled Lagrangians[C]//In Proceedings of the 36th IEEE Conference onDecision and Control. San Diego: CA, 1997:2356~2361.
    94 A. M. Bloch, N. E. Leonard, J. E. Marsden. Matching and Stabilization by theMethod of Controlled Lagrangians[C]//In Proceedings of the 37th IEEE Confer-ence on Decision and Control. Tampa: FL, 1998:1446~1451.
    95 A. M. Bloch, N. E. Leonard, J. E. Marsden. Potential Shaping and the Methodof Controlled Lagrangians[C]//In Proceedings of the 38th IEEE Conference onDecision and Control. Phoenix: AR, 1999:1653~1657.
    96 A. M. Bloch, D. E. Chang, N. E. Leonard, et al. Controlled Lagrangians and theStabilization of Mechanical Systems II: Potential Shaping[J]. IEEE Transactionson Automatic Control, 2001, 46(10):1556~1571.
    97 A. M. Bloch. Nonholonomic Mechanics and Control[M]. New York: Springer-Verlag, 2003.
    98孙卫华,李高凤.移动质心再入飞行器姿态的无源性控制[J].宇航学报,2008, 29(4):131~136.
    99梅生伟.现代鲁棒控制理论与应用[M].北京:清华大学出版社, 2003.
    100 G. Blankenstein, R. Ortega, A. J. van der Schaft. The Matching Conditions ofControlled Lagrangians and IDA-passivity Based Control[J]. International Journalof Control, 2002, 75(9):645~665.
    101 F. Gomez-Estern, R. Ortega, F. R. Rubio, et al. Stabilization of a Class ofUnderactuated Mechnical Systems via Total Energy Shaping[C]//In Proceedingsof the 40th IEEE Conference on Decision and Control. Orlando,Florida: USA,2001:1137~1143.
    102 J. A. Acosta, R. Ortega, A. Astolfi, et al. Interconnection and Damping Assign-ment Passivity-based Control of Mechanical Systems with Underactuation DegreeOne[J]. IEEE Transactions on Automatic Control, 2005, 50(12):1936~1955.
    103 R. Ortega, M. W. Spong, F. Gomez-Estern. Stabilization of a Class of Underactu-ated Mechanical Systems via Interconnection and Damping Assignment[J]. IEEETransactions on Automatic Control, 2002, 47(8):1218~1233.
    104 A. M. Bloch. Open Problem in Mathematical System and Control Theory[M].New York: Springer-Verlag, 1999.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700