大型柔性航天器动力学与振动控制研究进展
|
摘要
随着航天重大工程的逐步实施,航天器正朝着超高速、超大尺度、多功能的方向发展,其面临的发射和运行环境也更加恶劣.航天器发射过程中的振动及其主/被动控制、在轨运行中大型柔性航天器动力学建模与动态响应分析、结构振动与飞行器姿态的混合控制等问题越来越复杂且难于处理;航天器结构的大型化和柔性化(如大阵面天线和太阳翼等)也对其地面试验和半实物仿真提出了挑战.本文着重介绍大型柔性航天器涉及到的动力学与振动控制问题,包括航天器发射过程中的整星隔振,大型柔性结构动力学建模与振动响应分析,大型柔性航天器的结构振动与姿轨控耦合动力学及其混合控制等.提炼出航天动力学与控制领域中亟待解决的若干基础科学问题,包括:多刚柔体系统动力学建模与模型降阶(涉及大变形柔性体动力学建模、多求解器合作仿真、模型降阶、组合结构动力学建模的解析方法等);复杂结构状态空间模型构建方法与能控性(涉及状态空间模型构建的理论与实验方法、复杂结构振动控制系统的能观性与能控性等);航天器姿态运动与大型柔性结构振动的混合控制律设计(涉及姿态机动与结构振动的鲁棒混合控制、执行机构与压电控制器的协同控制等).
With the gradual implementation of the major projects in aerospace engineering, the spacecraft design is heading towards the direction of ultra-high speed, large scale and multi-function, and its launching and operating environmentis likely to worsen. The problems on vibration and active and/or passive control in spacecraft launching process, dynamic modeling and response analysis of large flexible spacecraft in orbit, and the hybrid control of structural vibration and attitude maneuver of the spacecraft are getting more and more complicated and difficult to deal with. The enlarged scale and increased flexibility of the spacecraft structure(such as the large aperture antenna and solar panels) present a challenge to the ground test and semi-physical simulation. The dynamics and control problems involved in the large-scale flexible spacecraft such as the whole-spacecraft vibration isolation in the spacecraft lunching process, the dynamic modeling and vibration response analysis of large-scale flexible structures, and the coupling dynamics and hybrid control of structural vibration and attitude and/or orbital maneuver of the large-scale flexible spacecraft are presented. The key scientific issues seriously in the fields of spacecraft dynamics and control could then be extracted as follows: the dynamic modeling and order reduction of multi-rigid/flexible body systems(including the dynamic modeling of the flexible structure with large deformation, the collaborate simulations with multi-solvers, model reductions, the analytical approach for the dynamic modeling of composite structures, etc.), the construction of state space model of complicated structures and its controllability investigation(including the theoretical and experiment methods of the state space model formulation, the observability and controllability of the control system for complex structures, etc.), and the design of hybrid control law of structural vibration and attitude maneuver for the large-scale flexible spacecraft(concerning the robust hybrid control of attitude maneuver and structural vibration, the collaborative control of actuating mechanism and piezoelectric actuator,etc.)
With the gradual implementation of the major projects in aerospace engineering, the spacecraft design is heading towards the direction of ultra-high speed, large scale and multi-function, and its launching and operating environmentis likely to worsen. The problems on vibration and active and/or passive control in spacecraft launching process, dynamic modeling and response analysis of large flexible spacecraft in orbit, and the hybrid control of structural vibration and attitude maneuver of the spacecraft are getting more and more complicated and difficult to deal with. The enlarged scale and increased flexibility of the spacecraft structure(such as the large aperture antenna and solar panels) present a challenge to the ground test and semi-physical simulation. The dynamics and control problems involved in the large-scale flexible spacecraft such as the whole-spacecraft vibration isolation in the spacecraft lunching process, the dynamic modeling and vibration response analysis of large-scale flexible structures, and the coupling dynamics and hybrid control of structural vibration and attitude and/or orbital maneuver of the large-scale flexible spacecraft are presented. The key scientific issues seriously in the fields of spacecraft dynamics and control could then be extracted as follows: the dynamic modeling and order reduction of multi-rigid/flexible body systems(including the dynamic modeling of the flexible structure with large deformation, the collaborate simulations with multi-solvers, model reductions, the analytical approach for the dynamic modeling of composite structures, etc.), the construction of state space model of complicated structures and its controllability investigation(including the theoretical and experiment methods of the state space model formulation, the observability and controllability of the control system for complex structures, etc.), and the design of hybrid control law of structural vibration and attitude maneuver for the large-scale flexible spacecraft(concerning the robust hybrid control of attitude maneuver and structural vibration, the collaborative control of actuating mechanism and piezoelectric actuator,etc.)
引文
1黄文虎,曹登庆,韩增尧.航天器动力学与控制的研究进展与展望.力学进展,2012,42(4):367-394(Huang Wenhu,Cao Dengqing,Han Zengyao.Advances and trends in dynamics and control of spacecraft.Advances in Mechanics,2012,42(4):367-394(in Chinese))
2孟光,周徐斌,苗军.航天重大工程中的力学问题.力学进展,2016,46(6):467-322(Meng Guang,Zhou Xubin,Miao Jun.Mechanical problems in momentous projects of aerospace engineering.Advances in Mechanics,2016,46:467-322(in Chinese))
3马兴瑞,于登云,韩增尧等.星箭力学环境分析与试验技术研究进展.宇航学报,2006,27(3):323-331(Ma Xingrui,Yu Dengyun,Han Zengyao,et al.Research evolution on the satellite-rocket mechanical environment analysis and test technology.Journal of Astronautics,2006,27(3):323-331(in Chinese))
4王庆伟,谭述君,吴志刚等.大型液体火箭姿控与跷振大回路耦合动力学建模与分析.力学学报,2015,47(5):789-798(Wang Qingwei,Tan Shujun,Wu Zhigang,et al.Dynamic modeling and analysis of large-loop coupled by attitude control and pogo for large liquid rockets.Chinese Journal of Theoretical and Applied Mechanics,2015,47(5):789-798(in Chinese))
5张军,谌勇,骆剑等.整星隔振技术的研究现状和发展.航空学报,2006,26(2):179-183(Zhang Jun,Chen Yong,Luo Jian,et al.Review of the whole-spacecraft isolation techniques.Acta Aeronauticaet Astronautica Sinica,2006,26(2):179-183(in Chinese))
6 Wilke PS,Johnson CD,Fosness ER.Whole-spacecraft passive launch isolation.Journal of Spacecraft and Rockets,1998,35(5):690-694
7 Wilke PS,Johnson CD.Recent launches using the softride wholespacecraft vibration isolation system//Proceedings of the AIAASpace 2001 Conference,Albuquerque,NM,2001:AIAA-2001-40788 Liu LK,Liang L,Zheng GT,et al.Dynamic design of octo-strut platform for launch stage whole-spacecraft vibration isolation.Journal of Spacecraft and Rockets,2005,42(4):654-662
9 Wang Z,Liu LK,Zheng GT.Optimal design of octo-strut vibration isolation platform.Journal of Guidance,Control,and Dynamics,2006,29(3):749-753
10 Zhang YW,Fang B,Chen Y.Vibration isolation performance evaluation of the discrete whole-spacecraft vibration isolation platform for flexible spacecraft.Meccanica,2012,47:1185-1195
11 Yang K,Zhang YW,Ding H,et al.Nonlinear energy sink for wholespacecraft vibration reduction.Journal of Vibration and Acoustics,2017,139:021011
12陆泽琦,陈立群.非线性被动隔振的若干进展.力学学报,2017,49(3):550-564(Lu Zeqi,Chen Liqun.Some recent progresses in nonlinear passive isolations of vibrations.Chinese Journal of Theoretical and Applied Mechanics,2017,49(3):550-564(in Chinese))
13 Thayer D,Campbell M,Vagners J.Six-axis vibration isolation system using soft actuators and multiple sensors.Journal of Spacecraft and Rockets,2002,39(2):206-212
14 Marneffe B,Avraam M,Deraemaeker A,et al.Vibration isolation of precision payloads:A six-axis electromagnetic relaxation isolator.Journal of Guidance,Control,and Dynamics,2009,32(2):395-401
15 Zhang Y,Zang J,Fang B,et al.Dynamic characteristics of integrated active and passive whole-spacecraft vibration isolation platform based on non-probabilistic reliability.Transactions of the Japan Society for Aeronautical and Space Sciences,2014,57(5):263-271
16 Yang X,Wu H,Li Y,et al.Dynamic isotropic design and decentralized active control of a six-axis vibration isolator via Stewart platform.Mechanism and Machine Theory,2017,117:244-252
17 Chi W,Cao D,Wang D,et al.Design and experimental study of a VCM-based Stewart parallel mechanism used for active vibration isolation.Energies,2015,8:8001-8019
18 Wu Y,Yu K,Jiao J,et al.Dynamic isotropy design and analysis of a six-DOF active micro-vibration isolation manipulator on satellites.Robotics and Computer-Integrated Manufacturing,2018,49:408-425
19 Tang J,Cao D,Yu T.Decentralized vibration control of a VCM-Based Stewart parallel mechanism:simulation and experiments.Journal of Mechanical Engineering Science,2018.DOI:10.1177/0954406218756941
20胡海岩,田强,张伟等.大型网架式可展开空间结构的非线性动力学与控制.力学进展,2013,43(4):390-414(Hu Haiyan,Tian Qiang,Zhang Wei,et al.Nonlinear dynamics and control of large deployable space structures composed of trusses and meshes.Advances in Mechanics,2013,43(4):390-414(in Chinese))
21曲广吉.航天器动力学技术的发展和挑战.强度与环境,2003,30(4):1-6(Qu Guangji.Development and challenge of spacecraft dynamics technology.Structure and Environment Engineering,2003,30(4):1-6(in Chinese))
22曲广吉.复合柔性结构航天器动力学建模研究.中国工程科学,1999,1(2):52-56(Qu Guangji.Dynamics modeling of spacecraft with composite flexible structures.Engineering Science,1999,1(2):52-56(in Chinese))
23缪炳祺,曲广吉,夏邃勤等.关于柔性航天器动力学模型降阶问题.中国工程科学,2001,3(11):60-64(Liao Bingqi,Qu Guangji,Xia Suiqin,et al.On the order reduction of dynamics models of flexible spacecraft.Engineering Science,2001,3(11):60-64(in Chinese))
24 Mettler E,Quadrelli MB.Multibody dynamics modeling of segmented booms of the mars express spacecraft.Journal of Spacecraft and Rockets,2005,42(3):523-529
25蒋建平,李东旭.带太阳帆板航天器刚柔耦合动力学研究.航空学报,2006,27(3):418-422(Jiang Jianping and Li Dongxu.Research on rigid-flexible coupling dynamics of spacecraft with solar panel.Acta Aeronauticaet Astronautica Sinica,2006,27(3):418-422(in Chinese))
26张越,赵阳,谭春林等.ANCF索梁单元应变耦合问题与模型解耦.力学学报,2016,48(6):1406-1415(Zhang Yue,Zhao Yang,Tan Chunlin,et al.The strain coupling problem and model decoupling of ANCF cable/beam element.Chinese Journal of Theoretical and Applied Mechanics,2016,48(6):1406-1415(in Chinese))
27章孝顺,章定国,洪嘉振.考虑曲率纵向变形效应的大变形柔性梁刚柔耦合动力学建模与仿真.力学学报,2016,48(3):692-701(Zhang Xiaoshun,Zhang Dingguo,Hong Jiazhen.Rigid-flexible coupling dynamic modeling and simulation with the longitudinal deformation induced curvature effect for a rotating flexible beam under large deformation.Chinese Journal of Theoretical and Applied Mechanics,2016,48(3):692-701(in Chinese))
29和兴锁,邓峰岩,张烈霞等.大型空间刚柔耦合组合体的动力学建模.机械科学与技术,2004,23(5):543-545(He Xingsuo,Deng Fengyan,Zhang Liexia,et al.Dynamics modeling of large coupled rigid flexible space platform system.Mechanical Science and Technology,2004,23(5):543-545(in Chinese))
29方柳,刘玉亮,赵桂平.考虑动力刚化的挠性航天器的动力学建模与分析.兵器装备工程学报,2017,38(9):67-72(Fang Niu,Liu Yuliang,Zhao Guiping.Dynamic modeling and analysis for flexible spacecraft with dynamic stiffening.Journal of Ordnance Equipment Engineering,2017,38(9):67-72(in Chinese))
30 Xu W,Meng D,Chen Y,et al.Dynamics modeling and analysis of a flexible-base space robot for capturing large flexible spacecraft.Multibody System Dynamics,2014,32(3):357-401
31郭其威,吴松,刘芳等.航天器柔性附件对整器固有振动特性影响因素及规律分析.振动与冲击,2016,35(6):187-191(Guo Qiwei,Wu Song,Liu Fang,et al.The effect and change rule of spacecraft flexible annex on system natural vibration characteristics.Journal of Vibration and Shock,2016,35(6):187-191(in Chinese))
32胡海岩,田强,张伟等.大型网架式可展开空间结构的非线性动力学与控制.力学进展,2013,43(4):390-414(Hu Haiyan,Tian Qiang,Zhang Wei,et al.Nonlinear dynamics and control of large deployable space structures composed of trusses and meshes.Advances in Mechanics,2013,43(4):390-414(in Chinese))
33王巍,于登云,马兴瑞.航天器铰接结构非线性动力学特性研究进展.力学进展,2006,36(2):233-238(Wang Wei,Yu Dengyun,Ma Xingrui.Advances and trends of non-linear dynamics of space joint-dominated structure.Advances in Mechnics,2006,36(2):233-
238(in Chinese))
34曹登庆,初世明,李郑发等.空间可展机构非光滑力学模型和动力学研究.力学学报,2013,45(1):3-15(Cao Dengqing,Chu Shiming,Li Zhengfa,et al.Study on the non-smooth mechanical models and dynamics for space deployable mechanisms.Chinese Journal of Theoretical and Applied Mechanics,2013,45(1):3-15(in Chinese))
35白争锋,赵阳,田浩.含铰间间隙太阳帆板展开动力学仿真.哈尔滨工业大学学报,2009,41(3):11-14(Bai Zhengfeng,Zhao Yang,Tian Hao.Dynamics and simulation of deployment for solar panels with hinge clearance.Journal of Harbin Institute of Technology,2009,41(3):11-14(in Chinese))
36阎绍泽,申永胜,陈洪彬.考虑杆件柔性和铰间隙的可展结构动力学数值模拟.清华大学学报(自然科学版),2003,43(2):145-
148(Yan Shaoze,Shen Yongsheng,Chen Hongbin.Dynamic performance of deployable structures with flexible members and clearance connections.J Tsinghua Univ(Sci&Tech),2003,43(2):145-148(in Chinese))
37尉飞,郑钢铁.具有非线性连接的航天器非线性振动分析.振动工程学报,2009,22(4):329-334(Wei Fei,Zheng Gangtie.Nonlinear dynamics of spacecraft with nonlinear joints.Journal of Vibration Engineering,2009,22(4):329-334(in Chinese))
38刘福寿,金栋平.环形桁架结构径向振动的等效圆环模型.力学学报,2016,48(5):1184-1191(Liu Fushou,Jin Dongping.Equivalent circular ring model for the radial vibration analysis of hoop truss structures.Chinese Journal of Theoretical and Applied Mechanics,2016,48(5):1184-1191(in Chinese))
39 Modi VJ.Attitude dynamics of satellites with flexible appendagesa brief review.Journal of Spacecraft and Rockets,1974,11(11):743-751
40 Likins P.Spacecraft attitude dynamics and control-a personal perspective on early developments.Journal of Guidance,Control,and Dynamics,1986,9(2):129-134
41尹婷婷,邓子辰,胡伟鹏等.空间刚性杆-弹簧组合结构轨道、姿态耦合动力学分析.力学学报,2018,50(1):87-98(Yin Tingting,Deng Zichen,Hu Weipeng,et al.Dynamic modelling and simulation of orbit and attitude coupling problems for structure combined of spatial rigid rods and spring.Chinese Journal of Theoretical and Applied Mechanics,2018,50(1):87-98(in Chinese))
42 Cai GP,Hong JZ,Yang SX.Model study and active control of a rotating flexible cantilever beam.International Journal of Mechanical Sciences,2004,46(6):871-889
43 Cai GP,Lim CW.Active control of a flexible hub-beam system using optimal tracking control method.International Journal of Mechanical Sciences,2006,48(10):1150-1162
44 Banerjee AK,Pedreiro N,Singhose WE.Vibration reduction for flexible spacecraft following momentum dumping with/without slewing.Journal of Guidance,Control,and Dynamics,2001,24(3):417-427
45 Hu QL,Shi P,Gao H.Adaptive variable structure and commanding shaped vibration control of flexible spacecraft.Journal of Guidance,Control,and Dynamics,2007,30(3):804-815
46胡军,张国琪,张志方等.可抑制航天器轨控过程中太阳翼大幅振动的新型轨控方法研究.载人航天,2011(2):15-23(Hu Jun,Zhang Guoqi,Zhang Zhifang,et al.New orbit control method to reduce solar panel vibration during orbit maneuvering.Manned Spaceflight,2011(2):15-23(in Chinese))
47 Lun L,Cao DQ.Dynamic modeling for a flexible spacecraft with solar arrays composed of honeycomb panels and its proportionalderivative control with input shaper.Journal of Dynamic Systems,Measurement,and Control-Transactions of the ASME,2016,138:08100848 Singh SN,Zhang R.Adaptive output feedback control of spacecraft with flexible appendages by modeling error compensation.Acta Astronautica,2004,54(4):229-243
49 Azadi M,Fazelzadeh S,Eghtesad M,et al.Vibration suppression and adaptive-robust control of a smart flexible satellite with three axes maneuvering.Acta Astronautica,2011,69(5):307-322
50 Hu QL.Sliding mode maneuvering control and active vibration damping of three-axis stabilized flexible spacecraft with actuator dynamics.Nonlinear Dynamics,2008,52:227-248
51 Hu Q,Cao J,Zhang Y.Robust backstepping sliding mode attitude tracking and vibration damping of flexible spacecraft with actuator dynamics.Journal of Aerospace Engineering,2009,22(2):139-152
52 da Fonseca IM,Rade DM,Goes LCS.Attitude and vibration control of a satellite containing flexible solar arrays by using reaction wheels,and piezoelectric transducers as sensors and actuators.Acta Astronautica,2017,139:357-366
53陶佳伟,张涛.控制受限的挠性航天器姿态机动控制和振动抑制.电机与控制学报,2018,22(3):105-113(Tao Jiawei,Zhang Tao.Robust adaptive attitude maneuvering and vibration reducing control of flexible spacecraft with input saturation.Electric Machines and Control,2018,22(3):105-113(in Chinese))
54袁国平,史小平,李隆.航天器姿态机动的自适应鲁棒控制及主动振动抑制.振动与冲击,2013,32(12):110-115(Yuan Guoping,Shi Xiaoping,Li Long.Adaptive robust attitude maneuver control of a flexible spacecraft with active vibration suppression.Journal of Vibration and Shock,2013,32(12):110-115(in Chinese))
55 Cao DQ,Song MT,Zhu WD,et al.Modeling and analysis of the inplane vibration of a complex cable-stayed bridge.Journal of Sound and Vibration,2012,331(26),5685-5714
56 Song MT,Cao DQ,Zhu WD.Dynamic analysis of a micro-resonator driven by electrostatic combs.Communications in Nonlinear Science and Numerical Simulation,2011,16(8):3425-3442
57 Wei J,Cao D,Wang L,et al.Dynamic modeling and simulation of flexible spacecraft with flexible joints.International Journal of Mechanical Sciences,2017,130:558-570
58 Brǘls O,Duysinx P,Golinval JC.The global modal parameterization for non-linear model-order reduction in flexible multibody dynamics.International Journal for Numerical Methods in Engineering,2007,69(5):948-977
59 Luo K,Hu H,Liu C,et al.Model order reduction for dynamic simulation of a flexible multibody system via absolute nodal coordinate formulation.Computer Methods in Applied Mechanics and Engineering,2017,324:573-594
2孟光,周徐斌,苗军.航天重大工程中的力学问题.力学进展,2016,46(6):467-322(Meng Guang,Zhou Xubin,Miao Jun.Mechanical problems in momentous projects of aerospace engineering.Advances in Mechanics,2016,46:467-322(in Chinese))
3马兴瑞,于登云,韩增尧等.星箭力学环境分析与试验技术研究进展.宇航学报,2006,27(3):323-331(Ma Xingrui,Yu Dengyun,Han Zengyao,et al.Research evolution on the satellite-rocket mechanical environment analysis and test technology.Journal of Astronautics,2006,27(3):323-331(in Chinese))
4王庆伟,谭述君,吴志刚等.大型液体火箭姿控与跷振大回路耦合动力学建模与分析.力学学报,2015,47(5):789-798(Wang Qingwei,Tan Shujun,Wu Zhigang,et al.Dynamic modeling and analysis of large-loop coupled by attitude control and pogo for large liquid rockets.Chinese Journal of Theoretical and Applied Mechanics,2015,47(5):789-798(in Chinese))
5张军,谌勇,骆剑等.整星隔振技术的研究现状和发展.航空学报,2006,26(2):179-183(Zhang Jun,Chen Yong,Luo Jian,et al.Review of the whole-spacecraft isolation techniques.Acta Aeronauticaet Astronautica Sinica,2006,26(2):179-183(in Chinese))
6 Wilke PS,Johnson CD,Fosness ER.Whole-spacecraft passive launch isolation.Journal of Spacecraft and Rockets,1998,35(5):690-694
7 Wilke PS,Johnson CD.Recent launches using the softride wholespacecraft vibration isolation system//Proceedings of the AIAASpace 2001 Conference,Albuquerque,NM,2001:AIAA-2001-40788 Liu LK,Liang L,Zheng GT,et al.Dynamic design of octo-strut platform for launch stage whole-spacecraft vibration isolation.Journal of Spacecraft and Rockets,2005,42(4):654-662
9 Wang Z,Liu LK,Zheng GT.Optimal design of octo-strut vibration isolation platform.Journal of Guidance,Control,and Dynamics,2006,29(3):749-753
10 Zhang YW,Fang B,Chen Y.Vibration isolation performance evaluation of the discrete whole-spacecraft vibration isolation platform for flexible spacecraft.Meccanica,2012,47:1185-1195
11 Yang K,Zhang YW,Ding H,et al.Nonlinear energy sink for wholespacecraft vibration reduction.Journal of Vibration and Acoustics,2017,139:021011
12陆泽琦,陈立群.非线性被动隔振的若干进展.力学学报,2017,49(3):550-564(Lu Zeqi,Chen Liqun.Some recent progresses in nonlinear passive isolations of vibrations.Chinese Journal of Theoretical and Applied Mechanics,2017,49(3):550-564(in Chinese))
13 Thayer D,Campbell M,Vagners J.Six-axis vibration isolation system using soft actuators and multiple sensors.Journal of Spacecraft and Rockets,2002,39(2):206-212
14 Marneffe B,Avraam M,Deraemaeker A,et al.Vibration isolation of precision payloads:A six-axis electromagnetic relaxation isolator.Journal of Guidance,Control,and Dynamics,2009,32(2):395-401
15 Zhang Y,Zang J,Fang B,et al.Dynamic characteristics of integrated active and passive whole-spacecraft vibration isolation platform based on non-probabilistic reliability.Transactions of the Japan Society for Aeronautical and Space Sciences,2014,57(5):263-271
16 Yang X,Wu H,Li Y,et al.Dynamic isotropic design and decentralized active control of a six-axis vibration isolator via Stewart platform.Mechanism and Machine Theory,2017,117:244-252
17 Chi W,Cao D,Wang D,et al.Design and experimental study of a VCM-based Stewart parallel mechanism used for active vibration isolation.Energies,2015,8:8001-8019
18 Wu Y,Yu K,Jiao J,et al.Dynamic isotropy design and analysis of a six-DOF active micro-vibration isolation manipulator on satellites.Robotics and Computer-Integrated Manufacturing,2018,49:408-425
19 Tang J,Cao D,Yu T.Decentralized vibration control of a VCM-Based Stewart parallel mechanism:simulation and experiments.Journal of Mechanical Engineering Science,2018.DOI:10.1177/0954406218756941
20胡海岩,田强,张伟等.大型网架式可展开空间结构的非线性动力学与控制.力学进展,2013,43(4):390-414(Hu Haiyan,Tian Qiang,Zhang Wei,et al.Nonlinear dynamics and control of large deployable space structures composed of trusses and meshes.Advances in Mechanics,2013,43(4):390-414(in Chinese))
21曲广吉.航天器动力学技术的发展和挑战.强度与环境,2003,30(4):1-6(Qu Guangji.Development and challenge of spacecraft dynamics technology.Structure and Environment Engineering,2003,30(4):1-6(in Chinese))
22曲广吉.复合柔性结构航天器动力学建模研究.中国工程科学,1999,1(2):52-56(Qu Guangji.Dynamics modeling of spacecraft with composite flexible structures.Engineering Science,1999,1(2):52-56(in Chinese))
23缪炳祺,曲广吉,夏邃勤等.关于柔性航天器动力学模型降阶问题.中国工程科学,2001,3(11):60-64(Liao Bingqi,Qu Guangji,Xia Suiqin,et al.On the order reduction of dynamics models of flexible spacecraft.Engineering Science,2001,3(11):60-64(in Chinese))
24 Mettler E,Quadrelli MB.Multibody dynamics modeling of segmented booms of the mars express spacecraft.Journal of Spacecraft and Rockets,2005,42(3):523-529
25蒋建平,李东旭.带太阳帆板航天器刚柔耦合动力学研究.航空学报,2006,27(3):418-422(Jiang Jianping and Li Dongxu.Research on rigid-flexible coupling dynamics of spacecraft with solar panel.Acta Aeronauticaet Astronautica Sinica,2006,27(3):418-422(in Chinese))
26张越,赵阳,谭春林等.ANCF索梁单元应变耦合问题与模型解耦.力学学报,2016,48(6):1406-1415(Zhang Yue,Zhao Yang,Tan Chunlin,et al.The strain coupling problem and model decoupling of ANCF cable/beam element.Chinese Journal of Theoretical and Applied Mechanics,2016,48(6):1406-1415(in Chinese))
27章孝顺,章定国,洪嘉振.考虑曲率纵向变形效应的大变形柔性梁刚柔耦合动力学建模与仿真.力学学报,2016,48(3):692-701(Zhang Xiaoshun,Zhang Dingguo,Hong Jiazhen.Rigid-flexible coupling dynamic modeling and simulation with the longitudinal deformation induced curvature effect for a rotating flexible beam under large deformation.Chinese Journal of Theoretical and Applied Mechanics,2016,48(3):692-701(in Chinese))
29和兴锁,邓峰岩,张烈霞等.大型空间刚柔耦合组合体的动力学建模.机械科学与技术,2004,23(5):543-545(He Xingsuo,Deng Fengyan,Zhang Liexia,et al.Dynamics modeling of large coupled rigid flexible space platform system.Mechanical Science and Technology,2004,23(5):543-545(in Chinese))
29方柳,刘玉亮,赵桂平.考虑动力刚化的挠性航天器的动力学建模与分析.兵器装备工程学报,2017,38(9):67-72(Fang Niu,Liu Yuliang,Zhao Guiping.Dynamic modeling and analysis for flexible spacecraft with dynamic stiffening.Journal of Ordnance Equipment Engineering,2017,38(9):67-72(in Chinese))
30 Xu W,Meng D,Chen Y,et al.Dynamics modeling and analysis of a flexible-base space robot for capturing large flexible spacecraft.Multibody System Dynamics,2014,32(3):357-401
31郭其威,吴松,刘芳等.航天器柔性附件对整器固有振动特性影响因素及规律分析.振动与冲击,2016,35(6):187-191(Guo Qiwei,Wu Song,Liu Fang,et al.The effect and change rule of spacecraft flexible annex on system natural vibration characteristics.Journal of Vibration and Shock,2016,35(6):187-191(in Chinese))
32胡海岩,田强,张伟等.大型网架式可展开空间结构的非线性动力学与控制.力学进展,2013,43(4):390-414(Hu Haiyan,Tian Qiang,Zhang Wei,et al.Nonlinear dynamics and control of large deployable space structures composed of trusses and meshes.Advances in Mechanics,2013,43(4):390-414(in Chinese))
33王巍,于登云,马兴瑞.航天器铰接结构非线性动力学特性研究进展.力学进展,2006,36(2):233-238(Wang Wei,Yu Dengyun,Ma Xingrui.Advances and trends of non-linear dynamics of space joint-dominated structure.Advances in Mechnics,2006,36(2):233-
238(in Chinese))
34曹登庆,初世明,李郑发等.空间可展机构非光滑力学模型和动力学研究.力学学报,2013,45(1):3-15(Cao Dengqing,Chu Shiming,Li Zhengfa,et al.Study on the non-smooth mechanical models and dynamics for space deployable mechanisms.Chinese Journal of Theoretical and Applied Mechanics,2013,45(1):3-15(in Chinese))
35白争锋,赵阳,田浩.含铰间间隙太阳帆板展开动力学仿真.哈尔滨工业大学学报,2009,41(3):11-14(Bai Zhengfeng,Zhao Yang,Tian Hao.Dynamics and simulation of deployment for solar panels with hinge clearance.Journal of Harbin Institute of Technology,2009,41(3):11-14(in Chinese))
36阎绍泽,申永胜,陈洪彬.考虑杆件柔性和铰间隙的可展结构动力学数值模拟.清华大学学报(自然科学版),2003,43(2):145-
148(Yan Shaoze,Shen Yongsheng,Chen Hongbin.Dynamic performance of deployable structures with flexible members and clearance connections.J Tsinghua Univ(Sci&Tech),2003,43(2):145-148(in Chinese))
37尉飞,郑钢铁.具有非线性连接的航天器非线性振动分析.振动工程学报,2009,22(4):329-334(Wei Fei,Zheng Gangtie.Nonlinear dynamics of spacecraft with nonlinear joints.Journal of Vibration Engineering,2009,22(4):329-334(in Chinese))
38刘福寿,金栋平.环形桁架结构径向振动的等效圆环模型.力学学报,2016,48(5):1184-1191(Liu Fushou,Jin Dongping.Equivalent circular ring model for the radial vibration analysis of hoop truss structures.Chinese Journal of Theoretical and Applied Mechanics,2016,48(5):1184-1191(in Chinese))
39 Modi VJ.Attitude dynamics of satellites with flexible appendagesa brief review.Journal of Spacecraft and Rockets,1974,11(11):743-751
40 Likins P.Spacecraft attitude dynamics and control-a personal perspective on early developments.Journal of Guidance,Control,and Dynamics,1986,9(2):129-134
41尹婷婷,邓子辰,胡伟鹏等.空间刚性杆-弹簧组合结构轨道、姿态耦合动力学分析.力学学报,2018,50(1):87-98(Yin Tingting,Deng Zichen,Hu Weipeng,et al.Dynamic modelling and simulation of orbit and attitude coupling problems for structure combined of spatial rigid rods and spring.Chinese Journal of Theoretical and Applied Mechanics,2018,50(1):87-98(in Chinese))
42 Cai GP,Hong JZ,Yang SX.Model study and active control of a rotating flexible cantilever beam.International Journal of Mechanical Sciences,2004,46(6):871-889
43 Cai GP,Lim CW.Active control of a flexible hub-beam system using optimal tracking control method.International Journal of Mechanical Sciences,2006,48(10):1150-1162
44 Banerjee AK,Pedreiro N,Singhose WE.Vibration reduction for flexible spacecraft following momentum dumping with/without slewing.Journal of Guidance,Control,and Dynamics,2001,24(3):417-427
45 Hu QL,Shi P,Gao H.Adaptive variable structure and commanding shaped vibration control of flexible spacecraft.Journal of Guidance,Control,and Dynamics,2007,30(3):804-815
46胡军,张国琪,张志方等.可抑制航天器轨控过程中太阳翼大幅振动的新型轨控方法研究.载人航天,2011(2):15-23(Hu Jun,Zhang Guoqi,Zhang Zhifang,et al.New orbit control method to reduce solar panel vibration during orbit maneuvering.Manned Spaceflight,2011(2):15-23(in Chinese))
47 Lun L,Cao DQ.Dynamic modeling for a flexible spacecraft with solar arrays composed of honeycomb panels and its proportionalderivative control with input shaper.Journal of Dynamic Systems,Measurement,and Control-Transactions of the ASME,2016,138:08100848 Singh SN,Zhang R.Adaptive output feedback control of spacecraft with flexible appendages by modeling error compensation.Acta Astronautica,2004,54(4):229-243
49 Azadi M,Fazelzadeh S,Eghtesad M,et al.Vibration suppression and adaptive-robust control of a smart flexible satellite with three axes maneuvering.Acta Astronautica,2011,69(5):307-322
50 Hu QL.Sliding mode maneuvering control and active vibration damping of three-axis stabilized flexible spacecraft with actuator dynamics.Nonlinear Dynamics,2008,52:227-248
51 Hu Q,Cao J,Zhang Y.Robust backstepping sliding mode attitude tracking and vibration damping of flexible spacecraft with actuator dynamics.Journal of Aerospace Engineering,2009,22(2):139-152
52 da Fonseca IM,Rade DM,Goes LCS.Attitude and vibration control of a satellite containing flexible solar arrays by using reaction wheels,and piezoelectric transducers as sensors and actuators.Acta Astronautica,2017,139:357-366
53陶佳伟,张涛.控制受限的挠性航天器姿态机动控制和振动抑制.电机与控制学报,2018,22(3):105-113(Tao Jiawei,Zhang Tao.Robust adaptive attitude maneuvering and vibration reducing control of flexible spacecraft with input saturation.Electric Machines and Control,2018,22(3):105-113(in Chinese))
54袁国平,史小平,李隆.航天器姿态机动的自适应鲁棒控制及主动振动抑制.振动与冲击,2013,32(12):110-115(Yuan Guoping,Shi Xiaoping,Li Long.Adaptive robust attitude maneuver control of a flexible spacecraft with active vibration suppression.Journal of Vibration and Shock,2013,32(12):110-115(in Chinese))
55 Cao DQ,Song MT,Zhu WD,et al.Modeling and analysis of the inplane vibration of a complex cable-stayed bridge.Journal of Sound and Vibration,2012,331(26),5685-5714
56 Song MT,Cao DQ,Zhu WD.Dynamic analysis of a micro-resonator driven by electrostatic combs.Communications in Nonlinear Science and Numerical Simulation,2011,16(8):3425-3442
57 Wei J,Cao D,Wang L,et al.Dynamic modeling and simulation of flexible spacecraft with flexible joints.International Journal of Mechanical Sciences,2017,130:558-570
58 Brǘls O,Duysinx P,Golinval JC.The global modal parameterization for non-linear model-order reduction in flexible multibody dynamics.International Journal for Numerical Methods in Engineering,2007,69(5):948-977
59 Luo K,Hu H,Liu C,et al.Model order reduction for dynamic simulation of a flexible multibody system via absolute nodal coordinate formulation.Computer Methods in Applied Mechanics and Engineering,2017,324:573-594