空间分离与伴飞的轨道控制研究
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摘要
本文针对子卫星弹射后的轨道控制问题进行研究,首先假设一颗子卫星被母卫星通过弹簧弹射,然后在控制作用下进行轨道过渡,并最终形成伴飞状态的过程。其中主要研究针对子卫星的轨道过渡段,由于子卫星控制力不完备,所以需要设计一种控制律,使其能够令子卫星追踪母卫星,最终形成伴飞状态,并满足工程要求。对此本文给出了子卫星相对母卫星的运动方程,并将飞行过程设计为:自由飞行段和控制飞行段。利用最优二次型控制方法,设计出了子卫星轨道过渡的控制律。在卫星的轨道动力学方程中,控制量为连续力,但一般实际工程中都是通过常值推力,所以利用PWPF方法,将连续力离散为常值推力。并在此基础上分为两种情况进行了仿真分析,给出了仿真结果:首先是控制力完备的情况,在这种情况下通过所设计的控制律,子卫星可以快速到达到伴飞状态,并且能够满足工程要求;其次是在子卫星轨道平面内,沿体坐标轴,有三个方向可以施加控制力,而一个方向没有控制力的控制力不完备情况,这种情况下,子卫星依旧可以通过设计的控制律到达伴飞状态,并满足工程要求,只是时间要相对增加不少。最后,分析了摄动对两星伴飞状态的影响,可以发现近地轨道上主要的摄动力将会对两颗卫星的伴飞状态造成影响,如不施加控制力进行调整,两卫星的伴飞状态将遭到破坏。
This paper presents the research on Sub-satellite orbital control problem after ejections. First of all, I assume Sub-satellite ejected from Main satellite by spring, and then progressive orbit transition under the control system, and engender formation flying finally. The main problem is the section of Sub-satellite orbit transition. Because the control force of Sub-satellite is incomplete, it require to design a control law, which could make Sub-satellite trace Main satellite, engender formation flying and satisfy requirements of engineering projects finally. This paper presents the relative motion equation between Sub-satellite and Main satellite, and split flying process into two parts: Free flight phase and Control flight phase, and then use quadratic type optimal control methods to design the control law of Sub-satellite orbit transition. In the orbit dynamics equations, control force is continued, but in engineering projects use we constant thrust control, so we need use PWPF method. And meanwhile, it conducts a comparison of the two conditions. The first condition is that the control force is complete. In such cases, Sub-satellite may achieve formation flying speedily by the control law, and could satisfy requirements of engineering projects. Secondly, in the Sub-satellite orbit plane, there are three directions control force in body-coordinate axis. In such cases, Sub-satellite may achieve formation flying by the control law also, and could satisfy requirements of engineering projects, but the time is increased. At the end of this article, it gives perturbation analysis for formation flying, and discover that major perturbative force in low earth orbit could make influence for the formation flying.
This paper presents the research on Sub-satellite orbital control problem after ejections. First of all, I assume Sub-satellite ejected from Main satellite by spring, and then progressive orbit transition under the control system, and engender formation flying finally. The main problem is the section of Sub-satellite orbit transition. Because the control force of Sub-satellite is incomplete, it require to design a control law, which could make Sub-satellite trace Main satellite, engender formation flying and satisfy requirements of engineering projects finally. This paper presents the relative motion equation between Sub-satellite and Main satellite, and split flying process into two parts: Free flight phase and Control flight phase, and then use quadratic type optimal control methods to design the control law of Sub-satellite orbit transition. In the orbit dynamics equations, control force is continued, but in engineering projects use we constant thrust control, so we need use PWPF method. And meanwhile, it conducts a comparison of the two conditions. The first condition is that the control force is complete. In such cases, Sub-satellite may achieve formation flying speedily by the control law, and could satisfy requirements of engineering projects. Secondly, in the Sub-satellite orbit plane, there are three directions control force in body-coordinate axis. In such cases, Sub-satellite may achieve formation flying by the control law also, and could satisfy requirements of engineering projects, but the time is increased. At the end of this article, it gives perturbation analysis for formation flying, and discover that major perturbative force in low earth orbit could make influence for the formation flying.
引文
1林来兴.空间交会对接技术的发展.中国航天,1993(6):15~19
2张万里.小型空间飞行器近距离追踪方法研究.哈尔滨工业大学硕士学位论文:2006:1~3
3周前祥,连顺国.航天器空间交会对接技术的进展.航天医学与医学工程.1998( 8):1~5
4 Jesse Leitner. Fornation Flightin Space: Distributed Spacecraft Systems Develop New GPS Capabilities. GPS World, February2002:2~4
5 William E, Wiese1. Optimal Impulsive Control of Relative Satellite Motion. Journal of Guidance, Control and Dynamics. 2003,26(1):74—78
6 Vaddi S S, Vadali S R, Alfriend K T. Formation Flying: Accommodating Nonlinearity and Eccentricity Perturbations. Journal of Guidance, Control and Dynamics.2003,26(2):214—223
7 B.M.Kiforenko, Z.V.Pasechnik, S.B.Kyrychenko, LYu.Vasiiiev. Minimum time transfer of low thrust rocket in strong gravity fields. Acta Astronautica. 2003,14(1):114~123
8 Liu Peiyu, Wang Jincheng, Wang Lin. General form of extended least squares method. Hefei: AMSE Conference“Modeling, Simulation & Control”.1993(2):252~255
9朱仁章,俞南嘉.航天器轨道交会的一般策略.中国空间科学技术.1999.4(2):27~33
10余韶华.航天飞行器相对运动动力学及其控制方法.宇航学报.1995.7(16):1~7
11谌颖,黄文虎.多冲量最优交会的动态规划方法.宇航学报.1998.4(2):1~7
12陈新海.陈文胜.航天器四冲量固定时间最优交会.宇航学报.1994.4(2):71~75
13王虎妹,李俊峰,杨卫.利用参照轨道要素研究卫星星座/编队的几何特性.工程力学.2006.11(23):177~182
14朱仁章,尹燕.论空间交会最终平移段制导设计.空间科学技术.2004.10(5):1~5
15唐玉灵.空间飞行器在目标机动下基于视线坐标系的交会方法研究.哈尔滨工业大学硕士学位论文.2006.6:20~40
16王颖.吴鸿鑫.解永春.空间交汇停靠视线知道控制方法.全国第十一届空间及运动体控制技术年会论文.176~182
17李新刚.空间交会对接制导策略与仿真研究.西北工业大学硕士学位论文.2000.3:15~20
18哈尔滨工业大学理论力学教研室.理论力学.高等教育出版社.2002: 244~318
19李心宏.理论力学.大连理工大学出版社.2004:430~458
20杨嘉墀.航天器轨道动力学与控制.宇航出版社,1995:79~148
21刘暾,赵钧.空间飞行器动力学.哈尔滨工业大学出版社.2003:12~114
22 D. Rex. Orbital mechanics and satellite missions. Technische Universtat Braunschwerg.1984:12~17
23王志刚,李卿,陈士橹等.伴随卫星伴随运动运动学分析.空军工程大学学报.2001,2(1):1~5
24林来兴.交会对接动力学模型与动力学特性.中国空间科学技术,1994: 34~89
25李文华.空间交汇对接动力学与控制研究.西北工业大学博士学位论文.2001:10~30
26 V.A. Sarychev. Dynamics of Two Connected Bodies in a Circular Orbit. Space flight Dynamics. Space flight Dynamics.1993:3-337
27 Brondino G, Legenne J, Hermes guidance. Navigation and control system for rendezvous phases. ESASP.1991,3(1):2~7
28张振民,许滨,孙兰.航天器相对运动与Hill解的适用性分析.空间科学技术.2002.4(3):1~8
29 S.D. Fernande. Optimal low-thrust limited power transfer between neighboring quasi-circular orbits of small inclinations around a no blate P lanet. Acta A stronautica,1989, 19(5):401~409
30黄文梅,杨勇,熊桂林,成晓明.系统仿真分析与设计.2001:182~186
31魏克新.控制系统计算机辅助设计.机械工业出版社.1997:57~264
32刘陪玉.最优控制系统设计.大连理工出版社.2000:287~334
33薛定宇.控制系统计算机辅助设计.清华大学出版社.1996:142~197
34章仁为.静止卫星的轨道和姿态控制.科学出版社.1987:74~98
35李亮.航天器轨道转移与交会最优控制研究.西北工业大学硕士学位论文.2005:4~23
36胡中楫,邹伯敏.控制原理及应用.1988:338~352
37刘林.航天器轨道理论.国防工业出版社.2000:143~177
38 V. J. Modi, A.C. Ng, A. Suleiman. An Efficient Approach to Dynamics and Control of Flexible Multibody systems. Space flight Dynamics.1993:3-332.
39 Sophie Geoffrey, Richard Eponym. Optimal low-thrust transfers with constraints-generalization of averaging techniques. Acta Astronautica. 1997,41(3):133-149
40 Schell W.A, Conway B.A. Optimization of very-low-thrust, many-revolution Spacecraft trajectories. Journal of Guidance, Control, and Dynamics.1994,17 (6):185-192
41 Li Junfeng, Meng Xin, Gao Yunfeng, Li Xiang. Study on Relative Orbital Configuration in Satellite Formation Flying. Acta Mechanica Sinica. 2002,1(3): 14~17
42 Carte T E. State Transition Matrices for Terminal Rendezvous Studies: Brief Survey and New Example. Journal of Guidance, Control and Dynamics. 1998,21(1):148~155
43 Gang Bing Song, Nick V. Buck, Brij N. Agrawal. Spacecraft Vibration Reduction Using Pulse-Width Pulse-Frequency Modulated Input Shaper. Journal of Guidance, Control and Dynamics. 1999,22(3):5~7
44李志敏.使用PWPF喷气推力器的挠性卫星输入成型姿态机动控制.哈尔滨工业大学硕士学位论文.2002:7~18
45 T, Anthony, Carroll. S. Pulse-Modulated Control Synthesis for a Flexible Spacecraft. Journal of Guidance, Control and Dynamics. 1990,13(6):1014 ~1021
46 Naoni Ehrich Leonard,William S. Levine. Using Matlab To Control System.“Modeling, Simulation & Control”.1997,23(2):104~221
47 Folta D C, Newman L K, Gardner T. Foundations of Formation Flying for Mission to Planet Earth and the New Millennium. Proceedings of the AIAA/AAS Astrodynamics Conference.1996,7(2):656—666
48 Milam M B, Petit N, Murray R M. Constrained Trajectory Generation for Micro-Satellite Formation Flying. AIAA 2001,4(3),2001:1~6
49 Schaub H, Vadali S R, Junkins J L. Spacecraft Formation Flying ControlUsing Mean Orbit Elements. The Journal of Astronautically Sciences. 2000,48(1):69~87
50李俊峰,孟鑫,高云峰,李响.项摄动对编队飞行卫星相对轨道构型的影响.清华大学学报.2004,44(2):1~5 J2
51韦娟,袁建平.小卫星编队飞行的相对运动学方程研究.飞行力学.2002,3(1):1~4
2张万里.小型空间飞行器近距离追踪方法研究.哈尔滨工业大学硕士学位论文:2006:1~3
3周前祥,连顺国.航天器空间交会对接技术的进展.航天医学与医学工程.1998( 8):1~5
4 Jesse Leitner. Fornation Flightin Space: Distributed Spacecraft Systems Develop New GPS Capabilities. GPS World, February2002:2~4
5 William E, Wiese1. Optimal Impulsive Control of Relative Satellite Motion. Journal of Guidance, Control and Dynamics. 2003,26(1):74—78
6 Vaddi S S, Vadali S R, Alfriend K T. Formation Flying: Accommodating Nonlinearity and Eccentricity Perturbations. Journal of Guidance, Control and Dynamics.2003,26(2):214—223
7 B.M.Kiforenko, Z.V.Pasechnik, S.B.Kyrychenko, LYu.Vasiiiev. Minimum time transfer of low thrust rocket in strong gravity fields. Acta Astronautica. 2003,14(1):114~123
8 Liu Peiyu, Wang Jincheng, Wang Lin. General form of extended least squares method. Hefei: AMSE Conference“Modeling, Simulation & Control”.1993(2):252~255
9朱仁章,俞南嘉.航天器轨道交会的一般策略.中国空间科学技术.1999.4(2):27~33
10余韶华.航天飞行器相对运动动力学及其控制方法.宇航学报.1995.7(16):1~7
11谌颖,黄文虎.多冲量最优交会的动态规划方法.宇航学报.1998.4(2):1~7
12陈新海.陈文胜.航天器四冲量固定时间最优交会.宇航学报.1994.4(2):71~75
13王虎妹,李俊峰,杨卫.利用参照轨道要素研究卫星星座/编队的几何特性.工程力学.2006.11(23):177~182
14朱仁章,尹燕.论空间交会最终平移段制导设计.空间科学技术.2004.10(5):1~5
15唐玉灵.空间飞行器在目标机动下基于视线坐标系的交会方法研究.哈尔滨工业大学硕士学位论文.2006.6:20~40
16王颖.吴鸿鑫.解永春.空间交汇停靠视线知道控制方法.全国第十一届空间及运动体控制技术年会论文.176~182
17李新刚.空间交会对接制导策略与仿真研究.西北工业大学硕士学位论文.2000.3:15~20
18哈尔滨工业大学理论力学教研室.理论力学.高等教育出版社.2002: 244~318
19李心宏.理论力学.大连理工大学出版社.2004:430~458
20杨嘉墀.航天器轨道动力学与控制.宇航出版社,1995:79~148
21刘暾,赵钧.空间飞行器动力学.哈尔滨工业大学出版社.2003:12~114
22 D. Rex. Orbital mechanics and satellite missions. Technische Universtat Braunschwerg.1984:12~17
23王志刚,李卿,陈士橹等.伴随卫星伴随运动运动学分析.空军工程大学学报.2001,2(1):1~5
24林来兴.交会对接动力学模型与动力学特性.中国空间科学技术,1994: 34~89
25李文华.空间交汇对接动力学与控制研究.西北工业大学博士学位论文.2001:10~30
26 V.A. Sarychev. Dynamics of Two Connected Bodies in a Circular Orbit. Space flight Dynamics. Space flight Dynamics.1993:3-337
27 Brondino G, Legenne J, Hermes guidance. Navigation and control system for rendezvous phases. ESASP.1991,3(1):2~7
28张振民,许滨,孙兰.航天器相对运动与Hill解的适用性分析.空间科学技术.2002.4(3):1~8
29 S.D. Fernande. Optimal low-thrust limited power transfer between neighboring quasi-circular orbits of small inclinations around a no blate P lanet. Acta A stronautica,1989, 19(5):401~409
30黄文梅,杨勇,熊桂林,成晓明.系统仿真分析与设计.2001:182~186
31魏克新.控制系统计算机辅助设计.机械工业出版社.1997:57~264
32刘陪玉.最优控制系统设计.大连理工出版社.2000:287~334
33薛定宇.控制系统计算机辅助设计.清华大学出版社.1996:142~197
34章仁为.静止卫星的轨道和姿态控制.科学出版社.1987:74~98
35李亮.航天器轨道转移与交会最优控制研究.西北工业大学硕士学位论文.2005:4~23
36胡中楫,邹伯敏.控制原理及应用.1988:338~352
37刘林.航天器轨道理论.国防工业出版社.2000:143~177
38 V. J. Modi, A.C. Ng, A. Suleiman. An Efficient Approach to Dynamics and Control of Flexible Multibody systems. Space flight Dynamics.1993:3-332.
39 Sophie Geoffrey, Richard Eponym. Optimal low-thrust transfers with constraints-generalization of averaging techniques. Acta Astronautica. 1997,41(3):133-149
40 Schell W.A, Conway B.A. Optimization of very-low-thrust, many-revolution Spacecraft trajectories. Journal of Guidance, Control, and Dynamics.1994,17 (6):185-192
41 Li Junfeng, Meng Xin, Gao Yunfeng, Li Xiang. Study on Relative Orbital Configuration in Satellite Formation Flying. Acta Mechanica Sinica. 2002,1(3): 14~17
42 Carte T E. State Transition Matrices for Terminal Rendezvous Studies: Brief Survey and New Example. Journal of Guidance, Control and Dynamics. 1998,21(1):148~155
43 Gang Bing Song, Nick V. Buck, Brij N. Agrawal. Spacecraft Vibration Reduction Using Pulse-Width Pulse-Frequency Modulated Input Shaper. Journal of Guidance, Control and Dynamics. 1999,22(3):5~7
44李志敏.使用PWPF喷气推力器的挠性卫星输入成型姿态机动控制.哈尔滨工业大学硕士学位论文.2002:7~18
45 T, Anthony, Carroll. S. Pulse-Modulated Control Synthesis for a Flexible Spacecraft. Journal of Guidance, Control and Dynamics. 1990,13(6):1014 ~1021
46 Naoni Ehrich Leonard,William S. Levine. Using Matlab To Control System.“Modeling, Simulation & Control”.1997,23(2):104~221
47 Folta D C, Newman L K, Gardner T. Foundations of Formation Flying for Mission to Planet Earth and the New Millennium. Proceedings of the AIAA/AAS Astrodynamics Conference.1996,7(2):656—666
48 Milam M B, Petit N, Murray R M. Constrained Trajectory Generation for Micro-Satellite Formation Flying. AIAA 2001,4(3),2001:1~6
49 Schaub H, Vadali S R, Junkins J L. Spacecraft Formation Flying ControlUsing Mean Orbit Elements. The Journal of Astronautically Sciences. 2000,48(1):69~87
50李俊峰,孟鑫,高云峰,李响.项摄动对编队飞行卫星相对轨道构型的影响.清华大学学报.2004,44(2):1~5 J2
51韦娟,袁建平.小卫星编队飞行的相对运动学方程研究.飞行力学.2002,3(1):1~4