空间拦截轨道的优化设计与控制
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摘要
随着战争格局的变化,空间拦截越来越受到各国的重视。拦截过程燃料消耗的多少很大程度上决定了拦截任务是否能够圆满完成,因此拦截轨道的优化和控制具有重要的意义。本文重点研究了空间拦截轨道优化和初始段、末端控制以及悬停问题,并开发了相应的设计软件。
对于空间拦截轨道优化,采用非线性规划方法进行优化和用主矢量法进行优化。利用非线性规划方法研究了多脉冲最优拦截问题。考虑地球扁率J2摄动影响,建立普遍适用的空间拦截数学模型。在此基础上建立了用于求解多脉冲最优拦截的非线性规划模型,并对双脉冲、三脉冲固定时间拦截轨道进行优化,得到了最优速度增量的大小、方向和作用时间,最后对单脉冲、双脉冲和三脉冲在不同时间的优化结果进行了比较,验证了此方法的有效性。利用主矢量原理判断在固定时间内近距离脉冲拦截轨道速度增量是否最优,并对非最优情况提出了优化策略。根据轨道动力学理论,建立了近距离空间拦截轨道的数学模型。根据主矢量理论给出了判断冲量拦截是否最优的理论依据,并给出了优化方法。对不同时间的空间拦截速度增量进行仿真比较分析,提出了速度增量最优的拦截策略。
对于空间拦截控制,利用微分修正法进行初始控制。在之前建立的普遍适用的空间拦截数学模型的基础上,基于状态转移矩阵不断迭代求解得出初始拦截所需的速度增量的大小和方向。采用这种控制方法能够补偿轨道摄动对拦截脱靶量的影响,并通过仿真验证了此方法的有效性。利用准滑模控制进行末端控制,针对空间拦截的非线性模型,考虑到发动机的实际工作特性,基于准滑模控制思想,设计了一种易于工程实现又可精度可控的控制律,克服了滑模控制的抖振问题,并对扰动有较强的鲁棒性。
对圆轨道悬停问题进行了研究。给出了卫星悬停的轨道动力学模型,不考虑地球扁率J2摄动影响,通过在一段时间内对轨道实施连续有限推力控制,使得卫星运行在新的轨道上,实现对目标卫星的悬停。通过数学仿真,验证了在一段时间内对目标卫星实现悬停的可行性。
As the war situation changed, more and more country pay attention to space interception. Whether the interception mission successfully completed is depended on the amount of fuel consumption in the interception process, thus orbit optimization and control is of great significance. This paper focuses on orbit optimization, initial control, terminal control and hovering, based on above corresponding software was developed.
Nonlinear programming and primer vector theory was used for orbit optimization. Optimal multiple-impulse interception was studied by nonlinear programming, considering the J2 perturbation. Based on normal Interception model, the nonlinear programming model was set up. Using this method,the times , magnitudes and directions of three-impulse Interception with time constraint were obtained. Finally, optimal results were compared for one-impulse interception, two-impulse interception and three-impulse interception with different time constrain. The simulation results show that the initial control is rational and efficient. Whether the fuel consumption was optimal in time-fixed interception was mainly studied by primer vector theory. Based on orbit dynamic theory,the close interception model was set up. According to primer vector theory, whether the interception optimal and how to optimize was given. Finally, a great lot of simulations were done to investigate the fuel consumption with different time and impulses restraint.
Initial control for space Interception was studied by differential correction method. Based on the mathematical model and the state transition matrix for orbit Interception, the magnitude and direction of velocity were attained. The miss distance caused by the effects of perturbation was compensated in this initial control. The simulation results show that the initial control is rational and efficient. Terminal control for space Interception was studied by quasi-sliding mode control. For the nonlinear models of the space interception and characteristics of the engines terminal guidance laws were proposed based on quasi-sliding mode control theory. The guidance law is easy to be realized in engineering. Numerical simulation is carried out with available and satisfactory results.
Circular orbit of satellite hovering over space target was studied. Dynamics analysis of hovering orbit was presented, not considering J2 perpetual. By implementing a continuous pulse thrust control, the satellite was kept in a period of time on a new hovering orbit other than Kepler orbit. Finally, numerical simulation shows that it was feasible to hover over space targets in a period of time.
对于空间拦截轨道优化,采用非线性规划方法进行优化和用主矢量法进行优化。利用非线性规划方法研究了多脉冲最优拦截问题。考虑地球扁率J2摄动影响,建立普遍适用的空间拦截数学模型。在此基础上建立了用于求解多脉冲最优拦截的非线性规划模型,并对双脉冲、三脉冲固定时间拦截轨道进行优化,得到了最优速度增量的大小、方向和作用时间,最后对单脉冲、双脉冲和三脉冲在不同时间的优化结果进行了比较,验证了此方法的有效性。利用主矢量原理判断在固定时间内近距离脉冲拦截轨道速度增量是否最优,并对非最优情况提出了优化策略。根据轨道动力学理论,建立了近距离空间拦截轨道的数学模型。根据主矢量理论给出了判断冲量拦截是否最优的理论依据,并给出了优化方法。对不同时间的空间拦截速度增量进行仿真比较分析,提出了速度增量最优的拦截策略。
对于空间拦截控制,利用微分修正法进行初始控制。在之前建立的普遍适用的空间拦截数学模型的基础上,基于状态转移矩阵不断迭代求解得出初始拦截所需的速度增量的大小和方向。采用这种控制方法能够补偿轨道摄动对拦截脱靶量的影响,并通过仿真验证了此方法的有效性。利用准滑模控制进行末端控制,针对空间拦截的非线性模型,考虑到发动机的实际工作特性,基于准滑模控制思想,设计了一种易于工程实现又可精度可控的控制律,克服了滑模控制的抖振问题,并对扰动有较强的鲁棒性。
对圆轨道悬停问题进行了研究。给出了卫星悬停的轨道动力学模型,不考虑地球扁率J2摄动影响,通过在一段时间内对轨道实施连续有限推力控制,使得卫星运行在新的轨道上,实现对目标卫星的悬停。通过数学仿真,验证了在一段时间内对目标卫星实现悬停的可行性。
As the war situation changed, more and more country pay attention to space interception. Whether the interception mission successfully completed is depended on the amount of fuel consumption in the interception process, thus orbit optimization and control is of great significance. This paper focuses on orbit optimization, initial control, terminal control and hovering, based on above corresponding software was developed.
Nonlinear programming and primer vector theory was used for orbit optimization. Optimal multiple-impulse interception was studied by nonlinear programming, considering the J2 perturbation. Based on normal Interception model, the nonlinear programming model was set up. Using this method,the times , magnitudes and directions of three-impulse Interception with time constraint were obtained. Finally, optimal results were compared for one-impulse interception, two-impulse interception and three-impulse interception with different time constrain. The simulation results show that the initial control is rational and efficient. Whether the fuel consumption was optimal in time-fixed interception was mainly studied by primer vector theory. Based on orbit dynamic theory,the close interception model was set up. According to primer vector theory, whether the interception optimal and how to optimize was given. Finally, a great lot of simulations were done to investigate the fuel consumption with different time and impulses restraint.
Initial control for space Interception was studied by differential correction method. Based on the mathematical model and the state transition matrix for orbit Interception, the magnitude and direction of velocity were attained. The miss distance caused by the effects of perturbation was compensated in this initial control. The simulation results show that the initial control is rational and efficient. Terminal control for space Interception was studied by quasi-sliding mode control. For the nonlinear models of the space interception and characteristics of the engines terminal guidance laws were proposed based on quasi-sliding mode control theory. The guidance law is easy to be realized in engineering. Numerical simulation is carried out with available and satisfactory results.
Circular orbit of satellite hovering over space target was studied. Dynamics analysis of hovering orbit was presented, not considering J2 perpetual. By implementing a continuous pulse thrust control, the satellite was kept in a period of time on a new hovering orbit other than Kepler orbit. Finally, numerical simulation shows that it was feasible to hover over space targets in a period of time.
引文
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[2]张莉英,张启信,王辉.反卫星武器技术及防御措施浅析[J].飞航导弹, 2004, (3): 28-30
[3]吴勤,高雁翎.美国空间对抗装备的新进展[J].航天电子对抗. 2007(3): 1-4
[4]葛之江,刘品雄,王乃东.美俄天基反卫星技术的发展[J].航天电子对抗: 2003(4):1-5
[5]冯志刚,方昌华.世界各国反卫星策略综述[J].中国航天:2006(3): 38-40
[6] D.G.Kubitschek. Impactor Spacecraft Targeting for the Deep Impact Mission to Comet Tempel-1.[J].AAS03-615
[7] Lawden D F. Optimal Trajectories for Space Navigation [M]. Butterworth, 1963.
[8] Lion P M, Handelsman. H. M. An efficient method for calculating optimal free-space n-impulse trajectories [J]. AIAA Journal, 1968, 6(11):2160-2165
[9] J.E. Prussing, L.J. Wellnitz. Optimal Impulsive Time-Fixed Direct-Ascent Interception. [J] Journal of Guidance, 1989,12(4): 487-494
[10] N. X. Vinh, P. Lu, R. M. Howe, E. G. Gilbert. Optimal Interception with Time Constraint. [J] Journal of Optimization Theory and Applications, 1990,9(3):361-389
[11] Battin R.H. Lambert’s Problem Revisited [J] AIAA Journal, 1997, 15(5):707-713
[12] Battin.R.H, Vaughan R.M. An elegant Lambert algorithm. [J]. Journal of Guidance and Control, 1984, 7(6):662-670
[13]白洪波,马书兴,朱丽萍,任新霞.空间作战中固定时间轨道拦截的仿真研究. [J].航天控制. 2006, 24(4):62-65
[14]徐晓静,张恒源,李智.空间作战中的轨道拦截建模与仿真. [J]装备指挥技术学院学报. 2005,16(5):60-63
[15]程龙,陈勇.一种拦截轨道的确定方法. [J].航天控制. 2005(1):65-68
[16]朱战霞,袁建平.一种远程快速拦截轨道设计方法. [J].飞行力学.2008,26(2):54-56
[17]贾沛然,汤建国.运用速度增益制导实现对目标卫星的拦截. [J]国防科技大学学报. 1992,14(2):72-77
[18]李晨光,肖业伦.多冲量C-W交会的优化方法. [J].宇航学报, 2006, 27(2):172-176
[19]谌颖,王旭东.多冲量最优交会. [J].航天控制, 1992, 10(1):25-32
[20]林来兴,王立新.空间交会对接的双冲量最优控制. [J].航天控制, 1996, 14(1):12-18
[21]齐映红,曹喜滨.三脉冲最优交会问题的解法. [J].吉林大学学报. 2006,36(4):608-612
[22] Optimal four-impulse fixed-time rendezvous in the vicinity of a circular orbit. [J] AIAA Journal, 1969, 7(5):928-935
[23] Prussing. J.E Optimal two and three-impulse fixed-time rendezvous in the vicinity of a circular orbit. [J] .AIAA Journal, 1970, 8(7):293-310
[24]程国采.航天飞行器最优控制理论与方法,.[M].北京:国防工业出版社. 1999
[25]王会利.空间作战拦截轨道设计与优化.[D]西安:西北工业大学.2007
[26]王朝珠,秦化淑.最优控制理论[M].北京:科学出版社. 2003
[27]周克强,高晓光,白奕.反卫星卫星攻击方式研究. [J].飞行力学. 2006,24(4):80-83
[28]周军,常燕.考虑地球扁率J2摄动影响的异面椭圆轨道多冲量最优交会[J].宇航学报, 2008(2):472-475
[29]用非线性规划求解有限推力最优交会[J].国防科技大学学报, 2003(5):9-13
[30]王华,唐国金.用遗传算法求解双冲量最优交会问题.[J].中国空间科学技术. 2003(1):26-30
[31]刘鲁华,汤建国,余梦伦.利用动态规划原理实现多冲量最优交会问题.[J]国防科技大学学报. 2006, 28(6):38-42
[32]谌颖,黄文虎,倪茂林.多冲量最优交会的动态规划方法.[J].宇航学报. 1993,14(2):1-7
[33]王石,祝开建,戴金海,等.用EA求解非固定时间轨道转移和拦截问题. [J]国防科技大学学报. 2001, 23(5):1-4
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