航天器气动力辅助变轨方法研究
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摘要
航天器进行轨道机动或转移往返于空间站与平台、卫星之间,它们的变轨可用冲量或连续推力方式,但是耗能比较大,而气动力辅助轨道转移可成为节省燃料的变轨方案。本文所研究的气动力辅助变轨方式由于有效的利用了航天器环绕星球上的大气这种自然资源,减少燃料消耗,从而使航天器获得了较大的有效载荷比。因此,研究气动力辅助变轨具有重要的意义。
本文分析了气动力辅助变轨飞行器的特点,研究了影响气动力变轨过程中的因素,确定了升阻比和滚转角作为主要的控制参数,燃料最省作为目标。首先,建立了大气层内运动学微分方程,并对方程进行了简化和无量纲化处理。
其次,在同面HEO-LEO的气动辅助变轨过程中,根据大气边界条件和最优目标确定性能指标,通过引入哈密顿函数,利用庞特里压金极大值方法,对性能指标进行分析,设计出关于升阻比的控制律,代入轨道运动学方程中进行最优控制。分别对升力系数受约束和不受约束两种不同情况进行仿真,并改变转移轨道近地点高度进行仿真。
再次,在异面HEO-LEO的气动辅助变轨过程中,分别以升阻比和滚转角控制参数,进行控制律设计,在大气飞行段对轨道倾角进行寻优,分别对不同的轨道倾角进行仿真分析。
最后,通过对同面辅助变轨和异面辅助变轨两种情况大量的仿真,分析了升力系数受约束和不受约对同面变轨的影响,同时分析转移轨道近地点高度对同面变轨的影响和轨道倾角的变化对异面变轨的影响,并与霍曼变轨进行对比,结果验证了本文算法的有效性和合理性。
Spacecraft commit to maneuver or transfer to and from the space station, platform and the satellites with thrust impulse or continuous mode, but consuming large energy, while aeroassisted orbit transferring can be efficient program for fuel saving. By using the planet's atmosphere surrounding this natural resource, the way of aeroassisted orbital transfer can reduce fuel consumption, which makes the vehicle gain a larger payload. Therefore, it is of great significance to study aeroassisted orbital transfer.
This paper analyzes the characteristics of the aeroassisted orbital transfer vehicle, studies the influence factors in orbit transferring, identifies lift-to-drag ratio as the main control parameters, minimum fuel consumption as the target. First, to establish the atmospheric kinematics equations and the equations have been simplified and non-dimensional quantities.
Second, with the process of the coplanar HEO-LEO aeroassisted orbital transfer, according to atmospheric boundary conditions and the optimal target it determines performance index, this paper analyzes performance index by introducing the Pontryagin maximum method and using the Hamiltonian function, it obtained the optimal control law of the lift coefficient, which is substituted into orbit kinematics control law equation, to commit the optimal control. To simulate when the lift coefficient is fettered and unfettered respectively, and change the transfer orbit perigee altitude to simulate.
Third, with the process of the nonplanar HEO-LEO aeroassisted orbital transfer, this paper designs the control law with the control parameters of the lift-drag ratio and roll angle. To find good of the orbital inclination in atmospheric flight segment, it is to simulate when the orbital inclination is different.
Finally, with a large number of optimization simulation experiments on both of the coplanar and nonplanar orbit transfer, this paper analyzes the impacts of the lift coefficient when it is fettered and unfettered respectively, and analyze the impacts of transfer orbit perigee height to the coplanar orbital transfer and the orbit inclination changes to the nonplanar orbital transfer, it presents the verification of the algorithm effective and reasonable.
本文分析了气动力辅助变轨飞行器的特点,研究了影响气动力变轨过程中的因素,确定了升阻比和滚转角作为主要的控制参数,燃料最省作为目标。首先,建立了大气层内运动学微分方程,并对方程进行了简化和无量纲化处理。
其次,在同面HEO-LEO的气动辅助变轨过程中,根据大气边界条件和最优目标确定性能指标,通过引入哈密顿函数,利用庞特里压金极大值方法,对性能指标进行分析,设计出关于升阻比的控制律,代入轨道运动学方程中进行最优控制。分别对升力系数受约束和不受约束两种不同情况进行仿真,并改变转移轨道近地点高度进行仿真。
再次,在异面HEO-LEO的气动辅助变轨过程中,分别以升阻比和滚转角控制参数,进行控制律设计,在大气飞行段对轨道倾角进行寻优,分别对不同的轨道倾角进行仿真分析。
最后,通过对同面辅助变轨和异面辅助变轨两种情况大量的仿真,分析了升力系数受约束和不受约对同面变轨的影响,同时分析转移轨道近地点高度对同面变轨的影响和轨道倾角的变化对异面变轨的影响,并与霍曼变轨进行对比,结果验证了本文算法的有效性和合理性。
Spacecraft commit to maneuver or transfer to and from the space station, platform and the satellites with thrust impulse or continuous mode, but consuming large energy, while aeroassisted orbit transferring can be efficient program for fuel saving. By using the planet's atmosphere surrounding this natural resource, the way of aeroassisted orbital transfer can reduce fuel consumption, which makes the vehicle gain a larger payload. Therefore, it is of great significance to study aeroassisted orbital transfer.
This paper analyzes the characteristics of the aeroassisted orbital transfer vehicle, studies the influence factors in orbit transferring, identifies lift-to-drag ratio as the main control parameters, minimum fuel consumption as the target. First, to establish the atmospheric kinematics equations and the equations have been simplified and non-dimensional quantities.
Second, with the process of the coplanar HEO-LEO aeroassisted orbital transfer, according to atmospheric boundary conditions and the optimal target it determines performance index, this paper analyzes performance index by introducing the Pontryagin maximum method and using the Hamiltonian function, it obtained the optimal control law of the lift coefficient, which is substituted into orbit kinematics control law equation, to commit the optimal control. To simulate when the lift coefficient is fettered and unfettered respectively, and change the transfer orbit perigee altitude to simulate.
Third, with the process of the nonplanar HEO-LEO aeroassisted orbital transfer, this paper designs the control law with the control parameters of the lift-drag ratio and roll angle. To find good of the orbital inclination in atmospheric flight segment, it is to simulate when the orbital inclination is different.
Finally, with a large number of optimization simulation experiments on both of the coplanar and nonplanar orbit transfer, this paper analyzes the impacts of the lift coefficient when it is fettered and unfettered respectively, and analyze the impacts of transfer orbit perigee height to the coplanar orbital transfer and the orbit inclination changes to the nonplanar orbital transfer, it presents the verification of the algorithm effective and reasonable.
引文
1 Loh, W.H.T. Hypervelocity Vehicles at Large Angles of Inclination .ARS Journal, July 1960,29(7)323～332
2 Austin.R.E. System Design Concepts and Requirements for Aeroassisted Orbit Transfer Vehicles, AIAA-82-1379
3 Warzecha.L.W. Performance and Design Consideration for Maneuvering Space Vehicles, 1960:59～60
4 Walbeg.G..D. A Survery of Aeroassisted Orbit Transfer, J.spacecraft 1985, 22(1):231～233
5 Miele A. Recent Advance in the Optimization and Guidance of Aeroassisted Orbital Transfer. Acta Astronautica, 1996,38(10):747～768
6 Miele A.,Basapur V K, Lee W Y. Optimal Trajectories For Aeroassisted Coplanar Orbital Transfer. The Journal of Optimization Theory and Applications, 1987,52(1):423～433
7 Miele A,Wang T, Deaton A W. Optimal Trajectories for Aeroassisted Noncoplanar Orbital Transfer. Journal of Optimization Theory and Application, 1991,69(1):315～318
8 Vinh N X. Gerneral theory of optimal trajectory for rocket flight in a resisting medium. J.of Optimization theory and application, 1973,11(3):189～202.
9 Hull D G, Buffington M. Maximizing the Probability of a Hypervelocity Glider Intercepting a Fixed Target.AIAA-92-4346
10荆武兴,杨涤,吴瑶华.AOTV极小时间控制.宇航学报,1992,(4):9～17
11李小龙,陈士橹.航天飞机的最优再入轨迹与制导.宇航学报,1993,(1):431～437
12李小龙,陈士橹,杨旭.航天器异面气动辅助变轨飞行段的最优轨迹.宇航学报,1995(2):95～101
13 Vinh N X,Ma D M.Optimal Multiple-Pass Aeroassisted Plane Change. Acta Astronautica, 1990,21(11): 749～758
14张海联,周建平,吴德隆,王小军.热流限制下的最优气动力辅助变轨.上海航天,1999,16,(4):1～6
15张海联,周建平,吴德隆,王小军.过载限制下的最优气动力辅助异面变轨.弹道学报,1999,11(3):45～51
16吴德隆,彭伟斌,张海联等.过载限制下气动力辅助变轨的最优解与平衡滑行解.导弹与航天运载技术.2003,(4):4～6
17 Horie K,B A Conway. Optimal Aeroassisted Orbital Interception. Journal of Guidance, Control, and Dynamics.1999,22(5):625～631
18 Spriesterbach T P and Ross I M. Effect of Heating Rate on the Fuel Efficiency of Aerocruise and Aerobang Maneuvers AIAA-92-4642
19 Ross I.M. Thrust Programming in Aeroassisted Maneuvers. AAS99-404:1607～1625
20 Casalino L.Singular Arcs During Aerocruise. Journal of Guidance ,Control ,and Dynamics.2000,23(1).118～122
21 Eugene P Bonfiglio, James M Longuski, Nguyen X Vinh. Automated Design of Aerogravity-Assist Trajectories. Journal of Spacecraft and Rockets, 2000, 37(6):768～775
22 AndrewsDG, F Bloetscher. Aerobraked Orbital Transfer Vehicle Definition. AIAA -81-0279
23 Grenich A F, W C Woods.Flow Field Investigation of Atmospheric Braking for High Drag Vehicles with Forward Facing Jets. AIAA-81-0293
24沈青.稀薄气体动力学.国防工业出版社, 2003:196~198
25 G. A. Bird. Application of the Direct Simulation Monte Carlo Method to the Full Shuttle Geometry. AIAA 5th Joint Thermophysics and Heat Transfer Conference, Seattle, WA, USA, 1990, AIAA-1990-1692
26沈青,王松皋,刘大有.稀薄气体动力学现状.力学进展. 1973,2(1):10～15
27沈青,樊菁,胡振华,徐晓燕.过渡领域三维绕流直接统计模拟位置元法的一种新方案.空气动力学学报. 1996,14(3):295～303
28吴其芬,陈伟芳,黄琳,石于中.稀薄气体动力学.国防科技大学出版社, 2004:264～286.
29林来兴,潘科炎.空间飞行器控制设计准则.科学出版社.1981,(9):92～109
30 Benjamin P. Graziano. Computational Modeling of Aerodynamic Disturbances on Spacecraft within a Concurrent Engineering Framework. Cranfield University, School of Engineering, PhD thesis. 2007.9:302～307
31 M.S. Ivanov, A.V. Kashkovsky, S.F. Gimelshein, G.N. Markelov. SMILE System for 2D/3D DSMC Computations. Proc. of 25th Int. Symp. on RGD., Saint-Petersburg (Russia, July 21-28, 2006), Publishing House of the Siberian Branch of the Russian Academy of Sciences, 2007:539~544
32 J.P.Marce, Optimal Space Trajectories,New York, NY, Elsevier,1979:212～219
33 C.Marchal, Transferts Optimaux entre orbites elliptiques coplanaires Astronautica Aeta, 1965,11(6):432～445.
34 R.F.Hoelker,R.Silber The bi-elliptic transfer between circular co-Planar orbits, Alabama, Army Ballistic Missile Agency, Redstone Arsenal,Jan.1959:315～321
35 H.L.Roth,Minimization of the velocity increment for a bi-elliptic transfer with plane change. Astronautica Acta 1967, 13(2):119～130.
36 J.E. Prussing, J.H.Chiu, Optimal multiple-impulse time-fixed rendezvous between circular orbits. Journal of Guidance, Control, and Dynamics, 1986,9(1):17～22.
37海宁·吐尔著.最优化方法.欧天恒,曹叔维译.机械工业出版社. 1982: 235～241
38庞特里压金.最佳过程的数学理论.陈祖浩等译.上海科学技术出版社. 1965:132～139
39谈庆明.钱学森对近代力学的发展所作的贡献.力学进展,2001,31(4):57～62
40 RossI M. Thrust Programming in Aeroassisted Maneuvers. AAS99-404,:1607～1625
41 Betts J T. Using Sparse Nonlinear Programming to Computer Low Thrust Orbital Transfer. The journal of the Astronautical Sciences, 1993,41(3):349～371
42 U.S. Standard Atmoshere.1976
43程国采.航天飞行器最优控制理论与方法.国防工业出版社,1999:268～270
44阮春荣.大气中飞行的最优轨迹.宇航出版社,1987:165～168
45 Istratie Vasile.Optimal profound entry into atmosphere with minimum heat and constraints.In. AIAA Atmospheric Flight Mechanics Conference and Exhibit. Montreal, Canada,2001:120～123
46 Vinh Nguyen X.,Ma D.M.Optimal Multiple-Pass Aeroassisted Plane Change. Acta Astronautica, 1990,21(11):749～758
47吴德隆,王小军.航天器气动力辅助变轨动力学与最优控制.中国宇航出版社,2006:150～156
48袁方.最优过程理论在飞行轨迹优化计算中的应用.飞行力学. 2000,18(1):50～53
49周浩,周韬,陈万春等.高超声速滑翔飞行器引入段弹道优化.宇航学报, 2006,27(5):970～973
50王大轶,李铁寿,马兴瑞.月球最优软着陆两点边值问题的数值解法.航天控制,2000,(3):44～49
51赵汉元.飞行器再入动力学和制导.国防科技大学出版社,1997:78～80
52 Shi Y.Y.,Nelson R.L.,Young D.H.The application of nonlinear programming and collocation to optimal aeroassisted orbital transfers. In. AIAA, Aerospace Sciences Meeting and Exhibit.Reno, NV, 1992:205～211
53 Luus R.Iterative dynamic programming: from curiosity to a practical optimization procedure . Control and Intelligent Systems,1998,26:1～8
54 Bousson Kouamana.Single Gridpoint Dynamic Programming for trajectory Optimization.In, AIAA Atmospheric Flight Mechanics Conference and Exhibit.San Francisco,California, 2005:151～155
55 Gang Chen,Min Xu,Zi-ming Wan,et al.RLV Reentry Trajectory Multi-objective Optimization Design Based on NSGA-II Algorithm. In. AIAA Atmospheri Flight Mechanis Conferene and Exhibit. San Francisco, California, USA, 2005:230～233
56林西强,张育林.设计参数对气动辅助异面变轨性能的影响.飞行力学. 2000(02):50～55
57林西强,张育林.近地点高度对气动辅助异面变轨性能的影响.中国空间科学技术. 2000(02):13～19
2 Austin.R.E. System Design Concepts and Requirements for Aeroassisted Orbit Transfer Vehicles, AIAA-82-1379
3 Warzecha.L.W. Performance and Design Consideration for Maneuvering Space Vehicles, 1960:59～60
4 Walbeg.G..D. A Survery of Aeroassisted Orbit Transfer, J.spacecraft 1985, 22(1):231～233
5 Miele A. Recent Advance in the Optimization and Guidance of Aeroassisted Orbital Transfer. Acta Astronautica, 1996,38(10):747～768
6 Miele A.,Basapur V K, Lee W Y. Optimal Trajectories For Aeroassisted Coplanar Orbital Transfer. The Journal of Optimization Theory and Applications, 1987,52(1):423～433
7 Miele A,Wang T, Deaton A W. Optimal Trajectories for Aeroassisted Noncoplanar Orbital Transfer. Journal of Optimization Theory and Application, 1991,69(1):315～318
8 Vinh N X. Gerneral theory of optimal trajectory for rocket flight in a resisting medium. J.of Optimization theory and application, 1973,11(3):189～202.
9 Hull D G, Buffington M. Maximizing the Probability of a Hypervelocity Glider Intercepting a Fixed Target.AIAA-92-4346
10荆武兴,杨涤,吴瑶华.AOTV极小时间控制.宇航学报,1992,(4):9～17
11李小龙,陈士橹.航天飞机的最优再入轨迹与制导.宇航学报,1993,(1):431～437
12李小龙,陈士橹,杨旭.航天器异面气动辅助变轨飞行段的最优轨迹.宇航学报,1995(2):95～101
13 Vinh N X,Ma D M.Optimal Multiple-Pass Aeroassisted Plane Change. Acta Astronautica, 1990,21(11): 749～758
14张海联,周建平,吴德隆,王小军.热流限制下的最优气动力辅助变轨.上海航天,1999,16,(4):1～6
15张海联,周建平,吴德隆,王小军.过载限制下的最优气动力辅助异面变轨.弹道学报,1999,11(3):45～51
16吴德隆,彭伟斌,张海联等.过载限制下气动力辅助变轨的最优解与平衡滑行解.导弹与航天运载技术.2003,(4):4～6
17 Horie K,B A Conway. Optimal Aeroassisted Orbital Interception. Journal of Guidance, Control, and Dynamics.1999,22(5):625～631
18 Spriesterbach T P and Ross I M. Effect of Heating Rate on the Fuel Efficiency of Aerocruise and Aerobang Maneuvers AIAA-92-4642
19 Ross I.M. Thrust Programming in Aeroassisted Maneuvers. AAS99-404:1607～1625
20 Casalino L.Singular Arcs During Aerocruise. Journal of Guidance ,Control ,and Dynamics.2000,23(1).118～122
21 Eugene P Bonfiglio, James M Longuski, Nguyen X Vinh. Automated Design of Aerogravity-Assist Trajectories. Journal of Spacecraft and Rockets, 2000, 37(6):768～775
22 AndrewsDG, F Bloetscher. Aerobraked Orbital Transfer Vehicle Definition. AIAA -81-0279
23 Grenich A F, W C Woods.Flow Field Investigation of Atmospheric Braking for High Drag Vehicles with Forward Facing Jets. AIAA-81-0293
24沈青.稀薄气体动力学.国防工业出版社, 2003:196~198
25 G. A. Bird. Application of the Direct Simulation Monte Carlo Method to the Full Shuttle Geometry. AIAA 5th Joint Thermophysics and Heat Transfer Conference, Seattle, WA, USA, 1990, AIAA-1990-1692
26沈青,王松皋,刘大有.稀薄气体动力学现状.力学进展. 1973,2(1):10～15
27沈青,樊菁,胡振华,徐晓燕.过渡领域三维绕流直接统计模拟位置元法的一种新方案.空气动力学学报. 1996,14(3):295～303
28吴其芬,陈伟芳,黄琳,石于中.稀薄气体动力学.国防科技大学出版社, 2004:264～286.
29林来兴,潘科炎.空间飞行器控制设计准则.科学出版社.1981,(9):92～109
30 Benjamin P. Graziano. Computational Modeling of Aerodynamic Disturbances on Spacecraft within a Concurrent Engineering Framework. Cranfield University, School of Engineering, PhD thesis. 2007.9:302～307
31 M.S. Ivanov, A.V. Kashkovsky, S.F. Gimelshein, G.N. Markelov. SMILE System for 2D/3D DSMC Computations. Proc. of 25th Int. Symp. on RGD., Saint-Petersburg (Russia, July 21-28, 2006), Publishing House of the Siberian Branch of the Russian Academy of Sciences, 2007:539~544
32 J.P.Marce, Optimal Space Trajectories,New York, NY, Elsevier,1979:212～219
33 C.Marchal, Transferts Optimaux entre orbites elliptiques coplanaires Astronautica Aeta, 1965,11(6):432～445.
34 R.F.Hoelker,R.Silber The bi-elliptic transfer between circular co-Planar orbits, Alabama, Army Ballistic Missile Agency, Redstone Arsenal,Jan.1959:315～321
35 H.L.Roth,Minimization of the velocity increment for a bi-elliptic transfer with plane change. Astronautica Acta 1967, 13(2):119～130.
36 J.E. Prussing, J.H.Chiu, Optimal multiple-impulse time-fixed rendezvous between circular orbits. Journal of Guidance, Control, and Dynamics, 1986,9(1):17～22.
37海宁·吐尔著.最优化方法.欧天恒,曹叔维译.机械工业出版社. 1982: 235～241
38庞特里压金.最佳过程的数学理论.陈祖浩等译.上海科学技术出版社. 1965:132～139
39谈庆明.钱学森对近代力学的发展所作的贡献.力学进展,2001,31(4):57～62
40 RossI M. Thrust Programming in Aeroassisted Maneuvers. AAS99-404,:1607～1625
41 Betts J T. Using Sparse Nonlinear Programming to Computer Low Thrust Orbital Transfer. The journal of the Astronautical Sciences, 1993,41(3):349～371
42 U.S. Standard Atmoshere.1976
43程国采.航天飞行器最优控制理论与方法.国防工业出版社,1999:268～270
44阮春荣.大气中飞行的最优轨迹.宇航出版社,1987:165～168
45 Istratie Vasile.Optimal profound entry into atmosphere with minimum heat and constraints.In. AIAA Atmospheric Flight Mechanics Conference and Exhibit. Montreal, Canada,2001:120～123
46 Vinh Nguyen X.,Ma D.M.Optimal Multiple-Pass Aeroassisted Plane Change. Acta Astronautica, 1990,21(11):749～758
47吴德隆,王小军.航天器气动力辅助变轨动力学与最优控制.中国宇航出版社,2006:150～156
48袁方.最优过程理论在飞行轨迹优化计算中的应用.飞行力学. 2000,18(1):50～53
49周浩,周韬,陈万春等.高超声速滑翔飞行器引入段弹道优化.宇航学报, 2006,27(5):970～973
50王大轶,李铁寿,马兴瑞.月球最优软着陆两点边值问题的数值解法.航天控制,2000,(3):44～49
51赵汉元.飞行器再入动力学和制导.国防科技大学出版社,1997:78～80
52 Shi Y.Y.,Nelson R.L.,Young D.H.The application of nonlinear programming and collocation to optimal aeroassisted orbital transfers. In. AIAA, Aerospace Sciences Meeting and Exhibit.Reno, NV, 1992:205～211
53 Luus R.Iterative dynamic programming: from curiosity to a practical optimization procedure . Control and Intelligent Systems,1998,26:1～8
54 Bousson Kouamana.Single Gridpoint Dynamic Programming for trajectory Optimization.In, AIAA Atmospheric Flight Mechanics Conference and Exhibit.San Francisco,California, 2005:151～155
55 Gang Chen,Min Xu,Zi-ming Wan,et al.RLV Reentry Trajectory Multi-objective Optimization Design Based on NSGA-II Algorithm. In. AIAA Atmospheri Flight Mechanis Conferene and Exhibit. San Francisco, California, USA, 2005:230～233
56林西强,张育林.设计参数对气动辅助异面变轨性能的影响.飞行力学. 2000(02):50～55
57林西强,张育林.近地点高度对气动辅助异面变轨性能的影响.中国空间科学技术. 2000(02):13～19