近程弹道导弹弹道优化方法研究
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摘要
自从第二次世界大战期间德国的V2弹道导弹诞生以后,作为战略武器的弹道导弹以其巨大的杀伤力、破坏力和威慑力受到世界各国的重视,尤其是近期武器火力全覆盖概念的提出,并伴随着美国“网火”系统的开发研制,各国不停地对弹道导弹进行研制、改进和生产。弹道导弹的弹道仿真与优化是弹道导弹总体设计的重要内容,贯穿于弹道导弹研制各个阶段。本文主要是针对近程弹道导弹的弹道设计要求,对弹道导弹的弹道仿真与优化展开了以下研究工作。
首先,本文根据弹道导弹的动力学特性,建立了导弹飞行的动力学、运动学模型,并针对弹道优化问题,忽略次要因素,进行合理假设,推导得出用于弹道设计的简化模型。
其次,分析了弹道优化问题的本质为动态优化问题,采用一般的优化方法很难得到解析优化解。因此本文根据弹道导弹的飞行特性以及设计经验分析、研究并最后采用了参数化方法,将弹道分段设计,把原问题转换为参数优化问题。
然后,分析研究了各种非线性优化方法,并针对本文的弹道优化问题采用遗传算法和单纯形混合算法对转换后的参数优化问题求解,给出合理的优化解,得到理论弹道。
最后,在六自由度模型中,对方案弹道阶段和末制导阶段分别采用内外环制导控制和比例导引过载控制法,完成全弹道的仿真实验,并针对目标机动的情况也进行了仿真实验。六自由度的仿真实验表明弹道设计满足任务要求,验证了弹道设计的正确性和合理性。
Since the coming of German V2 Rocket during the Second World War, as strategic weapons, ballistic missiles are given much of considerations for its huge execution and determent. Especially after the concept introduction of full coverage of weapon fire lately together with stimulation of the development of American Netfires system, the research and manufacture of ballistic missiles are carried out nonstop by many countries. The simulation and the optimization of trajectory for ballistic missiles are of great importance to the collectivity design, which will appear in every stage of ballistic development. This thesis is focused on the trajectory simulation and optimization for a certain type of ballistic missile according to its design task requirement.
First, this thesis builds up the mathematical kinetics model and motion model according to the dynamical characteristics of ballistic missile. Then this paper brings up proper hypothesis and neglects subordinate factors so the simplified model for trajectory optimization is derived.
Second, this paper analyzes the essential problem of trajectory optimization is the dynamic optimization problem which is hard to get the analytical solution. So after the consideration of the ballistic kinetics characteristics and design experience, the method of parameterization is proposed, which is to design the trajectory in different segments and convert the original problem into a parameter optimization problem.
Then, different nonlinear optimization methods are discussed and analyzed and finally the combination method of Genetic Algorithm and N-M Simplex method are selected to solve this problem. The optimization process is carried out and the optimal solution is given out. The ideal trajectory is obtained.
Last, the six-dimension simulation is carried out. The whole trajectory is divided into tow parts which are program trajectory and terminal guidance trajectory. The tow loops guidance control method is applied for the program trajectory and the proportional navigation guidance law is used for the terminal guidance trajectory. The six-dimension simulation is performed and the situation when objective’s moving is also discussed and researched. The results of the six- dimension simulation indicates that the design meets all the task requirements , which validates the correctness and rationality of trajectory design.
首先,本文根据弹道导弹的动力学特性,建立了导弹飞行的动力学、运动学模型,并针对弹道优化问题,忽略次要因素,进行合理假设,推导得出用于弹道设计的简化模型。
其次,分析了弹道优化问题的本质为动态优化问题,采用一般的优化方法很难得到解析优化解。因此本文根据弹道导弹的飞行特性以及设计经验分析、研究并最后采用了参数化方法,将弹道分段设计,把原问题转换为参数优化问题。
然后,分析研究了各种非线性优化方法,并针对本文的弹道优化问题采用遗传算法和单纯形混合算法对转换后的参数优化问题求解,给出合理的优化解,得到理论弹道。
最后,在六自由度模型中,对方案弹道阶段和末制导阶段分别采用内外环制导控制和比例导引过载控制法,完成全弹道的仿真实验,并针对目标机动的情况也进行了仿真实验。六自由度的仿真实验表明弹道设计满足任务要求,验证了弹道设计的正确性和合理性。
Since the coming of German V2 Rocket during the Second World War, as strategic weapons, ballistic missiles are given much of considerations for its huge execution and determent. Especially after the concept introduction of full coverage of weapon fire lately together with stimulation of the development of American Netfires system, the research and manufacture of ballistic missiles are carried out nonstop by many countries. The simulation and the optimization of trajectory for ballistic missiles are of great importance to the collectivity design, which will appear in every stage of ballistic development. This thesis is focused on the trajectory simulation and optimization for a certain type of ballistic missile according to its design task requirement.
First, this thesis builds up the mathematical kinetics model and motion model according to the dynamical characteristics of ballistic missile. Then this paper brings up proper hypothesis and neglects subordinate factors so the simplified model for trajectory optimization is derived.
Second, this paper analyzes the essential problem of trajectory optimization is the dynamic optimization problem which is hard to get the analytical solution. So after the consideration of the ballistic kinetics characteristics and design experience, the method of parameterization is proposed, which is to design the trajectory in different segments and convert the original problem into a parameter optimization problem.
Then, different nonlinear optimization methods are discussed and analyzed and finally the combination method of Genetic Algorithm and N-M Simplex method are selected to solve this problem. The optimization process is carried out and the optimal solution is given out. The ideal trajectory is obtained.
Last, the six-dimension simulation is carried out. The whole trajectory is divided into tow parts which are program trajectory and terminal guidance trajectory. The tow loops guidance control method is applied for the program trajectory and the proportional navigation guidance law is used for the terminal guidance trajectory. The six-dimension simulation is performed and the situation when objective’s moving is also discussed and researched. The results of the six- dimension simulation indicates that the design meets all the task requirements , which validates the correctness and rationality of trajectory design.
引文
1甘楚雄,刘冀湘.弹道导弹和运载火箭总体设计[M].北京:国防工业出版社. 1996.
2祝强军.弹道导弹弹道仿真与优化设计[D].西安:西北工业大学, 2007.
3 Christensen D E. Multiple Rocket Launcher characteristics and simulation Technique. AD-A025379.
4 http://mil.news.sohu.com/20081205/n261044852.shtml
5张毅,杨辉耀,李俊莉.弹道导弹弹道学.长沙:国防科技大学出版社, 1999.
6 Taur D R. Midcourse Trajectory Optimization for a SAM Against High-speed Target[R]. AIAA-2002-4514, 2002.
7 Phillips C A, Drake J C. Trajectory optimization for a missile using a multitier approach[J]. Journal of Spacecraft and Rockets.2000, 37(5): 653-662.
8 MustafT.弹道导弹飞行方案设计及弹道优化[D].北京:北京航空航天大学, 2003.
9陈宝林编著.最优化理论与算法.北京:清华大学出版社, 1989.
10李向前,何麟书,王书河.一种战术弹道导弹主动段飞行攻角优化的算法.导弹与航天运载技术, 2002.
11 Mordecai Avriel. Nonlinear Programming: Analysis and Methods. Dover Publishing, 2000.
12 Bryson, Ho. Applied Optimal Control. Blaisdell Publishing Company, 1969.
13程极泰.最优设计的数学方法.国防工业出版社. 1981.
14 C.R. Hargraves, S.W. Paris, W.G. Vlases. OTIS past, present and future. AIAA 92-4530
15 Betts JT. Survey of Numerical Methods for Trajectory Optimization[J]. JOURNAL OF GUIDANCE, CONTROL, AND DYNAMICS.1998, 21(2)
16 David W.Mile, Stephen M.Rock. Real-Time dynamic trajectory Optimization[C], 1996
17 Vathsal, Sarkar A.K. Optimal control of mission trajectory by an efficient variable transformation technique [C]. AIAA-2001-4203.
18 C.A. Phillips, J.C. Drake. Trajectory Optimization for a Missile Using a Multitier Approach. JOURNAL OF SPACECRAFT AND ROCKETS, 2000.
19钟世勇,王玉堂,曹国敏.弹道式导弹弹道多目标优化研究[D].现代防御技术, 1998.
20 Afzal MI.火箭弹道及运载火箭弹道的设计优化及仿真[D].北京:北京航空航天大学, 2004.
21 John T. Betts. Survey of Numerical Methods for Trajectory Optimization. Journal of Guidance, Control, and Dynamics, 1998, 21(2): (193-207).
22唐明亮.飞行器弹道仿真通用软件设计[D].西安:西北工业大学, 2006.
23尚磊云.空地导弹数学模型与系统仿真模型[D].西安:西北工业大学, 2004.
24罗亚中,唐国金.混合遗传算法及其在运载火箭最优上升轨道设计中的应用[J].国防科技大学学报. 2004
25 CHEN GANG.. Genetic Algorithm Optimization of RLV Reentry Trajectory[J]. AIAA-2005
26冯刚,陈昌敢.运载火箭弹道优化设计.中国航天科技集团公司八院805所, 2004.
27赵汉元.飞行器再入动力学和制导[M].长沙:国防科技大学出版社, 1997.
28姚文俊.遗传算法及其研究进展[J].计算机与数字工程. 2004, 32(4).
29 Jorge Nocedal and Stephen J. Wright. Numerical Optimization. Springer, 2006.
30 Sheu Donglong, Chen Yumin, Chang YuanJen. Optimal glide for maximum Range[R]. AIAA-98-4462.
31王凌.智能优化算法及其应用[M].北京:清华大学出版社, 2001.
32周明,孙树栋.遗传算法原理及应用[M].北京:国防工业出版社, 1999.
33 Grefenstette J J. Optimization of control parameters for genetic algorithms[J]. IEEE Trans. On Systems, Man, and Cybernetics, SMC216(1): 122-128.
34 Goldberg D. Genetic Algorithms in Search, Optimization, and Machine Learning [M]. Addison Wesley, Reading, MA, 1989.
35 R. A. Krohling, J. P. Rey. Design of Optimal Disturbance Rejection PID Controllers Using Genetic Algorithms. IEEE Transactions on Evolutionary Computation, 2001, 5(1): 78-82.
36秦莉,杨明,郭庆.遗传算法在质量矩导弹中姿态控制中的应用.北京航空航天大学学报, 2007, 33(7): 769-772.
37 Nelder J A, Mead R. A simplex method for function minimization[J]. Computer Journal, 1965, 7(2): 308-313.
38 Torczon V. Multi-directional Search: A direct search algorithm for parallelmachines. Ph.D. thesis, Texas: Rice University, 1989: 7-74.
39耿忠娟.对非线性规划单纯形算法的研究[D].中国优秀硕士学位论文全文数据库, 2008, (08).
40赵善友.防空导弹武器寻的制导控制系统设计[M].北京:宇航出版社, 1996.
41曾颖超,陆毓敏.战术导弹与姿态动力学[M].西安:西北工业大学出版社, 1997.
42高为炳.非线性控制系统导论.北京:科学出版社, 1988.
43 Guelman M, Shinar J. Optimal guidance law in the plane .Journal of Guidance, Control and Dynamics, 1984, 76, 7(6): 471-476.
44 M. Sharma, N. Richards. Adaptive, Integrated Guidance and Control for Missile Interceptors. AIAA-2004-4880.
45 Yuan P J, Chern J S. Analytic study of biased proportion navigation. Journal of Guidance, Control and Dynamics, 1992, 151, 15(1): 185-190.
2祝强军.弹道导弹弹道仿真与优化设计[D].西安:西北工业大学, 2007.
3 Christensen D E. Multiple Rocket Launcher characteristics and simulation Technique. AD-A025379.
4 http://mil.news.sohu.com/20081205/n261044852.shtml
5张毅,杨辉耀,李俊莉.弹道导弹弹道学.长沙:国防科技大学出版社, 1999.
6 Taur D R. Midcourse Trajectory Optimization for a SAM Against High-speed Target[R]. AIAA-2002-4514, 2002.
7 Phillips C A, Drake J C. Trajectory optimization for a missile using a multitier approach[J]. Journal of Spacecraft and Rockets.2000, 37(5): 653-662.
8 MustafT.弹道导弹飞行方案设计及弹道优化[D].北京:北京航空航天大学, 2003.
9陈宝林编著.最优化理论与算法.北京:清华大学出版社, 1989.
10李向前,何麟书,王书河.一种战术弹道导弹主动段飞行攻角优化的算法.导弹与航天运载技术, 2002.
11 Mordecai Avriel. Nonlinear Programming: Analysis and Methods. Dover Publishing, 2000.
12 Bryson, Ho. Applied Optimal Control. Blaisdell Publishing Company, 1969.
13程极泰.最优设计的数学方法.国防工业出版社. 1981.
14 C.R. Hargraves, S.W. Paris, W.G. Vlases. OTIS past, present and future. AIAA 92-4530
15 Betts JT. Survey of Numerical Methods for Trajectory Optimization[J]. JOURNAL OF GUIDANCE, CONTROL, AND DYNAMICS.1998, 21(2)
16 David W.Mile, Stephen M.Rock. Real-Time dynamic trajectory Optimization[C], 1996
17 Vathsal, Sarkar A.K. Optimal control of mission trajectory by an efficient variable transformation technique [C]. AIAA-2001-4203.
18 C.A. Phillips, J.C. Drake. Trajectory Optimization for a Missile Using a Multitier Approach. JOURNAL OF SPACECRAFT AND ROCKETS, 2000.
19钟世勇,王玉堂,曹国敏.弹道式导弹弹道多目标优化研究[D].现代防御技术, 1998.
20 Afzal MI.火箭弹道及运载火箭弹道的设计优化及仿真[D].北京:北京航空航天大学, 2004.
21 John T. Betts. Survey of Numerical Methods for Trajectory Optimization. Journal of Guidance, Control, and Dynamics, 1998, 21(2): (193-207).
22唐明亮.飞行器弹道仿真通用软件设计[D].西安:西北工业大学, 2006.
23尚磊云.空地导弹数学模型与系统仿真模型[D].西安:西北工业大学, 2004.
24罗亚中,唐国金.混合遗传算法及其在运载火箭最优上升轨道设计中的应用[J].国防科技大学学报. 2004
25 CHEN GANG.. Genetic Algorithm Optimization of RLV Reentry Trajectory[J]. AIAA-2005
26冯刚,陈昌敢.运载火箭弹道优化设计.中国航天科技集团公司八院805所, 2004.
27赵汉元.飞行器再入动力学和制导[M].长沙:国防科技大学出版社, 1997.
28姚文俊.遗传算法及其研究进展[J].计算机与数字工程. 2004, 32(4).
29 Jorge Nocedal and Stephen J. Wright. Numerical Optimization. Springer, 2006.
30 Sheu Donglong, Chen Yumin, Chang YuanJen. Optimal glide for maximum Range[R]. AIAA-98-4462.
31王凌.智能优化算法及其应用[M].北京:清华大学出版社, 2001.
32周明,孙树栋.遗传算法原理及应用[M].北京:国防工业出版社, 1999.
33 Grefenstette J J. Optimization of control parameters for genetic algorithms[J]. IEEE Trans. On Systems, Man, and Cybernetics, SMC216(1): 122-128.
34 Goldberg D. Genetic Algorithms in Search, Optimization, and Machine Learning [M]. Addison Wesley, Reading, MA, 1989.
35 R. A. Krohling, J. P. Rey. Design of Optimal Disturbance Rejection PID Controllers Using Genetic Algorithms. IEEE Transactions on Evolutionary Computation, 2001, 5(1): 78-82.
36秦莉,杨明,郭庆.遗传算法在质量矩导弹中姿态控制中的应用.北京航空航天大学学报, 2007, 33(7): 769-772.
37 Nelder J A, Mead R. A simplex method for function minimization[J]. Computer Journal, 1965, 7(2): 308-313.
38 Torczon V. Multi-directional Search: A direct search algorithm for parallelmachines. Ph.D. thesis, Texas: Rice University, 1989: 7-74.
39耿忠娟.对非线性规划单纯形算法的研究[D].中国优秀硕士学位论文全文数据库, 2008, (08).
40赵善友.防空导弹武器寻的制导控制系统设计[M].北京:宇航出版社, 1996.
41曾颖超,陆毓敏.战术导弹与姿态动力学[M].西安:西北工业大学出版社, 1997.
42高为炳.非线性控制系统导论.北京:科学出版社, 1988.
43 Guelman M, Shinar J. Optimal guidance law in the plane .Journal of Guidance, Control and Dynamics, 1984, 76, 7(6): 471-476.
44 M. Sharma, N. Richards. Adaptive, Integrated Guidance and Control for Missile Interceptors. AIAA-2004-4880.
45 Yuan P J, Chern J S. Analytic study of biased proportion navigation. Journal of Guidance, Control and Dynamics, 1992, 151, 15(1): 185-190.