弹道导弹的弹道设计与仿真
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摘要
在弹道导弹设计的各个阶段,需要进行不同精度的弹道设计和仿真。同时,不同种类的导弹的仿真模型也相差较大。弹道导弹的弹道设计与仿真是弹道导弹总体设计的重要内容,贯穿于弹道导弹研制的各个阶段。同一导弹选用不同姿态的弹道,会有不同的飞行性能。为正确使用和充分发挥导弹的技术性能,需要对弹道进行认真设计。为了得到准确的仿真结果,设计人员需要针对具体问题使用专门软件。
针对这一需要,本文致力于弹道设计、编写弹道仿真软件能实现不同类型的导弹在不同的发射方式下,进行不同自由度的多段弹道全数字仿真。为此,本研究主要集中在以下几个方面:
1)在理想状态环境下建立弹道仿真所需的子模块,包括坐标转换模块、地球引力模块、标准大气模块、飞行程序模块、发动机模块等。给出了弹道导弹的主动段运动方程、自由段椭圆运动方程和再入段运动方程。分析了引力和附加惯性力等因素对射程的影响。
2)论述了用参数选择法求解弹道仿真问题的方法。弹道导弹的弹道求解就是设计俯仰角程序,文中给出了俯仰角程序设计的工程方法。通过选择俯仰角程序的几个特殊参数,将弹道解算这样的动态问题转化为参数选择问题。针对弹道导弹飞行弹道的目标和多种约束要求,建立了参数数学和仿真模型。
3)编写程序,以便从输入文本中搜索提取有用数据,并使程序变得更加有效可靠和友好易懂。这有利于弹道设计和仿真等其他软件调用本软件时修改参数。
最后,本文结合具体算例对软件的使用进行了简要地说明介绍,验证了软件的可靠性。
In ballistic missile design of each phase, the need for different precision design and simulation of trajectory. At the same time, different kinds of missile simulation model is different. Ballistic missile trajectory design and simulation is a ballistic missile is an important content of the overall design, throughout all phases of ballistic missiles. The same gesture of ballistic missile chooses different, can have different flight performance. For the correct use and fully missile technology, need to carefully designed trajectory. In order to get accurate simulation results, the design for specific issues need to use special software.
In this paper, a need to ballistic trajectory simulation software design, write to achieve different types of missile launch in different ways in different degrees, of ef ficient digital simulation. Therefore, this research mainly in the following aspects:
1) In the ideal environment for establishment of trajectory simulation modules, including coordinate conversion module, gravity module, standard atmospheric module, flight program modules, engine modules etc. Given a ballistic missile active period of motion equation for freedom, the equation of motion and elliptic equations of motion segment. Analysis of gravity and additional force on the influence factors such as range.
2) Discussed with parameter selection method to solve the problem of trajectory simulation method. Solving ballistic missile trajectory design elevation Angle is presented, the procedure of the method of engineering program design elevation Angle. Through the choice of several special pitching Angle program, so the dynamic solution trajectory problem into the parameter selection problem. According to the target of ballistic missile flight trajectory, and many constraints, established mathematical and simulation model.
3)Program, to extract from the input text search, and make useful data become more effective and reliable program. Friendly This is helpful for ballistic design and simulation software calls the other software modification parameter.
Finally, combined with a concrete example of the use of software are briefly introduced, and verifies the software reliability.
针对这一需要,本文致力于弹道设计、编写弹道仿真软件能实现不同类型的导弹在不同的发射方式下,进行不同自由度的多段弹道全数字仿真。为此,本研究主要集中在以下几个方面:
1)在理想状态环境下建立弹道仿真所需的子模块,包括坐标转换模块、地球引力模块、标准大气模块、飞行程序模块、发动机模块等。给出了弹道导弹的主动段运动方程、自由段椭圆运动方程和再入段运动方程。分析了引力和附加惯性力等因素对射程的影响。
2)论述了用参数选择法求解弹道仿真问题的方法。弹道导弹的弹道求解就是设计俯仰角程序,文中给出了俯仰角程序设计的工程方法。通过选择俯仰角程序的几个特殊参数,将弹道解算这样的动态问题转化为参数选择问题。针对弹道导弹飞行弹道的目标和多种约束要求,建立了参数数学和仿真模型。
3)编写程序,以便从输入文本中搜索提取有用数据,并使程序变得更加有效可靠和友好易懂。这有利于弹道设计和仿真等其他软件调用本软件时修改参数。
最后,本文结合具体算例对软件的使用进行了简要地说明介绍,验证了软件的可靠性。
In ballistic missile design of each phase, the need for different precision design and simulation of trajectory. At the same time, different kinds of missile simulation model is different. Ballistic missile trajectory design and simulation is a ballistic missile is an important content of the overall design, throughout all phases of ballistic missiles. The same gesture of ballistic missile chooses different, can have different flight performance. For the correct use and fully missile technology, need to carefully designed trajectory. In order to get accurate simulation results, the design for specific issues need to use special software.
In this paper, a need to ballistic trajectory simulation software design, write to achieve different types of missile launch in different ways in different degrees, of ef ficient digital simulation. Therefore, this research mainly in the following aspects:
1) In the ideal environment for establishment of trajectory simulation modules, including coordinate conversion module, gravity module, standard atmospheric module, flight program modules, engine modules etc. Given a ballistic missile active period of motion equation for freedom, the equation of motion and elliptic equations of motion segment. Analysis of gravity and additional force on the influence factors such as range.
2) Discussed with parameter selection method to solve the problem of trajectory simulation method. Solving ballistic missile trajectory design elevation Angle is presented, the procedure of the method of engineering program design elevation Angle. Through the choice of several special pitching Angle program, so the dynamic solution trajectory problem into the parameter selection problem. According to the target of ballistic missile flight trajectory, and many constraints, established mathematical and simulation model.
3)Program, to extract from the input text search, and make useful data become more effective and reliable program. Friendly This is helpful for ballistic design and simulation software calls the other software modification parameter.
Finally, combined with a concrete example of the use of software are briefly introduced, and verifies the software reliability.
引文
1齐艳丽. 2006年国外战略弹道导弹发展综述.中国航天. 2007,(04):2~6
2张飞天.近程弹道导弹弹道优化方法研究.哈尔滨工业大学硕士论文2009:8~9
3甘楚雄,刘冀湘.弹道导弹和运载火箭总体设计.国防工业出版社. 1996: 59~103
4张毅,杨辉耀,李俊莉.弹道导弹弹道学.国防科技大学出版社. 1999:1~300
5唐明亮.飞行器弹道仿真通用软件设计.西北工业大学硕士论文2006:20~25,34~37
6王明海,李邦杰.弹道导弹弹道设计的一种快速迭代方法.飞行力学, 2007,(02) :18~25.
7 Doug Nelson,Qualitative and Quantitative Assessment of Optimal Trajectories by ImPlicit Simulation(OTIS) and Program to Optimize Simulated Trajectories (POST),April 26,2001:24~29
8吕学富.飞行器飞行力学.西北工业大学出版社. 1995:14~54
9祝强军.弹道导弹弹道仿真与优化设计.西北工业大学硕士论文2007.03:22~77
10贾沛然,陈克俊.何力.远程火箭弹道学.国防科技大学出版社. 1993: 62~92
11 Zarchan Paul. Tactical and Strategic Missile Guidance. Second Edition, Published by the American Institute of Aeronautics and Astronautics Inc., 1994:3~18
12郝磊,李邦杰,王明海.速燃弹道导弹飞行程序角设计方法.弹箭与制导学报. 2008,(02):21~28
13程文科,江琳,王华,杨光.基于Modelica的弹道导弹三自由度仿真.系统仿真技术.2009.07 5(3) 174~175
14强胜,申镇,易东云,涂先勤.基于导弹设计原理的弹道建模与仿真.战术导弹技术2008.4(4)
15张星奇,张合新,孙立江.地地弹道导弹空气动力系数的建模与仿真.战术导弹控制技术. 2006,(04):22~36 .
16肖滨,郭鹏程等.战术弹道导弹的弹道仿真.系统仿真技术. 2008.10, 4(4):214~215
17陈磊,吴瑞林,王军.战术弹道导弹的性能推测及仿真实现.现代防御技术. 2000,2.28(1):57~62
18 Der-Ren Taur and Jeng-Shing Chern,Optimal Side Jet Control Vertically Cold Launched Tactical Missiles. AIAA-2000-4164.2001:23~52
19 The ASDL Missile Design Team,DKM119 Fast Attack,Air Launched Air to Ground Missile,AIAA Missile Systems Technical Committee,1999:3~21
20李海军,黄显林,葛东明.基于轨迹线性化的再入机动飞行器控制器设计.战术导弹控制技术. 2009,(01):1~6
21雷刚,鲜勇.弹道导弹飞行弹道的三维仿真.计算机仿真. 2005.8,22(8): 33~34
22王芳,刘新学.弹道导弹再入机动弹道设计研究.计算机仿真.2008,(06):1~6
23 Kozai Y. the motion of a close erath satellite[J] .The Astronomical Journal, 1959, 64 (9) :367-377
24 Whiting, J K. Three-dimensional low-thrust trajectory optimization with applications. AIAA-2003-5260: 32~38
25 D. Hull. Conversion of Optimal Contrl Problems into Parameter Optimization Problems. AIAA?1996?3812.:44~53
26 CarlsonNA , Michael P , Berarducci Federated Kalman Filter Simulation Results Navigation,1994:41(3):290-331
27 Thomas R M, Timothy T C, Patrick E M. A Generic Common Simulation Framework based Starting Point for Missile 6DOF Simulations[R]. AIAA 2005-5887,2005:321~326
28 Timothy T C, Thomas R M. Challenges and Lessons Learned Establishing Simulation Reuse and Collaboration at Raytheon Missile Systems[R].AIAA 2006-6259. 2006:231~243
29高桂清,刘刚,郭锡监,姚应权.弹道导弹被动段雷达截面积仿真计算研究.系统仿真学报.2007,(16):15~26
30 Terril N H, Thomas R M, Louisa J G. Integrating Support for Statistical Design Methods within Missile 6DOF Simulation Experiments[R].AIAA 2006-6260,2006:212~218
31呼玮,杨建军,龙光正,王森.弹道导弹被动段动态RCS建模与仿真.电光与控制.2010,(04):25~38
32王子才.关于仿真理论的探讨.航空工业出版社. 1990:93~110
33 Richard L, Dongyu F, Jinho K. Using Matlab/Simulink for Launch Vehicle GN&C Validation[R].AIAA 2002-4687,2002:16~21
34 Robert G Sargent. Validation And Verification of Simulation Models. Proceedings of WSC05. 2005:43~53
35 Victoria H. Scene Generation Interation Into a Common Simulation Framework [R].SPIE vol.6239,2006:32~38
36祝庆国,刘刚,鲜勇.战术弹道导弹再入段机动弹道仿真研究.战术导弹技术, 2008,(01):122~127
37 Rauw M O.FDC 1.2-A Simulink Toolbox for Flight Dynamics and Control Analysis, Zeist, The Netherlands, 1997:34~65
38 Magni J F, Bennani S, Terlouw J. Robust Flight Control: A Design Challenge, Springer-Verlag London Ltd, 1997:12~26
39 M. Duran Toksari. Ant colony optimization for finding the global minimum. Applied Mathematics and Computation, 2006, 308~316
40 Computer Model and Simulation of a Theater Ballistic Missile(TBM) Counterforce Plan Involving a Lethal Unmanned Air Vehicle(UAV),Richard W. Kammann.September19,1995:22~27
41 Modelica Association. Modelica Tutorial--Modelica Conference 2008(ppt). http://www.Modelica.org/,2008.
42 Waldraff W, Finsterwalder R. Master Project Overview for the Development of a Modular Vehicle Simulator[R].AIAA, Aug 2001:6-9
43 Alejandro A, perez A.Modeling of a Gas Turbine with Modelica [D]. Sweden: Department of Automatic Control Lund Institue of Technology, 2001:12~16
44张靖男,赵兴锋等.战术导弹的弹道仿真模型.兵工自动化先进制造技术. 2006,25(8):29~30
45王强如,李兰友主编. C语言绘图与计算机仿真技术.北京航空航天大学出版社. 1995
46钱能. C ++程序设计教程.清华大学出版社. 1999
2张飞天.近程弹道导弹弹道优化方法研究.哈尔滨工业大学硕士论文2009:8~9
3甘楚雄,刘冀湘.弹道导弹和运载火箭总体设计.国防工业出版社. 1996: 59~103
4张毅,杨辉耀,李俊莉.弹道导弹弹道学.国防科技大学出版社. 1999:1~300
5唐明亮.飞行器弹道仿真通用软件设计.西北工业大学硕士论文2006:20~25,34~37
6王明海,李邦杰.弹道导弹弹道设计的一种快速迭代方法.飞行力学, 2007,(02) :18~25.
7 Doug Nelson,Qualitative and Quantitative Assessment of Optimal Trajectories by ImPlicit Simulation(OTIS) and Program to Optimize Simulated Trajectories (POST),April 26,2001:24~29
8吕学富.飞行器飞行力学.西北工业大学出版社. 1995:14~54
9祝强军.弹道导弹弹道仿真与优化设计.西北工业大学硕士论文2007.03:22~77
10贾沛然,陈克俊.何力.远程火箭弹道学.国防科技大学出版社. 1993: 62~92
11 Zarchan Paul. Tactical and Strategic Missile Guidance. Second Edition, Published by the American Institute of Aeronautics and Astronautics Inc., 1994:3~18
12郝磊,李邦杰,王明海.速燃弹道导弹飞行程序角设计方法.弹箭与制导学报. 2008,(02):21~28
13程文科,江琳,王华,杨光.基于Modelica的弹道导弹三自由度仿真.系统仿真技术.2009.07 5(3) 174~175
14强胜,申镇,易东云,涂先勤.基于导弹设计原理的弹道建模与仿真.战术导弹技术2008.4(4)
15张星奇,张合新,孙立江.地地弹道导弹空气动力系数的建模与仿真.战术导弹控制技术. 2006,(04):22~36 .
16肖滨,郭鹏程等.战术弹道导弹的弹道仿真.系统仿真技术. 2008.10, 4(4):214~215
17陈磊,吴瑞林,王军.战术弹道导弹的性能推测及仿真实现.现代防御技术. 2000,2.28(1):57~62
18 Der-Ren Taur and Jeng-Shing Chern,Optimal Side Jet Control Vertically Cold Launched Tactical Missiles. AIAA-2000-4164.2001:23~52
19 The ASDL Missile Design Team,DKM119 Fast Attack,Air Launched Air to Ground Missile,AIAA Missile Systems Technical Committee,1999:3~21
20李海军,黄显林,葛东明.基于轨迹线性化的再入机动飞行器控制器设计.战术导弹控制技术. 2009,(01):1~6
21雷刚,鲜勇.弹道导弹飞行弹道的三维仿真.计算机仿真. 2005.8,22(8): 33~34
22王芳,刘新学.弹道导弹再入机动弹道设计研究.计算机仿真.2008,(06):1~6
23 Kozai Y. the motion of a close erath satellite[J] .The Astronomical Journal, 1959, 64 (9) :367-377
24 Whiting, J K. Three-dimensional low-thrust trajectory optimization with applications. AIAA-2003-5260: 32~38
25 D. Hull. Conversion of Optimal Contrl Problems into Parameter Optimization Problems. AIAA?1996?3812.:44~53
26 CarlsonNA , Michael P , Berarducci Federated Kalman Filter Simulation Results Navigation,1994:41(3):290-331
27 Thomas R M, Timothy T C, Patrick E M. A Generic Common Simulation Framework based Starting Point for Missile 6DOF Simulations[R]. AIAA 2005-5887,2005:321~326
28 Timothy T C, Thomas R M. Challenges and Lessons Learned Establishing Simulation Reuse and Collaboration at Raytheon Missile Systems[R].AIAA 2006-6259. 2006:231~243
29高桂清,刘刚,郭锡监,姚应权.弹道导弹被动段雷达截面积仿真计算研究.系统仿真学报.2007,(16):15~26
30 Terril N H, Thomas R M, Louisa J G. Integrating Support for Statistical Design Methods within Missile 6DOF Simulation Experiments[R].AIAA 2006-6260,2006:212~218
31呼玮,杨建军,龙光正,王森.弹道导弹被动段动态RCS建模与仿真.电光与控制.2010,(04):25~38
32王子才.关于仿真理论的探讨.航空工业出版社. 1990:93~110
33 Richard L, Dongyu F, Jinho K. Using Matlab/Simulink for Launch Vehicle GN&C Validation[R].AIAA 2002-4687,2002:16~21
34 Robert G Sargent. Validation And Verification of Simulation Models. Proceedings of WSC05. 2005:43~53
35 Victoria H. Scene Generation Interation Into a Common Simulation Framework [R].SPIE vol.6239,2006:32~38
36祝庆国,刘刚,鲜勇.战术弹道导弹再入段机动弹道仿真研究.战术导弹技术, 2008,(01):122~127
37 Rauw M O.FDC 1.2-A Simulink Toolbox for Flight Dynamics and Control Analysis, Zeist, The Netherlands, 1997:34~65
38 Magni J F, Bennani S, Terlouw J. Robust Flight Control: A Design Challenge, Springer-Verlag London Ltd, 1997:12~26
39 M. Duran Toksari. Ant colony optimization for finding the global minimum. Applied Mathematics and Computation, 2006, 308~316
40 Computer Model and Simulation of a Theater Ballistic Missile(TBM) Counterforce Plan Involving a Lethal Unmanned Air Vehicle(UAV),Richard W. Kammann.September19,1995:22~27
41 Modelica Association. Modelica Tutorial--Modelica Conference 2008(ppt). http://www.Modelica.org/,2008.
42 Waldraff W, Finsterwalder R. Master Project Overview for the Development of a Modular Vehicle Simulator[R].AIAA, Aug 2001:6-9
43 Alejandro A, perez A.Modeling of a Gas Turbine with Modelica [D]. Sweden: Department of Automatic Control Lund Institue of Technology, 2001:12~16
44张靖男,赵兴锋等.战术导弹的弹道仿真模型.兵工自动化先进制造技术. 2006,25(8):29~30
45王强如,李兰友主编. C语言绘图与计算机仿真技术.北京航空航天大学出版社. 1995
46钱能. C ++程序设计教程.清华大学出版社. 1999