高斯伪谱法在变推力导弹弹道优化中的应用
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摘要
为实现对可变推力固体火箭发动机推进剂的充分利用,以近程导弹拦截目标为特定研究场景,在推进剂质量给定的情况下采用Gauss伪谱法进行弹道优化设计。该方法采用变推力控制,选用固体火箭发动机实现推力可调,由比例导引给出制导指令,研究Gauss伪谱法在变推力导弹弹道优化中的应用方法,最终得到目标函数及约束条件下的比例导引变推力优化方案。仿真结果表明了高斯伪谱法应用于可变推力导弹弹道优化设计的有效性,同时与传统发动机方案下的弹道进行对比,表明了变推力控制在导弹弹道性能上的优越性。
To make full use of variable solid rocket engine propellant,a short-range missile intercepting target is taken as a research scenario,and the Gauss pseudo-spectral method is adopted for trajectory optimization design under given propellant mass. Solid rocket engine can achieve thrust control and the guidance commands are given by proportional navigation method. The trajectory optimization is realized based on the Gauss pseudo-spectral method under the objective function and constraints. Simulation results show that the Gauss pseudo-spectral method is effective in trajectory optimization design of variable trust missile. Compared with the trajectory under the traditional solid rocket engine scheme,it shows the superiority of variable thrust control in missile trajectory performance.
To make full use of variable solid rocket engine propellant,a short-range missile intercepting target is taken as a research scenario,and the Gauss pseudo-spectral method is adopted for trajectory optimization design under given propellant mass. Solid rocket engine can achieve thrust control and the guidance commands are given by proportional navigation method. The trajectory optimization is realized based on the Gauss pseudo-spectral method under the objective function and constraints. Simulation results show that the Gauss pseudo-spectral method is effective in trajectory optimization design of variable trust missile. Compared with the trajectory under the traditional solid rocket engine scheme,it shows the superiority of variable thrust control in missile trajectory performance.
引文
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[13]孙勇.基于改进Gauss伪谱法的高超声速飞行器轨迹优化与制导[D].哈尔滨:哈尔滨工业大学,2012.SUN Yong. Trajectory Optimization and Guidance of Hypersonic Vehicle Based on Improved Gauss PseudoSpectral Method[D]. Harbin:Harbin Institute of Technology,2012.
[14]杨希祥,杨慧欣,王鹏.伪谱法及其在飞行器轨迹优化设计领域的应用综述[J].国防科技大学学报,2015(4):1-8.YANG Xi-xiang,YANG Hui-xin,WANG Peng. Overview of Pseudo-Spectral Method and Its Application in Trajectory Optimum Design for Flight Vehicles[J]. Journal of National University of Defense Technology,2015(4):1-8.
[15]张洪倩.基于高斯伪谱法的弹道优化设计与实现[D].南京:南京理工大学,2014.ZHANG Hong-qian. Trajectory Optimization Design and Realization Based on Gauss Pseudo-Spectral Method[D]. Nanjing:Nanjing University of Science and Technology,2014.
[16]张松.基于高斯伪谱法的空空导弹弹道优化策略[C]∥中国自动化学会控制理论专业委员会、中国系统工程学会.第三十二届中国控制会议论文集(C卷),中国自动,2013:5.ZHANG Song. Midcourse Trajectory Optimization Strategy for Air to Air Missile Based on Gauss Pseudo-spectral Method[C]∥Technical Committee on Control Theory,Chinese Association of Automation,Systems Engineering Society of China. Proceedings of the 32ndChinese Control Conference,2013:5.
[2]侯晓,付鹏,武渊.固体火箭发动机能量管理技术及其新进展[J].固体火箭技术,2017(1):1-6.HOU Xiao,FU Peng,WU Yuan. Energy Management Technology of SRM and Its Development[J]. Journal of Solid Rocket Technology,2017(1):1-6.
[3] RYAN J. A Legendre Pseudospectral Method for Rapid Optimization of Launch Vehicle Trajectories[J]. Massachusetts Institute of Technology,2001.
[4] Clarke,Kimberley A. Performance Optimization Study of a Common Aero Vehicle Using a Legendre Pseudospectral Method[J]. Massachusetts Institute of Technology,2003.
[5] Taylor,Christine P. Optimization Study of a Trans-Atlantic Abort for the U. S. Space Shuttle Using a Pseudospectral Legendre Method[J]. Massachusetts Institute of Technology,2003.
[6] STANTON S A. Optimal Orbital Transfer Using a Legendre Pseudospectral Method[J]. 2003.
[7] HAWKINS A M. Constrained Trajectory Optimization of a Soft Lunar Landing from a Parking Orbit[J]. Massachusetts Institute of Technology,2005.
[8] Benson David. A Gauss Pseudospectral Transcription for Optimal Control[J]. Massachusetts Institute of Technology,2005.
[9]曹喜滨,张相宇,王峰.采用Gauss伪谱法的小推力日-火Halo轨道转移优化设计[J].宇航学报,2013,34(8):1047-1054.CAO Xi-bin,ZHANG Xiang-yu,WANG Feng. Optimization Design of Small Thrust Daily-Fire Halo Orbit Transfer Using Gauss Pseudo-Spectral Method[J]. Journal of Astronautics,2013,34(8):1047-1054.
[10]杨希祥,张为华.基于Gauss伪谱法的固体运载火箭上升段轨迹快速优化研究[J].宇航学报,2011,32(1):15-21.YANG Xi-xiang,ZHANG Wei-hua. Trajectory Fast Optimization of Solid Launch Vehicle Rising Stage Based on Gauss Pseudo-Spectral Method[J]. Journal of Astronautics,2011,32(1):15-21.
[11]杨希祥,张为华.基于Gauss伪谱法的空空导弹最优中制导律设计[J].国防科技大学学报,2013,35(1):28-32.YANG Xi-xiang,ZHANG Wei-hua. Midcourse Guidance Law Optimal Design for Air-to-Air Missiles Based on Gauss Pseudo-spectral Method[J]. Hournal of National University of Defense Technology,2013,35(1):28-32.
[12]彭祺擘,李海阳,沈红新,等.基于Gauss伪谱法和直接打靶法结合的月球定点着陆轨道优化[J].国防科技大学学报,2012,34(2):119-124.PENG Qi-bo,LI Hai-yang,SHEN Hong-xin,et,al. Lunar Trajectory Optimization Based on Gauss Pseudo-Spectral Method and Direct Target Shooting Method[J]. Journal of National University of Defense Technology,2012,34(2):119-124.
[13]孙勇.基于改进Gauss伪谱法的高超声速飞行器轨迹优化与制导[D].哈尔滨:哈尔滨工业大学,2012.SUN Yong. Trajectory Optimization and Guidance of Hypersonic Vehicle Based on Improved Gauss PseudoSpectral Method[D]. Harbin:Harbin Institute of Technology,2012.
[14]杨希祥,杨慧欣,王鹏.伪谱法及其在飞行器轨迹优化设计领域的应用综述[J].国防科技大学学报,2015(4):1-8.YANG Xi-xiang,YANG Hui-xin,WANG Peng. Overview of Pseudo-Spectral Method and Its Application in Trajectory Optimum Design for Flight Vehicles[J]. Journal of National University of Defense Technology,2015(4):1-8.
[15]张洪倩.基于高斯伪谱法的弹道优化设计与实现[D].南京:南京理工大学,2014.ZHANG Hong-qian. Trajectory Optimization Design and Realization Based on Gauss Pseudo-Spectral Method[D]. Nanjing:Nanjing University of Science and Technology,2014.
[16]张松.基于高斯伪谱法的空空导弹弹道优化策略[C]∥中国自动化学会控制理论专业委员会、中国系统工程学会.第三十二届中国控制会议论文集(C卷),中国自动,2013:5.ZHANG Song. Midcourse Trajectory Optimization Strategy for Air to Air Missile Based on Gauss Pseudo-spectral Method[C]∥Technical Committee on Control Theory,Chinese Association of Automation,Systems Engineering Society of China. Proceedings of the 32ndChinese Control Conference,2013:5.