一种基于大气层外解析动力学模型的最优迭代制导方法
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摘要
固体火箭在实际飞行过程中其发动机参数会产生较大的摄动偏差,而传统的摄动制导很难保证较高的制导精度,甚至会发散。另外,采用动力学数值积分的显式制导算法进行实时计算又会带来较大的计算量,从而难以满足实际飞行的要求。针对这一问题,提出了一种基于大气层外解析动力学模型的最优迭代制导方法。首先在大气层外推导了解析动力学模型,然后基于Pontryagin极大值原理推导了最省燃料的推力控制方法,以共轭状态向量和飞行时间为迭代变量给出了带有多种终端约束的迭代制导算法。仿真分析了发动机参数和火箭初始状态在最大正偏差以及最大负偏差情况下迭代制导精度,并进行了蒙特卡罗打靶仿真。仿真结果表明,提出的基于大气层外解析动力学模型的迭代制导算法计算时间少、制导精度高、鲁棒性强,具有较好的工程应用价值。
The large perturbation deviations of engine parameters of solid rocket would appear in the process of actual flight,which is hard to guarantee superior guidance precision and even causes divergency. Additionally,a large amount of calculation would emerge in terms of explicit guidance of adopting numerical integration of dynamic model,which is hard to satisfy the requirements of the actual flight. To solve the problems,this paper presents an optimal iterative guidance method based on exoatmospheric analytical dynamics model. On the basis of flight dynamics model,the thrust control method of the most-saving fuel is deduced based on the Pontryagin maximum principle,and the iteration guidance algorithm whose iterative variables are conjugate state vector and flight time is given under the condition of a variety of terminal constraints. The iterative guidance precision is analyzed by simulation in the case of maximum positive and negative deviation concerned with solid rocket engine parameters and initial state,followed by monte carlo targeting simulation. The simulation results demonstrate that the proposed iterative guidance method based on exoatmospheric analytical dynamics model displays less computation,high precision,strong robustness and superior engineering application.
The large perturbation deviations of engine parameters of solid rocket would appear in the process of actual flight,which is hard to guarantee superior guidance precision and even causes divergency. Additionally,a large amount of calculation would emerge in terms of explicit guidance of adopting numerical integration of dynamic model,which is hard to satisfy the requirements of the actual flight. To solve the problems,this paper presents an optimal iterative guidance method based on exoatmospheric analytical dynamics model. On the basis of flight dynamics model,the thrust control method of the most-saving fuel is deduced based on the Pontryagin maximum principle,and the iteration guidance algorithm whose iterative variables are conjugate state vector and flight time is given under the condition of a variety of terminal constraints. The iterative guidance precision is analyzed by simulation in the case of maximum positive and negative deviation concerned with solid rocket engine parameters and initial state,followed by monte carlo targeting simulation. The simulation results demonstrate that the proposed iterative guidance method based on exoatmospheric analytical dynamics model displays less computation,high precision,strong robustness and superior engineering application.
引文
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[10]郑伟.地球物理摄动因素对远程弹道导弹命中精度的影响分析及补偿方法研究[D].长沙:国防科学技术大学,2006:123-126Zheng Wei.Research on Effect of Geophysical Disturbance Factors and the Compensation Method for Hit Accuracy of LongRange Ballistic Missile[D].Changsha,National University of Defense Technology,2006:123-126(in Chinese)
[2]郑军.灵活机动、便捷高效的固体弹道导弹[J].兵器知识,1999,2(10):31-33Zheng Jun.Flexible,Convenient and Efficient Solid Ballistic Missiles[J].Ordnance Knowledge,1999,2(10):31-33(in Chinese)
[3]宋征宇.从准确、精确到精益求精——载人航天推动运载火箭制导方法的发展[J].航天控制,2013,31(1):4-10Song Zhengyu.From Accurate,Precise to Perfect——Manned Space Promotes the Development of Guidance Method on Launch Vehicle[J].Aerospace Control,2013,31(1):4-10(in Chinese)
[4]Lu P,Pan B F.Highly Constrained Optimal Launch Ascent Guidance[J].Journal of Guidance,Control,and Dynamics,2010,33(2):404-414
[5]Huang P X,Wei C Z,Gu Y B,et al.A Symplectic Optimization Method for Rapid Endo-Atmospheric Ascent Trajectory Planning[J].International Journal of Modelling,Identification and Control,2015,24(3):196-205
[6]Mounir K Z,Denis A,Christophe L.Mixed Iterative Algorithm for Solving Optimal Impulsive Time-Fixed Rendezvous Problem[C]∥AIAA Guidance,Navigation,and Control Conference,2010,Toronto,Ontario Canada
[7]Jing W X,Zheng X,Wei P X,et al.An Ascent Iterative Guidance Algorithm for Solid Rocket Concerned with Multi-Constraints[C]∥27th Chinese Control and Decision Conference(CCDC),2015,Qingdao,China
[8]茹家欣.液体运载火箭的一种迭代制导方法[J].中国科学(E辑:技术科学),2009,39(4):696-706Ru Jiaxin.An Iterative Guidance Method for Liquid Rocket[J].Science in China(Series E),2009,39(4):696-706(in Chinese)
[9]傅瑜,陈功,卢宝刚,等.基于最优解析解的运载火箭大气层外自适应迭代制导方法[J].航空学报,2011,32(9):1696-1704Fu Yu,Chen Gong,Lu Baogang,et al.A Vacuum Adaptive Iterative Guidance Method of Launch Vehicle Based on Optimal Analytical Solution[J].Acta Aeronautica et Astronautica Sinica,2011,32(9):1696-1704(in Chinese)
[10]郑伟.地球物理摄动因素对远程弹道导弹命中精度的影响分析及补偿方法研究[D].长沙:国防科学技术大学,2006:123-126Zheng Wei.Research on Effect of Geophysical Disturbance Factors and the Compensation Method for Hit Accuracy of LongRange Ballistic Missile[D].Changsha,National University of Defense Technology,2006:123-126(in Chinese)