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高超末段机动突防/精确打击弹道建模与优化

李静琳 陈万春 闵昌万

李静琳, 陈万春, 闵昌万等 . 高超末段机动突防/精确打击弹道建模与优化[J]. 北京航空航天大学学报, 2018, 44(3): 556-567. doi: 10.13700/j.bh.1001-5965.2017.0308
引用本文: 李静琳, 陈万春, 闵昌万等 . 高超末段机动突防/精确打击弹道建模与优化[J]. 北京航空航天大学学报, 2018, 44(3): 556-567. doi: 10.13700/j.bh.1001-5965.2017.0308
LI Jinglin, CHEN Wanchun, MIN Changwanet al. Terminal hypersonic trajectory modeling and optimization for maneuvering penetration and precision strike[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(3): 556-567. doi: 10.13700/j.bh.1001-5965.2017.0308(in Chinese)
Citation: LI Jinglin, CHEN Wanchun, MIN Changwanet al. Terminal hypersonic trajectory modeling and optimization for maneuvering penetration and precision strike[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(3): 556-567. doi: 10.13700/j.bh.1001-5965.2017.0308(in Chinese)

高超末段机动突防/精确打击弹道建模与优化

doi: 10.13700/j.bh.1001-5965.2017.0308
详细信息
    作者简介:

    李静琳  女, 博士研究生。主要研究方向:弹道优化、制导导航与控制

    陈万春  男, 博士, 教授, 博士生导师。主要研究方向:飞行力学、制导导航与控制

    通讯作者:

    陈万春, E-mail: wanchun_chen@buaa.edu.cn

  • 中图分类号: V412+.4;TJ765.3

Terminal hypersonic trajectory modeling and optimization for maneuvering penetration and precision strike

More Information
  • 摘要:

    针对高超声速飞行器再入末段机动突防、精确打击问题,从最优控制角度出发,提出了一种考虑拦截弹动力学特性的最优机动突防弹道优化方法,获得了高超声速飞行器的最大机动能力。该方法将拦截弹运动模型引入突防弹道优化的模型中,通过施加约束限制拦截弹按照比例导引律飞行。根据飞行任务和交战双方的弹道特点分段,结合各段的任务和特性,分别提出了突防性能指标和精确打击性能指标等,并通过加权函数将各个独立、矛盾的性能指标统一,建立了多对象、多段、多约束机动突防弹道优化模型,采用Radau多段伪谱法(MRPM)进行求解。针对该问题求解的初值敏感、可行域窄等问题,提出了一系列弹道优化策略,提高了收敛速度和求解精度,最终获得了最优机动弹道,并通过协态映射原理对其最优性进行了验证。结果表明,该方法能充分发挥高超声速飞行器的机动能力,获得满足落点精度要求的突防弹道,相对已有方法,将脱靶量提高了1~2个量级。灵敏度分析表明,该弹道对拦截弹的发射时间不敏感。

     

  • 图 1  高超末段机动突防-对地打击示意图

    Figure 1.  Diagram of maneuvering penetration and ground attack in terminal phase of hypersonic trajectory

    图 2  弹道分段示意图

    Figure 2.  Schematic diagram of trajectory segment

    图 3  平滑性能指标对控制曲线的影响

    Figure 3.  Influence of smoothness performance index on control curves

    图 4  弹道优化流程图

    Figure 4.  Trajectory optimization flowchart

    图 5  可行性精度对比

    Figure 5.  Comparison of feasibility accuracy

    图 6  最优性精度对比

    Figure 6.  Comparison of optimality accuracy

    图 7  可行性精度收敛性

    Figure 7.  Feasibility accuracy convergence

    图 8  逐次迭代可行性精度收敛性

    Figure 8.  Feasibility accuracy convergence in iteration

    图 9  弹道分段嵌套优化流程

    Figure 9.  Nested multi-phase trajectory optimization process

    图 10  x-z曲线、x-y曲线和速度-时间曲线

    Figure 10.  x-z curves, x-y curves and velocity-time curves

    图 11  弹道倾角-时间曲线

    Figure 11.  Flight path angle-time curves

    图 12  突防弹攻角-时间曲线和倾侧角-时间曲线

    Figure 12.  Penetration missile attack angle-time curve and bank angle-time curves

    图 13  不同机动形式突防弹攻角-时间曲线和倾侧角-时间曲线

    Figure 13.  Penetration missile attack angle-time curve and bank angle-time curves of different motivations

    图 14  三维弹道曲线

    Figure 14.  Three-dimensional trajectory curves

    图 15  热流密度-时间,动压-时间,过载-时间曲线

    Figure 15.  Heat flux-time, dynamic pressure-time and overload-time curves

    图 16  哈密顿函数曲线

    Figure 16.  Hamiltonian function curves

    图 17  拦截弹发射时机影响

    Figure 17.  Impact of interceptor launch time

    表  1  突防弹初始及终端状态约束

    Table  1.   Initial and terminal state constraints of penetration missile

    时间 xA/m yA/m zA/m VA/(m·s-1) θA/(°) ψA/(°) αA/(°) σA/(°)
    t0 10 188.8 21 299.3 10 188.8 1 878.8 -18.9 135.0 10 -180
    tf -9 346 0 -9 346 (800, 1 100) (-90, -75) (0, 7)
    下载: 导出CSV

    表  2  拦截弹初始状态约束

    Table  2.   Initial state constraints of interception missile

    状态约束 xD0/
    m
    yD0/
    m
    zD0/
    m
    VD0/
    (m·s-1)
    θD0/
    (°)
    ψD0/
    (°)
    mD0/
    kg
    数值 -8 000 0 -8 000 1 000 38 -45 315
    下载: 导出CSV

    表  3  突防弹常规路径约束

    Table  3.   Path constraints of penetration missile

    路径约束 q/(N·m-2) ny
    数值 400 6×105 20
    下载: 导出CSV

    表  4  优化结果终端状态

    Table  4.   Terminal states of optimal results

    性能指标 xAf/m yAf/m zAf/m VAf/(m·s-1) θAf/(°) ψAf/(°) αAf/(°) σAf/(°)
    J1 -9 346.99 -1.00 -9 346.99 1 450.67 -84.37 132.49 6.00 -178.64
    J2 -9 344.99 -1.00 -9 344.99 1 515.68 -75.01 135.00 6.00 -180.01
    J3 -9 344.99 -1.00 -9 346.99 1 377.61 -75.01 180.01 6.00 -210.65
    J4 -9 344.99 -1.00 -9 346.99 1 018.95 -90.01 180.01 6.00 -180.20
    常值 -9 345.99 -1.81×10-12 -9 345.99 1 462.12 -84.62 135.01 10.00 -180.00
    下载: 导出CSV

    表  5  突防脱靶量对比

    Table  5.   Comparison of penetration miss distance

    性能指标 脱靶量/m
    J1 19.00
    J2 5.18
    J3 216.65
    J4 234.59
    常值 3.69
    下载: 导出CSV

    表  6  不同机动形式突防脱靶量对比

    Table  6.   Comparison of penetration miss distance of different motivations

    机动形式 最优机动 程序机动
    脱靶量/m 234.6 119.7
    下载: 导出CSV

    表  7  求解精度对比

    Table  7.   Comparison of solution accuracy

    求解精度 GPOPS初值生成器 分段嵌套优化
    节点数 41 105
    节点误差 0.293 5 8.313 9×10-5
    可行性 2.0×10-2 3.2×10-8
    最优性 9.4×10-3 7.2×10-6
    下载: 导出CSV
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出版历程
  • 收稿日期:  2017-05-15
  • 录用日期:  2017-08-11
  • 刊出日期:  2018-03-20

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