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常值推力下面内轨道优化的一种改进间接法

赵国伟 李德金 宋婷 武海雷

赵国伟, 李德金, 宋婷, 等 . 常值推力下面内轨道优化的一种改进间接法[J]. 北京航空航天大学学报, 2017, 43(5): 894-901. doi: 10.13700/j.bh.1001-5965.2016.0387
引用本文: 赵国伟, 李德金, 宋婷, 等 . 常值推力下面内轨道优化的一种改进间接法[J]. 北京航空航天大学学报, 2017, 43(5): 894-901. doi: 10.13700/j.bh.1001-5965.2016.0387
ZHAO Guowei, LI Dejin, SONG Ting, et al. An improved indirect method for in plane orbit optimization under constant thrust[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(5): 894-901. doi: 10.13700/j.bh.1001-5965.2016.0387(in Chinese)
Citation: ZHAO Guowei, LI Dejin, SONG Ting, et al. An improved indirect method for in plane orbit optimization under constant thrust[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(5): 894-901. doi: 10.13700/j.bh.1001-5965.2016.0387(in Chinese)

常值推力下面内轨道优化的一种改进间接法

doi: 10.13700/j.bh.1001-5965.2016.0387
基金项目: 

国家自然科学基金 11572016

详细信息
    作者简介:

    赵国伟, 男, 博士, 副教授。主要研究方向:航天飞行器设计、航天飞行器动力学与控制、在轨操作系统

    通讯作者:

    赵国伟, E-mail:zhaoguowei@buaa.edu.cn

  • 中图分类号: V412.4

An improved indirect method for in plane orbit optimization under constant thrust

Funds: 

National Natural Science Foundation of China 11572016

More Information
  • 摘要:

    针对常值推力下航天器面内轨道转移燃耗最省的轨道优化问题,利用极大值原理导出了最优轨迹下推力方向角应满足的控制方程,结合动力学方程建立了一种求解航天器面内最优转移轨道的改进间接法,及其在推力方向角调节能力受限条件下的应用方法。由于避免了协态变量微分方程组的求解,改进间接法相对于传统间接法降低了初值猜测的难度和计算量;与采用Gauss伪谱法求解相比,所建立的改进间接法求解结果精度更高,数值光滑性更好。仿真算例表明:推力方向角调节能力受限会改善推力方向角变化规律,降低推力方向角变化范围;就燃耗而言,推力越大燃耗越多,优化轨道节省燃耗更加显著。

     

  • 图 1  变量示意图

    Figure 1.  Illustration of variables

    图 2  改进间接法求解流程

    Figure 2.  Flowchart of improved indirect method

    图 3  Gauss伪谱法求解流程

    Figure 3.  Flowchart of Gauss pseudospectral method

    图 4  不同推力加速度下推力方向角变化曲线

    Figure 4.  Thrust angle vs time under different thrust acceleration

    图 5  ϕ″不受限时推力方向角变化规律

    Figure 5.  Change law of thrust angle when ϕ″ is free

    图 6  |ϕ″|≤0.008 (°)/s2时推力方向角变化规律

    Figure 6.  Change law of thrust angle when |ϕ″|≤0.008 (°)/s2

    表  1  不同条件下的转移轨道燃耗

    Table  1.   Fuel consumption of orbit transfer under different conditions

    推力加速度/
    (10-3m·s-2)
    速度变化量/(m·s-1)
    切向推力转移轨道 优化轨道
    Gauss伪谱法求解不限ϕ Gauss伪谱法求解|ϕ″|≤0.008 (°)/s2 改进间接法求解不限ϕ 改进间接法求解|ϕ″|≤0.008 (°)/s2
    0.02 13.205 12.757 12.757 12.757 12.757
    0.10 14.862 14.005 14.007 14.005 14.005
    0.15 12.858 12.713 12.713 12.713 12.713
    0.20 14.995 14.254 14.257 14.254 14.254
    0.40 22.588 20.645 20.722 20.645 20.670
    1.00 40.315 34.428 34.447 34.309 34.421
    4.00 100.270 72.974 73.007 72.856 72.937
    10.00 185.780 117.660 117.770 117.560 117.690
    下载: 导出CSV
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出版历程
  • 收稿日期:  2016-05-10
  • 录用日期:  2016-09-21
  • 网络出版日期:  2017-05-20

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