北京航空航天大学学报 ›› 2017, Vol. 43 ›› Issue (5): 894-901.doi: 10.13700/j.bh.1001-5965.2016.0387

• 论文 • 上一篇    下一篇

常值推力下面内轨道优化的一种改进间接法

赵国伟1, 李德金1, 宋婷2,3, 武海雷2,3   

  1. 1. 北京航空航天大学 宇航学院, 北京 100083;
    2. 上海航天控制技术研究所 研发中心, 上海 201109;
    3. 上海市空间智能控制技术重点实验室, 上海 201109
  • 收稿日期:2016-05-10 出版日期:2017-05-20 发布日期:2017-05-27
  • 通讯作者: 赵国伟,E-mail:zhaoguowei@buaa.edu.cn E-mail:zhaoguowei@buaa.edu.cn
  • 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。
  • 基金资助:
    国家自然科学基金(11572016)

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

ZHAO Guowei1, LI Dejin1, SONG Ting2,3, WU Hailei2,3   

  1. 1. School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
    2. Research and Development Centre, Shanghai Institute of Spaceflight Control Technology, Shanghai 201109, China;
    3. Shanghai Key Laboratory of Aerospace Intelligent Control Technology, Shanghai 201109, China
  • Received:2016-05-10 Online:2017-05-20 Published:2017-05-27
  • Supported by:
    National Natural Science Foundation of China (11572016)

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。

关键词: 轨道转移, 最优控制, 常值推力, 极大值原理, 共面轨道

Abstract: The transfer of a spacecraft between coplanar orbits under continuous constant thrust with minimum fuel consumption was investigated. A control equation of the optimal trajectory, which the steering angle must satisfy, was derived by using maximum principle. Combining the control equation with dynamic equations, we establish an improved indirect method to design optimal coplanar transfer orbit and propose an approximate application method for the condition when thrust direction adjustment ability was limited. Due to avoiding solving the Lagrange costate differential equations, the improved indirect method reduces difficulty of initial value estimation and calculation a lot than traditional indirect method. Compared with Gauss pseudospectral method, the improved indirect method can get higher precision and better numerical smoothness. Simulations show that a limitation on the magnitude of the second derivative of thrust angle can improve change law of thrust angle and reduce change range of thrust angle; as to the fuel consumption, the greater the thrust magnitude is, the more the fuel consumption is, and the optimal transfer orbit can save fuel consumption a lot under a certain large magnitude of thrust.

Key words: orbit transfer, optimal control, constant thrust, maximum principle, coplanar orbit

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