敏捷卫星姿态机动的奇异最优控制

印明威; 李京阳; 宝音贺西

doi:10.3788/OPE.20182604.0906

您当前的位置：

首页 >

文章列表页 >

敏捷卫星姿态机动的奇异最优控制

信息科学 | 更新时间：2020-07-05

- 敏捷卫星姿态机动的奇异最优控制
- Singular optimal control for three-axis reorientation of an agile satellite
- 光学精密工程 2018年26卷第4期页码：906-915
- 作者机构：
  
  清华大学航天航空学院, 北京 100084
- 作者简介：
  
  [ "印明威(1991-), 男, 湖北洪湖人, 博士研究生, 2013年于北京航空航天大学获得学士学位, 主要从事航天器姿态动力学与控制、敏捷卫星成像任务规划等方面研究。Email:ymw13@mails.tsinghua.edu.cn" ]
  [ "宝音贺西(1972-), 男, 内蒙古人, 博士, 教授, 国家杰出青年基金获得者, 1999年于哈尔滨工业大学获得博士学位, 主要从事航天器姿态控制、轨道优化等方面研究。E-mail:baoyin@tsinghua.edu.cn" ]
- 基金信息：
  
  国家杰出青年科学基金资助项目(11372150);中国博士后科学基金资助项目(2016T90086);中国博士后科学基金面上资助项目(2015M581080);国家自然科学基金资助项目(11602123)
- DOI：10.3788/OPE.20182604.0906
  中图分类号： V448.22
- 收稿日期：2017-08-09，
  
  录用日期：2017-12-8，
  
  纸质出版日期：2018-04-25
- 稿件说明：
移动端阅览
印明威, 李京阳, 宝音贺西. 敏捷卫星姿态机动的奇异最优控制[J]. 光学精密工程, 2018,26(4):906-915.

Ming-wei YIN, Jing-yang LI, He-xi BAOYIN. Singular optimal control for three-axis reorientation of an agile satellite[J]. Optics and precision engineering, 2018, 26(4): 906-915.
印明威, 李京阳, 宝音贺西. 敏捷卫星姿态机动的奇异最优控制[J]. 光学精密工程, 2018,26(4):906-915. DOI： 10.3788/OPE.20182604.0906.

Ming-wei YIN, Jing-yang LI, He-xi BAOYIN. Singular optimal control for three-axis reorientation of an agile satellite[J]. Optics and precision engineering, 2018, 26(4): 906-915. DOI： 10.3788/OPE.20182604.0906.

摘要

研究姿态机动的时间最优控制时，通常只考虑最优解为Bang-Bang控制的情况，假设了开关函数仅在有限个孤立点为零，本文对假设之外的奇异最优控制进行探讨。以球对称光学敏捷卫星为对象，根据姿态机动最优控制问题的数学模型，证明了开关函数的特殊性质。在不同边界条件下，结合一阶必要条件、广义勒让德-克莱伯西条件等，分析了最优控制包含奇异区间的所有情况，得到了奇异控制最优性的必要条件。结果表明，对于起止角速度为0，乃至起止角速度相同的所有工况，可以直接排除奇异控制最优的可能性，最优控制中各个分量在+1和-1之间切换；而起止角速度相异时，存在奇异控制最优的情况，且奇异分量的开关函数在全过程均为0，奇异阶数为无穷阶，文中给出了相应算例予以佐证。

Abstract

The possibility of singular optimal control in the time-optimal reorientation of an agile satellite with independent three-axis control was investigated in this paper. Generally

it is assumed that the switching functions take the value zero only at isolated points

which dictates that the controls are "bang-bang". However

some new results were found in this paper. An inertially symmetric rigid body was considered. Based on the optimum model

two propositions about the switching functions were derived. All possible optimal control strategies under different boundary conditions were identified. These included bang-bang solution

one control singular

two controls singular and all three controls singular. Using Pontryagin's principle and the Generalized Legendre-Clebsch condition

necessary conditions for optimality of singular control were obtained. The research illustrated that all three control components could not be simultaneously singular at any point on an optimal path. For rest to rest maneuvers

singular control was proved to be not optimal. Actually

for the boundary conditions that the initial and final angular velocities were equal

the possibility of singular optimal control could be completely dismissed. The components of the optimal control switch between +1 and -1. On the other hand

the cases of singular optimal control exist while the final angular velocity was different from the initial one

the switching function of the singular component remained at zero all the time

and the order of the singular control was infinite. Numerical examples of time-optimal solutions with one control singular and two controls singular were presented.

关键词

Keywords

references

LEMAIÎTRE M, VERFAILLIE G, JOUHAUD F, et al.. Selecting and scheduling observations of agile satellites[J]. Aerospace Science and Technology, 2002, 6(5):367-381.

王秀红, 李俊峰, 高彦平, 等.基于虚拟测距的单星光学监测空间目标定轨方法[J].光学精密工程, 2016, 24(7):1541-1549.

WANG X H, LI J F, GAO Y P, et al.. Orbit determination of space objects with single satellite optical observations and virtual range[J]. Opt. Precision Eng., 2016, 24(7):1541-1549. (in Chinese)

陈雪芹, 耿云海, 王峰, 等.敏捷小卫星对地凝视姿态跟踪控制[J].光学精密工程, 2012, 20(5):1031-1040.

CHEN X Q, GENG Y H, WANG F, et al.. Staring imaging attitude tracking control of agile small satellite[J]. Opt. Precision Eng., 2012, 20(5):1031-1040. (in Chinese)

徐开, 金光, 陈娟, 等.敏捷小卫星姿态机动切换算法[J].光学精密工程, 2008, 16(8):1528-1532.

XU K, JIN G, CHEN J, et al.. Switch algorithm for quick small satellite attitude maneuver[J]. Opt. Precision Eng., 2008, 16(8):1528-1532. (in Chinese)

ZHANG J R. The output torque estimation of MCMG for agile satellites[J]. Acta Mechanica Sinica, 2010, 26(1):141-146.

范国伟, 常琳, 戴路, 等.敏捷卫星姿态机动的非线性模型预测控制[J].光学精密工程, 2015, 23(8):2318-2327.

FAN G W, CHANG L, DAI L, et al.. Nonlinear model predictive control of agile satellite attitude maneuver[J]. Opt. Precision Eng., 2015, 23(8):2318-2327. (in Chinese)

SCRIVENER S L, THOMPSON R C. Survey of time-optimal attitude maneuvers[J]. Journal of Guidance Control and Dynamics, 1994, 17(2):225-233.

叶东. 敏捷卫星姿态快速机动与稳定控制方法研究[D]. 哈尔滨: 哈尔滨工业大学, 2013.

YE D. Research on fast maneuver and stabilization control for agile satellite [D]. Harbin: Harbin Institute of Technology, 2013. (in Chinese)

NGUYEN H, PHAM Q C. Time-optimal path parameterization of rigid-body motions:Applications to spacecraft reorientation[J]. Journal of Guidance Control and Dynamics, 2016, 39(7):1667-1671.

LI F Y, BAINUM P M. Numerical approach for solving rigid spacecraft minimum time attitude maneuvers[J]. Journal of Guidance Control and Dynamics, 1990, 13(1):38-45.

BILIMORIA K D, WIE B. Time-optimal three-axis reorientation of a rigid spacecraft[J]. Journal of Guidance Control and Dynamics, 1993, 16(3):446-452.

BAI X L, JUNKINS J L. New results for time-optimal three-axis reorientation of a rigid spacecraft[J]. Journal of Guidance Control and Dynamics, 2009, 32(4):1071-1076.

LI J. Analysis of the inertially symmetric rigid spacecraft time-optimal three-axis reorientation[J]. Optimal Control Applications and Methods, 2017, 38(1):59-74.

BOYARKO G A, ROMANO M, YAKIMENKO O A. Time-optimal reorientation of a spacecraft using an inverse dynamics optimization method[J]. Journal of Guidance Control and Dynamics, 2011, 34(4):1197-1208.

VENTURA J, ROMANO M, WALTER U. Performance evaluation of the inverse dynamics method for optimal spacecraft reorientation[J]. Acta Astronautica, 2015, 110:266-278.

KIRK D E. Optimal Control Theory:An Introduction[M]. London:Courier Corporation, 2012.

BELL D J, JACOBSON D H. Singular Optimal Control Problems[M]. Pittsburgh, U.S.A:Academic Press, 1975.

解学书.最优控制理论与应用[M].北京:清华大学出版社, 1986.

XIE X SH. Optimal Control Theory and Application[M]. Beijing:Tsinghua University Press, 1986. (in Chinese)

MARTINON P, BONNANS F, LAURENT-VARIN J, et al.. Numerical study of optimal trajectories with singular arcs for an Ariane 5 launcher[J]. Journal of Guidance Control and Dynamics, 2009, 32(1):51-55.

SEYWALD H, KUMAR R R. Singular control in minimum time spacecraft reorientation[J]. Journal of Guidance Control and Dynamics, 1993, 16(4):686-694.

LEE T, LEOK M, MCCLAMROCH N H. Time optimal attitude control for a rigid body[C]. Proceedings of 2008 American Control Conference , IEEE , 2008: 5210-5215.

FLEMING A, SEKHAVAT P, ROSS I M. Minimum-time reorientation of a rigid body[J]. Journal of Guidance Control and Dynamics, 2010, 33(1):160-170.

SHEN H J, TSIOTRAS R. Time-optimal control of axisymmetric rigid spacecraft using two controls[J]. Journal of Guidance Control and Dynamics, 1999, 22(5):682-694.

ROBBINS H M. A generalized Legendre-Clebsch condition for the singular cases of optimal control[J]. IBM Journal of Research and Development, 1967, 11(4):361-372.

焦宝聪, 王在洪, 时红廷.常微分方程[M].北京:清华大学出版社, 2008.

JIAO B C, WANG Z H, SHI H T. Ordinary Differential Equations[M]. Beijing:Tsinghua University Press, 2008. (in Chinese)

GOH B S. Necessary conditions for singular extremals involving multiple control variables[J]. SIAM Journal on Control, 1966, 4(4):716-731.

KELLEY H J. A second variation test for singular extremals[J]. AIAA Journal, 1964, 2(8):1380-1382.

KELLEY H J, KOPP R E, MOYER H G. 3 Singular extremals[J]. Mathematics in Science and Engineering, 1967, 31:63-101.

RAO A V, BENSON D A, DARBY C, et al.. Algorithm 902:GPOPS, A MATLAB software for solving multiple-phase optimal control problems using the gauss pseudospectral method[J]. ACM Transactions on Mathematical Software (TOMS), 2010, 37(2):22.

GARG D, PATTERSON M A, FRANCOLIN C, et al.. Direct trajectory optimization and costate estimation of finite-horizon and infinite-horizon optimal control problems using a Radau pseudospectral method[J]. Computational Optimization and Applications, 2011, 49(2):335-358.

浏览量

429

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

敏捷卫星姿态机动的非线性模型预测控制

敏捷小卫星对地凝视姿态跟踪控制