基于伪谱法的再入可达域影响因素分析

doi:10.16183/j.cnki.jsjtu.2022.256

摘要/Abstract

摘要：

再入可达域是飞行器机动能力的重要体现,可为轨迹规划与制导、着陆点选择等提供依据.为此,研究了一种基于伪谱法的可达域快速生成方法,并对可达域的影响因素进行仿真分析.将攻角、倾侧角同时作为控制量被离散化而形成非线性规划问题,并通过求解若干个不同纵程条件下的最大横程问题得到可达域.基于上述方法对影响可达域的相关因素进行仿真与分析.仿真结果表明,飞行器质量、气动参考面积、大气密度等在一定范围内不会导致可达域的变化;超出一定范围后,会对短纵程轨迹产生明显影响,影响可达域的左半部分,而基本不影响可达域的右半部分;升阻比对可达域的影响较大,其大小与可达域范围成正相关.

关键词: 再入可达域, 轨迹优化, 伪谱法, 影响因素, 升阻比

Abstract:

Entry footprint is an essential manifestation of vehicle maneuverability, which can provide the basis for trajectory planning and guidance, landing point selection, etc. A fast footprint-generation method based on the pseudospectral method is proposed. The influencing factors of footprint are simulated and analyzed. In this method, the attack and bank angles are simultaneously discretized as control quantities to form the nonlinear programming problem of the pseudospectral method, and the footprint is obtained by solving the maximum transverse range problem for several different longitudinal conditions. Moreover, the affecting factors of the footprint are studied. The simulation results show that the mass, reference area, atmospheric density, etc., do not cause the change of the footprint within a specific range. Beyond a certain range, the short longitudinal trajectory would be significantly affected. The left half of the footprint is affected, while the right half is not changed. The effect of the lift-to-resistance ratio on the footprint is significant, and its size is positively related to the footprint range.

Key words: entry footprint, trajectory optimization, pseudospectral method, influence factors, lift-to-resistance ratio

中图分类号:

V448.2

李兆亭, 周祥, 张洪波, 汤国建. 基于伪谱法的再入可达域影响因素分析[J]. 上海交通大学学报, 2022, 56(11): 1470-1478.

LI Zhaoting, ZHOU Xiang, ZHANG Hongbo, TANG Guojian. Analysis of Entry Footprint Based on Pseudospectral Method[J]. Journal of Shanghai Jiao Tong University, 2022, 56(11): 1470-1478.

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参考文献 30

[1]	曾夕娟, 钟范俊, 丁学良, 等. 一种可重复使用再入飞行器的覆盖区求解方法[J]. 载人航天, 2017, 23(1): 14-20.
	ZENG Xijuan, ZHONG Fanjun, DING Xueliang, et al. Method for landing footprint generation in reusable vehicles[J]. Manned Spaceflight, 2017, 23(1): 14-20.
[2]	常松涛, 杨业, 王永骥, 等. 计算再入飞行器可达区域的快速算法[J]. 华中科技大学学报(自然科学版), 2012, 40(7): 1-5.
	CHANG Songtao, YANG Ye, WANG Yongji, et al. A rapid algorithm for generating landing footprint for entry vehicles[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2012, 40(7): 1-5.
[3]	HE R Z, ZHANG Y L, LIU L L, et al. Feasible footprint generation with uncertainty effects[J]. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2019, 233(1): 138-150. doi: 10.1177/0954410017728971 URL
[4]	ZHANG Y L, CHEN K J, LIU L H, et al. Rapid generation of landing footprint based on geometry-predicted trajectory[J]. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2017, 231(10): 1851-1861. doi: 10.1177/0954410016662066 URL
[5]	LIU Q G, LIU X X, WU J, et al. A fast computational method for the landing footprints of space-to-ground vehicles[J]. Journal of Systems Engineering and Electronics, 2020, 31(5): 1062-1076. doi: 10.23919/JSEE.2020.000080 URL
[6]	ZHANG R, LI Z, SHI L. A general footprint generation approach for lifting re-entry vehicle[C]∥28th Congress of the International Council of the Aeronautical Sciences 2012. Brisbane, Australia: ICAS, 2012: 3137-3143.
[7]	章吉力, 周大鹏, 杨大鹏, 等. 禁飞区影响下的空天飞机可达区域计算方法[J]. 航空学报, 2021, 42(8): 525771. doi: 10.7527/S1000-6893.2021.25771
	ZHANG Jili, ZHOU Dapeng, YANG Dapeng, et al. Computation method for reachable domain of aerospace plane under the influence of no-fly zone[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(8): 525771. doi: 10.7527/S1000-6893.2021.25771
[8]	吴楠, 王锋, 赵敏, 等. 高超声速滑翔再入飞行器的可达区快速预测[J]. 国防科技大学学报, 2021, 43(1): 1-6.
	WU Nan, WANG Feng, ZHAO Min, et al. Fast prediction for footprint of hypersonic glide reentry vehicle[J]. Journal of National University of Defense Technology, 2021, 43(1): 1-6.
[9]	LI H F, ZHANG R, LI Z Y, et al. Footprint problem with angle of attack optimization for high lifting reentry vehicle[J]. Chinese Journal of Aeronautics, 2012, 25(2): 243-251. doi: 10.1016/S1000-9361(11)60384-1 URL
[10]	WANG T, ZHANG H B, LI Y Y, et al. An improved footprint generation method for entry vehicles[J]. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2017, 231(10): 1951-1956. doi: 10.1177/0954410016662060 URL
[11]	LU P, XUE S B. Rapid generation of accurate entry landing footprints[J]. Journal of Guidance, Control, and Dynamics, 2010, 33(3): 756-767. doi: 10.2514/1.46833 URL
[12]	杜昕, 刘会龙. 探月飞船跳跃式再入轨迹可达域分析[J]. 载人航天, 2017, 23(2): 163-167.
	DU Xin, LIU Huilong. Analysis of reachable sets of lunar module skip entry trajectory[J]. Manned Spaceflight, 2017, 23(2): 163-167.
[13]	乔浩, 李曾浩, 李新国, 等. 飞行器可达性问题的统一求解方法研究[J]. 弹道学报, 2017, 29(4): 9-14.
	QIAO Hao, LI Zenghao, LI Xinguo, et al. A unified numerical method for aircraft accessibility problems[J]. Journal of Ballistics, 2017, 29(4): 9-14.
[14]	明超, 孙瑞胜, 梁卓, 等. 多脉冲导弹可达域优化方法设计与分析[J]. 国防科技大学学报, 2016, 38(1): 143-149.
	MING Chao, SUN Ruisheng, LIANG Zhuo, et al. Design and analysis of footprint optimization method for multiple-pulse missile[J]. Journal of National University of Defense Technology, 2016, 38(1): 143-149.
[15]	樊朋飞, 郭云鹤, 凡永华, 等. HGV平衡滑翔式轨迹可达区域计算方法研究[J]. 计算机测量与控制, 2019, 27(5): 136-140.
	FAN Pengfei, GUO Yunhe, FAN Yonghua, et al. Footprint calculation of HGV with equilibrium gliding trajectory[J]. Computer Measurement & Control, 2019, 27(5): 136-140.
[16]	赵吉松, 张建宏, 李爽. 高超声速滑翔飞行器再入轨迹快速、高精度优化[J]. 宇航学报, 2019, 40(9): 1034-1043.
	ZHAO Jisong, ZHANG Jianhong, LI Shuang. Rapid and high-accuracy approach for hypersonic glide vehicle reentry trajectory optimization[J]. Journal of Astronautics, 2019, 40(9): 1034-1043.
[17]	蔺君, 何英姿, 黄盘兴. 基于差分进化算法的再入可达域快速计算[J]. 中国空间科学技术, 2020, 40(4): 54-60.
	LIN Jun, HE Yingzi, HUANG Panxing. Fast reentry landing footprint calculation using differential evolution algorithm[J]. Chinese Space Science and Technology, 2020, 40(4): 54-60.
[18]	梁巨平, 周韬, 周浩. 再入飞行器平稳滑翔可达区域计算分析[J]. 兵器装备工程学报, 2018, 39(5): 112-116.
	LIANG Juping, ZHOU Tao, ZHOU Hao. Footprint generation of steady glide reentry vehicle[J]. Journal of Ordnance Equipment Engineering, 2018, 39(5): 112-116.
[19]	赵江, 周锐. 基于粒子群优化的再入可达区计算方法研究[J]. 兵工学报, 2015, 36(9): 1680-1687. doi: 10.3969/j.issn.1000-1093.2015.09.012
	ZHAO Jiang, ZHOU Rui. Landing footprint computation based on particle swarm optimization[J]. Acta Armamentarii, 2015, 36(9): 1680-1687. doi: 10.3969/j.issn.1000-1093.2015.09.012
[20]	孙勇, 段广仁, 张卯瑞, 等. 基于拟能量的高超声速飞行器再入轨迹优化[J]. 上海交通大学学报, 2011, 45(2): 262-266.
	SUN Yong, DUAN Guangren, ZHANG Maorui, et al. Reentry trajectory optimization of hypersonic vehicle based on pseudo energy[J]. Journal of Shanghai Jiao Tong University, 2011, 45(2): 262-266.
[21]	王涛, 张洪波, 李永远, 等. Gauss伪谱法的再入可达域计算方法[J]. 国防科技大学学报, 2016, 38(3): 75-80.
	WANG Tao, ZHANG Hongbo, LI Yongyuan, et al. Landing footprint generation of entry vehicle based on Gauss pseudospectral method[J]. Journal of National University of Defense Technology, 2016, 38(3): 75-80.
[22]	李柯, 聂万胜, 冯必鸣. 助推-滑翔飞行器可达区域影响因素研究[J]. 现代防御技术, 2013, 41(3): 42-47.
	LI Ke, NIE Wansheng, FENG Biming. Affecting factor of footprint for boost-glide vehicle[J]. Modern Defence Technology, 2013, 41(3): 42-47.
[23]	WANG Z, YANG M, HU H X, et al. Landing footprint computation and simulation for spacecraft of reentry phase[C]∥Signal and Information Processing, Networking and Computers. Singapore: Springer, 2020: 387-393.
[24]	解永锋, 唐硕. 亚轨道飞行器再入可达域快速计算方法[J]. 飞行力学, 2011, 29(4): 72-76.
	XIE Yongfeng, TANG Shuo. Rapid calculation of entry footprint of suborbital launch vehicles[J]. Flight Dynamics, 2011, 29(4): 72-76.
[25]	XIE Y, LIU L H, LIU J, et al. Rapid generation of entry trajectories with waypoint and no-fly zone constraints[J]. Acta Astronautica, 2012, 77: 167-181. doi: 10.1016/j.actaastro.2012.04.006 URL
[26]	RICHIE G. The common aero vehicle—Space delivery system of the future[C]∥Space Technology Conference and Exposition. Reston, Virginia: AIAA, 1999: 4435.
[27]	GARG D, PATTERSON M, HAGER W W, et al. A unified framework for the numerical solution of optimal control problems using pseudospectral methods[J]. Automatica, 2010, 46(11): 1843-1851. doi: 10.1016/j.automatica.2010.06.048 URL
[28]	GILL P E, MURRAY W, SAUNDERS M A. SNOPT: An SQP algorithm for large-scale constrained optimization[J]. SIAM Review, 2005, 47(1): 99-131. doi: 10.1137/S0036144504446096 URL
[29]	WÄCHTER A, BIEGLER L T. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming[J]. Mathematical Programming, 2006, 106(1): 25-57. doi: 10.1007/s10107-004-0559-y URL
[30]	PATTERSON M A, RAO A V. Exploiting sparsity in direct collocation pseudospectral methods for solving optimal control problems[J]. Journal of Spacecraft and Rockets, 2012, 49(2): 354-377. doi: 10.2514/1.A32071 URL

状态	v/(m·s^-1)	θ/(°)	ψ/(°)	h/km	λ/(°)	φ_S/(°)	φ_N/(°)
起点状态	6500	0	90	70	0	0	0
过程状态下限	1000	-20	-360	30	0	-90	-2
过程状态上限	6500	+2	+360	70	λ_f	2	90
终点状态下限	1000	-3	-360	30	0	-90	-2
终点状态上限	1000	+0	+360	30	λ_f	2	90

序号	变量	拉偏比率/%
1	M	-5、0、+5
2	S	-5、0、+5
3	C_L	-10、0、+10
4	C_D	-10、0、+10
5	ρ	-5、0、+5