大气层内助推段广义标控脱靶量解析制导律

doi:10.12305/j.issn.1001-506X.2023.07.26

摘要/Abstract

摘要：

针对大气层内助推段的制导问题，提出了一种适用于多级助推器的广义标控脱靶量解析制导律。首先，给出了满足终端弹道倾角和高度约束的最优标控攻角曲线的求解方法。利用弹道解析解可将助推段动力学约束转换为关于插值节点处攻角值的函数，以此将攻角曲线优化问题离散为非线性规划问题, 并通过序列二次规划可求得其最优解。之后，在每个制导周期，基于当前状态量解析预测标控攻角曲线下的广义标控脱靶量；为了闭环修正终端误差，利用线性二次型最优控制推导了解析形式的制导指令修正量，其可表示为广义标控脱靶量的线性组合。仿真结果表明，该制导方法不仅所需过载小，且制导精度高，适用范围广。

关键词: 大气层内助推段, 助推段制导律, 广义标控脱靶量, 弹道解析解

Abstract:

An analytical generalized nominal miss distance guidance law suitable for multi-stage booster is proposed for the endo-atmospheric boost guidance. Firstly, the optimal nominal angle of attack curve satisfied the terminal flight-path angle and altitude constraints is given. Using the analytical solution of boost trajectory, the dynamical constraint is enforced by the arbitrary angle of attack values discretized in Chebyshev-Gauss-Legendre points. Therefore, the optimal angle of attack problem is discretized into the nonlinear programming problem and its solution can be derived by sequential quadratic programming. Then, in each guidance cycle, the generalized nominal effort miss (GNEM) is predicted analytically based on the current states. The linear quadratic optimal control is used to derive the analytical guidance correction, which can be expressed as a linear combination of the GNEM. The simulation results show that the proposed method not only performs well in providing the small guidance command, but also has high guidance accuracy and great applicability.

Key words: endo-atmosphere boost phase, guidance law for boost phase, generalized nominal effort miss (GNEM), trajectory analytical solution

中图分类号:

TN953

赵石磊, 陈万春, 杨良, 冯卓. 大气层内助推段广义标控脱靶量解析制导律[J]. 系统工程与电子技术, 2023, 45(7): 2150-2157.

Shilei ZHAO, Wanchun CHEN, Liang YANG, Zhuo FENG. Analytical generalized nominal effort miss guidance law for endo-atmosphere boost phase[J]. Systems Engineering and Electronics, 2023, 45(7): 2150-2157.

图/表 8

图1

图2

表1

图3

表2

表3

图4

表4

参考文献 26

1	宋征宇, 巩庆海, 王聪, 等. 长征运载火箭上升段的自主制导方法及其研究进展[J]. 中国科学: 信息科学, 2021, 51 (10): 1587- 1608.
	SONG Z Y , GONG Q H , WANG C , et al. Review and progress of the autonomous guidance method for Long March launch vehicle ascent flight[J]. Scientia Sinica Informationis, 2021, 51 (10): 1587- 1608.
2	郭玮林, 鲜勇, 张大巧, 等. 高超声速飞行器助推段弹道快速计算方法[J]. 中国惯性技术学报, 2018, 26 (1): 109- 114.
	GUO W L , XIAN Y , ZHANG D Q , et al. Fast calculation method of booster trajectory for hypersonic vehicle[J]. Journal of Chinese Inertial Technology, 2018, 26 (1): 109- 114.
3	LU P , SUN H , TSAI B . Closed-loop endoatmo-spheric ascent guidance[J]. Journal of Guidance, Control, and Dynamics, 2013, 26 (2): 283- 294.
4	MURILLO O, LU P. Fast ascent trajectory optimization for hypersonic air-Breathing vehicles[C]//Proc. of the AIAA Gui-dance, Navigation, and Control Conference, 2010.
5	LU P , PAN B F . Highly constrained optimal launch ascent guidance[J]. Journal of Guidance, Control, and Dynamics, 2010, 33 (2): 404- 414. doi: 10.2514/1.45632
6	LU P, ZHANG L J, SUN H S. Ascent guidance for responsive launch: a fixed-point approach[C]//Proc. of the AIAA Guidance, Navigation, and Control Conference and Exhibit, 2005.
7	LU B , CUI N G , FU Y , et al. Closed-loop atmospheric ascent guidance based on finite element method[J]. Aircraft Engineering and Aerospace Technology, 2015, 87 (5): 393- 401. doi: 10.1108/AEAT-02-2014-0021
8	DUKEMAN G, CALISE A. Enhancements to an atmospheric ascent guidance algorithm[C]//Proc. of the AIAA Guidance, Navigation, and Control Conference and Exhibit, 2003.
9	DUKEMAN G. Atmospheric ascent guidance for rocket-powered launch vehicles[C]//Proc. of the AIAA Guidance, Navigation, and Control Conference and Exhibit, 2002.
10	CHENG X M , LI H F , ZHANG R . Efficient ascent trajectory optimization using convex models based on the Newton-Kantorovich/Pse-udospectral approach[J]. Aerospace Science and Technology, 2017, 66, 140- 151. doi: 10.1016/j.ast.2017.02.023
11	DUAN H B , LI S T . Artificial bee colony-based direct collocation for reentry trajectory optimization of hypersonic vehicle[J]. IEEE Trans.on Aerospace and Electronic Systems, 2015, 51 (1): 615- 626. doi: 10.1109/TAES.2014.120654
12	FU W Z , WANG B , LI X , et al. Ascent trajectory optimization for hypersonic vehicle based on improved chicken swarm optimization[J]. IEEE Access, 2019, 7, 151836- 151850. doi: 10.1109/ACCESS.2019.2947297
13	PONTANI M . Particle swarm optimization of ascent trajectories of multistage launch vehicles[J]. Acta Astronautica, 2014, 94 (2): 852- 864. doi: 10.1016/j.actaastro.2013.09.013
14	GIRI R, GHOSE D. Differential evolution based ascent phase trajectory optimization for a hypersonic vehicle[C]//Proc. of the International Conference on Swarm, Evolutionary, and Memetic Computing, 2010.
15	PRASANNA H M, GHOSE D, BHAT M S, et al. Ascent phase trajectory optimization for a hypersonic vehicle using nonlinear programming[C]//Proc. of the International Confe-rence on Computational Science and its Applications, 2005.
16	SHI W , JING Z L , YANG Y S . Ascent trajectory optimisation for hypersonic vehicles via Gauss pseudospectral method[J]. International Journal of Space Science and Engineering, 2013, 1 (1): 64- 81. doi: 10.1504/IJSPACESE.2013.051769
17	YANG S B , CUI T , HAO X Y , et al. Trajectory optimization for a ramjet-powered vehicle in ascent phase via the Gauss pseudospectral method[J]. Aerospace Science and Technology, 2017, 67, 88- 95. doi: 10.1016/j.ast.2017.04.001
18	ZHOU J , LEI H M , ZHANG D . Online optimal midcourse trajectory modification algorithm for hypersonic vehicle interceptions[J]. Aerospace Science and Technology, 2017, 63, 266- 277. doi: 10.1016/j.ast.2016.12.022
19	ZHANG D , LIU L , WANG Y J . Online ascent phase trajectory optimal guidance algorithm based on pseudospectral method and sensitivity updates[J]. Journal of Navigation, 2015, 68 (6): 1056- 1074. doi: 10.1017/S0373463315000326
20	YANG L , ZHOU H , CHEN W C . Application of linear Gauss pseudospectral method in model predictive control[J]. Acta Astronautica, 2014, 96, 175- 187. doi: 10.1016/j.actaastro.2013.11.038
21	YANG L , YANG J , CHEN W C , et al. Entry guidance with no-fly zone avoidance using linear pseudospectral model predictive control[J]. IEEE Access, 2019, 7, 98589- 98602. doi: 10.1109/ACCESS.2019.2927995
22	YANG L , LIU X M , CHEN W C , et al. Autonomous entry gui-dance using linear pseudospectral model predictive control[J]. Aero-space Science and Technology, 2018, 80, 38- 55. doi: 10.1016/j.ast.2018.06.031
23	YANG L , CHEN W C , LIU X M , et al. Robust entry guidance using multi-segment linear pseudospectral model predictive control[J]. Journal of Systems Engineering and Electronics, 2017, 28 (1): 103- 125. doi: 10.21629/JSEE.2017.01.13
24	ZARCHAN P . Tactical and strategic missile guidance[M]. 6th ed Reston, Virginia: AIAA, 2012.
25	ZHAO S L , YANG L , CHEN W C . Endoatmospheric ascent optimal guidance with analytical nonlinear trajectory prediction[J]. International Journal of Aerospace Engineering, 2022, 2022, 5729335.
26	陈思远. 助推-滑翔导弹弹道优化及制导方法研究[D]. 北京: 北京理工大学, 2016.
	CHEN S Y. Study on trajectory optimization and guidance method for boost-glide missil e[D]. Beijing: Beijing Institute of Technology, 2016.

制导率	算例	弹道倾角误差/(°)	高度误差/m	终端攻角/(°)
本文制导律	1	-3.85E-05	1.86E-04	0.056 5
	2	-2.25E-05	-1.87E-04	0.017 3
	3	-3.49E-06	-1.91E-05	0.002 2
	4	-6.56E-05	-1.81E-04	-0.099 4
样条曲线制导律	1	2.36E-05	-1.26E-04	-3.056 7
	2	2.83E-05	7.44E-05	-4.548 3
	3	3.71E-05	7.13E-05	-4.456 0
	4	2.41E-04	3.51E-04	-6.775 6

参数	拉偏值(3σ)/%	参数	拉偏值(3σ)/%
升力系数	10	大气密度	10
阻力系数	10	发动机总冲	3

制导律	参数	弹道倾角误差/(°)	高度误差/m	终端攻角/(°)
本文制导律	平均值	1.64E-05	-1.66E-04	0.094 8
本文制导律	标准差	7.02E-05	2.57E-04	0.763 0
样条曲线制导律	平均值	-4.96E-05	1.44E-04	-3.000 3
样条曲线制导律	标准差	3.78E-05	2.28E-04	0.980 7

[1]	毕文豪, 周杰, 张安, 刘力. 杂波环境下基于最大熵模糊聚类的JPDA算法[J]. 系统工程与电子技术, 2023, 45(7): 1920-1927.
[2]	王森, 鲍庆龙, 潘嘉蒙, 祝茜. 基于改进概率假设密度滤波器的非合作双基地雷达目标跟踪[J]. 系统工程与电子技术, 2023, 45(7): 2002-2009.
[3]	张宏伟. 双站纯方位空时软约束无迹粒子滤波算法[J]. 系统工程与电子技术, 2023, 45(5): 1261-1269.
[4]	任明健, 胡国平, 周豪, 游致远, 张凌培. 基于耦合张量分解的稀疏阵列二维DOA估计算法[J]. 系统工程与电子技术, 2023, 45(4): 958-964.
[5]	刘政玮, 陈映, 鲁耀兵. 适用于多目标轨迹小角度交叉的PHD滤波器[J]. 系统工程与电子技术, 2023, 45(4): 982-990.
[6]	张育豪, 朱圣棋, 曾操, 崔森, 石琦剑. EPC-MIMO雷达主瓣距离欺骗式干扰抑制方法[J]. 系统工程与电子技术, 2023, 45(3): 690-698.
[7]	游致远, 胡国平, 周豪. 基于冗余阵元优化的双基地嵌套MIMO雷达目标DOD和DOA联合估计方法[J]. 系统工程与电子技术, 2022, 44(12): 3696-3702.
[8]	张瑜, 吴凯, 郭杰, 葛志闪, 张宝超. 基于数据质量评估的自适应序贯航迹关联算法[J]. 系统工程与电子技术, 2022, 44(11): 3477-3485.
[9]	刘浩楠, 宋骊平. 基于核Fisher判别的群结构更新模型及群目标跟踪算法[J]. 系统工程与电子技术, 2022, 44(10): 3012-3019.
[10]	孙照强, 王志贵, 孟飞, 李陆雨, 于中, 陈燕. 基于EKF及弹道方程的弹道目标跟踪滤波器设计[J]. 系统工程与电子技术, 2022, 44(10): 3207-3212.
[11]	万福海, 许京伟, 张振荣. FDA-MIMO雷达稳健抗主瓣距离欺骗式干扰技术[J]. 系统工程与电子技术, 2022, 44(9): 2809-2816.
[12]	侯子林, 程婷, 彭瀚. 基于量测转换序贯滤波的GMPHD机动目标跟踪[J]. 系统工程与电子技术, 2022, 44(8): 2474-2482.
[13]	刘红亮, 陈超, 黄昆伟, 卢博, 岳凯. 针对分布式雷达网的多帧联合航迹起始方法[J]. 系统工程与电子技术, 2022, 44(7): 2143-2147.
[14]	王伟, 王钦钊, 沈岚, 王波, 丁怀. 基于概率累积的非通视无源定位方法[J]. 系统工程与电子技术, 2022, 44(1): 64-69.
[15]	庞晓娇, 赵永波, 曹成虎, 胡毅立, 陈胜. 基于协方差拟合准则的降维空时自适应处理方法[J]. 系统工程与电子技术, 2022, 44(1): 86-93.