带视线角约束的三维超螺旋滑模协同制导律

doi:10.12305/j.issn.1001-506X.2023.07.25

摘要/Abstract

摘要：

针对三维情况下带视线角约束的多弹协同制导问题，基于二阶一致性理论和自适应超螺旋滑模控制方法提出了一种新的三维多弹协同制导律。在视线切向方向，设计了一种协同方法，并利用二阶一致性理论，证明了导弹的相对距离和相对速度能在有限时间内趋于一致。在视线高低角和方位角方向，设计了一个新的滑模面，并利用自适应超螺旋滑模控制方法，证明了在该制导律下导弹能够在有限时间内实现期望视线角且视线角速率收敛到0。所采用的自适应超螺旋滑模控制方法能有效解决传统的滑模抖振问题，且对机动目标有一定的鲁棒性。最后，在仿真实验中，通过对比分析验证了所提出的制导律具有更高的制导精度。

关键词: 协同制导, 一致性理论, 超螺旋滑模, 自适应控制

Abstract:

In view of the problem of three-dimensional multi-missile cooperative guidance with line-of-sight angle constraint, a three-dimensional multi-missile cooperative guidance law is proposed based on second-order consensus theory and adaptive super-twisting sliding mode control method. In the line-of-sight direction, the relative distance and relative velocity of the missile will converge to consensus in finite time. In the elevation direction and azimuth direction of line-of-sight, this paper proves that the missile can achieve the desire line-of-sight angle and the line-of-sight angle rate converges to zero in finite time. The adaptive super-twisting sliding mode control method adopted can effectively solve the chattering problem of traditional sliding mode and be robust to maneuvering targets. Finally, the effectiveness of the designed cooperative guidance law is demonstrated in the simulation experiment through the comparative analysis.

Key words: cooperative guidance, consensus theory, super-twisting sliding mode, adaptive control

中图分类号:

V448.133

游骏, 张科, 韩治国, 蔡天星, 张程. 带视线角约束的三维超螺旋滑模协同制导律[J]. 系统工程与电子技术, 2023, 45(7): 2138-2149.

Jun YOU, Ke ZHANG, Zhiguo HAN, Tianxing CAI, Cheng ZHANG. Three-dimensional super-twisting slide mode cooperative guidance law with line-of-sight angle constraint[J]. Systems Engineering and Electronics, 2023, 45(7): 2138-2149.

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参考文献 31

1	宋俊红, 宋申民, 徐胜利. 一种拦截机动目标的多导弹协同制导律[J]. 宇航学报, 2016, 37 (12): 1306- 1314.
	SONG J H , SONG S M , XU S L . A cooperative guidance law for multiple missiles to intercept maneuvering target[J]. Journal of Astronautics, 2016, 37 (12): 1306- 1314.
2	HE S M , LIN D F . Three-dimensional optimal impact time gui-dance for antiship missiles[J]. Journal of Guidance, Control, and Dynamics, 2019, 42 (4): 941- 948. doi: 10.2514/1.G003971
3	HOU Z W , YANG Y , LIU L , et al. Terminal sliding mode control based impact time and angle constrained guidance[J]. Aerospace Science and Technology, 2019, 93, 105142. doi: 10.1016/j.ast.2019.04.050
4	CHEN X T , WANG J Z . Nonsingular sliding-mode control for field-of-view constrained impact time guidance[J]. Journal of Guidance, Control, and Dynamics, 2018, 41 (5): 1214- 1222. doi: 10.2514/1.G003146
5	KIM H G , CHO D , KIM H J . Sliding mode guidance law for impact time control without explicit time-to-go estimation[J]. IEEE Trans. on Aerospace and Electronic Systems, 2018, 55 (1): 236- 250.
6	TSALIK R , SHIMA T . Circular impact-time guidance[J]. Journal of Guidance, Control, and Dynamics, 2019, 42 (8): 1836- 1847. doi: 10.2514/1.G004074
7	TANG Y , ZHU X P , ZHOU Z , et al. Two-phase guidance law for impact time control under physical constraints[J]. Chinese Journal of Aeronautics, 2020, 33 (11): 2946- 2958. doi: 10.1016/j.cja.2020.06.007
8	HU Q L , HAN T , XIN M . Sliding-mode impact time guidance law design for various target motions[J]. Journal of Guidance, Control, and Dynamics, 2019, 42 (1): 136- 148. doi: 10.2514/1.G003620
9	ERER K S , TEKIN R . Impact time and angle control based on constrained optimal solutions[J]. Journal of Guidance, Control, and Dynamics, 2016, 39 (10): 2448- 2454. doi: 10.2514/1.G000414
10	TEKIN R , ERER K S , HOLZAPFEI F . Adaptive impact time control via look-angle shaping under varying velocity[J]. Journal of Guidance, Control, and Dynamics, 2017, 40 (12): 3247- 3255. doi: 10.2514/1.G002981
11	KIM H G , LEE J Y , KIM H J , et al. Look-angle-shaping guidance law for impact angle and time control with field-of-view constraint[J]. IEEE Trans. on Aerospace and Electronic Systems, 2019, 56 (2): 1602- 1612.
12	赵世钰, 周锐. 基于协调变量的多导弹协同制导[J]. 航空学报, 2008, 29 (6): 1605- 1611. doi: 10.3321/j.issn:1000-6893.2008.06.031
	ZHAO S Y , ZHOU R . Multi-missile cooperative guidance using coordination variables[J]. Acta Aeronautica et Astronautica Sinica, 2008, 29 (6): 1605- 1611. doi: 10.3321/j.issn:1000-6893.2008.06.031
13	ZADKA B , TRIPATHY T , TSALIK R , et al. Consensus-based cooperative geometrical rules for simultaneous target interception[J]. Journal of Guidance, Control, and Dynamics, 2020, 43 (12): 2425- 2432. doi: 10.2514/1.G005065
14	刘翔, 梁晓庚. 攻击角约束多拦截弹协同制导控制一体化研究[J]. 西北工业大学学报, 2019, 37 (2): 273- 282. doi: 10.3969/j.issn.1000-2758.2019.02.009
	LIU X , LIANG X G . Integrated guidance and control of multiple interceptors with impact angle constraints considered[J]. Journal of Northwestern Polytechnical University, 2019, 37 (2): 273- 282. doi: 10.3969/j.issn.1000-2758.2019.02.009
15	ZHAO J B , YANG S X . Integrated cooperative guidance framework and cooperative guidance law for multi-missile[J]. Chinese Journal of Aeronautics, 2018, 31 (3): 546- 555. doi: 10.1016/j.cja.2017.12.013
16	YU H , DAI K R , LI H J , et al. Distributed cooperative guidance law for multiple missiles with input delay and topology switching[J]. Journal of the Franklin Institute, 2021, 358 (17): 9061- 9085. doi: 10.1016/j.jfranklin.2021.09.018
17	LI G F , WU Y J , XU P Y . Fixed-time cooperative guidance law with input delay for simultaneous arrival[J]. International Journal of Control, 2021, 94 (6): 1664- 1673. doi: 10.1080/00207179.2019.1662947
18	LYU T , GUO Y N , LI C J , et al. Multiple missiles cooperative guidance with simultaneous attack requirement under directed topologies[J]. Aerospace Science and Technology, 2019, 89, 100- 110. doi: 10.1016/j.ast.2019.03.037
19	KUMAR S R , MULJERJEE D . Cooperative salvo guidance using finite-time consensus over directed cycles[J]. IEEE Trans. on Aerospace and Electronic Systems, 2019, 56 (2): 1504- 1514.
20	WANG X X , LU H Q , HUANG X L , et al. Three-dimensional time-varying sliding mode guidance law against maneuvering targets with terminal angle constraint[J]. Chinese Journal of Aeronautics, 2022, 35 (4): 303- 319. doi: 10.1016/j.cja.2021.05.019
21	LI W , WEN Q Q , HE L , et al. Three-dimensional impact angle constrained distributed cooperative guidance law for anti-ship missiles[J]. Journal of Systems Engineering and Electro-nics, 2021, 32 (2): 447- 459. doi: 10.23919/JSEE.2021.000038
22	LYU T , LI C J , GUO Y N , et al. Three-dimensional finite-time cooperative guidance for multiple missiles without radial velocity measurements[J]. Chinese Journal of Aeronautics, 2019, 32 (5): 1294- 1304. doi: 10.1016/j.cja.2018.12.005
23	HE S M , KIM M , SONG T , et al. Three-dimensional salvo attack guidance considering communication delay[J]. Aerospace Science and Technology, 2018, 73, 1- 9. doi: 10.1016/j.ast.2017.11.019
24	AI X L , WANG L L , YU J Q , et al. Field-of-view constrained two-stage guidance law design for three-dimensional salvo attack of multiple missiles via an optimal control approach[J]. Aerospace Science and Technology, 2019, 85, 334- 346. doi: 10.1016/j.ast.2018.11.052
25	CHEN Y D , WANG J , WANG C Y , et al. Three-dimensional cooperative homing guidance law with field-of-view constraint[J]. Journal of Guidance, Control, and Dynamics, 2020, 43 (2): 389- 397. doi: 10.2514/1.G004681
26	CHEN Z Y , CHEN W C , LIU X M , et al. Three-dimensional fixed-time robust cooperative guidance law for simultaneous attack with impact angle constraint[J]. Aerospace Science and Technology, 2021, 110, 106523. doi: 10.1016/j.ast.2021.106523
27	ZUO Z Y . Nonsingular fixed-time consensus tracking for second-order multi-agent networks[J]. Automatica, 2015, 54, 305- 309. doi: 10.1016/j.automatica.2015.01.021
28	MORENO J A . On strict Lyapunov functions for some non-homogeneous super-twisting algorithms[J]. Journal of the Franklin Institute, 2014, 351 (4): 1902- 1919. doi: 10.1016/j.jfranklin.2013.09.019
29	BHAT S P , BERNSTEIN D S . Finite-time stability of continuous autonomous systems[J]. SIAM Journal on Control and Optimization, 2000, 38 (3): 751- 766. doi: 10.1137/S0363012997321358
30	YU S , YU X H , SHIRINZADEH B , et al. Continuous finite-time control for robotic manipulators with terminal sliding mode[J]. Automatica, 2005, 41 (11): 1957- 1964. doi: 10.1016/j.automatica.2005.07.001
31	ZHANG C , GUTIERREZ S V , PLESTAN F , et al. Adaptive super-twisting control of floating wind turbines with collective blade pitch control[J]. IFAC-PapersOnLine, 2019, 52 (4): 117- 122. doi: 10.1016/j.ifacol.2019.08.165

序号	x/m	y/m	z/m	v/(m/s)	θ/(°)	φ/(°)	q_εd/(°)	q_βd/(°)
导弹1	-3 000	20 000	-5 000	680	-10	-10	-15	-10
导弹2	0	20 000	5 000	680	-15	10	-23	10
导弹3	-2 000	20 000	1 000	680	-5	5	-18	0
导弹4	-1 000	20 000	-7 000	680	-5	-10	-25	-15
目标	20 000	8 000	0	200	0	0	-	-

编号	脱靶量/m	制导时间/s	高低角误差/(°)	方位角误差/(°)
导弹1(本文)	0.086 9	46.423 0	0.061 9	0.009 9
导弹2(本文)	0.533 8	46.422 0	0.026 9	0.014 9
导弹3(本文)	0.558 3	46.422 0	0.021 7	0.010 7
导弹4(本文)	0.246 2	46.422 0	0.042 2	0.013 6
导弹1([26])	0.020 0	48.303 0	0.163 5	0.032 2
导弹2([26])	0.409 5	48.302 0	0.035 5	0.055 7
导弹3([26])	0.574 2	48.302 0	0.034 8	0.036 3
导弹4([26])	0.554 8	48.302 0	0.032 7	0.049 0

编号	脱靶量/m	制导时间/s	高低角误差/(°)	方位角误差/(°)
导弹1(本文)	0.050 7	41.392 0	0.216 9	0.108 2
导弹2(本文)	0.287 2	41.402 0	0.184 2	0.168 1
导弹3(本文)	0.420 9	41.388 0	0.264 4	0.197 3
导弹4(本文)	0.359 9	41.383 0	0.171 5	0.095 2
导弹1([26])	0.239 3	41.701 0	0.411 7	0.003 2
导弹2([26])	0.398 2	41.716 0	0.431 9	0.573 3
导弹3([26])	0.457 8	41.696 0	0.301 7	0.347 5
导弹4([26])	0.019 7	41.691 0	1.027 7	0.036 0

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