三维自适应有限时间超螺旋滑模制导律

doi:10.12305/j.issn.1001-506X.2021.03.23

摘要/Abstract

摘要：

针对导弹以固定终端攻击角拦截机动目标的制导问题, 提出一种三维自适应有限时间超螺旋滑模制导律。首先，利用相对运动质点模型将三维制导问题转换为二阶视线角系统的控制问题。其次，构造一种多变量非奇异的快速终端滑模面, 结合改进型超螺旋算法, 设计了有限时间超螺旋滑模制导律。同时, 通过参数自适应增益实时在线估计目标机动引起的外部扰动上界, 设计了自适应有限时间超螺旋滑模制导律。然后，利用Lyapunov稳定性理论进行了闭环系统有限时间收敛性能分析。最后，通过仿真分析验证了所提方法在保证良好拦截精度的同时, 具有更强的鲁棒性和更高的终端攻击角控制精度。

关键词: 非奇异快速终端滑模, 终端攻击角约束, 超螺旋算法, 有限时间收敛, 三维拦截制导律

Abstract:

Aiming at the guidance problem of intercepting maneuvering target with fixed terminal attack angle, a three-dimensional adaptive finite-time super-twisting sliding mode guidance law is proposed. Firstly, the three-dimensional guidance problem is transformed into the control problem of the second-order line-of-sight angle system by using the relative motion particle model. Secondly, a multi-variable nonsingular fast terminal sliding surface is constructed, and the finite-time super-twisting sliding mode guidance law is designed by combining the improved super-twisting algorithm. At the same time, the upper bound of external disturbance caused by target maneavering is estimated online by parameter adaptive gain, and the adaptive finite-time super-twisting sliding mode guidance law is designed. Then, the finite-time convergence performance of the closed-loop system is analyzed by using the Lyapunov stability theory. Finally, the simulation results show that the proposed method has better robustness and higher terminal attack angle control accuracy while ensuring good interception accuracy.

Key words: nonsingular fast terminal sliding mode, terminal attack angle constraint, super-twisting algorithm, finite-time convergence, three-dimensional interception guidance law

中图分类号:

V448.133

李军, 廖宇新, 李珺. 三维自适应有限时间超螺旋滑模制导律[J]. 系统工程与电子技术, 2021, 43(3): 779-788.

Jun LI, Yuxin LIAO, Jun LI. Three-dimensional adaptive finite-time super-twisting sliding mode guidance law[J]. Systems Engineering and Electronics, 2021, 43(3): 779-788.

图/表 9

图1

图2

图3

图4

图5

图6

表1

表2

表3

参考文献 26

1	刘柏均, 侯明善, 余英. 带攻击角度约束的浸入与不变制导律[J]. 系统工程与电子技术, 2018, 40 (5): 1085- 1090.
	LIU B J , HOU M S , YU Y . Guidance law with impact angle constraints based on immersion and invariance[J]. Systems Engineering and Electronics, 2018, 40 (5): 1085- 1090.
2	CHEN X T , WANG J Z . Optimal control based guidance law to control both impact time and impact angle[J]. Aerospace Science and Technology, 2019, 84, 454- 463. doi: 10.1016/j.ast.2018.10.036
3	李晨迪, 王江, 李斌, 等. 过虚报交班点的能量最优制导律[J]. 航空学报, 2019, 40 (12): 178- 187.
	LI C D , WANG J , LI B , et al. Energy-optimal guidance law with virtual hand-over point[J]. Acta Aeronautica Et Astronautica Sinica, 2019, 40 (12): 178- 187.
4	孟克子, 周荻. 多约束条件下的最优中制导律设计[J]. 系统工程与电子技术, 2016, 38 (1): 116- 122.
	MENG K Z , ZHOU D . Design of optimal midcourse guidance law with multiple constraints[J]. Systems Engineering and Electronics, 2016, 38 (1): 116- 122.
5	SUN J L , LIU C S , YE Q . Robust differential game guidance laws design for uncertain interceptor-target engagement via adaptive dynamic programming[J]. International Journal of Control, 2017, 90 (5): 990- 1004. doi: 10.1080/00207179.2016.1192687
6	李伟, 黄瑞松, 王芳, 等. 基于SDRE具有终端碰撞角约束的非线性微分对策制导律[J]. 系统工程与电子技术, 2016, 38 (7): 1606- 1613.
	LI W , HUANG R S , WANG F , et al. Nonlinear differential games guidance law based on SDRE with terminal impact angular[J]. Systems Engineering and Electronics, 2016, 38 (7): 1606- 1613.
7	SUN L H , WANG W H , YI R , et al. A novel guidance law using fast terminal sliding mode control with impact angle constraints[J]. ISA Transactions, 2016, 64, 12- 23. doi: 10.1016/j.isatra.2016.05.004
8	SONG J H , SONG S M , GUO Y , et al. Nonlinear disturbance observer-based fast terminal sliding mode guidance law with impact angle constraints[J]. International Journal of Innovative Computing Information and Control, 2015, 11 (3): 787- 802.
9	王超伦, 宋保华, 常超. 考虑弹体动态特性的非奇异有限时间制导律[J]. 国防科技大学学报, 2018, 40 (2): 22- 27.
	WANG C L , SONG B H , CHANG C . Nonsingular finite-time guidance law with missile dynamic[J]. Journal of National University of Defense Technology, 2018, 40 (2): 22- 27.
10	赵国荣, 李晓宝, 刘帅, 等. 自适应非奇异快速终端滑模固定时间收敛制导律[J]. 北京航空航天大学学报, 2019, 45 (6): 1059- 1070.
	ZHAO G R , LI X B , LIU S , et al. Adaptive nonsingular fast terminal sliding mode guidance law with fixed-time convergence[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45 (6): 1059- 1070.
11	张凯, 杨锁昌, 张宽桥, 等. 带攻击角约束的有限时间收敛滑模制导律[J]. 电光与控制, 2017, 24 (1): 63- 66.
	ZHANG K , YANG S C , ZHANG K Q , et al. Finite-time convergent sliding mode guidance law with impact angle constraint[J]. Electronics Optics & Control, 2017, 24 (1): 63- 66.
12	LEVANT A , FRIDMAN L M . Accuracy of homogeneous sliding modes in the presence of fast actuators[J]. IEEE Trans.on Automatic Control, 2010, 55 (3): 810- 814. doi: 10.1109/TAC.2010.2040512
13	刘畅, 杨锁昌, 汪连栋, 等. 基于快速自适应超螺旋算法的制导律研究[J]. 北京航空航天大学学报, 2019, 45 (7): 1388- 1397.
	LIU C , YANG S C , WANG L D , et al. Guidance law based on fast adaptive super-twisting algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45 (7): 1388- 1397.
14	MENG K Z , ZHOU D . Super-twisting integral-sliding-mode guidance law considering autopilot dynamics[J]. Proceedings of the Institution of Mechanical Engineers Part G: Journal of Aerospace Engineering, 2017, 232 (9): 1787- 1799.
15	ZHAO Z H , YANG J , LI S H , et al. Drag-based composite super-twisting sliding mode control law design for Mars entry guidance[J]. Advances in Space Research, 2016, 57 (12): 2508- 2518.
16	BEHNAMGOL V , VALI A R , MOHAMMADI A . A new adaptive finite time nonlinear guidance law to intercept maneuvering targets[J]. Aerospace Science and Technology, 2017, 68, 416- 421.
17	CHO D , KIM H J , TAHK M . Fast adaptive guidance against highly maneuvering targets[J]. IEEE Trans.on Aerospace and Electronic Systems, 2016, 52 (2): 671- 680.
18	ZHANG Y , TANG S J , GUO J . An adaptive fast fixed-time guidance law with an impact angle constraint for intercepting maneuvering targets[J]. Chinese Journal of Aeronautics, 2018, 31 (6): 1327- 1344.
19	SHIN H S , TSOURDOS A , LI K B . A new three-dimensional sliding mode guidance law variation with finite time convergence[J]. IEEE Trans.on Aerospace and Electronic Systems, 2017, 53 (5): 2221- 2232.
20	LI G L , JI H B . A three-dimensional robust nonlinear terminal guidance law with ISS finite-time convergence[J]. International Journal of Control, 2016, 89 (5): 938- 949.
21	ZHOU D , SUN S , XU B . Finite time sliding sector guidance law with acceleration saturation constraint[J]. IET Control Theory & Applications, 2016, 10 (7): 789- 799.
22	SI Y J , SONG S M . Continuous reaching law based three-dimensional finite-time guidance law against maneuvering targets[J]. Transactions of the Institute of Measurement and Control, 2018, 41 (2): 321- 339.
23	SONG J H , SONG S M . Three-dimensional guidance law based on adaptive integral sliding mode control[J]. Chinese Journal of Aeronautics, 2016, 29 (1): 202- 214.
24	POLYAKOV A , FRIDMAN L . Stability notions and Lyapunov functions for sliding mode control systems[J]. Journal of the Franklin Institute, 2014, 351 (4): 1831- 1865.
25	YANG L , YANG J Y . Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems[J]. International Journal of Robust and Nonlinear Control, 2011, 21 (16): 1865- 1879.
26	YANG Y , QIN S Y , JIANG P . A modified super-twisting sliding mode control with inner feedback and adaptive gain schedule[J]. International Journal of Adaptive Control and Signal Processing, 2017, 31 (3): 398- 416.

制导律	拦截时间/s	脱靶量/m	θ_Lf误差/(°)	ϕ_Lf误差/(°)
FSTSMGL	7.519 0	0.555 1	0.172 0	0.089 2
AFSTSMGL	7.569 0	0.594 0	0.023 6	0.021 9
NTSMGL	7.511 0	0.807 5	0.349 8	0.104 4

制导律	拦截时间/s	脱靶量/m	θ_Lf误差/(°)	ϕ_Lf误差/(°)
FSTSMGL	7.612 0	0.682 8	0.110 6	0.070 8
AFSTSMGL	7.660 0	0.360 9	0.037 0	0.035 5
NTSMGL	7.605 0	0.331 6	0.281 3	0.101 6

制导律	拦截时间/s	脱靶量/m	θ_Lf误差/(°)	ϕ_Lf误差/(°)
FSTSMGL	7.674 0	0.562 3	0.103 3	0.106 1
AFSTSMGL	7.801 0	0.457 6	0.081 9	0.083 6
NTSMGL	7.697 0	0.632 1	0.271 0	0.132 2

[1]	罗世彬, 李晓栋, 王忠森, 徐骋. 并联式运载器上升段广义超螺旋有限时间控制[J]. 系统工程与电子技术, 2022, 44(5): 1626-1635.
[2]	刘文吉, 杜佳璐, 李健, 李诤. 基于超螺旋滑模的船载稳定平台镇定控制[J]. 系统工程与电子技术, 2022, 44(5): 1662-1669.
[3]	景亮, 张忠阳, 崔乃刚, 吴荣. 固定时间收敛扰动观测终端滑模制导律设计[J]. 系统工程与电子技术, 2019, 41(8): 1820-1826.
[4]	毛柏源, 李君龙, 张锐. 考虑自动驾驶仪动态特性的多约束中制导律[J]. 系统工程与电子技术, 2019, 41(2): 382-388.
[5]	刘正华, 温暖, 祝令谱. 变体飞行器有限时间收敛LPV鲁棒控制[J]. 系统工程与电子技术, 2018, 40(6): 1325-1330.
[6]	吕寿坤, 周荻, 孟克子, 王子才. 视线角约束自适应滑模中制导律[J]. 系统工程与电子技术, 2018, 40(4): 855-859.
[7]	李炯, 张涛, 雷虎民, 叶继坤, 王华吉. 非奇异快速终端二阶滑模有限时间制导律[J]. 系统工程与电子技术, 2018, 40(4): 860-867.
[8]	华玉龙, 孙伟, 迟宝山, 郭晓林, 刘国强. 非奇异快速终端滑模控制[J]. 系统工程与电子技术, 2017, 39(5): 1119-1125.
[9]	徐世许，马建敏. 不确定多变量线性系统的快速收敛滑模控制[J]. Journal of Systems Engineering and Electronics, 2011, 33(7): 1585-1589.
[10]	樊仲光1,3，梁家荣2，肖剑1. 不确定奇异系统的Terminal滑模控制[J]. Journal of Systems Engineering and Electronics, 2010, 32(1): 158-161.