基于鲁棒精确微分器的分数阶滑模制导律设计

doi:10.12305/j.issn.1001-506X.2023.01.21

Abstract

Abstract:

A fractional order terminal sliding mode guidance law with finite time convergence is proposed for maneuvering target interception with impact angle constraint. Firstly, the relative motion model of missile and target in two-dimensional plane is established. Secondly, the fractional order sliding surface and fractional order reaching law are selected respectively to design the fractional order terminal sliding mode guidance law, and the finite time stability of the guidance system is proved. At the same time, for the target maneuvering information acquisition, a target maneuvering acceleration estimation method based on robust precise differentiator is proposed to compensate the guidance law. Finally, the simulation results are compared with relevant guidance laws, the simulation results show that the proposed fractional order terminal sliding mode guidance law has a higher guidance accuracy and can effectively suppress sliding mode chattering.

Key words: differentiator, fractional calculus, sliding mode control, guidance law, finite time

CLC Number:

V412.1

Haoran LU, Wei ZHENG, Xiaohua CHANG. Fractional order sliding mode guidance law based on robust exact differentiator[J]. Systems Engineering and Electronics, 2023, 45(1): 175-183.

Figures/Tables 19

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References 29

1	LIU Y H , LI K B , CHEN L , et al. Novel augmented proportional navigation guidance law for mid-range autonomous rendezvous[J]. Acta Astronautica, 2019, 162 (9): 526- 535.
2	YANG C D , YANG C C . A unified approach to proportional navigation[J]. IEEE Trans.on Aerospace & Electronic Systems, 1997, 33 (2): 557- 567.
3	YANUSHEVSKY R , BOORD W . New approach to guidance law design[J]. Journal of Guidance, Control, and Dynamics, 2005, 28 (1): 162- 166. doi: 10.2514/1.6154
4	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 (1): 454- 463.
5	CHEN Z , SHIMA T . Nonlinear optimal guidance for intercepting a stationary target[J]. Journal of Guidance, Control, and Dynamics, 2019, 42 (11): 2418- 2431. doi: 10.2514/1.G004341
6	ZHU J W , SU D L , XIE Y , et al. Impact time and angle control guidance independent of time-to-go prediction[J]. Aerospace Science and Technology, 2019, 86 (3): 818- 825.
7	LIANG H Z , WANG J Y , WANG Y H , et al. Optimal guidance against active defense ballistic missiles via differential game strategies[J]. Chinese Journal of Aeronautics, 2020, 33 (3): 978- 989. doi: 10.1016/j.cja.2019.12.009
8	ZHANG Y X , SUN M W , CHEN Z Q . Finite-time convergent guidance law with impact angle constraint based on sliding-mode control[J]. Nonlinear Dynamics, 2012, 70 (1): 619- 625. doi: 10.1007/s11071-012-0482-3
9	SONG J H , SONG S M , ZHOU H B . Adaptive nonsingular fast terminal sliding mode guidance law with impact angle constraints[J]. International Journal of Control, Automation and Systems, 2016, 14 (1): 99- 114. doi: 10.1007/s12555-014-0155-8
10	KUMAR S R , RAO S , GHOSE D . Nonsingular terminal sliding mode guidance with impact angle constraints[J]. Journal of Guidance, Control, and Dynamics, 2014, 37 (4): 1114- 1130. doi: 10.2514/1.62737
11	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
12	ZHAO Z H , LI C T , YANG J , et al. Output feedback continuous terminal sliding mode guidance law for missile-target interception with autopilot dynamics[J]. Aerospace Science and Technology, 2019, 86, 256- 267. doi: 10.1016/j.ast.2019.01.012
13	杨芳, 张宽桥, 余磊. 自适应非奇异快速终端二阶滑模制导律[J]. 弹道学报, 2020, 32 (2): 7- 15.
	YANG F , ZHANG K Q , YU L . Adaptive nonsingular fast terminal second-order sliding mode guidance law[J]. Journal of Ballistics, 2020, 32 (2): 7- 15.
14	ZHOU B C, WANG W H. An improved nonsingular fast terminal sliding mode guidance law with impact angle constraints[C]//Proc. of the IEEE 8th International Conference on Intelligent Control & Information Processing, 2017: 8-15.
15	SLOTINE J J , SASTRY S S . Tracking control of nonlinear system using sliding surfaces with application to robot manipulators[J]. International Journal of Control, 1983, 38 (2): 465- 492. doi: 10.1080/00207178308933088
16	SHTESSEL Y B , FRIDMAN L , ZINOBER A . Higher-order sliding mode[J]. International Journal of Robust and Nonlinear Control, 2008, 18 (4/5): 381- 384.
17	LIN F J , WAI R J . Sliding-mode-controlled slider-crank mechanism with fuzzy neural networ[J]. IEEE Trans.on Industrial Electronics, 2001, 48 (1): 60- 70. doi: 10.1109/41.904553
18	PEI P, LIN D F, WANG J, et al. Global fast terminal sliding mode guidance law for maneuvering target interception[C]//Proc. of the IEEE CSAA Guidance, Navigation and Control Conference, 2018: 2-5.
19	ZHANG B T , PI Y G , LUO Y . Fractional order sliding-mode control based on parameters auto-tuning for velocity control of permanent magnet synchronous motor[J]. ISA Transactions, 2012, 51 (5): 649- 656. doi: 10.1016/j.isatra.2012.04.006
20	GOLESTANI M, AHMADI P, FAKHARIAN A. Fractional order sliding mode guidance law: improving performance and robustness[C]//Proc. of the IEEE International Conference on Control, 2016.
21	刘清楷, 陈坚, 汪立新, 等. 三维落角约束自适应分数阶滑模制导律设计[J]. 现代防御技术, 2018, 46 (2): 68- 74. doi: 10.3969/j.issn.1009-086x.2018.02.012
	LIU Q K , CHEN J , WANG L X , et al. Design of 3D adaptive fractional order sliding mode guidance law with impact angle constraints[J]. Modern Defence Technology, 2018, 46 (2): 68- 74. doi: 10.3969/j.issn.1009-086x.2018.02.012
22	周慧波. 基于有限时间和滑模理论的导引律及多导弹协同制导研究[D]. 哈尔滨: 哈尔滨工业大学, 2015.
	ZHOU H B. Study on guidance law and cooperative guidance for multi-missiles based on finite-time and sliding mode theory[D]. Harbin: Harbin Institute of Technolgy, 2015.
23	SAMKO S G , KILBAS A A , MARICHEV O I . Fractional integrals and derivatives, theory and applications[M]. Yverdon: Gordon and Breach, 1993.
24	MONJE C A , CHEN Y Q , VINAGRE B M , et al. Fractional-order systems and controls: fundamentals and applications[M]. New York: Springer, 2010.
25	PODLUBNY I . Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications[M]. New York: Academic Press, 1998.
26	MARCO T A , MORENO J A , FRIDMAN L . Robust exact uniformly convergent arbitrary order differentiator[J]. Automatica, 2013, 49 (8): 2489- 2495. doi: 10.1016/j.automatica.2013.04.034
27	EFE M O . Fractional fuzzy adaptive sliding-mode control of a 2-dof direct-drive robot arm[J]. IEEE Trans.on Systems, Man, and Cybernetics. Part B, Cybernetics, 2008, 38 (6): 1561- 1570. doi: 10.1109/TSMCB.2008.928227
28	谢子涵. 基于分数阶滑模的博弈制导方法研究[D]. 哈尔滨: 哈尔滨工业大学, 2020.
	XIE Z H. Research on game guidance method based on fractional sliding mode[D]. Harbin: Harbin Institute of Technolgy, 2020.
29	SHTESSEL Y , EDWARDS C , FRIDMAN L , et al. Sliding mode control and observation[M]. New York: Springer, 2014: 229- 230.

偏差项	偏差大小(3σ)
测距偏差/m	10
视线角测量偏差/rad	0.01

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Fractional order sliding mode guidance law based on robust exact differentiator

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