﻿ 带落角约束的新型二阶滑模三维制导律<sup>*</sup>
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Novel second-order sliding mode control based 3D guidance law with impact angle constraints
SHI Shaokun, ZHAO Jiufen, CHONG Yang, YANG Qisong, YOU Hao
College of Operational Support, Rocket Force University of Engineering, Xi'an 710025, China
Received: 2018-06-27; Accepted: 2018-07-27; Published online: 2018-09-05 09:03
Corresponding author. ZHAO Jiufen, E-mail:xiangcdx1994@163.com
Abstract: To deal with the problem of missile for attacking ground maneuvering target in 3D space, a 3D finite-time guidance law with impact angle constraints is proposed. In order to improve convergence speed and suppress chattering problem, the nonsingular fast terminal second-order sliding mode control based 3D guidance law with coupling terms is designed based on the nonsingular fast terminal sliding surface and the second-order sliding mode control theory. System model linearization is not needed and singular problem is avoided in the design process. A nonhomogeneous disturbance observer is designed to estimate and compensate the total disturbance, which is caused by target maneuvering information and coupling terms of line of sight. And the stability and finite-time convergent characteristics of the proposed guidance law are proved mathematically. The effectiveness and superiority of the proposed guidance law are verified by numerical simulation.
Keywords: impact angle constraint     fast terminal sliding mode     second-order sliding mode     3D guidance law     disturbance observer     finite-time convergence

1 三维空间末制导系统模型

 图 1 弹目相对运动关系 Fig. 1 Relative motion relationship between missile and target

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2 制导律设计

2.1 设计目标

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2.2 基于快速终端滑模面的二阶滑模制导律设计

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3 稳定性和有限时间收敛证明

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t≥max{tr1, tr2}，即系统状态收敛到滑模面s1=0, s2=0时，则式(9)变为

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证毕

4 仿真分析

4.1 多枚导弹仿真分析

 导弹 初始坐标/km θm0/(°) φm0/(°) qεd/(°) qβd/(°) M1 (0, 10, 0) -25 -20 -30 -30 M2 (2, 12, 1) -10 -30 -60 -20 M3 (-2, 9, 3) 10 10 -70 -60

 图 2 3枚导弹攻击目标仿真结果 Fig. 2 Simulation results of 3 missiles attacking targets

 导弹 脱靶量/m 视线倾角误差/(°) 视线偏角误差/(°) 飞行时间/s M1 0.206 9 0.011 6 0.025 7 29.768 0 M2 0.077 6 0.010 0 0.025 0 29.979 0 M3 0.296 2 0.029 3 0.015 9 30.362 0

4.2 不同制导律仿真对比

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 图 3 3种制导律仿真对比结果 Fig. 3 Simulation result comparison of 3 guidance laws

 制导律 脱靶量/m 视线倾角误差/(°) 视线偏角误差/(°) 飞行时间/s SO-NFTSMG 0.206 9 0.011 6 0.025 7 29.768 0 NTSMG1 0.268 1 0.023 6 0.026 1 29.706 0 NTSMG2 0.242 3 0.011 4 0.027 3 29.923 0

5 结论

1) 无需对系统模型作解耦处理，并且设计过程避免了奇异问题的出现。

2) 针对目标机动信息和视线角耦合带来的总扰动设计了非齐次干扰观测器进行估计，无需目标先验信息。

3) 通过2组实验仿真，结果表明：①本文提出的制导律能够控制不同位置不同状态下的多枚导弹以各自期望角度击中目标。②制导律对脱靶量和落角的控制能力强，飞行时间较NTSMG2缩短。③制导律收敛速度快，收敛过程中光滑无抖振现象出现，验证了本文提出制导律的快速收敛和抑制抖振能力强的优点。

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#### 文章信息

SHI Shaokun, ZHAO Jiufen, CHONG Yang, YANG Qisong, YOU Hao

Novel second-order sliding mode control based 3D guidance law with impact angle constraints

Journal of Beijing University of Aeronautics and Astronsutics, 2019, 45(3): 614-623
http://dx.doi.org/10.13700/j.bh.1001-5965.2018.0387