﻿ 基于碰撞航线的动能拦截器滑模制导律设计
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Sliding mode guidance law for KKV based on collision course
YANG Xu, ZHANG Jiao, LIU Yuanxiang
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
Abstract: Aimed at the problem of exoatmospheric kinetic kill vehicle(KKV) guidance law design for intercepting targets, a novel missile sliding mode guidance law with nonlinear disturbance observer (NDO) was derived base on collision course. Through steering angle of attack of missile, the direction of velocity of missile always pointed at the expected collision point. Missile could intercept the target with lower overload, faster speed via NDO, which was currently estimating and dynamically compensating to target acceleration. Moreover, comparison to the two interception strategies were obtained with interception trajectories, capture zones and velocity range. Another strategy was the sliding mode guidance law based on finite time convergence which aiming to steering the line of sight rate close to zero. The results show that the validities of the proposed sliding mode guidance law based on collision course in application for kinetic kill vehicle.
Key words: missile guidance     nonlinear disturbance observer     sliding-mode control     collision course     capture zone

1 弹目相对运动模型

 图 1 弹目拦截几何 Fig. 1 Missile and target engagement geometry

2 基于碰撞航线的制导律设计

tgo求导有

3 稳定性分析

t∈[t0,T(x0)),φ(t;t0,x0)∈U＼{0},那么系统的平衡点x=0是局部有限时间收敛的,如果U=Rn,则平衡点是全局有限时间收敛的.

4 仿真结果及分析

4.1 拦截非机动目标

 图 2 导弹和非机动目标相对运动轨迹 Fig. 2 Trajectories of missile and nonmaneuvering target relative motion

 图 3 导弹和非机动目标的攻角变化 Fig. 3 Variation of angle of attack for missile and nonmaneuvering target

4.2 拦截机动目标

 图 4 导弹和机动目标相对运动轨迹 Fig. 4 Trajectories of missile and maneuvering target relative motion

 图 5 导弹和机动目标的攻角变化 Fig. 5 Variation of angle of attack for missile and maneuvering target

 图 6 目标加速度的估计 Fig. 6 Estimation of target acceleration

 图 7 滑模面随时间变化曲线 Fig. 7 Curve of sliding mode surface changing with time

4.3 可拦截区域分析

 图 8 FTCG的拦截区域 Fig. 8 Capture zone of FTCG

 图 9 NDOGC的拦截区域 Fig. 9 Capture zone of NDOGC

NDOGC仅在γm0∈[90°,140°],γt0∈[0°,17°]的小部分区域难以拦截目标,在余下区域均可成功拦截.而FTCG在γt0∈[0°,17°]及γt0∈[34°,90°]的大部分区域都难以命中目标.故制导律NDOGC可适用的弹目初始航向角范围更广.

4.4 可拦截目标速度范围

 γm0/(°) FTCG Vt0/(m·s-1) NDOGC Vt0/(m·s-1) 20 0~4 472 0~5 832 40 0~2 586 0~3 905 60 0~2 163 0~3 877

5 结 论

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文章信息

YANG Xu, ZHANG Jiao, LIU Yuanxiang

Sliding mode guidance law for KKV based on collision course

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(11): 2095-2102.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0728