基于变幂次滑模的三维固定时间的多导弹打击比例导引律

doi:10.12382/bgxb.2024.0437

摘要/Abstract

摘要：

针对多导弹对重要目标同时攻击的问题,提出一种三维固定时间打击多弹比例导引律。建立三维空间内的导弹-目标动力学模型,为降低在三维空间内控制方法的设计难度,在三维空间内确定基准面,将导弹-目标三维空间状态向量分解平行和垂直于基准面两个分量,并在上述基准面内分别设计控制方法。其中,平行于基准面基于比例导引法,设计切向和法向加速度作为控制输入,驱使导弹在期望攻击时刻之前达成剩余飞行时间一致;在垂直基准面,基于变幂次改进传统滑模控制法设计导引律,实现多导弹系统前段控制快速收敛与末段控制稳定的兼容。当两个基准面分量都能在预设攻击时间内实现一致性控制时,在三维空间内多导弹系统可完成同步攻击。通过向所设计的导引律中补偿各导弹发射时延,实现多弹系统在异步发射场景下对目标的同步攻击。仿真验证结果表明,所设计的导引律具备快速收敛、稳定性高等特点,不仅适用于同步发射场景,在异步发射时只需将各发导弹发射时延补充至输入端,即可完成攻击时间一致性控制。

关键词: 导弹, 变幂次滑模控制, 比例导引律, 固定时间打击, 三维攻击场景

Abstract:

Aiming at the problem of simultaneous attack of multiple missiles against the important targets,a three-dimensional fixed-time attack proportional guidance law based on variable power sliding mode is proposed for multiple missiles.A missile-target dynamics model in three-dimensional space is established.To reduce the complexity of designing a control method in three-dimensional space,a reference plane is determined in three-dimensional space,and the missile-target state vector in three-dimensional space is decomposed into two components parallel and perpendicular to the reference plane.Control methods are designed separately in the reference plane.The method parallel to the reference plane is based on the proportional guidance method,The tangential and normal accelerations are designed as the control inputs to drive the missile to reach the remaining flight time consistency before the desired attack moment.Additionally,for the component perpendicular to the reference plane,a guidance law is designed using an improved sliding mode control method based on variable power to achieve the rapid convergence in the early stage and the stable control in the terminal stage for the multi-missile system.When the consistent control of both components along the reference plane is realized in a preset attack time,the multi-missile system can complete the synchronized attack in the three-dimensional space.Furthermore,the synchronized attack on the target by the multi-missile system in the asynchronous launching scenario can be realized by compensating the launch delay of each missile in the guidance law.The performance of the proposed three-dimensional guidance law is verified by simulation,which is characterized by fast convergence and high stability.The guidance law is not only applicable to synchronous launching scenarios,but also adds only the launch delay of each missile to the input to complete the consistency control of attack time.

Key words: missile, variable power sliding mode control, proportional guidance law, fixed-time attack, three-dimensional attack scenarios

中图分类号:

TJ301

李健, 刘鹏, 喻小昊, 于航, 李长生, 史云雷, 张合. 基于变幂次滑模的三维固定时间的多导弹打击比例导引律[J]. 兵工学报, 2025, 46(7): 240437-.

LI Jian, LIU Peng, YU Xiaohao, YU Hang, LI Changsheng, SHI Yunlei, ZHANG He. Three-dimensional Fixed-time Attack Proportional Guidance Law Based on Variable Power Sliding Mode for Multiple Missiles[J]. Acta Armamentarii, 2025, 46(7): 240437-.

图/表 7

图1 三维攻击场景示意图

Fig.1 Schematic diagram of a three-dimensional attack scenario

图2 导弹三维状态向量分解示意图

Fig.2 Schematic diagram of three-dimensional state vector decomposition of missile

图3 平行基准面导弹动力学模型

Fig.3 Missile dynamics model on parallel reference plane

表1 导弹初始参数

Table 1 Initial states of missiles

导弹与目标	位置信息/m	初始速度垂向分量/ (m·s^-1)	初始速度平行向分量/ (m·s^-1)	速度水平分量航向角/ rad
导弹1	(5000,5000,-50)	350	-35	0.09
导弹2	(4000,4500,80)	320	20	-0.10
导弹3	(3000,3000,-40)	270	-25	0.11
导弹4	(1000,4000,45)	400	22	-0.15
导弹5	(3500,2000,-60)	330	-35	0.12
目标	(15000,15000,0)

图4 三维空间轨迹及弹目距离

Fig.4 Three-dimensional spatial trajectory and missile-target distance

图5 垂直基准面导弹运动参数

Fig.5 Motion parameters of missile on vertical reference plane

图6 平行基准面导弹运动参数

Fig.6 Motion parameters of missile on vertical reference plane

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