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1. 火箭军工程大学 控制工程系, 西安 710025;
2. 火箭军工程大学 士官学院, 青州 262500

Cooperative guidance law based on MPSC and CPN guidance method
LI Xinsan1 , WANG Lixin1 , WANG Mingjian2 , YAN Xunliang1 , LIU Guohui2 , DING Bangping2
1. Department of Control Engineering, Rocket Military Engineering University, Xi'an 710025, China ;
2. Petty Officer Academy, Rocket Military Engineering University, Qingzhou 262500, China
Received: 2015-09-10; Accepted: 2015-11-20; Published online: 2015-12-08
Foundation item: National Natural Science Foundation of China (61203354)
Corresponding author. Tel.:029-84741536,E-mail:281167393@qq.com
Abstract: Cooperative guidance of multiple missiles satisfying terminal impact angle constraints is considered. A suboptimal guidance law is presented using the recently proposed model predictive spread control (MPSC) method and cooperative proportional navigation (CPN) guidance law. The basic principle of the MPSC method is given and the MPSC guidance law is designed on the assumption that the control is considered to be a function of quadratic formulation. The MPSC method requires a control history to begin the algorithmic sequence. Guess control history is computed using the CPN technique, subject to constraint on impact time. A stationary target is attacked by two missiles in the simulation. It is observed from the simulation that the impact time error and terminal impact angle error are within the specified convergence tolerance. The terminal impact angle constraint is well satisfied in salvo attack scenario.
Key words: guidance     cooperative guidance     model predictive spread control (MPSC)     impact angle constraint     impact time constraint

1 MPSC制导律设计 1.1 MPSC制导方法推导

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B k(k=1,2,…,N-1)为末端输出量与控制量 U k之间的误差系数矩阵，表达式为

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1.2 制导问题描述

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1) 通过第2节CPN制导律对初始控制量进行猜测，得到初始控制量acik，并确定飞行时间tk

2) 通过数值积分求解式(29)，得到导弹的末端状态 X f=(xif,yif,ψif)，末端状态偏差d Y N

 (33)

3) 如果末端状态偏差d Y N满足设计要求，程序结束；如果不满足要求，需要对法向加速度指令acik进行修正。计算 B N-10和 B N-1如下：

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4) 通过式(8)和式(9)计算 B kB k0(k=1,2，…,N-1)

5) 求解出 B k后，通过式(36)直接计算aibici

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6) 通过aibici计算导弹法向加速度指令acik

2 基于CPN制导方法的初始控制量猜测 2.1 CPN制导原理

 图 1 导弹和目标相对运动示意图 Fig. 1 Engagement geometry of missile and target

CPN制导方法[19]通过对式(37)中的比例导引系数 i进行调节，使各枚导弹飞行时间趋于一致，实现协同攻击。

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2.2 初始控制量猜测仿真

 参数 导弹1(M1) 导弹 2(M2) (xm,ym)/m (1 180.0,2 080.0) (0,0) σ/(°) -20 -5 V/(m·s-1) 290 300 (xT,yT)/m (13 100.0,4 100.0) (13 100.0,4 100.0)

 图 2 待飞时间变化历程 Fig. 2 Time-to-go variation histories
 图 3 待飞时间偏差变化历程 Fig. 3 Time-to-go error variation histories
 图 4 法向加速度指令变化历程 Fig. 4 Normal acceleration command variation histories
3 数值仿真

 导弹 导弹1(M1) 导弹2(M2) ψd /(°) 65.0 25.0

 图 5 两枚导弹飞行轨迹示意图 Fig. 5 Schematic diagram of flight trajectories of two missiles
 图 6 速度矢量与基准线夹角的变化历程 Fig. 6 Variation histories of angle between velocityvector and reference line

 末端时刻状态参数 导弹1(M1) 导弹2(M2) (xmf,ymf) /m (13 099.2,4 099.5) (13 100.3,4 100.8) ψmf/(°) 64.9 25.0

 图 7 初始控制量猜测法向加速度指令 Fig. 7 Normal acceleration command for initial control guess

CPN制导方法可以确定各枚导弹的攻击时间，攻击时间不用事先设定；MPSC制导方法可以对攻击角度进行控制。仿真表明，本文给出的MPSC制导体系的协同制导方法可以对攻击时间和攻击角度同时进行控制，实现多导弹协同攻击。与文献[20]给出的带有攻击角度和时间约束的协同制导律相比，本文方法角度偏差可控制在0.1°范围内，协同攻击时末端角度控制精度更高。

4 结 论

1) 基于MPSC和CPN制导方法实现了满足末端攻击角度约束的多导弹协同攻击。

2) 通过CPN制导方法对初始控制量进行猜测并确定协同攻击时间，运用MPSC制导方法实现末端攻击角度约束。

3) 下一步将对三维空间多约束条件下的协同制导律作更深入的研究。

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文章信息

LI Xinsan, WANG Lixin, WANG Mingjian, YAN Xunliang, LIU Guohui, DING Bangping

Cooperative guidance law based on MPSC and CPN guidance method

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(9): 1857-1863
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0592