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1. 北京理工大学 宇航学院, 北京 100081;
2. 航天系统仿真重点实验室 北京仿真中心, 北京 100854

Hardware-in-the-loop simulation method and influence analysis of missiles considering body elasticity
LIU Li1 , WANG Yansong1 , ZHOU Sida1 , ZHANG Wulong2
1. School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China;
2. Beijing Simulation Center, Science and Technology on Space System Simulation Laboratory, Beijing 100854, China
Received: 2015-04-21; Accepted: 2015-06-05; Published online: 2015-06-16 14:43
Foundation item: National Key Laboratory Foundation (9140C600205130C60)
Corresponding author. Tel.: 010-68914534 E-mail: liuli@bit.edu.cn
Abstract: With the increasing requirements of velocity and accuracy, the elasticity has been a non-ignorable factor in the dynamic analysis and design of missiles, which could evidently influence the flight performance and control accuracy. In this case, considering the elastic vibration of missiles would improve the precision while running a hardware-in-the-loop simulation of a flexible missile. A flight dynamic model considering the elasticity was developed, and the model of hardware-in-the-loop simulation system was established at the same time. The integrated simulation of math simulation model and hardware-in-the-loop simulation model was realized, based on which, the influences of the elastic vibration and the simulation equipment were analyzed. The results could provide a theoretical basis for the future hardware-in-the-loop simulation of missiles considering the elasticity.
Key words: missile dynamics     elasticity     math simulation     hardware-in-the-loop simulation     dynamics of turntable

1 弹性体导弹的动力学模型 1.1 参考系及转换矩阵

 图 1 参考系系统 Fig. 1 Reference coordinate systems

1.2 动力学方程

FaeMae分别为空气动力和空气动力矩,包括定常气动载荷和弹性振动引起的非定常气动载荷。其中,定常气动载荷有

1.3 控制方程

2 半物理仿真系统数学模型

 图 2 半物理仿真流程 Fig. 2 Flowchart of hardware-in-the-loop simulation

2.1 仿真计算机

2.2 自动驾驶仪

2.3 转台

2.4 弹上器件[8]

1)角速度陀螺仪

2)加速度计

3)导引头

4)舵机

2.5 半物理仿真的状态空间模型

3 算例

 编号 工况 符号 1 刚性体数学仿真模型 RMS 2 弹性体数学仿真模型 FMS 3 刚性体半物理仿真模型 RHILS 4 弹性体半物理仿真模型 FHILS

 参数 数值 参数 数值 导弹质量/kg 304 弹翼根弦长/m 0.68 导弹长度/m 4.64 弹翼梢弦长/m 0.53 弹身直径/m 0.25 弹翼展长/m 0.44 头部长度/m 0.58 舵面弦长/m 0.18 尾部长度/m 0.32 舵面展长/m 0.44
 图 3 RMS和RHILS 2种工况的弹道、俯仰角及俯仰角速度曲线 Fig. 3 Curves of trajectory, pitching angle, and pitching angular velocity of two examples of RMS and RHILS

 图 4 FMS、RHILS和FHILS 3种工况的弹道、俯仰角及俯仰角速度曲线 Fig. 4 Curves of trajectory, pitching angle, and pitching angular velocity of three examples of FMS, RHILS and FHILS

 图 5 RHILS和FHILS误差曲线 Fig. 5 History of errors between RHILS and FHILS

 图 6 导弹各时刻变形曲线 Fig. 6 Deformed curves of missile at each moment
 图 7 3 s之后俯仰角速度的频率特性曲线 Fig. 7 Curve of pitching angular velocity in frequency domain after 3 s
4 结 论

1)对大长径比导弹进行半物理仿真时,其弹性特性不可以被忽略,考虑弹性振动有利于提高大长径比导弹半物理仿真的精度。

2)在半物理仿真中,转台等仿真设备的动力学特性会对弹体的弹性振动效应产生影响。因此,在对弹性体导弹进行半物理仿真实验时,应该考虑转台动力学特性的影响,采用合适带宽的转台有利于半物理仿真精度的提高。

3)由于高精度、大长径比导弹研发需求的提高,实现考虑弹体弹性的导弹半物理仿真的新方法和新途径可能会成为未来弹性飞行器领域的研究热点之一。

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#### 文章信息

LIU Li, WANG Yansong, ZHOU Sida, ZHANG Wulong

Hardware-in-the-loop simulation method and influence analysis of missiles considering body elasticity

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(4): 639-645.
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0245