Nonlinear Region of Attraction Estimation for Projectile’s Angular Motion

Dongyang LI; Sijiang CHANG; Zhongyuan WANG

doi:10.12382/bgxb.2022.0417

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Nonlinear Region of Attraction Estimation for Projectile’s Angular Motion

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- Nonlinear Region of Attraction Estimation for Projectile’s Angular Motion
- Acta Armamentarii Vol. 44, Issue 8, Pages: 2329-2341(2023)
- 作者机构：
  
  南京理工大学能源与动力工程学院, 江苏南京 210094
- 作者简介：
- 基金信息：
- DOI：10.12382/bgxb.2022.0417
  CLC：
- Received：19 May 2022，
  
  Published Online：06 September 2023，
  
  Published：30 August 2023
- 稿件说明：
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Dongyang LI, Sijiang CHANG, Zhongyuan WANG. Nonlinear Region of Attraction Estimation for Projectile’s Angular Motion[J]. Acta Armamentarii, 2023, 44(8): 2329-2341.
DOI：

Dongyang LI, Sijiang CHANG, Zhongyuan WANG. Nonlinear Region of Attraction Estimation for Projectile’s Angular Motion[J]. Acta Armamentarii, 2023, 44(8): 2329-2341. DOI： 10.12382/bgxb.2022.0417.

摘要

为探索平方和规划方法在弹箭非线性吸引域估计中的应用

对计及高阶静力矩的无控尾翼弹平面角运动进行多项式化处理

并开展了非线性吸引域估计

通过构造李雅普诺夫函数并利用V-s迭代算法

得到了精度较高的吸引域估计;考虑法向力系数、俯仰力矩系数、赤道阻尼力矩系数以及马格努斯力矩系数的非线性

利用平方和优化得到脉冲末端修正迫弹空间角运动的非线性吸引域估计

由此获得脉冲参数(脉冲冲量和轴向作用位置)的有效组合范围

据此形成脉冲控制弹箭的参数设计方法。研究结果表明

利用平方和规划方法估计弹箭角运动的非线性吸引域

具有较高准确性

将估计结果用于弹箭参数设计是可行和有效的。

Abstract

This paper explores the application of the Sum of Squares Programming (SOSP) in the nonlinear region of attraction estimation for projectiles. Considering quantic static moment

the nonlinear planar angular motion for an unguided fin-stabilized projectile is expressed in polynomials and its region of attraction is estimated using Lyapunov functions and V-s iterative algorithm

leading to an accurate estimation. Considering the nonlinear items of normal force coefficient

pitching moment coefficient

equatorial damping moment coefficient

and Magnus moment coefficient

the nonlinear region of attraction of the spacial angular motion of a terminal trajectory corrected mortar projectile with impulses is also studied. Thus

the effective combination of impulse parameters (impulse magnitude and axial acting position) is obtained and then a method for designing impulse parameters is proposed. The findings show that the estimation of the nonlinear region of attraction for projectile’s angular motion obtained by SOSP is of relatively high accuracy. It is feasible and effective to apply the estimation to projectile design.

关键词

Keywords

references

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杨杰 , 常思江 , 魏伟 . 带扰流片旋转稳定弹动态稳定性 [J ] . 兵工学报 , 2021 , 42 ( 8 ): 1613 - 1623 . DOI: 10.3969/j.issn.1000-1093.2021.08.005 http://doi.org/10.3969/j.issn.1000-1093.2021.08.005 为发展一种新型弹道修正弹，以带扰流片旋转稳定弹为研究对象对其进行动态稳定性分析。推导带扰流片旋转稳定弹的动力学模型并简化得到其非齐次角运动方程，求得攻角在阶跃激励下的瞬态响应和稳态响应解析解。根据非线性角运动方程分析旋转弹结构参数、飞行参数和气动参数对系统分岔特性及稳定性的影响，通过数值计算分析带扰流片旋转稳定弹的修正能力。结果表明：求得的攻角解析解具有较高的精度；气动参数对动力学系统平衡点的稳定域影响较大；扰流片的控制效率很高。研究结果为带扰流片旋转稳定弹的结构参数设计提供了参考。

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