弹箭角运动的非线性吸引域估计  

Nonlinear Region of Attraction Estimation for Projectile's Angular Motion

作　　者：李东阳[1] 常思江[1] 王中原[1] LI Dongyang;CHANG Sijiang;WANG Zhongyuan(School of Energy and Power Engineering,Nanjing University of Science and Technology,Nanjing 210094,Jiangsu,China)

机构地区：[1]南京理工大学能源与动力工程学院,江苏南京210094

出　　处：《兵工学报》2023年第8期2329-2341,共13页Acta Armamentarii

基　　金：瞬态冲击技术重点实验室基金项目(6142606183107)。

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。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：攻角运动 非线性气动力 吸引域 平方和规划 稳定性 

分 类 号：TJ760.1[兵器科学与技术—武器系统与运用工程]