尾翼控制小型超空泡航行体运动稳定性分析

doi:10.12305/j.issn.1001-506X.2024.07.27

摘要/Abstract

摘要：

为探究可偏转尾翼对小型超空泡航行体运动状态的影响，建立了具备尾翼控制功能的小型超空泡航行体非线性动力学模型，对航行体动力学系统进行仿真计算，根据Lyapunov指数谱和相轨图对系统稳定性进行判定，运用非线性动力学方法，对不同尾翼反馈增益下的稳定系统、周期振荡系统以及混沌系统进行分析，得到了速度衰减情况下无动力小型超空泡航行体保持稳定运动的反馈增益参数区间，结果表明，无动力小型超空泡航行体可以通过调整尾翼的反馈增益参数进行姿态控制并实现稳定运动。

关键词: 超空泡航行体, 尾翼控制, 非线性动力学, 稳定性

Abstract:

In order to explore the influence of deflectable fin on the motion state of small supercavitating vehicle, a nonlinear dynamic model of small supercavitating vehicle with fin-controlled function is established. The dynamic system of the vehicle is calculated, and the stability of the system is judged by Lyapunov exponent spectrum and phase-orbit diagram. The stable system, periodic oscillation system, and chaotic system with different fin feedback gain are analyzed by nonlinear dynamic analysis method, and the feedback gain parameter interval of small non-power supercavitating vehicle maintaining stable motion under velocity attenuation is obtained. The results show that the unpowered small supercavitating vehicle can control its attitude and achieve stable motion by adjusting the feedback gain parameters of the fin.

Key words: supercavitating vehicle, fin-controlled, nonlinear dynamics, stability

中图分类号:

U661.3

严平, 李超畅. 尾翼控制小型超空泡航行体运动稳定性分析[J]. 系统工程与电子技术, 2024, 46(7): 2456-2464.

Ping YAN, Chaochang LI. Motion stability analysis of fin-controlled small supercavitating vehicle[J]. Systems Engineering and Electronics, 2024, 46(7): 2456-2464.

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参数名称	取值
重力加速度g/(m/s²)	9.8
质量M/g	113.9
航行体半径R/m	0.007 25
航行体长度L/m	0.154
阻力系数c_x0	0.065
转动惯量Izz/(g·mm³)	4 766.412
空化数σ	[0.001 1, 0.010 0]
密度比(航行体/水)m	7.9

σ	V/(m/s)	k_z	系统状态
0.001 1	600	[30, 59]	稳定
		[-26, -17];[12, 29]	周期振荡
		[68, 86]	混沌
		其他	发散
0.002 5	400	[28, 60]	稳定
		[-29, -14];[9, 27]	周期振荡
		[62, 85]	混沌
		其他	发散
0.01	200	[26, 63]	稳定
		[-30, -12];[10, 25]	周期振荡
		[51, 86]	混沌
		其他	发散

σ	V/(m/s)	k_θ	系统状态
0.001 1	600	[-9, -6]	稳定
		[-15, -9]	周期振荡
		其他	发散
0.002 5	400	[-4, -1]	稳定
		[-18, -8]	周期振荡
		其他	发散
0.01	200	[-6, -2]	稳定
		[-14, -7];[5, 52]	周期振荡
		其他	发散

σ	V/(m/s)	k_q	系统状态
0.001 1	600	[12, 19]	稳定
		[-16, -7];[20, 39]	周期振荡
		其他	发散
0.002 5	400	[16, 23]	稳定
		[-26, -17];[24, 38]	周期振荡
		其他	发散
0.01	200	[16, 27]	稳定
		[-18, -9];[28, 39]	周期振荡
		其他	发散

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