舵机动态响应下导弹阻尼回路稳定性

doi:10.12305/j.issn.1001-506X.2022.10.24

摘要/Abstract

摘要：

针对导弹控制参数稳定区域的研究大多忽略了舵机的动态响应过程对参数稳定区域的影响, 首先建立了阻尼驾驶仪控制的导弹动力学方程以及舵机的动力学方程, 然后考虑舵机的稳态响应和动态响应, 应用劳斯判据给出了非旋转弹阻尼反馈增益与舵机控制参数的动态关系。为推导旋转弹阻尼反馈增益的稳定区域, 分析了舵机在准弹体坐标系下的表达式, 然后采用复姿态角方法和Lyapunov稳定性判据, 给出了旋转弹动态稳定性条件。最后以某一导弹飞行参数为例进行了仿真, 验证了本文所得出的稳定性条件的有效性。

关键词: 导弹, 阻尼回路, 复姿态角方法, Lyapunov稳定性判据, 舵机动态响应

Abstract:

Most of the researches on the stability region of missile control parameters ignore the influence of the dynamic response process of the actuator. In this paper, the dynamic equations of the missile and the actuator are established firstly. Considering the steady-state response and dynamic response of the actuator, applying the Routh criterion, the dynamic relationship between the damping feedback gain of the non-spinning missile and the control parameters of the actuator is given. In order to deduce the stability region of the damping feedback gain of the spinning missile, the expression of the actuator in the quasi-body coordinate system is analyzed, then the dynamic stability condition of the spinning missile is given by using the complex attitude angle method and Lyapunov stability criterion. Finally, a missile flight parameter is taken as an example to verify the effectiveness of the stability conditions.

Key words: missile, damping pilot, complex attitude angle method, Lyapunov stability criterion, actuator dynamic response

中图分类号:

V249

周志明, 刘振, 易建强, 姚晓先. 舵机动态响应下导弹阻尼回路稳定性[J]. 系统工程与电子技术, 2022, 44(10): 3200-3206.

Zhiming ZHOU, Zhen LIU, Jianqiang YI, Xiaoxian YAO. Stability of missile damping loop under actuator dynamic response[J]. Systems Engineering and Electronics, 2022, 44(10): 3200-3206.

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符号	意义
α, β	准弹体坐标系下攻角与侧滑角
ϑ, ψ	准弹体坐标系下俯仰角与偏航角
δ_y, δ_z	等效舵偏角
C_D	阻力系数
C′_L	升力系数导数
C′_M	马格努斯力系数导数
C′_δ	舵偏升力系数导数
C′_S	静力矩系数导数
C′_μ	马格努斯力矩系数导数
C′_q	俯仰偏航阻尼系数
C_mq	控制力矩系数
I_x, I_t	赤道转动惯量与极转动惯量
$\dot{\gamma}$	弹体转速

参数名称	值
电机转动惯量J_m/(kg·m²)	1.667e-6
舵片转动惯量J_l/(kg·m²)	0.016 6
电阻R/Ω	7.8
反电动势系数K_e/(V·s·rad^-1)	0.04
电磁力矩系数K_m/(N·m·A^-1)	0.017 3
减速比N	600

参数	取值	参数	取值
V/(m·s^-1)	1 200	$\dot{\gamma} /\left(\operatorname{rad} \cdot \mathrm{s}^{-1}\right)$	20π
a₁	1.106	a₂	－2.07×10^－4
a₃	6.23×10^－4	b₃	251.1
b₁₁	-265.4	b₁₂	-3.326
b₂₁	0.552	b₂₂	1.297

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