基于非线性滤波器和动态面的指定时间预设性能导弹冷发射响应控制

doi:10.12382/bgxb.2024.0773

摘要/Abstract

摘要：

围绕车载导弹发射平台无依托垂直发射过程,提出一种通过液压执行器主动调节发射筒摆振进而控制弹体出筒姿态的思路,以保证发射安全性和车载导弹发射平台对发射场坪的适应性。考虑发射筒-适配器-弹筒之间的相互作用关系,建立6自由度发射系统动力学模型,并结合液压压力动态方程推导出7阶状态空间方程。为避免高阶非线性系统控制器反步设计存在的“微分爆炸”问题,引入一种基于光滑的非线性滤波器的动态面技术以简化控制器设计。为抑制难以建模因素对发射响应控制的影响,引入时延估计控制方法进行未建模误差和外部扰动的估计和衰减。结合指定时间预设性能控制方法,实现弹体跟踪快速收敛,并满足摆振幅度和角速度的预设指标。通过数学模型和有限元模型的仿真结果比较,验证了新提出的发射动力学模型的正确性。同时,对PID控制器、动态面控制器、动态面和时延估计结合的控制器以及在此基础上加入指定时间预设性能的控制器影响下的发射动态响应结果进行比较。新提出的控制器能够保证弹体出筒时刻弹体角度被约束在0.5 °之内,角速度被约束在1.5°/s之内,其控制性能更优越。

关键词: 导弹, 发射平台, 无依托垂直发射, 指定时间预设性能控制, 时延估计, 动态面控制

Abstract:

Focusing on the unsupported random vertical launching process of a vehicular missile launching system, this paper proposes an idea of actively regulating the oscillation of launch canister and hence controlling the attitude of missile through the hydraulic actuator, which ensures the launching safety and the adaptability of vehicular missile launching system to the launching site. A 6-DOF dynamics model of the launching system is established, which takes into account the interactions among the launch canister, adapters and missile. The seventh-order state-space equation is derived by combining with the pressure dynamic equation of the hydraulic system. For avoiding the problem of “differential explosion” in a backstepping controller design of the seventh-order nonlinear system, the dynamic surface technique based on a smooth nonlinear filter is introduced to simplify the controller design. Meanwhile, in order to suppress the influence of hard-to-modelling factors on the launch dynamics, a time delay estimation control method is introduced for the estimation and attenuation of unmodeled errors and external disturbances. The fast convergence of missile tracking is achieved and the prescribed indicators of oscillation amplitude and angular velocity are met by using the appointed-time prescribed performance control method. The calculation results of mathematical model are compared with the results from the finite element model to verify the correctness of the proposed launch dynamics model. In addition, the launch dynamic response results under the influences of proportion-iIntegral-differential (PID) controller, dynamic surface controller, controller with dynamic surface and time delay estimation, and controller with the appointed-time prescribed performance are compared. The results show that the proposed controller can be used to constrain the angle of missile within 0.5° and the angular velocity within 1.5°/s when a missile comes out of the launch canister.

Key words: missile, launching system, unsupported vertical launch, appointed-time prescribed performance control, time delay estimation, dynamic surface control

中图分类号:

TJ812+.6

于小川, 杨晓伟, 梁相龙, 朱威霖, 姚建勇. 基于非线性滤波器和动态面的指定时间预设性能导弹冷发射响应控制[J]. 兵工学报, 2024, 45(11): 4155-4174.

YU Xiaochuan, YANG Xiaowei, LIANG Xianglong, ZHU Weilin, YAO Jianyong. Appointed-time Prescribed Performance Control for Missile Cold Launch Response Based on Nonlinear Filters and Dynamic Surface[J]. Acta Armamentarii, 2024, 45(11): 4155-4174.

图/表 22

图1 车载导弹冷发射系统多刚体动力学模型

Fig.1 Multi-rigid body dynamic model of vehicular missile cold launching system

图2 弹体-适配器-发射筒之间几何关系示意图

Fig.2 Geometric relationships among missile, adapter and laun chcanister

图3 基于DSC和TDC的APPC控制系统示意图

Fig.3 Block diagram of APPC control system based on DSC and TDC

图4 发射系统有限元模型

Fig.4 Finite element model of launching system

表1 发射动力学模型参数

Table 1 Parameters of launch dynamics model

参数	数值	参数	数值
m₁/kg	38000	$y ¯ 1$ /m	0.591
m₂/kg	14950	$x ¯ 2$ /m	1.198
m₃/kg	42470	$y ¯ 2$ /m	-6.065
J₁/(kg·m²)	1.42×10⁶	D/m	2
J₂/(kg·m²)	2.98×10⁵	z₁/m	5.324
J₃/(kg·m²)	1.11×10⁶	z₂/m	1.634
k_l/(N·m^-3)	1.6×10⁷	z₃/m	-2.826
c_a/(N·m^-1·s^-1)	10	z₄/m	-7.226
k_s₁/(N·m^-1)	6×10⁷	μ	0.16
c_s₁/(N·m^-1·s^-1)	6×10⁵	β_e/Pa	7×10⁸
k_s₁/(N·m^-1)	6×10⁷	p_s/Pa	2.8×10⁷
c_s₂/(N·m^-1·s^-1)	6×10⁵	p_r/Pa	0
x_A₀/m	2.504	A₁/m²	0.0283
y_A₀/m	-0.845	A₂/m²	0.017
x_B₀/m	-0.009	V_c1/m³	0.051
y_B₀/m	7.02	V_c2/m³	0.0119
$x ¯ 1$ /m	-10.580	k_q	0.7

表1 发射动力学模型参数

Table 1 Parameters of launch dynamics model

参数	数值	参数	数值
m₁/kg	38000	$y ¯ 1$ /m	0.591
m₂/kg	14950	$x ¯ 2$ /m	1.198
m₃/kg	42470	$y ¯ 2$ /m	-6.065
J₁/(kg·m²)	1.42×10⁶	D/m	2
J₂/(kg·m²)	2.98×10⁵	z₁/m	5.324
J₃/(kg·m²)	1.11×10⁶	z₂/m	1.634
k_l/(N·m^-3)	1.6×10⁷	z₃/m	-2.826
c_a/(N·m^-1·s^-1)	10	z₄/m	-7.226
k_s₁/(N·m^-1)	6×10⁷	μ	0.16
c_s₁/(N·m^-1·s^-1)	6×10⁵	β_e/Pa	7×10⁸
k_s₁/(N·m^-1)	6×10⁷	p_s/Pa	2.8×10⁷
c_s₂/(N·m^-1·s^-1)	6×10⁵	p_r/Pa	0
x_A₀/m	2.504	A₁/m²	0.0283
y_A₀/m	-0.845	A₂/m²	0.017
x_B₀/m	-0.009	V_c1/m³	0.051
y_B₀/m	7.02	V_c2/m³	0.0119
$x ¯ 1$ /m	-10.580	k_q	0.7

图5 弹体角度计算结果比较

Fig.5 Comparison of calculatrf results for missile angle

图6 弹体角速度计算结果比较

Fig.6 Comparison of calculated results for missile angular velocity

图7 弹体角加速度计算结果比较

Fig.7 Comparison of calculated results for missile angular acceleration

图8 第一道适配器载荷计算结果比较

Fig.8 Comparison of calculated results for the first adapter load

图9 第二道适配器载荷计算结果比较

Fig.9 Comparison of calculationed results for the second adapter load

图10 第三道适配器载荷计算结果比较

Fig.10 Comparison of calculated results for the third adapter load

图11 第四道适配器载荷计算结果比较

Fig.11 Comparison of calculated results for the forth adapter load

图12 无控状态下有无集总干扰的弹体角度变化比较

Fig.12 Changes in missile angle with and without lumped disturbances in uncontrolled state

图13 无控状态下有无集总干扰的弹体角速度变化比较

Fig.13 Changes in missile angular velocity with and without lumped disturbances in uncontrolled state

图14 无控状态下有无集总干扰的弹体角加速度变化比较

Fig.14 Changes in missile angular acceleration with and without lumped disturbances in uncontrolled state

图15 4种控制器的弹体角度跟踪性能比较

Fig.15 Comparison of missile angle tracking performances using four kinds of controllers

图16 4种控制器的弹体角速度比较

Fig.16 Comparison of missile angular velocities using four kinds of controllers

图17 集总干扰的估计

Fig.1 Estimation of lumped disturbance d1

图18 集总干扰d2的估计

Fig.18 Estimation of lumped disturbance d2

图19 集总干扰d3的估计

Fig.19 Estimation of lumped disturbance d3

图20 集总干扰d4的估计

Fig.20 Estimation of lumped disturbance d4

表2 4种控制算法的控制效果比较

Table 2 Comparison of control effects of four kinds of controllers

控制算法	指标(≥0.6s)
控制算法	e_1sm/(°)	e_1max/(°)	$θ · 3 s m$ / (°·s^-1)	$θ · 3 m a x$ / (°·s^-1)
NC	3.1175	3.5019	3.3015	6.2344
PID	0.2246	0.4376	1.6847	4.3430
DSC	0.3047	0.3301	0.7324	1.2855
DSC+TD	0.2145	0.2478	0.7440	1.4857
DSC+TD+PPC	0.0844	0.1001	0.3927	1.1833

表2 4种控制算法的控制效果比较

Table 2 Comparison of control effects of four kinds of controllers

控制算法	指标(≥0.6s)
控制算法	e_1sm/(°)	e_1max/(°)	$θ · 3 s m$ / (°·s^-1)	$θ · 3 m a x$ / (°·s^-1)
NC	3.1175	3.5019	3.3015	6.2344
PID	0.2246	0.4376	1.6847	4.3430
DSC	0.3047	0.3301	0.7324	1.2855
DSC+TD	0.2145	0.2478	0.7440	1.4857
DSC+TD+PPC	0.0844	0.1001	0.3927	1.1833

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