新型迅捷弹箭动力学建模与姿态控制

doi:10.12382/bgxb.2023.0404

摘要/Abstract

摘要：

为大幅度提高弹箭的超大角度机动能力,提出一种新型迅捷弹箭动力学建模与姿态控制方法。通过在传统直接力/气动力复合控制敏捷弹箭尾部加装一类柔性可控圆伞,设计一种新型弹箭的几何构型,并划分新型迅捷转向的三个阶段。为回避牛顿欧拉力学在多体动力学建模过程中求解复杂约束力带来的一系列问题,以拉格朗日力学为基础,选取弹箭的位置、姿态和伞的姿态作为广义坐标,推导系统的动能,求解系统的广义力,建立以弹箭为主体的铅垂平面4自由度动力学模型。针对具有快时变性、强不确定性、强非线性等特点的柔性力/直接力/气动力复合控制律设计问题,建立系统姿态跟踪误差的状态方程,基于非奇异终端滑模面和双幂次趋近律设计具有有限时间收敛特性的姿态控制器,利用扩张状态观测器消除内外扰动对系统造成的负面影响,抑制抖振。通过仿真验证了新方法的合理性和有效性,并与传统敏捷弹箭进行仿真对比,验证了新方法有利于减小转弯半径、缩短转弯时间、减少能量消耗。

关键词: 弹箭, 敏捷转弯, 柔性可控圆伞, 拉格朗日力学, 滑模控制, 扩张状态观测器

Abstract:

A dynamic modeling and attitude control method for novel agile projectiles is proposed to improve the large-angle maneuverability of the projectiles. By adding a flexible and controllable circular parachute to the tail of the traditional reaction-jet and aerodynamic compound control agile projectile, a geometric configuration of the novel agile projectile is designed, and the novel agile turn is divided into three phases. To avoid a series of problems caused by Newton-Euler’s mechanics in solving complex constraints in the process of multi-body dynamics modeling, based on Lagrange mechanics, the position and attitude of projectile and the attitude of parachute are selected as the generalized coordinates, the kinetic energy of the system is derived, and the generalized force of the system is solved. Then a four-degree-of-freedom dynamic model with projectiles as the main body in the vertical plane is established. Finally, in order to design the flexible force, reaction-jet and aerodynamic compound control law for novel agile projectiles with fast time variability, strong uncertainty and strong nonlinearity, the equation of state for the system attitude tracking error is established, and the attitude controller with finite time convergence is designed based on the non-singular terminal sliding mode and the double power reaching law. The extended state observer is used to eliminate the negative impact of internal and external disturbances on the system and suppress chattering. The rationality and effectiveness of the proposed method are verified through simulation. Through the simulation and comparison of the novel and traditional agile projectiles, it is verified that the proposed method is beneficial for reducing turning radius, shortening turning time, and reducing energy consumption.

Key words: projectiles, agile turn, flexible and controllable circular parachute, Lagrange mechanics, sliding mode control, extended state observer

中图分类号:

赵新运, 于剑桥. 新型迅捷弹箭动力学建模与姿态控制[J]. 兵工学报, 2024, 45(7): 2182-2196.

ZHAO Xinyun, YU Jianqiao. Dynamic Modeling and Attitude Control for Novel Agile Projectile[J]. Acta Armamentarii, 2024, 45(7): 2182-2196.

图/表 21

图1 传统敏捷弹箭弹体配置

Fig.1 Configuration of traditional agile projectile

图2 传统敏捷弹箭掉头转弯

Fig.2 Heading reversal maneuver of traditional agile projectile

图3 新型迅捷弹箭弹体配置

Fig.3 Configuration of novel agile projectile

图4 新型迅捷弹箭掉头转弯

Fig.4 Heading reversal maneuver of novel agile projectile

图5 新型迅捷弹箭受力分析图

Fig.5 Force analysis diagram of novel agile projectile

图6 控制系统原理框图

Fig.6 Schematic diagram of control system

图7 弹箭飞行包络

Fig.7 Projectile flight envelope

表1 时间与能量消耗

Table 1 Time and energy consumption

传统、新型与效果	t_sim/ s	E_uR/ (N·s)	E_uT/ (N·s)	E_total/ (N·s)
传统	2.31	3732.78	40567.50	44300.28
新型	2.00	13440.31	24952.50	38392.81
效果	-13.27%	260.06%	-38.49%	-13.34%

图8 弹道曲线

Fig.8 Curves of trajectory

图9 俯仰角、攻角和弹道倾角变化曲线

Fig.9 Curves of pitch angle, attack of angle and flight path angle

图10 俯仰角速度变化曲线

Fig.10 Curves of pitch angular velocity

图11 法向加速度变化曲线

Fig.11 Curves of normal acceleration

图12 弹道倾角角速度变化曲线

Fig.12 Curves of flight path angular velocity

图13 速度曲线

Fig.13 Curves of velocity

图14 直接力指令曲线

Fig.14 Curves of reaction-jet command

图15 气动舵指令曲线

Fig.15 Curves of elevator deflection command

图16 柔性力指令曲线

Fig.16 Curve of flexible force command

图17 不确定量变化曲线

Fig.17 Curves of uncertainty

表B1 弹箭结构参数

Table B1 Structural parameters of projectiles

参数	数值
质量/kg	102.1573
转动惯量/(kg·m²)	69.1467
特征长度/m	0.1270
特征面积/m²	0.0127

表B2 弹箭气动参数

Table B2 Aerodynamic coefficients of projectiles

攻角/(°)	Ma	C_n_α	C_n_δ	C_m_α	C_m_δ
	0.3	16.094	12.307	-48.106	-123.266
10	0.6	13.212	12.485	-46.822	-124.985
	0.8	10.875	12.124	-44.777	-121.278
	2.0	10.015	6.520	-10.279	-67.076
	0.3	6.578	5.690	-68.927	-56.992
40	0.6	44.112	6.452	-103.362	-64.570
	0.8	52.443	6.976	-104.679	-69.683
	2.0	31.581	4.864	-58.786	-50.008
	0.3	10.796	0	0	0
80	0.6	11.156	0	0	0
	0.8	11.529	0	0	0
	2.0	0	0	0	0

表B3 伞的气动参数

Table B3 Aerodynamic coefficients of parachute

伞的攻角/(°)	Ma	C_N	C_T	C_mp
10	0.2	0.080	0.550	-0.018
	0.6	0.084	0.627	-0.020
20	0.2	0.150	0.480	-0.027
	0.6	0.179	0.592	-0.031
30	0.2	0.280	0.400	-0.035
	0.6	0.340	0.482	-0.042
40	0.2	0.400	0.280	-0.043
	0.6	0.510	0.335	-0.050

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