组合式飞行器多体动力学建模与飞行力学特性

doi:10.12382/bgxb.2022.0282

摘要/Abstract

摘要：

为精确、完整地描述组合式多体飞行器空间运动位形,基于拟坐标形式的Lagrange方程提出反映相对滚转运动的8自由度组合式三体飞行器动力学建模方法。采用计算流体力学方法建立考虑气动耦合效应的组合式飞行器系统气动力数据库。通过算例将所建模型与ADAMS软件的仿真结果进行对比,验证所建模型的准确性。在此基础上,进行配平方案及飞行力学特性研究,分析比较飞行器在不同配平状态的动力学特性,并基于串级PID控制方法进行增稳控制研究。研究结果表明:所建模型有效反映了组合式飞行器的相对运动;在给定配平方案及飞行工况后,该构型飞行器存在“对称下反”和“对称上反”两个配平状态,在两个状态下的相对滚转运动静稳定性显著不同;除了传统飞行力学模态,该构型飞行器还存在由相对滚转运动主导的4个新生运动模态,按运动特性可分为复合对称运动和复合反对称运动两类;针对在无控状态下该构型飞行器无法长期保持稳定飞行的问题,所提增稳控制方案合理有效,可以快速镇定发散的飞行力学系统;所提建模方法和增稳控制方案可为多体飞行器设计分析提供指导和参考。

关键词: 组合式飞行器, 多体动力学, 飞行力学特性, 拟坐标, 增稳控制

Abstract:

To precisely and completely describe the location and shape of the combined multibody aircraft, a dynamic modeling method of the 8 DOF combined three-body aircraft reflecting relative rolling motion is proposed using Lagrange’s equations with quasi-coordinates. The aerodynamic database of the combined multibody aircraft system considering the aerodynamic coupling effect is established by the CFD method. The accuracy of the model is verified by comparing the model with ADAMS software through a numerical example. Based on this, the trim scheme and flight dynamic characteristics of the aircraft in different trim states are studied. The stability augmentation control is studied based on the cascade PID control method. The results show that the established model effectively reflects the relative motion of the combined aircraft. With the given trim scheme and flight condition, the aircraft of this configuration has two trim states of "symmetrical lower inverse" and "symmetrical upper inverse", and the static stability of relative rolling motion in the two states is quite different. In addition to the traditional flight mechanics mode, there are 4 new motion modes dominated by relative rolling motion, which can be divided into composite symmetric motion and composite antisymmetric motion according to the motion characteristics. To address the problem that the aircraft with this configuration cannot keep stable flight for a long time without control, the stability augmentation control scheme is reasonable and effective, which can quickly stabilize the divergent flight mechanics system. The proposed modeling method and stabilization control scheme can provide guidance and reference for the design and analysis of multibody aircrafts.

Key words: combined aircraft, multibody dynamics, flight dynamic characteristics, quasi-coordinate, stability augmentation control

中图分类号:

V212.1

杜万闪, 周洲, 拜昱, 张志林, 王科雷. 组合式飞行器多体动力学建模与飞行力学特性[J]. 兵工学报, 2023, 44(8): 2245-2262.

DU Wanshan, ZHOU Zhou, BAI Yu, ZHANG Zhilin, WANG Keilei. Study on Multibody Dynamics Modeling and Flight Dynamic Characteristics of Combined Aircraft[J]. Acta Armamentarii, 2023, 44(8): 2245-2262.

图/表 29

图1 组合式三体飞行器示意图

Fig.1 Diagram of combined three-body aircraft

图2 组合式三体飞行器坐标轴系示意图

Fig.2 Diagram of coordinate system of combined three-body aircraft

图3 组合式三体飞行器模型

Fig.3 Example model of combined three-body aircraft

表1 飞行单元基本参数

Table 1 Basic parameters of single aircraft

参数	数值
质量/kg	3.75
参考展长/m	3.2
平均气动弦长/m	0.3
展弦比	10.6
参考面积/m²	0.87
对轴Ox的惯量I_xx/(kg·m²)	0.734
对轴Oy的惯量I_yy/(kg·m²)	0.41
对轴Oz的惯量I_zz/(kg·m²)	1.1
对轴Oz和Ox的惯性积I_zx/(kg·m²)	-0.01

图4 单体飞行器模型

Fig.4 Model of single aircraft

表2 气动力数据库建立方法

Table 2 Method of establishing aerodynamic database

CFD仿真内容	气动参数	计算方法
基本气动参数项	CD₀、CL₀等	雷诺平均Navier-Stokes (RANS)方法
气动耦合项	C $D ϕ b a$ 、C $D ϕ c a$ 等
静导数项	CD_α、CL_α等
操纵导数项	C $D δ e$ 、C $Y δ a$ 等
动导数项	CL_q、CY_p等	涡格法

表2 气动力数据库建立方法

Table 2 Method of establishing aerodynamic database

CFD仿真内容	气动参数	计算方法
基本气动参数项	CD₀、CL₀等	雷诺平均Navier-Stokes (RANS)方法
气动耦合项	C $D ϕ b a$ 、C $D ϕ c a$ 等
静导数项	CD_α、CL_α等
操纵导数项	C $D δ e$ 、C $Y δ a$ 等
动导数项	CL_q、CY_p等	涡格法

图5 单体飞行器网格分布

Fig.5 Diagram of grid distribution of single aircraft

图6 组合式三体飞行器网格分布

Fig.6 Diagram of grid distribution of combined three-body aircraft

图7 飞行单元气动参数随迎角α和侧滑角β变化

Fig.7 Curve of aerodynamic parameters of single aircraft varying with attack angle α and sideslip angle β

图8 飞行单元气动参数随相对滚转角ϕba变化

Fig.8 Curve of aerodynamic parameters of single aircraft varying with relative roll angle ϕba

图9 飞行单元a状态量响应

Fig.9 Diagram of state response of single aircraft a

表3 不同初始状态的相对滚转角

Table 3 Relative roll angles at different initial states

初始状态	ϕ_ba/(°)	ϕ_ca/(°)
1	10	-10
2	-10	10

图10 不同初始状态的相对滚转角响应

Fig.10 Diagram of relative roll angle response in different initial states

表4 配平分析结果

Table 4 Result of trim analysis

未知配平量	配平状态1	配平状态2
升降舵偏角/(°)	-0.2622	-0.1347
油门杆操纵量/%	35.5	35.5
方向舵偏角/(°)	0	0
飞行单元a副翼偏角/(°)	0	0
飞行单元b副翼偏角/(°)	1.6809	2.0557
飞行单元c副翼偏角/(°)	-1.6809	2.0557
相对滚转角ϕ_ba/(°)	6.4393	-6.6386
相对滚转角ϕ_ca/(°)	-6.4393	6.6386

图11 两种配平状态

Fig.11 Diagram of two trim states

图12 “对称下反”状态相对滚转运动静稳定性分析

Fig.12 Static stability analysis of relative rolling motion of “symmetrical lower inverse”

图13 “对称上反”状态相对滚转运动稳定性分析

Fig.13 Static stability analysis of relative rolling motion of “symmetrical upper inverse”

表5 配平状态运动模态分析

Table 5 Motion mode analysis of trim states

运动模态	“对称下反”配平点1				“对称上反”配平点2
运动模态	特征根	模态特征	阻尼比	时间常数/s	特征根	模态特征	阻尼比	时间常数/s
短周期模态	-7.1334±5.9653j	收敛	0.7671	1.0533	-7.1254±5.8959j	收敛	0.7704	1.0657
长周期模态	-0.0363±0.9628j	收敛	0.0377	6.5260	-0.0372±0.9639j	收敛	0.0386	6.5185
滚转模态	-56.2923	收敛	1	0.0123	-57.9442	收敛	1	0.0120
螺旋模态	0.1874	发散	1	3.6988	-0.1297	收敛	1	5.3442
荷兰滚模态	-0.6013±0.5190j	收敛	0.7570	12.1063	-0.3580±0.7475j	收敛	0.4319	8.4056
复合对称运动模态1	-17.288	收敛	1	0.0401	-17.8852	收敛	1	0.0388
复合对称运动模态2	-0.1579	收敛	1	4.3898	0.1200	发散	1	5.7762
复合反对称运动模态1	-9.4704	收敛	1	0.0732	-9.6093	收敛	1	0.0721
复合反对称运动模态2	-0.3058	收敛	1	2.2667	0.2888	发散	1	2.4001

表6 新生运动模态特征向量分析

Table 6 Feature vector analysis of new motion modes

配平状态	运动模态	Δp_a	Δϕ_a	Δq_a	Δθ_a	Δr_a	Δψ_a	Δω_ba	Δϕ_ba	Δω_ca	Δϕ_ca
“对称下反” 配平点1	复合对称运动模态1	-1.90× 10^-15	1.10× 10^-16	-0.0244	0.0014	2.37× 10^-18	-1.37× 10^-19	0.5766	-0.0334	-0.5766	0.0334
	复合对称运动模态2	1.01× 10^-15	-1.07× 10^-14	-0.0007	0.0043	-3.79× 10^-15	2.39× 10^-14	0.0942	-0.5962	-0.0942	0.5962
	复合反对称运动模态1	-0.7885	0.0833	-1.21× 10^-15	9.12× 10^-17	-0.0488	0.0052	0.4221	-0.0446	0.4221	-0.0446
	复合反对称运动模态2	-0.1118	0.3658	-8.87× 10^-16	1.32× 10^-15	-0.0208	0.0681	0.1840	-0.6018	0.1840	-0.6018
“对称上反” 配平点2	复合对称运动模态1	-1.89× 10^-16	1.39× 10^-18	-0.0261	0.0015	1.10× 10^-16	-6.16× 10^-18	-0.5566	0.0311	0.5566	-0.0311
	复合对称运动模态2	-5.98× 10^-14	-5.05× 10^-13	-0.0026	-0.0216	-1.27× 10^-14	-1.06× 10^-13	0.0755	0.6291	-0.0755	-0.6291
	复合反对称运动模态1	-0.7924	0.0825	1.07× 10^-14	-1.07× 10^-15	-0.0486	0.0051	0.3863	-0.0402	0.3863	-0.0402
	复合反对称运动模态2	0.1039	0.3596	-5.83× 10^-14	-2.06× 10^-13	-0.0345	-0.1195	-0.1795	-0.6214	-0.1795	-0.6214

表7 双机组合运动模态

Table 7 Motion modes of combined two-body aircraft

运动模态	特征根	模态特征
短周期模态	-1.0419±2.1693j	收敛
长周期模态	0.0643±0.0489j	发散
滚转模态	-4.4588	收敛
荷兰滚模态	-0.2048±0.8746j	收敛
复合运动模态1	-0.9696	收敛
复合运动模态2	0.9625	发散

图14 复合对称运动

Fig.14 Composite symmetric motion

图15 复合反对称运动

Fig.15 Composite antisymmetric motion

图16 “对称下反”配平点1处系统自由响应

Fig.16 System free response of “symmetrical lower inverse”

图17 “对称上反”配平点2处系统自由响应

Fig.17 System free response of “symmetrical upper inverse” at trim point 2

图18 配平点1处不对称扰动下系统自由响应

Fig.18 System free response under asymmetric disturbance at trim point 1

图19 增稳控制系统设计思路图

Fig.19 Diagram of design of stability augmentation control system

图20 Simulink仿真框图

Fig.20 Diagram of Simulink simulation

图21 增稳控制后配平点2处对称扰动响应

Fig.21 Response under symmetric disturbance at trim point 2 after stability augmentation control

图22 增稳控制后配平点1处不对称扰动响应

Fig.22 Response under asymmetric disturbance at trim point 1 after stability augmentation control

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