超声速飞机缩比模型飞行控制律参数相似设计准则

doi:10.7527/S1000-6893.2025.31885

Abstract

Abstract:

During the conceptual design phase of an aircraft， flight tests of scaled-model are often used to approximate the motion of full-size aircraft and validate the rationality of the design. Only similar design criteria have been investigated for scaled-model in the low-speed flight phase， however， no research has been carried out on similar design of overall parameters and flight control law parameters for supersonic aircraft. To conduct the flight test of high-gain supersonic aircraft with linear flight control law， it is necessary to systematically investigate the similarity of the overall parameters and flight control law parameters between the scaled-model and the full-size aircraft. First， the similarity criterions for the ontological parameters and the kinematic parameters of the scaled-model are derived based on the heavy model method. Second， the general similarity relationships applicable to all flight control law configurations and feedback signals are analyzed and derived. According to the differences in control principles， the flight control law parameters are categorized into two types： feedback gains and series dynamic links. For these two types of parameters， similar relations with generalization are derived based on similar system theory. Finally， the mathematical simulation of a closed-loop system with a control law is completed using a supersonic aircraft and its scaled- model as an example. The results show that the simulation results of the full-size aircraft and scaled-model with flight control laws satisfy the motion similarity relationship， validating the correctness of the research conclusions in this paper.

Key words: supersonic aircraft, similarity criterion, scaled-model, flight control law, flight simulation

CLC Number:

V212

Shang TAI, Lixin WANG, Yanguo HU, Haoze WU, Kai HUANG, Hailiang LIU, Ting YUE. Similarity criterion of flight control law parameters for scaled-model of supersonic aircraft[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(20): 531885.

Figures/Tables 19

Table 1

Table 2

Table 3

Similarity ratios of aircraft response variables （scaled-model/full-size aircraft）

参数	符号	相似比例
尺寸、高度变化量	k_l 、k_Δ_H	k
飞行速度	k_V	1
速度变化量	k_Δ_V	k^0.5
加速度	k_a	1
迎角、侧滑角、滚转角、俯仰角、偏航角	k_α 、k_β 、k_ϕ 、k_θ 、k_ψ	1
角速度	k_ω	k^-0.5
角加速度	$k ω ˙$	k^-1
时间	k_t	k^0.5

Table 3

Fig.1

Fig.2

Table 4

Table 5

Fig.3

Fig.4

Fig.5

Fig.6

Table 6

Comparison of flight control law parameters between scaled-model and full-size aircraft

控制律增益	相似比例	数值	全尺寸	缩比
K_q	k^0.5	1/2	0.90	0.45
K_Pnz	1	1	0.10	0.10
K_Inz	k^-0.5	2	0.30	0.60
K_nz	1	1	0.15	0.15
K_PV	k^-0.5	2	0.50	1.00
K_IV	k^-1	4	0.10	0.40
$K ϕ ˙$	k^0.5	1/2	0.07	0.04
K_fa	k^0.5	1/2	0.08	0.04
K_Ia	1	1	0.09	0.09
K_ny	1	1	0.22	0.22
K_r	k^0.5	1/2	0.80	0.10
K_Ir	k^-0.5	2	0.74	1.48
K_fr	1	1	1.85	1.85
T_w	k^0.5	1/2	3.00	1.50
τ_act	k^0.5	1/2	0.10	0.05
τ_p	k^0.5	1/2	3.00	1.50
τ_nf	k^0.5	1/2	0.20	0.10

Table 6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

Table 7

Goodness of fits of the processed scaled-model to the full-size aircraft simulation results

类型	拟合优度
纵向指令输入仿真结果	Δn_z	V	α	q	θ	H	Δn_x	γ	pla
纵向指令输入仿真结果	0.98	0.98	0.95	0.94	0.96	0.99	0.99	0.97	0.93
横向指令输入仿真结果	$ϕ ˙$	p	β	ϕ	r	ψ	y	δ_a	δ_r
横向指令输入仿真结果	0.98	0.96	0.94	0.99	0.93	0.94	0.99	0.97	0.92
航向指令输入仿真结果	β	ϕ	ψ	p	r	y	n_y	δ_a	δ_r
航向指令输入仿真结果	0.98	0.97	0.91	0.98	0.95	0.99	0.98	0.97	0.98

Table 7

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参数	符号	重模型法	轻模型法
平均气动弦长	c	k	k
重心位置	x_cg	1	1
机翼面积	S	k²	k²
质量	m	k²	k³
惯性矩	I	k⁴	k⁵
空气密度	ρ	1	1
马赫数	Ma	1	1

相似参数	重模型法	比例	轻模型法	比例
初始配平角度相等	满足	1	不满足
无量纲的质量密度分布函数相等	满足	1	满足	1
马赫数相等	满足	1	满足	1
雷诺数相等	不满足	k	不满足	k
斯特劳哈尔数相等	不满足	k^0.5	满足	1
密度比相等	不满足	k	满足	1
弗劳德数相等	不满足	k^-^0.5	不满足	k

参数		比例	全尺寸	缩比
构型参数	机翼展长/m	1/4	18	4.5
	平均气动弦长/m	1/4	11.5	2.88
	机翼面积/m²	（1/4）²	150	9.38
	质量/kg	（1/4）²	41 000	2 562
	俯仰转动惯量/（kg·m²）	（1/4）⁴	1 063 800	4 155
	偏航转动惯量/（kg·m²）	（1/4）⁴	1 144 200	4 470
	滚转转动惯量/（kg·m²）	（1/4）⁴	160 575	627
	惯性积/（kg·m²）	（1/4）⁴	18 083	70.6
状态参数	空气密度/（kg·m^-3）	1	0.193 7	0.193 7
	飞行速度/（m·s^-1）	1	531.1	531.1
	马赫数	1	1.8	1.8
	飞行高度/km	1	15	15

Similarity criterion of flight control law parameters for scaled-model of supersonic aircraft

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