﻿ 基于间隙度量的高超声速飞行器包线定量划分
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1. 北京航空航天大学 自动化科学与电气工程学院, 北京 100191;
2. 第二炮兵装备研究院, 北京 100085

Flight envelope quantitative division of hypersonic vehicle based on gap metric
He Chaofan1, Yang Lingyu1, Li Xin1, He Niannian2
1. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
2. The Second Artillery Equipment Institude, Beijing 100085, China
Abstract:Considering that the existing flight envelope division methods of hypersonic vehicle were too subjective and complicated, a new division method was introduced based on the theory of gap metric. The theory of gap metric was introduced, and the computing method of gap between linear systems was given. Here the gap metric was taken as the quantitative index to analyze the extent of the model characteristics' variation to confirm the frontier of subrange. Based on the result obtained above, the way of choosing the nominal state point was proposed by analyzing the gap metric of all points within the subrange. With the living example of some hypersonic vehicles, the analysis of amplitude-frequency characteristics for nominal state point and the simulations of closed-loop control system prove that the result of envelope division is reasonable, which indicates the method proposed is effective and able to increase the level of automation of envelope division.
Key words: hypersonic vehicle     flight envelope     amplitude-frequency characteristics     automation     gap metric

K为Hilbert空间中的线性算子:

K的图谱(graph)G(K)为{v,Kv}的集合,其中
G(K)∈H×H,D(K)称为K的域.若G(K)为H×H的闭子空间,则称K是闭合的.

δ21(G(K2),G(K1))定义类似.对任意的两个算子K1,K2,0≤δ(K1,K2)≤1,两个算子差异越小,则δ值越接近于0. 1.2 线性系统间隙度量计算方法

P的左右互质分解形式如式(4)所示:

1) 求传递函数,其中(A,B)稳定,(A,C)可观;

2) 求取矩阵FH,使得AF=A+BF,AH=A+HC稳定,并令

3) 互质分解形式为

 图 1 基于间隙度量的包线划分方法流程图 Fig. 1 Flowchart of envelope division method based on gap metric

1) 在飞行包线内建立一系列线性化模型,作为分析模型特性变化规律的基础.

2) 计算相邻状态点模型之间的间隙度量值,并对其进行分析,以确定区域边界.

3) 一般情况下,一个飞行区域内的标称点要满足与区域内其他状态点的模型特性差异最小,在以间隙度量为衡量指标情况下,确定标称点即为寻找子区域的“间隙度量极小点”.

2 包线划分举例验证

 图 2 同一马赫数下间隙度量随高度变化率 Fig. 2 Changing curves of gap metric with height at same mach
 图 3 同一高度下间隙度量随马赫数变化率 Fig. 3 Changing curves of gap metric with Mach at same height

 图 4 包线划分结果示意图 Fig. 4 Flight envelope division result

 图 5 间隙度量极小点示意图 Fig. 5 Schematic of gap metric minimum point

 图 6 Ea0点与其余状态点频域特性对比(滚转通道) Fig. 6 Comparison chart of frequency-domain charact- eristics between Ea0 and other state point (roll channel)
 图 7 Ea0点与其余状态点频域特性对比(偏航通道) Fig. 7 Comparison chart of frequency-domain charact- eristics between Ea0 and other state point (yaw channel)
 图 8 Ea0点与其余状态点频域特性对比(俯仰通道) Fig. 8 Comparison chart of frequency-domain charact- eristics between Ea0 and other state point (pitch channel)

 图 9 间隙度量极小点Ea0阶跃响应曲线 Fig. 9 Response curves for the state of gap metric minimum point Ea0
 图 10 子区域内所有网格点阶跃响应曲线 Fig. 10 Response curves for all states within the subrange

3 结 论

1) 间隙度量理论能够为包线划分提供依据，通过实例验证，结果表明基于间隙度量的包线定量划分方法能够实现飞行包线的合理划分；

2) 相较于传统划分方法，基于间隙度量的划分方法能够大幅降低包线划分的工作量，故更具有工程实用性.

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#### 文章信息

He Chaofan, Yang Lingyu, Li Xin, He Niannian

Flight envelope quantitative division of hypersonic vehicle based on gap metric

Journal of Beijing University of Aeronautics and Astronsutics, 2014, 40(9): 1250-1255.
http://dx.doi.org/10.13700/j.bh.1001-5965.2013.0592