高超声速飞行动态特性的特征值扰动分析

Eigenvalue perturbation analysis of thrust law effects on hypersonic flight dynamics

提出了一种基于特征值扰动理论的方法来分析推力特性对高超声速纵向飞行动态的影响,指出飞行动态的改变是飞行动态灵敏度和推力特性共同作用的结果。使用未扰矩阵的特征值条件数评价了各个运动模态的灵敏度,通过对扰动矩阵2范数的解析分析了各种推力特性的影响。结果表明:沉浮运动模态最容易受到推力特性的影响;飞行速度越高,飞行动态对外界扰动越敏感;推力/速度特性是影响飞行动态的主要推力特性。

A novel approach is proposed using the eigenvalue perturbation theory to analyze the thrust law effects of advanced air-breathing engines on hypersonic longitudinal dynamics. It is noticed that the influences of thrust laws are determined not only by the thrust characteristics, but also by the sensitivity of flight dynamics. By appropriate linear decomposition of the system matrix, the contributions of these two factors are analyzed using the eigenvalue perturbation theory. The influences of thrust laws are examined by their contributions to the 2-norm of the perturbation matrix. The sensitivities of the longitudinal modes of motion are examined according to their eigenvalue condition numbers. It is concluded that the phugoid mode is much more sensitive to thrust laws than the short period mode, and the thrust/speed dependence is the dominant factor that influences the flight stability. A detailed development of the method along with its application to a benchmark hypersonic vehicle Winged-cone as an example is included.