一类弹性飞行器动态特性的摄动估计

本文针对一类高速、细长体飞行器的动力学模型,应用矩阵谱的摄动与估计理论,分析了气动力非定常因素对飞行器动态特性的影响。结论表明,利用低阶的准定常系统结果可以十分准确地估计非定常系统特性,从而大大降低动力学方程的阶次,为弹性飞行器的降阶模型研究提供了理论依据,有助于飞行器主动控制系统的分析与设计。

Perturbation Evaluation of Dynamic Behavior of a Class of Elastic Vehicles

It is well known that aeroelastic state-space model of flight vehicle may be based either on indicial lift functions of unsteady aerodynamics or on quasisteady aerodynamics. As everyone knows, the order of the state-space model for unsteady aerodynamics is much larger than that for quasisteady aerodynamics. The large-order model makes it very difficult to analyze and design the active control system. Consequently, reducing the order of the state-space model has become the subject of a great deal of study. Numerous digital calculations indicate clearly that for higher speeds the unsteady part of aerodynamic forces has only a small effect on the dynamic behavior of elastic vehicle system1] 2]. But, unfortunately, there exists no engineering theory to assure that such is always the case. This paper attempts to present such an engineering theory for slender flight vehicle. In this paper, by employing a new mathematical tool called perturbation and evaluation theory for matrix eigenvalue5], we analyze the influence of unsteady aerodynamics on the dynamic behavior of slender flight vehicle system. Thus we obtain the first order perturbation solutions of system eigenvalues and also obtain the upper and lower bounds of the error of approximation. The digital calculations of this paper's numerical example show that the proposed method is accurate and effective for estimating the dynamic behavior of the elastic vehicle system from the vehicle model considering only quasisteady aerodynamic force under certain conditions as explained in the paper; the relative error of perturbation solution with respect to accurate solution is less than 10%.