高超声速飞行器飞行动力学特性不确定分析

Uncertainty Analysis of Flight Dynamic Characteristics for Hypersonic Vehicles

高超声速飞行器分析模型存在较大不确定性,其给出的动力学特性与真实值之间存在偏差,因此研究飞行动力学特性分析结果的可信度水平对控制系统设计具有重要意义。针对典型的乘波体构型高超声速飞行器,在建立气动/结构/推进相互耦合的动力学模型基础上,利用非概率区间来描述模型中的不确定参数,并将复特征根不确定范围求解问题转化为频率和阻尼比两个实数的不确定区间分别求解,给出了动力学模态特征根、频率及阻尼比的不确定边界。分别采用直接蒙特卡罗(DMC)模拟方法、基于泰勒展开的区间分析方法(TIAM)和基于多项式逼近的区间分析方法(CIAM)对高超声速飞行器飞行动力学不确定性进行了研究。结果表明:CIAM计算时间适中,且给出的边界更为准确、安全,适合在控制系统设计和验证过程中使用。

Knowledge of the dynamic characteristics bounds of hypersonic vehicles is necessary during the process of control law design and clearance due to the multi-sources and large magnitude of uncertainties arising from the inaccuracy of mathe- matical dynamic models. A coupled longitudinal dynamical model is developed in this paper for a typical hypersonic waverid- er with parametric uncertainties depicted as intervals. A comparative study is made of the open-loop/closed-loop eigenvalue bounds estimation by the three methods of Taylor expansion based interval analysis method （TIAM）, collocation interval analysis method （CIAM）, and direct Monte Cado （DMC） simulation method. For complex eigenvalues, the problems are transformed into two sub-problems of the intervals of the frequency and damping ratio, which are both real numbers. The re- sults indicate that ClAM can give comparatively more accurate and safe bounds estimation while keeping the computation cost low, which demonstrates its potential for application in robust controller design and assessment.