基于平衡截断方法的高超声速飞行器模型降阶

摘要

本文提出了一种适用于高超声速飞行器数学模型的模型降阶方法。该方法采用基于奇异值分解的投影技术，对高阶的高超声速飞行器数学模型进行平衡变换，进而通过截断获得低阶的微分方程，方便控制器的设计，达到模型降阶的目的。相比于传统的只适用于稳定系统的模型降阶方法，本文提出的模型降阶方法通过右互质分解可以应用于不稳定的系统的模型降阶。为了证明该模型降阶方法的准确性，本文通过平均灰色关联系数的计算，给出基于时域分析的定量验证结果。仿真部分成功应用该方法对美国空军实验室提出的弹性纵向模型实现了降阶，证明了该方法的有效性。%This paper presents a model reduction method applicable to the hypersonic vehicle mathematical model. The method uses projection technology based on the singular value decomposition to transform the high-level mathematical model of a hypersonic vehicle to a balance form to obtain a low-order differential equation by truncation, thus achieving the model reduction and facilitating the design of the controller. Compared to the traditional model reduction applied only to stable system, the model reduction method proposed in this paper can be applied to reduce the unstable system by using right coprime decomposition. In order to prove the accuracy of the model reduction method, we give quantitative validation results based on the time domain analysis through the calculation of the average gray relational coefficients. In the simulation part, we apply this method to achieve a reduced-order model of the elastic longitudinal model proposed by the US Air Force Research Laboratory successfully, which proves the effectiveness of this method.