CAJ | 학술논문

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。
본문제출료일충괄용우고초성속비행기수학모형적모형강계방법。해방법채용기우기이치분해적투영기술，대고계적고초성속비행기수학모형진행평형변환，진이통과절단획득저계적미분방정，방편공제기적설계，체도모형강계적목적。상비우전통적지괄용우은정계통적모형강계방법，본문제출적모형강계방법통과우호질분해가이응용우불은정적계통적모형강계。위료증명해모형강계방법적준학성，본문통과평균회색관련계수적계산，급출기우시역분석적정량험증결과。방진부분성공응용해방법대미국공군실험실제출적탄성종향모형실현료강계，증명료해방법적유효성。
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.