利用传统的一阶选频内平衡降阶方法进行降阶时,不但破坏了原二阶系统动力学结构,而且降阶过程中的选频Gramian矩阵的求解计算量大、数值稳定性差。利用解耦模态坐标的二阶柔性空间结构(FSS)方程的特殊性,给出了可控和可观Gramian矩阵的选频闭合解析解。为了将FSS动力学模型在指定频段进行降阶并保留原系统的二阶动力学结构,提出了几种不同的二阶选频降阶方法。数值仿真结果表明,所提出的降阶方法可以有效地在指定频段进行降阶,降阶精度可以达到或超过传统的一阶选频内平衡降阶方法。
The conventional first-order frequency-selective internal balanced truncation can destroy the dynamical properties of flexible space structures (FSS). Moreover, the calculation of frequency-selective Gramians is ineffective and unstable. Therefore, a controllable and observable closed-form solution of frequency-selective Gramians is presented considering special second-order form of FSS equation via frequency definition of Gramians. Several new second-order frequency-selective model reduction methods are proposed for preserving second-order structure and dynamical characteristics of FSS equation. The numerical results show that the new methods can not only achieve almost the same accuracy, but also preserve all the dynamic properties of original system compared with conventional first-order frequency-selective balanced truncation method.
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