Abstract: 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.

Key words: internal balanced, reduction, second-order system, flexible space structures, frequency-selective, Gramian matrix