重频模态可控可观性的度量与主模态概念

THE CONCEPT OF PRINCIPAL MODE SHAPES AND THE MEASURES OF CONTROLLABILITY AND OBSERVABILITY FOR MODE SHAPES WITH REPEATED FREQUENCIES

本文研究重频模态的可控性和可观性的定量度虽以及不变子空间的可控性结构和可观性结构问题，提出了一种利用奇异值来度量重频模态可控性和可观性的方法，同时提出了如何获得一组新的重频模态向量，使得在这组模态坐标下，子空间的可控性结构或可观性结构有更加明了的表达．

This paper studies how to measure the controllability and observability ofvibration mode shapes with repeated frequencies and how to show clearly the structure of thesubspace consisting of these mode shapes with repeated frequencies in terms of controllabilityand observability. Using singular value decomposition technique,a new set of mode shapesassociated with this repeated frequency and the corresponding singular values has beenfound out.This new set of mode shapes, called the principal mode shapes,can clearlyshow the structure of this subspace in terms of controllability and observability, and thesingular value associated with each principal mode shape can measure the controllabilityand observability of this principal mode sliape. The method of this paper is of importancefor vibration control of flexible space structures.