THE CONCEPT OF PRINCIPAL MODE SHAPES AND THE MEASURES OF CONTROLLABILITY AND OBSERVABILITY FOR MODE SHAPES WITH REPEATED FREQUENCIES
重频模态可控可观性的度量与主模态概念

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.