A New Method for Making a Reduced-Order Model of Flexible Structures using Unobservability and Uncontrollability and Its Application in Vibration Control

Abstract

This paper proposes a new method for modeling flexible structures with distributed parameters as reduced-order models with lumped parameters. Both prevention of spillover and physical correspondence at the modeling points are taken into consideration. When modern control theory is employed to control the vibration of flexible structures, because of restrictions on controller design, it is necessary to make a reduced-order model of the structure. When higher modes are ignored, the reduction of the model may result in vibration instability-spillover. Because of uncontrollability and unobservability, nodes of higher-order vibration modes are selected as modeling points to prevent spillover. The effctiveness of this method is demonstrated by applying vibration control to a flexible towerlike structure.