Active Wave Feedback Control of a Flexible Beam Using Wave Filter

Theoretical Verification of Basic Properties

Abstract

This paper deals with the active wave control of a flexible beam using wave filter which enables the direct sensing of a designated wave amplitude. It is the purpose of this paper to present the basic properties of active wave feedback control system based upon wave amplitude signal. First, the state equation of a flexible beam with arbitrary boundary condition is described by using a transfer matrix method. Then, two kinds of control laws are derived; one is for absorbing reflected wave and the other is for eliminating transmitted wave. Next, from a viewpoint of numerical analysis, the basic properties of control laws and its control effects are investigated. Finally, an active wave control system is found to be stable regardless of whether collocation holds or not, demonstrating the relation of stability between control and measurement point placement.