Active Wave Feedback Control at a Free End of a Flexible Beam Using a Wave Filter Constructed with Point Sensors (Theoretical Verification of Basic Properties)

Abstract

This paper deals with the feedback wave control of a flexible beam using the wave filter constructed with four point sensors. The objective of this paper is to theoretically lay out the active wave control at free end of the beam which is independent of the disturbance positions. Firstly, the transfer matrix method and wave filtering method are extended to the Laplace domain. Next, based on the relation between the incident and reflected wave vectors at a free end, the control laws and characteristic equation of the control system are derived. Moreover, the control effects are presented from a viewpoint of a numerical analysis. It is found that the proposed method can eliminate the designated wave even if a disturbance acts around the control point. Finally, the stability of the control system is clarified by using root loci, showing that all poles are close to the critical damping.