Cluster vector-based control of a flexible beam for generating a vibration-free region

This paper presents cluster vector-based control for generating a vibration-free state in the designated area of a target beam. Cluster control consisting of both cluster filtering and cluster actuation is shown, and the stability of a cluster control system is investigated. Cluster filtering aims at extracting the information necessary for control, while cluster actuation excites or suppresses the cluster filtering output without causing spillover. For generating a vibration-free state in the designated area of a beam, where neither progressive waves nor reflected waves exist, state variables governing the vibration of a beam must be extracted and suppressed. A cluster vector—the common link between cluster filtering and cluster actuation—is introduced for this purpose. It is found that the suppression of a performance index, expressed in terms of the cluster vector, generates a vibration-free state of a beam, whereas the suppression of conventional orthogonal contributors, such as radiation modes, does not. Numerical simulation is performed, followed by an experiment, to verify the validity of the results.