Keywords: cluster vector-based control, flexible beam, vibration-free state, feedback control, cluster filtering, cluster actuation.

Vibration control has long been considered as a control technique for augmenting the damping of structural modes. However, even after perfectly augmenting the damping of structural modes, vibrations still occur in the structure. Note that a perfect control performance over the frequency response of a structure, with dynamic compliance, dynamic mobility etc., results in convergence to the asymptote of the frequency response. Thus, a conventional control approach, even when ideally performed, may not produce a vibration-free state.

Currently, there is a strong demand for vibration-free structures, particularly in the field of nanotechnology. A recently disclosed technology road map, outlining a future generation of semi-conductor technology, shows that a 22-nm-wide (i.e. only 100 atoms wide) electrical lead wire is planned as a technological milestone. However, no existing technology can cope with this demand. Realizing future semiconductors, with highly sophisticated specifications, requires the resolution of many technological implementation problems. Among them, the establishment of a nano-infrastructure, which requires semiconductor fabrication machines with extremely low vibration levels, is essential.

Instead of further enhancing structural damping, which is the aim of traditional vibration control, a novel vibration control approach that can even eliminate micro-vibration is needed to keep pace with the demands for continually increased precision. Moreover, the final goal of vibration control is straightforward - the new method should generate a vibration free state of the target structure.

By expanding on the concept of active cluster control, this paper presents a novel control strategy that enables the creation of a stable, vibration-free state in the designated region of a flexible beam. This paper begins by discussing the cluster control system of a distributed-parameter beam for generating a vibration-free state in the designated area of a target beam. Next, cluster control consisting of both cluster filtering and cluster actuation is shown, and an investigation of the stability of a cluster control system is presented. Cluster filtering extracts 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, state variables governing beam vibration must be extracted and suppressed. For this purpose, a cluster vector that serves as the common link between cluster filtering and cluster actuation is introduced. Furthermore, a means of establishing the cluster vector is presented and its properties are clarified. It is found that the suppression of a performance index, expressed in terms of the cluster vector, leads to the generation of a vibration-free state, whereas the suppression of conventional orthogonal contributors, such as radiation modes (sometimes termed power modes), does not. Finally, numerical simulation and experiments verify the validity of the cluster control presented in the work.

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