Cluster Control of Distributed-Parameter Structures

Abstract

When suppressing the vibration of a distributed parameter structure, control designers face the problem of its infinite number of vibration modes. It is, however, possible to group all the structural modes into a finite number of clusters, wherein all the structural modes belonging to a particular cluster have the same common attributes. If the structural modes within a given cluster are orthogonal to those in other clusters, the clusters may be controlled independently, thereby enabling cluster control with a simple control strategy without causing spillover problems. Grouping all the structural modes into a finite number of clusters is called cluster filtering, while independent control of each cluster is termed cluster actuation. Utilizing both cluster filtering and cluster actuation, cluster control may be performed. Cluster control offers the benefits of stability and control law simplicity analogous to low authority control (LAC), while providing the high control performance and some flexibility of control gain assignment of high authority control (HAC) — hence middle authority control (MAC). Some examples are demonstrated for the purpose of clarifying cluster control. By expanding on the concept of cluster control, this paper further presents a control strategy that enables the creation of a stable, vibration-free state in the designated region of a targeted structure. To this end, a cluster vector that serves as the common link between cluster filtering and cluster actuation is introduced. It is shown 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.