Active vibration isolation via simultaneous left–right eigenvector assignment

Abstract

The objective of this research is to synthesize a simultaneous left and right eigenvectorassignment (SLREA) method for active vibration isolation. It is a pioneering effort toutilize such an eigenvector assignment concept for active isolator design, where theapproach can provide good physical insight into the problem. In this investigation, a newalgorithm for the synthesis of the desired left eigenvectors is developed, which is animprovement over the classical methods. The purpose of the right eigenvectorassignment method is to alter the closed-loop system modes such that the modalcomponents corresponding to the concerned region (isolation area of the isolator) haverelatively small vibration amplitude. Correspondingly, the design goal of the lefteigenvector assignment is to alter the left eigenvectors of the closed-loop system sothat they are as closely orthogonal to the system’s forcing vectors as possible.With the proposed approach, one can achieve both disturbance rejection andmodal confinement concurrently for the purpose of vibration isolation. In thisresearch, a new formulation is developed so that the desired left eigenvectorsof this integrated system are selected through solving a generalized eigenvalueproblem, where the orthogonality indices between the forcing vectors and the lefteigenvectors are minimized. The components of the right eigenvectors correspondingto the concerned region are minimized concurrently. It is shown that, with theSLREA technique, both disturbance rejection and modal confinement can beachieved, and thus vibration amplitude in the isolated region can be suppressedsignificantly.