Active vibration isolation via simultaneous left-right eigenvector assignment

摘要

The objective of this research is to synthesize a simultaneous left and right eigenvector assignment (SLREA) method for active vibration isolation. It is a pioneering effort to utilize such an eigenvector assignment concept for active isolator design, where the approach can provide good physical insight into the problem. In this investigation, a new algorithm for the synthesis of the desired left eigenvectors is developed, which is an improvement over the classical methods. The purpose of the right eigenvector assignment method is to alter the closed-loop system modes such that the modal components corresponding to the concerned region (isolation area of the isolator) have relatively small vibration amplitude. Correspondingly, the design goal of the left eigenvector assignment is to alter the left eigenvectors of the closed-loop system so that they are as closely orthogonal to the system's forcing vectors as possible. With the proposed approach, one can achieve both disturbance rejection and modal confinement concurrently for the purpose of vibration isolation. In this research, a new formulation is developed so that the desired left eigenvectors of this integrated system are selected through solving a generalized eigenvalue problem, where the orthogonality indices between the forcing vectors and the left eigenvectors are minimized. The components of the right eigenvectors corresponding to the concerned region are minimized concurrently. It is shown that, with the SLREA technique, both disturbance rejection and modal confinement can be achieved, and thus vibration amplitude in the isolated region can be suppressed significantly.