An adaptive left–right eigenvector evolution algorithm for vibration isolationcontrol

Abstract

The purpose of this research is to investigate the feasibility of utilizing an adaptive left andright eigenvector evolution (ALREE) algorithm for active vibration isolation. As depictedin the previous paper presented by Wu and Wang (2008 Smart Mater. Struct. 17015048), the structural vibration behavior depends on both the disturbance rejectioncapability and mode shape distributions, which correspond to the left and righteigenvector distributions of the system, respectively. In this paper, a novel adaptiveevolution algorithm is developed for finding the optimal combination of left–righteigenvectors of the vibration isolator, which is an improvement over the simultaneousleft–right eigenvector assignment (SLREA) method proposed by Wu and Wang(2008 Smart Mater. Struct. 17 015048). The isolation performance index used inthe proposed algorithm is defined by combining the orthogonality index of lefteigenvectors and the modal energy ratio index of right eigenvectors. Through theproposed ALREE algorithm, both the left and right eigenvectors evolve such that theisolation performance index decreases, and therefore one can find the optimalcombination of left–right eigenvectors of the closed-loop system for vibration isolationpurposes. The optimal combination of left–right eigenvectors is then synthesizedto determine the feedback gain matrix of the closed-loop system. The result ofthe active isolation control shows that the proposed method can be utilized toimprove the vibration isolation performance compared with the previous approaches.