Vibration Confinement by Minimum Modal Energy Eigenstructure Assignment

Abstract

A novel Eigenstructure Assignment (ESA) method for vibration confinement of flexible structures has been developed. This method is an output feedback control and determines the closed-loop systems that their eigenvectors are orthogonalized to the open-loop eigenvectors. This method is a numerical method and used Singular Value Decomposition (SVD) to find the null space of the closed-loop eigenvectors. The matrix that spans the null space can be used to regenerate the open-loop system as well as the systems that have orthogonal eigenvectors to the regenerated open-loop system. As a result the isolation of vibration is independent of the type of the disturbance. Also in this method, the energy of the closed-loop system is minimized. As an important outcome, the proposed method needs neither to specify the closed-loop eigenvalues nor to define a desired set of eigenvectors.

Active vibration cancellation of tonal disturbance using orthogonal eigenstructure control

“…When the open-loop eigenvalues with greatest distance from the origin are chosen as the operating eigenvalues, a more desirable closed-loop system can be achieved [8,10,13]. The index i is used to specify the equation for the i th operating eigenvalue.…”

“…The index i is used to specify the equation for the i th operating eigenvalue. eigenvectors are unity [8][9][10][11][12].…”

“…Orthogonal eigenstructure control is a novel approach proposed by the authors [8][9][10][11][12], as an active vibration cancellation method that is relatively easy to design and implement. OEC is an output feedback control applicable for structural vibration cancellation.…”