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16 May 2005 Vibration control via disturbance rejection through left eigenvector assignment
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The objective of this research is to investigate the feasibility of utilizing left eigenvector assignment for vibration disturbance rejection. In the previous study, it has been shown that through right eigenvector assignment and modal confinement, one can enhance the performance of periodic vibration isolators. However, it was also recognized that since vibration mode confinement is based on the concept of modal response, it does not guarantee that vibration will always be reduced in a forced excitation scenario. In this research, the left eigenvector assignment technique is utilized to achieve vibration suppression throughout a broad frequency range. The principle is to alter the left eigenvectors of the closed-loop system so that the system's forcing vectors are as closely orthogonal to each left eigenvector as possible. With such an approach, one can directly attack the forced response problem. 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 vector and the left eigenvectors are minimized. The integrated system with assigned left eigenvectors achieves to reject external disturbance of the complete electromechanical system. An integrated closed-loop system with state estimator is also developed so that the algorithm can be implemented realistically. Numerical simulations are performed to evaluate the effectiveness of the proposed method on disturbance rejection for an isolator design example. Frequency responses of the isolator in the selected frequency range are illustrated. It is shown that with the left eigenvector assignment technique, the system’s external disturbances are rejected and vibration amplitude of the isolated regions can be effectively suppressed.
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T. Y. Wu and K. W. Wang "Vibration control via disturbance rejection through left eigenvector assignment", Proc. SPIE 5760, Smart Structures and Materials 2005: Damping and Isolation, (16 May 2005);

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