Vibration Isolation Control via Simultaneous Left and Right Eigenvector Assignment

摘要

The objective of this research is to investigate the feasibility of utilizing the simultaneous left and right eigenvector assignment concept for vibration isolation feedback control design. 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 regions (isolation end of an isolator) have relatively small amplitude. Correspondently, the design goal of 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 this 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 vector and the left eigenvectors are minimized. The components of right eigenvectors corresponding to the concerned regions are minimized concurrently. To realistically implement the algorithm, an integrated closed-loop system with state estimator is developed. Numerical simulations are performed to evaluate the effectiveness of the proposed method on concurrent disturbance rejection and modal confinement for a isolator rod design. Frequency responses of the isolator in the selected frequency range are illustrated. It is shown that with the simultaneous left-right eigenvector assignment technique, both disturbance rejection and modal confinement can be achieved, and thus the vibration amplitude in the isolated regions can be suppressed significantly.