Vibration Suppression using Orthogonal Eigenstructure Control

Abstract

A novel control method called orthogonal eigenstructure control is developed for active vibration cancellation in structures. Orthogonal eigenstructure control is a feedback control method applicable to multi-input multi-output linear systems. While the available control design methodologies offer a large and complex design space of options that can often overwhelm a designer, this control method offers a significant simplification of the design task while still allowing some experience-based design freedom. For example, eigenstructure assignment methods need definition of a desired eigenvector for the closed-loop system. The controller designer may also be required to do pole placement. Considering the fact that there are no one-to-one relationships between the elements of the closed-loop eigenvectors of a model and the states of the system, this effort could be inefficient for many practical systems. Moreover, for large-scale systems, defining or shaping the eigenstructures become a relatively difficult task. Orthogonal eigenstructure control is a state feedback-like control law that is relatively easy to design and implement to multiple-input multiple-output systems. It allows control engineers to achieve good performing designs even with little design experience, while the existing methods are highly dependent on designer experience.

Orthogonal eigenstructure control is introduced and extended to be applicable to linear systems regardless of the number and location of the actuators and sensors. Also, the concept of progressive application of the proposed control method for increasing robustness is described. Finally, the result of application of the control method for vibration cancellation of a test plate is investigated through experiments for tonal and wideband disturbances. The results show a significant reduction of vibrations using the orthogonal eigenstructure control with relative ease in finding the control gain matrix.