Actuators’ Locations in Vibration Cancellation of a Plate Using Orthogonal Eigenstructure Control

Orthogonal eigenstructure control is a novel control method that recently has been developed by the authors as a method for active vibration cancellation. This method is a feedback control method, which is applicable to linear multi-input multi-output systems. The remarkable advantage of this method over most of the eigenstructure assignment methods is that it neither needs pole placement nor eigenvector shaping. By eliminating the requirement for defining desirable eigenvectors, the algorithmic error due to difference between achievable and desirable eigenvectors is no longer exist. Moreover, since the closed-loop poles are not required to be placed, the possibilities for excessive actuation forces are eliminated. The orthogonal eigenstructure control regenerates the open-loop eigenvectors and simultaneously finds the vectors orthogonal to them. Replacing the open-loop eigenvectors with those orthogonal vectors results in vibration suppression in the system. Furthermore, by eliminating the concept of desirable eigenvector for the closedloop system, the method has become suitable for the system with high degrees of freedom. To show that this control method is easily applicable to system with high degrees of freedom, it is applied to a finite element model of a plate, and the effect of the location of the control actuators in the cancellation of vibration has been investigated.