Eigenvalue Sensitivity Assignment by the Receptance Method

In this paper the problem of eigenvalue assignment in active vibration control by the receptance method using single-input state feedback is considered. The poles of the system and their sensitivities are assigned using measured vibration data from the open-loop system in the form of receptances, there being no need to evaluate or to know the system matrices M, C, K. The perturbation method is applied to a characteristic equation resulting in expressions for the derivatives of the pole eigenvalues with respect to the control gains. These sensitivities are expressed as a linear combination of the feedback control gains. The control effort necessary to assign the poles may be reduced by increasing the sensitivity of the poles. In addition, the uncontrolled poles in the system may be rendered insensitive for stability robustness. It is demonstrated that chosen eigenvalues may be rendered insensitive to all the control gain terms by choice of the distribution vector b. Numerical examples are provided to demonstrate how the technique works.