Receptance Method in Active Vibration Control

Abstract

The pole/zero assignment problem is addressed using a method based on measured receptances. The approach, which is well known in passive structural modification, has not been used before in active vibration control. A number of significant advantages are claimed over the conventional state-space approach that uses the mass, damping, and stiffness matrices formed, for example, by finite elements. In fact, because the method is based solely upon measured vibration data, there is no need to evaluate or to know the M, C, and K matrices. It is demonstrated that all the poles may be assigned actively by the equivalent of a rank-1 modification to the dynamic stiffness matrix of the system. The assignment of zeros has a special significance in vibration suppression, because the vibration response at coordinatep vanishes completely when sinusoidal excitation is applied at coordinate q at the frequency of a zero of receptance H nn . A pole ofH pq may be eliminated by assigning a zero at the same frequency.