Receptance-based partial eigenstructure assignment by state feedback control

Abstract

The partial eigenvalue assignment problem has drawn much attention for decades because of its usefulness and fascinating appeal in vibration control. It is also a mathematically challenging problem, particularly when the mathematical description is cast in the second-order formulation framework. Previous methods require either the system matrices, such as mass, damping or stiffness matrix, or the eigenvectors of the original system. Those data, especially the system matrices which are usually obtained from a finite element model, are not easy to obtain or very accurate. To overcome this drawback, a new partial eigenvalue assignment method by multi-input active control is proposed in this paper. Only part of the receptance matrix of the original system is required in this method. In addition, this method can simultaneously assign eigenvalues and the associated eigenvectors, including assigning nodes at desired locations. Three numerical examples are used to validate the proposed method and demonstrate the role of the control efforts. The robustness of the proposed method is analysed through a Monte-Carlo simulation. Numerical results show that this method is robust for the four-DoF damped system where there are 5% variations of the needed receptance matrix elements. This paper reports the first attempt to make partial eigenstructure assignment in the second-order eigenvalue framework using only the receptances.