An improved power method for solving eigenvalue problems in plant dynamics and control

This report describes an improvement of the power method which is applied to solve eigenvalue problems in the analysis of plant dynamics and control. These problems are taken from stability evaluation of an objective plant, modal analysis and modal control, calculation of optimal state-feedback control, and reduction method of dimension of a large-scale dynamical system. Usually there exist only a few modes of poor stability in plant dynamics. To analyze these modes the power method is applied after some modifications. The basic procedure of the method is to calculate first a maximum absolute eigenvalue and the corresponding eigenvector of a matrix, and then the remaining eigenvalues are calculated by the eigenvalue deflation method. The main improvement presented in this report is that the power method has been made applicable in the cases of both nearly equal eigenvalues and confluent ones. The effectiveness of the improved method is shown with some examples of different kinds of eigenvalues which were calculated using the computer code developed based on this method. In addition, the deflation method, which removes the calculated eigenvalue from the matrix and reduces the dimension of the matrix, is discussed in comparison with the ordinary deflation method. (author)