Formula omitted]-optimal vibration control using receptance-based regional eigenvalue assignment

Abstract

This paper proposes a method of H2-optimal vibration control using regional eigenvalue assignment based only on measured receptances, typically from a modal test. The sum of the squared weighted H2-norm of closed-loop receptance matrix and the transfer matrix from the external input to the control input is minimized by exploiting the flexibility from assigning the closed-loop eigenvalues to prescribed stable regions with single- or multiple-input control. It is found that regional eigenvalue assignment and the optimization of a free parameter matrix (in the multiple-input case) provide extra flexibility for improving the closed-loop performance over and above the selection of weighting matrices, as in standard H2 control. Therefore, the internal stability, satisfactory response, and minimum control energy are readily guaranteed by the proposed method, whereas the standard approach is dependent upon the arbitrarily chosen weighting matrices. The method inherits the advantages of both optimal control and eigenvalue assignment by the receptance method. The working of the method and its advantages over the standard H2 control are demonstrated numerically.