Eigenstructure assignment with gain suppression using eigenvalue andeigenvector derivatives

Abstract

Eigenstructure assignment is considered with gain suppression in which selected entries in the output feedback gain matrix are eliminated. This approach may yield a simpler controller with only a small effect on performance. Early results used partial derivatives of the eigenvalues with respect to the gains in order to determine which entries of the feedback gain matrix should be selected for elimination. In this paper, expressions for the partial derivatives of the eigenvectors with respect to the feedback gains are derived and used to compute the expected shift in the eigenvectors if the (/th feedback gain were eliminated. This establishes an improved design method for eigenstructure assignment with gain suppression by a priori choosing to eliminate those gains that have the smallest influence on both the eigenvalues and eigenvectors. An example of a fighter aircraft is presented that illustrates the importance of using both eigenvalue and eigenvector derivative information when choosing which feedback gains should be eliminated.