Assignment of reduced sensitivity eigenstructure

Abstract

The presented technique addresses the problem of maintaining the powerful design simplicity and visibility of eigenstructure assignment, while reducing closed-loop eigenstructure sensitivity to dominant parameter variations. The method results from consideration of the allowable eigenvector subspace as a complete description of the eigenstructure assignment problem. Variations in open-loop system dynamics can thus be visualised as movements of the closed-loop allowable subspace. If a nonlinear model is linearised about two operating points with intersecting subspaces, assignment from the intersection will yield the same closed-loop eigenstructure at both operating points. This hypothesis is proven, and the analysis extended to include the case of non-intersecting subspaces, where it has been shown that reduced sensitivity solutions may also be generated. This reduced subspace design method has been tested on an eighth-order helicopter model that exhibits significant nonlinearity when forward speed is varied. The results demonstrate a considerable reduction in variation of the closed-loop eigenstructure over conventional techniques. The method is found to be a simple variation to the standard projection technique, while offering implicit consideration of dominant parameter variations.