Optimal Eigenstructure Achievement with Robustness Guarantees

Abstract

A new aigenstructure. assignment procedure is presented. In this new method, the best eigenstructure achievable is attained by minimizing with respect to the eigenvalues and the inconsequential components of the desired eigenvectors. This is in contrast to existing techniques which fix the eigenvalues a priori, thereby freezing the subspaces within which the eigenvectors must reside. An added benefit of the technique is that the minimization can be performed subject to an algebraic Riccati constraint, thus providing the closed-loop system with the same gain and phase margins inherent in the linear quadratic regulator. With an estimator in the loop, the procedure can be modified to design a target feedback loop for loop transfer recovery, breaking the loop at either the plant's input or output. An example is given to illustrate the technique.