Stability Based Robust Eigenvalue Design for Tolerance

Abstract

A novel integrated approach is developed to design systems for stability and robustness. First, design parameters with large variation bounds are chosen to maintain system stability. Then, a robust eigenvalue design problem is considered to make the dynamic response less sensitive to parameter variations. A new complex sensitivity matrix is derived from the system dynamics with the eigenvalue variation approximated into a first-order model by means of the eigenvector orthogonal theory. Through a proper transformation, the complex eigenvalue sensitivity of the Jacobian matrix can still be processed by the traditional robust design approach. By minimizing the eigenvalue sensitivity, design parameters can be obtained for stability as well as robustness. Furthermore, the tolerance space of the selected parameters can be maximized to improve robust performance. A Laval rotor example is used to demonstrate the effectiveness of the proposed robust design method.