Robust Pole Assignment With Part Parameter Perturbation System

There are two types of methods for solving the problem of robust pole assignment: one considers the problem of closed-loop system eigenvalue sensitivity to small parameter variations in some, but not all, of the elements of the open-loop system matrices; the other considers the problem of closed-loop system eigenvalue sensitivity to parameter variations in all of the elements of the open-loop system matrices. The former is more practical significant because most of the practical systems often possess special forms and structure information about system parameter perturbations is usually known. In this dissertation the problem of robust state-feedback pole assignment in linear systems subject to parameter perturbations in some of the elements of the open-loop system matrices is investigated. Firstly, based on an application result of Gerschgorin theory, the dissertation establishs a new closed-loop eigenvalue sensitivity index, which measures closed-loop system eigenvalue sensitivity to perturbations in some of the elements of the open-loop system matrices. Since the Frobenius norm is used in the proposed index, gradient formula of index can be obtained easily. Secondly, using a parameter state-feedback pole assignment result, complete parametric expression for the index is given. For real closed-loop eigenvalues and complex-conjugate closed-loop eigenvalues, an explicit gradient formula of the index function is established. Thirdly, based on the proposed gradient formula of index function and three optimization methods which are Quasi-Newton method, conjugate-gradient method and Newton method, a simple effective algorithm for the problem of robust pole assignment is proposed. Finally, five examples are worked out to demonstrate the the proposed methods. Values of eigenvalue sensitivity index, condition number of eigenvector matrix and norm of state-feedback matrix are calculated by using the optimization parameters obtained from the algorithm, and closed-loop eigenvalues are assigned by the obtained state-feedback matrix. The results shows that robust pole assignment approach proposed in the dissertation is simple and effective, and gives control systems with better robustness.