Eigenstructure Assignment Problems In Vibration System

According to the theory and methods of the algebraic inverse eigenvalue problems, in this dissertation, we study the eigenstructure assignment problems on linear systems, undamped structural systems and damped structural systems. The main contribution is as follows.The robust eigenstructure assignment problem of linear system in a specified region is studied. The problem is formulated as an optimization problem. According to a Sun's measure of robustness, we analyze the properties of this problem, and suggest the formula of the gradient vector of the objective function. Then a new algorithm for solving this problem is presented. Numerical examples show that the problem of robust pole assignment in a specified region can be solved effectively.The eigenstructure assignment problems of undamped structural systems are considered. For the case that all the poles are prescribed, we give the conditions and the expressions of the solutions, and give a new measure of robustness according to the theory of matrix perturbation. Thus, we propose a numerical method for solving this problem. we study the preserve symmetric eigenstructure assignment problem, and give the conditions and the expressions of the solutions. We study the partial eigenstructure assignment problem of undamped structural systems, that is a few eigenvalues and eigenvectors of system are undesirable, and the rest of the eigenstructure invariant, and we give the conditions and the expressions of the solutions. According to a new measure of robustness, we give an algorithm for solving this problem. Moreover, in order to preserve the symmetry of the system, we consider the partial eigenstructure assignment problem using output feedback, and give a special solution of this problem. Lastly, we consider a structural dynamics model updating problem.The eigenstructure assignment problems of damping structural systems are investigated. For the case that all the poles are prescribed, we give two algorithms for solving this problem. The procedure of this method is easy to realize, and have a good numerical stability. For the partial eigenstructure assignment problems of damping structural systems, according to the perturbation theory of matrices, we give a method for choosing the assigned eigenstructure, and propose an algorithm for solving this problem. For general eigenstructure assignment problem, in the case of the assigned eigenvectors are given arbitrarily, we give a method for getting the control matrix and the feedback matrices in the condition of the control matrix is unknown.