Partial Pole Assignment Problems For Second And High Order Linear Systems

The pole assignment problem of second order and higher order linear systems arises in the fields of automatic control,structural dynamics and so on.In this thesis,the theory and method of inverse algebraic eigenvalue problems are used to study the partial pole assignment problem for second order and higher order linear systems.The main work is as follows:For the partial pole assignment problem of second order symmetric linear system,based on an orthogonality relation,an algorithm is proposed for solving the partial pole assignment problem of single input second order symmetric system,which is extended to the case of multi-input,and a multi-step method is presented for solving the partial pole assignment problem of multi-input second order symmetric linear system.For the partial pole assignment problem of large scale second order symmetric control system,the relationship among the poles to be assigned,the corresponding eigenvectors,the ideal poles and the control vector is established,and a new multi-step method for solving the partial pole assignment problem of multi-input linear control system is proposed.This method avoids solving many higher order linear systems.For the partial pole assignment problem of higher order control system,based on the higher order orthogonality relation,the parametric representation of the solution of partial pole assignment of higher order linear system is given,the gradient of the objective function with respect to the parameter matrix is derived,and a numerical method for calculating the minimum norm solution of partial pole assignment problem of higher order control system is proposed.Numerical experiments show that the proposed algorithms are effective.