Theory And Method Of The Partial Pole Assignment Problem

Pole assignment problem is one of the most important problems in control system.In general,the position of the poles in the control system matrix determines the stability of the system.The pole placement method is an important method to change the dynamic performance of the system.There are important applications of structural analysis of the problem in actual engineering project,such as in the spring and the bridge system,the system matrix is generally measured in a small part of the poles may make the system produce resonance phenomenon,which leads to a decrease in the stability of the whole system and reaction speed.Key to the pole assignment problem by selecting the appropriate state feedback matrix,the matrix makes the closed-loop control system of the desired pole configuration to the preset position,so as to ensure the whole system has good dynamic characteristics,which is part of the pole assignment problem.The core of the pole assignment problem is the analysis and control of the factors that affect the performance of the whole system,such as state feedback,time delay and the optimization of the solution.This paper mainly studies the theory and method of partial pole assignment problem,this paper first introduces the linear part of the system state feedback pole assignment problem,summarizes the theory and method of two order linear systems with state feedback part of the pole assignment problem,research and design a correlation algorithm and a numerical example is given,and then the theory and method of high order linear systems with state feedback part of the pole assignment problem,the solving algorithm is given and numerical examples show the effectiveness of the algorithm.Then focus on the part of the pole assignment problem with time delays and methods of previous studies on the two order delay system based on pole assignment problem,then based on the method of two order control system,an improved algorithm is proposed for solving the problem of partial pole assignment of high order delay system,the method of direct calculation no,the use of the response matrix and the solution of the Sylvester equation is avoided,the calculation process is more complex,more simple and effective solutions to the problems,finally,part of the pole assignment problem to study optimal,mainly through the minimum norm feedback matrix solution optimization problem,the algorithm design of minimum norm two order and high order system for the optimal part the pole assignment problem of solution are given.