部分极点配置问题的理论与方法研究

发布时间：2018-07-04 20:07

本文选题：部分极点配置 + 无溢出性　；参考：《成都理工大学》2017年硕士论文

【摘要】：极点配置问题是控制结构系统中的重要问题之一。一般情况下,在控制系统矩阵中极点的位置决定着系统的稳定性能,而极点配置法是比较常用的改变系统动态性能的重要方法。这类问题在实际工程项目前期的构造分析中有重要用途,比如在弹簧和桥梁系统中,一般测量得到的系统矩阵中有一小部分极点可能会使得系统产生共振现象,从而导致整个系统的稳定性和反应速度等性能下降。极点配置问题的关键就是通过选取适当的状态反馈矩阵,使得闭环控制系统中的矩阵所期望的极点配置到事先给定的位置上,从而保证整个系统具有良好的动态特性,即部分极点配置问题。部分极点配置问题的核心是对影响整个系统性能因素的分析和控制,状态反馈、时滞现象、解的优化等因素,这些问题有待进一步展开研究。本文主要研究部分极点配置问题的理论与方法,文中首先介绍了线性系统状态反馈的部分极点配置问题,总结了二阶线性系统状态反馈的部分极点配置问题的理论与方法,研究、设计出相关算法并给出了数值实例,然后研究高阶线性系统状态反馈的部分极点配置问题的理论与方法,给出了求解算法并结合数值实例说明了算法的有效性。接下来重点研究了受时滞影响的部分极点配置问题,基于总结前人关于二阶时滞系统极点配置问题的研究方法,然后在有关二阶控制系统的方法基础上,提出了一种求解高阶时滞系统的部分极点配置问题的改进算法,该方法中直接进行计算,没有使用响应矩阵和求解Sylvester方程,避免了比较复杂的计算过程,能更简单有效的解决问题,最后针对最优部分极点配置问题来研究,主要通过求反馈矩阵的最小范数解来优化问题,分别给出了求解二阶和高阶系统的最优部分极点配置问题的最小范数解的算法设计。
[Abstract]:Pole assignment 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, and pole assignment is an important method to change the dynamic performance of the system. Such problems have important applications in the structural analysis of the early stage of a practical engineering project. For example, in spring and bridge systems, a small number of poles in the system matrix obtained from general measurements may cause resonance in the system. As a result, the stability and reaction speed of the whole system are reduced. The key of pole assignment problem is to select appropriate state feedback matrix, so that the desired poles of the matrix in the closed-loop control system can be configured to a given position in advance, so as to ensure that the whole system has good dynamic characteristics. That is, the problem of partial pole assignment. The core of the partial pole assignment problem is the analysis and control of the factors affecting the performance of the whole system, the state feedback, the phenomenon of time delay, the optimization of the solution, and so on. These problems need to be further studied. In this paper, the theory and method of partial pole assignment problem are studied. Firstly, the partial pole assignment problem of linear system state feedback is introduced, and the theory and method of partial pole assignment problem of second order linear system state feedback are summarized. The related algorithm is designed and a numerical example is given. Then the theory and method of partial pole assignment problem with state feedback for high order linear systems are studied. The algorithm is given and the effectiveness of the algorithm is illustrated by a numerical example. Then, the partial pole assignment problem affected by time delay is studied, based on summarizing the previous research methods of pole assignment problem for second order delay systems, and then on the basis of the second order control system method. In this paper, an improved algorithm for solving partial pole assignment problem for high-order time-delay systems is proposed. In this method, the response matrix and Sylvester equation are not used to solve the problem, and the complicated calculation process is avoided. The problem can be solved more simply and effectively. Finally, the problem of optimal partial pole assignment is studied, and the problem is optimized by finding the minimum norm solution of the feedback matrix. The algorithm design for the minimum norm solution of the optimal partial pole assignment problem for the second order and higher order systems is given respectively.
【学位授予单位】：成都理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O231

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