线性系统D稳定极点配置问题的研究方法.doc

线性系统D稳定极点配置问题的研究方法 摘 要 20世纪50年代后期，控制理论由经典控制理论向现代控制理论转变，现代控制理论是在引入状态和状态空间概念的基础上发展起来的。与经典控制理论一样，现代控制系统中仍然主要采用反馈控制结构，但不同的是，经典控制理论中主要采用输出反馈，而现代控制系统中主要采用内部状态反馈。状态反馈可以为系统控制提供更多的信息反馈，从而实现更优的控制。闭环系统极点的分布情况决定于系统的稳定性和动态品质，因此，可以根据对系统动态品质的要求，规定闭环系统的极点所应具备的分布情况，把极点的配置作为系统的动态品质指标。这种把极点配置在指定的区域的过程称为极点配置。如果，这个区域是左半复平面D，并且无论系统如何变化，其极点都落在此区域内，则该系统具有D-稳定性。本论文对线性系统的D-稳定极点配置问题进行了研究，分别以左半平面、圆域及扇形区域为例与精确极点配置比较，利用线性矩阵不等式LMI处理方法，编写系统的MATLAB仿真程序，仿真结果证明D-稳定极点配置的可行性和正确性。 关键词: 线性系统；状态反馈；极点配置；线性矩阵不等式；D-稳定 Linear system D stability study method of the pole placement problem Abstract In the 1950s, control theory later by classical control theory to modern control theory shift, modern control theory is introducing state and state space concept developed on the basis of. As with classical control theory, modern control system still mainly USES the feedback control structure, but different is, classical control theory mainly USES the output feedback, and modern control system mainly USES the internal state feedback. State feedback control for system provide more information feedback, so as to achieve better control. The distribution of closed-loop system poles depends on system stability and dynamic quality, therefore, can according to the system dynamic quality request, provisions that poles of close-loop system should have the distribution of the pole, configuration of the system dynamic quality indicators. The poles in the designated area process called poles. If, this area is left after plane D, and no matter how the system changes, it fell on the regional pole, the system has within the D - stability. This paper the D - linear system steady poles were studied, by plane, round respectively left for example the sectorial domain and precise and poles comparison, by using the linear matrix inequality LMI treatment methods, writing system of MATLAB simulation program, using the simulation results prove D - stable correctness and feasibility of the poles. Keywords: Linear system; State feedback; Pol