非交换环上电网络系统结构能控性研究

项目名称： 非交换环上电网络系统结构能控性研究

项目编号： No.51307047

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 电工技术

项目作者： 马强

作者单位： 湖北文理学院

项目金额： 24万元

中文摘要： 目前在线性电网络系统中长期困扰设计人员的"不用专门设计的系统几乎都能控"的理论问题基本得到解决。对于非线性电网络系统针对此问题还未有比较圆满的理论分析，这是本项目的研究目的。非线性电网络系统前期的定性(如结构能控性)分析，以结构分析为基础，采用非交换多项式和图论两个数学工具，获得两类结论:(1)针对非线性电网络系统的结构能控性问题，基于非交换代数，研究结构能控性的代数判据；(2)依据非交换多项式与图的对应关系，研究非线性电网络系统的结构能控性图论判据。本项目从非线性电网络的前期特性分析着手，预期获得非线性电网络结构能控性的判据，为后期的稳定性设计提供理论依据。结构性质研究中所获得的结论不受系统参量对系统性质影响程度，因此结构性质分析过程对生产过程中参数的选择具有明确的指导意义。通过结构性质分析可以消除那些结构不能控的设计方案，可以减少设计的选择范围，节省人力、物力与财力，具有明显经济性。

中文关键词： 非线性电网络；结构能控性；非交换环；图论；控制器设计

英文摘要： The problem that the difficult and theoretic problem, which the unspecially designed system is almost all controllable, which puzzled enginneers in linear electrical network systems has been solved. But for nonlinear electrical networks there is little satisfactory theoretic analysis, which is the main purpose of this project. The previous qualitative analysis (such as structural controllability) based on structural analysis adopts the noncommutative polynomial and graph theory to get two classes of conclusion: (1)for the controllability of nonlinear networks, we will research the algebraic criterion based on noncommutative algebra; (2) according to the relationship between noncommutative polynomial and graph, we will research the graphic criterion of structrual controllability. In this project we focus on the previous character of nonlinear electrical networks in order to obtain the criterion of structrual controllability, which provides a theoretic basis for designing a stable network. The conclusions obtained in structural property research may not affected by parameters, and structural property analysis has clear guidance for the choice of parameters in producing process. Structural properties analysis can eliminate the structural uncontrollable design proposals, which can minimise the designing slecting ran

英文关键词： nonlinear electric network；structural controllability；noncommutative ring；graph theory；controller desgin