时滞反馈控制下三维节能减排系统的稳定性分析  

Stability Analysis of A Three-dimensional Energy Saving and Emission Reduction System under A Delayed Feedback Controller Feedback Controller

作　　者：张杰[1] 任祥[1] 杨坤一[1] 

机构地区：[1]北方工业大学理学院数学系,北京100144

出　　处：《数学的实践与认识》2016年第2期284-292,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61203058);北方工业大学"人才强校行动计划青年拔尖人才项目(XN131)";北方工业大学"科研创新团队建设计划项目(XN129)";实验室建设-公共数学网络教学平台建设(XN041)

摘　　要：考虑三维节能减排系统,施加时滞反馈控制,建立反馈控制下的节能减排系统,求解平衡点,分析系统稳定性,得到出现Hopf分支的条件.利用中心流形定理和Poincare规范型方法讨论Hopf分支的性质,给定参数进行数值模拟,验证理论结果的有效性.This paper considers a three-dimensional energy saving and emission reduction system. A delayed feedback controller is proposed to stabilize the system which was originally unstable. The stability properties of the equilibrium points are analyzed and the Hopf bifurcation appears under some conditions. By using the center manifold theorem and normal form method, the explicit formulae axe obtained revealing the properties of the periodic solutions of Hopf bifurcation to show stabilizing effects of the delayed feedback controller. Numerical simulations illustrate effectiveness of our results.

关 键 词：节能减排系统 时滞反馈控制 平衡点 HOPF分支 稳定性 

分 类 号：TK018[动力工程及工程热物理]