东北大学学报（自然科学版）

东北大学学报:自然科学版 ›› 2014, Vol. 35 ›› Issue (7): 1059-1063.DOI: 10.12068/j.issn.1005-3026.2014.07.033

• 数学 • 上一篇    

基于状态反馈和Washout滤波器的Qi系统Hopf分岔控制

张中华1，袁惠群2   

  1. (1东北大学 机械工程与自动化学院， 辽宁 沈阳110819; 2东北大学 理学院， 辽宁 沈阳110819)
  • 收稿日期:2013-08-26 修回日期:2013-08-26 出版日期:2014-07-15 发布日期:2014-04-11
  • 通讯作者: 张中华
  • 作者简介:张中华(1979-)，女，山东菏泽人，东北大学博士研究生，东北电力大学讲师;袁惠群(1954-)，男，辽宁沈阳人，东北大学教授，博士生导师.
  • 基金资助:
    国家自然科学基金资助项目(51275081).

Hopf Bifurcation Control of the Qi System Based on State Feedback and WashoutFilter〓

ZHANG Zhonghua1， YUAN Huiqun2   

  1. 1 School of Mechanical Engineering & Automation， Northeastern University， Shenyang 110819， China; 2 School of Sciences， Northeastern University， Shenyang 110819， China.
  • Received:2013-08-26 Revised:2013-08-26 Online:2014-07-15 Published:2014-04-11
  • Contact: ZHANG Zhonghua
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摘要： 针对一类Qi系统的Hopf分岔问题，首先，通过计算分岔稳定性指标判定系统的Hopf分岔类型;然后分别采用状态反馈控制器及Washout滤波器控制系统的分岔行为，并采用NormalForm(规范型)方法讨论控制参数对分岔位置及分岔极限环幅值的影响，同时借助Matlab软件对理论结果进行数值仿真.理论结果和数值仿真表明:控制器中的线性增益能提前、延迟甚至消除原系统Hopf分岔行为，控制器中的非线性增益能改变原系统的Hopf分岔类型.最后对两种控制方法进行对比，结果表明，Washout滤波器相对于含线性项和非线性项的状态反馈控制器而言，控制效果较明显.

关键词: Qi系统, Hopf分岔, 分岔控制, Washout滤波器, 规范型方法

Abstract: To control the Hopf bifurcation of a Qi system， the Hopf bifurcation type was firstly determined by bifurcation stability index. Then， the state feedback controller and Washout filteraided feedback controller were designed to control the Hopf bifurcation， respectively. The effects of controller parameters on the bifurcation position and the amplitude of limit cycle were discussed based on the Normal Form method. Simultaneously， the simulations using Matlab software were carried out to illustrate the results. Simulation charts and theoretical results show that the linear gain can change the position of Hopf bifurcation and even eliminate Hopf bifurcation， while the nonlinear gain can change the bifurcation type of original system. Finally， some conclusions were obtained with a comparison between the state feedback controller and the Washout filteraided ones.The results showed that the control effect based on Washout filter is better than the effect based on nonlinear state feedback controller.

Key words: Qi system, Hopf bifurcation, bifurcation control, Washoutfilter, Normal Form method

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