非线性振荡系统的Hopf分叉幅值控制  

Hopf Bifurcation Amplitude Control of Nonlinear Oscillation System

作　　者：刘向东[1] 黄文虎[1] 

机构地区：[1]哈尔滨工业大学航天工程与力学系

出　　处：《振动工程学报》1999年第1期21-26,共6页Journal of Vibration Engineering

摘　　要：研究了非线性连续系统Ｈｏｐｆ分叉的状态反馈控制方法，提出了Ｈｏｐｆ分叉幅值可控性的概念，获得了平面系统Ｈｏｐｆ分叉所产生的极限环幅值可控的充分条件，在此基础上采用非线性状态反馈控制来抑制Ｈｏｐｆ分叉引起的自激振动。数值仿真结果表明：Ｈｏｐｆ分叉控制是非线性振荡系统控制的一种切实有效的方法。The state feedback control method of the Hopf bifurcation in nonlinear continuous systems is studied, and the concept of amplitude controllability of Hopf bifurcation is presented, the sufficient conditions that the amplitude of a limit cycle arising from Hopf bifurcation can be controlled are derived. Nonlinear states feedback control to suppress the self sustained oscillation caused by Hopf bifurcation can be used. Numerial simulations show that Hopf amplitude bifurcation control method is an efficient approach for the control of nonlinear oscillation systems.

关 键 词：非线性振荡 HOPF分叉 极限环 状态反馈控制 

分 类 号：O322[理学—一般力学与力学基础]