Nonlinear feedback control of Hopf bifurcation in a relative rotation dynamical system

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Abstract
The Hopf bifurcation characteristic in a relative-rotation dynamical system with nonlinear damping force is analyzed and the necessary and sufficient condition of Hopf bifurcation is given under which the system has Hopf bifurcation emerging from the equilibrium. In order to make the Hopf bifurcation point transformed and control the stability and amplitude of limit cycle，a nonlinear feedback controller is proposed. The analytical results on controlling Hopf bifurcation points via the nonlinear controller agree well with the numerical results.

Keywords:
relatively rotation /

nonlinear feedback control /

Hopf bifurcation /

limit cycle
Authors and contacts
Liu Shuang²,

Liu Bin¹,

Shi Pei-Ming¹

(1)燕山大学电气工程学院，秦皇岛 066004; (2)燕山大学工业计算机控制工程河北省重点实验室，秦皇岛 066004；燕山大学电气工程学院，秦皇岛 066004
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