Stability and Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback  

作　　者：刘爽 赵双双 王兆龙 李海滨 

机构地区：[1]Key Laboratory of Industrial Computer Control Engineering of Hebei Province,Yanshan University [2]National Engineering Research Center for Equipment and Technology of Cold Strip Rolling,Yanshan University

出　　处：《Chinese Physics B》2015年第1期345-353,共9页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant No.61104040);the Natural Science Foundation of Hebei Province,China(Grant No.E2012203090);the University Innovation Team of Hebei Province Leading Talent Cultivation Project,China(Grant No.LJRC013)

摘　　要：The stability and the Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback are studied. By considering the energy in the air-gap field of the AC motor, the dynamical equation of the electromechanical coupling transmission system is deduced and a time delay feedback is introduced to control the dynamic behaviors of the system. The characteristic roots and the stable regions of time delay are determined by the direct method, and the relationship between the feedback gain and the length summation of stable regions is analyzed. Choosing the time delay as a bifurcation parameter, we find that the Hopf bifurcation occurs when the time delay passes through a critical value.A formula for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is given by using the normal form method and the center manifold theorem. Numerical simulations are also performed, which confirm the analytical results.The stability and the Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback are studied. By considering the energy in the air-gap field of the AC motor, the dynamical equation of the electromechanical coupling transmission system is deduced and a time delay feedback is introduced to control the dynamic behaviors of the system. The characteristic roots and the stable regions of time delay are determined by the direct method, and the relationship between the feedback gain and the length summation of stable regions is analyzed. Choosing the time delay as a bifurcation parameter, we find that the Hopf bifurcation occurs when the time delay passes through a critical value.A formula for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is given by using the normal form method and the center manifold theorem. Numerical simulations are also performed, which confirm the analytical results.

关 键 词：electromechanical coupling time delay Hopf bifurcation STABILITY 

分 类 号：TM34[电气工程—电机]