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

Abstract

Stability and Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback * Liu Shuang(刘 爽) a)b) , Zhao Shuang-Shuang(赵双双) a) , Wang Zhao-Long(王兆龙) a) , and Li Hai-Bin(李海滨) a)b) † a)

Stochastic P-bifurcation in a bistable Van der Pol oscillator with fractional time-delay feedback under Gaussian white noise excitation

“…The fractional derivative has the contributions of damping force and restoring force [44][45][46][47][48][49][50], hence, we introduce the equivalent system as follows:…”

“…Wen et al studied the deterministic and autonomous Duffing systems with fractional time-delay coupled feedback and noticed that fractional time-delay coupled feedback played the roles both of velocity time-delay feedback and displacement time-delay feedback [43]. Liu et al studied the Hopf bifurcation in a nonlinear electromechanical coupled system with timedelay feedback, obtained its characteristic root and stable domain, and finally, analyzed the relationship between feedback gain and stable domain [44]. Jiang et al considered a classical Van der Pol oscillator with general time-delay feedback and found the Bogdanov-Takens bifurcation, triple-zero and Hopf-zero singularities in the system by analyzing the distribution of associated characteristic roots [45].…”

Nonlinear Torsional Vibration Analysis and Nonlinear Feedback Control of Complex Permanent Magnet Semidirect Drive Cutting System in Coal Cutters

“…The breakdown diagnosis [16,17] and torsion vibration tests [18,19] of the transmission system by means of dynamic analysis have become research hot spots. Taking the torsional vibration system of rolling mill with nonlinear friction damping as the research object, Liu et al [20,21] analyzed the effects of both subcritical bifurcation and supercritical bifurcation on the system torsional vibration. With the introduction of the motor speed feedback, the nonlinear feedback controller was designed, in which the stator voltages of the drive motor were selected as the control variable, suppressing unstable vibrations for transmission system caused by Hopf bifurcation.…”

Nonlinear dynamic analysis of an electromechanical coupling transmission system: A case study on shearers

“…Liu et al. 21,22 analyzed the effects of subcritical bifurcation and supercritical bifurcation on the torsional vibration systems, taking nonlinear frictional damping as the research object. At the same time, the motor speed feedback was introduced to construct the nonlinear state feedback controller.…”

“…[13][14][15][16][17][18] With continuous in-depth study on the torsional vibration mechanism by the scholars, 19,20 it is found that the main cause of the torsional vibration is the nonlinear factors of the system, such as bifurcation and chaos, which is also the main reason for the system instability. Liu et al 21,22 analyzed the effects of subcritical bifurcation and supercritical bifurcation on the torsional vibration systems, taking nonlinear frictional damping as the research object. At the same time, the motor speed feedback was introduced to construct the nonlinear state feedback controller.…”