Bifurcation Analysis of a Fractional-Order Delayed Rolling Mill’s Main Drive Electromechanical Coupling System

Abstract

This work is focused on a rolling mill’s main drive electromechanical coupling system. Firstly, we equip electromechanical coupling system with fractional-order time delay. Secondly, we, respectively, derive the conditions for occurrence of Hopf bifurcation around equilibriums $E_0\left(0,0,0,0\right)$ and $E_1\left(x_1^{\ast },0,x_3^{\ast },0\right)$ . It is found that the fractional order $\alpha$ and time delay $\tau$ in the system play an important role on the system stability. Finally, numerical simulations are given to verify the analytic results.