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

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 E0ð0, 0, 0, 0Þ and E1ðx∗ 1 , 0, x∗ 3 , 0Þ. It is found that the fractional order α and time delay τ in the system play an important role on the system stability. Finally, numerical simulations are given to verify the analytic results.