Bifurcation control for electromechanical coupling torsional vibration in rolling mill system driven by DC motor

Bifurcation control for electromechanical coupling torsional vibration in rolling mill system driven by DC motor is studied in this paper. Considering the electromechanical devices under unsaturated magnetic circuit, the dynamical equation of electromechanical coupling vibration in rolling mill drive system is deduced by using the dissipation Lagrange equation. Analysing the system equilibrium point and characteristic roots. Choosing the torsional rigidity of rotating shaft as a bifurcation parameter and the necessary and sufficient conditions of Hopf bifurcation are given. The bifurcation characteristics of the system is investigated and the Washout filter is adopted to control the Hopf bifurcation, then the effect of the filter's time constant and the linear gain on the location of bifurcation point is analyzed. The Normal Form factor is obtained by using the Direct Normal Form method. It is revealed that, the nonlinear gain can modify the periodic solution's amplitude and Hopf bifurcation type. Numerical simulations are also performed, which confirm the analytical results.