Hopf bifurcation control of nonlinear electromechanical coupling main drive system of rolling mill

The nonlinear dynamic model of electromechanical coupling main drive system of rolling mill with nonlinear stiffness and frictional torque is established. The equilibrium point of the system is analyzed, the conditions of the Hopf bifurcation of the system are given, and the type of the bifurcation is studied. The Hopf bifurcation controller is obtained by using the exact feedback linearization method based on differential geometry and combining the quadratic optimal control theory. The controller does not change the type of the Hopf bifurcation, and by changing the location of the bifurcation point, the bifurcation characteristics of the nonlinear system are effectively delayed. The range of parameter that makes the equilibrium point of the system stable is increased, and the robustness and effectiveness of the controller are analyzed when the system has parameter perturbation or additive feedback control disturbance.