Study On Time Delay Feedback Control And Vibration Performance Of Rolling Mill’s Main Drive Electromechanical Coupling System

The main drive system as a core part of rolling mill plays an irreplaceable role in the process of production. The frequent phenomena of torsional vibration in main drive system will seriously affected the product quality and production, even cause damage of equipment and other serious consequences. Therefore, a study on instability mechanism of main drive system and the control strategy is of great practical significance. Rolling mill main drive system is composed of electric drive control system and mechanical drive system, the stability of the system is determined jointly by the two parts. Considering the coupling effect of electrical parameters and mechanical parameters, the nonlinear torsional vibration model of the main drive system is established in this paper. Nonlinear dynamic behaviors which may lead to the instability of the system are studied from the view point of electromechanical. A time delay feedback is also introduced to control the dynamic behaviors and the effects of time delay on vibration characteristics of the system are investigated.Firstly, considering the energy in air-gap field of AC motor, the dynamical equation of nonlinear electromechanical coupling torsional vibration system is deduced, the equilibrium and the eigenvalues are analyzed. Choosing the electromagnetic stiffness as a bifurcation parameter, the necessary and sufficient conditions of Hopf bifurcation are given, and the bifurcation characteristics are studied. The mechanism and conditions of system parameters for chaotic motions are investigated rigorously based on the Silnikov method. By using the undetermined coefficient method, the homoclinic orbit is found, therefore Smale horseshoe chaos occurs when electromagnetic stiffness changes. Finally, numerical simulations confirmed the analytical results.Secondly, the equivalent low-dimensional bifurcation equation is obtained by reducing the system dimensionality using the method of Lyapunov-Schmidt reduction and the bifurcation characteristic is analyzed using the singularity theory. In order to control the dynamic behaviors of the system, a time delay feedback is introduced and the distribution of the roots is studied. The analytical conditions which determine the control parameters are given based on the delay differential equation stability theory. The effects of the time-delay feedback control parameters on the system movement are analyzed combined with the system phase diagram and time history.Thirdly, the characteristic roots and the stable regions of time delay are determined by the Direct Method and the relationship between feedback gain and length summation of stable regions is analyzed under the time-delay feedback control. Choosing the time delay as a bifurcation parameter, the conditions of Hopf bifurcation under the time-delay nonlinear feedback control are analyzed. The direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are given by using the normal form method and center manifold theorem. Numerical simulations are also performed, which show the bifurcation behaviors of the system under different time delay and feedback gains.