Dynamics and nonlinear feedback control for torsional vibration bifurcation in main transmission system of scraper conveyor direct-driven by high-power PMSM

The main transmission system of a scraper conveyor direct-driven by the high-power permanent magnet synchronous motor (PMSM) is taken as a study object. With the effect of the nonlinear friction torque caused by the nonuniformity of the transported coal quality in the operation process considered, the torsional vibration bifurcation mechanism and the corresponding control measures for the main transmission system of the scraper conveyor are investigated. Firstly, based on the Lagrange–Maxwell principle, the global electromechanical-coupling dynamic models for the main transmission system of the scraper conveyor are constructed. Secondly, by the Routh–Hurwitz stability criterion, the Hopf bifurcation characteristics of the main transmission system are analyzed to reveal the influence of supercritical bifurcation and subcritical bifurcation on the torsional oscillation of the transmission shafting. Thirdly, in order to suppress the system unstable oscillation caused by the Hopf bifurcation, the motor speed is fed back to construct the nonlinear state feedback controller for the quadrature axis current of the PMSM by the (I_{d}=0) vector control strategy. Similarly, on the basis of the Routh–Hurwitz criterion, the influence of the linear feedback coefficient in the nonlinear state feedback controller on the system bifurcation position is discussed. Meanwhile, by the central manifold theory and canonical form theory, the effect of the square and cubic nonlinear feedback coefficients on the Hopf bifurcation type of the torsional vibration and the amplitude of the stable limit cycle are investigated. Finally, the numerical simulation results show the effectiveness of the designed controller.