Backstepping sliding mode control for continuous casting mold vibration displacement system driven by servo motor

Aiming at the time-varying load torque disturbance in the vibration displacement system of continuous casting mold driven by servo motor, an extended state observer (ESO) based backstepping sliding mode control method is proposed. Firstly, a mapping function is established to deal with the non-uniqueness of the nonlinear inverse relationship from eccentric shaft angle to mold displacement. Secondly, an ESO is constructed to estimate the time-varying load torque, and the estimate of load torque is employed to compensate the disturbance in controller. And a backstepping sliding mode controller is then developed for the vibration displacement system of continuous casting mold, which can guarantee the asymptotical stability and the robust stability of the resulting closed-loop system. Finally, simulation results are given to show the effectiveness of the proposed method.