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This paper concerns the problem of output regulation for the oscillation displacement system of continuous casting mold driven by servo motor with mismatched time varying disturbances. A composite control scheme combining the backstepping control with sliding mode control (SMC) and extended state observer (ESO) is proposed. Two novel nonlinear ESOs with high gain are first constructed to estimate the compound disturbance and the load torque, respectively, and the estimates are then introduced into the design of virtual control laws. A continuous sliding mode controller with adaptive gain is designed in each step of backstepping procedure, and a robust exact differentiator is introduced to obtain the first-order time derivative of the previous virtual control law. By using Lyapunov stability theorem, it can be proved that the estimation errors of the proposed ESOs are bounded and the upper bounds are dependent on the high gain; it can be shown that all the signals of the resulting closed-loop systems are bounded and the system states can be stabilized to the origin exponentially by choosing appropriate parameters. Finally, simulation results are given to illustrate the verification of the proposed control method.

Adaptive Backstepping Sliding Mode Control for the Oscillation Displacement System of Continuous Casting Mold With Mismatched Disturbances