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An adaptive backstepping control system using a recurrent neural network (RNN) is proposed to control the mover position of a magnetic levitation apparatus to compensate the uncertainties including the friction force in this study. First, the dynamic model of the magnetic levitation apparatus is derived. Then, an adaptive backstepping approach is proposed to compensate disturbances including the friction force occurring in the motion control system. Moreover, to further increasing of the robustness of the magnetic levitation apparatus, a RNN uncertainty estimator is proposed to estimate the required lumped uncertainty in the adaptive backstepping control system. Furthermore, an on-line parameter training methodology, which is derived using the gradient descent method, is proposed to increase the learning capability of the RNN. The effectiveness of the proposed control scheme is verified by some experimental results. With the proposed adaptive backstepping control system using RNN, the mover position of the magnetic levitation apparatus possesses the advantages of good transient control performance and robustness to uncertainties for the tracking of periodic trajectories.