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We propose an intelligent adaptive backstepping control system using a recurrent neural network (RNN) to control the mover position of a magnetic levitation apparatus to compensate for uncertainties, including friction force. First, we derive a dynamic model of the magnetic levitation apparatus. Then, we suggest an adaptive backstepping approach to compensate disturbances, including the friction force, occurring in the motion control system. To further increase the robustness of the magnetic levitation apparatus, we propose an RNN estimator for the required lumped uncertainty in the adaptive backstepping control system. We further propose an online parameter training methodology, derived by the gradient descent method, to increase the learning capability of the RNN. The effectiveness of the proposed control scheme has been verified by experiment. 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.Index Terms-Adaptive backstepping control, lumped uncertainty, magnetic levitation, recurrent neural network.

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A robust recurrent-neural-network (RRNN) sliding-mode control is proposed for a biaxial motion mechanism to allow reference contour tracking. The biaxial motion mechanism is a X-Y table of a computer numerical control machine that is driven by two field-oriented control permanent-magnet synchronous motors. The single-axis motion dynamics are derived in terms of a lumped uncertainty that includes cross-coupled interference between the two-axes. A RRNN sliding-mode control system is proposed based on the derived motion dynamics to approximate the control obtained by using sliding-mode control and the motions at the X-axis and Y-axis are controlled separately. The motion tracking performance is significantly improved using the proposed control technique and robustness to parameter variations, external disturbances, crosscoupled interference and frictional torque can be obtained as well. Experimental results on circular, four-leaf, window and star reference contours are provided to show that the dynamic behaviour of the proposed control system is robust with regard to uncertainties.

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