A direct modified Elman neural networks (MENNs)-based decentralized controller is proposed to control the magnets of a nonlinear and unstable multi-input multi-output (MIMO) levitation system for the tracking of reference trajectories. First, the operating principles of a magnetic levitation system with two moving magnets are introduced. Then, due to the exact dynamic model of the MIMO magnetic levitation system is not clear, two MENNs are combined to be a direct MENN-based decentralized controller to deal with the highly nonlinear and unstable MIMO magnetic levitation system. Moreover, the connective weights of the MENNs are trained online by back-propagation (BP) methodology and the convergence analysis of the tracking error using discrete-type Lyapunov function is provided. Based on the direct and decentralized concepts, the computational burden is reduced and the controller design is simplified. Furthermore, the experimental results show that the proposed control scheme can control the magnets to track various periodic reference trajectories simultaneously in different operating conditions effectively.
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