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The electromagnet levitation system (ELS) of low-speed maglev train is taken as the research object. The nonlinear dynamics and control law of ELS are discussed. Specifically, by employing the Euler-Lagrange's method, a nonlinear dynamic model is constructed for the single-ELS. Then, the linear control law is studied, which has a disadvantage of weak robustness. To improve the performance of the controller, a fuzzy sliding-mode control law is proposed. According to the dynamic nonlinear model, a novel sliding surface which can make the system reach the stable point within the finite time is presented. Moreover, the fuzzy inference method is utilized to slow down the speed of the states crossing the sliding surface. The simulation results demonstrate that the global robustness of external disturbance and parameter perturbation can be achieved through the proposed control law. And the chattering phenomenon can be reduced significantly. Finally, the experiments are also implemented to examine its practical dynamic performance of the proposed control law.

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The suspension system of Maglev vehicle needs strong robustness and anti-jamming ability in the process of operation and fluctuation control. In order to solve the open-loop instability and strong nonlinearity of the mechanical equation of the suspension system of the Maglev vehicle, the non-linear dynamic equation is established. At present, the research based on the single electromagnet and the rigid track is the most common. However, based on this method, it is impossible to study the coupled vibration caused by track factors. Therefore, based on the dynamic equation of a single span simply supported beam of flexible track and the non-linear equation of the suspended electromagnet itself, an overall control model is needed to discuss the control strategy. Based on this dynamic model, the singularities of the system are solved according to Hurwitz criterion, and the characteristic equation corresponding to the Jacobian matrix is obtained. The stability analysis shows that the system is unstable. At the same time, the necessity of using a feedback control method to control the air gap has been proved. On this basis, a sliding mode adaptive state feedback controller for the maglev system is designed based on the RBF network approximation principle. The corresponding simulation and experimental results are given. The simulation and experimental results show that the controller can ensure the vehicle's stable suspension and effectively suppress external interference. Compared with the traditional PID and fuzzy controllers, the controller can guarantee a faster dynamic response, stronger robustness, and smaller overshoot while considering the flexible track and external disturbances. INDEX TERMS Maglev system, flexible track, coupled vibration, RBF, sliding mode adaptive control.