Vertical Dynamic Response of the 2-DOF Maglev System considering Suspension Nonlinearity

In order to study the dynamic characteristics of the nonlinear system of the maglev train, a vibration model of the two-degree-of-freedom nonlinear suspension system of the maglev train is established in this paper. Based on the linearized model of the suspension control module, the suspension system is controlled by the state feedback method. Compared with the results of the Runge–Kutta method, the accuracy of the settlement results is verified. This paper analyzes the influence of system parameters and feedback control parameters on the system. The results show that the linear stiffness mainly affects the left-right migration of the resonance peak and the difference between the maximum and minimum of the resonance region of the suspension frame; the nonlinear stiffness mainly affects the slope of the resonance region of the car body and the suspension frame; displacement feedback control parameters can reduce the amplitude of the system, velocity feedback control parameters can make the state change of the suspension frame more smoothly, and acceleration feedback control parameters make the car body and the suspension frame have a strong coupling effect. According to the Hurwitz criterion of Hopf bifurcation, this paper deduces the conditions that the control parameters should satisfy when the equilibrium point is stable, and the instability produces periodic vibration under PID control. Through numerical simulation, it is found that the system has complex dynamic behavior, the results show that the system works under some conditions, and there are multiple stable and unstable limit cycles simultaneously. Therefore, the system will appear alternately between multiperiod and chaotic motion, which will affect the stability of the system.