Hopf bifurcation analysis of maglev vehicle–guideway interaction vibration system and stability control based on fuzzy adaptive theory

Abstract The vehicle–guideway interaction vibrations often occur when the parameters of the maglev system change. This phenomenon corresponds to the Hopf bifurcation in nonlinear dynamics. In order to solve the problem of maglev vehicle–guideway interaction vibration, the vehicle–guideway coupling dynamics model of maglev system considering the elasticity of the guideway is established firstly. Then, according to nonlinear dynamics theory and numerical simulations, the Hopf bifurcation rules of the maglev system are studied. Next, based on the Hopf bifurcation rules and the influence of control parameters on system vibration, the fuzzy inference method is used to establish the fuzzy control rules. A fuzzy adaptive tuning PID controller with variable parameter is designed for the vehicle–guideway interaction system. By identifying the disturbance or the change of the system parameters, the control parameters are adjusted automatically to keep the closed loop system away from the Hopf bifurcation point, which can restrain the vehicle–guideway interaction vibration. The simulation results show that the proposed fuzzy controller can adjust the levitation control proportional gain parameter K p ( t ) online, which can improve the dynamic performance of the system and make the maglev system obtain a large state stability range, thus restrain the vehicle–guideway interaction vibration effectively.