Purpose:
Magnetic levitation (MAGLEV) vehicles represent an advanced passenger transportation system that offers several advantages over conventional railways, including enhanced efficiency and performance. This study investigates the nonlinear vertical and lateral oscillations of a high-speed MAGLEV vehicle when subjected to steady and unsteady aerodynamic loading and centrifugal effects under primary resonance. The primary objective is to investigate the effect of a suggested controlling technique that employs an integral resonant controller (IRC), combined with a proportional-derivative (PD) controller, on the nonlinear vertical and lateral dynamics of the MAGLEV vehicle under the aforementioned circumstances.

Methods:
The vertical and lateral motions are modeled as independent nonlinear degrees of freedom. Using the multiple scales (MS) perturbation method, approximate second-order solutions are derived for both vertical and lateral vibrations under primary resonance, and their stability characteristics are analytically investigated using Lyapunov’s first method. Complementary numerical simulations are performed with the fourth-order Runge–Kutta (RK4) algorithm to verify the analytical predictions.

Results:
For both lateral and vertical motions, the results show that unsteady aerodynamic forces significantly increase vibration amplitudes and can cause instability close to resonance conditions. It is shown that the system moves toward stable operating regions when the strength of unsteady aerodynamic excitations is decreased. When the IRC is activated, additional effective damping factors are introduced. Consequently, vibration amplitudes are significantly reduced when higher IRC control gains are paired with lower internal feedback gains of the IRC, which results in larger stability regions.

Conclusion:
These findings demonstrate that the proposed IRC-PD control approach is effective, as it improves the dynamic stability and vibration suppression of the MAGLEV vehicle under aerodynamic disturbances, resulting in safer operation, improved ride comfort, and enhanced overall system performance.