The effect of model predictive control on the interplay between electromagnetic and wave-induced instability in hyperloop systems

Abstract

Hyperloop has emerged as a promising mode of transportation and has attracted strong interest from student teams and start-ups. Its potential lies in enabling faster and more sustainable transport. At the same time, the technology and characteristics of the hyperloop system may also lead to different instability mechanisms. This study focuses on two of these, namely electromagnetic instability and wave-induced instability. Previous studies have generally considered either conventional control strategies or simplified models of the vehicle-guideway dynamics. This study contributes by investigating the effect of an advanced control strategy, Model Predictive Control (MPC), on both sources of instability. MPC is applied because of its predictive nature and its ability to handle constraints.

The analysis first considers a simplified 1.5-degree-of-freedom (DOF) system to study the effect of MPC on electromagnetic instability. An eigenvalue analysis was conducted to examine the influence of the MPC parameters. It is found that linear MPC does not achieve stabilisation. Therefore, a nonlinear MPC is designed and compared with a PD controller, showing improved control performance.

To capture the influence of vehicle velocity on system stability, an infinite guideway with coupled vehicle-beam interaction is considered, allowing anomalous Doppler waves to arise at high velocities. In the supercritical velocity regime, where wave-induced instability becomes dominant, numerical simulations show that MPC can maintain stability for suitably tuned controller parameters over a wider range of velocities. Compared with the PD controller, MPC appears better able to achieve fast convergence while also suppressing wave-induced instability.

Overall, MPC showed improved control performance relative to the PD controller and appears to be a promising control strategy for application in magnetically levitated high-speed transportation systems. However, more research is needed to make nonlinear MPC feasible for real-time implementation. A more formal and comprehensive study of the stability of the vehicle is also needed.