Stability Analysis of a Maglev Vehicle-Guideway Coupled System Considering Dual Time Delays in Displacement and Velocity Feedback

To investigate the influence of dual feedback delays on the stability of a maglev vehicle-guideway coupled system, a coupled dynamic model consisting of the carbody, levitation frame, and flexible guideway beam is established under a stationary midspan levitation condition. Both displacement and velocity feedback delays are considered. Based on the linearized electromagnetic suspension force and the first-mode approximation of the guideway beam, the characteristic equation of the dual-delay system is derived, and stability is evaluated using the spectral abscissa criterion. The stability regions under different combinations of displacement and velocity delays are obtained, and the effects of control parameters, guideway structural parameters, and carbody mass on the stability boundary are analyzed. The results show that the system is stable without time delay, while increasing either feedback delay drives the dominant characteristic roots toward the right half-plane and reduces the stability margin. The two feedback delays exhibit a coupled effect, so the dual-delay stability boundary cannot be regarded as a simple superposition of single-delay critical values. DDE timedomain simulations agree with the characteristic-root-based results, supporting the reliability of the stability analysis. The results can provide guidance for levitation controller design, feedback-delay margin evaluation, and guideway parameter selection.