Stability analysis of railway vehicles with time-delayed active suspension control via Padé approximation

To investigate the influence of time delay in active suspension systems on the stability of railway vehicle systems, this paper proposes a stability analysis method for the time-delayed feedback control system via Padé approximation. First, the properties of the Padé approximation are introduced, followed by an analysis of the required approximation order. Subsequently, two models incorporating active lateral actuators were constructed: a simplified 17-DOF lateral dynamics model and a full-DOF multibody dynamics model of the whole vehicle. In addition, the influence of time delay on the dynamic performance indices under sky-hook damping control was explored. Then, the stability of the vehicle system with time-delayed feedback control was investigated, in which the critical time delay for instability was determined based on the eigenvalue method. Finally, the effects of the damping control gain and active suspension configurations on the critical time delay were analyzed. Numerical analysis indicates that the proposed stability analysis method can accurately determine the eigenvalues. For sky-hook damping control, excessive time delay may cause the damping ratios of carbody suspension modes to become negative, leading to system instability and abrupt deterioration of dynamic performance indices. Overall, a lower damping gain permits a larger time delay, and the active suspension configuration with fewer actuators exhibits greater delay robustness. The proposed stability analysis method is applicable to various mechanical systems with time-delayed linear feedback control and provides a basis for stability assessment.