Delay-robust nonlinear control for hunting stability of high-speed trains with active yaw dampers

To address the hunting stability of high-speed rail vehicles under wheel wear conditions, the nonlinear control method of active yaw damper (AYD) was investigated to improve delay robustness. A lateral simplified dynamic model was established for bifurcation and stability analysis. The analysis incorporated displacement and velocity feedback control strategies, utilizing both polynomial and piecewise nonlinear force laws. The passive vehicle system exhibited a subcritical Hopf bifurcation. With AYDs, the bifurcation characteristics were significantly influenced by the control gain and time delay. Under displacement feedback control, stability progressively deteriorated with increasing delay and was highly gain-dependent. Although nonlinear (e.g., quadratic, cubic) gains mitigated adverse stability effects near the equilibrium, they did not extend the maximum allowable delay (e.g., 25 ms at 110 m/s) or increase the maximum critical speed (e.g., 120 m/s at 20 ms). In contrast, the vehicle system regained stability across a broader delay range (10–50 ms) under velocity feedback control, but its stability switched as the gain increased. To counteract this, a dead zone was introduced, effectively mitigating the destabilizing effect. Full degree-of-freedom model simulations confirmed that the velocity feedback control with a dead zone provides improved robustness to variations in both gain and delay. In summary, displacement feedback performs better for delays below 10 ms, whereas the velocity feedback approach with dead-zone compensation is advantageous for longer delays (10–50 ms) due to its ability to mitigate the destabilizing effect of excessive gains.