Hunting stability analysis of high-speed trains with nonsmooth elements controlled by delayed yaw feedback

This paper presents a thorough bifurcation analysis of a 17 degrees-of-freedom high-speed train lateral dynamics model subject to delayed yaw feedback control, incorporating nonsmooth wheel-rail interaction. The control force provided by actuators replacing the yaw dampers is modeled as a polynomial function of the state variables. First, the eigenvalue analysis can be applied to identify the critical delay at which a Hopf bifurcation destabilizes the control systems with two actuators. Next, a single-parameter bifurcation diagram is obtained using the delay as the bifurcation parameter. From this, the critical delay and hunting frequency of the linear terms in the wheel-rail contact geometry are calculated. Then, the influence of feedback gains on the critical delay, hunting frequency, first Lyapunov coefficient, hunting amplitude, and control force is explored. Finally, the hunting stability of the passive system and the active system with various delay is compared under distinct wheel conicities and running speeds. These findings indicate that active control can stabilize a system that is inherently unstable when passive. While a moderate increase in delay enhances stability, excessive delay will once again lead to instability. In actively controlled vehicle systems, hunting stability can be improved more effectively through the careful choice of both linear and nonlinear feedback gains.