Advanced lagged slip ratio for stable analysis of wheel dynamics at low-speed and high-speed

Real-time interpretation of a vehicle is mainly used for the speed estimation of autonomous vehicles and hardware-in-the-loop simulation. For real-time analysis of vehicles, an explicit integrator is more suitable than an implicit integrator. The implicit integrator guarantees the stability of the numerical analysis, whereas the explicit integrator requires a smaller amount of computation, which enables quick analysis. However, the lagged slip ratio, which is the most typical slip ratio in the tire model for vehicle dynamics simulation, shows that the numerical results of the explicit integrator are unstable in low-speed and high-speed driving situations. This is because the pole of the wheel dynamics system applying the lagged slip ratio deviates from the stability region of the explicit integrator depending on the driving speed. Generally, the instability of the lagged slip ratio is eliminated by applying an arbitrary damper system. In this study, an advanced lagged slip ratio is proposed to maintain the pole of the wheel dynamics in the stability region using an explicit integrator. The validity and stability of the proposed method is confirmed by comparing the driving simulation results with the conventional slip ratio.