Stable regions of vehicle lateral dynamics in the parameter space of driver

In this paper, using the linear and non-linear vehicle-driver model, the effect of the driver's time delay on the vehicle lateral stability has been investigated. Driver's time delay is an unavoidable issue in vehicle handling dynamics. Apart from intrinsic time-delay in human sensory-motor response, the driver's health condition can potentially affect the reaction-time. Taking into account the driver time delay in the modeling, transforms the vehicle handling dynamics to a system of delay differential equations (DDE), which has infinite solution in mathematical sense. In this paper, to solve the follow-on DDE, the time delay is approximated via a Taylor series. Stability charts, demonstrating the acceptable regions for driver's proportional and derivative gains are provided for a specified driver time delay. The results show that as the time delay increases or the vehicle speed increases, the stability region becomes smaller. The critical value of driver time delay for a specified set of driver’s proportional and derivative gains is also calculated. This analysis shows that if the driver drives at higher speeds, he must react faster so that the vehicle does not become unstable. Numerical simulation of a vehicle driver model subjected to a rigorous lane change maneuver is carried out to verify the results obtained from the stability charts. In the simulation a nonlinear seven degrees of freedom of vehicle and a nonlinear tire model is used. The simulation results fully confirm the stability analysis results.