Bifurcation analysis of a car and driver model

The bifurcation analysis of a simple mathematical model describing a road vehicle with a driver is . The mechanical model of the car has two degrees of freedom and the related equations motion contain the nonlinear tyre characteristics. The driver is described by a well-known model in the literature. The road vehicle model has been validated in a case study. Bifurcation is adopted as the proper procedure for analysing both steady-state cornering and straight motion at different speeds. The importance of properly computing steady-state equilibria is . The effect of a skilled driver is to broaden the basin of attraction of stable equilibria and, in cases, to stabilise originally unstable behaviours.Asubcritical Hopf bifurcation is normally found limits the forward speed of either understeering or oversteering vehicles. A three-parameter analysis is performed to understand the influence on stability of driver gain, of driver time, of vehicle speed. It turns out, as expected from practice, that an oversteering vehicle more challenging to be controlled than an understeering one. The paper proposes an insight into –driver interaction. The stabilising or de-stabilising effect of the driver is ultimately explained to the existence of a Hopf bifurcation.