Bifurcation analysis of a car and driver model

Abstract

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