The straight running of the system composed by a car plus driver is studied. Straight running is an important case study for analysing stability. Despite the lateral slip angles of the tyres are small, the system is highly non linear, due essentially to the driver action. Following the simple model of McRuer, later developed by Mistschke and revised by many other authors, we have developed a mathematical model of a car plus driver. The dynamic behaviour of the mathematical model has shown the presence of limit cycles generated by so called Hopf-bifurcations. The mathematical model predicts that, despite the understeering vehicle is globally stable, the driver can make the whole system (car plus driver) unstable. This occurs in case an external disturbance is sufficiently strong. If the external disturbance is small, the understeering vehicle plus driver remains stable. There is a speed above which the understeering car plus driver is unstable, usually such a speed is much greater than the maximum speed of the car on high grip surface. The statements introduced above have been validated by employing the driving simulator of Danisi Engineering, Nichelino, Italy. We experimentally saw that limit cycles do exist and that the driver can make the understeering vehicle model of the simulator quite unstable. We were able to validate the mathematical model by including two humans in the driving loop. One driver was a professional driver, the other one was a novice. The same non linear behaviours were highlighted for the two drivers, however, the amplitudes of the limit cycles and the ability of controlling the car were higher for the professional driver. A question arises whether an electronic power steering (EPS) may reduce or cancel instability. The answer is that there are a number of possible solutions for ESP to counteract the effect of unstable limit cycle.

The stability of the straight ahead running motion of automobiles is studied with proper theoretical tools pertaining to bifurcation theory. The study is both theoretical and experimental. Four theoretical models have been employed. They refer, respectively, to one simple car model, one simple driver model, one complex car model and one complex driver model. The existence of bifurcations, namely Hopf bifurcations, is found for both the simple car/simple driver model combination and for the complex car/complex driver model combination. The experimental study refers to the employment of a driving simulator in which a human driver controls the complex car model. At the driving simulator, bifurcations are found which correspond to the ones predicted either with the simple car/simple driver model combination or the complex car/complex driver model combination. At the driving simulator a chaotic motion is found, after a subcritical Hopf bifurcation has occurred. Apparently, for the first time in the sector of vehicle system dynamics, the actual existence of bifurcations and chaos has been shown for a real system with a human driver in-the-loop. The driving simulator does not seem introducing factors affecting sensibly bifurcations, so the bifurcations that have been found appear to be real, i.e. bifurcations could be found in an actual car running straight ahead.