Straight running – stability analysis with a driving simulator

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.