Abstract:
A numerical method is presented for the time optimal control of the race car. The method
is then used to perform the role of the driver in numerical simulations of manoeuvres at the
limit of race car performance. The method does not attempt to model the driver but rather
replaces the driver with methods normally associated with numerical optimal control. The
use of constraints on the method is then considered to represent the performance limits of
the human driver. The method simultaneously finds the optimal driven line and the driver
control inputs (steer, throttle and brake) to drive this line in minimum time. The method is
in principle capable of operation with arbitrarily complex vehicle models as it requires only
limited access to the vehicle model state vector. It also requires solution of the differential
equation representing the vehicle model in only the forward time direction and is hence
capable of simulating the full vehicle transient response. The impact of various vehicle
parameters on minimum manoeuvre time, driven line and vehicle stability is shown for a
number of representative manoeuvres using a quasi-steady state vehicle model. A similar
process is then carried out to analyse the effect of suspension springs and dampers using a
fully dynamic sprung vehicle model. The presented transient time optimal control method
is then compared with results obtained from a traditional quasi-steady state manoeuvre
time simulation method. A thermodynamic tyre model is developed and the time optimal
control algorithm is used to evaluate dynamic tyre temperature effects on lap time and
vehicle stability.
