Abstract:
Motorsport has become a multidisciplinary sport in which skilled engineers and strategists play as big a part in the team’s success as the athlete driving the car. In Formula One it is common practice for teams to have dedicated resources on the track that are supported by a second team back at the home base who analyses telemetry data and performs simulations to refine the racing strategy.
Optimal control calculations are typically used to optimise vehicle setup parameters (such as ride height and heave spring stiffness) and driver inputs (such as braking and steering) specific to each track. Traditionally this approach has been employed by minimising time over a single lap. Although this is useful in qualifying simulations, there is an unexplored element of optimising a vehicle’s "race pace". Drivers complete qualifying laps using minimal fuel with new tyres to get the best possible lap time but this performance cannot be sustained throughout the whole race. Drivers need to manage their tyres so that they do not wear prematurely and have a detrimental effect on their performance.
This work places an emphasis on tyre modelling and in particular how optimal control can be used to optimise a tyre management strategy. A model has been presented that reduces grip as a function of tyre wear. This ensures that the qualifying pace cannot be sustained indefinitely. A thermodynamic model consisting of two states (surface and carcass temperature) is used to calculate tyre wear, which ultimately dictates how much grip can be provided by each tyre.
The objective function for the optimal control problem is to minimise time over multiple laps and the absolute tyre wear (in mm tread) is constrained to a predefined limit. This ensures that the consequences of pushing the car to its limits are considered: overheating temperatures and accelerated wear will be detrimental to racing performance. The optimal control solver needs to manage the tyre temperatures carefully over a racing distance. It has been shown that lap times degrade more severely as the tyres reach the end of their life. At some point in the race this drop off in performance will render the car uncompetitive and strategists can use this model to evaluate the performance of different tyre compounds at each track and to strategically plan pit stops during a race.
