Formula One (F1) is considered to be the forefront of innovation for the automotive and motorsport industry. One of the key provisions has been towards the inclusion of the Energy Recovery System (ERS) since 2014 in F1 regulations. ERS comprises Motor Generator Unit-Heat (MGU-H), Motor Generator Unit-Kinetic (MGU-K) and an Energy Storage (ES). This has not only converted the conventional powertrain into a hybrid power-split device, but also imposed constraints on the fuel energy available, energy recovered and deployed by MGU-K, and charge stored in ES, along with various other parameters. Although the objective for a F1 race is to minimize lap-time, it is obvious that there is no unique control path or decision to meet this objective. This builds up needs to optimally control the power-split and energy of the system.
In this study, we propose an energy optimal control strategy for a F1 car by constructing a detailed force-balanced mathematical model of the F1 powertrain, identifying state-space variables, as well as regulated constraints and weighted-cost functions and then solving for minimizing cost function based on model-based optimization inside GT-Suite© using Discrete Optimization and Genetic Algorithm. The obtained optimal trajectory is compared to the global optimum obtained by Dynamic Programming. Finally, the results are validated over in our high-fidelity GT-Drive based F1 powertrain simulator and also compared against conventional rule-based controls for added advantage to race performance and energy minimization. The result is the optimal strategy that results in minimal energy consumption for the provided speed trajectory over a single lap.