Optimal control policy tuning and implementation for a hybrid electric race car

Abstract

The Formula 1 car is a state-of-the-art hybrid electric vehicle. Its power unit is composed by a turbocharged gasoline engine and two electric motor/generator units connected to the traction system and to the turbocharger. Such a powertrain offers an additional degree of freedom and therefore requires an energy management system. This supervisory controller has a significant influence on the vehicle’s fuel consumption and on the achievable lap-time. Therefore, a thorough, systematic optimization of the energy management system is a crucial prerequisite to win a race. The complexity of the system and the strict regulations make the time-optimal energy management problem non-trivial to solve and an effective implementation of its solution on the car difficult to achieve. In Ebbesen, S. et al. (2016) and Salazar, M. et al. (2016) a convex numerical solver was designed and the optimal strategies were derived analytically using a non-smooth version of Pontryagin’s Minimum Principle, respectively. Building on these results, we design a nonlinear program to tune an efficient version of the optimal control policy, in order to precisely match various boundary conditions on the fuel consumption and on the battery usage. This allows a simple and robust implementation of the time-optimal control strategies on the vehicle, and guarantees compatibility with the FIA rules. A simulator is then used to test the obtained feedforward controls on one race lap in Barcelona. The results stand comparison with the optimal solutions obtained with the numerical solver and validate the effectiveness of this strategy.