Time-optimal control of the formula 1 hybrid electric power unit

Since 2014, Formula 1 racing cars have been equipped with a hybrid electric power unit composed of an electrically turbocharged internal combustion engine and an electric motor used for boosting and regenerative braking. The energy management system that controls this hybrid electric powertrain strongly influences the achievable lap time, as well as the consumption of fuel and battery energy. In this thesis we study models and control strategies to achieve the best possible lap time. First, we identify a convex model of the power unit and use it to numerically assess the time-optimal control strategies. Second, we leverage the convex model to analytically derive a time-optimal control policy that can be implemented on the ECU in a feedforward fashion and in compliance with the sporting regulations. Third, we develop two feedback control algorithms to counteract disturbances and track the optimal strategies in a lap-time-optimal way: the first one in the form of a two-level optimality tracking MPC scheme, and the second one inspired by ECMS and consisting of PID controllers continuously adjusting the optimal control policy in real-time. We perform numerical tests using convex and high-fidelity simulation environments to validate the optimality and the robustness of the proposed control approaches under realistic disturbances.