Minimum Lap Time Control of Hybrid Electric Race Cars in Qualifying Scenarios

Abstract

This paper presents models and control algorithms for the energy management of the Formula 1 race car in qualifying scenarios, whereby the car's performance is solely determined by the lap time achieved over a single lap. Specifically, we first extend an existing convex model of the Formula 1 car to include the waste-gate action, and analytically derive its lap-time-optimal control policy. Second, we combine nonlinear programming techniques with convex optimization to numerically compute the optimal solution for an out-lap-flying-lap sequence. Third, we devise equivalent lap time minimization strategies, whereby three PI controllers adapt the optimal control policy implemented on the car in real time, in order to track precomputed control strategies in a minimum-lap-time fashion. Finally, we benchmark the control algorithms presented against the optimal solution and validate their performance with high-fidelity simulations. The results obtained show the optimality and the robustness of the presented approach.