Time-Optimal Low-Level Control and Gearshift Strategies for the Formula 1 Hybrid Electric Powertrain

Camillo Balerna, Marc-Philippe Neumann, Nicolò Robuschi, Pol Duhr, Alberto Cerofolini, Vittorio Ravaglioli and Christopher Onder
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Camillo Balerna: Institute for Dynamic Systems and Control, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, Switzerland
Marc-Philippe Neumann: Institute for Dynamic Systems and Control, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, Switzerland
Nicolò Robuschi: Department of Mechanical Engineering, Politecnico di Milano, via La Masa 1, 20156 Milano, Italy
Pol Duhr: Institute for Dynamic Systems and Control, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, Switzerland
Alberto Cerofolini: Power Unit Performance and Control Strategies, Ferrari S.p.A., via Enzo Ferrari 27, 41053 Maranello, Italy
Vittorio Ravaglioli: Department of Industrial Engineering, Università di Bologna, Via Fontanelle 40, 47121 Forlì, Italy
Christopher Onder: Institute for Dynamic Systems and Control, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, Switzerland

Energies, 2020, vol. 14, issue 1, 1-30

Abstract: Today, Formula 1 race cars are equipped with complex hybrid electric powertrains that display significant cross-couplings between the internal combustion engine and the electrical energy recovery system. Given that a large number of these phenomena are strongly engine-speed dependent, not only the energy management but also the gearshift strategy significantly influence the achievable lap time for a given fuel and battery budget. Therefore, in this paper we propose a detailed low-level mathematical model of the Formula 1 powertrain suited for numerical optimization, and solve the time-optimal control problem in a computationally efficient way. First, we describe the powertrain dynamics by means of first principle modeling approaches and neural network techniques, with a strong focus on the low-level actuation of the internal combustion engine and its coupling with the energy recovery system. Next, we relax the integer decision variable related to the gearbox by applying outer convexification and solve the resulting optimization problem. Our results show that the energy consumption budgets not only influence the fuel mass flow and electric boosting operation, but also the gearshift strategy and the low-level engine operation, e.g., the intake manifold pressure evolution, the air-to-fuel ratio or the turbine waste-gate position.

Keywords: hybrid electric vehicles; Formula 1; optimal control; gearshift optimization; cylinder deactivation; outer convexification; neural networks; mixed-integer nonlinear optimization (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2020
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