Time-Optimal Low-Level Control and Gearshift Strategies for the Formula 1 Hybrid Electric Powertrain
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 e...
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| Format: | Article |
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MDPI AG
2020-12-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/14/1/171 |
| _version_ | 1797542837459353600 |
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| author | Camillo Balerna Marc-Philippe Neumann Nicolò Robuschi Pol Duhr Alberto Cerofolini Vittorio Ravaglioli Christopher Onder |
| author_facet | Camillo Balerna Marc-Philippe Neumann Nicolò Robuschi Pol Duhr Alberto Cerofolini Vittorio Ravaglioli Christopher Onder |
| author_sort | Camillo Balerna |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T13:37:05Z |
| format | Article |
| id | doaj.art-bde8080588984acaaaeb38d709d7547a |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-10T13:37:05Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-bde8080588984acaaaeb38d709d7547a2023-11-21T07:29:05ZengMDPI AGEnergies1996-10732020-12-0114117110.3390/en14010171Time-Optimal Low-Level Control and Gearshift Strategies for the Formula 1 Hybrid Electric PowertrainCamillo Balerna0Marc-Philippe Neumann1Nicolò Robuschi2Pol Duhr3Alberto Cerofolini4Vittorio Ravaglioli5Christopher Onder6Institute for Dynamic Systems and Control, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, SwitzerlandInstitute for Dynamic Systems and Control, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, SwitzerlandDepartment of Mechanical Engineering, Politecnico di Milano, via La Masa 1, 20156 Milano, ItalyInstitute for Dynamic Systems and Control, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, SwitzerlandPower Unit Performance and Control Strategies, Ferrari S.p.A., via Enzo Ferrari 27, 41053 Maranello, ItalyDepartment of Industrial Engineering, Università di Bologna, Via Fontanelle 40, 47121 Forlì, ItalyInstitute for Dynamic Systems and Control, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, SwitzerlandToday, 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.https://www.mdpi.com/1996-1073/14/1/171hybrid electric vehiclesFormula 1optimal controlgearshift optimizationcylinder deactivationouter convexification |
| spellingShingle | Camillo Balerna Marc-Philippe Neumann Nicolò Robuschi Pol Duhr Alberto Cerofolini Vittorio Ravaglioli Christopher Onder Time-Optimal Low-Level Control and Gearshift Strategies for the Formula 1 Hybrid Electric Powertrain Energies hybrid electric vehicles Formula 1 optimal control gearshift optimization cylinder deactivation outer convexification |
| title | Time-Optimal Low-Level Control and Gearshift Strategies for the Formula 1 Hybrid Electric Powertrain |
| title_full | Time-Optimal Low-Level Control and Gearshift Strategies for the Formula 1 Hybrid Electric Powertrain |
| title_fullStr | Time-Optimal Low-Level Control and Gearshift Strategies for the Formula 1 Hybrid Electric Powertrain |
| title_full_unstemmed | Time-Optimal Low-Level Control and Gearshift Strategies for the Formula 1 Hybrid Electric Powertrain |
| title_short | Time-Optimal Low-Level Control and Gearshift Strategies for the Formula 1 Hybrid Electric Powertrain |
| title_sort | time optimal low level control and gearshift strategies for the formula 1 hybrid electric powertrain |
| topic | hybrid electric vehicles Formula 1 optimal control gearshift optimization cylinder deactivation outer convexification |
| url | https://www.mdpi.com/1996-1073/14/1/171 |
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