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

Author

Listed:
  • Camillo Balerna

    (Institute for Dynamic Systems and Control, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, Switzerland
    These authors contributed equally to this work.)

  • Marc-Philippe Neumann

    (Institute for Dynamic Systems and Control, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, Switzerland
    These authors contributed equally to this work.)

  • 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)

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.

Suggested Citation

  • Camillo Balerna & Marc-Philippe Neumann & Nicolò Robuschi & Pol Duhr & Alberto Cerofolini & Vittorio Ravaglioli & Christopher Onder, 2020. "Time-Optimal Low-Level Control and Gearshift Strategies for the Formula 1 Hybrid Electric Powertrain," Energies, MDPI, vol. 14(1), pages 1-30, December.
    • Handle: RePEc:gam:jeners:v:14:y:2020:i:1:p:171-:d:472964
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    References listed on IDEAS

    as
    1. Balerna, Camillo & Lanzetti, Nicolas & Salazar, Mauro & Cerofolini, Alberto & Onder, Christopher, 2020. "Optimal low-level control strategies for a high-performance hybrid electric power unit," Applied Energy, Elsevier, vol. 276(C).
    2. Tobias Nüesch & Alberto Cerofolini & Giorgio Mancini & Nicolò Cavina & Christopher Onder & Lino Guzzella, 2014. "Equivalent Consumption Minimization Strategy for the Control of Real Driving NOx Emissions of a Diesel Hybrid Electric Vehicle," Energies, MDPI, vol. 7(5), pages 1-31, May.
    3. Pérez, Laura V. & Pilotta, Elvio A., 2009. "Optimal power split in a hybrid electric vehicle using direct transcription of an optimal control problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(6), pages 1959-1970.
    4. Liu, Xuze & Fotouhi, Abbas & Auger, Daniel J., 2020. "Optimal energy management for formula-E cars with regulatory limits and thermal constraints," Applied Energy, Elsevier, vol. 279(C).
    5. Tobias Nüesch & Philipp Elbert & Michael Flankl & Christopher Onder & Lino Guzzella, 2014. "Convex Optimization for the Energy Management of Hybrid Electric Vehicles Considering Engine Start and Gearshift Costs," Energies, MDPI, vol. 7(2), pages 1-23, February.
    6. Jonas Asprion & Oscar Chinellato & Lino Guzzella, 2014. "Optimal Control of Diesel Engines: Numerical Methods, Applications, and Experimental Validation," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-21, February.
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