Formula 1 Powertrain
The project Formula 1 Powertrain deals with the modeling and the optimal control of the power unit of the Formula 1 race car, in order to achieve the best possible lap time with the given hybrid electric architecture and in compliance with the FIA sporting regulations in force.
Hybrid Electric Powertrain
Since 2014, the Formula 1 car has been a hybrid electric vehicle with a turbocharged gasoline engine and electric motor/generator units connected to the axle, for kinetic energy recovery and boosting, and to the shaft of the turbocharger, mainly to recover waste heat from the exhaust gases. This system offers a new degree of freedom, namely the power split, which is the ratio of power delivered by the electric traction motor in comparison to the overall propulsive power.
Driver in the Loop and Regulations
The traction system is semi-autonomous. In the straights, where the driver usually requests 100% acceleration, regulations allow the implementation of a thrust controller, since only by limiting the acceleration power, the maximum allowed fuel consumption of 100kg gasoline per race can be achieved. Furthermore, there exist several operational constraints imposed by the regulations that need to be tracked.
Lap Time Optimal Control Strategies
In each moment of time, the energy management system of the vehicle needs to decide how much power to draw from the internal combustion engine and from the battery. These decisions have a huge impact on the energy efficiency of the vehicle and, therefore, on the achievable lap time, and turn out to be not trivial. Therefore, a proper understanding of the vehicle and its surrounding conditions is crucial for the development of an energy management algorithm. This problem belongs to the class of dynamic optimal control problems that can only be solved by using dedicated tools from the theory of optimal control.
Based on the expertise in control systems theory and hybrid vehicle propulsion systems, an optimal energy management strategy is developed at the Institute for Dynamic Systems and Control both in terms of theoretical research and numerical simulations.
We develop computationally efficient methods to evaluate the theoretic, optimal energy management strategy leading to the best possible lap time. By carefully introducing convex approximations and relaxations, we formulate the problem as a convex optimal control problem that can be solved efficiently using dedicated numerical solvers. The proposed method allows parameter studies to be conducted within a reasonable time frame of a few minutes, while the optimization results serve as a benchmark for any real-time energy management strategy ultimately to be used during a real race.
Combining the numerical optimization methods with an analytical approach based on Pontryagin's minimum principle, we derive real-time implementable energy management strategies minimizing the lap time, which can be adjusted for specific scenarios and are compatible with the regulations.
On-line Energy Management
The objective of the energy management strategy is to minimize the lap time, while ensuring compliance with the regulations. At the same time, all operational constraints of all components must be monitored and maintained. The development of on-line energy management systems aims to increase robustness with respect to modeling errors. Moreover, a feedback loop is necessary to track the optimal trajectories and properly react to unforeseen disturbances.
Journals
Soren Ebbesen, Mauro Salazar, Philipp Elbert, Carlo Bussi, and Christopher H. Onder, external page Time-optimal Control Strategies for a Hybrid Electric Race Car, IEEE Transactions on Control Systems Technology, 2017.
Mauro Salazar, Philipp Elbert, Soren Ebbesen, Carlo Bussi, and Christopher H. Onder, external page Time-optimal Control Policy for a Hybrid Electric Race Car, IEEE Transactions on Control Systems Technology, 2017.
Mauro Salazar, Camillo Balerna, Philipp Elbert, Fernando P. Grando, and Christopher H. Onder, external page Real-time Control Algorithms for a Hybrid Electric Race Car Using a Two-level Model Predictive Control Scheme, IEEE Transactions on Vehicular Technology, 2017.
Mauro Salazar, Pol Duhr, Camillo Balerna, Luca Arzilli, and Christopher H. Onder, external page Minimum Lap Time Control of Hybrid Electric Race Cars in Qualifying Scenarios, IEEE Transactions on Vehicular Technology, 2019.
Camillo Balerna, Nicolas Lanzetti, Mauro Salazar, Alberto Cerofolini, and Christopher Onder, external page Optimal low-level control strategies for a high-performance hybrid electric power unit, Applied Energy, 2020.
Pol Duhr, Grigorios Christodoulou, Camillo Balerna, Mauro Salazar, Alberto Cerofolini, and Christopher H. Onder, external page Time-optimal gearshift and energy management strategies for a hybrid electric race car, Applied Energy, 2021.
Camillo Balerna, Marc Neumann, Nicolò Robuschi, Pol Duhr, Alberto Cerofolini, Vittorio Ravaglioli and Christopher Onder, external page Time-Optimal Low-Level Control and Gearshift Strategies for the Formula 1 Hybrid Electric Powertrain, Energies, 2021.
Pol Duhr, Ashwin Sandeep, Alberto Cerofolini, and Christopher H. Onder, external page Convex Performance Envelope for Minimum Lap Time Energy Management of Race Cars, IEEE Transactions on Vehicular Technology, 2022.
Pol Duhr, Daniele Buccheri, Camillo Balerna, Alberto Cerofolini, and Christopher H. Onder, external page Minimum-Race-Time Energy Allocation Strategies for the Hybrid-Electric Formula 1 Power Unit, IEEE Transactions on Vehicular Technology, 2023.
Marc-Philippe Neumann, Giona Fieni, Camillo Balerna, Pol Duhr, Alberto Cerofolini, and Christopher H. Onder, external page Low-level Online Control of the Formula 1 Power Unit with Feedforward Cylinder Deactivation, IEEE Transactions on Vehicular Technology, 2023.
Conferences
Mauro Salazar, Carlo Bussi, Fernando P. Grando, and Christopher H. Onder, external page Optimal Control Policy Tuning and Implementation for a Hybrid Electric Race Car, IFAC-PapersOnLine, 2016.
Camillo Balerna, Mauro Salazar, Nicolas Lanzetti, Carlo Bussi, and Christopher H. Onder, Adaptation Algorithms for the Hybrid Electric Powertrain of a Race Car, FISITA World Congress, 2018.
Mauro Salazar, Camillo Balerna, Eugenio Chisari, Carlo Bussi, and Christopher H. Onder, external page Equivalent Lap Time Minimization Strategies for a Hybrid Electric Race Car, IEEE Conference on Decision and Control, 2018.
Pol Duhr, Maximilian Schaller, Luca Arzilli, Alberto Cerofolini, and Christopher H. Onder, external page Time-optimal Energy Management of the Formula 1 Power Unit with Active Battery Path Constraints, European Control Conference (ECC), 2021.
Pol Duhr, Maximilian Schaller, Luca Arzilli, Alberto Cerofolini, and Christopher H. Onder, external page Analysis of optimal energy management strategies for the hybrid electric Formula 1 car under consideration of the finite battery size, FISITA 2021 World Congress.
Marc-Philippe Neumann, Gioele Zardini, Alberto Cerofolini and Christopher H. Onder, On the Co-Design of Components and Racing Strategies in Formula 1, 35th IEEE Intelligent Vehicles Symposium (IV 2024), Jeju Island, Korea, June 2-5, 2024.