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Energy Optimal Control for Formula One Race Car
Technical Paper
2022-01-1043
ISSN: 0148-7191, e-ISSN: 2688-3627
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English
Abstract
Formula One (F1) is considered to be the forefront of innovation for the automotive and motorsport industry. One of the key provisions has been towards the inclusion of the Energy Recovery System (ERS) since 2014 in F1 regulations. ERS comprises Motor Generator Unit-Heat (MGU-H), Motor Generator Unit-Kinetic (MGU-K) and an Energy Storage (ES). This has not only converted the conventional powertrain into a hybrid power-split device, but also imposed constraints on the fuel energy available, energy recovered and deployed by MGU-K, and charge stored in ES, along with various other parameters. Although the objective for a F1 race is to minimize lap-time, it is obvious that there is no unique control path or decision to meet this objective. This builds up needs to optimally control the power-split and energy of the system.
In this study, we propose an energy optimal control strategy for a F1 car by constructing a detailed force-balanced mathematical model of the F1 powertrain, identifying state-space variables, as well as regulated constraints and weighted-cost functions and then solving for minimizing cost function based on model-based optimization inside GT-Suite© using Discrete Optimization and Genetic Algorithm. The obtained optimal trajectory is compared to the global optimum obtained by Dynamic Programming. Finally, the results are validated over in our high-fidelity GT-Drive based F1 powertrain simulator and also compared against conventional rule-based controls for added advantage to race performance and energy minimization. The result is the optimal strategy that results in minimal energy consumption for the provided speed trajectory over a single lap.
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Citation
Javed, H. and Samuel, S., "Energy Optimal Control for Formula One Race Car," SAE Technical Paper 2022-01-1043, 2022, https://doi.org/10.4271/2022-01-1043.Also In
References
- FIA 2021
- Boretti , A. KERS Braking for 2014 F1 Cars SAE 2012 Brake Colloquium & Exhibition - 30th Annual, SAE International 2012 https://doi.org/10.4271/2012-01-1802
- Wei , C. , Hofman , T. , Ilhan Caarls , E. , and van Iperen , R. A Review of the Integrated Design and Control of Electrified Vehicles Energies 13 20 2020 10.3390/en13205454
- Ying , L. , Wang , S. , and Xiaolin , H. Finding All Solutions of Piecewise-Linear Circuits using Mixed Linear Programming Algorithm Chinese Control and Decision Conference 2008 4204 4208 10.1109/CCDC.2008.4598121
- Bellman , R.E. The Theory of Dynamic Programming Santa Monica, CA RAND Corporation 1954
- Mange , J. and Kountanis , D. Non-Linear Programming Approach to Simulation of the General Adversarial Agents Problem MILCOM 2012 - 2012 IEEE Military Communications Conference 2012 1 5 10.1109/MILCOM.2012.6415645
- Alves , A.F. , Freitas , H.F.S. , Andrade , C.M.G. , and Ravagnani , M.A.S.S. MPC, Objective Function with Economic Cost IEEE Conference on Evolving and Adaptive Intelligent Systems (EAIS) 2016 157 161 10.1109/EAIS.2016.7502507
- Li , Y. , Jiao , X. , and Jing , Y. A Real-Time Energy Management Strategy Combining Rule-Based Control and ECMS with Optimization Equivalent Factor for HEVs Chinese Automation Congress (CAC) 2017 5988 5992 10.1109/CAC.2017.8243855
- Wang , H. , Huang , Y. , He , H. , Lv , C. et al. Chapter 5 - Energy Management of Hybrid Electric Vehicles Zhang , H. , Cao , D. and Du , H. Modeling, Dynamics and Control of Electrified Vehicles Woodhead Publishing 2018 159 206 10.1016/B978-0-12-812786-5.00005-7 978-0-12-812786-5
- Liu , J. and Peng , H. Modeling and Control of a Power-Split Hybrid Vehicle IEEE Transactions on Control Systems Technology 16 6 2008 1242 1251 10.1109/TCST.2008.919447
- Sciarretta , A. , Back , M. , and Guzzella , L. Optimal Control of Parallel Hybrid Electric Vehicles IEEE Transactions on Control Systems Technology 12 3 2004 352 363 10.1109/TCST.2004.824312
- Wu , X. , Du , J. , Hu , C. , and Ding , N. The Economic Analysis of a Plug-In Series Hybrid Electric Vehicle in Different Energy Management Strategy IEEE Vehicle Power and Propulsion Conference (VPPC) 2013 1 5 10.1109/VPPC.2013.6671716
- Finesso , R. , Spessa , E. , and Venditti , M. An Unsupervised Machine-Learning Technique for the Definition of a Rule-Based Control Strategy in a Complex HEV SAE International Journal of Alternative Powertrains 5 2 2016 308 327 https://doi.org/10.4271/2016-01-1243
- Sorniotti , A. and Curto , M. Racing Simulation of a Formula 1 Vehicle with Kinetic Energy Recovery System Motorsports Engineering Conference & Exposition, SAE International 2008 https://doi.org/10.4271/2008-01-2964
- Bengolea , F. and Samuel , S. Technology Choices for Optimizing the Performance of Racing Vehicles SAE 2016 World Congress and Exhibition, SAE International 2016 https://doi.org/10.4271/2016-01-1173
- Samuel , S. and Bopaiah , K. Analysis of Energy Recovery System of Formula One Cars SAE WCX Digital Summit, SAE International 2021 https://doi.org/10.4271/2021-01-0368
- Salazar , M. , Elbert , P. , Ebbesen , S. , Bussi , C. et al. Time-Optimal Control Policy for a Hybrid Electric Race Car IEEE Transactions on Control Systems Technology 25 6 2017 1921 1934 10.1109/TCST.2016.2642830
- Ebbesen , S. , Salazar , M. , Elbert , P. , Bussi , C. et al. Time-Optimal Control Strategies for a Hybrid Electric Race Car IEEE Transactions on Control Systems Technology 26 1 2018 233 247 10.1109/TCST.2017.2661824
- Salazar , M. , Balerna , C. , Elbert , P. , Grando , F.P. et al. Real-Time Control Algorithms for a Hybrid Electric Race Car Using a Two-Level Model Predictive Control Scheme IEEE Transactions on Vehicular Technology 66 12 2017 10911 10922 10.1109/TVT.2017.2729623
- Silvas , E. , Hofman , T. , Murgovski , N. , Etman , L.F.P. et al. Review of Optimization Strategies for System-Level Design in Hybrid Electric Vehicles IEEE Transactions on Vehicular Technology 66 1 2017 57 70 10.1109/TVT.2016.2547897
- Bopaiah , K. and Samuel , S. Strategy for Optimizing an F1 Car’s Performance Based on FIA Regulations SAE International Journal of Advances and Current Practices in Mobility 2 5 2020 2516 2530 https://doi.org/10.4271/2020-01-0545
- Grimm , D. Model Predictive Control for the Thermal System of an Electric Vehicle Sweden Chalmers University of Technology 2019
- Zhou , H. , Xu , Z. , Liu , L. , Liu , D. et al. A Rule-Based Energy Management Strategy Based on Dynamic Programming for Hydraulic Hybrid Vehicles Mathematical Problems in Engineering 2018 2018 9492026 10.1155/2018/9492026
- Samuel , S. Route Selection Strategy for Hybrid Vehicles Based on Energy Management and Real Time Drive Cycles WCX World Congress Experience, SAE International 2018 https://doi.org/10.4271/2018-01-0995
- Asfoor , M.Sh. , Beyerlein , S.W. , Lilley , R. , and Santora , M. Discrete Grid Optimization of a Rule-Based Energy Management Strategy for a Formula Hybrid Electric Vehicle SAE 2015 World Congress & Exhibition, SAE International 2015 https://doi.org/10.4271/2015-01-1212
- Eiben , A.E. and Smith , J.E. Introduction to Evolutionary Computing Berlin Heidelberg Springer-Verlag 2003 10.1007/978-3-662-05094-1 978-3-642-07285-7
- Stiegeler , M. , Sauter , M. , Lindenmaier , J. , and Kabza , H. Impact of Improved Cost Function-Based Torque Split Algorithm on Different Drive Train Topologies IEEE Vehicle Power and Propulsion Conference 1 5 2006 10.1109/VPPC.2006.364306