Time-optimal Control of Electric Race Cars under Thermal Constraints

Alessandro Locatello, Mouleeswar Konda, O.J.T. Borsboom, Theo Hofman, Mauro Salazar

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

10 Citations (Scopus)
264 Downloads (Pure)


This paper presents a quasi-convex optimization framework to compute the minimum-lap-time control strategies of electric race cars, accurately accounting for the thermal limitations of the electric motor (EM). To this end, we leverage a previously developed thermally-unconstrained framework and extend it as follows: First, we identify a thermal network model of an interior permanent magnet EM comprising its shaft, rotor, magnets, stator, windings and end-windings, including their individual loss-models. Second, we devise a convex battery model capturing the impact of the state of energy on the battery losses. Third, in order to cope with the nonlinearities stemming from the transcription of the problem from time-domain to a position-dependent representation, we leverage an iterative algorithm based on second-order conic programming to efficiently compute the solution. Finally, we showcase our framework on the Le Mans racetrack. A comparison with high-fidelity simulations in Motor-CAD reveals that our proposed model can accurately capture the temperature dynamics of the EM, revealing the end-windings and the magnets to be the limiting components in a cold-start and a long-run operation scenario, respectively. Furthermore, our numerical results underline the considerable impact of the EM thermal dynamics on lap time, while suggesting that using a continuously variable transmission could significantly improve lap time with respect to a fixed-gear transmission.

Original languageEnglish
Title of host publication2021 European Control Conference, ECC 2021
PublisherInstitute of Electrical and Electronics Engineers
Number of pages8
ISBN (Electronic)9789463842365
Publication statusPublished - 2021
Event2021 European Control Conference, ECC 2021 - Virtual, Delft, Netherlands
Duration: 29 Jun 20212 Jul 2021
Conference number: 19
https://ecc21.euca-ecc.org/ (conference website)


Conference2021 European Control Conference, ECC 2021
Abbreviated titleECC 2021
Internet address

Bibliographical note

Publisher Copyright:
© 2021 EUCA.


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