Time-optimal Control of Electric Race Cars under Thermal Constraints

Locatello, Alessandro; Konda, Mouleeswar; Borsboom, Olaf; Hofman, Théo; Salazar, Mauro

doi:10.23919/ecc54610.2021.9654968

Cited by 14 publications

(18 citation statements)

References 18 publications

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“…Moreover, we excluded the influence of thermal aspects in the study. In this case, a CVT may be even more beneficial than an FGT, as the CVT can help the EM to avoid overheating during certain demanding driving situations owing to its capability to operate the EM at any desirable working point [43]. Furthermore, a proper experimental validation on the models proposed in this thesis should be carried out in the future.…”

Section: Discussionmentioning

confidence: 99%

Decomposition-Based Integrated Optimal Electric Powertrain Design

Fahdzyana

Salazar

Donkers

et al. 2022

IEEE Trans. Veh. Technol.

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Section: Discussionmentioning

confidence: 99%

Decomposition-Based Integrated Optimal Electric Powertrain Design

Fahdzyana

Salazar

Donkers

et al. 2022

IEEE Trans. Veh. Technol.

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“…First, the relatively high fidelity of the proposed convex models could be leveraged for more general powertrain control and optimization problems [26]. Second, the methods could be extended to account for thermal dynamics [17]. Finally, the computational efficiency of our approach could be leveraged both in more comprehensive design studies (e.g., including the battery dynamics) and real-time control applications.…”

Section: Discussionmentioning

confidence: 99%

“…The components' size and the energy management strategy of an HEV has been optimized jointly, leveraging convex optimization [11] and particle swarm optimization [12], but without accounting for the transmission. Focusing on EVs, the transmission design and control problem has been studied analytically [13], and solved simultaneously using derivative-free methods [14] and convex optimization [15], which was also applied to e-racing in [16], [17]. However, all these approaches only consider FGTs or CVTs.…”

Section: Introductionmentioning

confidence: 99%

Energy-optimal Design and Control of Electric Vehicles' Transmissions

Hurk

Salazar

2021

2021 IEEE Vehicle Power and Propulsion Conference (VPPC)

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This paper presents models and optimization algorithms to jointly optimize the design and control of the transmission of electric vehicles equipped with one central electric motor (EM). First, considering the required traction power to be given, we identify a convex speed-dependent loss model for the EM. Second, we leverage such a model to devise computationally-efficient algorithms to determine the energyoptimal design and control strategies for the transmission. In particular, with the objective of minimizing the EM energy consumption on a given drive cycle, we analytically compute the optimal gear-ratio trajectory for a continuously variable transmission (CVT) and the optimal gear-ratio design for a fixed-gear transmission (FGT) in closed form, whilst efficiently solving the combinatorial joint gear-ratio design and control problem for a multiple-gear transmission (MGT), combining convex analysis and dynamic programming in an iterative fashion. Third, we validate our models with nonlinear simulations, and benchmark the optimality of our methods with mixed-integer quadratic programming. Finally, we showcase our framework in a case-study for a family vehicle, whereby we leverage the computational efficiency of our methods to jointly optimize the EM size via exhaustive search. Our numerical results show that by using a 2-speed MGT, the energy consumption of an electric vehicle can be reduced by 3% and 2.5% compared to an FGT and a CVT, respectively, whilst further increasing the number of gears may even be detrimental due to the additional weight.

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“…The original formulation was in the form of a second-order cone program [29]. Extensions included gearshift optimization with an iterative scheme [30], the optimization of a continuously variably transmission [31], the consideration of thermal constraints stemming from the electric motors using a quasi-convex formulation [32] and the optimization of the low-level operation of the F1 powertrain with NLP [33]. The maximum velocity profile has several drawbacks: While it can be easily measured at points on the circuit where the car was actually grip-limited, extrapolation backwards in distance at corner entries and forwards at corner exits is required to specify a useful constraint, relying either on imprecise heuristics or on complex vehicle dynamic simulations.…”

Section: A Literature Reviewmentioning

confidence: 99%

Convex Performance Envelope for Minimum Lap Time Energy Management of Race Cars

Duhr¹,

Sandeep²,

Cerofolini

et al. 2022

IEEE Trans. Veh. Technol.

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The optimization of the energy management of modern hybrid-electric or fully electric race cars for minimum lap time requires a description of the vehicle dynamics performance envelope, that is, of the tires' grip limit in corners, braking zones and during acceleration. In this paper, we present a computationally efficient performance envelope model in the form of convex constraints on the achievable longitudinal and lateral acceleration, on the assumption that the path on the track is given. The proposed acceleration limits are modeled velocity-dependent to take into account the effect of aerodynamic downforce present in many circuit race cars. The formulation as linear equality, inequality and second-order cone constraints allows to embed the model in a convex energy management optimization framework. To showcase the approach, we identify the model with data obtained from a state-of-the-art hybrid-electric Formula 1 car and present results for the Silverstone and Spa-Francorchamps circuits. The optimal energy management strategies can be evaluated with a computational time of less than 1 s. The optimal velocity profile subject to the performance envelope constraints is close to the measured one. The good agreement between the optimal solution and the measurement data shows that the proposed model captures the vehicle dynamics accurately enough for the purposes of energy management optimization.

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Time-optimal Control of Electric Race Cars under Thermal Constraints

Cited by 14 publications

References 18 publications

Decomposition-Based Integrated Optimal Electric Powertrain Design

Decomposition-Based Integrated Optimal Electric Powertrain Design

Energy-optimal Design and Control of Electric Vehicles' Transmissions

Convex Performance Envelope for Minimum Lap Time Energy Management of Race Cars

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