Time-optimal Control Strategies for Electric Race Cars with Different Transmission Technologies

Abstract

This paper presents models and optimization methods to rapidly compute the achievable lap time of a race car equipped with a battery electric powertrain. Specifically, we first derive a quasi-convex model of the electric powertrain, including the battery, the electric machine, and two transmission technologies: a single-speed fixed gear and a continuously variable transmission (CVT). Second, assuming an expert driver, we formulate the time-optimal control problem for a given driving path and solve it using an iterative convex optimization algorithm. Finally, we showcase our framework by comparing the performance achievable with a single-speed transmission and a CVT on the Le Mans track. Our results show that a CVT can balance its lower efficiency and higher weight with a higherefficiency and more aggressive motor operation, and significantly outperform a fixed single-gear transmission.

Time-optimal Control of Electric Race Cars under Thermal Constraints

“…1, frames the time-optimal control problem and proposes an iterative solution algorithm to effectively solve it. The electro-mechanical modeling of the powertrain and the proposed iterative optimization approach are inspired by our previous work [14]. In this paper, we identify and validate a thermal network meticulously characterizing the temperature dynamics of the EM's components and an accurate state-of-energy dependent battery model, which we include in the minimum-lap-time control problem.…”

“…In line with [4], [14], we formulate the time-optimal control problem in space domain, so that it becomes a finite-horizon optimal control problem accommodating positiondependent parameters such as the maximum speed profile. This way, our framework needs to be defined in terms of forces instead of power.…”

“…This section presents a convex model of the longitudinal vehicle dynamics in space domain taken from [4], [14]. The kinetic energy is related to speed in a relaxed convex form as…”

“…Statement of contribution: Against this backdrop, this paper presents an extension of the quasi-convex optimization framework outlined in [14] to compute the time-optimal control strategies of a battery electric race car, explicitly accounting for the thermal constraints on the EM and the impact of the transmission technology on the overall performance. In particular, we first derive an almost-convex model of the race car, including an LPTN capturing the temperature dynamics of the EM and a state-of-energy-dependent battery model.…”

A Convex Optimization Framework for Minimum Lap Time Design and Control of Electric Race Cars

“…Third, we showcase our convex framework with case studies comparing the performance of different transmission technologies and component sizes on the Le Mans race track. A preliminary version of this paper was presented at the 2020 IEEE Vehicular Power and Propulsion Conference [42]. In this extended version, we identify a CVT model that explicitly captures the dependence of its losses on input speed, output speed, and input power.…”