Human-in-the-loop Energy and Thermal Management for Electric Racing Cars through Optimization-based Control

This paper presents an energy and thermal management system for electric race cars, where we tune a lift-off-throttle signal for the driver in real-time to respect energy budgets and thermal constraints. First, we compute the globally optimal state trajectories in a real-time capable solving time, optimizing a 47-kilometer horizon in 2.5 seconds. Next, for safe operation with a human driver, we simplify it to a maximum-power-or-coast operation in full-throttle regions (straights). Thereby, both the positions from which the vehicle should start coasting and the optimal throttle map are subject to tuning. To this end, we define the coasting sections with a threshold on the co-state trajectory of the kinetic energy from the optimal solution. We devise an online implementable bisection algorithm to tune this threshold and adapt it using PI feedback. Finally, we validate the proposed approach for an electric endurance race car and compare three variants with varying implementation challenges: one re-optimizing and updating the kinetic co-state trajectory online, one applying only the bisection algorithm online, and one relying exclusively on feedback control. Our results show that, under typical racing disturbances, our energy management can achieve stint times ranging from less than 0.056\% to 0.22\% slower compared to offline optimization with a priori knowledge of disturbances, paving the way for on-board implementations and testing.