Time-optimal Design and Control of Electric Race Cars Equipped with Multi-speed Transmissions

This paper presents a framework to jointly optimize the design and control of an electric race car equipped with a multiple-gear transmission (MGT), specifically accounting for discrete gearshift dynamics. We formulate the problem as a mixed-integer optimal control problem (MIOCP), and deal with its complexity by combining convex optimization and Pontryagin's Minimum Principle (PMP) in a computationally efficient iterative algorithm satisfying necessary conditions for optimality upon convergence. Finally, we leverage our framework to compute the achievable lap time of a race car equipped with a fixed-gear transmission (FGT), a continuously variable transmission (CVT) and an MGT with 2 to 4 speeds, revealing that an MGT can strike the best trade-off in terms of electric motor control, and transmission weight and efficiency, ultimately yielding the overall best lap time.