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

Abstract

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

“…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.…”

“…12. Silverstone Circuit: Investigation of the split acceleration approach given in (31). Shown are the positive and negative components a + p and a − p of the propulsive acceleration, as well as their product.…”

Energy-optimal Design and Control of Electric Vehicles' Transmissions

“…Similarly to [15], [16], the motor mass m m is modeled linear in relation to the maximum motor power P m,max as…”

“…where P m,loss represents the EM losses. While previous convex EM models, such as the quadratic model from [16], explicitly depend on both the EM speed and power, in this paper we devise a different approach based on the fact that the mechanical EM power P m to be provided is known in advance. Specifically, for each EM power value at time t, P m , we determine the power loss as a function of the EM speed ω m (t):…”

“…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.…”