Abstract
A broad literature deals with torque-vectoring (TV) algorithms based on direct yaw moment control (DYC), which continuously generate longitudinal tire forces that are different on the left and right vehicle sides. Such set-ups enable desirable yaw rate and sideslip responses in normal and extreme driving conditions. However, they imply two electric powertrains per axle, or controllable differentials, and therefore the related controllers are not applicable to typical production electric vehicle layouts with a single centralized electric machine and open differential per axle. Nevertheless, in proximity of the limit of handling, the cornering response of conventional all-wheel-drive electric vehicles with one motor per axle can benefit from front-to-rear axle torque-vectoring (ATV), which, by controlling the longitudinal force distribution between the front and rear axles, indirectly modifies the yaw moment contribution due to the lateral tire forces. Only a few studies exploit this option, with limited coverage, e.g., without considering the energy efficiency aspects and the electronic stability control (ESC) function actuating the friction brakes. To address the gap, this paper presents real-time capable nonlinear model predictive controllers (NMPCs) for ATV and ESC, targeting: i) energy consumption reduction in normal driving, through powertrain and tire slip power loss limitation; and ii) yaw rate, sideslip angle and wheel slip control at the limit of handling, by considering the trade-off between powertrain and friction brake actuation. The performance is assessed through simulations with a validated vehicle model, and experiments on a vehicle demonstrator. With respect to benchmarking rule-based controllers, the results show that the NMPCs bring significant reductions of the yaw rate errors and friction brake power losses, while increasing the exit speed in acceleration-during-cornering conditions.