Abstract
A Vehicle with multiple drivetrains, like a hybrid electric one, is an over-actuated system that means there is an infinite number of combinations of torques that individual drivetrains can supply to provide a given total torque demand. Energy efficiency is considered as the secondary objective to determine the optimum solution among these feasible combinations. The resulting optimisation problem, which is nonlinear due to the multi-modal operation of electric machines, must be solved quickly to comply with the stability requirements of the vehicle dynamics. A theorem is developed for the first time to formulate and parametrically solve the energy-efficient torque distribution problem of a vehicle with multiple different drivetrains. The parametric solution is deployable on an ordinary electronic control unit (ECU) as a small-size lookup table that makes it significantly fast in operation. The fuel-economy of combustion engines, load transformations due to longitudinal and lateral accelerations, and traction efficiency of the off-road conditions are integrated into the developed theorem. Simulation results illustrate the effectiveness of the provided optimal strategy as torque distributors of on-road and off-road electrified vehicles with multiple different drivetrains.
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