Model predictive control for multimode power-split hybrid electric vehicles: Parametric internal model with integrated mode switch and variable meshing losses

Model predictive control (MPC) is one of the most promising energy management strategies for hybrid electric vehicles. However, owing to constructive complexity, the multimode power-split powertrain requires dedicated mathematical tools to model the mode switch and transmission power losses within the internal model of the controller. Thus, the transmission losses are usually neglected and the mode switch is optimised through offline simulations. This paper proposes an MPC internal model relying on a parametric approach available in the literature, which provides a unique formulation for modelling any power-split transmission and assesses the transmission meshing losses. The objectives, which cover a gap in the literature, are: 1) to integrate the discrete problem of the mode switch in a continuous formulation of the internal model; 2) to compare MPC internal models with different complexity, and evaluate how the consideration of meshing losses and efficiency of the electric machines affect the controller performance. The results on a case study vehicle, i.e., the Chevrolet Volt, suggest that a simplified internal model deteriorates the fuel consumption performance by less than 2 %, while the integrated mode switch is comparable to the offline strategy.