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The definition of the energy management strategy for a hybrid electric vehicle is a key element to ensure maximum energy efficiency. The ability to optimally manage the on-board energy sources, i.e., fuel and electricity, greatly affects the final energy consumption of hybrid powertrains. In the case of plug-in series-hybrid architectures, such as Range-Extender Electric Vehicles (REEVs), fuel efficiency optimization alone can result in a stressful operation of the range-extender engine with an excessively high number of start/stops. Nonetheless, reducing the number of start/stops can lead to long periods in which the engine is off, resulting in the after-treatment system temperature to drop and higher emissions to be produced at the next engine start.

The nonlinear behavior of automotive powertrains is mainly due to the presence of backlash between engaging components. In particular, during tip-in or tip-out maneuvers, backlash allows the generation of impacts that negatively affect the vehicle NVH performance. Due to the faster response of electric motors with respect to conventional internal combustion engines, this problem is even more critical for electric vehicles. In order to employ numerical optimal control methods for backlash compensation, the system states have to be known. In this paper, an electric powertrain is modeled as a two-mass oscillator with lumped backlash. This model estimates the system states when in no-contact mode while a Kalman filter that relies only on commonly available speed measurements is active in the contact phase. The powertrain model is validated using experimental data collected during vehicle testing and the online estimated half-shaft torque is shown.