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This paper describes the development of a control-oriented model that allows the simulation of the Internal Combustion Engine (ICE) thermodynamics, including pressure wave effects. One of the objectives of this work is to study the effects of a Variable Valve Timing (VVT) system on the behavior of a single-cylinder, four-stroke engine installed on a motor scooter. For a single cylinder engine running at relatively high engine speeds, the amount of air trapped into the cylinder strongly depends on intake pressure wave effects: it is essential, therefore, the development of a model that has the ability to resolve the wave-action phenomena, if successful simulation of the VVT system effects is to be performed.

While the Diesel Particulate Filter (DPF) is actually a quasi-standard equipment in the European Diesel passenger cars market, an interesting solution to fulfill NOx emission limits for the next EU 6 legislation is the application of a Selective Catalytic Reduction (SCR) system on the exhaust line, to drastically reduce NOx emissions. In this context, one of the main issues is the performance of the SCR system during cold start and warm up phases of the engine. The exhaust temperature is too low to allow thermal activation of the reactor and, consequently, to promote high conversion efficiency and significant NOx concentration reduction. This is increasingly evident the smaller the engine displacement, because of its lower exhaust system temperature (reduced gross power while producing the same net power, i.e., higher efficiency).

This paper presents an optimization algorithm, based on discrete dynamic programming, that aims to find the optimal control inputs both for energy and thermal management control strategies of a Plug-in Hybrid Electric Vehicle, in order to minimize the energy consumption over a given driving mission. The chosen vehicle has a complex P1-P4 architecture, with two electrical machines on the front axle and an additional one directly coupled with the engine, on the rear axle. In the first section, the algorithm structure is presented, including the cost-function definition, the disturbances, the state variables and the control variables chosen for the optimal control problem formulation. The second section reports the simplified quasi-static analytical model of the powertrain, which has been used for backward optimization. For this purpose, only the vehicle longitudinal dynamics have been considered.