The trend to reduce the engine size in automotive industry is motivated by more restrictive pollutant emissions standards. That is why engine technical definitions have become more and more complicated. The control challenge has also grown since engines are now considered as highly nonlinear multi-input multi-output systems with saturated actuators. In this context, the need for model-based control laws is bigger than ever. In this study we propose a nonlinear model predictive control strategy based on a physical engine model. Moreover, we also underline the benefit of using a thermodynamic engine term in the objective function. Finally, the design and calibration choices consciously fulfill the criterions of the use of an explicit approach for the real time implementation.