The intake manifold model of turbocharged engine is constructed and a high speed calculation algorithm is developed for model based predictive control in real time. The model is built according to the analysis of its thermodynamic and hydrodynamic characteristics and the sampled experiment data. The model equations are expressed by a set of differential equations with switching (bifurcation) on the right hand side. The switching surface is divided into two parts: sliding and crossing. We analyze the switching situations existing on the surface and develop the well-defined control semantics for managing the behavior discontinuities in the case of mode transition. The calculation algorithm can seamlessly integrate the continuous behavior and the discrete mode switching together. Using this method we can solve this model under entire region of input throttle angles. Furthermore the stability is greatly increased and the calculation time is greatly reduced for the real time control system.