Piston temperature model oriented to control applications in diesel engines

In this paper, the development of a control-oriented piston temperature model for diesel engines is discussed. Using the underlying energy balance at the piston, a one-state piston temperature model was developed based on a thermal resistance concept. The model is composed of five sub-models: an engine model, a heat distribution model, a piston temperature model, an initial piston temperature model, and a maximum piston temperature model. In the engine model, the combustion heat transferred to the engine is calculated based on the energy balance in the cylinder chamber. The heat distribution model, which is a main feature in this model, determines the heat transferred to the piston using two maps as a function of engine speed and fuel depending on the piston cooling jet (PCJ) operation. The energy balance at the piston is applied to calculate the mean piston temperature, and the initial piston temperature is determined by the arbitration between the piston and the oil temperatures. The maximum piston temperature is estimated using a simple linear correction to the mean piston temperature. Integrating all sub-models in the Simulink platform, the model was identified and validated using piston temperature measurements under steady-state fuel steps as well as transient tests. There is a good agreement between the modeled and the measured piston temperatures with less than 4.1 degrees C of root-mean-square-error (RMSE) over transient emissions cycles (FTP-75, LA92, and HWEFT). The modeled piston temperature can be used as an input to the control strategy of variable cooling devices, such as a variable displacement oil pump.