Control-Oriented Exhaust Gas Temperature Modelling Based on Wiebe Equation

Exhaust gas temperature is one of the main parameters under engine manufacturers' focus due to its effects on both turbocharger durability and catalyst efficiency. Typically, the measurement of such variable at the test bench is carried out by using thermocouples (TCs), which are not available for on-board applications. For this reason, an accurate and reliable model for Real-Time (RT) calculation of this variable is particularly important. In this work a control-oriented model for the estimation of exhaust temperature in Spark Ignition (SI) engines is developed and validated exploiting experimental data. A fundamental quantity that has to be necessarily known is the temperature of the gas within the exhaust manifold or at the Exhaust Valve Opening (EVO). The first part of this paper deals with the development of a zero-dimensional (0-D) combustion model, identifying the main parameters of the Wiebe function with an automatic optimization routine. Such method allows to accurately reproduce the in-cylinder pressure trace and calculate the temperature of the gas at EVO. Hence, an analytical function that converts such temperatures into the exhaust manifold ones is developed by analyzing the experimental measurements of TCs installed in the exhaust manifold under steady-state operating conditions. This is the main reason why the proposed approach cannot be considered fully empirical. The resulting 0-D model is not suitable for an RT application nor to be implemented in an Engine Control Unit (ECU) due to a differential equation that needs to be solved in the angular domain. For this reason, in the second part of the article, a control-oriented model is developed by using an analytical methodology, which exploits the combustion model and the temperature analytical function presented in the first part. Finally, the control-oriented model is coupled with a TC dynamics RT model, and both are validated under transient conditions.