Data-Based In-Cylinder Pressure Model with Cyclic Variations for Combustion Control: An RCCI Engine Application

Cylinder-pressure-based control is a key enabler for advanced pre-mixed combustion concepts. In addition to guaranteeing robust and safe operation, it allows for cylinder pressure and heat release shaping. This requires fast control-oriented combustion models. Over the years, mean-value models have been proposed that can predict combustion metrics (e.g., gross indicated mean effective pressure ((Formula presented.)), or the crank angle where 50% of the total heat is released (CA50)) or models that predict the full in-cylinder pressure. However, these models are not able to capture cycle-to-cycle variations. The inclusion of the cycle-to-cycle variations is important in the control design for combustion concepts, like reactivity-controlled compression ignition, that can suffer from large cycle-to-cycle variations. In this study, the in-cylinder pressure and cycle-to-cycle variations are modelled using a data-based approach. The in-cylinder conditions and fuel settings are the inputs to the model. The model combines principal component decomposition and Gaussian process regression. A detailed study is performed on the effects of the different hyperparameters and kernel choices. The approach is applicable to any combustion concept, but is most valuable for advance combustion concepts with large cycle-to-cycle variation. The potential of the proposed approach is successfully demonstrated for a reactivity-controlled compression ignition engine running on diesel and E85. The average prediction error of the mean in-cylinder pressure over a complete combustion cycle is (Formula presented.) bar and of the corresponding mean cycle-to-cycle variation is (Formula presented.) bar². This principal-component-decomposition-based approach is an important step towards in-cylinder pressure shaping. The use of Gaussian process regression provides important information on cycle-to-cycle variation and provides next-cycle control information on safety and performance criteria.