Autoregressive modeling of cycle-to-cycle correlations in homogeneous charge compression ignition combustion

Homogeneous charge compression ignition or gasoline controlled auto-ignition combustion is characterized by a strong coupling of consecutive cycles, which is caused by residuals from the predecessor cycle. Closed-loop combustion control is considered a promising technology to actively stabilize the process. Model-based control algorithms require precise prediction models that are calculated in real time. In this article, a new approach for the transient measurement of the auto-ignition process and the data-driven modeling of combustion phasing and load is presented. Gasoline controlled auto-ignition combustion is modeled as an autoregressive process to represent the cycle-to-cycle coupling effects. The process order was estimated by partial autocorrelation analysis of steady-state operation measurements. No significant correlations are found for lags that are greater than one. This observation is consistent with the assumption that cycle coupling is mainly caused by the amount of exhaust gas that is directly transferred to the consecutive combustion. Because steady-state operation results in a hard coupling of actuation and feedback variables, only minor variations of the test data can be achieved. The steady-state tests delivered insufficient data for the generalized modeling of the transient autoregressive effects. A new transient testing and measurement approach is required, which maximizes the variation of the predecessor cycle's characteristics. Dynamic measurements were performed with the individual actuation of the injection strategy for each combustion cycle. A polynomial model is proposed to predict the combustion phasing and load. The regression analysis shows no overfitting for higher polynomial orders; nevertheless, a first-order polynomial was selected because of the good extrapolation capabilities of extreme outliers. The prediction algorithm was implemented in MATLAB/Simulink and transferred to a real-time-capable engine control unit. The verification of the approach was performed by test bench measurements in dynamic operation. The combustion phasing was precisely predicted using the autoregressive model. The combustion phasing prediction error could be reduced by 53% in comparison to a state-of-the-art mean value-based prediction. This work provides the basis for the development of a closed-loop autoregressive model-based control for gasoline controlled auto-ignition combustion.