Experimental demonstration of safe and automated in-cylinder pressure shaping using constrained extremum seeking

To support decarbonization of transport, research is focusing on advanced and highly efficient combustion concepts running on low-carbon fuels. Optimizing the performance of these complex engines over a wide range of operating conditions results in exploded control calibration efforts for traditional calibration methods. In this paper, an automated engine calibration framework based on constrained Extremum Seeking (ES) control is proposed to effectively reduce calibration times. Contrary to previous research that optimizes an efficiency metric, the proposed ES algorithm directly shapes the entire in-cylinder pressure trace by decomposing it into Principal Components (PCs) and controlling the associated weights towards their optimal reference, defined by an Ideal Thermodynamic cycle. This method finds an optimal trade-off between controllability of the PC weights and optimality, while explicitly addressing combustion safety constraints using a novel gradient based projection method for the PC weights. The proposed ES controller was successfully implemented for fuel path calibration on a single cylinder engine running in dual-fuel (diesel-gasoline) mode. Besides demonstrating optimality and convergence of the ES concept within 4 min, the handling of an arbitrary constraint on maximal in-cylinder pressure is validated. Despite the under-actuated nature of the control problem for the PC weights, the resulting ES optimal operating point is close to the actual maximal thermal efficiency point. This work highlights the practical viability of automated calibration methods through a model-free in-cylinder pressure shaping approach.