Online optimisation of fuel consumption subject to NOx constraints

Abstract

Several variations of extremum seeking algorithms have been successfully used to optimise the fuel consumption in automotive engines, albeit without explicit consideration of the emissions constraints that dictate whether the engine meets legislated standards. By treating the emissions constraints as requiring satisfaction on average and assuming measurable tailpipe emissions, an augmented extremum seeking algorithm is proposed in this paper. The suggested approach utilises a constrained optimisation method developed for static plants that considers both the original cost function and a constraint function representing the satisfaction of the imposed average constraint. Existing theoretical results are modified to guarantee semi-global practical stability of the approach. The approach is then applied to a high fidelity engine and aftertreatment system simulation to find the optimal spark advance that minimises fuel consumption subject to an NOx constraint, under the assumption that appropriate sensor feedback is available. The simulation results demonstrate the potential of the proposed approach, and suggest other existing extremum seeking schemes can be readily augmented with the ability to satisfy constraints in an averaged sense.