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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 286538, 21 pages
Research Article

Optimal Control of Diesel Engines: Numerical Methods, Applications, and Experimental Validation

1Institute for Dynamic Systems and Control, ETH Zurich, Sonneggstraße 3, 8092 Zurich, Switzerland
2FPT Motorenforschung AG, Schlossgasse 2, 9320 Arbon, Switzerland

Received 6 October 2013; Revised 20 November 2013; Accepted 20 November 2013; Published 5 February 2014

Academic Editor: Hui Zhang

Copyright © 2014 Jonas Asprion et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In response to the increasingly stringent emission regulations and a demand for ever lower fuel consumption, diesel engines have become complex systems. The exploitation of any leftover potential during transient operation is crucial. However, even an experienced calibration engineer cannot conceive all the dynamic cross couplings between the many actuators. Therefore, a highly iterative procedure is required to obtain a single engine calibration, which in turn causes a high demand for test-bench time. Physics-based mathematical models and a dynamic optimisation are the tools to alleviate this dilemma. This paper presents the methods required to implement such an approach. The optimisation-oriented modelling of diesel engines is summarised, and the numerical methods required to solve the corresponding large-scale optimal control problems are presented. The resulting optimal control input trajectories over long driving profiles are shown to provide enough information to allow conclusions to be drawn for causal control strategies. Ways of utilising this data are illustrated, which indicate that a fully automated dynamic calibration of the engine control unit is conceivable. An experimental validation demonstrates the meaningfulness of these results. The measurement results show that the optimisation predicts the reduction of the fuel consumption and the cumulative pollutant emissions with a relative error of around 10% on highly transient driving cycles.