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

Abstract

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.

Dynamic Feedforward Control of a Diesel Engine Based on Optimal Transient Compensation Maps

“…Despite that, a cumulative constraint for soot emissions is anyways set during the optimization, but more permissive, otherwise the optimization could be negatively effected, resulting in a suboptimal solution for the main objective. Detailed information about the numerical methods required for optimal control of diesel engines may be found in [14].…”

“…This paper focuses on this topic, and presents the numerical methods and the testbench setup to derive optimal transient compensation maps, implementable in a FF control structure. The proposed approach is characterized by a combination of physics-based and set-point relative mathematical models, in synergy with optimal control of diesel engines [14,15].…”

Optimal Control ofWastegate Throttle and Fuel Injection for a Heavy-Duty Turbocharged Diesel Engine During Tip-In Throttle and Wastegate Developed for Optimal Control Applications

“…For a comprehensive treatment of modeling diesel engines for optimal control, the reader is referred to Asprion (2013), and for the modeling of hybrid electric powertrains for optimal control the reader is referred to Sivertsson (2015). Numerical optimal control is extensively treated in Betts (2010);Biegler (2010).…”

Optimal Control for Automotive Powertrain Applications

“…These studies, whose main characteristics are summarized in table 2.1, calculate the optimal trajectories for the engine controls but limiting to short transients that last 30 seconds in the best cases. It was in 2014 when Asprion et al addressed the complete control of an engine for longer driving cycles by calculating the optimal trajectories for fueling rate, VGT opening, SOI and rail pressure, minimizing fuel consumption [62]. This work focused on the capabilities of different DM approaches to address this OCP, as well as the potential of the solution to derive dynamic controls.…”

“…A long problem such as the one addressed in [62] is computationally expensive, and in many situations they can be avoided. For example, it is pointless to extend the OCP beyond a couple of seconds for a VGT control to perform a load transient where Table 2.1: Main characteristics of engine control related works that can be found in literature, namely the minimization objective, the controls whose trajectories are optimized, the optimization method and the control horizon.…”