Optimisation-oriented modelling of the NOx emissions of a Diesel engine

Asprion, Jonas; Chinellato, Oscar; Guzzella, Lino

doi:10.1016/j.enconman.2013.05.039

Cited by 38 publications

(25 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Since the model is evaluated a large number of times the model evalution needs to be fast, but still capture the qualitatitive phenomenons, be quantitatively accurate as well as have good extrapolation properties [3]. Further in order for gradient based optimization techniques to work well the model needs to be smooth in the region of interest.…”

Section: Modeling Of Diesel-electric Powertrainsmentioning

confidence: 99%

Optimal Control of Electrified Powertrains

Sivertsson

2015

View full text Add to dashboard Cite

The cover: Front: Formulation and solution of an optimal control problem, coincidentally the benchmark problem in Paper 6. Back: Positive and not so positive exit messages from the solvers used in the dissertation. Typeset with L A T E X 2εPrinted by LiU-Tryck, Linköping, Sweden 2015 i Abstract Vehicle powertrain electrification, i.e. combining the internal combustion engine (ICE) with an electric motor (EM), is a potential way of meeting the increased demands for efficient and low emission transportation, at a price of increased powertrain complexity since more degrees of freedom (DoF) have been introduced. Optimal control is used in a series of studies of how to best exploit the additional DoFs.In a diesel-electric powertrain the absence of a secondary energy storage and mechanical connection between the ICE and the wheels means that all electricity used by the EMs needs to be produced simultaneously by the ICE, whose rotational speed is a DoF. This in combination with the relatively slow dynamics of the turbocharger in the ICE puts high requirements on good transient control.In optimal control studies, accurate models with good extrapolation properties are needed. For this aim two nonlinear physics based models are developed and made available that fulfill these requirements, these are also smooth in the region of interest, to enable gradient based optimization techniques. Using optimal control and one of the developed models, the turbocharger dynamics are shown to have a strong impact on how to control the powertrain and neglecting these can lead to erroneous estimates both in the response of the powertrain as well as how the powertrain should be controlled. Also the objective, whether time or fuel is to be minimized, influences the engine speed-torque path to be used, even though it is shown that the time optimal solution is almost fuel optimal. To increase the freedom of the powertrain control, a small energy storage can be added to assist in the transients. This is shown to be especially useful to decrease the response time of the powertrain, but the manner it is used, depends on the time horizon of the optimal control problem.The resulting optimal control solutions are for certain cases oscillatory when stationary controls would have been expected. This is shown to be neither an artifact of the discretization used nor a result of the modeling assumptions used. Instead it is for the formulated problems actually optimal to use periodic control in certain stationary operating points. Measurements show that the pumping torque is different depending on whether the controls are periodic or constant despite the same average value. Whether this is beneficial or not depends on the operating point and control frequency, but can be predicted using optimal periodic control theory.In hybrid electric vehicles (HEV) the size of the energy storage reduces the impact of poor transient control, since the battery can compensate for the slower dynamics of the ICE. For HEVs the problem instead is how and when to use the b...

show abstract

Section: Modeling Of Diesel-electric Powertrainsmentioning

confidence: 99%

Optimal Control of Electrified Powertrains

Sivertsson

2015

View full text Add to dashboard Cite

show abstract

“…Because we are considering time scales in the order of entire driving cycles, the dynamics of the engine can be neglected, and the engine may be represented by a steady-state model with the inputs, engine speed ω e , torque T and control input u, * m CO 2 = f ω e , T, u (36) * m NOx = f ω e , T, u (37) The steady-state engine model, (36) and (37), is realized as a lookup table, which was derived from a validated dynamic engine model [34].…”

Section: Problem Settingmentioning

confidence: 99%

An Equivalent Emission Minimization Strategy for Causal Optimal Control of Diesel Engines

et al. 2014

Self Cite

View full text Add to dashboard Cite

One of the main challenges during the development of operating strategies for modern diesel engines is the reduction of the CO 2 emissions, while complying with ever more stringent limits for the pollutant emissions. The inherent trade-off between the emissions of CO 2 and pollutants renders a simultaneous reduction difficult. Therefore, an optimal operating strategy is sought that yields minimal CO 2 emissions, while holding the cumulative pollutant emissions at the allowed level. Such an operating strategy can be obtained offline by solving a constrained optimal control problem. However, the final-value constraint on the cumulated pollutant emissions prevents this approach from being adopted for causal control. This paper proposes a framework for causal optimal control of diesel engines. The optimization problem can be solved online when the constrained minimization of the CO 2 emissions is reformulated as an unconstrained minimization of the CO 2 emissions and the weighted pollutant emissions (i.e., equivalent emissions). However, the weighting factors are not known a priori. A method for the online calculation of these weighting factors is proposed. It is based on the Hamilton-Jacobi-Bellman (HJB) equation and a physically motivated approximation of the optimal cost-to-go. A case study shows that the causal control strategy defined by the online calculation of the equivalence factor and the minimization of the equivalent emissions is only slightly inferior to the non-causal offline optimization, while being applicable to online control.Energies 2014, 7 1231

show abstract

“…The mean-value model for the air path, adopted from [13], is extended to include the EGR, and an additional restriction representing the exhaust-gas ATS. The new model parts are briefly described next.…”

Section: Engine Modelmentioning

confidence: 99%

“…A simple mass balance is applied in the volume between turbine and ATS, and a momentum balance defines the change of the TC speed, see e.g., [1,13].…”

Section: Engine Modelmentioning

confidence: 99%

“…Hence, control oriented models (COM) of engines have been presented in several works [1,[10][11][12]. Although many COMs have been developed for the purpose of transient control of different types of engines, deriving accurate physics-based models, which cover the whole engine operating region, is a difficult and not always successfully achievable task [13]. For this reason, our approach relies on a custom-tailored model that is valid in a region around the actual state and input trajectories.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

et al. 2014

Self Cite

View full text Add to dashboard Cite

To satisfy the increasingly stringent emission regulations and a demand for an ever lower fuel consumption, diesel engines have become complex systems with many interacting actuators. As a consequence, these requirements are pushing control and calibration to their limits. The calibration procedure nowadays is still based mainly on engineering experience, which results in a highly iterative process to derive a complete engine calibration. Moreover, automatic tools are available only for stationary operation, to obtain control maps that are optimal with respect to some predefined objective function. Therefore, the exploitation of any leftover potential during transient operation is crucial. This paper proposes an approach to derive a transient feedforward (FF) control system in an automated way. It relies on optimal control theory to solve a dynamic optimization problem for fast transients. A partially physics-based model is thereby used to replace the engine. From the optimal solutions, the relevant information is extracted and stored in maps spanned by the engine speed and the torque gradient. These maps complement the static control maps by accounting for the dynamic behavior of the engine. The procedure is implemented on a real engine and experimental results are presented along with the development of the methodology.

show abstract

Optimisation-oriented modelling of the NOx emissions of a Diesel engine

Cited by 38 publications

References 45 publications

Optimal Control of Electrified Powertrains

Optimal Control of Electrified Powertrains

An Equivalent Emission Minimization Strategy for Causal Optimal Control of Diesel Engines

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

Contact Info

Product

Resources

About