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Oil & Gas Science and Technology – Rev. IFP, Vol. 62 (2007), No. 4, pp. 523-538

Oil & Gas Science and Technology – Rev. IFP, Vol. 62 (2007), No. 4, pp. 523-538 Copyright c 2007, Institut français du pétrole DOI: 10.2516/ogst:2007042 Modeling and Control of Turbocharged SI and DI Engines L. Eriksson Vehicular Systems, Dept. of Electrical Engineering Linköping University, SE-58183 Linköping - Sweden e-mail: larer@isy.liu.se Résumé — Modélisation et contrôle de moteurs suralimentés à allumage commandé et à injection directe — Une méthodologie pour la modélisation par composants de moteurs suralimentés est décrite et appliquée. Plusieurs modèles à composants sont considérés et évalués. De plus, de nouveaux modèles sont élaborés incluant l’efficacité du compresseur, le ﬂux dans le compresseur, et le ﬂux dans la turbine. Enﬁn, deux exemples d’application qui utilisent cette méthodologie et ces modèles de composants sont présentés. Les applications sont, d’une part, la conception d’observateurs et le contrôle du rapport air/carburant de moteurs à allumage commandé, et d’autre part la conception du contrôle de moteurs à injection directe incluant un turbocompresseur à géométrie variable et le recyclage de gaz d’échappe- ment. Abstract — Modeling and Control of Turbocharged SI and DI Engines — A component based mod- eling methodology for turbocharged engines is described and applied. Several component models are compiled and reviewed. In addition new models are developed for the compressor efficiency, compressor ﬂow, and turbine ﬂow. Two application examples are ﬁnally given where the modeling methodology and the component models have been used. The applications are, ﬁrstly, observer design and air/fuel ratio control of SI engines and, secondly, control design of DI engines with VGT and EGR. New Trends on Engine Control, Simulation and Modelling Avancées dans le contrôle et la simulation des systèmes Groupe Moto-Propulseur 524 Oil & Gas Science and Technology – Rev. IFP, Vol. 62 (2007), No. 4 INTRODUCTION Environmental concern coupled to pollutants and consump- tion of our ﬁnite resources is driving the technological devel- opment of engines and vehicles. Higher demands from leg- islators and customers are met by introducing new techno- logical solutions that give the system designer more degrees of freedom to utilize when optimizing a vehicles perfor- mance. One interesting path for improving the fuel eﬃ- ciency is to downsize and supercharge the engines [1-3]. These new systems combined with the already complex engines require proper control and gives the controls engi- neer a more complex task to handle. One way to handle the complexity is to utilize model-based methods where the components and the complex interactions between them are described by models. These models are utilized in a central way in the design of the control and supervision systems. Mean Value Engine Models (MVEM) have a complexity that is favorable for design of control and supervision sys- tems, where they form an excellent basis for e.g. control and observer design. Consequently have they been success- fully utilized in several aspects of engine management [4-6] and engine supervision [7, 8]. These MVEM are usually formulated as a non-linear Ordinary Diﬀerential Equation (ODE) which gives a model complexity suitable for control design, as opposed to wave action models based on partial diﬀerential equations that are used for more detailed (and computationally expensive) modeling. A modeling methodology for MVEM, based on a com- ponent view, was outlined in [9] and applied to a turbo charged spark ignited (SI) engine. This methodology, that focuses on the gas ﬂows in the engine, has been reﬁned and successfully applied in several projects. The methodology is based upon a component view of the system and many of the components used are well known and therefore the majority of modeling work in the paper is focused on new insights on component models that describe the compressor and turbine performance. Finally two control applications are described where the modeling methodology has success- fully been applied and where the models have been used in a central way in the development of the controller. 1 MODELING METHODOLOGY Eﬃcient reusage of models is important from an industrial perspective, where equations that have been implemented and thoroughly validated can be reused to give leverage in new projects. It is also beneﬁcial if the models also cover a wide variety of engines. Figure 1 shows two tur- bocharged engines, one gasoline and one diesel, the main diﬀerence between them is the absence of throttle in the diesel engine and a Variable Geometry Turbine (VGT) on the diesel engine instead of a wastegate (there are also diesel engines with wastegate and with a throttle on the intake side). As Figure 1 shows many components can be found on both engines and therefore a component based approach to the modeling can facilitate the reusage of the models in a wide variety of projects. The general modeling methodology applied here is to divide the system into components and then deﬁning bound- aries and interactions with the aid of physics and thermo- dynamics. The components are arranged according to a scheme where control volumes are placed in series with ﬂow governing components such as for example compres- sor, engine, or restrictions. These ﬂow governing compo- nents are here collectively named restrictions. Control vol- umes have the mass and energy conservation equations and the restrictions determine the transport of mass and energy. Examples of control volumes are those where mass is col- lected: intake manifold, exhaust manifold, all the sections of the pipes between components including the inlets and outlets of the upstream and downstream components respec- tively. Examples of restrictions are: air ﬁlter, compressor, intercooler, throttle, engine, turbine, catalyst, exhaust sys- tem. To exemplify this methodology the ﬁrst part of the intake system is realized as follows: Air ﬁlter-pipe-compressor-pipe-intercooler restr - CV - restr - CV - restr With this component view on the modeling it is easy to develop and maintain a library with a set of generic compo- nents. 2 COMPONENT MODELS With the division into components, given above, the compo- nent models have to be developed but there are also design choices with the interfaces. The main equations in the con- trol volumes are mass and energy balances and therefore the natural choice is to have the mass and energy ﬂows given by the restrictions. Furthermore it is also beneﬁcial to base the model equation on measurable quantities, such as mass ﬂow, pressure and temperature, since the models can then easily be tuned and validated. Consequently it is natural to select the pressure and the temperature as state variables for the control volumes and the mass ﬂow and temperature of the ﬂowing ﬂuid as the transported properties in the restrictions. 2.1 Control Volumes For control volumes there two options, either to use a sim- ple mass balance and the ideal gas state equation, or to use both the mass balance and energy balance. With the ﬁrst approach the diﬀerential equation for the pressure p in the control volume then becomes dp dt = RT V (Wi −Wo) L Eriksson / Modeling and Control of Turbocharged SI and DI Engines 525 Waste Turbine Compressor Turbine Shaft Gate Air filter Air flow meter Catalyst Engine Intercooler Throttle Manifold Exhaust Manifold Intake EGR Cooler VG Turbine Compressor Turbine Shaft EGR Valve Air filter Engine Manifold Exhaust Manifold Intake Aftercooler Exhaust Pipe Figure 1 Left: A sketch showing frequently used components in a turbocharged SI engine. Right: A sketch showing frequently used components in a turbocharged diesel (CI) engine. where W denotes mass ﬂow. This model violates the energy equation but it gives good agreement with measured pres- sures and it is simple to implement and tune to dynamic measurement data from engines. The other choice is to use both the energy and mass balance which gives the following diﬀerential equations for the pressure and temperature m = pV RT dT dt = 1 m cv Wicv(Ti −T) + R(TiWi −TWo) + ˙ Q dp dt = RT V (Wi −Wo) + mR V dT dt (1) For a longer discussion about these models and the dif- ferences between them see [10]. 2.2 Flow Restrictions 2.2.1 Components with Pressure Losses Several components that are placed the air path of the engine have pressure losses over them e.g. air ﬁlter, intercooler, catalyst, exhaust system, and pipe bends. They are well described by the equation for incompressible and turbu- lent ﬂow, see for example [11], where the pressure drop has a quadratic dependence on the mass ﬂow, pus −pds = C fr R Tus pus · W2, where pus is upstream pressure, pds is down- stream pressure, and Tus is upstream temperature. To ﬁt into the modeling framework it is rewritten so that it returns the mass ﬂow W as function of the pressure and temperature W = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ pus(pus−pds) CfrTus pus −pds ≥plin pus CfrTus pus−pds √plin otherwise (2) Another aspect that is important to take into account is that the uploads/Management/ modeling-and-control.pdf