On optimal control of the wastegate in a turbocharged SI engine

turbocharged SI engine

ROBERTO ARGOLINI - VIVIANA BLOISI

Master’s Degree Project

Stockholm, Sweden June 2007

Sommario

The project aims to improve positive torque transient response through more advanced wastegate controllers than what are used today. All controllers are developed for a standard General Motors turbocharged engine. In many tur-bocharged SI engines, a wastegate is used for preventing the turbine to overrun and to decrease the pumping loss. Today, the wastegate is controlled by a PI controller, which tries to fulfill a compromise between fuel consumption and torque response by regulating the wastegate position.

A nonlinear Mean Value Engine Model (MVEM) of this engine, with 13 states and linearized in 45 different working points, is used. The original mod-el, implemented in Matlab/Simulink, has been enriched with new features, like lambda and spark advance efficiencies and the related exhaust tempera-ture correction.

The project aims to do a theoretical analysis to find the optimal control of wastegate position, investigating also spark retard and fuel enrichment during a positive torque transient. First a solution for achieving optimal wastegate control is designed, based on Linear Quadratic (LQ) approach. Since the op-timal control strategy is expected to vary quite much for different working points, a gain scheduling architecture has been investigated.

An independent lambda controller has been developed, in order to maxi-mize the lambda efficiency and quicken the torque response during transient.

Since the system operates near a constraint boundary, another solution ba-sed on Model Predictive Control (MPC) of the wastegate has been investigated. The MPC design has been extended also to a MIMO formulation, adding the throttle and the air to fuel ratio as control inputs, and the trade off between fast torque response and fuel economy is analyzed. A complete realtime MPC im-plementation, with the capability for automatic code generation in the dSpace microAutobox environment, requires the model, now with 13 states, to be re-duced to a minimum state space order. The extent of model reduction that is required and the possible performance deterioration have been investigated.

Indice

2.2 Incompressible Flow restrictions . . . 8

2.2.1 Air Filter . . . 8

2.2.2 Intercooler . . . 8

2.2.3 Exhaust System . . . 9

2.3 Compressible Flow Restrictions . . . 10

2.3.1 Throttle flow . . . 10

2.3.2 Wastegate flow . . . 10

2.4 Engine . . . 10

2.4.1 Mass flow into the cylinders . . . 10

2.4.2 Volumetric efficiency . . . 11

2.4.3 Exhaust Manifold Out Temperature . . . 11

2.5 Compressor . . . 11

2.5.1 Compressor - Pressure Model . . . 12

2.5.2 Compressor - Air Mass Flow Model . . . 12

2.5.3 Compressor - Efficiency Model . . . 12

2.6 Turbine . . . 13

2.6.1 Turbine - Pressure Model . . . 13

2.7 Model Dynamics . . . 13

2.7.1 Control volumes . . . 14

2.7.2 Turbo Shaft Dynamics . . . 15

2.8 Torque generation . . . 16 v

2.9 Fuel path and (A/F)-ratio . . . 19 2.10 Fuel consumption . . . 19 2.11 Conclusions . . . 20 3 Simulink Model 21 3.1 Driver . . . 21 3.2 Car . . . 21 3.3 Engine Structure . . . 23 3.3.1 Model Simplifications . . . 25 3.3.2 Model Inputs . . . 26 3.3.3 Model States . . . 26 3.3.4 Model Output . . . 27

3.3.5 Maps for parameters representation . . . 28

3.4 Performance Limiting Factors . . . 28

3.4.1 Knock . . . 28

3.4.2 Surge . . . 29

3.4.3 Limits on air to fuel ratio . . . 29

3.5 Engine Management System (ECM) . . . 30

3.5.1 Map-Based Control . . . 31

3.5.2 Throttle control . . . 32

3.5.3 Lambda Control . . . 33

3.5.4 Fuel Control . . . 33

3.5.5 Spark Advance Control . . . 34

3.6 Turbo Control . . . 36

3.6.1 Wastegate Control . . . 36

3.7 System Modifications . . . 37

3.7.1 Bypass Valve . . . 37

3.7.2 Lambda and SA Efficiency . . . 37

3.7.3 Temperature Correction Map . . . 39

3.7.4 Volumetric Efficiency . . . 39

3.7.5 WG Pressure valve . . . 42

3.8 Changes in the ECM . . . 44

3.9 Conclusions . . . 44

4 Validation of the NonLinear Model 45 4.1 Experiment setup . . . 45

4.2 Data processing . . . 49

4.3 Validation . . . 49

5 Analysis of linearized model 55

5.1 Linearized Model . . . 55

5.1.1 Model linearization . . . 56

5.2 Validation of the linearized model . . . 58

5.3 Linear Analysis . . . 62

5.3.1 SISO Analysis . . . 63

5.3.2 Controllability and observability . . . 65

5.4 Open Loop system behavior . . . 66

5.4.1 Step in the WG . . . 66

5.4.2 Pulse in the WG with constant throttle . . . 66

5.4.3 Pulse in the WG with step in throttle . . . 69

5.5 Conclusions . . . 70

6 Optimal Wastegate Control 73 6.1 Spark-ignited engines . . . 73

6.2 Turbocharging . . . 74

6.3 Wastegate . . . 75

6.3.1 Transient response and turbo lag . . . 76

6.3.2 Open Loop System Characteristics . . . 79

6.3.3 Dealing with constraints . . . 80

6.3.4 Control Problem formulation . . . 81

6.4 Linear Quadratic Regulation (LQR) . . . 82

6.5 Optimal State Feedback . . . 83

6.5.1 Stability and robustness . . . 84

6.6 LQR for non-zero set points . . . 86

6.7 Tuning . . . 87

6.8 Integral action in LQ control . . . 88

6.9 Simulations . . . 90

6.9.1 LQ on Linearized System . . . 91

6.9.2 LQR on Nonlinear System . . . 94

6.10 Gain Scheduling Strategy for LQ Control . . . 99

6.10.1 Variable engine speed . . . 101

6.10.2 Variable engine speed with 3 controllers . . . 105

6.11 Conclusions . . . 105

7 Lambda and SA Control 109 7.1 Lambda . . . 109

7.2 Control Design . . . 111

7.2.2 Dynamic Lambda Control . . . 112 7.3 Simulations . . . 113 7.4 Spark Advance . . . 116 7.5 Conclusions . . . 116 8 MPC 119 8.1 MPC Overview . . . 119 8.1.1 Parameters Tuning . . . 122

8.2 Implementation in Simulink using Mpc Toolbox . . . 123

8.2.1 Building the MPC object . . . 124

8.2.2 Prediction Model . . . 126 8.2.3 Offsets . . . 127 8.2.4 State Estimation . . . 127 8.2.5 MPC Computation . . . 128 8.2.6 Setting MPC parameters . . . 128 8.3 System Consistency . . . 130 8.4 Simulations . . . 133

8.4.1 MPC on the Linearized Model . . . 133

8.4.2 Pumping Losses . . . 140

8.4.3 MPC on the Nonlinear Model . . . 140

8.5 Conclusions . . . 145

9 Model Reduction 149 9.1 Introduction . . . 149

9.2 Model Reduction Process . . . 150

9.3 Hankel Singular Values . . . 150

9.4 Overview of Model Reduction Techniques . . . 151

9.4.1 Truncation and Residualization . . . 152

9.4.2 Balanced truncation and residualization . . . 154

9.4.3 Optimal Hankel norm approximation . . . 154

9.4.4 Balanced stochastic model truncation (BST) . . . 155

9.5 Model Reduction Procedure . . . 155

9.5.1 Number of states to use in the reduced model . . . 156

9.5.2 Model Reduction Techniques. Comparison: Additive Me-thods . . . 156

9.6 Model Reduction Technique: Multiplicative Error Method . . . 160

9.6.1 Validate the model . . . 161

10 Multivariable System Analysis 171

10.1 Directions in multivariable systems . . . 171

10.2 Scaling the system . . . 173

10.3 Singular value decomposition . . . 174

10.4 Multivariable Poles and Zeros . . . 175

10.5 Input-output controllability . . . 176 10.5.1 MISO case . . . 177 10.5.2 MIMO case . . . 177 10.6 SVD Controller . . . 180 10.7 Conclusions . . . 182 11 MIMO Control 185 11.1 Introduction . . . 185

11.1.1 Best Fuel Consumption: formulation of the problem . . . 186

11.2 Control design . . . 189

11.2.1 Layout 1: Fuel Optimal Control . . . 189

11.2.2 Layout 2: Torque Optimal Control . . . 189

11.3 Simulations with MIMO MPC . . . 189

11.3.1 Simulation on the Linear Model . . . 190

11.3.2 Considering Pumping Losses . . . 192

11.3.3 Simulation on the Nonlinear Model . . . 195

11.3.4 Comparison of the two controller versions . . . 195

11.4 MIMO MPC on the Reduced Order Model . . . 198

11.5 MIMO MPC for α, WG and λ . . . . 200

11.6 Numerical errors . . . 201

11.7 Conclusions . . . 203

12 Conclusion 207

List of Notations

λst: λ stoichiometric

Kef f: efficiency coefficient ˙mair: air mass flow ˙mf uel: fuel mass flow

mAir_−Req: requested air mass

mF uel_−Req: requested fuel mass

MP red: predicted torque

nr: number of crank revolutions for each power stroke per revolution rpm: rounds per minute

˙Va: volume flow rate of air into the intake system ˙Vd: rate at which volume is displaced by the piston, WG: wastegate Numerical values: λstec=14.65 qHV = 44 ∗ 106J/kg Vd= 2 ∗ 10−3m3 R= 287.2J/(kgK) nr=2 η=0.3469 a0=857.748579470353/1000 a1=-5216.7334951752 xi

List of Abbreviations

BMEP: Brake Mean Effective Pressure IMEP: Indicated Mean Effective Pressure FMEP: Friction Mean Effective Pressure PMEP: Pumping Mean Effective Pressure RHP: Right Half Plane

ECM: Electronic Control Manager ECU: Electronic Control Unit

MIMO:Multiple Input Multiple Output MISO:Multiple Input Single Output SIMO:Single Input Multiple Output SISO:Singol Input Single Output SA: Spark Advance

SI: Sparked Ignited

SVD: Singular Value Decomposition

Introduction

This Master’s Degree Project is performed at Automatic Control Group at KTH, Stockholm, in cooperation with General Motors Power Train, S ¨odert¨alje (Swe-den).

The project concerns optimal control of a turbocharged SI engine, to improve positive torque response during the transient.

1.1

Background

The ever increasing governmental regulation of emissions and driver demands for fuel economy and drivability emphasize the need for advanced engine tech-nology and control. Among many other measures to improve the fuel con-sumption, one method is to apply a turbocharger. Investigations have shown a considerable potential for improvement in this area. In turbocharged engines energy from exhaust gases is used to compress the intake air and produce a higher intake manifold pressure. This is done by a turbine connected to the ex-haust. The increased intake pressure results in an increased amount of air into the combustion chamber and thus increases the power output that is available. A turbo also increases the inlet air temperature which can be cooled by an inter-cooler. The turbocharger speed and the resulting pressure after the compressor is controlled using a wastegate.

A wastegate is a valve that diverts exhaust gases away from the turbine wheel. Diversion of exhaust gases causes the turbine to lose speed, which in turn reduces the rotating speed of the compressor. The pressure above atmo-spheric pressure that the turbocharger is creating in the engine’s inlet manifold

is called boost pressure and the primary function of the wastegate is to stabilize this boost pressure, to protect the engine and the turbocharger.

Today, the wastegate is mechanically actuated, by means of a pressure valve which simply opens up the wastegate when the pressure over it is too high, and can be controlled by a simple PI controller. In all the other cases it is closed. This thesis investigates the possibility for a more advanced control of the wastegate, to improve the responsiveness of turbocharged SI engines.

The wastegate in state-of-the-art turbocharged engines is always closed in order to achieve the highest possible pressure before the turbine and thus the highest possible turbocharger speed. The higher the turbocharger speed, the smaller is the turbo lag, as the torque build-up time is highly sensitive to the turbocharger inertia. The wastegate is only opened to keep the boost pressure below a certain limit, i.e. for boost pressure control.

One possible way to reduce time lag is to control the turbo so that the tur-bo always keeps a relatively high speed and then use the throttle to reduce the flow into the intake manifold and the manifold pressure. In this way the driveability is improved by reducing the turbo lag but the fuel consumption is increased, since the intake manifold pressure is increased.

The turbo increases the intake manifold pressure and also the intake man-ifold temperature and with an intercooler the charger density is increased, which results in higher power output from the engine. An intercooler also gives better engine efficiency, since it can give the same mass flow through the engine at a lower pressure which in its turn requires less turbine pressure and in this way reduces the pumping losses.

1.2

Prior Work

This project continues the investigation started by Ida Kristoffersson in her Master Thesis[1]. For more details on engine modeling, [2] and [3] are rec-ommended. The problem of controlling the wastegate is handled in [4], with a pressure based approach, and in [5]. Multivariable design and nonlinear con-trol are extensively treated in [6],[7] and [8]. MPC is implemented in Matlab, using the MPCToolbox, based on [9].

1.3

Problem Formulation

In this work the control strategy is based on the idea of using turbocharg-ing and wastegate to reduce pumpturbocharg-ing losses durturbocharg-ing the transient and so

im-prove the torque response. Further investigations for improving the system responsiveness concerned also the air-to-fuel ratio and the spark advance.

The first part of the project focused on analyzing the main characteristics of a turbocharged engine, from a control point of view, in order to be able to understand the problems and so design the requested controllers.

A nonlinear Mean Value Engine Model (MVEM), with 13 states and lin-earized in 45 different working points, has been first studied and then used for simulations and control design. The original model, implemented in Mat-lab/Simulink, has been enriched with new features, like spark advance and lambda efficiencies and exhaust temperature correction depending on spark advance. A validation of the modified nonlinear model has been performed, recording data from the car in a driving test.

To check that the linearized model correctly captured the main dynamics of the system, it was compared and validated with respect to the nonlinear one. A mathematical analysis of the linearized model in all the 45 operating points was carried through, in order to point out the main characteristics and fundamental limitations of the system.

The proposed solution for achieving optimal wastegate control is based on Linear Quadratic (LQ) approach. For such controller a torque based de-sign is applied. Reference tracking is achieved adding a feedforward action in the LQ controller. To guarantee disturbance rejection, it was also enforced with integral action and with an anti wind-up solution, related to hard input constraints.

Since the optimal control strategy is expected to vary quite much for dif-ferent working points, a gain scheduling strategy based on engine working conditions, has been designed.

In order to improve the torque transient response, also the air-to-fuel ra-tio influence has been investigated and an independent lambda controller has been developed, in order to maximize the lambda efficiency during transient.

Since the system operates near a constraint boundary, another solution ba-sed on Model Predictive Control (MPC) has been investigated. The first step has been considering only the wastegate as manipulated variable. Later on a multivariable approach has been considered, adding the throttle as control input and the fuel consumption as a second output. A mathematical analysis of the resulting MIMO system has been performed, based on singular value decomposition.

The MPC was then extended to the MIMO formulation and some con-straints on the states were also included, in order to consider physical

limi-tations of the system. Different MPC configurations have been designed, to manage the trade-off between fast torque response and low fuel consumption. As last step, the air-to-fuel ratio was added to the manipulated variables, to verify if it is possible to get some benefit improving the transient torque response.

The complete realtime MPC implementation, with the capability for au-tomatic code generation in the dSpace microAutobox environment, requires the model, now with 13 states, to be reduced to a minimum state space order. The extent of model reduction that is required and the possible performance deterioration caused by the reduction have been investigated.

1.4

Thesis outline

Chapter 2 covers the modeling of a turbocharged SI engine and Chapter 3 de-scribes the Simulink model including the car, the driver and the ECM. In Chap-ter 4 the validation of the nonlinear model is shown, by comparing simulation results and data from a test on the car. Chapter 5 deals with the analysis of the linearized model, which is then used as a basis for the investigation of transient torque response and the possible approaches to its improvement. In Chapter 6 different ways to improve the engine response are investigated and a strategy based on LQ control is shown. Chapter 7 deals with control of Lambda and Spark Advance, and presents a strategy to improve torque response by max-imizing the Lambda efficiency. A strategy based on model predictive control (MPC) is investigated thoroughly in Chapter 8 with a model-based approach. In Chapter 9 the applicability of the strategy is discussed and a reduced order model is derived, in order to make the MPC computationally lighter. A dif-ferent formulation for the problem is given in Chapters 10 and 11, where mul-tivariable control theory is used and MPC is designed to control also throttle and Lambda together with the wastegate.

Engine Model

Turbocharged SI engines are a major possibility in the current trend of down-sized engines with preserved drivability performance. Downsizing refers to reducing the size of the engine without a loss in the amount of torque pro-duced, by adding a turbocharger, which connects a turbine placed before the exhaust system to a compressor placed after the air filter. This way the ener-gy in the exhaust gases is utilized to compress the incoming air more and the engine can produce more torque.

Considering control and supervision it is favorable to have a mean value model to be used. Such models of turbo engines are similar to those of natu-rally aspirated engines, but there are some special characteristics, e.g. the in-terconnected gas flows, the intercooler, the difference in relative sizes between the gas volumes (compared to naturally aspirated engines), the turbo, and the wastegate.

2.1

Mean Value Engine Model

In order to perform a model-based investigation and optimization of the dy-namic behavior of a turbocharged SI engine, a good model is necessary. A highly suitable model class is then mean value engine models (MVEMs) which describe the average behavior of the engine over one to several thousands of engine cycles[3] [2].

Fig. 2.1 shows a sketch of the turbocharged SI engine under consideration. The components that have to be modeled are: air filter, compressor, intercooler, throttle, engine, turbine, wastegate, and a lumped model for the catalyst and

exhaust. One benefit of this modelling strategy is that every component can be separately identified and then the engine model is built using the separate components. Each component is described in terms of equations, constants, parameters, states, inputs and outputs.

For mean value models, that describe variations slower than an engine cy-cle, the frequency range is within 0.1-50 Hz. Parameters in mean value models are usually physically interpretable. This is advantageous in simulations of principle concern.

General guidelines for MVEMs are:

• Changes that take in the order of 10-1000 cycles to reach their final state are expressed by differential equations.

• Changes that are faster are expressed by static relations.

The basic principle used here is that each engine component shown in Fig.2.1 is modeled as a flow restriction (or pump) that affects the thermodynamic state of the fluid (gaseous). The standard calculation causality of almost all restrictions is that they take pressure difference as input and gives the flow as a result. The volumes between the restrictions are modeled as reservoirs where normally the pressure in each reservoir represent a state in the model.

Whereas for the control volume there is only one type of model, for the restrictions there are two main components, namely compressible and incom-pressible fluids.

Abbreviated Nomenclature

It is natural to accompany the component based modeling with a system to name the variables. The main variables in the table to the left are specified by a subscript from the table to the right referring to its own component or the component before. As an example, Tcomprefers to the temperature after the compressor. Variables ˙m Mass flow P Power p Pressure T Temperature Tq Torque Π Pressure ratio

Subscripts amb Ambient af Air filter em Exhaust mannifold es Exhaust system Tq Torque ic Intercooler im Intake manifold t Turbine th Throttle

The following sections quickly describe the modelling of some important subsystems present in the MVEM, based on the model developed by Per An-derson in [3] and the components related to turbocharging are given in the turbo section (see [3] for more details).

Figura 2.1: Sketch of a turbocharged SI-engine, that illustrates how the engine is divided into subsystems to enable physical modeling.

2.2

Incompressible Flow restrictions

In many engine components the fluid flow can be regarded as incompressible and in-viscid. Under such conditions the pressure head losses caused by bends, valves, and sudden changes in area approximately follow the same relation

Δp= pbef ore− paf ter= ξ(Re)

RTbef ore˙m2

pbef ore (2.1)

where the ξ only has a weak dependence on the Reynolds number (Massey, 1998). In most cases ξ(Re)·R can be regarded as constant, here denoted H, and the equation can be used as a general model for incompressible flow through a restriction. Models for the air filter, intercooler, and exhaust system are all based on this relation.

2.2.1

Air Filter

The air filter is important to model since it produces a pressure drop that can be as high as 5%, which propagates trough the intake system and influences the whole engine. A sketch of the air filter is shown in Fig.2.2. It consists of three sudden changes in area, the filter itself, and the pipes in and out of it. As described above, Eq. 2.1 can be used to model pressure loss for several kinds of flow restrictions, which gives the following pressure loss over the air filter:

Δpaf = pamb− paf = Haf Tamb˙m2air pamb (2.2) m_air m_air p_amb T_amb p_af T_af

Figura 2.2: Sketch of the air filter showing the changes in flow area.

2.2.2

Intercooler

A heat exchanger, called intercooler, is used after the compressor to cool the compressed air back to near ambient temperature. It increases air density

which is advantageous, but in SI engines it is mainly used for knock reduc-tion. To achieve efficient cooling of the charge air, the tubes in the intercooler need to be rather thin so that the air is exposed as much as possible to the cool-ing medium. The result is that some of the gain in intake air density is lost. Therefore, beside the obvious need to model the outlet air temperature, also a model for the pressure head loss is needed.

Intercooler - Pressure Head Loss

Intercooler pressure head loss is modeled by [10] Δpic= Hic

Tcomp˙m2air,ic

pcomp (2.3)

where ˙mair,icis the air-mass flow through the intercooler. Intercooler - Temperature Head Loss

For all practical purposes of intercoolers the flow rate of the cooling fluid ˙mcool is greater than the air mass flow, ˙mair, through it. This suggests, (Holman, 1997), that the following equation can be used to measure the efficiency of the intercooler

= Tcomp− Tic

Tcomp− Tcool (2.4)

Solving this equation for Tic yields the desired expression for the intercooler outlet temperature, expressed in terms of the temperatures and the intercooler efficiency

Tic= Tc− (Tcomp− Tcool) (2.5)

Tcoolis the temperature of the cooling medium, in this case ambient air, Tcool=

Tamb. In order to predict the intercooler outlet temperature, a model for the intercooler efficiency, , is needed. We are not interested in details here, the description will not go deeper, but more can be found in [2].

2.2.3

Exhaust System

The exhaust system consists of changes in flow area and flow direction and the head losses can therefore also be modeled in the same way as the air filter, i.e. using Eq. 2.1: Δpt = pt− pamb= Hes Tes,in ˙m 2 air pt (2.6)

2.3

Compressible Flow Restrictions

Isentropically compressible mass flows (Taylor, 1994) are used to describe the flow through the throttle and the wastegate.

2.3.1

Throttle flow

The throttle is modeled with a butterfly type model,see Figure 2.3, where the angle of the throttle plate controls the flow area. In engine under consideration the throttle is controlled by the ECU through an electrical servo, thus provid-ing high flexibility in determinprovid-ing the behavior of the vehicle by designprovid-ing different profiles for the throttle behavior.

a

a0

Figura 2.3: Left: the throttle body. The angle a is the actual angle related to the throttle housing, while the angle a0 defines when the throttle is closed. Right: the flow areas are representd by the two moon crest shaped areas.

2.3.2

Wastegate flow

Wastegate flow is modeled using the standard model for a compressible re-striction, with variable area.

2.4

Engine

The engine produces a port air.mass flow, exhaust mass flow and exhaust tem-perature.

2.4.1

Mass flow into the cylinders

The air mass flow out of the intake manifold into the cylinders depends on many parameters, but mostly on engine speed N, intake manifold pressure

pim, and temperature Tim:

˙mac(N, pim, Tim) = ηvol(N, pim, . . .)

VdN pim

where ηvolis the volumetric efficiency, a parameter used to describe the effec-tiveness of the engine’s ability to induct new air into the cylinders; Vd is the displaced volume for the whole engine; nris the number of engine revolutions per cycle and R is the gas constant.

2.4.2

Volumetric efficiency

The intake system consisting of air filter, intercooler and throttle plate, intake port and intake valve restricts the amount of air that the engine can induct. The measure for the effectiveness of an engine’s induction process is the volumetric

efficiency, ηvol. The volumetric efficiency is defined as the volume flow rate of air into the intake system, ˙Va, divided by the rate at which volume is displaced by the piston, ˙Vd, ηvol= ˙Va ˙Vd = ˙manr ρaiVdηcylN (2.8) where ρaiis the air density in the inlet, ˙ma is the air mass flow, and nris the number of crank revolutions for each power stroke per revolution (nr= 1 for a two stroke engine and nr = 2 for a four stroke engine). The engine speed n is given in revolution per seconds. An equivalent definition of the volumetric efficiency is to use the mass of air in one cylinder directly

ma

ρai˙Vd

(2.9) The definition are equivalent but the mass of air is not easily determined.

The inlet density can be either be taken as the intake system density. Then

ηvolmeasures the efficiency for the pumping over the inlet valves and ports. Or ρ can be taken as atmospheric density, and then it measures the efficiency for the whole intake.

2.4.3

Exhaust Manifold Out Temperature

The temperature out of the exhaust manifold before entering the turbine can be modeled with sufficient accuracy as a function of air mass flow Tem = f( ˙maf) when the engine operates at stoichiometric conditions, (Eriksson, 2002).

2.5

Compressor

Compressor performance is determined in a flow bench where the compressor is run together with the turbine in a number of points and the state changes of

the fluid are measured. From this data a performance map of the compressor is constructed. The performance map is usually implemented in a look-up table which serves as the actual compressor model.

2.5.1

Compressor - Pressure Model

f an adiabatic process is assumed, compression from a state with pressure p01 and To1 to another state, with pressure p02requires an amount of specific en-ergy, wi, that obeys the following relation between the pressure ratio and the specific energy. In this case p01 = paf and p02 = pcomp, so

Πc= pcomp paf = (1 + win cpT01) γ γ−1 _(2.10)

An expression for the work can be derived, see e.g. (Mtiller et al., 1998), by considering the Euler equations for compressor blades and the losses due to friction and incidence, resulting in

win= U22(s1( ˙mair

U2 )

2_{+ s}

2( ˙mair

U2 ) + s3) (2.11) wehre U2is the rotor tip speed and siare constants that are tuned to measured data.

2.5.2

Compressor - Air Mass Flow Model

n mean value models it is desirable to represent the flow through the compres-sor as a function of pressure ratio and turbine shaft speed, rather than as in Eqs 2.10 and 2.11. To do this, the equations can be inverted to

˙mair = a1U2∓ a2U22+ a3Taf 

(Πγ−1γ

c − 1) (2.12)

where aiare tuning constants.

2.5.3

Compressor - Efficiency Model

he efficiency is defined by the ratio of the isentropic and the actual specific input work ηc= win win,act = (pc paf) γ−1 γ − 1 Tc Taf − 1 (2.13) where winis modeled by Eq.2.11.

2.6

Turbine

Dimensionless quantities are used when describing the turbine performance and the same definitions, as for the compressor, are applied. Here it is worth to stress that the dimensionless expressions are of higher importance for the tur-bine since it is exposed to more extreme variations in inlet conditions compared to the compressor; Temperatures vary from 500 K up to 1300 K and pressures at turbine inlet from atmospheric conditions up to 300 kPa.

For turbines the corrected mass flow and efficiency is normally plotted ver-sus pressure ratio Pem

pt = l/Πt. Turbine efficiency is determined from the flow

conditions and calculated using

ηt= 1 − Tt Tem 1 − ( pt pem) γ−1 γ (2.14)

In addition, the mechanical efficiency of the turbocharger might also be includ-ed in the turbine efficiency. Look-up tables derivinclud-ed from the map may serve as turbine models but it is also interesting to study parameterizations.

2.6.1

Turbine - Pressure Model

eglecting the corrected quantities and studying the mass flow alone shows that there exists a relationship between mass flow and pressure ratio for the turbine that is practically independent of turbine shaft speed. The connection between the flow and pressure ratio is almost independent of the compressor speed, therefore the speed dependence is neglected and the corrected air mass flow is modeled as a function of only the pressure ratioΠt = _pp_emt . The parallel flow in the wastegate also has a large effect and makes the validation of the turbine model difficult, when using engine data.

2.7

Model Dynamics

Two kind of dynamics are included in the model:

- Control volumes. All receivers are modeled as control volumes with filing and emptying dynamics using pressure and temperature as states.

- Turbo shaft dynamics. The axle connecting compressor and turbine has its own dynamics, driven by the turbine torque and loaded by the com-pressor and friction.

2.7.1

Control volumes

Control volumes are placed in between all flow restricting components and they determine some of the engines dynamic characteristics.

A control volume is a thermodynamical volume that stores mass and ener-gy. It has fixed volume V and as a storage it has filling and emptying dynamics. The increase or decrease o0f the mass is determined by the inlet and outlet air mass flow ˙minand ˙mout. The difference between the inflow and outflow of mass( ˙min− ˙mout) directly gives the rate of change in mass in the system

dm

dt = ˙min− ˙mout (2.15)

Energy is also conserved and stored in the system. Considering the energy there might be heat transfer ˙Qbut there is no mechanical work transfer to the control volume. Energy is also transferred to and from the system through the in-and outflows. For the open system that we are considering the first law (energy conservation) gives the following rate of change of the internal energy

dU

dt = ˙Hin− ˙Hout− ˙Q (2.16)

Since is difficult to measure mass and energy, these equations are manipu-lated and rewritten in terms of temperature and pressure. Assuming that

• the gas is ideal(pV = mRT )

• cpandcvare constant

the temperature can be determined from the internal energy and the mass through

U = mu(T ) = [cv− constant] = mcvT (2.17) and the pressure can be determined from the ideal gas law

pV = mRT (2.18)

Furthermore the enthalpy flows are given by ˙

Hin= ˙mincpTinand ˙Hout= ˙moutcpTout (2.19) where the temperature of the outflowing gas is the same as that in the control volume, i.e. Tout− Tin. Equations 2.15 to 2.19 give a system of equations that can be solved to give all information on the system and differential equations

can be formulated so that mass, pressure and temperature are the states in the model (see [2] for the detailed equations).

Control Volume p _U T m V H m_in T_in m_out T_out H Q

Figura 2.4: The control volume is marked with dashed line and in it the pres-sure, temperature, and mass states are shown. There are two flows across boundaries. There is no volume change (V is constant), except those from the flow, so there is no mechanical work exchange.

2.7.2

Turbo Shaft Dynamics

revious sections described models for compressor and turbine separately and to connect the two submodels Newton’s second law for a rotating system is used:

Tqt− Tqcomp= I ˙ω (2.20)

where Tqtis the driving torque and Tqcompdenotes braking torque acting on the rotating parts of the turbo charger spinning with the angular velocity ω. The power and torque are connected through P = Tqωso equation 2.20 becomes:

Pt− Pcomp= I ˙ωω (2.21) If the turbine and the compressor are treated as two separate thermodynamic systems, Pt and Pcompcan be calculated from the first law of thermodynam-ics. The heat transfer with the surroundings and change in potential energy is neglected.

−P = ˙m(hout− hin) = ˙mcp(Tout− Tin) (2.22) For the compressor, the net amount of produced power is negative, i.e. the compressor consumes energy, while for the turbine, the net amount of pro-duced energy is positive.

2.8

Torque generation

How large the torque is, depends on the work produced and consumed in the engine [2]:

Me=

Wig− Wf r− Wpump

nr2π (2.23)

where Wigis the indicated gross work produced, i.e. the mechanical work pro-duced, Wf ris the friction work consumed by the engine components as well as auxiliary devices, and Wpumpis the pumping work due to difference in intake and exhaust manifold pressures, while nris the number of engine revolutions per cycle. There exist different expressions for Wig, Wf r and Wpump. Often they are modeled as follows:

Wig = Vd·mf uel˙ qHV 2 Ns min (λ, 1) Vd ηe, (2.24) Wf r= Vd·  0.97 + 0.15  N 1000  + 0.05  N 1000 2 , Wpump= Vd· (pem− pim).

ηeis the engine raw efficiency, qHV the heating value (the amount of energy that the combustion of one unit of fuel can release when the fuel is in gaseous phase), Vd the displacement volume, N the engine speed in revolutions per minute and Nsthe engine speed in revolutions per second. The indicated gross work is coupled to the energy in the fuel and to operating conditions, which gives the model in the first equation above. In the equation (2.24) the pumping work is modeled as proportional to the difference in exhaust manifold pres-sure and intake manifold prespres-sure. The friction model comes from [11]. It accounts for three different kinds of friction: boundary friction (independent of engine speed), hydrodynamic friction (proportional to speed) and turbulent dissipation (proportional to speed squared).

Torque is a valuable measure of a particular engine’s ability to do work but it depends on engine size. Another useful parameter is the mean effective pressure (MEP) which is normalized with engine size and has the same unit as pressure [force per unit area][12]

M EP = work produced per cycle

volume displaced per cycle (2.25) Gross indicated work(IMEPg) is defined as the work delivered during the compression and expansion strokes while Net indicated work(IMEPn)

implies the work generated during the entire four-stroke cycle.

The difference between net and gross IMEP is called Pumping Mean Effec-tive Pressure, PMEP:

P M EP = IMEPg− IMEPn (2.26) From eq. 2.26 it is evident that a positive PMEP means negative work on the

Figura 2.5: Cylinder pressure versus V/Vmax for a turbocharged SI-Engine.

crankshaft. PMEP and IMEP can also be expressed by the areas formed in the pressure versus volume diagram, see Figure 2.5:

• PMEP = Area B + Area C

• IMEP= Area A + Area C

The usable power is usually referred to as brake power, so inserting the brake torque into the definition of MEP, the brake mean effective pressure (BMEP) is obtained:

BM EP = Pbnr VdccylN =

2πMbnr

Vdccyl (2.27) BMEP is estimated by subtracting pumping (PMEP) and friction work (FMEP)

from the supplied work from the fuel (IMEP):

BM EP = IMEP − P MEP − F MEP (2.28) In turbocharged engines the turbine power is generated by the energy in the exhaust flow. Figure 2.6 gives a schematic view of the theories behind turbocharged engines. Loop 1 to 4, in Figure 2.6 is the engine power stroke.

Figura 2.6: Schematic cylinder pressure versus volume diagram, showing the available exhaust energy.

The driving power of the turbine is the energy available at point 4 when the piston is at BDC. Area AT represents the available energy, which could be pro-duced by expanding the exhaust gases to atmospheric pressure after the ex-haust valves have opened. This energy is used to drive the compressor so that the intake pressure can be raised above the atmospheric pressure to the charg-ing pressure, which requires work, area Ap. For the ideal case area AT equals area Ap. In other words, the power generated by the turbine will be used in the compressor. The power is related to the mass flow through the turbine, ˙m and enthalpy, h , according to [10]:

where T is the temperature and cpthe specific heat.

The choice of turbine for a specific engine configuration is a compromise between low and high load performance of the engine. For commercial au-tomotive purposes low load performance is most often preferred. In order to ensure sufficient pressure at the turbine inlet at low load, the inlet area to the turbine needs to be limited. However at high load a small inlet area will gen-erate too high rotational speed of the turbine. Hence, it is necessary to limit the turbine rotational speed during high load due to mechanical constraints. This can be done by the wastegate, which leads part of the flow past the turbine, thereby decreasing the pressure at the turbine inlet.

2.9

Fuel path and (A/F)-ratio

The fuel flow into the cylinder is measured and controlled by a fuel injector, that is an electrically controlled valve. Only a fraction of the injected fuel is inducted into the cylinder directly, due to the wall wetting phenomenon, i.e., some amount of fuel is deposited on the intake walls either as a film or as puddles and does not mix with the air.

The result is that the following (A/F) mixture enters the cylinder

λ= ˙mac ˙mf c 1 A F s (2.30) where ˙macand ˙mf care the air and fuel flow into the cylinder respectively.

2.10

Fuel consumption

The fuel mass flow to the cylinder is proportional to the air mass flow ([3]): ˙mf uel= ˙m air λA F  s . whereA F 

sis the stoichiometric air/fuel ratio. An expression for the air mass flow is:

˙mair= (a0pim+ a1) VdNs

RTimnr (2.31)

where Vd is the displacement volume, Nsthe engine speed in revolutions per second, R is the gas constant and nr the number of engine revolutions per cycle. The constants a0 and a1are identified in [3] with the Matlabfunction lscurvefit

which uses a nonlinear least-squares technique. If the state Timand the input signal Nsis assumed constant, ˙maircan be expressed as a linear function of the state pim: ˙mair= k1pim+ k2 k1= a0_RTVdNs imnr k2= a1_RTVdNs imnr (2.32)

Assuming λ= 1, also the fuel mass flow is a linear function of pim: ˙mf= ˙m air _A F  s = k1pim+ k2 (2.33)

2.11

Conclusions

A mean value engine model (MVEM) is compiled in this chapter. It is a para-metrized component based model of the engine’s intake system and exhaust system, including the turbocharger and wastegate. Each component of the en-gine is described in terms of equations, constants, parameters, states, inputs and outputs. This class of models describe the average behavior of the engine over one to several thousands of engine cycles, so is very suitable for control design.

Simulink Model

This thesis is based on the model of a turbocharged SAAB 9-3 L850 2.0T, de-veloped at GM Power Train. The model is implemented in Simulink and has three fundamental components:

• the driver, who is basically modeled by the accelerator pedal signal;

• the car, which contains the Mean Value Engine Model (MVEM) and the block describing Transmission and Chassy. The MVEM was developed by Per Andersson [3];

• the ECM, which contains all the controllers. The top level diagram is shown in figure 3.1.

3.1

Driver

The behavior of the driver is modeled through the acceleration pedal, the gear box and the clutch. Setting some parameters inside the driver block it is pos-sible to simulate different driving scenarios: acceleration, constant speed or braking. The focus of the thesis is on improving the torque response during the transient, so the acceleration phase is considered and a step in the pedal is given as input to the engine model. The clutch and the gears will be disregard-ed, and only the signal representing the acceleration pedal will be considered as an input coming from the driver to the ECM.

3.2

Car

The car is represented by two main blocks:

Driv er Simple driver E C M D riv er S AAB 9-3 L 850 2. 0T M a nua l 5 G e a rs M e mory2 B U S

Inte rrupt G e ne ra tor

ECM_1_11_7_8

ECM P lantD ataB us

Figura 3.1: Top level diagram of the plant model implemented in Simulink.

t t t Acc_Ped Clutch Gear 1st 2nd 3rd Down Up

Figura 3.2: Driver: acceleration phase, from first to third gear. 0=clutch down, 1=clutch up.

• the Engine Model, that will be treated in detail in the next section;

• the Transmission and Chassi model: in this block the clutch and the shafts are assumed to be stiff and the transmission and the final drive are assumed to multiply the torque by the conversion ratio.

Making some change inside this block we had the possibility to fix the engine speed as constant.

3.3

Engine Structure

The components included in the model are the intercooler, engine, throttle, wastegate, turbine, compressor, exhaust system and various pipes or manifold connecting these components. These pipes or manifolds can be considered as

control volumes where the pressure and temperature of the gas inside depends

on the mass-flows into and out of the volume. Mass-flow are determined by

restrictions which are components that, given the pressure and the temperature

before and after the restriction, determine the mass-flow and temperature of the flow. The restrictions and control volumes are listed next:

Restrictions Air-Filter Compressor Intercooler Throttle Engine Turbine/wastegate Exhaust system Control volumes

Pipe between air-filter and compressor Pipe between Compressor and Intercooler Pipe between Intercooler and Throttle

Intake manifold connecting the the throttle and cylinders Exhaust manifold connecting the cylinders and the turbine/WG Pipe between turbine/WG and the exhaust system

To complete the model there are only two components left. First there is the tur-bocharger shaft, which is modeled as a rotating inertia, and second the engine torque model. Below the components are divided into groups:

w_ tc W_ ou t [ kg /s ] Q_d ot W_ in [ kg /s ] T_ in [ K] p [P a] T [K ] dT dp T_ in [ K] W_ in [ kg /s ] Q_d ot W_ ou t [ kg /s ] p [P a] T [K ] dT dp T_ in [ K] W_ in [ kg /s ] Q_d ot W_ ou t [ kg /s ] p [P a] T [K ] dT dp Q_d ot W_ in [ kg /s ] T_ in [ K] W_ ou t [ kg /s ] p [P a] T [K ] dT dp p_e s u_w g w_tc p_be f_ cm p p_a fte r_ cm p p_e m p_a mb T_ em T_ trb m_es Tq _t p _ imW G _ o p e n q _b ra ki n g _m e q _d ri v in g _m e to rq u e _ W G o p e n p_ e m W G _ o pe n T u p p u p ef f e c ti v e a rea p do w n m f lo w T f lo w T_ cool [K ] p_u p T_ up p_do wn W_ ic T_ fwd_ flo w [K ] T_i n [ K ] W_ in [ k g /s ] Q_ d o t W_ o u t [ k g /s ] p [ P a ] T [ K ] dT dp 2 Tq _b ra k in g Tq _d ri v in g w_ tc dw _ tc d T_ i d p_ ic [T _ c ] [p _ c ] [d T _ c ] [d p _ c ] [d w _ tc ] [W _ e sO u t] [W _ e sI n ] [W _ th ] [d T _ a f] [W _ ic ] [W _ c o m p ] [W _ a f] [w _ tc ] [p _ t] [T _ t] [d T _ t] [d p _ t] [p _ e m ] [T _ e m ] [d p _ a f] [T q _ c s] [W _ c y l] [d T _ e m ] [d p _ e m ] [p _ im] [T _ im ] [d T _ im] [dp_ im ] [p _ ic ] [T _ ic ] [T _ a f] [p _ a f] p do wn T up p up T flo w m flo w W_ ou t [ kg /s ] Q_d ot T_ in [ K] W_ in [ kg /s ] T [K ] p [P a] dT dp p em T_ am b w_e L_re q Fu el ma ss f lo w [ kg /s ] IM OP EM OP phi_ Ig nO ffs et phi_ Fin alA dva nc e p im T im mFlo w e T ti Tq _e air F lo w T_ af [K ] p_a f [ Pa ] w_tc [ra d/s ] p_c [P a] W_ c T_ c Tq _c eta _c 1 T up p up p do wn T flo w m flo w 2 1 Am b <V e E V P R _ T _ A m b ie n tA ir > T_es T_es p_ e s p_ e s W_ e s O u t T_em T_em W_ t W_ t p_ e m p_ e m Tq _c s W_ c y l T_i m p_ im p_ im <A _ th > W_ th T_i c T_i c p_ ic p_ ic T_i c W_ ic W_ ic T_c T_c p_ c W_ c o m p W_ c o m p T_a f T_a f p_ a f p_ a f p_ a f T_a f W _a f W_ a f < V eAAP R _ p _ Amb ie n tAi r> <A _ e f f [ 0 -2 c m 2 ]> <u _ W G [ 0 -1 0 0 ]> T_mi x <V e E V P R _ T _ A m b ie n tA ir > < V e A A P R _ p_ A m bie n tA ir > <w _ e > <l a m b d a > < V e T RQ R_ m _ F u e lRe q > < V e P H S R _ ph i_ In tC a m P o s A llC y ls > < V e P H S R _ p h i_ E x hC a m P o s A ll C y ls > W_ c y l W_ c y l < p hi _ O f f s e tN orm a l> <V e S P K C _ p h i_ F in a lA d v a n c >

Figura 3.3: Simulink implementation of MVEM. The model is implemented with control volumes connected to restrictions. In the center the turbocharger shaft dynamics block connects compressor and turbine/wastegate blocks. The shadowed backdrop indicated that dynamics (states) are present in the blocks.

1. Restrictions. These determine a mass-flow through the restriction with a temperature, given pressure and temperature before and after the restric-tion.

• Incompressible flow restrictions. Air-filter, intercooler and exhaust system.

• Compressible flow restriction. Throttle and wastegate.

• Custom restrictions. These restrictions are specific applications:

Engine Determines the port air-mass flow, exhaust mass-flow and

temperature of the gases to the exhaust manifold. This block also models the engine torque.

Compressor The compressor is a part of the turbocharger and it is

considered as a restriction as it produces a mass-flow through the compressor and models the mass-flow temperature. It also produces a loading torque to the turbine.

Turbine The turbine part of the turbocharger produces a mass-flow

through the turbine, models its temperature, and describes the torque produced by the turbine.

2. Adiabatic mixer. This component is used to adiabatically mix flows from two different restrictions, such as when the flows through the turbine and wastegate meet. The outputs are mass-flow and flow-temperature.

3. Model dynamics. Components which have one or more states.

• Control volume: A control volume is used to connect two restric-tions. It has two states, pressure and temperature. Control volumes are located between the restrictions: air-filter, compressor, intercool-er, throttle, turbine, and exhaust system. Inputs: mass-flows in and out of the control volume together with the flow temperatures.

• Inertia with friction: The axle in the turbocharger is modeled as a rotating inertia, where the inertia is the total inertia of the axle, com-pressor and turbine. The angular velocity of the shaft is represented by a state. The inertia is powered by the torque from the turbine and loaded by the compressor and axle friction. The inputs are: driving torque and loading torque. Output is speed.

3.3.1

Model Simplifications

- Flows run only in forward direction.

- No heat transfer to/from the gas inside of the control volumes.

- No compressor bypass valve.

- All gases are considered to be ideal.

3.3.2

Model Inputs

Inputs to the model are:

Name Description Unit

α Throttle angle mm2

N Engine speed RP M

uwg Wastegate opening. Range0 − 1 –

λ Normalized air/fuel ratio –

pa Ambient pressure P a

Ta Ambient temperature K

3.3.3

Model States

The model has states for pressures and temperatures in each control volume and one state for the turbocharger speed:

State Description

paf Pressure after air-filter

Taf Temperature after air-filter

pcomp Pressure after compressor

Tcomp Temperature after compressor

pic Pressure after intercooler

Tic Temperature after intercooler

pim Intake manifold pressure

Tim Intake manifold temperature

pem Exhaust manifold pressure

Tem Exhaust manifold temperature

pt Pressure after turbine

Tt Temperature after turbine

ωTC Turbocharger speed

Figure 3.4 shows a sketch of a turbocharged SI-engine, that illustrates how the engine is divided into subsystems to enable physical modeling and indi-cates all the states.

Engine T_im p_im T_em p_em Intake manifold Exhaust manifold Compressor Turbine u_wg Intercooler p_af T_af Throttle p_comp, T_comp m_c m_im m_em Air filter p_ic, T_ic Catalyst & Exhaust system p_t T_t w_t

Figura 3.4: Sketch showing the components that are modeled in a turbocharged SI-engine.

3.3.4

Model Output

If the state Timand the input signal N are assumed constant, the engine torque can be expressed as a linear function of the states pimand pem[1]:

Tq= k3pim+ k4pem+ k5 k3= Vd nr2π  k1_N2_s qHV λA F  s min (λ,1) Vd ηe+ 1  k4= − Vd nr2π k5= Vd nr2π  k2N2s qHV λA F  s min (λ,1) Vd ηe−  0.97 + 0.15  N 1000  + 0.05  N 1000 2

Furthermore it is assumed that the input signal λ does not change. The as-sumptions are only made for a certain operating point, i.e. the values of Tim, N and λ can change between operating points.

0 5 10 15 20 25 30 0 50 100 150 200 250 300 350 400 T intake M

3.3.5

Maps for parameters representation

Some of the components depend in a non-linear way on their inputs and might be difficult to derive analytically a function describing their behavior. If mea-surements data is available for these it is convenient to use maps or look up tables instead of a functional representation.

3.4

Performance Limiting Factors

A number of factors limit the performance of an engine; both the compressor ratio and air to fuel ratio are very important for the efficiency but there are some factors limiting their potential.

3.4.1

Knock

Knock is a fundamental problem in spark ignited engines. It can easily de-stroy an engine if the knocking is allowed to continue. Knock is a resonance phenomenon in the cylinder that originates from an abnormal combustion where some of the gas auto ignites before the flame front has arrived and burns uncontrollably.

Normal combustion

Under normal conditions the combustion is ignited by a spark plug that gives a small flame kernel. The flame kernel increases in size and develops into a turbulent flame that propagates through the full chamber and is extinguished at the cylinder walls. The complete combustion process takes around 60° to complete, which corresponds to a flame propagation that is much slower than the speed of sound. Therefore the cylinder pressure can be considered to be constant in the cylinder. The part of the air-fuel mixture that is in front of the flame front and has not yet burned is called end-gas.

Knocking combustion

Knock is the name given to the noise which is transmitted through the en-gine structure due to essentially spontaneous ignition of a portion of the end-gas. When this abnormal combustion process takes place there is an extremely rapid release of much of the chemical energy in the end-gas, causing a very high local pressure and the propagation of pressure waves across the combus-tion chamber. Knock is a disturbing source of noise and if it is let to continue, can significantly damage the engine.

Two theories explain the origin of knock phenomenon: the autoignition and the detonation theory. The first states that when the fuel-air mixture in the end gas region is compressed to sufficiently high pressures and temperatures, the fuel starts to oxidize spontaneously in part or all of the end-gas region. The second says that under knocking conditions the flame front accelerates to sonic velocity and burns the end gas much faster than under normal conditions.

Knock can be controlled using the spark advance.

3.4.2

Surge

The compressor operation is limited by the so called surge line. It shows in the compressor map the border of a region with unstable operation of the compres-sor flow. A centrifugal comprescompres-sor can only generate a pressure increase when there is a flow through it. An increase in pressure ratio over the compressor opposes the flow and gives a decreased mass flow. When the pressure ratio be-comes too high the compressor can not maintain the flow necessary to generate the pressure increase and the flow through the compressor breaks down. When the flow breaks down there can be an uneven distribution of forces around the compressor wheel. The instabilities induce vibrations in the compressor wheel and turbo shaft which can cause the blades to hit the casings or destroy the bearings.

Surge can easily occur when the throttle is suddenly closed. The remedy is to add a surge valve which reduces the pressure after the compressor by either a return pipe which leads the flow back in front of the compressor or a pipe that releases it directly to the ambient atmosphere. The surge valve is controlled by the engine control system which detects if there is a risk for surge and then opens the valve.

3.4.3

Limits on air to fuel ratio

The fundamental limitation for SI engines operating with homogeneous charge is that there is a combustion stability limit around λ= 1.3 where the fuel can no longer be ignited and combusted. Other limits are also imposed by the leg-islators, based on the levels of pollutant emissions from the engine.The current emission after treatment systems can not effectively handle pollutant emissions other than λ= 1.

3.5

Engine Management System (ECM)

An engine management system must meet and compromise between several goals, such as: produce good driveability, maximize the engine performance, minimize the fuel consumption, and give low emissions. Some of the steps towards this are: metering the amount of air and fuel according to quantity and ratio, forming a combustible mixture, distributing the air-fuel mixture to the cylinders, igniting the mixture at the optimum position, controlling exhaust emissions and controlling the non-exhaust emissions.

The control system comprises the control of the A/F ratio, the preparation of the air to fuel mixture, ignition timing, and ignition energy, that all influ-ence the engine performance regarding the combustion process and emission formation. Several sensors are positioned on the engine to measure the engine state. The signals are measured by the electrical control unit (ECM) that calcu-lates and executes the control actions.

The ECM is a complex control unit, that contains many controllers; among them the most important are:

• Throttle Control

• WG Control

• Lambda Control

• Fuel Control

• Spark Advance Control

As illustrated in Fig. 3.6, the ECM is formed by two main blocks: a Time Based Unit an an Angular Based Unit. They both receive inputs from the driver (Ac-celeration pedal position) and from the engine (mainly the engine speed N and the inlet air mass flow).

The Time Based unit generates the requested Lambda, that goes into the Angular Based and is used to calculate the requested fuel mass, the request-ed throttle position (see 3.5.2) and the signal to control the wastegate. The Angular based unit works with signals that refer to fuel and spark advance. The requested fuel mass is calculated through lambda request (coming from the Time based unit), given the engine speed and the inlet air mass flow. The

section related to SA, takes as input from the Time Based unit the signal cor-responding to the best spark advance timing (phi-MBT) and gives as outputs two signals (phi-offset and phi-ignition) that will be used to calculate the SA efficiency.

The aim of the thesis is to improve transient response through more ad-vanced controllers than what are used today, investigating if and how new different control of throttle, lambda and wastegate may quicken the torque re-sponse. So the Fuel Control and Spark Advance Control, implemented now on the car, will not be changed and a brief description will be given in the following sections. M Pred L Req KNOCK AIR Phi Ignition Acc Pedal v Vehicle N m Air Per Cyl

Phi min Offset Phi MAX Offset

Phi MBT Pct Throttle Pct WG L Req Phi Ignition Phi Offset Phi Offset Normal t Injection m Fuel Req ANGULAR BASED TIME BASED THROTTLE CONTROL WG CONTROL LAMBDA CONTROL FUEL CONTROL SA CONTROL SPARK FUEL PHI-IGNITION Phi Offset N m Air Per Cyl

TORQUE

FUEL

Figura 3.6: ECM

3.5.1

Map-Based Control

In current practice, lookup tables or maps are used extensively in the control system for parameter representation and directly for control (c.f. Section 2.1), even though there is a trend towards more model based techniques. When maps are used for control the basic idea is to use measured quantities, like en-gine speed and intake manifold pressure (i.e. load), as inputs and deliver the

control action directly as output. These maps usually implement open loop controllers and are obtained through calibration in an engine test bench. The procedure is simple but time consuming. The engine is controlled to the de-sired grid point in speed and load and the control outputs are tuned to achieve desired goals. Control outputs are then stored directly in the map.

The advantage with maps is that they are computationally efficient, easy to implement and easy to obtain if an engine is available. A major disadvan-tage is that they do not offer any extrapolation; when an engine is re-designed all maps might have to be re-calibrated which is a time consuming process. Another control paradigm is model based control where models are used to describe the functions and the complex interactions between inputs and out-puts. Models are interesting since they offer the benefit of extrapolation and in general require less measurements for calibration. Models are also interesting since they directly show the structure of the model and point out the important effects.

3.5.2

Throttle control

The Throttle control determines the throttle area request to satisfy the demand coming from the acceleration pedal. Figure 3.7 shows the path from the pedal (which represents the request of the driver) to the requested air mass flow.

Acc_Pedal M_Pred K_eff m_Fuel_Req L_st L_Req x x x m_Air_Req Pedal to Torque Torque to Fuel

Figura 3.7: Signals path from the pedal to the air mass request.

The pedal position (AccP edal) is converted into predicted torque(MP red), that takes into account the efficiency coefficient (Kef f). This coefficient con-siders the influence of Lambda and Spark Advance on the torque, in fact de-pending on the values of these two variables, the effective torque coming out from the engine is modified. Torque is then converted into requested fuel mass flow(mF uel−Req) and finally to requested air mass flow (mAir−Req) through the definition of lambda (see.2.30):

λReq = ˙m air

˙mf uelλst (3.1)

m_Air_Req _{e_Air} THROTTLE_AREA REQUEST PID Th_Pst_Req m_Air + -+ +

Figura 3.8: Throttle controller.

a PID acting on the error between the air mass reference mAir−Req and actual value mAir, and finally gives the throttle request.

3.5.3

Lambda Control

In an engine management system for SI engines there are several controllers and two of the most important are A/F control and ignition control. The main purpose of the A/F control loop is emission reduction. To achieve good emis-sion reduction is necessary to use both feedback and feedforward. Feedback is necessary for maintaining λ in the narrow band around λ = 1 where the cat-alyst operates best. Only an open loop will not be sufficiently accurate due to model uncertainties. Feedforward is necessary for fast transient response and it determines the basic amount of fuel to inject.

The main purpose of the ignition control loop is to get good fuel economy while avoiding knock. At low loads the engine runs with the most fuel effi-cient ignition while at high loads engine knock can pose a limit on the ignition timing and it has to be set later.

3.5.4

Fuel Control

The amount of fuel is controlled by the fuel injection system, which is respon-sible for mixture formation, mixture transport and mixture distribution. By mixture formation is meant the process of preparing the air and fuel mixture: some of the fuel drops that enter the inlet manifold evaporates (which is desir-able), while some other forms a film on the manifold walls (which is not de-sirable). Mixture transport is the transport of air-fuel mixture to the cylinders and mixture distribution is the distribution of air and fuel to each cylinder.

When the driver accelerates, the throttle position changes and so the inlet air flow changes. The fuel injection controls the amount of fuel injected so that at all times the air to fuel ratio is kept in a narrow band around λ = 1. This value of λ is chosen since gives good driveability and low emissions. The fuel control is based on the speed density principle [2], which determines the air mass flow into the cylindersm˙acthrough the volumetric efficiency, given the engine

displacement volume, intake density and engine speed ˙mac= ηvolρiVd

N nr

where the intake manifold density ρiis determined from the pressure and tem-perature in the intake using the ideal gas law. Then how much fuel to inject is determined based on the air flow into the cylinders and the requested λ.

˙mf i= ˙m ac λReq A F  s

Once the fuel mass flow is obtained, it is possible to calculate the desired injection opening time

tinj = ˙m f i

N c1 + t0(ubatt)

where ubattis the battery voltage, t0is the opening and closing time of the valve and c1is a constant including pressure influence (which is constant), injector constant, number of cylinders and the number of strokes per cycle.

3.5.5

Spark Advance Control

Spark advance control deals with determination of the engine position where the spark plug shall ignite the air-fuel mixture and start the combustion [13][14]. It is thus used to position the combustion and pressure trace relative to the crank shaft motion: work is lost to heat transfer and to compression if it is placed too early and expansion work is lost if it is placed too late. Spark tim-ing is one of the most important factors affecttim-ing the engine performance. The instant moment when the spark happens in the cycle is really crucial in deter-mining the produced power and torque. The combustion event must be prop-erly located relative to top-center (TC) in order to obtain maximum torque. The combustion process starts before the end of the compression stroke, continues through the early part of the expansion stroke and ends after the point in the cycle at which the peak cylinder pressure occurs. The combined duration of the flame development and propagation process is typically between 30 and 90 crank angle degree.

Thus, optimal spark advance positions the pressure trace in a way that compromise between the effects mentioned above. To define the position of the in-cylinder pressure relative to TDC, the peak pressure position (PPP) is used, Figure 3.9. The PPP is the position in crank angle where the in-cylinder pressure takes its maximum value.

Figura 3.9: The PPP (Peak Pressure Position).

If the start of the combustion process is progressively advanced before TC, the compression stroke work transfer (from the piston to the cylinder gases) increases. Also, if the end of the combustion process is progressively delayed by retarding the spark timing, the peak cylinder pressure occurs later in expan-sion stroke and the peak is smaller. So the work transfer from the cylinder gases to the piston is reduced. When the magnitudes of these two opposing trends just offset each other, the maximum brake torque (MBT) is produced. This is also the point where the optimum timing occurs. Also at this point, the maximum brake power and minimum brake specific fuel consumption is obtained. Any advanced or retarded timing from this optimum point will produce a lower torque.

Figura 3.10: Three different pressure traces resulting from three different spark advances. The optimal spark advance is close to SA2