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Doctoral Thesis

Performance and driveability optimization of turbochargedengine systems

Author(s): Frei, Simon A.

Publication Date: 2004

Permanent Link: https://doi.org/10.3929/ethz-a-004832975

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Diss. ETH No. 15510

Performance and Driveability

Optimization of Turbocharged

Engine Systems

A dissertation submitted to the

SWISS FEDERAL INSTITUTE OF TECHNOLOGY

ZURICH

for the degree of

Doctor of Technical Sciences

presented by

Simon Andreas Frei

Dipl. Masch.-Ing. ETH

born 28 July 1973

citizen of Leuggern, AG

accepted on the recommendation of

Prof. Dr. L. Guzzella, examiner

Prof. Dr. G. Rizzoni, co-examiner

Dr. C. Nizzola, co-examiner

2004

11

contact: [email protected]

ETeX2£

page size: DIN A4

documentclass: extbook

standard character size: 14 pt

Simon Frei

2004

"I believe in feedback"

Âström (2000)

Dedicated to my parents

V

Preface

This thesis is based on my research performed at the Measurement

and Control Laboratory of the Swiss Federal Institute of Technology

(ETH) in Zurich between 1999 and 2004. It was carried out with the

support of DaimlerChrysler AG, Germany.

I wish to thank my advisor, Professor Dr. Lino Guzzella, for the

initiation of the project and for providing support throughout the

course of this work.

Furthermore I would like to thank Professor Dr. Giorgio Rizzoni for

accepting to be my co-examiner and for being my host during my visit

at the Center of Automotive Research at The Ohio State University.A special thank you goes to Dr. Corrado Nizzola of DaimlerChrys¬

ler AG for his constant support and for accepting to be my second

co-examiner.

I immensely appreciated the fellowship and the support of the en¬

tire staff of the Measurement and Control Laboratory. In this context

I would like to especially thank Dr. Chris Onder for his constant inter¬

est and the many fruitful discussions, and Peter Spring for the goodbasis he provided me with the set-up of the test bench.

I would also like to thank all the people of DaimlerChrysler AG

who supported me during this work.

Finally, my thanks go to my parents whose support and encour¬

agement during all the years made this dissertation possible in the

first place.

Contents

Abstract xi

Zusammenfassung xiii

Nomenclature xv

1 Introduction 1

1.1 Spark-ignited engines 2

1.1.1 Basic principles 2

1.1.2 Efficiency 3

1.2 Downsizing and supercharging 4

1.2.1 Discussion of the concept 4

1.2.2 Mechanical supercharging 5

1.2.3 The pressure-wave supercharger 5

1.2.4 Turbocharging 6

1.2.5 Conclusion 7

1.3 Contributions 8

1.4 Structure of the thesis 9

2 Engine modeling 11

2.1 System description 12

2.2 Causality diagram 13

2.2.1 System decomposition and flow directions...

13

2.3 The subsystems 13

2.3.1 Receiver 13

2.3.2 Incompressible flow restriction 17

2.3.3 Compressible flow restriction 18

2.3.4 Throttle plate area 20

2.3.5 Radial compressor 21

vn

vm CONTENTS

2.3.6 Intercooler 23

2.3.7 Mass flow through the engine 23

2.3.8 Fuel mass flow 25

2.3.9 Torque generation 26

2.3.10 Torque loss due to delayed spark timing ....29

2.3.11 Engine out temperature 30

2.3.12 Temperature at turbine inlet 31

2.3.13 Turbine 33

2.3.14 Wastegate 35

2.3.15 Adiabatic mixer 36

2.3.16 Turbocharger inertia 37

2.4 Calibration of the model 38

2.4.1 Mass flow through the engine 38

2.4.2 Torque generation 40

2.4.3 Temperature before turbine 41

2.4.4 Mass flow through the catalytic converter...

42

2.5 Map fitting 42

2.5.1 Motivation for the map fitting 42

2.5.2 Compressor mass flow 44

2.5.3 Compressor efficiency 46

2.5.4 Turbine mass flow 47

2.5.5 Turbine efficiency 47

2.6 Static calibration of the model 48

2.6.1 Results 49

2.7 Dynamic calibration of the model 52

3 Longitudinal dynamics of a vehicle 55

3.1 Quantification of agility 56

3.1.1 Literature search on agility 57

3.1.2 Specifications for the new agility criterion...

58

3.2 Solutions for better agility 62

3.2.1 System analysis 62

3.2.2 Solutions with auxiliary devices 63

3.2.3 Solutions without auxiliary devices 66

4 Optimization 69

4.1 Model extension 69

4.1.1 Modeling of the clutch 70

IX

4.1.2 Modeling of the engine dynamics 71

4.2 The optimal control problem 73

4.2.1 Formulation of the optimal control problem . .73

4.2.2 Means to solve the optimal control problem . .75

4.2.3 Solving the optimal control problem 76

4.2.4 Solutions of the optimal control problem ....78

5 Experimental verification 85

5.1 Implementation on the test bench 85

5.1.1 Choice from the set of optimal solutions....

85

5.1.2 Results 87

5.2 Implementation of the clutch strategy 96

5.2.1 Clutch specifications 96

5.2.2 Emissions 97

5.2.3 Implementation without a priori knowledge ...98

5.2.4 Consumer acceptance 99

5.2.5 Discussion of possible implementations 101

6 Conclusion 103

A Technical data of the vehicle 105

B Implementation on the test bench 107

B.l System description 107

B.2 System analysis and modeling 107

B.3 Controller design 112

B.3.1 Feedforward controller 112

B.3.2 Feedback controller 112

XI

Abstract

The demand for individual mobility still increases inexorably, increas¬

ing the use of vehicles with combustion engines. Gasoline engines can

reach excellent emission values, but they suffer from a lower efficiencythan compression ignited engines.

A good way to increase the overall efficiency of an engine-vehicle

system is to improve its part-load efficiency. This can be achieved

by a turbocharger using the enthalpy in the exhaust gas to drive a

compressor, which in turn raises the pressure in the intake manifold.

This allows to reduce the engine displacement, which causes lower

friction and pumping losses.

The application of a turbocharger implicates two problems, namelythe low boost pressure at low engine speeds and the delayed torque

development, the latter being due to the additional inertia broughtinto the system by the rotor of the turbocharger. Whereas the former

issue can be reduced by a sophisticated design, the latter is still critical.

Many solutions to overcome this problem are presented in literature,but they all entail the need for additional hardware.

The new approach presented in this thesis only needs an automated

starting clutch. By opening the clutch partially during the acceleration

phase, the engine can speed up and thus increase the exhaust mass

flow to the turbine. As the turbine experiences a higher enthalpyflow it produces more torque and thus accelerates faster. The faster

increase in speed leads to a faster increase in intake manifold pressure,

yielding a faster torque build-up of the engine.

Opening the clutch creates a new degree of freedom which in turn

poses the problem of an optimal use of this new input into the system.Therefore a new quality function is defined which considers the driver's

wish for a fast as well as a comfortable acceleration.

Furthermore, a mean value model is developed, allowing dynamicsimulations of the torque development of turbocharged spark-ignited

engines. The quality function and the model are then used to find an

optimal torque development of the engine.The results from the clutch-opening strategy have been tested and

verified on a test bench. When starting at a representative load pointof the new European driving cycle (NEDC), the time to reach 90%

of the full-load torque can be reduced by more than 1.8 s. This is a

Xll

reduction in time of 60%.

This new strategy has the potential to increase the acceptance of

the fuel-efficient turbocharged engines considerably and thus reduce

the need for fossil fuels in individual mobility.

xm

Zusammenfassung

Die Nachfrage nach individuellen Verkehrsmitteln steigt nach wie vor

und mit ihr der Bedarf an Fahrzeugen mit Verbrennungsmotoren.Benzinmotoren verfügen über ein ausgezeichnetes Emissionsverhalten,aber unterliegen den Dieselmotoren bezüglich Wirkungsgraden.

Eine gute Möglichkeit, den Gesamtwirkungsgrad von Verbren¬

nungsmotor-Fahrzeugsystemen zu verbessern, besteht darin, den Teil¬

lastwirkungsgrad des Verbrennungsmotors anzuheben. Dies kann

durch einen Turbolader erreicht werden, welcher die Enthalpie im Ab¬

gasstrom nutzt, um einen Verdichter anzutreiben, welcher zu einer

Druckerhöhung im Einlasstrakt führt. Dadurch kann der Hubraum

des Motors verringert werden, welches zu geringeren Reibungsverlu¬sten führt.

Die Anwendung eines Turboladers bringt zwei Probleme mit sich.

Zum einen wird bei zu tiefen Drehzahlen ein zu geringer Ladedruck

erreicht, zum anderen verzögert sich der Drehmomentaufbau durch

die zusätzliche Massenträgheit, die mit dem Läufer des Turboladers in

das System eingebracht wird. Während der erste Punkt durch eine ge¬

schickte Auslegung des Turboladers überwunden werden kann, bleibt

der letztere kritisch. In der Literatur sind diverse Lösungen vorgeschla¬

gen worden, um dieses Problem zu bewältigen. Sie bedingen aber alle

zusätzliche Bauteile und Komponenten.In dieser Arbeit wird ein neue Lösung präsentiert, welche ein¬

zig eine automatisierte Anfahrkupplung benötigt. Durch teilweises

Offnen der Kupplung während der Beschleunigungsphase kann der

Motor hochdrehen und somit den Massenstrom durch die Turbine

erhöhen. Da die Turbine mit einem grösseren Enthalpiestrom versorgt

wird, kann diese mehr Drehmoment erzeugen und somit schneller be¬

schleunigen. Der schnellere Drehzahlaufbau führt zu einem schnelleren

Druckanstieg im Saugrohr und somit zu einer schnelleren Entwicklungdes Motordrehmoments.

Durch das Offnen der Kupplung entsteht ein neuer Freiheitsgrad,welcher die Frage nach dessen optimaler Nutzung aufwirft. Zur Beant¬

wortung dieser Frage wird ein Gütekriterium definiert, welches sowohl

den Wunsch des Fahrers nach einer schnellen, als auch nach einer

gleichmässigen Beschleunigung berücksichtigt.Weiter wird ein Mittelwertmodell des Motors entwickelt, welches

XIV

die dynamische Simulation der Drehmomententwicklung erlaubt. Das

Gütekriterium und das Modell werden anschliessend verwendet, um

den optimalen Drehmomentverlauf der Kupplung zu bestimmen.

Die Ergebnisse dieser so genannten Kupplungsstrategie wurden auf

einem dynamischen Motorenprüfstand getestet und bestätigt. Wird

ein typischer Lastpunkt aus dem neuen europäischen Fahrzyklus als

Startpunkt gewählt, so kann die benötigte Zeit um 90% des Voll¬

lastmomentes zu erreichen um mehr als 1.8 s reduziert werden. Dies

entspricht einer Reduktion der Zeit von 60 %.

Diese neue Strategie hat das Potenzial, die Akzeptanz von ver¬

brauchsgünstigen turboaufgeladenen Motoren markant zu verbessern

und damit den Verbrauch von fossilen Brennstoffen im Individualver-

kehr nachhaltig zu senken.

XV

Nomenclature

Abbreviations, Acronyms, Names

BMEP brake mean effective pressure

CI compression ignition

CVT continuously variable transmission

DOHC double overhead camshaft

DSC downsizing and superchargingFTP-75 American combined drive cycleFMEP friction mean effective pressure

IC internal combustion

mps mean piston speed

MSC mechanical superchargerNA naturally aspiratedNEDC new European driving cycleODE ordinary differential equation

PWSC pressure-wave supercharger

rpm revolutions per minute

SI spark ignition

TC turbochargerVTG variable turbine geometry

VVA variable valve actuation

VVT variable valve timing

XVI

Symbols

Symbol Description Unit

a acceleration m/s2A Area 2

nr

(A/F), stoichiometric air-to-fuel ratio -

B bore m

BSR blade speed ratio -

c specific heat J/kgKci comfort index -

cD discharge coefficient -

d diameter m

f frequency Hz

F force N

H enthalpy J

i gearbox ratio -

I length m

*

m mass flow kg/sn rotational speed rpm

k thermal conductivity w/mK

Kfr flow restriction constant Pa2 sykg2 K

m mass kgNu Nusselt number -

V pressure Pa

pi power index -

Pr Prandtl number -

Qhv lower specific heating value of fuel J/kg

Q heat J

r radius m

rc compression ratio -

R specific gas constant J/kgKRe Reynolds number -

T temperature K

Tq torque Nm

u input variable -

XVII

U

Uc

V

Vd

v

w

x

y

a

7

A

r]

K

(1

n

nw

o

C

p

Î

inner energy

circumferential speed of the compressor

volume

displaced volume

velocitywork

state variable

output variable

throttle angle

weight in agility index

difference

efficiencyratio of specific heats

air-to-fuel ratio

dynamic viscosity

pressure ratio

layout boosting ratio

head parameter of the compressor

normalized mass flow rate

mass moment of inertia

ignition angle

densityload factor auxiliary devices

rotational speed

m

m"

m2

mA

rad

kg/

kg m2

o

kg/m3

rad

Subscripts

Subscript Description

a

air

af

aux

ax

b

c

ambient

air

air filter

auxiliaryaxle

before

compressor, compression

XV111

cat catalytic converter

cb combustion

cl clutch

cd conduction

CS crank shaft

cv convection

cyl cylindercrit critical

ds downstream

D discharge

e engine

eff effective

eg exhaust gas

el electrical

em exhaust manifold

es exhaust system

ex exhaust

ext external

f fuel

fg fresh gas

fl full load

fr friction

flr flow restriction

gb gearboxht heat transfer

i inside

ic intercooler

ig gross indicated

ip intake pipe

im intake manifold

lin linear

m motor

mps mean piston speed

n net

0 outside, out

XIX

p pumping

pr,gl piston rings under gas load

qS quasi-static

r restriction

R receiver

rad radiation

s stoichiometric

sh shaft

t turbine

tb test bench

tc turbochargerth throttle

tot total

us upstream

vap vaporization

veh vehicle

vol volumetric

vvt variable valve timing

wg wastegate

wh wheel

Notational Conventions

Pressure ratios

The pressure ratio over a component, acting as a flow restriction or

pump, is a frequently used quantity. The pressure ratio is alwaysdefined as the pressure after the component (downstream) divided bythe pressure before the component (upstream).

-prPds

Pus

For instance, any device increasing the pressure has a pressure ratio II

above unity, such as the compressor. Any device lowering the pressure

has a pressure ratio II below unity, such as the intercooler or the

throttle.PRC

^ -, TT Pmin - ±^-

> i Uth =^ < 1

Lc th

PRaf PRi

XX

Derivatives

Time derivatives are represented by the respective fractions (Eq. (1)).The flow, which is a quantity transported through a certain area (A)per time unit (dt), is represented by an asterisk (Eq. (2)).

dx

~dt* K A :

x=^-

dt

Subscripts

Subscripts denote components, or refer to states in the control volumes

after the corresponding component.

(i)

(2)

Chapter 1

Introduction

For more than one hundred years internal combustion engines have

been used for automotive applications. Whereas in the first years

power density and reliability where the main development goals, the

set of requirements has become considerably wider. Through the dra¬

matic increase in individual traffic, emissions of the vehicles have be¬

come a serious problem. In the early 1960's emission standards for

automobiles were introduced first in California, then nationwide in

the United States of America [Heywood (1988)]. Emission standards

in Europe and Japan followed. These measures have decreased the

emissions by automobiles considerably. Since the late 1970's catalyticconverters have been used in spark-ignited (SI) engines, which allow a

drastic decrease of NOx, HC and CO emission levels. Despite recent

improvements of the emissions by compression ignited (CI) engines

[Johnson (2003)], they still do not reach the level of SI engines.As neither a replacement of the combustion engine in automotive

applications nor a reduced demand of individual means of transporta¬

tion can be expected anytime soon, further improvements in the ef¬

ficiency of combustion engines continue to be a major goal of the

ongoing research. Soltic (2000) presented a comprehensive compari¬son of different measures to reduce fuel consumption. The SI enginecombined with a catalytic converter is able to reach current and future

regulations on emissions, but it is less efficient than a CI engine. In

this thesis only spark-ignited (SI) engines will be investigated. The

efficiency deficit of SI engines is mainly due to the load control of the

engine, as the air mass flow is throttled in order to control the power

output.

1

2 CHAPTER 1. INTRODUCTION

Among many other measures to improve the fuel consumption,one method is to apply a turbocharger. Investigations have shown

a considerable potential for improvement in this area. In reality the

potential is hardly exploited, as drivers tend to drive in higher gears

and at lower load levels due to the delayed response of turbocharged

engines.

This thesis focuses on demonstrating a way to improve the respon¬

siveness of turbocharged SI engines.

With a model-based approach a new strategy is investigated thor¬

oughly and its applicability is shown on a test bench.

1.1 Spark-ignited engines

1.1.1 Basic principles

The mechanical power an engine can produce is determined by its

efficiency, the fuel it burns, and the lower heating value of the fuel.

Pe = r)e-rhf quv (1.1)

In order to use a three-way catalytic converter for the exhaust gas

aftertreatment of spark-ignited (SI) engines, the fuel has to be burned

at a stoichiometric air-to-fuel ratio (Ac& = 1). A certain power demand

thus leads directly to a corresponding demand for air mass flow.

rriatr = rrif (A/F)s Xcb (1.2)

As a first approach the air mass flow can be modeled as the productof the volume flow, the density of the air in the intake manifold and a

volumetric efficiency.

**

"lair V e 'Pirn '

ijvol

^eJr

Vim /-. 0n=

T~'

Vd'

~^F~' ^ (L3)

4 7T Ri-vm

Combining equations (1.1)-(1.3) yields:

d^e

T/Vim -L

/., ,\

P' = T,-V"-Rf^- "»' ' * '

(A/F), Xd>qHV (L4)

1.1. SPARK-IGNITED ENGINES 3

This equation reveals the dominant parameters of the power produc¬tion.

The rotational speed (ue) is limited by dynamical forces result¬

ing from the moving pistons and valves. For small enginesthis limit is usually not reached due to the bad consumer ac¬

ceptance, resulting from the high-frequency noise [Soltic and

Guzzella (2001)].

The displaced volume (V^) directly influences the dimensions of

the engine, which again is coupled to the friction losses.

Pressure in the intake manifold {jpim) For naturally aspirated

(NA) engines this pressure is limited by the ambient pressure.

The concept of using intake manifold pressures higher than am¬

bient is called supercharging.

1.1.2 Efficiency

Engines in automotive applications are operated in part-load very of¬

ten1. A good part-load efficiency is thus very important.The load in SI engines is controlled by throttling the air mass flow

to the engine, which influences the pressure in the intake manifold.

This method is simple and entails excellent dynamic behavior, but

induces pumping losses. Especially for low loads the efficiency of the

engine becomes very poor.

This characteristic is quite evident in Table 1.1, which lists the

different losses at 15% and at 85% load of an SI engine running at

2000 rpm. At 15% of full load the gas exchange consumes 12.2% of

the invested energy, whereas close to full load the pumping losses are

roughly 2%.

A high potential for improving the fuel consumption comes from

either reducing part-load operation or increasing the efficiency while

operating at low load by reducing pumping losses. Whereas the former

requires a transmission unit with many transmission ratios, e. g., a

CVT, there are several solutions to tackle the latter problem.

1According to Soltic (2000) an engine of 40 kW is operated on average at roughly 10% of its

rated power during the New European Driving Cycle (NEDC)


Table 1.1: Energy distribution in an SI engine operating at 2000 rpm

under different load conditions [Langen et al. (1993)].

Load 15% 85%

Exhaust gases 48.6% 48.5%

Incomplete combustion 2.6% 2.1%

Heat flux through the cylinder wall 9.0% 10.7%

Gas exchange 12.2% 2.1%

Friction 10.3% 6.7%

Work 17.3% 29.9%

Sum 100.0% 100.0%

Equation (1.4) shows that the product of Vd, Vim and ue charac¬

terizes the power output of the engine. All three parameters can be

chosen within certain limits. As the displaced volume directly corre¬

lates to the friction losses, it has to be reduced for better efficiency.This demands higher pressures in the intake manifold or higher ro¬

tational speeds of the engine. As higher rotational speeds are not

accepted by the consumer, the only practicable way is to increase the

pressure before the engine. This approach is known as downsizing and

supercharging (DSC).

1.2 Downsizing and supercharging

1.2.1 Discussion of the concept

As mentioned above downsizing and supercharging can influence the

part-load efficiency positively. A smaller displaced volume reduces the

dimensions of the engine which results in lower friction losses. As an

additional benefit, the operating temperature is reached faster due to

the smaller thermal mass of the engine block.

Three types of superchargers can be distinguished: mechanical

superchargers (MSC), pressure-wave superchargers (PWSC) and tur-

bochargers (TC). They all have some advantages and disadvantageswhich will be discussed below. In general, it can be said that they

1.2. DOWNSIZING AND SUPERCHARGING 5

all increase the system complexity and that they demand a lower in¬

ner compression ratio of the engine in order to avoid the problem of

knocking2.

1.2.2 Mechanical supercharging

For mechanical supercharging blowers, compressors or pumps can be

used. They all are driven from the crank shaft.

The use of a mechanical supercharger involves the following ad¬

vantages and disadvantages:

+ good dynamic response to load demand

+ high boost pressure at low engine speed

+ no heat sink in the exhaust tract, thus faster light-off of the

catalytic converter

- torque to drive compressor is taken from crank shaft

- the compressor must be switched off in part-load operation for

realizing efficiency gains, which results in comfort problems when

the compressor is engaged again

- the drive belt and the considerable volume of the charger con¬

strain the packaging

- noise from pressure fluctuations at the compressor outlet

- dimensions of the compressor scale linearly with dimensions of

the engine displacement, thus the MSC is not suitable for engineswith Vd > 31

1.2.3 The pressure-wave supercharger

The core of the machine is the so-called cell wheel, a set of open-endedchannels arranged on a rotor between two casings. During a rotation,

2Knocking is a form of abnormal combustion where the charge is ignited spontaneously at

exothermic centers in the fresh-gas It appears randomly, can cause damage and strongly dependson the fuel used


each cell is first passing the exhaust manifold, where the entering gas

triggers a shock wave which runs through the cell and compresses the

fresh air. This compressed air then leaves the cell in the direction of

the intake manifold.

The use of a pressure-wave supercharger entails the following ad¬

vantages and disadvantages:

+ high boost pressure at low engine speed

+ very good part-load efficiency

+ good transient behavior

+ external EGR possible without any further devices

- complex control algorithms

- need for additional actuators and sensors

- mixture of fresh gas and exhaust gas possible

1.2.4 Turbocharging

For turbocharging, a turbine in the exhaust path is used to drive a ra¬

dial compressor, which pumps air into the intake manifold. Figure 2.1

shows a system overview.

The use of a turbocharger results in the following advantages and

disadvantages:

+ improved part-load efficiency, as exhaust enthalpy is used to

drive the compressor

+ easily applicable

+ easily controllable (one additional actuator, but no additional

sensor is necessary)

+ cost-efficient and robust production techniques available

o no connection to the crankshaft, but a placing close to the ex¬

haust openings of the engine block is advantageous

1.2. DOWNSIZING AND SUPERCHARGING 7

- increased back pressure decreases full-load efficiency

- low boost pressure for low engine speeds

- delayed boost pressure rise in transient operating condition

- delayed light-off of the catalytic converter due to the heat ex¬

traction from the exhaust gas through the turbine

1.2.5 Conclusion

Langen et al. (1993) compared the gain in fuel consumption of different

DSC concepts and found that a turbocharged engine has the highest

potential for a reduced consumption. In real traffic, the potential is

often not exploited by the driver, as the engine produces less torqueat low speeds and in addition has a delayed torque development. This

so-called turbo lag is due to the need to speed up the turbochargerbefore it can pressurize the intake air. The driver tends to operate

the engine at higher engine speed and thus lower load, which in turn

reduces the benefit from the downsizing supercharging concept. In

Figure 1.1 the fuel consumption of a turbocharged and a mechanically

supercharged engine are compared against the fuel consumption of a

naturally aspirated engine. The left column of each pair represents the

consumption resulting from an American driving cycle (FTP-75). The

right column of each pair depicts the average improvements realized

by a group of drivers. Both columns are scaled independently to 100 %

for the naturally aspirated engine.The big discrepancy between the gain technically realizable by

turbocharging and the gain realized by the consumer demand for a

strategy to overcome the turbo lag. In the automotive industry two

approaches are known.

Reduction of the boost level By designing the engine for low

boost levels, the turbo lag becomes less dominant. On the other

hand lower boost levels also lessen the gain from supercharging.

Improvement of the dynamic response Many approaches are

known to increase the responsiveness of a turbocharged engine

by modifications in the hardware. They are briefly discussed in

Section 3.2.

CHAPTER 1. INTRODUCTION

100%

40%

20% -L-

3%

IFTP-75

Consumer

Group

NA TC MSC

Figure 1.1: Comparison of the gains in fuel economy [Langen et al.

(1993)]

In this work a new approach is presented. This new approach allows to

increase the dynamic performance as well as the comfort by actuatingthe starting clutch.

1.3 Contributions

A new approach to increase the acceptance of turbocharged engines is

developed and investigated thoroughly.In order to investigate the responsiveness problem of turbocharged

engines a mean value model is developed. Most of the components are

modeled with known approaches. One crucial part of the model of

a TC engine is the compressor. Due to the quantitative load control

applied in SI engines, the air mass flow can become very small in part-

load operation. The map of the compressor usually used to represent

its behavior lacks data in this important region of the map, as deterio¬

rating effects render measurements too inaccurate. Here, the approachof Jensen et al. (1991) is extended to the region of low mass flows and

low pressure ratios. This allows an extrapolation of the compressor

map and thus the simulation of this important region.

1.4. STRUCTURE OF THE THESIS 9

Many approaches are known that attempt to quantify the subjec¬tive impression a driver has of a vehicle. Although the problem of the

turbo lag has been discussed for a long time, no index to quantify its

impact on the initial phase of the acceleration has been presented in

the literature. A new, simple, and comprehensive agility index is thus

developed, rating the wish for a fast torque development as well as the

expectation of a predictable and comfortable response to the variation

in accelerator pedal position.A new strategy to overcome the turbo lag is then presented, using

a partially slipping clutch. The control problem arising from this

strategy was solved and verified on an engine test bench.

1.4 Structure of the thesis

Chapter 2 covers the modeling of a turbocharged SI engine. This

model is then used as a basis for the investigation of agility and the

possible approaches to its improvement.In Chapter 3 the reasons for the turbo lag are discussed in detail. A

new index for the quantification of agility is presented. Finally, several

ways to improve the agility are discussed and two new strategies are

shown. Since the strategy with a partially opened clutch offered the

best potential, this strategy is investigated thoroughly in Chapter 4

with a model-based approach. In Chapter 5 the results are verified on

an engine test bench, and finally the applicability of the strategy is

discussed.

Chapter 2

Engine modeling

In order to perform a model-based investigation and optimization of

the dynamic behavior of a turbocharged SI engine, a suitable model

is necessary. There are several methods available to model a dynamic

system:

PT1 model Static maps are extended with one or several PT1 ele¬

ments in order to depict the dynamic behavior of the system.

Calculation time for a step response = o(10ms)l

O-dimensional models Receivers are modeled with lumped param¬

eters for temperature and pressure.

Calculation time for a step response = o(100s)l

1-dimensional models The state variables of the fluid vary alongthe path of the fluid.

Calculation time for a step response = o(l h)l

The O-dimensional approach is also called mean value approach, as

all the state variables in the different receivers represent mean values

of the state variables. It is very suitable for the task formulated,as it provides a sufficient degree of detailing as well as acceptablecalculation times.

After a system overview, the causality diagram for the tur¬

bocharged engine will be presented in this chapter, followed by all

the necessary submodels. The fitting of the maps used to depict the

1on a Pentium III, 700 MHz computer with Matlab

11

12 CHAPTER 2. ENGINE MODELING

compressor and the turbine will be discussed in more detail. Finally,the static and the dynamic identification of the parameters will be

presented.

2.1 System description

Figure 2.1 shows a sketch of the engine under consideration. After the

air filter the fresh air is compressed with a radial compressor. The

intercooler then reduces its temperature before it passes the throttle

and enters the engine. The enthalpy in the exhaust gas drives the

turbine, mounted on the same shaft as the compressor. The wastegateis used to bypass the turbine in case of an excess supply of enthalpy.

receiver after

air filter (Raf)

intercooler (ic)

intake

throttle (th) manifold (im)

exhaust system (es)

catalyticconverter (cat)

p\ wastegate (wg)

exhaust

manifold (em)

crank shaft (cs)

Figure 2.1: Sketch of the turbocharged engine.

2.2. CAUSALITY DIAGRAM 13

2.2 Causality diagram

The causality diagrams for the turbocharged engine are shown in Fig¬ure 2.2. Note that the structure follows the principle of restrictions in

series with control volumes. The outputs of the control volumes are

pressure and temperature, whereas the outputs for the restrictions are

mass flow and temperature of the flowing fluid.

2.2.1 System decomposition and flow directions

The model is built up using control volumes in series with restrictions

and pumps. Whereas for the control volume there is only one typeof model, for the restrictions there are two main components, namely

compressible and incompressible fluids.

2.3 The subsystems

As shown in Figure 2.2 the total model of the TC SI engine consists

of several subsystems, which are described in this section. Each

description is divided into the following categories:

Inputs

Outputs

Parameters

Equations

Assumptions

Remarks

2.3.1 Receiver

There are several receivers in the system that are modeled the same

way. These are:

• Receiver after air filter

CHAPTER 2. ENGINE MODELING

«th

Pamb ^amb

PRaf

T"laf

o

n

Tc

PRi<

o PRc

T9c Tqt

LD

mo

Wtc

Tr1c

O

IE

"ith

£.^

//i

me, fg Se,f

1/"W"g

o

_/ w

III Tem JLt

an?o

Pern

Pu

nil

Tqt

PambPes I Te

T?cl

AC

Tqc

2.2: Causality diagram of a turbocharged SI engine.

2.3. THE SUBSYSTEMS 15

• Receiver after compressor

• Receiver after intercooler

• Intake manifold

• Receiver after turbine

The exhaust manifold is modeled in a special way since heat trans¬

fer through the walls is relevant there.

Each receiver is modeled as a dynamic element with two states

taking into account mass and energy balances.

Inputs

*

fflm kg/s Mass flow in

VTLout kg/s Mass flow out

T-*- us

K Temperature upstream

^Om J/s Heat flow into the system

Outputs

VR

Tr

Pa

K

Pressure in the receiver

Temperature in the receiver

Parameters

Vr9

m Volume of receiver

R J/kgK Gas constant

K - Ratio of specific heats

Equations The model for the receiver is based on mass and energy

conservation laws. The mass balance yields the following time deriva¬

tive for the mass in the receiver:

dm,R(t) * *

T~. fffm ffvout (2.1)


The receiver temperature is derived from the energy balance. The

internal energy in the receiver is:

UR = mRcvTR (2.2)

The complete time derivative of the inner energy is equal to the sum

of the energy flows crossing the system border:

dUR dmR dTR

dt dt dt

^ i^ ^

= Hm ~ Hout + Qm (2-3)

**

The enthalpy flow is H= mcpT. This yields the following expressionfor the time derivative of the temperature

dTR 1 ( *^

*„

dmR * \

—rr= m cPTus

- mout cpTR —— cv TR+ Qm (2.4)a t mR cv\ dt J

which can be rewritten as follows

dTR 1 / * * d mR Q

dt mR

[K,mmTus- KrhvutTds jt^Tr^ — ) (2-5)V at cv J

using the substitution: k = cp/cv.Finally, based on the ideal gas law the pressure is determined from

the mass and temperature

mRRTRVR =^^

(2.6)

Assumptions

• the fluid is a perfect gas

• constant temperature in the whole receiver

• immediate and complete mixture of the incoming gas

• no gas dynamics


2.3.2 Incompressible flow restriction

Flow restrictions are found in several places along the air flow pathof the engine. The engine components that can be modeled using a

standard equation for the pressure loss in an incompressible fluid are:

• air filter

• intercooler

• lumped model of catalytic converter and exhaust system.

Further details and a validation of how well the model structure fits

the components of an engine may be found in Eriksson et al. (2001).

Inputs

Vus Pa Pressure upstream

Vds Pa Pressure downstream

T-*- us


Outputs

*

m

T

kg/sK

Mass flow through restriction

Temperature of the flowing fluid

Parameters

Kfr

Vim

Paz sz

kg2K

Pa

Flow restriction resistance

Linearization limit

Equations The pressure drop for an incompressible flow over a com¬

ponent where there is wall friction, a change in area, or a change in

flow direction can be described by the following equation:

Ap/r = Vus ~ Vds = Kfr— (2.7)Vus


From this expression the mass flow can be solved

Vi

m= Jus

VVus-Vds (2.8)V KfrJ-us

This function has a derivative with respect to the upstream pressure

that m}-Pus> —>. — (X) when pus —> pd.s which can cause problems forMPus

the ODE solver. Therefore the second root is exchanged for a linear

component when the pressure difference is smaller than the limit p\m

Pus \Pus Pds

± I A/ Kr T Vus Vds—

Phn

m={ y KfrTus_ (2.9)KPusT PusPés otherwise-"-/r -*- us -yPlin

Under the assumption of an isenthalpic throttling process the temper¬ature of the flowing fluid is

T = TUS (2.10)

Assumptions Isenthalpic restriction with no temperature change of

the fluid.

Remark If pus < pds backflow occurs. In this case the equationsremain the same, but the pressure and temperature variables have to

be exchanged, i.e. pus ^ pds and Tus ^ T^s, furthermore the mass

flow given as output from the component is then negative.

2.3.3 Compressible flow restriction

The compressible fluid model is used when high velocities occur in the

flow through the restriction. This may be the case in the throttle,the valves and the wastegate, for instance. Since for these compo¬

nents the area of the restriction also changes, the area is added as

an input. When considering compressible fluids a distinction must be

made between choked and unchoked flows.


Inputs

Aeff2

nr Effective area

Vus Pa Pressure upstream

Vds Pa Pressure downstream

T-1- US


Tds K Temperature downstream

Outputs

*

m

T

kg/sK

Mass flow through restriction

Temperature of the flow

Parameters

R J/kgK

Ratio of specific heats

Ideal gas constant

Equations For a derivation of the throttle equations see for example

Appendix C in Heywood (1988). The mass flow through the restriction

is

Cd Ar pus*

m

yRTu^(n) 2.11

Ea± < 1. The product of the discharge coefficient Cd andPus

where II

the real flow area are lumped together to an effective area:

Aefj = Cd A7 ;2.i2)

The function ^/(II) separates the cases of when the flow is choked, i.e.

sonic conditions are reached in the flow restriction, and when it is not

choked

«GÄr)Ä> n<iw

(2.13)^2k

K-l

-K+l

i >n >ncritn« -n

The critical pressure ratio that determines when choking occurs is

( 2ncrit

K+ 12.14)


As the throttle is assumed to be isenthalpic, the temperature after the

throttle is the same as before the restriction.

T = T [2.15)

Assumptions Isenthalpic throttling process, i. e., no temperature

change over the restriction.

2.3.4 Throttle plate area

The throttle plate is used to control the pressure in the intake mani¬

fold. It is modeled as a compressible flow restriction, using the block

described in the previous section. The only addition here is a function

for the effective area.

Inputs

Uth — Throttle signal

Outputs

As2

nr Effective area

Parameters

Cü,th — Discharge coefficient

dth m Diameter of throttle pipe

th,max rad Max. throttle opening angle

a0 rad Throttle angle when closed

Equations The throttle control input uth is within the range [0,1]and the throttle angle is determined as follows:

a = Uth {pLth,max ~ «o) + «0 ;2.i6)

A simple function for the area of the throttle is given below. Figure 2.3

shows a sketch of how the angles used in the equation are defined

Ath(a)ndth

1cos a

cos ( «o;2.i7)


Finally the effective area is

A// = Ahipi) CD,th ;2.i8)

Figure 2.3: Sketch showing the angles used to model the throttle area.

Assumptions The assumptions for the compressible restriction de¬

scribed in Sec. 2.3.2 are valid as well.

2.3.5 Radial compressor

The compressor is mounted on a shaft together with the turbine. Both

devices work radially.

Inputs

^tc rad/s TC speed

VRaf Pa Pressure after air filter

VRc Pa Pressure after compressor

TRaf K Temperature after air filter

Outputs

Tqc Nm Compressor torque*

mc kg/s Compressor mass flow

T-L

CK Compressor temperature


Parameters

Cp J/kgK Specific heat*

mc kg/s Mass flow map = /(IIC, L)tc)Parameters from map fitting

Vc— Efficiency map = /(IIC, mtc)

Parameters from map fitting

Equations

Pr

*

TflrCnc Cp^air-L Raf

n;K-l

1 ;2.i9)

The characteristics of a compressor are measured on a turbochargertest bench and stored in a compressor map. In order to make the

measurements independent of the measuring conditions, the rotational

speed (üütc,tb) and the mass flow (mCjtb) are corrected with reference

Values (Vrefj Tref).

T

&tc — Utc±bref

T

mc = mctb

'T

Vraeas \\ -*- ref

J2.20)

:2.21)

*

m. f(£ütc, nc) map or fitted function J2.22)

The mass flow through the compressor is calculated from the corrected

mass flow:

*

mf

* VRafmc

T

ref

Vref V Tr,afJ2.23)

f]c = f(mc, IIC) map or fitted function J2.24)

Tqc =^Vtc

iffc Cp,air -L be

Ve^te

n;K-l

[2.25)


Tr = Tr

be 1 +n;

re-l

VeJ2.26)

2.3.6 Intercooler

The intercooler cools down the air heated by the compressor and

slightly restricts the air flow. The pressure drop over the intercooler

is modeled using the model flow restriction for incompressible fluids

(see Section 2.3.2). In the test bench setup, the original intercooler is

replaced with a water-air heat exchanger. Its output temperature is

controlled such that it cannot exceed a certain level. A model of the

heat exchanger is thus not necessary.

2.3.7 Mass flow through the engine

The mass flow through the engine is modeled using the volumetric

efficiency r\vo\ and the states of the fresh gas aspirated. The temper¬ature of the fresh gas is decreased by the vaporization energy of the

fuel and increased while it flows through the hot intake pipes.

Inputs

UJe rad/g Engine speed

Vim Pa Intake manifold pressure

Vera Pa Exhaust manifold pressure

T-*- im

K Intake manifold temperature

Outputs

*

iife,air kg/s Air mass flow into the engine

Parameters

vd m Displaced volume

R J/kgK Gas constant

rc — Compression ratio

K — Ratio of specific heat


^ifvap

Cl, c2

J/kg Specific vaporization enthalpyParameters describing heat transfer in

intake pipe

Equations The heat transfer from the wall to the inflowing fluid

was modeled by Zapf (1969) for a compression ignited engine, and

Wimmer et al. (2000) tested the same approach for a spark-ignited

engine. Mladek (2003) finally simplified the model such that it is

applicable for mean value models. The temperature increase due to

convection is:

AT;ht(%ip -ft-ip yJ-wall \-L vm T 2 ')

mfgCp

The heat transfer coefficient can be modeled as:

C2

aip c\ me Tvm +

AT;0.33

ht

J2.27)

J2.28)

The parameters c\ and c^ have to be identified with measured data.

The temperature decrease resulting from the vaporization of the

fuel can be derived with the energy conservation law and yields:

ATrrifAh.

'vap

vap (2.29)(rhf + mmr) cp

These two effects partly compensate each other. For small mass flows,convection from the walls is more important, whereas for high loads

and especially for enriched air-to-fuel ratios the vaporization effect

gains on importance.The temperature of the fluid in the cylinder thus becomes:

T,cyl Tm + ATht + AT- vap ;2.30)

The volumetric efficiency is linked to the residual gas fraction. Fox

et al. (1993) suggest a residual gas model that takes into account valve

overlap and pressures before and after the engine. As a highly boosted

engine is considered here, the valve overlap is very small, which avoids

scavenging losses. Therefore the residual gas fraction is only a function


of the intake and exhaust manifold states as well as of the clearance

volume. Assuming isentropic expansion or compression of the residual

gas, the volumetric efficiency is a function of the compression ratio (rc)and the pressures before and after the engine.

1/kPern,

rivoi,p = ^r (2-31)

The volumetric efficiency is the product of a speed-dependent, a

pressure-dependent and a valve-timing-dependent efficiency.The speed-dependent efficiency f]vo\^ is a curve representing the

speed-dependent effects.

r]voi = r]voi,Uu) r]Voi,p(Vimi Vem) • r)voi,vvt{ue, bmep) (2.32)

The mass flow equation finally becomes:

*/ rp \

_

Vd Ue pvm , .

iife,air\Uei Vimi -Lirai Vera) ijvol , r> m yZ.ooj

4:71 H 1 cyl

Assumptions

• Isentropic expansion of the residual gases from pem to pvm.

• Backflow and scavenging are neglected as valve overlap is as¬

sumed to be very small.

• The volumetric efficiency is modeled without the effects depend¬

ing on gas dynamics (e. g., ram effect) and engine speed.

2.3.8 Fuel mass flow

The fuel mass flow is calculated from the air mass flow into the engine,

considering Ac& as the air-to-fuel ratio in the combustion chamber.

Inputs

*

fffair

AC6

kg/s Air mass flow

Air-to-fuel ratio

26

Outputs

Parameters


fg*

mf

kg/s

kg/s

Mass flow fresh gas

Fuel mass flow

(A F) s— Stoichiometric air-to-fuel ratio

Equations

mf

*

mr,

(A/F)a Xcb

mfg = Tfff +mc

J2.34)

[2.35)

Assumptions It is assumed that the wall wetting dynamics are fully

compensated by the engine control unit and can therefore be neglected.

2.3.9 Torque generation

The torque produced by the engine is modeled as the sum of the three

addends gross indicated work, pumping work, and friction work. In

the torque model, the sum of the air and the fuel flows yields the total

mass flow through the engine into the exhaust manifold.

Inputs

rhe,f kg/s Fuel mass flow*

iife,air kg/s Air mass flow

Vim Pa Intake manifold pressure

Vera Pa Exhaust manifold pressure

UJe rad/g Engine speed


Outputs

Tqcs Nm Torque at crankshaft*

me kg/s Total engine mass flow

Tqi9 Nm Gross indicated torque

Tqfr Nm Friction torque

TqP Nm Pumping torque

Parameters

vd9

m Engine displacementB m Bore

qnv J/kg Lower heating value for the fuel

(A/F)s — Stoichiometric air-to-fuel ratio

Vig— Indicated gross efficiency

nw — Boost layout

Çaux— Factor for auxiliary devices

Cmpsl,2— Parameter for FMEP

cbmep — Parameter for FMEP

CTqli CTq2— Parameters for estimation of brake

mean effective pressure

Equations The model of the engine torque production is based on

three components: the gross indicated work per cycle, pumping work

from the difference in intake and exhaust manifold pressures, and fric¬

tion work consumed by the engine components as well as the auxiliarydevices.

TqcWn Wt„ -Wn-W-,

ig frJ2.36)

47T 47T

The pumping is modeled using the intake and exhaust manifold pres¬

sures.

Wp = Vd (Vem ~ Vim) J2.37)

The indicated work is modeled as

W,w mf qHv -^{XXAd^e J2.38)

In the current implementation the gross indicated efficiency is onlyassumed to be a function of the air-to-fuel ratio


fjtg(\, C, Vd, oje) = i]ig min(l, A) (2.39)

The spark timing will be considered in a separate subsystem (Sec¬tion 2.3.10) and its influence will be implemented as an additional

factor in the torque model (r]Tq,() •

The friction is modeled as

Wfr = Vd FMEP (2.40)

where friction mean effective pressure (FMEP) is based on the ETH

model [Inhelder (1996); Stöckli (1989)], a summary of which is givenin Soltic (2000). The model is derived from data published in papers

about engine friction. Its algebraic expression reads as follows:

FMEP = Çaux [{cmpsi + cmps2 nips1'8) • IIW • 105 + ...

/75\0'5• •• + cbmep BMEP] •

(—J (2.41)

where t;aux is the load from the auxiliary devices, 11^ is the boost layout

stemming from the effect that supercharging has on the dimensions of

the bearings, mps is the mean piston speed and B is the bore. One

disadvantage of this model is that it requires the brake mean effective

pressure (BMEP) to be known before FMEP can be calculated. How¬

ever, there are two solutions: one is to phrase the equations such that

BMEP can be solved from the model, the other is to approximateBMEP using for instance an affine function in the intake manifold

pressure.

BMEP = -cTqi + cTq2• Vim (2.42)

Assumptions The time-varying transport delays from fuel injectionto torque development are neglected.

Remarks There are currently no mean value engine models for in¬

dicated work and friction that can capture the influence of increased

exhaust back pressure.


2.3.10 Torque loss due to delayed spark timing

By delaying the spark timing the torque resulting from the combustion

of the fuel in the combustion chamber decreases and the temperature

of the exhaust gas increases due to a reduced efficiency.

Inputs

AC

Tqcb

0

Nm

Deviation from optimal spark timing

Torque from combustion

Outputs

Tqcb,cATe

Nm

K

Corrected torque from combustion

Temperature rise

Parameters

VTq,C - Torque efficiency due to ignition timing

Equations By analyzing more than 1000 SI engines Gerhardt et al.

(1998) found a heuristic relation between the angle by which the spark

timing was delayed from its optimal position and the resulting ef¬

ficiency of the combustion. This relation can be depicted with the

curve presented in Figure 2.4.

The torque from the combustion is reduced due to the efficiencyreduction resulting from the spark timing delay.

Tqcb,c = Tqcb r)Tq,ç [2 A3)

By reducing the torque the temperature of the exhaust gas is increased

by

Tqcb-ue • (1 -r]Tq,c)AT

^ ' iffeg

'

^p,eg

[2 A4)


O data

— fitted

0 10 20 30 40 50

AÇ[°]

Figure 2.4: Correlation between spark delay and efficiency [Gerhardtet al. (1998)]. For the use in the model, the data is fitted

with a polynomial of 4th order.

Assumptions Without the application of a spark delay AC the

spark timing is assumed to be optimal and the spark timing efficiencyis thus T)Tq,Ç = 1.

The additional enthalpy resulting from the delayed spark timingis flowing through the cylinder walls and to the exhaust gas in equalshares.

2.3.11 Engine out temperature

Eriksson (2002) suggests an affine approach for the engine out tem¬

perature. This approach is extended to non-stoichiometric operatingconditions with an affine approach in Xcb.

Inputs

meg kg/s Total engine mass flow

Outputs

T-L

eK Engine out temperature

0.8

cr

0.6

0.4

0.2

n


Parameters

Teo K Temperature at 0 mass flow

Crp *

1 e,raKs/kg Temperature rise with mass flow

cTe,Xcb K Temperature rise with Xcb

Equations Measured data show that the linear model is sufficient

to capture the temperature variations in the exhaust manifold,

ATTe = Te0 + meg

- (1 - min(Xcb, 1)) •

cTe,xcb (2.45)iff

eg,max

Te,m

where Te o is the asymptote of the engine output temperature at zero

mass flow, AT is the temperature rise over the whole engine flow

region, and meg^max is the maximum flow through the engine.

2.3.12 Temperature at turbine inlet

The temperature at turbine inlet is very important, as it influences

directly the enthalpy flowing through the turbine. Heat transfer from

the exhaust gases to the surroundings decreases the temperature of the

gases flowing through the pipes. The temperature reduction is mod¬

eled as a function of air mass flow and of the internal heat transfer co¬

efficient, which is determined by a user selected correlation. Eriksson

(2002) provides a detailed derivation and a description of the model.

Inputs

*

life,eg kg/s Exhaust mass flow

T-L

eK Temperature engine out

T-La

K Ambient temperature

Outputs

T-1 era

K Temperature before turbine


Parameters

d m Pipe diameter

I m Pipe lengthR J/kgK Gas constant

K — Ratio of specific heat

ß kg/ms Dynamic viscosity

k w/mK Heat transfer coefficient

ifpipe s

- Number of parallel exhaust pipes

Equations First the flow through each pipe is determined by divid¬

ing the total flow by the number of exhaust pipes

*

m

*

mf

pipen.

J2.46)pipes

The temperature drop through a pipe is modeled using a total heat

transfer coefficient from inside of the pipe to the environment. The

total heat transfer coefficient from the interior through the pipe wall

to the environment is:

1

ktot

A, I I 1— 1 1^io "Jcv,i f^cd "Jcv,ext * "Jcd,e T i^rad

[2A7)

In the implemented model this equation is simplified by using the fact

that ai/a0 « 1 and that the conduction through the walls is very highso that l/kcd « 0. In the engine model only the sum of the external

heat transfer coefficients (convection to ambient (kCVjext), conduction

to engine block (kcd,e), and radiation to environment (krad)), is given,i.e. they are lumped together as kext = kCVjext + kcdfi + krad. The total

heat transfer coefficient is then given by

1

ktot k

1 1— +

k[2 AS)

ext

The output temperature of the gas from the exhaust pipe is determined

by solving a simple partial differential equation for the temperature

drop of a fluid in the pipe. The result is the following equation:

ïiûi_

T-L p: Ta + (T, T

-L a.

k d I

g mpipe cP,eg J2.49)


Assumptions The derivation of the equation is based on flow

through a straight pipe with a constant temperature of the surround¬

ings. In this equation the heat transfer by radiation is approximated

by an equivalent linear heat transfer coefficient.

2.3.13 Turbine

The turbine takes energy from the exhaust gases and generates power

to drive the compressor. The turbine acts as a flow restriction and

also reduces the temperature of the fluid. The mass flow through the

turbine is modeled as the flow through a special kind of an orifice.

Inputs

Ute rad/g Turbocharger speed

Vera Pa Pressure exhaust manifold

Ves Pa Pressure exhaust systemT-1 em

K Temperature exhaust manifold

Outputs

Tqt Nm Turbine torque

Tt K Temperature turbine out

*

mt kg/s Mass flow turbine

Parameters

ct

h

cP,eg

kg'VK/s.Pa

J/kgK

Fitting constant for turbine mass flow

Fitting constant for turbine mass flow

Specific heat constant

Equations

Ilt = — <1 (2-50)Vera

Pt = mt- cPjeg ATt (2.51)


The efficiency is defined as

Vt

1--S-T-1- e,m,

[2.52)i-(nt)—

which leads to the following temperature difference over the turbine

AT = T,. 1 :u.K-l

The power of the turbine is defined as

±t lift '

Cp,eg' -L

e:1-OL

Vt

re-1

[2.53)

Vt [2.54)

and its torque can be calculated by dividing the power Pt by the

rotational speed of the turbocharger ujtc

Tqt^t *

Cp^eg* -L era

Utc

1 :n,K-l

^ [2.55)

The mass flow through the turbine is modeled as:

<5>t=ct\l-ll* Vem -r

mt = ,<P

v^

t

[2.56)

[2.57)em

The efficiency can be modeled as a parabolic function of the blade-

speed ratio (BSR) (Figure 2.5). For details see Guzzella and Onder

(2004).The blade-speed ratio is the quotient of the turbine tip speed and

the speed which exhaust gas reaches when it is expanded isentropicallyat the given pressure ratio Ut.

BSRnutc

£ Cp Iem \ 1 11^

(«-!)/«

[2.58)

m = m. '-{{BSR-0.6'

0.6[2.59)


lit,max

0 Ï.2 BSR

Figure 2.5: Model of the turbine efficiency, using a parabolic function

in the blade-speed ratio (BSR).

2.3.14 Wastegate

The wastegate (WG) is used to control the turbocharger speed and

the pressure in the receiver after compressor. The wastegate flow is

modeled as a flow restriction for a compressible fluid (Section 2.3.3).The only component described here is the area function.

Inputs

U"wg— Wastegate control signal

Outputs

Awg,eff2

m Effective wastegate area

Parameters

i'wg,raax m Maximum wastegate lift

Q"wg m Diameter of wastegate plate

Cj),wg — Discharge coefficient

36

Equations


Iwg,eff = mmu% I,

dwg

"wg ,jwg,maxi ,

^-wg,eff = ^D,wg ' ^wg,eff ' TT •

Uwg

J2.60)

;2.6i)

Assumptions Isenthalpic flow restriction, i.e. the temperature of

the fluid does not change while flowing through the throttle.

2.3.15 Adiabatic mixer

In the exhaust system after the wastegate and turbine there is a mixingof the gases. This mixing is modeled as an adiabatic process.

Inputs

Ti K Temperature of flow 1*

m\ kg/s Mass flow 1

T2 K Temperature of flow 2

*

m2 kg/s Mass flow 2

Outputs

T-1 mix

mtot

K

kg/s

Temperature of the mixed flow

Mass flow out

Parameters

cP,i

Cp,2

J/kgK

J/kgK

Specific heat of flow 1

Specific heat of flow 2

Equations The energy equation states that

(mi cPjl + m2 cp^)Tm%x = mx cPjl Tx + m2 cPj2 T2

which leads to the following temperature for the mixture

mi Cp^Ti + m2 cPj2T2

J2.62)

T

mi cPji + m2 cPj2

J2.63)


The mass flow out is just the sum of the mass flows

mtot = mi+m2 J2.64)

Assumptions

• Adiabatic mixing, no heat transfer.

• The mixing takes place at constant pressure.

2.3.16 Turbocharger inertia

The turbocharger speed is modeled using an element with a mass

moment of inertia. The friction in the turbocharger is usually taken

into consideration when calculating the efficiency of the turbine from

measurements. However, the addition of a friction term to the rotat¬

ing system has been reported to solve some problems occurring when

simulating the system.

Inputs

Tqc

Tqt

Nm

Nm

Compressor torque

Turbine torque

Outputs

Utc rad/s TC speed

Parameters

Cfr

kgm2

Nm-s/rad

Inertia of the turbochargerFriction coefficient

Equations The differential equation for the rotational speed ujtc is

dutc 1

dt G(Tqt - Tqc - cfr utc [2.65)

tc


2.4 Calibration of the model

After having defined the whole structure of the model, its parameters

have to be identified. First the parameters of single subsystems are

identified. The main purpose of the final model will be to predict the

torque. Therefore the parts lying between throttle signal and engine

torque are of special importance and will be discussed in detail.

After this step, the whole model is calibrated for steady-state con¬

ditions. Finally the model will be calibrated under dynamic condi¬

tions.

2.4.1 Calibration of the mass flow through the

engine

The mass flow through the engine is a function of many parameters,

as described in Section 2.3.7. Finally the parameters presented in

Table 2.1 were identified with a least square algorithm.

Table 2.1: Parameters identified for the mass flow through the engine

Parameter Symbol Value in

literature

Value

speed-dependent efficiency llvol,LU see Figure 2.6

Parameter 1 in Eq. (2.28) C\ 475 375

Parameter 2 in Eq. (2.28) c2 0.68 0.35

The result of the calibration is depicted in Figure 2.7.

Discussion of the parameters

The parameters found indicate that a heat exchange coefficient is less

dependent on the air mass flow than expected but the heat exchangevalue itself remains within reasonable boundaries.

The influence of the variable valve timing (i]voijVVt) was found to be

small and is only relevant in a small region of the engine map, namelyat high loads and low rotational speeds.

2.4. CALIBRATION OF THE MODEL 39

1

0.8

,0.6

p-S0.4

0.2

0

literature

fitted

0 1000 2000 3000 4000 5000 6000

ne [rpm]

Figure 2.6: Speed-dependent factor (rivoi^) of the volumetric efficiencyfrom Guzzella (1998) and identified values

x10

CO

Q.

2

1.5

1

0.5

0

m*.

[kq/s]

e.airL a J

0.01

0.005

0 1000 2000 3000

ne [rpm]

4000 5000

Figure 2.7: Calibration result of the air mass flow through the engine

The temperature of the intake pipes is assumed to be slightly

higher than the temperature of the cooling water, as the intake valve

is exposed to the combustion.


2.4.2 Calibration of the torque generation

The torque development is modeled as a function of the energy indi¬

cated by the fuel, the effect of the pressure difference over the engineand the losses from friction and auxiliary devices. Aside from the in¬

dicated gross efficiency r\ig three parameters of the friction term are to

be identified (Eq. (2.41)). The results of the identification are listed

in Table 2.2.

Table 2.2: Comparison of the parameters identified and found in

[Guzzella (1998) and Soltic (2000)] for the torque of the

engine


literature

Value

indicated gross efficiency

engine speed-dependent parameter 1

engine speed-dependent parameter 2

load dependent parameter

Vig

Cmpsl

Cmps2

cbmep

0.37

0.464

0.0072

0.0215

0.337

0.36

0.00084

0.0253

In Figure 2.8 the fuel mass per engine cycle is plotted versus its cor¬

responding torque. Note the affine correlation between the output and

the given input as described first by Willans [Urlaub (1994); Guzzella

(1998)]. The same approach is also used in a modified form for the

estimation of the brake mean effective pressure while calculating the

friction in Eq. (2.42).

Discussion of the parameters

The low value of cmps2 indicates a very low influence of the mean piston

speed on the friction, whereas the load dependence is slightly higherthan indicated in literature.

2.4. CALIBRATION OF THE MODEL 41

200

„

150

0 sim

+ meas

E-z.

«100ü

-

#**

50

0

0 0.5 1 1.5

m* / (f/2) [kg/cycle]x10

2

-4

Figure 2.8: Calibration result of the air mass flow through the engine

2.4.3 Calibration of the temperature before

turbine

For the modeling of the turbine inlet temperature, the engine out

temperature has to be identified. The parameters to be identified are

the engine out temperature for a very small air mass flow (Teo), the

slope of the temperature (c^eo) and the influence of the air-to-fuel-

ratio (cXcb).

Table 2.3: Parameters identified for the temperature before turbine


literature

Value

engine out temperature (m = 0)

engine out temperature slope

influence of Xcb

TeQ

CTeO

CAc6

1050 K

150Ks/kg

1170K

218Ks/kg678 K

In Figure 2.9 the temperature before turbine is plotted against the

mass flow. The plot of the temperature values shows an exponential

shape. Only for high mass flows, which correspond to high loads, the

temperature decreases due to the fact that Xcb < 1.


1400

1200

g 1000

I-0 800

600 $

â$# «?

400

o 0.02

$

0+

sim

meas

0.04

m*eg [kg/s]

0.06 C0.08

Figure 2.9: Calibration result of the temperature in the exhaust man¬

ifold, i. e., at turbine inlet

2.4.4 Calibration of the mass flow through the

catalytic converter

Figure 2.10 shows the good results, which can be achieved by modelingthe catalytic converter as an incompressible flow restriction.

Table 2.4: Parameter identified for the mass flow through the catalyticconverter


literature

Value

throttling parameter Kcat - 2- 108

2.5 Map fitting

2.5.1 Motivation for the map fitting

The mass flow through the compressor is a function of the pressure

ratio and the rotational speed of the turbocharger. Due to the difficult

2.5. MAP FITTING 43

$ $

2000 4000

*

6000

Pn ~ Pu

[pal"Res "amb

L J

*0

0 sim

+ meas

8000 10000

Figure 2.10: Calibration result of the air mass flow through the cat¬

alytic converter

flow conditions in the compressor (which is working close to the unsta¬

ble region, deceleration of the fluid), fully physically based models are

still not available for mean value models [Nasser and Playfoot (1999)].Instead of physical laws, maps can be used which represent the behav¬

ior of the compressor. This allows the simulation of the compressor

mass flow in a mean value model (see Eq. (2.21) in Sec. 2.3.5). The

efficiency is depicted in a similar way (Eq. (2.24)).The disadvantages of depicting the mass flow on the basis of maps

are as follows:

• The mass flow function around the surge line is very steep. When

simulating the compressor in this region, the calculated mass

flow becomes unsteady because of the interpolation in this steep

region.

• The finite number of sampling points induces unsteady first

derivatives. This is unfavorable for a numerical optimization.

• The map is the result of measurements on a test bench. The

region with very small mass flow is usually not available, as con-

vective heat transfer negatively affects the measurement of the

efficiency and manufacturers usually do not take measurements


in this particular region. For simulations in this region the data

thus have to be extrapolated.

One way to overcome the drawbacks of a map is to represent the

mass flow and the efficiency of the compressor with functions. The

procedure of finding these functions is called map fitting.

2.5.2 Compressor mass flow

Literature review

In order for the mass flow of the compressor to fit into the mean-value

model, it has to be expressed as a function of the pressure ratio and

the rotational speed.

mc = f(Tic Cute) (2.66)

Müller et al. (1998) suggest a physically based compressor map,

but they still need many parameters to tune the map. Isermann et al.

(2000) use a locally linear neural net to represent the compressor map.

Moraal and Kolmanovsky (1999) compare four different ways of fittinga function into a compressor map. They include an approach of Jensen

et al. (1991), which uses two dimensionless variables, which are: the

head parameter

*c = H- '- (2.67)2 c

and the normalized compressor flow rate

m d$c= °r

withUc=

^ÙJtc (2.68)^ -TTT7-

WithUc=

—

Pa\dlUc 2

The normalized compressor flow rate <ï>c is then approximated as fol¬

lows:

^ = hi ^ ~,h»

k* = ki + ^ Ma (2.69)K'2 + ^c

2.5. MAP FITTING 45

where Ma is the Mach number at the ring orifice of the compressor.

From the fitted compressor flow rate the mass flow can then be calcu¬

lated:

7ffc = /($c, Lute)= /($c(nc,ü>te,fe.),ü>fc) (2.70)

Results

The fitting of the function shown is done by a least-square method

(Gauss-Newton). This approach provides poor agreement, as the

speed lines intersect at an acute angle with the iso-pressure lines.

Much better results can be achieved when using the inverted ap¬

proach:

Uc = f(mC7Cütc) (2.71)

With this approach the speed lines intersect the mass flow lines almost

perpendicularly in the region of interest, which yields good fittingresults. The variables \I/ and <ï> are defined as above, and the fittingfunction becomes:

*' = *££The result of this fitting method is shown in Figure 2.11. The

suggested function is able to capture the shape of the speed lines,

especially at low load and speed that are of interest here. For pressure

ratios IIC < 2 the agreement is good. This is also the important region,as the boost pressure ratio will not be above 1.9.

A least-square algorithm is used to fit the function. The calculation

of the real mass flow (mc) is done according to Eq. (2.23).

Technical aspects of the map fitting

In order to obtain better fitting results in the region of interest (lowrotational speed) the error function was weighted with an affine, speed-

dependent function. This allows to weight the results in the important

region./ ~ \ 1

^tc Ldtc,max/n ,_0\

c{utc) = 1 z:

(2.73)^tc'raax


n [1000rpm]

2.5

„2

1.5

200

AfP^gQ^Q^^

0 0.02 0.04 0.06 0.08

m*c [kg/s]

0.1

Figure 2.11: Comparison of the measured and fitted compressor speedlines

2.5.3 Compressor efficiency

Guzzella (1998a) suggests a method using ellipsoids to depict the com¬

pressor efficiency.

Tlcyffci *-*-c) ilc,max a tyn X

X

tyr

*

m.

*

m,c'raaxi *-*-c

nc,max\

q\q2

q2q3

J2.74)

[2.75)

This method was adapted by scaling the y axis for the fitting:

nc - 1 + y/Uc-l J2.76)

The parameters mC;TOaa;, UCjmax, rimax, qi...3 are fitted using a least-

square algorithm. The results from the fitting can be seen in Fig¬ure 2.12.

2.5. MAP FITTING 47

2.5

„2

1.5

icM

0 0.02 0.04 0.06 0.08

m*c [kg/s]

0.1

Figure 2.12: Comparison of the measured and fitted efficiency of the

compressor.

2.5.4 Turbine mass flow

For the fitting of the turbine mass flow the function from equation

(2.56) is used. The parameters C, K are determined using a least-

square fitting. The results of the curve fitting are shown in Figure 2.13.

2.5.5 Turbine efficiency

The efficiency of the turbine is modeled using the blade-speed ratio,

(Figure 2.5). The parameters mjmax and BSR^max from Eq. (2.59) is

determined using a least square fitting algorithm. The result is shown

in Figure 2.14. For low exhaust mass flows the heat conduction in the

housing of the turbine becomes dominant such that the fluid is heated

after the turbine wheel, leading to too high measured values of the

temperature after turbine. According to Equation (2.52) this leads to

efficiency values that are too high. These values are omitted for the

fitting of the parabola.


Figure 2.13: Fitting of the mass flow through the turbine

1 -

*

• \

0.8

— 0.6 __————'^^— «

•

0.4 -

0.2 -

0 i i

• meas

— fitted

0.6 0.8 1

BSRt [-]

1.2

Figure 2.14: Fitting of the turbine efficiency

2.6 Static calibration of the model

For the static calibration of the engine model, all the subsystems are

joined together in accordance with the causality diagram shown in

Figure 2.2. The engine system has three inputs (angle of the throt¬

tle plate, position of the wastegate, and rotational speed). The only

2.6. STATIC CALIBRATION OF THE MODEL 49

relevant output is the torque at the crank shaft.

For the static calibration the rotational speed is set to a constant

value, as it was during the measurement. The wastegate is controlled

such a way that the pressure after the intercooler (vric) is the same

as during the measurement. Finally the throttle plate is controlled

such that the same air mass flow (me^ir) as in the measured operating

point is achieved.

Concerning the modeling of the turbocharger only the efficiencies

of the compressor and the turbine had to be saturated, such that theydid not drop below certain limits. The very low efficiency levels in the

lower left hand corner of the compressor map (Figure 2.11) result from

heat conduction in the turbocharger housing. In order to achieve the

good agreement of the turbocharger speed as presented in Figure 2.18,the compressor efficiency was not allowed to drop below a value of 0.54.

2.6.1 Results

The results from the static simulation are discussed in this section.

In Figure 2.15 and Figure 2.16 the most important elements of the

causality chain for torque generation are depicted. The causality chain

starts at the intake manifold pressure, continues to the to mass flow

through the engine and ends with the torque generated by the engine.

As the values are now plotted for a complete engine system, the fit¬

ting is no longer as accurate as for the single, unassembled subsystems.Nevertheless it remains within an acceptable range.

The important connection from the pressure in the intake manifold

to the torque produced by the engine is depicted in Figure 2.17. The

agreement of the simulation and measurement results is good.

Figure 2.18 shows the agreement between measured and simulated

turbocharger speed. The result is very good, especially in the regionof low loads and low rotational speeds. Points out of this region will

be used as starting values for the dynamic calibration, which will be

discussed in the next section.

After the static calibration of the whole model, its dynamics have

to be adjusted. This procedure will be described in the next chapter.


x10m*

.

[kg/s]e.air

L a J

2000 4000 5000

ne [rpm]

Figure 2.15: Comparison of the resulting air mass flow plotted versus

the engine speed and the pressure in the intake manifold

«T 0.05

0

Tqe [Nm]

1000 2000 3000 4000 5000

ne [rpm]

Figure 2.16: Comparison of the torque resulting form the mass flow

through the engine

2.6. STATIC CALIBRATION OF THE MODEL 51

x10 Tqe [Nm]

2

1.5

of*=- 1

E

d

0.5

0

0 1000 2000 3000 4000 5000

ne [rpm]

Figure 2.17: Correlation between the pressure in the intake manifold

and the torque at the crankshaft

150

E 100

50

ntc[1000 rpm]

1000 2000 3000 4000 5000

ne [rpm]

Figure 2.18: Resulting turbocharger speeds depicted in the engine map


2.7 Dynamic calibration of the model

In order to get a good agreement of the dynamic traces of the different

output signals, the dynamic elements, namely receiver volumes and

the inertia of the turbine, have to be adjusted.In the results shown below all the values of the volumes and the

inertia were be set to their physical values. The only adjustments had

to be made in the wastegate control.

Figure 2.19 shows a typical result from a comparison between mea¬

sured and simulated data. The initial condition is set to 2000 rpm and

20 Nm. The throttle signal is shown in the upper left-hand field. The

agreement between the pressure after the compressor (vrc) and the

pressure after the throttle plate Vim is good. In the lower right-handcorner the pressures before (pem) and after (pes) the turbine are de¬

picted.

2.7. DYNAMIC CALIBRATION OF THE MODEL 53

x 10

1.5

x:

Z3*"

0.5

°5

5

x10

meas

sim

10 15

TO

D.

1.5

0.5

0 55

x10

10 15

5 10 15

t[s]

1.5

TO

D.

a.

0.5

x 10

150

100

50

10 15

10 15

Figure 2.19: Comparison of the pressures, the turbocharger speed, and

the resulting torque at the crank shaft. Conditions: ne =

2000 rpm, initial load 20 Nm

Chapter 3

Longitudinal dynamicsof a vehicle

As mentioned in the introductory chapter, a turbocharger can be ap¬

plied to achieve the necessary boost pressures for a desired torque at

the crank shaft.

The concept of turbocharging provides the advantage of better fuel

efficiency, but entails some new challenges as well. The turbocharger is

a representative of the group of turbo-machines and works best around

its setpoint. A combustion engine works volumetrically and can thus

cope with any mass flow.

As the turbocharger-engine system is laid out for medium to high

power demands, the boost pressure for low air mass flows is poor, i. e.,

at low engine speeds the engine only develops a low torque.

This problem is not very serious in modern SI engines. If the

combination of the turbine, the compressor, and the engine is well

chosen, the boost level is not too high and a wastegate is applied.

A more serious problem arises from the low-pass characteristic,which is brought into the system by the inertia of the turbocharger.In order to build up boost pressure, the turbocharger has to speed up

after a tip-in by the driver. This leads to an erratic torque develop¬ment. First the boost pressure reaches ambient pressure very fast, but

then the turbocharger has to speed up before the desired torque can

be reached. Figure 3.1 shows this unsteady torque development.

55

56 CHAPTER 3. LONGITUDINAL DYNAMICS OF A VEHICLE

150

100

x10

1.5

cc

± 1

0.5

/

/

E

350

300

250

200

T3

^o 150

HT3

100

50

0

measured

desired

\

/y'V"v,W..n ^ .m

2 4

5x10

1.5

Jz, 1

0.5

/

/

2 4 6 8

t[s]

2 4 6 8

t[s]

Figure 3.1: Torque development after a tip-in at 3 s and its derivative

with the typical peak right after the tip-in

3.1 Quantification of agility

In order to allow an optimization of agility, a quality function and a

test case are necessary. The test case has to depict a critical situation

3.1. QUANTIFICATION OF AGILITY 57

for a turbocharged engine, as well as having to provide a good basis

for future investigations by granting high reproducibility. The qualityfunction has to depict the crucial initial phase of the acceleration. Not

only does it have to depict the power development, but it also has to

rate the comfort a driver experiences while accelerating.

3.1.1 Literature search on agility

For the description of good dynamic behavior there are several expres¬

sions used in literature, such as: good transient behavior, elasticity,reaction time, no turbo lag, agility, good load response, or sprint¬

ing capability. In this thesis the longitudinal behavior will be called

"agility".A number of publications present criteria for the quantification of

the agility of a car.

Singer (1985), Hiereth (1986), and Uthoff and Yakimow (1987)suggest tests in which full load accelerations are made in a certain

range of speeds. In all these tests the mass of the vehicle as well as

the rated power of the engine are very important, since most of the

time the engine is operated close to its peak power. Lundstrom and

Gall (1986) suggest accelerations in a high gear without gear shiftingand measure the time to reach a predefined boost pressure. That

test can be seen as a base for the new test case and quality function

suggested in this thesis. As the tests are executed in cars rather than

on test benches, the engine speeds are not constant, which influences

the results.

Baker et al. (1989) proposes a test where an engine is mounted on

a test bench and the throttle is opened according to a linear function.

The quality function is represented by the time to increase the brake

mean effective pressure by 0.35 bar. Comfort is not considered.

Only Lezhnev et al. (2002) take power as well as comfort into

consideration with a weighted sum. One addend is the time delay

experienced in torque build-up, whereas the other addend measures

the overshoot of the torque.

Besides these specific tests, there are several generally applied tests

may be found in literature:

• £o-iookm/h time to reach 100km/h


• ^0-200 km/h for sports cars

• t\ km time needed for the first km

The elasticity tests emphasize the full-load torque:

• ^60-iookm/h m the second-highest gear

• ^80-120 km/h in the highest gear

Neither of the tests presented so far fulfills all the requirements to

measure power as well as comfort of an acceleration. Most of these

approaches have the drawback that they grant too much weight to the

shape of the full load line and the peak power, whereas they do not

sufficiently consider the dynamic torque development in the first few

seconds.

In List and Schoeggel (1998) a commercial product is presentedwhich can quantify the agility of a vehicle. Fuzzy logic and generic

algorithms are used to find a correlation between vehicle behavior

and subjective impressions by the test drivers. Since a model-based

approach is used in this thesis that procedure is not suitable.

In SAE (1998) a standard is published for quantifying driveability.This procedure is only applicable for existing vehicles and providesa general value of the driveability of the vehicle tested. Thus this

standard is not applicable for the quantification of agility.Since all the presented procedures have certain drawbacks, a new

agility criterion is required.

3.1.2 Specifications for the new agility criterion

The new agility criterion has to reflect the important time period at

the beginning of an acceleration phase, especially when starting at low

load.

The test case

Hand in hand with the need for a new agility criterion comes the need

for a new test case. Especially high load demands at low rotational

speeds are crucial for good driveability. Such a case occurs for instance

when coasting in a high gear and then tipping in the driving pedal.


With this information the test case summed up in Table 3.1 can be

defined.

Table 3.1: The test case

vehicle mid-size car

initial condition cruising at 60 km/hin 4th gear

action tip-in to full load

Assumptions

A driver feels the force between his body and the seat. Linked via his

mass (mfdnver) this force is proportional to the acceleration he experi¬ences.

"driver/Q 1 \

(^driver V /

'f"driver

In order to simplify the problem of quantifying the quality of the

acceleration, the following assumptions are made:

Stiff vehicle For the vehicle under consideration we assume a stiff

drive-train. This assumption is justified, as a good torque developmentat the clutch results in a good acceleration of the vehicle.

No slip Slip between road and tire is assumed to be sufficientlysmall that it can be neglected. This assumption is justified, as all the

tests will be run in 4th gear (Table 3.1).

Consequences If we assume a stiff drive-train and no slip between

wheel and street, the acceleration of the vehicle and the torque appliedto the gear box (Tqci) are proportional.

"driver ^ ("vehicle ^ -^ Qcl V /

Therefore we only consider the torque applied to the gear box Tqc\ for

further investigations.


Analysis of the driver's demands

This allows us to analyze the behavior a driver likes when tipping in.

The driver wants two reactions when pressing the driver pedal

(tip-in):

• as much torque as possible as fast as possible

• a smooth and predictable torque development

The first point can be seen as a power issue whereas the second demand

is a comfort issue.

Both expectations can be fulfilled if the torque develops linearlywith time.

Based on this desired behavior a new cost functional can be de¬

rived. As outlined above, it is helpful to judge agility in terms of power

and comfort.

In the following paragraphs five indices are described. Figure 3.2

displays the torque development of a turbocharged engine and its cor¬

responding indices.

150

100

Ez

75cr

H

50

0

2468 2468

t [s] t [s]

Figure 3.2: Application of the different agility indices to the torque

and its corresponding derivative

90%Tq_

.-

•

e.max^

17-

Ez

cr

Ho

300

250

200

p150

100

50

n £_'NVV-''.UW ^ /


Power Index 1

The first power index (vh) is the inverted slope of the line connectingthe point before tip-in with the point where 90 % of the full load torque

is reached.

t_

( U-^ J- (Jcs,raax\(jJ=const ~ J- Ccs,tipin \(°i°i)

V ^0.9 — Uipm j

The lower this power index is the better.

Power Index 2

The second power index (vh) is the integral of the power consumed

by the clutch on the gear box side in the first 3 s after a tip-in. This

index is especially helpful to compare different strategies on the same

set-up.

Vh = J Tqdugb)tndt (3.4)

The higher it is the better.

Power Index 3

Power index 3 (pi3) measures the time between tip-in and the pointwhere 90 % of the full load are reached. This index does not allow to

compare different operating points or even different engines, but pro¬

vides a good access to the improvement realized by a certain strategy.

Comfort Index 1

The driver expects a predictable increase of the torque. Any deviation

from this optimal trace is penalized with the first comfort index. It

is calculated as the area between the real torque trace and a fictitious

linear trace (cl\ in Figure 3.2).

['t<3 9

dl = / \Tqd,real —Tqci,ideai\dt (3.5)


Comfort Index 2

The second comfort index (cl2) is the highest slope of the real torquetrace divided by the average slope, which is equal to a multiplicationwith the first power index.

^^16 Tgo g-TqUlnn \ dt I

^0 9 ^tipin

The smaller the comfort indices are, the better.

A summary of all the indices can be found in Table 3.2.

Table 3.2: Summary of the different agility indices

acronym description better if

ph inverted slope of the optimal Tq ramp \

Vh Jt0°+3S Pgb,mdtph At90%Tqfc-h J \Tqcijreai — Tqd,ideai\ dt

cl2 max(dT(ici/dt) • ph

While the first power index and the first comfort index will be used

for the optimization, the other indices give a better understanding of

the performance improvements. The indices used for the optimizationare set up such that the smaller they are, the better.

3.2 Solutions for better agility

3.2.1 System analysis

The causality diagram in Figure 2.2 on page 14 not only shows the

dependencies among the various subsystems, but also the inputs to

the engine system. They are listed in Table 3.3.

The ambient conditions (Ta, pa) cannot be controlled and are there¬

fore classified as disturbances.

3.2. SOLUTIONS FOR BETTER AGILITY 63

Table 3.3: Disturbances and inputs of a state-of-the-art turbocharged

engine

Disturbance Variable Input Variable

Ambient temperature Ta Throttle signal uth

Ambient pressure pa Wastegate opening uwg

Spark advance A(Clutch signal uc\

Air-to-fuel ratio Xcb

Although all inputs are potentially useful for increasing the agilityof a vehicle, not all of them can be used.

The air-to-fuel ratio cannot be chosen arbitrarily, because a cat¬

alytic converter is used for the exhaust gas after treatment, which

requires a stoichiometric combustion, i. e., Xcb = 1.

The wastegate in state-of-the-art turbocharged engines is alwaysclosed in order to achieve the highest possible pressure before the

turbine and thus the highest possible turbocharger speed. The higherthe turbocharger speed is, 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. Eriksson et al. (2002) show in

detail why the wastegate has to be closed for the best possible agility.

After all these constraints only two inputs remain, namely the

spark advance and the torque from the clutch. Whereas the sparkadvance can be controlled without any additional hardware, an auto¬

mated starting clutch has to be applied in order to make the torquetransmitted by the clutch controllable.

3.2.2 Solutions with auxiliary devices

As turbocharged engines have suffered from the turbo lag ever since

their invention, many devices have been developed to overcome this

drawback.


Continuously variable transmission

A continuously variable transmission (CVT) allows to shift the gear

ratio without any interruption of the torque on the wheels. This fact

can be used to increase the dynamics of the vehicle. Pfiffner (2001)presents a detailed investigation of the combination of a supercharged

engine and a CVT.

Integrated starter-alternator device

The integrated starter-alternator is mounted on the shaft between en¬

gine and clutch and allows to brake the engine as well as to drive it.

Among many other strategies this set-up allows to assist the combus¬

tion engine until it reaches its full-load. See Zeyen and Pels (1997) for

a more detailed discussion.

Variable valve actuation

Variable valve actuation (VVA) is implemented in order to improvethe filling of the cylinder under full load conditions. As it is alreadyused to maximize the torque output it cannot bring any further con¬

tribution to an increased torque output. Wirth et al. (2000) discuss

an approach to increase the agility of a gasoline direct injection enginewith a turbocharger using VVA.

Variable turbine geometry

At the current state of the art only compression ignition engines and

gasoline direct injection engines can be equipped with turbines with

variable geometries (VTG) as the guide wanes can not (yet) with¬

stand the high temperatures in the exhaust manifold of conventional

SI engines [Lezhnev et al. (2002)].

Combinations of charging devices

In order to improve the dynamic response of a turbocharger the enginecan be equipped with additional charging devices, such as a mechan¬

ically driven supercharger [Cantore et al. (2001)] or by installing a


second turbocharger and an intelligent piping [Tashima et al. (1991);Cantemir (2001)].

Electrically supported TC

By adding an electrical motor to the shaft of the turbocharger, its

dynamic can be improved as well as recuperation becoming also pos¬

sible [Kolmanovsky and Stefanopoulou (2001)]. The downside of this

device is the increased inertia of the turbocharger which is actually

counterproductive and the restrictions in speed of the turbochargerdue to the electrical engine being mounted on the same shaft.

Additional booster for intake manifold

A way to overcome the problem of additional inertia on the same shaft

is to install a second blower, driven by an electrical motor. The com¬

pressor is connected to the intake manifold with a non-return valve.

This blower only has to run during the crucial acceleration phase and

can thus be well dimensioned for its purpose. See Kattwinkel et al.

(2003) for a discussion of the arising control problems.

Additional receiver with pressurized air

Janach et al. (2002) investigate the advantage of storing compressedair in a phase of high boost pressure in order to use it during an

acceleration phase.

Modifications of the turbocharger

Baker et al. (1989) investigated the effect of ceramic turbine wheels

on the agility, whereas Watanabe et al. (1996) improved the agility

by replacing the fluid bearings by ball bearings and thus reducing the

friction.

All these devices achieve a better longitudinal dynamic behavior,but they all entail additional costs for hardware. Therefore further

investigations will focus on solutions requiring few or no additional

devices.


3.2.3 Solutions without auxiliary devices

As derived in Section 3.2.1 only the two inputs, namely the sparkadvance A( and the clutch signal Ud, can be used to influence the

agility of a car.

The ignition angle strategy

The spark advance can be used to help speed up the turbocharger

according to the argumentation summarized in Table 3.4.

Table 3.4: Use of spark advance for improved agility

tip-in

spark advance toward late

—> decreased combustion efficiency—> increased exhaust temperature

—> higher enthalpy flow to the turbine

—> higher torque development of the turbine

—> faster acceleration of the turbine and the compressor

=> faster increase of the intake manifold pressure

Results Preliminary investigations revealed that the strategy pro¬

vides a good means to correct the erratic torque development. The

impact on the agility is positive but very small.

The clutch strategy

In the clutch strategy we use the fact that a higher mass flow throughthe turbine results in a higher turbine speed. The argumentation is

outlined in Table 3.5.

Results In preliminary tests this strategy already revealed its po¬

tential and will thus be investigated in detail. A thorough discussion

of the strategy and its application follows in the next chapter.


Table 3.5: Use of the clutch for an improved agility of a vehicle

tip-in

controlled clutch opening

—> increased engine speed—> higher mass flow through the engine

—> increased pressure in the exhaust manifold

—> higher mass flow through the turbine

—> higher torque development of the turbine

—> faster acceleration of the turbine and the compressor

=> faster increase of the intake manifold pressure

Chapter 4

Optimization

4.1 Model extension

Figure 4.1 shows a sketch of a complete vehicle with engine, clutch,

gearbox, axle, tires and chassis. By applying the simplifications from

Section 3.1.2 the structure can be simplified to a combination of the

engine, the clutch and a well-defined input (see Figure 4.2). The inputwill be derived in the next section.

oooo

Figure 4.1: Sketch of the whole vehicle under consideration

According to these assumptions the engine model derived in Chap¬ter 2 needs only a little extension, namely the clutch model.

69

CHAPTER 4. OPTIMIZATION

oooo &Jgb,m Ç

b)

-> =>

Lüe Tqc Tqd —Tqd ugb,i

a

Figure 4.2: a) Sketch of the reduced system b) Model representationof the engine with its corresponding torques

4.1.1 Modeling of the clutch

The clutch has two subsystems which are alternately in charge, de¬

pending on whether the clutch is engaged or not. The distinction

between the two states of the clutch is made according to the follow¬

ing criterion.

Clutch switching criterion

The clutch disengages if the torque between the clutch plates (Tqd) is

larger than what the clutch can currently transmit.

Tqd > Tqd,r Ud (4.1)

The clutch closes if the speed of the two discs is exactly the same and

if the torque applied is smaller than the torque it can transmit:

UJe Ugb,m A Tqd < Tqd,r Ud (4.2;

4.1. MODEL EXTENSION 71

Modeling the open clutch

Inputs

Ud — Normalized clutch actuation signal

UJe rad/g Rotational speed of the engine

^gb,m rad/s Rotational speed of the gearbox in

shaft

Outputs

Tqd Nm Torque transmitted by the clutch

Parameters

Tqdoo

Tqdo

Nm

Nm

Maximal torque for gliding clutch discs

Maximal torque for adhering clutch

discs

Equations

Tqd,max(A.Lü)

Alu — uje — LUgbjîn

sign(Au) (Tqdoo ~ (Tqdo ~ Tqd

Tqd(Au) = ud Tqd,max(Auj)

|AuOO I

(4.3)

(4.4)

(4.5)

Modeling the closed clutch

In case of a closed clutch, its influence on the drive train disappearsand the inertias of the engine and the rest of the vehicle can be lumped

together.

EquationsGtot

e„ + a

Gveh,tot

e i ^veh,tot

wh "•" ^ ^whj[mveh rl,h + 4 G i2 -i2gb ax

(4.6)

(4.7)

4.1.2 Modeling of the engine dynamics

All pistons and rods, the crank shaft with all the auxiliary devices,and half the clutch are represented through one inertia.

72 CHAPTER 4. OPTIMIZATION

Tqdo

Tqdoo

-Tq{cloo

ALU

-Tqdo

Figure 4.3: Torque delivered by the clutch, depending on the difference

in angular speed

Inputs

Tqcs

Tqd

Nm

Nm

Torque at the crank shaft

Torque at the clutch

Outputs

UJe rad/g Rotational speed of the engine

Parameters

Ge kgm2 Mass moment of inertia

Equations The differential equation for the rotational speed ue is

düüP 1

dt G— (Tqcs - Tqcl I (4.!

Assumptions The friction in the engine and the torque resultingfrom the auxiliary devices are already included in the calculation of

the torque at the crankshaft (see Sec. 2.3.9 for details).

4.2. THE OPTIMAL CONTROL PROBLEM 73

4.2 The optimal control problem

The strategy outlined in Table 3.5 rises the question of how to open

and close the clutch in a way to maximize the agility. With the new

degree of freedom from the clutch opening, an optimal control problemhas thus to be solved.

Figure 4.4 shows all the inputs necessary in order to phrase an

optimal control problem.

quality function test case

(Chapter 3) (Chapter 3)

plant \ /

(Chapter 2) \ / constraints

C optimization problem ")

1optimal solution

Figure 4.4: Overview over the necessary inputs for solving an optimalcontrol problem

4.2.1 Formulation of the optimal control problem

The Plant

The plant is represented by the validated mean value model derived

in Chapter 2 extended by the clutch model derived in Section 4.1.

The inputs to the plant are the load pedal position (uth), the clutch

activation signal (ud), the rotational speed of the gearbox input shaft

(ugb,in), and the wastegate control signal (uwg). As the wastegate is

used to keep the turbocharger at the highest possible speed and for

controlling full-load torque, it is governed by a separate controller and

is thus not available for the optimization.


The quality function and the test case

The quality function and the test case are derived in Chapter 3. The

test case allows the model of the vehicle and of the drive train to be

simplified considerably. In fact they only contribute to the definition

of the boundary conditions of the optimization problem (Fig. 4.2a) ).The quality function is a weighted sum of the power index (pi)

and the comfort index (cl). These two indices represent partially

conflicting goals. Equation (4.9) defines the quality function value J.

The solution of the optimization problem will thus be a Pareto front

with the parameter 7 e [0..1].

J = 1-ph + (l-7)-c/i (4.9)

The constraints

As derived in Section 3.1.2, the speed of the shaft into the gearbox

(ugb,m) can be assumed to be constant.

The speed can be calculated from the torque equivalence when the

vehicle is cruising at the proposed speed of 60 km/h:

-L qgb,m \" drag T "roll T "grade) ^gb'

*ax' '

'wh U ^4.1UJVgb

The three dragging forces can be expressed very simply. The air re¬

sistance is a function of the square of the speed:

"drag ~^' Pair '

--drag' &w '

^veh V /

The rolling resistance is a function of the mass of the vehicle and its

rolling coefficient.

Froii = Ufnc mveh g (4-12)

The force from climbing is zero, as the experiment takes place on a

horizontal street.

Fgr-ade = 0 (4-13)

The rotational speed of the shaft into the gearbox can be calculated

from the vehicle speed:

UVehf a -\ a\

Ugb,m = ~. : (4.14)''gb

'

*ax'

'wh


Solving equations 4.10 and 4.14 with the parameters specified in

Appendix A yields Tqgbjin = 21.95 Nm and ngbjm = 1940 rpm. As

the optimization to follow is not used for the comparison with other

vehicles, but for the comparison with other load points in the engine

map, the following starting point will be used: Tqgbjin = 20.0 Nm and

ngb}Zn = 2000 rpm.

With these equations at hand all boundary conditions are defined.

4.2.2 Means to solve the optimal control problem

Although there is a lot of research going on in the field of optimal

control, there is no generally applicable solution for all optimal control

problems.Several ways exist to find a solution for an optimal control problem.

Figure 4.5 shows a condensed decision tree with some applicable tools

(in capitals).

optimal control problem

indirect methods

-BOUNDSOL

- OPTSOL

direct shooting direct colocation

- MATLAB SIMULINK - DIRCOL

-TOMP

Figure 4.5: Decision tree for optimal control tools

The indirect methods rely on the underlying optimization theory,i. e., they depend on adjoint variables, the Hamilton function, or the

maximum principle (e. g., by Pontryagin). This makes the calculation

often very difficult or even impossible.

direct methods


The direct methods can be divided in direct shooting methods and

direct collocation methods. The former have been known since the

1960's. They use a discretization of the input signals and fulfill the

differential equations of motion via numeric integration. The direct

collocation methods discretize the state variables as well and use col¬

location to satisfy the differential equations.As the order of the system changes when the clutch opens or closes,

the adjoint variables cannot be expressed explicitly. This renders the

indirect methods inapplicable.As all the models are directly at hand in Matlab code, this pro¬

gramming and simulation environment is used for the optimizationtask.

4.2.3 Solving the optimal control problem

The idea of parameterizing the input is fairly standard in the optimalcontrol literature, see e. g., Bryson (1998).

Many ways of parameterization of the input signal (Tqd) were

tested, such as sampling the input signal with fixed and variable sam¬

pling times, superposition of orthogonal polynomials (e. g., Cheby-cheff [Bronstein and Semenjajew (1977)]), but the best results were

obtained by using an educated guess and parameterizing the input sig¬nal by concatenating linear input elements as depicted in Figure 4.6.

The points marked with 'o' were finally used. As the points marked

with 'x' only increased calculation time and did not improve the result

considerably, they were not used for the final optimization.Of the n parameters, n — 1 parameters were chosen by the opti¬

mization algorithm, whereas the n-th parameter was used to attain a

smooth clutch engagement.

Implementation in Matlab For the programming in Matlab

a shell concept was used, as depicted in Figure 4.7. An m-function

generates an input signal in accordance with the n — 1 parameters

obtained from the optimization algorithm. The n-th parameter is

then determined by applying a Regula-Falsi1 algorithm in order to

1The Regula-Falsi method is a robust algorithm to determine the zeros of a function [Bronsteinand Semenjajew (1977)]


TqeJi

ttzpzn ^ S

Figure 4.6: Parameterization of the clutch torque.

ensure a smooth clutch engagement. When all the parameters are

determined, the quality function can be calculated and returned to

the optimization algorithm.

initial parameters parametrization technique

ammeterssignal

generation

u(t)^ l>L + y(t). qualityfunction

input signal output signal

1 optimal parameters

Simulink model

m-function

optimization routine

1 final value of the quality function

Figure 4.7: Shell concept for the implementation of the optimization

strategy in Matlab


4.2.4 Solutions of the optimal control problem

This section presents the results from the optimization. In a first stepthe weight 7 of the power index versus the comfort index is varied,which yields a so-called Pareto front. In a second step a choice of

traces with a specific weight are discussed in more detail.

In order to get the bench mark for the power index, a completeclutch disengagement is allowed for the calculation of a first Pareto

front. Figure 4.8 shows the optimized torque traces with varying

weights 7 at the clutch. For 7 = 0 the solution is a ramp, as comfort

only is demanded. The more 7 is increased, the more the torque drops

right after the tip-in at to = 3 s. Once the clutch is completely open,

the starting of the clutch closing is delayed more and more. Finallythe case of a pure optimization of the power index (7 = 1) is reached.

150

"e 100

15

I- 50

0

2 2.5 3 3.5 4 4.5 5

t[s]

Figure 4.8: Variation of the optimal clutch torque, depending on the

weight 7 G [0..1]

In Figure 4.9 the values of the corresponding power and comfort

indices are shown, representing the Pareto front of the problem.

Figure 4.10 shows the power optimized solution. The clutch is

opened completely up to the point where it can be directly closed

to the value of the full-load torque. The dot-dashed line representsthe torque development of a state-of-the-art engine. Its corresponding

torque at the clutch is equal to the engine torque. The dash-dotted


1

0.8

Jl 0.6

^0.4

0.2

0

0 0.2 0.4 0.6 0.8 1

Pl1 H

Figure 4.9: Calculated Pareto front resulting from the optimizationwith a torque drop.

line represents the torque development of the engine with the applied

strategy and the solid line depicts the torque applied to the gear box.

The time to reach 90 % of the full-load torque can be improved bymore than 2.4 s. Unfortunately, this improvement cannot be realized,as no driver would accept such a torque drop after hitting the load

pedal.

Figure 4.11 shows the optimized torque traces without a torque

drop. Again, the torque trace for the comfort-optimized strategy (7 =

0), is represented by a ramp. With an increasing weight of the power

index, the clutch engagement has to be delayed more and more.

The Pareto front depicted in Figure 4.12 is very similar to the case

with torque drop.Parameterizations with a finer segmentation were tested as well.

The resulting torque trace had the same shapes.

Figure 4.13 depicts the power-optimized case without a torque

drop. The torque rise is delayed as long as possible and then the

torque is directly raised to its final value.

The time to reach 90 % of the full-load torque is slightly worse,

whereas the comfort is improved, but this behavior is still not accept¬

able for an acceleration.

The result from weighting power index and comfort index equally


150

100 -

Ez

cr

50 -

/2.47s

y

/

Tq

Tq

Tq

cl.ref

cs, opt

cl.opt

400

5

t[s]

Figure 4.10: Power-optimized solution with torque drop, 7=1

(7 = 0.5) is depicted in Figure 4.14. The torque increase is only

delayed 100 ms. Thereafter it stays close to the comfort-optimal ramp.

The time to reach 90 % of the full-load torque is considerably longerthan in the power-optimized cases, but it is still more than with 1.8 s

better than the state-of-the-art strategy.The rise in engine speed is now less than 80rad/s.

Summary of the optimization results

Table 4.1 summarizes the results from the optimization of the three

important cases discussed above.


150

"E 100

50

y=0

n I i i i i i i

2 2.5 3 3.5 4 4.5 5

t[s]

Figure 4.11: Variation of the optimal clutch torque, depending on the

weight 7 G [0..1]

Figure 4.12: Calculated Pareto front resulting from the optimizationwithout a torque drop.

The first index is displayed in its inverted form, which represents

the slope of the helping line. As expected, the slope decreases with

the increasing comfort.

It is interesting to see that the work produced within the first 3 s

CHAPTER 4. OPTIMIZATION

150 F

„100 -

50

A-

/2.37s

/

Tq

Tq

Tq

cl.ref

cs, opt

cl.opt

5

t[s]

gure 4.13: Power-optimized solution without torque drop, 7=1

Table 4.1: Summary of the optimization results

Tq-

drop

7

H

(Pli)"1[Nm/S]

pl2

kJ

pl3

N

di

[s-Nm]

Fig.No

ref 36.9 71.0 2.9 80 -

yes

no

no

l

l

0.5

292.1

233.3

114.3

82.6

82.3

83.3

0.4

0.5

1.0

29

26

2

4.10

4.13

4.14


Ez

cr

150

//

1 1

/ /•'

____

—

—

100

/ 1.85s ,-

'

-

50 ~~

^cl.ref-

Tq'cs.opt

Tq^cl.opt

n

300

250 -

TO

200 -

150

5

t[s]

Figure 4.14: Agility-optimized solution without torque drop, 7 = 0.5

after tip-in is only little influenced by the chosen strategy, but in all

cases tested it is considerably higher than in the state-of-the-art case.

The strategy thus not only increases the comfort of the driver

considerably, but also the power output in the initial phase of the

acceleration.

Chapter 5

Experimentalverification

5.1 Implementation on the test bench

The results in Chapter 4 gained with a mean value model of the enginehave to be verified on a real engine. Therefore a turbocharged enginewas installed on a dynamic test bench. The detailed specifications of

the engine can be found in Appendix A.

The setup of the test bench is sketched in Figure 5.1. The engineis mounted on a frame and connected to an asynchronous motor with

a cardan shaft. The motor can be used to brake as well as to propelthe engine. The bandwidth of its torque output extends to 100 rad/s.The power electronics for the motor are controlled with a real-time

PC based system.The gearbox is bypassed and a direct feed-through is implemented

instead. The motor is thus used to emulate the whole vehicle including

gearbox and clutch. In Figure 5.2 the engine is depicted with the

turbocharger.A detailed discussion of the control strategy used to emulate the

clutch can be found in Appendix B.

5.1.1 Choice from the set of optimal solutions

In Section 4.2.4 a set of optimal solutions was presented. They all have

different ratios of power and comfort. By applying further conditions

85

CHAPTER 5. EXPERIMENTAL VERIFICATION

TC SI enginewith gearbox

asynchronous power PC with

motor electronics real time

I system

-o cH

data link

Figure 5.1: Setup of the test bench for the implementation of the clutch

strategy

11 four-cylinder SI engine coupling to electric motor with torque shaft

turbocharger gearbox in direct gear

Figure 5.2: Engine on the test bench equipped with a turbocharger

5.1. IMPLEMENTATION ON THE TEST BENCH 87

the most suitable solution from this set can be chosen. Because of

comfort considerations the torque is not allowed to drop. As a rule

of thumb, 100 ms after tip-in the driver wants to feel the acceleration

and from the set fulfilling these conditions the one with the highest

power index is chosen. These constraints are summarized in Table 5.1.

Table 5.1: Additional constraints for the choice of an optimal solution.

> no torque drop

> delay from tip in to torque increase not more than 100 ms

> highest possible power index

This set of applications leads to a weight 7 = 0.5. Its corresponding

torque trace can be seen in Figure 4.14.

5.1.2 Results

Results from the chosen starting point

The torque signal found to be optimal in the previous section was

applied on the engine on a test bench. Figure 5.3 shows the results.

The dashed lines represent the optimized strategy, whereas the solid

lines represent the state-of-the-art strategy. The torque signals are

filtered for better readability. In the optimized case the torque at

the clutch develops linearly, as desired. The emulated clutch openingresults in an increased engine speed, culminating about 80 rad/s above

the initial value. In the upper right-hand corner the turbocharger

speed is shown. Due to the clutch strategy the turbocharger can speed

up considerably faster. The graph in the lower right-hand corner shows

a comparison of different indices.

Note that the very promising results from the simulation in the

previous chapter are now verified experimentally. The time to reach

90 % of the full-load torque can be reduced from 3 s to 1.2 s. This very

nice result is achieved by only optimizing the control of the system.The hardware remains unchanged.

The power and the comfort index are normalized to be one for

the state-of-the-art case. As expected the power index as well as the

comfort index can be improved considerably.


x 10

400

350

300

^2502 200

150

100

50

0

/ \

v

4 6

t[s]

0

2 4 6

t[s]

3

2.5

2

1.5

1

0.5

t_90 pl_1 cl_1

Figure 5.3: Measurement of the agility improvement of a downsized

and supercharged engine, starting at 2000 rpm and 20 Nm

It is also interesting to note that this very good results are neither

achieved by optimizing the engine nor by optimizing the gearbox to¬

gether with the clutch. The good results are achieved by optimizingthe engine-clutch-gearbox system.


Varying starting points

In the Figures 5.4 - 5.8 the results from varying starting points are

presented. In Figure 5.9 each square represents a different starting

point. The darker a square is the more the time to reach 90 % of the

full-load can be improved.When starting at 2000 rpm the biggest improvement can be at¬

tained. For lower engine speeds the full-load torque becomes smaller

due to a lower boost pressure achievable. The less the turbochargercan contribute to the torque development, the smaller is its influence

on the dynamic torque development. This directly decreases the im¬

pact of the clutch strategy as well.

For engine speeds above 2000 rpm the impact decreases as well, but

for another reason. With higher engine speeds the mass flow increases,which leads to higher initial speeds of the turbine and compressor,

resulting in a faster response of the turbocharger. At 3000 rpm and a

load of 10 Nm the gain becomes very small, as shown in Figure 5.8.

With higher loads the air mass flow through the engine increases

as well. With higher air mass flows the initial turbocharger speedincreases and the turbo lag is thus less critical.

Although the region with a strong improvement is not very large, it

is a very important region. For the assessment of this fact a frequency

analysis of the new European driving cycle (NEDC) is used, as this

cycle is to represent an average driving habit. In Figure 5.10 the

frequency distribution of the operating points for a complete NEDC

is plotted for a VW GOL. The operating frequency is the operatingtime in the corresponding operation area divided by the total cycleduration. The engine's idling duration is taken into account but not

plotted.The points frequently used and thus of high importance lie exactly

in the region of where the clutch strategy can provide a considerable

benefit.

90 CHAPTER 5. EXPERIMENTAL VERIFICATION

Tq =20Nm, n = 1500rpm Tq =20Nm, n = 1750rpm

150 150

400 400

300

2 200

300

ST

2 200

100 100

0 0

2 4 6

t[s]

2 4 6

t[s]

2.5

1.5

0.5

2.5

2

1.5

0.5

t_90 pl_1 cl_1 t_90 pl_1 cl_1

Figure 5.4: Measurement of the agility improvement, initial load

20 Nm, initial speed 1500 rpm, 1750 rpm, respectively


Tq =40Nm, n = 1750rpm Tq = 10Nm, n = 2000rpm

150 150

F 100

400 400

300

ST

2 200

100

300

ST

2, 200

3

100

/ \

J_ A.

0

2 4 6

t[s]

2.5

0 L

2

3p

2.5

2

1.5

4 6

t[s]

0.5

t_90 pl_1 cl_1

II In Lt_90 pl_1 cl_1

Figure 5.5: Measurement of the agility improvement. Measurements

start with 1750 rpm and 2000 rpm. When starting at

2000 rpm the highest improvements can be achieved.


Tq = 20Nm, n = 2000rpm Tq = 40Nm, n = 2000rpm

150 150

F 100

50

400 400

300

ST

2 200

100

/ \

_^,

300

ST

2, 200

3

100

/ \

4 6

t[s]

4 6

t[s]3 3

2.5 2.5

2 2

1.5 1.5

1 1

0.5 1 1 0.5 1 10

1 L0

1 nt_.90 PL_1 cl_1 t_.90 PL_1 cl_1

gure5.6: Measurement of the agility improvement. Starting points:20 Nm/2000 rpm and 40 Nm/2000 rpm



ref

opt

150

F 100

50

400 400

300

ST

2 200

100

\

300

ST

]| 200

3

100

/ \

0

2 4 6

t[s]

t_90 pl_1 cl_1 t_90 pl_1 cl_1

Figure 5.7: Measurement of the agility improvement. Starting points:60 Nm/2000 rpm and 20 Nm/2250 rpm



150

100

400

300

ST

]| 200

0)

100

/ \

150

100

400

f\

300

2, 200

0)

100

0

2 4 6

t[s]

0

2 4 6

t[s]

2.5 2.5

1.5

:l l\ I Int_90 pl_1 cl_1 t_90 pl_1 cl_1

Figure 5.8: Measurement of the agility improvement. Starting points:40 Nm/2250 rpm and 10Nm/3000rpm. For the last start¬

ing point the improvement is very small due to good per¬

formance of the state-of-the-art solution.


150

E 100

CT

K50

0

0

12 16

1115 18 11

280

300

320 -^"g/kWh

0 29

1 9"

2000 4000 6000

ne [rpm]

w

o

Figure 5.9: Gain in £90 (time to reach 90% of the full-load torque) in

the engine map, fuel consumption specified in g/kWh

150

"e 100

<D

I- 50

0

1000 2000 3000 4000 5000 6000

ne [rpm]

Figure 5.10: Frequency plot of the different load and speed points in

the NEDC, applied to the vehicle under consideration.

Idling point is not displayed (24 %) for better resolution.

The fuel consumption is specified in g/kWh


5.2 Remarks on the implementation of

the clutch strategy in a car

5.2.1 Clutch specifications

So far the clutch strategy for an improved agility was tested with a

dynamic model and on a test bench. As it was not possible within

the constraints of the project to implement the strategy in a car, some

theoretical reflections are presented.As the name of the strategy already says, the clutch is the central

element of the strategy. It thus has to fulfill certain specifications:

Automated The clutch has to be automated in order for the torquein the clutch becoming an input into the system.

Design Because of the more frequent use of the clutch, it has to be

designed in a virtually wear-free way. According to Steinhagen

(1980) a wet clutch can fulfill this requirement.

Bandwidth Schreiber et al. (2003) present an automated clutch

which can realize a torque ramp of 320 Nm in 50 ms. A clutch

with these specifications allows the implementation of the clutch

strategy.

Torque adaption The responsiveness can be further improved by

continuously keeping the clutch torque just slightly above the

engine torque, so that the clutch actuator only has to travel

very little until the clutch opens [Fischer and Salecker (1997)].

When the clutch is operated in slipping mode, the question arises

whether it can absorb the heat produced during the acceleration phase.The heat flux to be absorbed is equal to the difference between the

inflowing and the outflowing power.

7,rin

r out

dt

= LüeTqd-LügbTqd (5.1)

5.2. IMPLEMENTATION OF THE CLUTCH STRATEGY 97

The energy to be absorbed during one strategy application is thus

the integral over time from the opening of the clutch (to) to the pointwhen the clutch engages again (ti).

Qd = ue- Tqd -

LOgb Tqd dt (5.2)Jto

The simulation of the proposed strategy yields the heat to be absorbed

by the clutch plates as Qd = 0.22 J/mm2.This value is well below the acceptable limits given by Winkelmann

and Hartmuth (1985):

Table 5.2: Acceptable heat to be absorbed in a clutch [Winkelmannand Hartmuth (1985)]

Action maximal heat density

Shifting in a car

Shifting in a light-weight truck

1 •J/mm21.2 J/mm2

For a clutch the start of the vehicle is the critical case. As the

clutch strategy is shorter and requires less differential speed between

the clutch plates, the energy to be absorbed becomes smaller and thus

less critical.

5.2.2 Emissions

The application of the clutch strategy increases the engine dynamics

considerably. The correct control of the air-to-fuel ratio and the spark

timing could therefore be problematic.

The steepest torque increase happens in the state-of-the-art as well

as in the optimized case between tip-in and the moment when the full-

load torque of the underlying naturally aspirated engine is reached.

The control of the emissions is thus not a more difficult task than in

a state-of-the-art set up.


5.2.3 Implementation without a priori knowledge

The implementation of the clutch strategy entails the problem that

the torque ramp has to be followed without knowing a priori how the

torque of the turbocharged engine evolves. As the torque of the en¬

gine and the engine speed correlate strongly, small errors in the clutch

torque can have a big influence on the smoothness of the clutch en¬

gagement. In the following paragraphs a robust strategy to overcome

this problem will be presented.The strategy will be verified on the most critical case, which is a

driver demanding maximum torque. Lower torque demands can be

fulfilled more easily.

Among the different solutions tested for the implementation the

most robust behavior can be achieved as follows:

• Choose a grid of starting points in the engine map

Determine the optimal solutions for all the starting points offline•

• Parameterize the resulting clutch speed difference by a polyno¬mial of hth order which fulfills the following boundary conditions:

— The speed difference between the two clutch plates at tip-inis zero

Aud(t)\to = 0 (5.3)

— The speed difference between the two clutch plates when

the engine reaches its full-load torque is zero.

Aud(t)\ti = 0 (5.4)

— The derivative of the speed difference between the two

clutch plates when the engine reaches its full-load torque is

zero.

dAujd(t)dt

= 0 (5.5)

Including these boundary conditions, only three free parameters

remain.

• Store the resulting parameters in a map


• Store the parameters describing the optimal clutch torque trace

for the same grid points

• Use gain scheduling to determine the parameters for any given

starting point

In Figure 5.11 the optimal solution with a correct parameterizationof the clutch speed as well as the result of a parameterization error

of ±10% is depicted. Even in case of wrong parameterization, the

torque rises in a constant manner before it reaches its maximum level.

If the speed signal is chosen too high, a slight jerk cannot be

avoided, as the additional energy stored in the engine's inertia has

to be brought back into the system somehow. A speed trace that is

parameterized too low is less problematic as the engine just does not

reach its full-load torque as fast as intended.

5.2.4 Consumer acceptance

After the discussion of all the technical aspects of the clutch strat¬

egy, the consumer acceptance has to be discussed as well. A driver

mainly perceives the application of the clutch strategy through an al¬

tered torque development and a changed sound during the acceleration

phase.

As no experiments with a car were possible, only theoretical con¬

siderations can be used. In Table 5.3 the expected effects are summa¬

rized.

The higher acceleration capability as well as the improved com¬

fort will increase the acceptance of vehicles with turbocharged enginessince the number of gearshifts necessary can be reduced.

The effect of the sound is the most difficult part to be rated. As

Figure 5.3 shows a short rise of the engine speed, culminating at 80 rad/sabove the value without the strategy. This raise is most probablyaudible. As this rapid change in engine speed occurs unexpectedly, it

could be rated negative. On the other hand, since it yields a better

acceleration, it might be accepted as a sign for the ongoing boosting.


200

Figure 5.11: Results of disturbed and optimal implementations ob¬

tained by simulation. The solid line represents the nom¬

inal case with correct parameterization, the dashed line

a too low parameterization of the engine speed and the

dash-dotted line a too high parameterization. The bot¬

tom graph shows the engine speeds and the top graph

depicts the corresponding torque development. Even for

such high parameterization errors as ±10% a constant

torque rise and an acceptable clutch engagement can be

achieved.


Table 5.3: Rating of the consumer acceptance of the clutch strategy

Consequencefrom the

clutch

strategy

improved

torque

build-up

improvedcomfort

change in

engine sound

Expected

Rating± ± o(-)

Effect

use of higher

gears —>

improved fuel

efficiencyx

Better

acceptance of

cars with TC

engines

-

5.2.5 Discussion of possible implementations

Frequency of use

The strategy can be used for different purposes. It can either be used

for any acceleration in which the uneven torque development could

bother the driver or it could be applied only in the case of kick-down,

providing the driver with a faster torque development. If the strategyis used only for kick-down, a dry clutch could be considered as well.

Torque converter

When a torque converter is installed, the suggested strategy is inher¬

ently implemented. If a soft torque converter is applied, the enginecan speed up, but the driver experiences a delayed response. A stiff

torque converter, however, causes the responsiveness to increases, but

it prevents any fast engine speed-up, which would have been a desir¬

able effect.

One way to overcome this problem would be to use a torque con¬

verter with either variable guide vanes or a controllable bypass clutch.

This would allow the application of the clutch strategy and to profit

See Section 1 2 for a detailed discussion


from the faster torque increase, if the dynamics of the actuator can

fulfill the conditions listed in Section 5.2.1.

Diesel engines

The clutch strategy has been developed and tested for spark ignited

engines. As compression ignited engines suffer from the turbo lag as

well, the same strategy can be applied as well. Since their variation

in air mass flow is far smaller, namely a factor of 6.5 instead of the 35

typical for SI engines, the turbocharger speed would remain on higherlevels and the gain from the clutch strategy would thus be smaller.

Heavy duty application

Heavy trucks are typically equipped with automated clutches, which

doubles the clutch lifetime compared to clutches in manually shifted

gearboxes. As wear is one of the main arguments for the automati¬

zation of the clutch, any strategy increasing the wear of the clutch is

not suitable.

Chapter 6

Conclusion

Turbocharging combustion engines provides a considerable potentialfor lower fuel consumption. However, due to delayed torque develop¬ment the driver tends to use lower gears, resulting in higher engine

speeds and lower loads. With this behavior most of the fuel saving

potential cannot be realized. This fact calls for a strategy eliminatingthe turbo lag or at least reducing it considerably.

For the investigation of the turbo lag, an agility criterion is sug¬

gested and used for the improvement of the dynamic torque devel¬

opment of the engine. The quality function weights the desire for a

fast torque increase as well as the need for a predictable and smooth

torque development.As turbocharged engines have suffered from the turbo lag ever

since their invention, many devices were developed to reduce the lag.In this work two strategies are investigated that do not require any

additional devices. The use of a modified spark timing improves the

comfort of the acceleration considerably, but the work output of the

engine is decreased. By applying the so-called clutch strategy, the

clutch is partially opened during the acceleration phase, allowing the

engine to speed up and thus increase the air mass flow. This in turn

increases the enthalpy flow to the turbine, forcing a faster speed-upof the turbine and the compressor. By closing the clutch again in a

suitable manner the kinetic energy from the inertia of the engine flows

back into the gear box, allowing the full load torque to be reached

even faster.

This strategy provides an accelerated torque development as well

as an increased comfort for the driver. This will not only increase

103

104 CHAPTER 6. CONCLUSION

the acceptance of turbocharged SI engines but also favor a more

consumption-optimized driving pattern.

The clutch strategy was developed based on models and verified on

an engine dynamometer. The experiments confirm the improvement

expected from the simulation. Accordingly, a patent has been filed

[DaimlerChrysler (2003)] that includes the main points of the clutch

strategy.In a next step the results will have to be verified with a vehicle

equipped with an automated clutch. This will allow to test the appli¬

cability of the strategy in different driving conditions and allow to gainresults on the influence of the clutch strategy on the driving pattern.

The only relevant premise is the use of an automated wet clutch or

a torque converter with a variable characteristic. Automated clutches

are already available in production type cars and the constructive

effort will thus be very small to realize this new technology.

By following a system oriented approach, combining the potentialof the turbocharged engine with an automated clutch, a considerable

improvement of the whole system has been achieved.

Appendix A

Technical data of the

vehicle

Table A.l: Technical data of VW GOL 1.0 turbo engine

engine VWGOL 1.0 16 V turbo

peak power 82 kW

rated torque 155 Nm@ 2100 rpm

displaced volume 999 cm3

stroke 67.1mm

bore 70.6 mm

compression ratio 10.5 : 1

number of cylinders 4, in a row

number of valves 16

valve train DOHC, 2-point VVT

105

106 APPENDIX A. TECHNICAL DATA OF THE VEHICLE

Table A.2: Technical data of VW GOL 1.0 turbo

gearbox 5 gears

I

II

III

IV

V

final transmission

driven wheels

3.9

2.12

1.29

0.97

0.8

2.951

front

vehicle compact car

mass

doors

1050 kg5

driving performance

top speed

t (0-100 km/h)

192 km/h9.5s

Table A.3: Other parameters of VW GOL 1.0 turbo, general values

from Bauer (1995)

air resistance parameter c%

rolling resistance ur

0.32

0.012

1 Identified with information from Automobilrevue (2002)

Appendix B

Implementation on the

test bench

The strategy suggested in Chapter 3 was tested on a test bench. For

the emulation of the clutch, a dynamic test bench was used. This

test bench will be described in the following section. Thereafter an

analysis of the system will be presented and a controller consisting of

a feedforward and a feedback path will be designed and tested.

B.l System description

A cardan shaft is used to connect the engine and the asynchronousmotor. The shaft is equipped with a torque measurement sensor, al¬

lowing to determine the torque produced by the engine. The installed

gearbox is bypassed and the clutch is only used while starting the

engine. The clutch is emulated with the electrical motor. A generaloverview of the test bench is provided in Figure 5.1.

B.2 System analysis and modeling

By opening the clutch in a real vehicle, all the inertias of the drive

train and the vehicle are decoupled.In order to allow the emulation of a disengaged clutch the inertia

of the electrical motor has to be compensated. The system thus has

to be identified in a first step.

107

108 APPENDIX B. IMPLEMENTATION ON THE TEST BENCH

The system to be emulated is shown schematically in Figure B.l,

a) representing the setup of the test bench, b) showing the system to

be emulated, and c) depicting the corresponding physical model of the

test bench.

a TC SI enginewith gearbox

asynchronousmotor

testbench setup

b)system to be

emulated

n n

nn

physical model

Tqcs Lüe Tq.sh Tq

-> <p

sh ujmTqtel

a Or

Figure B.l: The system to be emulated is compared with the setup

on the test bench and the physical model used for the

identification of the test bench.

Under the assumption of a stiff connection between the engine and

the electrical motor, the speeds of the engine and the motor are the

same.

Lüe= Lüm = Lütb (B.l)

B.2. SYSTEM ANALYSIS AND MODELING 109

The differential equations for the rotational speed of the two inertias

can be written using d'Alembert's law.

^ = ^(Tte-Tto) (B.2)

due 1

dt O—(Tqcs-Tqsh) (B.3)

e

Using equations (B.1-B.3) yields the differential equation for the ro¬

tational speed of the test bench.

^T- =

r,

l

r,(TVcs ~ Tqel) (B.4)

The analysis of Eq. (B.4) reveals an integrating behavior between the

electrical torque and the rotational speed of the test bench. In or¬

der to identify the transfer function, a frequency analyzer was used.

Figure B.2 shows the measured and identified Bode plots. The shapeof the transfer function can be depicted by a low-pass element much

better than by an integrator. This effect comes from the speed de¬

pendence of the torque of the engine Tqcs(u)e). For low excitation fre¬

quencies the engine speed changes considerably and the torque from

the engine does not remain constant, although the throttle position is

kept constant.

The PT1 element depicting the transfer function best is:

PTqel2^ = 9totS\ 0 6withetot = 0M (B.5)

At high frequencies the agreement of the magnitude is good, whereas

the phase decreases faster than identified. This can be explained with

delays and the resulting phase drop.For the identification of the transfer function from the electrical

torque (Tqei) to the torque in the shaft (Tqcs) the rotational speedsare set equal (B.l). By combining (B.2) and (B.3) the correlation

between the torques becomes

1

{Tqsh - Tqel) = )-(Tqcs - Tqsh) (B.6)m. C

e


20

QU

p.

O)

CD

-20

-40

-60

meas

id

10

co [rad/s]

Figure B.2: Bode plot depicting the transfer function from Tqd —> lvt

With some simple algebraic transformations the torque in the cardan

shaft Tqsh can be expressed as:

Tqsh1

0P + Or-(eeTqd + emTqe (B.7)

The torque at the shaft is related to the electrical torque in the motor

with the algebraic factor ee/(ee+em) < 1.

B.2. SYSTEM ANALYSIS AND MODELING 111

10

co [rad/s]

Figure B.3: Bode plot depicting the transfer function from

TqeJ - Tqsh

The expected result is only partially visible in the Bode plot. At

very low frequencies, the torque from the crank shaft (Tqcs) is not

constant. At frequencies higher than 100rad/s the magnitude rolls off

and a delay can be identified in the phase plot. The replacing trans¬

fer function is a linear combination of a zero and a pole, a second-

order low-pass element and a delay approximated with a Padé element


(Eq. (B.8)). Figure B.3 shows how good the agreement is.

PTqel2Tqsh = Pzp PPT2 Pdelay (B.*9r

-s + 0.2p, =e£+eI2—: /BQx

ps+ 0.2

v ;

with—^-— = 0.3 (B.10)G 4- G

P^2 = -2—T^—-^ (B.ll)

with C = 1 and lui = 110 rad/s

Pdelay = pade(T = 10 ms) (B.12)

Solving Equation (B.5) and Equation (B.10) for GTO and Ge yieldsthe following values for the inertias: GTO = 0.25 kg m2 and Ge =

O.llkgm2.

B.3 Controller design

B.3.1 Feedforward controller

For the best possible feedforward control, the identified transfer func¬

tion is partially inverted. For a good roll-off behavior, a second-order

low-pass element is connected in series with the inverted controller.

B.3.2 Feedback controller

Whereas the feedforward part of the controller is mainly used for a

highly dynamic response, the feedback part cannot be tuned as fast

and is used to eliminate stationary errors. It is designed as a PI

controller.

The final result is displayed in Figure B.4. The magnitude of the

closed-loop system is close to the desired 0 dB-line up to a frequencyOf 60 rad/s.

B.3. CONTROLLER DESIGN 113

20

inT3

CD

-20

-40

-60 L

io~

P

P with ff

P with ff & fb

010 10 10 10

Figure B.4: Bode magnitude plot of the transfer function

Tqci,ref —> Tqc\.

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Curriculum Vitae

Personal Data

Name: Simon Andreas Frei

Date of birth: July 28, 1973

Parents: Siegfried Frei and Bertha Frei-Alder

Education

1980-1986 Primary school in Warth-Weiningen TG, Switzerland

1986-1988 Secondary school in Hüttwilen TG, Switzerland

1988-1993 Gymnasium in Frauenfeld TG, Switzerland

1993 Matura certificate, type C

1993-1994 Military service

1994-1999 Studies in mechanical engineering, Swiss Federal

Institute of Technology (ETH) Zurich, Switzerland

Major in system dynamics

1999 Diploma as Dipl. Masch.-Ing. ETH

1999-2004 Doctoral student and research assistant at the Mea¬

surement and Control Laboratory, Swiss Federal

Institute of Technology (ETH) Zurich, Switzerland

Professional Experience

2000 Feasibility study of a new measurement concept for

Hilti AG, Liechtenstein

121

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