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Automotive Diesel Engine Transient Operation: Modeling, Optimization and

Control

Thesis · June 2014

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 Alma Mater Studiorum – Università di Bologna

DOTTORATO DI RICERCA IN

Meccanica e Scienze Avanzate dell’Ingegneria

INGEGNERIA DELLE MACCHINE E DEI SISTEMI ENERGETICI

Ciclo XXVI

Settore Concorsuale di afferenza: 09/C1

Settore Scientifico disciplinare: ING-IND/08

AUTOMOTIVE DIESEL ENGINE TRANSIENT OPERATION:

MODELING, OPTIMIZATION AND CONTROL

Presentata da: Giorgio Mancini

Coordinatore Dottorato Relatore

Prof. Vincenzo Parenti Castelli Prof. Nicolò Cavina

Esame finale anno 2014

Ai miei genitori
Abstract

Traditionally, the study of internal combustion engines operation has focused

on the steady-state performance. However, the daily driving schedule of
automotive engines is inherently related to unsteady conditions. In fact,
only a very small portion of a vehicle’s operating pattern is true steady-
state, e.g., when cruising on a motorway.
There are various operating conditions experienced by (diesel) engines
that can be classified as transient ; these may last from a few seconds up
to several minutes. Besides the variation of the engine operating point, in
terms of engine speed and torque, also the warm up phase can be considered
as a transient condition. Chapter 2 has to do with this thermal transient
condition; more precisely the main issue is the performance of a Selective
Catalytic Reduction (SCR) system during cold start and warm up phases
of the engine. The exhaust temperature is too low to allow thermal activa-
tion of the reactor and, consequently, to promote high conversion efficiency
and significant NOx concentration reduction. This is increasingly evident
the smaller the engine displacement, because of its lower exhaust system
temperature (reduced gross power while producing the same net power, i.e.,
higher efficiency). The proposal of the underlying work is to investigate
and identify optimal exhaust line heating strategies, to provide a fast ac-
tivation of the catalytic reactions on SCR. The main constraint is to limit
the potential fuel consumption increase, and possibly to even increase global
efficiency, and the chosen application is a small EU5-compliant diesel engine.
Chapters 3 and 4 focus the attention on the dynamic behavior of the
engine, when considering typical driving conditions. To satisfy the increas-
ingly stringent emission regulations and a demand for an ever lower fuel
consumption, diesel engines have become complex systems with many inter-
acting actuators. As a consequence, these requirements are pushing control
and calibration to their limits. The calibration procedure nowadays is still
based mainly on engineering experience, which results in a highly iterative
process to derive a complete engine calibration. Moreover, automatic tools
are available only for stationary operation, to obtain control maps that are
optimal w.r.t. some predefined objective function. Therefore, the exploita-
tion of any leftover potential during transient operation is crucial. Control
trajectories resulting from the solution of an optimal-control problem pro-

i
vide a guideline to the calibration engineer, serve as a benchmark, and might
be used for a partial automation of the calibration procedure. The common
approach to dynamic optimization involves the solution of a single optimal-
control problem. However, this approach requires the availability of models
that are valid throughout the whole engine operating range and actuator
ranges. In addition, the result of the optimization is meaningful only if the
model is very accurate.
Chapter 3 proposes a methodology to circumvent those demanding re-
quirements: an iteration between transient measurements to refine a purpose-
built model and a dynamic optimization which is constrained to the model-
validity region. Moreover all numerical methods required to implement this
procedure are presented. The crucial steps are analyzed in detail, and the
most important caveats are indicated. Finally, an experimental validation
demonstrates the applicability of the method and reveals the components
that require further development.
Chapter 4 proposes an approach to derive a transient feedforward control
system in an automated way. It relies on optimal control theory to solve a
dynamic optimization problem for fast transients. A partially physics-based
model is thereby used to replace the engine. From the optimal solutions, the
relevant information is extracted and stored in maps spanned by the engine
speed and the torque gradient. These maps complement the static control
maps by accounting for the dynamic behavior of the engine. The procedure
is implemented on a real engine and experimental results are presented along
with the development of the methodology.

ii
Sommario

Lo studio del funzionamento dei motori a combustione interna è tradizional-

mente focalizzato sulla prestazione in condizioni stazionarie. Tuttavia, il
ciclo di guida giornaliero dei motori automobilistici è per sua stessa natura
caratterizzato da condizioni non stazionarie. Infatti, solo una piccolissima
porzione del ciclo operativo di un veicolo è realmente stazionaria, ad esempio
quando si tiene una certa velocità di crociera in autostrada.
Le condizioni di funzionamento dei motori (diesel) che possono essere clas-
sificate come “transitorie” sono svariate; queste possono durare da pochi sec-
ondi fino a diversi minuti. Oltre alla variazione del punto di funzionamento
del motore, in termini di velocità e coppia, anche la fase di riscaldamento
può essere considerata come una condizione transitoria. Il Capitolo 2 tratta
esattamente questa condizione di transitorio termico; più precisamente il
problema principale è la prestazione di un sistema SCR (Selective Catalytic
Reduction) durante le fasi di avviamento a freddo e riscaldamento del mo-
tore. La temperatura di scarico è troppo bassa per consentire l’attivazione
termica del reattore e, di conseguenza, per promuovere un’elevata efficienza
di conversione e una significativa riduzione della concentrazione di NO x . Tale
comportamento è sempre più evidente quanto più piccola è la cilindrata del
motore, a causa della più bassa temperatura del suo sistema di scarico (ri-
dotta potenza lorda a parità di potenza netta, ovvero maggiore efficienza). Il
seguente lavoro si propone di individuare e identificare strategie di riscalda-
mento ottimo della linea di scarico, al fine di fornire una rapida attivazione
delle reazioni catalitiche in seno al SCR. Il vincolo principale è quello di
limitare il potenziale aumento del consumo di combustibile, e possibilmente
di riuscire persino a incrementare l’efficienza globale. L’applicazione scelta
è un piccolo motore diesel, che rispetta i limiti della normativa Euro 5.
I Capitoli 3 e 4 spostano l’attenzione sul comportamento dinamico del mo-
tore, considerato nelle tipiche condizioni di guida. Per soddisfare le sempre
più stringenti normative sulle emissioni e la richiesta di un sempre più basso
consumo di combustibile, i motori diesel sono diventati sistemi complessi con
molti attuatori interagenti. Di conseguenza, tali requisiti stanno spingendo
il controllo e la calibrazione ai loro limiti. La procedura di calibrazione
è ancora oggi basata principalmente sull’esperienza ingegneristica, il quale
richiede un processo altamente iterativo per poter derivare una calibrazione

iii
completa del motore. Inoltre, sono disponibili diversi sistemi di calibrazione
automatica applicabili al caso stazionario, al fine di ottenere mappe di con-
trollo che siano ottime rispetto a funzioni obiettivo predefinite. Pertanto, lo
sfruttamento di qualsiasi potenziale residuo durante il funzionamento tran-
sitorio è di cruciale importanza. Traiettorie di controllo risultanti dalla
soluzione di un problema di controllo ottimo forniscono una linea guida per
l’ingegnere di calibrazione, servono come punto di riferimento, e potrebbero
essere usate per una parziale automazione della procedura di calibrazione.
L’approccio comune all’ottimizzazione dinamica comporta la soluzione di un
singolo problema di controllo ottimo. Tuttavia, questo approccio richiede la
disponibilità di modelli validi su tutto il campo di funzionamento del motore
e degli attuatori. Inoltre, il risultato dell’ottimizzazione è significativo solo
se il modello è molto accurato.
Il Capitolo 3 propone una metodologia per aggirare tali requisiti esigenti:
un’iterazione tra misure transitorie, per perfezionare un modello realizzato
ad hoc, e un’ottimizzazione dinamica vincolata alla regione di validità del
modello. In aggiunta, vengono presentati tutti i metodi numerici necessari
per implementare tale procedura. I passi fondamentali sono analizzati nel
dettaglio, soffermandosi in particolar modo sui punti più critici. Infine,
una validazione sperimentale dimostra l’applicabilità del metodo e rivela gli
aspetti che richiedono un ulteriore sviluppo.
Il Capitolo 4 propone un approccio per realizzare un sistema di controllo
dei transitori in modo automatizzato. Esso si basa sulla teoria del controllo
ottimo, applicata per risolvere un problema di ottimizzazione dinamica di
transitori veloci. Un modello parzialmente basato sulla fisica viene quindi
usato per rimpiazzare il motore. Dalle soluzioni ottime vengono estratte le
informazioni rilevanti e archiviate in mappe dipendenti dalla velocità e dal
gradiente di coppia. Queste mappe compensano le mappe di controllo statico
tenendo conto del comportamento dinamico del motore. La procedura è
implementata su un motore reale e i risultati sperimentali vengono presentati
insieme allo sviluppo della metodologia.

iv
Contents

Abstract(English/Italiano) i

Nomenclature vii

1 Introduction 1
1.1 Background and motivation . . . . . . . . . . . . . . . . . . . 1
1.2 Transient operation fundamentals . . . . . . . . . . . . . . . . 2
1.3 Structure of the thesis . . . . . . . . . . . . . . . . . . . . . . 6

2 Transient thermal management of diesel engines 8

2.1 Control parameters sensitivity analysis . . . . . . . . . . . . . 9
2.1.1 Start of Injection (SOI) . . . . . . . . . . . . . . . . . 13
2.1.2 Variable Geometry Turbine (VGT) . . . . . . . . . . . 14
2.1.3 Throttle Valve (TVA) . . . . . . . . . . . . . . . . . . 16
2.1.4 SOI and VGT combined effects . . . . . . . . . . . . . 18
2.2 Heating strategy . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.1 The concept . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 27

3 Dynamic optimization of diesel engines 29

3.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2 Engine model . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.1 Mean-value model of the air-path . . . . . . . . . . . . 37
3.2.2 Exhaust Gas Recirculation . . . . . . . . . . . . . . . 52
3.2.3 Transient validation . . . . . . . . . . . . . . . . . . . 56
3.2.4 Time-resolved combustion model . . . . . . . . . . . . 60
3.3 Numerical optimal control . . . . . . . . . . . . . . . . . . . . 63
3.3.1 The Diesel-engine problem . . . . . . . . . . . . . . . . 64
3.3.2 Direct transcription . . . . . . . . . . . . . . . . . . . 64
3.3.3 Regularization . . . . . . . . . . . . . . . . . . . . . . 65
3.4 Transient model refinement . . . . . . . . . . . . . . . . . . . 66
3.4.1 Refinement of the dynamic air-path model . . . . . . . 66
3.5 Iterative procedure . . . . . . . . . . . . . . . . . . . . . . . . 67

v
 3.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.6.1 Transient air-path model refinement . . . . . . . . . . 69
3.6.2 Static combustion model . . . . . . . . . . . . . . . . . 71
3.6.3 Optimal control . . . . . . . . . . . . . . . . . . . . . . 71
3.6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 73

4 Transient control of diesel engines 74

4.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.1.1 The concept . . . . . . . . . . . . . . . . . . . . . . . . 75
4.1.2 Engine model . . . . . . . . . . . . . . . . . . . . . . . 78
4.1.3 Time-resolved combustion model . . . . . . . . . . . . 79
4.1.4 The optimal control problem . . . . . . . . . . . . . . 80
4.1.5 Optimization procedure . . . . . . . . . . . . . . . . . 82
4.1.6 From time-based to map-based optimal control . . . . 83
4.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 84
4.2.1 Dynamic optimization . . . . . . . . . . . . . . . . . . 87
4.2.2 Optimal control versus compensation maps . . . . . . 90
4.2.3 Validation . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 95

5 Summary and outlook 96

A Sensors 98
A.1 Temperature Sensors . . . . . . . . . . . . . . . . . . . . . . . 98
A.1.1 Thermoresistances . . . . . . . . . . . . . . . . . . . . 98
A.1.2 Thermocouples . . . . . . . . . . . . . . . . . . . . . . 98
A.2 Piezoresistive effect . . . . . . . . . . . . . . . . . . . . . . . . 100
A.3 Piezoelectric effect . . . . . . . . . . . . . . . . . . . . . . . . 102
A.4 Pressure Sensors . . . . . . . . . . . . . . . . . . . . . . . . . 103
A.5 Acceleremoters . . . . . . . . . . . . . . . . . . . . . . . . . . 105
A.5.1 Piezoelectric accelerometers . . . . . . . . . . . . . . . 105
A.5.2 Piezoresistive accelerometers . . . . . . . . . . . . . . 106
A.5.3 Capacitive accelerometers . . . . . . . . . . . . . . . . 106
A.6 Microphones . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
A.7 Turbocharger speed . . . . . . . . . . . . . . . . . . . . . . . 110
A.7.1 Variable Reluctance measurement system . . . . . . . 110
A.7.2 Optical measurement system . . . . . . . . . . . . . . 111
A.7.3 Eddy Current measurement system . . . . . . . . . . . 111
A.8 TDC measurement . . . . . . . . . . . . . . . . . . . . . . . . 111
A.9 Air Mass Sensors . . . . . . . . . . . . . . . . . . . . . . . . . 114

vi
Nomenclature
∗
The time derivative of a variable x is denoted by ẋ, whereas x represents a
flow of mass, heat or energy, for instance. Bold symbols indicate vectors and
matrices. The following list introduces the abbreviations and the symbols
that are used consistently throughout the text. Indices and specific symbols
that are used only in a narrow context are introduced and explained directly
at the corresponding locations in the text. For each symbol that can assume
different meanings, the respective context is indicated in brackets.

Symbols
σ0 Stoichiometric AFR [−]
λ Normalized Air-to-fuel ratio λ =AFR/σ0 [−]
w Speed [rad/s]
mfcc Mass of fuel injected per cycle per cylinder [kg/cc]
ϕSOI Start of main injection [°BTDC]
pIM Intake manifold pressure [Pa]
pEM Exhaust manifold pressure [Pa]
ϑIM Intake manifold temperature [K]
ϑEM Exhaust manifold temperature [K]
xbg,IM Burnt-gas ratio in the intake manifold [−]
xbg,EM Burnt-gas ratio in the exhaust manifold [−]
Neng Engine speed [rpm]
Teng Engine coolant temperature [K]

Acronyms and Abbreviations

AFM Air-flow Meter
AFR Air-to-fuel ratio
aTB after Turbine

vii
bTB before Turbine
bmep brake mean effective pressure
BSA back-sweep angle of the blade
BTDC Before Top Dead Center
CoV Coefficient of Variation
DC Dynamic Compensation
DOC Diesel Oxidation Catalyst
DPF Diesel Particulate Filter
ECU Electronic Control Unit
EGC Exhaust Gas Cooler
EGR Exhaust Gas Recirculation
EM Exhaust Manifold
FB Feedback
FC Fuel Consumption
FF Feedforward
IM Intake Manifold
IMEP Indicated Mean Effective Pressure
LIP Linear in Parameters
LSQ Linear least-squares
NEDC New European Driving Cycle
OCP Optimal-control Problem
ODE Ordinary Differential Equation
SCR Selective Catalytic Reduction
SOI Start Of Injection
VGT Variable Geometry Turbine
TB Time-based
TcatIN Temperature catalyst inlet
TVA Throttle Valve Actuator
TWC Three Way Catalyst

viii
Chapter 1

Introduction

1.1 Background and motivation

In recent years, the increasingly stringent exhaust emission regulations have
dominated the automotive industry, and forced manufacturers to new devel-
opments. Automotive diesel engines have experienced a significant techno-
logical development, resulting in increased requirements on calibration and
control [1]. For diesel engines, the emphasis is on reducing emissions of ni-
trogen oxides (NOx ) and particulate matter (PM), due to the toxicity of the
inhaled nanoparticles and because these pollutants are typically higher than
those from equivalent rated, port-injected gasoline engines equipped with
three-way catalysts.
Unfortunately, there is a trade-off between NO x and PM reduction, result-
ing in a complicated control strategy requiring complex after-treatment sys-
tems. Sophisticated, high-pressure common rail injection systems, exhaust
gas recirculation (EGR), or selective catalytic reduction (SCR), multi-valve
configurations with variable valve timing, variable geometry turbocharg-
ers (VGT), exhaust after-treatment systems with particulate traps or urea-
based deNOx are among the measures applied for pollutant emissions reduc-
tion and fuel consumption. For the research community, the introduction of
these systems has led to a number of challenging problems as far as control
and combustion research are concerned. In particular, the control of the
EGR [2] and the conjoint control of the EGR and VGT [3, 4, 5, 6] have
resulted in numerous publications.
Furthermore, carbon dioxide (CO 2 ) emissions are becoming increasingly
important owing to their connection with global warming; limiting CO 2 pro-
duction can be achieved, primarily, through improvements in fuel economy
and use of biofuels. Today’s diesel-engined automobiles not only demon-
strate greater fuel efficiency than ever before, but they also achieve emission
levels at least 50% lower than those of a few years ago.
Unsurprisingly, the various technological advances mentioned above have

1
Chapter 1. Introduction 2

also led to a significant increase in the complexity and cost of the engine
and its control system, and this trend is sure to continue.
Figures 1.1 and 1.2 show an overview of a typical modern diesel engine
as used in passenger cars. The comprehensive open- or closed-loop control
systems employed gather the signals from the various sensors located on the
engine, fuel pump and turbocharger (Figure 1.2), process them by means
of look-up tables (steady-state maps) or, better still, model-based control
theory with, for instance, feed-forward control, and eventually determine
the optimum position of the various valves, vanes, etc.
The main objective for electronic diesel-engine control-systems is to pro-
vide the required engine torque while minimizing fuel consumption and
complying with exhaust-gas emissions and noise level regulations. This re-
quires an optimal coordination of injection, turbocharger and exhaust-gas
recirculation systems in stationary and transient operating conditions. Tra-
ditionally, the control optimization is undertaken during the design stage
for steady-state operations, with the calibrated parameters, e.g., injection
strategy (pre-, main- and post-injection scheme, rate, timing and pressure
of injection), VGT vanes position, boost pressure, EGR valve position etc.,
stored in 3-D maps spanned by engine speed and load/fueling.
From a control-engineering point of view, there are three important paths
which have to be considered: fuel, air and EGR. Figure 1.3 shows a schematic
overview of the basic structure of a typical diesel-engine control-system,
clearly pointing out these three paths. Notice that a speed controller is
standard in diesel engines: the top speed must be limited in order to prevent
engine damage whereas the lower limit is imposed by the desired running
smoothness when idling.

1.2 Transient operation fundamentals

Traditionally, the study of internal combustion engines operation has fo-
cused on the steady-state performance, with minor, if any, attention paid to
the unsteady-state or more accurately termed transient operation. However,
the majority of daily driving schedule involves transient conditions. In fact,
only a very small portion of a vehicle’s operating pattern is true steady-state,
e.g., when cruising on a motorway. Historically, however, the research on
transient diesel engine operation dates back to 1960s, when the engine man-
ufacturers observed that when highly-rated, medium-speed diesel engines
were employed in sudden 0-100% step load changes, severe difficulties were
encountered, even leading to engine stall. In recent years, the global concern
about environmental pollution has led the respective studies to be intensi-
fied; particulate, gaseous and noise emissions typically go way beyond their
acceptable values following the extreme, non-linear and nonsteady-state con-
ditions experienced during dynamic engine operation. A few representative
Chapter 1. Introduction 3

Figure 1.1: Overview of a typical system structure of a Diesel engine ([7]).

Figure 1.2: Simplified diagram showing some major air-supply and fueling
controllable inputs (italics) and engine/vehicle outputs (bold), highlighting
the complexity of a modern diesel engine powertrain ([8].)
Chapter 1. Introduction 4

Figure 1.3: Basic diesel-engine control-system structure, variables as defined

in 1.1 ([7]).

results follow: cold- or warm-start emissions from heavy-duty diesel engines

have been found to exceed up to 15 times their steady-state values; 50% of
NOx emissions from automotive engines during the European Driving Cycle
stem from periods of acceleration, whereas instantaneous particulate matter
and NOx emissions during load increase transients have been measured to be
1 to 2 orders of magnitude higher than their respective quasi-steady values.
Starting from the 1980s, (diesel-engined) vehicles have been tested for
exhaust emissions, prior to type approval, using sophisticated standardized
transient tests (Transient Cycles); these are usually characterized by long
duration (up to 30 minutes) consisting of both speed and load changes un-
der varying operating schedules. A Transient Test Cycle is a sequence of
test points each with a defined vehicle speed to be followed by the vehicle
under study, or with a defined rotational speed/torque to be followed by
the engine under transient conditions; these test points are divided in time
steps, mostly seconds, during which acceleration is assumed constant. Such
standardization is necessary as it makes it possible to compare different
vehicles/engines that fulfill the same operation.
In order for the exhaust emission measurements to be representative of
real engine operation, Transient Test Cycles incorporate some or all of the
following driving conditions:

• cold and hot starting

• frequent accelerations and decelerations

Chapter 1. Introduction 5

• changes of load

• idling conditions typical of urban driving

• sub-urban or rural driving schedule

• motorway driving

By applying a Transient Cycle for the testing of new vehicles, the com-
plete engine operating range is tested and not just the maximum power or
torque operating points. Moreover, the serious discrepancies that are expe-
rienced during abrupt transients are taken into account. However, it should
be pointed out that the primary objective of a Transient Cycle procedure
is to establish the total amount of exhaust emissions rather than indicate
the specific parts or conditions under which these emissions are produced.
Further, legislative Test Cycles assume straight roads with zero gradient,
thus no account is taken of the respective road-dependent resistance torque.
Transient Cycles require highly sophisticated experimental facilities (a fully
automated testbench with electronically controlled motoring and dissipat-
ing (chassis) dynamometer, fast response exhaust gas analyzers, dilution
tunnels, etc.) in order to be accurately reproduced. Many countries in the
world have developed Transient Cycles for emission testing of their vehicles.
These Transient Cycles concern the testing of passenger vehicles, light-duty
(commercial) vehicles, heavy-duty vehicles, heavy-duty engines, and non-
road mobile engines. Passenger cars and light-duty vehicles usually undergo
a vehicle speed vs. time Test Cycle on a chassis dynamometer, and the
results are expressed in g/km.
There are various operating conditions experienced by (diesel) engines
that can be classified as transient ; these may last from a few seconds up to
several minutes. In this thesis, the term transient will be used to describe
any of the following three forced changes:

1. cold or hot starting

2. step change in pedal position (change in load request) resulting in

engine speed changes (acceleration) while keeping the same output
torque

3. load acceptance (change) at quasi-constant engine speed, mainly expe-

rienced in industrial applications, e.g., electrical generation, but also
observed in various propulsion applications, e.g., when a vehicle climbs
a hill;

These are the most fundamental transient cases, while their combination
results in:

• simultaneous speed and load changes

Chapter 1. Introduction 6

• whole vehicle propulsion schedule, e.g., gear shift

• Transient Cycles, which consist of all of the above mentioned transients

A number of typical transient cases will be described in the next chapters,

emphasizing the different responses of the engine as well as the requirements
of the engine control system.

1.3 Structure of the thesis

The core subject treated during the research activity, and presented in this
thesis, is the development of control strategies for diesel engine transient op-
eration. Independently of the specific transient pattern (see list above), the
control scheme derived is characterized by the same structure, shown in Fig-
ure 1.4. The “static-based controls” represent the typical outputs from the
feedforward control based on the steady-state set-point maps, whereas the
“transient-accounting controls” are obtained when applying the transient
compensation strategy to the static outputs. As can be noted, the inputs
to the steady-state set-point maps are engine speed (Neng ) and load or fuel
request (mf cc ), and they are independent of the specific transient pattern.
On the contrary, the transient compensation strategy strongly depends on
the transient effect to be accounted for, and so do the “transient-related
inputs” likewise. This is the crucial point: how to derive such compensa-
tion strategies, along with the best suited control inputs. Depending on the
control problem to be solved, different solutions are proposed.
In Chapter 2, the main issue is the performance of a Selective Catalytic
Reduction (SCR) system during cold start and warm up phases of a light-
duty diesel engine; it is thus focused on the transient condition 1, referring
to the list previously presented. Transient conditions 2 and 3 are considered
instead in Chapters 3 and 4, which focus mainly on the dynamic optimization
of diesel engines.

Figure 1.4: Transient control approach presented in the thesis.

Chapter 1. Introduction 7

Chapter 3 presents the numerical methods and the testbench setup re-
quired to perform an iterative dynamic optimization of diesel engines over
prescribed driving profiles. Through the synergy of engine modeling and
optimal-control theory, control trajectories resulting from the solution of an
optimal-control problem are derived. The results achieved are then applied
in Chapter 4, where a methodology to derive a transient feedforward control
system in an automated way is proposed.
It has to be pointed out that each subject has been tackled with the same
approach, which is in logical order:

• analysis of the problem and definition of the main objectives

• experimental and/or numerical methods definition

• development of the methodology

• experimental validation through a systematic and reliable approach

• implementation on a real engine

• final experimental validation and presentation of results

Chapter 2

Transient thermal
management of diesel engines

As is well known, Euro 6 (EU6) regulation is about to introduce in Europe

a particularly severe reduction of the allowed NO x emission levels for Diesel
passenger cars [9]. Due to the lean composition of diesel engines exhaust gas,
Three Way Catalysts (TWCs) prove inefficient to reduce NOx species, and
other solutions have been investigated in recent years. Especially in heavy-
duty applications, the most widely adopted solution is the installation of
Selective Catalyst Reduction (SCR) systems [10, 11, 12]. The use of a SCR
system on a diesel engine exhaust line is now becoming a valid solution also
for passenger cars, with the aim of drastically reducing NO x emissions, in
an effort to comply with forthcoming EU6 regulations. In [13, 14] a pre-
liminary study about the application of a SCR system on a EU5 B-segment
vehicle has been presented, analyzing possible solutions for obtaining high
NOx conversion efficiency values from the after-treatment device. Several
simulations have been performed, using the New European Driving Cycle
(NEDC) as a benchmark test to compare the results. They show that the ex-
haust gas temperature tends to be too low at SCR inlet to allow for optimal
catalyst operation. So, for the considered vehicle (B-segment), the simula-
tion demonstrated the need for a specific heating strategy to rapidly light-off
the SCR catalyst, and to subsequently control its operating temperature at
optimal values.
This chapter presents the analysis and application of thermal management
strategies for the exhaust line, with the constraint of limiting additional fuel
consumption [15]. Firstly, a few NEDC cycles have been performed on the
roll bench dynamometer, to collect exhaust line temperature dynamics ex-
perimental data of the production calibration (EU5), as a reference starting
point. Figure 2.1 shows the exhaust line layout selected for this study (Fiat
1.3L Doblò Multi-Jet), with the SCR and its related components installed
specifically for this project. The exhaust gas path, from the engine to the

8
Chapter 2. Transient thermal management of diesel engines 9

SCR inlet (where urea injection takes place), is particularly long. The chal-
lenge is to reach a temperature of approximately 190°C as fast as possible
[16], far away from the exhaust valves and without compromising fuel con-
sumption.
Figure 2.2 shows the temperature trend of the exhaust gas at SCR inlet,
during NEDC operation (the vehicle speed is reported in the right y-axis).
As clearly shown, the target temperature mentioned above is reached almost
at the end of the driving cycle (around t=900 s), suggesting the impossibility
to effectively take advantage of the selective catalyst reactor. From a more
general point of view, during engine warm-up the significant NOx reduction
that should be provided by the SCR system seems to be unfeasible, and this
consideration is true the farther the SCR system is located from the engine.
To find a possible solution to this issue, an experimental investigation has
been performed, focusing the attention on the main engine control parame-
ters that are available to the Engine Control Unit (ECU). The proposal is
to analyze the effects on the combustion and the resulting exhaust gas tem-
perature (and composition), by changing the parameters that mostly affect
the engine efficiency, reported in the following list (see also Figure 2.3):

• Injection phasing, by controlling the Start Of Injection (SOI) position

of the pre-selected injection pattern.

• Turbine efficiency, and engine back-pressure, by controlling the Vari-

able Geometry Turbine (VGT) actuation.

• Exhaust Gas Recirculation (EGR) rate, for its impact on NO x produc-

tion and pumping losses, by controlling the engine EGR valve position.

• Intake pressure and composition, by controlling the engine Throttle

Valve Actuation (TVA) system.

After this first analysis, performed on a test bench with the same en-
gine layout set on the vehicle, several calibration strategies have been de-
veloped and validated. Afterwards, calibration profiles derived from the
validation process have been applied on the vehicle while executing other
NEDC tests. Final results show the improvement reached with the heating
strategy methodology, enhancing a faster SCR activation.

2.1 Control parameters sensitivity analysis

In the first phase of the work, different approaches on how to rapidly warm-
up the exhaust line have been evaluated, taking into consideration two po-
tential strategies [17, 18, 19]:
Chapter 2. Transient thermal management of diesel engines 10

Table 2.1: Engine characteristics.

engine type: FIAT 1.3 Multi-Jet EU5
displacement: 1248 cm3
compression ratio: 16.8
EGR: high pressure, cooled
turbocharger: VGT, charge-air cooler
injection system: common rail DDI
valves/cyl.: 4
max. torque: 200 Nm (1500-3500 rpm)
max. power: 66 kW (4000 rpm)

Figure 2.1: Exhaust line layout.

Chapter 2. Transient thermal management of diesel engines 11

Figure 2.2: Temperature trend at SCR inlet during NEDC cycle without
heating strategy (EU5 calibration).

Figure 2.3: Layout of the diesel engine used for the experiments.
Chapter 2. Transient thermal management of diesel engines 12

• “Hard” strategy : late or post injections to promote oxidation processes

in the exhaust line (after Diesel Oxidation Catalyst DOC activation).
It implies the need to increase the amount of injected fuel, with a
consequent predictable fuel penalty.

• “Soft” strategy : identify control strategies and calibration parameters,

with particular focus on the ones that mainly influence combustion
efficiency.

The second choice has been preferred, since it could have the desired effect
of satisfying both the exhaust heating and the fuel consumption constraint.
As already mentioned, and with reference to Figure 2.3, the main control
parameters are SOI, EGR, TVA, and VGT, while the main engine charac-
teristics are presented in Table 2.1. The final effect, in terms of exhaust
temperature, must be evaluated downstream of the turbine and upstream
of after-treatment devices, so that the measured temperature is not affected
by the operating condition of DOC and DPF systems.
The standard ECU calibration (EU5) is the result of a trade-off between
engine performance (maximum torque and optimum drivability) and mini-
mum fuel consumption and emissions, so any modification should in princi-
ple result in a worse engine behavior. Nevertheless, the addition of a SCR
system downstream of DOC and DPF systems introduces new perspectives.
It is now possible to identify new calibration parameter combinations that
optimize the overall engine (and aftertreatment system) behavior. For in-
stance, the NOx reduction task can be completely handled by the SCR
system, once it has been thermally activated. Therefore, starting from this
consideration and given the previous simulation results, the effects of SOI,
VGT and TVA have been evaluated on a test bench, performing several
steady-state measurements.
The engine operating points have been extrapolated from the ECE driving
cycle. Figure 2.4 shows the four operating points (red triangles) in which the
engine behavior can be approximately considered stationary; it follows that
each point is characterized by a speed-bmep combination, as shown in Table
2.2 (bmep represents the engine normalized output torque). In order to take
into consideration also engine transient operation, a fifth operating point has
been identified as the average condition in terms of engine speed and bmep.
The operating conditions chosen for the sensitivity analysis have been n.
1, n. 3, and n. 5, with the aim of minimizing the number of tests while
guaranteeing a substantial representation of the engine operating range.
The EGR valve actuation has not been directly considered, leaving to the
ECU the priority to handle it, dependently from the air flow resulting from
VGT and TVA positions. The EGR rate has therefore not been externally
controlled during the experimental tests, but it depends on the other devices
involved in the air-path controller.
Chapter 2. Transient thermal management of diesel engines 13

Table 2.2: Engine operating points extrapolated from the ECE driving
cycle. Only n. 1, n. 3 and n. 5 have been used for the sensitivity analysis.

# Speed [rpm] bmep [bar]

1 2200 1.81
2 2400 1.51
3 2500 2.52
4 1700 2.11
5 1800 5.03

2.1.1 Start of Injection (SOI)

Considering a determined steady state operating point, in a maximum ef-
ficiency condition, apparently the only way to increase the exhaust tem-
perature is to shift the combustion toward the exhaust phase. This action
reduces combustion efficiency, therefore a greater amount of injected fuel is
needed to guarantee the same engine torque. The main control parameter
of the combustion phase in a diesel engine is the SOI position (expressed
in crankshaft degrees Before Top Dead Center BTDC). If not differently
specified the SOI refers to the main injection in a multiple injection pattern.
The figures below show the exhaust gas temperature and fuel consump-
tion responses to SOI sweeps performed in different steady state conditions.
ΔSOI is defined as the difference between reference (EU5) SOI value and
actual SOI value, while ΔTcatIN and ΔFuelConsumption respectively rep-
resent the exhaust gas temperature difference between actual and ref. value
(with ref. SOI), and the percentage difference between actual and ref. fuel
consumption values. Positive values in the x-axis of Figures 2.5 through 2.7
therefore represent retarded injection phases with respect to reference val-
ues. Figure 2.5 confirms that the higher is the combustion delay, the higher
is the exhaust gas temperature. As previously shown in Table 2.2, tests have
been performed while controlling speed and bmep at constant values, so that
the efficiency reduction that comes with the combustion delay needs to be
compensated by increasing fuel consumption, as clearly visible in Figure 2.6.
Furthermore, the same figure confirms that in the ΔSOI ≈ 0 range the fuel
consumption is minimum, proving that the SOI ref value had been correctly
identified.
It is also true that the applied SOI corrections reduce the combustion
chamber temperatures, thus decreasing the thermal NO x production. This
explains why sometimes the SOI ref may in other cases prove to be sub-
optimal, in terms of efficiency, to limit such type of emissions. Finally,
Figure 2.7 shows the Indicated Mean Effective Pressure (IMEP) Coefficient
Chapter 2. Transient thermal management of diesel engines 14

Figure 2.4: Vehicle speed profile in the ECE cycle and operating points
investigated.

of Variation, CoV(IMEP), for cylinders 2 and 3, to prove that up to a SOI

delay of 12 CA, the combustion stability is always guaranteed. CoV(IMEP)
is defined as the ratio between IMEP standard deviation and its mean value,
expressed as a percentage value, and it is widely recognized as an indirect
but accurate measure of combustion stability [20].

2.1.2 Variable Geometry Turbine (VGT)

As it has been previously mentioned, another important control parameter
within this context is the VGT position. In the given control system, a VGT
position=100% corresponds to a fully closed condition, and vice versa the
distributor is fully open with a VGT position=0%. In other words, when
the VGT is fully closed (100%) it means that the turbine, under steady state
flow conditions, generates the highest backpressure, correspondent to that
mass flow, and therefore the pressure drop through the turbine is maximum.
In this condition, the turbine produces its maximum power, increasing the
turbocharger speed, with the consequent increase of the intake manifold
pressure.
The tests performed have the aim to increase the distributor opening with
respect to reference (EU5) calibration, in order to reduce the enthalpy drop
and to increase the temperature downstream of the turbine.
As shown in Figure 2.8, where negative ΔVGT values correspond to a
Chapter 2. Transient thermal management of diesel engines 15

50

40

30
ΔTcatIN[°C]

20

10

-10
-4 -2 0 2 4 6 8 10 12 14 16
ΔSOI[CA]

Figure 2.5: Effect of SOI variation on TcatIN.

18

15
ΔFuelConsumption[%]

12

-3
-4 -2 0 2 4 6 8 10 12 14 16
ΔSOI[CA]

Figure 2.6: Effect of SOI variation on Fuel consumption.

4
cyl2
3.5 cyl3

3
CoV(IMEP)[%]

2.5

1.5

1
-4 -2 0 2 4 6 8 10 12 14 16
ΔSOI[CA]

Figure 2.7: Effect of SOI on CoV(IMEP), cylinders 2 and 3.

Chapter 2. Transient thermal management of diesel engines 16

0.5

0
Δλ[-]

-0.5

-1
-30 -26 -22 -18 -14 -10 -6 -2 2
ΔVGTposition[%]

Figure 2.8: Effect of VGT on λ.

wider opening position with respect to reference values, by reducing the

VGT position the normalized air-to-fuel ratio (λ) value slightly decreases.
This effect is quite predictable, because the fuel mass flow does not change
(constant load and essentially constant engine efficiency) while the air mass
flow decreases due to intake pressure reduction. During the tests, a lower
saturation has been imposed on λ, to guarantee acceptable smoke levels. In
this case there is a positive effect both on exhaust gas temperature and fuel
consumption (Figure 2.9, Figure 2.10). The first effect is due to the turbine
energy conversion reduction, and to a lower λ value (richer combustion, due
to reduced excess air mass and therefore reduced thermal capacity of the
charge), while the fuel consumption reduction is mainly due to the reduced
engine backpressure (higher pumping efficiency). As shown in Figure 2.11,
the CoV(IMEP) is rather unaffected by the VGT variation, except for rel-
atively large opening positions, implying lowest boost pressure and lowest
lambda. Generally, large deviations from nominal turbocharger operating
conditions are not allowed, to avoid negative effects on turbo lag response
and vehicle drivability.

2.1.3 Throttle Valve (TVA)

The throttle valve is placed at the intake manifold inlet, before the EGR
path outlet (Figure 2.3), and during engine operation the valve is typi-
cally fully opened. The same valve is actuated only when the pressure
drop across the EGR valve is not sufficient to guarantee the requested ex-
haust gas recirculation amount. By forcing the throttle valve closing, while
controlling EGR and VGT at constant position, the intake manifold pres-
sure may be significantly reduced. Figures 2.12, 2.13 and 2.14 highlight
the effects of intake pressure reduction (with respect to the levels achieved
with reference TVA calibration) on the most significant engine operating
Chapter 2. Transient thermal management of diesel engines 17

40

35

30

25
ΔTcatIN[°C]

20

15

10

-5
-30 -26 -22 -18 -14 -10 -6 -2 2
ΔVGTposition[%]

Figure 2.9: Effect of VGT on TcatIN.

1.5
ΔFuelConsumption[%]

-1.5

-3

-4.5

-6
-30 -26 -22 -18 -14 -10 -6 -2 2
ΔVGTposition[%]

Figure 2.10: Effect of VGT on fuel consumption.

4
cyl2
3.5 cyl3

3
CoV(IMEP)[%]

2.5

1.5

1
-30 -26 -22 -18 -14 -10 -6 -2 2
ΔVGTposition[%]

Figure 2.11: Effect of VGT on CoV(IMEP), cylinders 2 and 3.

Chapter 2. Transient thermal management of diesel engines 18

-0.5

-1
Δλ[-]

-1.5

-2

-2.5

-3
-500 -450 -400 -350 -300 -250 -200 -150 -100 -50
ΔPmanifold[mbar]

Figure 2.12: Effect of TVA on λ.

50

40

30
ΔTcatIN[°C]

20

10

-10

-20
-500 -450 -400 -350 -300 -250 -200 -150 -100 -50
ΔPmanifold[mbar]

Figure 2.13: Effect of TVA on TcatIN.

parameters. ΔPmanifold represents the difference between reference intake

manifold pressure values and the ones measured during the tests. The main
effect is a large λ value reduction, which causes the exhaust gas tempera-
ture to increase. On the other hand, the specific fuel consumption responds
negatively, especially when the intake manifold pressure is lower than the
ambient pressure (see Figure 2.14). Even if there is a positive effect on
the temperature, this kind of strategy has been discarded, because of the
large fuel penalty introduced by pumping losses related to throttle opening
reduction.

2.1.4 SOI and VGT combined effects

Summarizing what presented so far, Figures 2.15 and 2.16 show the effects
of SOI and VGT variations on exhaust gas temperatures and fuel consump-
Chapter 2. Transient thermal management of diesel engines 19

15

10
ΔFuelConsumption[%]

-5
-500 -450 -400 -350 -300 -250 -200 -150 -100 -50
ΔPmanifold[mbar]

Figure 2.14: Effect of TVA on fuel consumption.

tion, respectively. It is evident that SOI positive variations are essential

for achieving a significant increase of the exhaust temperature, while VGT
negative variations can compensate for the fuel penalty while at the same
time contributing to make the temperature higher.
Given the considerations presented so far, and considering the knowledge
gained by simulating the whole system, a possible solution for heating the
exhaust line while limiting the fuel consumption penalty can be found by
considering the combined effects of SOI and VGT. A more detailed analysis
has been carried out in order to define potential heating strategies based
on this concept. In Figures 2.17, 2.18 and 2.19, catalyst intake temperature
(TcatIN), Fuel Consumption (FC), and NO x trends are shown, in relation to
SOI and VGT, referring to one engine operating point (number 5 in Table
2.2). The main result is that SOI and VGT carry out a synchronous ac-
tion on TcatIN, increasing the exhaust gas temperature up to about 50 °C
with respect to reference conditions, if both control parameters are forced
towards their allowed limits. For what concerns the fuel consumption, it
is interesting to notice that in a limited region of SOI-VGT combinations,
the fuel penalty is almost insignificant, if not even negative (higher fuel effi-
ciency). To complete this scenario, it has also been reported the NO x trend
(Figure 2.19), showing that, as expected, the higher the TcatIN tempera-
ture, the lower the combustion chamber temperature, and therefore the NO x
production decreases.

2.2 Heating strategy

Summarizing what has been presented so far, and adding some other con-
siderations, it comes out that if it was possible to separately optimize one
parameter at a time, it would be possible to define the following list of
Chapter 2. Transient thermal management of diesel engines 20

20 20

10 0

ΔVGTposition[%]
ΔSOI[CA]

0 -20

-10 -40
-10 0 10 20 30 40 50
ΔTcatIN[°C]

Figure 2.15: Effects of SOI and VGT on Exhaust Temperature Variations.

20 20

15

10 0
ΔVGTposition[%]
ΔSOI[CA]

0 -20

-5

-10 -40
-20 -10 0 10 20 30 40 50 60 70 80
ΔFuelConsumption[%]

Figure 2.16: Effects of SOI and VGT on Fuel Consumption Variations.

Chapter 2. Transient thermal management of diesel engines 21

control priorities:

• maxΔT catIN : to reach the highest admissible exhaust temperature,

using both SOI and VGT at their limits, as shown in Figure 2.17.

• minΔF C: to minimize the fuel consumption without considering ex-

haust temperature, by trying to work in the small region shown in
Figure 2.18.

• ΔF C = 0: rather similar to the previous target, with the slight dif-

ference to try to work in a zero fuel penalty region, without searching
for its minimum.

• ΔP boost(100): by analyzing the effect of VGT on TcatIN (see Figure

2.9) it has been verified that the higher is the VGT opening, the lower
is the boost pressure and the higher is TcatIN. It follows that the boost
pressure can be reduced, in order to increase TcatIN, but being careful
to not exceed smoke limits and drivability constraints (turbo lag). So
this control piority refers to a maximum boost pressure reduction of
about 100 mbar.

Figure 2.20 shows all these control objectives, represented as SOI-VGT

combinations in a diagram prepared as a guideline of a possible control
strategy calibration. This synthetic representation makes it quite easy to
have a general idea of the engine behavior, when forced to operate under
different control (and calibration) conditions. Depending on the priority,
a particular region of the plane can be chosen, and not all targets can be
achieved at the same time. This graphical representation is a starting point
to define optimal heating calibration strategies, to be tested on the vehicle
during driving cycle operation.

2.2.1 The concept

The main idea is to apply the results of the previous analysis, while taking
into consideration other aspects concerning the vehicle and the driving cycle.
For example, all tests performed on the test bench have been executed with
a warmed up engine, while the NEDC presents a cold start phase that is
quite relevant for what concerns fuel consumption and emissions production.
Depending on the engine (and aftertreatment systems) thermal state, the
strategy should be able to smoothly adapt SOI and VGT position.
A typical feedforward control strategy based on steady-state actuator set-
point maps is implemented in the ECU; it is thus the starting control struc-
ture, as shown in the upper part of Figure 2.21. In order to account for
transient operation (thermal transient in this case), the control structure
needs to be adapted. The steady-state control maps are spanned by engine
Chapter 2. Transient thermal management of diesel engines 22

70

60

50
ΔTcatIN[°C]

40

30

20

10

0
5 12
0 10
-5 8
-10
-15 6
-20 4
-25 2
-30 0
ΔVGTposition[%] ΔSOI[CA]

Figure 2.17: Combined effect of SOI and VGT on TcatIN (1800 rpm, 5.03
bmep).

8
ΔFuelConsumption[%]

-2
5 12
0 10
-5 8
-10 6
-15
-20 4
-25 2
-30 0
ΔVGTposition[%] ΔSOI[CA]

Figure 2.18: Combined effect of SOI and VGT on fuel consumption (1800
rpm, 5.03 bmep).
Chapter 2. Transient thermal management of diesel engines 23

-20
ΔNOx[ppm]

-40

-60

-80
0 5
2 0
4 -5
-10
6 -15
8 -20
10 -25
12 -30
ΔVGTposition[%]
ΔSOI[CA]

Figure 2.19: Combined effect of SOI and VGT on NO x (1800 rpm, 5.03
bmep).

-5

-10
ΔVGTposition[%]

-15

-20
ΔFC≈0
minΔFC
-25
maxΔTcatIN
ΔPboost(100)

-30
0 2 4 6 8 10 12
ΔSOI[CA]

Figure 2.20: Representation of combined VGT and SOI position effects on

engine behavior.
Chapter 2. Transient thermal management of diesel engines 24

speed (Neng ) and load (mfcc ). The latter variable has not been introduced
yet: mfcc is the fuel quantity injected per cycle in each cylinder, and it can
be intended as the load request (bmep). If no other corrections were ap-
plied, the two control outputs would be SOI ref and VGTref , which are solely
set-point dependent, regardless of the thermal condition.
On one hand it can be argued that such a control structure is not suit-
able to account for dynamic phenomena, on the other hand it represents a
standard architecture in automotive ECUs. As a consequence, enhancing its
control efficacy while keeping the main structure intact may be achieved by
adding transient compensation maps. The sensitivity analysis presented in
preceding sections may be seen as a tool to derive the compensation maps.
More precisely, referring to Figure 2.21, correction maps (spanned by Neng
and mfcc ) of SOI and VGT have been extracted from the information pro-
vided by the calibration table in Figure 2.20. The corrective factors SOI corr
and VGTcorr rely on Neng and mfcc at the same way as the reference val-
ues, therefore the thermal-related compensation is given by the third map
shown in the figure. Depending on the engine coolant temperature (Teng ),
the modulation factors TSOI,corr and TVGT,corr act on the steady-state cor-
rection values, by keeping them unchanged (T i,corr = 1) or eliminating their
effect (Ti,corr = 0).
Figure 2.22 gives an overview of the ideal control action to be satisfied.
A NEDC cycle is considered as a driving profile; as is well known the urban
part of the cycle (ECE) is repeated four times, therefore the engine operates
in the same operating points (Neng and mfcc ). Since the correction maps are
spanned by the same input variables, their outputs remain unvaried for each
ECE repetition. Supposing to define the target correction with a rectangular
area in Figure 2.22, one might want to shift this rectangle over the calibration
table, depending on the desired effect (maximize TcatIN versus minimize
FC) along the driving profile. This action cannot be accomplished with a
single map, therefore the temperature-dependent map helps to fulfil such
request.
The bottom plot of Figure 2.22 shows a typical engine coolant tempera-
ture trend during the NEDC considered. It can be argued that the results
presented so far suit only this specific driving profile, invalidating this ap-
proach when considering a different cycle. The global validity is instead
guaranteed, since the engine coolant temperature is the key factor used for
compensating the set-point related correction factors. Finally, whenever a
cold start takes place the heating strategy is activated, speeding up the
aftertreatment systems’ light-off.
Chapter 2. Transient thermal management of diesel engines 25

Figure 2.21: Control structure derived for managing SOI and VGT during
the engine warm-up.

2.3 Results
Figure 2.23 shows the results achieved by implementing different heating
strategies on the vehicle, during roll bench dynamometer NEDC tests. The
blue line refers to the original temperature profile without any heating strat-
egy (EU5 reference calibration, also shown in Figure 2.2), while the other
ones refer to the various temperature profiles that have been recorded with
different control strategies and calibration datasets. In all test cases the
target temperature is reached about 600 s earlier than the original behavior,
thus highly improving the chances to quickly start catalytic reactions on
SCR, enhancing NOx reduction efficiency. The temperature profiles (and
the corresponding heating strategies) differ one from each other because of
different SOI and VGT calibrations, confirming the ability to control their
effect on exhaust temperature and engine behavior, according to the specific
request.
Table 2.3 presents a synthetic comparison in terms of fuel consumption,
highlighting that the heating strategy corresponding to the red line (“C”)
introduces a very limited increase in fuel consumption (+1.47 %). This result
is of particular interest, also because “hard” heating strategies based on late
or post-injection events typically imply much greater fuel penalties. Heating
strategy “C” is based on the implementation of a specific SOI control law,
which will be briefly described below.
Some specific considerations need to be expressed, as far as the SOI is
concerned. The optimal SOI is typically calibrated on the test bench, as a
Chapter 2. Transient thermal management of diesel engines 26

Figure 2.22: Ideal application of different calibration strategies during the

engine warm-up. The NEDC cycle has been taken into consideration as
exemplary cycle. The calibrations derived as well as the final results achieved
can be extended to any driving profile.
Chapter 2. Transient thermal management of diesel engines 27

Figure 2.23: SCR inlet temperatures, for NEDC tests with different exhaust
line heating strategies.

trade-off between maximum combustion efficiency (minimum fuel consump-

tion) and combustion chamber temperature containment, in order to limit
NOx production. Therefore the ECU cannot always apply maximum ef-
ficiency SOI, being forced to delay the combustion process to reduce its
temperature. In the system under exam, this dual functionality can be real-
ized by two different control actions, thanks to the SCR system availability,
which can reduce NOx emissions with a higher efficiency if compared to SOI
delay action. Referring to the red line (strategy “C”), as soon as the engine
temperature approaches the warmed up condition, SOI and VGT corrections
gradually decrease. When the final pattern of the driving cycle starts, the
engine is substantially warm and the heating strategy adapts again to the
new conditions. This part of the cycle is characterized by an higher load,
and higher exhaust gas temperatures: the heating strategy is not necessary
anymore, and the maximum efficiency SOI is selected, together with a slight
increase of VGT opening position, to minimize fuel consumption.

2.3.1 Conclusion
In this chapter, the development of exhaust line heating strategies, based on
experimental investigations and previously developed simulation analysis,
Chapter 2. Transient thermal management of diesel engines 28

Table 2.3: Fuel consumption variation with respect to the reference temper-
ature profile (no heating strategy).
heating strategy: A B C
ΔFuelConsumption[%]: + 6.76 + 7.39 + 1.47

has been presented. The case study is represented by the SCR installation
in a small diesel engine exhaust line, to enhance NO x reduction in an effort
to comply with upcoming EU6 regulations. The challenge was to reach a
pre-specified temperature (of approximately 190°C) as fast as possible, far
away from the exhaust valves and without compromising fuel consumption.
The experimental investigation, supported by a modeling activity that had
previously been carried out, allowed the identification of the main effects of
the available control parameters on exhaust gas temperature, by considering
at the same time eventual negative effects on fuel consumption. The control
strategy (and the correspondent calibration dataset) has been based on such
approach, and different solutions have been tested on a roll dynamometer,
while performing homologation driving cycles (NEDC). The interesting re-
sult is that a substantial SCR light-off time reduction (around 600 s) may
be achieved with minor fuel penalties, and this may be obtained by imple-
menting a control strategy that is designed to respect different priorities
depending on the SCR thermal state. The proposed approach consists of
starting with low NOx production and higher exhaust gas temperature tar-
gets until the SCR has been thermally activated, and switching to maximum
efficiency priority (with SCR active thermal state constraint) afterwards.
Possible further improvement could be achieved by exploring the effect of
the EGR valve partial closing, which can be possible thanks to the increase
in NOx reduction due to the higher efficiency of the SCR after-treatment
system. A fuel consumption reduction is foreseen because of the double
effect of a better combustion efficiency and a further reduction of VGT
closing at constant boost pressure (due to the higher enthalpy available at
the turbocharger inlet).
Chapter 3

Dynamic optimization of
diesel engines

Optimal control of Diesel engines is becoming increasingly important. More

stringent emission regulations [7, 8] require the exploitation of the remaining
potential to further reduce the pollutant emissions, especially during tran-
sient operation [21, 22]. At the same time, the fuel consumption has to be
minimized for economical and environmental reasons. Nowadays, deriving
an engine calibration is a highly time demanding task, owing to the many
degrees of freedom provided by current diesel engines and to the requirement
to consider transient operation. Optimal control is a tool that can support
the calibration engineer. The optimal control trajectories indicate directions
for the calibration, disclose shortcomings of a chosen control structure and
serve as a benchmark.
The common approach to dynamic optimization is to use a large amount
of stationary and/or transient measurement data to identify a globally valid
model. Relying on this model, the optimal-control problem (OCP) is solved
at once. This approach assumes that all influences on the relevant outputs
are captured by the model and the selected set of control inputs.
Similar approaches were already used in the early days of automated en-
gine calibration [23, 24]. However, due to limitations in computer hard-
ware and software, a predefined structure of the control system had to be
assumed. Furthermore, the transient measurements were used to directly
construct gradient information for the optimization, since the vast amount
of model evaluations required to numerically solve a nonlinear OCP would
have been prohibitive at that time. Nowadays, such computing power is
readily available.
This thesis presents the development of an alternative approach to dy-
namic optimization. It involves an iteration between the dynamic optimiza-
tion, restricted to the current model-validity range, and the refinement of
the model using specific transient measurements [25]. This approach avoids

29
Chapter 3. Dynamic optimization of diesel engines 30

measurements in irrelevant regions. Furthermore, refining the model us-

ing transient measurements on the driving cycle at hand allows accounting
for the effect of all influences that are missing in the model. This com-
pensation mechanism allows for the use of a simple mean-value model for
the air path as well as empirical setpoint-relative emission models. It is
thus not required to develop sophisticated combustion models that have
to provide reliable far-field extrapolation. The accuracy of the air-path
model is increased by applying a “generalized Kalman filter”. All OCPs
occurring within the methodology are solved numerically by transcribing
the continuous-time problem into a finite-dimensional nonlinear program
(NLP).
The drawback of this method is that multiple runs of the transient cycle
have to be performed during each iteration. The procedure is thus best
suited for compact test cycles containing all relevant transient patterns in a
condensed form.
In this chapter, all models and numerical methods required to implement
the iterative procedure are described and analyzed. Furthermore, the exper-
imental setup and the testbench-software interfaces are presented. Finally,
one iteration of the procedure is executed on an engine testbench and the
results are analyzed and discussed.

3.1 Experimental setup

The experimental activity has been carried out on a light-duty engine that
is used mainly in EU4 C-segment passenger car. It is a 3.0 l V6 diesel en-
gine, equipped with a high-pressure injection system, a high-pressure cooled
EGR (Exhaust Gas Recirculation) circuit and a VGT (Variable Geometry
Turbine) turbocharger (Table 3.1).
The engine testbench is equipped with a dynamic brake which allows not
only steady-state performance but also transient operation. This character-
istic is of crucial importance whenever driving cycles are needed to be carried
out, in order to reproduce as closely as possible the real operating condi-
tion of the vehicle. The brake controller is remotely connected and driven
by a dSPACE rapid prototyping system, in which all algorithms needed to
control the desired engine speed and load torque are implemented.
Before focusing on the engine control unit (ECU), it is important to de-
scribe the layout of sensors installed on the engine. Generally speaking,
every testbench setup follows some common rules or guidelines, which can
vary accordingly to the particular research activity conducted. What makes
the testbench such an important environment for engine testing, is the pos-
sibility of installing several sensors, mainly “laboratory sensors” which are
not implemented on the production vehicle, because of their cost, short-term
reliability and duration.
Chapter 3. Dynamic optimization of diesel engines 31

Figure 3.1 shows the layout of all sensors that were available when this
activity has been carried out. It can be noticed that only a minority of
sensors are related to the ECU, which typically are in the minimum number
to properly control the engine. In recent control systems there is a growing
tendency to use virtual sensors (models) rather than physical ones, since
the main objective is to reduce the overall cost of the engine system, while
keeping the same amount of information provided by the sensors. Deriving
reliable models often relies on the type of sensors installed on the engine dur-
ing the experiments, for instance the availability of cylinder-pressure signals
provides a huge amount of information about the combustion phenomena.
Furthermore, several temperature and pressure sensors are usually installed
all over the engine, to acquire as much information as possible, which can
be used both to identify engine models or to enhance the supervision of the
engine. During the calibration activity performed on the testbench, fuel
consumption and pollutant emissions are typically measured by means of
sophisticated and expensive measurement devices, not usually available in
on-board applications. Referring to Figure 3.1, the following sensors and
devices have been used during the research activity at hand:

• pressure sensors based on piezoresistive effect: widely used for

measuring the pressure of fluids (both air and liquid) in various parts
of the engine, like in the air-path or in the fuel line. The piezoresistive
effect describes change in the electrical resistivity of a semiconductor
or metal when mechanical strain is applied. These sensors are robust,
reliable and quite inexpensive, therefore they are typically standard
sensors (ECU sensors).

• pressure sensors based on piezoelectric effect: more sophisti-

cated, accurate and expensive than piezoresistive sensors. Particularly
spread in the automotive field for the cylinder-pressure measurement.
In this specific case the engine is equipped with six cylinder-pressure
sensors, to monitor the combustion process in each cylinder.

• temperature: measured by means of thermoresistances and thermo-

couples. The former are used for on-board application (ECU sensors)
while the latter exclusively on the testbench or, more generally, for de-
velopment applications. Thermocouples are more accurate than ther-
moresistances, they cover a wider range of temperatures (also high
temperatures) and their dynamics may be faster, depending on their
size.

• air-flow meters: there are several types, based on different principles

and dedicated for various applications. Here the standard AFM (Air-
flow Meter) sensors have been used, one for each engine bank. They
are based on the hot-film anemometer measuring principle.
Chapter 3. Dynamic optimization of diesel engines 32

Table 3.1: Main data of the engine used for this research activity.
engine type: Diesel, V6
displacement: 2987 cm3
EGR: high pressure, cooled
compression ratio: 15.5
turbocharger: VGT, charge-air cooler
bore/stroke: 83/92 mm
injection: CDI 4, max. 1600 bar
valves/cyl.: 4
max. torque: 400 Nm (1400–3800 rpm)
rated power: 165 kW (3800 rpm)

• turbocharger speed: there are various kinds of possible solutions,

based on different measuring principles. In this case, it is an eddy
current turbocharger speed measurement system (micro-epsilon tur-
boSPEED DZ135).

• Nitrogen oxide (NOx) emissions: the NOx emissions are measured

by means of two different types of devices, namely a Cambustion fNOx
400 Fast CLD and a UniNOx sensor. The accurate but slow signal from
the latter has been used to calibrate the fast but drifting signal of the
fNOx 400.

• Soot emissions: the soot emissions are recorded by means of an AVL

Micro Soot Sensor. Further details about this measurement device are
presented in (4.1.3).

A quite comprehensive list of sensors typically employed in automotive,

along with some fundamental measuring principles, are presented in Ap-
pendix A.

Electronic Control Unit (ECU) The engine is controlled by a develop-

ment ECU, which slightly differs from the end of line version implemented
on the production vehicle. The Ethernet-based ETK interface by ETAS
provides direct access to the control variables and parameters of the ECU
via the parallel data and address bus, or via a serial microcontroller testing
or debugging interface. Due to its extremely compact design, the ETK can
be accommodated inside the housing of the production ECU. Moreover, the
ETK interface is real-time capable, and provides a universal ECU interface
for sophisticated applications in the development and calibration of engine
ECUs. The interface is supported across the board by ETAS hardware mod-
ules, the INCA calibration tool (Figure 3.2) as well as the INTECRIO and
ASCET development tools. The high standards in terms of performance,
safety, responsiveness, drivability, fuel savings and emissions met by today’s
Chapter 3. Dynamic optimization of diesel engines 33

Figure 3.1: Layout of the diesel engine used in this work, showing the various
types of sensors installed.

vehicles would not be attainable without the deployment of ECUs featuring

a multitude of sophisticated functions. Powerful measuring and calibration
access constitutes an essential prerequisite for developing these functions
and calibrating the function parameters. With INCA, ETAS offers a flexible
family of software products for calibration, diagnostics, and validation. The
need to develop, add and/or bypass some control structures implemented on
the ECU has been fulfilled by the utilization of a Rapid Prototyping Module
(ES910), in combination with the software package INCA-EIP (Experimen-
tal Target Integration Package). INCA-EIP enables real-time function de-
velopers to use the measurement and calibration functionality of INCA while
the ECU software functions are executed on the ES910. The ES910 proto-
typing and interface module combines high computing performance with all
common ECU interfaces in a compact and robust housing (Figure 3.3). A
schematic representation of its interaction with the ECU and the Host PC
is shown in Figure 3.4. CAN and LIN interfaces provide the connection
of the ES910 module to the ECU bus and to the external CAN-modules
(Input/Output operations). This setup provides complete control over all
relevant control inputs of the engine.
The prototyping tool INTECRIO is used to set up the rapid-prototyping
models, previously designed in Simulink (MathWorks), on the ES910. Dur-
ing the INTECRIO experiment the user has runtime access to the model
Chapter 3. Dynamic optimization of diesel engines 34

Figure 3.2: Screen shots of the calibration tool INCA.

executed by the ES910 module. With such an experimental setup any ECU
function can be bypassed, allowing for the development and the implemen-
tation of custom control algorithms, needed to perform the dynamic opti-
mization procedure that is presented in this chapter.

3.2 Engine model

From a modeling point of view, the engine treated in this work can be seen
as a nonlinear dynamic system with two dynamic feedback loops coupled
to each other, namely the EGR and the turbocharger. Referring to Figure
3.1, the fresh air path (light blue and blue) and the exhaust gas path (red)

Figure 3.3: ETAS ES910 prototyping and interface module.

Chapter 3. Dynamic optimization of diesel engines 35

Figure 3.4: Hardware, software, and interfaces of the testbench setup.

are not separate, but connected in different ways. The first coupling is due
to the mechanical connection between the compressor and the turbine: the
enthalpy in the exhaust gas is transformed by the turbine into mechanical
energy (torque) to speed up the turbocharger, and then this mechanical
energy is transferred to the intake air by the compressor. The EGR system
extracts part of the exhaust gas flow (upstream of the turbine for high-
pressure EGR) and drives it to the intake manifold (downstream of the
compressor). So, on the one hand the enthalpy related to this EGR mass
flow is not available anymore to the turbine to drive the turbocharger, but
on the other hand it increases the pressure in the intake manifold and thus
also the mass flow into the cylinders (and the composition).
Due to this coupling, the effects of the two actuators associated with the
turbocharger and the EGR depend on each other. The EGR valve controls
the EGR mass flow, while the turbocharger is equipped with a variable-
geometry turbine (VGT). Thanks to the adjustable vanes position, the open-
ing area of the turbine can be modified in order to change the restriction
of the flow. While the EGR valve positioning has an intuitive convention,
as EGR=0% means fully closed and no gas recirculation, a clarification for
the VGT position might be useful for the reader. In the given control sys-
tem, a VGT position=100% corresponds to a fully closed condition, and vice
versa the distributor is fully open with a VGT position=0%. In other words,
when the VGT is fully closed (100%) it means that the turbine, under steady
state flow conditions, generates the highest backpressure correspondent to
that mass flow rate, and therefore the pressure drop through the turbine
is at the maximum. In this condition, the turbine produces its maximum
power, increasing the turbocharger speed, with the consequent increase of
the intake manifold pressure.
To recap, capturing and modeling all the physical processes in a modern
diesel engine, equipped with VGT and EGR, is a demanding task. The final
purpose has to be clear from the beginning, when deriving an engine model,
since its structure and characteristics are strongly related to its intended use.
A model able to catch the waves effect in the intake and exhaust manifolds,
Chapter 3. Dynamic optimization of diesel engines 36

Figure 3.5: Structure of the engine model.

or the emission species formation into the combustion chamber, is hugely

more complex than a linearized, control-oriented model that runs online on
the ECU. The model derived in this work is close to the latter category,
but it may be defined as an optimization-oriented rather than a control-
oriented model. The intended use of the model is to be part of a dynamic
optimization framework, in which an iterative optimization routine is run
by using the engine model as plant. For the results of the optimization to
be of any relevance, the model on which the optimization relies has to be
sufficiently accurate and must capture all influences of each control input.
The vast amount of model evaluations during the iterative optimization
requires the model to be fast, which is primarily achieved by keeping the
structure simple. Finally, the model has to be smooth since an efficient
optimization relies on (first and even second) derivatives. The combustion
processes are especially hard to describe by models that combine all those
requirements.
In Figure 3.5 the schematic of the engine model derived is shown. The air-
path model is presented in details in Sec. 3.2.1, and the combustion model
in Sec. 3.2.4. The model can be subdivided into a dynamic and a static
part. The subscripts denote the intake and exhaust manifolds (IM/EM),
the volume between the turbine and the exhaust-gas aftertreatment system
(ATS), and the turbocharger (TC). The positions of the variable-geometry
turbine (VGT) and the exhaust-gas recirculation valve (EGR) are pulse-
width modulation signals with a range of [0,1]. The SOI is specified in
degrees before top dead center. Finally, the burnt-gas fraction in the intake
manifold is denoted by xbg,IM .
All dynamics are induced by the air path, i.e. the turbocharger inertia
and the volumes. The full model is represented in state-space form as:

ẋ(t) = f (x(t), u(t)), (3.1a)

y(t) = g(x(t), u(t)), (3.1b)

where nx = 6 state variables, nu = 4 control inputs, and the state, control

Chapter 3. Dynamic optimization of diesel engines 37

and output vectors are:

T
x = pIM , ϑIM , xbg,IM , pEM , pATS , ωTC ,
∗ ∗
T
u = uVGT , uEGR , ϕSOI , mfuel )T , y = mNOx , msoot , Tload .
The engine speed (Neng ) is treated as time-varying parameter.

3.2.1 Mean-value model of the air-path

The models for the air path are based on many related works. Most of
the modeling components are based on [7], while other publications are
referenced along the text.
In the following paragraphs, all the air-path components needed to build
the engine model are presented. Their mathematical formulation is de-
scribed, highlighting the set of parameters that have to be determined for
each model. The numerical methods that have been applied to identify such
parameters are detailed later, while the set of experimental measurements,
needed to run the identification routines as well as the validation runs, is
now described. In addition, Figure 3.6 shows a schematic representation of
the air-path model that has been derived. It may be helpful to go through
the nomenclature used when describing the models.

Measurement data Figure 3.7 shows an overview of the measuring points,

spanned by engine speed and load torque. Once the engine is warmed-up,
the first measuring point is reached by setting the engine speed, on the test-
bench management system, and the torque request on INCA. Afterwards,
the engine is considered to be in a stationary condition when the variations
of the main physical variables (intake/exhaust temperature and pressure,
turbocharger speed, etc.) are not relevant. Finally the first measurement
can start. The recording time is at least 20 seconds, so that meaningful
average values can be calculated during the post-processing phase. In or-
der to discard meaningless recorded data, resulting for instance from a not
real steady-state condition, the post-processing code calculates, besides the
average value, the CoV (Coefficient of Variation), and highlights those mea-
surements with an over threshold CoV (defined by the user). All the scripts
are written in MatLab 2012b.
The EGR and VGT positions are controlled manually, bypassing the ECU
control functions. In doing so, sweeps of both actuators can be performed.
A set of measurements is performed without exhaust-gas recirculation, by
keeping the EGR valve closed, while VGT sweeps are applied. For each
measuring point, approximately ten VGT positions are swept and, obvi-
ously, recorded. The following models are identified and validated by using
this set of data: compressor mass-flow, compressor enthalpy, turbine mass-
flow, turbine efficiency, restriction mass-flow, cylinder mass-flow, engine-
out temperature. As a general rule, half of the measurement data are used
Chapter 3. Dynamic optimization of diesel engines 38

Figure 3.6: Schematic of the air-path model described in this work.

Chapter 3. Dynamic optimization of diesel engines 39

180

120
T load [Nm]

60

0
500 1500 2500 3500 4500
Engine Speed [rpm]

Figure 3.7: Grid of operating points measured on the testbench for iden-
tification and validation of the models. For each measuring point (overall
roughly 90), the engine is brought in steady-state condition, and then VGT
and EGR sweeps are performed.

for the identification, and the other half for the validation. This approach
ensures that the prediction quality of the model, assessed by the validation
data, is unrelated to the measurements carried out. Once these models are
identified, only the EGR mass-flow and the EGR cooler remain to be an-
alyzed. Similar to the previous case, EGR sweeps are performed, from the
lowest mass-flow through the EGR valve to the highest (but tolerable by
the engine) one.
Looking back to Figure 3.7 it can be noticed that, while the engine speed
range spanned is coherent with its speed limits (1000-4000 rpm), the load
torque is significantly below the reachable limit. This apparently not spread
experimental plane does not invalidate the results obtained, because the op-
erating region is defined by the levels of pressure and temperatures reached
in the intake and exhaust manifolds. In other words, by sweeping the VGT
position the extreme conditions for the turbocharger speed can be reached,
bringing the intake manifold pressure up to its limit (approx. 2.7 bar abso-
lute). Once the border conditions are reached, there is no need to further
increase the output torque (by increasing the fuel injected), especially con-
sidering that the measured torque is not accounted for when deriving the
air-path models.

Compressor mass-flow The model is based on [26]. According to the

original literature, the ellipse equation should be solved for the pressure
ratio, if a surge model is included. The engine is operated strictly out of
the surge region of the compressor, thanks to constraints imposed by the
optimal control problem. Hence, surge has not been considered in this case,
Chapter 3. Dynamic optimization of diesel engines 40

resulting in the solution of the ellipse equation for the mass flow instead of
the pressure ratio. The speed lines need to have a positive slope towards
lower mass flows. The equations of the original model are presented below:

k
Πs = 1 + kπ,1 ∙ nTC
π,e
(3.2a)
∗ km,e
ms = 0 + km,1 ∙ nTC (3.2b)
∗
mmax = kmax,0 + kmax,1 ∙ nTC (3.2c)
   1
∗ ∗ ∗ ∗ ΠCP c2 c1
mCP = ms + (mmax − ms ) ∙ 1 − (3.2d)
Πs
where the index s denotes the surge limit. For every turbocharger speed
nTC , these equations define the ellipse-like curve:

 c 2 ∗ ∗
! c1
ΠCP mCP − ms
+ = 1. (3.3)
Πs ∗
mmax − ms
∗

where the denominators are the semi-axes (for an ellipse c1 = c2 = 2).

By adopting this kind of model formulation, two potential problems can
arise. The first one has to do with the surge line, because when it is ap-
proached, a high sensitivity from pressure ratio to mass flow can easily
result. Moreover, when the surge line is crossed, the mass flow is not even
defined. The solution found has been to shift the ellipses, in order to obtain
a constant slope at the surge line, and then to extend it to the abscissa
∗
mCP = 0.
The second problem concerns the extrapolation of the speed lines. For the
model identification, an appropriate set of experimental data has been used,
in order to achieve good interpolation behavior of the model. Outside this
experimental region, the model needs to extrapolate, leading to unstable
behavior. For instance the mass flow could increase with an increasing
pressure ratio. Given these considerations, the model (shown in Figure
3.8 a)) has been modified by replacing the surge line with a vertical line
∗
ms = const.(< 0), which is achieved by modifying equations (3.2a) and
(3.2b) to:

k
Πs = kπ,0 + kπ,1 ∙ nTC
π,e
(3.4a)
∗
ms = km,0 (< 0) (3.4b)
To provide sufficient degrees of freedom to the model, the shape of the
ellipses may change as a function of the turbocharger speed:

c2 = c2,0 + c2,1 ∙ nTC + c2,2 ∙ n2TC . (3.5)

Chapter 3. Dynamic optimization of diesel engines 41

Figure 3.8: a)Original compressor mass-flow model, critical extrapolation of

speed lines (dashed speed-lines) and usual operating region on the engine
(shaded area). b) Modified compressor mass-flow model.

The modified version of the model, shown in Figure 3.8 b), has been found
to be reliably identified by an automated fitting procedure, and exhibits
good accuracy for all mass-flow ranges and sufficient flexibility with a small
number of parameters.
For the identification, the compressor map, usually provided by the man-
ufacturer, was not available, therefore only experimental data have been
used. Stationary measurements have been performed as explained above.
During these experiments the EGR valve has been kept closed, while VGT
sweeps have been carried out with the aim of exploring all the operating
region of the compressor. A compromise between the absolute and the rel-
ative squared error has been used as the objective function. The weighting
between the two has been tuned to obtain a balanced fit, which showed a
satisfying accuracy at low as well as at high mass-flows. The simplex method
in MATLAB’s fminsearch revealed itself to be successful in finding a suit-
able set of parameters. Multiple iterative runs have been performed, each
one initialized with the optimized parameter set from the previous itera-
tion. Figure 3.9 shows the results of the identification, while the parameters
identified are listed in the final Table 3.2.

Compressor enthalpy The specific enthalpy increase over the compres-

sor can be expressed by the isentropic enthalpy change, and the isentropic
Chapter 3. Dynamic optimization of diesel engines 42

0.2 2.8

2.6
0.17
engine data model
5% error 2.4 measured
measured m*CP [kg/s]

0.14 2.2

ΠCP [-]
0.11
1.8

0.08 1.6

1.4
0.05
1.2

0.02 1
0.02 0.05 0.08 0.11 0.14 0.17 0.2 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
modeled m* [kg/s] m*CP [kg/s]
CP

Figure 3.9: Results of the identification of the compressor mass-flow model.

efficiency:

ΔhCP = cp ∙ (ϑCP,out − ϑCP,in ) (3.6a)

 κ−1 
ΔhCP,is = cp ∙ ϑCP,in ∙ ΠCP − 1
κ
(3.6b)

ΔhCP,is
ηis = (3.6c)
ΔhCP
Instead of this common formulation, the specific enthalpy transferred to
the gas can alternatively be calculated through a momentum balance [27],
resulting in the Euler equation:

ΔhCP = U2 Cϑ2 − U1 Cϑ1 (3.7)

where U2 is the speed of the blade tip. The tangential speed of the gas
at the inlet Cϑ1 is assumed to be zero (axial flow). The tangential speed of
the gas at the outlet Cϑ2 may be described by the radial component, and
the back-sweep angle (BSA) of the blade (assuming no slip):

Cϑ2 = U2 − Cr2 cot(β2 ) (3.8)

Cr2 is proportional to the mass-flow divided by the density at the impeller

outlet. Research in [28] shows how the assumption ρ2 = ρ1 may be reason-
able, so if (3.8) is inserted in (3.7), all constant parameters are merged, and
a constant slip factor is introduced, the specific enthalpy increase over the
compressor becomes:

" ∗
#
m
ΔhCP = kslip ∙ U22 − kBSA ∙ U2 ∙ (3.9)
ρ1
Chapter 3. Dynamic optimization of diesel engines 43

⋅
14 14

12
model
12 engine data measured
measured ΔhCP [J/kg K] ⋅ 10-4

5% error
10

ΔhCP [J/kg K] ⋅ 10-4

10

8
8
6

6
4

4
2

2 0
2 4 6 8 10 12 14 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
modeled ΔhCP [J/kg K] ⋅ 10-4 m*CP [kg/s]

Figure 3.10: Results of the identification of the compressor enthalpy model.

Considering that for single-stage turbocharging the gas density at the inlet
ρ1 can reasonably be assumed constant, and rearranging the equations, the
following compressor enthalpy model has been derived:

∗
ΔhCP = kh,1 ∙ n2TC − kh,2 ∙ m ∙ nTC (3.10)

Once ΔhCP is known, the temperature after the compressor can be cal-
culated by means of (3.6a) as:
ΔhCP
ϑCP,out = ϑamb + . (3.11)
cp
The two parameters of the model have been identified by a linear least-
squares (LSQ) regression, since (3.10) is linear in the parameters kh,i . Since
cp appears in both formulations, it is only used to yield a physical quantity
(enthalpy). Moreover its value has been chosen to be constant at cp =
1000 J/(kg ∙ K), since the inlet temperature hardly changes. The identified
parameters are shown in Table 3.2. The fit of the model is shown in Figure
(3.10).

Intercooler The mass flow through the intercooler has not been modeled
explicitly. Therefore, the pressure drop due to the intercooler can be taken
into account directly in the compressor mass-flow model, by using the pres-
sure value in the intake manifold when defining Π CP . In other words, the
pressure ratio in (3.2d) is ΠCP = pIM /pamb . By doing so, one state variable
(pressure between compressor and intercooler) and an orifice function can
be eliminated. The intercooler model is based on a simple stationary energy
balance:

 
ϑCP + ϑIC ∗
kIC ∙ − ϑcool = mCP ∙ (ϑIC − θCP ) (3.12)
2
Chapter 3. Dynamic optimization of diesel engines 44

Intercooler
90

80

70 engine data
5% error
measured ϑout [°C]

60

50

40

30

20

10
10 20 30 40 50 60 70 80 90
modeled ϑout [°C]

Figure 3.11: Comparison between modeled and measured temperature after

the intercooler (ϑIC ).

As representative temperature, the average between the inflow and outflow

temperatures has been used. The efficiency parameter kIC depends on the
mass flow, so the model has been derived as:

∗ ∗2
kIC = kIC,0 + kIC,1 ∙ mCP + kIC,2 ∙ mCP . (3.13)
The value of kIC has been calculated from the measurement data and an
LSQ regression has been applied to identify the model. Figure 3.11 shows
the comparison between measured and modeled outflow temperature.

Turbine mass-flow The turbine mass flow can be treated as an orifice,

with a variable area in the case of variable nozzle turbines and a blade speed
dependent discharge coefficient cd . While in the compressor the mass flow
is driven by its rotation, in the case of the turbine the difference between
the upstream and downstream pressure drives the fluid in a nonlinear way
through the restriction. A detailed description of fluid dynamics formula-
tions used for deriving the turbine mass-flow model can be found in [7].
Only the main definitions are summarized below, starting from the depen-
dent variables of the model chosen:
1. ΠTB = pTB,in /pTB,out : the pressure drop across the turbine is the main
factor responsible for the flow generation.
2. uVGT : in the case of variable nozzle turbines, the orifice area varies
accordingly to the VGT position.
Chapter 3. Dynamic optimization of diesel engines 45

3. nTC : the turbine rotation restricts the flow due to centrifugal accelera-
tion, therefore the discharge coefficient cd , which appears in the orifice
equation, is blade speed dependent.

The variable ΠTB (1) is included in the flow function term Ψ(∙), which in
this case has been considered in its simplified form

s  
2 1
ΨTB = ∙ 1− (3.14)
ΠTB ΠTB
∗
Concerning the mass flow mTB , usually the normalized mass flow

p
∗ ∗ ϑTB,in
μTB = mTB ∙ (3.15)
pTB,in
is used instead, to make the measurement data obtained on the engine
comparable to the manufacturer-supplied turbine map. In order to apply an
LSQ regression, the following selection of regressors has been found suitable
to fit the experimental data:
∗
μTB = (kTB,0 + kTB,1 ∙ uVGT + kTB,2 ∙ uVGT 2 ) ∙ ΨTB + kTB,3 ∙ nTC
(3.16)

Since the EGR mass-flow is still null (EGR valve closed), the entire mass
of engine-out gas flows through the turbine, therefore the exhaust mass flow
∗ ∗ ∗
is simply the sum of the fresh air and fuel mass-flows: mTB = mCP + mfuel .
Results of the identification are shown in the left-hand plot of Figure 3.12.

Turbine efficiency The turbine efficiency can be expressed as:

ΔhTB cp ∙ (ϑTB,in − ϑTB,out )

ηTB = =   (3.17)
ΔhTB,is 1−κ
cp ∙ ϑTB,in ∙ 1 − ΠTBκ

It could be easily calculated from experimental data, since each term

is measured and a constant value for κ is assumed. However, the enthalpy
change over the turbine ΔhTB may be overestimated when using the exhaust
temperatures directly (upstream and downstream of the turbine), because
of the heat losses in the exhaust manifold. In other words, the temperature
decrease due to heat losses is attributed to the enthalpy that the turbine
extracts from the gas, leading to an overestimated turbine power:

∗
PTB = wT C ∙ TTB = ΔHTB = mTB ∙ ΔhTB (3.18)
Chapter 3. Dynamic optimization of diesel engines 46

This effect is ever more emphasized the higher is the turbine case tem-
perature, therefore another approach has been adopted. Considering the
energy balance across the turbine

dwTC ΔHTB − ΔHCP − ΔHfric

ΘTC ∙ = TTB − TCP − Tfric = (3.19)
dt wT C
dwTC
in a steady-state condition (i.e. dt = 0) it becomes:

ΔHTB = ΔHCP + ΔHfric (3.20)

Sometimes, a more general mechanical efficiency is used instead of a fric-

tion torque. However, supposing the neglection of the friction contribution,
it can be imposed that the enthalpy change over the turbine matches the
enthalpy that the compressor transfers to the air, resulting in:

∗
mCP ∙ ΔhCP
ΔhTB = ∗ (3.21)
mTB
This matching ensures an accurate prediction of the turbocharger speed
and eliminates the influence of stationary heat losses in the exhaust mani-
fold. Given the considerations so far, the following LIP (linear in parame-
ters) model has shown a good fit (right-hand plot of Figure 3.12) with the
measurement data:

ηTB = hTB,0 + hTB,1 ∙ uVGT + hTB,2 ∙ u2VGT + hTB,3 ∙ ΠTB (3.22)

Once the efficiency has been determined, the temperature after the turbine
and before the aftertreatment system (ATS) can be calculated by applying
the following equations:

ΔhTB = ΔhTB,is ∙ ηTB (3.23a)

ΔhTB
ΔϑTB = (3.23b)
cp
ϑATS = ϑEM − ΔϑTB (3.23c)

where ϑEM is the temperature in the exhaust manifold, which is later

defined in Eq. (3.29).
Chapter 3. Dynamic optimization of diesel engines 47

0.2

0.18 0.7
model
5% rel.err 0.65
0.16
model
0.6 measured
measured m*TB [kg/s]

0.14
0.55

ηTB [-]
0.12
0.5
0.1
0.45
0.08
0.4

0.06 0.35
3.5
0.04 3
2.5 100
0.02 2 80
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
1.5 60
modeled m*TB [kg/s] 40
ΠTB [-] 1 20
u [%]
VGT

Figure 3.12: Results of the identification of the mass-flow and enthalpy

models for the turbine.

Restriction mass-flow The aftertreatment system has been modeled as

simple flow restriction, by adopting the approximation of the flow function
for compressible flows, already used for the turbine in Eq. (3.14). Since
the pressure ratio never reaches critical conditions, no case distinction is
necessary. The final model is expressed as

s  
∗ pATS 2 1
mATS = kATS,0 + kATS,1 ∙ √ ∙ ∙ 1− (3.24)
ϑAT S ΠATS ΠATS

with ΠATS = pATS /pamb . Figure (3.13) shows that the usual model for-
mulation (with kATS,0 = 0 ) exhibits a systematic error. For this reason the
model has been extended by adding the parameter kATS,0 .

Cylinder mass-flow Under normal engine operating conditions, the total

∗
mass flow mcyl entering the cylinders, is composed by a mixture of fresh air,
∗
driven from the compressor ( mCP ), and exhaust gas, recirculated from the
∗
exhaust manifold (mEGR ) through the EGR valve. Since the EGR valve has
been kept closed for the air-path model identification, there is no recircula-
∗
tion of exhaust gas (mEGR = 0). As a result, the total mass flow equals the
∗ ∗
compressor mass flow (mcyl = mCP ).
Regarding the mass flow entering the cylinders, the engine itself can be
approximated as a volumetric pump, i.e. a device that enforces a volume
flow approximately proportional to its speed. A typical formulation for such
a model is:

∗ ∗ pIM V d Neng
mcyl = ρIM ∙ V cyl = ηvol,rel ∙ ∙ ∙ (3.25)
R ∙ ϑIM 2 60
Chapter 3. Dynamic optimization of diesel engines 48

3.5

2.5
ext. model
measured
orig. model
2

1.5

0.5
1 1.1 1.2 1.3 1.4 1.5 1.6
ΠATS [-]

Figure 3.13: Model for the flow restriction representing the aftertreatment
system (ATS). The original model formulation suffers a systematic error.

The variable ρIM is the density of the gas at the engine’s intake, related
to the intake pressure and temperature by the ideal gas law. The parameter
ηvol,rel is the relative volumetric efficiency, which describes how far the engine
differs from a perfect volumetric device (ηvol,rel = 1). Several effects degrade
the ideal volumetric efficiency to a typical value of 0.7 - 0.95. For instance a
volume of residual gas, larger than the volume of the combustion chamber at
top dead centre (TDC), may be captured in the cylinder, or flow restrictions
causing a reduction of the pressure gradient may cause such an effect. These
effects are influenced mainly by the valve timing, which is invariable for the
given engine. Finally, the model formulation remains strict to the concept of
volumetric efficiency introduced in Eq. (3.25), so the mass of fresh mixture
aspirated in each cylinder is calculated as

pIM

mcyl = ∙ kcyl,0 + kcyl,1 ∙ Neng + kcyl,2 ∙ Neng
2
+ kcyl,3 ∙ Neng
ϑIM
(3.26)

and consequently the total mass flow into the engine is expressed as

∗ Neng ∙ ncyl
mcyl = mcyl ∙ (3.27)
120

The model reproduces the mass flow in the cylinders with a relative error
within 5%, as shown in Figure 3.14.
Chapter 3. Dynamic optimization of diesel engines 49

0.2

0.17 engine data

1.2
5% error
1.1 measured
measured m*cyl [kg/s]

0.14
1
modeled

mcyl [g]
0.9
0.11
0.8
0.7
0.08
0.6
0.5
0.05 700 5000
600 4000
500 3000
0.02
0.02 0.05 0.08 0.11 0.14 0.17 0.2 400 2000
modeled m*cyl [kg/s] pIM/θIM [Pa/K] 300 1000
Neng [rpm]

Figure 3.14: Model for the cylinder mass-flow. In right-hand plot, the mea-
sured mass entering each cylinder is plotted over the engine speed and the
density at engine’s intake. The model accurately reproduces all measure-
ment data.

Engine-out temperature The engine-out temperature is calculated by

an ideal-gas dual cycle (also known as the Seiliger cycle), splitting the com-
bustion process into an isochoric and an isobaric part. To be precise, a
distinction between the cylinder-outlet and the turbine-inlet temperature
would be needed, because of the occurring heat losses from the exhaust
manifold walls. In this engine at hand, the exhaust pipe is rather short,
placing the turbine very close to the cylinders-outlet. For this reason the
exhaust gas temperature along the connecting pipe between engine and tur-
bine is assumed to be constant.
The temperature of the aspirated gas is adjusted to compensate for resid-
ual gases, heat transfers, turbulence and friction phenomena. The aspirated
charge is heated from the hot valves, piston and cylinder walls. In addition,
turbulence and flow friction also increase the charge temperature. However,
the highest contribution is due to the hot residual gas from the previous
combustion cycle. Rather than calculating its temperature (and estimating
its fraction) iteratively, correction factors are introduced which also account
for the other effects. A linear dependence in engine speed and intake man-
ifold temperature has been found to be sufficient. Therefore, the initial
temperature ϑcylInit of the cylinder charge is given by:

ϑcylInit = hcylInit,1 ∙ ϑIM + hcylInit,2 ∙ Neng (3.28a)

After defining the pressure ratio over the cylinder block as

pexhaust p3
Πeng = = (3.28b)
pintake p2
Chapter 3. Dynamic optimization of diesel engines 50

550

500
measured engine-out temperature [°C]
engine data
450 5% error

400

350

300

250

200

150
150 200 250 300 350 400 450 500 550
modeled engine-out temperature [°C]

Figure 3.15: Model for the engine-out temperature.

and the “energy density” of the combustion process

∗
mfuel ∙ Hl
q̃ = ∗ , (3.28c)
min
the ideal-gas Seiliger cycle (diesel formulation in this case) has been used to
calculate the engine-out temperature as follows:
  1 −1  
1− 1 q̃ κ q̃
ϑEM = ηcomb ∙Πengκ ∙r1−κ ∙ 1+ ∙ + ϑcylInit ∙ r κ−1
cv ∙ rκ−1 ∙ ϑcylInit cv
(3.29)

The parameter ηcomb is a constant correction factor to compensate additional

heat losses and incomplete combustion, while r is the engine compression
ratio. The MATLAB’s function fminsearch has been adopted to find the
best set of parameters, which are listed in Table 3.2. The prediction accuracy
of the model is shown in Figure 3.15.

Dynamic elements In order to present the dynamics of the air-path, the

concept of receiver needs to be introduced [7]. A receiver is a fixed volume
in which the thermodynamic states (pressures, temperatures, composition,
etc.) are assumed to be the same over the entire volume (lumped parameter
system). As shown in Figure 3.16 , the inputs and outputs of the receiver
are the mass and enthalpy flows, the storage quantities are the mass and the
internal energy, and the state variables are the pressure and the temperature.
Assuming no heat or mass transfer through the walls, and no substantial
Chapter 3. Dynamic optimization of diesel engines 51

changes in potential or kinetic energy in the flow, the following two coupled
differential equations describe the receiver dynamics:

d ∗ ∗
m(t) = min (t) − mout (t) (3.30a)
dt
d ∗ ∗
U (t) = H in (t) − H out (t) (3.30b)
dt
The coupling between these two equations, under the assumption that the
fluids can be modeled as ideal gases, is given by the following relations:

p(t) ∙ V = m(t) ∙ R ∙ ϑ(t) (3.31a)

1
U (t) = cv ∙ ϑ(t) ∙ m(t) = ∙ p(t) ∙ V (3.31b)
κ−1
∗ ∗
H in (t) = cp ∙ ϑin (t) ∙ min (3.31c)
∗ ∗
H out (t) = cp ∙ ϑ(t) ∙ mout (3.31d)

Note that the temperature ϑout (t) of the out-flowing gas is assumed to
be the same as the temperature ϑ(t) of the gas in the receiver (lumped
parameter approach).
Substituting (3.31) into (3.30), the following two differential equations
for the level variables pressure and temperature are obtained after some
algebraic manipulations (time dependencies omitted):

d R ∗ ∗
p= ∙ κ ∙ [min ∙ ϑin − mout (t) ∙ ϑ] (3.32a)
dt V
d ϑ∙R ∗ ∗ ∗ ∗
ϑ= ∙ [cp (min ∙ ϑin − mout ∙ ϑ) − cv ∙ ϑ ∙ (min − mout )]
dt p ∙ V ∙ cv
(3.32b)
Moving the attention towards the air-path model described so far, there
are two receivers, namely the intake and exhaust volumes. Therefore, pres-
sure and temperature in the intake and exhaust manifolds would be easily
determined through equations (3.32), if there wasn’t a connection between
these two receivers. Indeed, they are connected through a pipe of small di-
ameter, in which the flow is determined by the pressure difference and by a
valve opening area, which serves as a regulation device. Since a higher level
of pressure prevails in the exhaust side than in the intake one, the flow is
driven in a non linear way through such valve, and as a consequence, part
of the exhaust gas is recirculated into the intake manifold. This system,
also known as EGR (Exhaust Gas Recirculation), connects the intake and
exhaust receivers, therefore it has to be taken into account when defining
the balance equations (3.30).
Chapter 3. Dynamic optimization of diesel engines 52

Figure 3.16: Inputs, outputs and level variables of a receiver.

3.2.2 Exhaust Gas Recirculation

The EGR valve has been modeled as a modified form of the simplified isen-
tropic orifice [7] with a variable effective cross-sectional area. An approxi-
mate flow function has been used, i.e.

s  
1 1
Ψ̃(ΠEGR ) = ∙ 1− (3.33a)
ΠEGR ΠEGR

with ΠEGR = pEM /pIM . The mass flow through the EGR may be expressed
as:
∗
mEGR = AEGR ∙ pEM ∙ Ψ̃(ΠEGR ) (3.33b)

and it is influenced by the term AEGR , which is related to the geometrical

opening area of the valve, reduced by a discharge coefficient. Since the
opening area is proportional to the EGR valve command uEGR , a relation
with this parameter has been identified and the fitting model is:

∗
mEGR
AEGR = = (kEGR,0 ∙ uEGR + kEGR,1 ∙ u2EGR + kEGR,2 ∙ u3EGR ) (3.34)
pEM ∙ Ψ̃
Figure 3.17 shows such relation, while the final results for the EGR mass-
flow model are shown in the left-hand plot of Figure 3.18.
It can be noticed that the prediction accuracy is slightly poorer compared
to the models previously presented. Most likely this result is due to the EGR
mass-flow estimation, which has been calculated as the difference between
the cylinder and compressor mass-flows. While the compressor mass-flow is
measured by the AFM, the cylinder mass-flow ∗has been estimated by using
the model itself (3.26), thereby the quantity m̃cyl has been predicted over
the entire experimental plan.
∗ ∗ ∗
mEGR = m̃cyl − mCP . (3.35)

Consequently, the error in estimating the cylinder mass-flow (Figure 3.14),

may lead to a potential propagation of the prediction error when calculating
the EGR mass-flow.
Chapter 3. Dynamic optimization of diesel engines 53

-7
x 10
4

3.5

measured
3
model
mEGR / (pEM ⋅ ΨEGR )

2.5

1.5
*

0.5

0
10 20 30 40 50 60 70 80
uEGR [%]

Figure 3.17: Model for the EGR valve. Fitting of the variable effective
cross-sectional area.

EGR cooler The recirculated exhaust gas passes through a heat ex-
changer, called EGR cooler (EGC), with the aim of cooling the gas before
mixing inside the intake manifold with the compressed air, which comes
from the compressor. For the temperature difference across the EGC, a
simple stationary energy balance is evaluated. The average of the inflow
and outflow temperatures is used as the representative temperature, which
yields:

 
ϑEM + ϑEGR ∗
kEGC ∙ − ϑclf = mEGR ∙ (ϑEM − ϑEGR ) (3.36a)
2

The temperature of the cooling-fluid is assumed to be constant, i.e. ϑclf =

360K, and the efficiency parameter kEGC depends on the mass flow:
∗ ∗2
kEGC = kEGC,1 ∙ mEGR + kEGC,2 ∙ mEGR (3.36b)

The right-hand plot of Figure 3.18 shows the results of the model. As al-
ready explained above, the inaccurate estimation of the EGR mass-flow may
be the main factor responsible for the poor prediction accuracy achieved.

Dynamic elements with EGR Now that the models related to the EGR
system have been introduced, the final balance equations can be defined
and the air-path dynamics summarized. Since the objective was to derive
a simple air-path model in the first place, the EGR dynamics need to be
introduced in accordance with the following assumptions:
Chapter 3. Dynamic optimization of diesel engines 54

0.02 350

engine data
0.016 engine data 300 5% error
5% error
measured m*EGR [kg/s]

measured θEGR [°C]

0.012 250

0.008 200

0.004 150

0 100
0 0.004 0.008 0.012 0.016 0.02 100 150 200 250 300 350
modeled m*EGR [kg/s] modeled θEGR [°C]

Figure 3.18: EGR mass-flow in left-hand plot. EGR cooler in right-hand

plot. For both cases the relative error is above 5 %, this inaccuracy might
be due to the approximation made when estimating the realEGR mass-flow.

• No transport delay of the mass through the EGR system. In a plug-

flow, the flow through the EGR valve instantly pushes the same flow
into the intake manifold.

• No gas dynamics from the exhaust ports to the EGR valve. In ac-
cordance with the plug-flow assumption, no mixing or diffusion takes
place.

• No transport delay of the gas composition through the EGR system.

The flow entering the intake manifold is assumed to have the compo-
sition of the exhaust gas leaving the exhaust ports at the same time.

• Perfectly mixed gas in the intake manifold. This assumption is com-

mon to all mean-value modelling approaches (lumped parameters).

• The EGR cooler is installed close enough to the valve that the two
parts can be represented by a single flow restriction with a variable
opening area.

• The mixture is stoichiometric or lean (but not rich). For diesel engines,
this is a normal operating condition.

Some of these assumptions may appear quite strong but, as long as the
EGR path is short, they can be accepted without significantly degrading the
quality of the model.
The differential equations (3.32) are now applied to the intake receiver,
where there are two input and one output flows, as shown in Figure (3.6).
The fresh air coming from the compressor mixes with the exhaust gas, con-
sequently the gas in the intake manifold can be subdivided into two species,
namely burnt gas and air. Burnt gas denotes the fraction of mixture that
actually burned during the combustion, accordingly to its stoichiometric
Chapter 3. Dynamic optimization of diesel engines 55

factor, thereby no oxygen is left in it. Hence, the burnt-gas fraction in the
exhaust manifold (bg,EM) is

∗ ∗
xbg,IM ∙ mcyl + (1 + σ0 ) ∙ mfuel
xbg,EM = ∗ ∗ (3.37)
mcyl + mfuel
where σ0 is the stoichiometric air-to-fuel ratio. Due to the distinction of
the two species in the intake volume, two mass-balance equations result:

d ∗ ∗ ∗
mIM,air = mCP,air + mEGR,air − mcyl,air
dt
∗ ∗ ∗
= mCP + mEGR ∙ (1 − xbg,EM ) − mcyl ∙ (1 − xbg,EM ) (3.38a)
d ∗ ∗
mIM,bg = mEGR ∙ xbg,EM − mcyl ∙ xbg,IM (3.38b)
dt
Concerning the energy balance (3.30b), constant and uniform specific heats
are assumed:
 
d dϑIM dmIM
(cv ∙ mIM ∙ ϑIM ) = cv ∙ mIM ∙ + ϑIM ∙
dt dt dt
∗ ∗ ∗

= cp ∙ mCP ∙ ϑIC + mEGR ∙ ϑEGC − mcyl ∙ ϑIM .
(3.38c)

where mIM = mIM,air + mIM,bg . The solution of the equation system for
the pressure, the temperature and the mass fraction is given by applying
the ideal gas law (3.31a):

d R ∗ ∗ ∗

f1 = pIM = κ mCP ϑIC + mEGR ϑEGC − mcyl ϑIM , (3.39a)
dt VIM
d RϑIM h  ∗ ∗ ∗
f2 = ϑIM = cp mCP ϑIC + mEGR ϑEGC − mcyl ϑIM
dt pIM VIM cv
∗ ∗ ∗
i
−cv ϑIM mCP + mEGR − mcyl , (3.39b)
d RϑIM  ∗ ∗

f3 = xbg,IM = mEGR ∙ (xbg,EM − xbg,IM ) − mCP xbg,IM .
dt pIM VIM
(3.39c)

An alternative option would have been to consider the exhaust-gas fraction

rather than the burnt-gas fraction. In that case, the fraction of exhaust
gas would be equal to 1 in the exhaust manifold, but the derivation of the
balance equations for the intake manifold would not change. The choice of
using the burnt-gas fraction has been guided by the fact that the burnt-
gas composition depends only on the air composition. During transient
Chapter 3. Dynamic optimization of diesel engines 56

2200

2000 150
s
1800
Neng [rpm]

1600

1400

1200

1000

800
0 200 400 600 800 1000 1200
time [s]

Figure 3.19: Transient validation of the air-path model. A sub-part of the

NEDC cycle (highlighted in dark grey) has been used for the validation.

operation a more accurate prediction of the mixture composition in the

intake manifold can be accomplished, since it can be influenced only by the
ambient conditions, which can be assumed to be constant or, at least, to
change significantly more slowly than the EGR dynamics.
To complete the set of differential equations describing the air-path model
dynamics, the following equations for the turbocharger speed, the exhaust
manifold and the ATS are here listed:

d R ∙ ϑEM  ∗ ∗ ∗

f4 = pEM = κ mEM − mTB − mEGR , (3.39d)
dt VEM
d R ∙ ϑATS  ∗ ∗

f5 = pATS = κ mTB − mATS , (3.39e)
dt VATS
∗ ∗
dwTC mTB ΔhTB − mCP ΔhCP
f6 = ΘTC ∙ = TTB − TCP = . (3.39f)
dt wTC

3.2.3 Transient validation

In the previous sections, the prediction accuracy of each sub-model has
been shown in the respective figures. It results that every model predicts
the measurement data with an error below 5%, except for the EGR models
which fall slightly short of expectations. All parameters identified are listed
in Table 3.2.
Finally, a transient driving cycle has been performed in order to assess
the quality of the entire air-path model. Hence, a NEDC (New European
Chapter 3. Dynamic optimization of diesel engines 57

2000 200
Neng [rpm]

Tload [Nm]
1500 100

1000 0
0 50 100 150
time [s]

Figure 3.20: Engine speed (blue) and load torque (green) requested during
the validation driving cycle.

0.05

model
measure
0.04 5 % error
mCP [kg/s]

0.03

0.02

0.01
0 50 100 150
time [s]

Figure 3.21: Comparison between the modeled and measured compressor

mass-flows. The light grey lines delimit the region characterized by a relative
error of 5%.
Chapter 3. Dynamic optimization of diesel engines 58

5 5
x 10 x 10
1.7 2.4
model
1.6 2.2
measure
1.5 10% error
2
1.4

pEM [Pa]
pIM [Pa]

1.8
1.3
1.6
1.2
1.4
1.1

1 1.2

0.9 1
0 50 100 150 0 50 100 150
5
x 10
400 1.15

380 1.1

360 1.05
pATS [Pa]
ϑIM [K]

340 1

320 0.95

300 0.9
0 50 100 150 0 50 100 150
4
x 10
0.35 12

0.3 model
10 measure
0.25 20% error
8
nTC [rpm]
xbg,IM [-]

0.2
6
0.15
4
0.1

0.05 2

0 0
0 50 100 150 0 50 100 150
time [s] time [s]

Figure 3.22: Results of the air-path model including the dynamic part.
The results related to the six equations expressed in (3.39) are plotted, in
comparison with the recorded data. If not differently specified, the error
region showed in the plots above is 10%.
Chapter 3. Dynamic optimization of diesel engines 59

Table 3.2: Identified parameters for the engine model.

model parameter value equation
compressor mass-flow kπ,0 8.5224 (3.4a)
kπ,1 7.2326 ∙ 10−15 (3.4a)
kπ,e 2.7310 (3.4a)
km,0 -0.2784 (3.4b)
kmax,0 0.0097 (3.2c)
kmax,1 1.1097 ∙ 10−6 (3.2c)
c1 1.5796 ∙ 10−11 (3.2d)
c2,0 12.2056 (3.2d), (3.5)
c2,1 4.1484 ∙ 10−11 (3.5)
c2,2 3.0921 ∙ 10−10 (3.5)
compressor enthalpy kh,1 6.99 ∙ 10−5 (3.10)
kh,2 2.1380 (3.10)
intercooler kIC,0 0.0215 (3.13)
kIC,1 1.3144 (3.13)
kIC,2 0.3853 (3.13)
turbine mass-flow kTB,0 3.1697 ∙ 10−5 (3.16)
kTB,1 −2.1797 ∙ 10−7 (3.16)
kTB,2 −7.2556 ∙ 10−10 (3.16)
kTB,3 2.7540 ∙ 10−11 (3.16)
turbine efficiency hTB,0 0.2584 (3.22)
hTB,1 0.0113 (3.22)
hTB,2 -1.1033 ∙10−4 (3.22)
hTB,3 0.0634 (3.22)
restriction mass-flow kATS,0 0.0300 (3.24)
kATS,1 5.2651 ∙ 10−4 (3.24)
cylinder mass-flow kcyl,0 1.2120 ∙ 10−6 (3.26),(3.27)
kcyl,1 2.5939 ∙ 10−10 (3.26),(3.27)
kcyl,2 −6.0851 ∙ 10−14 (3.26),(3.27)
kcyl,3 2.1706 ∙ 10−8 (3.26),(3.27)
engine-out temperature hcylInit,1 1.0393 (3.28a)
hcylInit,2 0.0320 (3.28a)
κ 1.2513 (3.29)
ηcomb 0.8169 (3.29)
EGR mass-flow kEGR,0 -1.7193∙10−9 (3.34)
kEGR,1 2.4500 ∙10−10 (3.34)
kEGR,2 -2.0968∙10−12 (3.34)
EGR cooler kEGC,1 1.2512 (3.36b)
kEGC,2 -33.1900 (3.36b)
Chapter 3. Dynamic optimization of diesel engines 60

Driving Cycle) has been carried out on the testbench, and a short sub-part
of 150 seconds has been taken into consideration. Looking at Figure 3.19,
the driving cycle considered is highlighted in dark grey, and corresponds to
the extra-urban cycle. This choice has been made since a sufficiently large
region of the engine operating range can be investigated. Furthermore, the
load profile, shown in Figure 3.20, is quite demanding as to allow for an
actual transient operation of the engine.
The first result presented is the compressor mass-flow model, in Figure
3.21. There are two visible regions, corresponding both to a low-speed and
low-load condition, in which the model is clearly far from the measure. These
operating conditions can be considered difficult to be accurately modeled
when deriving the compressor mass-flow model, since the mass flow and
the turbocharger speed are rather low. In Figure 3.22, where the intake
manifold pressure is plotted, it can be noted how low the pressure value is
in the region under discussion, confirming that the turbocharging effect is
almost absent. Such conditions are considered critical for the turbocharger
to work properly. Except for this unstable region, the prediction capability is
significantly accurate, being the model enclosed within the 5% error region.
Concerning the dynamic equations (3.39), the results obtained are plotted
in Figure 3.22. As explained at the beginning of this chapter, the primary
goal was to design a simple model, fast to be executed but still able to cap-
ture the main dynamic phenomena concerning the air-path. The attention
has to be especially focused on its ability to catch the trend of the physical
variables during transient operation. Since no thermal dynamics have been
introduced, it should not be surprising that the modeled intake manifold
temperature ϑIM shows different dynamics w.r.t the measured value.
The overall result is satisfying, therefore the next step involves deriving
the combustion model.

3.2.4 Time-resolved combustion model

Time-variable quadratic setpoint-deviation models are used for the emissions
and for the combustion efficiency. The cross-terms of the full second-order
Taylor expansion are omitted since the nu (nu − 1)/2 cross variations would
also need to be performed to reliably identify the corresponding model co-
efficients. The model coefficients are identified around the current reference
trajectory during each iteration. The vector w = (pIM , xbg,IM , ϕSOI , mfuel )T
denotes all inputs to the combustion model. The model for each output thus
reads:

yi (t) = yref,i (t) + klin (t)T ∙ Δw(t) + Δw(t)T ∙ K quad (t) ∙ Δw(t), (3.40a)
Chapter 3. Dynamic optimization of diesel engines 61

Figure 3.23: Exemplary static and dynamic references over a load step, and
the validity regions of the corresponding setpoint-relative models.

with


K quad (t) = diag kquad,1 (t), . . . , kquad,4 (t) , (3.40b)
Δw(t) = w(t) − wref (t). (3.40c)

Such setpoint-relative models are often used for control and optimisation
applications [29, 30]. However, usually the references for the inputs w are
stored as a static lookup map over engine speed and load. During transient
operation such as a load step, the actual values of the dynamic inputs (pIM
and xbg,IM in the case at hand) can be far from the steady-state reference
values. By using time-resolved reference values and correction factors, the
validity range of the model is relocated to the actual relevant region, which
is illustrated in Fig. 3.23.
The outputs of the air-path model, i.e. the dynamic inputs to the com-
bustion model, are denoted by v := (pIM , xbg,IM )T , with
 
1 0 0 0 0 0
v(t) = g AP (x(t), u(t)) = C AP ∙ x(t) = ∙ x(t). (3.41)
0 0 1 0 0 0

Identification The models for the emissions and the torque production
are re-identified at each iteration. In the final version of the algorithm, all
data collected so far should be used during the identification to successively
expand the model validity region over the iterations. It is subject to debate
whether the model structure should be adapted, i.e. its complexity increased
according to the data available. Alternatively, the measurements could be
weighted by their distance to the current w(t) to yield a tradeoff between
the representation of local and far-field trends. For now, only the variations
Chapter 3. Dynamic optimization of diesel engines 62

around the initial trajectory are considered, and the quadratic setpoint-
relative model described above is used.
A fast measurement of the instantaneous emissions is required. The NO x
emissions are measured by a Cambustion fNOx 400 FastCLD. The soot
emissions are recorded by means of an AVL Micro Soot Sensor. The dynamic
response of this device is identified by performing several stepwise variations
of the injected fuel mass at different operating points. A constant delay of
0.95s and a first-order element with a time constant of 0.25s are found to
closely compensate the sensor dynamics.
A slight averaging w.r.t. time is performed to suppress measurement
noise and to provide a smooth model, which is advantageous in the context
of optimization. A windowed Gauss curve is used to weight the preceding
and consecutive samples for the identification of the model at each time
instant,
 2
p
exp − Δt , if |Δt| < −σ 2 ∙ loge (θcut ),
θ(Δt) = σ 2
(3.42)
0, else.
The parameter θcut defines the value for θ at which the Gauss curve is
cut. Figure 3.24 shows the curve for the parameter values σ = 0.4s and
θcut = 0.5%, which are found to be a reasonable choice.
For each output yi , a weighted linear least-squares regression is used to
identify the coefficients at each sampling point tk . The Nm −1 variations are
used, which are again denoted by the superscript index in round brackets.
The equation system

(X T W X) ∙ p = X T W Δy i , (3.43a)

is solved for p, where

T
p = klin,1 (tk ), . . . , klin,4 (tk ), kquad,1 (tk ), . . . , kquad,4 (tk ) , (3.43b)
 
y i (t−l ) − y ref,i (t−l )

Δy i =  .. 
(3.43c)
. ,
y i (tl ) − y ref,i (tl )
 
Δw1 (t−l ) ∙ ∙ ∙ Δw4 (t−l ) Δw1 (t−l )2 ∙ ∙ ∙ Δw4 (t−l )2

X= .. .. .. .. 
. . . . ,
Δw1 (tl ) ∙ ∙ ∙ Δw4 (tl ) Δw1 (tl )2 ∙ ∙ ∙ Δw4 (tl )2
(3.43d)


W = diag θ(t−l − tk ) ∙ I Nm −1 , . . . , θ(tl − tk ) ∙ I Nm −1 . (3.43e)

Here, l is the number of samples inside the window in both directions, and
(1) (N −1)
I Nm −1 is the identity matrix. Each vector Δwj := wj −wref,j , . . . , wj m −

T
wref,j stacks all variations (similarly for y i ). Here, Δw2j denotes element-
wise squaring.
Chapter 3. Dynamic optimization of diesel engines 63

Figure 3.24: Windowed Gauss function used for the time-averaging of the
combustion model. The dashed lines delineate the window.

3.3 Numerical optimal control

A continuous-time optimal control problem (OCP) consists of an objective
function to be minimized (or maximized), and a set of ordinary differential
equations (ODE) that need to be satisfied, yielding dynamic constraints:

Z T
min L x(t), u(t), π(t)) dt (3.44a)
x(∙),u(∙) 0


s.t. ẋ(t) − f x(t), u(t), π(t) =0, t ∈ [0, T ] (3.44b)


The integral
cost L x(t), u(t) is called the Lagrange term, and the end
cost E x(T ) is known as Mayer term. The combination of the two is
called a Bolza objective. In the remainder of this work, only a Lagrange
term is considered. Every (differentiable) Mayer term can be replaced by an
equivalent Lagrange term, but the Lagrange formulation is preferable from
a numerical point of view [31].
A common extension of the unconstrained OCP (3.44) is to prescribe an
initial state x(0) = x0 , or to enforce some conditions on the end state x(T ).
Often, “simple bounds” are imposed directly on the state variables x and
on the control inputs u. These limits stem from the ranges of the physical
actuators represented by the control inputs, or mechanical limits on certain
state variables such as rotational speed or temperature. More general “path
constraints” may be imposed, which are nonlinear functions of the state
variables and the control inputs.
Integral equalities or inequalities are another type of constraint that often
arise in the formulation of engineering problems. These constraints may
also represent a Mayer term that is rewritten in Lagrange form. Since the
problem to be tackled in this thesis has to be formulated using time-variable
parameters π(t), this special case is explicitly included in the formulation
of the general OCP, which becomes:
Chapter 3. Dynamic optimization of diesel engines 64

Z T
min
L x(t), u(t), π(t)) dt (3.45a)
x(∙),u(∙) 0


s.t. ẋ(t) − f x(t), u(t), π(t) =0, t ∈ [0, T ] (3.45b)
Z T
g x(t), u(t), π(t)) dt − ĝ ≤ 0 (3.45c)
0
u(t) ≤ u(t) ≤ u(t), t ∈ [0, T ] (3.45d)
x(t) ≤ x(t) ≤ x(t), t ∈ [0, T ] (3.45e)

A detailed description about optimal control theory applied to diesel en-

gines can be found in [32].

3.3.1 The Diesel-engine problem

Since the main objective is to minimize the fuel consumption while main-
taining the same emission levels, the Diesel-engine problem can be cast in
the form of the following OCP:
 Z tf 
∗

min mfuel = mfuel x(t), u(t), ñeng (t) dt (3.46a)
x(∙),u(∙) 0
s.t. ẋ(t) − f (x(t), u(t), ñeng (t)) = 0 (3.46b)
Z tf
∗
mem (x(t), u(t), ñeng (t)) dt − m̂em ≤ 0 (3.46c)
0
T̃ (t) − Tload (x(t), u(t), ñeng (t)) ≤ 0 (3.46d)
u(t) ≤ u(t) ≤ u(t), x(t) ≤ x(t) ≤ x(t) (3.46e)
∗ ñ
The instantaneous fuel consumption mfuel = mfcc ∙ 120
eng
∙ Ncyl is integrated
to yield the cumulative fuel consumption mfuel . The dynamic constraints
(3.46b) enforce the model equations and (3.46c) limit the cumulative emis-
sions. The engine speed prescribed by the driving cycle, ñeng (t), is consid-
ered a time-varying parameter. The desired load torque T̃ (t) is imposed as
a time-local inequality constraint (3.46d).

3.3.2 Direct transcription

The continuous-time OCP (3.46) is transformed into a finite-dimensional
mathematical program by direct transcription. An integration scheme is
applied to approximate all continuous signals. Due to the stiffness of the
system, the method of choice is the family of Radau collocation schemes [33].
These stiffly accurate schemes provide stiff decay and algebraic stability [34].
Their implicit nature is irrelevant when used in the context of direct tran-
scription. The first-order representative, the well-known Euler-backward
Chapter 3. Dynamic optimization of diesel engines 65

discretization, is used for the solution of the OCPs in this study. It is found
to be very robust and it provides the solution on a uniform discretization
grid, which can be consistently implemented on the testbench.
The set of continuous ordinary differential equations (3.46b) is trans-
formed to

xk+1 = xk + h ∙ f (uk+1 , xk+1 , ñeng,k+1 ) (3.47)

adopting the notation xk := x(tk ). A uniform step size of h = 0.1s is used,

yielding a grid of N points 0 = t0 < t1 < . . . < tN −1 = tf . Accordingly, all
integrals are approximated as sums

Z tf N
X −2
∗ ∗
m• (u(t), x(t), ñeng (t)) dt ≈ h ∙ m• (uk+1 , xk+1 , ñeng,k+1 ). (3.48)
0 k=0

The bounds on the controls and on the state variables are imposed at the
grid points.
This discretization of the problem yields a sparse NLP. Sparsity signi-
fies that only a few entries in the Jacobian matrix, which contains the
first partial derivatives of the constraints, are non-zero. In fact, (3.47) re-
veals that they are only related in neighboring sets of two. Furthermore,
the control inputs and the state variables appear in nonlinear form only in
f (uk+1 , xk+1 , ñeng,k+1 ) and in the output function g. Thus, only the partial
derivatives of the model functions f and g w.r.t. the control inputs and the
state variables at each discretization point have to be calculated to construct
the Jacobian of the NLP. Assembling the first-derivative information of the
NLP from the model derivatives corresponds to a perfect exploitation of the
problem sparsity [35].
The derivatives of the model equations are calculated by forward finite
differences. Therefore, one additional model evaluation is required for each
partial derivative. The solver SNOPT 7.2 [36] is used to solve the sparse
NLP. It approximates the second partial derivatives by iterative updates
using the first-derivative information along the solution steps.

3.3.3 Regularization
Singular arcs are time intervals during which the Hamiltonian (the combina-
tion of the objective and the appropriately weighted constraint violations)
becomes affine in the controls. During such intervals, the second derivatives
vanish, which results in spurious oscillations when applying direct tran-
scription to solve the OCP. A more detailed analysis of this phenomenon is
provided in [37].
Chapter 3. Dynamic optimization of diesel engines 66

In the aforementioned thesis, a regularization based on the “piecewise

derivative variation of the control” is proposed as a countermeasure. The
regularization term, for a scalar control input u, is
N −1
˙ 2 (u• ) = creg 1X
Lreg (u• ) := cN ∙ Var tN ∙ |sl+1 − sl |2 , (3.49)
(N − 3)(N − 1)2 2
l=3

where sl = (ul − ul−1 )/(tl − tl−1 ) is the slope of the control in each dis-
cretization interval l. The factor (N − 3) in cN accounts for the number of
summation terms, whereas (N − 1)2 is an approximation of the average step
size. This formulation scales the regularization term according to the cho-
sen resolution of the approximation, such that the effect of the user-specified
parameter creg is invariant. The regularization term (3.49) is summed over
all control inputs and added to the discretized form of the objective (3.46a).

3.4 Transient model refinement

This section describes the methods to refine the dynamic part of the model.
The interaction between the air-path and combustion models is indicated at
the appropriate locations in the text.

3.4.1 Refinement of the dynamic air-path model

A generalization of a Kalman filter is applied to the dynamic part of the
model [38]. In order to correct for systematic model errors, the model equa-
tions are augmented by the dynamic and the static corrective variables x̃f
and x̃g ,

ẋ(t) = f (x(t), u(t)) + K f ∙ x̃f (t), (3.50a)

xcorr (t) = x(t) + K g ∙ x̃g (t). (3.50b)

The matrices K f and K g define which dynamics are adjusted and for which
state variables the absolute values are corrected.
The optimal-control framework described in Sec. 3.3.1 is used to derive
the trajectories of the corrective variables. As objective, the minimization of
the integrated squared error in the corrected state variables is used, yielding
a least-squares fit of these trajectories. The original state variables remain in
the OCP, but the control inputs become time-varying parameters. Instead,
the corrective variables x̃(t) = (x̃Tf (t), x̃Tg (t))T are optimised in the OCP,

Z tf
2
min bT ∙ K Tg ∙ x(t) + K g ∙ x̃g (t) −x̂(t) dt (3.51a)
x(t),x̃(t) 0 | {z }
xcorr (t)
Chapter 3. Dynamic optimization of diesel engines 67

s.t. ẋ(t) = f (x(t), û(t)) + K f ∙ x̃f (t). (3.51b)

Quantities with a hat, e.g. x̂, denote measured signals. The vector b con-
tains the weights to put more emphasis on the accuracy of some of the
corrected state variables. The regularization term introduced in Sec. 3.3.3
can be used to penalize fast changes of corrective variables. In fact, smooth
trajectories are desirable since the model errors are assumed to be of a sys-
tematic nature.
If the data from a single measurement is used to identify the corrective
variables by solving (3.51), a perfect match of the corrected state trajectories
is obtained by adjusting x̃g only. Therefore, multiple measurements need
to be considered simultaneously. In the optimal-control framework, Nm
instances of the model are stacked to yield a new system with Nm ∙ nx
state variables. The error in the relevant outputs is cumulated over all
measurements.

Nm Z
X tf
2
min bT ∙ K Tg ∙ x(k) (t) + K g ∙ x̃g (t) −x̂(k) (t) dt
x(1) (t),...,xNm (t),x̃(t) 0 | {z }
k=1 (k)
xcorr (t)
(3.52a)

   
ẋ(1) (t) f (x(1) (t), û(1) (t)) + K f ∙ x̃f (t)
s.t.
 ..   .. 
 . = .  . (3.52b)
ẋ(Nm ) (t) f (x(Nm ) (t), û(Nm ) (t)) + K f ∙ x̃f (t)

3.5 Iterative procedure

As introduced at the beginning of this chapter, the main purpose was to
set up a framework for the iterative dynamic optimization of diesel engines.
Building up such a framework has been possible thanks to the great flexi-
bility provided by the experimental setup.
The iterative procedure relies on two modes of operating the engine:

A) The ECU with its standard calibration controls the engine. The test-
bench controller is used to follow the desired profiles of the engine
speed (by controlling the brake torque) and the load torque (by con-
trolling the fuelling). This mode is used for the initialization of the
iterative procedure. The resulting trajectories of the controls, includ-
ing the injected fuel mass, are recorded.
Chapter 3. Dynamic optimization of diesel engines 68

B) Time-resolved trajectories are prescribed for all control inputs using

the rapid-prototyping module and the bypasses of the ECU. The test-
bench controller is only used to follow the engine-speed profile. This
mode is used for validation runs as well as for all variations.

The inputs to the procedure are a transient driving profile (3.25), consist-
ing of engine speed and load torque trajectories, and any calibration of the
ECU that is able to operate the engine along this profile.

1. Initialization: drive the profile in mode A. Save the resulting trajecto-

ries of the control inputs, set them as the “current controls” u(t). Set
the corrective variables x̃(t) to constant zero.

2. Perform 1 + 2 ∙ nu testbench runs in mode B. Thereby, apply

(a) the current controls u(t), and

(b) isolated perturbations of all controls in both directions,
i.e. ui (t) ← ui (t) ± Δui , for i = 1, . . . , nu .

3. Use the measurement data from step 2 to identify the corrective vari-
ables x̃(t) by solving (3.52). Run simulations of the refined air-path
model for all variations, and save the resulting corrected state trajec-
tories xcorr (t).

4. Use the state trajectories of the air-path model from step 3 to iden-
tify the torque and emission models around the current references by
solving (3.43).

5. Solve the control and state constrained OCP (3.46) to derive the im-
proved control trajectories u∗ (t). Thereby, set

u(t) = u(t) − ku ∙ Δu, u(t) = u(t) + ku ∙ Δu, (3.53a)

x(t) = kx ∙ min{x(t)(k) | k = 1, . . . , 1 + 2 ∙ nu }, (3.53b)
x(t) = kx ∙ max{x(t) (k)
| k = 1, . . . , 1 + 2 ∙ nu }. (3.53c)

6. Set u(t) ← u∗ (t), repeat steps 2.-5. until the change in the controls is
small.

Using the simulated state trajectories during the identification of the com-
bustion model in step 4 ensures a consistent prediction of the emissions and
of the torque inside the validity region. This fact is important since the
optimization in step 5 is also restricted to this region. This “trust region”
can be slightly expanded by the factors ku and kx .
Since the identification of the models for the air path and for the com-
bustion are identified separately, the physical causality is preserved. More
Chapter 3. Dynamic optimization of diesel engines 69

300

[Nm]
200
load desired
100
T
achieved
0
0 5 10 15
time [s]

Figure 3.25: The desired load-torque profile and the trajectory achieved by
the testbench controller.

precisely, there is no way that the combustion model corrects errors in the
air-path model or vice-versa. Although a combined identification could yield
a slightly higher accuracy, it would introduce unphysical cross corrections.
Furthermore, the identification procedure would become more complex and
non-convex.

3.6 Results
A short test cycle is used to evaluate the methods presented in the preceding
sections. The engine is operated at a constant speed of 2500 rpm, and the
desired load-torque profile is shown in Fig. 3.25. As variations, an additive
offset of ±5% PWM is applied to the VGT and EGR positions, and ±2◦ to
the SOI. A multiplicative factor of 1.05 defines the variation of the fuel mass.
These variations are referred to as the small variations in the remainder of
the text. To assess the accuracy of interpolation and extrapolation, large
variations with offsets of ±8% for the VGT, ±10% for the EGR, ±4◦ for the
SOI and a factor of 1.1 for the fuel mass are performed. Since the VGT and
the EGR both dynamically affect the burnt-gas fraction and the pressure
in the intake manifold, the four cross variations of these two actuators are
additionally recorded.
For the identification of the combustion model, it would be desirable to
have a constant offset in w. However, the EGR-VGT controller cannot
perfectly follow reference trajectories for the burnt-gas fraction and the boost
pressure. After initial tests, it has been found that applying constant offsets
directly to the two dynamic controls is the best choice.

3.6.1 Transient air-path model refinement

The turbocharger speed and the pressure in the exhaust manifold represent
the relevant dynamics in a turbocharged engine system with EGR. The boost
Chapter 3. Dynamic optimization of diesel engines 70

2.5
[bar]

2
IM

1.5
p

1
0.3
[bar]
IM,ref

0
- p
IM
p

-0.3
0 5 10 15 0 5 10 15

Figure 3.26: Effects of the dynamic model refinement, VGT variations. Mea-
surement data (grey) versus model outputs (black). Line styles: reference
(bold), small variations (solid), large variations (dashed).

pressure closely follows the turbocharger speed and the EGR mass-flow is
defined, aside from the position of the EGR valve, by the pressure ratio
between exhaust and intake manifolds. Therefore, it is sufficient to correct
these two dynamics.
Since for the combustion model only the relative accuracy is of interest,
it is not necessary to require v(t) to be accurate in terms of absolute values.
Rather, the state variables that are critical for a safe engine operation should
be matched to the measured trajectories to enable an accurate limitation
of these quantities in the OCP. Since no limits on any state variables are
included in the OCP as of yet, the pressures in the exhaust and intake
manifolds have been chosen to illustrate the methodology. The choice of the
dynamics and the state variables to be corrected are represented by

   
0 0 0 0 0 1 1 0 0 0 0 0
K Tf = , K Tg = . (3.54)
0 0 0 1 0 0 0 0 0 1 0 0

The errors in the two pressures are equally weighted, i.e. bT = (1 1).
The top plot in Fig. 3.26 shows the measured trajectories of the intake
pressure along with the model output before and after the refinement. The
refinement is performed using only the small variations. The resulting good
match for the large variations indicates that the model errors in fact are sys-
tematic. For example, the too fast speedup of the turbocharger predicted
by the model might be caused by the omission of the thermal models. The
Chapter 3. Dynamic optimization of diesel engines 71

Table 3.3: Static combustion model: average magnitude of the relative error
in % for the instantaneous NOx and soot emissions, and the torque Tload
ident. data: small variations small & cross vars. large variations
NOx soot Tload NOx soot Tload NOx soot Tload
small vars.: 0.14 0.89 0.09 0.70 4.45 0.25 1.14 7.70 0.75
cross vars.: 2.85 15.84 0.82 1.60 12.41 0.27 2.60 18.92 0.73
large vars.: 3.31 20.56 2.36 3.46 21.17 2.11 0.19 1.10 0.09

heat losses to the manifold walls are neglected and consequently, the en-
thalpy available to the turbine is overestimated.
The bottom plot shows the difference of the variations to the reference
trajectory. Obviously, the refinement has no influence on the predicted
difference. Therefore, the refinement of the air-path model is not critical for
the combustion model but rather a tool that allows an accurate limitation
of any state variable, e.g. maximum turbocharger speed, exhaust-manifold
pressure and temperature, etc.
In the context of the generalized Kalman filter, the regularization de-
scribed in Sec. 3.3.3 may be used to enforce smooth trajectories of the cor-
rective variables x̃. The demand for smooth trajectories is justified by as-
suming the model errors to be of a systematic nature and thus not to exhibit
a stochastic or arbitrarily fast changing behavior. For the results presented
here, a value of creg = 50 is used.

3.6.2 Static combustion model

The results presented here are all derived using the time averaging intro-
duced in Sec. 3.2.4. Interpolation and extrapolation are not influenced by
the time averaging. Table 3.3 shows the errors of the combustion model
when identified using three different data sets, namely the small variations,
the small and the cross variations, and the large variations. The figures
indicate that the model identified using the small variations is able to accu-
rately predict the cross variations, except for the soot emissions. Further-
more, interpolation is significantly more reliable than extrapolation. This
fact encourages the use of rather large variations and small factors ku and
kx instead of the reliance on small variations and extrapolation.

3.6.3 Optimal control

For the OCP, the regularization was set to creg = 100. This choice suc-
cessfully suppresses oscillating solutions while not affecting the parts that
exhibit smooth trajectories anyway. Especially for the SOI, which has no
influence on the air-path dynamics, fast oscillations result when no regu-
Chapter 3. Dynamic optimization of diesel engines 72

Figure 3.27: Controls resulting from the solution of the constrained OCP.

larization is applied. The time averaging during the identification of the

combustion model has a similar effect to the regularization. Determining
which approach provides the most plausible solutions and the fastest con-
vergence of the iterative procedure, is left to be analyzed in more detail.
Figure 3.27 shows the optimal control trajectories obtained when using
the model identified by the small variations only, or by the small and the
cross variations. In both cases, no extrapolation is performed, i.e. ku = 1
and kx = 1. The limits for the cumulative emissions, m̂em , are chosen
such that the brake-specific emissions of the reference are maintained. The
torque profile resulting from the reference control trajectories is imposed by
(3.46d).
The optimal control trajectories are experimentally validated on the en-
gine testbench. To account for possible deviations in the resulting torque,
the emissions and the fuel consumption are related to the integrated engine
power. Figure 3.28 summarizes the measured cumulative emissions and the
fuel consumption.
Five runs are recorded for each set of trajectories. The average as well as
the minimum and maximum values are shown in the plots. The emissions
remain within the measurement uncertainty, while the fuel consumption is
reduced. The soot measurement exhibits a large variability, which is also
present in the identification data. Therefore, the corresponding model is
not reliable and possibly hinders a more effective reduction of fuel consump-
tion. Furthermore, due to this inconsistency, the model quality seems not
to improve when including the cross variations in the identification data.
Chapter 3. Dynamic optimization of diesel engines 73

100.1 105
relative change [%]

130 reference
102.5
99.9 120 optimal,
100 small
110
97.5 optimal,
99.7 100 small & cross
95
90
99.5 92.5
fuel (264.2 g/kWh) NO (5.0 g/kWh) soot (0.032 g/kWh)
x

Figure 3.28: Experimental results of the first iteration. The error bars
indicate the range (minimal to maximal values) of the five measurements.

3.6.4 Conclusion
In conclusion, this chapter has presented the numerical methods and the
testbench setup, required to perform an iterative dynamic optimization of
diesel engines over prescribed driving profiles. One exemplary iteration has
been performed and experimentally validated, in order to assess the validity
of the methodology. A recognizable progress towards lower fuel consumption
while maintaining the emission levels has been observed.
Further development of the methodology focused firstly on the replace-
ment of the fast but manually calibrated, failure-prone and high-maintenance
emission-measurement devices by standard instrumentation, and secondly
on a fully automated implementation of the iterative procedure.
These mentioned further developments, along with an application of the
presented methodology exclusively oriented to engine control during tran-
sient operation, will be the subject of next chapter.
Chapter 4

Transient control of diesel

engines

Due to ever more challenging goals, in terms of fuel economy improvement

and reduction of exhaust emissions, noise and vibration, complexity of en-
gine systems has proportionally increased. New technologies help to fulfill
such demanding requests, but they come at a price. The increased com-
plexity and the exploitation of the entire hardware potential introduce two
important subjects, which are optimal engine calibration and transient con-
trol. The aim of the present thesis is to merge these two requirements, or
rather to apply the optimal control theory to achieve an incisive transient
control.
Static optimization of the control inputs of an engine is the first step to-
wards the calibration of an engine control unit. This optimization can be
carried out directly on the real engine or by utilizing models to represent
the engine [39, 40]. The number of actuations influencing the engine perfor-
mance is increasing, and, as a consequence, the effort in the calibration of
control parameters can be very costly and demanding. Often, with the aim
of speeding up the calibration process several methodologies can be applied,
for e.g. statistical tools [41] or automatic calibration procedures carried out
along engine transients [42, 43]. The resulting steady-state maps usually
constitute the first step to parameterize the engine control unit in form of a
feedforward control structure. Without any further manipulation, this kind
of control system cannot capture dynamic phenomena, leading to high emis-
sion peaks and fuel inefficiency during transient operation. An alternative
approach could take into account engine dynamics through mathematical
models, in order to implement a model-based rapid transient calibration
optimization process [44].
The following chapter is still focused on transient operation of diesel en-
gines, but it shifts the attention towards a control-oriented approach [45]. In
order to derive a transient controller, engine modelling for control purposes

74
Chapter 4. Transient control of diesel engines 75

is the first step. Hence, control oriented models (COM) of engines have
been presented in several works [7, 46, 47, 48]. Although many COMs have
been developed for the purpose of transient control of different types of en-
gines, deriving accurate physics-based models, which cover the whole engine
operating region, is a difficult and not always successfully achievable task
[49]. For this reason, in this context an alternative approach is proposed; it
involves a custom-tailored model that is valid in a region around the actual
state and input trajectories.
With the difficulties in estimating engine responses, transient control of
engines can be realized by using feedforward controls, based on steady-state
actuator set-point maps, and transient compensation maps. However, gen-
erating compensation maps suitable for transient operation is of crucial im-
portance. This role often relies on engineering experience more than on
engine physics, resulting in a highly iterative calibration process, which is
not systematically repeatable and provides only suboptimal results.
Chapter 3 focused on the numerical methods needed to derive optimal
control trajectories over a predetermined driving cycle. Besides the validity
and the usefulness of the methodology in itself, it might be utilized as a
tool to derive optimal transient compensation maps, implementable in a
feedforward control structure, as it will be shown in next paragraphs. From
the optimal solutions, the relevant information may in fact be extracted and
stored in maps spanned by the engine speed and the torque gradient. These
maps complement the static control maps by accounting for the dynamic
behavior of the engine. The procedure is implemented on a real engine
and experimental results are presented along with the development of the
methodology. The experimental setup is the one already presented in Sec.
3.1.

4.1 Methods
Although most methods used in this context have been presented in details in
Chapter 3, in some sections they need to be reminded for completeness, and
their application will be clarified whenever it differs from the one previously
illustrated.

4.1.1 The concept

The top left corner of Figure 4.1 shows a typical feedforward control struc-
ture based on steady-state control maps, spanned by engine speed (Neng )
and load (mfcc ). In a diesel engine, if neither torque limitation nor smoke
limitation are active, the load request directly corresponds to a specific fuel
quantity injected per cycle in each cylinder (mfcc ). To investigate the typi-
cal dynamic behavior of the engine, load transients at constant engine speed
are performed by operating the engine over load ramps, and the results are
Chapter 4. Transient control of diesel engines 76

Figure 4.1: Feedforward (FF) control based on the steady-state actuator

set-point maps

analyzed in terms of fuel consumption and emissions. With the aim of ex-
ploring the entire load range, fuel ramps from 10 to 85 percent of maximum
load and with different durations, have been carried out on the testbench
(see Figure 4.1).
Looking at Figure 4.2, the slowest ramp (30 s duration) can be considered
to represent the static case, i.e. to consist of a sequence of steady-state
conditions. The results in Table 4.1 show cumulative fuel consumption,
NOx and soot emissions variations with respect to this stationary-like pro-
file. From now on, the values of the three quantities just mentioned are
always normalized with respect to the integrated engine power, to allow for
meaningful comparisons. It turns out that the higher is the load gradient,
the higher is the specific fuel consumption. Despite this statement could
be quite predictable, figuring out the responsible physical effect is of sure
interest. The third graph in Figure 4.2 shows that the increasing pumping
effect corresponding to increasing gradients, is probably the main reason for
the fuel penalty. In other words, the faster is the transient the higher is the
negative backpressure effect caused by the turbine. This effect disappears
as soon as quasi-static state conditions are reached.
This is the crucial point: a stationary lookup map by nature is not able to
account for dynamic effects, so it sets the actuator set-point to the value that
will be appropriate when the transient is over. This yields, for instance, a
VGT position that increases the engine backpressure with negative effect on
efficiency. When the VGT is closed in order to increase the intake manifold
pressure (pIM ), the exhaust pressure (p EM ) increases too, but with a faster
dynamic, resulting in a growing effect of the backpressure. This is proven
by the third graph, which shows the ratio between p EM and pIM . Moreover,
it is also true that the air handling system has a slower dynamic than the
Chapter 4. Transient control of diesel engines 77

T: ramp duration
1
(normalised)
mfcc

0.5

load gradient
0
0 5 10 15 20 25 30
1
(normalised)
load torque

0.5

load gradient
0
0 5 10 15 20 25 30
1.8
(pumping effect)

1.6
pEM / pIM

1.4

1.2 load gradient

1
0 5 10 15 20 25 30
3

2.5 load gradient

lambda

1.5

1
0 5 10 15 20 25 30
time [s]

Figure 4.2: Ramp profiles performed at 1950 rpm.

Table 4.1: Effect of increasing load gradients: fuel, NOx and soot related
to the integrated engine power (normalized quantities).
3
ramp duration [s] d
dt mfcc [ mm
s ] fuel NOx soot
30 1 0%(ref) 0%(ref) 0%(ref)
12 2.5 2.77% 21.44% -15.37%
8 3.75 4.34% 30.91% -15.53%
6 5 4.42% 41.46% -18.81%
5 6 5.31% 44.42% -19.24%
4 7.5 5.79% 51.58% -10.42%
3 10 6.73% 57.55% -3.79%
2 15 8.30% 65.48% 31.83%
Chapter 4. Transient control of diesel engines 78

fuelling system, so an air reservoir is needed to prevent an excessive air-

to-fuel ratio (AFR) reduction during a positive load gradient. The fourth
graph proves this statement, showing the drop of the lambda value, ever
more accentuated as the load gradient increases. The phenomenon just
explained does not depend only on the turbocharger, but also on the EGR
rate, so that the combined effect of these two control levers has to be taken
into account.
Obviously all the considerations presented so far have an influence also on
exhaust emissions, as shown in Table 4.1. Concerning NOx emissions, there
is a combined effect of the reduced amount of air entering the cylinders and
the delayed effect of the EGR, which together lead to a higher combustion
temperature. The soot trend is not as monotone as the NO x one, and the
reason can be related to several aspects. First of all, the measurement device
is not fast enough to capture the transient peaks, resulting in a potentially
misleading cumulative value. It is also reminded that raw emissions have
been measured, while the traditional use of the engine at hand sees a DPF
installed on the exhaust line, resulting in a drastic reduction of tailpipe soot
emissions. Moreover, this aspect does not invalidate the presented results,
since, as remarked later, soot emissions are considered in this context as a
qualitative quantity not to be widely exceeded.
Another control lever which strongly effects fuel efficiency and NO x emis-
sions is the crank angle corresponding to the start of injection (SOI). This
control input directly influences the combustion process, therefore it does
not involve any dynamics. However, it may be used to compensate for the
transient effects described above, which is also proposed in [50]. For this rea-
son, the SOI is included in the dynamic optimization procedure proposed
below.
Once that the indisputable effect of transients has been remarked, it comes
out that finding the perfect combination of multiple cross-coupled control
inputs is a difficult engineering problem, which cannot be solved with just
a calibration-based approach. Before describing the new control structures
derived, all methods concerning engine models and optimal control are out-
lined in the next sections.

4.1.2 Engine model

The nomenclature is consistent with the one previously introduced, therefore
the reader may refer to Figure 3.6. The model structure (Figure 4.3) is
basically the same, except for the number of inputs. In this case, not only
the engine speed (Neng ) but also the fuel mass injected (mfcc ) is treated as
a time-varying parameter, moreover both are fixed during the optimization
procedure.
Chapter 4. Transient control of diesel engines 79

Figure 4.3: Structure of the engine model.

The model is represented in state-space form as:

ẋ(t) = f (x(t), u(t)), (4.1a)

y(t) = g(x(t), u(t)), (4.1b)

where the nx = 6 state variables, the nu = 3 control inputs, and the outputs
are:

T
x = pIM , ϑIM , xbg,IM , pEM , paTB , ωTC ,
∗ ∗
T
u = uVGT , uEGR , ϕSOI )T , y = mNOx , msoot , Tload .

The air-path model and all related sub-models remain unvaried (see Sec.
3.2.1).

4.1.3 Time-resolved combustion model

Time-variable quadratic setpoint-deviation models are used for the emissions
and for the combustion efficiency. The vector w = (pIM , xbg , ϕSOI )T denotes
all inputs to the combustion model. The model for each output thus reads

yi (t) = yref,i (t) + klin (t)T ∙ Δw(t) + Δw(t)T ∙ K quad (t) ∙ Δw(t), (4.2a)

with


K quad (t) = diag kquad,1 (t), . . . , kquad,3 (t) , (4.2b)
Δw(t) = w(t) − wref (t). (4.2c)

As it can be noted, the input to the combustion model is not exactly

the vector w, but rather its variation with respect to a reference vector.
A detailed description of the identification procedure is presented in 4.1.5,
however the reference condition is nothing other than the starting ramp
profile, while the real input Δw is generated by performing several variations
of the control inputs along the reference trajectory.
Chapter 4. Transient control of diesel engines 80

Sensor dynamics of the NO x and soot sensors A further critical as-

pect regarding empirical modelling of engine-out emissions, is the phase shift
between transient engine events and transient emission measurements. In
the case at hand the NOx emissions are measured by a Continental UniNOx
sensor, while the soot emissions are recorded by means of an AVL Micro
Soot Sensor.
Accounting for the transient transport delays and sensor lags, which to-
gether constitute the phase shift, is very important for the quality of the
model prediction. For this reason, the dynamic characteristic of the sensor
signals has been modelled as a first-order lag element, with a time delay
resulting from the transport of the gas to the sensor. The signal ξs,i of emis-
sion sensors, can thus be expressed by the differential equation (4.3), where
i corresponds to the emission species NO x or soot:
d 1
ξs,i (t) = − ∙ [ξs,i (t) − ψi (t − Δts,i )] . (4.3)
dt τs,i

The variable ψi refers to the corresponding engine-out emission species that

reaches the sensor after a delay of Δts,i . In order to influence the engine-out
emissions separately, measurements with stepwise changes in the SOI and
in the EGR valve have been carried out, for several engine speeds and loads.
The recorded emission signals have then been used to identify the sensor
dynamics of the NOx and soot sensors, respectively. Figure 4.4 shows the
results of the identification. Interesting correlations with the NO x mass flow
(mdNOx in figure) and the total exhaust mass flow (md EM in figure) have
been observed, respectively for the NO x and soot sensors. For this reason,
the fitted curves shown in red dots have been used to account for the sensors
dynamics within the combustion model.
Regarding the soot measurement, the dynamic characteristics of the Micro
Soot Sensor are significantly influenced by the dilution ratio. In the event
of low ambient temperatures or insufficiently diluted exhaust gas there is
the risk of the formation of condensate in the measuring chamber. In order
to avoid condensate formation, sufficient dilution of the exhaust gas should
be provided for. On the other hand, the delay and the time constant are
smaller for low dilution ratios. As a compromise a dilution ratio of five (in
a range of 2 to 20) has been used for the experiments.

4.1.4 The optimal control problem

The optimal control problem (OCP) needs a different formulation with re-
spect to the previous one (Sec. 3.3.1), thus it reads:

 Z tf 


max Eload = Tload x(t), u(t), mfcc (t) ∙ Neng dt (4.4a)
u(∙),x(∙) 0
Chapter 4. Transient control of diesel engines 81
4
Measured
3 Fitted

τs,NOx [s]
2

0
0 0.02 0.04 0.06 0.08 0.10 0.12
1.5
Δts,NOx [s]

0.5

0
0 0.02 0.04 0.06 0.08 0.10 0.12
mdNOx ⋅ 104 [kg/s]
2

1.5
τs,soot [s]

0.5

0
0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045
1.8

1.6
Δts,soot [s]

1.4

1.2

1
0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045
mdEM [kg/s]

Figure 4.4: Trend of the time constant τs,i and the time delay Δts,i identified
for the NOx and soot sensors respectively.

s.t. ẋ(t) − f (x(t), u(t), mfcc (t), Neng ) = 0, (4.4b)

Z tf
∗
mem (x(t), u(t), mfcc (t), Neng ) dt − m̂em ≤ 0, (4.4c)
0
u(t) ≤ u(t) ≤ u(t), x(t) ≤ x(t) ≤ x(t). (4.4d)

with mem = mNOx , msoot )T .

The cost function is the integrated power over the load ramp profile, called
∗ Neng
Eload in (4.4a). The instantaneous fuel mass flow mfuel = mfcc ∙ 120 ∙ncyl is in-
tegrated to yield the cumulative fuel consumption mfuel . The true objective
would be the minimization of the specific fuel consumption, which can be
expressed as := E mfuel
[ g ] , but the fuel quantity is assigned for each ramp,
load kW h
so it never changes. Consequently, the target becomes the maximization
of the energy released, in other words the net engine power (or Tload being
Neng constant). The dynamic constraints (4.4b) enforce the model equations
and equation (4.4c) limits the cumulative emissions. Considering that the
soot measurements exhibit a large variability, which is also present in the
identification data, the corresponding model is not as reliable as the NO x
model. Despite that, a cumulative but more permissive constraint for soot
emissions is set during the optimization anyway; otherwise the optimization
Chapter 4. Transient control of diesel engines 82

could be negatively effected, resulting in a suboptimal solution for the main

objective.

4.1.5 Optimization procedure

Differently from the preceding case (Sec. 3.5), the dynamic optimization
procedure is not meant to be iterative. Similarly to the iterative procedure,
it relies on two modes of operating the engine, but it has been adapted to
the different problem at hand:

A) The ECU with its standard calibration controls the engine, in partic-
ular it prescribes the fuel profile related to each ramp. The testbench
controller has to guarantee the desired engine speed (constant in this
case). This mode is used for the initialization of the optimization pro-
cedure. The resulting trajectories of the controls (VGT, EGR and
SOI) are recorded.

B) Time-resolved trajectories are prescribed for all control inputs using

the rapid-prototyping module and the bypasses of the ECU. The test-
bench controller has exactly the same task as in mode A). This mode
is used for all variations runs as well as for validation.

The inputs to the procedure are the transient profiles of Figure 4.2, per-
formed one at a time, by using a standard engine calibration that is able
to operate the engine along these profiles. The following list describes the
individual steps of the dynamic optimization:

1. Initialization: drive the profile in mode A. Save the resulting trajecto-

ries of the control inputs u(t).

2. Perform 1 + 4 ∙ nu testbench runs in mode B. Thereby, apply

(a) the reference controls u(t), and

(b) two perturbations of all controls towards each direction, i.e.
ui (t) ← ui (t) ± {0.5 ∙ Δui , Δui }, for i = 1, . . . , nu .

Run simulations of the air-path model for all variations.

3. Use the state trajectories of the air-path model and the measured
emission and torque trajectories from step 2, to identify the torque
and emission models around the current references.

4. Solve the control and state constrained OCP (4.4) to derive the im-
proved control trajectories u∗ (t). Thereby, set

u(t) = u(t) − Δu, u(t) = u(t) + Δu. (4.5)

Chapter 4. Transient control of diesel engines 83

In order to automate the optimization procedure, it has been necessary

to remotely manage some basic functionalities provided by INCA, such as
setting calibrations, reading signals and recording measurements. This ad-
ditional functionality can be achieved through several methods; in this par-
ticular case a COM communication between Matlab and INCA has been
established, by means of an in-house Matlab script.

4.1.6 From time-based to map-based optimal control

The optimal control input set, achieved with the optimization procedure, is
non causal and valid only for the specific profile used for the optimization, as
opposed to a conventional table or map-based control structure. Moreover,
referring to Figure 4.1, there is not a unique optimal trajectory for a given
speed, but several, corresponding to each ramp performed.
Finding a way to transform these control trajectories to an operating point
based representation, while preserving the information about the optimal
solution, is thus of particular interest. In view of the fact that keeping intact
the content of the time-resolved control vector is unfeasible, its information
could be stored in a scalar value of a new lookup table, namely the transient
compensation map. Since this map has to be activated only when transients
occur, a direct dependency with the load gradient is needed. Therefore,
the second quantity, besides the engine speed, that spans the compensation
maps is the derivative of the fuel quantity, while the fuel quantity itself is
used for the steady-state maps.
Figure 4.5 shows the two solutions proposed, both based on compensa-
tion maps that contain the information derived from the solution of the
OCP. What distinguishes the two control structures is the way the cylin-
der charge is managed, while the SOI is treated identically. Controlling the
cylinder charge is equivalent to controlling the intake manifold pressure pIM
and the burnt-gas fraction xbg,IM , by means of EGR and VGT, which rep-
resent the relevant actuators. In the first case, shown in Figure 4.5a, the
physical conditions in the intake manifold are not considered at all, resulting
in a feedforward (FF) control based on the steady-state actuator set-point
maps. Because of its simplicity, this control structure is still used as basic
layer in engine control systems. Unfortunately, as soon as a transient occurs
all its limits come to light, suggesting that a pure steady-state approach is
not satisfactory anymore. Enhancing its performance, by adding informa-
tion related to transient operation, can be an interesting solution, especially
if such a simple structure can be preserved. The compensation maps are
highlighted, and their outputs are the dynamic compensation (DC) factors
to be applied to VGT and EGR. If the load request gradient is below a
certain threshold, set within the compensation map, there is no alteration
of the stationary actuator set-point.
The second case, shown in Figure 4.5b, is characterized by an alternative
Chapter 4. Transient control of diesel engines 84

and more complex kind of cylinder charge control, called air-path control.
In this case the actuation of VGT and EGR are feedback (FB) controlled,
therefore the set-point variables are pIM and xbg,IM . The implementation
of this advanced control structure has been possible thanks to the RCP
system presented in Sec. 3.1. All details about the air-path controller im-
plemented and used during the experimental validation, can be found in
[51]. Differently from the previous case, the lookup tables store the steady-
state set-points of the two state variables mentioned above. At the same
time, the compensation maps act directly on these references for the FB
controller. If the correction was applied directly to the actuators (uVGT,FB
and uEGR,FB ), it would act as a disturbance that the feedback controller
would try to compensate. Regardless of the control structure, the dynamic
compensation maps have the goal to reproduce as strictly as possible the
optimal trajectories. Figure 4.6 helps explaining how they have been de-
rived, for one exemplary ramp profile. The first row shows the comparison
between the reference trajectory, obtained by using a standard engine cal-
ibration with the ECU running in mode A, and the optimized trajectory
(Sec. 4.1.5). VGT and EGR profiles are the real optimal control inputs de-
rived from the optimization procedure, while pIM and xbg,IM profiles are the
corresponding measurements. Since one single ramp profile is considered,
which means a single value of the fuel derivative, a single scalar value has
to capture the information coming out from this comparison.
The second row shows how the scalar value is calculated. For VGT and
EGR, it is the mean value of the difference between optimal and reference
trajectory, starting 0.5 seconds after the actual ramp starts (dash-dot line),
since the initial conditions of reference and optimal controls coincide. For
pIM and xbg,IM , the final value of, respectively the ratio and the difference
between the trajectories is considered.
The third and final row highlights the differences between optimal solu-
tions and dynamically compensated reference control inputs. Coherently
with the distinction made between the two control structures, VGT and
EGR refer to case (a) while pIM and xbg,IM refer to case (b). For what con-
cerns the SOI, its compensation is identical, no matter the control structure,
and likewise to the VGT and EGR cases, the average difference is used to
calculate the correction factor (last column).

4.2 Results and discussion

Firstly, the results obtained from the dynamic optimization are presented,
by focusing on the capabilities of the optimization tool. Afterwards, the
potential of this novel approach to dynamic feedforward control is assessed
by the validation procedure. Since the goal was to stimulate the dynamic
response of the engine, a transient demanding cycle has been employed.
Chapter 4. Transient control of diesel engines 85

Figure 4.5: a) Feedforward (FF) control based on the steady-state actuator

set-point maps: compensation of actuator set-point values. b) Feedback
(FB) control of the state variable set-point maps: compensation of state
variable set-point values.
Chapter 4. Transient control of diesel engines 86

6
4
time [s]
SOI

0.5s

2
final value

6
4
time [s]
xbg,IM

mean value

2
6
4
time [s]
ratio (opt/ref)
pIM

2
reference + DC
reference
optimal

reference
optimal

6
difference (ref-opt)

4
time [s]
EGR

0.5s

2
6
4
time [s]
VGT

0.5s

2
0

Figure 4.6: Example of calculation of the dynamic compensation factor,

for the 6s ramp. First row: comparison between reference and optimal
trajectories. Second row: difference (blue line) and ratio (black line) between
optimal and reference trajectories. Compensation factors are derived by
using either the average (green line) or the final value (red line) of the
respective compensation vectors. Third row: comparison between optimal
solutions and dynamically compensated reference control inputs.
Chapter 4. Transient control of diesel engines 87

100
VGT [%]

90

80

70
0 1 2 3 4 5 6
100 validity region
reference
EGR [%]

50
optimal

0
0 1 2 3 4 5 6
5
SOI [°BTDC]

-5
0 1 2 3 4 5 6
time [s]

Figure 4.7: Optimal control-input trajectories for 6s duration ramp.

4.2.1 Dynamic optimization

The outputs resulting from the solution of the OCP laid inside the validity
region (4.4d) without being constrained. This fact implies that the variations
of the inputs chosen, namely ΔuVGT = 0.05, ΔuEGR = 0.05 and ΔuSOI = 2,
yield a good compromise between model quality and broadness of the validity
region. If such outputs were limited by the validity limits, a second dynamic
optimization would be necessary, shifting the validity region in order to leave
the optimizer work properly.
Figure 4.7 shows an exemplary solution coming out from the optimization
framework. Table 4.2 shows the relative changes between the optimal and
the reference time-based control input set, in terms of fuel consumption
and emissions, related to the total energy released. In addition, Figure 4.8
assesses the repeatability of the measurements, performed five times for each
ramp, both for reference and for optimal conditions. The objective was to
minimize fuel consumption, without penalizing NO x emissions (4.4c) and
keeping soot emissions below an acceptable level. Regarding the former,
a significant improvement of fuel efficiency has been accomplished, except
for the slowest ramp (30 s duration). The result is plausible since that
ramp is sufficiently slow to represent stationary operation. This result is
also consistent with the assertion made in Sec. 4.1.1, where this ramp has
been considered as the reference condition, in order to assess the effect of
transient operation on fuel consumption.
Another proof of the effectiveness of the optimization is the reduction of
Chapter 4. Transient control of diesel engines 88

T=2s T=3s T=4s T=5s T=6s T=8s T=12s T=30s

Relative change [%]

100
99
reference = 100%
98
(fuel)

97
96
95
Relative change [%]

110
reference = 100%
(NOx)

100

90

80
Relative change [%]

100
reference = 100%
(soot)

80

60

40

Figure 4.8: Relative change of fuel consumption, NO x and soot emissions

after the optimization. Average value and error bars calculated by repeating
the measurement five time for each ramp.

the pumping effect, as compared to suboptimal control of VGT and EGR

performed by the production ECU. Figure 4.9 shows a comparison between
the reference and the optimal solutions. The negative backpressure effect has
been reduced, consistently with the observed fuel consumption reduction,
without compromising the air-to-fuel ratio. Likewise to EGR and VGT, the
SOI plays a fundamental role, due to its strong effect on fuel efficiency and
NOx emissions.
The usefulness of the optimization framework can be evaluated also from
an other perspective. For example, by supposing that the controller is asked
to fulfill higher or lower NOx emissions. In the first case, for instance, an
even lower fuel consumption can be achieved, while accepting the increase
of NOx emissions (that could afterwards be reduced by means of an after-
treatment system). This result can be obtained only if the engine model
correctly predicts the NO x -fuel tradeoff, and the optimization tool is able
to cope with changing constraints. In order to assess this ability, NO x
constraint targets have been altered in positive or negative direction, for
two cases representing fast and slow ramps. The results are listed in Table
4.3, and demonstrate that the optimization framework is sensitive to the
different requests of NOx target, showing that lower NOx emissions allow
for higher improvement of fuel efficiency, and vice versa.
Chapter 4. Transient control of diesel engines 89

Table 4.2: Results of the dynamic optimization for each ramp. Relative
changes between optimal and reference condition (average value over 5
repetitions).

ramp duration [s] fuel,measured NOx , measured soot,measured

2 -2.81% 3.96% -40.84%
3 -4.58% 10.4% -28.66%
4 -3.93% -1.53% -13.58%
5 -4.58% -3.85% -5.63%
6 -3.91% -12.92% 0.75%
8 -4.50% -15.87% -0.92%
12 -3.79% -14.73% -4.09%
30 -0.6% -0.49% -30.70%

1.8
(pumping effect)

1.6
IM
/p

1.4
EM
p

1.2

1
0 5 10 15 20 25 30
3

2.5 342
reference
1
optimal
0 5
lambda

1.5

1
0 5 10 15 20 25 30
time [s]

Figure 4.9: Comparison of the pumping effect and the air-to-fuel ratio be-
tween reference and optimal ramp profiles.

Table 4.3: Sensitivity analysis of the optimization framework, analyzed for

two cases representing fast and slow ramp. Arrows indicate the NO x target
in qualitative form.

ramp NOx target NOx measured fuel measured

5s ↓ -16.86% 0.15%
30s ↑ 10.37% -0.57%
Chapter 4. Transient control of diesel engines 90

Table 4.4: Effect of the implementation of the compensation maps, for

three cases representing very fast, fast and medium ramps. Comparison
to optimal time-based control, in terms of relative change with respect to
reference trajectories.

ramp duration[s] fuel NOx soot

2, optimal -2.81% 3.96% -40.84%
ref + compens -0.68% -8.39% 31.67%
5, optimal -4.58% -3.85% -5.63%
ref + compens -2.92% 4.33% 26.63%
8, optimal -4.5% -15.87% -0.92%
ref + compens -3.00% -1.89% 16.86%

4.2.2 Optimal control versus compensation maps

As explained in Sec. 4.1.6, the time-based optimal control trajectories need
to be transformed into a causal form, in order to be used for online control.
Moreover, a simple map-based structure is chosen so that the transient com-
pensation strategy may be directly implemented in a standard production
ECU (Figure 4.5a). Since the impossibility to exactly copy out the optimal
trajectories, an analysis of the effects when going from the non-causal to the
causal and implementable structure has been conducted.
To perform this analysis, a specific control structure has been used (Figure
4.10). The ramp is performed and the air-path controller runs on the ECU,
without any transient compensation. The control signals are recorded and
then set as reference trajectories for the validation run. These control signals
are referred as TB (time-based), and they can be applied only when using
the ECU in B mode. The dynamic compensation maps act directly on
the reference trajectories. This case, from now on called (TB + DC), is
not implementable outside dedicated testbench setup, but it is the closest
one to the optimal time-based control. Therefore, this procedure highlights
the effects of switching from the non-causal optimal solution to the map-
based representation, isolated from other influences. Table 4.4 displays the
relative changes with respect to the reference trajectories. As expected,
a deterioration of the fuel efficiency is unavoidable, but the positive effect
produced by the dynamic compensation is still recognizable.

4.2.3 Validation
Figure 4.11 shows the validation cycle. It is important to remind that all the
methodology described has been applied for one engine speed (1950 rpm),
therefore that speed has been used also for the validation cycle. Three cases,
Chapter 4. Transient control of diesel engines 91

Figure 4.10: time-based (TB) control of actuator set-points: compensation

of the time-resolved reference values.

corresponding respectively to three different control structures, have been

compared:

1. T B + DC The non-implementable solution presented in Sec. 4.2.2

(Figure 4.10).

2. F F + DC. The feedforward control based on the steady-state ac-

tuator set-point maps runs on the ECU (Figure 4.5a). This is the
easiest implementation possible, the compensation maps act on the
feedforward actuator outputs.

3. F B + DC. The air-path control introduced in Figure 4.5b runs on

the ECU. Only the reference values for the air-path controller are
changed, except for the SOI, which is the same as in case 2. Although
this implementation is as straightforward as the previous case, the
basic control structure, to which the compensation maps are added, is
more complex.

In order to analyze the effect of the transient compensation in more detail,

two different types of result are presented. Beside the overall effect of the
dynamic compensation, the sub-part of the cycle where the compensation
is active can be considered, i.e. where the fuel derivative is non negative
(Figure 4.12). Table 4.5 summarizes both results for the three cases under
discussion.
It turns out that the best result is achieved by implementing case 1, as
could be expected. It serves as a benchmark or a guideline to design alterna-
tive near-optimal control structures. The case 3 is very promising, especially
if considered the fact that it can be applied easily, once an air-path control
is available. The case 2 falls slightly short of expectations, because even
Chapter 4. Transient control of diesel engines 92

300 60
load torque [Nm]

Vfcc [mm3/c]
200 40

100 20

0 0
0 5 10 15 20 25 30 35 40
time [s]

Figure 4.11: Validation cycle at constant engine speed of 1950 rpm. V fcc is
the volume of fuel injected per cycle per cylinder.

Table 4.5: Performance of the compensation-map based control systems on

the validation cycle, in terms of relative change with respect to reference
trajectories.

implementation case 1)TB+DC 2)FF+DC 3)FB+DC

fuel, overall -2.08% -1.68% -1.22%
sub-part -2.62% -2.00% -1.68%
NOx , overall 0.28% 17.11% -4.96%
sub-part -0.19% 15.07% -1.65%
soot, overall -0.67% -30.37% 18.05%
sub-part -0.55% -36.80% 25.96%

if there is a significant fuel reduction, it substantially increases the NO x

emissions. Most likely NOx emissions might be reduced to the detriment
of fuel efficiency, according to the well known trade-off between these two
quantities. However, these results can be further explained by comparing
the different control trajectories, as shown in Figure 4.13. It turns out that
the higher is the deviation of the control signals from the “optimal” solution
(TB+DC), the worse is the result. In fact, there is a discrepancy between
the three cases in terms of approximation of the optimal trajectories, es-
pecially for the EGR valve position in case 2. Regarding the latter, the
control inputs generated by using the ECU maps are rather far away from
the optimal solution, and the transient maps cannot fully compensate such
a deviation, resulting in a suboptimal result. However, the simplest case 2,
as opposed to the near-optimal but not implementable case 3 which serves
as a benchmark, has been employed to assess the effectiveness of the overall
methodology.
Chapter 4. Transient control of diesel engines 93

40

40

40
dmfcc/dt (scaled)
TB (reference)
TB+DC
35

35

35
30

30

30
25

25

25
time [s]
20

20

20
15

15

15
10

10

10
5

5
0

0
0

2
80

60

40

50
100

100

-2

VGT[%] EGR[%] SOI[°BTDC]

Figure 4.12: Control signals for case 1. In order to highlight when the
compensation occurs, the fuel derivative trend is superimposed on the graph.
Chapter 4. Transient control of diesel engines 94

40

40

40
1) TB+DC

3) FB+DC
2) FF+DC
35

35

35
30

30

30
25

25

25
time [s]
20

20

20
15

15

15
10

10

10
5

5
0

0
0

0
80

60

40

50
100

100

-2

VGT [%] EGR [%] SOI [°BTDC]

Figure 4.13: Comparison between the three cases tested.

Chapter 4. Transient control of diesel engines 95

4.2.4 Conclusion
A methodology to derive compensation maps suitable for the transient con-
trol of a diesel engine has been presented and experimentally validated.
These maps are obtained by means of a dynamic optimization process, of
which a beginning-to-end implementation and validation has been detailed.
A significant improvement of fuel efficiency, without compromising emis-
sion levels, can be achieved by applying the methodology developed during
the doctorate. Moreover, the optimization framework shows a good sensi-
tivity to the NOx-fuel tradeoff when changing the NOx emission constraints.
As a consequence, the optimization tool can provide different levels of fuel
reduction correspondingly to different tunings of the emission level targets.
Since the main goal was to test the overall validity of the methodology,
only a single engine speed has been used. In order to cover the full op-
erating range, the same procedure has to be repeated for different engine
speeds. Thanks to the automated optimization procedure developed, the to-
tal time needed to perform a full calibration of the transient maps is directly
proportional to the number of engine speeds spanned.
As concluded in Sec. 4.2.3, the transient maps cannot fully recover large
deviations, typical of static control inputs significantly far away from the
optimal solution. Therefore, further development of the methodology will
focus on different approaches to extend the performance of the compensation
maps to that case. An improvement could be achieved by deriving multi-
dimensional maps, which should be able to reproduce the optimal solution
with more accuracy.
Chapter 5

Summary and outlook

The research activity carried out during the doctorate, and presented in
this thesis, focused on the development of control strategies for diesel engine
transient operation.
In Chapter 2, the development of exhaust line heating strategies, based
on experimental investigations and previously developed simulation analysis,
has been presented. The case study is represented by the SCR installation
in a small diesel engine exhaust line, to enhance NO x reduction in an effort
to comply with upcoming EU6 regulations. The challenge was to reach a
pre-specified temperature (of approximately 190°C) as fast as possible, far
away from the exhaust valves and without compromising fuel consumption.
The interesting result is that a substantial SCR light-off time reduction
(around 600 s) may be achieved with minor fuel penalties, and this may
be obtained by implementing a control strategy that is designed to respect
different priorities depending on the SCR thermal state. Possible further
improvement could be achieved by exploring the effect of the EGR valve
partial closing, which can be possible thanks to the increase in NO x reduction
due to the higher efficiency of the SCR after-treatment system. A fuel
consumption reduction is foreseen because of the double effect of a better
combustion efficiency and a further reduction of VGT closing at constant
boost pressure (due to the higher enthalpy available at the turbocharger
inlet).
Chapter 3 has presented the numerical methods and the testbench setup,
required to perform an iterative dynamic optimization of diesel engines over
prescribed driving profiles. One exemplary iteration has been performed and
experimentally validated, in order to assess the validity of the methodology.
A recognizable progress towards lower fuel consumption while maintaining
the emission levels has been observed.
In Chapter 4, a methodology to derive compensation maps suitable for the
transient control of a diesel engine has been presented and experimentally
validated. These maps are obtained by means of a dynamic optimization

96
Chapter 5. Summary and outlook 97

process, of which a beginning-to-end implementation and validation has been

detailed. A significant improvement of fuel efficiency, without compromis-
ing emission levels, can be achieved by applying the methodology developed
during the doctorate. Moreover, the optimization framework shows a good
sensitivity to the NOx-fuel tradeoff when changing the NOx emission con-
straints. As a consequence, the optimization tool can provide different levels
of fuel reduction correspondingly to different tunings of the emission level
targets.
As concluded in Sec. 4.2.3, the transient maps cannot fully recover large
deviations, typical of static control inputs significantly far away from the
optimal solution. Therefore, further development of the methodology will
focus on different approaches to extend the performance of the compensation
maps to that case. An improvement could be achieved by deriving multi-
dimensional maps, which should be able to reproduce the optimal solution
with more accuracy.
Appendix A

Sensors

As far as performing measurement is concerned, sensors play a primary role.

In this Appendix several kinds of sensors are analyzed, both automotive
sensors and “laboratory” sensors, being the latter pretty much utilized in
a testbench environment. The list presented below does not fully cover all
measurements potentially achievable in a test cell, but focuses on the most
widespread sensors in automotive field while highlighting their measuring
principle.

A.1 Temperature Sensors

Temperatures are measured by means of thermoresistances and thermocou-
ples. The main distinction to be made lays in their different applicability,
being the former type more suitable for production application whereas the
second type is exclusively relegated to the testbench environment.

A.1.1 Thermoresistances
Most temperature measurements in the automotive utilize the temperature
sensitivity of electric resistance materials with negative temperature coeffi-
cient (NTC). The strong nonlinearity enables a large temperature range to
be covered (Figure A.1).
For applications with very high temperatures (exhaust gas temperatures
up to 1000°C), platinum sensors are employed. The change in resistance
is converted into an analog voltage by a voltage grading circuit with an
optional parallel resistance to the linearization.

A.1.2 Thermocouples
A thermocouple is a sensor for measuring temperature. It consists of two
dissimilar metals, joined together at one end. When the junction of the two
metals is heated or cooled a voltage is produced that can be correlated back

98
Appendix A. Sensors 99

Figure A.1: Typical characteristics of temperature sensors (NTC).

to the temperature. The thermocouple alloys are commonly available as

wire.
A thermocouple is available in different combinations of metals or calibra-
tions. The four most common calibrations are J, K, T and E. There are high
temperature calibrations R, S, C and GB. Each calibration has a different
temperature range and environment, although the maximum temperature
varies with the diameter of the wire used in the thermocouple. Although
the thermocouple calibration dictates the temperature range, the maximum
range is also limited by the diameter of the thermocouple wire. That is, a
very thin thermocouple may not reach the full temperature range.
Since a thermocouple measures in wide temperature ranges and can be
relatively rugged, thermocouples are very often used in industry. The fol-
lowing criteria are used in selecting a thermocouple:
• Temperature range
• Chemical resistance of the thermocouple or sheath material
• Abrasion and vibration resistance
• Installation requirements (may need to be compatible with existing
equipment; existing holes may determine probe diameter)
The response time is an important characteristic to be considered when
choosing a thermocouple. A time constant has been defined as the time
required by a sensor to reach 63.2% of a step change in temperature under a
specified set of conditions. Five time constants are required for the sensor to
approach 100% of the step change value. An exposed junction thermocouple
is the fastest responding. Also, the smaller the probe sheath diameter, the
faster the response, but the maximum temperature may be lower. It has
to be noticed that sometimes the probe sheath cannot withstand the full
temperature range of the thermocouple type.
Appendix A. Sensors 100

A.2 Piezoresistive effect

Piezoresistivity is a common sensing principle for micromachined sensors.
First discovered by Lord Kelvin in 1856, the piezoresistive effect is a widely
used sensor principle. In a few words, an electrical resistor may change its
resistance when it experiences a strain and deformation. This effect provides
an easy and direct energy/signal transduction mechanism between the me-
chanical and the electrical domains. Today, it is used in the MEMS (Micro
Electro-Mechanical Systems) field for a wide variety of sensing applications,
including accelerometers, pressure sensors, gyro rotation rate sensors, tactile
sensors, flow sensors, sensors for monitoring structural integrity of mechan-
ical elements, and chemical/biological sensors.
The resistance value of a resistor with the length l and the cross-sectional
area A is given by
l
R=ρ (A.1)
A
The resistance value is determined by both the bulk resistivity ρ and the
dimensions. Consequently, there are two important ways by which the resis-
tance value can change with applied strain. First, the dimensions, including
the length and cross section, will change with strain. This is easy to un-
derstand, though the relative change in dimensions is generally small. Note
that transverse strains may be developed in response to longitudinal load-
ing. For example, if the length of a resistor is increased, the cross section
will likely decrease under finite Poissons ratios. Secondly, the resistivity of
certain materials may change as a function of strain. The magnitude of
resistance change stemming from this principle is much greater than what is
achievable from the first one. By strict definition, piezoresistors refer to re-
sistors whose resistivity changes with applied strain. Metal resistors change
their resistance in response to strain mainly due to the shape deformation
mechanism. Such resistors are technically called strain gauges. The resis-
tivity of semiconductor silicon changes as a function of strain. Silicon is
therefore a true piezoresistor.
Focusing now on the macroscopic description of the behavior of a piezore-
sistor under a normal strain, the change in resistance is linearly related to
the applied strain, according to
ΔR ΔL
=G∙ (A.2)
R L
The proportional constant G in the above equation is called the gauge
factor of a piezoresistor. We can rearrange the terms in this equation to
arrive at an explicit expression for G:
ΔR
ΔR
G= R
Δl
= (A.3)
l
εR
Appendix A. Sensors 101

The resistance of a resistor is customarily measured along its longitudinal

axis. Externally applied strain, however, may contain three primary vector
components: one along the longitudinal axis of a resistor and two arranged
90° to the longitudinal axis and each other. A piezoresistive element behaves
differently towards longitudinal and transverse strain components.
The change of measured resistance under the longitudinal stress compo-
nent is called longitudinal piezoresistivity. The relative change of measured
resistance to the longitudinal strain is called the longitudinal gauge factor.
On the other hand, the change of resistance under transverse strain compo-
nents is called transverse piezoresistivity. The relative change of measured
resistance to the transverse strain is called the transverse gauge factor. For
any given piezoresistive material, the longitudinal and transverse gauge fac-
tors are different.
It is important to realize that longitudinal and transverse strains are often
present at the same time though one of them may play a clearly dominat-
ing role. The total resistance change is the summation of changes under
longitudinal and transverse stress components, namely

   
ΔR ΔR ΔR
= + = Glongit ∙slongit +Gtransv ∙stransv (A.4)
R R longit R transv

Resistance changes are often read using the Wheatstone bridge circuit
configuration. A basic Wheatstone bridge consists of four resistors connected
in a loop. An input voltage is applied across two junctions that are separated
by two resistors. Voltage drop across the other two junctions forms the
output. One or more resistors in the loop may be sensing resistors, whose
resistances change with the intended variables. In the bridge shown in Figure
A.2a, one resistor (R1 ) is variable by strain. The other resistors (R2 , R3
and R4 ) are made insensitive to strains by being located in regions where
mechanical strain is zero, such as on rigid substrates.
The output voltage is related to the input voltage according to the fol-
lowing relationship,

 
R2 R4
Vout = − ∙ Vin (A.5)
R 1 + R 2 R 3 + R4

In many practical applications, all four resistors share an identical nominal

resistance value. A representative case is shown in Figure A.2b. In this case,
the resistance of the variable resistor (sensor) is represented as

Rs = R + ΔR (A.6)
Appendix A. Sensors 102

Figure A.2: Wheatstone bridge circuits.

whereas the nominal resistance values of other three resistors are denoted
R. The output voltage is linearly proportional to the input voltage according
to

 
−ΔR
Vout = ∙ Vin (A.7)
2R + ΔR

Most piezoresistors are temperature sensitive. For the purpose of elimi-

nating the effect of changing environmental temperature on the output, the
Wheatstone bridge is particularly effective. Variation of environmental tem-
perature would cause changes to all resistances in the bridge with the same
percentage. Hence, the temperature variation would cause the numerator
and the denominator of the right-hand terms of (A.7) to be scaled by an
identical factor. The temperature effect is therefore cancelled out.

A.3 Piezoelectric effect

The piezoelectric effect produces an opposed accumulation of charged parti-
cles on the crystal. This charge is proportional to applied force or stress. A
force applied to a quartz crystal lattice structure alters alignment of positive
and negative ions, which results in an accumulation of these charged ions
on opposed surfaces. These charged ions accumulate on an electrode that is
ultimately conditioned by transistor microelectronics.
There are two types of piezoelectric material that are used for PCB ac-
celerometers: quartz and polycrystalline ceramics. Quartz is a natural crys-
tal, while ceramics are man-made. Each material offers certain benefits, and
material choice depends on the particular performance features desired of
the accelerometer.
Quartz is widely known for its ability to perform accurate measurement
tasks and contributes heavily in everyday applications for time and frequency
measurements. Examples include everything from wrist watches and radios
Appendix A. Sensors 103

to computers and home appliances. Accelerometers benefit from several

unique properties of quartz. Since quartz is naturally piezoelectric, it has
no tendency to relax to an alternative state and is considered the most
stable of all piezoelectric materials. This important feature provides quartz
accelerometers with long-term stability and repeatability. Also, quartz has
virtually no pyroelectric effect (output due to temperature change), which
provides stability in thermally active environments. Because quartz has a
low capacitance value, the voltage sensitivity is relatively high compared to
most ceramic materials, making it ideal for use in voltage-amplified systems.
Conversely, the charge sensitivity of quartz is low, limiting its usefulness in
charge-amplified systems, where low noise is an inherent feature. The useful
temperature range of quartz is limited to approximately 600 °F (315 °C).
A variety of ceramic materials are used for accelerometers, depending on
the requirements of the particular application. All ceramic materials are
man-made and are forced to become piezoelectric by a polarization process.
This process, known as ”poling,” exposes the material to a high-intensity
electric field. This process aligns the electric dipoles, causing the material
to become piezoelectric. Unfortunately, this process tends to reverse itself
over time until it exponentially reaches a steady state. If ceramic is exposed
to temperatures exceeding its range or electric fields approaching the poling
voltage, the piezoelectric properties may be drastically altered or destroyed.
Accumulation of high levels of static charge also can have this effect on
the piezoelectric output. PCB uses three classifications of ceramics. First,
there are high-voltage-sensitivity ceramics that are used for accelerometers
with built-in, voltage-amplified circuits. There are high-charge-sensitivity
ceramics that are used for charge mode sensors with temperature ranges to
400 °F (205 °C). This same type of crystal is used in accelerometers that
use built-in charge-amplified circuits to achieve high output signals and high
resolution. Finally, there are high-temperature ceramics that are used for
charge mode accelerometers with temperature ranges to 600 °F (316 °C) for
monitoring of engine manifolds and superheated turbines.

A.4 Pressure Sensors

Different sensor types are employed in order to meet the various demands
of the pressures to be measured.

Piezoresistive sensors The micromachined pressure sensor was one of

the earliest demonstrations of micromachining technology. It is commer-
cially very successful because of several important traits, including high
sensitivity and uniformity. Bulk microfabricated pressure sensors with thin
deformable diaphragms made of singlecrystal silicon are the earliest prod-
ucts and still dominate the market today. One example is shown in Figure
Appendix A. Sensors 104

Figure A.3: Piezoresistive pressure sensor.

A.3. Piezoresistors are located in the center of four edges. The location of
these piezoresistors corresponds to regions of maximum tensile stress when
the diaphragm is bent by a uniformly applied pressure difference across the
diaphragm. Four resistors are connected in a full Wheatstone bridge con-
figuration. A fully functional on-chip signal-processing unit consists of two
stage amplifiers, compensation circuitry, and two forms of output (frequency
and voltage). In the Wheatstone bridge configuration, the temperature sen-
sitivity of the piezoresistors cancels each other. The diaphragm with em-
bedded piezoresistors is made by using silicon bulk micromachining steps.
Piezoresistors are made by selectively doping the silicon diaphragm.
Using microfabrication, the diaphragm thickness can be controlled pre-
cisely (at approximately 25μm or below). The sensor chip provides a sensi-
tivity of 4 mV/mm Hg, with the nonlinearity lower than 0.4% over the full
scale. The temperature coefficient of the sensitivity is less than 0.06%/°C
in the temperature range of to -20 to 110°C.

Piezoelectric sensors Piezoelectric pressure sensors measure dynamic

pressures. They are generally not suited for static pressure measurements.
Dynamic pressure measurements including turbulence and engine combus-
tion under varying conditions may require sensors with special capabilities.
Fast response, ruggedness, high stiffness, extended ranges, and the ability
to also measure quasi-static pressures are standard features associated with
these quartz pressure sensors.
Piezoelectric pressure sensors are available in various shapes and thread
configurations to allow suitable mounting for various types of pressure mea-
surements. Quartz crystals are used in most sensors to ensure stable, repeat-
able operation. The quartz crystals are usually preloaded in the housings to
ensure good linearity. When the crystal is stressed, a charge is generated.
This high-impedance output must be routed through a special low-noise
cable to an impedance-converting amplifier, such as a laboratory charge
Appendix A. Sensors 105

amplifier or source follower. High insulation resistance must be maintained

in the cables and connections. The primary function of the charge or voltage
amplifier is to convert the high-impedance output to a usable low-impedance
voltage signal for recording purposes. Laboratory charge amplifiers provide
added versatility for signal normalization, ranging, and filtering. Miniature
in-line amplifiers are generally of fixed range and frequency.
Typical applications in automotive field are in-cylinder pressure measure-
ments, but also intake/exhaust manifold pressure measurements whenever
the dynamic effects need to be captured.

A.5 Acceleremoters
Acceleration is the rate of change of velocity. Measurement units for accel-
eration include m/s2 , ft/s2 , and g.
An accelerometer is a sensor, or transducer, which is designed to gener-
ate an electrical signal in response to acceleration (or deceleration) that is
applied along (parallel with) its sensitive axis.
The applied, or experienced acceleration can fall into one or more of the
following categories:

• Constant Acceleration - acceleration that does not change during

an event. Examples include the acceleration due to earth’s gravity or
the centrifugal acceleration of a merry-go-round at constant rotational
speed.

• Transient Acceleration - acceleration that varies over the duration

of the event, but is not repetitive. Examples include the deceleration
that an automobile undergoes during braking or the acceleration ef-
fects experienced by a roller coaster as it negotiates its track. Transient
acceleration is the result of discontinuous motion.

• Periodic Acceleration - acceleration that continuously varies over

the duration of the event, and is quite repetitive. Examples include
the vibration of rotating machinery such as motors and bearings or
the acceleration experienced by a free-swinging pendulum. Periodic
acceleration is the result of continuous motion.

A.5.1 Piezoelectric accelerometers

Piezoelectric accelerometers employ either natural quartz crystals or man-
made polycrystalline ceramics as their sensing elements. A proof mass is
mated with the crystal and output is generated when a force is imposed
upon the crystal during acceleration. This force causes stress in the crystal,
which then generates an electrical charge that is relative to the applied force
Appendix A. Sensors 106

- the piezoelectric effect. The amount of force is proportional to applied ac-

celeration as governed by Newton’s law of motion F = m ∙ a. Piezoelectric
accelerometers cannot measure constant acceleration because they are in-
herently AC coupled, however, they are typically the most versatile and
economic choice for measuring fast transient and periodic acceleration. In
an accelerometer, the stress on the crystals occurs as a result of the seismic
mass imposing a force on the crystal. Over its specified frequency range, this
structure approximately obeys Newton’s law of motion, F=ma. Therefore,
the total amount of accumulated charge is proportional to the applied force,
and the applied force is proportional to acceleration. Electrodes collect and
wires transmit the charge to a signal conditioner that may be remote or built
into the accelerometer. Sensors containing built-in signal conditioners are
classified as Integrated Electronics Piezoelectric (IEPE) or voltage mode;
charge mode sensors require external or remote signal conditioning. Once
the charge is conditioned by the signal conditioning electronics, the signal
is available for display, recording, analysis, or control.
A very widespread accelerometer, as far as Spark Ignition engines are
concerned, is the so called “knock sensor”. The name obviously originates
from the abnormal combustion of the same name (knock). The functional
principle of a knock sensor is typically based on a piezoceramic ring that
converts the engine vibrations into electrically processable signals using a
superimposed (seismic) mass.
Sensor sensitivity is expressed in mV/g or pC/g and is practically constant
over a wide frequency range. The transmission behavior of the knock sensor
can be adapted by the choice of the seismic mass.

A.5.2 Piezoresistive accelerometers

Piezoresistive accelerometers may be fabricated from metal strain gauges,
piezoresistive silicon, or as a MEMS device. In such designs resistive material
is typically bonded to a cantilever beam that undergoes bending under the
influence of acceleration. This bending causes deformation of the resistor,
leading to a change in its resistance. The resistors are normally configured
into a Wheatstone bridge circuit, which provides a change in output volt-
age that is proportional to acceleration. Piezoresistive accelerometers are
capable of measuring constant, transient, and periodic acceleration.

A.5.3 Capacitive accelerometers

Capacitive accelerometers utilize the properties of an opposed plate capaci-
tor for which the distance between the plates varies proportionally to applied
acceleration thus altering capacitance. This variable is used in a circuit to
ultimately deliver a voltage signal that is proportional to acceleration. Ca-
pacitive accelerometers are capable of measuring constant as well as slow
Appendix A. Sensors 107

transient and periodic acceleration.

A.6 Microphones
When an object vibrates in the presence of air, the air molecules at the
surface will begin to vibrate, which in turn vibrates the adjacent molecules
next to them. This vibration will travel through the air as oscillating pres-
sure at frequencies and amplitudes determined by the original sound source.
The human eardrum transfers these pressure oscillations, or sound, into
electrical signals that are interpreted by our brains as music, speech, noise,
etc. Microphones are designed, like the human ear, to transform pressure
oscillations into electrical signals, which can be recorded and analyzed to
tell us information about the original source of vibration or the nature of
the path the sound took from the source to the microphone. The typical
audible range of a healthy human ear is 20 to 20000 Hz. Like the human
ear, microphones are designed to measure a very large range of amplitudes,
typically measured in decibels (dB) and frequencies in hertz (Hz).
In order to convert acoustical energy into electrical energy, microphones
are used. There are a few different designs for microphones. The more
common designs are Carbon Microphones, Externally Polarized Condenser
Microphones, Prepolarized Electret Condenser Microphones, Magnetic Mi-
crophones, and Piezoelectric Microphones.
The carbon microphone design is a value-oriented design. This design is
a very low quality acoustic transducer type. An enclosure is built. This
enclosure houses lightly packed carbon granules. At opposite ends of the
enclosure, electrical contacts are placed, which have a measured resistance.
When the pressure from an acoustical signal is exerted on the microphone, it
forces the granules closer together. This force presses the granules together,
which decreases the resistance. This change in resistance is measured and
output.
A condenser microphone operates on a capacitive design. The cartridge
from the condenser microphone utilizes basic transduction principles and
will transform the sound pressure to capacitance variations, which are then
converted to an electrical voltage. This is accomplished by taking a small
thin diaphragm and stretching it a small distance away from a stationary
metal plate, called a back plate. A voltage is applied to the back plate to
form a capacitor. In the presence of oscillating pressure, the diaphragm will
move which changes the gap between the diaphragm and the back plate.
This produces an oscillating voltage from the capacitor, proportional to the
original pressure oscillation. The back plate voltage can be generated by two
different methods. The first is an externally polarized microphone design
where an external power supply is used. The power source on this traditional
design is 200 volts. The second or newer design is called a prepolarized
Appendix A. Sensors 108

microphone design. This modern design utilizes an electret layer placed on

the backplane, which contains charged particles that supply the polarization.
A magnetic microphone is a dynamic microphone. The moving coil design
is based on the principal of magnetic induction. This design can be simply
achieved by attaching a coil of wire to a light diaphragm. Upon seeing
the acoustical pressure, the coil will move. When the wire is subjected to
the magnetic field, the movement of the coil in the magnetic field creates a
voltage, which is proportional to the pressure exerted on it.
A Piezoelectric microphone uses a quartz or man-made ceramic crystal
structure, which is similar to electrets in that they exhibit a permanent
polarization and can be coupled with an IEPE design. Although these sensor
type microphones have very low sensitivity levels, they are very durable
and are able to measure very high amplitude (decibels) pressure ranges.
Conversely, the floor noise level on this type of microphone is generally very
high. This design is suitable for shock and blast pressure measurement
applications.
The most popular test and measurement microphones are the capacitor
condenser designs.
When choosing the optimum microphone, the parameters to look at in-
clude the type of response field, dynamic response, frequency response, po-
larization type, sensitivity required, and temperature range. There are also
a variety of specialty type microphones for specific applications. In order to
select and specify a microphone, the first criteria that needs to be looked at
is the application and what the sound and environment represent.

Microphones Field Types There are three common application fields

for precision condenser microphones. The first and most common is the
free-field type. The free-field microphone is most accurate when measuring
sound pressure levels that radiate from a single direction and source, which
is pointed directly (0° incidence angle) at the microphone diaphragm, and
operated in an area that minimizes sound reflections.
The second type is called a Pressure Field. A Pressure Field microphone is
designed to measure the sound pressure that exists in front of the diaphragm.
It is described to have the same magnitude and phase at any position in the
field. It is usually found in an enclosure, or cavity, which is small when
compared to wavelength. The microphone will include the measurement
changes in the sound field caused by the presence of the microphone. The
sound being measured is typically coming from a single source.
The third type is called a Random Incident Microphone. This is also re-
ferred to as a Diffuse Field Type. The Random Incident type of microphone
is designed to be omni-directional and measure sound pressure coming from
multiple directions, multiple sources and multiple reflections. The Random
Incident type microphone will have typical correction curves for different
Appendix A. Sensors 109

angles of incidence. The random incidence microphone will compensate for

its own presence in the field. An average of the net effect of all the calibrated
incidence angles will be taken into account, in order to come up with a net
zero correction factor.

Dynamic Response The main criteria to describe sound, is based upon

the amplitude of the sound pressure fluctuations. The lowest amplitude that
a healthy human ear can detect is 20 millionths of a Pascal (20mPa). Since
the pressure numbers represented by Pascal’s are generally very low and not
easily managed, another scale was developed and is more commonly used,
called the Decibel (dB). The decibel scale is logarithmic and more closely
matches the response reactions of the human ear to the pressure fluctuations.
Manufacturers specify the maximum decibel level based on the design and
physical characteristics of the microphone.
In order to calculate the maximum output for a microphone, using a spe-
cific preamplifier and its corresponding peak voltage, you first need to cal-
culate the pressure in Pascals that the microphone can accept. The amount
of pressure can be calculated by using the following formula:
V oltage(mV )
P =

Sensitivity mV
Pa

where P = Pascal’s (Pa) and V oltage is the preamps output peak voltage.
Once the maximum pressure level that the microphone can sense at its peak
voltage is determined, this can then be converted to decibels (dB), using the
following logarithmic scale:
 
P
dB = 20 ∙ log
P0
where P is the pressure in Pascal’s and P0 is the reference value (0.00002
Pa). The above formula will provide the maximum rating that a microphone
(when combined with a specific preamplifier) can be capable of measuring.

Frequency Response Once the type of microphone field response and

dynamic range has been taken into consideration, the frequency range (Hz)
of interest, for the test requirement should be reviewed. Upon inspecting
the microphones specification sheet you will find the usable frequency range
of the specific microphone. Smaller diameter microphones will usually have
a higher upper frequency level capability. Conversely, larger diameter mi-
crophones will be able to detect lower frequencies, generally better.

Polarization Type As explained previously, test and measurement mi-

crophones can be broken down into two categories, traditional Externally
Polarized microphones and modern Prepolarized microphones. For most
Appendix A. Sensors 110

applications either type will work well. The prepolarized tend to be more
consistent in humid applications. They are recommended when changes
of temperature may cause condensation on the internal components. This
may short-out externally polarized microphones. Conversely, at high tem-
peratures, between 120-150° C, externally polarized microphones are a bet-
ter choice, since the sensitivity level is more consistent in this temperature
range.

Temperature Range Temperature has an effect on the microphones per-

formance. Sensitivity levels can be directly affected by extreme environmen-
tal conditions. As the temperature approaches the maximum specifications
of the microphone, its sensitivity specification will decrease. The owner
needs to be aware of not only the operating temperature, but also the stor-
age temperature of the microphones. If operated and/or stored in extreme
conditions, the microphone can be adversely affected and also require to be
calibrated more often.

A.7 Turbocharger speed

Turbocharger speed mainly depends on the exhaust and the conditions un-
der which the engine is running. Under certain circumstances the speed can
reach critical values for the safety and lifetime of the turbocharger. As the
need for higher pressure values and hence higher nominal turbo speeds has
constantly increased over recent years, it has become more and more impor-
tant to know the instantaneous speed of the turbo. This is valid for nearly
all sizes of turbochargers from the very small and fast rotating passenger
car turbochargers up to the large units used in 2-stroke ship engines.
There are three main concepts of sensors used in this application: VRS
(Variable Reluctance Sensors), optical sensors and eddy current sensors.

A.7.1 Variable Reluctance measurement system

A variable reluctance sensor (VRS) is used to measure position and speed of
moving metal components. This sensor consists of a permanent magnet, a
ferromagnetic pole piece, a magnetic pickup, and a rotating toothed wheel.
As the teeth of the rotating wheel (or other target features) pass by the face
of the magnet, the amount of magnetic flux passing through the magnet and
consequently the coil varies. When the gear tooth is close to the sensor, the
flux is at a maximum. When the tooth is further away, the flux drops off.
The moving target results in a time-varying flux that induces a proportional
voltage in the coil. Subsequent electronics are then used to process this signal
to get a digital waveform that can be more readily counted and timed.
Regarding turbocharger applications, a strong magnet and a coil system
build the core of these sensors. The target is normally a disc which is located
Appendix A. Sensors 111

in the bearing section of the turbocharger. That disc has notches or holes
so that the air-gap alters at these sections when the disc rotates with the
turbo. The induced voltage is the desired output signal. Many different
sizes and housings are available to adapt the sensors to the properties and
specific mechanical needs of the application.

A.7.2 Optical measurement system

Specially designed for non contact measurement of turbochargers running
at speed up to 200000 rpm, for purposes of measurement in stationary and
transient engine-mode. A Laser-beam is sent to the compressor wheel, scat-
tered back by means of a reflecting mark once each revolution. The scattered
light is detected and converted into a periodical sequence of voltage signals
that is available for further processing. The large optical range (usually
more than 300mm) enables measurement without changes in design.

A.7.3 Eddy Current measurement system

Eddy currents (also called Foucault currents) are electric currents induced
within conductors by a changing magnetic field in the conductor. These cir-
culating eddies of current have inductance and thus induce magnetic fields.
These fields can cause repulsion, attraction, propulsion, drag, and heating
effects. The stronger the applied magnetic field, the greater the electrical
conductivity of the conductor, and the faster the field changes, the greater
the currents that are developed and the greater the fields produced.
As far as turbocharger speed measurement is concerned, a coil is potted
in the sensor case and is energized by a high frequency alternating current.
The electromagnetic field from the coil generates eddy currents in the turbo-
charger blade. Every blade generates a pulse. The controller identifies the
speed (analog 0...10V) by considering the number of blades.
A potential problematic of this kind of sensor is related to EMC (Electro-
magnetic compatibility) emissions. Particularly where multi-test cells are in
use, very high levels of EMC emissions are causing effect on test cell instru-
mentation. New generations of controller offer a new electronic circuit which
‘boosts’ signal levels from the sensor and also dramatically improves circuit
shielding. The eddy current measurement technique is also immune to the
effects of oil, dirt, carbon particles that can be found in the engine, which
can affect the measurement output quality of other measurement principles,
particularly optical measurement technologies.

A.8 TDC measurement

In engine indicating measurements, special attention should be given to the
correct identification of the TDC (Top Dead Center) position, as small errors
Appendix A. Sensors 112

in this measurement lead to significant errors in the evaluation of indicated

work as well as combustion heat release rate. For instance, concerning the
imep, a deviation of only 0.1 ° crank angle from the true top dead location
already results in an error of several percentage points in the imep value.
In order to achieve adequate precision in determining the TDC position it
is recommended to perform a dynamic measurement, running the engine
motored and unfired or, alternatively, preventing combustion only in the
cylinder where the measurement is going on, while the other cylinders func-
tion fired to keep the engine running. When performing dynamic measure-
ment, the inaccuracies that would be generated by the bearing clearances
are eliminated. Such measurement is usually carried out with a capacitive
proximity sensor, or in the absence of such a sensor, the TDC position can
be inferred from the motored-engine pressure data.
The capacitive proximity sensor uses two conductive objects separated
by a dielectric material. A voltage difference applied to the conductive ob-
jects generates an imbalance of electrical charges between them, originating
an electric field in the dielectric material. When this voltage is alternated
the electrical charges move continuously, going from one of the conductive
objects to the other and generating an alternating electric current, which is
the output signal of the sensor. The amount of current flow is determined
by the capacitance, and the capacitance depends on the proximity of the
conductive objects. Closer objects cause greater current than more distant
ones.
In the capacitive sensors used to determine the TDC position, one of the
conductive objects is the sensor probe itself, while the piston plays the role
of the second conductive object (Figure A.4). The sensor is mounted in the
head in such a way that when the engine is running the piston will move
closer or away from the sensor, but without actually touching it. Thus, the
sensor will produce a signal with amplitude, which is inversely proportional
to the distance between the TDC sensor tip and the piston top. The exact
TDC position will correspond to the maximum amplitude of the TDC sensor
signal, which can be determined with great accuracy because of the high
degree of symmetry of the signal.
When using the motored-engine pressure data for identifying the
TDC position, the main arising difficulty is that the peak pressure pre-
cedes the actual TDC position, which corresponds to the minimum volume.
This occurs due to heat transfer and mass losses, and the angle interval
between these events is named “loss angle” (Figure A.5). Several enough
accurate methods have been proposed for determining the loss angle, and
usually manufacturers of indicating equipment include in their manual rec-
ommendations to estimate loss angle values, which depend on the kind of
the engine (spark ignition or diesel) and compression ratio.
The advantage of direct determination of TDC, compared with determin-
ing the position of pressure maximum from the motored-engine pressure
Appendix A. Sensors 113

Figure A.4: The capacitive TDC sensor.

Figure A.5: Definition of loss angle.

curve, is that there is then no need for a correction involving the degree of
the thermodynamic loss angle.
Appendix A. Sensors 114

A.9 Air Mass Sensors

Hot-film Anemometer Practically all air mass sensors employed in the
automobile today follow this principle. A heated element dissipates energy
to the surrounding air. The dissipated heat energy is dependent on the air
flow and can be used as a measurement parameter.
The HFM consists of a tubular housing with flow straightener (honeycomb-
lattice combination), sensor guard, and the sensor module. The tube di-
ameter is adapted to the air mass range required in each case. Sensors,
electronics, connecting elements, and plug are integrated into the sensor
module.
Two temperature-dependent metallic-film resistors on a glass substrate
(RS and RT ) are positioned inside the tube in the direct intake air stream.
These two resistors, in combination with R1 and R2 , are linked in a Wheat-
stone bridge circuit, Figure A.6. The voltage at R2 is a measure of the
air mass flow rate. Depending on the intaken air mass flow, RS is cooled
more or less strongly. The electronics control the necessary heating current
through RS so that there is always a constant temperature difference (e.g.
130 K) at RS to the air temperature measured at RT . The heating current
is transformed into a voltage signal at resistor R2 .
The resistors RS and RT are matched to one another in such a way that
the map is independent of the air temperature. The map also exhibits
(thanks to the physics) an advantageous nonlinear characteristic permitting
a practically constant proportional resolution.
Thanks to the use of materials specially adapted to the conditions in the
automobile engine compartment, flow control, circuiting technology, and the
mechanical configuration, the HFM signal is more or less independent of the
temperature, pressure, and soiling.
Internal combustion engines with four or fewer cylinders create extreme
pulsations in the intake manifold at wide-open throttle or in the case of
no throttle valve (e.g. in diesel engines). At certain engine speeds, at the
resonance point, a pulsating return flow occurs that with conventional HFM
results in a positive measurement error as the air passes over the sensor
three times.
The air mass flow (Q) is calculated as a function of the degree of modu-
lation (m) to

Q =Qmean ∙ [1 + m ∙ sin(wt)]
Q̂
m=
Qmean
This effect can be compensated with an additional heating resistor RH
(booster). Returning air is heated by the booster and passes over the heating
Appendix A. Sensors 115

Figure A.6: Principle of a hot-film air mass meter.

resistor RS . This prevents RS from being cooled again by the returning air.
Overheating the returning air produces an overcompensation that ensures
that the air flowing toward the engine again is not measured a second time.
The return-flow compensation is independent of the resonance frequencies,
temperature, and air pressure.
In many applications the temperature sensor (NTC resistor) for deter-
mining the intake air temperature is also integrated into the HFM.

Ultrasonic transit-time differential method With the ultrasonic run-

time method, the time taken for a sound wave to travel from the transmitter
to the receiver is measured. This parameter enables the flow velocity to be
measured and, in combination with air density and temperature, the mass
flow to be determined.
The measuring principle is based on the ultrasonic transit-time differen-
tial method. In this method, two ultrasonic pulses are sent simultaneously
from Transmitter 1 (T1) and Transmitter 2 (T2) right through the flowing
medium. One pulse is propagating into and the other one against flow direc-
tion. The interaction between the speed of sound c and the velocity of flow
v accelerates the pulse on one of the paths and decelerates the pulse on the
other path. This effective propagation velocity results in different transit
times through the medium: the signal at Receiver 2 (R2) arrives faster than
the signal arriving at Receiver 1 (R1) (Figure A.7). The device measures
the speed of sound traveling either way, corresponding to t1→2 and t2→1 .

• T - Transmitter

• R - Receiver
Appendix A. Sensors 116

Figure A.7: Principle of ultrasonic flow measurement according to the

transit-time differential method.

• c - speed of sound
• v - flow Media velocity
• α - inclination angle
A pulse travelling with the current from T1 to R2 needs a transit time of:
D 1
t1→2 = ∙
sinα (c + v ∙ cosα)

A pulse travelling against the current from T2 to R1 needs a transit time

of:
D 1
t2→1 = ∙
sinα (c − v ∙ cosα)
The time difference of both pulses comes to:
t2→1 ∙ t1→2 ∙ sin(2α)
Δt =t2→1 − t1→2 = v ∙
D
D t2→1 − t1→2
v= ∙
sin(2α) t2→1 ∙ t1→2
The flow rate Q is determined from the mean flow velocity. In a pipeline
with circular cross-section the following applies:
D2
Q =v ∙ A = v ∙ π ∙
4
π ∙ D3 t2→1 − t1→2
Q= ∙
4 ∙ sin(2α) t2→1 ∙ t1→2
Appendix A. Sensors 117

The transit time difference is therefore a precise linear measure of the mean
flow velocity v along the measuring path (ultrasonic beam).
Additionally, the sound velocity c can be determined on-line from the sum
total of transit times t1→2 , t2→1 :
X 1 2D
t =t2→1 + t1→2 = ∙
c sinα
2D 1
c= ∙
sinα t2→1 + t1→2
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