Drivetrain Modelling and Clutch Temperature Estimation in Heavy Duty Trucks

Drivetrain Modelling and Clutch Temperature Estimation in Heavy Duty Trucks
Drivetrain Modelling and Clutch
Temperature Estimation in Heavy
Duty Trucks
Examensarbete utfört i Fordonssystem
vid Tekniska högskolan vid Linköpings Universitet
av
Johan Thornblad
LiTH-ISY-EX--14/4784--SE
Södertälje 2014
Drivetrain Modelling and Clutch
Temperature Estimation in Heavy
Duty Trucks
Examensarbete utfört i Fordonssystem
vid Tekniska högskolan vid Linköpings Universitet
av
Johan Thornblad
LiTH-ISY-EX--14/4784--SE
Handledare:
Anders Larsson, Scania CV
Andreas Myklebust, ISY, Linköpings Universitet
Examinator:
Lars Eriksson, ISY, Linköpings Universitet
Södertälje, 10 Juni 2014
Presentationsdatum
Institution och avdelning
Institutionen för systemteknik
2014-06-13
Publiceringsdatum (elektronisk version)
Department of Electrical Engineering
-
Språk
Typ av publikation
ISBN (licentiatavhandling)
Svenska
X Annat (ange nedan)
Licentiatavhandling
X Examensarbete
C-uppsats
D-uppsats
Rapport
Annat (ange nedan)
ISRN
Engelska
Antal sidor
63
LiTH-ISY-EX--14/4784--SE
Serietitel (licentiatavhandling)
Serienummer/ISSN (licentiatavhandling)
URL för elektronisk version
http://www.ep.liu.se
Publikationens titel
Drivetrain Modelling and Clutch Temperature Estimation in Heavy Duty Trucks.
Författare
Johan Thornblad
Sammanfattning
En existerande drivlinemodell med temperaturdynamik i kopplingen har använts för att simulera beteendet hos en lastbil.
Vid implementation av modellen i MATLAB/Simulink betonades vikten av en enkel och modulär struktur. Detta gjordes för
att underlätta användning av modellen i olika applikationer samt för att göra den lätt att förstå. De huvudsakliga bidragen i
uppsatsen är anpassningen av en temperatur- och slitageobeservatör på kopplingen för användning i realtid av växellådans
styrenhet. För att ta observatören från simulerings- till realtidsmiljö måste styrenhetens konfiguration och begränsningar
beaktas samt gränssnittet hos observatören anpassas. Konkret betyder detta att hänsyn till begränsningarna hos de olika
datatyper som används i kopplingens styrenhet tagits, att den negativa inverkan som brusiga mätsignaler kan få begränsats
samt att skillnader i dynamik hos de olika sensortyper som används i kopplingen kompenserats för. Med simuleringar har
prestandan hos den anpassade observatören studerats samt dess förmåga att kompensera för värmeutvidgning och slitage i
kopplingen visats.
Abstract
An existing drivetrain model with clutch temperature dynamics has been used to simulate the behaviour of a heavy duty
truck. During the implementation of the model in MATLAB/Simulink modularity and simplicity was greatly emphasized.
This was done in order to facilitate the use of the model in various applications as well as making it easy to understand.
The main contributions of the thesis is however the adaptation of a clutch temperature and wear observer for use in an online application in the gearbox management system (GMS). The process of taking the observer from an off-line simulation
environment to running on-line includes taking into consideration the configuration and limitations of the GMS as well as
adapting the interface of the observer. Concretely this means dealing with the limitations of the available data types in the
GMS, compensating for the effect of biased measurements as well as accounting for the different dynamics of the sensortypes used in the clutch. In a simulation environment the performance of the adapted observer has been studied and its ability
to compensate for heat expansion and wear in the clutch shown.
Nyckelord
Drivetrain, Modelling, Clutch, Temperature, Estimation, EKF
Abstract
An existing drivetrain model with clutch temperature dynamics has been used to
simulate the behaviour of a heavy duty truck. During the implementation of the
model in MATLAB/Simulink modularity and simplicity was greatly emphasized.
This was done in order to facilitate the use of the model in various applications
as well as making it easy to understand.
The main contributions of the thesis is however the adaptation of a clutch temperature and wear observer for use in an on-line application in the gearbox management
system (GMS). The process of taking the observer from an off-line simulation environment to running on-line includes taking into consideration the configuration
and limitations of the GMS as well as adapting the interface of the observer. Concretely this means dealing with the limitations of the available data types in the
GMS, compensating for the effect of biased measurements as well as accounting
for the different dynamics of the sensor-types used in the clutch.
In a simulation environment the performance of the adapted observer has been
studied and its ability to compensate for heat expansion and wear in the clutch
shown.
VII
Sammanfattning
En existerande drivlinemodell med temperaturdynamik i kopplingen har använts
för att simulera beteendet hos en lastbil. Vid implementation av modellen i MATLAB/Simulink betonades vikten av en enkel och modulär struktur. Detta gjordes
för att underlätta användning av modellen i olika applikationer samt för att göra
den lätt att förstå.
De huvudsakliga bidragen i uppsatsen är anpassningen av en temperatur- och slitageobeservatör på kopplingen för användning i realtid av växellådans styrenhet. För
att ta observatören från simulerings- till realtidsmiljö måste styrenhetens konfiguration och begränsningar beaktas samt gränssnittet hos observatören anpassas.
Konkret betyder detta att hänsyn till begränsningarna hos de olika datatyper som
används i kopplingens styrenhet tagits, att den negativa inverkan som brusiga
mätsignaler kan få begränsats samt att skillnader i dynamik hos de olika sensortyper som används i kopplingen kompenserats för.
Med simuleringar har prestandan hos den anpassade observatören studerats samt
dess förmåga att kompensera för värmeutvidgning och slitage i kopplingen visats.
IX
Acknowledgements
I would like to thank my examiner Lars Eriksson at Linköpings University and
Henrik Flemmer, head of pre-development of engine system platforms at Scania
for giving me this great opportunity. Most of all I wish to thank my supervisor
Andreas Myklebust at Linköpings University for his invaluable feedback and for
letting me base the thesis on his research. Further I wish to thank Anders Larsson
from Scania for taking time to guide and support me during all phases of the work.
For his thoughtful input throughout the thesis I also want to thank my opponent
Svante Löthgren.
Finally i wish to say thank you to Emelie for your support and for proofreading
the report.
Johan Thornblad
Södertälje, June 2014
XI
Contents
1 Introduction
1.1
1.2
1.3
1
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.1
The drivetrain . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.2
Clutch control . . . . . . . . . . . . . . . . . . . . . . . . .
2
Aims and objectives . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.2.1
Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.2.2
Clutch control . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.2.3
Implementation in truck . . . . . . . . . . . . . . . . . . . .
4
1.2.4
Evaluate performance at low speeds . . . . . . . . . . . . .
4
Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.3.1
5
Chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Related research
7
2.1
Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
2.2
The clutch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
2.3
Clutch control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
2.4
Gearshift comfort analysis . . . . . . . . . . . . . . . . . . . . . . .
8
2.5
Position and cruise control . . . . . . . . . . . . . . . . . . . . . . .
8
3 Modelling
11
3.1
Variable and subscript definitions . . . . . . . . . . . . . . . . . . .
12
3.2
Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
3.3
Clutch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
3.3.1
Clutch overview . . . . . . . . . . . . . . . . . . . . . . . .
13
3.3.2
Clutch torque transmissibility . . . . . . . . . . . . . . . . .
13
3.3.3
Temperature Dynamics . . . . . . . . . . . . . . . . . . . .
14
3.3.4
Lock-Up/Break-Apart Logic . . . . . . . . . . . . . . . . . .
16
XIII
3.3.5
Torsional Part . . . . . . . . . . . . . . . . . . . . . . . . .
18
3.4
Gearbox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
3.5
Propeller Shaft . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
3.6
Final Drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
3.7
Drive Shafts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
3.8
Vehicle Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
3.9
Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
4 Clutch observer
22
4.1
Observer variable definitions . . . . . . . . . . . . . . . . . . . . . .
22
4.2
Extended clutch model . . . . . . . . . . . . . . . . . . . . . . . . .
23
4.3
Observability analysis . . . . . . . . . . . . . . . . . . . . . . . . .
25
4.3.1
Operating modes . . . . . . . . . . . . . . . . . . . . . . . .
25
4.3.2
Combined observability . . . . . . . . . . . . . . . . . . . .
25
4.4
Choice of observer type . . . . . . . . . . . . . . . . . . . . . . . .
26
4.5
Extended Kalman filter set up
. . . . . . . . . . . . . . . . . . . .
26
4.5.1
Discretisation of the model . . . . . . . . . . . . . . . . . .
26
4.5.2
The filter . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
4.6
Selection of covariance matrices . . . . . . . . . . . . . . . . . . . .
28
4.7
Initiation and limitation of the uncertainty matrix . . . . . . . . .
29
4.7.1
Uncertainty of the temperature states . . . . . . . . . . . .
29
4.7.2
Uncertainty of the zero position state . . . . . . . . . . . .
30
4.7.3
Initial uncertainty matrix . . . . . . . . . . . . . . . . . . .
31
5 Clutch controller
33
5.1
Fixed trajectory look-up table . . . . . . . . . . . . . . . . . . . . .
33
5.2
Temperature compensation . . . . . . . . . . . . . . . . . . . . . .
34
5.3
Engine torque feedback . . . . . . . . . . . . . . . . . . . . . . . .
34
5.4
Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
6 Implementation on GMS
37
6.1
Specify data types . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
6.2
Transformation the clutch torque transmissibility curve . . . . . .
38
6.3
Data type precision issues . . . . . . . . . . . . . . . . . . . . . . .
40
6.4
Biased measurements . . . . . . . . . . . . . . . . . . . . . . . . . .
41
6.5
Requesting clutch position . . . . . . . . . . . . . . . . . . . . . . .
42
XIV
6.6
6.5.1
Relating the clutch piston position to motor position . . . .
42
6.5.2
The distance between the clutch motor and piston . . . . .
43
Avoid division by zero . . . . . . . . . . . . . . . . . . . . . . . . .
44
6.6.1
45
EKF Update method . . . . . . . . . . . . . . . . . . . . . .
7 Results
7.1
7.2
7.3
7.4
47
Complete driveline model with clutch temperature dynamics . . .
47
7.1.1
Model residuals . . . . . . . . . . . . . . . . . . . . . . . . .
47
7.1.2
Correcting for the torque drift . . . . . . . . . . . . . . . .
49
Clutch temperature and zero-position observer . . . . . . . . . . .
49
7.2.1
Convergence of the zero position . . . . . . . . . . . . . . .
49
7.2.2
Convergence of individual states . . . . . . . . . . . . . . .
50
Temperature compensation in the clutch controller . . . . . . . . .
52
7.3.1
Effect on launch quality . . . . . . . . . . . . . . . . . . . .
52
7.3.2
Effect on produced engine torque . . . . . . . . . . . . . . .
54
Observer implemented on GMS . . . . . . . . . . . . . . . . . . . .
55
8 Conclusions and future work
8.1
8.2
57
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
8.1.1
Complete drivetrain model . . . . . . . . . . . . . . . . . .
57
8.1.2
Clutch observer on GMS . . . . . . . . . . . . . . . . . . . .
57
Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
8.2.1
Tire dynamics . . . . . . . . . . . . . . . . . . . . . . . . .
58
8.2.2
Backlash dynamics . . . . . . . . . . . . . . . . . . . . . . .
58
8.2.3
Adding the clutch motor . . . . . . . . . . . . . . . . . . . .
59
8.2.4
Implementing new engine model . . . . . . . . . . . . . . .
59
XV
Nomenclature
Acronym
AMT
HDT
PID
MPC
LQG
CC
ACC
GMS
EMS
ICE
RAM
Meaning
Automated Manual Transmission
Heavy Duty Truck
Proportional Integration Derivation
Model Predictive Control
Linear Quadratic Gaussian
Cruise Control
Adaptive Cruise Control
Gearbox Management System
Engine Management System
Internal Combustion Engine
Random Access Memory
XVI
Chapter 1
Introduction
This master thesis report presents work on Drivetrain Modelling and Clutch Temperature Estimation in Heavy Duty Trucks. The thesis was written at Scania CV
and the division of Vehicular Systems, department of Electrical Engineering at
Linköping University. This section contains some background to the thesis, the
aims and objectives of the thesis and the general outline of the report.
1.1
Background
Customer as well as government demands on the drivetrain of a heavy duty truck
(HDT) in terms of fuel efficiency, driveability and comfort are ever increasing and
are today larger than ever. There is no reason to think that this trend will come
to an end in the near future.
Another clear trend in today’s transportation industry is a movement towards a
higher degree of automatisation that aims at reducing both manual labour and
costs as well as increasing the level of safety and security of a given transportation
system.
To be able to meet those demands it is essential for automotive companies to build
a better understanding about the components of the drivetrain, their characteristics and interactions.
1.1.1
The drivetrain
The choice of drivetrain configuration has great impact on the performance of a
HDT. A type of configuration that is able to combine the efficiency of a manual
transmission with the driveability and comfort of an automatic transmission is the
automated manual transmission (AMT) [1]. This type of drivetrain is however
rather complex and therefore requires more refined control strategies than classic
types of drivetrains.
A fundamental problem with drivetrain control is the flexibility of its components.
For example this means that the propeller shaft and drive shafts of the vehicle
1
are exposed to torsion. This can be seen in Figure 1.1 where the torsion of the
driveshafts is seen. It should be noted that the torsion changes when the clutch
torque increases at 1 and 4 seconds and when the clutch locks-up at 8.6 seconds.
These properties can induce large torque oscillations [5] which often are perceived
negatively by the driver and can also be stressful for the drivetrain components.
Figure 1.1: The upper plot shows the clutch torque and the lower plot shows the
torsion of the driveshafts during a simulated launch.
1.1.2
Clutch control
In the future it is desired that HDT’s become more autonomous and are able
to deal with a wider range of driving situations without driver interference. An
example of this is a cruise controller that functions through the entire speed range.
When the speed of a vehicle drops low enough the clutch must change state from
closed to slipping since the engine idle velocity is too high. When the clutch is
slipping energy is dissipated and the clutch heats up. As can be seen in Figure 1.2
the clutch characteristics are very dependant on temperature where the transferred
torque at a certain clutch position can vary to up to 900 Nm depending on the
clutch temperature.
2
1500
80
Clutch Torque [Nm]
60
1000
40
20
500
0
4
Time [s]
5
6
7
8
9
Piston Pos. [mm]
10
11
12
Figure 1.2: The figure shows the clutch output torque when the clutch position
is ramped back and forth with increasing temperature as a result. The figure is
taken from [24].
To be able to develop a well functioning cruise controller for low speeds it is
therefore essential to have good knowledge about the current clutch temperature
and how this effects its operation.
1.2
Aims and objectives
The main objectives of this thesis is to adapt an existing drivetrain model for
use by Scania and the development and evaluation of a control strategy for the
clutch. Especially the possibilities of using the developed clutch model for use in
autonomous applications are to be examined.
1.2.1
Modelling
A complete drivetrain model that captures the dominating oscillating behaviour
of a heavy duty truck is to be developed. The model described in [25] is to be
used as the foundation of the drivetrain model that is used throughout the thesis.
The model is to be adapted to the model-structure that is currently being used
by Scania. Concretely this means that the structure of the model needs to be
modular and that the different blocks of the model should correspond to a physical
component. This together with no signals running on buses will result in a model
3
that is simple to understand and easy to use in a wide range of applications. This
part of the thesis is covered in Chapter 3.
1.2.2
Clutch control
The clutch is to be controlled using a feed-forward link that translates the desired
engine torque to a corresponding clutch piston position. In parallel with the feedforward a feedback link is used to compensate for differences between requested
engine torque and measured engine torque. The desired clutch stroke is also to
be corrected for the effects of thermal swelling and wear in the clutch. To do this
the clutch-observer described in [5] needs to be implemented. The clutch control
part of the thesis is covered in Chapter 5.
1.2.3
Implementation in truck
The developed clutch controller is to be modified and configured in a way that
makes it possible to generate in C-code and build onto the gearbox management
system (GMS). This means that both the limited processing power as well as
memory capacity of the GMS must be taken into consideration when designing
the clutch controller. The work done to implement the clutch controller in the
GMS can be seen in Chapter 6.
1.2.4
Evaluate performance at low speeds
The possibility to use the clutch temperature and wear observer for positioning
and use in an application for low speed autonomous driving is to be evaluated. An
important aspect of this is to survey the existing literature on the subject which
is done in Chapter 2.
1.3
Thesis outline
The first and second chapters of the thesis are dedicated to presenting the reader
with a short introduction to the report as well as some technical background and
a literature review on the subject. The following chapters can basically be divided
in two parts. The first part covers the modelling of the driveline and clutch that
has been performed. The second part describes the process of taking the clutch
temperature observer from the simulation environment and building it onto the
truck gearbox management system . At the end of the report the obtained results
are shown and discussed together with suggestions on future work. In Figure 1.3
a flow chart over the work process of the thesis can be seen.
4
Figure 1.3: The figure shows the different phases of the thesis.
1.3.1
Chapters
In this section the outline of the report can be seen.
Chapter 1 - Introduction
A short background to the thesis together with the aims and objectives.
Chapter 2 - Related research
In this chapter a review on literature on driveline modelling, clutch modelling and
clutch control is given.
Chapter 3 - Modelling
The different components of the model are explained and related equations are
stated.
Chapter 4 - Clutch observer
In this chapter the construction of the clutch temperature and wear observer is
explained.
Chapter 5 - Clutch controller
In this chapter it is described how the different part of the clutch controller are
put together
Chapter 6 - Implementation on GMS
All the changes made to the observer in order to build it on the GMS are described
here.
Chapter 7 - Results
The results are presented and discussed.
Chapter 8 - Conclusions and future work
Here the suggestions of future work are given.
5
Chapter 2
Related research
An important aspect in the thesis is to survey the existing research on the subject.
This is to give a deeper understanding of the challenges and possibilities in the
area.
2.1
Modelling
In this thesis most of the work is done in a simulation environment. Therefore it
is reasonable to start by surveying what possibilities there are when choosing a
model-structure. The primary choice is about what flexibilities in the drivetrain
that needs to be modelled and which can be neglected. When doing this it is
important to have the intended usage of the model in mind. For some applications
high simulation speed is important and therefore only one flexibility is included.
In other cases more flexibilities are considered to be able to capture to drivetrain
dynamics better.
In [4] three flexibilities are modelled; the clutch, the propeller shaft and the drive
shafts. In [8] only one flexibility between the transmission and the wheels is
modelled since it is dominating. In [7] the dynamics of the wheel tires and their
dependence on temperature are also studied.
2.2
The clutch
Since the quality of a gearshift mainly depends on how the clutch is controlled it
is essential to understand how torque is transferred through the clutch. Among
others this is examined in [5] where the clutch-properties dependence on temperature and wear are modelled. In [9] it is also analysed how heat influences the
functionality of the clutch.
7
2.3
Clutch control
In later years the AMT has received a lot of attention as a research area. Here follows a selection of the more interesting and in the literature frequently mentioned
control strategies. In [12] an adaptive PID-controller that utilizes a Q-learning
algorithm to adapt the controller to the present conditions is proposed. Further
there is extensive literature that covers the use of Fuzzy-logic [11] coupled with
extensive knowledge of the gear shift process and interpretation of the drivers intentions. As the computational capabilities of the onboard computers are getting
larger it has become more interesting to try model predictive controllers (MPC)
to control the drivetrain [10]. In [2] a linear quadratic Gaussian controller (LQG)
is developed that in an intuitive fashion interprets the intentions of the driver by
adjusting the weight-matrixes of the controller.
2.4
Gearshift comfort analysis
When performing a gear change it is according to [2] basically three parameters
that are important to pay respect to; minimizing the time-duration of the gear
shift, minimizing the friction losses and achieving smooth acceleration to assure
the comfort of the driver. An important property when it comes driver-comfort
is vehicle jerk which is defined as the rate at which the acceleration of the vehicle
changes or the third derivative of the position [3].
2.5
Position and cruise control
A possible driving scenario where the clutch temperature and wear observer might
prove useful is driving in queues. In this particular scenario the clutch is frequently
operated which raises the temperature of the clutch. This is one reason to why
ordinary cruise controllers do not function at low speeds. In order to better understand the requirements of a cruise controller in terms of clutch control performance
a review of the literature on the subject has been made.
Ordinary cruise control (CC) that makes a vehicle, called host vehicle, follow
a chosen set speed has been around for many decades. In later years more and
more automotive companies have started to introduce the more advanced adaptive
cruise control (ACC) [18]. This driver assisting application can apart from the
functionality of the ordinary cruise control also detect if an other slower vehicle,
called lead vehicle, appears in front of the host and then take action to keep an
appropriate inter-vehicle distance.
A basic approach when it comes to the control algorithm of an ACC is to use a cascaded controller structure of PID regulators with a feed-forward link on the inner
loop. This must also be coupled with some logic to decide when to switch between
operating in CC-mode to ACC-mode [19]. In [22] a exciting CC is expanded to
an ACC by adding the inter-vehicle distance control in form of a regulator that
utilizes fuzzy-logics.
8
According to [20] the different and over time changing driving habits of different
drivers can have a negative effect on the ACC controllers performance. It has been
proposed to address this by developing an adaptive controller that measures the
driving habits of the current driver during normal driving and then taking this
into account in the ACC controller [21].
9
Chapter 3
Modelling
This chapter covers the modelling work in the thesis. The model used is based
on existing models developed by several PhD students at Linköping University
in cooperation with Scania CV under the LINK-SIC research incubator program.
The original drivetrain model was developed in [4] which has been expanded with
more detailed clutch dynamics in [5]. The model is parametrized towards the
truck Ernfrid that previously has been used at Scania’s research facilities. A great
emphasize was put on making the model modular to facilitate its use in various applications such as the design of different clutch control strategies, driveline
damping and truck position control.
Figure 3.1: The figure shows an overview of the drivetrain components as well as
the modelled flexibilities.
In Figure 3.1 a schematic figure of the drivetrain is seen. The modelled flexibilities
are found in the clutch, propeller shaft and drive shafts and are represented as
spring/damper-systems.
11
3.1
Variable and subscript definitions
If not otherwise stated the following definitions and subscripts are used in the
thesis.
Variable
tq
x
x0
T
θ
ω = θ̇
θ̈
J
i
v
a
Meaning
Torque
Clutch piston position
Clutch piston zero position
Temperature
Angle
Angular speed
Angular acceleration
Inertia
Gear ratio
Longitudinal speed
Longitudinal acceleration
Table 3.1: Model variables
Subscript
ice
fw
c
gb
ps
fd
ds
b
h
d
w
i
amb
coolant
b2h
ice2b
d2b
h2amb
k
s
trans
Meaning
Engine
Flywheel
Clutch
Gear box
Propeller shaft
Final drive
Drive shafts
Clutch body
Clutch housing
Clutch disc
Wheels
Gear number
Ambient
Engine coolant
Body to clutch housing
Engine to clutch body
Clutch disc to clutch body
Clutch housing to ambient
Dynamic/Kinetic
Static
Transferred in the clutch
Table 3.2: Model subscripts
12
unit
[Nm]
[mm]
[mm]
[◦ C]
[rad]
[rad/s]
[rad/s2 ]
[kgm2 ]
[-]
[m/s]
[m/s2 ]
3.2
Engine
The engine model produces the engine torque which is given as a model input.
It is important to note that the engine model output torque is the net (brake)
torque.
3.3
Clutch
The clutch model consists of four separate parts that describes its torque transmissibility, temperature dynamics, lock-up/break-apart dynamics and torsional
behaviour.
3.3.1
Clutch overview
In Figure 3.2 an overview of the different components of the clutch can be seen.
Also the definition of the different clutch measurements and how they are related
to one and other are shown.
Figure 3.2: An overview of the clutch. The figure is taken from [24].
3.3.2
Clutch torque transmissibility
The clutch piston position x is translated to a dynamically transmittable torque
tqref using the third order polynomial in 3.1. The shape of the torque transmissi-
13
bility curve can be seen in Figure 3.3.
(
a(x − xisp )2 + b(x − xisp )3
tqref (x) =
0
, if x < xisp
, if x ≥ xisp
(3.1)
Where xisp is the kiss point, x the clutch piston position and a and b are estimated
curve-fit constants.
It should be noted that the clutch torque transmissibility curve depends heavily
on temperature. According to [5] a reference temperature of 60 ◦ C was used when
identifying the shape of the curve seen in Figure 3.3.
Figure 3.3: The clutch torque transmissibility curve identified at 60 ◦ C. It should
be noted that the clutch kiss point is at 11.5 mm.
3.3.3
Temperature Dynamics
When modelling the temperature effects on the torque transmissibility it has been
shown that there are three different temperatures that need to be modelled: The
clutch disc temperature Td , the clutch body (flywheel and pressure plate) temperature Tb and the clutch housing temperature Th . The equations that describes
the temperature states can be seen in 3.2, 3.3, 3.4 and 3.5.
(mcp )b T˙b = kice2b (Tcoolant − Tb ) + kb2h (Th − Tb ) + kd2b (Td − Tb )
14
(3.2)
(mcp )h T˙h = kb2h (Tb − Th ) + kh2amb (Tamb − Th )
(3.3)
(mcp )d T˙d = kd2b (Tb − Td ) + P
(3.4)
Where kx2y is heat transfer coefficients between parts x and parts y in the clutch.
P is the dissipated power that goes into the clutch and is calculated as.
P = tqtrans,k (wice − wc )
(3.5)
In Figure 3.4 the change in clutch temperatures during a simulated launch can be
seen. The clutch starts slipping at 9 seconds and closes at 12 seconds. It can be
seen that it is mostly the clutch disc that is affected during the slipping phase.
The clutch housing temperature on the other hand is hardly affected due to its
slow dynamics.
Figure 3.4: The figure shows the temperatures of the clutch during a simulated
launch where the clutch starts slipping at 9 seconds and closes at 12 seconds. It is
seen that it is primarily the temperature of the clutch disc that is affected during
the launch.
15
The clutch temperatures are used to calculate the thermal expansion of the clutch
using 3.6 where kexp,X are thermal expansion coefficients.
∆x0 = (kexp,1 + kexp,2 )(Tb − Tref ) + kexp,2 (Td − Tb )
(3.6)
The clutch piston position is then adjusted with regard to the thermal expansion
in 3.7.
xcor = x − ∆x0
(3.7)
The dynamically transmittable torque can now be calculated as,
tqtrans,k = tqref (xcor )
(3.8)
The way the model works is that an increase in the clutch temperatures gives a
larger xcor that results in an increase in tqtrans,k . If the ratio kµ between the static
friction coefficient over the kinetic friction coefficient is used the maximum static
transmittable torque can be calculated using 3.9
tqtrans,s = kµ tqtrans,k
3.3.4
(3.9)
Lock-Up/Break-Apart Logic
The clutch is operated in two different modes when driving, locked mode and
slipping/open mode. When the clutch is locked to the flywheel it constitutes a
one mass system with one degree of freedom. When the clutch is in slipping/open
mode it is represented as a two mass system with two degrees of freedom. This
means that the clutch torque can change if care is not taken in the control design
when the clutch goes from one state to another. This can be seen as a torque
dip in Figure 3.5 where the clutch lock up at roughly 9 seconds leads to driveline
oscillations.
The conditions for going from slipping/open to locked mode are:
θ̇ice = θ˙c
(3.10)
tqtrans,k ≤ tqtrans,s
(3.11)
The condition for going from locked to slipping/open mode is:
tqtrans,k > tqtrans,s
16
(3.12)
Figure 3.5: The figure shows the clutch torque during lock-up. It is seen that if the
slipping and static torque are not matched a torque dip with resulting driveline
oscillations occurs.
The equations for the clutch when in locked mode are:
tqice − tqc = (Je + Jfw + Jc )θ̈ice
(3.13)
θ̇c = θ̇ice
(3.14)
tqtrans =
tqice Jc + tqc (Je + Jfw )
Je + Jfw + Jc
(3.15)
The equations for the clutch when in slipping/open mode are:
tqtrans = sgn(θ̇ice − θ̇c )tqtrans,k
(3.16)
tqe − tqtrans,k = (Je + Jfw )θ̈ice
(3.17)
tqtrans − tqc = Jc θ̈c
(3.18)
17
3.3.5
Torsional Part
The clutch flexibility which mainly comes from the torsion springs in the clutch
disc is modelled as a torsional spring and damper in 3.19.
tqc = cc (θ̇c − θ̇gb ) + kc (θc − θgb )
(3.19)
Where cc and kc are damper and spring coefficients.
3.4
Gearbox
The gearbox is modelled using inertia, viscous friction and gear ratio. The model
does not contain any synchronisers and cannot engage neutral gear. Shifting will
therefore be instantaneous. The equations that describes the gearbox are:
tqgb = tqc igb,i
(3.20)
(Jgb,i + Jps ) = tqgb − bgb θ̇ps − tqps
(3.21)
θ̇gb = θ̇ps igb,i
(3.22)
Where bgb is a viscous friction coefficient.
3.5
Propeller Shaft
The flexibility in the propeller shaft is modelled the same way as the clutch torsional part. The equations are:
tqps = cps (θ̇ps − θ̇fd ) + kps (θps − θfd )
(3.23)
Where cps and kps are damper and spring coefficients.
3.6
Final Drive
The final drive is assumed to act symmetrically on the two drive shafts and is
modelled as an inertia and a fixed gear ratio.
(Jps i2fd + Jfd + Jds )θ̈ds = tqps ifd − bfd θ̇ds − tqds
(3.24)
θ̇fd = θ̇ds ifd
(3.25)
Where bfd is a viscous friction coefficient.
18
3.7
Drive Shafts
The two drive shafts contains the main flexibility of the driveline. Assuming a
symmetrical differential the drive shafts can be modelled the same way as the
propeller shaft and the clutch torsional part. The equation can be seen in 3.26.
tqds = cds (θ̇fd − θ̇w ) + kds (θfd − θw )
(3.26)
Where cds and kds are damper and spring coefficients.
3.8
Vehicle Dynamics
In this section the forces on the vehicle not coming from the driveline will be
explained together with the corresponding equations according to [5]. In this
thesis the tires are modelled without any dynamics as a radius together with an
inertia and a rolling resistance force.
The air drag is calculated as.
Fa = 0.5cd Af ρa v 2
(3.27)
Where cd is an aerodynamic constant, ρa is the air density and Af is the vehicle
cross-sectional area.
The road slope acts on the vehicle according to.
Fg = mg sin(α)
(3.28)
Where α is the road-slope angle.
The rolling resistance is calculated using.
Fr = f (v) ∗ (cr1 + cr2 |v|)mg
(3.29)
Where f (v) is a smoothing function used to improve the simulation performance
and cr1 and cr2 are rolling resistance coefficients.
Using Newtons second law an expression for the acceleration of the vehicle can
now be formulated as.
tqd
Jw + Jd
− sgn(v)(Fa + Fr + Fb ) − Fg = (m +
)a
2
rw
rw
(3.30)
Where Fb is the braking force
3.9
Implementation
The equations specified earlier in this chapter have been implemented in MATLAB/simulink using MATLAB function blocks. This makes the code easy to
19
read and also allows the code to be commented to help understanding. The lockup/break-apart logic is implemented using a state flow chart that switches between
the two operating modes of the clutch. Together with the fact that no signals are
on buses makes the model very intuitive to understand and to use. The model
is divided in several separate parts that each corresponds to a certain physical
component. This is shown in Figure 3.6 where the structure of the top layer of
the model can be seen.
Figure 3.6: The figure shows the top layer of the model structure. No signals are
sent on busses in order to make the model easy to understand.
20
Chapter 4
Clutch observer
In this thesis a model of how the clutch characteristics changes with temperature
has been implemented in a complete driveline model. It is desirable to use this
model to enhance the performance of clutch control in Scania’s trucks. Therefore
the observer described in [24] has been adapted for use in an on-line application.
The observer is of the extended kalman filter type (EKF).
4.1
Observer variable definitions
Variable
A/Ad
B/Bd
C/Cd
D/Dd
Gd
p
Ts
q
X
U
Ỹ
Y
w
v
Q
R
P
Ht
Ft
Gt
Meaning
Continuous/discrete state-space matrix
Continuous/discrete state-space matrix
Continuous/discrete state-space matrix
Continuous/discrete state-space matrix
Discrete state-space matrix
Differential operator
Sample time
Shift operator
State vector
Input vector
Intermediate output vector
Measurable output vector
Process noise
Measurement noise
Process noise covariance matrix
Measurement noise covariance matrix
Estimate error covariance matrix
Kalman matrix
Kalman matrix
Kalman matrix
Table 4.1: EKF variables
22
unit
[-]
[-]
[-]
[-]
[-]
[-]
[s]
[-]
[-]
[-]
[-]
[-]
[-]
[-]
[-]
[-]
[-]
[-]
[-]
[-]
4.2
Extended clutch model
It is desirable that the observer is insensitive to poorly chosen initial values and
also that it is able to adjust for the level of wear of the clutch. To do this a fourth
state is added to the existing clutch temperature model 3.2, 3.3 and 3.4 according
to 4.1. With this definition the fourth state holds information about the zero
position of the clutch piston at reference temperature.
ẋ0,ref = 0
(4.1)
It is important to note that the clutch zero position at reference temperature x0,ref
and the clutch zero position x0 are not the same. x0,ref is defined by.
x0,ref = x0 − ∆x0
(4.2)
Where x0 is the measured clutch position for a fully closed clutch and ∆x0 represents the heat expansion in the clutch.
The observer state vector is now defined as.
X = [Tb Th Td x0,ref ]T
(4.3)
The input vector is defined as.
U = [xp P Tcoolant Tambient ]T
(4.4)
Where xp is the measured clutch position.
The output of the system is given in the intermediate variable Ỹ according to 4.5.
Ỹ = [x0 xcor ]T = [y˜1 y˜2 ]T
(4.5)
Now the extended model together with 3.6, 3.7, 4.2, 3.8 and 3.1 can be written on
the form.
Ẋ = AX + BU
(4.6a)
Ỹ = CX + DU + [−1 1]T kexp,1 Tref
(4.6b)
Where A, B, C and D are defined as.
 kb2h +kice2h +kd2b
−
(mcp )b

kb2h

(mcp )h
A=
kd2b

(mc )
kb2h
(mcp )b
+kh2amb
− kb2h(mc
p )h
0
0
p d
0
23
kd2b
(mcp )b
0
kd2b
− (mc
p )d
0
0

0


0
0
(4.7)

0

0
B=
0
0
0
kiec2b
(mcp )b
0
0
0
0
1
(mcp )d
0
0

kh2amb 
(mcp )h 

0
0
(4.8)

kexp,1 − kexp,2 0 kexp,2
1
C=
−kexp,1 + kexp,2 0 −kexp,2 −1
0 0 0 0
D=
1 0 0 0
(4.9)
(4.10)
The measurable outputs of the system are.
Y = [x0 tqtrans,k ]T = [ỹ1 tqref (ỹ2 )]T
(4.11)
In 4.11 the measurement of x0 only exists when the clutch is fully closed and the
measurement of the clutch slipping torque tqtrans,k only when the clutch is slipping.
It should be noted that the term tqref (ỹ2 ) contains the non-linearity of the system
which is seen in 3.1.
24
4.3
Observability analysis
Before the observer is constructed the observability of the system must be analysed
in order to better understand how to design the observer as well as what limitations
are present. The analysis is made in [24] where the observability of the system is
thoroughly examined. The result is summarized below.
4.3.1
Operating modes
The clutch basically has four different operating modes; open, slipping, locked and
closed. As stated above there are two measured signals that can be used by the
observer. However these measurements are not available in some modes.
Open clutch
During open clutch the transmitted torque is zero and x0 can not be measured.
This means that the system is not observable in this mode.
Slipping clutch
The observability analysis in [24] states that it is only the temperature states that
are observable in this mode. However in this thesis a change to the observer was
made in 4.9 so that x0,ref enters Ỹ when the clutch is in slipping mode. Because
of this change all states are observable when the clutch is slipping.
Locked but not closed clutch
During locked but not fully closed clutch there is no measurable information about
the system which therefore is not observable.
Fully closed clutch
When the clutch is fully closed the zero position x0 is directly measurable and the
system is therefore observable.
4.3.2
Combined observability
Conveniently enough the most frequently visited modes are driving with a closed
clutch and slipping clutch. This means that the system as a whole is sufficiently
observable. When visiting an unobservable mode the EKF runs an open loop
simulation of the system and the uncertainty-matrix P grows which makes the
states converge faster when the system again becomes observable.
25
4.4
Choice of observer type
The temperature model used by the observer is not linear since it has a nonlinearity on the output, tqtrans,k . This means that a ordinary Kalman filter can not
be used for the estimation. Instead an extended Kalman filter is used that is able
to deal with the non-linearity. There are two main reasons to why the observer
type EKF is a good choice. Firstly it is well tested technology that is straight
forward in its implementation and also relatively intuitive and easy to interpret.
Secondly the EKF brings with it the possibility to adapt the estimation process
depending on the current operating mode of the clutch and what measurements
that are presently available.
4.5
Extended Kalman filter set up
In the following section a general description of how the extended Kalman filter
works is given.
4.5.1
Discretisation of the model
In order to be able to use the model described in Section 4.2 when constructing the
EKF for implementation in the GMS it is necessary to transfer it from continuous
form to discrete form. The simplest way to do this is to use a basic euler forward
method. Since using this method may lead to stability issues the discretisation
is instead performed using Tustin’s formula where the differential operator p is
defined as.
p=
2 (1 − q −1 )
Ts (1 + q −1 )
(4.12)
Where Ts is the system sample time and q is the shift operator defined by 4.13
with k = 0, 1, 2, ....
q −1 u(kT s) = u(kT s − T s)
(4.13)
After the discretisation is performed the model is described on state-space form
with the intermediate output variable Ỹt .
Xt+1 = Ad Xt + Bd Ut + Gd w = f (Xt )
Ỹt = Cd Xt + Dd Ut + v
(4.14a)
(4.14b)
Where w and v are gaussian process noises with zero mean and covariance matrices
Q and R respectively.
26
The measurable outputs are defined in 4.15. The non-linearity of the system is
included in the term tqref (ỹt2 ) which can be seen in 3.1.
Yt = [x0 tqtrans,k ]T = [ỹt1 tqref (ỹt2 )]T = h(Xt )
4.5.2
(4.15)
The filter
The idea the extended Kalman filter is based on is to update and the mean and
covariance of the estimates in a way that minimizes the covariance of the estimate
error. This process can be divided into two phases. During the measurement
update phase the estimate is adjusted using the current measurements. In the
time update phase the dynamics of the system are simulated in order to predict
the future behaviour of the system.
The variables used by the observer are defined as.
• P is the estimate error covariance matrix.
• The observation transition matrix Ht is defined by 4.16
Ht = (∇X h(X)|X=X̂
t|t−1
)T
(4.16)
Where h is defined by 4.15. It is important to note that Ht will change depending on the current operating mode of the clutch and what measurements
are available.
• The state transition matrix Ft is defined by 4.17
Ft = (∇X f (X, 0)|X=X̂ )T
t|t
(4.17)
Where f is defined by 4.14a.
• The process noise transition matrix Gt is defined by 4.18
Gt = (∇w f (X̂t|t , w)|w=0 )T
(4.18)
Where f is defined by 4.14a.
Measurement update phase
In this phase the available measurements in Yt and predicted estimate error covariance in Pt|t−1 is used to update the estimate X̂t|t using the following algorithm.
Kt = Pt|t−1 HtT (Ht Pt|t−1 HtT + Rt )−1
(4.19a)
Pt|t = (I − Kt Ht )Pt|t−1
(4.19b)
X̂t|t = X̂t|t−1 + Kt (Yt − h(X̂t|t−1 ))
(4.19c)
27
Time update phase
During the time update phase the system is simulated one sample ahead and the
estimate error covariance for the next iteration is also predicted. This is done by
performing the calculations described by 4.20a and 4.20b.
X̂t+1|t = f (X̂t|t )
Pt+1|t =
Ft Pt|t FtT
(4.20a)
+
Gt Qt GTt
(4.20b)
Initiation
The extended Kalman filter does not contain any information about the nominal
trajectory of the system at the start of each iteration. To deal with this the filter
takes the last known estimate and performs a linearisation to attain a trajectory.
This means that the filter must be initiated with values on P and X̂.
4.6
Selection of covariance matrices
The EKF covariance matrices has been chosen according to [5] where R is the
covariance matrix for the measurement noise and Q is the covariance matrix for
the process noise. Each element of the matrices is however multiplied by a factor
10 since they were identified at 10Hz and the observer used in this thesis runs at
100Hz. The values of R and Q are choosen as follows.
−1
10
0
R=
0
103
(4.21)
 0

10
0
0
0
 0 10−2 0
0 

Q=
0
 0
0
10
0 
0
0
0 10−7
(4.22)
It is worth noting that the in comparison small value of Q(4, 4) is due to the
fact that the fourth state x0,ref varies at a extremely slow rate compared to the
temperature states.
28
4.7
Initiation and limitation of the uncertainty matrix
As stated earlier when one or more states are not observable the corresponding
elements of the uncertainty matrix P grows. An example of this is that P (4, 4)
grows when the clutch is open which means that the fourth state x0,ref is not
observable. This could potentially cause numerical problems if the clutch stays
in an unobservable mode for a prolonged time, for instance standing still with an
open clutch.
4.7.1
Uncertainty of the temperature states
When further analysing the growth of the P -matrix for unobservable states it
is realised that the uncertainty related to states one to three (Tb , Th , Td ) will
not grow indefinitely but will rather converge to a certain value since they have
stable dynamics. These values can be found by calculating the static kalman
observer P -matrix or by simply running a simulation where the clutch is kept in
an unobservable mode. Since the normal starting mode of an HDT is standing
still with an open clutch it is intuitive to initiate the elements corresponding to
states one to three of the P -matrix with their static open clutch values which are
seen in 4.23. In Figure 4.1 the convergence of the uncertainty for states one to
three can be seen.
Figure 4.1: The figure shows the covariance of states on to three when the clutch
is kept open for 10000 seconds. The values can be compared to the computed
values in 4.23.
29
4.7.2
Uncertainty of the zero position state
The uncertainty corresponding to the fourth state x0,ref however does not converge
to a certain value when in an unobservable mode but will grow towards infinity
if not limited. This behaviour can be seen in Figure 4.2. According to [23] it
is the elements in the diagonal of P that decides the behaviour of the observer.
Therefore the off diagonal elements related to x0,ref are not limited and only a
limit on P (4, 4) is set.
Figure 4.2: The figure shows the covariance of the fourth state when the clutch
is kept open for 10000 seconds. It should be noted that the scale on the y-axis is
too large to represent the small values P (4, 4) continuously grows with.
To decide what initial value to use for the uncertainty of the fourth state a simulation of a launch is run to identify the level that P (4, 4) converges to when
x0,ref is observable. In Figure 4.3 it can be seen that the uncertainty in P (4, 4)
converges to a value of roughly 0.001 when the clutch is in an observable mode. It
should be noted that clutch starts slipping at 9 seconds, locks-up at 12 seconds and
then stays locked in the simulated driving scenario. The initial value of P (4, 4) is
then set to roughly 10 times the value it converges to when x0,ref is observable.
This is to ensure that the observation of x0,ref converges quickly when the state is
observable.
30
Figure 4.3: The change in the estimate-error covariance matrix for position (4,4)
for a simulated launch. Clutch lock-up occurs at roughly 12 seconds
4.7.3
Initial uncertainty matrix
This combined gives a initial P-matrix as follow.


2.452
0
0
0
 0
0.753
0
0 

P0 = 
 0
0
2.452
0 
0
0
0
10−2
31
(4.23)
Chapter 5
Clutch controller
The clutch controller works by taking the requested torque and translating this
to a corresponding clutch piston position through a look-up table. The requested
position is then adjusted with regard to clutch temperature. According to [5]
this is a natural choice since torque based driveline control is common in the
automotive industry. In the simulation environment it is also possible to add a
feedback-link from the engine torque if wanted. In Figure 5.1 the structure of the
clutch controller unit can be seen.
Figure 5.1: The figure shows the structure of the clutch controller unit. It should
be noted that the inputs to the clutch temperature and wear observer are not
included in the figure.
5.1
Fixed trajectory look-up table
The first part of the clutch controller consists of a look-up table that is used as a
feedforward-link from desired torque to clutch piston position. The look-up table
is basically an inversion of the torque transmissibility curve at 60◦ C which can be
seen in Figure 3.3.
33
5.2
Temperature compensation
According to [9] it is not only the lifetime of the clutch that is greatly affected
by operating at high temperatures but also its ability to transfer torque. This
in turn has a significant effect on the clutch control quality. A common way of
dealing with this is to implement an static adaptation that adapts the clutch kiss
point every time the clutch is engaged. This is however not optimal since with
this methodology the clutch controller only receives information about the past
and not the present.
In this thesis the observer described in Chapter 4 that estimates both the wear and
the temperature of the clutch is used instead. It is then possible to continuously
adjust the desired clutch piston position for temperature and wear.
5.3
Engine torque feedback
Besides the fixed trajectory control look-up table and the temperature compensation a feedback controller is also constructed that drives the clutch torque to
converge towards the desired level. This controller is only implemented in the
simulation environment as a PI-controller that acts on the difference between the
requested torque and the measured engine torque.
5.4
Validation
To validate the clutch controller a launch scenario has been simulated. In order
to test the temperature compensation of the clutch the torque request during the
launch was specified in a way that makes the clutch stay in the slipping mode
for about 7 seconds. Both launches with and without feedback control has been
simulated.
In the top plot of Figure 5.2 the clutch stroke during a launch when the clutch
controller consists of a fixed trajectory look-up table with temperature compensation can be seen. The torque request profile as well as the actual clutch torque
during the launch can be seen in the left plot in Figure 5.3. It should be noted
that the clutch starts slipping at 1.6 seconds and closes at 8.8 seconds. In the
bottom plot the clutch stroke during the slipping phase is shown. It can be seen
that the temperature compensation adjusts the clutch stroke as the clutch heats
up when it is slipping.
In the left plot in Figure 5.3 the clutch torque can be seen when there is no feedback
link used in the controller. It is seen that during the slipping phase between 1.6
and 8.8 seconds this results in a static error in the clutch torque compared to the
requested torque. In the right plot where the feedback link was used it can be
seen that there is no error in the clutch torque. It should be noted that the torque
dip at 8.8 seconds when the clutch closes occurs since the clutch controller does
not include matching of the dynamic and static clutch torque.
34
Figure 5.2: The upper plot shows the clutch stroke during a launch where the
clutch controller consists of a fixed trajectory look-up table and temperature compensation. The bottom plot shows the clutch stroke during only the slipping
phase of the launch where it is seen that the temperature compensation adjusts
the clutch piston position as the clutch heats up.
Figure 5.3: The left plot shows the clutch torque when no feedback from the engine
torque was used. In the right plot feedback was used. It is seen that the feedback
link removes the static torque error when the clutch is slipping.
35
Chapter 6
Implementation on GMS
When taking the clutch temperature observer and controller from the simulation
environment in MATLAB/Simulink and implementing them in the gearbox management unit there are a number of modifications that are required to be done
first. This is due to the fact that the GMS has very limited storage capacity
compared to a normal computer and the fact that it operates using different data
types. Also noise and uncertainty in the used signals needs to be considered and
dealt with. It should be noted that there is no feedback-link in the controller that
was implemented on the GMS. This is to make it easy to distinguish the effect the
temperature compensation has on the clutch control.
6.1
Specify data types
When programming in MATLAB and running simulations off-line in Simulink
there is often no need to pay attention to what data types that are used. By
default MATLAB will specify variables using the double precision floating-point
data format. Double precision means that each variable uses 64 bits to represent
its value.
When programming for on-line use of the temperature observer in the gearbox
management unit it is instead the 32 bit single precision floating-point data type
that is commonly used. This is done since the GMS has a very limited data storage
capacity and processing power.
Some signals that are used by the observer or sent as control signals are specified
as 16 bit integer values, int16. The 16 bit integer data type is able to write
all integers between -32,767 and +32,767. In order to obtain the desired level of
precision signals that are represented as int16 are often scaled. An example of this
the clutch motor position which ranges from 0 mm to 22 mm. Without scaling
this signal it would only be possible to request positions with steps of 1 mm. By
scaling the signal with a factor 1000 the range instead becomes [0.000 22000] with
a step size of 0.001 mm.
37
6.2
Transformation the clutch torque transmissibility
curve
When implementing the clutch torque transmissibility curve in a look-up table in
MATLAB/Simulink the curve must be monotonically increasing. As can be seen in
Figure 3.3 that is not the case if clutch position x goes from zero to the kiss point.
One way to ”trick” MATLAB to get around this is letting the clutch position x
go from the kiss point to zero. This works when the clutch torque transmissibility
curve defined by 3.1 is used in the model. When implementing the observer in the
GMS it is desirable to also be able to take a certain clutch position and calculate
the corresponding torque level, which is then used by the engine management
system (EMS). This means that the clutch torque transmissibility curve needs to
be invertible. One realises that the ”trick” used earlier will not work since the
inversion of the curve will not be monotonically increasing.
With the convention used when identifying the clutch torque transmissibility curve
the clutch operates in the range [0 mm, 22 mm] which translates to [Closed, Open].
A more intuitive way to describe the clutch range is [0, 1] = [Open, Closed].
This combined means that the clutch torque transmissibility should be transformed according to Figure 6.1. It should be noted that the original torque transmissibility curve that is in the range [Closed, KissPoint] has been extended to
[Closed, Open] before being transformed.
Figure 6.1: The figure shows a schematic overview of how the shape of the torque
transmissibility curve and how it is transformed. The range of the curve has also
been extended to [Closed, Open] instead of [Closed, KissPoint].
38
To transform coordinates from the range [0 mm, 22 mm]=[Closed, Open] to [0,
1]=[Open, Closed] the linear function shown in 6.1 is used.
y = kx + m = g(x)
(6.1)
The constants k and m are calculated using the conditions in 6.2a and 6.2b.
A2 = g(A1)
(6.2a)
B2 = g(B1)
(6.2b)
Where the definition of A1, A2, B1 and B2 can be seen in Figure 6.1.
In the top plot of Figure 6.2 the transformed clutch torque transmissibility curve
for the full clutch range [Closed, Open] can be seen. In the bottom plot the
inverted curve is seen.
Figure 6.2: In the top figure the transformed clutch torque transmissibility curve
for the full clutch range is seen. The bottom figure shows the inversion of the top
graph.
39
6.3
Data type precision issues
As stated before it is mostly the 36 bit single precision data type that is used by
the observer when run on the GMS. In the single data format 1 bit is allocated
as a sign bit and 12 bits as exponential bits. The last 23 bits are allocated as
precision bits which permits the use of 7 decimals after the first non-zero value of
a certain number. The following variable is used to denote the maximum single
precision.
precision, single = 10−7
(6.3)
This causes problems in the time-update phase of the observer for the fourth state
x0,ref when the next value of the estimate-error covariance matrix P is calculated.
Due to the the definition (zero-elements) of Ft and Gt it is only position (4, 4) of
P that is problematic to update.
The problem can be exemplified by looking at the first time update of the P -matrix
according to 4.20b. As seen in 4.23 the initial value of P (4, 4) is P0 (4, 4) = 10−2 .
With the definition of Ft and Gt the first time-update of P is evaluated as.
P1|0 (4, 4) = Ft (4, 4)P0 (4, 4)Ft (4, 4)T + Gt (4, 4)Qt (4, 4)Gt (4, 4)T )
−2
= 1 ∗ 10
∗ 1 + 10
−2
−7
∗ 10
−2
∗ 10
−2
= 10
+ 10
−11
(6.4a)
(6.4b)
In 6.4b there is a factor 10−9 between the two numbers that are added to attain
P1|0 (4, 4). This is a bigger difference than the maximum possible difference defined
in 6.3. Hence the term 10−11 will be equal to zero when added to 10−2 .
In order to remedy this a help variable S is introduced to which the second term of
4.20b is summed until S has grown to a point that it is possible to add to P (4, 4).
The algorithm to perform this is described by equations 6.5 - 6.7.
St+1 = St + Gt (4, 4)Qt (4, 4)Gt (4, 4)T
(6.5)
if |S| > P (4, 4) × precision, single
Pt+1|t (4, 4) = Ft (4, 4)Pt (4, 4)Ft (4, 4)T + S
S=0
(6.6a)
(6.6b)
else
Pt+1|t (4, 4) = Ft (4, 4)Pt (4, 4)Ft (4, 4)T
(6.7)
end
Where P (4, 4) is the current value of the covariance exclusively related to x0,ref .
40
6.4
Biased measurements
When the clutch is open the clutch disc does not touch the flywheel. Therefore
there can be no friction work and no heat can be dissipated into the clutch.
However the dissipated power is not measured directly but calculated according
to 3.5 as a function of the measured slip speed and measured engine torque.
This can cause severe problems for the observer if there is a bias in the engine
torque measurement that tells the observer that there is heat flow into the clutch
although it is open. The observer will then try to adapt its states in order to
explain the dissipated power. In 6.3 it is seen how the estimates of the clutch
temperatures are adapted to explain a bias in the measured torque when the
clutch is open.
Figure 6.3: The figure shows how the estimates of the clutch temperature changes
when there is a bias of 2 % of the max torque when the truck is standing still with
a open clutch.
There are many ways to take care of this. One method is to simply set the engine
torque to zero when under a certain threshold. In this thesis the dissipated power
is instead set to zero when the clutch is open. In this way the difficulties with
choosing a proper threshold relative the noise level of the torque signal is avoided.
41
6.5
Requesting clutch position
When the observer and clutch controller is implemented in the simulation environment the control signal to the clutch acts directly on the position of the clutch
piston xp . In reality though the control signal goes to an electric clutch motor
that actuates to a clutch motor position that through a motor (master) piston,
xm , pushes on some hydraulic fluid that moves the clutch piston (slave), xp . An
overview of the relations of the clutch motor and clutch piston can be seen in
Figure 6.4.
Figure 6.4: The figure shows the clutch positioning system where the measured
signals are xm and xp .
6.5.1
Relating the clutch piston position to motor position
The torque transmissibility curve, seen in Figure 3.3 is identified for the clutch
piston position x. Therefore the control signal from the clutch controller must
also request a position on the clutch piston. However it is the clutch motor that
actuates the system. Hence a way to translate a desired clutch piston position to
a desired motor position xm,req must be found.
The requested clutch piston position at reference temperature is denoted xreq,ref
and is given as a function of the inverted torque transmissibility (from torque to
position).
Compensating xreq,ref for the current clutch temperature gives.
xreq = xreq,ref + ∆x0
Where ∆x0 is the thermal expansion of the clutch.
42
(6.8)
Adding the zero position gives.
xp,req = xreq + x0,ref
(6.9)
Where x0,ref is taken from the observer in order to account for the wear of the
clutch.
Considering that the change in piston position should be equal to the change in
motor position gives.
xp,req − xp = xm,req − xm
(6.10)
Using equations 6.8, 6.9 and 6.10 the requested clutch motor position xm,req can
now be calculated according to 6.11.
xm,req = xreq,ref + (∆x0 + x0,ref ) + (xm − xp )
(6.11)
The brackets on the right side of 6.11 are there to emphasize that xm,req is a
function of xreq,ref plus temperature and wear compensation (first bracket) and
the measured distance between the motor and the piston (second bracket).
6.5.2
The distance between the clutch motor and piston
When calculating xm,req the measurement term xm − xp is not constant and needs
to be measured. To do this directly is however problematic. This is basically
due to physical reasons and also the difference in performance of the two sensors
involved
Physical reasons
The distance between the clutch motor and piston changes with temperature.
This is since the hydraulic fluid expands somewhat with increasing temperature
together with the fact that the volume of the hydraulic piping increases as well.
An other aspect is that the clutch motor piston passes the bleeding hole (opening
to the hydraulic fluid reservoir) with different characteristics from time to time.
This is partly remedied by making sure that the bleeding hole is passed at the
same speed every time.
Measurement issues
The two sensors that measure the clutch motor position xm and clutch piston
position xp respectively are not the same type of sensors. The one measuring motor
position has higher resolution and faster dynamics than the sensor measuring the
piston position. This causes problems during transients in xm − xp which can be
seen as large dips in Figure 6.5.
43
Solution
Due to the reasons discussed earlier it is not a good idea to simply use xm − xp at
all times. Instead the distance between motor and piston position is only updated
when there are no large transients in clutch position. This can be seen as the
areas circled in red in 6.5.
Figure 6.5: The figure shows the clutch motor position xm minus the clutch piston
position xp . The areas circled in red are the areas in between transients which are
used to update xm − xp .
6.6
Avoid division by zero
When running simulations off-line an accidental division by zero will only have
the effect that the simulation breaks down. In an on-line application however the
consequences may be more sever. Either the GMS resets or the the variable in
which division by zero occurred is set to ”NaN”. Therefore it is essential that the
code is written in a way that the possibility of division by zero is removed.
When running the EKF it is the update of Kt according to 4.19a during the measurement update phase that division by zero might occur. Specifically it is the
calculation of matrix inversions that may cause problems. This is remedied by
looking at the determinant of an matrix before deciding to calculate its inverse.
The algorithm used is seen below.
44
if det(Ht Pt|t−1 HtT + Rt ) > 10 ∗ eps
Kt = Pt|t−1 HtT (Ht Pt|t−1 HtT + Rt )−1
(6.12)
Kt = Kt−1
(6.13)
else
end
Where eps is the smallest number that the GMS is able to represent.
6.6.1
EKF Update method
The way the extended Kalman filter is described in Section 4.5.2 gives a very
straightforward implementation. It is important to note that there are other implementation methods that are more stable. One such method is the more complex
”array implementation” which propagates the square root of the covariance matrix. In this thesis however the standard implementation was used since there is
a limited amount of RAM as well as processing power available in the GMS.
45
Chapter 7
Results
In this chapter the main results of the the thesis are presented. The validity and
output of the driveline model is discussed together with the performance of the
clutch temperature and wear observer. Also how the observer runs on the gearbox
management system is presented.
7.1
Complete driveline model with clutch temperature dynamics
A complete driveline model from engine to the wheels has been implemented. In
this section the validity and performance of the model is presented.
The discussion of the model validity in this section is based on [24] and [25]. The
clutch model has been validated towards several separate data sets different from
those used for parameter identification.
7.1.1
Model residuals
The residuals between the measured clutch torque and the modelled clutch torque
that are seen in Figure 7.1 are never larger than 200 Nm. Most of the time the
residuals are well below 100 Nm which corresponds to 3 % of the maximum engine
torque with a mean relative error of 0.3 %. In the top plot in Figure 7.2 it can be
seen how the modelled clutch torque (dotted purple) with the dissipated power
calculated and not measured follows the actual measured clutch torque (dotted
green).
Further conclusions are that the model is able to capture both the amplitude and
frequency of the driveline torque oscillations during launch and that the lockup/break-apart logic performs the mode-switches at the proper time. The model
does not however capture the torque oscillations that arises when the requested
torque goes from positive to negative. This is due to the fact that the model does
not contain any backlash dynamics for when the torque switches sign.
47
120
100
80
Residuals [Nm]
60
40
20
0
−20
−40
−60
−80
−100
150
200
250
300
350
1200 1250 1300 1350
Time [s]
Clutch Torque [Nm]
Figure 7.1: The figure shows the residuals between the measured clutch output
torque and the modelled clutch output torque. The figure is taken from [24]
600
400
Measurement
Static Model
P Measured
P Modeled
200
0
150
200
250
300
350
1150
1200
1250
1300
1350
1300
1350
600
Temperature [C]
160
400
140
Body
Housing
Disc
engine
120
100
200
0
80
60
150
200
250
300
350
1150
Time [s]
1200
1250
Figure 7.2: The top figure shows the measured clutch output torque (dotted
green). Both when measuring (dashed black) and calculating (dotted purple) the
dissipated power a much better result is attained compared to the static model
(red) that does not include any temperature dynamics. The bottom plot shows
the temperatures of the engine and clutch. The figure is taken from [24]
48
7.1.2
Correcting for the torque drift
When using the model described in Section 3.3.3 to explain the torque drift with
increasing clutch temperature and to correct the clutch torque the graphs in Figure
7.3 are attained. It can be seen that the clutch temperature model is able to quiet
well explain the torque drift due to temperature increase. The clutch torque when
not corrected for temperature can be seen in Figure 1.2.
1500
80
Clutch Torque [Nm]
60
1000
40
20
500
0
4
Time [s]
5
6
7
8
9
10
Double Exp. Corrected Pos. [mm]
11
12
Figure 7.3: The figure shows the clutch torque which has been corrected for the
clutch temperature when the clutch position is ramped back and forth. The figure
is taken from [24]
7.2
Clutch temperature and zero-position observer
The aim of the observer is to estimate the current true zero position of the clutch.
This position is dependant on two parameters. The most dominant parameter is
the clutch heat expansion. The second parameter is the clutch wear which changes
very slowly over time.
7.2.1
Convergence of the zero position
In order to test the convergence of the estimated zero position the initial temperatures of the observer has been set 10 ◦ C lower than the initial temperatures of
49
the clutch model when simulating a launch. Also the initial value of the clutch
wear has been set 0.65 mm lower than the value used in the model.
As can be seen in Figure 7.4 the estimated zero position x0 that includes both the
wear and heat expansion terms converge even though both the temperature and
wear states of the observer are given poor initial values.
Figure 7.4: The figure shows the convergence of the estimated zero position x0
compared to the modelled zero position. The temperature states was initiated 10
◦ C lower in the observer compared to the model. The reference zero position x
0,ref
was initiated 0.65 mm to short.
7.2.2
Convergence of individual states
As was seen in Figure 7.4 the zero position x0 estimate converges well with the
modelled zero position when all states were given bad initial values in the observer.
However when the different states are studied separately it is seen that the observer
is not able to distinguish the wear effect from the effect from heat expansion in
x0 . In the top plot of Figure 7.5 the clutch disc temperature can be seen, in
the middle plot the clutch body temperature and in the bottom plot the clutch
housing temperature. In Figure 7.6 the estimation of the zero position at reference
temperature can be seen.
50
Figure 7.5: The figure shows from top to bottom the modelled and estimated
clutch disc, body and housing temperatures during a simulation. The temperature
states was initiated 10 ◦ C lower in the observer compared to the model. The
reference zero position x0,ref was initiated 0.65 mm to short.
51
Figure 7.6: The figure shows the estimated zero position at reference temperature x0,ref compared to the modelled zero position. The temperature states was
initiated 10 ◦ C lower in the observer compared to the model. The reference zero
position x0,ref was initiated 0.65 mm to short.
7.3
Temperature compensation in the clutch controller
The developed observer is able to keep track of the temperatures of the clutch
and the clutch heat expansion. This is then used by the controller to adjust the
desired clutch piston position. In this section it is shown how using temperature
compensation can improve clutch control and the effect it has on the performance
of a HDT.
7.3.1
Effect on launch quality
To exemplify the effect of temperature compensation the following driving scenario
has been studied. A HDT with a slightly warm clutch launches from standstill.
The clutch temperatures were initiated using [tb , th , td ] = [100, 90, 100]◦ C. The
clutch controller consists of an inversion of the clutch torque transmissibility curve
with and without temperature compensation. To evaluate the launch quality the
vehicle jerk is calculated and compared for the different cases.
In Figure 7.7 the vehicle jerk can be seen in the upper plot when temperature
compensation is used by the clutch controller. When looking at Figure 7.8 it is
seen that the vehicle jerk is about 90% higher when no temperature compensation
is used. It should be noted that the same torque request was used for both cases.
52
Figure 7.7: The figure shows the vehicle jerk in the upper plot as a measure of
launch quality (comfort) when temperature compensation is used by the clutch
controller. The bottom plot shows the engine and clutch speeds.
Figure 7.8: The figure shows the vehicle jerk in the upper plot as a measure of
launch quality (comfort) when no temperature compensation is used by the clutch
controller. The bottom plot shows the engine and clutch speeds.
53
7.3.2
Effect on produced engine torque
Whether clutch temperature compensation is used or not has a profound effect on
the produced engine torque. In Figure 7.9 it can be seen how the produced engine
torque relates to the requested torque during a simulated launch with a slightly hot
clutch. The clutch temperatures was initiated with [tb , th , td ] = [100, 90, 100]◦ C.
In the top figure where temperature compensation is used in the clutch controller
the engine produces the requested torque (graphs overlap). However when looking
at the lower plot where no temperature compensation was used the engine torque
drifts as the clutch temperature increase. When no temperature compensation
is used the maximum torque error is 300 Nm or 107% of the requested torque
right before lock up. As a consequence of this a lot of heat is dissipated in the
clutch unnecessarily. This affects both the lifetime of the clutch as well as the fuel
consumption of the vehicle negatively.
Figure 7.9: The upper plot shows the requested and actual engine torque, which
overlaps, when the clutch controller uses temperature compensation. In the lower
plot no temperature compensation was used.
54
7.4
Observer implemented on GMS
The clutch temperature and wear observer together with all the changes specified
in Chapter 6 has been implemented on a GMS and successfully connected to
Vision which is a program used by Scania for monitoring signals in the gearbox
management system.
In Figure 7.10 it can be seen how the observer and clutch controller has been
implemented in the GMS. The observer/controller block has been put as a separate unit high up in the controller structure. The block ct2p lvpc in the figure
contains the observer and is continuously evaluated. The stateflow chart to the
right contains a function called ”clutchTorqueToPosition”. This function uses the
inverted clutch torque transmissibility curve to transform a requested torque to a
corresponding clutch position which is then compensated for temperature.
The function ”clutchTorqueToPosition” is only run when called upon and can be
called from anywhere in the GMS using a stateflow chart as a function caller.
Figure 7.10: The figure shows how the observer is implemented in the GMS. The
block ct2p lvpc to the left contains the observer and the stateflow chart to the
right is an inversion of the torque transmissibility curve.
55
Chapter 8
Conclusions and future work
This chapter presents the main contributions and conclusions of this thesis together with recommendations on future work on the subject.
8.1
Conclusions
The main contributions of this thesis is the implementation of a clutch temperature
and wear observer in the gearbox management system of a HDT. Also a complete
drivetrain model that is able to simulate the dynamics of a heavy duty truck has
been implemented in MATLAB/Simulink.
8.1.1
Complete drivetrain model
The drivetrain model used in this thesis has flexibilities in the clutch, propeller
shaft and drive shafts in order to capture the dynamics of a real heavy duty truck.
The model has a modular structure that is easy to understand and facilitates its
use in various applications.
The clutch model apart from the flexibility also includes temperature dynamics.
This is essential when simulating driving scenarios where the clutch is frequently
operated in a slipping mode in order to get good results.
8.1.2
Clutch observer on GMS
The main contribution above others in the thesis is the adaptation of a clutch
temperature and wear observer for use in an on-line application on the gearbox
management system of a truck. In a simulation environment the observer has
been shown to be able to track the zero position of the clutch even when given
bad initial estimates. The different adjustments that needed to be done to the
observer can be seen in the list below.
• Specification of data types.
57
• Transforming the clutch torque transmissibility curve.
• Resolve data type precision issues.
• Consider effects of biased measurements.
• Compensating for the dynamics between the position of the clutch motor
and piston.
• Removing the possibility of division by zero.
• Choosing an update method that saves performance on the GMS.
8.2
Future work
In this section suggestions on future work and possible improvements to both the
model and observer are given.
8.2.1
Tire dynamics
In the model used in this thesis the dynamics of the tires are neglected and no
slipping condition is assumed. To improve the performance of the model tire
dynamics could be added according to [7]. This should be especially interesting if
simulating high speed driving scenarios since the tire dynamics are temperature
dependant.
8.2.2
Backlash dynamics
In reality when the engine torque switches sign there is some backlash since there
is a distance between the cogs that must be closed before torque can be transferred
again. This is something that may be interesting to look at in the future. In Figure
8.1 an explaining figure of the backlash phenomena can be seen.
Figure 8.1: The figure shows the cause to the backlash phenomenon. When the
engine torque switches sign the gears must cover the distance marked by red arrows
before torque can be transferred again.
58
8.2.3
Adding the clutch motor
In the implemented drivetrain model the clutch piston position is directly controlled. The piston position is also the only measured position on the clutch. In
reality however it is the clutch motor position that is controlled and there are two
measurements available, motor and piston position. This can be confusing and in
some cases a reason to making errors when simulating different clutch controllers.
Therefore it is a good idea to try to incorporate the clutch motor in the model.
8.2.4
Implementing new engine model
The driveline model is constructed in a modular way. One reason to this was to
prepare for the implementation of a more advanced engine model developed in
[26]. In order for the two models to work together they must both run on the
same type of solver. From Scania there was a wish to use a discrete solver to make
the combined model able to run together with the management units of a real
truck, for example the GMS. This however caused problems with the model when
evaluating the lock-up/break-apart logic in the clutch. These problems have not
been solved and are left as future work.
59
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Linköping University Electronic Press
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