SIMULATION, ESTIMATION, AND EXPERIMENTATION OF VEHICLE
LONGITUDINAL DYNAMICS THAT EFFECT FUEL ECONOMY
Except where reference is made to work of others, the work described in this thesis is my
own or was done in collaboration with my advisory committee. This thesis does not
include proprietary or classified information
Matthew Evan Heffernan
Certificate of Approval:
George T. Flowers
Professor
Mechanical Engineering
David M. Bevly, Chair
Assistant Professor
Mechanical Engineering
Thomas E. Burch
Visiting Assistant Professor
Mechanical Engineering
Stephen L. McFarland
Dean
Graduate School
SIMULATION, ESTIMATION, AND EXPERIMENTATION OF VEHICLE
LONGITUDINAL DYNAMICS THAT EFFECT FUEL ECONOMY
Matthew Evan Heffernan
A Thesis
Submitted to
the Graduate Faculty of
Auburn University
in Partial Fulfillment of the
Requirements for the
Degree of
Masters of Science
Auburn, Alabama
August 7, 2006
iii
SIMULATION, ESTIMATION, AND EXPERIMENTATION OF VEHICLE
LONGITUDINAL DYNAMICS THAT EFFECT FUEL ECONOMY
Matthew Evan Heffernan
Permission is granted to Auburn University to make copies of this thesis at
its discretion, upon the request of individuals or institutions and
at their expense. The author reserves all publication rights.
Signature of the Author
Date of Graduation
iv
THESIS ABSTRACT
SIMULATION, ESTIMATION, AND EXPERIMENTATION OF VEHICLE
LONGITUDINAL DYNAMICS THAT EFFECT FUEL ECONOMY
Matthew Evan Heffernan
Master of Science, August 7, 2006
(B.M.E., Auburn University, 2003)
144 Typed Pages
Directed by David M. Bevly
In this thesis, longitudinal vehicle dynamics are researched with an emphasis on
heavy trucks and fuel economy. Commercial vehicles display large variations in their
parameters, and due to many current trends in transportation systems, estimating these
parameters has been the subject of much research. Additionally, fuel economy
enhancement has become a major issue due to man-kind?s reliance on oil. In this research
a longitudinal truck model is developed and the longitudinal dynamics are simulated in
various conditions. Algorithms are developed to estimate vehicle parameters and are used
in simulation to perform an analysis of their accuracy. Simulated results show the
difficulty of estimating individual vehicle parameters in the presence of sensor noise and
low levels of vehicle excitation, such as with the heavy trucks at the Auburn University
National Center for Asphalt Technology facility. Finally, a class 8 commercial vehicle is
instrumented as a test-bed. Estimation results from the test bed support the simulation,
v
while simple parameters are shown to be identified with reasonable accuracy. Road load
data for fuel economy evaluation was also collected on the trucks and variations over the
asphalt sections are shown.
vi
ACKNOWLEDGEMENTS
I would like to thank the National Center for Asphalt Technology for allowing me
this research opportunity. Special thanks go to Buzz Powell, the NCAT test track
manager, who has always been helpful and gone the extra mile for me. I?d also like to
thank Dr. Ray Brown, the NCAT director, and Ronald and Margaret Kenyon for
providing the support for this research.
Special thanks to my faulty advisor Dr. David Bevly for guiding me through this
process and I thank you for the opportunity to further my education. Thanks to Dr. Tom
Burch and Dr. George Flowers for serving on my advisory committee.
To all the folks in the GPS and Vehicle Dynamics Lab, thank you for the
technical expertise, advice, and laughter. Special thanks to Rob Daily who has answered
a ton of questions and given me a lot of help and knowledge in my years here.
I?d also like to thank Dr. Larry Benefield, Dean of Engineering, for such strong
support of the engineering programs at Auburn University. Your efforts have enriched
my education and experience at Auburn University.
Without love and support, my college career would not have been possible. I
would like to thank my mother and father, Vickie and Alan Heffernan, and my entire
family for constantly encouraging me. I love you all and dedicate this to you?
vii
Style of Journal Used:
ASME Journal of Dynamic Systems, Measurement, and Control
Computer Software Used:
Microsoft Word 2003
viii
TABLE OF CONTENTS
LIST OF FIGURES....................................................................................................... xi
LIST OF TABLES........................................................................................................ xiv
1. INTRODUCTION
1.1 Motivation.................................................................................................. 1
1.2 Back Ground and Literature Review......................................................... 3
1.3 Purpose of Thesis and Contribution........................................................... 6
1.4 Outline of Thesis........................................................................................ 6
2. MODELING
2.1 Introduction................................................................................................ 8
2.2 Longitudinal Model................................................................................... 8
2.3 Loss Components....................................................................................... 10
2.3.1 Air Drag......................................................................................... 11
2.3.2 Road Grade.................................................................................... 13
2.3.3 Rolling Resistance......................................................................... 14
2.4 Turning Losses........................................................................................... 18
2.5 Fuel Economy Effects................................................................................ 21
2.6 Truck Simulations...................................................................................... 23
2.7 Conclusions................................................................................................ 28
3. ADVANCED MODELING
3.1 Introduction................................................................................................. 30
ix
3.2 Advanced Longitudinal Model................................................................... 30
3.3 Simulations of Vehicle Models, Simple and Complex............................... 33
3.3.1 Acceleration Simulations............................................................... 33
3.3.2 Deceleration Simulations............................................................... 35
3.3.3 NCAT Track Simulations.............................................................. 37
3.3.4 Model Validation........................................................................... 39
3.3.5 Model Variations........................................................................... 41
3.4 Noisy Sensor Models and Vehicle Simulations.......................................... 43
3.5 Modeling Conclusions................................................................................ 52
4. INDENTIFCATION IN SIMULATION
4.1 Introduction................................................................................................ 54
4.2 Identification Background.......................................................................... 54
4.3 Estimation Modeling.................................................................................. 58
4.4 Mass and Loss Estimation In Simulation................................................... 61
4.3.1 Simulations and Data Treatment.................................................... 61
4.3.2 Investigating Sensor Noise In Estimations.................................... 65
4.5 Conclusions................................................................................................ 72
5. IDENTIFICATION ON TRACK
5.1 Introduction................................................................................................ 74
5.2 NCAT Facility............................................................................................ 74
5.3 Road Grade Estimation.............................................................................. 76
5.4 Kalman Filter Background......................................................................... 78
5.5 Drive Force Estimation/CAN Data Verification........................................ 81
5.6 Test Data Estimation.................................................................................. 84
5.6.1 Data Treatment............................................................................ 84
x
5.6.2 Identification of Sample Data..................................................... 87
5.7 NCAT Road Load Results......................................................................... 90
5.8 Conclusions................................................................................................ 97
6. CONCLUSIONS
6.1 Summary................................................................................................... 99
6.2 Recommendation for Future Work........................................................... 101
REFERENCES.............................................................................................................. 103
APPENDICES............................................................................................................... 106
A Vehicle Properties...................................................................................... 107
B NCAT Facility: Experiment Setup and Data Acquisition.......................... 109
C GPS&INS Heavy Truck Cruise Control.................................................... 117
xi
LIST OF FIGURES
1.1 NCAT Fuel Economy Vs. Pavement Roughness (Courtesy Buzz Powell
@NCAT).......................................................................................................... 2
2.1 Longitudinal FBD............................................................................................ 9
2.2 Model of Power Losses Involved In Air Drag................................................. 13
2.3 Model of Power Losses Involved In Road Grade............................................ 14
2.4 Rolling Tire FBD............................................................................................. 15
2.5 Model of Power Losses Involved In Rolling Resistance................................. 17
2.6 Model of Non-Linear Power Losses Involved In Rolling Resistance............. 18
2.7 Tire Force FBD................................................................................................ 19
2.8 Tire Cornering Losses on a Constant Radius Turn......................................... 20
2.9 Magnitude of Energy Losses in a Vehicle (Reprinted from [LaClair, 2005]). 21
2.10 Magnitude of Power Losses in a Class 8 Truck.............................................. 22
2.11 Longitudinal Simulation Results...................................................................... 24
2.12 Measured NCAT Test Track Elevation Data................................................... 25
2.13 NCAT Test Track Slope................................................................................... 26
2.14 Magnitude of Loss Components at NCAT Track............................................ 27
2.15 Class 8 Truck Acceleration Performance with NCAT Track Road Profile..... 28
3.1 Advanced Longitudinal FBD........................................................................... 31
3.2 Drivetrain FBD................................................................................................. 32
3.3 Advanced Longitudinal Model Simulation, Acceleration Case....................... 34
3.4 Equivalent Masses Modeled, Acceleration Case............................................. 35
3.5 Advanced Longitudinal Model Simulation, Coast Down Case....................... 36
3.6 Advanced Longitudinal Model Simulation, NCAT Track Velocities.............. 38
3.7 Longitudinal Advanced Model Simulation, NCAT Track Longitudinal
Accelerations....................................................................................................
39
3.8 Longitudinal Advanced Model Simulation Validation with TruckSim........... 40
3.9 Model Differences, NCAT Track Simulation.................................................. 41
3.10 Comparison of Velocity Differences Between Models while Varying Mass.. 42
3.11 Model Velocity Differences as a Function of Effective Mass Ratio................ 43
3.12 Representative Sensor Simulation.................................................................... 45
3.13 Noisy Advanced Longitudinal Model, Acceleration Simulation..................... 46
3.14 Noisy Advanced Longitudinal Model Simulation, NCAT Track Velocities... 47
3.15 Noisy Longitudinal Advanced Model Simulation, NCAT Track
Accelerations.................................................................................................... 48
3.16 Static GPS Velocity, Analyzed for One
?
Bounds......................................... 49
3.17 Static Accelerometer Data, Analyzed for One
?
Bounds............................... 50
3.18 Static Accelerometer Data, Analyzed for One
?
Bounds............................... 51
3.19 Static GPS Acceleration, Analyzed for One
?
Bounds.................................. 52
4.1 Representation of 3-D Data Plane (Model 1), Indicating of Mass, Air Drag,
and Rolling Resistance Coefficients................................................................
60
4.2 Representation of 2-D Data Line (Model 2), Indicating Coefficients of Mass
and Losses........................................................................................................
60
4.3 Longitudinal Acceleration Simulation in 3-D Format..................................... 62
4.4 Noisy Longitudinal Acceleration Simulation Data for Identification.............. 63
4.5 Noisy Longitudinal Acceleration Simulation, 3-D with Theoretical Data
Plane Background............................................................................................ 64
4.6 3-D Planar Data Showing Background Planes Representing Model 1 and
Model 2............................................................................................................ 65
4.7 Averaging of GPS Measured Velocity............................................................. 66
4.8 Averaging of Measured Acceleration.............................................................. 67
4.9 Plot of Accuracy vs. Number of Iterations, or Loops Performed.................... 69
4.10 Estimation Accuracy as a Function of GPS Sensor Noise............................... 71
4.11 Estimation Accuracy as a Function of Longitudinal Force Noise................... 72
5.1 NCAT Test Track Layout from GPS............................................................... 76
5.2 NCAT Test Track Asphalt Section Layout...................................................... 76
xii
xiii
5.3 Road Grade Estimation.................................................................................... 78
5.4 Measured and Estimated Longitudinal Drive Force........................................ 84
5.5 Truck Test Data................................................................................................ 85
5.6 Truck Test Data, 3-D Representation............................................................... 86
5.7 Truck Test Data, 2-D Representation............................................................... 87
5.8 Truck Test Data, 2-D Representation with Linear Fit...................................... 88
5.9 Truck Test Data, Acceleration......................................................................... 89
5.10 Truck Acceleration Test Data with Linear Fit................................................. 90
5.11 Uncorrected Road Load Measurements........................................................... 91
5.12 Road Load Measurements with Section Averages........................................... 92
5.13 Road Load Averages by Section...................................................................... 92
5.14 Corrected Road Load Measurements and Averages........................................ 93
5.15 Slope Corrected Road Load Comparison........................................................ 94
5.16 Road Load and Asphalt Sections. ................................................................... 95
5.17 Road Load and Asphalt Roughness................................................................. 97
B.1 Data Acquisition Layout.................................................................................. 110
B.2 Data Acquisition and Sensors Inside Vehicle Cab........................................... 111
B.3 NCAT Test Truck with Starfire GPS Unit Indicated....................................... 112
B.4 Data Acquisition Power Schematic.................................................................. 113
C.1 Block Diagram of State Feedback Cruise Control........................................... 121
C.2 Block Diagram of Typical State Space Controller and Estimator................... 122
C.3 Block Diagram of State Space Controller and Estimator................................. 124
C.4 State Space Controller and Estimator Results................................................. 125
C.5 State Space Estimator Velocity Results........................................................... 126
C.6 Block Diagram of State Space Controller and Estimator with Rolling
Resistance Disturbance....................................................................................
127
C.7 State Space Controller and Estimator Results with Small Rolling Resistance
Disturbance......................................................................................................
128
C.8 State Space Controller and Estimator Results with Large Rolling Resistance
Disturbance.......................................................................................................
129
xiv
LIST OF TABLES
A.1 Vehicle Parameters.......................................................................................... 108
B.1 Hardware Summary......................................................................................... 114
B.2 Measurement Summary................................................................................... 115
B.3 SAEJ1939 Measurement Summary................................................................. 116
1
CHAPTER 1
INTRODUCTION
1.1 Motivation
This research was first motivated by the National Center for Asphalt Technology
(NCAT), at Auburn University. The test facility operates a trucking fleet, whose main
goal is to perform accelerated asphalt wear experiments. The test bed includes a 1.7 mile
oval test track located in Opelika, Alabama, on which 5 trucks drive the track
approximately 16 hours per day, over a two year test period. During the inaugural
construction of the NCAT pavement test track, fuel consumption of the trucks was
measured as the two year period elapsed. A decrease in fuel consumption was seen as the
asphalt degraded, as shown in Figure 1.1. This sparked an interested in studying the
effect of asphalt on fuel economy.
y = -0.07x + 9.26
R
2
= 0.53
3.00
3.50
4.00
4.50
5.00
5.50
6.00
65.0 66.0 67.0 68.0 69.0 70.0 71.0 72.0 73.0 74.0 75.0
International Roughness Index (inches/mile) for Entire Track
A
v
e
r
ag
e F
u
e
l
U
se (
m
p
g
)
fo
r
A
l
l
F
o
u
r
Tr
a
c
k R
i
g
s
Figure 1.1. NCAT Fuel Economy Vs. Pavement Roughness (Courtesy Buzz Powell
@NCAT)
During the 1970?s and 1980?s, fuel economy research took much priority due to
widespread oil and fuel shortages. Today, emphasis is again being put on researching
measures to reduce man-kind?s overall consumption of oil products and make use of
alternative fuels. Vehicle researchers and manufacturers strive to increase efficiency and
develop new technologies to reduce fuel consumption in vehicles, especially heavy
highway transport vehicles. Approximately 28% of the energy consumed today is in the
transportation sector, where heavy trucks consume approximately 15 to 20% of the
nation?s highway fuel usage [EIA, 2004]. This represents a significant amount of energy
and there is the potential to have a dramatic effect on the nation?s fuel usage by even
small improvements.
Much of this research to improve vehicle fuel economy is based around
improving the tires rolling efficiency, or rolling resistance which, along with many other
facets of vehicle research, is purely based on improving the vehicle. The motivation for
2
3
this thesis however, is to determine the effect of pavement types and construction to
improve efficiency. This study was performed using the heavy trucks as a test bed to
analyze the asphalt?s influence on fuel consumption. This opportunity provides a unique
experimental test environment as it involves measuring the truck?s vehicle dynamics to
develop information about the longitudinal dynamics and losses.
1.2 Back Ground and Literature Review
Many factors effect fuel economy, such as engine efficiency, rolling resistance,
air drag, and friction from various components. Much research has studied the reduction
of these effects as they all promise increases in vehicle efficiency and corresponding
increases in fuel economy. Because the interest for this research is relating the road to
fuel economy, the direct connection to vehicle performance is through reductions in
rolling resistance.
Research has been produced to both measure and simulate rolling resistance
coefficients and fuel economy effects. It has been shown that experimental tests can give
rolling resistance coefficients that match laboratory tests by using corrections derived
from fuel economy measurements [Knight, 1982]. The force applied to overcome rolling
resistance losses comes from the engine which thereby affects the fuel consumption
behavior of the powertrain. Studies have developed a relation between fuel economy and
rolling resistance values and were validated with various road experiments [Schuring,
1982]. Other long term studies have been performed on heavy trucks to capture the
4
engine and drive cycle behaviors for simulating the long term fuel economy benefits of
reducing rolling resistance of heavy truck tires [LaClair, 2005].
Much research has been done on tire behavior and the mechanisms that contribute
to rolling resistance and the modeling of those effects. Tire parameters that effect rolling
resistance behavior have been accurately quantified and used to predict their effect on
fuel economy [Glemming, 1975; Knight 1979]. More complex tire models have been
developed to analyze the heat generation in a rolling tire with the intention of simulating
tire temperatures and temperature gradients [Song, 1999]. Models have also been
developed to include new parameters such as expanding the Society of Automotive
Engineers (SAE) mathematical specification for rolling resistance forces [Grover, 1999],
or including tire velocity transients and tire temperature effects into the rolling resistance
coefficient [Nielsen, 2002].
The majority of rolling resistance research is focused on examining and
improving the tire for the benefit of fuel economy. The motivation for this research
however, is to discover a relationship between the asphalt and fuel economy by
examining the asphalts effect on rolling resistance. Research has provided conclusive
results showing that asphalt indeed has a realizable impact on vehicle fuel consumption.
Experiments using coast down tests on various road surfaces show that even with a
simple energy based engine model, road surface had up to a 20% effect on fuel
consumption [duPlessis, 1990]. Similar research using coast down experiments shows an
18% effect in fuel economy between the best and worst case surfaces tested [Bester,
1984]. Other research utilized a towed implement to measure rolling resistance forces and
showed very distinct trends of increasing rolling resistance with increases in surface
5
texture and roughness of both micro and macro-texture. Rolling resistance coefficients in
that research showed variations of 38%, which would yield fuel economy variations of
9% [Descornet, 1990].
The available research studying the effect asphalt has on rolling resistance and
fuel economy is somewhat limited compared to that of tire behavior research. Most
research tests only limited numbers of asphalt types that have large variations their
properties. The NCAT facility is an opportune test facility to do such research due to the
controlled environment and forty-five varieties of asphalts on the track. The fuel
economy research in this thesis had to be unobtrusive to the current pavement testing.
This necessitates different techniques for studying rolling resistance and required the use
of the moving truck as the measurement test bed. The research, therefore, investigated the
estimation of rolling resistance and truck longitudinal force as the trucks are driving, a
technique new to studying fuel economy and rolling resistance.
Due the constraints on the test bed, the project becomes heavily reliant on the
understanding of longitudinal vehicle dynamics and the ability to perform parameter
estimation. Accurately identifying parameters such as vehicle mass, longitudinal losses,
and road information, such as road grade and road friction, has been shown to provide
useful information for systems such as intelligent cruise control, automated vehicle
platooning, and advanced stability control systems for commercial vehicles [Bae, 2000;
Bae, 2001; Bevly, 2000; Anderson, 2004; Peterson, 1998]. Therefore, this research uses
such techniques, which have been shown capable for other systems, to perform road load,
fuel economy, and rolling resistance studies.
6
1.3 Purpose of Thesis and Contribution
The purpose of this thesis to provide a fundamental background and
understanding of vehicle longitudinal dynamics with the intent on using such knowledge
to perform fuel economy studies. Such a study relies on the understanding of the
vehicle?s behavior, the vehicle?s longitudinal losses, and estimation techniques suitable
for identifying parameter variations effected by varying rolling losses.
This thesis presents two longitudinal vehicle dynamic models and evaluates these
models for accuracy in an original simulation. The results are used to investigate the
various losses and fuel economy effects that would be experienced in various dynamic
conditions. This model is validated against commercial software and also used with a
sensor simulation to simulate expected signals. The model is then used to perform
sensitivity analysis on an estimation model to predict estimation errors as a function of
sensor noise. A data acquisition system was constructed for use on the vehicles at NCAT
and other vehicle dynamics testing. Data taken on the system was used to perform real
world estimation schemes and provide results for the fuel economy/road load research.
1.4 Outline of Thesis
This thesis begins by presenting an overview of vehicle longitudinal dynamics
with emphasis on the longitudinal losses such as rolling resistance and air drag. The
effects are then numerically simulated in a longitudinal model. Chapter 3 presents a more
advanced vehicle model that includes the effects of inertial losses on the vehicle. Various
simulations are performed where the vehicle is accelerating, decelerating, and driving the
7
NCAT track. Variations in longitudinal load around the track are examined by simulating
asphalts that would theoretically have varying levels of rolling resistance.
After the fundamentals and analyses of the vehicle?s longitudinal dynamics are
laid out, Chapter 4 presents a background on parameter estimation and sets out to
perform such estimations in simulation. Various vehicle parameters are estimated and an
in depth treatment of sensor noise is performed. Chapter 5 continues with parameter
estimation results which are performed on the real world test-bed at the NCAT facility.
Finally, overall conclusions and recommendations are provided in Chapter 6.
Additionally, an overview of the vehicle properties, data acquisition system, and a
discussion of the cruise control system can be found in the Appendices.
8
CHAPTER 2
VEHICLE MODEL
2.1 Introduction
In this chapter a longitudinal model of a rolling vehicle is developed to provide an
introduction to longitudinal vehicle dynamics. This model is used to describe longitudinal
dynamics of vehicle and contains the most significant longitudinal losses that affect the
vehicle. These losses are then mathematically and physically described in detail to outline
the mechanisms involved in each loss. Simulations are provided to show the magnitude
of each loss and their power requirements and how they affect overall vehicle efficiency
and fuel economy. Finally simulations are performed on the longitudinal model to show
vehicle motion.
2.2 Longitudinal Model
To describe the longitudinal motion of a vehicle, the dynamics are derived from
the loads on the vehicle, from which position, velocity, and acceleration of the vehicle
can be determined. Longitudinal vehicle dynamics typically include many losses such as
rolling resistance, air drag, and road grade or slope as shown. The developed model has
one degree of freedom and was derived using the equations of motion for the free body
diagram shown in Figure 2.1.
9
Figure 2.1. Longitudinal FBD
The governing equation of motion is derived from Newtonian dynamics and is
shown in Equation 2.1.
xmFFFFFF
AirDragcesisRollingSlopeBrakeDrive
&&=????=?
tanRe
2.1
where:
Drive
F = Drive force provided by engine
Brake
F = Vehicle braking force
Slope
F = Longitudinal force due to road grade
cesisRolling
F
tanRe
= Rolling resistance force
AirDrag
F = Force due to air drag
m = Vehicle mass
x&& = Longitudinal Acceleration
?
F
rolling resistance
+
F
air drag
F
drive / brake
+
F
brake
+
F
slope
This model is widely accepted as a standard longitudinal vehicle dynamics model
for modeling losses and vehicle drive behavior and is used for simulating vehicles in the
longitudinal vehicle coordinate frame [Gillespie, 1992].
2.3 Loss Components
The major losses of the moving vehicle are air drag, rolling resistance, and road
grade or slope. The following equations (2.1 through 2.5) mathematically describe each
of these components.
22
DragAir
2
1
F VCVAC
dffrdair
== ?
2.2
?sinF
Slope
mg= 2.3
mgC
rr
=
Resistance Rolling
F 2.4
tire
R
mechanicaldrive finalontransmissiengine
engine
NN
F
??
=
2.5
where:
air
? = Air density
d
C = Aerodynamic drag coefficient
fr
A = Vehicle frontal area
V = Vehicle speed
df
C = Vehicle air drag coefficient
10
rr
C
= Rolling resistance coefficient
g
= Gravity
engine
? = Engine torque
ontransmissi
N = Transmission reduction ratio
drive final
N = Final gear reduction ratio
mechanical
? = Overall mechanical efficiency
tire
R = Rear tire radius
2.3.1 Air Drag
Air drag force arises from two sources, form drag and viscous friction, which
result from fluid flow around the vehicle. Air drag forces are quite significant in long
haul truck and trailers due to their high frontal areas and poor aerodynamics [Wood,
2003]. Air drag is a function of the vehicle?s velocity squared which is due to the
dynamic pressure, or form drag, shown in Equation 2.6.
2
2
1
VP
airdynamic
?=
2.6
This dynamic pressure, multiplied by the vehicle aerodynamic drag coefficient and
frontal area, yields an aerodynamic drag force, as shown previously in Equation 2.2. For
convenience, air drag force on a specific vehicle is often simplified to an air drag
coefficient, which is the vehicle?s drag coefficient standardized with frontal area and
11
fluid properties. This results in a coefficient that can be used to easily compare the
aerodynamic efficiencies of different vehicles.
Power can be described as energy per time or force times distance per time.
Equations 2.7 and 2.8 describe the power consumed for a give force in the longitudinal
dynamics.
distForceEnergy *= 2.7
))(( VForce
time
energy
Power ==
2.8
Figure 2.2 shows a calculated road load of air drag for a constant vehicle mass
and frontal area as a function of vehicle speed and air drag coefficient. The plot shows
the non-linear velocity relationship and the significant power that can be necessary to
overcome air drag forces in a vehicle such as a class 8 truck.
12
0
0.2
0.4
0.6
0.8
1
0
10
20
30
0
50
100
150
200
250
Drag Coefficient
Vehicle Speed (m/s)
Powe
r
Cons
ume
d
(
k
W)
Figure 2.2. Model of Power Losses Involved In Air Drag
2.3.2 Road Grade
Road grade contributes to the longitudinal dynamics by adding a component of
the vehicle mass (on which gravity acts) in the longitudinal direction. These forces can be
significant especially in heavy vehicles such as long haul trucks. The force from road
grade is proportional to the vehicle mass and the sine of the road angle, as expressed
previously in Equation 2.3. Figure 2.3 shows the magnitude of the power consumed
driving over different road grades at various speeds for a constant vehicle mass of
68,000kg.
13
0
1
2
3
4
0
10
20
30
0
500
1000
1500
2000
Slope (deg)
Vehicle Speed (m/s)
P
o
w
e
r D
i
ssip
ated
(k
W
)
Figure 2.3. Model of Power Losses Involved In Road Grade
2.3.3 Rolling Resistance
Rolling resistance losses occur due to phenomenon of a rolling tire and comes
from many different sources of losses within the tire. Rolling resistance is of primary
concern due to its direct effect on vehicle longitudinal losses, and is the primary effect
roads have on fuel consumption. Much research has been done on rolling resistance as a
function of tire properties and asphalt composition as described in Section 1.2. An
understanding of rolling resistance can be obtained by examining the free body diagram
of the free rolling tire is shown in Figure 2.4.
14
F
z
15
Figure 2.4. Rolling Tire FBD
where:
z
F
= Normal force or weight
rr
F
= Rolling resistance force
res
F = Reaction force of road
d = Distance to centroid of contact pressure
x
F = Force of tow
zr
F
= Reaction of normal force
V = Velocity
loaded
R = Loaded tire radius
d
V
F
x
R
loaded
F
rr
F
zRF
res
The free body diagram is representative of a free rolling tire, defined as ?one that
is towed (or pushed) straight ahead in an upright position with all applied moments
(internal and external) about the wheel spin axis to be nearly zero and longitudinal wheel
slip to be negligible? [Gillespie, 1992]. Because the center of pressure of the tire?s
contact patch is forward of the wheel centerline, a phenomenon of a rolling tire, the
rolling resistance force and normal force also act in front of the wheel?s centerline. This
creates a resultant force that points to the center line of the wheel, with both horizontal
and vertical components. The horizontal component of the force denoted , is the
rolling resistance fore that is required to tow the wheel due to rolling resistance losses.
Fx
It is important to note that different variations of this free body diagram can be
shown where rolling resistance is a pure couple about the wheels centerline as a product
of the force, and distance, . This would indicate that the rolling resistance couple
increases linearly with either an increase in , or vehicle weight, . Figure 2.5 shows
a calculation of power losses due to rolling resistance as a function of vehicle mass and
speed, where the rolling resistance force is increased linearly with mass.
Fz d
Fz mg
16
0
1
2
3
4
5
6
x 10
4
0
10
20
30
0
20
40
60
80
100
Mass (kg)
Vehicle Speed (m/s)
Powe
r
Di
s
s
i
pa
t
e
d (
k
W)
Figure 2.5. Model of Power Losses Involved In Rolling Resistance
Generally, rolling resistance is caused by many complicated mechanisms within
the tire itself. Primary energy losses occur in the tire sidewall or contact area and tread
elements as the tread travels through the contact patch with energy being dissipated in the
hysteretic and viscoelastic friction of the rubber and carcass elements. Rubber exhibits
viscoelastic behavior, where stress is a function of strain rate, and thus dissipates energy
which accounts for 80-95% of total rolling resistance [LaClair, 2005]. Other losses occur
due to tire slip in the lateral and longitudinal directions, energy loss from bumps,
deflection of the road surface, tire temperatures, tire inflation pressure, tire design, and
other sources [Milliken, 1995]. Because the tire construction materials are strain rate
sensitive, meaning the materials exhibit some damping, the rolling resistance coefficient
is usually a function of the tires rolling speed. The most common model that accounts for
17
more external parameters is described in the SAE specification J2452 that gives the
rolling resistance force to be a function of tire inflation pressure, normal load, and
velocity in a second order relationship, as shown in Equation 2.9.
[ ]
2
cVbVaFPF
ZtireRR
++=
??
2.9
Figure 2.6 shows the power consumed by rolling resistance using the SAE J2452 rolling
resistance models and sample heavy truck steer tire parameters.
0
1
2
3
4
5
6
x 10
4
10
20
30
0
20
40
60
80
100
120
140
Mass (kg)Vehicle Speed (m/s)
P
o
we
r
Di
s
s
i
p
a
t
e
d
(
k
W)
Figure 2.6. Model of Non-Linear Power Losses Involved In Rolling Resistance
2.4 Longitudinal Turning Losses
The generation of lateral force with a pneumatic tire produces a longitudinal drag
force [Dixon, 1996].
18
Velocity
19
Figure 2.7. Tire Force FBD
The tire diagram in Figure 2.7, shows a tire heading vector and a tire velocity
vector, or actual path the tire is traveling. The angle between these two vectors is called
the tire slip angle,? , and is necessary to generate lateral force. The lateral force
generated by the tire is produced perpendicular to the tire?s carcass or heading which
results in a component that acts as drag force. This drag component arises due to the slip
angle and is therefore a function of that tire?s slip angle, as shown in Equation 2.10.
)sin(?
lateralforce
ForceDrag = 2.10
This equation can be examined to show how much energy is being put into the
tire, or lost from longitudinal forces in order to quantify how much longitudinal drive
force from the engine has to be applied in cornering to maintain constant speed. The total
?
Lateral Force
Component
Tire Force
?
Heading
Drag Component
energy consumed and power consumed by tire cornering forces and slip angle is shown in
Equations 2.11 and 2.12.
))())(sin((* dtVForcedistForceEnergy
lateral
?== 2.11
)))(sin(( VForce
time
energy
Power
lateral
?==
2.12
Figure 2.8 shows a plot of power consumed when a class 8 truck goes around the
corner of the National Center for Asphalt Technology. As shown in the figure, power
losses due to lateral force can be very significant, especially at high velocities or high slip
angles.
0
5
10
15
20
25
0
2
4
6
0
200
400
600
Vehicle Speed (m/s)
Slip Angle (deg)
Powe
r
Di
s
s
i
pa
t
e
d
(
k
W
)
Figure 2.8. Tire Cornering Losses on a Constant Radius Turn
20
2.5 Fuel Economy Effects
Because the losses described in this chapter contribute to longitudinal drive
inefficiency, the engine must provide some force to overcome these forces. This force
comes at some expense, mainly fuel consumption. The fuel consumed by an engine goes
not only to drive forces but to many different inefficiencies, which include engine
inefficiencies, friction and pumping losses, vehicle losses, and the losses described in the
model developed in the chapter. The relative magnitudes of these losses are described in
Fig 2.9.
Figure 2.9. Magnitude of Energy Losses in a Vehicle (Reprinted from [LaClair, 2005])
Fuel economy effects from losses are significant. Fuel consumed can be
approximated as being proportional to power necessary to overcome these losses which
has been shown for each individual loss in Figures 2.2 through 2.5. Figure 2.10 shows the
magnitudes of power consumed due to rolling resistance and air drag losses for a Class 8
21
truck at the NCAT facility, assuming pure longitudinal motion, ie: no turning, and no
road grade.
0 5 10 15 20 25 30 35
0
50
100
150
200
250
Velocity (m/s)
Pow
e
r
Co
ns
um
e
d
(
k
W
)
Air Drag
Rolling Resistance (linear)
Rolling Resistance (non-linear)
Summation (linear RR)
Summation (non-linear RR)
Figure 2.10. Magnitude of Power Losses in a Class 8 Truck
22
Research has been done to show the realizable effect of improving rolling
resistance has on fuel economy. Trends clearly show that an increase in road texture
yields an increase in fuel consumption [DeRaad, 1978]. Most research assumes a linear
energy based fuel consumption map. However, work has been done to develop an actual
engine map to quantify engine fuel usage as a function of engine speed and load (brake
mean effective pressure) [LaClair, 2005]. This works shows the ability to quantity fuel
usage and the results show that the economy improvements are indeed proportional, with
some scale factor, to the rolling resistance for a given drive cycle. For example in a
23
highway drive cycle, the most common cycle, LeClair shows a decrease of 2.3% fuel
consumption with a decrease of 10% rolling resistance coefficient.
2.6 Truck Simulations
Numerically integrating the equation of motion shown in Equation 2.1, a
simulation of longitudinal vehicle motion can be performed using known vehicle
parameters. Figure 2.11 shows a Freightliner truck as equipped and loaded as the NCAT
vehicles, accelerating from a standstill under full power.
0 5 10 15 20 25 30
0
5
10
15
Time (sec)
V
e
lo
cit
y
(m
/s)
0 5 10 15 20 25 30
0
1
2
Time (sec)
A
c
ce
le
rati
o
n
(m
/s
2
)
0 5 10 15 20 25 30
0
1000
2000
3000
Time (sec)
Engi
n
e
RP
M
0 5 10 15 20 25 30
0
2
4
6
Time (sec)
G
ear
Figure 2.11. Longitudinal Simulation Results
To analyze road load at the NCAT test track in more detail, track elevation data
was taken. Vertical survey measurements for inside and outside truck wheel-paths were
taken at specific locations on the track. The inside and outside wheel paths were averaged
to get an average road height as the vehicles center of gravity will tend to be positioned
about the center of the road. The resulting surface elevation as a function of track position
24
is shown in Figure 2.12. Then a high order polynomial was fit to the data to yield a
function representing the track surface.
0 500 1000 1500 2000 2500 3000
190
190.5
191
191.5
192
192.5
193
193.5
194
Distance (m)
E
l
ev
at
io
n
(m
)
Raw Measurement
Polynomial Fit
Figure 2.12. Measured NCAT Test Track Elevation Data
Turns
Straight-aways
To calculate road load due to elevation changes, it is necessary to know the road
slope. Discretely calculating slope between data points can produce noisy results, so an
analytical polynomial fit was applied to the data. Both this analytical fit, and the original
raw data, were differentiated to achieve a road slope measurement, as shown in Figure
2.13.
25
0 500 1000 1500 2000 2500 3000
-1
-0.5
0
0.5
1
1.5
Distance (m)
S
l
o
p
e (d
eg
)
Slope from analytical fit and derivative
Slope from raw data derivative
Figure 2.13. NCAT Test Track Slope
This road grade calculation was used to perform a road load analysis for the
NCAT track, calculating the individual losses as described earlier in this chapter. Figure
2.14 shows the magnitudes of each loss for a constant speed simulation of 20.11 m/s (45
mph). Air drag force and rolling resistance force are almost equal at the simulated speed,
where the road grade induced longitudinal force around the track causes large swings in
the overall vehicle longitudinal loading.
26
500 1000 1500 2000 2500
-1
-0.5
0
0.5
1
x 10
4
Distance (m)
F
o
rce (N
)
Force due to slope (analytical)
Force due to slope (raw)
Force due to rolling resistance
Force due to air drag
Figure 2.14. Magnitude of Loss Components at NCAT Track
The elevation data can be used to further simulate vehicle performance at the
track. A non-constant velocity simulation was performed of an accelerating vehicle, as in
Section 2.6, where the road grade of the test track was introduced. Figure 2.15 shows the
vehicle?s acceleration and the influence the small elevations changes can have on the
vehicle?s performance. It is shown to loose acceleration in the steepest section of the
track at about 25 m/s even while under full power.
27
0 20 40 60 80 100 120
5
10
15
20
25
Time (sec)
V
e
lo
city
(m
/s)
0 20 40 60 80 100 120
0
0.5
1
1.5
Time (sec)
A
cceleratio
n
(m
/s
2
)
Figure 2.15. Class 8 Truck Acceleration Performance with NCAT Track Road Profile
2.7 Conclusions
A mathematical model representing the longitudinal dynamics of vehicles has
been developed and simulated. This model includes loss terms that have been described
individually and mathematically modeled to understand their relative magnitudes and
impact on longitudinal vehicle dynamics. Inefficiencies and losses are shown to have
significant impact on fuel economy and their magnitudes are simulated. The model is
then numerically simulated to show heavy truck longitudinal behavior and performance.
28
29
Further simulations of road load are applied specifically to the NCAT test track and are
shown to have significant performance effects.
30
CHAPTER 3
ADVANCED MODELING
3.1 Introduction
In this chapter, more advanced topics of longitudinal vehicle dynamics are
discussed. A more complex longitudinal model of a rolling vehicle that includes inertias
is developed and simulated. This chapter also includes models for sensors that are
included in the vehicle simulations to predict sensor outputs when measuring the
longitudinal vehicle dynamics. These models are then used to predict longitudinal truck
behaviors in various environments, including those at the NCAT test track.
3.2 Advanced Longitudinal Model
The advanced longitudinal model developed in this chapter has one degree of
freedom and was derived using the equations of motion for the free body diagrams shown
in Figure 3.1. This figure is similar to that in Chapter 2, except Figure 3.1 includes an
additional inertia force.
31
Figure 3.1. Advanced Longitudinal FBD
To increase the model?s fidelity and more accurately simulate the longitudinal
dynamics, the mechanical systems through which the engines power is transmitted must
be modeled. The amount of torque delivered to the wheels in a system which is
accelerating/decelerating is reduced by inertial losses in addition to the viscous and
friction losses in the drivetrain. The previous model accounts for these by using an
efficiency term, but here a more advanced model is developed.
The advanced model which contains driveline dynamics due to inertia effects
consists of three distinct stages, the engine ( ), transmission ( ), and final drive
assembly ( ), as shown in Figure 3.2.
E
I
T
I
D
I
?
F
rolling resistance
+
F
air drag
F
drive / brake
+
F
brake
+
F
slope
+
F
inertia
32
Figure 3.2. Drivetrain FBD
The engine stage includes the vehicle?s engine, clutch, and first driving gear of
the transmission. The transmission includes all internal gearing and equivalent inertias
which drive the final drive and wheel axle assembly.
Deriving the equations of motion for the three stages, including loss terms as a
constant and function of rotational velocity, results in Equation 3.1.
SlopeResistance RollingDragAir Loss
FFFF ?????
?
?
?
?
?
?
= xb
R
NN
xm
eff
w
DTe
eff
&&&
?
3.1
1
2
R
R
N
T
=
3.2
3
4
R
R
N
D
=
3.3
I
T
loss3
w
T
loss2
T
e
T
e
I
e
I
1
?
1
T
loss1
F
1
F
1
I
2
I
3
F
2
?
2
F
2
I
4
R
4 ?
3
F
D
R
1
R
3
R
2
This equation of motion contains new terms for effective mass, effective damping, and
forces from losses. These additional mass, damping, and loss coefficients are described in
Equations 3.4 through 3.5.
?
?
?
?
?
?
+++=
22
2
2
22
w
D
w
DT
w
DTE
eff
R
I
R
NI
R
NNI
mm
3.4
?
?
?
?
?
?
++=
ww
D
w
DT
eff
R
b
R
Nb
R
NNb
b
3
2
2
2
2
22
1
3.5
?
?
?
?
?
?
++=
w
loss
w
Dloss
w
DTloss
RR
N
R
NN
321
loss
F
???
3.6
where:
1
III
eE
+= 3.7
32
III
T
+= 3.8
wD
III +=
4
3.9
The effective mass term includes the effects of the various inertias in the driveline
relating to vehicle longitudinal motion (i.e.: acceleration). Viscous losses, which act as a
function of velocity, and constant losses are included for each stage as well. This model
is more accurate as it will be shown that the effective mass can be significant in the
longitudinal performance.
3.3 Simulations of Vehicle Models, Simple and Complex
3.3.1 Acceleration Simulations
Continuing the simulations performed in Section 2.6 (mass model), a longitudinal
simulation with the model described in Section 3.2 (inertia model) is shown in Figure 3.3.
33
0 5 10 15 20 25 30
2
4
6
8
10
12
14
Time (sec)
V
e
lo
c
ity
(m
/s)
0 5 10 15 20 25 30
0.5
1
1.5
2
Time (sec)
A
c
c
e
le
ra
tio
n
(m
/s
2
)
0 5 10 15 20 25 30
500
1000
1500
2000
Time (sec)
RPM
0 5 10 15 20 25 30
0
2
4
6
Time (sec)
Ge
a
r
Mass Model
Inertia Model
Figure 3.3. Advanced Longitudinal Model Simulation, Acceleration Case
The model that includes inertias and losses shows a small difference in the
behavior of an accelerating truck from the model in the previous chapter. Velocities
reached after thirty seconds were approximately 2% lower than that of the model that
ignores these additional components. However, the new model does capture dynamics in
34
the drivetrain components that contribute to slowing the vehicle?s acceleration, especially
at lower speeds when the angular accelerations of these components are higher than later
in the run. This behavior can also be described by examining the values of
throughout the run. In lower gears, the values of are the highest and therefore
have the largest effect on acceleration performance, which is shown in Figure 3.4.
eff
m
eff
m
0 5 10 15 20 25 30
7.9
8
8.1
8.2
8.3
8.4
8.5
x 10
4
Time (sec)
Ma
s
s
Mass (m)
Mass & Inertia (Meff)
Figure 3.4. Equivalent Masses Modeled During Acceleration Case
3.3.2 Deceleration Simulations
Inertias and losses can have a similar effect on vehicle deceleration. Figure 3.5
shows a simulated truck coast-down with no drive force and only longitudinal vehicle
35
losses. The simulation assumes the transmission is in the neutral position and the only
inertia that effects the dynamics are those of the last stage, including the wheels, rear-
end/differential, drive shaft, and the driven transmission shaft.
0 20 40 60 80 100 120 140
5
10
15
20
25
Time (sec)
V
e
lo
city
(m
/s)
0 20 40 60 80 100 120 140
-0.18
-0.17
-0.16
-0.15
-0.14
-0.13
Time (sec)
A
cceleratio
n
(m
/s
2
)
Inertia Model
Mass Model
Figure 3.5. Advanced Longitudinal Model Simulation, Coast Down Case
The plot shows that the vehicle decelerates slower with the inertias included in the model
due to the increase in the term. In the above analysis the slopes of Figure 3.5 are
representative of the and terms, where the non-linearities are caused by losses,
which are functions of velocity.
eff
m
m
eff
m
36
37
3.3.3 NCAT Track Simulations
Vehicle simulations were performed to simulate a heavy truck traveling around
the 1.7 mile oval test track at the NCAT facility. The NCAT track surface is paved with
45 discrete sections of asphalt which are simulated by producing a matrix of 45 varying
rolling resistance values. The values are chosen to be +/- 5% of nominal values given in
Appendix A. The vehicles dynamics shown in Equation 3.1 were simulated using a
constant drive force provided by the engine. This constant force is the equivalent road
load associated with a velocity of 20.11m/s (45mph) and an average of the rolling
resistance values for the asphalt sections.
Figure 3.6 shows a plot of vehicle velocity around the NCAT facility. The mass
and inertia models are shown, with variations occurring due to the increased effective
mass component in the inertia model. The modeled inertia acts to decrease the high
vehicle speeds and increase the lower vehicle speeds, much like a filter.
0 500 1000 1500 2000 2500 3000
20.085
20.09
20.095
20.1
20.105
20.11
20.115
20.12
20.125
20.13
20.135
Distance (m)
V
e
l
o
city
(m
/s)
Mass Model
Inertia Model
Figure 3.6. Advanced Longitudinal Model Simulation, NCAT Track Velocities
Figure 3.7 shows the vehicle?s acceleration behavior in the two models, and more
clearly shows that peak accelerations are decreased in the inertia model, as decelerations
are also reduced.
38
0 500 1000 1500 2000 2500 3000
-4
-3
-2
-1
0
1
2
3
4
x 10
-3
Distance (m)
A
cceleratio
n
(m
/s
2
)
Mass Model
Inertia Model
Figure 3.7. Longitudinal Advanced Model Simulation, NCAT Track Longitudinal
Accelerations
3.3.4 Model Validation
To validate the model presented in this chapter, simulations were performed using
the commercial software package TruckSim. This provides a comparison to a source that
is accepted as accurate without doing experiments that would disturb existing
experiments at the NCAT test track and provide too much wear and tear on the vehicles
due to their aggressive nature. A TruckSim model was developed using the same engine,
transmission, and vehicle parameters used previously and the vehicle dynamics were
39
simulated in a full acceleration run. Figure 3.8 shows the results of this simulation plotted
against those of the model in this chapter.
0 5 10 15 20 25 30
2
4
6
8
10
12
14
Time (sec)
V
e
lo
city
(m
/s)
Chapter 3 Model
TrucksSim Commercial Software
0 5 10 15 20 25 30
0
0.5
1
1.5
2
Time (sec)
A
cceleratio
n
(m
/s
2
)
Figure 3.8. Longitudinal Advanced Model Simulation Validation with TruckSim
The simulations show very good agreement, with the largest error sources due to the
algorithms used during gear shifts. The higher degree of freedom model of TruckSim
shows additional dynamics in the gear changes which is most likely due to the very quick
shifts that were simulated and modeling the dynamics involved. There are also additional
dynamics during the acceleration portions that may be due to unmodeled drivetrain
40
dynamics from elasticity of components and tires. Overall, the differences between the
models are small and of an acceptable magnitude.
3.3.5 Model Variations
Figure 3.9 shows the variations between the two models are small when
simulating the NCAT test track. Looking at the magnitude of the velocity differences, the
velocity result does not vary more that 1 millimeter/second. This variance remains very
small for low dynamic situations.
0 500 1000 1500 2000 2500 3000
20.09
20.1
20.11
20.12
20.13
Distance (m)
V
e
lo
city
(m
/s)
Mass Model
Inertia Model
0 500 1000 1500 2000 2500 3000
-10
-5
0
5
x 10
-4
Distance (m)
D
i
fferen
ce (m
/s)
Model Difference
Figure 3.9. Model Differences, NCAT Track Simulation
41
Considering the acceleration simulation case, the variance between model results
is significantly larger than that of the NCAT track. It is quite evident that larger inertia, or
smaller mass, results in a more significant difference between the models. To quantify
this effect, the mass can be varied in simulation while looking at the RMS difference
between the two models? velocities. Figure 3.10 shows a plot of increased vehicle mass,
holding the total inertia constant, and the difference produced by the two models.
1 2 3 4 5 6 7 8 9 10
x 10
4
0
0.01
0.02
0.03
0.04
0.05
0.06
Mass (kg)
V
e
l
o
city
D
i
ffe
ren
ce (m
/s R
M
S
)
Figure 3.10. Comparison of Velocity Differences Between Models While Varying Mass
Figure 3.11 shows similar results with the values of inertia represented as a ratio
to mass ( ). Again, the trends show increasing model differences with the
increase in inertia. In simulating and experimenting with the trucks at NCAT these
mmm
eff
/)( ?
42
simulations give an indication of how much error can be expected from a model based on
either inertia or mass errors.
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
0
0.01
0.02
0.03
0.04
0.05
0.06
Effective Inertia / Mass
V
e
lo
city
D
i
fferen
ce (m
/s R
M
S
)
Figure 3.11. Model Velocity Differences as a Function of Effective Mass Ratio
3.4 Noisy Sensor Models and Vehicle Sensor Simulations
In order to analyze truck dynamics at the NCAT facility, modeling and simulating
sensor signals is necessary. Using the simulation results of the advanced vehicle model,
sensor signals can be simulated by adding noise characteristics of the sensors. A simple
43
sensor model contains terms that include a scale factor ( ), constant bias or offset ( ),
moving bias ( ), and noise ( ), as shown in Equation 3.10 [Flenniken, 2005].
SF c
b w
wbcSFxy +++= 3.10
Sensor scale factor is the linear component that relates the scale of the input to
output. Sensor noise, often called wide band noise, is of particular interest because it
degrades the accuracy of the sensor by some magnitude. The sensor noise is typically
modeled as a random zero-mean fashion with a standard deviation that can be found in
sensor specifications.
[ ]
s
fwE
22
?=
3.11
It should be noted that the noise variance increases with the sample rate ( ) [Demoz,
2003]. Sensor bias is typically composed of constant (stationary) and walking (non-
stationary) components. Sensor quality affects the magnitude and stability of these biases.
The non-stationary, or moving bias is often modeled as a first order Markov Process,
which simulates first order filtered noise with values for noise and a time constant.
s
f
Figure 3.12 shows an example of a signal corrupted by the major sensor
inaccuracies. Each noise effect is modeled and added on a linear signal to show their
effects on corrupting the original signal or true state. These sensor effects are important
for accurately simulating the measurements obtained on the trucks.
44
0 5 10 15 20 25 30 35 40 45 50
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
Time
M
easu
r
em
en
t
Noisy Signal
Noisy Signal with Scale Factor and Bias Errors
Noisy Signal with Moving Bias
Uncorrupted Linear Signal
Figure 3.12. Representative Sensor Simulation
This sensor model can be included to the truck simulations to predict sensor
outputs. Using noise statistics provided by sensor manufactures, random white noise can
be generated and added to the true vehicle states to simulate what a sensor?s output would
be if used in the vehicle. This simplification to the sensor model assumes a bias free and
calibrated sensor and one that is stable enough that the moving bias errors are small.
Figure 3.13 shows simulated velocity and acceleration measurements from the
longitudinal acceleration simulation, using the advanced model. Using sensor specs for
the Navcomm ?Starfire? GPS, velocity noise for the measurement is modeled as 1? =
0.05m/s and for the Crossbow IMU the accelerometer noise is 1? = 0.00687 m/s
2
.
45
0 5 10 15 20 25 30
0
5
10
Time (sec)
V
e
lo
city
(m
/s)
0 5 10 15 20 25 30
0
0.5
1
1.5
Time (sec)
A
cceleratio
n
(m
/s
2
)
Simulated State
Simulated Measurement
Figure 3.13. Noisy Advanced Longitudinal Model, Acceleration Simulation
Applying the same sensor models to the NCAT track simulation shows the larger
influence noise has on the smaller dynamic variations involved in circling the track.
Figure 3.14 shows that, due to the small relative velocity differences between asphalt
sections, the noise is very dominant over the true signals.
46
0 500 1000 1500 2000 2500 3000
20
20.05
20.1
20.15
20.2
20.25
20.3
20.35
Distance (m)
V
e
l
o
city
(m
/s)
Simulated Velocity Measurement
Simulated Velocity
Figure 3.14. Noisy Advanced Longitudinal Model Simulation, NCAT Track Velocities
Additionally, Figure 3.15 shows the small changes in acceleration between the asphalt
sections because rolling resistance changes are overwhelmed by accelerometer noise.
47
0 500 1000 1500 2000 2500 3000
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
Distance (m)
A
cceleratio
n
(m
/s
2
)
Simulated Acceleration Measurement
Simulated Acceleration
Figure 3.15. Noisy Longitudinal Advanced Model Simulation, NCAT Track Accelerations
Static sensor data was taken to verify the bounds on the random noise the sensors?
outputs. GPS and accelerometer data was taken in the cab of the NCAT truck and
analyzed for the one sigma bounds. Figure 3.16 shows static GPS velocity noise taken
with the truck?s engine running. The noise on the ?Starfire? velocity had a standard
deviation of 0.0411 m/s.
48
0 100 200 300 400 500 600 700 800 900 1000
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Time (sec)
V
e
l
o
city
(m
/s)
Static GPS Velocity Data
Noise Std, 0.0411 m/s
Figure 3.16. Static GPS Velocity, Analyzed for One ? Bounds
Static accelerometer data was taken using the Crossbow manufactured IMU
mounted on the trucks, as shown in Appendix A. Figure 3.17 shows the data that was
taken and its standard deviation on what should be a static signal. It is important to note
that the noise values shown, 0.2118 m/s
2
, are higher than the values printed in the sensor
data sheets. This is primarily due to the inclusion of process noise which is inserted into
the measurement from unknown dynamics, which in this case, is primarily cab vibrations
from the vehicle?s running engine.
49
0 100 200 300 400 500 600 700 800 900
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Time (sec)
A
cceleratio
n
(m
/s
2
)
Static Accelerometer Measurements
Noise Std. 0.2118m/s
2
Figure 3.17. Static Accelerometer Data, Analyzed for One ? Bounds
Purely static data was taken with the accelerometer and is shown in Figure 3.18.
Looking at the plot, the data is so clean that most error is discritization error and the noise
standard deviation is approximately seventy times smaller than when mounted in the
trucks, at 0.002975 m/s
2
.
50
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
Time (sec)
A
c
celeratio
n
(m
/s
2
)
Static Accelerometer Measurements
Noise Std. 0.002975m/s
2
Figure 3.18. Static Accelerometer Data, Analyzed for One ? Bounds
Because such a large amount of noise is injected into the accelerometer measurement
when mounted on the trucks, another alternative measurement can be used by
differentiating GPS velocity. This results in an estimate of acceleration which is actually
slightly cleaner than that shown in Figure 3.17, with a standard deviation on the noise of
0.1416 m/s
2
.
51
0 100 200 300 400 500 600 700 800 900 1000
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Time (sec)
G
P
S
A
cceleratio
n
(m
/s
2
)
GPS Accel
Noise Std. 0.1416 m/s
2
Figure 3.19. Static GPS Acceleration, Analyzed for One ? Bounds
This increase in noise characteristics will have an effect on the vehicle measurements and
will be analyzed in more detail in the following chapter.
3.5 Modeling Conclusions
This chapter presents a more extensive and slightly more accurate longitudinal
vehicle dynamic model compared to what was presented in Chapter 2. This new model
contains additional dynamic effects that act on the vehicle, mainly inertias. The model is
shown in simulation and a discussion of the differences between the model presented in
52
53
Chapter 2. The model is also compared to that in a commercial vehicle dynamics
modeling package and showed good agreement. Analytical sensor models are presented
and then applied to the vehicle simulations. Sensor noise was small when looking at high
dynamic truck measurements but the noise had a large impact when analyzing small
variations in velocity and acceleration.
The vehicle models presented capture similar dynamics with small differences in
the overall vehicle behavior, with the most significant difference occurring in high
dynamic situations. Sensor noise is shown to have a significant effect on what can be
expected of measurements in real world tests, especially those which experience low
dynamic excitation and will be analyzed more in depth in Chapter 4.
54
CHAPTER 4
IDENTIFICATION IN SIMULATION
4.1 Introduction
This chapter investigates, in simulation, the feasibility of identifying various
vehicle parameters in the presence of sensor noise. First, identification algorithms are
presented mathematically and are then applied to the vehicle models shown in Chapters
2&3. Simulated data is presented in a unique way to show the parameters to be identified
and the noise on the measurements for two different models. Estimations are performed
on the simulations with and without sensor noise. Finally, a sensitivity analysis of how
noise affects the estimation accuracy is performed and conclusions are drawn based on
the results.
4.2 Identification Background
There are several methods that can be used for identifying parameters such as
Least Squares, Recursive Least Squares, and the Kalman Filter. These numerical
techniques are based on determining the states that minimize a cost function [Stengel,
1994]. When the states are parameters of a mathematical model, this technique is
commonly called parameter estimation.
Parameter estimation frequently uses a method that is based on the minimization
of a quadratic cost function, known as Least Squares. This technique gets its name from
the linear system defined by Equation 4.1.
ny
nHxz
+=
+=
4.1
where:
z = Measurements
H = Observation matrix
x = Constant state vector
y
= Error-free output vector
n = Error
The goal is to compute estimates of the states, contained in the vector denoted , from
the measurements in z. This leads to Equation 4.2 below that describes the estimate of the
output.
x?
vxHy += ?? 4.2
where:
y? = Estimates of the output
x? = State estimate vector
v = Measurement Noise
55
The state residual error is defined by Equation 4.3 below.
xx
x
??=? 4.3
The measurement residual error is defined by the following equation.
zz
z
??=? 4.4
The state residual error, , represents the difference between the actual state and the
estimated state, while the measurement residual,
x
?
z
? , represents the difference between
the measured (ie: noisy) state and the (calculated) output. As previously mentioned, the
least squares technique requires the minimization of a quadratic cost function. Ideally, a
cost function would be defined such that the state residual error, , is minimized.
However, this is not feasible as the true states are unknown, hence the need for an
estimation algorithm. This cost function is therefore defined to contain terms of the
measurements and the output vector, as shown in Equation 4.5. This equation can be
solved without prior knowledge of the systems true states or noise values. Assuming that
the noise is zero mean, minimizing the cost function in z also minimizes the state residual
error.
x
?
)?()?(
2
1
)?()?(
2
1
2
1
)(
xHzxHz
yzyzzJ
T
T
z
T
z
??=
??=??=
4.5
56
Equation 4.5 above can be simplified to the following shown in Equation 4.6.
)????(
2
1
)( xHHxzHxxHzzzzJ
TTTTTT
+??=
4.6
To solve for its minimum, the gradient of the cost function is set to equal zero, as in
Equation 4.7.
)(zJ
0)?(
?
)(
=?=
?
?
TTT
zHxHH
x
zJ
4.7
This can be solved for to result in the least square estimator, as shown below in
Equation 4.8.
x?
zHHHx
TT 1
)(?
?
=
4.8
In the solution for , the term x? [ ]
TT
HHH
1?
is called the pseudoinverse, which reduces to
L
H as shown in Equation 4.9.
zHx
L
=?
4.9
The derivation above is typically called Batch Least Squares which refers to the
process being performed on a complete set of data. However on real systems, it becomes
beneficial to perform real time estimates. The recursive least squares (RLS) algorithm is
one that propagates, or calculates the estimates, through discrete time steps. It is possible
57
to append measurements to the measurement matrix as they are received and recalculate
the least squares estimates. However, recursive least squares uses a more computationally
efficient algorithm that uses the previous estimates as its starting point and propagates the
estimates through time. The RLS equations are [Stengel, 1994]:
)?(??
11 ?+
?+=
kkkkkk
xHzKxx 4.10
1
11
)(
?
??
+=
k
T
kkk
T
kkk
RHPHHPK
4.11
111
1
)(
???
?
+=
kk
T
kkk
HRHPP
4.12
Where:
x? = State estimates
k
K = Recursive least squares gain matrix
k
P = State estimate covariance matrix
4.3 Estimation Modeling
It has been shown that least squares is a suitable and practical method to provide
estimates for simple vehicle parameters [Bae, 2001]. Applying the longitudinal model
from Chapter 3 to a least squares structure (Equation 4.13) results in the following model:
[]
?
?
?
?
?
?
?
?
?
?
=
rr
dfDrive
F
C
m
VxF
?
?
?
1
2
&&
4.13
58
This satisfies the least squares form in Equation 4.2. In estimating the air drag and rolling
resistance the individual components cannot be distinguished when the vehicle system is
not sufficiently excited (i.e. when the vehicle travels at constant speed, which is similar to
the operations performed by the trucks at NCAT). Therefore this necessitates a different
estimation model form if the air drag and rolling resistance components are not
distinguishable, which is shown in Equation 4.14 below.
[]
?
?
?
?
?
?
=
const
Drive
loss
m
xF
?
1&&
4.14
As the vehicle travels around the NCAT test track, it travels through turns at the
east and west ends of the track. This correspondingly increases the longitudinal force on
the trucks proportional to that of the slip angle and lateral forces generated by the tires as
described in Section 2.4. This force is neglected in the estimation algorithm and will be
lumped into the total losses. Thus, this force is not distinguished from the rolling
resistance and air drag losses of the vehicle in the turns on the track.
Because system Model 1 contains three parameters to be estimated, plotting a 3-D
representation of these parameters shows a planar spread of data, as shown in Figure 4.1.
59
Figure 4.1. Representation of 3-D Data Plane (Model 1), Indicating of Mass, Air Drag,
and Rolling Resistance Coefficients
The data for Model 2 can also be represented in a plot that reduced the plane of Model 1
to a line as shown in Figure 4.2.
Figure 4.2. Representation of 2-D Data Line (Model 2), Indicating Coefficients of Mass
and Losses
60
61
4.4 Mass and Loss Estimation In Simulation
4.4.1 Simulations and Data Treatment
Further investigation of system excitation and sensor accuracies were performed
using a longitudinal tractor trailer simulation. Trucks were simulated accelerating from a
stand-still as in Chapter 3.
Parameter estimates were performed using the simulation data to verify the ability
to estimate parameters in simulation. Estimates of mass, air-drag, and rolling resistance
values were obtained using the least squares technique and were accurate to the values
used to produce the simulation data, given the noise free states. The following figure, 4.3,
represents the three dimensional planar view of the simulated data without noise,
showing the distinct forces in each gear as the vehicle speed increases and drive force
decreases.
0
1
2
3
0
50
100
150
200
250
0
0.5
1
1.5
2
x 10
5
Acceleration (m/s)
2
Velocity Squared (m
2
/s
2
)
D
r
i
v
e F
o
rce
(N
)
Figure 4.3. Longitudinal Acceleration Simulation in 3-D Format
The vehicle acceleration simulation provides a good range of drive forces,
velocities, and accelerations on which to perform identification. Noisy signals were
generated based on noise statistics found from static data tests performed in the trucks, as
shown in Section 3.4. Using these noise values a simulation of the vehicle is performed
with results shown in Figure 4.4.
62
Figure 4.4. Noisy Longitudinal Acceleration Simulation Data for Identification
Reapplying the 3-view technique to the simulated noisy data in Figure 4.4 results in the
plots shown in Figure 4.5. The background planes shown in the figure represent the
planes upon which clean data would lie. This gives an indication in each view how the
noise effects the measurement of each vehicle state.
63
Figure 4.5. Noisy Longitudinal Acceleration Simulation, 3-D with Theoretical Data Plane
Background
Re-plotting this data with background planes that represent the fits of Model 1
and Model 2 allows visualization of the effect the velocity squared term has on losses, as
shown in Figure 4.6. The velocity squared term in Model 1 represents a significant slope
difference in these planes and, therefore, model 2 is not valid for this condition where
velocity contains significant excitation.
64
Figure 4.6. 3-D Planar Data Showing Background Planes Representing Model 1 and
Model 2.
4.4.2 Investigating Sensor Noise in Estimations
Sensor noise was shown in Chapter 3 and in the previous section to have a
significant effect on expected measurements in real world tests, especially those which
experience low dynamic excitation. The heavy trucks at the NCAT facility drive repeated
laps for extended periods which can present an opportunity to increase measurement
accuracy by reducing noise through averaging repetitive measurements. This technique
uses simulated vehicle measurements of a heavy truck driving repeated laps around the
NCAT facility. This simulated noisy data of velocity and acceleration is taken at specific
points on the track. These repeated data points can then be averaged, effectively reducing
the random noise content. This creates a cleaner signal through averaging the random
65
noise at each point due to the characteristic that the noise is zero mean. Taking the data
points from each lap and lining them up as a function of distance around the track
removes process noise that would otherwise be introduced if averaging data that occurred
at different points on the track.
Figure 4.7 and 4.8 show these simulated vehicle measurements in blue and the
vehicle?s true state in black. These noisy sensor signals can then be averaged at the points
on the track to reduce noise level, as shown in red.
0 500 1000 1500 2000 2500
19.95
20
20.05
20.1
20.15
20.2
20.25
20.3
GPS Measured Distance Travelled (m)
M
e
asu
r
ed
V
e
lo
city
(m
/s)
Figure 4.7. Averaging of GPS Measured Velocity
66
0 500 1000 1500 2000 2500
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
Actual Distance Travelled (m)
A
c
c
e
l
e
ra
tio
n
(m
/s
2
)
Figure 4.8. Averaging of Measured Acceleration
These averaged signals represent the confidence that can be had if repeated runs
are created and measurements are averaged to filter noise. A specific analysis was
performed to show the reduction in noise as more laps were repeated and averaged to
reduce noise. Track simulations were performed to generate noisy data. This data was
then averaged and a noise value over the true state was calculated. This noise value is
plotted against the number of laps, or simulation loops, in Figure 4.9.
There is a clear trend reducing the noise as a function of laps whose data points
were averaged. This empirical simulation has an analytical fit described in Equation 4.21
which is derived by using the propagation of uncertainty, shown in Equation 4.15.
67
2
1
?
?
?
?
?
?
?
?
?
?
=
?
=
I
i
xi
i
y
x
y
??
4.15
The average signal is defined by Equation 4.16.
?
=
=
N
i
iave
x
N
x
1
1
4.16
Expanding the signal?s average to include noise is shown in Equation 4.17.
avetrueave
vxx += 4.17
The average noise is defined as follows.
2
1
?
?
?
?
?
?
?
?
?
?
=
?
=
N
j
x
j
ave
avg
x
x
v ?
4.18
The partial derivative of the average signal with respect to the signal is shown in
Equation 4.19.
Nx
x
j
ave
1
=
?
?
4.19
Finally, the propagation or uncertainty is simplified to Equation 4.20.
68
NN
v
x
N
j
xavg
2
1
2
1 ?
? =
?
?
?
?
?
?
=
?
=
4.20
Equation 4.21 shows the analytical solutions that represents the decrease in the original
noise, ? , as a function of number of laps.
laps
ave
#
2
?
? =
4.21
Figure 4.9. Plot of Accuracy vs. Number of Iterations, or Loops Performed
In the truck acceleration simulation, various levels of GPS velocity noise statistics
can be injected into the system and estimations can be performed to evaluate how the
69
70
noise effects the estimation accuracy. The longitudinal simulation was looped many
times, each time increasing the GPS velocity noise statistics. Errors on the state estimates
were calculated and plotted for each loop so that accuracy as a function of noise can be
analyzed. The results from estimating the three parameters of Model 1 are shown in
Figure 4.10. These plots show a very distinct trend of a decrease in estimation accuracy
with increasing noise in the velocity measurement. With perfect measurements, near
perfect estimates can be obtained with slight inaccuracies due to the aliasing effect a 5Hz
GPS measurement can have on the dynamics during the vehicle?s gear changes.
However, this effect could be reduced in with the inclusion of a Kalman filter technique
using additional measurements or a recursive least squares with a forgetting factor
[Vahidi, 2003]. Increasing the noise statistics just beyond the point of our known GPS
accuracies, it is shown that estimate errors become large very quickly. The mass estimate
shows the best performance of all three terms, and shows promise as it is of the most
interest in vehicle estimation scheme.
Figure 4.10. Estimation Accuracy as a Function of GPS Sensor Noise
A similar analysis can be performed using the longitudinal simulation without
adding velocity noise but with noise on the drive force from the CAN data. Figure 4.11
shows how the noise on the force measurements affects errors in the state estimates.
Again, the mass estimate is the most accurate and overall these estimates are less affected
by noise on the force measurement than that on the other inertial sensors.
Figure 4.10 showed biased estimates with the inclusion of GPS noise. However,
Figure 4.11 shows a zero-mean error is produced in the estimates with the inclusion of
noise on the force measurement. The trends shown in Figure 4.11 also show that
increasing the standard deviation on the drive force noise increases the standard deviation
on the estimate error. Recalling the Equation 4.2, the GPS noise enters into the H
71
matrix, resulting in the growing errors in the state estimate matrix, . However, drive
force noise enters into the systems estimate of the output, , which produces the zero
mean error on the system, hence the zero mean trend in the state estimates .
x?
y?
x?
Figure 4.11. Estimation Accuracy as a Function of Longitudinal Force Noise
4.5 Conclusions
This chapter provides a foundation for performing estimation techniques in real
vehicles by analyzing these techniques? performance in simulation. A background was
given on various estimation techniques and these techniques were applied to the
mathematical longitudinal vehicle dynamics models shown in the previous chapters. A
unique visual data treatment was provided to show the effects of sensor noise and
72
73
modeling differences. Simulations results provide estimation results for longitudinal
vehicle estimate techniques and simulate the expectations of their accuracy. Estimates
were shown to vary significantly depending on the excitation of the system and the
quality of measurements taken. This shows that the estimation variability should be taken
into consideration for any long term vehicle estimation schemes.
74
CHAPTER 5
IDENTIFICATION ON TRACK
5.1 Introduction
This chapter investigates, using real experiments, the feasibility of identifying
various vehicle parameters in the presence of sensor noise. A background on the test
facility is given and road grade estimation around the facility is performed for future use
in the parameter estimation data. Another technique for parameter estimation, known as
Kalman Filtering, is presented and used to validate measurements from the on-board
vehicle computer. Test data is presented in the format shown in previous chapters and
parameter estimation is performed on driving, accelerating, and coasting data sets.
Results are discussed regarding parameter estimation quality and further longitudinal
loading data is analyzed for the benefit of studying road load and its effects at the NCAT
facility.
5.2 NCAT Facility
The test bed for this research is an instrumented class 8 truck on Auburn
University?s National Center for Asphalt Technology (NCAT) oval test track. The NCAT
75
facility is a civil engineering research facility whose primary function is to perform
accelerated asphalt testing and wear studies. This is accomplished on a 1.7 mile oval test
track on which there are various types of asphalt test mixes and constructions. Five
Freightliner trucks travel the track 16 hours per day in two shifts, five days a week.
Historically the track has had two year test sessions with a small downtime between them
for track reconstruction. These trucks give an opportunity to validate the accuracy,
performance, and practicality of various estimation methods in heavy vehicles.
The track is broken into 200-foot sections of different pavement types and has
near zero-grade through the straight-aways. This gives many different asphalt varieties to
test on and also allows the verification, if necessary, of rolling resistance estimations
using the straight-aways. Detailed information on each section of the track is monitored
including rut depth and coefficient of friction. Additionally, influence of temperature and
humidity on the data can be can be minimized by comparing data collected under similar
testing conditions and/or analyzing existing weather station data.
Data collection hardware was installed on the trucks and is outlined in Appendix
A. Figure 5.1 below shows GPS data recorded on the 1.7 mile oval test track and Figure
5.2 outlines the asphalt section layout.
Figure 5.1. NCAT Test Track Layout from GPS
Figure 5.2. NCAT Test Track Asphalt Section Layout
76
5.3 Road Grade Estimation
It has been shown that a bias free estimate of road grade can be obtained by
comparing the vertical and heading velocities measured by a single GPS unit [Bae, 2001;
77
Ryu, 2004]. This method is favorable over a dual antenna unit because it does not contain
biases from vehicle pitch and it has no initialization bias. Vehicle bounce motions can
however, be a factor in this type of measurement. Because the road grade dynamics are
typically much slower than road dynamics that effect the vehicle?s vertical suspension
dynamics, vehicle bounce motions can be reasonably filtered using simple low pass
filters or more complex techniques such as a Kalman Filter [Bae, 2001].
Using a single GPS antenna, a track profile can be generated using the lateral,
longitudinal, and vertical measurements. The test track was designed and constructed
with the goal of minimizing road grade. Results from test track elevation data in Section
2.6 shows that the track is quite level in the straight-aways, with approximately a 3 meter
elevation difference between the north and south straight-aways, which results in a small
slope through the turns. The estimation results using vertical and heading velocities are
shown in Figure 5.3. Due to a relatively small data set and the type of GPS receiver used,
a single antenna non-differential unit, the data is noisy and inaccurate during the straight-
aways. The GPS unit?s velocity accuracy is approximately 10 cm/s vertically and 5 cm/s
horizontally. Because the slope estimation is a function of the inverse tangent of the ratio
of vertical and horizontal velocities, the overall accuracy becomes a function of the
magnitude of the heading velocity. Based on other research, more accurate receivers are
needed for precise vehicle state measurements using GPS [Bevly, 2001]. Therefore, for
this research, the elevation data provided by NCAT was deemed more accurate and
therefore used later to remove road grade effects from the road load.
0 50 100 150 200 250 300
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Time (sec)
G
PS Sl
ope
(
d
e
g
)
Figure 5.3. Road Grade Estimation
5.4 Kalman Filter Background
The Kalman Filter is a set of equations used in estimation, to provide an estimate
of the states of a system by minimizing a quadratic cost function, like least squares
presented in the previous chapter. A Kalman Filter minimizes the estimate error
probability density which is a cost function subject to dynamic constraints [Stengel,
1994].
The Kalman Filter estimates the states of a system that are defined by the
following discretized state-space dynamic equation, shown in Equation 5.1.
111 ???
++=
kkdxdk
wuBxAx 5.1
78
The system?s output, is as shown in Equation 5.2.
k
y
kkdk
vxCy += 5.2
The variables and represent process and measurement noise respectively. Their
noise statistics are assumed to be zero mean, white, normally distributed, and
uncorrelated as shown in Equations 5.3 through 5.9.
w v
[ ] 0=wvE
5.3
[ ] 0=wE
5.4
[ ] 0=vE
5.5
[ ]
2
w
T
d
wwEQ ?==
5.6
[ ]
2
v
T
d
vvER ?==
5.7
[ ]
d
QNw ,0~ 5.8
[ ]
d
RNv ,0~ 5.9
There are five distinct steps to the recursive algorithm that makes up the Kalman
Filter, which are given in Equations 5.10 through 5.14. The first step of the Kalman Filter
is to compute the state estimate extrapolation shown in Equation 5.10.
( ) ( )
kdkdk
uBxAx +=
+?
+
??
1
5.10
79
Along with the state estimate is the state error covariance matrix extrapolation shown in
Equation 5.11.
( ) ( )
k
T
dkdk
QAPAP +=
+?
+1
5.11
The next step of the Kalman Filter is to compute the filter gain, or Kalman gain, using the
following equation.
() ()
[ ]
1?
??
+=
k
T
dkd
T
dkk
RCPCCPL
5.12
This gain is then used in a linear combination of
( )?
k
x? and a weighted difference between
the actual measurement and a predicted measurement. This value of
( )
( )
?
?
kdk
xCy ? is
known as the measurement innovation and is multiplied by the Kalman gain calculated in
the previous step to produce the state estimate update as shown in Equation 5.13.
() ( ) ( )
( )
??+
?+=
kdkkkk
xCyLxx ???
5.13
Finally, the state error covariance matrix is updated using Equation 5.14.
( )
( )
( )?+
?=
kdkk
PCLIP
5.14
If the measurement noise covariance matrix, R , goes to zero the Kalman Gain, ,
approaches values of . In this limit, the actual measurement is trusted completely and
the predicted measurement thrown out. If the state estimation error covariance,
k
L
1?
d
C
( )?
k
P ,
80
approaches zero, the Kalman Gain approaches values of zero. If this occurs, the predicted
measurement (state estimate) is trusted more.
5.5 Drive Force Estimation/CAN Data Verification
Engine torque is available on the controller area network (CAN) bus of the
Freightliner trucks used in this research. It is however, an estimate of torque that is
calculated by the engine computer. Because the accuracy of the CAN force data is
unknown, adding additional sensors and using a Kalman filter allows the estimation of a
clean or more accurate drive force as well as verifying the CAN measurement?s quality.
For this more accurate drive force estimation, the CAN drive force, longitudinal
acceleration, and vehicle mass must all be known. Because mass is typically unknown or
would vary significantly in use, this wouldn?t have applications in real world vehicle
systems. However, for the sake of this research, using the known mass will allow the
quality of the CAN data to be verified using a preliminary data set.
The engine force can be described by Equation 5.15.
tire
R
mechanicaldrive finalontransmissiengine
engine
NN
F
??
=
5.15
81
Because the trucks have a manual transmission and use only one transmission gear for
these verification experiments the reductions, , shown in Equation 5.16 can be
found from data sheets or empirically.
total
N
ncecircumfereenginevelocity
C
total
NV ?= 5.16
The tire radius in the above equation is 0.5311m as equipped from the manufacturer.
Therefore using vehicle speed and engine speed from the CAN, the total reduction
was determined to be 3.904 using Equation 5.16.
total
N
Using a Kalman filter, a cleaner, higher fidelity drive force can be estimated for
later use in the vehicle parameter estimation schemes. The Kalman filter model used is
arranged as shown in Equations 5.17 through 5.18.
vCxy
wF
+=
+= 0
&
5.17
[ ] [ ]
[]
long
long
longlong
Force
xaccelmass
Forcemeasured
ForceorceF
?
?
?
?
?
?
=
?
?
?
?
?
?
=
1
1
_*
_
]0[
&
5.18
As shown in Equation 5.17 above, the outputs are measured CAN drive force and
measured longitudinal acceleration, and the estimated state is drive force.
The longitudinal acceleration measurement in the system can be first run through
a Kinematic Kalman filter to remove the sensor bias using GPS velocity [Bevly, 2001].
An understanding of the noise statistics for both the CAN drive force and the longitudinal
82
accelerometer are necessary to obtain good force estimates. The CAN drive force noise
statistics used for the Kalman Filter are chosen in simulation to obtain good quality
estimates and filtering of the signal. The accelerometer noise statistics were obtained
from the static tests discussed in Section 3.4.
The Kalman filter noise statistics are normally distrubted zero mean with variance
summarized in Equations 5.19 and 5.20.
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
2
_
2
2
_
0
0
,
0
0
xaccel
measforce
m
Nv
?
?
5.19
g
Newtons
xaccel
measforce
022.0
100
_
_
=
=
?
?
5.20
Figure 5.4 shows the results of the Kalman Filter drive force estimate compared
with the actual measurement on the CAN bus from the engine computer. The noise
covariance for the sensors and initial uncertainties were chosen to give good estimator
performance without effecting the higher dynamics of the data. As seen in Figure 5.4 the
CAN force estimate does not vary significantly from the measured force, which indicates
the force estimate from the engine computer is fairly accurate. It may, however, be
possible to increase the accuracy of the force estimate with a higher precision
accelerometer. However, from this experiment, the raw force measurement from the
engine computer was deemed sufficient for the following estimation schemes in this
thesis.
83
Figure 5.4. Measured and Estimated Longitudinal Drive Force
50 100 150 200 250
2000
3000
4000
5000
6000
7000
8000
Time (sec)
Dr
i
v
e
F
o
r
c
e
,
N
KF Estimated State
Measured Force
5.6 Test Data Estimation
5.6.1 Data Treatment
Truck data was sampled during a normal shift, where the trucks drive the track at
a 45 mph target speed under the action of the vehicle?s cruise controller. Very long
sessions of data of up to 24 hours were taken and a sample of this data is shown in Figure
5.5. Lap repetitions are clearly shown by the test data, where approximately fifty laps of
the trucks were sampled in this test, shown below.
84
0 1000 2000 3000 4000 5000 6000 7000
0
5000
10000
15000
D
r
iv
e F
o
rce (N
)
0 1000 2000 3000 4000 5000 6000 7000
-0.2
0
0.2
A
cceleratio
n
(m
/s
2
)
0 1000 2000 3000 4000 5000 6000 7000
21
21.5
22
22.5
Time (sec)
V
e
lo
cit
y
(m
/s)
Figure 5.5. Truck Test Data
Applying the data shown above to the 3-view format first presented in Section 4.3, allows
for the visualization of the quality of the data. The top right plot of Figure 5.6 shows the
extended track session data plotted in 3-view, where the noise free data would lie on a
plane. Viewing this three dimensional data from each side of the plot shows specific
information about various parameters and the excitation in those parameters. The upper
left hand plot shows the excitation in the air drag parameter to be identified. Ideally, this
plot would yield a line, given significant excitation in the parameter and noise free
measurements. The lower right hand plot shows the excitation and noise in the mass
parameter. It too would ideally yield a line, whose slope would be the mass of the
85
vehicle. Finally the lower left hand plot shows a view of overall excitation in terms of
velocity and acceleration and should have a slope of the air drag coefficient divided by
the vehicle mass, with an offset of constant losses.
440 460 480 500
0
5000
10000
15000
Velocity squared (m/s)
2
D
r
iv
e F
o
rce (N
)
-0.02
0
0.02
460
480
2000
4000
6000
8000
10000
12000
14000
Acceleration
(m/s
2
)
Velocity squared (m/s)
2
D
r
iv
e F
o
rce
(N
)
-0.05 0 0.05
440
460
480
500
Acceleration (m/s
2
)
V
e
lo
city
sq
u
a
red
(m
/s)
2
-0.05 0 0.05
0
5000
10000
15000
D
r
iv
e F
o
rce (N
)
Acceleration (m/s
2
)
Figure 5.6. Truck Test Data, 3-D Representation
The figure above visually shows the magnitude of the noise on the sensors and how they
corrupt the shape of the line to be estimated. Figure 5.7 below shows a closer view of
what lies in the lower right hand plot of the figure above. The slope of a linear data fit of
this figure would represent the mass of the truck. Again, noise has a distinct effect in the
clarity of any linear fit that may be applied to this data, resulting in poor mass estimates.
86
-0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04
0
5000
10000
15000
D
r
iv
e F
o
rce (N
)
Acceleration (m/s
2
)
Figure 5.7. Truck Test Data, 2-D Representation
5.6.2 Identification of Sampled Data
Using both Models 1 & 2 as detailed in Section 4.3, least squares parameter
identification was performed on the experimental truck data. These models are again
shown in Equations 5.21 and 5.22.
Model 1: []
?
?
?
?
?
?
?
?
?
?
=
rr
dfDrive
F
C
m
VxF
?
?
?
1
2
&&
5.21
87
Model 2: []
?
?
?
?
?
?
=
const
Drive
loss
m
xF
?
1&&
5.22
The results using model 1 for identification showed very poor estimates (>50%) of mass,
air drag, and rolling resistance/constant losses. Performing a fit of Model 2 to the truck
data resulted in a reasonable quality fit with approximately 10% error on the mass
estimate and 10% error on the constant losses, when compared to known values.
This accuracy can be attributed to the simple linear model and the abundant
amounts of data which least squares can average the noise effects. The equivalent results
of doing the least squares fit can be plotted as a linear fit of the data shown in Figure 5.7
above. The results are shown in Figure 5.8, where the slope represents the mass
parameter and the y intercept represents the constant losses.
-0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02
-2000
0
2000
4000
6000
8000
10000
12000
14000
16000
D
r
iv
e F
o
rce (
N
)
Acceleration (m/s
2
)
Data
Linear Fit
Figure 5.8. Truck Test Data, 2-D Representation with Linear Fit
88
Similar analysis can be performed on acceleration data taken on the trucks at the
NCAT facility. The data shown in Figure 5.9 was taken during a truck accelerating at
near full capability to NCAT track speed.
0 10 20 30 40 50 60 70
-5
0
5
x 10
4
D
r
iv
e F
o
rce (N
)
0 10 20 30 40 50 60 70
-0.5
0
0.5
1
A
cceleratio
n
(m
/s
2
)
0 10 20 30 40 50 60 70
1000
1500
2000
Time (sec)
Engi
n
e
RPM
Figure 5.9. Truck Test Data, Acceleration
As with the regular driving data, the results for Model 1 show poor agreement
with that of known values. However, Model 2 shows again, reasonable agreement with
mass error of 15% and constant loss values of approximately 15%. This again can be
attributed to using the simpler model, as shown in Figure 5.10 below.
89
-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
-3
-2
-1
0
1
2
3
4
5
x 10
4
D
r
iv
e F
o
r
c
e
(N
)
Acceleration (m/s
2
)
y = 4.5e+004*x + 6.2e+003
data 1
linear
Figure 5.10. Truck Acceleration Test Data with Linear Fit
5.7 Test Data Road Load Results
Data was taken with the intention of analyzing the total road load on the vehicle
as they travel the NCAT test track. Interest in studying the individual asphalt sections for
their effect on fuel economy has led to the analysis of longitudinal load as a function of
track position. Data in Figure 5.11 shows the applied drive force of the trucks in 3-view
as a function of track position. The plane indicated in red represents the average percent
load, while red circles indicate the location of changes in the asphalt sections.
90
-1000
-500
0
-300
-200
-100
0
20
40
60
80
GPS Position East (m)
GPS Position North (m)
D
r
iv
e F
o
rce (%
)
Measured % Torque
Asphalt Section Markers
Track Layout, Representing Ave % Load
Figure 5.11. Uncorrected Road Load Measurements
To accurately analyze the truck data, the exact location of the GPS antenna must be taken
into account. The GPS antenna is mounted just behind the roof of the truck?s cab so an
algorithm must be written to translate this measurement to the vehicles longitudinal
center. It is also necessary to consider the trucks length in any analysis as data is sampled
where the truck is passing over asphalt transitions and is therefore on two sections at one
time. This data that has truck measurements on two surfaces should not be considered
when analyzing average road load per section. Figure 5.12 below compensates for both
GPS antenna offset and truck length and calculates an average longitudinal load for each
asphalt section, shown in black. Figure 5.13 shows only the averaged road load per
section for more clarity.
91
-1000
-800
-600
-400
-200
0
200
-300
-200
-100
0
20
40
60
80
GPS Position East (m)
GPS Position North (m)
D
r
iv
e
F
o
rc
e (%
)
Figure 5.12. Road Load Measurements with Section Averages
-1000
-800
-600
-400
-200
0
200
-300
-200
-100
0
20
40
60
80
GPS Position East (m)
GPS Position North (m)
D
r
iv
e
F
o
rc
e
(%
)
Figure 5.13. Road Load Averages by Section
Road load is impacted by the road slope as discussed in Section 2.6. As the vehicle
travels the track the cruise controller varies the engine?s torque, or drive force in an
attempt to maintain a constant vehicle speed. Using the track elevation data presented in
92
Section 2.6, a road grade for each section is computed, and a corresponding longitudinal
force is calculated based on the known vehicle mass during the experiments. Figure 5.14
shows the average longitudinal load per asphalt section after the force due to the road
grade is removed. As is shown, the average loading deviates from the raw measurements,
indicating the significance road grade has on the trucks, even at such small amplitudes as
the NCAT test track.
-1000
-800
-600
-400
-200
0
200
-300
-200
-100
0
2000
4000
6000
8000
10000
12000
14000
GPS Position East (m)
GPS Position North (m)
D
r
iv
e F
o
rce (N
)
Figure 5.14. Corrected Road Load Measurements and Averages
Figure 5.15 compares the original averaged road load to the road load shown previously
in Figure 5.13 where the forces due to slope are removed. The load shows small
differences on the track?s straight sections, as would be expected with a quite flat surface.
93
However, the uphill climb through the west end shows reduced loading when the slope is
removed. The opposite effect happens in the east end of the track, where the vehicle
travels on a downhill slope to the north side of the track. This corrected force represents
an estimate of the magnitude of the sum of the losses due to the air drag, rolling
resistance, and driveline of the vehicle.
-1000
-800
-600
-400
-200
0
200
-300
-200
-100
0
2000
4000
6000
8000
10000
12000
14000
GPS Position East (m)
GPS Position North (m)
D
r
iv
e F
o
rce
(N
)
Asphalt Section Markers
Test Track Path, Average Force Plane
Slope Corrected Longitudinal Force
Longitudinal Force Per Section
Figure 5.15. Slope Corrected Road Load Comparison
Figure 5.16 shows the magnitudes of both the averaged measurements and the slope
corrected measurements as a function of track surface. The force due to the slope of the
road is also shown.
94
0 5 10 15 20 25 30 35 40 45
0
5000
10000
15000
F
o
rce
(N
)
Mean Force Per Section
Slope Correct Force Per Section
0 5 10 15 20 25 30 35 40 45
-4000
-2000
0
2000
4000
F
o
rce (N
)
Asphalt Section
Force Due To Road Slope
Figure 5.16. Road Load and Asphalt Sections
Analyzing the road load results shows the impact the road grade has on the
vehicle loading around the track. Removing the road grade from the force measurement
should show the magnitude of the remaining losses in the vehicle. This however does not
explain trends seen in the curves, where the correct road load values are increased over
the average in the west end turn, and decreased over average in the east curve. In other
words, the results show increased losses in the west curve and decreased losses in the east
curve. This trend in the plot actually has the behavior that the road grade in the turns was
underestimated which would indicate that the accuracy of the survey data is suspect.
95
96
However, this is not likely the case, as the average slope based on the elevation change
between the north and south ends and the radius of the turn supports the average slope
seen in the corners. This data can be verified in the future by taking dedicated GPS
vertical measurements as discussed in Section 5.3. The irregularity in the force could also
be due to a south wind. To account for the differences seen in the force, which are
approximately 2000N, would require a 10.6 m/s (23.7 mph) wind speed. This wind would
also have to remain fairly constant due to the repeatability of the data over the 4 hour test
session. This is possible and should be considered in future tests and may require
additional sensors on the vehicle, such as dynamic pressure sensors. The average force
irregularity could also be partially due to the behavior of the truck?s electronic fuel and
cruise controller behavior and would require adding cruise controller dynamics to better
validate the behavior of the truck?s controller.
Figure 5.17 shows the road load and asphalt roughness data collected at the test
track. The middle plot represnts asphalt roughness, starting at section N1, in the
Internation Roughness Index (IRI) scale. The IRI value is representative of large scale
irregularities which are typically described as those felt in the vehicle. The bottom plot
represents the Mean Texture Depth (MTD), which is shorter wavelength irregularities
more commonly heard in the vehicle. When comparing the roughness data with the road
force data no distinct relation can be shown with either macro or micro texture, which
also doesn?t account for the large road force trends seen in the trucks.
0 5 10 15 20 25 30 35 40 45
4000
6000
8000
10000
12000
14000
F
o
rce
(N
)
0 5 10 15 20 25 30 35 40 45
0
50
100
150
200
I
n
e
r
n
a
t
i
o
n
a
l
Ro
ughn
e
s
s
I
nde
x (
i
n
/
mi
)
Asphalt Section
0 5 10 15 20 25 30 35 40 45
0
0.5
1
1.5
Me
a
n
Te
xt
ur
e
De
pt
h
Asphalt Section
Mean Force Per Section
Slope Correct Force Per Section
Ave. Slope Corrected Force
IRI
Ave.
MTD
Ave.
Figure 5.17. Road Load and Asphalt Roughness
97
5.8 Conclusions
This chapter has presented an overview of the test bed and experimental testing of
the methods proposed in this thesis. A new estimation technique was presented and used
98
to verify unknown measurements available on the trucks. This measurement was then
used in combination with others to measure the trucks vehicle dynamics under various
tests. This data was used to estimate heavy truck parameters and a discussion of the
results is given. Much inaccuracy in the estimation results was seen due to various
reasons, including lack of dynamic excitation and sensor noise and accuracy.
The estimation results provided poor estimates in the experimental data, except
when applying the simplest of fits. Recall that Chapter 4 showed under adequate
excitation, the accuracy of estimating parameters in the presence of sensor noise. In the
estimation performed in this chapter, the excitation levels were consistently low. In the
case of the acceleration and deceleration experiments, the amount of data points available
were not adequate to provide accurate results. This shows the necessity of a direct study
on excitation in the presence of sensor noise, which is inherently described by the signal
to noise ratio.
99
CHAPTER 6
CONCLUSIONS
6.1 Summary
An investigation of vehicle longitudinal dynamics in simulation and experimental
tests has been presented. A vehicle model was developed and validated for studying
longitudinal vehicle dynamics and the losses therein. The vehicle dynamics model was
used to studying the effects and magnitudes of the various losses with in the moving
vehicle with the intention of quantifying the energy losses and therefore fuel economy
effects. Estimation techniques were used on the vehicle models in a unique test bed that
involved performing estimation in a non-typical environment. A sensitivity analysis was
performed in simulation showing the effects various sensor noise statistics have on
estimation accuracy. A heavy truck test bed was instrumented and data was used for
performing estimation results. Long term test longitudinal force data was also analyzed
for evaluating road load around a test track to deduce the losses involved with the asphalt
sections.
The following paragraphs summarize the information provided in the chapters of
this thesis. Chapter 2 presented a simple vehicle model that is widely used to describe the
longitudinal vehicle motion on forces on the vehicle. The model was simulated with
100
results showing vehicle behavior and performance. The individual losses were simulated
for their magnitudes on losses and in depth discussions of each are given.
Chapter 3 presented a more advanced derivation of longitudinal vehicle dynamics
that includes inertial effects of the driveline. More advanced simulations were performed,
which included acceleration, deceleration, and constant speed driving in varying
parameters as would be expected and the NCAT test track. Sensor modeling is also
presented and used in the vehicle simulations to produce results to mimics those that
would be measured in a real world test.
Using the models and simulations developed in Chapter 3, Chapter 4 gave a
background on parameter estimation techniques using least squares, and presents models
for estimating the major vehicle parameters involved in longitudinal vehicle dynamics.
These estimation models were used with the results from simulating various vehicle
maneuvers to perform parameter estimates in simulation. The simulated sensor outputs
were used to perform parameter estimates and a sensitivity analysis was performed to see
the effects of sensor noise on estimation accuracy.
Chapter 5 then described the vehicle test facility and shows real world tests on the
work shown in the previous chapters. Road grade around the track and its influences
discussed in previous chapters is backed up with real world measurements. An alternative
estimation technique utilizing a Kalman Filter is presented and applied to verify the
accuracy of the load measurement available from the vehicle on board electronics.
Estimation is then performed on various experiments and the results show the feasibility
of identifying mass and difficulty distinguishing the various longitudinal losses. Test data
101
is also analyzed for road load behavior for the direct comparison of road load to asphalt
section, or track position.
6.2 Recommendations for Future Work
Ultimately, the work in this thesis should be extended to include vehicle
estimation results in test environments other than that of the test track. As shown in
Chapter 4, the amount of data and the quality of data has a very large effect on the
estimation algorithms? performance. Having access to more high quality data will
improve the quality of the results presented in this thesis.
System excitation, or the magnitude of dynamic excitation, is also essential to
providing accurate estimation results. This effect is amplified by the inclusion of sensor
process and measurement noise. Direct studies on system excitation will yield more
comprehensive sensitivity to noise analysis. This will add more dimensions to
understating the estimation algorithms performance.
Much work has been done on correlating asphalt roughness to fuel economy
effects [duPlessis, 1990; Bester, 1984; Descornet, 1990]. However, this work is
somewhat limited in the amount of surfaces tested, and doesn?t always have a means to
validate the measurements taken. The NCAT test facility is an excellent resource for
continuing the work started in this thesis. However, some simple recommendations can
be made for improving the existing test bed. Because road grade has such a large effect
on the longitudinal loading of the vehicle, a GPS system capable of very accurate vertical
measurements should be used to estimate the road grade. This could be inserted into more
102
advanced estimation schemes that will allow the varying rolling resistance estimates to be
performed. Higher accuracy GPS will also be capable of providing more accurate
acceleration measurements and position for averaging data over a test section.
To fully understand and simulate fuel economy benefits, a more accurate engine
map should also be considered. This can be done by measuring various engine parameters
while driving under significant excitation. A fuel consumption map can be generated
using measurements of brake mean effective pressure (fuel flow as a function of output),
engine load, and engine rpm. This allows the individual engine?s characteristics to be
analyzed as part of the complex vehicle system and true fuel efficiency benefits
estimated. Understanding the engine control system also involves characterizing the
vehicle?s cruise controller. It is important to understand its control behavior as this will
effect fuel use outside of road loading. Appendix C shows a sample cruise control and the
effect it can have on the vehicle.
Another option for continuing the research is the construction of a dedicated
rolling resistance test rig. Typically rolling resistance measurements are made using a
towed implement with a force measuring device. The current estimation schemes could
be adapted to estimate rolling resistance in a fully instrumented test rig that could be
towed around the track on a regular basis. This device could also be made to measure the
rod irregularities directly, and therefore provide a direct rolling resistance versus surface
quality measurement.
103
REFERENCES
[1] Anderson, R., and Bevly, D.M., Estimation of Slip Angles using a Model Based
Estimator and GPS, Proceedings of the American Control Conference,
2004, pp. 2122-2127.
[2] Ardalan, V, Anna Stefanopoulou, Huei Peng, Recursive Least Squares with
Forgetting for Online Estimation of Vehicle Mass and Road Grade:
Theory and Experiments, Vehicle System Dynamics, Jan 16, 2003.
[3] Bae, H.S., and Gerdes, J.C., Parameter Estimation and Command Modification for
Longitudinal Control of Heavy Vehicles, AVEC 2000, Ann Arbor,
Michigan, August 2000.
[4] Bae, H.S., Ryu, J., and Gerdes, J.C., Road Grade and Vehicle Parameter
Estimation for Longitudinal Control Using GPS, IEE ITS 2001, Oakland
CA, August 2001.
[5] Bester, C.J., ?Effect of Pavement Type and Condition on the Fuel Consumption of
Vehicles,? Transportation Research Record 1000, National Research
Council, Washington D.C., 1984, pp.28-32.
[6] Bevly, D.M., Gerdes, J. C., Wilson, C., and Zhang, G., The Use of GPS Based
Velocity Measurements for Improved Vehicle State Estimation,
Proceedings of the American Control Conference, 2000, pp. 2538-2542.
[7] Bevly, D. M., Ryu, J., Sheridan, R., Gerdes, J. C, ?Integrating INS Sensors with
GPS Velocity Measurements for Continuous Estimation of Vehicle Side-
Slip and Tire Cornering Stiffness,? Proceedings of the 2001 American
Control Conference, Vol.1, June 2001, pp.25-30.
[8] Demoz, G.E., ?Design and Performance Analysis of a Low-Cost Aided Dead
Reckoning Navigator.? A Dissertation submitted to the Department of
Aeronautics and Astronautics and the committee on graduate studies of
Stanford University, Stanford University 2003.
104
[9] DeRaad, L.W., ?The Influence of Road Surface Texture on Tire Rolling
Resistance,? SAE Paper No. 780257, 1978.
[10] Descornet, G., ?Road-Surface Influence on Tire Rolling Resistance,? Surface
Characteristics of Roadways: International Research and Technologies,
American Society for Testing and Materials, Philadelphia, 1990, pp. 401-
415.
[11] Dixon, J. C., ?Tires, Suspension and Handling? Society of Automotive Engineers.
Warrendale, PA. ISBN: 1-56091-831-4, 1996.
[12] duPlessis, H.W., Visser, A.T., and Curtayne, P.C., ?Fuel Consumption of Vehicles
as Affected by Road-Surface Characteristics,? Surface Characteristics of
Roadways: International Research and Technologies, American Society
for Testing and Materials, Philadelphia, 1990, pp. 480-496.
[13] EIA, ?2004 Annual Energy Review,? 2004, The Energy Information
Administration: U.S. Dept of Energy, http://www.eia.doe.gov/emeu/aer/.
[14] Flenniken, W.S. IV., ?Characterization of Various IMU Error Sources and the
Effect on Navigation Performance,? Proceedings of The Institute of
Navigation?s GNSS Meeting, Long Beach, CA, September 2005.
[15] Gillespie, T. D. 1992. ?Fundamentals of Vehicle Dynamics.? Society of
Automotive Engineers. Warrendale, PA. ISBN: 1-56091-199-9.
[16] Glemming, D.A., Bowers, P.A., ?Tire Testing for Rolling Resistance and Fuel
Economy,? SAE Paper No. 750457, 1975.
[17] Grover, P.S., Bordelon, S.H., ?New Parameters for Comparing Tire Rolling
Resistance,? SAE Paper No. 1999-01-0787, 1999.
[18] Knight, R.E., ?Correlation of Truck Tire Rolling Resistance as Derived From Fuel
Economy and Laboratory Tests,? SAE Paper No. 821266, 1982.
[19] Knight, R.E., ?Tire Parameter Effects on Truck Fuel Economy,? SAE Paper No.
791043, 1979.
[20] LaClair, T.J., ?Rolling Resistance,? The Pneumatic Tire, National Highway Traffic
Safety Administration, Washington D.C., 2005, pp. 475-532.
[21] LaClair, T.J., Truemner, R., ?Modeling of Fuel Consumption for Heavy-Duty
Trucks and the Impact of Tire Rolling Resistance,? SAE Paper No. 2005-
01-3550, 2005.
105
[22] Milliken, D. L. and Milliken, W. F. 1995. Race Car Vehicle Dynamics. Society of
Automotive Engineers. Warrendale, PA. ISBN: 1-56091-526-9.
[23] Nielsen, L., Sandberg, T., ?A New Model For Rolling Resistance of Pneumatic
Tires,? SAE Paper No. 2002-01-1200, 2002.
[24] Petersen, E., Neuhaus, D., Glabe, K., Koschorek, R., and Reich, T., ?Vehicle
Stability Control for Trucks and Busses,? SAE Paper No. 982782, 1998.
[25] Schuring, D.J., Redfield, J.S., ?Effect of Tire Rolling Loss on Fuel Consumption
of Trucks,? SAE Paper No. 821267, 1982.
[26] Song, T.S, et. Al, ?Rolling Resistance of Tires- An Analysis of Heat Generation,?
SAE Paper No. 980255, 1998.
[27] Stengel, Robert F, Optimal Control and Estimation, Dover Publications, New
York, 1994.
[28] Vahidi, A, Stefanopoulou, A., and Peng, H., ?Experiments for Online Estimation
of Heavy Vehicle?s Mass and Time-Varying Road Grade?, in Proceedings
of ASME World Congress, Washington, D.C, 2003.
[29] Wood, R., and Bauer, S., ?Simple and Low-Cost Aerodynamic Drag Reduction
Devices for Tractor-Trailer Trucks,? SAE Paper No. 2003-01-3377, 2003.
106
APPENDICES
107
APPENDIX A
VEHICLE PROPERTIES
A.1 Introduction
Appendix A contains a list and description of the vehicle properties used in the
vehicle model developed in Chapter 2 and 3.
108
A.2 Simulation Vehicle Properties
Table A.1 contains a list and value of the vehicle properties used in this thesis,
unless otherwise stated.
Table A.1: Vehicle Parameters
Description Value Units
Total Vehicle Mass 68000 kg
Air Drag Coefficient 0.6 unitless
Rolling Resistance Coefficient (ave.) 0.0058 unitless
Front Area 10.3 m
2
Tire Rolling Radius 0.504 m
10.5
7.37
5.21
3.78
2.76
1.95
1.38
1.0
Gear Ratios (Low; 1-8)
0.73
unitless
Final Drive Reduction 3.70 unitless
Inertias:
Engine Inertia 0.35 kg-m
2
=N-m-s
2
Clutch 0.15 kg-m
2
Transmission (each gear, 1 side) 0.005 kg-m
2
Rear Axle and Input Gear 0.015 kg-m
2
Differential 0.005 kg-m
2
Tire & Wheel 11.1 kg-m
2
Efficiencies:
Driveline Overall 0.85 unitless
Driveline Each Stage (Transmission,
final drive, brake losses, ea.)
0.95 unitless
Engine Torque Approximation tq = -1.81*10^-3*RPM^4
+1.56*10^-7*RPM^3
-1.217*10^-3*RPM^2
+2.571*RPM
lbf-ft
109
APPENDIX B
NCAT FACILITY: EXPERIMENTAL SETUP AND DATA
ACQUISITION
B.1 Introduction
Appendix B contains information about the National Center for Asphalt
Technology, the hardware, and the experimental setup.
B.2 Experimental Setup & Data Acquisition
Using the National Center for Asphalt Technology?s test track and the
Freightliner vehicles as a test bed, instrumentation was setup to do real world estimations
and fuel economy studies.
For the data collection, a PC/104 computer based data acquisition system was
developed. This small form factor computer provides a robust solution to on-board data
acquisition. The computer is housed in an extruded aluminum case that serves to isolate
the computer hardware from harsh environments, while allowing quick access to
computer functions and connections. The operating system used is real-time Unix based
QNX, primarily chosen for its stability, low memory and processing requirements, and
real-time functionality. Software was written using C++ to interface and data log the
various sensors in the system, shown in Figure B.1.
Figure B.1. Data Acquisition Layout
110
Sensors include a 6 DOF inertial measurement unit, ?Starfire? GPS, and CAN
data from the Freightliner?s engine computer. The PC, corresponding hardware, and
inertial sensors were mounted in the vehicle?s cab under the passenger seat, as shown in
Figure B.2.
Figure B.2. Data Acquisition and Sensors Inside Vehicle Cab
The NavComm manufactured Starfire GPS unit was mounted by attaching a
bracket to the vehicle structure just rear of the cab out of necessity for adequate satellite
view. This placed the receiver high enough to clear obstructions and placed the unit on
the vehicle?s centerline as shown in Figure B.3.
111
Figure B.3. NCAT Test Truck with Starfire GPS Unit Indicated
To solve issues of powering the complete data acquisition unit, without draining
the trucks battery when the truck is not running, a unique switching solid state power
management device was used. All the sensors are powered directly from switched (key)
power on the vehicle, but the computer needed to stay on at all times.
A power management device, made up of rectifier diodes, is used to switch
between the backup battery when the engine is off and the vehicle charging system when
the engine is on. It is also capable of recharging the separate backup battery using a
recharging circuit when the vehicles charging system is functional. This allowed the data
112
acquisition unit to be left unattended to take data, without requiring any user input or
necessity for restarting the computer. The total power system is outlined in Figure B.4.
Figure B.4. Data Acquisition Power Schematic
113
114
B.3 Hardware Manufacturer Summary
The following table, B.1, outlines the hardware used in data acquisition and the
corresponding manufactures.
Table B.1: Hardware Summary
Device Manufacturer
Bobcat Data Aq Computer w/Enclosure Versalogic Corp
Computer LCD/keyboard Earth Computer Technologies, Inc
DC to AC Power Inverter Sima
Data Aq Computer Power Supply Tri-M
IMU-400CD Crossbow Technology Inc.
Starfire GPS Receiver Navcomm
CAN Controller Lawicel
12 Volt Lead Acid Battery PowerSource
Solid State Power Management West Mountain Radio
115
B.4 Measurement Capability Summary
The following table shown below outlines the measurement capability of the data
acquisition system.
Table B.2: Measurement Summary
Measurement Source Data Format
Longitudinal
Acceleration
Xbow IMU Serial RS-232 Data Packets
Lateral Acceleration Xbow IMU Serial RS-232 Data Packets
Vertical Acceleration Xbow IMU Serial RS-232 Data Packets
Pitch Rotation Rate Xbow IMU Serial RS-232 Data Packets
Yaw Rotation Rate Xbow IMU Serial RS-232 Data Packets
Roll Rotation Rate Xbow IMU Serial RS-232 Data Packets
Latitude Starfire GPS NMEA-RMC Serial GPS Message
Longitude Starfire GPS NMEA-RMC Serial GPS Message
Ground Speed Starfire GPS NMEA-RMC Serial GPS Message
Heading Starfire GPS NMEA-RMC Serial GPS Message
Time Starfire GPS NMEA-RMC Serial GPS Message
Electronic Engine
Controller 3
Freightliner Engine
Computer
SAEJ1939 CAN Specification:
Parameter Group Number 61247
Electronic Engine
Controller 2
Freightliner Engine
Computer
SAEJ1939 CAN Specification:
Parameter Group Number 61443
Electronic Engine
Controller 1
Freightliner Engine
Computer
SAEJ1939 CAN Specification:
Parameter Group Number 61444
Cruise
Control/Vehicle
Speed
Freightliner Engine
Computer
SAEJ1939 CAN Specification:
Parameter Group Number 65265
Fuel Economy Freightliner Engine
Computer
SAEJ1939 CAN Specification:
Parameter Group Number 65266
The information in Table B.3 shown below represents the measurements
contained in the data packets logged in this research. The Society of Automotive
Engineers publishes and maintains the SAE J1939, Truck and Bus Control and
Communications Network Standards Manual. This manual describes the controller area
116
network (CAN) protocol used in many heavy vehicle systems and provides a standard
format and communications protocol for the manufactures if the choose to utilize them.
On the Freightliner trucks at the NCAT facility the CAN protocol has been unlocked and
made available to us for this research. Within the SAE specification are different
Parameter Group Numbers (PGNs) which describe the data packets being sent and
received and are functionally organized. Not all available PGNs on the vehicle were used
but the following data shown below outlines the PGNs which were used in this research.
Table B.3: SAEJ1939 Measurement Summary
Parameter Group
Number
Name Data Available
Nominal Friction % Torque 65247 Electronic Engine Controller 3
Engine?s Desired Operating
Speed
Selected Gear
Actual Gear Ratio
Current Gear
Transmission Requested Range
61443 Electronic Engine Controller 2
Transmission Current Range
Driver?s Demand Engine %
Torque
Actual Engine % Torque
61444 Electronic Engine Controller 1
Engine Speed
Wheel based Vehicle Speed 65265 Cruise Control/Vehicle Speed
Cruise Control Set Speed
Fuel Rate
Instantaneous Fuel Economy
Average Fuel Economy
65266 Fuel Economy
Throttle Position
117
APPENDIX C
GPS&INS Heavy Truck Cruise Control
C.1 Introduction
Appendix C contains a model derivation and simulation of a state-space vehicle
velocity (cruise) controller. This has applications to the Freightliner National Center for
Asphalt Technology Trucks because they travel the track under the action of the
Freightliner cruise control system. It has been shown previously in this thesis that is
important to understand the behavior of the control system and how it effects fuel
consumption.
This appendix investigates a cruise control that uses GPS and inertial sensors as
the inputs instead of the traditional wheel speed sensors. The system to be controlled is
the trucks longitudinal dynamics while rolling over asphalts of varying rolling resistance.
C.2 Cruise Control Model and Simulation
Typical cruise control systems are fairly simple in that their only input is usually a
wheel speed sensor. Their control variable is throttle position up to certain limits, usually
utilizing a proportional-integral-derivative controller. This simulation however, will use a
state feedback control. Longitudinal load variations from surface variations, turns
scrubbing off speed, and bank angle on the track, necessitate cruise control to vary the
throttle (or the engine control unit?s engine load calculation in this case, due to the diesel
engines lack of engine air flow throttle mechanisms). A GPS unit?s velocity
measurement and longitudinal acceleration are the inputs. Combining the sensors creates
an essentially cleaner, faster, and more accurate input to control the longitudinal
dynamics.
The system dynamics for this simulation are described as follows:
xmFFFF
AirDragcesisRollingDrive
&&=??=?
tanRe
C.1
where:
Drive
F =Drive force provided by engine
cesisRolling
F
tanRe
= Rolling resistance force
AirDrag
F = Force due to air drag
m = Vehicle mass
x&& = Longitudinal Acceleration
118
It is generally assumed that air drag is related to velocity squared via an air drag
coefficient, labeled as follows in Equation C.2.
2
1
VCF
AirDrag
=
C.2
Rolling resistance is related to mass with a linear coefficient as shown in Equation C.3.
ccesisRolling
mgCF
2tanRe
=
C.3
This simplifies the assumed model to:
xmVCmgCF
cDrive
&&=??
2
12
C.4
Note that this system includes nonlinear dynamics. In order to put this plant into
state space format we?ll have to linearize about some reference point. This is also
necessary to calculate the state feedback control gains. In the case of our cruise control
system we?ll linearize about the target velocity and . This assumes prior knowledge
of the rolling resistance and air drag coefficients as shown below:
Drive
F
2
1
=C
C.5
01.0
2
=C
C.6
Which results in:
M
V
g
M
F
x
c
d
2
2
01.0 ??=&&
C.7
Using the Jacobian to linearize Equation C.7:
119
ulin
xlin
u
ulin
xlin
x
fB
fA
uxfx
?=
?=
= ),(&
C.7
Looking at u indicated in Equation C.7 at steady state : 0==Vx
&
&&
gMxu
gMxu
M
V
g
M
F
refref
ssss
c
d
01.02
01.02
2
01.00
2
2
..
2
+=?
+=
??=?
C.8
Taking:
g
M
x
M
u
f 01.0
2
2
??=
C.9
Results in:
M
B
M
x
A
ref
1
4
=
?
=
C.10
Arranging the plant into state space format results in the following:
Vy
F
M
V
M
V
x
where
DuCxy
BuAxx
d
=
+
?
=
+=
+=
14
:
&
&
C.11
Therefore our plant matrices are:
120
[]
mphV
where
D
C
M
B
M
V
A
ref
ref
45
:
0
1
1
4
=
=
=
?
?
?
?
?
?
=
?
?
?
?
?
??
=
C.12
Using the Matlab ?place? command, the system poles can be placed to be
however fast we like. The state-space control poles were placed such that the system had
a response resembling the longitudinal dynamics of a ground vehicle (settling time of 10
seconds) and a limit was put on the Fdrive command to a value of force equating to
0.5g?s of longitudinal acceleration. Also, to make the system more accurate, the plant
model in the simulation is that of the second order system, where the linearized system
was only used to pick the feedback gains. The following is the block diagram for the
simple state feedback cruise control with noise added to the system output.
Figure C.1. Block Diagram of State Feedback Cruise Control
121
The next step is to add an observer to the system, which will allow the use of both
GPS and a longitudinal accelerometer to estimate a cleaner velocity to serve as the input
to the controller. The typical form a state space controller and estimator is as follows in
Figure C.2.
Figure C.2. Block Diagram of Typical State Space Controller and Estimator
For the system studied in this thesis, the truck plant and estimator plant are
different and therefore the standard estimator model will not function, as the state matrix
varies between the two. The first option is to create two separate systems, a plant and
estimator and feed the estimator output to the input of the truck plant. However, this can
be simplified to the following system, which will be used for the GPS/INS cruise
control.
For the estimator:
122
[]
[]
?
?
?
?
?
?
=
?
?
?
?
?
?
+
?
?
?
?
?
?
?
?
?
?
?
? ?
=
+=
+=
ax
x
ax
b
V
y
a
b
V
x
where
DuCxy
BuAxx
01
0
1
00
10
:
&
&
C.13
With the following system matrices:
[]
0
01
0
1
00
10
=
=
?
?
?
?
?
?
=
?
?
?
?
?
? ?
=
D
C
B
A
C.14
The estimator gains are found similarly to the state feedback gains with the
matlab pole placement function, but settle time is chosen to be about 10 times faster than
that of the plant. The estimator above is essentially taking an acceleration input,
subtracting the accelerometer bias and integrating to add a correction to the GPS velocity
measurement. Both the accelerometer and velocity have random noise added to them,
with specs obtained from sensor data sheets. The accelerometer also has a constant turn
on bias modeled. The system block diagram is shown in Figure C.3.
123
Figure C.3. Block Diagram of State Space Controller and Estimator
Simulations were run to verify the performance of the cruise controller and to
assure that the estimator was providing some measurement benefits and removing the
sensor bias.
124
0 20 40 60 80 100 120
0
20
40
Time (sec)
V
e
lo
city
(m
/s)
GPS Velocity
Clean/Estimated Velocity
0 20 40 60 80 100 120
-2
0
2
Time (sec)
A
c
c
e
lero
m
e
ter
B
i
a
s
E
s
tim
ate (m
/s
2
)
Bias Estimate, with simulated constant bias of 1 m/s
2
0 20 40 60 80 100 120
0
1
2
x 10
5
Time (sec)
Cont
r
o
l
I
nput
,
D
r
iv
e
F
o
rce (N
)
Figure C.4. State Space Controller and Estimator Results
The controller also seems to be giving very good response with no overshoot and zero
steady state error, discounting the noise. The following plots provide a closer look at the
raw velocity measurement and the estimated velocity.
125
15 20 25 30 35 40 45
19.85
19.9
19.95
20
20.05
20.1
20.15
Time (sec)
V
e
lo
city
(m
/s)
GPS Velocity
Clean/Estimated Velocity
Figure C.5. State Space Estimator Velocity Results
Next, random rolling resistance variation was added to the system. This will serve
as a disturbance much like the NCAT trucks experience on their test track as they pass
over various asphalts and small slope changes. The technique for this was essentially
generating different random calculations of rolling resistance that each lasted for 20
seconds. The system block diagram is in the following figure.
126
Figure C.6. Block Diagram of State Space Controller and Estimator with Rolling Resistance
Disturbance
Figure C.7 shows a simulation of very small changes in rolling resistance and the
velocity response.
127
0 50 100 150 200 250
19
19.5
20
20.5
21
Time (sec)
V
e
lo
ci
ty
(m
/
s
)
Clean/Estimated Velocity
GPS Velocity
0 50 100 150 200 250
-0.0102
-0.01
-0.0098
Time (sec)
R
o
llin
g
R
e
sistan
c
e
C
o
e
f
ficien
t
Small Longitudinal Disturbance, Mean Value: 0.01, 10% variance
0 50 100 150 200 250
0
2000
4000
6000
8000
10000
Time (sec)
D
r
iv
e F
o
rce
(N
)
Figure C.7. State Space Controller and Estimator Results with Small Rolling Resistance
Disturbance
Figure C.8 shows a much larger disturbance in the rolling resistance parameter.
This causes the controller to command larger force variations to try to maintain the target
speed. It?s also interesting to note, that due to the large variance of rolling resistance
coefficients, some actually went to positive values, indicating that the loss was actually a
gain, or a force propelling the vehicle. An example would be a down-hill situation. In this
case, the controller obeyed its limits, commanding zero drive force.
128
0 50 100 150 200 250
19
19.5
20
20.5
21
Time (sec)
V
e
lo
city
(m
/s)
Clean/Estimated Velocity
GPS Velocity
0 50 100 150 200 250
-0.1
0
0.1
Time (sec)
R
o
llin
g
R
e
sistan
ce C
o
e
fficien
t
Small Longitudinal Disturbance, Mean Value: 0.01, 100% variance
0 50 100 150 200 250
0
5000
10000
15000
20000
Time (sec)
D
r
iv
e F
o
rc
e (N
)
Figure C.8. State Space Controller and Estimator Results with Large Rolling Resistance
Disturbance
This cruise control is an interesting study on the state feed back/state space
control techniques and gives the opportunity to use sensor fusion in a common
application. The controller/estimator implemented performs very well. The controller
tracked disturbances well within the realm of vehicle longitudinal dynamics. The
linearization to design the feedback gains didn?t seem to have any measurable effect on
the controller?s performance. The estimator improved the GPS reading as well as quickly
129
130
estimated out the accelerometer bias, within the time frame of what?s necessary upon
initializing a cruise control.
There exists opportunities to verify the drive force commands and estimated
velocity measurements accuracy on the trucks to make this cruise control?s behavior
match that of the real trucks to further other research. It is important to understand the
controller properties and behaviors if looking at the vehicle dynamics. Certain under and
overshoot of the controller may skew results for fuel economy studies.