Development of a Traction Control System for a

Development of a Traction Control System for a
Development of a Traction Control System for a Parallel-Series PHEV
THESIS
Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in
the Graduate School of The Ohio State University
By
Amanda Nicole Hyde
Graduate Program in Mechanical Engineering
The Ohio State University
2014
Master's Examination Committee:
Professor Giorgio Rizzoni, Professor Shawn Midlam-Mohler
Copyright by
Amanda Nicole Hyde
2014
Abstract
The work presented in this thesis details the development of a traction control system for a
parallel-series plug-in hybrid electric vehicle created by the Ohio State EcoCAR 2 team.
The test vehicle is a rebuilt 2013 Chevrolet Malibu features a 1.8L ethanol engine, an 80
kW permanent magnet electric machine, and a 6-speed automated manual transmission to
power the front axle while another 80 kW electric machine and a fixed speed gear box
power the rear axle. A 340 V lithium ion battery pack acts as the energy storage system for
the electric drivetrain components. The front and rear powertrains are not mechanically
coupled and thus act independently of one another allowing the vehicle substantial
flexibility of three major operating modes to achieve maximum efficiency without
sacrificing vehicle range. While the slip detection and traction control algorithms
developed in this work were intended specifically for the Ohio State EcoCAR 2 vehicle,
they could be easily adapted to any vehicle with independent front and rear drivetrains.
The existing quasi-static simulator of the test vehicle was expanded to account for the
inertias and stiffnesses present in the powertrain and create a dynamic simulator. This was
accomplished using the SimDriveline toolbox available in The Mathworks’ Simulink
software. This model also incorporates longitudinal tire dynamics using the Pacejka Magic
Formula and a longitudinal vehicle model. The resulting simulator is a suitable plant model
ii
for traction control development, though further refinement is required for complete
functionality in all modes.
Using the dynamic plant model, a slip detection algorithm capable of detecting slip on
either axle or both simultaneously is developed. The algorithm uses six wheel speed
comparisons to determine the vehicle current slip scenario without requiring knowledge of
the current vehicle speed. Next the traction control algorithm was developed to act
independently on each axle if slip is detected. The system creates axle torque limits on the
outputs of the operating strategy that reduce torque until wheel slip stops and then gradually
reapplies the torque until the full driver torque request has been restored with no wheel
slip. Software-in-the-Loop results for a large variety of tests show significant improvement
in vehicle performance on low friction surfaces. Large decreases in peak wheel speed, peak
slip ratio, and maximum slip interval were observed in all cases. In-vehicle validation was
performed for a limited number of tests but adequately demonstrated real-world
functionality of the slip detection and torque control algorithms on the vehicle.
iii
Vita
May 2007 .......................................................Parkview High School
2011................................................................B.S. Mechanical Engineering, University of
Oklahoma
2014................................................................M.S. Mechanical Engineering, Ohio State
University
Publications
Hyde, A., Midlam-Mohler, S., and Rizzoni, G., "Development of a Dynamic Driveline
Model for a Parallel-Series PHEV," SAE Int. J. Alt. Power. 3(2):2014
Fields of Study
Major Field: Mechanical Engineering
iv
Table of Contents
ABSTRACT ................................................................................................................................................ II
VITA ........................................................................................................................................................ IV
LIST OF TABLES ........................................................................................................................................ IX
LIST OF FIGURES ....................................................................................................................................... X
CHAPTER 1: MOTIVATION ........................................................................................................................ 1
1.1
THESIS OVERVIEW ..................................................................................................................................3
CHAPTER 2: LITERATURE REVIEW ............................................................................................................. 5
2.1
ELECTRIC AND HYBRID VEHICLES ...............................................................................................................5
2.1.1
Introduction .............................................................................................................................5
2.1.2
Classifications ..........................................................................................................................6
2.1.3
EcoCAR 2 ................................................................................................................................10
2.2
THE TRACTION CONTROL PROBLEM .........................................................................................................15
2.2.1
2.3
Intro to Tire Physics ...............................................................................................................16
CURRENT TRACTION CONTROL SOLUTIONS................................................................................................27
2.3.1
Torque Management Devices ................................................................................................27
2.3.2
Four-Wheel and All-Wheel Drive ...........................................................................................31
2.3.3
Traction Control Systems .......................................................................................................33
2.3.4
The OSU EcoCAR 2 Traction Control Problem ........................................................................38
v
CHAPTER 3: SYSTEM AND COMPONENT MODELING .............................................................................. 40
3.1
TRACTION CONTROL PHILOSOPHY ...........................................................................................................40
3.2
REQUIREMENTS ...................................................................................................................................40
3.3
ASSUMPTIONS .....................................................................................................................................41
3.4
POWERTRAIN MODELING ......................................................................................................................42
3.4.1
Engine ....................................................................................................................................43
3.4.2
Front Electric Motor ...............................................................................................................44
3.4.3
Transmission ..........................................................................................................................45
3.4.4
Rear Electric Machine and Gearbox ......................................................................................46
3.4.5
Front and Rear Axles ..............................................................................................................48
3.4.6
Wheel Dynamics ....................................................................................................................48
3.4.7
Tire Model ..............................................................................................................................49
3.4.8
Vehicle Model ........................................................................................................................52
CHAPTER 4: SIMULATION AND VEHICLE CONTROLS ............................................................................... 55
4.1
INTRODUCTION ....................................................................................................................................55
4.2
EXISTING SIMULATION TOOLS: ECOSIM2 .................................................................................................55
4.3
VEHICLE CONTROL STRATEGY .................................................................................................................58
4.4
SIMULATION FOR TRACTION CONTROL: ECOSIM2 – DYNAMIC .....................................................................60
4.5
ECOSIM2-DYNAMIC INITIAL VALIDATION .................................................................................................62
4.6
ECOSIM2-DYNAMIC RESULTS ................................................................................................................63
CHAPTER 5: TRACTION CONTROL DEVELOPMENT .................................................................................. 69
5.1
VEHICLE CONFIGURATION ......................................................................................................................69
5.2
ALGORITHM PLACEMENT .......................................................................................................................70
5.3
ACTIVATING TRACTION CONTROL ............................................................................................................72
vi
5.3.1
Detecting Wheel Slip..............................................................................................................73
5.3.2
Determining Slip Scenario ......................................................................................................78
5.3.3
Handling for Non-Unique Slip Signatures ..............................................................................82
5.3.4
Setting Slip Flags ....................................................................................................................82
5.4
TRACTION CONTROL ALGORITHM ............................................................................................................84
5.5
IMPLEMENTATION ................................................................................................................................86
5.5.1
Controls Hardware .................................................................................................................87
5.5.2
Required Signals and Sensors ................................................................................................88
5.6
PARAMETER OPTIMIZATION ...................................................................................................................89
5.7
SYSTEM PERFORMANCE METRICS............................................................................................................91
5.8
SENSITIVITY TO ROAD FRICTION ..............................................................................................................92
CHAPTER 6: TESTING AND RESULTS ........................................................................................................ 97
6.1
SOFTWARE-IN-THE-LOOP (SIL) TESTING ...................................................................................................97
6.2
CHARGE DEPLETING MODE - SOFTWARE-IN-THE-LOOP (SIL) RESULTS ...........................................................99
6.2.1
Results Summary ...................................................................................................................99
6.2.2
Detailed Results – All Wheels on Low Friction .....................................................................100
6.3
CHARGE DEPLETING MODE – IN VEHICLE RESULTS ...................................................................................105
6.3.1
Launch with All Wheels on Low Friction ..............................................................................105
6.3.2
Launch with Left Wheels on Low Friction ............................................................................107
6.4
CHARGE SUSTAINING SERIES MODE – SIL RESULTS...................................................................................109
6.4.1
Results Summary .................................................................................................................109
6.4.2
Detailed Results – All Wheels on Low Friction .....................................................................111
CHAPTER 7: CONCLUSIONS AND FUTURE WORK .................................................................................. 114
7.1
CONCLUSIONS ...................................................................................................................................114
vii
7.2
FUTURE WORK ..................................................................................................................................115
BIBLIOGRAPHY ..................................................................................................................................... 117
viii
List of Tables
Table 1: EcoCAR 2 Vehicle Technical Specifications ..................................................... 12
Table 2: Gear and Drive Ratios of the Transmission ........................................................ 46
Table 3: Friction Coefficient Variance Convention.......................................................... 64
Table 4: Typical Friction Coefficients [11], [22].............................................................. 64
Table 5: Conditions for Slip Scenario 1 ............................................................................ 79
Table 6: Conditions for Slip Scenario 2 ............................................................................ 80
Table 7: Conditions for Slip Scenario 3 ............................................................................ 80
Table 8: Conditions for Slip Scenario 4 ............................................................................ 81
Table 9: Slip Flag Determination...................................................................................... 83
Table 10: Simulation Optimized Parameter Values.......................................................... 91
Table 11: Friction Distributions ........................................................................................ 92
Table 12: Results Summary for Charge Depleting Operation in SIL ............................... 99
Table 13: Results Summary for Charge Sustaining Series Operation in SIL ................. 110
ix
List of Figures
Figure 1: Oil Consumption in Select Regions 1965-2010 [1] ............................................ 1
Figure 2: Sample Series Hybrid Architecture [3] ............................................................... 7
Figure 3: Sample Parallel Hybrid Vehicle Architecture [3] ............................................... 8
Figure 4: Sample Power-Split Hybrid Architecture [3] ...................................................... 9
Figure 5: OSU Powertrain Architecture ........................................................................... 13
Figure 6: Powertrain Configurations for Vehicle Operating Modes ................................ 14
Figure 7: Tire Contact Mechanisms [2] ............................................................................ 17
Figure 8: Brush Model Representation of Tires [2] .......................................................... 19
Figure 9: Characteristic Curve of Longitudinal Tire Force as a Function of Slip Ratio [8]
........................................................................................................................................... 22
Figure 10: Example Slip-Slope Curves [11] ..................................................................... 24
Figure 11: Free Body Diagram of Wheel During Acceleration [1] .................................. 26
Figure 12: Clutch Type Limited Slip Differential [2], [15] .............................................. 29
Figure 13: Viscous Coupling Type Limited Slip Differential [2]..................................... 30
Figure 14: Driveline Dynamic Model ............................................................................... 42
Figure 15: SAE Tire Axis System [14] ............................................................................. 50
Figure 16: Vehicle Model Block Diagram [22] ................................................................ 52
Figure 17: Torque/Speed Structure of EcoSIM2 .............................................................. 56
x
Figure 18: EcoSIM2 User Interface .................................................................................. 57
Figure 19: PHEV Powertrain Subsystem in EcoSIM2 ..................................................... 58
Figure 20: EcoSIM2 – Dynamic User Interface ............................................................... 60
Figure 21: Initial Validation for EcoSIM2-Dynamic........................................................ 63
Figure 22: Actuator Torques and Speeds During US06 Cycle - 𝝁𝒙 = 1.0........................ 65
Figure 23: Wheel Speeds and Wheel Slip During Zero-to-Sixty Acceleration - 𝝁𝒙 = 1.065
Figure 24: Actuator Torques and Speeds During US06 Cycle - 𝝁𝒙 = 0.26...................... 66
Figure 25: Wheel Speeds and Slips During US06 Cycle - 𝝁𝒙 = 0.26 .............................. 67
Figure 26: Control Strategy Flow Chart ........................................................................... 71
Figure 27: Slip Scenarios .................................................................................................. 74
Figure 28: Torque Reduction Strategy Flow Chart........................................................... 85
Figure 29: Traction Control Illustration ............................................................................ 86
Figure 30: dSpace MicroAutoBox II ................................................................................ 88
Figure 31: Friction Study Results Per Axle ...................................................................... 93
Figure 32: Overall Performance Metric Value for Friction Study .................................... 94
Figure 33: Simulation for Friction Distribution A – Overall Performance Metric = 559. 95
Figure 34: Simulation for Friction Distribution G – Overall Performance Metric = 302. 96
Figure 35: Scenarios for SIL Testing ................................................................................ 97
Figure 36: Typical Accelerator Pedal Command.............................................................. 98
Figure 37: Wheel Speeds and Slip – All Wheels on Low Friction – Traction Control Off
......................................................................................................................................... 101
Figure 38: Vehicle Speed and Pedal Profile ................................................................... 102
xi
Figure 39: Wheel Speeds and Slip – All Wheels on Low Friction – Traction Control On
......................................................................................................................................... 102
Figure 40: Axle Torque Commands from Traction Control System .............................. 103
Figure 41: Vehicle Acceleration Performance ................................................................ 104
Figure 42: All Wheels on Ceramic Tiles – Traction Control Off ................................... 106
Figure 43: All Wheels on Ceramic Tiles – Traction Control On .................................... 107
Figure 44: Left Wheels on Low Friction – Traction Control Off ................................... 108
Figure 45: Left Wheels on Low Friction – Traction Control On .................................... 109
Figure 46: Wheel Speeds and Slip – All Wheels on Low Friction – Traction Control Off
......................................................................................................................................... 111
Figure 47: Wheel Speeds and Slip – All Wheels on Low Friction – Traction Control On
......................................................................................................................................... 112
Figure 48: Axle Torque Commands of Traction Control System................................... 113
Figure 49: Vehicle Acceleration Performance ................................................................ 113
xii
Chapter 1: Motivation
Petroleum is a non-renewable resource that is depleting with time. However the global
population continues to be reliant on petroleum products and petroleum energy to power
mobility around the world. Developing countries also contribute to a rapidly increasing
demand for petroleum products. Global consumption of oil has nearly tripled since 1965
[1] as seen in Figure 1.
Figure 1: Oil Consumption in Select Regions 1965-2010 [1]
1
Because oil supplies are finite in nature, the peak and eventual decline of oil production
rates are inevitable as adequate new supplies cannot be consistently found and brought to
production at reasonable cost and in a timely manner. Over time, this has driven up the
price of oil significantly. Much of the demand for oil in the United States is due to use as
fuel in transportation and in automobiles in particular. As oil and fuel prices increase, the
demand for fuel efficient vehicles, which can maximize the distance travelled per dollar,
also increases. This demand is also pushed forward by ever increasing regulations limiting
allowable emissions and mandating greater overall fuel economy.
The response from automotive manufacturers has been to pursue various avenues for
increasing fuel economy, decreasing emissions, and ensure sustainability into the future.
One method pursued is advancements in efficiency for internal combustion engines.
Another is the reduction of vehicle road loads with low rolling resistance tires, lightweight
materials, low drag body designs, and active aerodynamics. A third avenue is the use of
alternative fuels such as biodiesel, ethanol, natural gas, hydrogen, and electricity.
A final common and promising solution that manufacturers are developing is hybrid
electric vehicles. These are vehicles which use a minimum of two energy converters and
minimum two energy sources which are stored on-board and used for vehicle propulsion
[2]. Many types of hybrid vehicle are available on the market today including hybrid
electric vehicles (HEV), plug-in hybrid electric vehicles (PHEV), and extended range
electric vehicles (EREV). Hybrids provide a high level of flexibility in the powertrain
2
configuration which increases the capability of the vehicles over that of conventional
vehicles to meet increasingly stringent fuel economy and emissions goals.
It is not enough to assume that the existence of hybrids will make them attractive to
consumers. In order to boost the sale of hybrids and encourage them to permeate both the
market and the road, safety and consumer acceptability features must be comparable to or
exceed those of modern conventional vehicles. Traction control is a feature important both
to safety and consumer acceptability that is becoming standard on vehicles sold today. For
this reason, the development of traction control for hybrid vehicles is a necessary endeavor.
1.1
Thesis Overview
The work presented in this thesis discusses the development of a traction control system
for Ohio State EcoCAR 2 competition vehicle. This includes the creation of a dynamic
plant model of the vehicle powertrain, the development of a versatile slip detection
algorithm, and finally the development of a traction control algorithm for the Ohio State
EcoCAR 2 vehicle.
The organization of this thesis is as follows:

Chapter 2 provides background information on common types of hybrid vehicles,
the EcoCAR 2 competition, and on the experimental vehicle architecture. It also
explains the background information related to tire contact and traction control
including explanations of current traction control solutions.
3

Chapter 3 details the development of a dynamic powertrain model necessary for
use as the plant model in traction control development.

Chapter 4 outlines the implementation of the model developed in Chapter 3 to
create a simulator in Simulink

Chapter 5 describes the simulation and control development of the slip detection
strategy and the traction control algorithm

Chapter 6 details the testing of the developed algorithm and the results obtained
through simulation and in-vehicle testing

Chapter 7 summarizes the work presented in the thesis and gives recommendations
for future work on the topic
4
Chapter 2: Literature Review
2.1
2.1.1
Electric and Hybrid Vehicles
Introduction
The expanding prevalence of powertrain electrification demonstrates its popularity as a
means to increase fuel economy and reduce emissions. An electrified powertrain can be
either an electric vehicle (EV) or a hybrid electric vehicle (HEV). Electric vehicles do not
contain an internal combustion engine and are propelled solely by one or more electric
machines that are powered by a high voltage battery pack. Electric vehicles entirely
eliminate the need for liquid fuel in the vehicle and as a result have zero tailpipe emissions.
Electric vehicles also benefit from the high efficiency of electric machines in converting
electrical energy to mechanical power and the ability to recapture some amount of
mechanical energy and return it to the battery pack through the use of regenerative braking.
The disadvantages of electric vehicles include a limited range between charges (<100
miles) and long charge times which make EVs impractical for use outside of cities where
total daily commutes can be short. Other disadvantages to EVs include high purchase
prices, lack of charging station infrastructure, and concerns over the life-span of a high
voltage battery pack.
5
Hybrid electric vehicles combine the electric machines and battery pack of an EV with an
internal combustion engine and liquid fuel to propel the vehicle. There are a variety of
liquid fuels commonly used in hybrids including gasoline, E85, natural gas, and diesel. The
combination of power sources allows the engine size to be reduced compared to that of
conventional powertrains without sacrificing the vehicle’s ability to meet driver power
demands. The addition of liquid fuel also extends the range of the vehicle to be equivalent
to the range of conventional vehicles. Hybrid vehicles are also able to recapture mechanical
energy as electric energy through regenerative braking just as in EVs. The disadvantages
of hybrid vehicles are similar to those of electric vehicles including high purchase price,
charging infrastructure, and life of the battery pack.
2.1.2
Classifications
Hybrids are divided further into three main classifications: series, parallel, and power split.
These classifications are based upon the powertrain architecture used in the vehicle. Each
type of hybrid has a unique configuration that comes with certain advantages and
disadvantages.
2.1.2.1 Series Hybrid
Series hybrids are among the simplest of hybrid architectures. In a series hybrid all of the
propulsive power to the wheels is provided by an electric machine. Another electric
machine is driven by an engine to provide power directly to the battery pack. The
advantages of a series architecture include ease of packaging since the two motors need
6
not be near each other and a simple control strategy relative to other hybrid architectures
since only one torque source is connected to the driven wheels. Engine efficiency and
emissions can also be optimized since the engine is not mechanically coupled to the wheels
and thus can remain at predetermined optimal operating points at all times. An example
series architecture is given in Figure 2.
Figure 2: Sample Series Hybrid Architecture [3]
A disadvantage of the series architecture is the requirement for a large electric motor to be
used for traction and the requirement of at least two electric motors. The powertrain also
has inherent losses associated with the multiple energy conversions from mechanical to
electrical and back to mechanical.
7
2.1.2.2 Parallel Hybrid
Parallel hybrids have both an engine and electric machine coupled to the wheels through
some mechanical coupling. A multi-gear transmission can also be used with the engine
much like a conventional vehicle. The electric machine can be coupled before or after the
transmission in the driveline. Also, the electric machine can be used to help propel the
vehicle or act as a generator while the engine alone propels the vehicle. An advantage of
the parallel architecture is that only one electric machine is required and both the engine
and electric machine can be downsized since the sum of the power sources is used to drive
the wheels. The parallel architecture also allows for compact packaging. The disadvantages
of a parallel architecture include the inability to maintain the engine at optimal operating
points and increased complexity of the control strategy since torque and speed must be
balanced between multiple devices while also balancing the battery state of charge. An
example of a parallel hybrid architecture is given in Figure 3.
Figure 3: Sample Parallel Hybrid Vehicle Architecture [3]
8
2.1.2.3 Power-Split Hybrid
Power-Split hybrids contain the functionality of both series and parallel configurations and
are able to switch between the two. To obtain the ability to run in both modes, a powersplit hybrid typically contains two electric machines, one internal combustion engine, and
a configuration of clutches and gear sets, typically planetary gear sets, that allow the vehicle
to switch between modes. Power-split hybrids have the most complex controls problem of
the three hybrid classifications due to the large number of actuators involved. Packaging
can also be challenging due to the number of components involved. The main advantage
of a power-split hybrid is the flexibility of the powertrain which increases the capability
for improving fuel economy and emissions while maintaining vehicle performance [2]. An
example of a power-split hybrid architecture is given in Figure 4.
Figure 4: Sample Power-Split Hybrid Architecture [3]
9
2.1.3
EcoCAR 2
The rapidly advancing vehicle technology used in industry demands a particular skill set
and experience for effective development. Many of the nation’s top engineering
universities do not focus on or teach students about these new technologies as a part of
their degree programs, causing new engineering graduates to be inexperienced or ignorant
of advanced vehicle technology prior to their first day on the job. To help fill this
knowledge gap, the Advanced Vehicle Technology Competition (AVTC) series began and
continues to the present where EcoCAR 2 is the currently active competition sequence.
EcoCAR 2 and all AVTCs give students the opportunity to work first hand with the design
and implementation of state of the art automotive technologies while still enrolled in
school.
EcoCAR 2 is an AVTC sponsored by General Motors and the US Department of Energy
that challenges students to redesign a 2013 Chevrolet Malibu in order to obtain higher fuel
economy and lower emissions without sacrificing performance, safety, or consumer
acceptability. Fifteen teams across the US and Canada are participating in the competition
with the task of designing, building, and optimizing a new powertrain for the Malibu
culminating in a showroom ready vehicle by the end of the competition cycle. The vehicles
are judged over a full range of criteria including fuel economy, emissions, drivability,
acceleration, and braking performance, and consumer acceptability features.
The competition runs for three years, each of which represent a distinct phase of the design
process. Year 1 focuses on the design and computer simulation of the vehicles.
10
The year begins with an architecture selection phase which is followed by component
selection, in depth packaging studies, development of the vehicle and component
simulation plant models, and early development of the vehicle control strategy using
Hardware-in-the-Loop testing equipment. Early in Year 2 teams receive the production
vehicle from GM. Throughout the year each team tears down the stock Malibu and
integrates the team designed powertrain and controls. The teams should have a functional
mule vehicle capable of participating in dynamic driving events by the end of Year 2. Year
3 allows teams to refine and optimize the mechanical, electrical, and controls systems with
the ultimate goal of a near production ready vehicle by the end of Year 3.
2.1.3.1 EcoCAR 2 Vehicle Technical Specifications
The competition provides a set of vehicle technical specifications (VTS) that act as
performance targets for the vehicle during development. Table 1 below gives a selection
of relevant VTS for EcoCAR 2. The values for each metric for the stock 2013 Chevrolet
Malibu are provided in the table as well as the competition target value and the 2014
predicted value for the Ohio State team vehicle. The values for the Ohio State proposed
design are found using the simulation tools discussed later in Chapter 4.
Table 1 clearly illustrates the competition goals of reducing emissions and improving fuel
economy while maintaining performance and utility. This presents a significant design
challenge for the competing teams. For example, the acceleration times of the vehicle must
11
remain comparable to the stock vehicle despite a significant increase in vehicle mass due
to hybridization.
Table 1: EcoCAR 2 Vehicle Technical Specifications
Production 2013
Malibu
Competition
Design Target
OSU Proposed
Design
Acceleration 0-60 mph
8.2 sec
9.5 sec
10 sec
Acceleration 50-70 mph (Passing)
8.0 sec
8.0 sec
4.6 sec
143.4 ft
(43.7 m)
10+%
@ 60 mph
16.3 ft3
5
1589 kg
<2 sec
2012 155 mm
736 km
[457 mi] (CAFE)
8.83
(lge/100 km)
[787 Wh/km]
143.4 ft
(43.7 m)
3.5%
@ 60 mph
16.3 ft3
>=4
<2250 kg
<2 sec
155 mm
322 km
[200 mi]*
7.12
(lge/100 km)
[634 Wh/km]
143.4 ft
(43.7 m)
3.5+%
@ 60 mph
10 ft3
5
2075 kg
<10 sec
>127 mm
>398 km
[247 mi]*
1.36
(lge/100km)
[121.1 Wh/km]
N/A
**
141.8 (Wh/km)
787 (Wh/km)
634 (Wh/km)
262.9 (Wh/km)
774
(Wh PE/km)
253
(g GHG/km)
Tier 2 Bin 5
624
(Wh PE/km)
204
(g GHG/km)
Tier 2 Bin 5
43.1
(Wh PE/km)
123.5
(g GHG/km)
<Tier 2 Bin 5
Specification
Braking 60-0 mph
Highway Gradeability @ 20 min
Cargo Capacity
Passenger Capacity
Vehicle Mass
Starting Time
Ground Clearance
Vehicle Range
Utility Factor (UF)-Weighted Fuel
Energy Consumption*
UF-Weighted AC Electric Energy
Consumption*
UF-Weighted Total Energy
Consumption*
UF-Weighted WTW Petroleum
Energy (PE) Use*
UF-Weighted WTW GHG
Emissions*
Criteria Emissions
The competition also evaluates qualitative consumer acceptability features such as interior
noise, drive quality, ride, fit and finish, and stability. Though not listed in Table 1, these
metrics are judged during the competition and thus were kept in mind throughout vehicle
development process.
12
2.1.3.2 Ohio State Vehicle Architecture
The OSU vehicle architecture is a Parallel-Series PHEV shown in Figure 5. The front axle
is powered by a 1.8L Honda high compression ratio engine that can be coupled or
decoupled from the transmission input with a clutch. An 80 kW permanent magnet electric
machine is connected via belt drive to the transmission input shaft. The transmission itself
is a 6-speed automated manual transmission. The rear axle is powered by another 80 kW
electric machine connected to a fixed ratio gearbox which drives the rear wheels. The
electric drivetrain components are powered by a 340 V, 18.9 kWh lithium-ion battery pack.
This architecture has great versatility in its operation due to the independent front and rear
drives and the transmission’s ability to be used as an additional clutch when set to neutral
or one of the six gear ratios. This allows the vehicle to operate in a charge depleting mode
and a charge sustaining mode with both parallel and series configurations.
Figure 5: OSU Powertrain Architecture
13
For charge depleting operation, the engine is decoupled from the transmission while both
electric machines provide power to the wheels. For charge sustaining series operation, the
transmission is shifted to neutral and the engine clutch is closed so that the engine charges
the battery pack using the front electric machine as a generator and the rear electric machine
drives the vehicle. For charge sustaining parallel operation, the clutch is closed and the
transmission is in gear such that all three torque actuators are connected to the wheels.
Diagrams showing the vehicle configuration for each mode are shown in Figure 6.
Figure 6: Powertrain Configurations for Vehicle Operating Modes
14
An important intermediate operating mode is the engine start mode. During engine start,
the powertrain configuration is the same as series configuration. All driver requested torque
is sent to the rear electric machine and the front wheels are disconnected from the front
actuators with the transmission in neutral. The engine clutch closes to couple it with the
transmission input shaft and the secondary belt pulley. The front electric machine is then
used to spin up the engine to the required starting speed as the engine begins firing.
2.2
The Traction Control Problem
Active vehicle dynamics controls serve several important purposes. These include
increasing the range of conditions under which a vehicle behaves predictably as well as
enhancing vehicle comfort and response [4]. Traction control in particular maximizes
longitudinal and lateral tractive forces between the vehicle’s tires and the road for
acceleration and cornering performance. This is accomplished using control inputs and
available actuators to target an appropriate driven wheel slip. When thoroughly
implemented, traction control allows inexperienced drivers to perform as well as or better
than experienced drivers on slippery roads [4]. To understand traction control, it is
necessary first to understand the fundamental physics of tire contact and traction. This
chapter will give an introduction to traction physics that includes tire and vehicle forces,
tire contact, and wheel slip. A survey of popular traction control methods currently used in
conventional vehicles and novel traction control methods proposed for hybrid vehicles will
also be given. The section will conclude with a detailed explanation of the unique traction
control problem presented by the experimental vehicle.
15
2.2.1
Intro to Tire Physics
Vehicle motion is primarily caused by forces generated at the contact patch between tires
and the road. These forces are also produce the greatest non-linearity and uncertainty in the
control of vehicle dynamics [4]. To address this problem, highly non-linear models are
used to represent tire dynamics. However, only the underlying principles of tire contact
will be presented here.
2.2.1.1 Contact Mechanisms
A vehicle’s ability to accelerate or decelerate is often limited by the frictional coupling
between the tire and the road. The frictional coupling is a result mainly of two mechanisms:
adhesion and hysteresis. Adhesion is the result of intermolecular bonds between rubber in
the tire and aggregate in the road surface. Hysteresis represents energy loss as a result of
deformation in the rubber as it slides over the road surface [5]. Both of these forces, as
friction forces, rely upon some amount of slip occurring in the contact patch. Adhesion and
hysteresis are illustrated in Figure 7.
16
Figure 7: Tire Contact Mechanisms [2]
2.2.1.2 Effective Rolling Radius
An important concept that affects accurate tire modeling is the effective rolling radius. The
effective rolling radius of the wheel relates the angular velocity and linear velocity of the
wheel as it moves through the contact patch. The effective rolling radius differs from the
nominal tire radius due to the linear deformation of the tire in the contact patch. It is
important because typical vehicle operation occurs with a slip ratio of 10% or less for which
the calculation is significantly impacted by small changes in tire radius [2].
The basic relationship between angular and linear velocity that defines effective rolling
radius for a free rolling wheel is given by
𝑅𝑒𝑓𝑓 =
𝑉𝑥
𝜔𝑤
( 1)
17
where 𝑉𝑥 is the longitudinal speed of the wheel center and 𝜔𝑤 is the angular velocity of the
wheel [6]. In order to calculate the effective rolling radius without detecting wheel speed,
alternative calculations exist. One such alternative is given by [2]
𝑅𝑒𝑓𝑓
𝑟
sin {cos−1 ( 𝑠𝑡𝑎𝑡𝑖𝑐
𝑟𝑤 )}
=[
] 𝑟𝑤
𝑟
cos −1 ( 𝑠𝑡𝑎𝑡𝑖𝑐
)
𝑟𝑤
( 2)
where 𝑟𝑤 and 𝑟𝑠𝑡𝑎𝑡𝑖𝑐 represent the relaxed wheel radius and static wheel radius respectively.
Static wheel radius is defined by [2]
𝑟𝑠𝑡𝑎𝑡𝑖𝑐 = 𝑟𝑤 −
𝐹𝑧
𝑘𝑡
( 3)
𝐹𝑧 is the normal load on the tire and 𝑘𝑡 is the vertical tire stiffness. The vertical tire stiffness
can be calculated using test data from the tire manufacturer.
2.2.1.3 Brush Model
The brush model views the tire as a series of infinitesimal tread elements that reach laterally
over the contact patch. These elements can be thought of as individual spring elements that
can deform independently [2], [7]. The brush model also divides the contact patch into
sliding and adhesion regions. In the adhesion region, the tread elements adhere to the road
and the force generated is influenced by static friction. In the sliding region, the tread
elements slide against the road surface and the forces developed are influenced by kinetic
friction [7]. The sliding and adhesion forces cause the tread elements to bend as seen in
Figure 8.
18
Figure 8: Brush Model Representation of Tires [2]
Considering the longitudinal and angular velocities defined previously, the net velocity of
the treads through the length of the contact patch, 𝑙𝑐𝑝 , can be expressed as
𝑣𝑡𝑟𝑒𝑎𝑑 = 𝑅𝑒𝑓𝑓 𝜔𝑤 − 𝑉𝑥
( 4)
For a driving wheel, 𝑅𝑒𝑓𝑓 𝜔𝑤 is greater than 𝑉𝑥 implying that the net tread velocity is
opposite the direction of the longitudinal velocity. If the net tread velocity is relatively
small, the adhesion region exists which means that the tip of the element entering the
adhesion region has zero velocity at the point of contact with the ground and a velocity of
𝑣𝑡𝑟𝑒𝑎𝑑 at the other end of the tread element. This speed difference causes the tread elements
19
to bend in the direction of longitudinal vehicle motion as shown in Figure 8 [8]. At the
point at which the tire deformation exceeds the capability of static friction between the tire
and the road the tread element enters the sliding region of the contact patch. When the tread
element exits the contact patch entirely it returns to a relaxed state [2].
For a braking wheel, 𝑟𝑒𝑓𝑓 𝜔𝑤 is less than 𝑉𝑥 implying that the net tread velocity is in the
same direction as the longitudinal speed. This causes the tread elements to bend in the same
manner but opposite direction of that shown in Figure 8 [2], [8]. It also results in the
positions of the sliding and adhesion regions being switched from that shown in Figure 8
with respect to the direction of vehicle motion. In the case of a freely rolling wheel,
meaning that no driving or braking torque is applied, the tread elements remain vertical
throughout the contact patch and thus develop no propulsive force [6].
2.2.1.4 Wheel Slip
From the net tread velocity and the understanding of the maximum bending capability of
the tread elements explored above the slip ratio can be derived. The slip ratio is a unitless
metric that defines how the maximum deflection of the tread element is proportional to the
ratio of slip velocity in the contact patch to longitudinal velocity of the vehicle [5], [8].
Various expressions for wheel slip ratio exist, but for this work, the slip ratio is given by:
𝜅=
𝑅𝑒𝑓𝑓 𝜔𝑤 − 𝑉𝑥
𝑉𝑥
20
( 5)
This expression yields positive slip ratios when the vehicle is accelerating and negative slip
ratios when the vehicle is braking. Often a very small constant is added to the denominator
of the expression to prevent the slip ratio from becoming undefined as the vehicle speed
approaches 0. This yields a slip expression of:
𝜅=
𝑅𝑒𝑓𝑓 𝜔𝑤 − 𝑉𝑥
𝑉𝑥 + 𝜀𝑥
( 6)
where 𝜀𝑥 is the small constant.
2.2.1.5 Tire Friction Characteristics
One of the most important features necessary for traction control is the ability to estimate
friction between the tire and the road surface, or more specifically, the wheel-slip vs.
adhesion-coefficient characteristics of the tire. The coefficient of friction depends on
numerous variables and must be estimated in real time making it one of the greatest
challenges in traction control development [9], [10]. Some of the involved factors include
surface topography of the road, tread design, contaminants, tire speed, and the viscoelastic
properties of the rubber compound which vary with temperature and pressure.
Due to the complexity of the problem, tire friction characteristics are generally determined
from experimental observations and an empirical formulation is created. One frequently
used solution in current vehicles is the use of look-up tables based on experimental trials.
While deemed adequate for many driving conditions, these are limited in their capability
due to being a fixed control type. This means the tables are tuned to accommodate worst
21
case scenarios with poor road conditions which doesn’t allow optimal performance in good
conditions [9], [10].
Tire friction exhibits specific characteristics of peak and sliding friction. The peak
coefficient, 𝜇𝑝𝑒𝑎𝑘 , denotes the maximum friction force that can be created between the tire
and the road. Once the shear load between tire and road exceeds the force capability of the
vertical load on the tire combined with static friction, the wheel begins to slip and sliding
friction becomes the governing force [2]. This results in the total tractive force decreasing
continuously until the wheel locks entirely for braking or pure sliding occurs for
acceleration [10]. A typical characteristic curve of longitudinal tire force as a function of
the slip ratio is shown in Figure 9.
Figure 9: Characteristic Curve of Longitudinal Tire Force as a Function of Slip Ratio [8]
22
Considering only the longitudinal direction, the friction coefficient is given by
𝜇=
𝐹𝑥
𝐹𝑧
( 7)
2.2.1.6 Estimating Tire Friction Coefficient
There are numerous methods in use or proposed for estimating tire friction coefficient in
real-time. Some methods focus on detecting the many factors that affect friction and then
analytically predicting the peak friction coefficient. These methods frequently utilize
specialized sensors such as lubricant sensors or optical sensors which look at road
reflections [11]. Other methods look at the effects created by tire friction and then backcalculate to determine the friction coefficient. The effects typically utilized are acoustic
characteristics, tread deformation, and wheel slip. The first two again use specialized
sensors, an acoustic sensor for acoustic characteristics and a sensor affixed to the inner
surface of the tire to detect tread deformation, and rely on an understanding of very
complex characteristics that make it difficult to obtain an accurate estimation [8], [11].
Friction estimation based on wheel slip utilizes wheel speed and input force data to observe
the correlation between the tire slip at a given force to determine the friction coefficient.
Finally, there are methods of friction estimation that utilize longitudinal vehicle dynamics
to estimate tire friction coefficient. The most well-known of these methods is the “slipslope” method. The slip-slope method uses predetermined maps of slip-slope and friction
data to estimate 𝜇 in real-time based on the slip-slope calculated from sensor data [8]. A
generic example of the type of maps used with the slip-slope method is shown in Figure
23
10. This method does have several drawbacks. First, it is only valid for low slip ratios.
Second, driven wheel speed is usually used to determine vehicle speed which leaves allwheel drive vehicles such as the Ohio State EcoCAR 2 vehicle without an accurate source
of absolute vehicle speed. This has been solved in some vehicles by adding a 5th nondriven wheel to the vehicle or utilizing GPS speedometers [8], [11]. This method also
requires experimental data for the particular type of vehicle and tires in order to obtain
accurate slip-slope curves since the factors affecting the peak and shape of the curves is
different for each vehicle.
Figure 10: Example Slip-Slope Curves [11]
2.2.1.7 Longitudinal Tractive Force
At low slip ratios, the longitudinal tractive force of the tire can be given by [2]:
24
𝐹𝑥 = 𝐾𝑇 𝜅
( 8)
where 𝐾𝑇 represents the longitudinal stiffness of the tire. This linear slip-slope region can
be seen easily in Figure 9. The linear region ends at the inflection point 𝜇𝑝𝑒𝑎𝑘 . Beyond this
point at high slip ratios the relationship becomes highly non-linear as traction is lost [2],
[8]. Also, once the peak friction point has been passed, the tire force response is saturated
causing the longitudinal force to decrease continuously until the wheels either lock or reach
a complete spin [10].
2.2.1.8 Tire Rolling Resistance
Due to internal damping of the tire material, not all of the energy used to deform the tire as
it rolls is recovered when the tread elements exit the contact patch and return to their
original shape. Also, the distribution of the normal load on the tire becomes asymmetric
when the tire is rotating. This is because the spring elements are not purely elastic but
instead have viscous dissipation which prevents the force used to compress the springs
from being recovered in the rear half of the contact patch [8]. This shifts the normal load
distribution towards the forward portion of the contact patch. The loss of energy can be
represented as a force on the tires which opposes the motion of the vehicle. This force,
called the tire rolling resistance, can be represented by [12]:
𝐹𝑅𝑅 = 𝑀𝑔 cos(𝛼) 𝐶𝑟
( 9)
For this equation, 𝑀, 𝑔, and 𝛼 represent the vehicle mass, acceleration of gravity, and grade
angle of the road respectively. 𝐶𝑟 is a rolling resistance coefficient that is a function of
25
vehicle speed. It is also dependent on the type of tire, inflation pressure, temperature,
vehicle mass, and road surface characteristics [12]. 𝐶𝑟 is typically approximated as a
constant with values in a range of 0.013-0.02 for smooth pavement. For a passenger vehicle
with radial tires on a normal road surface, the value is assumed at 0.015. A lower limit that
can be reached with special low rolling resistance tires is 𝐶𝑟 =0.008 [8], [12].
2.2.1.9 Wheel Dynamics
The free body diagram given in Figure 11 shows the primary forces acting on a wheel
during acceleration. 𝑇𝑎𝑥 is the torque transmitted to the wheels by the half-shafts, 𝑇𝑅𝑅 is
the torque from rolling resistance, 𝐽𝑤 is the combined inertia of a wheel and tire, and 𝜔̇ 𝑤 is
the angular acceleration of the wheel.
Figure 11: Free Body Diagram of Wheel During Acceleration [1]
26
𝑥 represents the direction of motion and 𝐹𝑥 is the longitudinal tractive force. From this
diagram, Newton’s second law can be applied to derive the basic dynamic expression for
the wheels:
1
𝜔̇ 𝑤 = ( ) 𝑇𝑎𝑥 − 𝑇𝑅𝑅 − 𝐹𝑥 𝑅𝑒𝑓𝑓
𝐽𝑤
2.3
( 10)
Current Traction Control Solutions
Various systems are currently in use to address the traction control problem. Many of these
systems use active and passive devices to manage the torque transmitted to the wheels.
Some systems employ the use of additional, specialized control strategies to detect and
reduce wheel spin. The following sections address the most common methods of traction
control currently in use and some proposed traction control strategies for the unique
traction control problem presented by hybrid vehicles.
2.3.1
Torque Management Devices
Torque management devices (TMD) are the primary hardware used for traction control.
These devices can be passive or actively controlled. Passive TMDs engage automatically
when certain conditions are met based on their mechanical design. They can activate based
on speed or torque. Active TMDs use a hydraulic or electronic actuator to engage a clutch
pack or similar mechanism. When one or more wheels lose traction, these devices help to
redirect torque in the powertrain towards the wheels with traction. The following are
several of the common torque management devices used in vehicles and traction control
systems [13].
27
2.3.1.1 Open Differential
Differentials allow the inside and outside wheels on an axle to spin at different speeds as
the vehicle turns around a corner while continuing to deliver torque. Open differentials
send an equal amount of torque to each of the two wheels. The wheel with the least traction
limits the amount of torque that can be delivered by the wheels to the road. This means that
if one of the wheels comes off the ground or is on a very low-µ surface, both wheels lose
their ability to transmit torque to the road [2]. This is the major drawback of open
differentials in a traction control application.
2.3.1.2 Limited-Slip Differential
To address the drawbacks of an open differential, a limited slip differential can be used.
The limited slip differential adds a semi-rigid coupling between the gears of an open
differential. This is a passive torque management device. The semi-rigid coupling causes
the gears to resist spinning at different speeds. The result is that when one wheel loses
traction, the other is still able to transmit some torque to the road [2]. While the amount of
torque transmitted is small, it is still an improvement upon the open differential as it allows
the vehicle to continue forward motion.
Two common types of limited slip differential are a clutch type and a viscous coupling
type. A clutch-type limited slip differential uses a spring pack to push the gears against the
clutches which provides the resistance against rotation at different speeds [2]. A cutaway
view of a clutch type limited slip differential can be seen in Figure 12. A viscous coupling
28
type uses two sets of plates inside of a thick fluid. Each set of plates is connected to one of
the output shafts. When one output shaft spins faster than the other, the viscous friction of
the fluid causes some torque to continue being transferred to the other shaft [2]. A cross
sectional view of a viscous coupling type limited slip differential can be seen in Figure 13.
Clutch
Spring
Figure 12: Clutch Type Limited Slip Differential [2]
29
Figure 13: Viscous Coupling Type Limited Slip Differential [2]
Actively controlled limited slip differentials are also available. Electronically actuated
differentials use an electric motor to engage the clutch pack when necessary. Advantages
of actively controlled electronic differentials include that they weigh less, can transmit
higher torques, and require smaller speed differences to activate [13].
2.3.1.3 Locking Differential
Active control allows for the creation of a locking differential. Typically used in serious
off-road vehicles, a locking differential uses an electric, pneumatic, or hydraulic
mechanism to lock the differential such that it behaves like a solid axle. This means that
both wheels receive the same amount of torque and rotate at the same speed regardless of
the road surface. Locking differentials are generally manually activated with a switch by
the driver [2].
30
2.3.1.4 Torque Sensing Differential
A torque sensing differential uses a set of gears designed to bind together when a torque
differential develops across the two output shafts. When equal torque is being delivered to
each wheel, the torque sensing differential behaves as an open differential. When a torque
differential develops, the gears multiply the torque of the slipping wheel and transmits it to
the other wheel. The factor by which the torque is multiplied is called the torque bias ratio
and is determined by the design of the gears [2]. This unique type of differential transmits
a relatively large amount of torque to the non-slipping wheel without needing an active
mechanism.
2.3.2
Four-Wheel and All-Wheel Drive
The most widely used and known passive systems for traction control are four-wheel drive
and all-wheel drive. Four wheel drive typically refers to a part time system that can be
engaged or disengaged by the driver using some type of switch. When disengaged, the
vehicle has only two driven wheels. All-wheel drive systems are full time systems such
that the vehicle has four driven wheels at all times. These systems cannot typically be
switched off.
Four and all-wheel drive systems are very similar in composition. One of the key
components is a transfer case which divides power between the front and rear axles.
Transfer cases in four-wheel drive systems are able to decouple one of the axles from the
power input when the system is disengaged. Transfer cases for all-wheel drive systems
31
contain a viscous coupling or similar type of differential to allow a speed difference
between the two axles allowing the system to function properly on any surface since it
cannot be turned off [2], [13].
Four and all-wheel drive systems also must contain a differential on each axle. Four-wheel
drive systems often contain locking differentials that allow for multiple four-wheel drive
modes [2], [13]. Typical modes include 4HI in which the transfer case is engaged to
activate four-wheel drive and the differentials are left open, 4LO in which the transfer case
and differentials are locked, and auto-4WD in which the transfer case is used as a limitedslip differential. 4HI is useful when four-wheel drive is needed but it is not likely that
several wheels will encounter a low coefficient of friction all at once. With the front and
rear differentials open, such conditions would result in insufficient torque transfer to the
road. 4LO directs an identical amount of torque to each wheel regardless of the road
conditions. This is useful for serious off-road driving, however turning becomes difficult
since there can be no speed difference between any of the wheels [2].
All-wheel drive systems take further advantage of the limited slip capabilities of the
transfer case. An on-demand all-wheel drive system primarily uses one axle to drive the
vehicle but transfers torque to whichever axle has traction if the wheels of one axle being
to slip [13]. A full-time all-wheel drive system utilizes torque sensing differentials rather
viscous couplings is the transfer case to transfer torque to all wheels at all times based on
the torque bias ratios of the differentials [2].
32
2.3.3
Traction Control Systems
Passive, mechanical systems such as the ones discussed in the previous sections can be
highly beneficial for certain conditions, however their utility is very limited due to being
primarily or entirely passive systems. To enhance the response and capability of traction
control, actively controlled systems have been developed. The objective of an actively
controlled system is to control wheel slip by estimating the friction between the tire and
road surface and using a control system to regulate the wheel slip. The result is improved
vehicle stability and traction.
2.3.3.1 Anti-lock Braking System (ABS)
The first active traction control system was the anti-lock braking system (ABS) [4]. ABS
was designed to eliminate high slip during braking that results from the wheels locking. By
preventing wheel-lock, ABS is very effective at improving driver control, steerability, and
stopping distance during heavy braking. Work on ABS led to the development of traction
control systems as the acceleration analog of ABS [4]. Traction control (TC) systems work
to control vehicle acceleration by targeting a certain driven wheel slip. The target slip value
is based on the driver steering input and accelerator pedal position. At high pedal input and
low steering input, a higher driven slip will be targeted to achieve maximum longitudinal
force for acceleration. When a higher steering input is detected, the target slip will decrease
because lateral traction peaks at lower slip levels than longitudinal slip [4].
33
2.3.3.2 Traction Control in Conventional Vehicles
Modern traction control in conventional vehicles relies on reducing engine torque, applying
brakes to the spinning wheel, or some combination of the two [13]. In some cases, such as
driving on a surface of uniform friction, reducing the torque output from the powertrain is
sufficient for traction control. Changes in spark advance and air/fuel ratio are widely used
methods for engine torque control, however cylinder cutting, shifting the transmission, and
electronic throttle control are also used. Careful control must be used when combining
these methods since each has its own operational bandwidth and engine emissions can be
affected [4].
If the driving surface friction is not uniform such that the driven wheels encounter different
coefficients of friction, the use of brakes in the traction control system is necessary [4].
Traction control systems utilizing the brakes are generally used in conjunction with an open
differential. The application of brakes to the spinning wheel allows a higher torque output
from the wheel with traction thus allowing the vehicle to accelerate [13]. The same applies
to four or all-wheel drive vehicles whose transfer case is an open differential. When one
axle loses traction, brakes are applied to both wheels of the axle to allow torque to be
transmitted to the axle with traction. However braking the spinning wheel or wheels wastes
a significant portion of the engine torque being produced so the resulting acceleration is
still far from optimal and excessive system noise can also result [4], [13]. Brake based
systems also have the disadvantage of being very difficult to tune, particularly tuning the
brake and powertrain controls so they function smoothly in tandem [4].
34
2.3.3.3 Modern Advances in Traction Control
Advancement in vehicle control and the introduction of electronic and hybrid drivetrains
has led to vast improvements in the control capabilities of traction control systems. There
have also been adaptations of existing traction control strategies to apply them to new
hybrid and electric drivetrains. There has also been development of a new kind of traction
control system that works to monitor and control wheel slip at all times. This works to
prevent wheel slip from occurring in the first place, rather than activating only to fix the
problem once it has occurred. These systems can provide the added benefit of maximizing
traction at all times because they are able to continuously target the optimum wheel slip in
all conditions. Systems have also been developed to address the problem of detecting
vehicle speed and wheel slip on four-wheel drive vehicles where there are no non-driven
wheels from which to determine an accurate vehicle speed. This section will discuss several
advancements in these areas.
In [14], a continuously functional system was developed for an EV with two hub motors.
The maximum tractive force of the wheels under current conditions is calculated and used
to limit the torque requests to the motors. This creates a half closed loop system when the
wheels are not slipping because the feedback Tmax has no effect on the system and thus it
functions as an open loop system. The loop automatically closes when the wheels begin
slipping causing the maximum effective torque to dip below the reference torque and limit
the torque request. This system has the advantage of being simple to implement, however
it depends on the two driven wheels being independent of each other and it depends upon
35
non-driven wheels to obtain vehicle speed and thus its usefulness in all-wheel drive
vehicles is limited.
[15] proposed a general traction control law that makes use of a simplified vehicle model
and detected wheel slip. The test vehicle was primarily a front wheel drive vehicle with a
rear powertrain that was activated only when additional power was needed for acceleration
or when wheel slip was detected. The proposed traction control strategy minimizes an
objective function, which represents the combined wheel slip of front and rear wheels, with
respect to the motor torque. The resulting motor torque is then applied to the rear electric
drive of the powertrain to assist in controlling the vehicle and regaining traction with the
front wheels. The performance of the system was limited, however, by lack of coordination
with the engine for reduction of torque on the front wheels.
A simple “bang-bang” type controller was employed by [9] on an electric drivetrain. The
control strategy transmitted the requested torque to the wheels until wheel slip above a set
threshold was detected. At that point the torque request was set to zero until the detected
slip dropped back into the stable region and the driver requested torque was again
transmitted to the wheels. This controller is effectively an acceleration version of ABS and
depends on the inertia of the wheels and vehicle to “smooth” the torque modulation. A
state-observer was used with knowledge of current slip to estimate the road load on the
drivetrain and determine the allowable slip threshold value.
36
The traction control system proposed by [16] goes beyond correcting for loss of traction
and works to maximize the vehicle’s longitudinal force and acceleration at all times by
actively optimizing wheel slip at all time. The goal of the system is to maintain the slip
ratio at the point of peak friction at all times. This is accomplished by slightly varying the
slip target and noting any resulting change in longitudinal force and vehicle acceleration.
Positive changes in acceleration indicate the slip target is below the current optimal value
and the slip target is incrementally increased. When the change in acceleration becomes
negative it indicates that the peak point has been passed and the slip target will be
decreased. The amount of increase or decrease is determined by a PID controller. This
continuous testing ensures that the optimum slip point is always tracked without a need for
large stored look-up tables, prior knowledge of the road or tire characteristics, large
equations, or complicated logic. The strategy is computationally light and can be
implemented on a standard embedded platform, but requires the ability to accurately
determine and control slip.
Fuzzy logic control techniques have been developed by several researchers in recent years
for use in various electronic control systems including transmission control, engine control,
and ABS [9]. They have generally found them to have better performance than traditional
control algorithms [17]. Fuzzy logic has the advantage of being able to efficiently model
highly complex and non-linear systems. It can also handle uncertainty and noise in data
effectively [9].
37
2.3.4
The OSU EcoCAR 2 Traction Control Problem
The traction control problem presented by the Ohio State EcoCAR 2 vehicle is unique in
many ways. Because the vehicle is a prototype built for the specific purpose of competing
in the EcoCAR 2 competition, its powertrain configuration and the components therein are
not seen in any other vehicle. The competition rules and team goals also introduced a set
of specific constraints to the traction control problem. First, the final traction control
algorithm needs to be largely self-contained. This means that all functions directly
pertaining to traction control should exist in a single area of the vehicle’s supervisory
control and have no interaction with the low level controls. Second, the traction control
algorithm must be designed such that it can be easily and directly integrated with the
existing controls architecture created during the first two years of the competition without
major modifications to any other portion of the code.
The competition rules specifically prohibit any controls action which interferes with or
modifies the operation of ABS and normal braking action in any way. The end result of
this rule places two constraints on the traction control development. One is that the traction
control can only function during acceleration and the vehicle will rely upon the stock ABS
system as the means of traction control during heavy braking. The second is that the traction
control system cannot actuate the brakes in order to slow a spinning wheel that has lost
traction or to transfer torque across the open differentials. Another constraint was placed
in order to prevent the vehicle from exceeding the competition maximum weight
requirement, no additional torque splitting components could be added to the vehicle. This
38
means that the open differentials included in the gearboxes on the vehicle are the only
available means for the vehicle to divide torque between the left and right wheels on an
axle. Open differentials are not controllable so the traction control algorithm must be
designed with an uncontrolled left-to-right torque split in mind. Finally, to avoid additional
weight on the vehicle and to avoid unnecessary complication of the vehicle wiring and
controls, the addition of sensors to the vehicle was to be minimized or avoided altogether.
39
Chapter 3: System and Component Modeling
3.1
Traction Control Philosophy
Because the plant model is intended for traction control development, the intended traction
control strategy is an important factor to consider in model development. The intended
traction control strategy, which will be discussed in detail in a later chapter, takes
advantage of the electric motors to control the torque to the wheels during a traction control
event. The control strategy of the vehicle utilizes a charge depleting mode for heavy
acceleration in which the electric motors accelerate the vehicle while the engine is off and
disconnected from the rest of the powertrain. This is when an acceleration traction control
event is most likely to occur. If a traction control event occurs while the vehicle is using
the charge depleting mode traction control will be applied directly. If the battery state-ofcharge is too low to allow the vehicle to function in charge depleting mode, the vehicle will
enter the charge sustaining series mode for traction control. The series mode leaves the
front axle with no propulsive torque input from the powertrain and the rear electric motor
to control the torque transmitted to the rear wheels in order to maintain traction.
3.2
Requirements
Based on the background given in the previous sections, the requirements for the plant
model can be described:
40

High fidelity of the model to capture high frequency vibrations is not required as
only lower frequency dynamics will be important for traction control

The model must be capable of modeling slip on all four wheels and demonstrating
differential action between the two wheels on a given axle

The model must be available for SIL work prior to mechanical realization of the
vehicle
3.3
Assumptions
The following assumptions were used in the development of the dynamic model, driven by
the requirements listed above.

Only longitudinal vehicle dynamics are considered

The torsional stiffness of shafts and gears except half shafts are assumed to be
infinitely large

Environmental factors such as temperature, pressure, and humidity are not taken
into consideration

Drivetrain losses are represented by lumped efficiency and friction models
The supervisory control strategy developed for the test vehicle converts a percentage-based
torque request from the pedals into actual torque requests for each of the three torque
generating components based on the optimization of fuel economy and emissions. The
dynamic model presented here focuses on translating the torque requests into the torque
41
realized by the engine and motors and how it propagates through the powertrain to the
wheels. The following sections will describe each of the model components in detail.
3.4
Powertrain Modeling
It is necessary to derive dynamic equations to describe the components of the powertrain.
Figure 14 shows the model of the driveline upon which the derived equations are based.
The component models are designed to translate engine and motor torque requests into the
torque realized by the actuators and to trace how the torque produced and its effects on
component speeds propagate through the system. The following sections will describe each
of the model components in detail.
Figure 14: Driveline Dynamic Model
42
3.4.1
Engine
A detailed thermodynamic model describing engine dynamics does not provide substantial
additional information for the validation of a traction control oriented dynamic vehicle
model, particularly because the engine will not be used to transmit torque to the wheels in
the intended traction control strategy as described previously. Such detailed models are
often used for the design of engine control systems, however for this work a simplified
representation of the engine model is used to reflect the dynamics between torque request
and resulting engine speed. The engine is modeled as an ideal torque actuator with a
constant inertia connected through the crankshaft to the rest of the powertrain. The
resulting crankshaft dynamics are given by:
𝜔̇ 𝑒 = (
1
) 𝑇 − 𝑇𝑒,𝑓𝑟 − 𝑇𝐶
𝐽𝑒 + 𝐽𝐶1 𝑒
( 11)
Where
𝜔̇ 𝑒
= engine angular acceleration
𝑇𝑒
= engine indicated torque
𝑇𝑒,𝑓𝑟
= engine friction torque
𝑇𝐶
= torque transmitted by the clutch
𝐽𝑒
= lumped engine inertia
𝐽𝐶1
= inertia of the clutch flywheel attached to the engine
The engine friction is modeled by a lookup table constructed from experimental data. A
delay between torque request and torque generation is included in the model to account for
the induction-to-power stroke transport delay.
43
3.4.2
Front Electric Motor
Because the pulleys on which the belt is mounted are coupled directly to the electric
machine and transmission, they are modeled as lumped inertias with those components.
The primary pulley, denoted by the subscript s1, is coupled to the output shaft of the electric
machine. Belt dynamics are ignored. Taking into account these assumptions, the dynamics
of the front electric machine are given by:
1
𝜔̇ 𝐹𝑀 = (
) 𝑇 − 𝑇𝐹𝑀,𝑓𝑟 − 𝑇𝑏𝑒𝑙𝑡
𝐽𝐹𝑀 + 𝐽𝑠1 𝐹𝑀
( 12)
Where
𝜔̇ 𝐹𝑀
= Front electric machine angular acceleration
𝑇𝐹𝑀
= Front electric machine torque
𝑇𝐹𝑀,𝑓𝑟
= Front electric machine internal friction torque
𝑇𝑏𝑒𝑙𝑡
= Torque transmitted by the belt
𝐽𝐹𝑀
= Front electric machine inertia
𝐽𝑠1
= Inertia of primary belt pulley
The front electric machine friction term is modeled as the combined friction of all
components at the node of the front electric machine, the belt and pulleys, and the
transmission primary shaft when the engine clutch is open.
44
3.4.3
Transmission
The clutch disk and secondary belt pulley are coupled directly to the input shaft of the
transmission so they are modeled as a lumped inertia. A highly detailed dynamic model of
the transmission would not provide significant useful information for the development of
traction control because the vehicle will be kept in a fixed gear during a traction control
event so a simplified model was chosen to prevent unnecessary model complexity and
maintain an efficient model based design. The simplified model represents the torque on
the input and output shafts of the transmission by a static multiplication by the gear ratio
as shown in ( 13).
The dynamics of the transmission input are given by
𝜔̇ 𝐺𝐵1 = (
1
𝐽𝐶2 + 𝐽𝑠2 + 𝐽𝐺𝐵1
) 𝑇𝐶 + 𝐵 ∙ 𝑇𝑏𝑒𝑙𝑡 − 𝑇𝐺𝐵1
Where
𝜔̇ 𝐺𝐵1
= Transmission input angular acceleration
𝐵
= Belt ratio
𝑇𝐶
= Torque transmitted by the clutch
𝑇𝐺𝐵1
= Torque transmitted to transmission primary shaft
𝐽𝐶2
= Clutch disk inertia
𝐽𝑠2
= Inertia of belt pulley attached to transmission input
𝐽𝐺𝐵1
= Equivalent transmission primary shaft inertia
The dynamics of the transmission output are given by
45
( 13)
1
𝜔̇ 𝐺𝐵2 = (
) 𝑅 ∙ 𝑇𝐺𝐵1 − 𝑇𝑎𝑥,𝑓
𝐽𝐺𝐵2
( 14)
Where
𝜔̇ 𝐺𝐵2
= Transmission output angular acceleration
𝑇𝑎𝑥,𝑓
= Torque transmitted to the front wheels
𝐽𝐺𝐵2
= Equivalent transmission secondary shaft inertia
𝑅
= Transmission gear ratio
Table 2 contains the gear ratios for the transmission and final drive.
Table 2: Gear and Drive Ratios of the Transmission
3.4.4
Gear
Ratio
1st
3.8180
2nd
2.1580
3rd
1.4750
4th
1.0670
5th
0.8750
6th
0.7440
Differential
3.941
Efficiency
0.962
Rear Electric Machine and Gearbox
Similar to the engine and front electric machine, the rear electric machine is modeled as a
lumped inertia, ideal torque actuator. The rear powertrain dynamics can be described with
a lumped model that reflects all inertias to the rear electric machine output shaft.
46
𝜔̇ 𝑅𝑀 = (
1
𝐽𝑔2
𝐽𝑅𝑀 + 𝐽𝑔1 + 2
𝑟
) 𝑇𝑅𝑀 − 𝑇𝑅𝑀,𝑓𝑟 −
𝑇𝑎𝑥,𝑟
𝑟
( 15)
Where
𝜔̇ 𝑅𝑀
= Rear electric machine angular acceleration
𝑇𝑅𝑀
= Rear electric machine torque
𝑇𝑅𝑀,𝑓𝑟
= Rear electric machine friction torque
𝑇𝑎𝑥,𝑟
= Torque transmitted to the rear wheels
𝐽𝑅𝑀
= Rear electric machine inertia
𝐽𝑔1
= Gearbox primary shaft inertia
𝐽𝑔2
= Gearbox secondary shaft inertia
𝑟
= Gearbox gear ratio
The rear electric machine friction term is modeled as the combined friction of the rear
electric motor and gearbox.
Electric machines experience a small lag between torque request and torque output which
can be represented with a pure delay with a time constant 𝜏𝐸𝑀 of 0.01s. A delay of 0.01s
represents the typical lag exhibited by electric machines [2], [18]. This delay precedes ( 12)
and ( 15) in the implementation of the model and can be represented as [18]
𝑇̇𝐸𝑀 =
1
𝜏𝐸𝑀
(𝑇𝐸𝑀,𝑟𝑒𝑞 − 𝑇𝐸𝑀 )
47
( 16)
𝑇𝐸𝑀,𝑟𝑒𝑞 and 𝑇𝐸𝑀 represent the torque request and actual torque output of the electric
machine. This is represented generically here but applies to both the front and rear electric
machine individually.
3.4.5
Front and Rear Axles
The torsional stiffness and damping of the axle shafts are taken into account for this work.
Keeping this in mind, the torque transmitted to the wheels by the front and rear half shafts
can be given by the following relationship
𝑇𝑎𝑥,𝑖 = 𝑘𝑎𝑥,𝑖 (𝜃̇𝑎𝑥,𝑖 ) + 𝑏𝑎𝑥,𝑖 (∆𝜔𝑎𝑥,𝑖 )
( 17)
The subscript 𝑖 = {𝑓, 𝑟} is used to indicate the front and rear axles, 𝑘𝑎𝑥,𝑖 is the stiffness of
a single half-shaft on axle 𝑖, and 𝑏𝑎𝑥,𝑖 is the damping coefficient of a single half-shaft on
axle 𝑖. The torsional displacement on a half-shaft and the relative angular speed are given
as
𝜃̇𝑎𝑥,𝑖 = ∆𝜔𝑎𝑥,𝑖 = {
𝜔𝐺𝐵2 − 𝜔𝑤,𝑓 , 𝑖 = 𝑓
𝜔𝑔2 − 𝜔𝑤,𝑟
𝑖=𝑟
( 18)
where 𝜔𝑤,𝑖 is the wheel speed.
3.4.6
Wheel Dynamics
The free body diagram given in Figure 11 shows the simple forces acting on a wheel during
acceleration. From this diagram, Newton’s second law can be applied to derive the basic
dynamic expression for the wheels
48
1
𝜔̇ 𝑤,𝑖 = ( ) 𝑇𝑎𝑥,𝑖 − 𝑇𝑅𝑅 − 𝐹𝑥,𝑖 𝑅𝑒𝑓𝑓
𝐽𝑤
( 19)
Rolling resistance is given by [1, 4]
𝐹𝑅𝑅 = 𝑀𝑔 cos(𝛼) 𝐶𝑟
( 20)
The mass of the vehicle, acceleration due to gravity, and grade angle of the road are given
by 𝑀, 𝑔, and 𝛼 respectively. 𝐶𝑟 the rolling resistance coefficient assumed for this work to
have a value of about 0.015 as explained in Chapter 2 [12]. The torque due to rolling
resistance can be determined by multiplying the rolling resistance force from ( 20) by the
tire’s effective rolling radius. Due to the weight distribution in the vehicle, each wheel has
a slightly different effective rolling radius.
3.4.7
Tire Model
In the development of traction control, modeling of the tire-road interaction and forces is
very important. Due to the non-linear behavior of tires and the great variance in vehicle
handling caused by the tires, it is important that a realistic non-linear tire model is used.
Existing tire models are predominantly semi-empirical in nature which use experimental
data to determine the model parameters [19]. One of the most prevalent tire models in use
is the Pacejka ‘Magic Formula’ model. This work uses the Pacejka ‘Magic Formula’ model
in a form considering only longitudinal forces to model tire behavior. This model was
chosen in part due to its prevalence which allowed the necessary empirical coefficients to
be directly obtained from the tire manufacturer. It was chosen over popular theoretical
49
models because theoretical models generally must be based on simplifying assumptions
which limits their practical use and makes them undesirable for use in traction control
development [7].
The following sign conventions were used:

Angles, forces, and moments use sign conventions consistent with SAE definitions
as shown in Figure 15.

Longitudinal sip 𝜅 is positive during acceleration and negative during braking as
given by ( 6) which is repeated here for clarity
𝜅=
𝑅𝑒𝑓𝑓 𝜔𝑤 − 𝑉𝑥
𝑉𝑥 + 𝜀𝑥
Figure 15: SAE Tire Axis System [14]
50
( 6)
The magic formula is given by
𝐹𝑥0 = 𝐷𝑥 ∙ sin(𝐶𝑥 ∙ arctan[{𝐵𝑥 𝜅𝑥 − 𝐸𝑥 ∙ [𝐵𝑥 𝜅𝑥 − arctan(𝐵𝑥 𝜅𝑥 )]}])
+ 𝑆𝑉𝑥
( 21)
The coefficients B, C, D, and E are dimensionless coefficients that are functions of the tire
load. They are the stiffness factor, shape factor, peak value, and curvature factor
respectively. The load dependent coefficients are defined by
𝐷𝑥 = 𝜇𝑥 𝐹𝑧
( 22)
𝜇𝑥 = 𝐷𝑥1 + 𝐷𝑥2 ∙ 𝑑𝑓𝑧
( 23)
𝐹𝑧 ∙ (𝐾𝑥1 + 𝐾𝑥2 ∙ 𝑑𝑓𝑧 )𝑒 𝐾𝑥3 ∙𝑑𝑓𝑧
𝐵𝑥 =
𝐶𝑥 𝐷𝑥 + 𝜀𝑥
( 24)
𝐸𝑥 = (𝐸𝑥1 + 𝐸𝑥2 ∙ 𝑑𝑓𝑧 + 𝐸𝑥3 ∙ 𝑑𝑓𝑧 2 )(1 − 𝐸𝑥4 ∙ 𝑠𝑖𝑔𝑛(𝜅𝑥 ))
( 25)
Where
𝑑𝑓𝑧 =
(𝐹𝑧 − 𝐹𝑧0 )
𝐹𝑧
( 26)
𝜅𝑥 = 𝜅 + 𝑆𝐻𝑥
( 27)
𝑆𝐻𝑥 = 𝐻𝑥1 + 𝐻𝑥2 ∙ 𝑑𝑓𝑧
( 28)
𝑆𝑉𝑥 = 𝐹𝑧 ∙ (𝑉𝑥1 + 𝑉𝑥2 ∙ 𝑑𝑓𝑧 )
( 29)
𝑆𝑉𝑥 and 𝑆𝐻𝑥 represent an offset to the slip and longitudinal force. 𝜇𝑥 is the load-dependent
friction coefficient in the longitudinal direction. 𝜀𝑥 is a small constant intended to avoid
division by zero as the vertical load approaches zero [20]. The tires for the test vehicle are
being custom developed for this team for light weight and low rolling resistance. The
rolling resistance will be approximately half that of a normal tire. As the tire development
51
is completed, the empirical coefficients for the tire model will be obtained by the tire
manufacturer through testing and provided for use in this work.
3.4.8
Vehicle Model
The motion of the vehicle results from the sum of all forces acting on the vehicle body.
These forces are shown in Figure 16.
Figure 16: Vehicle Model Block Diagram [20]
In this diagram,
𝑎, 𝑏
= Distance of front and rear axles, respectively, from the plane of the
vehicle center of gravity (CG)
𝑉𝑥
= Longitudinal velocity of vehicle
𝐹𝑑
= Force of aerodynamic drag
𝐹𝑥𝑓 , 𝐹𝑥𝑟
= Longitudinal force generated between the road and the front and rear
wheels, respectively
52
𝐹𝑧𝑓 , 𝐹𝑧𝑟
= Normal forces on the front and rear wheels, respectively
ℎ
= Height of vehicle CG above ground
𝑚
= Vehicle mass
𝑔
= Acceleration of gravity (9.81 m/s2)
𝛽
= Angle of incline of the road
The vehicle model is based upon the following properties and assumptions:

Two axles with two equally sized wheels on each axle

The vehicle axles are parallel

Only longitudinal motion is considered

Longitudinal motion occurs perpendicular to the axles

The normal z direction is always perpendicular to the axle plane

Vehicle weight and aerodynamic drag act through the center of gravity

Pitch and vertical motion are not considered
Newton’s second law as applied to the vehicle model is given as:
𝑚𝑉𝑥̇ = 𝐹𝑥 − 𝐹𝑑 − 𝑚𝑔 sin 𝛽
( 30)
The longitudinal force is determined by
𝐹𝑥 = 2(𝐹𝑥𝑓 + 𝐹𝑥𝑟 )
( 31)
The aerodynamic drag force is given by
𝐹𝑑 =
1
𝐶 𝜌𝐴(𝑉𝑥 − 𝑉𝑤 )2 ∙ 𝑠𝑖𝑔𝑛(𝑉𝑥 − 𝑉𝑤 )
2 𝑑
53
( 32)
where 𝑉𝑤 represents the headwind speed.
The normal forces on the wheels are found by
𝐹𝑧𝑓 =
−ℎ(𝐹𝑑 + 𝑚𝑔 sin 𝛽 + 𝑚𝑉𝑥̇ ) + 𝑏𝑚𝑔 cos 𝛽
𝑛(𝑎 + 𝑏)
( 33)
ℎ(𝐹𝑑 + 𝑚𝑔 sin 𝛽 + 𝑚𝑉𝑥̇ ) + 𝑏𝑚𝑔 cos 𝛽
𝑛(𝑎 + 𝑏)
( 34)
𝐹𝑧𝑟 =
and must satisfy the condition
𝐹𝑧𝑓 + 𝐹𝑧𝑟 = 𝑚𝑔 cos 𝛽/𝑛
Equations ( 30) through ( 35) comprise the vehicle model [20].
54
( 35)
Chapter 4: Simulation and Vehicle Controls
4.1
Introduction
The model described in Chapter 3 is designed for implementation as a simulator. The Ohio
State EcoCAR 2 team utilizes Simulink from The MathWorks in order to create simulators
for use in control development during the three years of the competition. This chapter
contains a discussion of the primary simulator used by the team to illustrate why an
additional, unique simulator was necessary for the development of traction control. The
development of the new simulator is also discussed as well as a brief description of the
primary control algorithms used in the vehicle around which the traction control
development was focused.
4.2
Existing Simulation Tools: EcoSIM2
The primary simulator utilized by the Ohio State team is an energy based quasi-static model
called EcoSIM2. The simulator is based on the concept of feed-forward torque which is
delivered from the actuators and through the powertrain gearing to the wheels where a
longitudinal force is generated which acts on the vehicle mass to propel the vehicle
forward. The forward acceleration is determined by dividing the force by the vehicle mass.
It is then integrated to determine the vehicle velocity. Vehicle velocity is then converted to
a wheel rotational velocity once divided by the wheel radius. The rotational velocity is then
55
fed back through the powertrain and the gearing to determine the actuator rotational speeds.
This concept is illustrated in Figure 17.
Figure 17: Torque/Speed Structure of EcoSIM2
EcoSIM2 is used to evaluate fuel economy and to develop control strategies and perform
basic tuning of controls for the vehicle. The simulator is quasi-static meaning that the time
constants of components in the system are considered negligible when compared to the
greatest inertia which is the vehicle itself [21]. With this assumption, the components in
EcoSIM2 are modeled based on static maps, simple transfer functions, and simplified soft
ECUs [22]. This allows the model to be computationally inexpensive and run quickly for
rapid controls iterations. The simulator is comprised four primary segments as seen in the
user interface shown in Figure 18.
56
The Driver subsystem is a PID controller that uses the difference between a vehicle speed
trace and the current vehicle speed to generate accelerator and brake pedal commands.
Typical speed traces include the Federal Urban Driving (FUDS) cycle, Federal Highway
Driving (FHDS) cycle, US06 cycle, and team created cycles designed for fault or
performance testing.
Figure 18: EcoSIM2 User Interface
The PHEV Powertrain subsystem contains the aforementioned maps, transfer functions,
and soft ECUs that model the components of the drivetrain. The PHEV Powertrain
subsystem can be seen in Figure 19. The EcoCAR2 Vehicle subsystem contains a version
57
of the vehicle body model that uses dynamometer coefficients to calculate the road loads
on the vehicle. The MABX Primary Controller subsystem contains the control algorithms
used to govern vehicle mode, gear, and transitions between modes. This subsystem is
where vehicle control development occurs.
Figure 19: PHEV Powertrain Subsystem in EcoSIM2
Additional blocks in the primary user interface include an Inputs subsystem to load
variables from the workspace into the model, an Outputs subsystem to save variables from
the model into the workspace, and the Economy subsystem to display selected vehicle
status indicators and performance metrics during simulation.
4.3
Vehicle Control Strategy
The vehicle control strategy determines operating mode based on the battery state of charge
(SOC) and vehicle speed. On a full charge, the vehicle starts in charge depleting mode
58
using the electric machines to propel the vehicle. When the SOC drops below 18%, the
vehicle transitions to charge sustaining mode. Once charge sustaining mode is activated,
the vehicle selects between charge sustaining series and charge sustaining parallel based
on the vehicle speed. When vehicle speed is less than 50 kph, charge sustaining series is
selected. Above 50 kph, the vehicle transitions to charge sustaining parallel. Within each
mode, efficiency is maximized to produce maximum fuel economy and vehicle range.
The energy management in the control strategy is performed by an algorithm called the
Equivalent Consumption Minimization Strategy (ECMS) to determine the optimal power
split between the torque actuators in the powertrain during charge sustaining modes. A
modified version is used during charge depleting mode to determine the most efficient split
between the two electric machines. ECMS reduces a global optimization problem to an
instantaneous, local optimization method [23]. ECMS assigns both electricity and liquid
fuel a cost function designed to balance energy use and power output. The control strategy
minimizes the energy cost function while maintaining the power output necessary to meet
the requested torque and then assigns torque commands to the torque actuators accordingly.
More detailed information on ECMS can be found in [24].
Another important aspect of the vehicle control strategy is the gear shifting process. When
a shift is requested, the transmission first shifts to neutral. While in neutral, the front electric
machine is used to control the speed of the transmission input and match it to the speed of
59
the transmission output for the new gear prior to engaging the gear. This minimizes any
grinding of the synchronizers and allows for a smooth feel to shifting in the vehicle.
4.4
Simulation for Traction Control: EcoSIM2 – Dynamic
EcoSIM2 is very useful for its primary purpose of control development for improved fuel
economy and basic performance. However, the model does not account for powertrain
dynamics such as inertias and shaft stiffnesses. The model also assumes the wheels behave
as rigid discs and that perfect contact exists between the wheels and the road with no slip.
For these reasons, the model is insufficient for traction control development.
Figure 20: EcoSIM2 – Dynamic User Interface
60
To accommodate the desired development, a new model was developed which expanded
upon EcoSIM2 to take the powertrain dynamics into account and incorporate the Pacejka
Magic Formula tire model. EcoSIM2 – Dynamic is a model derived from EcoSIM2 that
uses Simulink’s SimDriveline toolbox to implement the dynamic model described in
Chapter 3. The user interface of EcoSIM2 – Dynamic is shown in Figure 20. The structure
of the model was kept almost identical. All changes were made within the plant models for
each component subsystem shown in Figure 19.
Implementing the dynamics and the use of the SimDriveline toolbox required an important
modification to the original simulator. SimDriveline systems are best used with a variable
step solver. However the MABX controller simulator must be run at a fixed time step to
most accurately model the functionality of the controller hardware which is a digital
system. To accomplish this, the MABX Primary Controller subsystem was isolated as an
atomic subsystem and all continuous functions within it were discretized with a time step
of 0.01 sec to match the time step of the controller hardware. Another change was the
addition of a feedback loop directly from the vehicle subsystem to the powertrain
subsystem which brings the calculated normal forces to the tire model.
A limitation of the simulator using SimDriveline is the inability to accurately simulate
speed control for the motors. The electric motors can be controlled in a torque control mode
or a speed control mode. When in torque control mode, the inverter controls the motor by
sending it a torque set point based on the torque commands from the MABX and allowing
61
the speed to vary naturally based upon the torque. In speed control mode, the inverter
commands a specific motor speed and continuously varies the torque in order to meet the
speed command. Because the torque variance in speed control mode is performed by the
inverter and not in the supervisory controller, it is not captured in the simulator.
Furthermore, speed control mode is only used during gear shifting to match the
transmission input and output speeds while in neutral during a shift. EcoSIM2 is able to
mimic the speed control functionality by directly commanding the front electric machine
speed rather than back propagating as shown in Figure 17. However, the structure of the
SimDriveline model requires torque control to be used at all times. Therefore, speed
matching does not properly occur.
Another limitation of the model is that the coefficient of friction for each wheel must
remain constant throughout the simulation. This makes it impossible to accurately model a
wheel transitioning from low friction to high friction or from high friction to low friction.
For example, if a simulation begins with the front wheels on a low friction surface and the
rear wheels on a high friction surface, the rear wheels will never enter the low friction zone
during the simulation even if the vehicle displacement is large.
4.5
EcoSIM2-Dynamic Initial Validation
To validate the updates to the EREV powertrain subsystem from the creation of EcoSIM2Dynamic, data collected from the vehicle during a zero-to-sixty acceleration is compared
to data generated from the model. The actuator torque commands recorded from the vehicle
62
were used as inputs to the model and the resulting vehicle speed in the model is compared
to the actual vehicle speed recorded in the data. The simulator behavior mimics that of the
vehicle quite well with slight inaccuracy in the speed. The simulator speed slightly lags the
actual speed for about 10 seconds and reaches a peak speed approximately 2 kph greater
than the actual vehicle speed. Based upon these results, further refinement of the EcoSIM2Dynamic plant model is not necessary for the development of traction control.
Vehicle Speed [kph]
120
100
80
60
40
Vehicle Data
Simulation Data
20
0
0
5
10
time [s]
15
20
Figure 21: Initial Validation for EcoSIM2-Dynamic
4.6
EcoSIM2-Dynamic Results
To demonstrate the simulator’s ability to model friction between the tires and the road,
several simulations were run. Sample results are given below. Realistically, driving
surfaces are imperfect and non-uniform causing each wheel to experience a slightly
different friction coefficient. To simulate this, the friction coefficient for each wheel can
be varied slightly in the simulation. Throughout this work, the following convention will
63
be used for variance in friction coefficient unless otherwise specified. In Table 3, 𝜇𝑥
represents the nominal friction coefficient.
Table 3: Friction Coefficient Variance Convention
Left Wheel
Right Wheel
Front Axle
𝜇𝑥 – 0.01
𝜇𝑥 – 0.03
Rear Axle
𝜇𝑥 – 0.03
𝜇𝑥
Typical nominal friction coefficients for various road surfaces are given in Table 4.
Table 4: Typical Friction Coefficients [11], [20]
Surface
Dry Pavement
Wet Pavement
Snow
Ice
Nominal Friction
Coefficient
0.9 – 1.0
0.7 - 0.8
0.3 - 0.4
0.1 - 0.25
The initial simulation was performed with a longitudinal load-dependent friction
coefficient (𝜇𝑥 in equation ( 23) ) of 1. This is the value of the coefficient provided for the
Magic Formula model to represent dry pavement [20], [25]. Figure 22 shows the torque
and rotational speed of the torque actuators as well as a plot of vehicle speed compared to
the speed trace defined by the drive cycle. The wheel speeds and wheel slip values as
defined by ( 6) are shown in Figure 23. For clarity, only the first 60 seconds are shown.
64
Torque [Nm]
200
FEM
REM
ICE
100
0
Speed [rpm]
-100
0
6000
4000
10
20
30
40
50
60
10
20
30
40
50
60
20
30
time [s]
40
50
60
FEM
REM
ICE
2000
Speed [kph]
0
0
100
Vehicle velocity
Cycle Velocity
50
0
0
10
Figure 22: Actuator Torques and Speeds During US06 Cycle - 𝝁𝒙 = 1.0
0.02
FR
FL
Wheel Slip
200
0
-0.01
0
0
600
Wheel Speed [rpm]
0.01
400
20
40
-0.02
0
60
FR
FL
10
20
30
40
50
60
20
30
time [s]
40
50
60
0.02
RR
RL
0.01
400
Wheel Slip
Wheel Speed [rpm]
600
200
0
-0.01
0
0
20
40
-0.02
0
60
time [s]
RR
RL
10
Figure 23: Wheel Speeds and Wheel Slip During Zero-to-Sixty Acceleration - 𝝁𝒙 = 1.0
65
The wheel speeds and slip clearly illustrate the oscillations in the powertrain captured by
EcoSIM2-Dynamic that are absent from the quasi-static simulations in EcoSIM2. Traction
was maintained throughout the simulation as evinced by slip values that stay very low. The
maximum slip seen by the wheels is 0.019.
Next, the same simulation was run with a nominal friction coefficient of 0.26 which
represents a low friction driving surface such as a snow covered road. Plots of the actuator
torques and speeds and of the wheel speeds and slip are given in Figure 24 and Figure 25.
Torque [Nm]
200
0
Speed [kph]
Speed [rpm]
-200
0
4
x 10
2
FEM
REM
ICE
10
20
30
40
50
60
0
0
100
10
20
30
40
50
60
80
Vehicle velocity
Cycle Velocity
20
30
time [s]
40
50
60
1.5
1
FEM
REM
ICE
0.5
60
40
20
0
0
10
Figure 24: Actuator Torques and Speeds During US06 Cycle - 𝝁𝒙 = 0.26
66
11
10
FR
FL
5000
4000
3000
2000
1000
0
0
6
4
2
0
20
40
-2
0
60
4000
10
20
30
40
50
60
50
60
12
RR
RL
3000
RR
RL
10
Wheel Slip
Wheel Speed [rpm]
FR
FL
8
Wheel Slip
Wheel Speed [rpm]
6000
2000
1000
8
6
4
2
0
0
0
20
40
60
-2
0
10
20
time [s]
30
time [s]
40
Figure 25: Wheel Speeds and Slips During US06 Cycle - 𝝁𝒙 = 0.26
A comparison shows much higher wheel speeds and slip values for Figure 25 where the
friction between the tires and the road is low than for Figure 23 where friction is optimal.
For the low friction simulation the slip on the front axle peaks at a value of 10. Figure 25
also illustrates the effect of a non-uniform surface on wheel slip. For example, the rear left
wheel accelerates to a speed several times that of the rear right wheel due to the open
differential and the lower friction experienced by the rear left wheel. Because the friction
experienced by the left wheel is lower, it is the first of the two to lose traction. Once the
left wheel breaks loose, the differential transfers all of the torque to the left wheel and none
to the right. The right wheel maintains traction due to lack of input torque and continues
spinning at a rate directly proportional to vehicle speed since the vehicle is the force driving
the right wheel. This phenomenon is also seen on the front axle.
67
An examination of Figure 24 shows a sharp increase in the speed of the electric machines
disproportionate to the increase in input torque during the times that the wheels lose
traction. The sudden loss of load, because it is uncontrolled and because the torque input
is sustained as if the load were still present, causes the electric machines to far exceed the
rated operating speeds of the electric machines. Accordingly, the wheels are accelerated to
excessive speeds as well. On a vehicle rather than in simulation, these kinds of effects
would cause significant damage to the vehicle and danger to the driver, further emphasizing
the need for effective traction control.
68
Chapter 5: Traction Control Development
5.1
Vehicle Configuration
When determining the approach for traction control on the Ohio State EcoCAR 2 vehicle,
the constraints described in Chapter 2 must be taken into consideration. The constraint
prohibiting the use of the brakes dictates that the traction control approach will use the
reduction of input torque to the powertrain as the sole mechanism to reduce and eliminate
wheel slip. It is desirable to use the electric machines for torque reduction on the EcoCAR
2 as they provide the most direct and best controlled avenue for torque reduction as well
as offering the ability to reduce to zero or negative torque if necessary. The engine is only
able to reduce to idle speed and torque without stalling or potentially damaging the engine.
When the vehicle is in the charge depleting configuration, the electric machines are the
only sources of torque so their use for torque reduction can be easily implemented. When
in the charge sustaining series configuration, the rear wheels are the only driven wheels so
the rear electric machine is the natural avenue for torque reduction. In the charge sustaining
parallel configuration, however, the engine is connected to both the wheels and front
electric machine. If torque reduction occurs on the front axle in this configuration, it is
necessarily limited by the engine in order to prevent the engine from stalling. Energy
management also becomes a concern if traction control is applied in the charge sustaining
69
parallel configuration. Thus, the traction control strategy needs to transition the vehicle
from the parallel configuration to the series configuration if wheel slip is detected while
the vehicle is in charge sustaining configuration.
5.2
Algorithm Placement
As discussed in Chapter 2, there are many methods by which wheel slip and traction can
be managed. It was necessary to determine which of these methods would be utilized for
the Ohio State vehicle. First a determination of whether an active system, passive system,
or both would be used. Because the vehicle contains open differentials and it is impractical
to replace them with limited slip or torque sensing differentials, no passive approach is
possible. As such, the Ohio State vehicle must rely entirely upon an active traction control
strategy implemented in the vehicle controls.
There are two primary methods of implementing traction control within the vehicle control
strategy. First, traction control can be implemented as an operating mode that is entirely
separate from the normal operating modes and is activated upon detection of wheel slip as
seen in [2]. The other option is to implement traction control as a modification to the torque
request within the existing operating modes. Examples of this option presented in Chapter
2 include the on-off torque request of the bang-bang controller presented in [9], the half
closed loop system in [14], and several others. The creation of additional modes for traction
control in multiple powertrain configurations would add considerable complexity to the
mode selection and mode transition logic of the controller. To prevent this, it was decided
70
that traction control would be implemented as a modification to the torque request within
the existing operating mode algorithms, almost entirely eliminating the need for
modification to mode selection and transition algorithms. One transition condition must
still be added to ensure the vehicle moves to the charge sustaining series configuration
when wheel slip is detected during charge sustaining operation. To illustrate the final
structure of the vehicle control strategy, a diagram of the control strategy is shown in Figure
26.
Figure 26: Control Strategy Flow Chart
The logic to determine the reduced torque request can be self-contained in a subsystem
independent from the rest of the operating mode logic. The only necessary point of
71
interaction with existing control is an override of the torque request with the final reduced
torque request at an appropriate place within the algorithm. This structure satisfies the
necessity to minimize impact on the existing controls architecture.
5.3
Activating Traction Control
First, the conditions under which traction control will be activated must be determined.
Because the front and rear powertrains operate independently with no rigid connection
between the axles, traction control can act on each axle separately. To accomplish this, two
slip flag variables were introduced: 𝑅𝑒𝑑𝑢𝑐𝑒_𝐹𝑟𝑜𝑛𝑡 and 𝑅𝑒𝑑𝑢𝑐𝑒_𝑅𝑒𝑎𝑟. Both variables are
Boolean indicators where a value of 1 indicates that slip has been detected on the front or
rear axle, respectively. If either of these variables is set to 1 while the vehicle is in charge
depleting mode or charge sustaining series mode, traction control strategy within those
modes will be activated and no changes to the vehicle configuration will occur. If either
variable is set to 1 while in charge sustaining parallel, the transmission will be moved to
neutral to activate charge sustaining series mode and the traction control strategy within
series mode will be activated as well. If either variable is set to 1 while the vehicle is in
engine start mode, traction control can be activated within engine start mode since the mode
occurs in the series powertrain configuration which is desirable for traction control. Once
the engine has started, the controls can pass into charge sustaining series mode and activate
traction control within series mode without any changes to the powertrain configuration
that could interfere with wheel traction.
72
Another case to be considered is when the vehicle is in charge depleting mode with traction
control active and the battery SOC drops below 18%. To prevent draining the battery pack
beyond a safe limit, the vehicle will still be passed to engine start mode by shifting the
transmission to neutral and then to charge sustaining series, all with traction control still
active.
5.3.1
Detecting Wheel Slip
Next, an algorithm to detect slip and set the 𝑅𝑒𝑑𝑢𝑐𝑒_𝐹𝑟𝑜𝑛𝑡 and 𝑅𝑒𝑑𝑢𝑐𝑒_𝑅𝑒𝑎𝑟 flags to 1
must be developed. The slip flags will be triggered dependent upon what slip scenario the
vehicle is experiencing. A wide range of slip scenarios are possible in the vehicle and
should be considered for detection. These scenarios include:
1. Launch under low mu conditions on all four wheels
2. Launch with low mu on one axle (front or rear)
3. Launch with low mu on one side of vehicle (left or right)
4. Launch with low mu on any one of the four wheels
5. Left-right split mu encountered while driving
6. Temporary front-rear split mu while driving if a patch of low mu is entered or exited
while driving
An example of these scenarios is illustrated in Figure 27.
73
5
1
2
3
4
6
Figure 27: Slip Scenarios
Wheel slip in vehicles is typically determined by comparing the speeds of driven wheels
to the vehicle speed and determining if the current wheel speeds properly correspond to the
vehicle speed. The vehicle speed is determined from non-driven wheels on the vehicle
since they are driven by the vehicle inertia and thus do not slip during acceleration. The
challenge presented by the Ohio State vehicle is that all four wheels are driven and thus
there is not guaranteed to be a reliable source of vehicle speed at all times, particularly
when all four wheels are on a low friction surface. To combat this problem, the slip
detection algorithm was designed in such a way that knowledge of the vehicle speed is not
necessary. This was accomplished by using several different comparisons of the wheel
speeds on the vehicle to determine which scenario the car has encountered and thus which
slip flag should be activated.
This method of slip detection is predicated on the assumption that the only time that all
four wheels will be at approximately the same speed is when all four wheels have traction.
74
This is true for the Ohio State vehicle even if slip occurs on all four wheels simultaneously
on an ideal surface with uniform friction because the front and rear axles will never have
an equal axle torque input under normal operation. The differing total gear ratios for the
front and rear powertrains, different normal forces on each wheel, and the torque split
determined by the operating strategy ensure that there will always be a meaningful
difference between the front axle and rear axle torque. If the torque at the axle is different
for each axle, one axle will spin its wheels faster than the other and this difference in speeds
can be captured by one of the wheel speed comparisons elaborated in this section.
The following naming convention is used throughout this work to designate each wheel:
𝜔𝐹𝑅
= Front Right wheel speed
𝜔𝐹𝐿
= Front Left wheel speed
𝜔𝑅𝑅
= Rear Right wheel speed
𝜔𝑅𝐿
= Rear Left wheel speed
Three speed differentials are calculated to help determine the slip scenario. The first two
differentials are right versus left wheel speed across the front axle and right versus left
wheel speed across the rear axle. The differentials are calculated and four resulting
intermediate indicators (𝐷1 , 𝐷2 , 𝐷3 , 𝐷4 ) are designated as shown:
𝐷1 = 1
𝑖𝑓
𝜔𝐹𝑅 − 𝜔𝐹𝐿 ≥ 𝜀𝑠
( 36)
𝐷2 = 1
𝑖𝑓
𝜔𝐹𝐿 − 𝜔𝐹𝑅 ≥ 𝜀𝑠
( 37)
𝐷3 = 1
𝑖𝑓
𝜔𝑅𝑅 − 𝜔𝑅𝐿 ≥ 𝜀𝑠
( 38)
𝐷4 = 1
𝑖𝑓
𝜔𝑅𝐿 − 𝜔𝑅𝑅 ≥ 𝜀𝑠
( 39)
75
The indicators 𝐷1 , 𝐷2 , 𝐷3 , and 𝐷4 are Booleans that default to false unless the conditions
in ( 36) - ( 39) are met. The threshold value 𝜀𝑠 that the speed differentials must exceed in
order to become true is a variable threshold that takes into account normal variances in
wheel speeds that occur during driving as well as signal noise in the wheel speed sensors.
An additional buffer is included to ensure significant wheel slip is occurring. The threshold
is calculated as:
𝜀𝑠 = 𝜀𝑛 + 𝜀𝑏 + 𝜀𝜃
( 40)
Where
𝜀𝑛
= Allowable speed differential due to signal noise and normal variance
between wheels
𝜀𝜃
= Allowable speed differential due to steering angle
𝜀𝑏
= Buffer for speed differential
The value of 𝜀𝑛 was determined from analyzing wheel speed data from several driving tests
combined with an analysis of the typical noise in the signal remaining after filtering the
wheel speed signals. To avoid high latency, a simple filter was used which contained noise
within approximately a 6 rpm band around the actual wheel speed. Normal variance
between the wheel speeds during straight line driving peaked around 20 rpm between the
wheels on the front axle and 15 rpm between the wheels on the rear axle. The normal
variance seen between the front and rear axle speeds peaked at about 20 rpm as well. The
value of 𝜀𝑏 was determined through data analysis and calibration which set it at a final
value of 10 rpm. The value of 𝜀𝜃 was determined from analyzing vehicle data from constant
76
radius tests and autocross tests and was implemented as a gain placed upon the steering
angle, 𝜃, as shown:
𝜀𝜃 = 0.08 ∗ 𝜃
( 41)
An important feature of the 𝐷1 -𝐷4 indicators is that no more than two of them can be true
at any one time since only one wheel from each axle can be faster than the other. This
means that at any time either 𝐷1 or 𝐷2 can be true but not both. Similarly, either 𝐷3 or 𝐷4
can be true but not both. This is an inherent property of the indicators since they represent
opposite ends of a single comparison.
The third differential is a comparison between the front and rear axle speeds. The axle
speed is defined as the average of the speeds of the two wheels on the axle. The third
differential and its two intermediate indicators are given as
𝜔𝐹𝑅 + 𝜔𝐹𝐿
𝜔𝑅𝑅 + 𝜔𝑅𝐿
𝐷5 = 1 𝑖𝑓 (
)−(
) ≥ 𝜀𝑠
2
2
( 42)
𝜔𝑅𝑅 + 𝜔𝑅𝐿
𝜔𝐹𝑅 + 𝜔𝐹𝐿
𝐷6 = 1 𝑖𝑓 (
)−(
) ≥ 𝜀𝑠
2
2
( 43)
This differential exhibits the same property as the left-right differential. Either 𝐷5 or 𝐷6
can be true at any point in time but not both. The 𝜀𝜃 term was excluded in the calculation
of 𝜀𝑠 for the 𝐷5 and 𝐷6 differentials because steering angle was seen to have a negligible
effect on the difference between average axle speeds. Because both axles contain open
differentials, the differences between left and right wheels on each axle is approximately
77
the same and thus the average speed of the axle is changed the same for front and rear
leaving the variances between them the same as when the vehicle is traveling straight.
5.3.2
Determining Slip Scenario
The combination of these six indicators is enough to isolate the slip scenario being
experienced by the vehicle with a significant degree of accuracy. Simulations were run
with several variations of friction distribution across the wheels in order to confirm the
necessary combinations of indicators. This includes an ideal scenario of uniform friction
distribution so that each tire experiences exactly the same friction coefficient. While this is
not realistic, it is important to include this case to develop a robust slip detection algorithm.
Each possible configuration of slipping wheels is enumerated below with the
corresponding conditions.
First, the conditions for slip scenario 1 from Figure 27 are shown in Table 5. Slip scenario
1 is characterized by the presence of a 𝐷1 -𝐷4 indicator from each axle as well as the
presence of 𝐷5 or 𝐷6 . Either 𝐷5 or 𝐷6 can be true for this configuration depending upon
which gear the transmission is in and the current torque input to each axle. All permutations
of indicators meeting these conditions can indicate slip scenario 1.
The permutations in the first two columns which are highlighted in the lighter gray in Table
5 contain 𝐷1 -𝐷4 indicators that correspond to wheels on opposite corners of the vehicle
spinning, either front right and rear left or front left and rear right. These permutations are
78
wholly unique to slip scenario 1. The permutations highlighted in darker gray correspond
to wheels on the same side of the vehicle spinning. The far right column corresponds to the
case of ideal uniform friction distribution so both wheels on each axle slip at the same
speed and none of the left-right comparisons are set true. Neither of these are unique as
will be explained later in this section.
Table 5: Conditions for Slip Scenario 1
Case
Indicator
Values
𝐷1 (FR Slip)
All Wheels on Low Mu
0
1
0
1
0
𝐷2 (FL Slip)
1
0
1
0
0
𝐷3 (RR Slip)
1
0
0
1
0
𝐷4 (RL Slip)
0
1
1
0
0
𝐷5 (Faxle Slip)
0
1
0
1
0
1
0
1
0
1
𝐷6 (Raxle Slip)
1
0
1
0
1
0
1
0
1
0
The conditions for slip scenario 2 are given in Table 6. The two possible configurations
within slip scenario 2 are front wheels on low friction or rear wheels on low friction. In
either configuration, the axle that is on low friction will trigger the corresponding 𝐷5 or 𝐷6
indicator and one of the 𝐷1 -𝐷4 indicators will be set true corresponding to one of the wheels
on the appropriate axle. In the rare case of uniform friction distribution, both wheels on the
slipping axle will slip at the same speed and none of the 𝐷1 -𝐷4 indicators will be set true.
These conditions are also not unique. Handling for these will be discussed in section 5.3.3.
79
Table 6: Conditions for Slip Scenario 2
Case
Indicator
Values
𝐷1 (𝜔𝐹𝑅 > 𝜔𝐹𝐿 )
𝐷2 (𝜔𝐹𝐿 > 𝜔𝐹𝑅 )
𝐷3 (𝜔𝑅𝑅 > 𝜔𝑅𝐿 )
𝐷4 (𝜔𝑅𝐿 > 𝜔𝑅𝑅 )
𝐷5 (𝜔𝐹𝑎𝑥𝑙𝑒 > 𝜔𝑅𝑎𝑥𝑙𝑒 )
𝐷6 (𝜔𝑅𝑎𝑥𝑙𝑒 > 𝜔𝐹𝑎𝑥𝑙𝑒 )
Front on
Low Mu
0
1
1
0
0
0
1
0
Rear on
Low Mu
0
0
0
0
0
1
0
1
1
0
0
0
The conditions for slip scenario 3 are given in Table 7. Slip scenario 3 represents a splitmu configuration for which there are two possible cases: left wheels on low friction or right
wheels on low friction. These configurations are primarily characterized by the appearance
of 𝐷1 and 𝐷3 together or 𝐷2 and 𝐷4 together. Either 𝐷5 or 𝐷6 can be true for either splitmu configuration depending upon which gear the transmission is in and the current torque
input to each axle. The permutations in Table 7 are identical to permutations highlighted
in darker gray from slip scenario 1 rendering them non-unique to either scenario. Handling
for these will be discussed in section 5.3.3.
Table 7: Conditions for Slip Scenario 3
Case
Indicator
Values
𝐷1 (𝜔𝐹𝑅 > 𝜔𝐹𝐿 )
Left on
Low Mu
Right on
Low Mu
0
1
𝐷2 (𝜔𝐹𝐿 > 𝜔𝐹𝑅 )
1
0
𝐷3 (𝜔𝑅𝑅 > 𝜔𝑅𝐿 )
0
1
𝐷4 (𝜔𝑅𝐿 > 𝜔𝑅𝑅 )
1
0
𝐷5 (𝜔𝐹𝑎𝑥𝑙𝑒 > 𝜔𝑅𝑎𝑥𝑙𝑒 )
0
1
0
1
𝐷6 (𝜔𝑅𝑎𝑥𝑙𝑒 > 𝜔𝐹𝑎𝑥𝑙𝑒 )
1
0
1
0
80
There are four possible configurations for slip scenario 4, shown in Table 8, representing
each individual wheel on a low friction surface. Each case is characterized by the 𝐷1 -𝐷4
indicator corresponding to the specific wheel that is slipping being set true while the other
three remain false. The 𝐷5 or 𝐷6 indicator corresponding to the axle containing the spinning
wheel will also be true. The permutations for slip scenario 4 are identical to those for slip
scenario 2 rendering them non-unique to either scenario. Handling for these is discussed in
section 5.3.3.
Table 8: Conditions for Slip Scenario 4
Case
FR on
Low Mu
FL on
Low Mu
RR on
Low Mu
RL on
Low Mu
𝐷1 (𝜔𝐹𝑅 > 𝜔𝐹𝐿 )
1
0
0
0
𝐷2 (𝜔𝐹𝐿 > 𝜔𝐹𝑅 )
0
1
0
0
𝐷3 (𝜔𝑅𝑅 > 𝜔𝑅𝐿 )
0
0
1
0
𝐷4 (𝜔𝑅𝐿 > 𝜔𝑅𝑅 )
0
0
0
1
𝐷5 (𝜔𝐹𝑎𝑥𝑙𝑒 > 𝜔𝑅𝑎𝑥𝑙𝑒 )
1
1
0
0
𝐷6 (𝜔𝑅𝑎𝑥𝑙𝑒 > 𝜔𝐹𝑎𝑥𝑙𝑒 )
0
0
1
1
Indicator
Values
For detection purposes, slip scenario 5 will appear the same to the slip detection algorithm
as scenario 4 when one axle has entered the low friction surface and will appear the same
as scenario 3 when both axles have entered the low friction surface. Similarly, scenario 6
will appear the same as scenario 2 or scenario 1. This means that scenario 5 and 6 are
already covered by the analysis above and further analysis specific to these scenarios is not
necessary.
81
5.3.3
Handling for Non-Unique Slip Signatures
There are identical permutations of slip indicators for slip scenarios 1 and 3 as well as for
slip scenarios 2 and 4. This makes it impossible to determine the exact combination of
wheels that are slipping. Fortunately, the indicators give enough information for the
purposes of traction control that it is not necessary to obtain additional information. For
example, cases that are indistinguishable include a single wheel on low friction or both
wheels of an axle on low friction. A traction control system can react to a spinning wheel
in one of two ways: reducing the input torque to the wheel or braking the spinning wheel.
In either scenario, one wheel or both wheels of an axle on low friction, the traction control
system would react by either reducing the input torque to the axle or braking the wheel that
is spinning faster to control the wheel speed and aid in transferring torque to the other
wheel of the axle. Thus it is not necessary to distinguish further which scenario the vehicle
is experiencing.
5.3.4
Setting Slip Flags
As demonstrated in section 5.3.2 and section 5.3.3, the proposed slip detection algorithm
determines the slip scenario with enough accuracy to determine which slip flag,
𝑅𝑒𝑑𝑢𝑐𝑒_𝐹𝑟𝑜𝑛𝑡 or 𝑅𝑒𝑑𝑢𝑐𝑒_𝑅𝑒𝑎𝑟, should be set to true. The appropriate slip flag or flags
to be set true based on detected slip scenario is shown in Table 9. This logic is implemented
as a truth table in the vehicle controller.
82
Table 9: Slip Flag Determination
Slip Flag
Slip Scenario
Normal Traction
𝑹𝒆𝒅𝒖𝒄𝒆_𝑭𝒓𝒐𝒏𝒕 𝑹𝒆𝒅𝒖𝒄𝒆_𝑹𝒆𝒂𝒓
0
0
All Wheels on Low Mu (Scenario 1)
1
1
Front on Low Mu (Scenario 2)
1
0
Rear on Low Mu (Scenario 2)
0
1
Left Side on Low Mu (Scenario 3)
1
1
Right Side on Low Mu (Scenario 3)
1
1
FR on Low Mu (Scenario 4)
1
0
FL on Low Mu (Scenario 4)
1
0
RR on Low Mu (Scenario 4)
0
1
RL on Low Mu (Scenario 4)
0
1
After the truth table logic, hysteresis is added to the slip flags to prevent them from rapidly
switching on and off. It also prevents a slip flag from signaling true if the speed difference
goes out of range for a very short amount of time. The hysteresis holds the final slip flags
at false until the truth table output of the flag remains true for longer than 𝑡𝑑𝑒𝑙𝑎𝑦_𝑜𝑛 seconds.
More importantly, the hysteresis holds the slip flags on and prevents them from becoming
false until the truth table output of the flag is false for longer than 𝑡𝑑𝑒𝑙𝑎𝑦_𝑜𝑓𝑓 seconds. This
allows for a continuous torque reduction action in the traction control strategy when the
wheels are struggling to gain traction and experience speed oscillations around the slip
threshold.
The fact that this method of slip detection does not require any measure of vehicle speed
to determine slip as is required by the traditional slip calculation given in ( 5) gives it a
distinct advantage over traditional slip detection methods. It also has an advantage over
83
previously used methods of slip detection on all wheel drive vehicles which considered
only the differential between front and rear axle speeds to detect slip. The addition of the
left to right comparisons on each axle grants the ability to detect when both axles are
slipping simultaneously.
5.4
Traction Control Algorithm
The approach taken for traction control in the Ohio State EcoCAR 2 vehicle is to reduce
the input torque to the axle experiencing wheel slip. The torque reduction is implemented
as a maximum axle torque limit imposed upon the torque requests output from the control
strategy for the current operating mode. This limit acts as a maximum allowable torque for
the axle meaning that the driver requested torque will be overridden by the traction control
limit if it is greater than the limit, however the driver torque request will be followed if it
is below the traction control limit. A flow chart of the torque reduction and reapplication
process is illustrated using the front axle as an example in Figure 28. In Figure 28, t
indicates the amount of time that the current state has been active.
When no wheel slip is detected, the torque limit is set well above the driver torque request
to ensure that torque does not become unnecessarily limited. When slip is detected, the axle
torque limit for the appropriate axle is instantly reduced by a value of 𝑇𝑑𝑟𝑜𝑝 Nm below the
current front or rear, respectively, axle torque request. The limit is then reduced linearly
from that value at a rate of 𝑇𝑟𝑒𝑑𝑢 Nm/time step until slip is no longer detected.
84
Figure 28: Torque Reduction Strategy Flow Chart
To avoid unwanted regenerative braking, a safety mechanism in the traction control
algorithm saturates the traction control torque limit at 0 Nm and so will not allow the
algorithm to request a negative torque. A negative torque request is never necessary for
traction control as a torque request of zero will always allow the wheels to regain traction
as they will be driven by the inertia of the vehicle through road contact. A negative torque
request also risks the introduction of negative slip. However, if the driver requested torque
becomes negative, that torque request would still be passed out of the control system to the
actuators.
85
Once the slip flag has been set to 0 again, the torque limit will continue to reduce at the
same rate for a short period of time, 𝑡𝑟𝑒𝑑𝑢 , to add a small safety factor and will then be held
at the reduced value for a predetermined amount of time, 𝑡ℎ𝑜𝑙𝑑 , after which it will be
linearly increased at a rate of 𝑇𝑖𝑛𝑐 Nm/time step until the torque limit again exceeds the
driver commanded torque. During the torque reduction, hold, and torque increase stages,
if the slip flag is set to 1 again at any time the torque begins reducing again even if the full
process has not completed. Figure 29 illustrates this process on an exaggerated time scale
for clarity.
Figure 29: Traction Control Illustration
5.5
Implementation
With the traction control algorithm determined on paper, implementation in EcoSIM2Dynamic follows as well as final implementation on the Ohio State vehicle. The algorithm
86
is first implemented into code and tested within the dynamic simulator. Once development
in software is complete, the algorithm can be implemented in the vehicle and tested on the
ceramic tile surfaces at the Transportation Research Center in East Liberty, Ohio.
5.5.1
Controls Hardware
The traction control algorithm is located within the vehicle’s supervisory controller. The
highly complex architecture chosen by the Ohio State team demands an extensive
supervisory control strategy capable of optimizing a complex system in real time. To
accommodate the control strategy, the controller hardware must meet several requirements
including:

3 ADC inputs and DAC outputs

3 CAN busses

Ability to execute complex controls in real time

Allows for rapid-prototyping and tuning

Robust hardware that can withstand vibration and temperatures experienced in
vehicle cabin
The Ohio State team chose a dSpace MicroAutoBox II (MABX II) for the EcoCAR 2
vehicle because it suitably met these criteria with a large amount of computing power, the
ability to compile and flash code quickly, and a record of reliability with the Ohio State
team during several past AVTCs. Full manufacturer specifications for the MABX II are
given in [26]. A view of the MABX II controller can be seen in Figure 30.
87
Figure 30: dSpace MicroAutoBox II
5.5.2
Required Signals and Sensors
Necessary signals for proper function of the traction control algorithm are:

Front Right wheel speed

Front Left wheel speed

Rear Right wheel speed

Rear Left wheel speed

Current electric machine torque outputs

Current gear command

Current electric machine torque commands
The wheel speeds are obtained from the stock hall-effect wheel speed sensors and
transmitted to the MABX by CAN from the stock brake controller. The wheel speed
sensors have a resolution of 48 ticks/rev. The current electric machine torques are obtained
via CAN from the inverters and the current gear is obtained via CAN from the transmission
controller. Current actuator torque and gear commands are calculated within the MABX at
88
its operating time step of 0.01 sec and the values are routed directly into the traction control
algorithm. The incoming signals are appropriately mapped or converted from their original
signals prior to use in the traction control algorithm.
5.6
Parameter Optimization
The final slip detection and traction control algorithm contain a total of 7 tunable
parameters for each axle. These parameters are 𝑡𝑑𝑒𝑙𝑎𝑦_𝑜𝑛 , 𝑡𝑑𝑒𝑙𝑎𝑦_𝑜𝑓𝑓 , 𝑇𝑑𝑟𝑜𝑝 , 𝑇𝑟𝑒𝑑𝑢 , 𝑡𝑟𝑒𝑑𝑢 ,
𝑡ℎ𝑜𝑙𝑑 , and 𝑇𝑖𝑛𝑐 . To optimize these parameters, a genetic algorithm optimization was used
with the results of the algorithm implemented in EcoSIM2-Dynamic. The objective
function to be minimized considered the difference between the appropriate wheel speeds
for the current vehicle speed and the actual wheel speeds. This could be accomplished in
simulation because the vehicle speed during wheel slip can be found in simulation through
the magic formula and vehicle body models. An acceleration performance term was also
included in the objective function that considers the vehicle’s ability to continue
accelerating during traction control operation by comparing the target vehicle speed to the
actual speed achieved during simulation. The objective function to optimize the parameters
using the genetic algorithm is given as
𝐸𝑟𝑟 = (∫
𝑣𝑣𝑒ℎ
𝑣𝑣𝑒ℎ
− ∫ 𝜔𝐹𝑅 ) + (∫
− ∫ 𝜔𝐹𝐿 )
𝑟𝑒𝑓𝑓,𝐹𝑅
𝑟𝑒𝑓𝑓,𝐹𝐿
𝑣𝑣𝑒ℎ
𝑣𝑣𝑒ℎ
+ (∫
− ∫ 𝜔𝑅𝑅 ) + (∫
− ∫ 𝜔𝑅𝐿 )
𝑟𝑒𝑓𝑓,𝑅𝑅
𝑟𝑒𝑓𝑓,𝑅𝐿
+ 6|𝑣𝑡𝑎𝑟𝑔𝑒𝑡 − 𝑣𝑓𝑖𝑛𝑎𝑙 |
89
( 44)
Where
𝑣𝑡𝑎𝑟𝑔𝑒𝑡
= Target speed for acceleration test in mph
𝑣𝑓𝑖𝑛𝑎𝑙
= Final vehicle speed achieved during simulation in mph
The objective function acts as an overall performance metric for the traction control
system. It will be used throughout the remainder of this work and referred to as the overall
performance metric. While a term to consider vehicle performance is included in the
optimization, its relative weight as compared to the other terms is much less. Typical
differences between target and final speed seen during these simulations are less than 8
mph. Typical values for the terms considering wheel speeds are on the order of 60-100.
This means that even when multiplied by two in the objective function, the performance
term carries considerably less weight than the other terms. Performance considerations
were given such a small weight because the safety concerns surrounding the control of
wheel speeds are of much higher importance than acceleration performance during that
time.
The simulation for use with the genetic algorithm optimization considered a 0-30 mph
acceleration with all wheels on low friction and a perfectly uniform low friction surface
with a nominal coefficient of friction of 0.26. This scenario was used because it represents
a worst case scenario. The final values for the parameters generated by the optimization
are given in Table 10.
90
Table 10: Simulation Optimized Parameter Values
5.7
Parameter
Front Axle Value
Rear Axle Value
𝒕𝒅𝒆𝒍𝒂𝒚_𝒐𝒏
0.014 sec
0.008 sec
𝒕𝒅𝒆𝒍𝒂𝒚_𝒐𝒇𝒇
0.040 sec
0.015 sec
𝒕𝒓𝒆𝒅𝒖
0.346 sec
0.050 sec
𝒕𝒉𝒐𝒍𝒅
0.408 sec
0.248 sec
𝑻𝒓𝒆𝒅𝒖
11.0 Nm
23.7 Nm
𝑻𝒊𝒏𝒄
7.0 Nm
5.86 Nm
𝑻𝒅𝒓𝒐𝒑
499.0 Nm
500 Nm
System Performance Metrics
Before presenting any simulation results, it is important to outline some metrics to help
measure the performance improvement granted by the traction control. The following
metrics will be looked at for each axle in all test scenarios:

Maximum wheel speed (𝜔𝑚𝑎𝑥 )

Maximum slip ratio value (𝜅𝑚𝑎𝑥 )

Maximum interval of slip (𝑡𝑠𝑙𝑖𝑝,𝑚𝑎𝑥 )

Overall Performance Metric (OPM)
Slip ratios are defined in ( 6). The maximum interval of slip is defined as the longest
interval for which a slip flag is active. The overall performance metric is defined as the
objective function value as given by ( 44). For all metrics, lower values are more desirable.
91
5.8
Sensitivity to Road Friction
To ensure that the system is effective across a wide range of conditions, the worst case
scenario of all wheels on low friction was repeated using a variety of friction distributions
across the tires and the resulting performance was compared. Table 11 shows the friction
distributions that were considered.
Table 11: Friction Distributions
Distribution Front Left Front Right
Rear Left
Rear Right
𝜇𝑥
𝜇𝑥
𝜇𝑥
𝜇𝑥 − 0.03
𝜇𝑥 − 0.01
𝜇𝑥 − 0.01
𝜇𝑥
𝜇𝑥
𝜇𝑥 − 0.02
𝜇𝑥 − 0.01
𝜇𝑥
𝜇𝑥 − 0.02
𝜇𝑥 − 0.03
𝜇𝑥 − 0.01
𝜇𝑥
𝜇𝑥
𝜇𝑥
𝜇𝑥 − 0.04
𝜇𝑥
𝜇𝑥
𝜇𝑥
A
B
C
D
E
F
G
𝜇𝑥
𝜇𝑥 − 0.01
𝜇𝑥 − 0.02
𝜇𝑥
𝜇𝑥 − 0.03
𝜇𝑥 − 0.03
𝜇𝑥
The 0-30 mph simulation was run with traction control active for each friction scenario.
The results for each of these scenarios is summarized in Figure 31. The effect on each axle
is shown separately in the plot. The results show clear trends in the behavior of each
performance metric as the friction difference increases between the right and left wheels
on an axle.
92
Wheel Speed [rpm]
400
Front
Rear
350
300
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Slip Interval [s]
Slip Ratio
8
6
Front
Rear
4
1
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Front
Rear
0.8
0.6
0.4
0
0.005
0.01
0.015 0.02 0.025
Difference in Mu
0.03
0.035
0.04
Figure 31: Friction Study Results Per Axle
The following trends can be seen:

For both axles, 𝜔𝑚𝑎𝑥 peaks when there is a slight difference in friction between the
wheels, but then rapidly declines as the friction differential grows.

The maximum slip ratio, 𝜅𝑚𝑎𝑥 , for the rear axle stays somewhat constant as it
oscillates within a small band of values, however the front axle maximum slip ratio
increases steadily as the friction differential increases.

The slip interval increases slightly for the front wheels and decreases slightly for
the rear wheels.
93
While these trends display that there is some change in the performance of the system, the
scale of the change is relatively small. A better illustration of this is seen in Figure 32 where
the change in the overall performance metric is seen as a function of the maximum deviance
from the nominal coefficient of friction seen by one of the wheels. This is particularly
useful as an overall measure of the performance of the system that takes both axles into
account rather than only one axle at a time. There is a clear trend of improved performance
with a diminishing return as the maximum friction differential increases. It is important to
note, however, that the system is still effective and capable of adequately controlling slip,
Overall Performance Metric
even in the worst case scenario of a uniform low friction surface.
600
500
400
300
0
0.005
0.01
0.015 0.02 0.025 0.03
Maximum Difference in Mu
0.035
0.04
Figure 32: Overall Performance Metric Value for Friction Study
Overall performance metric values less than 1000 indicate that traction control is functional
and at least moderately effective whereas overall performance metric values for
simulations with no traction control active is typically on the order of 104. Examples of this
can be seen in Table 12 and Table 13 in Chapter 0. Figure 33 and Figure 34 show the results
94
of the simulation with overall performance metric of 559 and 302, respectively, to illustrate
the difference in vehicle performance associated with each overall performance metric
4
400
300
Wheel Slip
FR
FL
200
100
0
0
5
10
FR
FL
3
2
1
0
15
400
0
8
300
6
Wheel Slip
Wheel Speed [rpm]
Wheel Speed [rpm]
value.
200
RR
RL
100
0
0
5
10
time [s]
15
5
10
15
RR
RL
4
2
0
0
5
10
time [s]
15
Figure 33: Simulation for Friction Distribution A – Overall Performance Metric = 559
95
Wheel Slip
200
100
0
0
300
5
10
0
5
10
time [s]
2
0
5
10
15
8
100
0
4
0
15
RR
RL
200
FR
FL
6
Wheel Slip
Wheel Speed [rpm]
Wheel Speed [rpm]
8
FR
FL
300
15
RR
RL
6
4
2
0
0
5
10
time [s]
15
Figure 34: Simulation for Friction Distribution G – Overall Performance Metric = 302
96
Chapter 6: Testing and Results
6.1
Software-in-the-Loop (SIL) Testing
The traction control algorithm was first tested in EcoSIM 2 – Dynamic. Several slip
scenarios were tested in the software configuration. Due to the limitations discussed in
Chapter 4, the most accurate slip scenarios for simulation are launch under low mu
conditions for all four wheels and launch with a left-right split-mu scenario. To test the slip
detection and flexibility of the traction control algorithm, front-rear split mu scenarios and
a single wheel on low-mu were tested as well. Figure 35 shows the subset of scenarios from
Figure 27 that were chosen for SIL testing.
Figure 35: Scenarios for SIL Testing
97
The test results were all gathered from a 15 second simulation of a 0-30 mph acceleration.
The driver commands for the acceleration are to press the accelerator to 100% at t = 1.5
sec and hold it at 100% until the vehicle speed nears the target speed of 30 mph. As the
vehicle speed approaches 30 mph, the accelerator percent is reduced such that the vehicle
continues at a constant 30 mph once the speed has been achieved. A sample accelerator
command is shown in Figure 36 for a vehicle with regular traction performing a 0-30 mph
acceleration test. Figure 36 demonstrates that for SIL simulations, the driver torque request
remains at maximum throughout the simulation unless the target speed is met. It is not
reduced based on lack of traction as it likely would be by a human driver in a vehicle. This
means that for SIL results, all traction control comes from the traction control algorithm
Speed [mph] and Pedal Percent
and is not a result of a decreased pedal input.
100
Vehicle Velocity
Target Velocity
Accelerator Position
80
60
40
20
0
0
5
10
time [s]
Figure 36: Typical Accelerator Pedal Command
98
15
6.2
6.2.1
Charge Depleting Mode - Software-in-the-Loop (SIL) Results
Results Summary
In total, seven configurations of the wheels on low friction were used to fully exercise the
traction control algorithm in SIL. A summary of the important metrics for all of the cases
both with and without traction control are given in Table 12. A case is then shown in more
detail to provide an in depth look at the operation and effectiveness of the traction control
system.
Table 12: Results Summary for Charge Depleting Operation in SIL
Wheels on Low
TC
Friction
All Wheels
Front Wheels
Rear Wheels
Left Wheels
Right Wheels
Front Left
Wheel
Rear Right
Wheel
Off
On
Off
On
Off
On
Off
On
Off
On
Off
On
Off
On
Front Axle
Rear Axle
𝒕𝒔𝒍𝒊𝒑,𝒎𝒂𝒙 𝝎𝒎𝒂𝒙
𝒕𝒔𝒍𝒊𝒑,𝒎𝒂𝒙
𝝎𝒎𝒂𝒙
𝜿𝒎𝒂𝒙
𝜿𝒎𝒂𝒙
OPM
3455
343
2094
365
376
365
3641
344
3988
368
2250
365
375
365
56140
324
13105
145
16741
187
41967
293
39469
314
8689
125
11761
173
(rpm)
9.72
5.99
5.54
5.82
0.024
0.025
10.46
5.19
11.47
6.82
6.15
4.83
0.024
0.025
(sec)
(rpm)
13.13
0.43
8.76
0.43
0
0
12.18
0.37
12.45
0.44
8.03
0.37
0
0
3165
315
373
367
2653
368
2995
328
2239
382
373
366
2012
367
(sec)
18.45
6.82
0.022
0.022
14.76
5.42
17.36
6.44
15.08
6.29
0.022
0.022
12.67
4.99
11.71
0.57
0
0
10.55
0.55
11.24
0.56
10.31
0.56
0
0
9.23
0.55
Table 12 shows a significant improvement in all of the important metrics for every case
when traction control is applied. Without traction control, the maximum wheel speed on
any axle with wheels on low friction reaches dangerously high speeds that would cause
99
component damage and initiate vehicle spin. These speeds are reduced by an order of
magnitude with traction control applied to values that do not exceed typical wheel speeds
for driving. The maximum slip ratios are also reduced significantly by the traction control
system reaching ratios peaking in the range of 5-7 with traction control rather than values
as high as 19 without. Finally, the maximum slip intervals are reduced by the traction
control to an average of 0.41 sec on the front axle and 0.56 sec on the rear axle. Without
traction control, the slipping wheel or wheels typically did not regain traction for most or
all of the simulation once slip began.
6.2.2
Detailed Results – All Wheels on Low Friction
The case to be explored in detail is a launch with all four wheels on a low friction surface
corresponding to slip scenario 1. The results of the simulation with traction control turned
off are shown in Figure 37. It is clear that traction was lost and wheel spin began to occur
immediately at t = 1.5 sec when the accelerator is initially pressed to 100 percent. On the
front axle, both wheels received enough torque input to spin up to high speeds. In contrast,
the rear wheels experience a greater friction differential across the wheels that causes the
rear differential to divert torque away from the wheel with higher friction. The result is that
the rear left wheel spins up very fast while the rear right wheel is driven primarily by the
vehicle inertia. This combination of traction loss and high wheel speeds would incite a spin
or fishtail in a vehicle.
100
10
FR
FL
3000
2000
1000
0
0
4000
5
10
FR
FL
0
5
10
15
20
RR
RL
3000
5
0
15
Wheel Slip
Wheel Speed [rpm]
Wheel Slip
Wheel Speed [rpm]
4000
2000
1000
RR
RL
15
10
5
0
0
0
5
10
15
time [s]
0
5
10
15
time [s]
Figure 37: Wheel Speeds and Slip – All Wheels on Low Friction – Traction Control Off
Figure 38 shows the vehicle speed and accelerator commands for the simulation. As the
vehicle reaches and exceeds the target speed the accelerator input is reduced as the driver
PID attempts to reduce the vehicle speed back to the target speed. The resulting negative
torque request from the motor, slight brake application, and rapid speed reduction of the
rear left wheel is so severe that it overshoots the target wheel speed and experience negative
slip for 1.46 sec.
101
Speed [mph] and Pedal Percent
100
Vehicle Velocity
Target Velocity
Accelerator Position
Brake Position
80
60
40
20
0
0
5
10
time [s]
15
Figure 38: Vehicle Speed and Pedal Profile
Simulation results with traction control applied are given in Figure 39 where significant
8
400
Wheel Slip
FR
FL
300
200
100
0
0
5
10
400
4
2
0
5
10
15
8
RR
RL
300
100
0
5
10
time [s]
RR
RL
6
200
0
FR
FL
6
0
15
Wheel Slip
Wheel Speed [rpm]
Wheel Speed [rpm]
reduction in all of the important metrics is visible.
15
4
2
0
0
5
10
time [s]
15
Figure 39: Wheel Speeds and Slip – All Wheels on Low Friction – Traction Control On
102
An interesting aspect to note is the appearance of several shorter slip events rather than one
large one. This is the result of the functioning of the traction control algorithm. Once
traction has been regained, the traction control strategy begins to increase the torque limit
to meet the driver request, however the torque becomes greater than the friction between
the wheels and road before reaching the driver torque request so the wheels begin to slip
again. At that point the torque reduction cycle begins again. Because such a low friction
surface is used for the simulation, this repeats several times since the driver torque request
is consistently higher than the tractive capacity of the wheels. An illustration of the action
Front Axle
Torque [Nm]
of the traction control system upon the axle torque requests is shown in Figure 40.
1000
500
0
0
5
15
Driver Request
Limit
Output
2000
Rear Axle
Torque [Nm]
10
1500
1000
500
0
0
5
time [s]
10
Figure 40: Axle Torque Commands from Traction Control System
103
15
Both axles follow the driver torque request as it quickly reaches a maximum, but as wheel
slip begins the limit drops below the driver request causing the output torque from the
operating strategy to drop along with it. Each cycle of traction being regained and torque
reapplied can be seen. The front axle very nearly reaches the driver request each time but
the wheels are unable to accommodate the full request and so begin to slip again. The rear
axle is able to accommodate a higher torque input before slip occurs, however it remains
further from meeting the driver torque request than the front axle.
A trade-off of the use of a traction control system like this one is a reduction in acceleration
performance. When the traction control system is active and the torque inputs reduced, the
vehicle is unable to meet the target vehicle speed by the end of the simulation. The
acceleration performance is shown in Figure 41.
Speed [mph]
30
20
10
0
Vehicle Velocity
Target Velocity
0
5
10
15
time [s]
Figure 41: Vehicle Acceleration Performance
The line denoting vehicle speed in the plot is wavy as a reflection of the continuously
decreasing and increasing output torque of the vehicle shown in Figure 40. These
104
reductions in performance and drivability are an acceptable trade-off for the traction
control system because increased safety and stability during loss of traction are of the
highest importance.
6.3
Charge Depleting Mode – In Vehicle Results
After implementing the algorithm on the vehicle, testing was conducted on the low
coefficient of friction ceramic tiles at the Transportation Research Center. Because there
was a very limited time available for testing, only a few configurations were able to be
tested. The traction control system was able to be tested during a launch with all wheels,
only the left wheels, and only the right wheels on the tiles. All tests were conducted with
the accelerator pedal pressed to 100%.
6.3.1
Launch with All Wheels on Low Friction
Figure 42 shows the results of a vehicle launch with all four wheels on the ceramic tiles
without traction control.
105
Torque [Nm], Percent Wheel Speed [rpm] Wheel Speed [rpm]
FR
FL
200
100
0
0
5
10
15
20
RR
RL
300
200
100
0
0
5
10
15
1500
20
Faxle
Raxle
Accel Pedal x10
1000
500
0
0
5
10
time [s]
15
20
Figure 42: All Wheels on Ceramic Tiles – Traction Control Off
The wheels can be seen to start slipping at t = 3.4 sec. The accelerator pedal was lifted
quickly to prevent dangerous wheel speeds and vehicle spin. Figure 43 shows the same test
with the traction control system turned on. The rear wheels begin slipping at approximately
t = 3.75 sec. With the accelerator pedal remaining at 100% throughout the test, the wheel
speed is controlled and slipping wheels are recovered by the traction control system alone.
106
Torque [Nm], Percent Wheel Speed [rpm] Wheel Speed [rpm]
300
FR
FL
200
100
0
0
5
10
15
20
5
10
15
20
300
RR
RL
200
100
0
0
1500
Faxle
Raxle
Accel Pedal x10
1000
500
0
0
5
10
time [s]
15
20
Figure 43: All Wheels on Ceramic Tiles – Traction Control On
Once slip began, the rear wheel speeds increased only 80 rpm during the first slip event
before the traction control was able to begin reducing slip. In contrast, without traction
control the rear wheel speeds increased over 150 rpm and would have continued to increase
if the driver had not released the pedal.
6.3.2
Launch with Left Wheels on Low Friction
Figure 44 shows the results of a launch with only the left wheels on the ceramic tiles
without traction control. Both of the left wheels are seen to begin to spin at approximately
107
t = 4 sec. Again, the driver released the pedal to prevent excessive wheel or motor speeds
Torque [Nm], Percent Wheel Speed [rpm]
Wheel Speed [rpm]
and vehicle spin.
FR
FL
300
200
100
0
0
2
4
6
8
10
12
14
16
300
18
RR
RL
200
100
0
0
2
4
6
8
10
12
14
16
18
1500
Faxle
Raxle
Accel Pedal x10
1000
500
0
0
2
4
6
8
10
time [s]
12
14
16
18
Figure 44: Left Wheels on Low Friction – Traction Control Off
The results of the same test with traction control turned on are seen in Figure 45. Again,
the traction control is able to eliminate the wheel slip while the accelerator remains
pressed to 100%. The largest increase in wheel speed seen during a slip event was only
100 rpm whereas the increase without traction control was over 130 rpm and would have
increased further if the driver had not released the pedal.
108
Torque [Nm], Percent Wheel Speed [rpm] Wheel Speed [rpm]
300
FR
FL
200
100
0
0
5
10
15
20
400
RR
RL
200
0
0
5
10
15
2000
Faxle
Raxle
Accel Pedal x10
1000
0
20
0
5
10
time [s]
15
20
Figure 45: Left Wheels on Low Friction – Traction Control On
6.4
6.4.1
Charge Sustaining Series Mode – SIL Results
Results Summary
To test charge sustaining series mode in SIL, the same 0-30 mph acceleration was used to
allow for direct comparison. Because only the rear wheels are driven by the powertrain in
the series configuration, fewer combinations of wheels on low friction had to be tested in
order to thoroughly test the system. In total, four configurations were chosen. A summary
of the results is shown in Table 13.
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Table 13: Results Summary for Charge Sustaining Series Operation in SIL
Wheels on Low
TC
Friction
All Wheels
Left Wheels
Right Wheels
Rear Right
Wheel
Off
On
Off
On
Off
On
Off
On
Front Axle
Rear Axle
𝒕𝒔𝒍𝒊𝒑,𝒎𝒂𝒙 𝝎𝒎𝒂𝒙
𝒕𝒔𝒍𝒊𝒑,𝒎𝒂𝒙
𝝎𝒎𝒂𝒙
𝜿𝒎𝒂𝒙
𝜿𝒎𝒂𝒙
(rpm)
246
167
247
168
278
212
278
212
0
0.005
0
0.005
0
0.005
0
0.005
(sec)
(rpm)
0
0
0
0
0
0
0
0
4161
250
4286
250
3147
314
3147
314
OPM
(sec)
26.8
8.8
32.3
8.8
27.0
9.0
27.0
9.0
13.16
0.49
13.16
0.49
13.13
0.55
13.13
0.55
33131
218
33434
217
26430
269
26430
269
The very low slip ratio of 0.005 on the front axle is indicative of the fact that the front
wheels are non-driven wheels in the series configuration. For the rear wheels, significant
improvement is again seen in every case when traction control is applied. The maximum
wheel speeds and slip ratios both with and without traction control applied are notably
higher than those seen during charge depleting mode. This is because the entire driver
torque request is sent to the rear axle in this mode and a higher torque input to the wheels
causes them to accelerate faster once they begin to slip. With fewer driven wheels, the
vehicle’s ability to accelerate during the launch while wheel slip is occurring is reduced
even further. The combination of lower vehicle speed and higher torque input causes the
maximum slip ratio to peak higher. The slip intervals with the traction control applied are
also slightly longer than those seen in charge depleting mode because it takes longer for
the traction control to reduce the wheels from their higher slip speed.
110
6.4.2
Detailed Results – All Wheels on Low Friction
The case to be explored in detail is a launch with all four wheels on a low friction surface.
This corresponds to slip scenario 1 but for charge sustaining operation is effectively the
same as slip scenario 2 with the rear wheels on low friction. Simulation results with traction
x 10
300
Wheel Slip
200
100
0
0
6000
5
10
15
0
5
10
time [s]
-1
-2
5
10
15
15
RR
RL
20
2000
0
FR
FL
0
30
RR
RL
4000
-4
0
FR
FL
Wheel Slip
Wheel Speed [rpm]
Wheel Speed [rpm]
control turned off are shown in Figure 46.
10
0
0
5
10
time [s]
15
Figure 46: Wheel Speeds and Slip – All Wheels on Low Friction – Traction Control Off
The front wheels are driven by the inertia of the vehicle so they maintain traction and slip
ratios on the order of 10-3 throughout the simulation. The torque input on the rear wheels
is great enough to overcome the friction differential between the rear wheels and spin both
of them to dangerous speeds. The rear right wheel eventually regains traction due to the
111
transfer of torque to the left wheel since the left wheel experiences a slightly lower friction
coefficient. The rear left wheel continues to spin up to higher speeds throughout the
x 10
200
FR
FL
Wheel Slip
150
100
50
0
0
5
10
15
300
RR
RL
200
100
0
0
5
10
time [s]
15
-4
FR
FL
2
1
0
-1
-2
0
10
Wheel Slip
Wheel Speed [rpm]
Wheel Speed [rpm]
simulation. This would cause a severe fishtail in the vehicle.
5
10
15
RR
RL
5
0
0
5
10
time [s]
15
Figure 47: Wheel Speeds and Slip – All Wheels on Low Friction – Traction Control On
Figure 47 shows the results of the simulation with traction control applied. The front
wheels again maintain traction throughout the simulation. The rear wheels exhibit the
behavior of several small periods of slip as seen in the charge depleting mode. A view of
the torques within the traction control algorithm is shown in Figure 48. In this case, the
rear axle is never able to meet the driver torque request without inciting wheel slip.
112
Rear Axle Torque [Nm]
Driver Request
Limit
Output
2000
1500
1000
500
0
0
5
10
15
Figure 48: Axle Torque Commands of Traction Control System
The vehicle acceleration performance suffers much more in charge sustaining mode since
the entire torque request is handled by the rear axle. When the torque is reduced to regain
traction, there is no assistance from the front axle to continue propelling the vehicle. As
with charge depleting mode, this is an acceptable tradeoff for the gain in vehicle safety.
The vehicle velocity shows more pronounced velocity fluctuations which is reflective of
the greater torque reduction necessary to regain traction in this mode.
35
Speed [mph]
30
25
Vehicle Velocity
Target Velocity
20
15
10
5
0
0
5
10
time [s]
Figure 49: Vehicle Acceleration Performance
113
15
Chapter 7: Conclusions and Future Work
7.1
Conclusions
The hybrid powertrain configuration of the Ohio State EcoCAR 2 vehicle was analyzed
and the fundamental powertrain dynamics necessary to describe the powertrain were
investigated. The powertrain dynamics and longitudinal vehicle dynamics were coupled
with concepts of tire force generation and tire slip to create a vehicle model and
corresponding simulator called EcoSIM 2 - Dynamic implemented in Simulink from The
MathWorks. This model allowed for the development of a traction control system tailored
to the vehicle’s unique powertrain.
A multi-faceted slip detection algorithm was created to adequately detect slip on both axles.
A series of wheel speed comparisons allow the algorithm to determine if one or both axles
are slipping at any point in time in order to activate the necessary corrective actions from
the traction control system. The traction control algorithm presented in this work is an
effective solution to the problems presented by uncontrolled wheel slip in the Ohio State
EcoCAR 2 vehicle. Simulations demonstrate the effectiveness of the algorithm for
reducing the duration and maximum ratio of wheel slip and preventing the wheels from
reaching dangerous speeds. These improvements to wheel slip management lead to
increased vehicle stability and safety. The tests performed in simulation include vehicle
114
launch in multiple operating modes with one, two, or all four wheels on a low friction
surface. A comparison of results for these tests with and without the traction control active
demonstrate that the system is robust and effectively manages loss of traction in the vehicle
though there is a tradeoff in acceleration performance due to the torque reduction inherent
in the strategy. Finally, while the slip detection and traction control algorithms presented
within this work are designed specifically for the Ohio State EcoCAR 2 vehicle, they could
be easily adapted for implementation on any vehicle with independent front and rear
drivetrains.
7.2
Future Work
The traction control system presented here provides a strong basis upon which
improvements and further development can be carried out. If further development is done
outside of the scope of the competition, the addition of brake based control could be used
to more rapidly reduce wheel speeds and more effectively transfer torque to wheels
maintaining traction for improved acceleration performance under low friction conditions.
Another way the acceleration performance could be increased would involve further
integration of the traction control algorithm with the mode operation algorithms. Rather
than simply acting as an override on the output, the torque limits could be taken into
account by the operating strategy so that wheels with traction could receive an increased
torque request to compensate for the decreased torque input to wheels without traction.
This would allow the vehicle to output the maximum possible torque at all times.
115
Modifications to the torque increase process could also improve acceleration performance.
Torque increase could be made a multistage process that initially increases the torque
quickly then slows as the vehicle approaches the torque level at which it initially lost
traction. The higher average torque input would allow the vehicle to accelerate faster,
however it increases the risk of losing traction again and thus would require careful design
and tuning to ensure stability.
Another future development is to expand the traction control strategy to take energy
management concerns into account. If energy management is considered, traction control
could request negative torque as a means of rapidly reducing wheel speeds. This would
also provide the opportunity for potential improvements to vehicle efficiency by including
regenerative braking as a part of the traction control strategy.
Improvements should be made to EcoSIM 2 – Dynamic as well. First, a method may be
possible for properly modeling speed control for the motors to allow more accurate
modeling of gear shifts. This could expand the simulator’s utility to include drivability
testing as well. The model could also be expanded to model lateral vehicle dynamics. The
full Magic Formula model includes lateral forces and all moments present in the contact
patch, but the capabilities of SimDriveline do not currently include these forces. However,
the tire model could be implemented through other Simulink toolboxes as well as the lateral
vehicle dynamics which also are currently limited by SimDriveline.
116
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