Modeling and Simulation of a Hy
Vehicle for the Challenge X Co
Submitted to:
The Engineering Honors Commi
119 Hitchcock Hall
College of Engineering
The Ohio State University
Columbus, OH 43210
By
Michael Arnett 4091 Millsboro Rd W
Mansfield, OH 44903
Dr. Giorgio Rizzoni, Adviso
May 20, 2005
brid Electric
mpetition
ttee
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Abstract:
As the market shifts toward larger vehicles and growing concerns regarding
petroleum consumption and emissions emerge, automakers have begun to explore new
vehicle propulsion solutions. General Motors and The Department of Energy have joined
together to create the Challenge X competition to explore hybrid-electric vehicles as one
such solution. Seventeen teams across the United State will experience “real-world” HEV
development over the three year competition. This process begins with vehicle
architecture selection, modeling and simulation. A dynamic model of a hybrid-electric
powertrain is developed here. This model is then implemented into two Simulink based
simulators: the quasi-static cX-SIM, the dynamic cX-DYN. These simulators are used to
validate the control strategy being developed for the Challenge X vehicle. Verification
will include optimal performance in regards to fuel consumption, battery state-of-charge,
and drivability. Techniques of validating the model and simulators using a rolling chassis
are also being implemented. Preliminary data from the quasi-static simulator and the
rolling chassis is presented herein.
Acknowledgements:
I would like to thank Dr. Giorgio Rizzoni, Joe Morbitzer, Osvaldo Barbarisi,
Kerem Koprubasi, Jason Disalvo, John Neal and Christopher C. Mabry, for all of the help
and support they have given me throughout the duration of this research.
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Table Contents
CHAPTER 1: INTRODUCTION ............................................................................................................... 6 1.1 MOTIVATION ....................................................................................................................................... 6 1.2 VEHICLE ARCHITECTURE................................................................................................................... 8
1.2.1 Classifications of HEVs .............................................................................................................. 8 1.2.2 Vehicle Components.................................................................................................................. 10 1.2.3 Modes of Operation................................................................................................................... 11
CHAPTER 2: MODELING....................................................................................................................... 14 2.1 MODEL OF THE DRIVELINE .............................................................................................................. 14
2.1.1 Dynamic Equations of the Front Driveline.............................................................................. 15 2.1.2 Dynamic Equations of Rear Driveline ..................................................................................... 17 2.1.3 Dynamic Equation of the Vehicle............................................................................................. 17
2.2 DYNAMIC SIMULINK MODEL OF THE FRONT DRIVELINE ................................................................ 18 2.2.1 ICE Model ................................................................................................................................. 19 2.2.2 Clutch Model ............................................................................................................................. 19 2.2.3 Front Gearbox Model ............................................................................................................... 20 2.2.4 Transmission ............................................................................................................................. 21 2.2.5 Front Axle ................................................................................................................................. 22 2.2.6 Front Brakes ............................................................................................................................. 23 2.2.7 Front Wheels ............................................................................................................................. 24
2.3 DYNAMIC SIMULINK MODEL OF THE REAR DRIVELINE .................................................................. 25 2.3.1 Electric Motor ........................................................................................................................... 25 2.3.2 Rear Gearbox ............................................................................................................................ 26 2.3.3 Rear Axle ................................................................................................................................... 27 2.3.4 Rear Brakes ............................................................................................................................... 28 2.3.5 Rear Wheels............................................................................................................................... 29
CHAPTER 3: SIMULATION RESULTS................................................................................................ 31 3.1 CX-SIM ............................................................................................................................................. 31
3.1.1 Driver......................................................................................................................................... 32 3.1.2 HEV Powertrain........................................................................................................................ 33 3.1.3 Vehicle ....................................................................................................................................... 34
3.2 CX-DYN ............................................................................................................................................ 34 3.3 CX GRAPHICS .................................................................................................................................... 36
3.3.1 Set Layout for Plots Driver ....................................................................................................... 37 3.3.2 Set Layout for Plots Vehicle...................................................................................................... 38 3.3.3 Set Layouts for Plots Acceleration Test.................................................................................... 39 3.3.4 Set Layout for Plots HEV Operation........................................................................................ 40 3.3.5 Set Layout Plots for Conventional Operation .......................................................................... 41 3.3.6 Set Layout Plots for Electric Powertrain.................................................................................. 42
CHAPTER 4: RESULTS & MODEL VERIFICATION........................................................................ 45 4.1 CX-SIM ............................................................................................................................................. 45 4.2 CX-DYN ............................................................................................................................................ 52 4.3 ROLLING CHASSIS............................................................................................................................. 52
4.3.1 Launch Test............................................................................................................................... 53 4.3.2 Model Verification & Mapping................................................................................................. 57 4.3.3 cX Test ....................................................................................................................................... 60
CHAPTER 5: CONTROL STRATEGY DEVELOPMENT .................................................................. 62 5.1 OVERVIEW......................................................................................................................................... 62 5.2 ECMS................................................................................................................................................ 63 5.3 BATTERY STATE-OF-CHARGE .......................................................................................................... 64
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5.4 DRIVABILITY ..................................................................................................................................... 65 REFERENCES ........................................................................................................................................... 67 APPENDIX ................................................................................................................................................. 68
List of Figures:
Figure 1. Ohio State Challenge X Vehicle Architecture [5]. ............................................ 10 Figure 2. Dynamic Model of the Driveline [8]. ................................................................ 15 Figure 3. Simulink Diagram of ICE & ISA....................................................................... 19 Figure 4. Simulink Diagram of the Clutch. ....................................................................... 20 Figure 5. Simulink Diagram of the Front Gearbox. .......................................................... 21 Figure 6. Simulink Diagram of the Automatic Transmission. .......................................... 22 Figure 7. Simulink Diagram of the Front Axle. ................................................................ 23 Figure 8. Simulink Diagram of the Front Brakes. ............................................................. 23 Figure 9. Simulink Model of the Front Wheels and Differential. ..................................... 24 Figure 10. Simulink Diagram of the Traction Motor. ....................................................... 26 Figure 11. Simulink Block Diagram of the Rear Gearbox. ............................................... 27 Figure 12. Simulink Diagram of the Rear Axle................................................................. 28 Figure 13. Simulink Diagram of the Rear Brakes. ............................................................ 29 Figure 14. Simulink Diagram of the Rear Wheels. ........................................................... 30 Figure 15. cX-SIM Top Layer. ......................................................................................... 32 Figure 16. cX-SIM Powertrain Subsystem. ...................................................................... 33 Figure 17. cX-DYN Top Layer......................................................................................... 35 Figure 18. cX-DYN Powertrain Subsystem. .................................................................... 35 Figure 19. cX Graphics Top Layer. .................................................................................. 37 Figure 20. Driver Plot Options Screen.............................................................................. 38 Figure 21. Vehicle Plot Options Screen............................................................................ 39 Figure 22. Acceleration Test Parameter Selection Screen................................................ 40 Figure 23. HEV Operation Plot Options Screen............................................................... 41 Figure 24. Conventional Powertrain Plot Options Screen. ............................................... 42 Figure 25. Electric Powertrain Plot Options Screen. ........................................................ 44 Figure 26. Actual & Desired Velocity from cX-SIM Preliminary Simulation................. 46 Figure 27. Deviation of Actual & Desired Vehicle Speed of cX-SIM Simulation........... 46 Figure 28. Total Output and Requested Torque during the cX-SIM Preliminary Simulation. ........................................................................................................................ 47 Figure 29. Deviations Between Actual & Desired Torque of HEV Powertrain. .............. 48 Figure 30. ICE Operating Points during cX-SIM Preliminary Simulation....................... 49 Figure 31. Operating Points of the EM during the cX-SIM Preliminary Simulation. ...... 50 Figure 32. ISA Power during the cX-SIM Preliminary Simulation. ................................ 51 Figure 33. Battery SOC during cX-SIM Preliminary Simulation..................................... 52 Figure 34. Rolling Chassis Experimental Set-Up. ............................................................ 55 Figure 35. Launch Test EM Motor Speed -40% Torque Limit. ....................................... 55 Figure 36. Launch Test Vehicle Speed- 40% Torque Limit. ............................................ 56 Figure 37. Launch Test EM Motor Speed--50% Torque Limit. ....................................... 56
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Figure 38. Launch Test Vehicle Speed-- 50% Torque Limit............................................ 57 Figure 39. EM Torque Mapping Test: Vehicle Speed (B=30). ........................................ 59 Figure 40. EM Torque Mapping Test: Acceleration (B=30). ........................................... 60 Figure 41. cX Test Top Layer........................................................................................... 61 Figure 42. cX -Test Graphics............................................................................................ 61 Figure 43. Control Strategy Schematic............................................................................. 63
List of Tables:
Table 1. Summary of Challenge X Vehicle Technical Specifications [9, 5]. ..................... 7 Table 2. Vehicle Operating Modes [8]. ............................................................................ 12 Table 3. Nomenclature...................................................................................................... 68
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Chapter 1
Introduction
The motivation for this research stems from the growing concern of energy
consumption and environmental impacts of current automobiles. These issues have lead
to the creation of Challenge X and Ohio State’s participation in this competition. Hybrid-
electric vehicle architecture is developed using the general classifications of HEVs while
considering the advantages and disadvantages of each solution. The components to drive
this architecture and various modes of operation are also defined.
1.1 MotivationAs the global economy begins to strain under the pressure of raising petroleum
prices and environmental concerns, automobile manufacturers constantly strive to
produce more fuel efficient and environmentally friendly vehicles. The primary objective
of manufacturing automobiles subject to such constraints is to ensure consumer mobility.
Given the current resources and technologies, the most feasible solution is hybrid electric
vehicles. In order to accelerate the research involved with creating these vehicles, the
General Motors Corporation and The Department of Energy have created the Challenge
X Competition. This is a three year long competition that requires 17 universities across
the United States to design, develop, and build a hybrid-electric Chevrolet Equinox sport-
utility vehicle. The goal of this competition is to secure consumer sustainable mobility.
The first, and current, year involves the preliminary design of the vehicle,
component selection, control strategy development, and vehicle modeling and simulation.
General Motors and The Department of Energy have created a list of goals each team is
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to achieve with the development of their hybrid electric vehicle. These “Vehicle
Technical Specifications” can be seen in Table 1. The idea behind such specifications is
to maintain stock Chevrolet Equinox performance and capacity while decreasing fuel
consumption and emissions. Throughout the first year each team must develop and
simulate a hybrid electric vehicle architecture that meets, or surpasses, these goals.
Table 1. Summary of Challenge X Vehicle Technical Specifications [9, 5].
DESCRIPTION COMPETITION GOAL
OHIO STATE VTS
IVM – 60 MPH < 9.0 S < 10.0 S 50 – 70 MPH < 6.8 S < 7.0 S VEHICLE MASS < 4400 LBS < 4275 LBS
COMBINED FUEL ECONOMY
> 32.0 MPGGE > 35.0 MPGGE
HIGHWAY RANGE > 200 MI > 275 MI
PASSENGER CAP. 5 PASSENGERS 5 PASSENGERS
EMISSIONS LEVEL TIER 2, BIN 5 TIER 2, BIN 5 TRAILERING CAP. 2500 LBS 2500 LBS STARTING TIME < 5.0 S < 2.0 S
During the second and third year, each team then integrates their HEV
configuration onto the actual vehicle to compete. Upon receiving their Equinox during
the second year, each team must implement their hybrid electric architecture onto the
vehicle. Confirming the developed architecture meets competition specifications is the
objective for the second year. The actual competition involving a “show room” Equinox
hybrid is be held during the third year. Here each team competes against one another in
the hopes that their hybrid electric vehicle best achieves the aforementioned
specifications.
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1.2 Vehicle Architecture The most critical task to achieve the goals listed in Table 1 is selecting and
developing an effective HEV architecture. Performance of the vehicle automatically
increases with a hybrid electric configuration due to increased fuel savings, reduced
energy losses with regenerative braking, and emissions control. Hybrid electric vehicle
architectures are organized into three classes: parallel, series and power-split hybrids.
1.2.1 Classifications of HEVs
The parallel configuration allows for the electric machine(s) and the internal
combustion engine to provide mechanical power to the driveline. Parallel hybrids can be
further classified in two ways: electrical assist parallel hybrids and ICE assist parallel
hybrids. In the electrical assist architecture, the ICE operates only within the optimal
region to reduce emissions and fuel consumption. The EM assists whenever necessary in
order to uphold this constraint. The ICE assist architecture involves the ICE only being
turned on for hard accelerations, hill climbing, and high speeds. This also reduces
emissions and fuel consumption as the EM acts as the primary actuator for vehicle
motion [1].
The other configuration is a series hybrid. In a series HEV, the vehicle is
propelled solely by the EM. The EM obtains the required energy from either a battery, or
a motor-generator set. The MG set supplies power to the EM and an energy storage
device (i.e. a battery or super capacitor). The purpose of the energy storage device is to
allow more power to be drawn by the EM during more demanding driving conditions
(hill climbing, hard accelerations, etc.) [6].
Both configurations have their own distinct advantages. The parallel configuration
allows for the ICE and EM to be reduced in size since their propelling power can be
summed to meet driver demand. Moreover, efficiency increases with this configuration
since fewer energy conversions take place. However, a parallel configuration is far more
complex than the series architecture. The series architecture allows for easier packaging
since the EM and MG set do not need to be close together. The control problem for this
type of HEV is also far less complex [1, 6]. Moreover, the series configuration allows for
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direct battery charging and electric power supply which is essential for effective hybrid
travel.
There are two additional types of HEVs when not speaking of the vehicle
architecture: charge-sustaining and grid dependent. If the HEV can sustain the charge of
the battery in every driving condition without the assistance of an outside electrical
power grid, the HEV is considered charge-sustaining. If the vehicle needs to be integrated
with an outside electrical power grid from time-to-time to recharge the battery, the
vehicle is referred to as grid-dependent [6]. Charge-sustaining HEVs, although more
complex, are more appealing to the consumer. This is due to the longer range of the HEV
over a conventional vehicle without sacrificing performance [6]. Ohio State has chosen to
develop a charge-sustaining HEV.
In order to obtain the benefits from both HEV architecture configurations, the
Ohio State Challenge X team has chosen to develop the third class of HEV: power-split.
[5]. This configuration combines both parallel and series architectures. To accomplish
this, the powertrain is divided into two independent sections. The first is the conventional
powertrain. This consists of an ICE coupled with an integrated starter/alternator (ISA)
that powers the front axle of the Equinox. An electric powertrain drives the rear wheels of
the HEV. To do this, an electric machine, with a gearbox appropriately sized for vehicle
propulsion, is used [7]. This vehicle architecture is represented in Figure 1.
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(ISA)
Integrated StarterAlternator
Traction Motor& Gearbox
(EM)
(ISA)
Integrated StarterAlternator
Traction Motor& Gearbox
(EM)
(ISA)
Integrated StarterAlternator
(ISA)
Integrated StarterAlternator
Traction Motor& Gearbox
(EM)
(ICE)
(AT)
Front Back
Figure 1. Ohio State Challenge X Vehicle Architecture [5]. 1.2.2 Vehicle Components
With the architecture defined, the individual components that make up the vehicle
are chosen. The main actuator of the conventional powertrain is a diesel engine.
Specifically, a Fiat 1.9L diesel engine is used. This is one of the engines provided by the
Challenge X organizers as being acceptable for use during the competition. Diesel
engines are more efficient than gasoline powered internal combustion engines due to
higher compression ratios and lack of engine pumping loses. To reduce emissions,
Biodiesel B20 is the selected fuel [7].
As shown in Figure 1, an ISA rigidly connects to the diesel engine via the
crankshaft. The ISA is simply an electric machine that is capable of being used to start
the diesel engine, or be used by the diesel engine as an alternator to provide electrical
energy. This is one of the components that make this HEV charge-sustaining. The ISA
can also supply a minimal amount of torque to the front wheels for propulsion assistance
[5].
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The EM, referred to as the “Traction Motor” the Figure 1, is the electrical
propulsion unit used to the power the EV1 electric car by General Motors. This 103 kW
electric motor and gearbox is now used to drive the rear wheels of the Equinox HEV. Not
only can this unit provide power to the wheels, but it can also absorb power from the
wheels and be used as a generator. This process occurs when the driver requests stopping
torque. At this point, the EM absorbs torque from the rear axle slowing the vehicle, and
will use this torque to generate energy for the replenishment of the battery [5]. This is
another feature that classifies this HEV as charge-sustaining.
Initially, the Ohio State Challenge X team agreed to use an automated manual
transmission [7]. However, these types of transmissions are hard to acquire, so the
automatic transmission that accompanies the Fiat diesel engine is used. Automatic
transmissions are not as efficient as automated manual or manual transmissions, but they
are the most acceptable to the consumer [5].
Only one nickel-metal hydride battery pack powers both electric machines and the
vehicle accessories. As shown above, there are two separate inverters for the EM and the
ISA, as well as, a DC-to-DC converter to power 12 volt vehicle accessories (interior
lamps, radio, head lights, etc.). A switch box routes high-voltage flow [5]. One of the
main reasons for selecting a charge-sustaining HEV configuration involves current
battery technology. The market is filled with low efficiency, low energy storage capacity,
and long charge time solutions [1]. As previously stated, to cater to the desires of the
consumer, a charge-sustaining strategy eliminates these undesirable issues.
1.2.3 Modes of Operation
With the architecture depicted in Figure 1, various operating modes for the
vehicle can be achieved. These operating modes have been summarized in Table 2.
During a typical driving mission, the HEV operates in both hybrid, and conventional
modes [1]. This can be seen in the table below.
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Table 2. Vehicle Operating Modes [8].
MODE ICE ISA EM TRAN.
Idle Off Off Off Neutral
ICE, EM, AND ISA ARE SHUTOFF. ELECTRICAL ACCESSORIES.
ELECTRIC LAUNCH OFF MOT. OFF NEUTRAL
VEHICLE STARTED FROM REST WITH EM.
ENGINE START START MOT. MOT. NEUTRAL
AT A CERTAIN VEHICLE SPEED, ICE QUICKLY STARTED BY ISA.
NORMAL ON MOT. OR GEN.
MOT. OR GEN. DRIVE
TORQUE REQUESTS DETERMINED BY PRIMARY CONTROL STRATEGY.
DECELERATION ON OR OFF GEN. GEN. DRIVE OR
NEUTRAL REGENERATIVE BRAKING BY EM AND ISA AS BATTERY ALLOWS.
4WD ON GEN. OROFF MOT. DRIVE
EM RECEIVES CONTINUOUS POWER THROUGH DC BUS FROM ISA.
With each of these, the fuel efficiency increases and the emissions decrease immensely.
During the idle mode, and decelerating cases the ICE is be turned off, unless recharging
of the battery requires this to drive the ISA to provide the necessary power (series HEV).
The fuel efficiency can increase by as much as 10% simply by eliminating fuel flow to
the ICE during braking and idling situations [5]. This concept accompanies the general
rule that the EM should be used during launch and immediate power request situations
[6]. This is because electric actuators can deliver high torque at low speeds while
emitting no environmentally harmful by-products. This general rule is satisfied during
Electric Launch mode when the EM motors (MOT.) the vehicle.
After a set speed, the ICE turns on during the Engine Start mode. Once the ICE is
up to speed, the automatic transmission engages and the ICE becomes the primary
actuator for vehicle propulsion. At this point, the vehicle enters the Normal mode.
Between the Electric Launch and Normal mode, the HEV satisfies the constraints of
being a parallel HEV as previously defined. Note that during Normal mode, the EM can
be used to supply regenerative power to the battery; moreover, the EM can draw power
12
from the battery and assist the ICE with motoring the vehicle during four-wheel drive
situations. The ISA shares similar options during Normal mode. Basically, the 4WD
mode is merely a derivative of the Normal mode with the EM motoring and the ISA
generating the electrical power needed (a series/parallel hybrid combination).
The vehicle enters Deceleration mode when the driver uses the brakes to slow the
vehicle. Here the concept of “Regenerative braking” is implemented. Regenerative
braking involves the process of using the resistance between the field and armature of the
EM to generate power to replenish the battery. As the driver applies the brake, for a set
distance of pedal travel, the mechanical braking system does not activate and the EM
absorbs torque off of the rear axle. This mechanical energy is converted to electrical
energy and sent to the battery [6].
The power-split HEV solution with a charge-sustaining focus has been selected
by the Ohio State Challenge X team. This particular configuration leads to alternate
modes of operation all of which increase the efficiency of the vehicle. With the
architecture, and components thereof, defined, modeling of the HEV can begin.
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Chapter 2
Modeling
With the vehicle architecture and components selected modeling of the Challenge
X HEV is performed. The entire driveline is first visually represented by a figure which
leads to the development of the mathematical expressions governing the behavior of the
HEV. These expressions are then configured into Simulink block diagrams for further
analysis and simulation.
2.1 Model of the Driveline The dynamic model of the driveline is displayed in Figure 2. Refer to Table 3 of
the Appendix for a list of the nomenclature. Only the necessary inertias are included in
the model. The inertias of the smaller components (the axles, brake assemblies, and
wheels) do not have a drastic effect on the dynamics of the system and can be ignored for
simplicity. Unnecessary damping and spring effects such as those intrinsic to the
automatic transmission and rear gearbox are also eliminated to further simplify the
model. Disregarding these dynamic effects does not alter the accuracy of the model since
they are insignificant in comparison to other driveline components (i.e. ICE, EM, and
ISA). The equations that follow are developed by the author, as well as separately
developed by others and represented in the referenced publications [2, 5, 7, 8].
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Figure 2. Dynamic Model of the Driveline [8].
2.1.1 Dynamic Equations of the Front Driveline
Due to the fact that the ISA is rigidly connected to the ICE, they can be
considered as one lumped inertia (JICE+JISA) accelerating at the same rate as the
ICE ( . The torque converter divides the front driveline into two parts. The first
includes the dynamic behavior of every component from the ICE and ISA to the pump
side of the torque converter. This relationship is as follows:
)ICEω&
_( )ICE ISA ICE ICE ISA ICE ICE TC PJ J T T b Tω ω+ = + − −& (1)
Here the inertias of the ICE and ISA are combined and have the same rotational
speed ICE( )ω . This inertial force must be equivalent to the torque of the ICE (TICE) and
ISA (TISA), as well as the damping effect of the ICE (bICEωICE), and torque of the pump
side of the torque converter (TTC_P). When the torque converter is not locked, the
dynamic behavior of each component from the turbine side of the torque converter to the
wheels can be modeled as:
15
_
( )TC T VEH VEH
TR TR F TR F TRTR F F
T xJ k bg r
ω θ ωτ
⎛ ⎞ ⎛= − − − −⎜ ⎟ ⎜
⎝ ⎠ ⎝&
vr
⎞⎟⎠
(2)
The rotational inertia of the transmission accelerates ( TR TRJ ω& ) as a result of the excitation
imposed by the following quantities. Torque from the transmission depends on the gear
ratio (τTR (g)), which in turn depends on the current gear (g). Each gear results in a
different torque on the turbine side of the torque converter (TTC_T). Coming off of the
transmission are the spring and damping ( dynamic effects introduced by the
front axles (half shafts). These quantities are functions the transmission rotational speed
(ω
( )Fk )Fb
TR) and angular position (θTR). Vehicle speed (vVEH) and vehicle position (xVEH) are
manipulated by the wheel radius (rF) to be used here as well. Note the dynamic effects of
the front brakes have been ignored, and are only considered as a torque (TB_F). This
torque is zero until the driver begins to demand stopping power. When this occurs,
equation (2) becomes:
__( )
TC T VEH VEHTR TR F TR F TR B F
R F F
T x vJ k bg r r
ω θ ωτ
⎛ ⎞ ⎛ ⎞= − − − − −⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠& T (3)
The above equations are derived assuming that the torque converter is not locked.
When the torque converter is locked, the fluid coupler becomes a rigid link connecting
the ICE and ISA inertia directly to the inertia of the automatic transmission through the
gears. This also means that the torque the pump side and turbine side are equal (TTC), or:
_ _TC P TC T TCT T T= = (4)\
However, the specific dynamic equations for the driveline when the torque converter is
locked have yet not been developed. Currently, the Ohio State Challenge X Team is not
concerned with such a model. This concludes the development of the dynamic equations
for the conventional (front) driveline.
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2.1.2 Dynamic Equations of Rear Driveline
The rear driveline is not nearly as complex as the front as there is no torque
converter. The rotational inertia of the EM is excited ( EM EMJ ω& ) by the torque of the EM
(TEM) and the intrinsic damping of the EM (bEM). The spring (kR) and damping (bR)
characteristics of the axle add to the dynamic response of this component as well. Here,
the angular speed ( )EMω and angular position ( )EMθ of the EM are manipulated by the
ratio of the gearbox ( )GBτ and this interacts with the previously defined vehicle
parameters to yield the appropriate dynamic response from the rear axle. This portion of
the vehicle is modeled as follows:
VEH VEHEM EM EM EM EM GB R EM GB R EM GB
R R
x vJ T b k br r
ω ω τ θ τ ω τ⎡ ⎤⎛ ⎞ ⎛
= − − − + −⎞
⎢ ⎥⎜ ⎟ ⎜⎝ ⎠ ⎝
⎟⎠⎣ ⎦
& (4)
Again, the dynamics of the rear brakes are disregarded and their effect is represented by a
torque (TB_R). This torque is zero until the driver commands otherwise. If the brakes are
being applied, then (4) becomes:
_VEH VEH
EM EM EM EM EM GB R EM GB R EM GB B RR R
x vJ T b k b Tr r
ω ω τ θ τ ω τ⎡ ⎤⎛ ⎞ ⎛ ⎞
= − − − + − −⎢ ⎥⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎣ ⎦
& (5)
2.1.3 Dynamic Equation of the Vehicle
The final expressions to derive are those of the vehicle. This component will be
affected by not only the tractive force (F) input from the powertrain, but also the
opposing forces due to aerodynamic drag (FDRAG), rolling resistance (FRR), and forces
from the road grade (FRD). These equations can be seen below.
VEH VEH RR DRAG RDm v F F F F= + + −& (6)
cos( )RR VEH rF m gC ϕ= (7)
212DRAG AIR d f VEHF C Aρ= v (8)
17
sin( )RD VEHF m g ϕ= (9)
The rolling resistance is the product of the vehicle mass (mVEH), the gravitational
acceleration due to gravity (g), the rolling resistance coefficient (Cr) and the cosine of the
grade angle of the road measured from the horizontal plane (φ). Air drag on the vehicle is
represented by the standard drag equation that includes the density of air (ρAIR), the drag
coefficient of the vehicle (Cd), the frontal area of the vehicle (Af) and the vehicle velocity
(vVEH). Finally, the force resulting from the grade of the road is merely a product of the
mass of the vehicle, the acceleration due to gravity, and the sine of the grade angle [6].
With all of the dynamic equations derived for the entire driveline, models can be created
in Simulink for further analysis and simulation.
2.2 Dynamic Simulink Model of the Front Driveline
One of the most convent ways to analyze dynamic equations such as those
previously derived is with Simulink modeling software. Each of the above equations are
represented by a block diagram. Each individual diagram is connected to create the entire
system. Then an input can be introduced and the response of this system can be analyzed
in great detail. When this Simulink model was initially developed, the Ohio State
Challenge X team was considering using a manual transmission; therefore, the model
presented below is slightly different than the aforementioned vehicle model. Also, the
variables seen in these diagrams are different than those seen in Figure 2. This is done for
programming convenience. Finally, the version of the front driveline developed here is
not used for the HEV vehicle simulator discussed later; however, this model, after slight
alterations, is used by another for initial testing of the control strategy that is discussed in
a subsequent chapter [2].
In general, torque, or speed in some cases, flows forward through the following
model component by component. The speed, or torque in some cases, and position are
then fed back when necessary. This model operates on an initial torque request from the
“driver.” This request acts as an input to each actuator. The particular actuator then
converts this input to an output torque and a feed back speed. The output torque then
18
serves as the input of the next component in the driveline. This process continues until
torque is delivered to the wheels, and vehicle speed is fed back to the “driver.” The driver
is ultimately represented by a Simulink subsystem that can be seen in Figure 15.
2.2.1 ICE Model
The Simulink block diagram of the ICE can be seen in Figure 3 along with the
dynamic equation that governs this model. Note that the inertia of both the ICE and ISA
are lumped together into one variable ( F ICE EJ J J M= + ) as seen in the diagram. The first
two inputs represent the torque command for the ICE (TICE) and ISA (TISA). The third
input is the opposing torque coming from the clutch of the manual transmission (Tc). This
torque is subtracted from the other input torques. The output from the inertia gain is
integrated twice: once for speed ( ICEω ), and the other for position ( )ICEθ . The value of the
ICE speed is sent to the clutch, but the value of ICE position is used only for observation
purposes. The dynamic equation is as follows:
(10) ( )ICE ISA ICE ICE ISA ICE ICE CJ J T T b Tω ω+ = + −& −
Figure 3. Simulink Diagram of ICE & ISA.
2.2.2 Clutch Model
The speed and position of the ICE and ISA enter the clutch. The clutch is fairly
simple and operates under the assumption that no slip occurs. This is a valid assumption
for modeling purposes as predicting and modeling the magnitude of any slip presents a
rather complex problem. However, provisions have been made in the model for the
19
damping ( ) and stiffness ( intrinsic to the clutch and are represented in the
respective gain blocks of Figure 4. The input, γ, is a command sent to the clutch by the
driver that either engages, or disengages, the clutch. This value can either be 0 to
represent the clutch being disengaged, or 1 to represent the clutch being engaged. If the
driver is shifting and has the clutch disengaged, the product will be zero, and no torque
passes through the clutch. When the driver has the clutch engaged, the speeds will be
multiplied by 1 with the product block and the torque flows through this device and onto
the gearbox. The clutch speed
cb )ck
( )cω is an input here and is sent from the gearbox as a
feedback. The governing equation of the clutch is:
( ) ( )c C ICE C C ICE CT b kγ ω ω θ θ= − + −⎡⎣ ⎤⎦ (11)
Figure 4. Simulink Diagram of the Clutch.
2.2.3 Front Gearbox Model
The torque from the clutch enters the front gearbox. This block diagram can
be seen in Figure 5. Here the torque and speed are manipulated according to the gear and
the respective gear ratio. The only inputs are the torque from the clutch, the gear
command, the feed back speed
( )cT
( )Tω and position ( )Tθ of the transmission. These inputs
will be manipulated to result in an output torque , speed@( C TT ) ( )cω , and position ( )cθ .
20
The ratios for each gear are contained within the look-up table and provide the
appropriate constants for accurate speed reduction and torque increase. To ensure ideal
operation, a switch allows torque to pass through the clutch if the clutch command is 1
(engaged). Otherwise, the switch will force the output torque to be zero. Torque, speed,
and position are calculated as follows:
( )@C
C TTR
TTgτ
= (12)
( )C TR g Tω τ= ω (13)
( )C TR g Tθ τ= θ (14)
Figure 5. Simulink Diagram of the Front Gearbox.
2.2.4 Transmission
The transmission resembles that of the ICE and is shown in Figure 6. The inertia
and damping affect the input torque from the gearbox. The resistive torque of
the front axle is subtracted from the torque input . This result is integrated for
speed
( )TJ ( )Tb
@( C TT )
( )Tω and position ( )Tθ respectively. These quantities are fed back to the gearbox
21
and sent on to the front axle. The dynamic equation for this process is represented in (15)
below.
@ 1T T C T X f TJ T T bω ω= + −& (15)
Figure 6. Simulink Diagram of the Automatic Transmission.
2.2.5 Front Axle The front axle is assumed to be a mass-less component that only contributes a
torsional damping and stiffness to the system. As seen in Figure 7, the axle is
a very simple model with input speeds and positions from both the transmission and the
wheels (
1( Xb ) )1( Xk
)Fω . The output is merely the torque experienced at the axle . This is
somewhat backwards from the previous components, but effective for modeling this
particular device. The individual expression representing the axle is shown in (16) below.
1( XT )
( ) ( )1 1 1X X f t X f tT b kω ω θ= − + −θ (16)
22
Figure 7. Simulink Diagram of the Front Axle.
2.2.6 Front Brakes
The front brakes simply apply a torque to the powertrain that counter-acts the
motion of the vehicle when the driver demands to do so. As previously mentioned, beta
(β), the input command from the driver, ranges from 0 to 1 corresponding to the position
of the brake pedal. This value is 0 at rest and 1 when the pedal is completely depressed.
The other input is rotational speed of the front wheels ( )Fω . Using these values along
with the damping coefficient of the brakes , results in an output torque from the
front brakes . This torque is sent to the wheels. Figure 8 is the Simulink model while
(17) is the mathematical representation of this figure.
( )BFb
( )BFT
BF BF FT b ω β= (17)
Figure 8. Simulink Diagram of the Front Brakes.
23
2.2.7 Front Wheels
The model of the wheels is displayed in Figure 9. The front wheels convert the
torque from the axle and potential torque from the brakes into a tractive force ( )fF that is
sent to the vehicle. The vehicle speed and position ( )Fv ( )Fx are used to provide an
output rotational speed and position for feed back to the brakes and axle. The effect of the
front differential ratio is considered along with the wheel radius ((diff ) )FR . Equations
18, 19 and 20 represent this process mathematically.
( 11 1
FF
F Tdiff R
⎛ ⎞⎛ ⎞= ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
)X BFT− (18)
FF
diffFx
Rθ = (19)
FF
diff vR
ω = F (20)
Figure 9. Simulink Model of the Front Wheels and Differential.
24
2.3 Dynamic Simulink Model of the Rear Driveline
The development of an acceptable model for the rear driveline of the chosen
vehicle architecture is the one of the main thrusts of this thesis. Each model seen below
was developed specifically for the simulators discussed in a Chapter 3. Because of this,
the nomenclature seen in the figures to follow is significantly different than that of the
models previously discussed. The nomenclature of the models developed for the rear
driveline matches that of the early versions of cX-SIM and cX-DYN (See Chapter 3).
The nomenclature also differs from that of the previously seen dynamic equations for
convenience during programming. Each component is modeled as dynamic, but only the
more dominant dynamic characteristics are considered. Hence, the inertia of the axle is
once again ignored due to the smaller magnitude of this quantity when compared to that
of the EM.
2.3.1 Electric Motor
The electric motor, seen in Figure 10, is modeled identically to the ICE. There is
an input torque command from the “driver” that is affected by a gain equal to that
of the inertia of the EM . This value is then integrated twice for position
( )EMT
( )EMJ ( )EMθ and
speed ( )EMω . The intrinsic damping of the EM is included. The output of the EM
diagram is rotational speed
( )EMb
( )EMω and position ( )EMθ . The feed back to the EM is the
torque from the rear gearbox . The green box is another method of signal routing in
Simulink that is utilized to simplify the appearance of the system model seen in Figure 15.
The dynamic equation for this component is (21).
( )RGBT
EM EM EM RGB EM EMJ T T bω ω= − −& (21)
25
Figure 10. Simulink Diagram of the Traction Motor.
2.3.2 Rear Gearbox
The speed of the EM enters the gearbox and is reduced according to the gear ratio
( GB )τ as seen in Figure 11. From the data given to Ohio State by General Motors, the
reduction ratio was found to be 10.946. The third input to this block is the torque from
the rear axle . After applying the ratio to these inputs, gearbox rotational speed ( )RGBT
( RGB )ω and position ( )RGBθ , as well as torque, become outputs. This process is modeled
with the following equations. Note the rear gearbox is far less complex than the front
counterpart. This is because the gearbox attached to the EV1 motor has only one
reduction and no “driver selectable” gears to be considered. The EM is either motoring,
regenerating, or off depending on commands received by this device.
RGB GB RAxleT Tτ= (22)
EMRGB
GB
ωωτ
= (23)
EMRGB
GB
θθτ
= (24)
26
Figure 11. Simulink Block Diagram of the Rear Gearbox.
2.3.3 Rear Axle
The rear axle is an exact replica of the front axle as seen in Figure 12. Assumed to
be mass- less, the axle only contributes a damping ( and stiffness to the
dynamics of the rear driveline. Inputs to the rear axle match that of the outputs of the gear
box. By implementing the appropriate damping and stiffness values, the rear gearbox
speed and position are converted to an output torque .This torque is sent to the
rear brakes and fed back to the rear gearbox as previously stated. The values of stiffness
and damping have yet to be determined. Expression (25) mathematically represents the
process seen in Figure 12.
)RAxleb ( )RAxlek
( )RAxleT
( ) ( )RAxle RAxle RGB RBrake RAxle RGB RBrakesT b kω ω θ θ= − + − (25)
27
Figure 12. Simulink Diagram of the Rear Axle.
2.3.4 Rear Brakes
The rear brakes behave exactly as the front brakes. They are considered to have
no mass, and only impose a torque that will resist the torque driving the vehicle.
There are differences in this model when compared to the front counterpart as seen in
Figure 13. For modeling purposes, the actual damping coefficient of the brakes is a very
difficult number to estimate. Keeping this in mind, the brake torque is determined by
multiplying the brake command from the driver by a proportional gain (λ
( )RBrakeT
RBrakes). This
result is subtracted from the incoming torque to the brakes. This effectively reduces the
torque flowing between the rear axle and the wheels. The value of the gain is simply the
percentage of the total braking power that is provided by the rear brakes. In this case the
value equals 40%, or 0.4. The incoming brake command, determined by the control
strategy, accurately provides a value that is manipulated by this gain. The simple
expression representing this process is:
RBrakes RBrakes RAxleT Tβλ= (26)
28
Figure 13. Simulink Diagram of the Rear Brakes.
2.3.5 Rear Wheels
The model of the rear wheels provides semblance to that of the model of the front
wheels. However, no differential is included here since this does not exist on the
Chevrolet Equinox. The only reduction of the rear driveline occurs at the gearbox
attached to the EM. This model uses the inputs of brake torque ( , vehicle
speed ( , and vehicle position (
)RBrakeT
)VEHv )VEHθ , and creates the three outputs using the wheel
radius as seen in Figure 14. The outputs include wheel rotational speed (( )RWheelr )RWheelω
and position ( )RWheelθ , as well as, the tractive force to be given to the vehicle.
The wheel radius is determined from the specifications of the Equinox released by
General Motors for this competition. The dynamics of the wheels are relatively small
compared to the other dynamic phenomena present in the rear driveline. Thus, the
stiffness and damping of the wheels are not considered in the following model. The
effects of the wheel are mathematically represented in the equations below.
( )RWheelF
RBrakesRWheel
RWheel
TFr
= (27)
RWheel RWheel VEHr xθ = (28)
29
RWheel RWheel VEHr vω = (29)
Figure 14. Simulink Diagram of the Rear Wheels.
The individual components of the driveline have been represented both
mathematically and by Simulink diagrams. Each of these can now be connected together
to create a model of the entire vehicle powertrain. Completing this task results in the
creation of two HEV simulators that will be extensively used to evaluate the performance
of the hybrid Equinox.
30
Chapter 3
Simulation Results
With all of the modeling complete, two comprehensive HEV simulators are
created. One is a quasi-static simulator that is effective for monitoring energy
consumption. The other is a dynamic simulator for the evaluation of the drivability of the
HEV. Both work together in conjunction with a graphics program that is developed here.
These three items give the Ohio State Challenge X team extensive capability to study of
all aspects of HEV operation.
3.1 cX-SIM The first simulator is called cX-SIM and the top layer of this Simulink model can
be seen in Figure 15. This is a quasi-static HEV simulator, meaning the dominant
dynamics of the system are solely the vehicle. The vehicle reacts much slower than every
other component in the system thus the time constant of the vehicle is quite large. This
fact allows for the time constants of all other components to be assumed zero [6].
However, there is one caveat; the inertia of the ICE is included to ensure proper operation
of the dynamic model of the torque converter. With only these two dynamic
characteristics included, this simulator is computationally inexpensive and the results are
acquired in a rather timely fashion. This is ideal for monitoring fuel consumption and
energy usage. Since the models of the previous chapter result in a convoluted system
when integrated together, they are each converted into a subsystem. This collects of the
31
various parts of the aforementioned models into one block. These are the subsystems seen
in cX-SIM.
Figure 15. cX-SIM Top Layer.
3.1.1 Driver
As shown in Figure 15, cX-SIM is divided into three main parts. The first
represents the Driver. Contained within this subsystem are all of the components that
mimic the behavior of an actual vehicle operator. There is an input velocity profile that
can be set to match that of the Federal Urban Driving Cycle (FUDS) or Federal Highway
Driving Cycle (FHDS). This input enters a PID controller, which receives a feedback
signal of the actual velocity from the vehicle. The controller minimizes the discrepancy
between the desired and actual vehicle velocity. Not only is the difference in velocity
rectified, but also two signals are generated and sent from the driver subsystem. The first
signal, alpha (α), represents the accelerator pedal position. The second represents the
brake pedal position, beta (β). These commands are then sent to the HEV Powertrain
subsystem.
32
3.1.2 HEV Powertrain
The diagram of the HEV Powertrain subsystem is shown in Figure 16. Here, the
models seen in the previous chapter are integrated together to effectively represent the
driveline of the Ohio State Challenge X Equinox. The driver commands, α and β, enter
the controller bock. Within this subsystem lies the control strategy. The inputs from the
driver are manipulated to create torque requests for each of the actuators, as well as, state
commands, the gear command, and the brake command. The torque request enters the
appropriate component and the conversion of torque and speed according to the
characteristic of the device begins. Note that the axles of the driveline have been removed
because these dynamics are being ignored for this particular simulator. Moreover, the
inertias of the EM and the AT have also been ignored for the reasons previously
described. A look-up table containing the appropriate data is included in place of the
inertia. The result from this subsystem, as mentioned in Chapter 2, is a tractive force from
both the front and rear driveline, which are summed together and sent on to the vehicle.
Figure 16. cX-SIM Powertrain Subsystem.
33
3.1.3 Vehicle
The final subsystem in cX-SIM is the Vehicle. The contents of this subsystem are
merely the Simulink block representations of equations 6-9. Forces due to air drag,
vehicle rolling resistance, and road grade are subtracted from the total tractive force given
to the vehicle from the powertrain. Also, the inertia of the vehicle is included to give cX-
SIM the quasi-static classification previously defined. Once all of the force effects on the
vehicle have been calculated, and output vehicle speed is sent from this subsystem back
to driver. This entire process then repeats throughout the predetermined driving cycle.
3.2 cX-DYN A quasi-static simulator cannot effectively analyze vehicle dynamics, particularly
drivability. So a second HEV simulator is created to accomplish this. The second
simulator is called cX-DYN and is used primarily to analyze the drivability of the
vehicle. Drivability refers to the vibrations felt by the operator. In order to maintain
consumer favorability and fulfill one of the competition goals, this detail must be
precisely controlled. cX-DYN allows for this type of control, as well as the ability to
monitor all dynamic responses of the vehicle.
The construction of cX-DYN resembles that of cX-SIM. As can be seen in Figure
17, there are three main parts: Driver, HEV Powertrain, and Vehicle. The functions of the
driver and vehicle subsystems are exactly the same as those in the quasi-static
counterpart. However, the HEV Powertrain includes additional components to make the
simulator more dynamic. Mainly the dynamics of the axles and inertias of the EM and
AT are included. Figure 18 displays the HEV Powertrain of cX-DYN with these
additional components included.
34
Figure 17. cX-DYN Top Layer.
Figure 18. cX-DYN Powertrain Subsystem.
35
One main disadvantage to cX-DYN is that the included vehicle dynamics make
this simulator computationally more expensive. Therefore, this simulator must be run in
Simulink’s “Accelerator” mode in order to obtain results in a more time efficient manner.
Both cX-SIM and cX-DYN have their advantages and disadvantages, but they are used
together to analyze all aspects of HEV operation.
3.3 cX Graphics In order to obtain visual knowledge of the functions of the Challenge X Equinox
after running one of the aforementioned simulators, a graphical user interface program is
developed. The interface of this program is shown in Figure 19. Appropriately named cX
Graphics, this program can monitor every quantity of the HEV and visually represent
them. Moreover, the user has the option of selecting which exactly quantities to view.
This is done by dividing the data into the “Set layout for plots” categories as seen in
Figure 19: Driver, Vehicle, Acceleration, HEV Operation, Conventional Powertrain, and
Electric Powertrain. Statistical information of some of the quantities within these
categories can be viewed as well. A key feature of cX Graphics is that the user can select
to view their particular quantity is English, or SI units. This is done to increase the
versatility of this program; as well as, to enhance the Challenge X simulation analysis
experience by giving the users of cX-SIM, or cX-DYN, a detailed visual link between the
simulated operation of the HEV and the occurrences therein.
36
Figure 19. cX Graphics Top Layer.
3.3.1 Set Layout for Plots Driver
The plot options for the Driver are seen in Figure 20. Here, the accelerator and
brake pedal positions can be viewed over the entire drive cycle. Also, the commands
from the PID controller within the driver block can be monitored. The pedal positions
reflect how an actual driver behaves in order to match the velocity profile of the set
driving cycle being simulated. The output of the PID controller will be continuously
adjusted to in order to meet the desired velocity command.
37
Figure 20. Driver Plot Options Screen.
3.3.2 Set Layout for Plots Vehicle
Plot options for the vehicle are displayed in Figure 21. The actual velocity of the
vehicle can be generated, as well as the desired vehicle velocity according to the driver.
Both of the curves can be graphed together to analyze the error. The user also has the
option of setting a customized range for both the horizontal and vertical axis. The default
values are maximums and minimums of the particular simulation. Not only can the speed
be displayed, but also the desired and actual power at the wheels can be visualized.
Statistical data such as the rms, maximum and minimum deviations for the velocities and
powers can be also displayed.
38
Figure 21. Vehicle Plot Options Screen.
3.3.3 Set Layouts for Plots Acceleration Test
Prior to running the simulator, the user has the option of selecting an Acceleration
Test. After the simulation is complete, the user can then open the appropriate plot options
screen in cX Graphics (Figure 22) and define the parameters of this test. Once the cX
Graphics program is executed, the results appear in both a figure and table. The figure
shows the actual velocity and the table will contain the statistical information previously
aforementioned. The units for this can also be interchanged between SI and English.
39
Figure 22. Acceleration Test Parameter Selection Screen.
3.3.4 Set Layout for Plots HEV Operation
Since the main output signal of the control strategy is the torque request for each
driveline component, the most important aspect of analyzing this HEV is monitoring
these requests and device output. Thus, every torque request and output torque for each
actuator in the driveline can be visualized with cX Graphics. Figure 23 shows the plot
options for HEV operation. Deviations of the actual torque and torque request, as well as,
the shifting sched ontrol strategy is
plemented, the options to see the potential for energy recuperation and Sankey
ake cX Graphics a vital tool for
ule can also be displayed if desired. Once the c
im
Diagrams will be fully developed. These options m
energy management analysis. Such an analysis leads to minimal fuel consumption,
fulfilling one of the primary goals of Challenge X.
40
Figure 23. HEV Operation Plot Options Screen.
3.3.5 Set Layout Plots for Conventional Operation
The u conventional
owertrain with the options seen in Figure 24. These options include only those variables
uest and actual torque delivered by the
vering positive torque, hence why only
ser has the option of only viewing the results from the
p
that are related to the ICE. Again, the torque req
ICE can be examined. To enhance this comparison, statistical data between these two
values can also be shown. Not only can the speed and torque be viewed independently,
but they can also be displayed on the efficiency and fuel consumption map for the Fiat
1.9L diesel engine. Features like this, and others shown below, give cX Graphics the
capability to extensively audit the functions of the conventional powertrain. Unlike the
electric actuators, the ICE is only capable of deli
41
the first quadrant of the torque, speed, and efficiency/fuel consumption map is shown
when this option is selected (see Figure 30).
Figure 24. Conventional Powertrain Plot Options Screen.
3.3.6 Set Layout Plots for Electric Powertrain
Not only can the conventional powertrain be independently viewed, but the
electric powertrain can be as well. Figure 25 displays the plot options screen for this task.
All aspects of the battery—voltage, current, and state-of-charge—can be analyzed.
However, all of the limits for these quantities are still being investigated by other
members of the Ohio State Challenge X team. These limits will be properly implemented
here once conclusive values have been obtained.
The next component that can be monitored is the EM. Speed and torque can be
viewed independently, as well as on the efficiency map for the EV1 motor. Of course, the
statistical deviations between actual and desired torque can also be shown. Displaying the
power used by the EM is an option as well. It is important to note that the speed listed
42
here is that of only the EM, the angular speed seen at the half shafts is this value divided
by the gearbox ratio of 10.946. As previously stated, the EM is capable motoring the
vehicle and absorbing kinetic energy from the vehicle to replenish the battery. Thus, both
positive and negative torque, as well as power, is seen here throughout any given driving
cycle (see Figure 31).
The final set of options includes presenting the quantities produced by the ISA.
However, the efficiency map of the ISA does not currently exist since the Ohio State
Challenge X team has not yet received the actual device. The operating data of this
component is a modified version of a similar ISA that has been analyzed by others. Once
the actual ISA is been received and examined, the appropriate changes will be made in
cX-SIM and cX-DYN, as well as cX Graphics, to reflect this. Nonetheless, the delivered
torque and torque request can be viewed along with the statistics that quantify their
differences. The efficiency and power of this component are also display options. Keep in
mind that this component, just like the EM, can deliver torque (positive power) and
absorb torque (negative power) to recharge the battery. Therefore, both positive and
negative torque and power values will appear here.
43
Figure 25. Electric Powertrain Plot Options Screen.
The quasi-static cX-SIM is developed for the task of monitoring energy and fuel
consumption while the dynamic cX-DYN is used to the study drivability of the HEV. An
in-depth visual analysis is performed by cX Graphics once the simulators produce results.
Now that the vehicle can be actively simulated and analyzed, preliminary results are
obtained and verified to ensure the simulators are accurate to the designed vehicle.
44
Chapter 4
Results & Model Verification
As discussed in the previous chapter, both a quasi-static and dynamic simulator
are being developed. At the present time, only cX-SIM is functional and only a few of the
mod ry.
dditional work on these simulators will continue until both are fully capable of
roviding the Ohio State Challenge X team with the appropriate analysis. Techniques to
verify of these simulators are developed and also presented.
4.1 cX-SIM
es of operation are available. Therefore, the results presented here are prelimina
A
p
Only the Idle, Launch, Engine Start and Deceleration modes of operation are
functional when the preliminary results from cX-SIM are obtained. cX Graphics is then
used to create the figures seen below. Using a Federal Urban Driving Cycle (FUDS), a
sim 6
ows the actual and desired velocity curves. In a perfect system, the two curves would
ulation was performed for approximately the first 3 minutes of the cycle. Figure 2
sh
lay precisely on top one another; however, since this system design mimics the behavior
of an actual driver, the discrepancy seen in Figure 26 is very realistic. Nonetheless, the
deviation between the desired and actual velocity is not that outlandish. Figure 27 shows
the screen shot of the statistical data created by cX Graphics. The rms deviation is only
~2.0 kph-- an acceptable value given the nature of this simulation.
45
Figure 26. Actual & Desired Velocity from cX-SIM Preliminary Simulation.
Figure 27. Deviation of Actual & Desired Vehicle Speed of cX-SIM Simulation.
Using the Set Layout Plots HEV Operation option of cX Graphics the sum of the
total torque desired from the powertrain (ICE, ISA and EM combined) as well as the total
torque delivered from the powertrain is visually represented in Figure 28. The total torque
request can never be negative because the control strategy lacks the appropriate
algorithms for this case. In order for negative torque to be requested from the powertrain,
46
the battery state-of-charge must be approaching the acceptable lower bound. Since no
state-of-charge control is effectively implemented to date, the control strategy never
requests torque to replenish the battery. However, this does not mean that the powertrain
cannot deliver negative torque. As the vehicle slows down, the EM and ISA, as seen by
the resulting output torque curve of Figure 28, absorb the kinetic energy of the vehicle.
This results in the rather high deviations between total torque request and total torque
output seen in Figure 29.
Figure 28. Total Output and Requested Torque during the cX-SIM Preliminary
Simulation.
47
Figure 29. Deviations Between Actual & Desired Torque of HEV Powertrain.
n be
iewed in Figure 30. Keep in mind that these are not necessarily sequential, and the
The operating points of the ICE as selected by the current control strategy ca
v
control strategy selects the operating points of the ICE based only one of the three control
strategy objectives (See Chapter 5). Further more, the appearance of this figure will be
different once the complete control strategy is integrated into cX-SIM. However, the Fiat
ICE proves to be an efficient choice. As long as the torque of the ICE remains above ~50
Nm, the efficiency of this device never decreases below 33%-- a favorable result for the
Ohio State Challenge X team. However, as the torque demand increases the efficiency
reaches values in the upwards of 41%-- a good value for ICE’s.
48
Figure 30. ICE Operating Points during cX-SIM Preliminary Simulation.
The components of the electrical powertrain are also analyzed after the
preliminary simulation. Figure 31 displays the operating points of the EM on the
efficiency map on the EV1 motor. Again, these points are not necessarily sequential, and
are selected by the control strategy according to Figure 43 (See Chapter 5). The operating
points do appear to lie more so in the negative torque (regeneration) region than the
positive torque (motoring) region. This is another result of the incomplete control
strategy. The operating points seen in Figure 31 are not optimal for minimal fuel
onsumption and SOC control as a completed control strategy forces them to be.
onetheless, the EM tends to operate in the 60-75% efficiency region throughout this
particular driving cycle.
c
N
49
Figure 3 ulation. 1. Operating Points of the EM during the cX-SIM Preliminary Sim
Since no efficiency map of the ISA exists to date, the power of the ISA is shown
below. Note that the ISA power is zero, until the control strategy moves from Launch
mode into Engine Start mode. At this point, the power will spike as seen at ~15 seconds
into the drive cycle. Here, the ISA turns ON in order to start the ICE. The negative power
seen in Figure 32 represents the ISA being driven by the ICE in order to generate
electrical power. As previously aforementioned, this figure will also look differently once
the complete control strategy is implemented.
50
F
l component analyzed during this preliminary simulation is that of the
igure 32. ISA Power during the cX-SIM Preliminary Simulation.
The fina
battery. Figure 33 displays the SOC of the battery throughout the driving cycle. This
figure does not accurately represent how the SOC behaves during a given driving cycle,
as no SOC control is provided. However, this figure does display how the SOC increases
during replenishment, and decreases during power demand. The current limits of 60%
and 80% are initial boundaries set with the knowledge of past HEV development research
at Ohio State [6]. These limits will be optimized to accommodate the batteries being used
in the Ohio State Challenge X Equinox.
51
Figure 33. Battery SOC during cX-SIM Preliminary Simulation.
4.2 cX-DYN
No preliminary results for cX-DYN have been acquired to date. Since cX-SIM is
a more efficient simulator, computationally speaking, for optimizing two of the main
parts of the control strategy, the primary focus has been directed toward completing the
quasi-static simulator. Key deadlines for the Challenge X competition (reports and Year 1
competition) have also shifted the focus on gaining full functionally of cX-SIM prior to
cX-DYN. However, once cX-SIM is fully operational, the changes to be made in order to
make cX-DYN operational will be trivial.
4.3 Rolling Chassis
In order to validate the modeling and simulations mentioned in Chapters 2 and 3,
the Ohio State Challenge X team has created a Rolling Chassis. One of the obsolete
future truck vehicles was taken and cut down to only the floor pan, firewall, frame, axles
and wheels. The driver seat and steering wheel were left as well. This serves as a
52
platform on which all of the components described in Chapter 1 will be mounted for
initial testing. Once all of the actuators are assembled and the control strategy hardware
and software is installed, the complete verification process will begin. This will not only
verify the simulators, but also the ability for each of the aforementioned components to
be integrated together and behave according to the desired vehicle architecture.
4.3.1 Launch Test
Currently, only the EM is ready for testing and validation. The EM is attached to
the rolling chassis, and placed on a dynamometer as seen in Figure 34. Tests have been
conducted to analyze the effectiveness of the EM during electric launch. The figures that
follow show speed data from one such test. The pedals of the rolling chassis are used to
accelerate and decelerate the EM on the dynamometer. This approach accurately
resembles the accelerator pedal positions during the launch of the actual vehicle. With the
inertial and frictional values of the Equinox programmed into the dynamometer, the
accelerator pedal is pushed to the maximum position to generate a replication of a vehicle
launch.
In order to preserve the mechanical integrity of each device involved, there is a
torque request limit placed on the system. One of the tests has a limit of 40% torque
request. The second has a limit of 50%. This means that when the accelerator pedal is
completely depressed, only 40% of the total torque capacity of the EM is available for
delivery to the dynamometer. Figure 35 shows the EM motor speed during the 40%
limited test. Figure 36 displays the vehicle speed generated throughout the duration of
this test. The vehicle reaches a speed of ~24 kph (~15mph) in just under 10 seconds. The
launch is also performed with the torque output limit of 50%. Figure 37 and 38 show the
EM motor speed and vehicle speed, respectively, for this experiment. The vehicle reaches
a speed of approximately 37kph (~23 mph) in approximately 15 seconds. Recall that the
EM only provides motoring torque during launch for a short period of time (Launch
Mode), and then the ICE is started (Engine Start Mode) and then reigns as the primary
motoring device (Normal Mode). Considering the output of the EM is limited, initial
observations would suggest this actuator is capable of being a part of the system to meet
the goals specified in Table 1.
53
There are a few factors that exist which alter n below. The most
prominent involves the experimental set-up. Doing a repeated launch test is very taxing to
the battery, so a power supply is used. However, the DC output of this power supply
fluctuates immensely. In order to stabilize this output, the power supply is connected in
parallel to a lead-acid battery pack. The pack serves as an “electrical shock absorber”, or
large capacitor. This configuration stabilizes the voltage going into the EM at rest;
however, when the launch is performed, the power oscillates slightly. This oscillation is
reflected in the speed figures seen below. The torque request is constant, but the speed
fluctuates due to a changing power input. Since the pack can respond more rapidly than
the power supply, as the launch initially begins the battery pack supplies the elec
energy until the power supply “catches up.” Once the power supply is up to speed, it
provides more than the requested power in order to charge the battery, as well as run the
EM. The battery abs shoot” and the power supply then decreases output to
the point where the battery once again supplies power. The power supply detects this
drop in the battery his process would
repeat until a steady-state supply environment is reached between the two sources.
However, the launch test is not performed for this length of time.
the data see
trical
orbs this “over
and once again provides an “overshoot” of energy. T
54
Lead-Acid Battery Pack
EV1 Motor & Inverter
Chassis Dynamometer
Rolling Chassis
Figure 34. Rolling Chassis Experimental Set-Up.
Figure 35. Launch Test EM Motor Speed -40% Torque Limit.
55
Figure 36. Launch Test Vehicle Speed- 40% Torque Limit.
Figure 37. Launch Test EM Motor Speed--50% Torque Limit.
56
Figure 38. Launch Test Vehicle Speed-- 50% Torque Limit.
4.3.2 Model Verification & Mapping
The EM was ori algin ly the propulsion device for the EV1 electric car as
reviously mentioned. After deciding to use this component for Challenge X, the Ohio
tate team sent this drive unit to be rebuilt. When th
However, there is no method of requesting an exact torque from the EM, but merely a
aximum torque capacity. Therefore, a series of tests will be
peration. Once this extensive “torque mapping” exercise is completed, a modified
ersion of cX-SIM will investigated for simulator a
The mapping process will be quite extensive. Unfortunately, the chassis
p
S e rebuilt unit arrived testing began.
rough percentage of the m
conducted to create a map, so that known torque requests can be sent to the EM during
o
v ccuracy.
dynamometer is not calibrated correctly to yield an accurate power reading. Thus, the
torque mapping procedure involves varying the friction coefficient of the dynamometer
and running the EM at certain torque requests. Once the chassis reaches steady-state
speed, the torque being provided by the EM can be found. Effectively, the result of this
procedure will be the torque-speed map of the EM. The dynamometer specifies 3
57
coefficients that make up the total load that is placed on the vehicle. However, these
coefficients are represented by the horsepower at 50 miles per hour and require some
manipulation to be used for this mapping. The general expression of the dynamometer
load is:
Friction A B C= + + (30)
where A is the rolling resistance, B is the intrinsic friction, and C is the air drag. The
variable of interest is the friction coefficient, B. Each of these variables has units of
HP@50 mph [10]. Knowing this fact we can relate this horsepower at a rated speed to
the force of the dynamometer, Fdyno (N):
dynoSS
BFvλ
= (31)
In this expression, λ represents all of the conversion factors necessary and vSS is the found
steady-state speed (mph). This force, along with the wheel radius, rwheel, is used to find
the torque at
the wheel, Twheel:
wheel dyno wheelT F r= (32)
Using the gear ratio, τGB, the torque of the EM (TEM :) can be found.
wheelEM
GB
TTτ
= (33)
Figure 39 represents the vehicle speed of one such test. Notice how the vehicle reaches a
steady-state speed of approximately 8 kph (~5mph). To ensure this is in fact the steady-
state speed the derivative of this curve, acceleration, is found. In order to do this, a
second order polynomial was fit to the speed data and is shown in Figure 39. The
derivative of this curve is shown in Figure 40. The derivative approaches zero toward the
58
end of the test, meaning the vehicle speed has reached a quasi-steady state value that can
be used in the aforementioned calculations. The result of this particular test is an EM
torque of 313.9 Nm.
Figure 39. EM Torque Mapping Test: Vehicle Speed (B=30).
59
Figure 40. EM Torque Mapping Test: Acceleration (B=30).
This process will be repeated over a large range of friction coefficients and torques to
create a very detailed map. These output torques will be entered, with their corresponding
percentage torque request, into a look-up table. This will allow for an input torque value
in standard units (e.g. Nm) to be sent to the EM for operation. Once this table is
plemented, the verification odified form of cX-
M.
im of the model will be done with the m
SI
4.3.3 cX Test
This version of cX-SIM is called cX-Test and can be seen in Figure 41. Basically,
this model is the rear driveline and vehicle cut from the parent simulator. The vehicle is
included because the dynamometer simulates vehicle drag, rolling resistance, and grade
resistance. Here, a torque request is sent to the EM, and the model reacts accordingly.
This simulation is analyzed with the condensed version of cX Graphics seen in Figure
2—cX-Test Graphics. The same torque request is given to the actual EM on the rolling
hassis, and the resulting data is compared to the cX-Test data to ensure the model is
alid.
4
c
v
60
Figure 41. cX Test Top Layer.
Figure 42. cX -Test Graphics.
Preliminary results from cX-SIM have been obtained and visually represented
using cX Graphics. Once cX-SIM is
fully functional, cX-DYN will be brought on-line as
well. Verifying both simulators is done via the rolling chassis; however, this task could
not be completed before the conclusion of this thesis. Not only will finishing the
simulators and verification be a task of the future, developing and integrating a robust
control strategy also needs to be completed.
61
Chapter 5
Control Strategy Development
Future work includes performing the mapping and verification described in the
previous chapter, as well as developing a fully functional control strategy. With cX-SIM
nearing completion, and cX-DYN soon to follow, a suitable control strategy must be
implemented so the verification process can continue. The basics of the currently
considered control strategy are presented here. The ultimate design and fabrication of the
controllers necessary is left for future work on this project.
5.1 Overview rimary focus of this research is modeling and simulation of the rear The p
driveline of the Ohio State Challenge X Equinox. Development of the control strategy is
a task being pursued by other members of the OSU Challenge X team. However, the
literature has been investigated in regards to control of HEVs and the author has
participated in the development of the control strategy for the Hybrid Equinox. Therefore,
a brief summary of the control strategy is presented here.
The main objective of the control strategy is to reduce fuel consumption and
emissions while maximizing drivability by taking advantage of the multiple vehicle
modes. This is achieved by the potential energy recovery during braking, as well as the
availability of the additional degrees of freedom with respect to the power split to satisfy
62
driver demand [7]. The control strategy being developed for the Ohio State Challenge X
Equinox is divided into two parts: primary control and secondary control. The primary
ontrol strategy commands the drivetrain components in real time as dependent on driver
requests, the state of each component, and of course the control strategy algorithm. The
secondary control monitors the state of each component, such as temperature, to ensure
fe operation [5]. The focus here is on the primary control strategy.
This con
State-of-charge, and Drivability [2, 5]. Each are considered independently and then
crea
c
sa
trol signal is decomposed into three “decoupled” signals: ECMS, Battery
summed together to te the final control signal. The process for obtaining the ultimate
control signal is described by Figure 43 below.
Figure 43. Control Strategy Schematic.
5.2 ECMS The first factor considered by the control strategy is fuel consumption. Compliant
with the goals of Challenge X, the objective is to minimize this quantity. To accomplish
is, Ohio State chooses to use the Equivalent Consumption Minimization Strategy
CMS). The basis of ECMS is that all energy consumed by t
fuel tank [2]. In the case of HEVs, two fuel tanks are considered. The first is the
th
(E he vehicle comes from the
conventional fuel storage tank and the second is the battery, or some other energy storage
device. For ECMS purposes, the battery is modeled as a reversible fuel tank that can exist
in two states. First, the battery could be recharging, so fuel must be consumed, or kinetic
energy absorbed, to replenish this electrical energy. The second state is the battery could
63
be using electrical energy to alleviate some of the load from the ICE to save fuel [4]. The
governing equation for ECMS is as follows:
( )* ,* ,
( ) i ji j
i j LHV
x um x u
x u Qη=& (34)
where ( )* ,i jm x u& is the mass flow of “fuel” for component *, ( )* ,i jx uη is the efficiency of
component *, and LHVQ is known as the low-heating value of fuel. The quantity xi is a
state vector that includes the speeds of the ICE, AT, EM, and vehicle, as well as, the
positions of the AT, EM and vehicle. The control vector iu contains the torque of each of
the three actuators [2]. At any time during vehicle operation, the entire range of operating
points for ICE, ISA, and EM will be examined and equivalent flows will be found [4].
The point which minimizes the total equivalent fuel consumption—the sum of each
* ,( )i jm x u& -- will be chosen as the ECMS control input.
5.3 Battery State-of-Charge One of the most important aspects to consider for effective HEV operation is
battery state-of-charge. The capacity of the battery as stated by the manufacturer cannot
reflect the change in this quantity due to usage. By maintaining the SOC, the degradation
of the battery capacity as a result of use can be significantly slowed. The SOC is defined
p-hour capacity of the battery and the total amp-hour capacity as the ratio of the used am
of the battery.
( ) ( )( )
1USEDCAP t t
SOC t tCAP t t
δδ
δ+
+ = −+
(35))
Here, USEDCAP represents the energy used (Ah) and CAP is the total capacity of the
attery
when necessary. The acceptable range varies according to the type of battery being used.
b (Ah) [1]. Keeping this value within a certain range not only preserves battery life,
but also allow for additional “room” to absorb excess power and deliver additional power
64
Ohio State is currently investigating this range for the Nickel Metal-hydride batteries to
be used for Challenge X.
In Figure 26, ECMS and SOC control are grouped together. This is due to the fact
that ECMS and SOC control cannot be completely decoupled from one another. The
battery state-of-charge has a large impact on ECMS because if the SOC falls too low,
diesel fuel would need to be consumed in order to replenish the battery. Built into ECMS
is a penalty function that shifts the optimal power split up or down according to the actual
C and the SOC range. This penalty function shifts the power split according to three
ases. The first requires that the SOC is within the range and the selected
rating point is valid. The second case involves the SOC being too high,
us the power split is shifted to promote discharging of the battery. Finally, the SOC
ould be too low and the operating point is shifted to emphasize battery recharging.
thers have stated that in a charge sustaining control strategy the net consumption of
lectrical power is zero [4]. This is not true due to the set range of battery SOC. For
xample, a given drive cycle begins with a SOC of 75% and the acceptable range is
etween 60% and 80% SOC. The drive cycle could easily end with the battery SOC
eing 63%, meaning more electrical power was consumed, rather than replenished, over
e cycle. Hence, the net consumption of electrical power over this drive cycle is not
zero. Since the control strategy keeps the SOC within a range, the net consumption of the
electrical power over a given driving cycle does not necessarily have to be zero and most
likely will not be.
5.4 Drivability
SO
possible SOC c
power split ope
th
c
O
e
e
b
b
th
Drivability refers to the smooth operation of the vehicle. In this case, the control
strategy maximizes drivability by ensuring the shift from one operating mode to another
does not result in any undesirable vibrations or jerks. Such anomalies are also minimized
as the vehicle shifts gears. Drivability is to be evaluated by cX-DYN; however, no
drivability control has been implemented at this point.
Fuel consumption minimization and emissions reduction are two of the primary
goals of Challenge X. Drivability is also a primary goal being considered. All three of
65
these aspects of the HEV Equinox will be controlled to meet the standards of the
petition,
owev ed and the experiments detailed herein
nd
t the rolling chassis once
com as well as consumer standards.
Many unforeseen technical difficulties hindered the progress of this research.
er, once all of these issues have been resolvH
are conducted, the model of the Ohio State Challenge X HEV will prove to be valid a
e. Moreover, both simulators will also be validated using accura
the control strategy is in place.
66
References [1] X. He and J. W. Hodgson, “Modeling nd Simulation for Hybrid Electric
Vehicles—Part I: Modeling,” in IEE Transactions on Intelligent Transportation Systems, vol. 3, no. 4, pp. 235-243, 2002.
] O. Barbarisi, E.R. Westervelt, G. Rizzoni, and F. Vasca, “ Power Management
Decoupling Control for a Hybrid Electric Vehilce,” 2005. [3] X. He and J. W. Ho tion for Hybrid Electric
Vehicles t II: S E Transactions on Intelligent Transpo Syst pp. 244-251, 2002.
[4] G. Pagan . Erc c, and G. Rizzoni, “A General
Formula r the Charge Sustaini rid E
[5] F. Ohlem r, G. R iman, “Challenge X 2005 Report #3:
Control System Har e Development”, submitted to the Challeng organiz
[6] C. Musardo and Benedetto Staccia, “Energy Management Strategies for Hybrid
Electric les,” D [7] F. Ohlem , G. R ort #2:
Vehicle itectur bmitted to the Cha org 4.
[8] F. Ohlem r, G. R man, “Challenge X 2005 Report #4:
Contro Dev o the Challenge X organizers Nov
[9] “Challen websi
aE
[2
dgson, “Modeling and Simula—Par imulation,” in IEErtation ems, vol. 3, no. 4,
elli, G ole, A. Brahma, Y. Guezennetion fo Instantaneous Control of the Power Split in
001. ng Hyb lectric Vehicles,” 2
ache izzoni, and A. Solrdware and Softwa
e X ers March 2005.
Vehic octor of Philosophy Dissertation, 2003.
acher izzoni, and A. Soliman, “Challenge X 2005 Repe Selection for the Challenge X Competition”, su A
llenge Xrch
anizers November 200
ache izzoni, and A. Solil System elopment”, submitted t
ember 2004.
ge X te,” 2005 www.challengex.org. [10] Horiba Dynamomet
er Operation Manual, June 1992.
67
Appendix
Table 3. Nomenclature.
Abbreviation Description
HEV cle Hybrid Electric VehiICE Internal Combustion Engine EM Electric Machine M G Motor/Generator ISA Integrated Starter/Alternator AT Automatic Transmission
MOT Motoring, or providing propulsion power 4WD Four Wheel Drive JICE Inertia of the ICE JISA Inertia of the ISA JTR Inertia of the AT JEM Inertia of the EM TICE Torque of the ICE TISA Torque of the ISA
T P Converter TC_ Torque on Pump Side of TorqueTTC_T Torque on Turbine Side of Torque Converter TTC Torque of Torque Converter (locked case only)
TF, TX1 Torque of Front Axle TB_F Torque of Front Brakes TEM Torque of the EM
TR, Axle TR Torque of Rear Axles TB_R brakes, TR Torque of Rear Brakes
TC Torque of the Clutch TC@T Torque at Manual Transmission TRGB Torque of Rear Gearbox Twheel Torque of Wheel on Dynamometer
Jf JICE + JISA
ICEω& Angular Acceleration of the ICE
TRω& Angular Acceleration of the AT
EMω& Angular Acceleration of the EM ωICE Rotational Speed of the ICE ωT tR, ω Rotational Speed of the AT ωF Rotational Speed of Front Axle ωEM Rotational Speed of the EM ωR Rotational Speed of the Rear Axle ωC Rotational Speed of the Clutch
68
ω Gearbox RGB Rotational Speed of RearωRbrakes Rotational Speed of Rear Brakes ωRwheel Rotational Speed of Rear Wheel ωwheel Rotational Speed of Wheel on Dynamometer bICE Damping of the ICE
bF, bX1 Damping of Front Axle bEM Damping of the EM
b e Axle R, bRaxl Damping of Rear bC Damping of Clutch
kF, kX1 Spring Constant of Front Axle kR, kRaxle Spring Constant of Rear Axle
kC Spring Constant of Clutch τT ) R(g AT Gear Ratio τGB Gear Ratio of Rear Gearbox
rF f, R Radius of Front Wheels rR, heel els rRw Radius of Rear Whe
mVEH Mass of the Vehicle vVEH,, vf Velocity of the Vehicle
FRD Frictional Force of the Road FRR Rolling Resistance Force due to
FDRAG Force due to Air Drag F rain Tractive Force from PowertFf Tractive Force of Front Wheel
FRwhee el l Tractive Force of Rear WheFdyno Force of Dynamometer θTR, θt Angular Position of AT θ osition of the EM EM Angular Pθ the ICE ICE Angular Position of θF Angular Position of Front Axle θC Angular Position of the Clutch θRGB Angular Position of Rear Gearbox θRbrakes Angular Position of Rear Brakes θRwheel Angular Position of Rear Wheel x , xf Distance Traveled by Vehicle VEH
VEHx&& Acceleration of the Vehicle g Acceleration due to Gravity Cr Frictional Coefficient of Rolling Resistance φ Road Grade Angle ρAIR Density of Air Cd Drag Coefficient of the Vehicle Af Frontal Area of the Vehicle α Accelerator Position/Command β Brake Pedal Position/Command γ Clutch Command
69
70
λ BRbrakes B Rear Brake Proportional Constant diff Front Differential Ratio
cX-SIM Quasi-Static HEV Simulator cX-DYN Dynamic HEV Simulator
cX Graphics Graphical User Interface for simulators cX-Test Quasi-Static Model of Rear Driveline
PID Proportional, Integral, Derivative ECMS Equivalent Consumption Minimization Strategy SOC State-Of-Charge
FUDS Federal Urban Driving Cycle FHDs Federal Highway Driving Cycle
Friction Load of the Chassis Dynamometer A Rolling Resistance of dynamometer B Friction Coefficient of Dynamometer C Air Drag Coefficient of Dynamometer λ Conversion Factor from HP to lb using Speed
vBSSB Steady-state Speed ( )* ,i jm x u& Governing equation of ECMS representing
equivalent mass fuel flow from component * ix State vector including { ωBICE B ωBTR BωBEM BvBVEH BθBTR
BθBEM BxBVEH B} ju Control Vector including { TBICE BTBISAB TBEMB}B B
( )* ,i jx uη Efficiency of component *
LHVQ Low-heating value of fuel CAP Specified total capacity of the battery (Ah)
USEDCAP Used energy of the battery (Ah) t Time (s) δt Interval of time (s)
