Int. J. of Vehicle Systems Modelling and Testing , Vol. x, No. x, xxxx
Real-time dynamic simulation of vehicles with
electronic stability control: Modeling and validation
Weidong Pan and Yiannis E. Papelis
National Advanced Driving Simulator, The University of Iowa,
2401 Oakdale Blvd., Iowa City, IA 52242-5003, USA
E-mail: wpan@nads-sc.uiowa.edu, yiannis@nads-sc.uiowa.edu
Abstract: This paper presents an approach to real-time dynamic simulation of
vehicles with electronic stability control (ESC). The approach involves the
integration of ESC software into the powertrain and brake models of the realtime vehicle dynamic simulation environment of the National Advanced
Driving Simulator (NADS). The ultimate goal of this integration is the use of
ESC equipped vehicles in simulator-based human factors experimentation
assessing the effectiveness of ESC in avoiding loss of control accidents. The
effectiveness of this approach in simulating ESC is demonstrated through the
development and validation of two vehicle models, one for a 2003 Ford
Expedition and the other for a 2002 Oldsmobile Intrigue, both equipped with
ESC. Results show close correlation of vehicle behavior between the test data
and the simulation data. In addition, the timing and magnitude of the simulated
ESC activity correlate closely with the test results.
Keywords: active safety systems, driving simulator, electronic stability
control, multibody vehicle dynamics, real-time vehicle dynamic simulation,
vehicle modeling and validation
Reference to this paper should be made as follows: Pan, Weidong, and Papelis,
Yiannis E. (xxxx) ‘Real-time dynamic simulation of vehicles with electronic
stability control: Modeling and validation’, Int. J. of Vehicle Systems Modelling
and Testing, Vol. X, No. Y, pp. 000-000.
Biographical notes: Weidong Pan is an associate research engineer at the
National Advanced Driving Simulator. He earned his Ph.D. in mechanical
engineering from the University of Iowa. His academic and research career has
focused on flexible multibody dynamics, vehicle dynamics modeling and realtime simulation, and high-fidelity tire-soil and tool-soil interaction modeling
and simulation technology. He has published in journals such as Computer
Methods in Applied Mechanics and Engineering and Mechanics of Structures
and Machines.
Dr. Yiannis Papelis is a research scientist and chief technical officer at the
National Advanced Driving Simulator. He earned a Ph.D. in electrical and
computer engineering from the University of Iowa and has been involved in
driving simulation research for the past 15 years. Dr. Papelis has initiated and
led numerous transportation safety research projects focusing on in-vehicle
devices and vehicle design. He has also consulted with industry on simulator
development projects in the U.S., Europe, and Asia. His research interests
include transportation safety research, synthetic environment modeling, and
simulation, and he has published in journals such as IEEE Computer and
Transactions on Software Engineering, as well as in numerous conference
proceedings.
Copyright © 200x Inderscience Enterprises Ltd.
1
W. Pan and Y. Papelis
1
Introduction
Vehicle design has evolved significantly over the last decade, with new safety features
available on more and more vehicles. The latest addition is electronic stability control
(ESC). During severe maneuvers, such as obstacle avoidance, the ESC senses impending
loss of control and selectively brakes individual wheels and intervenes in the enginemanagement system to help the driver maintain control of the vehicle. Early statistical
studies have shown that vehicles with ESC have fewer accidents than vehicles without;
however, there has been no empirical study of ESC effectiveness with normal drivers.
Testing a new design or studying the effectiveness of an existing safety system like
ESC in the real world is difficult because such systems are designed to prevent accidents
and thus function only in severe and risky situations. High-fidelity driving simulation,
where the virtual environment ensures maximum driver immersion without the risks
associated with the driving situations necessary to exhibit the potential benefits of ESC, is
an ideal alternative. However, properly testing ESC on a driving simulator requires the
modeling and integration of ESC into the vehicle dynamics used in the real-time
simulation.
Real-time vehicle dynamics simulation is a key enabling technology in a high-fidelity
driving simulator. Given the driver control over the steering wheel, brake pedal,
accelerator pedal, and gear shift, vehicle dynamics must predict all information required
by the motion system (velocity and acceleration), visual system (position and
orientation), and audio system (powertrain, tires), in real time. The development of the
NADSdyna software a decade ago represents an early effort to achieve this capability
(CCAD, 1995). The software, with incremental enhancements over the years, now runs at
the National Advanced Driving Simulator at the University of Iowa.
There are several challenges when integrating an ESC model into real-time dynamics
code. First, the ESC system is only activated during very aggressive maneuvers, at which
point, there are severe nonlinearities in the vehicle suspension and tires. The vehicle
dynamics model must be of adequate fidelity and utilize high-quality data. For example,
the tire model must adequately simulate large slip angles and slip ratios. This problem
was addressed by obtaining, in a test laboratory environment, tire data for large slip
angles and slip ratios. This data was used to calibrate the simulation models, thus
ensuring close match to real-world aggregate vehicle performance.
Secondly, the ESC system implementation uses complicated proprietary algorithms
that are not easily reproduced. In this case, this problem was addressed by two ESC
manufacturers willingness to provide a library containing the actual software that runs in
the vehicle ESC controller to the University of Iowa. This software was integrated into
the NADS vehicle model, thus ensuring identical behavior of the ESC system between
the real world and the simulation.
The two ESC-equipped vehicles that were modeled are the 2003 Ford Expedition and
the 2002 Oldsmobile Intrigue. The ultimate purpose of this modeling effort was to utilize
these models in a simulator-based human factors study comparing loss of control with
and without ESC, under typical loss-of-control driving situations (Papelis et al., 2004).
This paper is organized as follows. The approach to incorporating ESC software into
NADSdyna is presented in Section 2. In Section 3, the development of the real-time
Real-time dynamic simulation of vehicles with electronic stability control:
Modeling and validation
model of a passenger car and the real-time model of a sports utility vehicle (SUV) is
presented. In Section 4, effectiveness of the vehicle dynamics modeling approach is
demonstrated by comparing simulation results and test data for several relevant
maneuvers. The integration time step-size for all simulations presented in this paper is
1/960 second, and the sampling rate of ESC software is 960 Hz.
2
Incorporating ESC into powertrain and brake model
Before the advent of ESC, the most popular active driving safety systems were the
Antilock Brake System (ABS) and the Traction Control System (TCS). The primary
function of ABS is to control the brake slip of the wheels to within a narrow range around
the slip value at which the longitudinal tire force peaks. The range is also where the tire
lateral force response to slip angle is usually sufficient to keep the vehicle stable and
steerable (Pacejka, 2002). ABS uses wheel speed sensors to compute wheel slip and
achieves its control objectives by modulating wheel brake pressure.
The primary function of TCS is to control the drive slip of the driven wheels so that it
is around the slip value at which the longitudinal tire force peaks. A TCS system uses the
same wheel speed sensors as the ABS but calculates drive slip as input to the control
algorithm that decides the appropriate brake pressure at driven wheels. To obtain optimal
results, TCS sometimes intervenes with the engine management to reduce engine power.
TCS prevents wheel spin during straight-line acceleration. It also prevents skidding when
accelerating too much in a turn.
Both ABS and TCS monitor wheel speed and take action based on the value of
computed wheel slip (brake slip and drive slip, respectively). ESC contains all the
capabilities of ABS and TSC. In addition, it also monitors steering wheel angle,
accelerator position (read from engine ECU), primer pump pressure in the brake system,
vehicle lateral acceleration, and vehicle yaw rate (Robert Bosch GmbH, 1999a). Based on
this additional information, the ESC estimates driver intention, computes vehicle
behavior, and then develops a control strategy to steer and/or slow the vehicle through
brake application and engine intervention during situations where the vehicle is about to
go out of control.
For TCS/ESC to intervene with engine management, an electronic throttle control
(ETC), also known as drive-by-wire, must replace the conventional mechanical linkage
between the accelerator pedal and the internal combustion engine throttle valve (or diesel
injection pump). Let ˆ   0,90 be the accelerator pedal angle,   0,1 be the
commanded throttle by the TCS/ESC system, and I etc be a Boolean variable with a 1
indicating the TCS/ESC command should be honored and a 0 indicating the command
should be disregarded. An ETC model can be expressed using the following equation:

if I etc  1

(1)
 
ˆ

 / 90 if I etc  0
where  is the actual throttle passed to engine model. Note that in a drive-by-wire
system, control commands from TCS/ESC have higher priority than commands from the
driver (Robert Bosch GmbH, 1999b).
W. Pan and Y. Papelis
2.1 Definition of the inputs and outputs of driving safety systems
Based on the above discussion, one can summarize that an ESC takes three groups of
information--driver inputs; chassis and wheel translational and rotational velocity and
acceleration (vehicle states); and powertrain states--and achieves its control objectives
through braking and engine/powertrain intervention. Thus, a generic interface for
describing ESC in the context of vehicle dynamic simulation can be defined as shown in
Fig. 1. The interface is general because all driver, vehicle, and powertrain information is
included as input and different types of brake and engine intervention are included as
output. It is expected that the interface will cover current and future driving safety
systems to a great extent. Details of the inputs and outputs are described in the following
paragraphs. Information that is not used by today’s ESC systems is intentionally
included, with the assumption that future sensor technology and vehicle control
algorithms will lead to more advanced driving safety systems that can use the
information.
The vector of driver inputs consists of accelerator pedal position ˆ , brake pedal
force Fbpedal , steering wheel angle  , steering wheel velocity  , and current gear
selection I selector ; i.e.,
T
(2)
x1  ˆ, Fbpedal , , , I selector 
The vector of wheel kinematic information consists of wheel spin velocity i ,
i  1,
i ,
, 4 and wheel spin acceleration
i  1,
, 4 at previous time step; i.e.,
x 2  1 , 2 , 3 , 4 , 1 , 2 , 3 , 4 
T
(3)
The vector of powertrain information consists of engine speed e , engine output
torque Te , the current gear in transmission gear box I gear , transmission output torque TTR ,
powertrain operation model I mode (two-wheel drive, four-wheel drive, or all-wheel drive),
differential operation mode J mode (locked, unlocked, or controllable), transfer case
operation mode K mode , and transfer case torque split ratio tcase ; i.e.,
T
x3  e , Te , I gear , TTR , I mode , J mode , K mode ,tcase 
(4)
The vector of chassis kinematic information, assuming use of the SAE vehicle
coordinate system, is
T
x4   x , y , z , x ,  y , z , x ,  y , z , vx , vy , vz , ax , a y , az 
(5)
where  x| y| z are the roll, pitch, and yaw angles;  x| y| z are the roll, pitch, and yaw rates;
x| y| z are the roll, pitch, and yaw accelerations at the previous time step; v x| y | z are the
longitudinal, lateral, and vertical velocities at the center of gravity; and a x| y| z are the
longitudinal, lateral, and vertical acceleration at the center of gravity at the previous time
step. These quantities can be computed from chassis location r1 , orientation matrix A1 ,
angular velocity ω1 , and CG location ρ1 relative to the origin of the chassis body
reference frame, all reported by multibody dynamics, using the following equations:
Real-time dynamic simulation of vehicles with electronic stability control:
Modeling and validation


 x  atan2  A1 , A1  ,  y  atan2  A1 , A12  A12 ,  z  atan2  A1 , A1
32
33
T
31
11
21
21
T
x ,  y , z   A1T ω1 , x ,  y , z   A1T ω1
The contents of
T

(6)
(7)

vx , vy , vz   A1T  r1  ω1ρ1  ,  ax , a y , az   A1T r1  ω1ρ1  ω1ω1ρ1
T
11

(8)
x 5 depends on the ESC software to be integrated. While some of
these values are often hard-coded, for the purpose of simulation it is beneficial to have
the ability to disable ESC to facilitate the necessary comparison. Thus, a Boolean flag
I esc is included in the x5 vector and is defined as follows:
I esc
0 : disable all safety feature

1: enable ABS


2
:
enable ABS/TCS

 3 : enable ABS/TCS/ESC
(9)
On the output side, the generic interface lists three quantities for engineintervention; y1 , y2 , and y3 . They are redundant, and only one is active for a specific
ESC model. The redundancy is necessary to make the interface useful for integrating
ESC software developed by different manufacturers. A flag, I eng , must be included in the
y 6 vector to indicate which channel is to be used by multibody vehicle dynamics. The
flag is defined as follows:
0 : to disregard y1 , y2 , y3

1: to honor y1

I eng  
(10)
2 : to honor y2


3 : to honor y3
Similarly, the brake intervention quantities, y 4 and y 5 , are redundant, and only one is
active for a specific ESC model. Another flag, Ibrk , must be defined in the y 6 vector, as
follows:
0 : to honor y 4
I brk  
1: to honor y 5
(11)
2.2 Integration into vehicle dynamics
As shown in Section 2.1, ESC outputs are directed to powertrain (via engine intervention)
and brake systems. In real-time vehicle dynamics formulation, a powertrain model
consists of models for the engine, torque converter, automatic transmission, transfer case,
differential, and final drive. The inputs to the engine model are throttle opening and
current engine speed; the output is engine torque. The inputs to the torque converter are
engine torque and the speed ratio of torque convert input shaft (which equals engine
speed) to the transmission input shaft speed. Outputs are the load applied on the engine
W. Pan and Y. Papelis
flywheel and the driving torque applied on the transmission input shaft. The primary
function of all other components, including transmission, transfer case (if applicable),
differential, and final drive, is to transmit the torque at the transmission input shaft to
individual driven wheels through a sequence of gear pairs and shafts connected by
universal joints or constant velocity joints. Depending on the value of I eng , the ESC
engine intervention is achieved in different ways involving different components of the
powertrain model.
When I eng  1 , ESC directly computes the desired engine throttle engine  . This
control can be realized by simply feeding the desire throttle to the ETC model in Eq. 1;
i.e.,
  y1 , I etc  1
(12)
In the case of I eng  2 , the ESC model computes desired engine torque. Because
engine torque is an output of the engine model, a controller such as a ProportionalIntegral-Derivative (PID) controller must be designed to use the difference between the
engine output torque and the ESC-desired torque to gradually adjust the throttle until the
difference diminishes, as shown in Fig. 2. A much simpler approach is to ignore the
torque computed by the engine model and directly use the desired torque as an input to
the torque converter. This approach is equivalent to having an infinitely powerful
controller in Fig. 2 that brings the throttle to the desired value instantly. Such
implementation is shown in Fig. 3.
Some ESC software computes only the desired torque at the transmission output axle,
which corresponds to I eng  3 . In this case, a controller must be introduced to adjust the
throttle until the desired axle torque equals the torque computed from the powertrain
model, as shown in Fig. 4. It is generally not acceptable to directly apply the desired
torque at the transmission output shaft in order to maintain consistency in the powertrain
model formulation.
The model for the conventional brake system in real-time vehicle dynamics
formulation contains a model of a pneumatic/hydraulic system that transforms brake
pedal force into caliper pressure at individual wheel brakes and a model that converts
caliper pressure into brake torque for each wheel. Thus, depending on the value of I brk ,
the brake intervention function of ESC can be brought into the vehicle dynamics model in
two ways, as shown in Figs. 5 and 6. When I brk  0 , the ESC system computes the
desired caliper pressure at each wheel. The pressure is then passed to the second part of
the conventional braking system model to compute wheel brake torque. When Ibrk  1 ,
the ESC system computes the desired wheel torque at individual wheels. In this case, the
desired torque is directly applied to the wheels. Thus, the conventional brake model is
entirely bypassed. In either case, brake pressure dynamics are handled by ESC software.
The complexity of the brake pressure dynamics model in ESC software varies.
As a final note, almost all ESC software contains digital controllers, which usually
require a sampling rate of as high as 1000 Hz. When vehicle dynamics equations of
motion are integrated at the same rate, vehicle information at the current time step can be
directly passed into ESC software. When the equations of motion are integrated at a
lower rate, computed vehicle information should be re-sampled, and multiple calls to
ESC software must be made for each integration time step of vehicle dynamics.
Real-time dynamic simulation of vehicles with electronic stability control:
Modeling and validation
3
Modeling of two ESC-equipped vehicles
Two vehicle models are described in this section. All model data, except for the
powertrain and aerodynamics, were derived from measurements made by SEA, Inc. and
its subcontractors (S.E.A. Inc., 2003a; S.E.A. Inc., 2003b).
3.1 2003 Ford Expedition
The Expedition employs a short-long arm (SLA) or double A-arm suspension on all four
wheels. For each wheel a lower control arm, upper control arm, and knuckle are modeled
as bodies. The upper and lower control arms are connected to the chassis with revolute
joints and to the knuckles with spherical joints. The Expedition uses rack and pinion
steering. Only the rack is modeled as a body, and it is connected to the chassis using a
translational joint. The ratio of steering wheel angle to rack displacement is 121.0 rad/m.
The tie rods connecting the front knuckles to the rack and the lateral links connecting the
rear knuckles to the chassis are not modeled as bodies but as distance constraints to save
computational effort. The wheels are not modeled as rigid bodies; only the rotational
degree of freedom relative to the knuckle it attaches to is modeled as a state equation.
The rotational inertia for the front wheels is 2.5462 kg- m 2 and the rotational inertia for
2
the rear wheels is 2.2642 kg- m . Mass and inertia of the wheels (except rotational
inertia) are added to the knuckle bodies. A topology map showing how the bodies are
connected is shown in Fig. 7.
The mass, initial position of center of gravity (CG), and inertia of each of the bodies
are shown in Table 1. The CG locations are relative to a global coordinate system whose
origin is located at ground level directly below the front axle and at the vehicle centerline
and whose axes follow the SAE convention; i.e., x forward, y to the right, and z down.
The local coordinates used to define the inertia properties in Table 1 for the chassis are
the SAE vehicle coordinates. The x axis of the upper and lower control arms is the line
of the pivot of the revolute joint connecting the control arms to the chassis. The y axis is
normal to the line of pivot through the point of the spherical joint connecting the control
arm to the knuckle. The z axis is then normal to each of these axes. The y axis for the
knuckles is the rotation axis of the wheel pointing to the right of the vehicle. The x axis
is in the forward direction, and the z axis is downward. The x axis for the rack is along
its direction of motion. The y and z axes are arbitrarily chosen as normal to the x axis.
For each corner of the suspension, the locations of the ten points shown in Fig. 8 are
measured. Global positions of the points describing the driver-side front and rear
suspension are shown in Table 2. Symmetry is assumed about the vehicle’s centerline to
describe the passenger-side suspensions. These points are used to define the joints and
force elements on each body by converting the global coordinates into the body’s local
coordinate system.
The curves for the front and rear suspension springs and shocks are shown in Fig. 9.
The roll stiffness of the front stabilization bar is set to 125000N/rad. The roll stiffness of
the rear stabilization bar is set to 25000N/rad. These values are determined via a trialand-error procedure so the simulated roll angle best matches the test data for steering
maneuvers.
W. Pan and Y. Papelis
The powertrain model for the Expedition is based the model used for the 1997 Jeep
Cherokee (Salaani, Guenther, and Heydinger, 1999), with the following changes:


The engine map is scaled such that it generates 260 horsepower at 4500 RPM and
350 Lb-ft torque at 2500 RPM. The speed of the engine is limited to 628.3 rad/s or
6000 rpm.
Gear ratios for the Expedition’s 4-speed automatic transmission are 2.84, 1.55, 1.00,
and 0.70 for the forward gears and -2.32 for the reverse gear.

The final drive gear ratio is 3.55.
The steady-state tire model by Allen et al. (Allen, Rosenthal, and Chrstos, 1997) is
used in conjunction with the transient slip and slip angle formulation (Bernard and
Clover, 1995) to compute real-time tire forces and moments. The tire model relies
heavily on test data for accurate simulations. A full description of the model is given by
Allen, Rosenthal, and Chrstos (1997), Bernard and Clover (1995), and Salaani and
Heydinger (1998). Tire parameters for computing normal force FN , transient slip, and
transient slip angle are: tire free radius 0.397 m, tire rolling radius 0.37338 m, radial
stiffness 270394 N/m, lateral relaxation length 0.5916168 m, radial damping 2000 Nsec/m, longitudinal damping coefficient 5000 N-sec/s, lateral damping coefficient 5000
N-sec/s, and longitudinal relaxation length 0.1 m. In addition, rolling resistance is set to
2% of normal force, and the nominal friction coefficient in both longitudinal and lateral
directions is set to 0.85. Parameters for computing tire forces and moments are as
follows, where the “ft-lbf” unit system is used for all parameters unless otherwise
indicated. Meanings of the symbols can be found in references 9 and 11.
Tw  10.4 in, FZT  2403 lbf, Tp  35 psi
A0  1063.4, A1  21.169, A2  4794.7, A3  0.87326, A4  29825
Ka  0.0365, Kx  0.3014, K y  7.9655 105  0.45091FN
B1y  1.9037 104 , B3 y  1.1947, B4 y  2.2025 108
K  0.9, CSFZ=17.7325, K1  1.1993 104
C1  0.6633, C2  0.2184, C3  0.4867, C4  0.1622, C5  1.2732
G1  1.3139, G2  1.0
B1x  4.7226 104 , B3x  1.2688, B4 y  2.879 107 , K  x  0.303
Klt  3.0012  108  3.514  105  FN
The coefficients
 B1x , B3x , B4 x 
are obtained by curve-fitting the peak longitudinal
force coefficient,  px , to test data using a second-order polynomial (Allen, Rosenthal,
and Chrstos, 1997); i.e., .
 px  B3x  B1x FN  B4 x FN2
(13)
Real-time dynamic simulation of vehicles with electronic stability control:
Modeling and validation
The maximum normal load for all straight-line braking/traction tests is 1000 lb, which
is exceeded during simulation because the curb load per rear wheel is 1410 lb. It is
observed from test data that  px approaches a constant value as normal force approaches
1000 lb. Simple calculation using Eq. 13 yields an erroneous prediction when the normal
load is larger than 1000 lb. To avoid this problem, Eq. 13 is modified as follows:
 px  B3 x  B1x  min 1000, FN   B4 x  min 10002 , FN2 
(14)
The aerodynamics model and data for the Expedition are taken from the Jeep
Cherokee model in reference 8, with the cross-sectional area increased to 2.750 m 2 and
the wheelbase increased to 3.018 m.
The ESC software for the Expedition was provided by Continental-Teves. This
software models all the logic of the onboard computer that determines when to activate
the ABS, TCS, or ESC and models the hydraulics of the braking system. This software
was integrated into NADSdyna with Ibrk  1 and I eng  3 . The PID controller parameters
are
K P  0.06 / 90, K I  30 / 90, K D  1.5 / 90
(15)
3.2 2002 Oldsmobile Intrigue
The Intrigue employs a MacPherson strut suspension on the front and rear. In the front,
each wheel has a lower control arm, knuckle, and piston modeled as bodies. The lower
control arms are connected to the chassis with revolute joints and to the knuckle with
spherical joints. Each piston body is connected to the chassis with a translational joint,
and the knuckles are connected with a spherical joint. In the rear, each wheel has two
lateral links, a knuckle, and a piston modeled as bodies. The lateral links are connected to
the chassis with universal joints, and the knuckles are connected with spherical joints. As
in the front, the pistons are connected to the chassis with a translational joint, and the
knuckles are connected with a spherical joint. The Intrigue uses rack and pinion steering.
Only the rack is modeled as a body, and it is connected to the chassis using a translational
joint. The ratio of steering wheel angle to rack displacement is -141.8 rad/m. The tie rods
connecting the front knuckles to the rack and the lateral links connecting the rear
knuckles to the chassis are not modeled as bodies, but rather as distance constraints to
save computational effort. Similar to the Expedition model, the wheels are not modeled
as rigid bodies; only the rotational degree of freedom is modeled as a state equation. The
2
inertia for the front wheels is 1.3992 kg- m , and the inertia for the rear wheels is 1.3437
2
kg- m . Mass and inertia of the wheels (except rotational inertia) are added to the
knuckle bodies. A topology map showing how all bodies are connected is shown in Fig.
10.
The mass, initial position of CG, and inertia of each of the bodies are shown in Table
3. The CG locations are relative to a global coordinate system whose origin is located at
ground level directly below the front axle and at the vehicle centerline and whose axes
follow the SAE convention.
The local coordinates used to define the inertia properties in Table 3 for the chassis
are the SAE coordinates. For the front suspension, the x axis of the lower control arms is
the line of the pivot of the revolute joint connecting the control arms to the chassis. The
W. Pan and Y. Papelis
y axis is normal to the line of pivot through the point of the spherical joint connecting
the control arm to the knuckle, and the z axis is then normal to each of these axes. The
pistons have the z axis along the motion of the translational joint, and the x and y axes
are arbitrarily chosen normal to the z axis. The y axis for the knuckles is the rotation
axis of the wheel pointing to the right of the vehicle. The x axis is in the forward
direction, and the z axis is downward. The x axis for the rack is along its direction of
motion. The y and z axes are arbitrarily chosen as normal to the x axis.
For the rear suspension, the pistons have the z axis along the motion of the
translational joint, and the x and y axes are arbitrarily chosen normal to the z axis.
The lateral links have the x axis s along the length of the tubular bodies, and the y and
z axes are arbitrarily chosen normal to the x axis. The y axis for the knuckles is the
rotation axis of the wheel pointing to the right of the vehicle. The x axis is in the
forward direction, and the z axis is downward.
In addition to the body CG location, several “hard points” shown in Fig. 11 were
measured. The points describing the driver-side front and rear suspension are shown in
Table 4. Symmetry is assumed about the vehicle’s centerline to describe the passengerside suspensions. The measurements are relative to the global coordinate system--the
same as the CG locations. These points are used to locate the joints and force elements on
each body by converting the global coordinates into the body’s local coordinate system.
The curves for the front and rear suspension springs and shocks are shown in Fig. 12.
The roll stiffness of the front stabilization bar is set to 37500N/rad. The roll stiffness of
the rear stabilization bar is set to 5000N/rad. These values are determined via a trial-anderror procedure so the simulated roll angle best matches the test data for steering
maneuvers.
The powertrain model for the Intrigue is based on the model used for the 1998
Chevrolet Malibu (Salaani, Heydinger, and Grygier, 20001), with the following changes:

The engine map is scaled so it generates 215 horsepower at 5600 RPM and 230 lb-ft
at 4400 RPM. The speed of the engine is limited to 586.5 rad/s or 5600 rpm.

Gear ratios for Intrigue’s four-speed automatic transmission are 2.92, 1.57, 1.0, and
0.71 for the forward gears and -2.39 for the reverse gear. The shifting logic map for
the Jeep (Salaani, Guenther, and Heydinger, 1999) is used instead of the Malibu’s.

The final drive gear ratio is 3.29.
Tire parameters for computing tire normal force, transient slip, and transient slip
angle are: tire free radius 0.339 m, tire rolling radius 0.327 m, radial stiffness 209530
N/m, lateral relaxation length 0.5873496 m, radial damping 2000 N-sec/m, longitudinal
damping coefficient 5000 N-sec/s, lateral damping coefficient 5000 N-sec/s, and
longitudinal relaxation length 0.1 m. In addition, rolling resistance is set to 2% of normal
force, and the nominal friction coefficient in both longitudinal and lateral directions is set
to 0.85. Parameters for computing tire forces and moments are as follows, where the “ftlbf” unit system is used for all parameters unless otherwise indicated.
Tw  6.39 in, FZT  1609 lbf, Tp  34 psi
A0  309.41, A1  20.059, A2  3567.6, A3  0.74501, A4  8454
Real-time dynamic simulation of vehicles with electronic stability control:
Modeling and validation
Ka  0.0441, Kx  0.0088, K y  1.8821104  0.64896FN
B1y  3.6045 104 , B3 y  1.348, B4 y  6.4635 108
K  0.9, CSFZ=19.4019, K1  1.5125 104
C1  0.7566, C2  0.6061, C3  0.7454, C4  0.2879, C5  1.2732
G1  1.1904, G2  1.0
B1x  1.6071105 , B3x  1.0656, B4 y  2.2099 108 , K x  0.2732
K lt  6.1435 108  7.3796 10 5  FN
The peak longitudinal force coefficient,  px , is computed using the following
equation:
 px  B3 x  B1x  min 1250, FN   B4 x  min 12502 , FN2 
(16)
Aerodynamics model and data for the 1998 Malibu (Salaani, Heydinger, and Grygier,
2001) is used, with the wheelbase increased to 2.769 m.
The ESC software for the Intrigue was provided by Bosch. This software models all
the logic of the onboard computer that determines when to activate the ABS, TCS, or
ESC, and models the hydraulics of the braking system. This software was integrated into
the NADSdyna with Ibrk  1 and I eng  2 with the simplified approach shown in Fig. 3.
4
Validation
To validate the vehicle models presented in Section 3, a 2002 Oldsmobile Intrigue and a
2003 Ford Expedition were instrumented and run through a series of maneuvers in a
proving ground by Bosch and Continental-Teves, respectively. The driver response for
each of these maneuvers; i.e., steering wheel angle, accelerator pedal position, and brake
pedal force, was measured. The measured driver inputs were passed through a low-pass
Butterworth filter with a frequency cutoff of 4 Hz and then used to drive the simulated
vehicle. The measured vehicle data was compared to the simulated data for each
maneuver.
There are some known discrepancies between the NADSdyna simulation and the test
vehicle. First, outriggers were installed on the vehicle for some maneuvers for safety
reasons but were not modeled in NADSdyna as the effects were assumed to be small.
Also, acceleration values were taken at the chassis CG location in NADSdyna. The exact
location of the instruments on the test vehicle is unknown but is assumed to be fairly
close to the CG.
4.1 Straight-line acceleration
The straight-line acceleration maneuver is intended to validate the powertrain model,
including the engine torque map, transmission shifting curves, gear ratios, and torque
converter. For the Expedition model, simulations were performed to accelerate the
W. Pan and Y. Papelis
vehicle from 0 to 70 mph with throttle values of 25%, 50%, 75%, and 100%. The vehicle
speed is shown in Fig. 13. For all simulations, the speed was very close to the test data.
For the Intrigue model, simulations were performed to accelerate the vehicle from 20
to 70 mph with throttle values of 25%, 50%, 75%, and 100%. The vehicle speed
comparison is shown in Fig. 13. For the 25% throttle maneuver, the vehicle speeds are
very close throughout the simulation. The other maneuvers are not as close, but are still
fairly good.
4.2 Straight-line braking
The straight-line braking maneuver is intended to test the overall performance of the
braking system. For the Expedition, two maneuvers were performed; the results are
shown in Fig. 14. Also shown in the Fig. 14 are the time histories of brake pedal force
that were measured during the field test and fed into the simulation model. For each
maneuver, the test vehicle has a slightly larger longitudinal acceleration than the
simulation vehicle, which is seen in the vehicle speed.
For the Intrigue, simulations were performed to brake the vehicle with initial vehicle
speeds of approximately 25, 40, and 60 mph; the vehicle speed is shown in Fig. 14. Also
shown in Fig. 14 are the time histories of brake pedal force that are fed to simulation
model. Note that only brake pedal displacement was measured during the field test and
that the brake pedal force fed to simulation is computed from brake pedal displacement
using a steady-state relation between them. For each maneuver, the simulated vehicle
stops before the test vehicle. The most likely reason for the discrepancy is the lack of
actual brake pedal force time histories experienced during field test.
4.3 Pulse steer
The pulse steer maneuver is a very quick steering input to test the transient directional
dynamics of the vehicle. For the Expedition, one maneuver was performed, and the
results are shown in Fig. 15. Also shown in the figure is the time history of steering
wheel angle that was measured during the field test and fed into the simulation model. As
shown in Fig. 15, the roll rate, yaw rate, and lateral accelerations are all very close except
for the peaks of the maneuvers.
For the Intrigue, one maneuver was performed; the results are shown in Fig. 15. Also
shown in the figure is the time history of steering wheel angle that was measured during
the field test and fed into the simulation model. The steering maneuver was severe
enough to cause the intervention of ESC. The vehicle speed, lateral acceleration, and yaw
rate all match very well, which points to good overall correlation of the directional
dynamics of the vehicle.
4.4 Double lane change
The double lane change is used to test the handling of the vehicle. This maneuver is
important because it most resembles the types of maneuvers that the ESC responds to in
order to help prevent vehicle spin-out. For the Expedition, the maneuver was first
performed with ESC activated (i.e., I esc  3 in Eq. 9), and the results are shown in Fig.
17. As illustrated, there are some differences in the lateral accelerations and yaw rate
Real-time dynamic simulation of vehicles with electronic stability control:
Modeling and validation
between the test vehicle and the simulated vehicle. The brake pressures shown in Fig. 18
indicate that the ESC is activated at similar times, except for a small activation around
two seconds for the simulated vehicle. Next the maneuver was performed without ESC,
and the results are shown in Fig. 16. Here the lateral acceleration and yaw rate diverge a
little more than with ESC activated.
For the Intrigue, two double lane change maneuvers are performed at 60 mph with
and without ESC. Both maneuvers, shown in Figs. 16 and 17, give similar results. In both
cases, the lateral acceleration and yaw rate remain close until the return to the original
lane, when the simulated vehicle maintains better control and the results diverge. Brake
pressures shown in Fig. 18 indicate that the ESC is activated at very similar times, except
for the rear right wheel.
5
Conclusions
The approach to incorporating ESC software into a real-time vehicle dynamics simulation
environment is described, and its effectiveness is demonstrated through integration of
ESC software provided by Continental-Teves and Bosch. Vehicle models of a 2003 Ford
Expedition and a 2002 Oldsmobile Intrigue, both come equipped with ESC, were
developed. The results of these models have been compared with test data for several key
maneuvers, including straight-line accelerations, straight-line braking, pulse steer, and
double lane change. Results show that the timing and magnitude of the ESC activity
correlate very closely with the test results and that the simulated vehicles behave very
similarly to the test vehicles.
Areas that could use improvement are the stabilization bar model, the shock absorber
model, and the tire model. The stabilizer bar stiffness is treated as a constant, although it
is very likely that the stiffness of the stabilizer bars is nonlinear. The current shock
absorber model does not include any dependence on the frequency of the motion,
although the test data shows a clear dependence on frequency. In order to improve
accuracy in very aggressive maneuvers, a more physical-based tire model is need.
Acknowledgments
We would like to thank Continental-Teves and Bosch for their support in this effort.
Also, we would like to thank M. Kamel Salaani of the Transportation Research Center,
Inc. and Gary J. Heydinger of S.E.A., Inc. for supporting the modeling efforts in this
study.
References
Allen, R.W., Rosenthal, T.J., and Chrstos, J.P. (1997) ‘A vehicle dynamics tire model for both
pavement and off-road conditions’, Technical Paper 970559, SAE.
Bernard, J.E. and Clover, C.L. (1995) ‘Tire modeling for low-speed and high-speed calculations’,
Technical Paper 950311, SAE.
Center for Computer-Aided Design (CCAD) (1995), ‘NADS Vehicle Dynamics Simulation,
Release 4.0’, The University of Iowa, Iowa City, IA.
W. Pan and Y. Papelis
Pacejka, H.B. (2002) Tyre And Vehicle Dynamics. Butterworth-Heinemann, Oxford.
Papelis, Y., Brown, T., Watson, G., Holtz, D., and Pan, W. (2004) ‘Study of ESC assisted driver
performance using a driving simulator’, Technical Report N04-003, The National Advanced
Driving Simulator, The University of Iowa, Iowa City, IA.
Robert Bosch GmbH (1999a) Driving-safety systems [Editor-in-chief, Horst Bauer; translation,
Peter Girling], 2nd edition. Robert Bosch GmbH, Stuttgart, Germany.
Robert Bosch GmbH (1999b) Automotive electrics and electronics [Editor-in-chief, Horst Bauer;
translation, Peter Girling], 3rd edition. Robert Bosch GmbH, Stuttgart, Germany.
S.E.A. Inc. (2003a) ‘Vehicle inertia measurement facility, suspension kinematics and compliance,
shock absorber, suspension component geometric and inertia, and tire test measurement
results, 2003 Ford Expedition’, Report for Continental Teves, Continental Teves.
S.E.A. Inc. (2003b) ‘Vehicle inertia measurement facility, suspension kinematics and compliance,
shock absorber, suspension component geometric and inertia, and tire test measurement
results, 2002 Oldsmobile Intrigue’, Report for Bosch, Bosch.
Salaani, M.K. and Heydinger, G.J. (1998) ‘Powertrain and brake modeling of the 1994 Ford Taurus
for the National Advanced Driving Simulator’, Technical Paper 981190, SAE.
Salaani, M.K., Guenther, D.A., and Heydinger, G.J. (1999) ‘Vehicle dynamics modeling for the
National Advanced Driving Simulator of a 1997 Jeep Cherokee’, Technical Paper 1999-010121, SAE.
Salaani, M.K., Heydinger, G.J., and Grygier, P.G. (2001) ‘Parameter determination and vehicle
dynamics modeling for the NADS of the 1998 Chevrolet Malibu’, Technical Paper 2001-010140, SAE.
Real-time dynamic simulation of vehicles with electronic stability control:
Modeling and validation
y1 : Requested throttle opening
x1 : Driver inputs
y2 : Requested engine torque
x 2 : Wheel kinematic info
x3 : Powertrain info
x 4 : Chassis kinematic info
x5 : ABS/TCS/ESC parameters
Figure 1
y3 : Requested axle torque
ABS/TCS/ESC
Model
y 4 : Brake pressure at each wheel
y 5 : Brake torque at each wheel
y 6 : ABS/TCS/ESC status
Inputs and outputs of a generic ABS/TCS/ESC model
I esc
ˆ


ETC
Model
Engine
W. Pan and Y. Papelis
Flywheel, Torque
Converter, and
Transmission Models
Te

PID
Figure 2


y2
Integration of ESC engine intervention into powertrain system I eng  2
TTR
ˆ
Engine
Real-time dynamic simulation of vehicles with electronic stability control:
Modeling and validation
Te
min
Flywheel, Torque
Converter, and
Transmission Models
TTR
y2
Figure 3
Simpler integration of ESC engine intervention into powertrain system I eng  2
I esc
ˆ

ETC
Model

PID
Engine
W. Pan and Y. Papelis
Flywheel, Torque
Converter, and
Transmission Models
Te



y3
Figure 4
Integration of ESC engine intervention into powertrain system I eng  3
TTR
Real-time dynamic simulation of vehicles with electronic stability control:
Modeling and validation
Tb 4
Wheel 4
p1
Pnematic/Hydraulic
System Model
p4
y4 1
Figure 5
Tb1
Wheel 1
Wheel Brake 1
Wheel Brake n
y4  4 
Integration of ESC brake intervention into brake system I brk  0
W. Pan and Y. Papelis
Wheel Brake 1
Tb1
Pnematic/Hydraulic
System Model
Wheel Brake n
Tb 4
y5 1
Figure 6
Integration of ESC brake intervention into brake system when Ibrk  1
Wheel 4
p4
Wheel 1
p1
y5  4 
Real-time dynamic simulation of vehicles with electronic stability control:
Modeling and validation
2003 Expedition
-------------------------------1 Chassis
2 Steering Rack
3 Front Right Upper Control Arm
4 Front Right Lower Control Arm
5 Front Right Knuckle
6 Front Left Upper Control Arm
7 Front Left Lower Control Arm
8 Front Left Knuckle
9 Rear Right Upper Control Arm
10 Rear Right Lower Control Arm
11 Rear Right Knuckle
12 Rear Left Upper Control Arm
13 Rear Left Lower Control Arm
14 Rear Left Knuckle
r: revolute joint
t: translational joint
s: spherical joint
d: distance constraint (tie rod
or lateral link)
Figure 7
2
d
d
8
s
t
6
7
4
r
r
d
d
12
r
r
9
r
s
s
s
3
r
r
1
14
5
s
s
s
r
11
13
10
Graphical representation of a multibody model of a 2003 Ford Expedition
s
W. Pan and Y. Papelis
Figure 8
Expedition points where joints and force elements are connected
Real-time dynamic simulation of vehicles with electronic stability control:
Modeling and validation
Figure 9
Expedition suspension spring and shock absorber curves
W. Pan and Y. Papelis
2002 Intrigue
----------------1 chassis
2 strrack
3 piston_fr
4 lca_fr
5 knuckle_fr
6 piston_fl
7 lca_f1
8 knuckle_f1
9 piston_rr
10 latlink1_rr
11 latlink2_rr
12 knuckle_rr
13 piston_rl
14 latlink1_rl
15 latlink2_rl
16 knuckle_rl
d
d
2
8
5
t
s
t
t
6
s
s
7
s
3
4
r
r
d
16
t
d
13
s
s
s
1
s
u
u
14
15
u: universal r: revolute
s: spherical t: translational
d: distance (tie rod or trailing arm)
u
u
t
9
12
s
10
11
Figure 10 Graphical representation of a multibody model of a 2002 Oldsmobile Intrigue
s
Real-time dynamic simulation of vehicles with electronic stability control:
Modeling and validation
Figure 11 Intrigue points where joints and force elements are connected
W. Pan and Y. Papelis
Figure 12 Intrigue suspension spring and shock absorber curves
Real-time dynamic simulation of vehicles with electronic stability control:
Modeling and validation
Figure 13 Straight-line acceleration at 25%, 50%, 75%, and 100% throttle (left: Expedition, right:
Intrigue)
W. Pan and Y. Papelis
Figure 14 Straight-line braking (left: Expedition, right: Intrigue)
Real-time dynamic simulation of vehicles with electronic stability control:
Modeling and validation
Figure 15 Pulse steer maneuver (left: Expedition, right: Intrigue)
W. Pan and Y. Papelis
Figure 16 Double lane change maneuver with ESC off (left: Expedition, right: Intrigue)
Real-time dynamic simulation of vehicles with electronic stability control:
Modeling and validation
Figure 17 Double lane change maneuver with ESC on (left: Expedition, right: Intrigue)
W. Pan and Y. Papelis
Figure 18 Brake pressure during double lane change maneuver with ESC on (left: Expedition,
right: Intrigue)
Real-time dynamic simulation of vehicles with electronic stability control:
Modeling and validation
Table 1
Expedition mass, CG, and inertia properties (base units: kg for mass, meter for length)
W. Pan and Y. Papelis
Table 2
Initial position of the points that define joints and force elements (unit: meter)
Real-time dynamic simulation of vehicles with electronic stability control:
Modeling and validation
Table 3
Intrigue mass, CG, and inertia properties (base units: kg for mass, meter for length)
W. Pan and Y. Papelis
Table 4
Initial position of the points that define joints and force elements (unit: meter)