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Performance comparison of electric-vehicle drivetrain architectures from a
vehicle dynamics perspective
Article in Proceedings of the Institution of Mechanical Engineers Part D Journal of Automobile Engineering · August 2019
DOI: 10.1177/0954407019867491
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Original Article
Proc IMechE Part D:
J Automobile Engineering
1–21
Ó IMechE 2019
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DOI: 10.1177/0954407019867491
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Performance comparison of electric-
vehicle drivetrain architectures from a
vehicle dynamics perspective
Kerem Bayar
Abstract
Recent electric vehicle studies in literature utilize electric motors within an anti-lock braking system, traction-control
system, and/or vehicle-stability controller scheme. Electric motors are used as hub motors, on-board motors, or axle
motors prior to the differential. This has led to the need for comparing these different drivetrain architectures with each
other from a vehicle dynamics standpoint. With this background in place, using MATLAB simulations, these three drive-
train architectures are compared with each other in this study. In anti-lock braking system and vehicle-stability controller
simulations, different control approaches are utilized to blend the electric motor torque with hydraulic brake torque;
motor ABS, torque decomposition, and optimal slip-tracking control strategies. The results for the anti-lock braking sys-
tem simulations can be summarized as follows: (1) Motor ABS strategy improves the stopping distance compared to the
standard anti-lock braking system. (2) In case the motors are not solely capable of providing the required braking torque,
torque decomposition strategy becomes a good solution. (3) Optimal slip-tracking control strategy improves the stop-
ping distance remarkably compared to the standard anti-lock braking system, motor anti-lock braking system, and torque
decomposition strategies for all architectures. The vehicle-stability controller simulation results can be summarized as
follows: (1) higher affective wheel inertia of the on-board and hub motor architecture dictates a higher need of wheel
torque in order to generate the tire force required for the desired yaw rate tracking. A higher level of torque causes a
higher level of tire slip. (2) Optimal slip-tracking control strategy reduces the tire slip trends drastically and distributes
the traction/braking action to each tire with the control-allocation algorithm specifying the reference slip values. This
reduces reference tire slip-tracking error and reduces vehicle sideslip angle. (3) Tire slip trends are lower with the hub
motor architecture, compared to the other architectures, due to more precise slip control.
Keywords
Vehicle dynamics, electric-vehicle drivetrain architecture, anti-lock braking system, vehicle stability control
Date received: 16 November 2018; accepted: 10 July 2019
Introduction
Recently, there has been an increasing volume of
research carried out on experimental setups and proto-
type vehicles to target performance improvement of
vehicle’s active safety features using electric motors.
These studies consider motor braking/traction working
either solely or in tandem with the hydraulic brake
within an anti-lock braking system (ABS),1–4
traction-
control system (TCS),5,6
and/or vehicle-stability con-
troller (VSC)7–9
scheme. The general idea here is that
by utilizing the electric motor actuation, some impor-
tant performance criteria can be improved, such as a
lower stopping distance during ABS braking, or better
reference yaw rate tracking and lower vehicle sideslip
angle during active VSC. In these studies, which are
summarized below, various hydraulic–electric motor
torque-blending strategies are considered. This has led
to the need of comparing different torque-blending
strategies with each other from a vehicle dynamics
standpoint. Especially ABS and VSC systems need to
be analyzed.
Rosenberger et al.1
analyzed a drivetrain topology
named as ‘‘on-board’’ motor with side-shafts architec-
ture. The rear-wheel brake torques commanded by a
production ABS algorithm pass through the electric
Orta Dogu Teknik Universitesi, Ankara, Turkey
Corresponding author:
Kerem Bayar, Orta Dogu Teknik Universitesi, 06800 Ankara, Turkey.
Email: kbayar@metu.edu.tr

motor torque-control module first, so that the torque
commands can be overwritten. In Zhang et al.’s study,2
a pneumatic ABS actuates in coordination with electric
motor torque such that they complement each other to
get the optimal tire slip value, for an electric bus.
Through hardware-in-the-loop (HIL) simulations, it is
shown that this optimization approach enhances decel-
eration performance, that is, it reduces the stopping dis-
tance. Wang et al.3
developed an optimal predictive
control law for an electric vehicle with in-wheel motor
topology, based on state equations with the scaled vehi-
cle speed and wheel speed taken as state variables. The
proposed controller ensures robustness against vehicle
parameter uncertainties such as payload changes and
under-inflated tires. The blending strategy is that the
hydraulic brake system provides the low-frequency por-
tion of the net desired brake torque, whereas the electric
motor provides the quickly varying, high-frequency
part of it. The proposed control law is compared with
two other control laws through brake maneuver simula-
tions, sliding-mode control, and a simple proportional–
integral (PI) control law. The proposed control algo-
rithm outperforms both of these laws in terms of fol-
lowing the reference slip ratio, despite the fact that all
of them loose precision at low speeds. Ivanov et al.4
tracked an optimal slip value with a simple PI controller
for an on-board drivetrain architecture. The road test
results show that splitting the torque between the fric-
tion brakes and the electric motor results in shorter
stopping distances compared to the conventional ABS
operation without electric motor actuation.
Jalali et al.5
applied a fuzzy rule–based slip-control
algorithm for traction-control purpose, considering an
electric vehicle with four in-wheel motors. The same
control algorithm is extended for slip control during
braking maneuvers as well. Through an operator-in-
the-loop simulation scenario, the fuzzy control law is
shown to work efficiently, even under conditions such
as a split-m condition.
Chen et al.,6
performed a vehicle state estimation
using an extended Kalman filter. A simple propor-
tional–integral–derivative (PID) control law is devel-
oped for traction-control purpose, and its effectiveness
is shown through simulation work considering normal
and split-m road conditions.
Ceng et al.7
designed a state observer for an in-wheel
motored electric vehicle with direct yaw moment con-
trol using a fuzzy control approach. The local observer
design was based on the Kalman filter theory and was
combined with an interpolating mechanism which pro-
vided the link between the underlying local dynamics.
Wang et al.8
considered a vehicle lateral motion con-
trol method for an in-wheel motor drivetrain architec-
ture. The control method applied is a linear parameter-
varying-based HN control method, whose low-level
control considers tire force constraints to allocate the
control action to four wheels. Simulation results under
various driving scenarios and on different road
conditions show the effectiveness of the proposed con-
trol approach.
In De Novellis et al.’s study,9
a gain scheduling PID
controller is given, which aims at keeping vehicle side-
slip angle within the stable limits. The algorithm utilizes
an active set–based control-allocation algorithm with
respect to a typical cost function representing a balance
between control accuracy and energy. In addition to
these control laws, the algorithm includes an active
vibration control, which increases the torsional damp-
ing of the drive shafts, allowing a more precise yaw
moment modulation. The effectiveness of the devel-
oped algorithms has been demonstrated experimentally
on a test vehicle.
The literature given above possess some common
features. First one is the structure of the controller: a
high-level control algorithm, dictating a certain amount
of yaw moment and/or brake–tractive torque on the
vehicle, depending on whether the system will function
as an ABS and traction control in addition to yaw
moment control. Then this desired control action is
allocated to the electric motor torques, through an opti-
mization routine. If hydraulic friction brakes are still
actively used in the vehicle, which is the case in all pro-
duction vehicles, the final part is the blending strategy:
blending between electric motor torque and hydraulic
brake torque.
Blending electric motor (positive or negative) torque
with hydraulic brake torque is an interesting topic from
a control engineering standpoint. There are two basic
reasons of this: (1) Electric motor and hydraulic brake
are two separate actuators with different torque genera-
tion dynamics. This requires a flawless coordination
strategy for a satisfactory control performance. For
instance, in Wang et al.’s study,3
it is mentioned that
the high-frequency portion of the net desired wheel tor-
que is satisfied by the electric motor, whereas the
remaining steady portion by the hydraulic brake.
However, it is not explicitly explained how blending is
formulated. (2) The control modules that control the
electric motor torque and the hydraulic brake torque
communicate with each other through in-vehicle com-
munication networks such as controller area network
(CAN). This communication involves torque com-
mands and sensor signals (such as vehicle yaw rate and
wheel speed) as well. It is reported in previous works1,10
that time-varying delays of signals due to network com-
munication between different modules could degrade
the control performance of the entire system or even
make the system unstable. Therefore, the motor-
hydraulic brake torque blending strategy should miti-
gate the adverse effects of these signal delays. There are
linear quadratic regulator–based HN control methods
in literature, taking communication delays into account
within the controller structure.11,12
Simulation studies
show that the control system becomes robust against
signal delays with these control methods in both of
these studies.
2 Proc IMechE Part D: J Automobile Engineering 00(0)

The second commonly observed aspect in the given
literature summary is the driveline vibration-damping
control algorithms, commonly named as active motor
damping (AMD). This control feature works indepen-
dently of the high-level yaw moment/traction/braking
controller, such as explained in previous works.9,13
These control algorithms aim at damping the drive-
shaft vibrations that are caused by excitation of the dri-
veline with high-level brake/traction/yaw moment–
control algorithms. The requirement of such a damping
feature comes from the fact that the addition of electric
motors to the driveline together with their torque-
multiplying gearboxes (especially Architectures 1 and 2
in Figure 1) increases the effective inertia at wheel level.
That is to say, the inertia that ABS/TCS/VSC acts on
increases. This increases the possibility of these control
features and/or any friction brake–motor torque blend-
ing strategy to interact with the now lower drive-shaft
resonant frequency. This would not only increase the
risk of damaging the shafts, joints, or mounts but also
cause degradation in the performance of these control
features. This is observed through simulation results
that are given in coming sections of this study as well.
A conclusion on the literature summary given above
is as follows: there exist different drivetrain architec-
tures and control/blending strategies applied for electric
vehicles in the literature, but they have not been com-
pared with each other in terms of specific vehicle
dynamics performance criteria so far, except a few pub-
lished work.14,15
This observation leads to the motiva-
tion of this work with respect to the research
need regarding the literature summary given above:
Comparing (1) Different electric-vehicle drivetrain
architectures from a vehicle dynamics performance
standpoint (2) Different electric motor torque hydraulic
brake torque blending strategies for ABS and VSC pur-
pose. The expected contribution of this work to litera-
ture is as follows: an assessment with respect to clearly
expressed metrics of vehicle dynamics control, such as
stopping distance for ABS, and reference yaw rate
tracking and vehicle sideslip angle for VSC,16
and stat-
ing advantages and disadvantages of these different
architectures and blending strategies over each other.
There are five main sections in this article. In the
next section, different electric-vehicle architectures stud-
ied in literature and the simulator used to compare
them with each other are explained. In ABS and VSC
Simulations sections, ABS and VSC simulation results
are reported, respectively. The study is finalized with
the Conclusion section.
Different electric-vehicle drivetrain
architectures
Studies in literature that utilize electric motors for
active safety can be classified from a vehicle drivetrain
perspective: in-wheel motors at each corner,3,5–8
axle
motors prior to the differential, and on-board motor
drives with side shafts that are capable of commanding
separate torques to right and left wheels.1,4,10
These
combinations are illustrated in Figure 1. The architec-
ture that is observed in today’s mass produced hybrid
and/or electric vehicles is the first one: axle motor prior
to the differential.13
In-wheel motors provide significant advantages: (1)
Eliminating mechanical energy loss due to numerous
sophisticated and heavy power-transmission mechan-
isms between the motor and the wheel—clutch, trans-
mission, drive shafts, and differentials. (2) Eliminating
these driveline components provide significant weight
and manufacturing cost savings.
Despite these advantages, in-wheel motors for pas-
senger vehicles are yet to stay at a prototype level in
industry. The difficulties with in-wheel motor technol-
ogy can be summarized as follows:
1. In-wheel motors (to be more precise, any type of
electric motor) cannot be the sole source of brak-
ing a passenger or commercial vehicle due to the
following safety concerns: the space inside the
wheel is not sufficient to package an electric motor
that is powerful enough to provide braking power
during heavy braking conditions at high speeds.17
Therefore, the friction braking actuator must stay
in the vehicle. Given that the friction brakes must
remain, it is preferred to package the motor in a
location such that the friction brake assembly is
left unmodified. However, suspension components
inside the wheel hub and different types of suspen-
sion architectures enforce redesign of the in-wheel
assembly. Previous studies by Watts et al.17
and
Murata18
are examples where the redesign of the
wheel assembly is kept at a minimum level.
There are also in-wheel motor designs with gear
reducer mechanisms in literature.19,20
However,
using a reducer brings some disadvantages such as
Figure 1. Illustration of different drivetrain architectures in
literature that utilize electric motors for active safety features.
Bayar 3

complex structure with an increased number of
components and weight. The advantage though is
that, the torque requirement for the motor can be
reduced, which allows for a smaller motor size,
resulting in a more compact and lighter in-wheel
motor as a whole.
2. The weight of the electric motors increases the
unsprung mass, which affects ride comfort and
handling. The effect of unsprung mass increase on
ride can simply be illustrated using a simple 2-
degrees-of-freedom quarter car model, as shown in
Figure 2 (left). The values of the parameters for
unsprung and sprung mass, stiffness, and damping
coefficients are abbreviated by zM, zm, kM, km, and
cM, respectively. With increasing unsprung mass,
the magnitude of the sprung mass acceleration fre-
quency response function increases in the 4 to 8 Hz
band, emphasized by the shaded area in Figure 2
(right). This reduces the ride comfort level because
this is the band that the human body has the high-
est sensitivity level to vertical vibrations, according
to ISO 2631-1:1997.21
On the other hand, on-board motor architecture
with side shafts (Architecture 2 in Figure 1) is advanta-
geous from two perspectives: the wheel assembly does
not need to be modified, as the wheels are driven by
side shafts similar to a conventional vehicle.
Furthermore, gear reduction can be implemented
between the motor and the wheel satisfying high torque
requirements at the wheel.1,10
However, with such a
drivetrain architecture, the torsional vibration of the
side shafts need to be addressed exclusively, as men-
tioned above. This is simply because the torque com-
mand by the electric motors do not reach the wheel
directly as in hub motors; they pass through the elastic
half shafts. Two other factors are mass distribution and
packaging, regarding this architecture. The on-board
motors effect the mass distribution of the vehicle, this
would affect the understeering/oversteering tendency of
the vehicle. This may be prevented though, as shown in
this work as well, through controlling the electric
motors appropriately at the onset of VSC activation,
rather than traditional hardware-based chassis para-
meters such as mass distribution and suspension elasto-
kinematics.14
Packaging issue on the other hand has
been solved for the prototype vehicles according to
recent literature.9,10
The simulator used in the study
Simulink based vehicle dynamics simulator representing
a Sport Utility Vehicle (SUV) that is used in this study
is a full non-linear integrated performance, handling
and ride model that involves all degrees of freedom of
the vehicle body in space: roll, pitch, yaw, fore-aft, side-
slip, and vertical dynamics together with sprung and
unsprung mass motion, wheel and tire dynamics. The
tire force generation model is the Pacejka tire model for
combined slip.22
Tire force characteristic for asphalt
road surface is provided in Figure 3.
The driver model generates three main outputs in
order to keep a certain speed and track a specific lane:
throttle, brake, and steering wheel inputs. These out-
puts from the driver model and the signals that specify
the motion of the vehicle such as wheel speed, yaw rate,
and lateral and longitudinal acceleration measurements
(along with the associated sensor noise levels) are mod-
eled in the simulator as well considering the sampling
rate of each sensor. The sensor signals are transmitted
to the brake- and motor-control modules having 5- and
1-ms sampling periods, respectively. For the details of
the mathematical models used in the simulator, the
reader is referred to studies of Bayar and colleagues23–25
for
brevity. The parameters used for the simulator (sprung/
unsprung masses, drivetrain inertias, brake system para-
meters, etc.) belong to the hybrid electric vehicle mentioned
by Bayar et al.23,24
A picture showing the overview of the
drivetrain architecture for this vehicle is given in Figure 4.
The data for the hydraulic friction brakes were not
parametrized through experiments, rather the values
were taken from another SUV of the same class, from
dSPACE.26
Separate drivetrain models were built for
each of the electric-vehicle drivetrain architectures
Figure 2. (Left) Quarter car model and (right) the effect of
unsprung mass increase from 30 to 60 kg on ride comfort.
The parameters used: M=454kg, kM =22,000N/m, cM =900Ns/m,
km =176,000N/m.
Figure 3. Tire longitudinal force versus longitudinal slip for
asphalt road surface at a nominal tire load of 4000 N.

shown in Figure 1. The electric motor and differential
model parameters used for Architecture 1 are modified
from the values used by Bayar et al.24
The electric
motor parameters for on-board motors with side-shafts
architecture are from Goggia et al.10
and hub motor
parameters are from Watts et al.17
For electric motor
efficiency maps as a function of motor torque and
speed, the reader is referred to the corresponding refer-
ence. The torque actuation dynamics of the electric
motors is modeled with a simple first-order transfer
function: 1/1(ts + 1).
Note that despite having different powertrain config-
urations, all three architectures have identical hydraulic
brake systems. Furthermore, critical parameters that
affect vehicle dynamics performance such as the sprung
mass, vehicle mass moment of inertia, and suspension
parameters are identical as well. For a few road test
results regarding the validation of the vehicle dynamics
simulator used in the work, the reader is referred to
Bayar.27
Some of the important simulator parameters
are provided in Table 1.
ABS simulations
In the simulation scenario used for comparison of dif-
ferent drivetrain architectures and blending strategies,
Figure 4. The prototype vehicle with two axle motors prior to the differential.
Table 1. Simulator parameters.
Simulator parameters
Vehicle mass (kg) 2215
Unsprung mass (kg)
Architecture 1 Architecture 2 Architecture 3
45 45 80
Vehicle yaw moment of inertia (kg m2
) 3887 3887 3887
Vehicle roll moment of inertia (kg m2
) 723 723 723
Vehicle pitch moment of inertia (kg m2
) 3701 3701 3701
Front roll stiffness (N m/rad) 40,000 40,000 40,000
Rear roll stiffness (N m/rad) 44,750 44,750 44,750
Roll damping (N m s/rad) 5000 5000 5000
Pitch stiffness (excluding suspension) (N m/rad) 34,750 34,750 34,750
Side-shaft stiffness (N m/rad) 15,000 15,000 15,000
Side-shaft damping (N m s/rad) 65 65 65
Suspension spring stiffness (N/m) 35,000 35,000 35,000
Suspension damping coefficient (N s/m) 1500 1500 1500
Spring stiffness of tyre (N/m) 400,000 400,000 400,000
Wheel inertia (kg m2
) 1.5 1.5 2.85
Electric motor output shaft inertia (kg m2
) Architecture 1 Architecture 2 Architecture 3
0.013 0.013 –
Electric motor gear reduction ratio 10 10 –
Electric motor peak torque (N m) Front Rear 238 1000
306 271
Electric motor max speed (r/min) 10,000 10,000 10,000 1600
Bayar 5

the driver floors the brake pedal where the initial vehi-
cle speed is 50 km/h and the mean friction coefficient is
0.3; it is modeled such that it changes randomly
between 0.27 and 0.33 for each tire; representing the
uncertainty of the road profile.
The simulation results given in this section compare
different drivetrain architectures and control-blending
strategies with respect to five important criteria as
follows:
Stopping distance: the distance covered during braking
up until the vehicle completely stops.
Mean deceleration: obtained by dividing the initial
speed by the time period spent during braking,
expressed in (g).
Deviation from optimal slip: the root mean square (rms)
value of the deviation of the actual tire slip from the
ideal value (for a mean friction coefficient of mmean =
0.3, the optimal tire slip is 8% to 10% with the tire
and road adhesion model used) during braking.
The mean front and rear tire slip: the mean value for the
front and rear tire slip during braking.
Side-shaft angle of twist: The shafts’ angle of twist (the
shafts between the differential and the wheels for
Architecture 1, the shafts between the axle motor and
the wheels for Architecture 2) for the first and second
drivetrain architectures. Excessive angle of twist or
high-frequency vibrations on the shafts may degrade
the performance of ABS unless damped.
The four blending strategies evaluated for providing
the desired net braking torque at wheel level are as
follows:
Standard ABS: the standard ABS algorithm that
sequentially cuts and releases the wheel brake pressure
build-up. For the simple proportional feedback, ABS
control algorithm used in this study, the controller
gains are tuned heuristically such that the tire slip is
kept in a wider range of ( 15%) compared to the
standard conservative range of ( 7–8%) as shown in
Figure 5, so that the stopping distance is decreased.
This is achieved by keeping average tire slip closer to
the slip value corresponding to the peak tire force.
Motor ABS: in this control approach, the brake torque
pulsations commanded to the hydraulic brakes by the
ABS algorithm to regulate tire slip, is commanded to
the electric motors. The objective is to make use of three
advantages of electric motors over hydraulic brake sys-
tem in this control strategy:
1. Torque command realization of an electric motor
has a higher frequency bandwidth compared to
hydraulic friction brakes, which improves perfor-
mance (open-loop torque response bandwidth
comparison of internal combustion engine, hydrau-
lic friction brake, and electric motor can be found
in Yu’s study28
).
2. Motor torque realization is highly accurate in com-
parison to internal combustion engine and hydrau-
lic friction brakes. This is simply because current
control in an electric motor to realize the com-
manded torque can be handled with less number
of uncertainties, in comparison to internal combus-
tion engine’s and hydraulic friction brake’s torque
realization. For instance, in hydraulic braking, the
brake pad friction coefficient may change due to
wear in time; therefore, errors may be encountered
in translating the measured pressure into brake
torque
Tb = 2mbrbAbP ð1Þ
where mb is the brake pad friction coefficient (may
change with respect to vehicle speed, temperature,
and wear), rb is the effective radius between the pad
contact area and the center of the wheel, Ab is the
brake pad contact area, and P is the hydraulic pres-
sure in the brake wheel cylinder. This advantage of
motor ABS enables control designs for tracking the
desired slip more accurately within an ABS scheme.
3. A more accurate knowledge of the motor torque
enhances the estimation of the road friction coeffi-
cient and therefore the tire slip as well.29
However, ‘‘Motor ABS’’ strategy, differs from one
architecture to the other:
1. Motor ABS for Architecture 1: As shown in
Figure 1, axle motor is incapable of delivering dif-
ferent levels of torque to each side of the differen-
tial due to the open differential. Therefore, the net
brake torque demand at wheel level generated by
the ABS algorithm running in the motor-control
module is delivered according to the following sim-
ple approach: supply brake torque to the wheel
that needs a lower level of brake torque with the
electric motor and, for the remaining wheel on the
same axle that requires a higher level of brake tor-
que, generates the difference by hydraulic braking.
Figure 5. Wheel speeds for ABS simulation on asphalt.

There is an important difference between running
the ABS algorithm in the brake or the motor-control
module, with respect to ABS performance. The brake-
control module has 5-ms sampling period, whereas the
electric motor-control module has 1-ms sampling
period; by means, it becomes possible for the ABS
algorithm to command brake torque pulsation at a
higher frequency. For this reason, the ABS algorithm
developed and parametrized for 5-ms sampling period
is re-parametrized for 1-ms sampling period.
Another important aspect that was mentioned in the
introduction section is that electric motor torque com-
mand is transmitted from the brake-control module to
the motor-control module through the in-vehicle com-
munication network. The network-induced delay shows
a variable characteristic, though it is observed to be on
the order of 10 ms by Bayar et al.30
This delay is mod-
eled in the simulator as well.
2. Motor ABS for Architectures 2 and 3: As shown in
Figure 1, the aforementioned restriction for
Architecture 1 does not exist for Architectures 2
and 3; the electric motors are capable of delivering
different levels of torque to each wheel.
Torque decomposition: in this blending strategy explained
in detail by Yu and colleagues,28,31
the approach is basi-
cally decomposing the net required brake torque into two
components: a high-frequency and a low-frequency com-
ponent. For the decomposition purpose, a fourth-order
low-pass Butterworth filter is used. The low-frequency
component is commanded to the brake-control module,
whereas the high-frequency one is satisfied by the electric
motor. The torque command signal transmitted from the
motor-control module to the brake-control module is
again exposed to a 10-ms communication delay. The rea-
son of keeping the control algorithm in the motor-control
module is its faster sampling rate.
Optimal slip tracking: this control approach is based on
tracking a reference tire slip value during braking. This
method which is also applied for the VSC purpose in
VSC Simulations section applies sliding-mode control
method, which is robust against uncertainties and non-
linearities. The objective of the slip-tracking controller
is to track the reference slip values generated by a
control-allocation algorithm, which is explained in
detail by Bayar et al.24
In this algorithm, the control-
effectiveness matrix is derived as
B =
∂v
∂u
=
∂
P
Fx
∂u
∂
P
M
∂u
8
<
:
9
=
;
=
∂Fxfl
∂sfl
cos (d)
∂Fyfl
∂sfl
sin (d) a
∂Fxfl
∂sfl
sin (d) +
t
2
∂Fxfl
∂sfl
cos (d) + a
∂Fyfl
∂sfl
cos (d)
t
2
∂Fyfl
∂sfl
sin (d)
∂Fxfr
∂sfr
cos (d)
∂Fyfr
∂sfr
sin (d) a
∂Fxfr
∂sfr
sin (d)
t
2
∂Fxfr
∂sfr
cos (d) + a
∂Fyfr
∂sfr
cos (d) +
t
2
∂Fyfr
∂sfr
sin (d)
∂Fxrl
∂srl
b
∂Fyrl
∂srl
+
t
2
∂Fxrl
∂srl
∂Fxrr
∂srr
b
∂Fyrr
∂srr

t
2
∂Fxrr
∂srr
8

:
9

=

;
T
ð2Þ
and the optimization problem can be stated as
J = arg min
U
=
1
2
Bu v
ð ÞT
Wv Bu v
ð Þ +
1
2
uT
Wuu
ð3Þ
Subject to
u
j j4uthr m, a
ð Þ
where u is tire slip vector [sfl sfr srl srr]T
, constrained by
the tire slip value corresponding to the peak point of
the tire force versus slip curve.
Equation (2) is derived from the longitudinal force
and yaw moment equilibrium for the vehicle body
M( _
Vx Vyr) + Mshsr _
f
=
X
Fx = Fxfl cos (d) Fyfl sin d
ð Þ + Fxfr cos d
ð Þ
Fyfr sin d
ð Þ + Fxrl + Fxrr 0:047CDAfVx
2
ð4Þ
and
Izz _
r =
X
Mz = a Fxfl sin d
ð Þ + Fyfl cos d
ð Þ

+ Fxfr sin d
ð Þ + Fyfr cos d
ð ÞÞ b Fyrl + Fyrr

+
t
2
Fxfl cos d
ð Þ Fyfl sin d
ð Þ Fxfr cos d
ð Þ

+ Fyfr sin d
ð Þ + Fxrl FxrrÞ
ð5Þ
where Vx and Vy represent the longitudinal and the lat-
eral speeds with respect to the body-fixed reference
frame, r and _
f are the yaw and roll rates, d is the steer-
ing wheel angle, CD is the aerodynamic drag coefficient,
and Af is the vehicle frontal area. Ms represents the
sprung mass and M represents the total vehicle mass. a
and b are the distance of the center of mass to front
and rear axles, respectively.
The control-allocation algorithm takes the estimated
road adhesion coefficient as an input; it is used in the
∂Fxi/∂si expressions in equation (2); therefore, estimat-
ing m correctly is essential for this control strategy. The
reader is referred to previous works.32,33
The controller
starts with taking the slip dynamics into account
_
si =
r2
wFxi
IwVi

_
Vi
Vi
si
_
Vi
Vi
+
rw
IwVi
Ti + w ð6Þ
where rw is the rolling radius of the tire, Iw is the rota-
tional mass moment inertia of the wheel, Vi is the
Bayar 7

velocity component across wheel plane, Ti is the net
torque at wheel level, treated as the control input, and
w is the bounded disturbance term: bounded by the
maximum rate of change of tire slip due to the uncer-
tainty of road parameters and tire relaxation length.
The tire relaxation length is the parameter that directly
specifies how fast tire slip may physically vary. Its
importance is analyzed in detail in previous works34,35
rvvi Vi = Visi + s_
si ð7Þ
where vi is the angular speed of the wheel, and s is the
tire relaxation length.
The sliding surface is defined as
S = c s sdes
ð Þ + d
ð
s sdes
ð Þdt ð8Þ
where c and d are positive constants and picking the
control law as
Ti =
Iw 2cg + Vi max k + cr + 2d + c:Vi: max
smin

h i
rwc
sat S
ð Þ + rwFxi
ð9Þ
where Vimax is the maximum speed across wheel plane
(which is around the maximum speed of the vehicle), g
is the gravitational acceleration, r is the maximum rate
of change of the desired slip value as constrained by
the electric motor actuation rate and the tire relaxation
length, smin is the minimum possible tire relaxation
length, k is a positive constant affecting the rate of
attractivity of the sliding surface, Fxi is the estimated
longitudinal tire force, and sat denotes the saturation
function that typically replaces the sign function to
avoid chattering, which ensures the attractivity of the
sliding surface. The mathematical proof that states the
attractivity of the sliding surface with this control law
is not re-stated here; it can be found in Bayar et al.’s
study.24
The correct estimation of tire slip and tire longitudi-
nal forces in real time is essential for proper functional-
ity of this method. The accuracy of tire slip estimation
on the other hand depends on the correct estimation of
vehicle speed and tire rolling radius
si =
rw:wi
Vi

1 ð10Þ
Estimation of vehicle speed is carried out with the
commonly used Kalman filter approach.16
The filter is
explained in detail below.
The state equations for the vehicle speed and the
longitudinal acceleration are
ax(k + 1)
Vx(k + 1)

=
1 0
t 1
ax(k)
Vx(k)

+
1 0
0 1
z1(k)
z2(k)

ð11Þ
with ax and Vx representing the longitudinal accelera-
tion and speed, respectively. t is the sampling period
which may be 5 or 1 ms depending on whether the esti-
mation is being performed in the brake-control module
or the motor-control module. z1 and z2 represent zero
mean white noise terms due to modeling errors.
The measurement is
ax measured(k)
Vfrom fl(k)
Vfrom fr(k)
Vfrom rl(k)
Vfrom rr(k)
8

:
9

=

;
=
1 0
0 1
0 1
0 1
0 1
2
6
6
6
6
4
3
7
7
7
7
5
ax(k)
Vx(k)

+
na(k)
nfl(k)
nfr(k)
nrl(k)
nrr(k)
2
6
6
6
6
4
3
7
7
7
7
5
ð12Þ
where ax_measured represents the longitudinal accelera-
tion. The other four measurements, on the other hand,
namely Vfrom_fl,fr,rl,rr represent the vehicle speed, which
are obtained using the speeds across wheel plane for the
four corners. The expressions for each corner can be
written as follows
Vfrom fl =
Vfl Vysin d
ð Þ r asin d
ð Þ + t
2 cos d
ð Þ

cos d
ð Þ
Vfrom fr =
Vfr Vysin d
ð Þ r asin d
ð Þ t
2 cos d
ð Þ

cos d
ð Þ
Vfrom rl = Vrl
t
2
r
Vfrom rr = Vrr +
t
2
r
ð13Þ
where d is the steering wheel angle and Vy is the lateral
speed, which is estimated separately (explained in VSC
Simulations section). Note that Figure 6 representing
the planar vehicle motion is used to obtain equation
(13). Vfl, Vfr, Vrl, and Vrr in equation (13) are expres-
sions of tire slip and wheel speeds
Vi =
rivi
si + 1
ð14Þ
where s is obtained using the slip-slope method; making
use of the wheel dynamics equation
_
v =
Ths Tb rFx
Iw
ð15Þ
where Ths is the half-shaft torque (for Architecture 3, it
is the electric motor torque directly), Tb is the brake
torque, obtained from pressure measurement, Fx is the
longitudinal force, and Iw is the wheel inertia.
Neglecting _
vIw term, as it is quite smaller than the
expression in the numerator, one can express the tire
slip as
s =
Ths Tb
Cx:r
ð16Þ
where Cx is the longitudinal stiffness of the tire, which
is a function of wheel load and tire slip angle as well.
Therefore, estimation of these dynamic variables accu-
rately is essential for the estimation of tire slip using the
slip-slope method.

Note that, the slip estimation given by equation (16)
is not the final slip estimate of the control algorithm; it
is just an intermediate stage to estimate the vehicle
speed through the Kalman filter equations (11) and
(12). Once vehicle speed is estimated accurately, tire slip
is simply an expression of velocity across wheel plane,
rolling radius and wheel rotational speed, as given by
equation (10).
In Kalman filter, the effect of a possible acceler-
ometer signal offset on speed and acceleration equa-
tions are considered, for obtaining the elements of the
covariance matrix Q232 representing the modeling
error.
For the last four diagonal elements of the matrix
R5x5 representing the covariance of the measurement
noise, different values are taken in order to represent
the noise covariance levels of the expressions given in
equation (13) correctly. This is because estimated Vy
term, measured yaw rate, and steering wheel angle all
affect these expressions differently. These values,
including the wheel speed measurement noise can easily
be quantified through simple measurements from a
vehicle. The same holds for longitudinal acceleration
measurements, utilized for representing the covariance
of na (k).
The noise covariance factors for the longitudinal
acceleration and wheel speeds are modified dynamically
in real time with a look-up table. The look-up table is
tuned such that at high decelerations, such as during
ABS operation, the noise covariance values for nfl,fr,rl,rr
are increased considering wheel speeds would have a
high error in terms of representing the actual vehicle
speed due to high amount of brake slip.
Estimation of the tire longitudinal forces on the
other hand is carried out using the conventional
method of making use of wheel speed and brake pres-
sure measurements36
Fxi =
Tihs TBi Iv _
vi
rv
ð17Þ
where Tihs is the half (side) shaft torque, Tb is the brake
torque given by equation (1). One major advantage of
an electric drivetrain is that the side-shaft torque Tihs
can be estimated with a much higher accuracy as
explained in the ‘‘Motor ABS’’ section, compared to a
conventional vehicle with an internal combustion
engine powertrain. The highest accuracy is naturally
observed for Architecture 3, where there is no drive-
shaft stiffness and damping that should be considered
in the estimation algorithm.
The restriction for Architecture 1 explained above
for motor ABS strategy is valid for torque decomposi-
tion and optimal slip-tracking control-blending strate-
gies as well; the smaller magnitude brake torque
demand is satisfied by the electric motor, whereas the
difference due to the higher magnitude brake torque
demand is generated by the corresponding side’s
hydraulic brake torque. Note that since the hydraulic
brake torque and electric motor torque time response
characteristics are much faster than the vehicle chassis
dynamics (the reader is referred to Yu28
again), the
actuation rate constraints do not pose a critical limiting
factor on chassis control with this torque-splitting
strategy. However, the effect of this split strategy on
drivetrain dynamics, and designing a robust shaft
vibration-damping control algorithm that works in
coordination with the higher level ABS will be the
focus of the next phase of this research.
One final comment about all four aforementioned
control strategies, considering all architectures, is that
in case an electric motor fails, the hydraulic brake tor-
que would act as a backup. Furthermore, there are
fault-tolerant control approaches in literature, that are
activated in case any of the in-wheel motors for
Architecture 3 fails. For an example of such a study,
the reader is referred to Wang and Wang.37
ABS simulation results
1. Standard ABS control approach gives slightly dif-
ferent results for all architectures: best is
Architecture 3, 53 m; Architecture 2, 59 m; and
Architecture 1, 63 m, follows from a stopping dis-
tance standpoint, as given in Table 2.
The drivetrain component that is unique for
Architecture 1 is the open differential mechanism that
delivers equal amount of torque to each side, shown in
Figure 7. In this figure, vem and Tem represent electric
motor speed and torque (torque is 0 for standard
ABS); Iinput is the inertia of the gear connecting the
electric motor and the differential; imain is the main gear
reduction ratio; Icage, Iin, Ir, and Il represent the inertias
of the cage, inner bevel gear, and right and left gears;
and vleft and vright are the rotational speeds of the left
Figure 6. The vehicle and the body-fixed coordinate frame in
planar motion. Vx and Vy represent the longitudinal and lateral
velocities, r is the yaw rate, b is the vehicle sideslip angle, and a
and b represent the distance between the center of gravity and
the front and rear axles, respectively.
Bayar 9

and right shafts connected to the wheels, respectively
(assuming an infinitely high torsional stiffness—equa-
tion (18) is derived with this assumption; i.e. shaft
speed is equal to wheel speed).
With this mechanism, the effective inertia at wheel
level on which the net brake torque acts on increases,
as mentioned in the Introduction section. The wheel
dynamics equation with the open differential can be
expressed as follows
_
vleft =
0:5imainTem TBleft rFxleft
Icage + Iinput + Iem
ð Þi2
main
2 + Il + Iwheel
ð18Þ
where Tleft and Fxleft represent the left wheel brake tor-
que and tire brake force, respectively, and Iem represents
the electric motor output shaft inertia.
Since there is no differential in Architecture 2, the
effective inertia at wheel level is relatively higher
Itotal = Iw + IemI2
main ð19Þ
Because of this reason, the ABS algorithm needed to
be re-parametrized for Architecture 2. Another concern
is that vibration-damping control strategies that were
mentioned in the previous section to dampen the side-
shaft vibrations caused by this increase in effective
wheel inertia have not yet been developed at the current
stage of this research, thus the adverse effects of these
vibrations on ABS performance is another reason for
reparametrizing the ABS algorithm. By letting tire slip
Table 2. ABS simulation results.
Stopping
distance (m)
Mean
deceleration
(g)
Deviation from
optimal slip
(% rms)
Mean tire slip Side-shaft angle
of twist (°)
Front Rear
(%) (%)
Architecture 1
Axle motor prior to differential
Standard ABS 63 0.15 8 2 2 –0.9 to 1.2
Motor ABS 58 0.18 10 4 3 –5.4 to 0.6
Torque decomposition 62 0.16 8 2.7 2.2 –4.8 to 1.8
Optimal slip tracking 27 0.37 2 13 11 –4.5 to 0
Architecture 2
On-board motor with side shafts
Standard ABS 59 0.16 8 3.4 2.7 –0.9 to 1.5
Motor ABS 59 0.16 10 4.8 4.2 –6 to 0.6
Torque decomposition 60 0.16 8 3.0 2.5 –6 to 2.4
Optimal slip tracking 27 0.37 2 16 14 –4.5 to 0
Architecture 3
Hub motor
Standard ABS 53 0.16 8 2 1.3 –
Motor ABS 50 0.19 8 4 3 –
Torque decomposition 53 0.18 8 4 4 –
Optimal slip tracking 25 0.39 2 16 14 –
Figure 7. Open differential mechanism and associated inertias
and speeds.
Figure 8. Simple AMD strategy damping the high-frequency
component of the side-shaft vibration.

vary in a wider range (this can be observed from mean
tire slip values of Table 2). Standard ABS achieves a
better stopping distance for Architecture 2 (59 m) com-
pared to Architecture 1 (63 m).
On the other hand, there is neither differential nor
side shaft for Architecture 3; however, the hub motors
weighing 35 kg each increases the wheel inertia from 1.5
to 2.85 kg m2
. The ABS algorithm was re-parametrized
again, considering this change for Architecture 3. This
time, as there are no side-shaft vibrations that affect
ABS performance, the best stopping distance, 53 m, for
this standard approach follows.
2. With the motor ABS algorithm, the tire slip can be
controlled more precisely, by getting closer to the
peak point of the force versus slip curve, due to the
superiority of the electric motor as an actuator.
This improves the stopping distance, compared to
the standard ABS algorithm (reduces to 58 m for
Architecture 1, and 50 m for Architecture 3).
Another result that needs to be emphasized is the
increase in side shafts’ angle of twist due to the
motor ABS algorithm. The brake torque com-
manded at a higher frequency with the electric
motor increases the shaft angle of twists by a factor
of three compared with the ones for the standard
ABS algorithm (increases from a range of 2° to a
range of 6° on average, for Architectures 1 and 2)
due to lack of shaft vibration–damping strategies.
The reason of this is the fact that increasing the fre-
quency of the commanded torque may end up
interfering with the natural frequency of the drive-
line, as mentioned earlier. Simulation results
obtained by activating a simple AMD control
strategy based on pole-placement control method
are shown in Figure 8. It is observed that the high-
frequency component of the side-shaft vibration
for Architecture 2 may resonate the shaft and cause
the overall twist angle to increase in an uncon-
trolled way unless taken care of.
3. Torque decomposition strategy induces an increase
in side-shaft angle of twist variation, by an amount
of 1° on average for Architectures 1 and 2, com-
pared to motor ABS. This is because of the need to
add the low-frequency hydraulic brake torque with
positive motor torque occasionally, in order to
obtain the required net brake torque at wheel level,
as illustrated in Figure 9. This imposes extra side-
shaft angle of twist. Therefore, unless a driveline
vibration-damping strategy is applied, torque
decomposition strategy is recommended to be
applied only for Architecture 3, where this condi-
tion will not be an issue.
Another aspect of torque decomposition blending
strategy is the fact that it is superior to motor ABS
especially for Architectures 2 and 3. As mentioned
previously, the simulation results of Table 2 represent a
braking scenario where the initial vehicle speed is
50 km/h and mean friction coefficient is 0.3. However,
for a braking scenario where the initial speed is much
higher and the ground is asphalt, the maximum brake
torque the motors can generate will not suffice to
achieve the desired deceleration level, which is observed
in the next subsection Split-m simulations. In such a
case, there will be a need to add hydraulic brake torque
at the top of motor torque within the context of a coor-
dination strategy such as torque decomposition.
4. Optimal slip-tracking control strategy is the best
among four strategies in terms of stopping dis-
tance, with tire slip values staying closest to the
peak point of the longitudinal force versus tire slip
curve (the reader is referred to Figure 10 for wheel
and vehicle speed simulation results). Stopping dis-
tance improvement is remarkable; 50% on average
compared to standard ABS, motor ABS, and tor-
que decomposition strategies for all architectures.
Split-m Simulations
Another braking maneuver that needs to be considered
for simulation to compare different drivetrain architec-
tures and blending strategies is the ‘‘split-m’’ condition.
Figure 9. Torque commands for the hydraulic brake and the
electric motor, for Architecture 2 torque decomposition
strategy, during ABS maneuver. Second (multiplied by the gear
ratio) and third rows add up and yield the first row, that is, the
net desired wheel torque.
Bayar 11

Table 3 shows simulation results of a braking scenario
on such a surface where the initial vehicle speed is
90 km/h, left wheels are on asphalt (m = 1) right wheels
are on a surface with m = 0.3 and the brake pedal is
floored. The control strategies compared are the stan-
dard ABS and the optimal slip tracking. Motor ABS
and torque decomposition strategies are not simulated
because it was already concluded in the previous sec-
tion that optimal slip tracking is the best one in terms
of stopping distance improvement. Simulation results
can be assessed as follows:
1. In standard ABS strategy, brake torque applied on
left and right wheels generate a lower slip level for
the left wheels (1% for all architectures) compared
to the right wheels that are on a more slippery sur-
face (8% for front ones and 5% for rear ones on
average, considering all architectures), as can be
observed in Figure 11—left. Although these differ-
ent levels of slip generate (almost) equal amount of
brake force which prevents unintended yawing of
the vehicle, the deceleration level of the vehicle is
restricted by the right wheels that are on the
slippery surface. It leads to a quite high level of
stopping distance, 140m on average considering
all architectures.
2. Optimal slip-tracking strategy is based on tracking
reference tire slip values, as mentioned above. The
critical point in the split-m braking scenario is how
the reference values are selected. If the vehicle is
unintentionally yawing without any steering wheel
input during ABS braking, the control-allocation
algorithm automatically sets reference tire slip val-
ues for each tire such that the net yaw moment of
the vehicle is made 0. These values correspond to
9% and 2% on average for the right and left wheels.
The reason of these specific reference tire slip values
comes from tire force generation characteristics, it
can be found considering Figure 3 (with no slip
angle) and the longitudinal force characteristic on a
surface with an adhesion coefficient m 0.3. By
means, the braking forces on each side of the vehicle
become equal and unintentional yawing of the vehi-
cle is avoided. Here, it should be stated that this
strategy does not let any uncontrolled vehicle yaw at
all. Adhesion coefficient and normal load for each
tire is estimated separately anyway; therefore, in the
small time gap between flooring, the brake pedal
and ABS activation, where the control allocation
sets the aforementioned reference tire slip values, the
amount of vehicle yaw is almost 0; in the simulation,
it comes out to be just 3°/s. It should also be stated
at this point that in the vehicle simulator, the driver
is modeled such that, during the initial phase of
braking, at the onset of an unintentionally yaw, right
before the control algorithm acts, the driver does
not give any steering input to the vehicle to correct
the yawing. This is automatically achieved by the
control allocation algorithm.
3. In both strategies, the deceleration is limited
because of the right wheels that are on the slippery
Figure 10. Results of the simulation for optimal slip-tracking
strategy for Architecture 3. The tire slip settling at its optimal value
optimizes the deceleration level and stopping distance as well.
Table 3. ABS split-m simulation results.
Stopping distance (m) Mean deceleration (g) Mean tire slip Side-shaft angle of twist (°)
Front–rear (%)
Architecture 1
Standard ABS 145 0.22 1 8 1 6 –0.4 to 0.75
Optimal slip tracking 79 0.45 5 12 4 11 –3.75 to 0
Architecture 2
On-board motor with side shafts
Standard ABS 140 0.22 1 8 1 5 –0.25 to 0.5
Optimal slip tracking 81 0.44 3 11 2 9 –7.5 to 0
Architecture 3
Hub motor
Standard ABS 137 0.24 1 7 1 3 –
Optimal slip tracking 69 0.5 4 11 2 10 –

surface; however, since the reference slip values are
tracked better with the optimal slip-tracking strat-
egy, thanks to the sliding-mode controller as seen
in Figure 11 (right), the stopping distance and
mean deceleration performances are much better.
Stopping distance improvement is around 40% on
average, considering all architectures.
4. With the optimal slip-tracking strategy for
Architecture 2, an average net brake torque of
1500, 730, 950, and 600 Nm for the front-left,
front-right, rear-left, and rear-right wheels, respec-
tively, is provided by the electric motor solely,
thanks to the torque multiplication with the single-
speed gearbox, without any hydraulic braking.
However, for Architecture 3, the hub motors are
not able to generate sufficient braking torque for
tracking the desired tire slip values, due to the tor-
que limit of the hub motor. Figure 12 shows the
simulation result for the motor torque and the
brake torque for the front-left wheel for this man-
euver. They add up and provide the required total
brake torque for tracking the average reference slip
value of 2% for this tire.
VSC simulations
In the VSC simulation scenario, the initial vehicle speed
is 90 km/h, and the mean tire–road friction coefficient
is 1, representing dry asphalt (modeled in such a way
that varies between 0.97 and 1.03 randomly). The driver
gives the following handwheel angle input as shown in
Figure 13 for a lane-change maneuver.
The results given in Table 4 in subsection Evaluation
of the VSC Simulation Results compare different archi-
tectures and blending strategies in terms of five perfor-
mance metrics:
Yaw rate error: the deviation of the actual yaw rate of
the vehicle from the ideal one specified by the reference
Figure 11. Architecture 2 simulation results; wheel speeds and vehicle speed: (left) standard ABS strategy and (right) optimal slip-
tracking strategy. Optimal slip-tracking strategy tracks the reference slip values much better which yields better braking performance.
Figure 12. Optimal slip-tracking strategy split-m simulation results for Architecture 3. Front-left brake torque, and the motor
torque, saturating at its maximum limit 1000 Nm. Together they provide the required net brake torque.
Figure 13. Lane-change maneuver steering wheel input for the
VSC simulations.
Bayar 13

bicycle model as the vehicle is steered, shown in Figure
14. The desired yaw rate expression given by
rd(s) =
aV2
xM
2lCr
s + Vx
MIzV2
x
4lCfCr
s2
Cf + Cr
ð ÞIzVx + MVx a2Cf + b2Cr
ð Þ
2lCfCr
s + kusV2
x + l
d(s)
ð20Þ
is saturated by (g.m)/Vx; that is road adhesion limits,
where m is the estimated adhesion coefficient, kus is the
understeer coefficient, and is usually selected to be 0
kus 1 to have a control that will yield a slightly
understeer stable vehicle. Bayar et al.24
showed that by
tuning the understeer coefficient appropriately, exces-
sive sideslip angles can be avoided.
Maximum vehicle sideslip angle: the maximum value of
the angle that determines the stability and steerability
of the vehicle that is intended to be kept in a certain
band rather than regulating directly. It is the angle b
shown in Figure 14, as well as in Figure 6.
Deviation from the initial vehicle speed: the maximum
deviation from the initial vehicle speed during the man-
euver after activation of VSC.
Maximum tire longitudinal slip: an indication of how
much tire force is utilized to generate the required cor-
rective yaw moment.
Side-shaft angle of twist: the shafts’ angle of twist (the
shafts between the differential and the wheels for
Architecture 1, the shafts between the axle motor and
the wheels for Architecture 2) for the first and second
drivetrain architectures. It was mentioned in the ABS
section that, excessive angle of twist or high-frequency
vibrations on the shafts may degrade the performance
of ABS unless damped. Same condition holds for VSC.
Three different control/blending strategies are evalu-
ated as follows:
Standard VSC: this control algorithm, explained by
Van Zanten36
and attempted to be modeled by
Bayar,27
aims at tracking the reference yaw rate gener-
ated by the bicycle model and keeping the vehicle side-
slip angle at a certain stable band. Inner-rear wheel is
braked against understeering, and outer-front wheel is
braked against oversteering.
Torque decomposition: the blending strategy that was
explained and used for the ABS simulations in the previ-
ous section as well. This time, the net brake torque
request generated by the VSC algorithm (running in the
brake-control module with a 5 ms sampling rate) is
decomposed into a low-frequency and a high-frequency
component, the former provided by the hydraulic brake,
whereas the latter is satisfied by the electric motor.
Optimal slip tracking: the control algorithm that gener-
ates the brake torque for tracking the reference yaw
rate and distributes it to the hydraulic brakes and the
Table 4. VSC simulation results for lane change on dry asphalt.
Maximum
reference yaw
rate tracking
error (°/s)
Maximum
vehicle
sideslip
angle (°)
Deviation from initial
vehicle speed (km/h)
Maximum tire slip Side-shaft angle
of twist (°)
FL FR RL RR
(%) (%) (%) (%)
Architecture 1
Standard VSC 4.6 4.8 1.6 10 10 3 3 0.15 to 3.6
Torque decomposition – – – – – – – –
Optimal slip tracking 3.2 6.4 1.6 3 3 3 4 –1.2 to 3.9
Architecture 2
On-board motors with side shafts
Standard VSC 5.6 5.0 0.9 17 21 4 5 0 to 4.53
Torque decomposition 5.5 4.8 0.9 10 14 3 4 –3 to 6
Optimal slip tracking 3.2 6.7 1 2 2 3 4 –1.8 to 5.7
Architecture 3
In-wheel motor
Standard VSC 4.1 4.6 1.0 10 15 3 3 –
Torque decomposition 3.8 4.6 1.0 10 13 3 3 –
Optimal slip tracking 3.0 5.7 0.6 2 2 2 2 –
FL: front left; FR: front right; RL: rear left; RR: rear right.
Figure 14. Bicycle model used to generate the reference yaw
rate, where, d is the steering angle; Vx and Vy are the longitudinal
and lateral speed of the vehicle; r is yaw rate; b is vehicle sideslip
angle; af and ar are the front and rear slip angles; Fxf, Fyf, Fxr, and
Fyr represent the front and rear tire longitudinal and lateral
forces; a and b are distances form front and rear axles to the
center of mass; l is the wheelbase; and dom denotes the
direction of motion of the vehicle.

electric motor. Figure 15 shows this hierarchical con-
troller for tracking the reference yaw rate and vehicle
speed without causing excessive vehicle sideslip angles
that would cause instability. The inputs to the control-
ler are measured yaw rate, wheel speeds, lateral and
longitudinal accelerations (ax and ay in the figure), and
accelerator, brake pedal, and steering wheel input (a, g
and d) that come from the driver. The outputs of the
controller are motor and brake torque commands
(TEMi and TBi) that are fed into the powertrain and the
brake models. The control-allocation algorithm that is
run in the electric motor-control module was explained
by equations (2)–(5) in the ABS section, it is not re-
explained here for brevity, it may be found in Bayar et
al.’s study.24
An important variable that is estimated in the algo-
rithm is the lateral speed, or the sideslip angle. The
method used for estimation is the classical approach
adopted from Van Zanten.36
In this approach, vehicle
sideslip angle is first obtained by two different ways.
The first one is using the accelerometer and yaw rate
signals, together with the estimated longitudinal speed
_
b =
ay
Vx
r b ax
Vx
b tan b
ð Þr
1 + b2
ð21Þ
The second one is first estimating the lateral forces,
by properly filtering the expression below (recall
Fx_estimated is obtained through equation (17))
Fy estimated = Fx estimated
Csa
Cxs
ð22Þ
where a is the tire slip angle, Cs and Cx are the tire cor-
nering and longitudinal stiffness values, respectively.
Once Fy values are computed, lateral speed can be
obtained through the following equation, which can be
derived from Figure 6, neglecting roll motion of the
vehicle
Vy =
ð P
Fy
M
Vxr

dt ð23Þ
This approach can be found in Tseng et al.’s38
study
as well.
Next is the decision of fusing the two methods with
each other, depending on tire slip condition. When slip
is low, the weighting of equation (21) is increased,
whereas during heavy braking which causes tire slip to
increase, weighting of the above expression is increased.
The reason of this is that in order for equation (22) to
give accurate results, tire slip should not be at low val-
ues. The look-up table used for this purpose is shown in
Figure 16. The weighting factor is applied with respect
to the following equation
best = 1 l
ð Þbfrom Eq17 + lbFbased ð24Þ
where bfrom_Eq17 is the integral of the expression given
by equation (21) and bFbased comes from equations (22)
and (23).
Evaluation of the VSC simulation results
1. It is observed from the lane-change maneuver on
dry asphalt simulation results of Table 4 that with
each architecture with the standard VSC algo-
rithm, the vehicle speed reduction is avoided. The
deviation from the initial vehicle speed of 90 km/h
is kept at 1 km/h on average, considering all archi-
tectures. The reason of this is that the outer wheel
is braked to prevent oversteering during the man-
euver (which can be observed from the high front
tire slip values of Table 4 for the standard VSC
algorithm—10% for Architecture 1, 19% for
Architecture 2, and 13% for Architecture 3),
Figure 15. Overall structure for the optimal slip-tracking
strategy, along with the inputs coming to it from the vehicle and
the driver.
Figure 16. The weighting factor as a function of tire slip values.
Bayar 15

whereas the driver is simultaneously applying the
accelerator pedal, in order to keep vehicle speed
constant. The rapid actuation capability of the
electric motors enables reacting to this input com-
ing from the driver. In addition to this, by allowing
a yaw rate tracking error of 4.6°/s with this algo-
rithm, the vehicle sideslip angle was kept in a sta-
ble band below around 5° on average considering
all architectures. This result is shown in Figure 17
as well. If it is predicted by the algorithm that the
vehicle sideslip angle would increase to a value
exceeding the steerability limit of the vehicle, then
the understeer coefficient is tuned such that yaw
rate tracking is sacrificed by a small amount. This
is done heuristically with the rule-based fuzzy con-
trol toolbox of MATLAB-Simulink within the
simulator,27
for the standard VSC algorithm. The
vehicle steerability threshold is formulated by the
following equation from Kiencke and Nielsen16
bmax = m 108
78 V
40 m=s
2
#
ð25Þ
The difference of Architecture 2 and Architecture 3
from Architecture 1 is the increase in front tire slip val-
ues (from 10% in Architecture 1% to 19% for
Architecture 2 and to 13% for Architecture 3). It was
explained by equations (18) and (19) that the higher
affective wheel inertia of Architecture 2 and
Architecture 3 dictates a higher need of wheel torque in
order to generate the tire force required for the desired
yaw rate tracking. A higher level of torque on the other
hand causes a higher level of tire slip and a wider range
of side-shaft angle of twist (for Architecture 2). The
ABS algorithm had to be re-parametrized for
Architecture 2 and 3 simulations in order to prevent
the ABS from blocking the high front tire slip values
generated with this VSC algorithm.
2. Torque decomposition blending/control strategy
would not be very meaningful for Architecture 1,
since the axle motor prior to differential distributes
the same amount of torque to each side, and the
yaw moment generation would be achievable only
by adding hydraulic brake torque to one side
again. Therefore, this algorithm is applied to
Architectures 2 and 3 only.
With this VSC algorithm, the high-frequency compo-
nent of the net wheel torque is satisfied by the electric
motor in a more rapid and precise fashion compared to
standard VSC. This results in achieving the same refer-
ence yaw rate tracking and sideslip angle performance,
with a lower tire slip trend, especially for Architecture 2;
mean front tire slip decreases from 19% to 12% for
Architecture 2, and from 13% to 12% for Architecture 3.
The comment that was made for the ABS simula-
tions is valid for the VSC simulations considering stan-
dard VSC and torque decomposition control strategies:
the addition of a vibration-damping strategy would fur-
ther improve the performance of these VSC strategies,
controlling the net wheel torque more precisely by elim-
inating the undesired vibrations in the side shafts.
3. Optimal slip-tracking control strategy is superior to
the other two control strategies in terms of refer-
ence yaw rate tracking and maximum tire slip val-
ues; maximum yaw rate tracking error is reduced
by 30% on average, considering all architectures.
This is achieved along with a great reduction in tire
slip values; they are in the 2% to 3% range, track-
ing the desired slip values dictated by the control-
allocation algorithm. The cost is a slight, yet negli-
gible increase in vehicle sideslip angle; 1.6°, 1.7°,
and 1.1° increase compared to the standard VSC,
for Architectures 1, 2, and 3, respectively (still
within the boundary specified by equation (25),
7.8° for this maneuver). Furthermore, the vehicle
speed was kept almost constant during the maneu-
ver; the speed reduction is 1 km/h on average, con-
sidering all architectures, similar to the standard
VSC control algorithm. This shows the other main
benefit of using this control algorithm compared to
the previous control algorithms. This control
Figure 17. Standard VSC algorithm control performance for Architecture 2. Sideslip angle increase is avoided between the 4th and
5th seconds and the 6.5th and 7th seconds by sacrificing reference yaw rate tracking.

algorithm utilizes the capability of accelerating the
front inner wheel in addition to braking the outer
one against oversteering of the vehicle automati-
cally, with the accelerator pedal position
unchanged during the maneuver. This can be
achieved with a higher accuracy level for
Architecture 2 and 3, since the electric motor tor-
que delivered to the left and right wheels are inde-
pendent of each other.
Results of applying optimal slip-tracking control
strategy for different steering maneuvers on different
road-tire adhesion conditions for Architecture 1 can be
found in Bayar et al.’s study.24
Tables 5–7 show a sum-
mary of the simulation results of applying this control
strategy for all architectures, considering a lane-change
maneuver on a road surface with an average m = 0.5
representing wet asphalt, and J-turn maneuver on aver-
age m = 1 and m = 0.5 surfaces. The results are
compared with the standard VSC control strategy. The
steering wheel angle input for each maneuver is shown
in Figure 18. For the J-turn maneuver, the driver
brakes and simultaneously steers the vehicle at around
t = 1.5 s in order to follow a desired speed trajectory,
which is also shown in Figure 18.
The main observation from Table 5 is that both stan-
dard VSC and optimal slip-tracking strategies achieve a
good performance of tracking the desired yaw rate; the
yaw rate tracking error is kept at around 2.4°/s and
2.1°/s on average for standard VSC and optimal slip-
tracking control strategies, respectively, considering all
architectures. The error is reduced for Architecture 2
(from 2.9° to 2.5°) and Architecture 3 (from 2.4° to
1.7°) with the optimal slip-tracking control strategy,
compared to the standard VSC strategy. Vehicle side-
slip angle on the other hand is kept below the steerabil-
ity limit during this maneuver, except the optimal slip-
tracking strategy Architecture 1. The limit computed by
Table 5. VSC simulation results for lane change on wet asphalt.
Maximum
reference yaw
rate tracking
error (°/s)
Maximum
vehicle
sideslip
angle (°)
Deviation
from initial
vehicle speed
(km/h)
of twist (°)
FL FR RL RR
(%) (%) (%) (%)
Architecture 1
Standard VSC 2.0 3.4 0.9 8 7 1 1 0–2.1
Architecture 2
Standard VSC 2.9 3.4 0.5 10 6 1 2 0–2.4
Architecture 3
In-wheel motor
Standard VSC 2.4 3.2 0.6 7 4 1 1 –
Table 6. VSC simulation results for J-turn on dry asphalt.
Maximum reference
yaw rate tracking
error (°/s)
Maximum vehicle
sideslip angle (°)
Deviation
from initial
vehicle speed
(km/h)
Maximum tire slip Side-shaft
angle of twist (°)
FL FR RL RR
(%) (%) (%) (%)
Architecture 1
Standard VSC 3.2 4.9 1.3 15 1 3 3 –2.1 to 2.4
Optimal slip tracking 4.4 7.7 1.7 9 2 9 1 –3 to 3
Architecture 2
Standard VSC 6.5 7.3 1.4 26 2 4 1 –0.6 to 1.5
Architecture 3
In-wheel motor
Standard VSC 4.3 5.5 1.5 15 3 2 1 –
Bayar 17

equation (25) is 4° for this maneuver; it is exceeded by
0.6°, which can be easily compensated by an average
driver. Furthermore, the maneuver is handled without
any loss in vehicle longitudinal speed. This is achieved
differently for the standard VSC and the optimal slip-
tracking control strategies. In standard VSC, the front
outer wheel is hydraulically braked to prevent over-
steering (which can be observed from the high front tire
slip values of Table 5, 8% on average for Architecture 1
and 2, and 6% for Architecture 3), whereas the electric
motors are responding to the driver’s accelerator pedal
position input and generating positive torque to keep
speed constant.
On the other hand, with the optimal slip-tracking
control strategy, the reference tire slip values are com-
puted with the control-allocation algorithm (taking the
adhesion coefficient and normal tire load into account)
and are tracked by the sliding-mode slip-tracking con-
troller formulated by equation (9). By means, the same
performance can be achieved with a much lower tire
slip trend; maximum 2% on average considering all
architectures.
The same observations made for Table 4 hold for
Table 6 as well; the front outer tire braking to prevent
oversteering yields very high tire slip values; 15% for
Architecture 1, 26% for Architecture 2%, and 15% for
Architecture 3 (recall the ABS was re-parametrized to
avoid blocking the VSC torque commands). On the
other hand, with the optimal slip-tracking control algo-
rithm, this braking action is automatically split between
front and rear outer tires; to 8% considering
Architectures 2 and 3. Reference yaw rate tracking is
enhanced for Architecture 2, from 6.5°/s to 5.4°/s, side-
slip angle is decreased by 1°, from 7.3° to 6.3°. For
Architecture 1, the standard VSC performs better in
terms of reference yaw rate tracking, but again the
outer-front tire slip values are much lower for the opti-
mal slip-tracking strategy, 9% on average.
Similar observations hold for the VSC simulation
results for J-turn on wet asphalt, Table 7. Reference
yaw rate–tracking error decreases from 4.3°/s to 3.6°/s
for Architecture 2, and from 4.3°/s to 3.1°/s for
Architecture 3. Vehicle sideslip angle is decreased as
well, from 3.8° to 3.3° for Architecture 2 and from 3.5°
to 2.9° for Architecture 3. Vehicle speed deviation from
the desired speed is quite close for both standard VSC
and optimal slip-tracking control strategies. Other than
these results, the same observation made for Tables 5
Table 7. VSC simulation results for J-turn on wet asphalt.
Maximum reference
yaw rate tracking
error (°/s)
Maximum vehicle
sideslip angle (°)
Deviation from
initial vehicle
speed (km/h)
of twist (°)
FL FR RL RR
(%) (%) (%) (%)
Architecture 1
Standard VSC 2.3 3.4 1 11 1 1 1 –1.5 to 1.5
Optimal slip tracking 3.4 3.4 2 9 2 10 1 –2.4 to 2.4
Architecture 2
Standard VSC 4.3 3.8 1.1 13 1 1 0.5 –0.3 to 1.05
Optimal slip tracking 3.6 3.3 1.4 4 1 3 1 –3.6 to 0
Architecture 3
In-wheel motor
Standard VSC 4.3 3.5 1.1 8 1 1 0.5 –
Figure 18. Driver handwheel angle input for lane change and j-turn maneuvers on dry and wet asphalt surfaces, on the left, and at
the middle. Desired speed profile for j-turn maneuver on dry and wet asphalt, on the right.

and 6 holds for Table 7 as well: This enhanced perfor-
mance is achieved with much lower tire slip trends;
obtained by tracking the optimal slip values specified
by the control-allocation algorithm. The corrective yaw
moment obtained by braking the front outer tire with
the standard VSC strategy—11%, 13%, and 8%—con-
sidering Architectures 1, 2, and 3, respectively—is split
to both front and rear outer tires—9% and 10%, 4%
and 3%, and 3% and 3% considering Architectures 1,
2, and 3, respectively—with the optimal slip-tracking
control strategy. The side-shaft angle of twist range
does not change much for Architectures 1 and 2; simi-
lar ranges are observed for both architectures.
The comment made for the simulation results for the
standard VSC strategy for lane change on dry asphalt,
Table 4, is valid for lane change wet asphalt, J-turn dry
asphalt and J-turn wet asphalt as well. Higher affective
wheel inertia of Architectures 2 and 3 dictates a higher
need of wheel torque in order to generate the tire force
required for the desired yaw rate tracking. A higher
level of torque on the other hand causes a higher level
of tire slip, as a general trend. This can be observed by
comparing Architecture 2 to Architecture 1 and
Architecture 3, for the same control strategy, in Tables
4–7. Architecture 3 yields lower slip trends than
Architecture 2 in general, due to more precise tire slip
control with hub motors; 2% and 1% on average con-
sidering all tires for lane change on dry and wet asphalt,
and a maximum tire slip of 8% and 3% considering J-
turn on dry and wet asphalt, for the optimal slip-
tracking control strategy, respectively. This is due to
the fact that with hub motors, an AMD for damping
shaft vibrations is not needed, contrary to Architectures
1 and 2; more accurate reference tire slip tracking
follows.
Conclusion
It has been observed that utilization of a faster
actuator-like electric motor for providing the brake tor-
que requirement generated by the ABS algorithm,
named as motor ABS strategy in this study, improves
the performance of tire slip regulation. Being able to
command torque faster, and realizing the commanded
torque with a higher certainty with the electric motors,
yields staying closer to the peak point of the longitudi-
nal force versus slip curve. The improvement in stop-
ping distance performance is around 7%, and 6%
considering Architectures 1 and 3, compared to the
standard ABS control strategy.
In case the motors are not capable of providing the
required braking torque solely, torque decomposition
strategy becomes a good solution. For Architectures 1
and 2 where the side-shaft dynamics are important as
well, motor ABS and torque decomposition strategies
are recommended to be used with an AMD strategy to
dampen the driveline vibrations. Otherwise, the high-
frequency excitation of the shafts yields an increase in
the side-shaft angle of twist from a range of 2°–6°,
which degenerates the ABS performance.
Optimal slip-tracking control strategy improves the
stopping distance by a factor of 50% on average com-
pared with standard ABS, motor ABS, and torque
decomposition strategies for all architectures. The stop-
ping distance improvement is 40%, for the split-m brak-
ing. Furthermore, the control allocation–based optimal
slip-tracking control strategy does not let any uncon-
trolled yawing motion of the vehicle during ABS brak-
ing, by setting the reference tire slip values accordingly.
VSC simulation results for lane-change maneuver on
dry asphalt shows that with the torque decomposition
strategy, the same reference yaw rate tracking and vehi-
cle sideslip angle performance, obtained with the stan-
dard VSC can be obtained this time with lower tire slip
values; mean front tire slip decreases from 19% to 12%
for Architecture 2, and from 13% to 12% for
Architecture 3. The tire slip values are further
decreased, to the range of 3% on average for all tires,
considering all architectures, with the optimal slip-
tracking control strategy. Furthermore, reference yaw
rate tracking error is reduced by 30% on average, con-
sidering all architectures, compared to the standard
VSC strategy. The cost is a slight, yet negligible
increase in vehicle sideslip angle; which stays within the
vehicle steerability limits.
Simulation results for the lane change on wet
asphalt, j-turn on dry and wet asphalt surfaces all have
common trends: with the optimal slip-tracking control
strategy, the reference yaw rate tracking is enhanced,
for Architectures 2 and 3, compared to the standard
VSC strategy. The mean value of this improvement for
all three maneuvers is 16% for Architecture 2, and
21% for Architecture 3. Furthermore, this improve-
ment is achieved with much lower tire slip trends;
evenly distributed to the tires, in the 1–2% range for
the lane-change maneuver on wet asphalt, compared to
7–10% range for the front outer tires for the standard
VSC strategy, considering all architectures. For the j-
turn maneuver on dry asphalt, the front outer tire slip
goes up to 15%, 26%, and 15% for Architectures 1, 2,
and 3, with the standard VSC control strategy, whereas
it goes up to a maximum of 9% with the optimal slip-
tracking control strategy, and evenly distributed to
each outer tire. The same observations hold for j-turn
maneuver on wet asphalt; better yaw rate tracking and
sideslip angle performance with Architectures 2 and 3,
achieved with a much lower tire slip trend, distributed
to both outer tires.
As a general trend, higher affective wheel inertia of
Architectures 2 and 3 dictates a higher need of wheel
torque in order to generate the tire force required for
the desired yaw rate tracking. A higher level of torque
on the other hand causes a higher level of tire slip. Due
to the lack of an AMD strategy for Architecture 2, slip
levels are even higher, compared to Architecture 3. This
result is another justification for the need of an AMD
strategy for Architecture 2. In the next stage of this
Bayar 19

research, different AMD algorithms will be developed
with the objective of more accurate tire slip control dur-
ing ABS and VSC operation.
Acknowledgement
This study was conducted under The Scientific and
Technological Research Council of Turkey (Tübitak)
project number 117C015.
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest
with respect to the research, authorship, and/or publi-
cation of this article.
Funding
The author(s) received no financial support for the
research, authorship, and/or publication of this article.
ORCID iD
Kerem Bayar https://orcid.org/0000-0002-2051-8347
References
1. Rosenberger M, Uhlig RA, Koch T, et al. Combining
regenerative braking and anti-lock braking for enhanced
braking performance and efficiency. SAE technical paper
2012-01-0234, 2012.
2. Zhang J, Kong D, Chen L, et al. Optimization of control
strategy for regenerative braking of an electrified bus
equipped with an anti-lock braking system. Proc
IMechE, Part D, J Automobile Engineering 2011; 226:
494–506.
3. Wang B, Huang X, Wang J, et al. A robust wheel slip
ratio control design combining hydraulic and regenera-
tive braking systems for in-wheel-motors-driven electric
vehicles. J Franklin Inst 2015; 352: 577–602.
4. Ivanov V, Savitsky D, Augsburg K, et al. Electric vehi-
cles with individually controlled on-board motors: revi-
siting the ABS design. In: International conference on
mechatronics, Nagoya, Japan, 6–8 March 2015. New
York: IEEE.
5. Jalali K, Uchida T, McPhee J, et al. Development of a
fuzzy slip control system for electric vehicles with in-
wheel motors. SAE Int J Alt Power 2012; 1: 46–64.
6. Chen G, Zong C and Guo X. Traction control logic
based on extended Kalman filter for omni-directional
electric vehicle. SAE technical paper 2012-01-0251, 2012.
7. Ceng C, Mostefai L, Denai M, et al. Direct yaw-moment
control of an in-wheel-motored electric vehicle based on
body slip angle fuzzy observer. IEEE Trans Ind Electron
2009; 56: 1411–1419.
8. Wang R, Zhang H, Wang J, et al. Robust lateral motion
control of four-wheel independently actuated electric
vehicles with tire force saturation consideration. J Frank-
lin Inst 2014; 352: 645–668.
9. De Novellis L, Sorniotti A, Gruber P, et al. Direct yaw
moment control actuated through electric drivetrains and
friction brakes: theoretical design and experimental
assessment. Mechatronics 2015; 26: 1–15.
10. Goggia T, Sorniotti A, De Novellis L, et al. Integral slid-
ing mode for the torque-vectoring control of fully electric
vehicles: theoretical design and experimental assessment.
IEEE Trans Veh Technol 2015; 64: 1701–1715.
11. Shuai Z, Zhang H, Wang J, et al. Combined AFS and
DYC control of four-wheel-independent-drive electric
vehicles over CAN network with time-varying delays.
IEEE Trans Veh Technol 2014; 63: 591–602.
12. Zhu X, Zhang H, Wang J, et al. Robust lateral motion
control of electric ground vehicles with random network-
induced delays. IEEE Trans Veh Technol 2013; 64: 4985–
4995.
13. Liang W, Doering JA, Wang X, et al. Hybrid electric
vehicle driveline active damping and transient smoothness
control. Patent application 20140277875, USA, 2014.
14. De Novellis L, Sorniotti A and Gruber P. Design and
comparison of the handling performance of different elec-
tric vehicle layouts. Proc IMechE, Part D: J Automobile
Egineering 2014; 228: 218–232.
15. De Novellis L, Sorniotti A, Gruber P, et al. Comparison
of feedback control techniques for torque-vectoring con-
trol of fully electric vehicles. IEEE Trans Veh Technol
2014; 63: 3612–3623.
16. Kiencke U and Nielsen L. Automotive control systems.
Berlin: Springer, 2001.
17. Watts A, Vallance A, Fraser A, et al. Integrating in—
wheel motors into vehicles—real-world experiences. SAE
Int J Alt Power 2012; 1: 289–307.
18. Murata S. Innovation by in-wheel-motor drive unit. Veh
Syst Dyn 2012; 50: 807–830.
19. Makino T, Ishikawa A, Itou C, et al. Recent technology
trends of in-wheel motor system for automotive. NTN tech-
nical review no. 81, 2013, https://www.ntnglobal.com/en/
products/review/pdf/NTN_TR81_en_022-029p.pdf
20. Woodard TP. Multi-speed electric hub drive wheel design.
Master’s Thesis, The University of Texas at Austin, Aus-
tin, TX.
21. ISO 2631-1:1997. Mechanical vibration and shock—
evaluation of human exposure to whole-body vibration
part 1: general requirements.
22. Pacejka HB. Tyre and vehicle dynamics. Amsterdam: Else-
vier Science Technology, 2012.
23. Bayar K, Biasini R, Onori S, et al. Modelling and control
of a brake system for an extended range electric vehicle
equipped with axle motors. Int J Veh Des 2011; 58: 399–
426.
24. Bayar K, Wang J and Rizzoni G. Development of a vehi-
cle stability control strategy for a hybrid electric vehicle
equipped with axle motors. Proc IMechE, Part D: J Auto-
mobile Engineering 2012; 226: 795–814.
25. Bayar K and Ünlüsoy YS. Steering strategies for multi-
axle vehicles. Int J Heavy Veh Syst 2008; 15: 208–236.
26. dSPACE. Automotive simulation models 2008: Brake
hydraulics reference, https://www.dspace.com/en/inc/
home/products/sw/automotive_simulation_models.cfm
27. Bayar K. Development of a vehicle stability control strat-
egy for a hybrid electric vehicle equipped with axle motors.
PhD Dissertation, Mechanical Engineering Department,
The Ohio State University, Columbus, OH, 2011.
28. Yu H. Central electric-motoring-assisted handling control
system for electrified vehicles. IEEE Trans Veh Technol,
2015; 64: 912–925.
29. Wang R and Wang J. Tire-road friction coefficient and
tire cornering stiffness estimation based on longitudinal

tire force difference generation. Contr Eng Prac 2013; 21:
65–75.
30. Bayar K, McGee R, Yu H, et al. Regenerative braking
control enhancement for the power split hybrid architec-
ture with the utilization of hardware-in-the-loop simula-
tions. SAE Int J Alt Power 2013; 2: 127–134.
31. Yu H, Bayar K and Crombez DS. Regenerative braking
in the presence of an antilock braking system control event.
Patent 9156358B2, USA, 2015.
32. Gustafsson F. Slip-based tire-road friction estimation.
Automatica 1997; 33: 1087–1099.
33. Wang J, Alexander L and Rajamani R. Friction estima-
tion on highway vehicles using longitudinal measure-
ments. J Dyn Syst Meas Contr 2004; 126: 265–275.
34. Vantsevich VV and Gray JP. Relaxation length review
and time constant analysis for agile tire dynamics con-
trol. In: Proceedings of the international design engineering
technical conferences computers and information in engi-
neering conference, Boston, MA, 2–5 August 2015. New
York: ASME.
35. Song Z, Li J, Wei Y, et al. Interaction of in-wheel perma-
nent magnet synchronous motor with tire dynamics. Chin
J Mech Eng 2015; 28: 470.
36. Van Zanten AT. Bosch ESP systems: 5 years of experi-
ence. SAE technical paper 2000-01-1633, 2000.
37. Wang R and Wang J. Passive actuator fault-tolerant con-
trol for a class of overactuated nonlinear systems and
applications to electric vehicles. IEEE Trans Veh Technol
2013; 62: 972–985.
38. Tseng HE, Ashrafi B, Madau D, et al. The development
of vehicle stability control at ford. IEEE/ASME Trans
Mechatron 1999; 4: 223–234.
Appendix
Notation
a distance from front axle to the center of
mass
ax longitudinal acceleration
Ab brake pad contact area
b distance from rear axle to the center of
mass
cM suspension damping coefficient
Cx tire longitudinal stiffness
dom direction of motion
fl front left
fr front right
Fx/yi longitudinal/lateral force generated by the
ith tire
Fyf front tire lateral force
Fyr rear tire lateral force
imain main gear reduction ratio
Icage inertia of the differential cage
IEM electric motor output shaft inertia
Iin inertia of the differential inner bevel gear
Iinput inertia of the gear connecting the electric
motor and the differential
Il inertia of the differential left gear
Ir inertia of the differential right gear
Iw wheel rotational inertia
kM suspension spring stiffness
km tire spring stiffness
l wheelbase
P hydraulic pressure in the brake wheel
cylinder
Q modeling error covariance
r yaw rate
rb effective radius between the pad contact
area and the center of the wheel
rl rear left
rr rear right
R measurement noise covariance
si tire longitudinal slip for the ith tire
sdes desired tire slip
t track
TBi brake torque for the ith wheel
TEM electric motor torque
Ti net wheel torque
Tihs side-shaft torque for the ith wheel
na measurement noise for longitudinal
acceleration
Vfrom_i vehicle speed obtained by speed across
wheel plane for the ith wheel
ni measurement noise for speed, using ith
corner
Vi velocity component across wheel plane
Vimax maximum speed across wheel plane
Vx longitudinal speed of the vehicle
Vy lateral speed of the vehicle
z0 road profile
zm unsprung mass
zM sprung mass
af front slip angle
ar rear slip angle
b vehicle sideslip angle
best estimated sideslip angle
d front wheel steering angle
dh handwheel angle
l weighting for vehicle sideslip angle
estimation
mb brake pad friction coefficient
mmean mean road adhesion coefficient
t sampling time of the controller
vleft left side-shaft speed
vright right side-shaft speed
Bayar 21
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