Development of Antilock Braking System using Electronic Wedge Brake Model
DEVELOPMENT OF ANTILOCK BRAKING SYSTEM
USING ELECTRONIC WEDGE BRAKE MODEL
V. R. Aparow1*, K. Hudha2, F. Ahmad3, H. Jamaluddin4
, Department of Mechanical Engineering, Faculty of Engineering,
Universiti Pertahanan Nasional Malaysia, Kem Sungai Besi,
57000 Kuala Lumpur, Malaysia
1 2
Smart Material and Automotive Control (SMAC) Group,
Department of Automotive Engineering,
Faculty of Mechanical Engineering,
Universiti Teknikal Malaysia Melaka,
76109 Durian Tunggal, Melaka, Malaysia
3
Faculty of Mechanical Engineering,
Universiti Teknologi Malaysia (UTM), 81310 UTM Skudai,
Johor Bahru, Malaysia
4
ABSTRACT
The development of an Antilock Braking System (ABS) using a quarter
vehicle brake model and electronic wedge brake (EWB) actuator is presented.
A quarter-vehicle model is derived and simulated in the longitudinal
direction. The quarter vehicle brake model is then used to develop an
outer loop control structure. Three types of controller are proposed for
the outer loop controller. These are conventional PID, adaptive PID and
fuzzy logic controller. The adaptive PID controller is developed based on
model reference adaptive control (MRAC) scheme. Meanwhile, fuzzy logic
controller is developed based on Takagi-Sugeno technique. A brake actuator
model based on Gaussian cumulative distribution technique, known as
Bell-Shaped curve is used to represent the real actuator. The inner loop
controls the EWB model within the ABS control system. The performance
of the ABS system is evaluated on stopping distance and longitudinal slip of
vehicle. Fuzzy Logic controller shows good performance for ABS model by
reducing the stopping distance up to 17.4% compared to the conventional
PID and Adaptive PID control which are only 7.38% and 12.08%.
KEYWORDS: Anti-lock braking system; Electronic wedge brake; MRAC;
Adaptive PID control; Fuzzy logic
* Corresponding author email: vimalrau87vb@gmail.com
ISSN: 2180-1053
Vol. 6
No. 1
January - June 2014
37
Journal of Mechanical Engineering and Technology
1.0INTRODUCTION
Currently, vehicles have become major assets for every human in their
daily life usage. Owning personal vehicles will tend to reduce time and
save energy for humans to travel from one place to another, but this
has significantly increased the risks to the human’s life. According to
the Malaysian Institute of Road Safety Research (MIROS), there were
3.55 deaths per 10,000 vehicles and 28.8 deaths for 100,000 populations
in Malaysia every year (MROADS, 2009; Ghani & Musa, 2011). Based
on statistical analysis by MIROS, the main cause of vehicle accidents
is instability condition in which drivers lost control of the vehicle by
steering, throttle or braking input (Ghani & Musa, 2011). The major
effects of driver losing control of the vehicle are rollover and skidding
effect during cornering and braking input.
Furthermore, vehicle skidding may cause oversteer where the rear end
of vehicle slides out of the road or understeer, a condition where the
front vehicle turns over outside the road without following the curve
of the road. Other major skid effect is called four wheels skid where all
the four wheels lock up and the vehicles starts to slip in the direction
of forward momentum of the vehicle. During this condition occurring,
there is a high possibility for the wheels to stop from rotating before
the vehicle approaches to a halt. This process is known as ‘locking up’
where the braking force on the wheel is not being transferred efficiently
to stop the vehicle because of the wheels skid on the road surface (Li &
Yang, 2012). This leads to increase in the stopping distance of a vehicle
since the grip between the wheel and the road has reduced drastically.
Hence, it leads to high risk for a driver to lose control of the vehicle and
unable to avoid the disturbance (Cabrera et al., 2005).
Henceforth, a new type of braking technology has been designed
and developed by automotive designers by considering after effects
of vehicle skidding. A wide range of controllable braking technology
has been invented by including the conventional braking system with
electrical and electronics components (Aparow et al., 2013a). This type of
braking technology is commonly known as active braking system such
as electronic brake distribution (Laine & Andreasson, 2007), electronic
stability control (Zhao et al., 2006; Piyabongkarn et al., 2007), automatic
braking system (Littlejohn et al., 2004; Avery & Weekes, 2009) and also
antilock braking system (Oudghiri et al., 2007; Aparow et al., 2013a).
All this controllable braking system has been enhanced by automotive
designers as part of safety system in vehicle. However, automotive
designers have focused more on antilock braking system (ABS) since
this active braking system has high potential to avoid wheel lock up
and reduce stopping distance once emergency brake is applied. 38
ISSN: 2180-1053
Vol. 6
No. 1
January - June 2014
Development of Antilock Braking System using Electronic Wedge Brake Model
Basically, active braking known as antilock braking system was first
introduced in aircraft technology to reduce the stopping distance
of an aircraft. However, automotive researchers have adopted the
knowledge of this active braking to ground vehicle design as vehicle
safety system. Automotive researchers realized the capability of this
system to reduce stopping distance in a safer method (Oniz et al., 2009;
Aparow et al., 2013a). This active braking system was developed in
order to control locking of the wheel during sudden braking (Oudghiri
et al., 2007). In general, this type of active braking can be classified into
three categories. Firstly, ABS via hydraulic system which is developed
using hydraulic fluid used as a medium to transfer brake force from
brake pedal to brake pad and rotors (Junxia & Ziming, 2010). Secondly,
ABS via pneumatic system is designed by using air as a medium to
transfer brake pressure which has been implemented in early 60’s.
Unfortunately, this type of active braking system is applied mainly in
commercial heavy vehicle such as truck, lorry and bus (Zhang et al.,
2009; Zhang et al., 2010). Thirdly, ABS via combination of electronic and
mechanical system is invented which used combination of electronic
and mechanical systems (Yang et al., 2006). This type of braking system
is the latest technology which is also invented based on aircraft and this
technology is known as brake-by-wire.
Many types of control strategies have been developed as the results
of extensive research on antilock braking system (ABS). Control
strategies used in order to control the ABS using electro hydro brake
(EHB) and recently introduced for electronic wedge brake (EWB).
Intelligent control strategies that have been applied for ABS using EHB
are adaptive fuzzy-PID controller (Li et al., 2010), fuzzy logic control
used by Aly et al., (2011), fuzzy sliding mode controller proposed by
Oudghiri et al., (2007) and PID-particle swarm optimization (PSO)
control technique proposed by Li and Yang (2012). Since ABS via EWB is
still a new technology, many researchers such as Nantais and Minaker
(2008) and Kim et al. (2010) have put their effort in designing ABS using
simulation and applied in passenger vehicle. Moreover, Han et al.
(2012) has initiated the controller research using sliding mode control
using EWB actuator to estimate clamping force for braking. Most of
the researchers used basic control algorithm such as PID to control
ABS via EWB. However, the researchers do not identify a suitable
controller by studying different controllers and make evaluation of
their performance.
Based on previous research works such as by Oudghiri et al. (2007),
(Li et al., 2010) and Aly et al., (2011) for ABS using electro hydro brake
and Nantaiz and Minaker (2008), Kim et al. (2010), Han et al. (2012)
ISSN: 2180-1053
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January - June 2014
39
Journal of Mechanical Engineering and Technology
for ABS using electronic wedge brake, an antilock braking system is
proposed in this study. The antilock braking system was developed
using electronic wedge brake model using Bell-Shaped curve. The
proposed ABS-EWB model is a hydraulic free active braking system
where this system tends to help humans to control vehicle steering and
stability under heavy braking by preventing the wheels from locking
up. Moreover, the proposed ABS-EWB model represents an active
braking system based on brake-by-wire technology. Meanwhile, three
types of control strategy are proposed and compared in this study for
ABS-EWB model. The controllers are conventional PID, adaptive PID
and fuzzy logic controller. The main purpose of proposing these types
of controller is to identify a suitable control scheme for ABS-EWB by
evaluating the performance of the model in terms of wheel longitudinal
slip and also stopping distance of a vehicle. Adaptive PID control is
developed using model reference adaptive control (MRAC) technique
based on MIT rule while fuzzy logic is developed using Takagi-Sugeno
configuration method.
The paper is organized as follows: The second section presents the
dynamic model of the vehicle in longitudinal direction. The following
section presents the proposed control structure for the ABS inner loop
control using EWB model and outer loop control using validated
quarter vehicle model. The next section describes the integration of
both outer loop and inner loop control structures to develop an ABS
control scheme using PID, adaptive PID, fuzzy logic as the closed loop
controller. The sixth section presents the performance evaluation of the
proposed ABS control systems. The last section contains the conclusions
of this study.
2.0
DEVELOPMENT OF A QUARTER VEHICLE BRAKE
MODELING
Referring to works done by Oniz et al. (2009) and Li and Yang (2012),
the brake modeling for a single wheel with quarter vehicle mass can be
derived as mathematical equations. There are few types of responses
of the vehicle due to brake input from driver and one of the response
analyze in this study is skidding due to excessive braking. Four types
of output response can be obtained using quarter vehicle brake model
which are vehicle velocity, wheel velocity, longitudinal slip and
stopping distance of a vehicle. The following section describes in detail
on the development of the quarter vehicle model.
40
ISSN: 2180-1053
Vol. 6
No. 1
January - June 2014
Development of Antilock Braking System using Electronic Wedge Brake Model
2.1
Quarter Vehicle Brake Mathematical Modeling
The free
body diagram
a quarter
vehicle
modelThe
is as
shownsection
in Figure
wheel velocity,
longitudinal
slip and of
stopping
distance
of a vehicle.
following
describes
detail on the
of themotion
quarter vehicle
1 in
describes
thedevelopment
longitudinal
of themodel.
vehicle and angular motion
of the wheel during braking. Even though the model is quite general
wheel velocity,
slip and stopping
distance of a vehicle. The following section
2.1 Quarter
Vehiclelongitudinal
Brake Mathematical
Modeling
but it can sufficiently represent the actual vehicle system’s fundamental
describes in detail on the development of the quarter vehicle model.
et al.,
2009).
There
several
assumptions
made
The freecharacteristics
body diagram of(Oniz
a quarter
vehicle
model
is as are
shown
in Figure
1 describes the
wheel
velocity,
longitudinal
slip
and
stopping
distance
of
a
vehicle.
The
following
section
deriving
dynamic
of of
the
First,braking.
the vehicle
2.1 in
Quarter
Vehicle
Mathematical
Modeling
longitudinal
motion
of the
theBrake
vehicle
and equations
angular motion
thesystem.
wheel during
Even is
describes
in detail
on thegeneral
development
ofcan
the quarter
vehicle
wheel
slip but
and it
stopping
distance
ofrepresent
a model.
vehicle.
Theactual
following
section
though
the velocity,
model
islongitudinal
quite
sufficiently
the
vehicle
considered
in
a longitudinal
direction.
The
lateral
and
vertical
motion
describes
in
detail
on
the
development
of
the
quarter
vehicle
model.
Theoffree
body
diagram
of
a
quarter
vehicle
model
is
as
shown
in
Figure
1
describes
system’s
fundamental
characteristics
(Oniz
et
al.,
2009).
There
are
several
assumptions
the vehicle
is neglected.
Secondly,
the rolling resistance forcethe
is
Vehicle
Brake
Mathematical
Modeling
longitudinal
of
theequations
vehicle
and
angular
motion
wheelisduring
braking.
made2.1
in Quarter
deriving motion
the dynamic
of the
system.
First,ofthethevehicle
considered
in aEven
ignored
since
itlateral
is very
small
during
braking.
Thirdly,
it actual
is assumed
2.1
Quarter
Vehicle
though
the model
isBrake
quite Mathematical
general
but motion
it Modeling
can of
sufficiently
the Secondly,
vehicle
longitudinal
direction.
The
and vertical
the vehiclerepresent
is neglected.
The
free
body
diagram
of
a
quarter
vehicle
model
is
as
shown
in
Figure
1
describes
that
there
is
no
interaction
between
four
wheels
of
the
vehicle
(Oniz
et
system’s
fundamental
al.,small
2009).
Therebraking.
are several
assumptions
the rolling
resistance
force characteristics
is ignored since(Oniz
it is et
very
during
Thirdly,
it is the
longitudinal
motion
of
the
and
angular
motion
of
the
wheel
during
braking.
Theal.,
free
body
diagram
of avehicle
quarter
vehicle
model
isofas
shown
in (Oniz
Figure
describes
Li
&interaction
Yang,
2012).
Figure
1system.
shows
non-braking
condition
made
in2009;
deriving
the
dynamic
equations
of the
First,
the
vehicle
iset1considered
inthea
assumed
that
there
is
no
between
four
wheels
thethe
vehicle
al.,
2009;Even
though
model
isofThe
general
but
it can
sufficiently
represent
the actual
motion
the
vehicle
angular
motion
wheel
braking.
direction.
lateral
vertical
motion
ofof
thethe
vehicle
isduring
neglected.
Secondly,
Li &longitudinal
Yang,
2012).
Figure
1quite
shows
theand
non-braking
condition
and
braking
condition
ofvehicle
aEven
and the
braking
condition
of
aand
quarter
vehicle
model.
system’s
fundamental
characteristics
(Oniz
et
al.,
2009).
There
are
several
assumptions
though
themodel.
model is force
quite isgeneral
it can
represent
the actual
vehicle
the
rolling
resistance
ignoredbut
since
it is sufficiently
very small during
braking.
Thirdly,
it is
quarter
vehicle
made
in deriving
equations
of the
system.
First,
thevehicle
vehicle
is considered
in a
system’s
fundamental
(Oniz
et
al.,wheels
2009).
are several
assumptions
assumed
that
therethe
is dynamic
nocharacteristics
interaction
between
four
ofThere
the
(Oniz
et al., 2009;
longitudinal
direction.
The lateral
andthe
vertical
ofFirst,
the vehicle
is
neglected.
Secondly,
made
in deriving
theFigure
dynamic
equations
of themotion
system.
theand
vehicle
is considered
in a
Li
& Yang,
2012).
1 shows
non-braking
condition
braking
condition
of
the
rolling
resistance
force
is ignored
since itmotion
is veryofsmall
during isbraking.
Thirdly,
it is
longitudinal
direction.
The lateral
and vertical
the vehicle
neglected.
Secondly,
𝑀𝑀
𝑀𝑀
quarter
vehicle
model.
𝑣𝑣
𝑣𝑣
𝑉𝑉𝑉𝑉
𝑉𝑉𝑉𝑉
assumed
that
there is no
interaction
between
wheels
of the
vehicle
(OnizThirdly,
et al., 2009;
the rolling
resistance
force
is ignored
since itfour
is very
small
during
braking.
it is
Li
& Yang,
1 shows between
the non-braking
condition
braking
condition
of a
assumed
that2012).
there isFigure
no interaction
four wheels
of theand
vehicle
(Oniz
et al., 2009;
quarter
vehicle
model.
𝑚𝑚
𝑤𝑤
𝑀𝑀
Li 𝑚𝑚
&𝑊𝑊Yang,
2012).
Figure
1
shows
the
non-braking
condition
and
braking
condition
of a 𝑉𝑉
𝑀𝑀
𝑣𝑣
𝑣𝑣
𝑇𝑇𝑏𝑏
𝑉𝑉
𝑉𝑉𝑉𝑉
𝜔𝜔
quarter vehicle
model.
𝑤𝑤
R
R
𝜔𝜔𝑊𝑊
𝑀𝑀𝑣𝑣
𝑀𝑀𝑣𝑣
𝑚𝑚𝑤𝑤 𝑉𝑉𝑉𝑉
𝑚𝑚𝑊𝑊
𝑉𝑉𝑉𝑉
𝑇𝑇𝑏𝑏
𝑇𝑇𝑡𝑡
𝑇𝑇𝑡𝑡
𝜔𝜔
𝑀𝑀
𝑀𝑀
𝑤𝑤
𝑣𝑣
𝑣𝑣
R
𝑉𝑉
R
𝑉𝑉𝑉𝑉
𝐹𝐹𝑓𝑓 𝜔𝜔 𝑉𝑉
𝑊𝑊
𝑚𝑚
𝑚𝑚𝑊𝑊
𝑤𝑤
𝑇𝑇𝑏𝑏
(a)
(b)
𝜔𝜔𝑤𝑤
𝑚𝑚𝑤𝑤
𝑚𝑚𝑇𝑇
R
𝑡𝑡𝑇𝑇al., 2009)
𝑊𝑊𝑡𝑡 1(a). R
Figure
Non-braking condition
and (b) braking condition (Ahmad𝑇𝑇et
𝑏𝑏 condition
Figure 1(a). Non-braking
condition and (b) braking
𝜔𝜔𝐹𝐹𝑊𝑊
𝜔𝜔𝑤𝑤
𝑓𝑓
R
R
(Ahmad
et
al.,
2009)
Based on Newton’s
second
law,
the
equation
of
motion
for
the
simplified
vehicle
model
𝜔𝜔
(a)
(b)
𝑊𝑊
𝑇𝑇𝑡𝑡
𝑇𝑇𝑡𝑡
can be expressed
as: 1(a). Non-braking condition and (b) braking condition (Ahmad
Figure
et al., 2009)
𝐹𝐹
𝑇𝑇𝑡𝑡
Based𝑇𝑇𝑡𝑡on Newton’s second law, the equation of motion
for the simplified𝑓𝑓
𝐹𝐹𝑓𝑓
(a)
(b)
Based
on Newton’s
law,
the
model
𝐹𝐹𝑓𝑓 =be
−((𝑀𝑀
𝑚𝑚𝑤𝑤 ) ×
vehicle
model second
can
expressed
as:𝑎𝑎𝑣𝑣of) motion for the simplified vehicle(1)
𝑣𝑣 + equation
Figure
1(a).
Non-braking
condition
and
(b)
braking
condition
(Ahmad
et
al.,
2009)
can be expressed(a)
as:
(b)
Figurethe
1(a).
Non-braking
and
(b) braking
condition (Ahmad
et al.,mass
2009) and 𝑎𝑎
where 𝑀𝑀𝑣𝑣 represents
total
mass ofcondition
a vehicle
body,
𝑚𝑚𝑤𝑤 represents
the wheel
𝑣𝑣
Based on Newton’s second𝐹𝐹 law,
the equation
of
motion
for the simplified vehicle model
=
−((𝑀𝑀
+
𝑚𝑚
)
×
𝑎𝑎
)
represents
the
acceleration
of the
the tire friction force and (1)
𝑓𝑓 vehicle 𝑣𝑣while𝑤𝑤𝐹𝐹𝑓𝑓 represents
𝑣𝑣
can
be
expressed
as:
Newton’s
second
law, the equation
of motion for the simplified vehicle model
basedBased
on theonlaw
of Coulomb
is represented
by:
can
be 𝑀𝑀
expressed
as:
where
represents
the
total
mass
of
a
vehicle
body, 𝑚𝑚𝑤𝑤 represents the wheel mass and 𝑎𝑎𝑣𝑣
𝑣𝑣
(1)
𝐹𝐹𝑓𝑓 =the
−((𝑀𝑀
𝑚𝑚𝑤𝑤 ) × of
𝑎𝑎𝑣𝑣 )a vehicle body, m represents
where
Mvacceleration
represents
total
𝑣𝑣 + mass
w
represents
the
of𝐹𝐹𝑓𝑓the= vehicle
while
𝐹𝐹𝑓𝑓 represents the tire friction
force
(2) and
𝜇𝜇𝑠𝑠 𝐹𝐹𝑁𝑁
(1)
𝐹𝐹
=
−((𝑀𝑀
+
𝑚𝑚
)
×
𝑎𝑎
)
the
wheel
mass
and
a
represents
the
acceleration
of
the
vehicle
while
𝑣𝑣
𝑤𝑤
𝑣𝑣
based on the law of Coulomb𝑓𝑓 isv represented
by:
where
𝑀𝑀
represents
the
total
mass
of
a
vehicle
body,
𝑚𝑚
represents
the
wheel
mass
and
𝑣𝑣
𝑤𝑤
𝑣𝑣
Ff represents the tire friction force and based on the law of Coulomb𝑎𝑎is
Thusrepresents
the
acceleration
of
the
vehicle
while
𝐹𝐹
represents
the
tire
friction
force
and
𝑓𝑓
where
𝑀𝑀
represents
the
total
mass
of
a
vehicle
body,
𝑚𝑚
represents
the
wheel
mass
and
𝑎𝑎
𝑣𝑣
𝑤𝑤
represented
by:−(𝑀𝑀𝑣𝑣 + 𝑚𝑚𝑤𝑤𝐹𝐹)𝑓𝑓×=𝑎𝑎𝑣𝑣 𝜇𝜇=𝑠𝑠 𝐹𝐹𝜇𝜇𝑁𝑁𝑠𝑠 𝐹𝐹𝑁𝑁
(3) (2)𝑣𝑣
based on thethelaw
of Coulomb
represented
by: 𝐹𝐹𝑓𝑓 represents the tire friction force and
represents
acceleration
ofis the
vehicle while
based on the law of Coulomb is represented by:
Thus
(2)
𝐹𝐹 = 𝜇𝜇 𝐹𝐹
(3)
−(𝑀𝑀𝑣𝑣 + 𝑓𝑓𝑚𝑚𝑤𝑤 ) ×𝑠𝑠𝑎𝑎𝑣𝑣𝑁𝑁 = 𝜇𝜇𝑠𝑠 𝐹𝐹𝑁𝑁
(2)
𝐹𝐹𝑓𝑓 = 𝜇𝜇𝑠𝑠 𝐹𝐹𝑁𝑁
Thus
Thus
(3)
−(𝑀𝑀𝑣𝑣 + 𝑚𝑚𝑤𝑤 ) × 𝑎𝑎𝑣𝑣 = 𝜇𝜇𝑠𝑠 𝐹𝐹𝑁𝑁
Thus
(3)
−(𝑀𝑀𝑣𝑣 + 𝑚𝑚𝑤𝑤 ) × 𝑎𝑎𝑣𝑣 = 𝜇𝜇𝑠𝑠 𝐹𝐹𝑁𝑁
ISSN: 2180-1053
Vol. 6
No. 1
January - June 2014
41
Journal of Mechanical Engineering and Technology
In Equations (2) and (3), FN represents the total normal load while the
road adhesion coefficient, μs is a function of vehicle velocity and wheel
slip.
In Equations (2) and (3), 𝐹𝐹𝑁𝑁 represents the total normal load while the road adhesion
During𝜇𝜇𝑠𝑠deceleration,
torque
iswheel
applied
coefficient,
is a function ofbraking
vehicle velocity
and
slip. to the wheels to reduce
wheel speed and vehicle speed. The rolling resistance force occurred at
During
braking torque
to much
the wheels
to reduce
speedforce
and
the deceleration,
wheel is neglected
sinceisitapplied
is very
smaller
thanwheel
friction
vehicle speed. The rolling resistance force occurred at the wheel is neglected since it is very
between (2)
theand
wheel
road (Oniz
et al.,
2009).
According
Newton’s
In Equations
(3), and
𝐹𝐹𝑁𝑁 represents
the total
normal
load
while the to
road
adhesion
much smaller than friction force
between the wheel and road (Oniz et al., 2009). According
coefficient,
𝜇𝜇
is
a
function
of
vehicle
velocity
and
wheel
slip.
second
law,
the
equation
of
motion
of
the
wheel
can
be
written
as:
𝑠𝑠
In Newton’s
Equationssecond
(2) and
(3),
the total
normal
while
the as:
road adhesion
𝑁𝑁 represents
to
law,
the𝐹𝐹equation
of motion
of the
wheelload
can be
written
coefficient,
𝜇𝜇𝑠𝑠 (2)
is aand
function
vehicle
velocity
and wheel
slip.
In Equations
(3), 𝐹𝐹of𝑁𝑁torque
represents
the total
normal
loadto while
roadspeed
adhesion
During
deceleration,
braking
is applied
to the
wheels
reducethe
wheel
and
(4)
∑
𝑇𝑇
=
𝑇𝑇
−
𝑇𝑇
𝑤𝑤
𝑡𝑡
𝑏𝑏
coefficient,
𝜇𝜇
is
a
function
of
vehicle
velocity
and
wheel
slip. is neglected since it is very
𝑠𝑠 The rolling resistance force occurred at the wheel
vehicle
speed.
During
deceleration,
is applied
to the
wheels
reducethe
wheel
and
In
Equations
(2) andbraking
(3), 𝐹𝐹𝑁𝑁torque
represents
the total
normal
loadto while
roadspeed
adhesion
much
smaller
than
friction
force
between
the
wheel
and
road
(Oniz
et al., 2009).
According
vehicle
The
rolling
resistance
occurred
at
the
wheel
neglected
since
it is
very
coefficient,
𝜇𝜇𝑠𝑠wheel
is aand
function
vehicle
velocity
and
wheel
slip.
where
𝑇𝑇speed.
torque,
while
𝑇𝑇force
𝑇𝑇𝑡𝑡 total
represent
the
brake
torque
and
torque
During
deceleration,
braking
applied
to the
the
wheels
toisbe
reduce
wheel
speed
and
𝑤𝑤 issecond
𝑏𝑏is
In
Equations
(2)
(3),
𝐹𝐹of
represents
the
normal
load
while
the
roadtire
adhesion
to Newton’s
law,
theforce
equation
ofand
motion
of
wheel
can
written
as:
𝑁𝑁torque
much
smaller
than
friction
between
the
wheel
and
road
(Oniz
et
al.,
2009).
According
respectively,
Based
on
Equation
(4),
the
following
equations
are
derived
as:
vehicle
speed.
resistance
force
occurred
at the
since ittorque
is very
where
wheel
torque,
while
Tband
and
Tt wheel
represent
the brake
coefficient,
𝜇𝜇T𝑠𝑠wThe
isisa rolling
function
of vehicle
velocity
wheel
slip. is neglected
to
Newton’s
second
law,
theforce
equation
of applied
motion
of
written
as: According
During
deceleration,
braking
torque
is
to the
the
wheels
tobereduce
wheel
speed and
where
the
wheel
torque,
𝑇𝑇respectively,
much
smaller
than
friction
between
andwheel
road can
(Oniz
et
al., 2009).
𝑤𝑤 , is ∑
and
tire
torque
Equation
(4),
thesince
following
(4)
𝑇𝑇𝑤𝑤force
= 𝑇𝑇the
− wheel
𝑇𝑇𝑏𝑏 on
𝑡𝑡Based
vehicle
speed.
The
rolling
resistance
occurred
at
the
wheel
is
neglected
it is very
to Newton’s
second
law,
the equation
of applied
motion of
cantobereduce
writtenwheel
as: speed
During
deceleration,
braking
torque
is
to the
thewheel
wheels
and
equations
are
derived
as:
(4)
∑between
much smaller than friction force∑
and road (Oniz et al., 2009). According
𝑇𝑇𝑤𝑤 =
= 𝐼𝐼𝑇𝑇the
− wheel
𝑇𝑇𝑏𝑏 at
𝑡𝑡 ×
(5)
vehicle
The rolling
resistance
the the
wheel
is neglected
since
very
𝜔𝜔occurred
𝜔𝜔
where
𝑇𝑇speed.
wheel
torque,
while𝑇𝑇𝑤𝑤𝑇𝑇force
𝑇𝑇𝑡𝑡 𝛼𝛼represent
brake
torque and
tireit is
torque
𝑤𝑤 issecond
𝑏𝑏ofand
to
Newton’s
law,
the equation
motion
of
the
wheel
can
be
written
as:
(4)
much smallerBased
than friction
force∑
between
and road are
(Oniz
et al.,as:
2009). According
𝑇𝑇𝑤𝑤the
= following
𝑇𝑇the
𝑇𝑇𝑏𝑏 equations
𝑡𝑡 − wheel
respectively,
on
Equation
(4),
derived
where
wheel
torque,
while
𝑇𝑇𝑡𝑡 represent
the can
brake
torque
tire the
torque
where
wheel
torque,
T𝑇𝑇w𝑏𝑏,ofand
ismotion
where
I𝑇𝑇ω𝑤𝑤 wheel
isisthe
the
wheel
inertia,
angular
acceleration
represented
by 𝛼𝛼𝜔𝜔 ,and
tire
to Newton’s
second
law,
the, equation
of theiswheel
be written
as:while
where
the
torque,
𝑇𝑇
is
𝑤𝑤
(4)
respectively,
on
Equation
(4),
the
∑
𝑇𝑇𝑤𝑤are
= following
𝑇𝑇𝑡𝑡 − 𝑇𝑇𝑏𝑏 equations are derived as:
torque,
tire friction
force,
𝐹𝐹
where 𝑇𝑇𝑇𝑇𝑤𝑤𝑡𝑡 and
is Based
wheel
torque,
while
𝑓𝑓 , 𝑇𝑇
𝑏𝑏 and 𝑇𝑇𝑡𝑡 represent the brake torque and tire torque
,
is
where
the
wheel
torque,
𝑇𝑇
𝑤𝑤
respectively, Based on Equation∑
(4),
(4)
∑
𝑇𝑇 the
= following
− 𝛼𝛼
𝑇𝑇𝑏𝑏 equations are derived as:
(5)
𝐼𝐼𝑇𝑇𝜔𝜔𝑡𝑡 ×
𝜔𝜔
where the
𝑇𝑇𝑤𝑤 wheel
is wheel
torque,
while𝑇𝑇𝑤𝑤𝑤𝑤𝑇𝑇𝑏𝑏= and
𝑇𝑇 represent
the brake torque and tire torque
where
torque,
𝑇𝑇𝑤𝑤 , is
(6)
𝑇𝑇𝑡𝑡 = 𝐹𝐹𝑓𝑓𝑡𝑡 × 𝑅𝑅𝑟𝑟
(5)
respectively, Based on Equation∑(4),
the
following
equations
are
derived
as:
𝑇𝑇
=
𝐼𝐼
×
𝛼𝛼
𝑤𝑤𝑇𝑇 and
𝜔𝜔 𝑇𝑇 represent
𝜔𝜔
where
𝑇𝑇𝑤𝑤 isis the
wheel
torque,
while
the brake torque
and
tire the
torque
𝑏𝑏
𝑡𝑡
where
I
wheel
inertia,
angular
acceleration
is
represented
by
𝛼𝛼
,
while
tire
ω wheel torque, 𝑇𝑇𝑤𝑤 , is
𝜔𝜔
where
the
(5),
∑𝐹𝐹
respectively,
Based
onwheel
Equation
(4),
following
equations are derived
as:
𝑇𝑇𝑤𝑤 the
= angular
𝐼𝐼𝜔𝜔 × 𝛼𝛼𝜔𝜔 acceleration
and
where
is wheel
the
inertia,
is represented
by α
torque,
tire
friction
force,
𝑓𝑓 , are acceleration is represented by 𝛼𝛼𝜔𝜔 , while the tire
ω
where
I𝑇𝑇ω𝑡𝑡 and
isIωthe
inertia,
angular
where
the
wheel
torque,
𝑇𝑇
,
is
𝑤𝑤
while
thetire
tire
torque,
T∑t𝐹𝐹𝑓𝑓and
tire
friction
force, Ff, are
(5)
𝑇𝑇
=
𝐼𝐼
×
𝛼𝛼
torque,
𝑇𝑇
and
friction
force,
,
are
𝑤𝑤
𝜔𝜔
𝜔𝜔
𝑡𝑡
where Iω is the wheel inertia, angular𝐹𝐹𝑓𝑓acceleration
is represented by 𝛼𝛼𝜔𝜔 , while the tire
(7)
(6)
𝑇𝑇𝑡𝑡 == 𝐹𝐹𝑓𝑓𝜇𝜇𝑠𝑠×𝐹𝐹𝑁𝑁𝑅𝑅𝑟𝑟
(5)
torque, 𝑇𝑇𝑡𝑡 and tire friction force,∑𝐹𝐹𝑓𝑓𝑇𝑇,𝑤𝑤are
= 𝐼𝐼𝜔𝜔 × 𝛼𝛼𝜔𝜔
where Iω is the wheel inertia, angular
acceleration
is
represented
by
𝛼𝛼
,
while
the
tire
(6)
𝑇𝑇𝑡𝑡 = 𝐹𝐹𝑓𝑓 × 𝑅𝑅𝑟𝑟
𝜔𝜔
where
𝑅𝑅
is
the
radius
of
the
wheel.
By
substituting
Equations
(5),
(6)
and
(7)
into
(4),
and
torque, I𝑇𝑇𝑟𝑟𝑡𝑡 and
tirewheel
frictioninertia,
force, angular
𝐹𝐹𝑓𝑓 , are acceleration is represented by 𝛼𝛼 , while the tire
where
is
the
(6)
𝑇𝑇𝑡𝑡 = 𝐹𝐹𝑓𝑓 × 𝑅𝑅𝑟𝑟
𝜔𝜔
Equationω (8) can be obtained as
and
torque, 𝑇𝑇𝑡𝑡 and tire friction force, 𝐹𝐹𝑓𝑓 , are
(7)
𝐹𝐹
=
𝜇𝜇
𝐹𝐹
(6)
𝑇𝑇 𝑓𝑓= 𝐹𝐹 𝑠𝑠× 𝑁𝑁𝑅𝑅
(8)
andand
𝜇𝜇𝑠𝑠 𝐹𝐹𝑁𝑁 × 𝑅𝑅𝑡𝑡 𝑟𝑟 − 𝑇𝑇𝑓𝑓𝑏𝑏 = 𝑟𝑟𝐼𝐼𝜔𝜔 × 𝛼𝛼𝜔𝜔
(7)
𝐹𝐹
=
𝜇𝜇
𝐹𝐹
(6)
𝑇𝑇𝑡𝑡 𝑓𝑓= 𝐹𝐹𝑓𝑓 𝑠𝑠× 𝑁𝑁𝑅𝑅𝑟𝑟
where
By substituting Equations (5), (6) and (7) into (4),
and 𝑅𝑅𝑟𝑟 is the radius of the wheel. 𝐹𝐹
(7)
=
𝜇𝜇
𝐹𝐹
,
is
where
the
total
normal
load,
𝐹𝐹
𝑓𝑓
𝑠𝑠
𝑁𝑁
𝑁𝑁
Equation
(8) can be obtained as
where
and 𝑅𝑅𝑟𝑟 is the radius of the wheel. By substituting Equations (5), (6) and (7) into (4),
(7)
= 𝜇𝜇+𝑠𝑠 𝐹𝐹𝑚𝑚
Equation
obtained
𝑓𝑓(𝑀𝑀
𝑁𝑁 )𝑔𝑔
(9)
=𝐹𝐹
where 𝑅𝑅𝑟𝑟(8)
is can
the be
radius
of theas
By
substituting
Equations (5), (6) and (7) into (4),
𝑁𝑁 𝑅𝑅
𝑣𝑣
𝑤𝑤
(8)
𝜇𝜇𝑠𝑠wheel.
𝐹𝐹𝑁𝑁𝐹𝐹×
𝑟𝑟 − 𝑇𝑇𝑏𝑏 = 𝐼𝐼𝜔𝜔 × 𝛼𝛼𝜔𝜔
= 𝜇𝜇𝑠𝑠 𝐹𝐹𝑁𝑁 By substituting Equations (5), (7)
where
is the radius of the𝐹𝐹𝑓𝑓wheel.
(6)
Equation
(8)Rcan
r be obtained as
where
𝑅𝑅
is
the
radius
of
the
wheel.
By
substituting
Equations
(5),
(6)
and
(7)
into
(4),
𝜇𝜇
𝐹𝐹
×
𝑅𝑅
−
𝑇𝑇
=
𝐼𝐼
×
𝛼𝛼
𝑟𝑟 Equation (9) into Equation
𝑠𝑠 𝑁𝑁 (8)𝑟𝑟 and rearrange
𝑏𝑏
𝜔𝜔 to𝜔𝜔obtain angular acceleration, 𝛼𝛼 (8)
substitute
𝜔𝜔 ,
and
into
(4), load,
Equation
(8) can be obtained as
where
the(7)
total
𝐹𝐹as
𝑁𝑁 , is
Equation
(8)
cannormal
be obtained
(8)
𝐹𝐹𝑁𝑁 × 𝑅𝑅By
−
𝑇𝑇
=
𝐼𝐼
×
𝛼𝛼
where 𝑅𝑅𝑟𝑟 is the radius of the𝜇𝜇𝑠𝑠wheel.
substituting
Equations
(5),
(6)
and
(7)
into
(4),
𝑟𝑟
𝑏𝑏
𝜔𝜔
𝜔𝜔
where
the(8)
total
load, 𝐹𝐹as
[𝜇𝜇 (𝑀𝑀 +𝑚𝑚 )𝑔𝑔×𝑅𝑅𝑟𝑟 ]− 𝑇𝑇𝑏𝑏
𝑁𝑁 , is
Equation
cannormal
be obtained
𝛼𝛼𝜔𝜔 𝐹𝐹
=𝑁𝑁 =𝑠𝑠 (𝑀𝑀𝑣𝑣𝑣𝑣 +𝑤𝑤𝑚𝑚𝑤𝑤 )𝑔𝑔
(10)
(9)
(8)
𝜔𝜔 𝐼𝐼𝜔𝜔 × 𝛼𝛼𝜔𝜔
is𝑁𝑁 × 𝑅𝑅𝑟𝑟 − 𝑇𝑇𝑏𝑏 𝐼𝐼=
where the total normal load, 𝐹𝐹𝑁𝑁𝜇𝜇,𝑠𝑠 𝐹𝐹
(9)
𝐹𝐹
=
(𝑀𝑀
+
𝑚𝑚
)𝑔𝑔
𝑁𝑁
𝑣𝑣
𝑤𝑤
𝜇𝜇 𝐹𝐹𝑁𝑁 ×(8)
𝑅𝑅𝑟𝑟 and
− 𝑇𝑇rearrange
𝛼𝛼𝜔𝜔obtain angular acceleration, 𝛼𝛼 (8)
𝑏𝑏 = 𝐼𝐼𝜔𝜔 × to
substitute
(9) load,
into
Equation
,
𝜔𝜔
The
longitudinal
wheel
speed,
,
and
vehicle
speed,
𝑉𝑉
,
is
represented
in
Equations
(11)
where
the Equation
total normal
𝐹𝐹𝑁𝑁 ,𝑠𝑠𝑉𝑉is
𝑤𝑤 𝐹𝐹 = (𝑀𝑀 + 𝑚𝑚 )𝑔𝑔 𝑣𝑣
(9)
𝑁𝑁
𝑣𝑣
𝑤𝑤
and
(12): the total
where
normal
load,[𝜇𝜇 F(𝑀𝑀
, isrearrange to obtain angular acceleration, 𝛼𝛼𝜔𝜔 ,
substitute
(9) load,
into Equation
and
N +𝑚𝑚 )𝑔𝑔×𝑅𝑅𝑟𝑟 ]− 𝑇𝑇
where the Equation
total normal
𝐹𝐹𝑁𝑁 , is (8)
𝑏𝑏
𝛼𝛼𝜔𝜔 𝐹𝐹
=𝑁𝑁 =𝑠𝑠 (𝑀𝑀𝑣𝑣𝑣𝑣 +𝑤𝑤𝑚𝑚𝑤𝑤 )𝑔𝑔
(9)
(10)
𝐼𝐼𝜔𝜔
substitute Equation (9) into Equation (8)
and𝐹𝐹rearrange
to obtain angular acceleration, 𝛼𝛼𝜔𝜔
,
[𝜇𝜇𝑠𝑠 (𝑀𝑀𝑣𝑣 +𝑚𝑚
𝑓𝑓 𝑤𝑤 )𝑔𝑔×𝑅𝑅𝑟𝑟 ]− 𝑇𝑇𝑏𝑏
(11)
𝛼𝛼𝜔𝜔=𝐹𝐹
=𝑁𝑁∫ =
𝑉𝑉𝑣𝑣 = ∫ 𝑎𝑎𝑣𝑣 𝑑𝑑𝑑𝑑
−(𝑀𝑀
𝑑𝑑𝑑𝑑
(vehicle
speed)
(10)
(9)
+
𝑚𝑚
)𝑔𝑔
𝑣𝑣
𝑤𝑤
𝐼𝐼
(𝑀𝑀𝑣𝑣 +𝑚𝑚
𝜔𝜔
𝑤𝑤 )
substitute
Equation
(9) into
Equation
(8)
and
rearrange
to
angular acceleration, 𝛼𝛼𝜔𝜔
,
[𝜇𝜇𝑠𝑠vehicle
(𝑀𝑀
𝑇𝑇𝑏𝑏,obtain
𝑣𝑣 +𝑚𝑚𝑤𝑤 )𝑔𝑔×𝑅𝑅
𝑟𝑟 ]− 𝑉𝑉
The longitudinal
wheel
speed,
, and
speed,
(11)
𝑣𝑣 is represented in Equations (10)
and
𝛼𝛼𝑉𝑉𝑤𝑤
𝜔𝜔 =
𝐼𝐼
𝜔𝜔
and
substitute
Equation
(9) into
Equation
(8)
and rearrange
to
obtain angular acceleration, 𝛼𝛼 (11)
,
The (12):
longitudinal
wheel
speed,
𝑉𝑉𝑤𝑤 , and
speed,
[𝜇𝜇𝑠𝑠vehicle
(𝑀𝑀𝑣𝑣 +𝑚𝑚𝑤𝑤 )𝑔𝑔×𝑅𝑅
𝑇𝑇𝑣𝑣𝑏𝑏, is represented in Equations 𝜔𝜔
𝑟𝑟 ]− 𝑉𝑉
𝛼𝛼
=
(10)
substitute
Equation
(9)
into
Equation
(8)
and
rearrange
to
obtain
𝜔𝜔
and
𝐼𝐼
The (12):
longitudinal wheel speed, 𝑉𝑉𝑤𝑤 , and
vehicle
𝐹𝐹 𝜔𝜔speed,
]− 𝑉𝑉
𝑇𝑇𝑣𝑣𝑏𝑏, is represented in Equations (11)
acceleration,
α𝛼𝛼ω𝜔𝜔,==∫[𝜇𝜇−𝑠𝑠(𝑀𝑀𝑣𝑣 +𝑚𝑚𝑓𝑓𝑤𝑤)𝑔𝑔×𝑅𝑅
(11)
𝑉𝑉𝑣𝑣 = ∫ 𝑎𝑎𝑣𝑣 𝑑𝑑𝑑𝑑
𝑑𝑑𝑑𝑑𝑟𝑟 (vehicle
speed)
(10)
andangular
(12):
𝐼𝐼𝜔𝜔𝑤𝑤 )
(𝑀𝑀𝑣𝑣𝐹𝐹
+𝑚𝑚
𝑓𝑓
The
longitudinal
wheel
speed,
𝑉𝑉
,
and
vehicle
speed,
𝑉𝑉
,
is
represented
in
Equations
(11)
𝑣𝑣
(11)
𝑉𝑉𝑣𝑣 = ∫ 𝑎𝑎𝑣𝑣 𝑑𝑑𝑑𝑑𝑤𝑤= ∫ − (𝑀𝑀 +𝑚𝑚 ) 𝑑𝑑𝑑𝑑 (vehicle
speed)
and
𝑣𝑣𝐹𝐹 𝑤𝑤
and (12):
𝑓𝑓 speed, 𝑉𝑉 , is represented in Equations (11)
The
longitudinal
wheel
speed,
𝑉𝑉
,
and
vehicle
𝑣𝑣
and
(11)
𝑉𝑉𝑣𝑣 = ∫ 𝑎𝑎𝑣𝑣 𝑑𝑑𝑑𝑑𝑤𝑤= ∫ − (𝑀𝑀 +𝑚𝑚 ) 𝑑𝑑𝑑𝑑 (vehicle
speed)
and42(12):
ISSN: 2180-1053
Vol.𝑣𝑣𝐹𝐹6 𝑤𝑤 No. 1 January - June 2014
𝑓𝑓
and
(11)
𝑉𝑉𝑣𝑣 = ∫ 𝑎𝑎𝑣𝑣 𝑑𝑑𝑑𝑑 = ∫ −
𝑑𝑑𝑑𝑑 (vehicle speed)
(𝑀𝑀 +𝑚𝑚 )
𝑣𝑣𝐹𝐹
𝑓𝑓
𝑤𝑤
where the total normal load, 𝐹𝐹𝑁𝑁 , is
(9)
(9)
𝐹𝐹𝑁𝑁 = (𝑀𝑀𝑣𝑣 + 𝑚𝑚𝑤𝑤 )𝑔𝑔
substitute Equation (9) into Equation (8) and rearrange to obtain angular acceleration, 𝛼𝛼𝜔𝜔 ,
substitute Equation (9) into Equation (8) and rearrange to obtain angular acceleration, 𝛼𝛼𝜔𝜔 ,
[𝜇𝜇 (𝑀𝑀 +𝑚𝑚 )𝑔𝑔×𝑅𝑅𝑟𝑟 ]− 𝑇𝑇𝑏𝑏
𝛼𝛼𝜔𝜔 = 𝑠𝑠 𝑣𝑣 𝑤𝑤𝐼𝐼
(10)
𝜔𝜔
[𝜇𝜇𝑠𝑠 (𝑀𝑀𝑣𝑣 +𝑚𝑚𝑤𝑤 )𝑔𝑔×𝑅𝑅
𝑟𝑟 ]− 𝑇𝑇𝑏𝑏
𝛼𝛼𝜔𝜔 =
(10)
𝐼𝐼𝜔𝜔
The longitudinal wheel speed, 𝑉𝑉𝑤𝑤 , and vehicle speed, 𝑉𝑉𝑣𝑣 , is represented in Equations (11)
The
(12):longitudinal wheel speed, Vw, and vehicle speed, Vv, is represented
The and
longitudinal
wheel speed, 𝑉𝑉 , and vehicle speed, 𝑉𝑉 , is represented in Equations (11)
𝐹𝐹𝑁𝑁 = (𝑀𝑀𝑣𝑣 + 𝑚𝑚𝑤𝑤 )𝑔𝑔
Development of Antilock Braking System using Electronic Wedge Brake Model
𝑤𝑤
𝑣𝑣
in Equations (11) and (12):
and (12):
𝐹𝐹𝑓𝑓
𝑉𝑉𝑣𝑣 = ∫ 𝑎𝑎𝑣𝑣 𝑑𝑑𝑑𝑑 = ∫ −
𝑑𝑑𝑑𝑑 (vehicle speed)
(𝑀𝑀 +𝑚𝑚 )
and
and
and
𝑉𝑉𝑣𝑣 = ∫ 𝑎𝑎𝑣𝑣 𝑑𝑑𝑑𝑑 =
𝑉𝑉𝑤𝑤 = ∫ 𝑎𝑎𝜔𝜔 𝑑𝑑𝑑𝑑 = ∫
𝑣𝑣
𝑤𝑤
𝐹𝐹𝑓𝑓
∫ − (𝑀𝑀 +𝑚𝑚 ) 𝑑𝑑𝑑𝑑
𝑣𝑣
𝑤𝑤
(vehicle speed)
[𝜇𝜇𝑠𝑠 (𝑀𝑀𝑣𝑣 +𝑚𝑚𝑤𝑤 )𝑔𝑔×𝑅𝑅𝑟𝑟 ]− 𝑇𝑇𝑏𝑏
𝑑𝑑𝑑𝑑
𝐼𝐼𝜔𝜔
(wheel speed)
(11)
(11)
(12)
The rotational velocity of the [𝜇𝜇wheel
would
be𝑟𝑟 ]−
similar
with the forward velocity of the
)𝑔𝑔×𝑅𝑅
𝑇𝑇𝑏𝑏
The𝑉𝑉rotational
of𝑣𝑣+𝑚𝑚
the𝑤𝑤wheel
would
be similar
the forward
𝑠𝑠 (𝑀𝑀
= ∫ 𝑎𝑎𝜔𝜔operating
𝑑𝑑𝑑𝑑velocity
= ∫ conditions.
𝑑𝑑𝑑𝑑 (wheel
speed)with
vehicle under
Once
the
brakes
are applied,
braking forces(12)
are
𝑤𝑤 normal
𝐼𝐼𝜔𝜔
velocity
of
the
vehicle
under
normal
operating
conditions.
generated at the interface between the wheel and road surface. The braking force will Once
cause
thetobrakes
applied,
braking
arethegenerated
the interface
wheel
reduce are
thethe
speed.
Increasing
theforces
forces at
wheel
will at
increase
The the
rotational
velocity
of
wheel
would be
similar
with the
forward
velocityslippage
of the
between
the
wheel
and
road
surface.
The
braking
force
willthan
cause
between the tire and road surface and this will cause the wheel speed to be lower
the
vehicle under normal operating conditions. Once the brakes are applied, braking forces are
vehicle the
speed
(Oniz to
et al.,
2009).the
Thespeed.
parameter
used to obtain
the
slippage
occurring
atwill
the
wheel
reduce
Increasing
the
forces
at
the
wheel
generated at the interface between the wheel and road surface. The braking force will cause
wheel using
both vehicle
andbetween
wheel velocity
is known
as wheel
slip, 𝜆𝜆,and this will cause
increase
slippage
the
tire
and
road
surface
the wheel to reduce the speed. Increasing the forces at the wheel will increase slippage
speed
to be
than
the vehicle speed (Oniz et al., 2009).
between thethe
tirewheel
and road
surface
andlower
this will
cause
𝑉𝑉𝑣𝑣 −
𝑉𝑉𝜔𝜔 the wheel speed to be lower than the
𝜆𝜆
=
The
parameter
usedThe
to obtain
the slippage
occurring
at the
wheel using
vehicle speed
(Oniz
et al., 2009).
parameter
to obtain
the slippage
occurring
at(13)
the
𝑚𝑚𝑚𝑚𝑚𝑚(𝑉𝑉used
𝑣𝑣 ,𝑉𝑉𝜔𝜔)
andwheel
wheel
velocity
is known
as wheel
wheel usingboth
both vehicle
vehicle and
velocity
is known
as wheel
slip, 𝜆𝜆,slip, λ,
The forward velocity and tire rolling speed are equal when the slip ratios of the vehicle
𝑉𝑉𝑣𝑣 − 𝑉𝑉𝜔𝜔 of either engine torque or brake torque. A
approach zero. Zero slip ratio implies
𝜆𝜆 = absence
(13)
𝑚𝑚𝑚𝑚𝑚𝑚(𝑉𝑉𝑣𝑣 ,𝑉𝑉𝜔𝜔)a greater finite forward velocity with the
positive slip ratio implies the vehicle approaches
tire having a positive finite rolling velocity. While a negative slip ratio implies the tire has a
The greater
forwardequivalent
velocity and
tire rolling speed
equal when
slip ratios
the forward
vehicle
positive
velocityaremeanwhile
thethe
vehicle
has a of
finite
The forward
velocity and
tire rolling speed
are equal
when
the slip
velocity
(Short
2004).
Two
conditions
occurred
approach
zero.
Zero et
slipal.,
ratio
implies
absence
of either
enginewhen
torquetheor longitudinal
brake torque.slip
A
of +1
theorthe
vehicle
approach
zero.
Zerofinite
ratio implies
absence
approaches
either
-1.vehicle
The conditions
are
wheel
isslip
‘spinning’
with
the vehicle
at
positive
slipratios
ratio
implies
approaches
athegreater
forward
velocity
with the
either
engine
torque
orzero
brake
torque.
Aslip
positive
slip
ratio
implies
zero speed
or the finite
wheel
is ‘locked’
at
speed.
The longitudinal
is mathematically
tire having
aofpositive
rolling
velocity.
While
a negative
ratioslip
implies
the tire
has a
thewhen
vehicle
approaches
a velocities
greater
finite
forward
with the
the
tire
undefined
both tires
and vehicle
are equal
zero. velocity
Figure
graph
greater
equivalent
positive
rolling
velocity
meanwhile
theto vehicle
has 2a shows
finite
forward
having
aal.,positive
rolling
a the
negative
slip ratio
with wheel
slip, velocity.
𝜆𝜆 (Aparow
et when
al., 2013a).
relating
friction
velocity
(Short
et coefficient,
2004).𝜇𝜇𝑠𝑠 finite
Two
conditions
occurredWhile
longitudinal
slip
a greater
equivalent
positive with
rolling
velocity
approaches implies
either +1 the
or -1.tire
Thehas
conditions
are the
wheel is ‘spinning’
the vehicle
at
vehicleathas
a finite
velocityslip
(Short
et al., 2004).
zero speed meanwhile
or the wheel the
is ‘locked’
zero
speed. forward
The longitudinal
is mathematically
undefined when
tires andoccurred
vehicle velocities
are longitudinal
equal to zero. Figure
2 shows theeither
graph
Twoboth
conditions
when the
slip approaches
relating friction
coefficient,
𝜇𝜇
with
wheel
slip,
𝜆𝜆
(Aparow
et
al.,
2013a).
+1 or -1. The conditions
are the wheel is ‘spinning’ with the vehicle at
𝑠𝑠
zero speed or the wheel is ‘locked’ at zero speed. The longitudinal slip
is mathematically undefined when both tires and vehicle velocities are
equal to zero. Figure 2 shows the graph relating friction coefficient, μs
with wheel slip, λ (Aparow et al., 2013a).
Figure 2. Experiment data for 𝜇𝜇𝑠𝑠 vs slip (Aparow et al., 2013a)
The value of friction coefficient, 𝜇𝜇𝑠𝑠 , is obtained using a lockup table based on the
experiment on normal
road2180-1053
surface. These
gathered
from
ISSN:
Vol. values
6 No.were
1 January
- June
2014tire experiment43
conducted on a normal surface road. The response from the variation of friction coefficient
approaches either +1 or -1. The conditions are the wheel is ‘spinning’ with the vehicle at
zero speed or the wheel is ‘locked’ at zero speed. The longitudinal slip is mathematically
Journal
of Mechanical
andvelocities
Technologyare equal to zero. Figure 2 shows the graph
undefined
when
both tiresEngineering
and vehicle
relating friction coefficient, 𝜇𝜇𝑠𝑠 with wheel slip, 𝜆𝜆 (Aparow et al., 2013a).
FigureFigure
2. Experiment
data for μ vs slip (Aparow et al., 2013a)
2. Experiment data for 𝜇𝜇 s vs slip (Aparow et al., 2013a)
𝑠𝑠
The value
of friction
coefficient,
μs, is obtained
lockup
table
The value
of friction
coefficient,
𝜇𝜇𝑠𝑠 , is obtained
using a using
lockupa table
based
on the
basedononnormal
the experiment
onThese
normal
roadwere
surface.
These
values
were
experiment
road surface.
values
gathered
from
tire experiment
gathered
from surface
tire experiment
conducted
normalofsurface
conducted
on a normal
road. The response
fromon
theavariation
friction road.
coefficient
with slip
ratio
is used as
the input
for quarterofvehicle
brake
model. with slip ratio is
The
response
from
the variation
friction
coefficient
used as the input for quarter vehicle brake model.
2.2
Description of Simulation Model
The vehicle dynamics model is developed based on the mathematical
equations from the previous quarter vehicle model by using MATLAB
SIMULINK.
Figure
thebased
simulation
model of
the quarter
The
vehicle dynamics
model3 isshows
developed
on the mathematical
equations
from the
vehiclequarter
brakevehicle
modelmodel
withbya step
the brakeFigure
input.3 The
step
previous
using function
MATLABas
SIMULINK.
shows
the
simulation
model
of the quarter
model
with afrom
step function
the brake
input.
response
represents
thevehicle
brakebrake
torque
input
brake aspedal
during
The
step response
brakeintorque
input fromvehicle
brake pedal
during
This
braking.
Thisrepresents
signal isthe
used
the quarter
model
forbraking.
dynamic
signal is used in the quarter vehicle model for dynamic performance analysis in
performance analysis in longitudinal direction only. Meanwhile, the
longitudinal direction only. Meanwhile, the parameters for the quarter vehicle model are
parameters
listed
in the Tablefor
1. the quarter vehicle model are listed in the Table 1.
2.2 Description of Simulation Model
Figure 3.
Quarter
vehicle
Matlab
SIMULINK
Figure
3. Quarter
vehiclemodel
model in in
Matlab
SIMULINK
Table 1. Simulation model parameters for the vehicle model (Ahmad et al., 2009)
44
Description
Wheel Inertia
ISSN: 2180-1053
Brake coefficient
Vehicle mass
Vol. 6
No. 1
Symbol
Value
5 kgm2
𝐼𝐼𝜔𝜔
January
- June 2014
0.8
𝐾𝐾𝑏𝑏
690 kg
𝑀𝑀𝑣𝑣
Development of Antilock Braking System using Electronic Wedge Brake Model
Figure 3. Quarter vehicle model in Matlab SIMULINK
Table 1. Simulation model parameters for the vehicle model
Table 1. Simulation model parameters
foret
theal.,
vehicle
model (Ahmad et al., 2009)
(Ahmad
2009)
Description
Wheel Inertia
Brake coefficient
Vehicle mass
Wheel mass
Tire radius
Gravitational acceleration
Coefficient of friction
Vehicle speed
3.0
Symbol
𝐼𝐼𝜔𝜔
𝐾𝐾𝑏𝑏
𝑀𝑀𝑣𝑣
𝑚𝑚𝑤𝑤
𝑅𝑅𝑡𝑡
g
𝜇𝜇
v0
Value
5 kgm2
0.8
690 kg
50 kg
285 mm
9.81 m/s 2
0.4
25 m/s
EWB MODELING
USING BELL-SHAPED
CURVE
3.0EWB
MODELING
USING BELL-SHAPED
CURVE
By refering
to Aparowto
et Aparow
al. (2013b),et
a mathematical
using Bell-Shaped
curve has
been
By refering
al. (2013b),equation
a mathematical
equation
using
used toBell-Shaped
developed electronic
equation
can represent
the
curvewedge
has brake
beenmodel.
usedThetomathematical
developed
electronic
wedge
actual force and brake torque produced by a real EWB actuator. The derived mathematical equation
brake model. The mathematical equation can represent the actual
force and brake torque produced by a real EWB actuator. The derived
mathematical equation using trigonometric function such as tangential
function (Aparow et al., 2013b). In this study, Bell-Shaped curve, a nonusing
trigonometric
function
such asdescribed
tangential function
linear
equation
is used
by (Aparow et al., 2013b). In this study, BellShaped curve, a non-linear equation is used described by
𝑥𝑥−𝑐𝑐 2𝑏𝑏
where
𝐹𝐹𝑀𝑀 = 𝐹𝐹𝑐𝑐𝑐𝑐 [1/(1 + �
𝑎𝑎
� )
(14)
𝐹𝐹𝑀𝑀 where
is the maximum clamping force for EWB system (output)
𝐹𝐹𝑐𝑐𝑐𝑐 is
clamping force
of EWB system
FMthe
isreal
thetime
maximum
clamping
force for EWB system (output)
𝑥𝑥 is the
piston displacement (input)
F
is
the
real
time
clamping
force
of EWB system
𝑎𝑎 andcsb are the width of the curve
the ofpiston
𝑐𝑐 isxtheiscenter
the curvedisplacement (input)
a and b are the width of the curve
Thecparameters
used in
is the center
ofthe
theEquation
curve (14) such as a, b and c are estimated to sufficiently the
behaviour of EWB simulation model to replace an EWB actuator. The parameters of a, b and c are
estimated through trial and error technique and the data has been analyzed using root mean
Theerror
parameters
used in The
the Equation
(14)Equation
such as(14)
a, bisand
c arebased
estimated
square
(RMSE) technique.
parameters for
obtained
on the
sufficiently
of The
EWB
simulation
model
an
leasttoerror
results fromthe
the behaviour
RMSE analysis.
parameters
is listed
in Tableto2 replace
based on the
simulation
and experiment
work of EWB.ofAccording
Equation
(14), the
input oftrial
the
EWB actuator.
The parameters
a, b and to
c are
estimated
through
proposed
equation
is obtainedand
fromthe
the data
worm has
pinion
displacement
while
the output
of this
and error
technique
been
analyzed
using
root mean
model represents the clamping force of EWB model. Hence, brake torque of the EWB
square error (RMSE) technique. The parameters for Equation (14) is
model using Bell-Shaped curve can be obtained using Equation (15) which was obtained
obtained
on the least error results from the RMSE analysis. The
from
Rahman etbased
al., (2012)
parameters is listed in Table 2 based on the simulation and experiment
= 𝐹𝐹𝑓𝑓𝑓𝑓 𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒 (14), the input of the proposed
work of EWB. According to𝑇𝑇𝑏𝑏Equation
where
𝐹𝐹𝑓𝑓𝑓𝑓 = 2𝜇𝜇is𝑓𝑓 𝐹𝐹obtained
equation
from the worm pinion displacement while the
𝑁𝑁
output of this model represents the clamping force of EWB model.
Hence
it can be
conclude
that of the EWB model using Bell-Shaped curve can
Hence,
brake
torque
ISSN: 2180-1053
where
𝑇𝑇𝑏𝑏 = 2𝜇𝜇𝑓𝑓 𝐹𝐹𝑁𝑁 𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒
Vol. 6
No. 1
January - June 2014
(15)
45
estimated through trial and error technique and the data has been analyzed using root mean
The square
parameters
in theintechnique.
Equation
(14)
such
as a,asbfor
andbEquation
cand
arec estimated
to sufficiently
errorused
(RMSE)
The(14)
parameters
(14)
is obtained
basedthe
on the
The
parameters
used
the Equation
such
a,
are
estimated
to sufficiently
the
behaviour
of EWB
simulation
model
to replace
an EWB
actuator.
Theisparameters
of a, of
b2 and
cand
are
behaviour
of
EWB
simulation
model
to
replace
an
EWB
actuator.
The
parameters
a,
b
are
least
error
results
from
the
RMSE
analysis.
The
parameters
listed
in
Table
based
onc the
Journal
of
Mechanical
Engineering
and
Technology
estimated through trial and error technique and the data has been analyzed using root mean
estimated
trial and error
the data to
hasEquation
been analyzed
using
rootof
mean
simulationthrough
and experiment
worktechnique
of EWB.and
According
(14), the
input
the
square
errorerror
(RMSE)
technique.
The
parameters
forpinion
Equation
(14) (14)
is obtained
based
on the
square
(RMSE)
technique.
The
parameters
for Equation
iswhile
obtained
based
on this
the
proposed
equation
is obtained
from
the
worm
displacement
the
output
of
leastleast
errorerror
results
fromfrom
the RMSE
analysis.
TheEWB
parameters
listed
inbrake
Table
2 based
on
results
the RMSE
analysis.
The parameters
is listed
in Table
2 of
based
on
the
model
represents
the
clamping
force
of
model.isHence,
torque
thethe
EWB
be using
obtained
using
Equation
(15)
which
obtained
from
Rahman
et
simulation
experiment
work
of can
EWB.
According
towas
Equation
(14),
the
input
ofobtained
the
simulation
and
experiment
work
of be
EWB.
According
to Equation
thewas
input
of the
model and
Bell-Shaped
curve
obtained
using
Equation
(15)(14),
which
al.,
(2012)
proposed
equation
is
obtained
from
the
worm
pinion
displacement
while
the
output
of
this
proposed
equation
obtained from the worm pinion displacement while the output of this
from Rahman
et al.,is(2012)
model
represents
the clamping
forceforce
of EWB
model.
Hence,
brakebrake
torque
of the
model
represents
the clamping
of EWB
model.
Hence,
torque
of EWB
the EWB
model
usingusing
Bell-Shaped
curvecurve
can be
using
Equation
(15)
which
was
obtained
model
Bell-Shaped
canobtained
be
obtained
using
Equation
(15)
which
was
obtained
𝑇𝑇𝑏𝑏 = 𝐹𝐹𝑓𝑓𝑓𝑓 𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒
fromfrom
Rahman
et
al.,
(2012)
Rahman
et
al.,
(2012)
where 𝐹𝐹𝑓𝑓𝑓𝑓 = 2𝜇𝜇𝑓𝑓 𝐹𝐹𝑁𝑁
where
Hence
conclude that
where
𝐹𝐹𝑓𝑓𝑓𝑓 it=𝐹𝐹can
2𝜇𝜇𝑓𝑓be
𝐹𝐹2𝜇𝜇
𝑁𝑁 𝑓𝑓 𝐹𝐹𝑁𝑁
where
𝑓𝑓𝑓𝑓 =
𝑇𝑇𝑏𝑏 =𝑇𝑇𝐹𝐹𝑏𝑏𝑓𝑓𝑓𝑓=𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒
𝐹𝐹𝑓𝑓𝑓𝑓 𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒
𝑇𝑇𝑏𝑏 = 2𝜇𝜇𝑓𝑓 𝐹𝐹𝑁𝑁 𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒
Hence
itHence
canit be
that
Hence
canconclude
conclude
that
itbecan
be
conclude
that
(15)
where
𝑇𝑇 = 2𝜇𝜇 𝐹𝐹𝑁𝑁 𝑓𝑓𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒
(15) (15)
𝐹𝐹𝑁𝑁 𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒
𝑇𝑇𝑏𝑏 is the brake torque produced 𝑏𝑏 𝑇𝑇𝑏𝑏 =𝑓𝑓 2𝜇𝜇
𝐹𝐹𝑓𝑓𝑓𝑓 is the friction force generated at the contact interface
where
𝑟𝑟where
is the effective pad radius
𝑒𝑒𝑒𝑒𝑒𝑒where
𝑇𝑇𝑏𝑏 is𝑇𝑇the
brakebrake
torque produced
𝐹𝐹𝑏𝑏𝑁𝑁 is
is the
the normaltorque
forceproduced
𝐹𝐹𝑓𝑓𝑓𝑓 is𝐹𝐹𝑓𝑓𝑓𝑓
theisfriction
forceforce
generated
at the contact
interface
the
friction
generated
contact
interface
𝜇𝜇𝑓𝑓 is the friction coefficient
of on at
thethe
surface
𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒 𝑟𝑟is𝑒𝑒𝑒𝑒𝑒𝑒
the
pad
radius
Tisbeffective
is
the
brake
torque
produced
the effective pad radius
force
𝐹𝐹𝑁𝑁 isIt
Fnormal
the
friction
force generated
at of
thefriction
contact
interface
is
theisnormal
forceto define
𝐹𝐹the
necessary
the coefficient
between
disc and pad contact
𝑁𝑁 is
fcalso
𝜇𝜇𝑓𝑓 is𝜇𝜇
the
friction
ofpad
on
surface
coefficient
ofthe
on
the surface
interface
to
calculate
the
brake
torque.
The coefficient of friction is dependent on the
refftheisfriction
thecoefficient
effective
radius
𝑓𝑓 is
braking
such force
as disc speed, temperature of the disc, brake line pressure and other
F isconditions
the normal
It is It
also
necessary
to
define
theAparow
coefficient
friction
between
disc disc
and and
pad pad
contact
is Nalso
necessary
to2012;
define
the coefficient
friction
between
contact
factors
(Rahman
et
al.,
et al., of
2013b).
μftoiscalculate
the friction
coefficient
of
theofsurface
interface
the brake
torque.
Theon
coefficient
of friction
is dependent
on the
interface
to calculate
the brake
torque.
The
coefficient
of friction
is dependent
on the
braking
conditions
suchsuch
as disc
speed,
temperature
of theofdisc,
brakebrake
line pressure
and other
braking
conditions
as disc
speed,
temperature
the disc,
line pressure
and other
factors
(Rahman
al.,et2012;
Aparow
et al.,etthe
2013b).
It is(Rahman
alsoet necessary
toAparow
define
of friction between disc and
factors
al., 2012;
al., coefficient
2013b).
pad contact interface to calculate the brake torque. The coefficient of
friction is dependent on the braking conditions such as disc speed,
temperature of the disc, brake line pressure and other factors (Rahman
et al., 2012; Aparow et al., 2013b).
Table 2. Simulation parameters for bell-shaped curve and brake torque
Table 2. Simulation parameters for bell-shaped curve and brake torque
Description
𝐹𝐹𝑐𝑐𝑐𝑐
𝜇𝜇𝑓𝑓
𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒
a
b
c
4.0
Value
3500 N
0.45
0.15 m
6.295×10−4 m
2.820×10−4 m
9.570×10−4 m
CONTROL STRUCTURE DESIGN
4.0
CONTROL STRCTURE DESIGN
In the previous section, the development of a quarter vehicle model and electronic wedge
brake model using Bell-Shaped curve has been discussed in detail. In this section, an active
braking
system,
Anti-lock
Brakingthe
System
(ABS) is developed
usingvehicle
the quarter
vehicle
In the
previous
section,
development
of a quarter
model
brakeand
model
and
EWB
model.
Figure
4
shows
the
proposed
outer
and
inner
loop
control
electronic wedge brake model using Bell-Shaped curve has been for
ABS model. Two control loops are needed to be designed in developing an ABS model
discussed in detail. In this section, an active braking system, Anticontrol scheme using both quarter vehicle model and EWB model. These control loops are
lock
Braking
System
is developed
theloop
quarter
known
as an
inner loop
control(ABS)
and outer
loop control.using
The inner
controlvehicle
is used to
control the actuator of the proposed system. In this study, EWB model is also used as the
actuator for the ABS control system.
46
ISSN: 2180-1053
Vol. 6
No. 1
January - June 2014
The actuator model is the focus of on electronic wedge brake mechanism (EWB) (Rahman
a
6.295×10−4 m
b
2.820×10−4 m
−4
Development of Antilock
Braking
System
using Electronic
c
9.570×10
m Wedge Brake Model
brake CONTROL
model andSTRUCTURE
EWB model. DESIGN
Figure 4 shows the proposed outer and
4.0
inner loop control for ABS model. Two control loops are needed to
In
previous section,
the development
a quarter
vehiclescheme
model and
electronic
bethe
designed
in developing
an ABSofmodel
control
using
both wedge
brake
model
using model
Bell-Shaped
been discussed
in detail.
In this
an active
quarter
vehicle
and curve
EWBhas
model.
These control
loops
aresection,
known
braking
system,
Anti-lock
Braking
System
(ABS)
is
developed
using
the
quarter
as an inner loop control and outer loop control. The inner loop control vehicle
brake
model
EWBthe
model.
Figure 4ofshows
the proposed
outer and
control for
is used
to and
control
actuator
the proposed
system.
Ininner
this loop
study,
ABS model. Two control loops are needed to be designed in developing an ABS model
EWB model is also used as the actuator for the ABS control system.
control scheme using both quarter vehicle model and EWB model. These control loops are
known as an inner loop control and outer loop control. The inner loop control is used to
The actuator
model
is the
focus of
on electronic
wedge
brake
mechanism
control
the actuator
of the
proposed
system.
In this study,
EWB
model
is also used as the
(EWB) for
(Rahman
al., 2012)
actuator
the ABS et
control
system.system since the brake actuator model is
developed based on brake-by-wire concept. Meanwhile, the outer loop
control for ABS system is to control the quarter vehicle model. Initially,
The actuator model is the focus of on electronic wedge brake mechanism (EWB) (Rahman
the longitudinal slip for quarter vehicle model is controlled without
et al., 2012) system since the brake actuator model is developed based on brake-by-wire
involving
brake actuator
model
or inner
loop
control.
The controller
concept.
Meanwhile,
the outer loop
control
for ABS
system
is to control
the quarter vehicle
for
this
model
will
control
the
quarter
vehicle
model’s
slipwithout
model. Initially, the longitudinal slip for quarter vehicle model is wheel
controlled
directly brake
without
any model
interference
the actual
longitudinal
involving
actuator
or inner until
loop control.
The wheel
controller
for this model will
control
quarter that
vehicle
model’s
wheel
slip the
directly
without
any longitudinal
interference until the
slip is the
obtained
closely
follow
with
desired
wheel
actual
wheel longitudinal
slip is
obtained
that closely
follow with
the desired
slip (Aparow
et al., 2013a).
Similar
procedure
is applied
for inner
loop wheel
longitudinal
slip (Aparow
al.,control
2013a).brake
Similartorque.
procedure is applied for inner loop control
control model
in orderetto
model in order to control brake torque.
Figure 4.outer
Proposed
outer
and loop
inner loop
controls
forABS
ABS model
model
Figure 4. Proposed
and
inner
controls
for
Then, both loop controls are integrated to become a closed loop model known as ABSThen, both loop controls are integrated to become a closed loop model
EWB model to control the wheel longitudinal slip and stopping distance of quarter vehicle
known
asproposed
ABS-EWB
modelfortoinner
control
wheel
longitudinal
slipthree
andtypes of
model.
The
controller
loop the
control
is PID
controller while
stopping
distance
of
quarter
vehicle
model.
The
proposed
controller
controller, namely PID, adaptive PID and fuzzy logic controllers are proposed for the
for inner loop control is PID controller while three types of controller,
namely PID, adaptive PID and fuzzy logic controllers are proposed
for the overall ABS-EWB control structure. The results using all three
controllers are compared and most optimum controller is proposed for
ABS-EWB model.
4.1
PID controller
PID algorithm stil is remain as one of the most widely used controller
in industrial process control. It is not only because PID algorithm
has a simple structure whereby easy to implement but also provides
adequate performance in most applications. PID controller may also be
considered as a phase lead-lag compensator with one pole formation
ISSN: 2180-1053
Vol. 6
No. 1
January - June 2014
47
4.1 PID controller
Journal of Mechanical Engineering and Technology
PID algorithm stil is remain as one of the most widely used controller in industrial process
control. It is not only because PID algorithm has a simple structure whereby easy to
at twobut
points
which is
at the performance
origin andinother
infinity. PID
A standard
implement
also provides
adequate
most at
applications.
controller
is as
known
“ three-term”
controller
the transfer
mayPID
also controller
be considered
a phaseaslead-lag
compensator
with one where
pole formation
at two
points
which
is
at
the
origin
and
other
at
infinity.
A
standard
PID
controller
is
known
as “
function of PID is generally written in the “parallel form” or “ideal
three-term”
controller
where
the
transfer
function
of
PID
is
generally
written
in
the
form”
“parallel form” or “ideal form”
𝑈𝑈(𝑠𝑠)
𝐺𝐺𝑃𝑃𝑃𝑃𝑃𝑃 (𝑠𝑠) = 𝐸𝐸(𝑠𝑠) = 𝐾𝐾𝑝𝑝 + 𝐾𝐾𝑖𝑖 /𝑠𝑠 + 𝐾𝐾𝑑𝑑 𝑠𝑠
𝐺𝐺𝑃𝑃𝑃𝑃𝑃𝑃 (𝑠𝑠) = 𝐾𝐾𝑝𝑝 (1 +
1
𝑇𝑇𝑖𝑖 𝑠𝑠
+ 𝑇𝑇𝑑𝑑 𝑠𝑠)
(16)
(17)
where U(s) is the control signal acting on the error signal E(s), 𝐾𝐾𝑝𝑝 is the proportional gain,
where
U(s) gain,
is the𝐾𝐾𝑑𝑑control
signalgain,
acting
onintergal
the error
signal E(s),
is
𝐾𝐾𝑖𝑖 is
the intergal
the derivative
𝑇𝑇𝑖𝑖 the
time constant
and 𝑇𝑇𝑑𝑑Kpthe
derivative
time constant. gain,
In thisKstudy,
PIDintergal
controllergain,
is used
inthe
thederivative
inner loop system
to
the proportional
is
the
K
gain,
T
i
d
i
regulate
the brake time
torqueconstant
from the electronic
wedge
brake (EWB).
output from
the
the intergal
and Td the
derivative
timeThe
constant.
In this
inner loop control is used as an input for the outer loop control.The output from the outer
controller
is used in
innerthe
loop
system
regulate
the
loopstudy,
controlPID
is the
wheel longitudinal
slipthe
to avoid
vehicle
fromtoskidding
during
brake
torque
from
the
electronic
wedge
brake
(EWB).
The
output
from
braking. The PID parameter are tuned using Knowledge Based Tuning (KBT) method
the inneret loop
control
is used
as torque
an input
for the
outermodel
loopis control.
(Calvo-Rolle
al., 2011)
until actual
brake
produced
by EWB
same as
desired
torque
in order
to control
wheel is
longitudinal
sliplongitudinal
of quarter vehicle
Thebrake
output
from
the outer
loopthe
control
the wheel
slip
model.
to avoid the vehicle from skidding during braking. The PID parameter
are tuned using Knowledge Based Tuning (KBT) method (Calvo-Rolle
et al., 2011) until actual brake torque produced by EWB model is same
desired
brake torque
in to
order
the wheel
longitudinal
slip
An as
adaptive
mechansim
is needed
tune to
thecontrol
PID parameters
to make
overall system
behaves
as the reference
of quarter
vehicle model.
model.Therefore, a model reference adaptive control (MRAC)
4.2 Outer loop Control Design using Adaptive PID controller
using MIT rule is proposed as an adaptive mechanism for PID controller (Adrian et al.,
2008). The adaptive PID controller which is applied in the outer loop model is shown in
4.2
Outer loop Control Design using Adaptive PID controller
Figure 5 while mathematical derivations is described by the following equations.
An adaptive mechansim is needed to tune the PID parameters to make
overall system behaves as the reference model. Therefore, a model
reference adaptive control (MRAC) using MIT rule is proposed as
an adaptive mechanism for PID controller (Adrian et al., 2008). The
adaptive PID controller which is applied in the outer loop model is
shown in Figure 5 while mathematical derivations is described by the
following equations.
Figure 5. Adaptive PID using MIT Rule for outer loop model
Figure 5. Adaptive PID using MIT Rule for outer loop model
The adaptive PID controller parameters are adjusted to give desired closed-loop
performance for ABS model. The controller parameters are estimated to cause the desired
change
in plant transfer
function so that
can- June
be made
48
ISSN: 2180-1053
Vol. the
6 actual
No. 1 output
January
2014 similar to the
reference model (Swarnkar et al., 2011).
Development of Antilock Braking System using Electronic Wedge Brake Model
The adaptive PID controller parameters are adjusted to give desired
closed-loop performance for ABS model. The controller parameters are
estimated to cause the desired change in plant transfer function so that
the actual output
can
be made
similar
to the
reference
model (Swarnkar
Figure
5. Adaptive
PID using
MIT Rule
for outer
loop model
et al., 2011).
The adaptive PID controller parameters are adjusted to give desired closed-loop
performance
for ABS model.
4.2.1 Reference
modelThe controller parameters are estimated to cause the desired
change in plant transfer function so that the actual output can be made similar to the
reference
model (Swarnkar
et al., 2011).
Normally,
the reference
model will be the desired overall system’s
performance by the designer. The adaptive mechanism is developed
based on the error between the output response of the plant with the
reference
model. The
controller
is designed
force the by
plant
Normally,
the reference
modeladaptive
will be the
desired overall
system’s to
performance
the
modelThe
to act
similar
to reference
model.
Model
output,
λm, is compared
designer.
adaptive
mechanism
is developed
based
on the
error between
the output
response
the plantoutput,
with the λ
reference
The adaptive
designed
to force
to theof actual
, and model.
the difference
is controller
used to is
adjust
feedback
p
the PID
plantcontroller
model to act
similar
to
reference
model.
Model
output,
𝜆𝜆
,
is
compared
to the
𝑚𝑚
parameters. The reference model used for the adjustment
actual output, 𝜆𝜆𝑝𝑝 , and the difference is used to adjust feedback PID controller parameters.
mechanism is
4.2.1 Reference model
The reference model used for the adjustment mechanism is
𝜆𝜆𝑚𝑚 (𝑠𝑠)
𝜆𝜆𝑝𝑝(𝑠𝑠)
𝐾𝐾𝜔𝜔 2
= 𝑠𝑠2 +2𝜀𝜀𝜀𝜀 𝑛𝑛𝑠𝑠+𝜔𝜔
𝑛𝑛
𝑛𝑛
(18)
2
where, 𝜔𝜔𝑛𝑛 is the undamped natural frequency, 𝜀𝜀, is the damping ratio while K is the gain of
is the undamped natural frequency, ε, is the damping ratio
the where,
system. ω
The
n value of 𝜔𝜔𝑛𝑛 = 15 rad/s, 𝜀𝜀 = 0.65, K = 1. These values are chosen for the
closed
loopKsystem
haveofmaximum
overshoot
5% atofrise
s andεpeak
timeKat=
while
is the to
gain
the system.
The ≤
value
ωntime
= 150.1
rad/s,
= 0.65,
0.251.s These
when excited
with
step function.
values
area chosen
for the closed loop system to have maximum
overshoot ≤ 5% at rise time 0.1 s and peak time at 0.25 s when excited
with a step function.
4.2.2 Transfer Function for Quarter Vehicle Brake Model
The inner loop model is ignored in this stage in order to develop outer loop ABS model.
The4.2.2
purpose
of ignoring
the inner
modelVehicle
is to avoid
interference
Transfer
Function
forloop
Quarter
Brake
Model during the
development of the adaptive control. The Laplace transfer function of the quarter vehicle
The𝐺𝐺inner
loop model is ignored in this stage in order to develop outer
model,
𝑝𝑝 , is needed to derive the adjustment mechanism. This transfer function model is
loop ABS
Thesingle
purpose
of ignoring
loop model
is the
to
developed
usingmodel.
single input
output (SISO)
concept.the
Theinner
step response
is used as
brake
inputinterference
for both quarter
vehicle
model and first
order
transfer control.
function. The
The
avoid
during
thebrake
development
of the
adaptive
comparison
of the
quarter of
vehicle
brake model
and the
approximation
of the
Laplaceresults
transfer
function
the quarter
vehicle
model,
Gp, is needed
response as a first order system are shown in Figure 6.
to derive the adjustment mechanism. This transfer function model is
developed using single input single output (SISO) concept. The step
response is used as the brake input for both quarter vehicle brake
model and first order transfer function. The comparison results of the
quarter vehicle brake model and the approximation of the response as
a first order system are shown in Figure 6.
ISSN: 2180-1053
Vol. 6
No. 1
January - June 2014
49
Journal of Mechanical Engineering and Technology
Graph longitudinal wheel slip versus time
1
2DOF
1st order function
Graph longitudinal wheel slip versus time
0.9
1
0.8
longitudinal
longitudinal
wheel slip
longitudinal
wheel slip
longitudinal
wheel slip
wheel slipwheel slip
longitudinal
0.9
0.7
1
0.8
0.6
0.9
0.7
0.5
1
0.8
0.6
0.4
0.9
0.7
0.5
0.3
1
0.8
0.6
0.4
0.2
0.9
0.7
0.5
0.3
0.1
0.8
0.6
0.4
0.20
0.7
0
0.5
0.3
0.1
0.6
0.4
0.2
0
0
0.5
0.3
0.1
Graph longitudinal wheel slip versus time
2DOF
1st order function
Graph longitudinal wheel slip versus time
2DOF
1st order function
Graph longitudinal wheel slip versus time
2DOF
1st order function
2DOF
1st order function
0.5
1
1.5
time, t
2
2.5
3
3.5
0.5
1of
1.5
2 function
2.5 and
3
3.5
Figure 6.
Comparison
order
transfer
quarter
vehicle
Figure
6. Comparison
of1st
1st order
transfer
function
and quarter
vehicle
model
time, t
0.4
model
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
Transfer
function
plant model,
quarter
vehicle
model
is model
shown
in Equation
Figureof
6. Comparison
of 1st𝐺𝐺order
transfer
and quarter
vehicle
0.3
𝑝𝑝 , using
time, function
t
0.1
(19)
0.2
0
Transfer
function
of plant model,
Gfunction
using
quarter
vehicle
model
is
0
2.5 vehicle model
3
3.5
p, 2 vehicle
Figure 0.5
6. Comparison1 of 1st order1.5
transfer
and quarter
Transfer
quarter
model
is shown
in Equation
t
0.1 function of plant model, 𝐺𝐺𝑝𝑝 , using time,
shown
in
Equation
(19)
𝑏𝑏
0.002385
(19)
0
st
𝐺𝐺1𝑝𝑝of=1�𝐺𝐺
� =quarter
�function
� quarter
0.5
1.5
2 vehicle
2.5 vehicle
3
3.5 (19)
Figureof
6. Comparison
transfer
and
model
Transfer 0function
plant model,
,1 +𝑎𝑎
using
model
is shown
in Equation
𝑎𝑎𝑝𝑝order
𝑠𝑠
0
time, t 1+0.25𝑠𝑠
(19)
𝑏𝑏
0.002385
st
(19)
𝐺𝐺𝑝𝑝 of
= 1�𝐺𝐺
� =quarter
�function
� quarter
Transfer
function
of6. Comparison
plant
, using
vehicle
model
is shown
Figure
transfer
and
vehicle
model in Equation
Meanwhile
the
output
frommodel,
plant
model,
𝑎𝑎𝑝𝑝order
1 +𝑎𝑎0𝜆𝜆𝑠𝑠𝑝𝑝 , is 1+0.25𝑠𝑠
𝑏𝑏
0.002385
(19)
(19)
𝐺𝐺𝑝𝑝 = �
� =quarter
� 2 vehicle
� model is shown in Equation
Transfer
function
of plant
𝐺𝐺𝑎𝑎𝑝𝑝1,+𝑎𝑎
using
0.002385
Meanwhile
the output
from model,
plant
model,
𝜆𝜆0𝐾𝐾𝑝𝑝𝑠𝑠𝑝𝑝 𝑠𝑠+𝐾𝐾
, is 𝑖𝑖 +𝐾𝐾1+0.25𝑠𝑠
𝑑𝑑 𝑠𝑠
(20)
𝜆𝜆
=
�
�
�
�
�𝜆𝜆
−
𝜆𝜆
�
𝑝𝑝
𝑑𝑑
𝑝𝑝
𝑏𝑏
(19)Meanwhile the output 1+0.25𝑠𝑠
𝑠𝑠 0.002385
λp�, is
(19)
𝐺𝐺𝑝𝑝 from
= � plant
=model,
�
�
2
Meanwhile the output from plant
model,
, is𝑖𝑖 +𝐾𝐾1+0.25𝑠𝑠
𝑎𝑎1 +𝑎𝑎𝜆𝜆
𝑠𝑠𝑠𝑠+𝐾𝐾
𝐾𝐾
0𝑝𝑝
0.002385
𝑝𝑝
𝑑𝑑 𝑠𝑠
𝜆𝜆𝑝𝑝 =the
� difference
��
� �𝜆𝜆𝑑𝑑 −
𝜆𝜆𝑝𝑝 � and actual response for(20)
desired
input
the
where 𝜆𝜆𝑑𝑑 − 𝜆𝜆𝑝𝑝 represents
1+0.25𝑠𝑠 𝑏𝑏 between
𝑠𝑠 0.002385
(19)
𝐺𝐺𝑝𝑝 = �
=� 2
�
�
𝐾𝐾
𝑠𝑠+𝐾𝐾
+𝐾𝐾
𝑠𝑠
,
is
Meanwhile
output
from plant
model,
outer loop the
model.
Rearrange
Equation
(20)
to
obtain
the
closed
function
of
outer
loop
0.002385
𝑎𝑎1 +𝑎𝑎𝜆𝜆
𝑠𝑠
1+0.25𝑠𝑠
𝑝𝑝
𝑑𝑑
𝑖𝑖
(20)
𝜆𝜆 = � 1+0.25𝑠𝑠 � � 0𝑝𝑝 𝑠𝑠
� �𝜆𝜆 − 𝜆𝜆𝑝𝑝 �
between desired𝑑𝑑 input
and actual response for the
where
model 𝜆𝜆𝑑𝑑 − 𝜆𝜆𝑝𝑝 represents𝑝𝑝 the difference
2
𝐾𝐾
, isto
Meanwhile
the output
from plant
model, 𝜆𝜆
0.002385
outer loop model.
Rearrange
Equation
(20)
the closed function of outer loop
𝑝𝑝
𝑑𝑑 𝑠𝑠
𝑖𝑖 +𝐾𝐾obtain
𝑝𝑝𝑠𝑠+𝐾𝐾
𝜆𝜆𝑝𝑝 =
� difference
� � between
� �𝜆𝜆 − 𝜆𝜆𝑝𝑝 �and actual response for(20)
−
𝜆𝜆
represents
the
desired
the
where
𝜆𝜆
𝜆𝜆
0.002385(𝐾𝐾
𝑠𝑠+𝐾𝐾
+𝐾𝐾𝑑𝑑 𝑠𝑠2𝑑𝑑) input
1+0.25𝑠𝑠
𝑠𝑠
𝑑𝑑
𝑝𝑝
𝑝𝑝
𝑝𝑝
𝑖𝑖
model
= �(0.25+0.002385𝐾𝐾 )𝑠𝑠2 +(1+0.002385𝐾𝐾
�
(21)
𝜆𝜆represents
)𝑠𝑠+0.002385𝐾𝐾
outer
loop λ
model.
Rearrange
Equation
(20)
closed
function
outer
loop
+𝐾𝐾obtain
𝑠𝑠2
where
-λ
the
difference
between
desired
and
actual
0.002385
𝑝𝑝the
𝑑𝑑
𝑑𝑑 𝐾𝐾
𝑖𝑖 inputof
𝑝𝑝 𝑠𝑠+𝐾𝐾to
𝑑𝑑
𝑖𝑖
d
p
𝜆𝜆𝑝𝑝 =
� � between
� �𝜆𝜆2𝑑𝑑 −
𝜆𝜆𝑝𝑝 �and actual response for(20)
represents
the� difference
desired
input
the
where
𝜆𝜆𝑑𝑑 − 𝜆𝜆𝑝𝑝 for
model
𝜆𝜆𝑝𝑝the outer
1+0.25𝑠𝑠
𝑠𝑠𝑠𝑠+𝐾𝐾
𝑝𝑝
𝑖𝑖 +𝐾𝐾𝑑𝑑 𝑠𝑠 )
response
loop0.002385(𝐾𝐾
model.
Rearrange
Equation
(20) to obtain
=
�
�
(21)
2 +(1+0.002385𝐾𝐾
outer loop model.𝜆𝜆𝑑𝑑Rearrange
Equation𝑑𝑑)𝑠𝑠(20)
to obtain 𝑝𝑝the
closed function
of
outer
loop
(0.25+0.002385𝐾𝐾
)𝑠𝑠+0.002385𝐾𝐾
𝑖𝑖
the𝜆𝜆closed
function
of difference
outer0.002385(𝐾𝐾
loop model
𝜆𝜆MIT
+𝐾𝐾𝑑𝑑value
𝑠𝑠2 ) input
represents
the
response
for the
where
model
By applying
gradient
rule, thebetween
adaptation
for and
PIDactual
controller
parameters
𝑝𝑝
𝑝𝑝 𝑠𝑠+𝐾𝐾𝑖𝑖desired
𝑑𝑑 − 𝜆𝜆𝑝𝑝the
=�
�
(21)
2 +(1+0.002385𝐾𝐾 )𝑠𝑠+0.002385𝐾𝐾
𝜆𝜆𝑑𝑑Rearrange
(0.25+0.002385𝐾𝐾
outer
model.
Equation
(20)
obtain 𝑝𝑝based
the closed function
of outer loop
𝑑𝑑 )𝑠𝑠
𝑖𝑖
𝐾𝐾𝑝𝑝 , 𝐾𝐾𝑖𝑖loop
and 𝐾𝐾
The
parameters
aretoderived
𝑑𝑑 are obtained.
𝜆𝜆𝑝𝑝
𝑠𝑠2 )
𝑝𝑝 𝑠𝑠+𝐾𝐾𝑖𝑖 +𝐾𝐾𝑑𝑑value
model
By
applying the MIT
rule,0.002385(𝐾𝐾
the adaptation
for PID �controller parameters
= gradient
�(0.25+0.002385𝐾𝐾
(21)
2 +(1+0.002385𝐾𝐾
𝜆𝜆
)𝑠𝑠
𝑑𝑑𝑑𝑑
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
𝑝𝑝 )𝑠𝑠+0.002385𝐾𝐾
𝑑𝑑
𝑑𝑑
𝑖𝑖
𝑥𝑥
𝐾𝐾𝑝𝑝 , 𝐾𝐾𝑖𝑖 and 𝐾𝐾𝑑𝑑 are obtained. The
parameters
are
derived
based
=
𝛾𝛾
(
)
=
𝛾𝛾
[(
)(
)(
)]
(22)
𝑝𝑝
𝑥𝑥
2
𝑑𝑑𝑑𝑑
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
𝜆𝜆𝑝𝑝
𝑠𝑠 ) 𝜕𝜕𝜕𝜕for
By applying the MIT
gradient
rule,0.002385(𝐾𝐾
the
adaptation
PID controller parameters
𝑥𝑥
𝑥𝑥
𝑝𝑝 𝑠𝑠+𝐾𝐾𝜕𝜕𝜕𝜕
𝑖𝑖 +𝐾𝐾𝑑𝑑value
=
�
�
(21)
2
𝜆𝜆𝑑𝑑
(0.25+0.002385𝐾𝐾
𝐾𝐾𝑝𝑝 , 𝐾𝐾𝑖𝑖 and 𝐾𝐾𝑑𝑑 are obtained.
are derived
𝑑𝑑𝑑𝑑𝑥𝑥The parameters
𝜕𝜕𝜕𝜕 𝑑𝑑 )𝑠𝑠 +(1+0.002385𝐾𝐾
𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕based
𝜕𝜕𝜕𝜕
𝑝𝑝 )𝑠𝑠+0.002385𝐾𝐾
𝑖𝑖
=or- Intergral
𝛾𝛾rule,
) =adaptation
- 𝛾𝛾
[(𝜕𝜕𝜕𝜕)(𝜕𝜕𝜕𝜕
)(𝜕𝜕𝜕𝜕
)] PID
(22)
𝑝𝑝 (𝜕𝜕𝜕𝜕the
𝑥𝑥 Derivative
⁄𝜕𝜕𝜕𝜕controller
⁄𝜕𝜕𝜕𝜕PID
where
𝐾𝐾applying
(P)
or
(D),
= value
𝑒𝑒 and 𝜕𝜕𝜕𝜕
= 1.
By
applying
the MIT
value
parameters
𝑑𝑑𝑑𝑑
𝑥𝑥 = Proportional
𝑥𝑥 (I)
𝑥𝑥for 𝜕𝜕𝜕𝜕
By
thegradient
MIT
gradient
rule,
the
adaptation
for
Equation
(22)
has
been
derived
mathematically
in
order
to
develop
an
adjustment
𝑑𝑑𝑑𝑑
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
𝐾𝐾
,
𝐾𝐾
and
𝐾𝐾
are
obtained.
The
parameters
are
derived
based
𝑥𝑥
𝑝𝑝 controller
𝑖𝑖
𝑑𝑑
= -K𝛾𝛾p𝑝𝑝,K
( i and
) = - 𝛾𝛾K𝑥𝑥 d[(are
)( obtained.
)(𝜕𝜕𝜕𝜕 )] The parameters (22)
parameters
are
𝑑𝑑𝑑𝑑 or Intergral
𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕
mechanism
for
controller.
⁄𝜕𝜕𝜕𝜕controller
⁄𝜕𝜕𝜕𝜕 = 1.
where
𝐾𝐾𝑥𝑥 = Proportional
(P)
or Derivative
(D),
= 𝑒𝑒 and 𝜕𝜕𝜕𝜕
𝑥𝑥 (I)
𝑥𝑥for𝜕𝜕𝜕𝜕
By
applying
thePID
MIT
gradient
rule,𝜕𝜕𝜕𝜕
the
adaptation
value
PID
parameters
derived
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 in
𝜕𝜕𝜕𝜕 order
𝜕𝜕𝜕𝜕
Equation
has
been𝑑𝑑𝑑𝑑derived
mathematically
to develop an adjustment
𝑥𝑥The parameters
𝐾𝐾
𝐾𝐾𝑑𝑑based
are
obtained.
𝑝𝑝 , 𝐾𝐾𝑖𝑖 and(22)
= - 𝛾𝛾𝑝𝑝 ( ) =
-are
𝛾𝛾 derived
[( )( based
)( (D),)] 𝜕𝜕𝜕𝜕⁄𝜕𝜕𝜕𝜕 = 𝑒𝑒 and 𝜕𝜕𝜕𝜕⁄𝜕𝜕𝜕𝜕 (22)
where
𝐾𝐾𝑥𝑥 = for
Proportional
(P)
= 1.
𝑑𝑑𝑑𝑑 or Intergral
𝜕𝜕𝜕𝜕𝑥𝑥 (I) or𝑥𝑥 Derivative
𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕
mechanism
PID controller.
𝑥𝑥
Equation (22) has been𝑑𝑑𝑑𝑑derived
mathematically
to develop an adjustment
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 in
𝜕𝜕𝜕𝜕 order
𝜕𝜕𝜕𝜕
𝑥𝑥
= - 𝛾𝛾𝑝𝑝 ( ) =
- 𝛾𝛾 [( )( )( (D),)] 𝜕𝜕𝜕𝜕⁄𝜕𝜕𝜕𝜕 = 𝑒𝑒 and 𝜕𝜕𝜕𝜕⁄𝜕𝜕𝜕𝜕 (22)
where
𝐾𝐾𝑥𝑥 = for
Proportional
(P)
= 1.
mechanism
PID controller.
𝑑𝑑𝑑𝑑 or Intergral
𝜕𝜕𝜕𝜕𝑥𝑥 (I) or𝑥𝑥 Derivative
𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕𝑥𝑥
Equation (22) has been derived mathematically in order to develop an adjustment
mechanism
PID controller.
where
𝐾𝐾𝑥𝑥 = for
Proportional
(P) or Intergral (I) or Derivative (D), 𝜕𝜕𝜕𝜕⁄𝜕𝜕𝜕𝜕 = 𝑒𝑒 and 𝜕𝜕𝜕𝜕⁄𝜕𝜕𝜕𝜕 = 1.
Equation (22) has been derived mathematically in order to develop an adjustment
mechanism for PID controller.
50
ISSN: 2180-1053
Vol. 6
No. 1
January - June 2014
Development of Antilock Braking System using Electronic Wedge Brake Model
where Kx = Proportional (P) or Intergral (I) or Derivative (D), ∂J⁄∂e= e
and ∂e⁄∂y = 1. Equation (22) has been derived mathematically in order
to develop an adjustment mechanism for PID controller.
𝜕𝜕𝜕𝜕𝑝𝑝
𝜕𝜕𝜕𝜕𝑝𝑝
𝜕𝜕𝜕𝜕𝑖𝑖
𝜕𝜕𝜕𝜕𝑝𝑝
𝜕𝜕𝜕𝜕𝑝𝑝
𝜕𝜕𝜕𝜕=
𝑝𝑝
𝜕𝜕𝜕𝜕𝑑𝑑
𝜕𝜕𝜕𝜕𝑖𝑖
= �(0.25+0.002385𝐾𝐾
𝑑𝑑 )𝑠𝑠
= 𝑝𝑝
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕𝑝𝑝
0.002385𝑠𝑠
2 +(1+0.002385𝐾𝐾 )𝑠𝑠+0.002385𝐾𝐾
𝑝𝑝
𝑖𝑖
0.002385
�(𝜆𝜆𝑑𝑑 − 𝜆𝜆𝑝𝑝 )
�
�(𝜆𝜆𝑑𝑑 − 𝜆𝜆𝑝𝑝 )
0.002385𝑠𝑠
i 𝑑𝑑 − 𝜆𝜆𝑝𝑝 )
= � (0.25+0.002385Kd)s2 2 +(1+0.002385Kp)s+0.002385K
�(𝜆𝜆
(0.25+0.002385𝐾𝐾𝑑𝑑 )𝑠𝑠 +(1+0.002385𝐾𝐾𝑝𝑝 )𝑠𝑠+0.002385𝐾𝐾𝑖𝑖
0.002385s2
�(0.25+0.002385K )s2 +(1+0.002385K
�(𝜆𝜆𝑑𝑑 − 𝜆𝜆𝑝𝑝 )
0.002385
=
�(0.25+0.002385K
�(𝜆𝜆𝑑𝑑 − 𝜆𝜆𝑝𝑝 )
p )s+0.002385Ki
d
)s2 +(1+0.002385K )s+0.002385K
p
d
i
(23)
(24)
(23)
(25)
(24)
By refering to𝜕𝜕𝜕𝜕Equations (23) to (25),0.002385s
the adaptation
value for PID parameters are obtained
2
𝑝𝑝
=
�
�(𝜆𝜆equations
(25)
as Equations
(26)
to
(28)
using
1st
order
transfer
function.
This
will be
used
as
By refering
to
Equations
(23)
to
(25),
the adaptation
for
PID
𝑑𝑑 − 𝜆𝜆𝑝𝑝 )value
2
𝜕𝜕𝜕𝜕𝑑𝑑
(0.25+0.002385Kd )s +(1+0.002385Kp )s+0.002385K
i
adjustment
mechanism
for the PID
of outer
loop
control
to 1st
develop
antransfer
adaptive
parameters
are obtained
ascontroller
Equations
(26) to
(28)
using
order
controller
usingThis
By refering
toPID.
Equations
(23) towill
(25),be
theused
adaptation
value for PIDmechanism
parameters arefor
obtained
function.
equations
as adjustment
the
as
Equations
(26)
to
(28)
using
1st
order
transfer
function.
This
equations
will
be
used as
PID
controller
of
outer
loop
control
to
develop
an
adaptive
controller
𝑑𝑑𝑑𝑑𝑝𝑝
𝜕𝜕𝜕𝜕
0.002385𝑠𝑠
adjustment
the PID controller
of outer loop control to� (𝜆𝜆
develop
an adaptive
= - 𝛾𝛾𝑝𝑝 PID.
(𝜕𝜕𝜕𝜕 mechanism
) = - 𝛾𝛾𝑝𝑝 𝑒𝑒[�for
(26)
𝑑𝑑 − 𝜆𝜆𝑝𝑝 )]
2
𝑑𝑑𝑑𝑑using
𝑝𝑝
controller
using
PID. (0.25+0.002385𝐾𝐾𝑑𝑑)𝑠𝑠 +(1+0.002385𝐾𝐾𝑝𝑝 )𝑠𝑠+0.002385𝐾𝐾𝑖𝑖
𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑
∂J
0.002385
𝑖𝑖 𝑝𝑝
0.002385𝑠𝑠
= - γ ( 𝑝𝑝 () 𝜕𝜕𝜕𝜕
= -) =
γi -e[�
� (λ�d(𝜆𝜆−𝑑𝑑 λ−p )]
𝛾𝛾𝑝𝑝(0.25+0.002385𝐾𝐾
𝑒𝑒[�(0.25+0.002385𝐾𝐾
𝜆𝜆𝑝𝑝 )]
2 +(1+0.002385𝐾𝐾
𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 = i- 𝛾𝛾∂K
𝑝𝑝 )𝑠𝑠+0.002385𝐾𝐾
𝑑𝑑 )𝑠𝑠 𝑑𝑑
i 𝜕𝜕𝜕𝜕𝑝𝑝
𝑖𝑖
)𝑠𝑠2 +(1+0.002385𝐾𝐾
𝑝𝑝 )𝑠𝑠+0.002385𝐾𝐾
𝑖𝑖
2
𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑖𝑖
𝜕𝜕𝜕𝜕 ∂J
0.002385𝑠𝑠
0.002385
= - 𝛾𝛾=𝑑𝑑 -(𝜕𝜕𝜕𝜕
) = )- =𝛾𝛾𝑑𝑑- γ𝑒𝑒[�
�� (𝜆𝜆
γ
(
e[�
(λ𝑑𝑑d − 𝜆𝜆λp𝑝𝑝)]
2 +(1+0.002385𝐾𝐾
2
i
i
𝑑𝑑𝑑𝑑
(0.25+0.002385𝐾𝐾
)𝑠𝑠
)𝑠𝑠+0.002385𝐾𝐾
𝑑𝑑𝑑𝑑
(0.25+0.002385𝐾𝐾
)𝑠𝑠+0.002385𝐾𝐾𝑖𝑖𝑖𝑖
𝑝𝑝𝑝𝑝
𝑑𝑑 ∂Ki
𝑑𝑑 𝑑𝑑 )𝑠𝑠 +(1+0.002385𝐾𝐾
(27)
(26)
(28)
(27)
𝑑𝑑𝑑𝑑𝑑𝑑𝛾𝛾 represents
𝜕𝜕𝜕𝜕 the learning rate of the adaptation
0.002385𝑠𝑠2 mechanism and 𝜀𝜀 are the defined
where
= - 𝛾𝛾𝑑𝑑 ( ) = - 𝛾𝛾𝑑𝑑 𝑒𝑒[�
� (𝜆𝜆 − 𝜆𝜆𝑝𝑝 )]
(28)
2 +(1+0.002385𝐾𝐾 )𝑠𝑠+0.002385𝐾𝐾
𝑑𝑑𝑑𝑑
𝜕𝜕𝜕𝜕
(0.25+0.002385𝐾𝐾
)𝑠𝑠
𝑝𝑝
error based on the𝑑𝑑 difference between actual𝑑𝑑 output and desired
output. 𝑖𝑖The 𝑑𝑑parameters
for
the adjustment mechanism in the Equations (18) to (28) are obtained from linearization of
𝛾𝛾 represents
rate value
of theofadaptation
mechanism
and 𝜀𝜀 linearization
are the defined
the where
controller
gain with the
the learning
desired slip
antilock braking,
𝜆𝜆. Before
is
error
based
on the to
difference
output
and desired
The parameters
for
made,
it is
necessary
identify between
the PID actual
controller
parameter
for output.
the braking
model using
where
γ represents
the
rate
of
adaptation
mechanism
and
the adjustment
mechanism
in learning
the
Equations
(18)
tothe
(28)
areis obtained
linearization
sudden
braking test
input. The
identified
PID
controller
used asfrom
a bench
mark inof
εtheare
the
defined
error
based
theofdifference
between
actual
output
controller
gain with
the desired
slipon
value
antilockThe
braking,
𝜆𝜆. Before
linearization
developing
adaptation
mechanism
for
MRAC
model.
initial
values
of the
PIDis
made,desired
it is necessary
identify
the
PID in
controller
for the
braking
and
output.
Therate
parameters
forparameter
the
adjustment
mechanism
controller
parameters
andtolearning
used
this model
are shown
in Table
3. model using
sudden
test input.
identified
PID controller
is used
as a bench of
mark
in
the braking
Equations
(18) The
to (28)
are obtained
from
linearization
thein
developing adaptationTable
mechanism
forandMRAC
The initial values of the PID
3. Controller
learning model.
rate parameters
controller
gain with
desired
slipinvalue
of antilock
controller parameters
and the
learning
rate used
this model
are shownbraking,
in Table 3.λ. Before
linearization
is made, it is necessary to
identify Value
the PID controller
Description
Symbol
P 3. Controller
550
Table
and learning
parametersbraking
𝐾𝐾𝑝𝑝sudden
parameter Proportional
for the gain,
braking
model
usingrate
test input.
Intergal gain, I
2950
𝐾𝐾𝑖𝑖
The identified
PID
controller
is used as Symbol
a bench mark
Description
Valuein developing
Derivative
gain,
D
10
𝐾𝐾
𝑑𝑑
Proportional
P MRAC model.𝛾𝛾The
550
𝐾𝐾
adaptationLearning
mechanism
initial
values
of the PID
rate of gain,
P for
0.001
𝑝𝑝 𝑝𝑝
Intergal
gain,
I
2950
𝐾𝐾
𝑖𝑖
Learning rate of I and learning rate used
0.05
𝛾𝛾𝑖𝑖
controller parameters
in
this
model
are
shown
Derivative
gain,
10
Learning
rate of
D D
0.05
𝛾𝛾𝑑𝑑𝐾𝐾𝑑𝑑
in Table 3. Learning rate of P
0.001
𝛾𝛾𝑝𝑝
Learning rate of I
𝛾𝛾𝑖𝑖
4.3 Outer loop Control
Design using Fuzzy Logic controller
Learning rate of D
𝛾𝛾𝑑𝑑
0.05
0.05
Another
advance
fuzzyusing
logic,Fuzzy
was developed
in this study based on Takagi4.3 Outer
loopcontroller,
Control Design
Logic controller
Sugeno method for the outer loop control system besides adaptive PID controller. In this
Another advance controller, fuzzy logic, was developed in this study based on TakagiSugeno method for the outer loop control system besides adaptive PID controller. In this
ISSN: 2180-1053
Vol. 6
No. 1
January - June 2014
51
made, it is necessary to identify the PID controller parameter for the braking model using
sudden braking test input. The identified PID controller is used as a bench mark in
developing
mechanismand
forTechnology
MRAC model. The initial values of the PID
Journal ofadaptation
Mechanical Engineering
controller parameters and learning rate used in this model are shown in Table 3.
3. Controller and learning rate parameters
Table Table
3. Controller
and learning rate parameters
Description
Proportional gain, P
Intergal gain, I
Derivative gain, D
Learning rate of P
Learning rate of I
Learning rate of D
Symbol
𝐾𝐾𝑝𝑝
𝐾𝐾𝑖𝑖
𝐾𝐾𝑑𝑑
𝛾𝛾𝑝𝑝
𝛾𝛾𝑖𝑖
𝛾𝛾𝑑𝑑
Value
550
2950
10
0.001
0.05
0.05
4.3 Outer loop Control Design using Fuzzy Logic controller
4.3
Outer loop Control Design using Fuzzy Logic controller
Another advance controller, fuzzy logic, was developed in this study based on TakagiAnother advance controller, fuzzy logic, was developed in this study
Sugeno method for the outer loop control system besides adaptive PID controller. In this
0.2
Desired
input, 𝜆𝜆𝑑𝑑
+
_
𝑑𝑑⁄𝑑𝑑𝑑𝑑
Inference
Rule Base
Defuzzificatio
Error
Fuzzification
based on Takagi-Sugeno method for the outer loop control system
besides adaptive PID controller. In this network model, the controller
consists of three stages which are known as fuzzification, rule base and
defuzzification (Ping et al., 2010). Figure 7 shows the overall control
structure of fuzzy logic control using Gaussian membership function
for the outer loop. The inputs to the fuzzy controller are error and
error rate. These fuzzy or linguistic variables are obtained through
network
model, the controller
of three of
stages
known as fuzzification,
fuzzification
process.consists
The output
the which
fuzzyarecontroller
is gap control
rule of
base
and
defuzzification
(Ping
et
al.,
2010).
Figure
7
shows
the
overall
brake piston in EWB actuator. Membership functions of control
the input
structure of fuzzy logic control using Gaussian membership function for the outer loop. The
and
outpu
fuzzy
variables
are
defined.
The
output-input
variables
inputs to the fuzzy controller are error and error rate. These fuzzy or linguistic variables
are
are through
linkedfuzzification
by rules. process.
The membership
functions
and rules
are defined
obtained
The output of the
fuzzy controller
is gap control
of
brakebased
piston in
EWB
actuator.
Membership
functions
of
the
input
and
outpu
fuzzy
variables
on expert experinece. Finally, defuzzification method converts
are defined. The output-input variables are linked by rules. The membership functions and
the fuzzy output into a crisp signal and become the command input for
rules are defined based on expert experinece. Finally, defuzzification method converts the
plant
fuzzythe
output
intomodel.
a crisp signal and become the command input for the plant model.
Two DOF
vehicle model
Actual
output, 𝜆𝜆𝑝𝑝
Error
rate
Fuzzy Logic controller
Figure
7. Fuzzy
logic controller
Gaussian
membership
Figure
7. Fuzzy
logic controller
using Gaussianusing
membership
function for
outer loop modelfunction
for outer loop model
In the Figure 7, the inputs of the fuzzy controller i.e. slip error and slip error rate are
defined
duringFigure
the initialization
stage andofallthe
fuzzy
membership
functions
defined
in
In the
7, the inputs
fuzzy
controller
i.e.areslip
error
order to form the complete rules. A Gaussian membership function is used and defined by
and
slip error rate are defined during the initialization stage and all fuzzy
𝑥𝑥 − 𝑐𝑐in order to form the complete rules.
membership functions are defined
(29)
𝜇𝜇 = 𝑒𝑒 −0.5( 𝜎𝜎 )
A Gaussian membership function is used and defined by
where
x is the Gaussian input from error and error rate
c is the center of the curve
𝜎𝜎 is the spread of the curve
The52
fuzzy logic network
model
used a singleton
Gaussian
membership
input
ISSN:
2180-1053
Vol. 6fuzzification,
No. 1 January
- June
2014
using two variables such as centers, 𝑐𝑐𝑗𝑗𝑖𝑖 , and spreads, 𝜎𝜎𝑗𝑗𝑖𝑖 , output membership function uses
Figure 7. Fuzzy logic controller using Gaussian membe
y logic controller
using
Gaussian
membership
function
for outer
loop model
In the
Figure
7, the
inputs of
the fuzzy
controller
i.e. slip error and slip error rate are
of Antilock
System
using7,
Electronic
Wedge
Brake
In the
Figure
the
ofdefined
the Model
fuzzy
7. Fuzzy
logicDevelopment
controllerstage
using
Gaussian
membership
function
for
outerinputs
loop
model
definedFigure
during
the initialization
and all Braking
fuzzy
membership
functions
are
in
controller
defined
during
the
initialization
stage
and
all fuzzy
order
to
form
the
complete
rules.
A
Gaussian
membership
function
is
used
and
defined
by
e inputs of the fuzzy controller i.e. slip error and slip error rate are
order
to
form
the
complete
rules.
A
Gaussian
member
In
the
Figure
7,
the
inputs
of
the
fuzzy
controller
i.e.
slip
error
and
slip
error
rate
are
initialization stage and all fuzzy membership functions𝑥𝑥 −are
defined in
𝑐𝑐
defined
during
the
initialization
stage
and
all
fuzzy
membership
functions
are
defined
in
−0.5(
)
(29)
omplete rules. A Gaussian membership function
is 𝑒𝑒used and
𝜎𝜎 defined by
𝜇𝜇 =
𝑥𝑥 − 𝑐𝑐
order to form the complete rules. A Gaussian membership function is used and defined by
𝜇𝜇 = 𝑒𝑒 −0.5( 𝜎𝜎 )
where 𝜇𝜇 = 𝑒𝑒 −0.5( 𝑥𝑥 𝜎𝜎− 𝑐𝑐)
(29)
𝑥𝑥 − 𝑐𝑐
where
)
(29)
= 𝑒𝑒 −0.5(
x is the Gaussian input from error and𝜇𝜇 error
rate 𝜎𝜎where
x
is
the
Gaussian
input
from
error
and
error
rate
c is the center of the curve
x is the Gaussian input from error and error rate
is theofcenter
of the curve
where
𝜎𝜎 is thecspread
the curve
c is the center of the curve
put from error
andσGaussian
error
is therate
spread
of the
x is the
input from
errorcurve
and error rate 𝜎𝜎 is the spread of the curve
e curve cThe
fuzzy
logic
is the
center
of network
the curvemodel used a singleton fuzzification, Gaussian membership input
𝑖𝑖
he curve 𝜎𝜎
is the
spread
of thesuch
curve
using
two
variables
as centers,
𝑐𝑐𝑗𝑗𝑖𝑖 , and
spreads,
𝜎𝜎fuzzy
membership
function
The
fuzzy
logic
network
model
used
alogic
singleton
The
network fuzzification,
model
useduses
a singleton fuzz
𝑗𝑗 , output
𝑖𝑖
,
product
for
the
implication
and
also
center
average
defuzzification.
The
final
center 𝑏𝑏
𝑖𝑖
using
two
variables
such
as
centers,
𝑐𝑐
Gaussian
membership
input
using
two
variables
such
as
centers,
𝑗𝑗 , and spreads,
work model
used
a singleton
fuzzification,
Gaussian
membership
inputGaussian membership input
The
fuzzy
logic network
model
used
a singleton
fuzzification,
equation
representing
the
network
model
is
𝑖𝑖
𝑖𝑖 output membership
𝑖𝑖 𝑏𝑏𝑖𝑖 , uses
center
product
the implication
,𝑐𝑐and
usesfor
center
bi, product
such as centers,
andspreads,
spreads,
output membership
function
using two
such 𝜎𝜎as
𝑐𝑐𝑗𝑗𝑖𝑖 , and spreads,
𝜎𝜎function
usesand also cent
𝑗𝑗 , variables
𝑗𝑗 , centers,
𝑗𝑗 , output membership function
equation
representing
the
network
model
is
𝑖𝑖
𝑖𝑖
for
the
implication
and
also
center
average
defuzzification.
The
final
for the implication
alsofor
center
average defuzzification.
𝑥𝑥𝑗𝑗average
−𝑐𝑐𝑗𝑗 final defuzzification. The final
product
the implication
and also
centerThe
center 𝑏𝑏𝑖𝑖 , and
∑𝑅𝑅
𝑏𝑏𝑖𝑖 ∏𝑛𝑛
𝑒𝑒𝑒𝑒𝑒𝑒 [−0.5 𝑖𝑖 ]
𝑖𝑖=1
𝑗𝑗=1
equation
representing
network
model𝜎𝜎𝑗𝑗is
ng the network
model
is
equation
representing
the network the
model
is
(30)
f(x|𝜃𝜃) =
𝑅𝑅
𝑛𝑛
𝑥𝑥𝑖𝑖 −𝑐𝑐𝑖𝑖
f(x|𝜃𝜃) =
𝑥𝑥𝑖𝑖𝑗𝑗−𝑐𝑐𝑖𝑖𝑗𝑗
𝑛𝑛
∑𝑅𝑅
]
𝑖𝑖=1 𝑏𝑏𝑖𝑖 ∏𝑗𝑗=1 𝑒𝑒𝑒𝑒𝑒𝑒 [−0.5
𝜎𝜎𝑖𝑖𝑗𝑗
𝑥𝑥𝑖𝑖𝑗𝑗−𝑐𝑐𝑖𝑖𝑗𝑗
𝑛𝑛
∑𝑅𝑅
𝑖𝑖=1 ∏𝑗𝑗=1 𝑒𝑒𝑒𝑒𝑒𝑒 [−0.5 𝜎𝜎𝑖𝑖 ]
𝑗𝑗
f(x|𝜃𝜃) =
𝑗𝑗
𝑗𝑗
𝑛𝑛
∑𝑅𝑅
𝑖𝑖=1 ∏𝑗𝑗=1 𝑒𝑒𝑒𝑒𝑒𝑒 [−0.5 𝑥𝑥𝑖𝑖𝑖𝑖−𝑐𝑐𝑖𝑖]
𝜎𝜎𝑗𝑗𝑗𝑗 𝑗𝑗
𝑛𝑛
∑𝑅𝑅
𝑖𝑖=1 𝑏𝑏𝑖𝑖 ∏𝑗𝑗=1 𝑒𝑒𝑒𝑒𝑒𝑒 [−0.5
𝑖𝑖 ]
𝜎𝜎𝑗𝑗
𝑥𝑥𝑖𝑖𝑗𝑗−𝑐𝑐𝑖𝑖𝑗𝑗
𝑛𝑛
∑𝑅𝑅
𝑖𝑖=1 ∏𝑗𝑗=1 𝑒𝑒𝑒𝑒𝑒𝑒 [−0.5
𝜎𝜎𝑖𝑖𝑗𝑗
(30)
]
f(x|𝜃𝜃) =
∑𝑖𝑖=1 𝑏𝑏𝑖𝑖 ∏𝑗𝑗=1 𝑒𝑒𝑒𝑒𝑒𝑒 [−0
𝑅𝑅
𝑛𝑛
∑𝑖𝑖=1 ∏𝑗𝑗=1 𝑒𝑒𝑒𝑒𝑒𝑒 [−0.
(30)
where
inputtotothe
thefuzzy
fuzzynetwork,
network,
number
where 𝑥𝑥𝑗𝑗𝑖𝑖 is input
j =j =1,1,…,…,n n(n(nis is
thethe
number
of inputs) and
𝑖𝑖
where
𝑥𝑥
is
input
to
the
fuzzy
network,
j
=
1,
…,
n
(n
is
the
number
of
inputs) and
of
inputs)
and
i
=
1,
…,
R
(R
is
the
number
of
rules
and
it
will
be
𝑗𝑗
R (R is the number of rules and it will be determined during the initialization
determined
the
initialization
stage
fixed during
Rfixed
(R isduring
the during
number
ofstage).
rules
and parameter
it will
beand
duringlearning
the initialization
learning
The
𝑏𝑏determined
𝑖𝑖 is the center of i th consequent fuz
stage).
The
b
is
the
center
of
i
th
consequent
fuzzy
set
andfunctionsfuzz
𝑖𝑖
𝑖𝑖 parameter
fixed
during
learning
stage).
The
parameter
𝑏𝑏
is
the
center
of
i
th
consequent
𝑖𝑖
membership
at
𝑐𝑐𝑗𝑗 and σ𝑗𝑗 are center andi spread of Gaussian antecedent
𝑖𝑖
𝑖𝑖
center
and
spread
of
Gaussian
antecedent
membership
and
σ
are
center
and
spread
of
Gaussian
antecedent
membership
functions
at
𝑐𝑐input
𝑗𝑗
j, 𝑗𝑗respectively. In order to develop the Fuzzy Logic controller, slip error an
functions
at rule as
i and
input
j, respectively.
Invariables
order
toreflect
develop
input
j,
respectively.
In order
develop These
the Fuzzy
Logic
controller,
slip error
error are
chosen
the
input to
variables.
thethe
fuzzy
inputand
se
Fuzzy
Logic
controller,
slip
error
and slip
rate variables
error are reflect
chosen the
as the
error
are
chosen
as
the
input
variables.
These
fuzzy
input
se
closed loop model which is shown in Figures 8 and 9. The parameter of cen
input
variables.
These
variables
reflect in
theFigures
fuzzy input
sets9.for
theparameter
closed
closed
which
is shown
and
The
spread,loop
𝜎𝜎 aremodel
determined
based
on the range
of 8maximum
and minimumofofcent
the
loop
model
which
is
shown
in
Figures
8
and
9.
The
parameter
of
center,
spread,
𝜎𝜎
are
determined
based
on
the
range
of
maximum
and
minimum
of
the
error rate values. The range is measured from the outer loop control structure u
cerror
and rate
spread,
σ areThe
determined
based on the
range
of maximum
and structure u
values.
range
is structure
measured
from
theasouter
loop
control
controller
since
this
control
is
used
the
benchmark
to develop
minimum of the error and error rate values. The range is measured from
controller
since
this
control
structure
is
used
as
the
benchmark
to
develop
controllers.
the parameter
is determined
based
on the
maxi
the
outer loopMeanwhile,
control structure
using PID bcontroller
since this
control
controllers.
Meanwhile,
the
parameter
b braking
is determined
based
on the
maxim
minimum
brake
torque
required
during
a
vehicle
in
order
to
avoid
structure is used as the benchmark to develop advance controllers.
minimum
brake torque required during braking a vehicle in order to avoid
disturbance.
Meanwhile,
the parameter b is determined based on the maximum and
disturbance.
minimum brake torque required during braking a vehicle in order to
In order
to improve
fuzzification speed, Gaussian function is proposed as the me
avoid
skidding
disturbance.
In
order to
improve
speed,
Gaussian
is proposed
as theofme
function
(Ping
et al.,fuzzification
2010). Figures
8 and
9 show function
the membership
functions
in
function
(Ping
et
al.,
2010).
Figures
8
and
9
show
the
membership
functions
of
in
variables
Figurefuzzification
10 for the output
variable
where
the range of slip erro
In
order toand
improve
speed, fuzzy
Gaussian
function
is proposed
variables
10 foristhe
output
fuzzy
variable
where
the
slip
erro
0.01)
andand
slipFigure
rate function
error
(-0.154,
Meanwhile,
Figure
119 range
shows
range
as
the membership
(Ping
et 0).
al.,
2010).
Figures
8 and
show ofthe
0.01)
and
slip rate
error is (-0.154,
0).
Meanwhile,
Figure
11 shows
the range
fuzzy
variable
is afunctions
singleton
within
to 700
and the
relationship
between
slip
the
membership
of
input-700
fuzzy
variables
and
Figure
10
fuzzy
variable
is
a
singleton
within
-700
to
700
and
the
relationship
between
slip
for
therateoutput
fuzzy
variable
where
range of slip error is (-0.8,
error
and brake
torque
output
in 3Dthe
surface.
error and
rate slip
and brake
torque
output in
surface. Figure 11 shows the
0.01)
rate error
is (-0.154,
0).3D
Meanwhile,
range of output fuzzy variable is a singleton within -700 to 700 and the
relationship between slip error, slip error rate and brake torque output
in 3D surface.
ISSN: 2180-1053
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No. 1
January - June 2014
53
In order to improve fuzzification speed, Gaussian function is proposed as the membership
In order to improve fuzzification speed, Gaussian function is proposed as the membership
function (Ping et al., 2010). Figures 8 and 9 show the membership functions of input fuzzy
function (Ping et al., 2010). Figures 8 and 9 show the membership functions of input fuzzy
variables
Figure 10 for the output
fuzzy variable where the range of slip error is (-0.8,
Journal
of and
Mechanical
and Technology
variables
and FigureEngineering
10 for the output
fuzzy variable where the range of slip error is (-0.8,
0.01) and slip rate error is (-0.154, 0). Meanwhile, Figure 11 shows the range of output
0.01) and slip rate error is (-0.154, 0). Meanwhile, Figure 11 shows the range of output
fuzzy variable is a singleton within -700 to 700 and the relationship between slip error, slip
fuzzy variable is a singleton within -700 to 700 and the relationship between slip error, slip
error rate and brake torque output in 3D surface.
error rate and brake torque output in 3D surface.
Figure
8. Slip
error
variable
Figure
8. Slip
error input
input variable
Figure 8. Slip error input variable
FigureFigure
9. Slip
error
input
variable
9. Slip
errorrate
rate input
variable
Figure
10.10.
Brake
torquetorque
output fuzzy
variables
Figure
Brake
output
fuzzy
Figure 10.
Brake
torque output fuzzy
variables
variables
Figure 9. Slip error rate input variable
Figure
Output-input relation
Figure
11.11.
Output-input
relation
Figure
11. Output-input relation
The fuzzy sets for the input fuzzy variables are defined as positive
(POS), zero (ZERO) and negative (NEG). The variables are maintained
to initial condition since this inputs itself is sufficient to control the
ABS longitudinal slip. Since there are 3 elements of each fuzzy set, the
probability of 9 types of fuzzy rules has been used as base rule for this
controller. The output fuzzy set representing brake torque is defined as
positive big (PB), positive small (PS), zero (ZERO), negative small (NS)
and negative big (NB).
The rules in Table 4 are derived basically using a combination of
experience, trial and error approach and the knowledge of the response
of the ABS system. In this study, ABS control system using PID controller
is used as a benchmark to develop fuzzy logic rules. The error and error
rate from ABS control system using PID controller is used to derive
the combinations rules for ABS using fuzzy logic controller. Normally,
the rules are determined using “if and then rules” condition. For an
example, if slip error is positive and slip error rate is positive then the
output is positive big. This means that the output signal is increasing
and responding as overshoot response.
54
ISSN: 2180-1053
Vol. 6
No. 1
January - June 2014
The rules in Table
are ABS
derived
basically
combinationNormally,
of experience,
trial and
combinations
rules 4for
using
fuzzyusing
logica controller.
the rules
are
error
approach
and“ifthe
knowledge
ofcondition.
the response
ABS system.
In this
study, ABS
determined
using
and
then rules”
For of
anthe
example,
if slip error
is positive
and
control
system
PIDthen
controller
is used
as a benchmark
toElectronic
develop
fuzzy
logic
rules.
slip error
rate isusing
positive
theofoutput
is positive
big. This
means
that the
output
signal
is
Development
Antilock
Braking
System
using
Wedge
Brake
Model
The
error and
rate from
control
system using PID controller is used to derive the
increasing
anderror
responding
as ABS
overshoot
response.
combinations rules for ABS using fuzzy logic controller. Normally, the rules are
determined using “if and then rules”Table
condition.
example, if slip error is positive and
FuzzyFor
rule an
Table 4. 4.
Fuzzy
rulebase
base
slip error rate is positive then the output is positive big. This means that the output signal is
Input variable
increasing and responding
as overshoot response. Slip error rate
POS
ZERO
NEG
PB (rule 9)
PS (rule 8)
ZERO (rule 7)
Table 4. Fuzzy rule base
PS (rule 6)
ZERO (rule 5)
NS (rule 4)
ZERO (rule 3)
NS (rule 2)
NB (rule 1)
Slip error rate
POS
ZERO
NEG
4.4 Inner loop
control
PBEWB
(rule 9)model PS (rule 8)
ZERO (rule 7)
Slip
error design
POS using
4.4
Inner loop ZERO
control design
EWB
PS (rule 6)using
ZERO
(rule model
5)
NS (rule 4)
ZERO
3)
NS
(rule 2)brake (EWB)
NB (rulemechanism.
1)
NEG
Inner loop control was developed
for the(rule
electronic
wedge
Slip error
POS
ZERO
NEG
Input variable
From
Inner loop control was developed for the electronic wedge brake (EWB)
the previous section, the Bell-Shaped curve has been used as the model for the EWB
mechanism.
the previous
section,
theclosely
Bell-Shaped
curve
has
been
4.4
InnerSince
loop control
design
EWB
modelcurve
actuator.
theFrom
behaviour
ofusing
the Bell-Shaped
follows the
actual
behaviour
used
as
the
model
for
the
EWB
actuator.
Since
the
behaviour
of
the
of the EWB actuator, this mathematical equation is used as the plant model of theBellinner
Inner
loop control
developed
for of
the
electronic
wedge
brakehas
(EWB)
mechanism.
loop
control.
The was
desired
trajectory
the
inner loop
control
been
set upactuator,
to 420From
Nm
Shaped
curve
closely
follows
the
actual
behaviour
of
the EWB
the
previous
section,
theofBell-Shaped
curve
has Figure
been used
as the the
model
for thecontrol
EWB
based
on
brake
torque
a
passenger
vehicle.
12
shows
proposed
this mathematical equation is used as the plant model of the inner loop
actuator.
behaviour
structure Since
using the
EWB
model. of the Bell-Shaped curve closely follows the actual behaviour
desired
trajectory equation
of the inner
has ofbeen
set
ofcontrol.
the EWB The
actuator,
this mathematical
is usedloop
as thecontrol
plant model
the inner
upcontrol.
to 420The
Nmdesired
basedtrajectory
on brake
torque
a passenger
vehicle.
12
loop
of the
inner of
loop
control has been
set upFigure
to 420 Nm
based
on brake
torque of control
a passenger
vehicle. using
Figure EWB
12 shows
the proposed control
shows
the proposed
structure
model.
structure using EWB model.
Figure 12. Proposed control structure using EWB model
Figure
12. Proposed
control structure
structure using
EWB EWB
model model
Figure 12.
Proposed
control
using
Figure 12 shows the proposed control structure using EWB model
to develop an inner loop controller. The reference input to the EWB
model is the wheel brake torque. Meanwhile, PID controller is used to
control the error of the inner loop control. Refering to Figure 12, there
are two PID controllers used in this control structure. The primary PID
controller is used to control brake torque obtained from the EWB model
as described in Equation (14) and (15). The secondary PID controller
is used specifically to command the DC motor to actuate the desired
value from the primary PID controller (Aparow et al., 2013c).
The rotational displacement from the DC motor is converted to linear
displacement (gapping mode). This will be the input to the BellShaped curve which represents the EWB actuator. The EWB force will
be converted to wheel brake torque and feedback to the comparator.
The actual brake torque is compared with the desired brake torque by
measuring the difference between actual and desired values in order
to obtain minimum error. The performance of EWB model has been
discussed in Aparow et al., (2013c).
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January - June 2014
55
Journal of Mechanical Engineering and Technology
4.5 Proposed ABS-EWB closed loop control structure
For an ABS-EWB closed loop scheme, the disturbance is measured
in the form of wheel slip occurred after brake being applied and a
corrective action is taken to maintain the wheel slip to 0.2. The outer
loop model is developed using the quarter vehicle model as the plant
to be controlled. Meanwhile, EWB model is used as the plant model
for inner loop model. Since the outer closed loop is developed using
a quarter vehicle brake model, only a single wheel brake torque is
needed to be controlled by the controller. Besides, validated electronic
wedge brake model is used as an inner loop control. The input for inner
loop control is obtained from the controller of the outer loop control.
Based on the proposed inner and outer loop controls, an ABS model is
developed by integrating both inner loop and outer loop into a system.
The desired trajectory used a constant slip value of 0.2. The response
from inner loop control is used as brake torque for the plant model and
the wheel slip is feedback and compared with the desired trajectory.
4.5.1 Closed Loop Control Design using Quarter Vehicle and EWB
Model
The ABS control system using three type of controllers which are
conventional PID, adaptive PID and fuzzy logic control are studied.
For comparison, the adaptive PID and fuzzy logic controller are
compared with both conventional PID controller and passive system.
The performance of the controllers are evaluated by examining the
vehicle braking performance namely vehicle and wheel velocity,
stopping distance and vehicle longitudinal slip. Figures 13 and 14
show the closed loop control structure of the proposed ABS model
using adaptive PID and fuzzy logic control.
Figure 13. Control structure of ABS-EWB closed loop control using
Figure 13. Control structure of ABS-EWB closed loop control using adaptive PID
adaptive PID
56
ISSN: 2180-1053
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January - June 2014
Development of Antilock Braking System using Electronic Wedge Brake Model
Figure 13. Control structure of ABS-EWB closed loop control using adaptive PID
Figure 14. Control structure of ABS-EWB closed loop control using fuzzy logic
Figure
14. Control structure of ABS-EWB closed loop control using
fuzzy
The actual response of longitudinal slip from
thelogic
quarter vehicle model will be feedback to
the comparator. The error is obtained from the difference between the predefined trajectory
ofThe
ABSactual
slip andresponse
actual longitudinal
slip from theslip
plantfrom
model.the
Thequarter
error willvehicle
be used asmodel
the
of longitudinal
input
the feedback
controller to to
optimize
and reduce the error
the actual
value willfrom
closelythe
willto be
the comparator.
Theuntil
error
is obtained
follow the reference value. According to the ABS concept, the wheel of the quarter vehicle
difference
between slip
theinpredefined
trajectory
of ABS
slip
andsudden
actual
should
produce longitudinal
the range of 0.15
to 0.25. Wheel
skidding
during
longitudinal
slip iffrom
the plantwheel
model.
error will
be the
used
asofthe
braking
can be reduced
the longitudinal
slip isThe
maintained
between
range
0.15
to 0.25.
wheel speed
stopping and
distance
of the vehicle
are also
determined.
input
to Further,
the controller
to and
optimize
reduce
the error
until
the actual
value will closely follow the reference value. According to the ABS
the wheel
of the quarter vehicle should produce longitudinal
5.0concept,
SIMULATION
RESULTS
slip in the range of 0.15 to 0.25. Wheel skidding during sudden braking
The
simulation
resultsifofthe
thelongitudinal
ABS closed loop
controlslip
structure
using PID, adaptive
PIDthe
can
be reduced
wheel
is maintained
between
using model reference adaptive control (MRAC) technique, and fuzzy logic control using
range of 0.15 to 0.25. Further, wheel speed and stopping distance of the
Gaussian membership function compared with conventional braking. This control system
vehicle
arebased
alsoon
determined.
was
developed
the outer loop control using quarter vehicle model and inner loop
control using electronic wedge brake (EWB) actuator model as shown in Figures 13 and 14.
The control structure is analyzed using sudden braking test where the brake is applied when
the velocity of the vehicle is 25 m/s and stopping distance, longitudinal slip and velocities
5.0
SIMULATION RESULTS
of vehicle and wheel are observed. ABS is developed by controlling the brake torque
obtained from the EWB actuator.
The simulation results of the ABS closed loop control structure using
PID, adaptive PID using model reference adaptive control (MRAC)
technique, and fuzzy logic control using Gaussian membership
function compared with conventional braking. This control system
was developed based on the outer loop control using quarter vehicle
model and inner loop control using electronic wedge brake (EWB)
actuator model as shown in Figures 13 and 14. The control structure is
analyzed using sudden braking test where the brake is applied when
the velocity of the vehicle is 25 m/s and stopping distance, longitudinal
slip and velocities of vehicle and wheel are observed. ABS is developed
by controlling the brake torque obtained from the EWB actuator.
Brake torque from EWB model is used as input to the quarter vehicle
model. Conventional PID controller is used as the benchmark for the
adaptive PID and fuzzy logic to control the brake torque of a single
wheel. The brake torque will control the longitudinal wheel slip to
be in between 0.15 to 0.25. This will reduce the stopping distance of
the vehicle and managed to halt wheel velocity without skidding. The
results of the study are shown in Figures 15 to 18 which compare the
ISSN: 2180-1053
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January - June 2014
57
Brake torque from EWB model is used as input to the quarter vehicle model. Conventional
PID controller is used as the benchmark for the adaptive PID and fuzzy logic to control the
brake torque of a single wheel. The brake torque will control the longitudinal wheel slip to
be in between 0.15 to 0.25. This will reduce the stopping distance of the vehicle and
vehicle and
wheel
longitudinal
slipresults
and the
vehicle
managed
to halt
wheelvelocities,
velocity without
skidding. The
of the
study stopping
are shown in
distance.
Figures
and 16the
show
theand
comparison
of vehicle
andslip
wheel
Figures
15 to
18 which15compare
vehicle
wheel velocities,
longitudinal
and the
vehicle
stopping
distance.
Figures
15
and
16
show
the
comparison
of
vehicle
and
wheel
velocity of the quarter vehicle model using conventional PID, adaptive
velocity
of
the
quarter
vehicle
model
using
conventional
PID,
adaptive
PID,
fuzzy
logic
PID, fuzzy logic and conventional braking.
and conventional braking.
Journal of Mechanical Engineering and Technology
Figure
Comparison ofof
vehicle
velocity
Figure 16.
of wheel
Figure
15. 15.
Comparison
vehicle
Figure
16.Comparison
Comparison
ofvelocity
wheel
velocity
velocity
Conventional braking causes the wheel to lock up causing skidding after 0.6 seconds brake
is applied. Meanwhile, ABS model using conventional PID, adaptive PID and fuzzy logic
Conventional
causes
the wheel
to from
lock locking
up causing
skidding
control
the brake braking
torque in order
to avoid
the wheel
during braking.
ABS
after
0.6
seconds
brake
is
applied.
Meanwhile,
ABS
model
using
using conventional PID shows the wheel stops decelerate at 3.65 second and ABS
using
adaptive
PID stops
at 3.5adaptive
second. However,
for ABS-EWB
usingcontrol
fuzzy logic
conventional
PID,
PID and
fuzzy logic
thecontrol,
brakethe
vehicle
is
able
to
halt
at
3.3
second.
ABS-EWB
using
fuzzy
logic
control
has
improve
torque in order to avoid the wheel from locking during braking. ABSthe
performance of the wheel velocity by reducing jerking motion occurred in a wheel during
using conventional PID shows the wheel stops decelerate at 3.65 second
braking compared to the other two controllers. Skidding of the wheel has been reduced and
andimproving
ABS using
adaptive
PIDofstops
at 3.5 second. However, for ABSthus
the stopping
distance
the vehicle.
EWB using fuzzy logic control, the vehicle is able to halt at 3.3 second.
Figure
17 shows
the comparison
of the
response
longitudinalthe
wheel
slip during sudden
ABS-EWB
using
fuzzy logic
control
hasof improve
performance
of
braking.
It canvelocity
be seen that
braking results
approaches
+1 in
aftera 0.6
second
the wheel
by conventional
reducing jerking
motion
occurred
wheel
which represents wheel locking during braking and the vehicle starts to skid until stops at
during braking compared to the other two controllers. Skidding of the
3.9 second. Three type of controllers are used to reduce address issue occurring in the
wheelbyhas
been reduced
and thusslip
improving
the stopping
distance
wheel
controlling
wheel longitudinal
to 0.2. Conventional
PID and
adaptiveof
PID
the
vehicle.
controllers are used in this study to control longitudinal slip of wheel to be equal to 0.2
once brake is applied. The performance of both controllers is investigated and the responses
show
that17
ABS
usingthe
PIDcomparison
controller reached
settling
time condition
for longitudinal
wheel
Figure
shows
of the
response
of longitudinal
wheel
slip
within
2.0
second
with
minor
jerk
before
halt.
Meanwhile,
ABS
using
adaptive
slip during sudden braking. It can be seen that conventional brakingPID
results approaches +1 after 0.6 second which represents wheel locking
during braking and the vehicle starts to skid until stops at 3.9 second.
Three type of controllers are used to reduce address issue occurring in
the wheel by controlling wheel longitudinal slip to 0.2. Conventional
PID and adaptive PID controllers are used in this study to control
longitudinal slip of wheel to be equal to 0.2 once brake is applied.
The performance of both controllers is investigated and the responses
show that ABS using PID controller reached settling time condition for
longitudinal wheel slip within 2.0 second with minor jerk before halt.
Meanwhile, ABS using adaptive PID controller is also able to reach
58
ISSN: 2180-1053
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January - June 2014
Development of Antilock Braking System using Electronic Wedge Brake Model
settling time condition within 1.5 second with jerking slighly better
than previous controller.
Jerking condition as shown in Figure 17 is occurred because of overshoot
response in wheel longitudinal slip before approaching steady state
conditions.Generally, adaptive PID works better than conventional
PID because of the parameter of PID will change by the adjustment
controller
is also until
able to reach
time condition
within 1.5
second However,
with jerking slighly
mechanism
they settling
converge
to optimal
values.
the
better
than previous
controller.for adaptive PID will take some time and this
parameter
adjustment
has been effected the simulation to slow down the longitudinal slip
Jerking condition as shown in Figure 17 is occurred because of overshoot response in wheel
response slip
to before
reach approaching
0.2 in shortest
time.
Even tough theadaptive
result PID
shows
longitudinal
steady state
conditions.Generally,
works
overshoot
response
using
both
conventional
PID
and
adaptive
PIDthe
better than conventional PID because of the parameter of PID will change by
adjustment
mechanism
until they
values.
controllers,
the system
still converge
unable to
to optimal
produce
fast However,
responsethetoparameter
reach
adjustment
for adaptive
PID will
take some
time and
this has
beenas
effected
simulation
steady-state
condition.
Hence,
by using
fuzzy
logic
ABS the
controller
tothe
slow
down stopping
the longitudinal
slip response
reach 0.2 in
shortest time.This
Evensystem
tough the
wheel
capability
has to
improved
drastically.
result shows overshoot response using both conventional PID and adaptive PID controllers,
is system
able tostillreach
0.58
second even
tough
theby
the
unablesteady-state
to produce fastcondition
response toin
reach
steady-state
condition.
Hence,
wheel
longitudinal
slip shows
overdamped
behaviour.
Additionally,
using
fuzzy
logic as ABS controller
the wheel
stopping capability
has improved
drastically.
This
is able
to reach
in 0.58 second
evenfor
tough
the wheel
thissystem
system
is also
ablesteady-state
to avoid condition
jerking which
occurred
adaptive
longitudinal
shows overdamped
behaviour.
thistosystem
is also able
PID at 0.6slipsecond
to 1.5 second
andAdditionally,
0.72 second
1.8 second
forto
avoid
jerking
which
occurred
for
adaptive
PID
at
0.6
second
to
1.5
second
and
0.72
second
conventional PID.
to 1.8 second for conventional PID.
Jerking
Figure 17. Comparison of Figure 18. Comparison of Figure 18. Comparison of vehicle distance travel
longitudinal slip
vehicle distance travel
Figure 18 shows the distance travelled by the vehicle after the brake input is applied. The
figure
shows
logic
is able
to reduce
travelled
vehicle
Figure
18 fuzzy
shows
thecontroller
distance
travelled
bythe
thedistance
vehicle
after by
thethebrake
compared
to
other
controllers
and
conventional
braking
system.
The
distance
travel
by the
input is applied. The figure shows fuzzy logic controller is able
vehicle controlled by fuzzy logic control is about 12.3 meter and the vehicle stops 3.3
to reduce the distance travelled by the vehicle compared to other
second after braking. Meanwhile, vehicle with adaptive PID and conventional PID
controllers
andtoconventional
system.travelled
The distance
travel
controllers
are able
stop 3.5 secondsbraking
with the distance
of 13.8 meter
and by
3.65
the vehicle
controlled
by fuzzy
logic
control
is about
12.3 meter
seconds
with the
distance travelled
of 14.9
meter
respectively.
By controling
the and
wheel
longitudinal
slip,
the distance
travel after
bu the
vehicle has
been improved
significantly
the vehicle
stops
3.3 second
braking.
Meanwhile,
vehicle
with
compared
conventional
braking system.
At controllers
the same time,are
fuzzy
logic
adaptiveto PID
and conventional
PID
able
to controller
stop 3.5 is
shown to halt the vehicle with the shortest distance compared to other controllers.
Figure 17. Comparison of longitudinal slip
seconds with the distance travelled of 13.8 meter and 3.65 seconds
with 19
theshows
distance
travelled
of 14.9velocity
meterand
respectively.
Figure
the comparison
of vehicle
wheel velocityBy
of acontroling
vehicle using
fuzzy logic controller. The ABS-EWB model using fuzzy logic controller shows a good
performance by stopping the vehicle and wheel at the same time without any jerking
ISSN: 2180-1053
Vol. 6
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January - June 2014
59
Journal of Mechanical Engineering and Technology
the wheel longitudinal slip, the distance travel bu the vehicle has been
improved significantly compared to conventional braking system. At
the same time, fuzzy logic controller is shown to halt the vehicle with
the shortest distance compared to other controllers.
Figure 19 shows the comparison of vehicle velocity and wheel velocity
of a vehicle using fuzzy logic controller. The ABS-EWB model using
fuzzy logic controller shows a good performance by stopping the
vehicle and wheel at the same time without any jerking problems in
the wheel. Besides, the stopping distance has been reduced compared
to ABS model using conventional PID and adaptive PID. The proposed
problems
in the shows
wheel. Besides,
stopping distance
been reduced
ABS
controller
better the
performance
in has
controlling
thecompared
vehicleto and
model using conventional PID and adaptive PID. The proposed controller shows better
EWB brake model to produce a good ABS model.
performance in controlling the vehicle and EWB brake model to produce a good ABS model.
Graph of comparison between vehicle and wheel velocity versus time
Comparison of vehicle and wheel velocity, m/s
90
vehicle
wheel
80
70
60
50
40
30
20
10
0
0
2
4
6
time, t
8
10
12
Figure
Comparison
between
vehicle
for
ABS
Figure 19.
19. Comparison
between
wheel andwheel
vehicle and
velocity
for ABSvelocity
using fuzzy
logic
using fuzzy logic
6.0
CONCLUSION
6.0CONCLUSION
A comprehensive study of the ABS model using Electronic wedge brake (EWB)
A comprehensive
of the ABS
wedge
mechanism
and the design study
of the conventional
PID,model
adaptiveusing
PID andElectronic
fuzzy logic controller
have
been (EWB)
presented.mechanism
A quarter vehicle
is modeled
and validated
using CarSim
brake
and model
the design
of the
conventional
PID,
simulator.
A mathematical
model
using
Bell-Shaped
is used
represent an A
EWB.
This
adaptive
PID and fuzzy
logic
controller
have
beentopresented.
quarter
model is used to represent the actual EWB behaivour. An outer loop model has been
vehicle model is modeled and validated using CarSim simulator. A
proposed using validated quarter vehicle model and EWB model is used to develop an inner
mathematical
model
using
Bell-Shaped
to develop
represent
an EWB.
loop
model. Both outer
and inner
loop
are integratedisinused
order to
the overall
ABS
Thissystem.
model
used to studies
represent
the actual
EWB
behaivour.
An outer
closed
Theissimulation
considered
three types
of controllers
for ABS
model.
Comparison
has been
the proposed
ABSvalidated
model to investigate
performance
of
loop model
has made
beenfor
proposed
using
quarterthe
vehicle
model
theand
proposed
controllers.
From
the
simulation
results,
the
Fuzzy
Logic
controller
shows
EWB model is used to develop an inner loop model. Both outer and
good
performance
forintegrated
ABS-EWB control
structure
by reducing
theoverall
stoppingABS
distance
up to
inner
loop are
in order
to develop
the
closed
17.4 % compared to the conventional PID and Adaptive PID control is 7.38% and 12.08 %.
system.
Thecontrol
simulation
three
types of
controllers
for
The
proposed
schemestudies
is able considered
to improve the
stopping
distance
and wheel
ABS
model.
Comparison
has
been
made
for
the
proposed
ABS
model
longitudinal slip of vehicle during braking. Hence, it can be concluded that fuzzy logic
controller
could provide
better active brake
performance
the adaptive
PID the
and
to investigate
the performance
of the
proposedthan
controllers.
From
conventional
PIDresults,
control. the Fuzzy Logic controller shows good performance
simulation
ACKNOWLEDGEMENT
60
ISSN: 2180-1053
Vol. 6
No. 1
January - June 2014
This work is supported by the University Teknikal Malaysia Melaka (UTeM) through short
Development of Antilock Braking System using Electronic Wedge Brake Model
for ABS-EWB control structure by reducing the stopping distance up
to 17.4 % compared to the conventional PID and Adaptive PID control
is 7.38% and 12.08 %. The proposed control scheme is able to improve
the stopping distance and wheel longitudinal slip of vehicle during
braking. Hence, it can be concluded that fuzzy logic controller could
provide better active brake performance than the adaptive PID and
conventional PID control.
ACKNOWLEDGEMENT
This work is supported by the University Teknikal Malaysia Melaka
(UTeM) through short term grant project entitled “Safety and Stability
Enhancement of Automotive Vehicle using ABS with Electronic Wedge
Brake Mechanism” led by Fauzi Bin Ahmad at the Universiti Teknikal
Malaysia Melaka. This financial support is gratefully acknowledged.
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