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Fuzzy Controllers of Antilock Braking System: A Review
Abdollah Amirkhani
1
•Mahdi Molaie
1
Received: 9 March 2022 / Revised: 24 June 2022 / Accepted: 18 July 2022
ÓThe Author(s) under exclusive licence to Taiwan Fuzzy Systems Association 2022
Abstract This paper provides a review of the common
fuzzy system-based controllers as one of the most powerful
approaches in the control problem of antilock braking
systems (ABSs) which have been employed in various
research works. Because of model nonlinearities and the
uncertainties of the braking process, designing proper
controllers for ABSs has become a challenging task. Fuzzy
systems are considered to be a highly useful and applicable
tool for designing effective ABS controllers. In this survey,
first, the preliminary information regarding the ABS con-
trol, such as vehicle dynamics and tire models, is pre-
sented. Then, various type-1 (T1) and type-2 (T2) fuzzy
logic systems and the structures of ABS controllers are
examined and classified into distinct general categories.
Finally, different research papers published in this field on
different types of fuzzy logic-based control systems (e.g.,
fuzzy proportional integral derivative, fuzzy sliding-mode
controllers, fuzzy neural networks, etc.) and also on other
control techniques based on T1 and T2 fuzzy systems are
compiled and reviewed. Moreover, in each section, the
details regarding the cited research works are listed in a
separate table.
Keywords Antilock braking system Fuzzy systems
Vehicle safety Intelligent control
1 Introduction
Although the technologies employed in the manufacture of
vehicles have experienced numerous changes and
improvements, one thing hasn’t changed and that is the
human driver operating the vehicle. In fact, the majority of
car accidents on the road can be attributed to human error
and mainly to the loss of vehicle control by the drivers
[1,2]. Hence, the reduction of these problems has become
one of the most fundamental concerns of the researchers in
the auto manufacturing industry [3]. These research efforts
have led to the development and application of driver-as-
sistance systems such as the lane keeping and adaptive
cruise control mechanisms [4,5]. By assisting the drivers
in the unusual and critical circumstances, these schemes
have led to a considerable reduction in the number of road
accidents. Using the information they receive from the
onboard cameras and sensors, the driver-assistance systems
can help reduce the driving accidents or minimize the
severity of the damages by punctually alerting the drivers
and sometimes by directly interfering in a vehicle’s oper-
ation [6]. Nevertheless, such systems are not complete and
their capabilities are continually expanding with the
advancement of technology. As one of the oldest and most
important of these mechanisms, the antilock braking sys-
tem (ABS) plays a vital role in preserving the stability of a
vehicle and reducing its stopping distance during hard
braking [7].
If the wheels of a car lock during braking, it will lose its
maneuverability in the lateral direction; consequently, the
vehicle will no longer be steerable and the probability of
potential accidents will increase tremendously. However,
the ABSs can continually analyze the feedbacks they get
from the sensors installed in the wheels and compare these
data with vehicle velocity in the longitudinal direction; and
&Abdollah Amirkhani
amirkhani@iust.ac.ir; amirkhani@ieee.org
1
School of Automotive Engineering, Iran University of
Science and Technology, Tehran 16846-13114, Iran
123
Int. J. Fuzzy Syst.
https://doi.org/10.1007/s40815-022-01376-y
thus, the locking of the wheels will be constantly checked.
When the wheels lock, the ABS can reduce or increase the
braking force applied to the wheels. This is exactly what a
driver does in this situation by pressing and releasing the
brake pedal. Of course, an ABS can do this at a much faster
rate and prevent the wheels from locking during the
braking action [8]. Therefore, the most important goals of
the ABSs are to preserve the traction and provide the
necessary adhesion between tires and road so that a suffi-
cient friction force can be produced for stopping a vehicle
on-time [9].
In the precise design of each type of ABS controller, for
attaining shorter braking distances, some challenging
conditions and requirements have to be met and satisfied.
For example, the control approaches that are based on the
proportional integral (PI)/ proportional derivative (PD)/
proportional integral derivative (PID) controllers, sliding
mode method and the fuzzy learning techniques require the
precise measurement or estimation of vehicle velocity to
compute the tire slip. The determination (or the precise
estimation) of the optimal value of instantaneous wheel slip
is another condition that has to be considered in the design
of controllers. The lack of a direct method for measuring
the wheel velocity and finding an exact technique for the
approximation of velocity has become one of the main
challenges in the controller design process [10]. Moreover,
measuring the road-tire friction is also a difficult task and
may require very complex sensors for this purpose. As an
external factor, the variation of road surface conditions also
affects the performance and the theoretical basis of the
ABS control approaches; and the disturbances caused by
such fluctuations may lead to undesired consequences if
not dealt with properly. Based on the above statements, we
could say that the main difficulties and challenges in the
design of ABS controllers stem from the existing nonlin-
earities and uncertainties [9].
The majority of the research efforts regarding the ABS
control methods have focused on the passenger cars
equipped with hydraulic brake systems [11]. The goal in
most of these works is to avoid the locking of the wheels
and also to reduce the braking distance. To this end, a
criterion called the wheel slip ratio has been defined, which
indicates the state of a car’s wheels. A slip ratio of zero
means the vehicle is moving fast and no braking has been
applied. On the other hand, a slip ratio of one (1) means
that the wheels have been locked and the vehicle is in
danger of losing its stability. Therefore, managing the slip
ratio is one of the utmost control objectives is many
research works [10,12]. Normally, for achieving and pre-
serving the maximum amount of road-tire friction and
adhesion force, the prospective controllers try to keep the
slip ratio in the range of 0.1 to 0.3, which is referred to as
the stable region [13].
System stability and robustness are also considered as
two fundamental precepts in the control theory [14]. In the
literature, the concept of uncertainty usually accompanies
the notion of fuzzy systems. The managing and modeling
of uncertainties is the most prominent feature and capa-
bility of fuzzy systems; which is considered and exploited
in many control applications. In this paper, we review
recent research works on the ABS control techniques which
are based on fuzzy logic, fuzzy systems, and their com-
ponents, and we explore the common approaches in this
field.
The remainder of this paper has been organized as fol-
lows. To examine the road–tire interactions, the models
related to tire force and vehicle dynamics have been pre-
sented in Sect. 2. The type-1 (T1) and type-2 (T2) fuzzy
logic systems (FLSs) have been reviewed in Sect. 3and the
structures of the ABS control systems have been studied.
Various types of fuzzy logic based control strategies have
been introduced in Sect. 4; and the paper has been con-
cluded in Sect. 5.
2 Preliminary Information
A structural model which is commonly used in designing
ABS controllers is the quarter vehicle model and the
dynamics associated with it. Here, the equations governing
such a system will be presented and its modeling procedure
will be fully explained. Moreover, the models that express
the relationship between road and tire forces are usually
used in the modeling of ABS as well. Thus, here we will
survey some of the more frequently used tire force models.
2.1 Vehicle Dynamics
To design a controller for a vehicle, one needs to have the
necessary information about the specifications of its dif-
ferent parts. This, however, is practically impossible, due
to the complexity of the various systems used in a vehicle.
For this purpose, one should employ the kind of models
that describe the basic characteristics of different vehicle
components [9]. Thus, in this section, we present the
quarter vehicle model as one of the most frequently used
models in the literature. The forces applied to an automo-
bile tire during braking are illustrated in Fig. 1. The
equations of the quarter vehicle model are as follows [15]:
_
v¼Fx
Mð1Þ
123
International Journal of Fuzzy Systems
_
x¼1
Ix
RFxsb
ðÞ ð2Þ
M= 1
4msþmwð3Þ
In the above equations, v,Fx,x,Ix,R,sb,msand mw
represent the vehicle longitudinal velocity, longitudinal
braking force, angular velocity, wheel moment of inertia,
wheel radius, braking torque, vehicle sprung mass and
wheel mass, respectively.
The longitudinal wheel slip ratio is calculated from
Eq. (4).
k¼vRx
vð4Þ
The aim of the ABS control method is to generate a
control signal so that the slip ratio defined in Eq. (4) is able
to follow the reference slip ratio.
2.2 Modeling the Tire Forces
The models that express the behavior of tires during road–
tire interactions are often used to compute the forces
applied to tires. Selecting each of these models and its level
of complexity depends on the considered objectives of
system analysis. For example, the Fiala [16] and the
Dugoff [9] models are usually employed for detection
purposes because of their high precision, structural sim-
plicity and the limited number of model parameters; while
the other highly accurate models such as the Magic For-
mula [17] and the tire-road dynamics [8] are less frequently
used because of their dependence on a large number of
parameters and different variables [10]. Three of the more
common and famous models in this filed, namely the
Dugoff model, Magic formula, and the Burckhardt model
[18], will be reviewed below and their governing equations
will be fully described.
2.2.1 The Dugoff Model
When the amount of wheel slip is small, a linear rela-
tionship exists between the longitudinal tire force and slip.
As the wheel slip increases, the longitudinal force becomes
saturated, because the specific amount of tire slip, which is
determined by the road-tire friction, reaches its maximum
value. As a result, the dynamic vehicle parameters become
nonlinear. Moreover, a saturated tire force is always con-
sidered as an important factor in jeopardizing the safety of
the vehicles in motion. Thus, with the help of the nonlinear
Dugoff tire model, the forces applied to tires in the lon-
gitudinal and lateral directions can be computed with
regards to the saturation properties of these forces [19]. The
computational relations of the Dugoff model have been
expressed in Eqs. (5) through (9).
Fx¼l:Fz:Cs:s
1s:fðLÞð5Þ
Fy¼l:Fz:Ca:tanðaÞ
1s:fðLÞð6Þ
fLðÞ¼ Lð2LÞ;L\1
1;L1
ð7Þ
where, Fxand Fydesignate the longitudinal and transverse
tire forces, respectively, Fzis the vertical load applied to
tire, Csand Caare the longitudinal and transverse stiffness
values, respectively, lis the road friction factor, sis the
longitudinal slip ratio, and ais the side angle of tire. The
value of Lis obtained from Eq. (8)[19].
L¼ð1sÞð1evffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðCssÞ2þðCatan aÞ2
qÞ
2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðCssÞ2þðCatan aÞ2
qð8Þ
In (8), edenotes the speed influence factor and vis the
longitudinal velocity of vehicle.
In addition, the vertical tire load has two components; a
static component arising from the distribution of vehicle
mass and a dynamic component caused by load shifting
during braking [9]. The magnitude of Fzis calculated from
Fz¼Mg mvshcg
2l
€
xð9Þ
where l,hcg and gindicate the distance between the two car
axles, height of the car’s center of gravity, and the gravi-
tational acceleration, respectively.
Considering the preceding Dugoff model equations,
Fig. 2illustrates the changes of longitudinal tire force
versus wheel slip. Clearly, the best point for controlling the
braking torque is the peak of the force–slip curve; because
the maximum value of road-tire adhesion occurs at this
point. In view of this figure, the maximum amount of tire
force is approximately obtained at the slip ratio of 0.15
Fig. 1 The forces applied to a car wheel during braking
123
A. Amirkhani, M. Molaie: Fuzzy Controllers of Antilock Braking System
(k¼0:15). To avoid the tracking error, which leads to the
generation of an excessive control force at the initial
moments of braking, and considering the transient state
response of the reference model, the following system can
be used as the desired slip model [9].
kref ðtÞ¼kopt kopte#tð10Þ
In (10), kopt and #indicate the optimal wheel slip and a
time constant, respectively.
2.2.2 The Magic Formula Model
Another tire model used in the literature is the Magic
Formula; which was presented for the first time by Bakker
et al. [20]. Pacejka and Bakker [21] introduced a new and
more improved version of the Magic Formula model that
was capable of modeling the tire behavior more precisely
in steady state. The Magic Formula has demonstrated a
high ability in the exact modeling of torque, braking force
and lateral force features [22]. Pacejka and Besselink [23]
presented a more improved version of the Magic Formula
for modeling the tire behavior in unsteady state. In addi-
tion, a comparison was made in [24] between the empirical
data and Magic Formula model results obtained under
different road conditions. The Magic Formula equation is
expressed as follows [25]:
yðxÞ¼DsinfCtan1½Bx EðBx tan1BxÞ ð11Þ
FxðxÞ¼yðxÞþSv;x¼XþShð12Þ
where, Fxcould stand for longitudinal force, lateral force,
or the self-aligning torque. The parameters of Eqs. (11) and
(12) have been listed in Table 1.
Using the parameters in Table 1, the Magic Formula
model provides tire-related quantities such as the peak
values of tire force, tire slip, and stiffness [22].
2.2.3 The Burckhardt Model
Another model used for determining the road-tire interac-
tions is the Burckhardt model, which expresses the rela-
tionship between the slip ratio and longitudinal force [26].
Knowing the slip ratio and using the Burckhardt’s relation
(Eq. (13)), the longitudinal tire force can be computed [27].
FxðkÞ¼c1ð1ec2kÞc3kð13Þ
In (13), c1,c
2and c3are, respectively, proportional to
the peak point of the friction curve, shape of the friction
curve, and the difference between the friction values at the
maximum value of curve and at the value in slip ratio of 1.
Figure 3shows the longitudinal tire force versus the slip
ratio based on the Burckhardt model. Similar to the graphs
of other models, the graphs of tire force versus slip ratio in
Fig. 3are divided into two steady and unsteady regions
[28]. If the wheel slip falls in an unsteady region, wheel
velocity will decrease and cause the slip ratio to increase;
as a result, the braking force will diminish until the wheel
is locked [27].
3 Methodology of the Fuzzy ABS Controllers
By scrutinizing the existing research works in this area, we
were able to classify these control strategies into several
different subgroups. Figure (5) shows these classifications
and their interrelationship with each other (Fig. 4). As was
mentioned earlier, the fuzzy controllers are the most
common and frequently used controllers in this field [10].
In the rest of this section, we will present a general over-
view of the T1 and T2 fuzzy logic approaches. We will
then describe the ABS control strategies and provide some
information and explanations regarding the cited and
reviewed papers.
3.1 Type-1 and Type-2 Fuzzy Sets
Following the initial introduction of the T1 fuzzy sets (FSs)
by Zadeh [29] in 1965, there was a proliferation of research
in this field in the years that followed. Ten years later, in
1975, Zadeh [30] presented an upgraded version of his
proposed system, which was termed as T2-FSs. Contrary to
the T1-FSs in which the membership functions (MFs) have
a specific and definite value, the MFs in T2-FSs are
themselves fuzzy functions [31]. Hence, the T2-FSs are
also known as fuzzy-fuzzy sets [32]. In the literature, we
can see the application of fuzzy logic in a variety of fields,
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Slip Ratio
0
500
1000
1500
2000
2500
3000
3500
Dry
Wet
Icy
Fig. 2 Graphs of longitudinal tire force versus wheel slip for the dry,
wet, and icy road surface conditions
123
International Journal of Fuzzy Systems
including machine learning [33], signal and image pro-
cessing [34,35], medical engineering [36], robotics [37],
etc. Also, ‘‘control’’ is another important research field in
which fuzzy logic has been employed [38,39].
FSs are able to manage and process the data affected by
various uncertainties [40]. While it is very difficult to
determine the exact values of uncertain and indeterminate
measurements and data by classical logic, the FSs show a
much better capability for this purpose. Although a T2-FS
is much more capable of modeling the uncertainties than a
T1-FS, due to its greater computational load relative to the
latter, it should be applied to the systems that suffer from a
greater degree of uncertainty. Nevertheless, both approa-
ches are very common and frequently used in various
control applications [41].
The general formulations of the T1-FSs and T2-FSs are
expressed by Eqs. (14) and (15), respectively [40].
F¼Zx2X
lFxðÞ
=xð14Þ
~
F¼Zx2XZu2Jx
l~
Fx;uðÞ
x;uðÞ;Jx0;1½ ð15Þ
In the above equations, Fand
~
Frepresent a T1-FS and a
T2-FS, respectively. In (14), lFxðÞdenotes a T1 fuzzy MF,
where x2Xand lFxðÞ 2 0;1½. Also, a T2-FS is desig-
nated by the MF l~
Fx;uðÞ, in which x2Xand
u2Jx0;1½. In a T2-FS, Jx0;1½indicates the pri-
mary MF xand l~
Ax;uðÞis a T1-FS known as the secondary
MF [41]. Later on, a simpler version of Eq. (15) was pre-
sented, which came to be known as the interval T2-FSs
(IT2-FSs). In these sets, the secondary MF is the same for
all the members and has a value of 1 [42]. The overall
formulation for IT2-FS is expressed as Eq. (16).
~
F¼x;uðÞ;l~
Ax;uðÞ
j8x2X;8u2Jx0;1½
ð16Þ
Every FLS is specified by IF–THEN rules. A T1-FS
and T2-FS comprises a fuzzifier section, fuzzy rule base,
fuzzy inference engine, and a defuzzifier section. The T2-
FS also includes a type-reducer unit, which is absent in the
T1-FS. The fuzzifier section maps the crisp inputs to fuzzy
MFs. The structure of the rules in a T1-FS and T2-FS is the
same; except that in the T2-FS, the antecedent and the
consequent sections are determined by means of a T1-FS.
In addition, implications are carried out in the inference
section. The Zadeh, Godel, Denis-Rescher, and the Mam-
dani implications are the more famous implications that we
can mention [43]. In fuzzy systems, the inference engine
combines the rules and maps the fuzzy inputs to the fuzzy
outputs. In a T2-FS, the type-reducer unit maps a T2-FS to
a T1-FS. There are different type-reduction techniques,
including the common methods of Centroid [44], Center-
of-Sets [45], Karnik–Mendel (KM) [46], Enhanced Kar-
nik–Mendel (EKM) [47], Iterative Algorithm with Stop-
ping Condition (IASC) [48], and the Enhanced Iterative
Algorithm with Stopping Condition (EIASC) [49]. Among
these, the KM and its upgraded version EKM are consid-
ered to be more common [47]. In addition, in the
defuzzifier unit, a fuzzy quantity is converted to a definite
value.
3.2 Structure of ABS Controller
The structure of a fuzzy logic-based ABS control system
has been depicted in Fig. 5. According to this figure, the
control system input is the error signal obtained by taking
the difference between the output wheel slip and the ref-
erence slip. Naturally, the error signal has a crisp value,
which is converted to a fuzzy value by considering pre-
defined FSs. Using a predetermined rules base, the input
error is mapped from input to output; and ultimately, after
defuzzification, the output value is again converted to a
crisp value and applied to the considered ABS.
ABS comprises different components, including the
physical brakes, hydraulic modulator unit, electronic con-
trol unit (ECU), and various sensors. All these components
are interdependent and the disturbance and malfunction of
each one will affect the whole system [50]. Fuzzy con-
trollers can effectively handle such failures, whether they
occur at the component level or at the aggregate level. In
these cases, the number of fuzzy rules can be increased to
better deal with any unknown environmental parameter;
although the increase of these rules will require more
complex analysis [10]. Another advantage of fuzzy con-
trollers is that they can be combined with the other control
methods that are capable of computing the control laws
offline. However, this requires a large volume of memory
for data storage. Therefore, in real-world applications, it is
more feasible to employ the online methods.
Table 1 Parameters of the Magic Formula model
Parameter Description
B Stiffness factor
C Shape factor
D Peak factor
E Curvature factor
ShHorizontal shift
SvVertical shift
Xslip angle or longitudinal slip
123
A. Amirkhani, M. Molaie: Fuzzy Controllers of Antilock Braking System
3.3 Statistics
In the present investigation, we have examined a total of
110 papers. These research works have been presented in
the forms of journals, conferences, and book sections, and
published within the years 1993–2022. Figure (8) shows
the numbers and percentages of the reviewed papers based
on their types of presentation. 66 of these 110 papers are
journal publications. The journals of ‘‘IEEE Transactions
on Vehicular Technology’’ and ‘‘SAE Technical Paper’’
have the highest numbers of published papers; and 5 papers
from each of these journals have been examined here.
Table 2contains the relevant information on the published
papers surveyed based on the journals in which they have
appeared, the publishers, number of papers, and their
rankings according to the SJR, 2021 database.
There are two major reasons for using fuzzy logic in
ABS controllers: (1) the nonlinear behavior of vehicle tires,
(2) the presence of uncertainty and noise in the state
variables. Hence, in addition to the other types of appli-
cations, the fuzzy controllers have long been used for
controlling the ABS as well. Figure 9 shows the papers
published on the subject of fuzzy ABS control from 1993
to Jan. 2022, based on the Scopus database. According to
this figure, the average number of the papers containing the
terms ‘‘fuzzy’’ and ‘‘antilock braking system’’ and pub-
lished from 1993 to 2008 is much less than that published
in the last 13 years; which shows a growing number of the
published papers in recent years.
4 Different Types of Fuzzy-Based Control
Strategies
Numerous studies and various schemes and strategies are
implemented to enhance the performance of the ABSs in
the vehicles with internal combustion engines and electric
motors. Of these different techniques, the use of fuzzy
controllers has attracted the attention of more researchers.
Fig. 4 Classification of various ABS control strategies in the former research works
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Slip Ratio
0
500
1000
1500
2000
2500
3000
Dry
Wet
Icy
Fig. 3 Longitudinal tire force versus slip ratio based on the
Burckhardt model
123
International Journal of Fuzzy Systems
According to the reported research findings [50], by con-
trolling the ABSs via fuzzy logic in different ways, the
performance of these systems can be improved under
varying road conditions. For instance, a common method
of enhancing the ABS performance is to optimize the
control parameters by means of fuzzy logic. Nevertheless,
the performance of ABSs cannot be fully improved by just
using fuzzy logic. Therefore, as time has passed, the fuzzy
logic technique has been combined with other methods and
a more powerful tool has been developed for ABS control
optimization and vehicle safety enhancement (Figs. 6,7).
For example, by integrating a fuzzy controller with the
discrete sliding mode scheme, a robust and stable fuzzy
adaptive sliding mode control (SMC) system has been
achieved in [51]. The trend of research works conducted on
the fuzzy controllers for ABS is presented in Fig. 8.
In this section, we will review the studies on ABS
control methods based on fuzzy logic. In general, different
types of fuzzy ABS controllers can be divided into four
groups (see Fig. 9).
4.1 Fuzzy Controllers
Two categories of fuzzy controllers are investigated in the
research works that have been surveyed: (1) pure FLCs,
and (2) combined fuzzy logic controllers. The details of
these research works are as follows:
4.1.1 Pure Fuzzy Logic Controllers
By combining a reference-learning fuzzy-model with
threshold-based controller, Layne et al. [52] designed a
fuzzy controller that could deal with the uncertainties
arising from road conditions. Their controller was able to
keep the amount of wheel skid fixed in the presence of
disturbances. They also demonstrated that by applying the
fuzzy logic concept, the controller command can be com-
puted faster and in less time relative to the adaptive iden-
tification control methods. These researchers evaluated
their proposed system on a quarter vehicle model. In this
evaluation process, they assumed a vehicle with nonlinear
elastics suspension and also considered uneven and rough
road conditions in the presence of noise. The distinguished
work of Mauer [62] on the subject of ABS control via
fuzzy logic has attracted a lot of attention. In this research,
for detecting and dealing with the current road conditions,
Mauer has proposed a controller which combines fuzzy
logic with a logical decision-making network. By merging
the past and the present wheel slip and brake pressure data,
this controller is able to generate a brake pressure signal for
ABS control. For evaluating his proposed technique, Mauer
has used a quarter-vehicle model. He has also assumed a
nonlinear elastic suspension system in his evaluations and
considered the robustness of hic controller in a rough and
uneven road environment and under noisy conditions. For
comparing his proposed method, he has used a proportional
integral controller as a benchmark. This comparison has
revealed that many parameters in the fuzzy controller
should be meticulously tuned in order to achieve a more
desirable control performance compared to the PI
controller.
Cabrera et al. [63] presented a fuzzy logic-based con-
troller which uses the ‘‘recursive least square’’ method to
approximate the values of road-tire friction coefficient and
vehicle velocity. Aided by fuzzy logic, they determined the
optimal amount of wheel slip with regards to the slip and
friction values obtained. To test their controller, these
authors evaluated it on a steel-belt-tire test bench. For
achieving the ideal wheel slip, reducing the vehicle speed
and attaining the maximum tensile force for tires, Mirzaei
Fig. 5 A fuzzy ABS controller
123
A. Amirkhani, M. Molaie: Fuzzy Controllers of Antilock Braking System
Table 2 The classification of the published papers based on the journal, publisher, number of papers, and quartiles (SJR, 2021)
Quartile #
Publications
Publisher Journals
2 1 MDPI Actuators
3 1 SAGE Publications Inc Advances In Mechanical Engineering
2 1 Ain Shams University Ain Shams Engineering Journal
2 1 MDPI Applied Sciences
1 1 Elsevier Applied Soft Computing
1 1 Elsevier Automatica
2 1 MDPI Electronics
2 2 MDPI Energies
1 1 Elsevier Engineering Applications of Artificial Intelligence
NA
*
1 Dionisios Pylarinos Engineering, Technology & Applied Science Research
1 2 IEEE IEEE Access
1 3 IEEE IEEE Transactions on Control Systems Technology
1 1 IEEE IEEE Transactions on evolutionary computation
1 4 IEEE IEEE Transactions on Fuzzy Systems
1 1 IEEE IEEE Transactions on Industrial Electronics
1 5 IEEE IEEE Transactions on Vehicular Technology
1 1 Wiley International Journal of Adaptive Control and Signal Processing
2 2 Korean Society of Automotive Engineers International Journal of Automotive Technology
2 1 Institute of Control, Robotics and Systems International Journal of Control and Automation
1 2 Springer International Journal of Fuzzy Systems
4 1 Inderscience Enterprises Ltd International Journal of vehicle Autonomous Systems
3 2 Inderscience Enterprises Ltd International Journal of vehicle Design
4 1 Inderscience Enterprises Ltd International Journal of vehicle Safety
NA 1 No data International journal on sciences and techniques of automatic control
NA 1 Fast track publications International Research Journal of Engineering and Technology
1 1 Springer Journal of Ambient Intelligence and Humanized Computing
NA 1 Iran University of Science & Technology Automotive Science and Engineering
2 2 The American Society of Mechanical Engineers
(ASME)
Journal of Dynamic Systems, Measurement, and Control
3 2 Kuwait University Journal of Engineering Research
1 1 American Institute of Aeronautics and Astronautics
Inc. (AIAA)
Journal of Guidance, Control, and Dynamics
2 2 IOS Press Journal of Intelligent and Fuzzy Systems
2 1 SAGE Publications Ltd Journal of Intelligent Material Systems and Structures
NA 1 University of Babylon Journal of University of Babylon
NA 1 Japan Society of Mechanical Engineers JSME International Journal, Series C: Mechanical Systems, Machine Elements
and Manufacturing
2 1 Korean Society of Mechanical Engineers KSME International Journal
NA 1 IAU Majlesi Majlesi Journal of Mechatronic Systems
3 1 Hindawi Mathematical Problems in Engineering
1 1 Elsevier Mechatronics
1 1 Springer Neural Computing and Applications
1 1 Elsevier Neurocomputing
1 1 Springer Nonlinear Dynamics
2 1 SAGE Publications Inc Proceedings of the Institution of Mechanical Engineers, Part D: Journal of
Automobile Engineering
2 5 SAE International SAE Technical Paper
NA 1 SAE International SAE Transactions
1 1 MDPI Sustainability
*
Not Available
123
International Journal of Fuzzy Systems
et al. [64] presented a controller which was based on the
Takagi–Sugeno-Kang (TSK) fuzzy system. They employed
an error-based optimization technique for reaching a faster
convergence in wheel slip; and also for tuning the param-
eters of their system, they used the genetic algorithm (GA)
in conjunction with the error-based optimization method.
For evaluating the proposed method, they considered the
vehicle’s dynamic model as well as the hydraulic dynam-
ics. In the performed simulations, the vehicle’s dynamic
load was transferred from the rear axle to the front axle,
and the proposed system was evaluated under the dry and
icy road surface conditions. Their technique was able to
reduce the stopping distance of a car with locked wheels by
20 m. Mane et al. [65] used T1 fuzzy logic to control the
ABS in motorcycles and to reduce their stopping distance
while preserving their controllability. Lee and Zak [53]
presented a fuzzy controller and employed the GA to
optimize the parameters of this fuzzy system. Their pro-
posed controller comprises a neural optimizer for finding
the optimal value of wheel slip and a fuzzy component for
calculating the amount of braking torque used to track the
optimal slip. The details of the cited papers and of some
other research works on ABS control with fuzzy controller
are presented in Table 3.
4.1.2 Combined Fuzzy Logic-Based controller
The ‘‘robust’’, ‘‘adaptive’’, ‘‘fractional’’ controllers and the
other control systems of this sort are considered as the
other fuzzy system -based controllers. As an example of the
controllers in this category, El-Garhy et al. [100] presented
a T1 fuzzy system-based controller. They used a vehicle’s
dynamic model along with the Magic Formula tire model
to simulate their system. They also applied the GA to
optimize the system parameters. Precup et al. [101] pro-
posed the use of a TSK fuzzy controller for controlling
ABS. They employed the nature-inspired particle swarm
optimization (PSO) and the simulated annealing (SA)
algorithms to optimize the parameters of the fuzzy MFs.
A fuzzy robust controller has been proposed in [102] for
ABS control and for managing vehicle stability in complex
braking maneuvers. An evolving fuzzy control model for
ABS has been presented in [103] and implemented
experimentally. In the surveyed literature, fuzzy controllers
have also been used for managing the ABS of motorcycles
as well as vehicle models. Ferna
´ndez et al. [66] developed
a T1-FLC for controlling the wheel slip rate under
changing road conditions. Their approach used two Kal-
man filters for estimating the road-tire interaction forces.
They also employed a co-evolutionary optimization
methodology based on GA to optimize the parameters of
their method. For improving the performance of aircraft
brakes under fault-perturbed conditions, Zhang et al. [104]
presented an Adaptive fuzzy active-disturbance rejection
control-based reconfiguration controller for aircraft anti-
skid braking systems. Their proposed controller estimates
the applied disturbances via an adaptive extended state
observer and rectifies the undesired effects by combining
fuzzy logic with nonlinear state error feedbacks. The
numerical results obtained by simulating under different
conditions reveal that the developed controller is robust
and ensure that the faulty brakes perform satisfactorily. The
details of the cited papers and some other research works
performed on the subject of ABS control by means of the
other fuzzy control techniques have been presented in
Table 4.
4.2 Fuzzy PID Controllers
The PID controllers, which are employed in many indus-
trial applications and processes, include a closed-loop
algorithm and control technique that uses the feedback
concept. The three important components of ‘‘propor-
tional’’, ‘‘integral’’ and ‘‘derivative’’ form the general
framework of the PID controllers. In practice, each of the
said components takes an error signal as an input and
performs some operations on it; and finally, the outputs of
these components are added together. In order to correct an
error, the output of this set (i.e., the output of the PID
controller) is fed back to the system.
Since their advent, some ABS controllers have exhibited
certain functional limitations and, therefore, some of their
requirements and parameters have had to be amended and
improved. Regarding the weaknesses of the PID con-
trollers, we can point out their large dead zone, poor
Journals
# 66, 60%
Conferences
# 42, 38%
Book Sections
# 2, 2%
Fig. 6 The numbers and percentages of published papers based on
their types
123
A. Amirkhani, M. Molaie: Fuzzy Controllers of Antilock Braking System
0
2
4
6
8
10
12
14
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
Documents
Year
Fig. 7 The number of papers on the fuzzy systems and ABS control and published from 1993 to Jan. 2022 based on the Scopus database
Fig. 8 Trend of the fuzzy controllers for ABS
Fig. 9 Classification of fuzzy system-based ABS controllers
123
International Journal of Fuzzy Systems
stability, and their inability to tune the parameters online.
In addition, some studies have shown that these controllers
are not so effective when dealing with time-varying and
nonlinear systems. To solve these problems and improve
the performance of the PID controllers, different control
strategies have been presented, the most important of
which is the fuzzy PID (FPID) control method [119]. In
this approach, the PID parameters are tuned by combining
the fuzzy controllers with certain algorithms; while the
values of these same parameters are very difficult to obtain
in the conventional PID controllers. It should be men-
tioned, however, that the FPID controllers are not so easy
to design. For example, obtaining the rules base in any field
requires a lot of experience, which can only be provided by
the experts in that field. In addition, there are some limi-
tations in the selection of the MFs [120]. The MFs should
be chosen so that the highest performance is achieved with
the least number of variables (i.e., with the least com-
plexity). Fuzzy logic rules can be used to obtain more
appropriate system responses in the presence of nonlinear
factors. Based on the fuzzy rules, a fuzzy controller first
converts the received inputs, and then the outputs, into
fuzzy variables; and eventually, a defuzzification mecha-
nism transforms these fuzzy outputs into acceptable out-
puts for the system [121].
For reducing the braking distance and keeping the wheel
slip ratio within a desired range, Sharkawy [122] proposed
an FPID controller with a self-tuning ability. Aided by
fuzzy logic and GA, this self-tuning ability could not only
overcome the system uncertainties but also help optimize
the controller parameters. Wang et al. [123] studied the
PID control of ABS based on the identification of various
road surfaces. They used the fuzzy logic capabilities to
tune the controller parameters in different road scenarios.
For the purpose of improving the low slip rate and dealing
with the effects of poor braking performance, Feng et al.
[59] presented a fuzzy adaptive PID controller that could
enhance vehicle stability and passenger safety. They used a
fuzzy system to tune the parameters of the PID controller.
Kejun and Chengye [124] designed a FPID control system
that considers an error and its derivative as the inputs and
creates a hydraulic brake pressure as the output. In their
proposed approach, as soon as the wheel slip error reaches
6%, the controller is stopped, the integration coefficient is
set to zero and the proportional gain is maximized so as to
minimize the response time. The details of the cited papers
and some other research works conducted on the subject of
ABS control by the FPID controllers have been presented
in Table 5.
4.3 Fuzzy Sliding-Mode Controllers
The SMCs are designed in two basic steps: the sliding step,
and the step of reaching a sliding surface. In the sliding
phase, a sliding surface is designed so that the asymptotic
stability of a system can be guaranteed if that system was
on the said sliding surface. In the phase of reaching a
sliding surface, a control signal is designed so that the state
variables of a system could converge to a sliding surface in
finite time and with the least effect from the considered
uncertainties. The first important attribute of the sliding
model is that by choosing an appropriate sliding function,
the desired dynamic behavior of a system can be ensured.
And its second characteristic is that there is no interde-
pendency between the closed-loop responses of a system
and uncertainties. Thus, the SMCs can be employed in
nonlinear processes and in the presence of disturbances
[132]. However, along with the mentioned, the sliding-
mode approaches suffer from certain drawbacks. The most
crucial flaw of these models is their chattering problem.
Chattering refers to a state in which oscillations of limited
frequency and amplitude occur in a system [133]. There-
fore, researchers have always tried to deal with such
drawbacks and to improve the performance of these con-
trollers. Using the fuzzy logic concept is one way of
improving the performance of the SMCs. In designing a
FSMC, the sliding surface can be chosen in fixed or vari-
able form. The main difference between a variable sliding
surface and a fixed one is that the parameter kin a variable
sliding surface is a linear and time-dependent function and
cannot be easily obtained in a closed form. In a controller
design process, the sliding surface should be chosen so that
the error dynamics of the system is globally stable [134].
Since the SMC approach reduces the order of a system, the
most important advantage of using the FSMC method in
the ABS control is that fewer rules are needed in the pro-
cess [50]; and the other advantage is the high robustness of
the SMC model [10].
In 2003, a self-learning fuzzy controller was combined
with the SMC approach and a new ABS control method
was developed [54]. This technique is able to automatically
tune the fuzzy rules and reduce their numbers. In additon,
an error estimation method for determining the error
boundary was investigated. The devised controller has two
sections. In the first section, a fuzzy controller that imitates
the behavior of an ideal controller is used as the main
tracking controller. The second section includes a robust
controller for compensating the approximation errors (i.e.,
the errors between the fuzzy controller and the ideal
123
A. Amirkhani, M. Molaie: Fuzzy Controllers of Antilock Braking System
Table 3 The ABS control methods based on T1 and T2 fuzzy logic approaches
Control
Approach
Vehicle model Tire model Optimization
algorithm
Changing in
road
condition
Adaptive
controller
Stability
analysis
Experimental
simulation
FLC [62] 4-Wheel vehicle Magic formula 94999
FLC [66] Motorcycle Magic formula Methodology based
on coevolution
using GA
4944
FLC [67]NA NA 99994
FLC [68] 4-Wheel vehicle Allen model Simulated
Annealing
9999
FLC [69] 4-Wheel vehicle Dugoff model 99994
FLC [70] Quarter vehicle Magic formula 99999
FLC
[71,72]
NA NA 99994
FLC [73] Single-track model
(bicycle model)
Magic formula 94999
FLC [74] A two-axle vehicle
model
Magic
formula ?Piecewise
linear model
99999
FLC [75] Quarter
vehicle ?hydraulic
servo brake actuator
system
Dugoff model 99999
FLC [76] 6800 series light bus NA 99999
FLC [77] Heavy vehicle dynamics Burckhardt model 99999
FLC [78] Quarter vehicle NA 99999
FLC [79] 4-Wheel vehicle Magic formula 99994
FLC [80] Quarter vehicle Burckhardt model 99994
FLC [81] Quarter vehicle Magic formula 99994
FLC [82] 4-Wheel vehicle NA 99999
FLC [83] 4-Wheel
vehicle ?hardware in
loop test
Magic formula 94944
FLC [84] Half vehicle ?brake
system model
Magic formula 99999
FLC [85] 4-Wheel
vehicle ?hydraulic
braking system model
Magic formula 99994
FLC [86] Truck model NA 99999
FLC [87] Brake system model NA GA 9999
FLC [88] 4-Wheel vehicle Magic formula GA 4999
FLC [89] Quarter vehicle Approximation of slip-
friction
99994
FLC [90] Quarter vehicle NA LQR optimization 9994
FLC [91] 4-Wheel vehicle ?brake
system model
NA GA 4999
FLC [92] Experimental test bench NA 94994
FLC [63] Quarter vehicle IMMa tire test bench 94994
FLC [93] Airplane brake model NA 94999
FLC [94] 4-Wheel vehicle Magic formula 94999
FLC [95] Quarter vehicle NA 99994
FLC [96] 4-Wheel vehicle Allen model 99999
FLC [65] Motorcycle Tire-road dynamics 99999
123
International Journal of Fuzzy Systems
controller). All the parameters of the designed controller
have been tuned according to the Lyapunov sense, and the
stability of the system has been verified. To evaluate their
proposed method, the authors of this paper tested their
controller for two different road scenarios and compared its
performance with that of a SMC and a fuzzy SMC. The
simulation results and comparisons show that although the
proposed method needs less tuning, it is a very simplified
model and its evaluation under realistic conditions is dif-
ficult and complex.
Guo et al. [135] presented a FSMC controller for opti-
mal wheel slip management. Their method was able to
achieve brake stability and improve the conversion energy.
For the prevention of wheels locking, Tang et al. [58]
proposed an adaptive fuzzy fractional-order SMC, which
had a fractional-order sliding mode part and a fuzzy part.
They also applied the Lyapunov theory to obtain the
adaptation rules. For improving the ABS performance and
reducing the braking distance in vehicles, Sun et al. [136]
developed a FSMC and presented an electrical ABS which
was able to quickly process the brake signals. In this way,
they were able to avoid the hydraulic delay that usually
exists in conventional ABS and improve the brake per-
formance to a large extent. Some of the advantages of their
proposed system include the road detection and the ability
to manage the disturbances and uncertainties in vehicle
mass and road surface conditions and also to prevent tire
and road wear and tear.
For maintaining the stability of UAVs during landing,
Zhang and Lin [137] presented a backstepping FSMC
strategy that was able to improve the performance of the
electromechanical actuator in these flying vehicles. The
results show that the proposed method helps the UAVs to
adapt to the runway conditions. The details and the infor-
mation of the cited papers and other research works on the
subject of ABS control via the FSMC approach are pre-
sented in Table 6.
4.4 Fuzzy Neural Networks and Neuro-Fuzzy
Controllers
As we explained in the previous sections, a significant
advantage of these controllers is their ability to model the
nonlinear systems and to manage the system uncertainties.
Therefore, using the fuzzy NN (FNN) controllers and a
neuro-fuzzy is considered as an effective way of dealing
with the key challenges in ABS control. In this respect, A
neuro-fuzzy controller has been presented in [91], which
needs the desired wheel slip data for ABS control. The
optimal reference wheel slip is obtained via a non-deriva-
tive neural optimization procedure. The authors in this
work have also used the GA to optimize the fuzzy system
parameters. For the purpose of ABS control, Chen et al.
[150] devised an observer-based direct adaptive fuzzy-
neural controller. One of their assumptions was that wheel
slip can be measured. For tracking the optimal wheel slip,
they combined an observer-based output feedback control
law with an online tuning law for the fuzzy-neural system
parameters.
Numerous research works have been conducted, espe-
cially in recent years, to mitigate the negative effects of
faults and disturbances on the ABSs. For example, for the
first time, Pan et al. [151] have managed to design a ‘2
‘1=H1control scheme for the fuzzy-model-based (FMB)
systems and to enhance the control performance by
applying an online learning policy. This gradient descent-
based learning policy is able to model the norm control
effects while it significantly accelerates the cost function
convergence [152]. In another research aimed at reducing
the performance loss of a system against the denial of
service (DoS) attacks, a novel and resilient event-triggered
security control technique has been designed for nonlinear
networked control systems (NCSs) [153].
For tracking the wheel slip in the ABS, Wang et al.
[154] presented a control method that combines a fuzzy
Table 3 continued
Control
Approach
Vehicle model Tire model Optimization
algorithm
Changing in
road
condition
Adaptive
controller
Stability
analysis
Experimental
simulation
FLC [64] 4-Wheel vehicle Tire-road dynamics GA ?error-base
optimization
4999
FLC [97] Quarter vehicle NA 99999
FLC and
PID
[98]
Quarter
vehicle ?hydraulic
braking system model
Experimental data 99999
FLC [99] 4-Wheel vehicle ?brake
system model
Magic formula 99999
123
A. Amirkhani, M. Molaie: Fuzzy Controllers of Antilock Braking System
inference system with a NN. Topalov et al. [155] devel-
oped a neuro-fuzzy ABS control technique by using a
sliding-mode incremental learning algorithm and consid-
ering nonlinear and unknown dynamic systems subjected to
various disturbances. Their proposed mechanism consisted
of a fuzzy-neural feedback controller along with a pro-
portional derivative (PD) controller. Lin et al. [8] intro-
duced an IT2 adaptive fuzzy controller for the control of
ABS. They employed the self-organizing method for cre-
ating enough rules in the neuro-fuzzy system and control-
ling the network size. In this approach, the input data are
considered as clusters, and a rule is defined in accordance
with each cluster. They also used the gradient descent
method to tune the indefinite parameters such as the mean
and variance of the Gaussian MFs and the coefficients of
Table 4 The ABS control methods based on the other types of T1-FS and T2-FS approaches
Control Approach Vehicle model Tire model Optimization
algorithm
Changing
in road
condition
Adaptive
controller
Stability
analysis
Experimental
simulation
Hybrid FLC [105] 4-Wheel vehicle Burckhardt
model
94999
Ordinary FLC ?self-learning
FLC [106]
Motorcycle model Magic formula 99999
Adaptive fuzzy log control
[107]
4-Wheel
vehicle ?brake
system model
Burckhardt
model
99449
FLC ?sliding-mode
obserbver [108]
Bus dynamics Truck tire
295/75R22.5
99999
Fuzzy model reference learning
controller [52]
4-Wheel vehicle Experimental
data
94499
Robust controller based on
fuzzy system and neural
network (NN) [109]
Aircraft dynamic NA 99999
Continuous-time and discrete-
time Takagi–Sugeno (T-S)
fuzzy controller [57]
Quarter vehicle
hardware in loop
NA 99994
FLC ?sliding mode controller
(SMC) [110]
Quarter vehicle Magic formula 99999
Fuzzy threshold
controller ?SMC [111]
4-Wheel vehicle
hardware in loop
NA 99999
FLC ?logic threshold
controller [112]
4-Wheel vehicle Non-steady
semiempirical
tire model
99994
Discriminative hierarchical
evolutionary fuzzy system
[113]
Brake system
model
NA GA 9999
Adaptive fuzzy controller [114] 5 DOF non-linear
consider as
‘‘Black Box’’
Consider as
‘‘Black Box’’
99499
Fuzzy genetic controller [115] Monocorner Magic formula GA 9994
Fuzzy life-extending control
[100]
4-Wheel vehicle Magic formula GA 9999
Robust fuzzy controller [102] 4-Wheel vehicle Magic formula 94999
IT2-FLC [60] 4-Wheel vehicle Magic formula 94999
Optimal fuzzy controller [116] Quarter vehicle Tire-road
dynamics
SA 9994
Adaptive fuzzy active-
disturbance rejection control
[104]
Aircraft dynamics Magic formula 94499
123
International Journal of Fuzzy Systems
the output equation and applied the PSO algorithm for
optimizing the learning rate.
Le [156] proposed an intelligent controller based on the
T2 fuzzy-neural system. This controller was able to
maintain the slip ratio at an appropriate level with regards
to the varying road conditions. He also used the PSO
algorithm for optimizing the system parameters. Recently,
a new ABS control structure based on the indirect T2-FNN
is presented in [61]. In this approach, the control system
parameters are optimized with Grasshopper algorithm and
the Lyapunov function is employed to verify the stability.
The proposed method is tested for different road and
driving scenarios and the obtained results have confirmed
the enhanced performance of the ABS. The details
regarding the cited papers and some other research works
on the subject of ABS control based on the neuro-fuzzy
systems are presented in Table 7.
5 Conclusion
Considering the un-modeled uncertainties as well as the
nonlinearity of the ABS, designing a controller for such
systems is a very challenging undertaking. Numerous
studies have been conducted on this subject in recent years.
In the past several decades, the fuzzy logic approaches
have been increasingly applied to the solving of various
control problems. Also, more researchers have become
interested in using the fuzzy systems for controlling and
managing the antilock braking mechanisms. Thus, in this
paper, we decided to review the research works that have
concentrated on the fuzzy logic-based ABS control sys-
tems. In this survey, first, the preliminary information and
the governing equations related to the dynamic models of
the tires and vehicles were presented. In the next step, by
reviewing the relevant research works, a general
Table 5 The ABS control methods based on the FPID approach
Control Approach Vehicle
model
Tire model Optimization
algorithm
Changing in
road condition
Adaptive
controller
Stability
analysis
Experimental
simulation
Adaptive PID-fuzzy control [55] Quarter
vehicle
Dugoff
model
94494
Fuzzy adaptive PID control [59] 4-Wheel
vehicle
Magic
formula
99499
Fuzzy self-tunning PID
controller [122]
Quarter
vehicle
Burckhardt GA 4999
FS-point weighted PID
controller [125]
Quarter
vehicle
Tire force
model
Firefly
algorithm ?GA
9999
FPID controller [126] Quarter
vehicle
Dugoff
model
99999
PI-fuzzy controller [127] Quarter
vehicle
Magic
formula
99994
FPID controller [123] 4-Wheel
vehicle
Burckhardt 94999
Fuzzy fractional PID gain
controller [128]
4-Wheel
vehicle
Magic
formula
99994
Adaptive neuro-fuzzy self-
tuning PID controller [56]
Quarter
vehicle
Burckhardt 99499
FPID controller [129] 4-Wheel
vehicle
Magic
Formula
99999
FPID control with S-function
[124]
4-Wheel
vehicle
NA 99999
Neuro fuzzy self-tuning PID
controller [130]
4-Wheel
vehicle
Burckhardt 94999
Fuzzy immune adaptive PID
control [131]
4-Wheel
vehicle
Bilinear
model
99499
123
A. Amirkhani, M. Molaie: Fuzzy Controllers of Antilock Braking System
Table 6 The ABS control methods based on the FSMC
Control Approach Vehicle model Tire model Optimization
algorithm
Changing in road
condition
Adaptive
controller
Stability
analysis
Experimental
simulation
FSMC [135] 4-Wheel vehicle Burckhardt model 99 999
Fuzzy sliding mode wheel slip
ratio control [136]
4-Wheel vehicle Magic formula 94999
FSMC [138] 4-Wheel vehicle Magic formula 99 994
FSMC [139] 4-Wheel vehicle NA 99 999
Robust FSMC [140] Quarter vehicle Burckhardt model 94499
Robust sliding mode-like FLC
[141]
Half ?quarter vehicle model ?hydraulic
brake system model
Dugoff model 99 949
FSMC [142] Quarter vehicle Burckhardt model 94949
Adaptive fuzzy fractional-order
SMC [58]
4-Wheel vehicle Tire-road
dynamics
94449
Adaptive FSMC [143] 4-Wheel vehicle The laboratory
ABS model
99 499
Robust FSMC [144] Quarter vehicle Burckhardt model 99 999
FSMC [145] 4-Wheel vehicle Burckhardt model 99 999
Extreme seeking-based adaptive
FSMC [146]
Quarter vehicle Burckhardt model 99 449
FSMC [147] 4-Wheel vehicle Magic formula 94444
Discrete-time adaptive FSMC
[148]
Quarter vehicle Magic formula 94499
Self-learning FSMC [54] Quarter vehicle Tire force model 94949
FSMC [149] 4-Wheel vehicle Burckhardt model 99 994
FLC and a sliding-mode observer
[108]
Bus dynamics model Dugoff model 99 999
123
International Journal of Fuzzy Systems
Table 7 The ABS control methods based on the FNN and neuro-fuzzy controllers
Control Approach Vehicle
model
Tire model Optimization
algorithm
Changing in road
condition
Adaptive
controller
Stability
analysis
Experimental
simulation
Adaptive network-based fuzzy inference system [157] Wheelchair Tire-road
dynamics
99 994
Neuro-fuzzy [158] Quarter
vehicle
Dugoff model 94499
Neuro-fuzzy [159]NANA99 994
FNN [160]NANA99 999
Indirect T2-FNN [61] Quarter
vehicle
Modified dugoff
model
Grasshopper
Algorithm
4449
Direct adaptive fuzzy-neural controller [161] Quarter
vehicle
LuGre friction
model
99 449
Adaptive neuro-fuzzy controller ?PD controller [162] Quarter
vehicle
NA 94449
Self-evolving function-link T2-FNN [156] Quarter
vehicle
Magic formula PSO 4449
IT2-FNN controller [8] Quarter
vehicle
Tire-road
dynamics
PSO 4449
Observer-based direct adaptive fuzzy-neural controller [150] Half vehicle Dugoff model 94449
Hierarchical Takagi–Sugeno (T–S) fuzzy-neural control
[163]
Quarter
vehicle
Tire-road
dynamics
99 449
Neuro-fuzzy control using sliding mode incremental learning
algorithm [155]
4-Wheel
vehicle
Tire force model 99 444
An observer-based direct adaptive fuzzy-neural controller
[154]
4-Wheel
vehicle
LuGre friction
model
94449
Adaptive fuzzy-neural control [164] Half vehicle Dugoff model 94449
Fuzzy-neural controllers [165] 4-Wheel
vehicle
LuGre friction
model
94449
Adaptive exponential-reaching SMC ?a functional
recurrent FNN [166]
Quarter
vehicle
Tire force model 94449
Adaptive neuro-fuzzy control with sliding mode learning
algorithm [167]
Quarter
vehicle
Tire force model 94449
FNN-SMC [168] Bycicle
model
Tire force model 94949
Neuro-fuzzy controller [158] Quarter
vehicle
Dugoff model 94494
Self-organizing function-link fuzzy cerebellar model
articulation controller [169]
4-Wheel
vehicle
Experimental
data
94449
Functional recurrent FNN uncertainty
estimator ?exponential SMC [170]
4-Wheel
vehicle
Experimental
data
94449
123
A. Amirkhani, M. Molaie: Fuzzy Controllers of Antilock Braking System
classification of the ABS control strategies was outlined
and the fuzzy controllers, as the most applied type of
control method, were examined in depth. Brief explana-
tions were then provided regarding the T1-FLS and T2-
FLS. The research works related to the different fuzzy
logic-based control approaches were subsequently sur-
veyed and evaluated. These methods included the FPID,
FSMC, FNN, and the other control techniques based on T1-
FLS and T2-FLS. At the start of each section, the structure
of the relevant control method was briefly explained. In
addition, the full details about the research papers reviewed
in each section were listed in a separate table.
References
1. Voinea, G.D., Postelnicu, C.C., Duguleana, M., Mogan, G.L.,
Socianu, R.: Driving performance and technology acceptance
evaluation in real traffic of a smartphone-based driver assistance
system. Int. J. Environ. Res. Public Health 17(19), 7098 (2020)
2. Zahabi, M., Razak, A.M.A., Shortz, A.E., Mehta, R.K., Manser,
M.: Evaluating advanced driver-assistance system trainings
using driver performance, attention allocation, and neural effi-
ciency measures. Appl. Ergon. 84, 103036 (2020)
3. Wang, L., Sun, P., Xie, M., Ma,S., Li, B., Shi, Y., Su, Q.:
Advanced driver-assistance system (ADAS) for intelligent
transportation based on the recognition of traffic cones. Adv.
Civ. Eng. (2020)
4. Mahdinia, I., Arvin, R., Khattak, A.J., Ghiasi, A.: Safety,
energy, and emissions impacts of adaptive cruise control and
cooperative adaptive cruise control. Transp. Res. Rec. 2674(6),
253–267 (2020)
5. Jiang, B., Li, X., Zeng, Y., Liu, D.: A maneuver evaluation
algorithm for lane-change assistance system. Electronics 10(7),
774 (2021)
6. Jime
´nez, F., Naranjo, J.E., Anaya, J.J., Garcı
´a, F., Ponz, A.,
Armingol, J.M.: Advanced driver assistance system for road
environments to improve safety and efficiency. Transportation
Research Procedia 14, 2245–2254 (2016)
7. Rafatnia, S., Mirzaei, M.: Adaptive Estimation of Vehicle
Velocity From Updated Dynamic Model for Control of Anti-
Lock Braking System. In: IEEE Transactions on Intelligent
Transportation Systems, 2021
8. Lin, C.-M., Le, T.-L.: PSO-self-organizing interval type-2 fuzzy
neural network for antilock braking systems. Int. J. Fuzzy Syst.
19(5), 1362–1374 (2017)
9. Mirzaeinejad, H.: Robust predictive control of wheel slip in
antilock braking systems based on radial basis function neural
network. Appl. Soft Comput. 70, 318–329 (2018)
10. Pretagostini, F., Ferranti, L., Berardo, G., Ivanov, V., Shyrokau,
B.: Survey on wheel slip control design strategies, evaluation
and application to antilock braking systems. IEEE Access 8,
10951–10970 (2020)
11. Yong, J., Gao, F., Ding, N., He, Y.: Design and validation of an
electro-hydraulic brake system using hardware-in-the-loop real-
time simulation. Int. J. Automot. Technol. 18(4), 603–612
(2017)
12. Savitski, D., Schleinin, D., Ivanov, V., Augsburg, K.: Robust
continuous wheel slip control with reference adaptation:
Application to the brake system with decoupled architecture.
IEEE Trans. Industr. Inf. 14(9), 4212–4223 (2018)
13. Wei, Z., Xuexun, G.: An ABS control strategy for commercial
vehicle. IEEE/ASME Trans. Mechatron. 20(1), 384–392 (2014)
14. Yang, D., Gu, Y., Thakor, N.V., Liu, H.: Improving the func-
tionality, robustness, and adaptability of myoelectric control for
dexterous motion restoration. Exp. Brain Res. 237(2), 291–311
(2019)
15. D. T. Le, D. T. Nguyen, N. D. Le and T. L. Nguyen, ‘‘Traction
control based on wheel slip tracking of a quarter-vehicle model
with high-gain observers,’’ International Journal of Dynamics
and Control, pp. 1–8, 2021
16. Kritayakirana, K., Gerdes, J.C.: Using the centre of percussion
to design a steering controller for an autonomous race car. Veh.
Syst. Dyn. 50(sup1), 33–51 (2012)
17. V. Krishna Teja Mantripragada and R. Krishna Kumar, ‘‘Sen-
sitivity analysis of tyre characteristic parameters on ABS per-
formance,’’ Vehicle System Dynamics, vol. 60, no. 1, pp. 47–72,
2022
18. Y. He, C. Lu, J. Shen and C. Yuan, ‘‘Design and analysis of
output feedback constraint control for antilock braking system
based on Burckhardt’s model,’’ Assembly Automation, 2019
19. Xiong, H., Liu, J., Zhang, R., Zhu, X., Liu, H.: An accurate
vehicle and road condition estimation algorithm for vehicle
networking applications. IEEE Access 17, 17705–17715 (2019)
20. E. Bakker, L. Nyborg and H. B. Pacejka, ‘‘Tyre modelling for
use in vehicle dynamics studies,’’ SAE Transactions,
pp. 190–204, 1987
21. Pacejka, H.B., Bakker, E.: The magic formula tyre model. Veh.
Syst. Dyn. 21(S1), 1–18 (1992)
22. Besselink, I.J.M., Schmeitz, A.J.C., Pacejka, H.B.: An improved
Magic Formula/Swift tyre model that can handle inflation
pressure changes. Veh. Syst. Dyn. 48(S1), 337–352 (2010)
23. Pacejka, H.B., Besselink, I.J.M.: Magic formula tyre model with
transient properties. Veh. Syst. Dyn. 27(S1), 234–249 (1997)
24. Wassertheurer, B., Gauterin, F.: Investigations on winter tire
characteristics on different track surfaces using a statistical
approach. Tire Science and Technology 43(3), 195–215 (2015)
25. Alagappan, A.V., Rao, K.V.N., Kumar, R.K.: A comparison of
various algorithms to extract Magic Formula tyre model coef-
ficients for vehicle dynamics simulations. Veh. Syst. Dyn. 53(2),
154–178 (2015)
26. Leng, B., Jin, D., Xiong, L., Yang, X., Yu, Z.: Estimation of tire-
road peak adhesion coefficient for intelligent electric vehicles
based on camera and tire dynamics information fusion. Mech.
Syst. Signal Process. 150, 107275 (2021)
27. He, Y., Lu, C., Shen, J., Yuan, C.: A second-order slip model for
constraint backstepping control of antilock braking system based
on Burckhardt’s model. Int. J. Model. Simul. 40(2), 130–142
(2020)
28. D. P. Madau, F. Yuan, L. I. Davis and L. A. Feldkamp, ‘‘Fuzzy
logic anti-lock brake system for a limited range coefficient of
friction surface. In; [Proceedings 1993] Second IEEE Interna-
tional Conference on Fuzzy Systems, pp. 883–888, 1993
29. Mardani, A., Hooker, R.E., Ozkul, S., Yifan, S., Nilashi, M.,
Sabzi, H.Z., Fei, G.C.: Application of decision making and
fuzzy sets theory to evaluate the healthcare and medical prob-
lems: a review of three decades of research with recent devel-
opments. Expert Syst. Appl. 137, 202–231 (2019)
30. Zadeh, L.A.: The concept of a linguistic variable and its appli-
cation to approximate reasoning—I. Inf. Sci. 8(3), 199–249
(1975)
31. Castillo, O., Melin, P.: A review on the design and optimization
of interval type-2 fuzzy controllers. Appl. Soft Comput. 12(4),
1267–1278 (2012)
32. D. Wang, M. Wang and Y. Li, ’’Genetic and fuzzy fusion
algorithm for coal-feeding optimal control of coal-fired power
123
International Journal of Fuzzy Systems
plant. In; 2020 International Symposium on Computer, Con-
sumer and Control (IS3C), pp. 500–503, 2020
33. M. El Midaoui, M. Qbadou and K. Mansouri, ‘‘A fuzzy-based
prediction approach for blood delivery using machine learning
and genetic algorithm.,’’ International Journal of Electrical &
Computer Engineering (2088–8708), vol. 23, no. 1, 2022
34. Li, Y., Wang, S., Yang, Y., Deng, Z.: Multiscale symbolic fuzzy
entropy: An entropy denoising method for weak feature
extraction of rotating machinery. Mech. Syst. Signal Process.
162, 108052 (2022)
35. C. Militello, L. Rundo, M. Dimarco, A. Orlando, V. Conti, R.
Woitek, I. D’Angelo, T. Bartolotta, Vincenzo and G. Russo,
‘‘Semi-automated and interactive segmentation of contrast-en-
hancing masses on breast DCE-MRI using spatial fuzzy clus-
tering,’’ Biomedical Signal Processing and Control, vol. 71,
p. 103113, 2022
36. N. F. Soliman, N. S. Ali, M. Aly, A. D. Algarni, W. El-Shafai
and F. E. Abd El-Samie, ‘‘An efficient breast cancer detection
framework for medical diagnosis applications,’’ CMC-Comput-
ers Materials & Continua, vol. 70, no. 1, pp. 1315–1334, 2022
37. Zaare, S., Soltanpour, M.R.: Adaptive fuzzy global coupled
nonsingular fast terminal sliding mode control of n-rigid-link
elastic-joint robot manipulators in presence of uncertainties.
Mech. Syst. Signal Process. 163, 108165 (2022)
38. Chang, X.-H., Jin, X.: Observer-based fuzzy feedback control
for nonlinear systems subject to transmission signal quantiza-
tion. Appl. Math. Comput. 414, 126657 (2022)
39. Silva, F.L., Silva, L.C.A., Eckert, J.J., Lourenc¸ o, M.A.M.:
Robust fuzzy stability control optimization by multi-objective
for modular vehicle. Mech. Mach. Theory 167, 104554 (2022)
40. Castillo, O., Melin, P.: A review on interval type-2 fuzzy logic
applications in intelligent control. Inf. Sci. 279, 615–631 (2014)
41. Mittal, K., Jain, A., Vaisla, K.S., Castillo, O., Kacprzyk, J.: A
comprehensive review on type 2 fuzzy logic applications: Past,
present and future. Eng. Appl. Artif. Intell. 95, 103916 (2020)
42. Liang, Q., Mendel, J.M.: Interval type-2 fuzzy logic systems:
theory and design. IEEE Trans. Fuzzy Syst. 8(5), 535–550
(2000)
43. Mas, M., Monserrat, M., Torrens, J., Trillas, E.: A survey on
fuzzy implication functions. IEEE Trans. Fuzzy Syst. 15(6),
1107–1121 (2007)
44. Y. Chen, ‘‘Study on centroid type-reduction of interval type-2
fuzzy logic systems based on noniterative algorithms,’’ Com-
plexity, vol. 2019, 2019
45. Khanesar, M.A., Khakshour, A.J., Kaynak, O., Gao, H.:
Improving the speed of center of sets type reduction in interval
type-2 fuzzy systems by eliminating the need for sorting. IEEE
Trans. Fuzzy Syst. 25(5), 1193–1206 (2016)
46. Ontiveros-Robles, E., Melin, P., Castillo, O.: New methodology
to approximate type-reduction based on a continuous root-
finding karnik mendel algorithm. Algorithms 10(3), 77 (2017)
47. Chen, Y., Wang, D.: Study on centroid type-reduction of general
type-2 fuzzy logic systems with weighted enhanced Karnik-
Mendel algorithms. Soft. Comput. 22(4), 1361–1380 (2018)
48. D. Wu and M. Nie, ‘‘Comparison and practical implementation
of type-reduction algorithms for type-2 fuzzy sets and systems.
In; 2011 IEEE International Conference on Fuzzy Systems
(FUZZ-IEEE 2011), pp. 2131–2138, 2011
49. C. Chen, D. Wu, J. M. Garibaldi, R. I. John, J. Twycross and J.
M. Mendel, ’’A comprehensive study of the efficiency of type-
reduction algorithms,‘‘ IEEE Transactions on Fuzzy Systems,
2020
50. Aly, A.A., Zeidan, E.-S., Hamed, A., Salem, F.: An antilock-
braking systems (ABS) control: A technical review. Intell.
Control. Autom. 2(03), 186 (2011)
51. B. K. Dash and B. Subudhi, ’’A fuzzy adaptive sliding mode slip
ratio controller of a HEV. In; 2013 IEEE International Confer-
ence on Fuzzy Systems (FUZZ-IEEE), pp. 1–8, 2013
52. Layne, J.R., Passino, K.M., Yurkovich, S.: Fuzzy learning
control for antiskid braking systems. IEEE Trans. Control Syst.
Technol. 1(2), 122–129 (1993)
53. Y. Lee and S. H. Zak, ‘‘Genetic neural fuzzy control of anti-lock
brake systems. In; Proceedings of the 2001 American Control
Conference.(Cat. No. 01CH37148), vol. 2, pp. 671–676, 2001
54. Lin, C.M., Hsu, C.F.: Self-learning fuzzy sliding-mode control
for antilock braking systems. IEEE Trans. Control Syst. Tech-
nol. 11(2), 273–278 (2003)
55. Chen, C.K., Shih, M.C.: PID-Type fuzzy control for anti-lock
brake systems with parameter adaptation. JSME Int J., Ser. C
47(2), 675–685 (2004)
56. N. Raesian, N. Khajehpour and M. Yaghoobi, ’’A new approach
in anti-lock braking system (ABS) based on adaptive neuro-
fuzzy self-tuning PID controller. In; the 2nd International
Conference on Control, Instrumentation and Automation,
pp. 530–535, 2011
57. Precup, R.E., Spa
˘taru, S.V., Ra
˘dac, M.B., Petriu, E.M., Preitl, S.,
Dragos¸ , C.A., David, R.C.: Experimental results of model-based
fuzzy control solutions for a laboratory antilock braking system.
Human-Computer Systems Interaction: Backgrounds and
Applications 2, 223–234 (2012)
58. Tang, Y., Wang, Y., Han, M., Lian, Q.: Adaptive fuzzy frac-
tional-order sliding mode controller design for antilock braking
systems. J. Dyn. Syst. Meas. Contr. 138(4), 041008 (2016)
59. X. Feng and J. Hu, ‘‘Discrete fuzzy adaptive PID control algo-
rithm for automotive anti-lock braking system,’’ Journal of
Ambient Intelligence and Humanized Computing, pp. 1–10,
2021
60. Lv, L., Wang, J., Long, J.: Interval type-2 fuzzy logic anti-lock
braking control for electric vehicles under complex road con-
ditions. Sustainability 13(20), 11531 (2021)
61. Amirkhani, A., Shirzadeh, M., Molaie, M.: An indirect type-2
fuzzy neural network optimized by the grasshopper algorithm
for vehicle ABS controller. IEEE Access 10, 58736–58751
(2022)
62. Mauer, G.F.: A fuzzy logic controller for an ABS braking sys-
tem. IEEE Trans. Fuzzy Syst. 3(4), 381–388 (1995)
63. Cabrera, J.A., Ortiz, A., Castillo, J.J., Simon, A.: A fuzzy logic
control for antilock braking system integrated in the IMMa tire
test bench. IEEE Trans. Veh. Technol. 54(6), 1937–1949 (2005)
64. Mirzaei, A., Moallem, M., Dehkordi, B.M., Fahimi, B.: Design
of an optimal fuzzy controller for antilock braking systems.
IEEE Trans. Veh. Technol. 55(6), 1725–1730 (2006)
65. N. M. Mane and N. V. Vivekanandan, ‘‘Design and analysis of
antilock braking system with fuzzy controller for motorcycle,’’
International Research Journal of Engineering and Technology
(IRJET) e-ISSN, pp. 0056–2395, 2019
66. Ferna
´ndez, J.P., Vargas, M.A., Garcı
´a, J.M.V., Carrillo, J.A.C.,
Aguilar, J.J.C.: Coevolutionary optimization of a fuzzy logic
controller for antilock braking systems under changing road
conditions. IEEE Trans. Veh. Technol. 70(2), 1255–1268 (2021)
67. D. E. Nelson, R. Challoo, R. A. McLauchlan and S. I. Omar,
‘‘Implementation of fuzzy logic for an antilock braking system.
In; 1997 IEEE International Conference on Systems, Man, and
Cybernetics. Computational Cybernetics and Simulation, vol. 4,
pp. 3680–3685, 1997
68. C. Sobottka and T. Singh, ’’Optimal fuzzy logic control for an
anti-lock braking system. In; Proceeding of the 1996 IEEE
International Conference on Control Applications IEEE Inter-
national Conference on Control Applications held together with
IEEE International Symposium on Intelligent Contro, pp. 49–54,
1996
123
A. Amirkhani, M. Molaie: Fuzzy Controllers of Antilock Braking System
69. E. C. Yeh, J. H. Ton and G. K. Roan, ‘‘Development of fuzzy
controller for anti-skid brake systems with a single chip
microcontroller. In; Proceedings of the Intelligent Vehicles’ 93
Symposium, pp. 129–134, 1993
70. R. E. Precup, S. Preitl, M. Balas and V. Balas, ’’Fuzzy con-
trollers for tire slip control in anti-lock braking systems. In; 2004
IEEE International Conference on Fuzzy Systems (IEEE Cat.
No. 04CH37542), vol. 3, pp. 1317–1322, 2004
71. P. Khatun, C. M. Bingham, N. Schofield and P. H. Mellor, ‘‘An
experimental laboratory bench setup to study electric vehicle
antilock braking/traction systems and their control. In; Pro-
ceedings IEEE 56th Vehicular Technology Conference, vol. 3,
pp. 1490–1494, 2002
72. P. Khatun, C. M. Bingham and P. H. Mellor, ’’Comparison of
control methods for electric vehicle antilock braking/traction
control systems,‘‘ SAE Technical Paper, no. 2001–01–0596,
2001
73. L. Jun, Z. Jianwu and Y. Fan, ’’An investigation into fuzzy
control for anti-lock braking system based on road autonomous
identification,‘‘ SAE Technical Paper, no. 2001–01–0599, 2001
74. D. Zhang, H. Zheng, J. Sun, Q. Wang, Q. Wen, A. Yin and Z.
Yang, ’’Simulation study for anti-lock braking system of a light
bus. In; Proceedings of the IEEE International Vehicle Elec-
tronics Conference (IVEC’99)(Cat. No. 99EX257), pp. 70–77,
1999
75. Z. Zhao, Z. Yu and Z. Sun, ‘‘Research on fuzzy road surface
identification and logic control for anti-lock braking system. In;
2006 IEEE International Conference on Vehicular Electronics
and Safety, pp. 380–387, 2006
76. S. Jun, ’’Development of fuzzy logic anti-lock braking system
for light bus,‘‘ SAE Technical Paper, no. 2003–01–0458, 2003
77. D. P. dos Santos and E. L. L. Cabral, ’’A novel method for
controlling an ABS (Anti-lock Braking System) for heavy
vehicle,‘‘ ,SAE Technical Paper, no. 2008–36–0039, 2008
78. Mousavi, A., Davaie-Markazi, A.H., Masoudi, S.: Comparison
of adaptive fuzzy sliding-mode pulse width modulation control
with common model-based nonlinear controllers for slip control
in antilock braking systems. J. Dyn. Syst. Meas. Contr. 140(1),
11014 (2018)
79. A. Aksjonov, V. Ricciardi, V. Vodovozov and K. Augsburg,
’’Trajectory phase-plane method-based analysis of stability and
performance of a fuzzy logic controller for an anti-lock braking
system. In; 2019 IEEE International Conference on Mecha-
tronics (ICM), vol. 1, pp. 602–607, 2019
80. V. N. and D. A. M. F. Spandan Waghmare, ‘‘Experimental
validation of fuzzy Logic based anti-lock braking system used in
quarter car model,’’ ,International Journal of Control and
Automation, vol. 13, no. 02, pp. 332–348, 2020
81. K. A. Augsburg, A. A. Aksjonov, V. V. Vodovozov and E.
P. Petlenkov, ‘‘Blended antilock braking system control method
for all-wheel drive electric sport utility vehicle. In; Collection of
Open Chapters of Books in Transport Research, 2020
82. A. A. Umnitsyn and S. V. Bakhmutov, ’’Intelligent anti-lock
braking system of electric vehicle with the possibility of mixed
braking using fuzzy logic. In; Journal of Physics: Conference
Series, vol. 2061, no. 1, pp. 12101, 2021
83. Aksjonov, A., Ricciardi, V., Augsburg, K., Vodovozov, V.,
Petlenkov, E.: Hardware-in-the-loop test of an open-loop fuzzy
control method for decoupled electrohydraulic antilock braking
system. IEEE Trans. Fuzzy Syst. 29(5), 965–975 (2020)
84. J. Shao, L. Zheng, Y. N. Li, J. S. Wei and M. G. Luo, ‘‘The
integrated control of anti-lock braking system and active sus-
pension in vehicle. In; Fourth International Conference on Fuzzy
Systems and Knowledge Discovery (FSKD 2007), vol. 4,
pp. 519–523, 2007
85. Zhang, L., Yu, L., Pan, N., Zhang, Y., Song, J.: Cooperative
control of regenerative braking and friction braking in the
transient process of anti-lock braking activation in electric
vehicles. Proceedings of the Institution of Mechanical Engi-
neers, Part D: Journal of Automobile Engineering 230(11),
1459–1476 (2016)
86. M. L. Akey, ’’Development of fuzzy logic ABS control for
commercial trucks,‘‘ SAE Transactions, pp. 780–788, 1995
87. Lennon, W.K., Passino, K.M.: Intelligent control for brake
systems. IEEE Trans. Control Syst. Technol. 7(2), 188–202
(1999)
88. Chen, F.W., Liao, T.L.: Nonlinear linearization controller and
genetic algorithm-based fuzzy logic controller for ABS systems
and their comparison. Int. J. Veh. Des. 24(4), 334–349 (2000)
89. M. B. Ra
˘dac, R. E. Precup, S. Preitl, J. K. Tar and K. J. Burn-
ham, ’’Tire slip fuzzy control of a laboratory anti-lock braking
system. In; 2009 European Control Conference (ECC),
pp. 940–945, 2009
90. R. E. Precup, S. V. Spa
˘taru, E. M. Petriu, S. Preitl, M. B. Ra
˘dac
and C. A. Dragos¸ , ‘‘Stable and optimal fuzzy control of a lab-
oratory antilock braking system. In; 2010 IEEE/ASME Inter-
national Conference on Advanced Intelligent Mechatronics,
pp. 593–598, 2010
91. Lee, Y., Zak, S.H.: Designing a genetic neural fuzzy antilock-
brake-system controller. IEEE Trans. Evol. Comput. 6(2),
198–211 (2002)
92. Khatun, P., Bingham, C.M., Schofield, N., Mellor, P.H.:
Application of fuzzy control algorithms for electric vehicle
antilock braking/traction control systems. IEEE Trans. Veh.
Technol. 52(5), 1356–1364 (2003)
93. Ursu, I., Ursu, F.: Airplane ABS control synthesis using fuzzy
logic. Journal of Intelligent & Fuzzy Systems 16(1), 23–32
(2005)
94. Aksjonov, A., Vodovozov, V., Augsburg, K., Petlenkov, E.:
Design of regenerative anti-lock braking system controller for 4
in-wheel-motor drive electric vehicle with road surface estima-
tion. Int. J. Automot. Technol. 19(4), 727–742 (2018)
95. A. Aksjonov, V. Vodovozov and E. Petlenkov, ’’Design and
experimentation of fuzzy logic control for an anti-lock braking
system. In; 2016 15th Biennial Baltic Electronics Conference
(BEC), pp. 207–210, 2016
96. Yazicioglu, Y., Unlusoy, Y.S.: A fuzzy logic controlled anti-
lock braking system (ABS) for improved braking performance
and directional stability. Int. J. Veh. Des. 48(3–4), 299–315
(2008)
97. H. Du, W. Li and Y. Zhang, ‘‘Tracking control of wheel slip
ratio with velocity estimation for vehicle anti-lock braking
system. In; The 27th Chinese Control and Decision Conference
(2015 CCDC), pp. 1900–1905, 2015
98. Aparow, V.R., Fauzi, A., Hassan, M.Z., Hudha, K.: Develop-
ment of antilock braking system based on various intelligent
control system. Appl. Mech. Mater. 229, 2394–2398 (2012)
99. A. M. A. Soliman and M. M. S. Kaldas, ’’An Investigation of
anti-lock braking system for automobiles,‘‘ SAE Technical
Paper, 2012
100. El-Garhy, A., El-Sheikh, G.A.M., El-Saify, M.H.: Fuzzy life-
extending control of anti-lock braking system. Ain Shams
Engineering Journal 4(4), 735–751 (2013)
101. Precup, R.E., Sabau, M.C., Petriu, E.M.: Nature-inspired opti-
mal tuning of input membership functions of Takagi-Sugeno-
Kang fuzzy models for anti-lock braking systems. Appl. Soft
Comput. 27, 575–589 (2015)
102. Aksjonov, A., Augsburg, K., Vodovozov, V.: Design and sim-
ulation of the robust ABS and ESP fuzzy logic controller on the
complex braking maneuvers. Appl. Sci. 6(12), 382 (2016)
123
International Journal of Fuzzy Systems
103. R. E. Precup, C. A. Bojan-Dragos, E. L. Hedrea, I. D. Borlea and
E. M. Petriu, ’’Evolving fuzzy models for anti-lock braking
systems. In; 2017 IEEE International Conference on Computa-
tional Intelligence and Virtual Environments for Measurement
Systems and Applications (CIVEMSA), pp. 48–53, 2017
104. Zhang, Z., Yang, Z., Zhou, G., Liu, S., Zhou, D., Chen, S.,
Zhang, X.: Adaptive fuzzy active-disturbance rejection control-
based reconfiguration controller design for aircraft anti-skid
braking system. Actuators 10(8), 201 (2021)
105. Habibi, M., Yazdizadeh, A.: A new fuzzy logic road detector for
antilock braking system application. IEEE ICCA 2010,
1036–1041 (2010)
106. Shiao, Y., Nguyen, Q.A., Lin, J.W.: A study of novel hybrid
antilock braking system employing magnetorheological brake.
Adv. Mech. Eng. 6, 617584 (2014)
107. Harifi, A., Rashidi, F.: Design of an adaptive fuzzy controller for
antilock brake systems. Automotive Science and Engineering
10(1), 3158–3166 (2020)
108. Park, J.H., Kim, D.H., Kim, Y.J.: Anti-lock brake system control
for buses based on fuzzy logic and a sliding-mode observer.
KSME International Journal 15(10), 1398–1407 (2001)
109. Tseng, H.C., Chi, C.W.: Aircraft antilock brake system with
neural networks and fuzzy logic. J. Guid. Control. Dyn. 18(5),
1113–1118 (1995)
110. G. Yin and X. Jin, ‘‘Cooperative control of regenerative braking
and antilock braking for a hybrid electric vehicle,’’ ,Mathe-
matical Problems in Engineering, p. 2013, 2013
111. Chu, L., Wang, X., Zhang, L., Yao, L., Zhang, Y.S.: Integrative
control of regenerative braking system and anti-lock braking
system. Advanced Materials Research 706, 830–835 (2013)
112. Peng, D., Zhang, Y., Yin, C.L., Zhang, J.W.: Combined control
of a regenerative braking and antilock braking system for hybrid
electric vehicles. Int. J. Automot. Technol. 9(6), 6 (2008)
113. Rattasiri, W., Wickramarachchi, N., Halgamuge, S.K.: An
optimized anti-lock braking system in the presence of multiple
road surface types. Int. J. Adapt. Control Signal Process. 21(6),
477–498 (2007)
114. G. Kokes and T. Singh, ‘‘Adaptive fuzzy logic control of an anti-
lock braking system. In; Proceedings of the 1999 IEEE Inter-
national Conference on Control Applications (Cat. No.
99CH36328), vol. 1, pp. 646–651, 1999
115. Fargione, G., Tringali, D., Risitano, G.: A fuzzy-genetic control
system in the ABS for the control of semi-active vehicle sus-
pensions. Mechatronics 39, 89–102 (2016)
116. R. C. David, R. B. Grad, R. E. Precup, M. B. Ra
˘dac, C.
A. Dragos¸ and E. M. Petriu, ’’An approach to fuzzy modeling of
anti-lock braking systems. In; Soft Computing in Industrial
Applications, 2014, pp. 83–93
117. Bansal, H.O., Sharma, R., Shreeraman, P.R.: PID controller
tuning techniques: a review. Journal of Control Engineering and
Technology 2(4), 168–176 (2012)
118. Huba, M., Chamraz, S., Bistak, P., Vrancic, D.: Making the PI
and PID controller tuning inspired by ziegler and nichols precise
and reliable. Sensors 21(18), 6157 (2021)
119. Liu, Y., Fan, K., Ouyang, Q.: Intelligent traction control method
based on model predictive fuzzy PID control and online opti-
mization for permanent magnetic maglev trains. IEEE Access 9,
29032–29046 (2021)
120. Chao, C.T., Sutarna, N., Chiou, J.S., Wang, C.J.: An optimal
fuzzy PID controller design based on conventional PID control
and nonlinear factors. Appl. Sci. 9(6), 1224 (2019)
121. Wang, Y., Jin, Q., Zhang, R.: Improved fuzzy PID controller
design using predictive functional control structure. ISA Trans.
71, 354–363 (2017)
122. Sharkawy, A.B.: Genetic fuzzy self-tuning PID controllers for
antilock braking systems. Eng. Appl. Artif. Intell. 23(7),
1041–1052 (2010)
123. Wang, B., Lu, P.P., Guan, H., Jing, J.: Fuzzy PID control of
ABS based on real-time road surface identification. Appl. Mech.
Mater. 597, 380–383 (2014)
124. J. Kejun and L. Chengye, ‘‘Application study of fuzzy PID
control with S-function on automotive ABS. In; 2010 Interna-
tional Conference on Future Information Technology and
Management Engineering, vol. 1, pp. 467–470, 2010
125. Boopathi, A.M., Abudhahir, A.: Firefly algorithm tuned fuzzy
set-point weighted PID controller for antilock braking systems.
Journal of Engineering Research 3(2), 1–16 (2015)
126. Dang, B.Y.: Study on the control of anti-lock braking system
simulation based on fuzzy PID control. Advanced Materials
Research 950, 239–244 (2014)
127. M. B. Ra
˘dac, R. E. Precup, S. Preitl, J. K. Tar and E. M. Petriu,
’’Linear and fuzzy control solutions for a laboratory anti-lock
braking system. In; 2008 6th International Symposium on
Intelligent Systems and Informatics, pp. 1–6, 2008
128. Ahmad, F., Mazlan, S.A., Hudha, K., Jamaluddin, H., Zamzuri,
H.: Fuzzy fractional PID gain controller for antilock braking
system using an electronic wedge brake mechanism. Int. J. Veh.
Saf. 10(2), 97–121 (2018)
129. Liu, Y., Jin, L.Q., Liang, X.L., Zheng, Z.A.: Research on BP
based fuzzy-PID controller for anti-lock braking system. Appl.
Mech. Mater. 365, 401–406 (2013)
130. A. A. Aldair, ‘‘Design of neurofuzzy self tuning PID controller
for antilock braking systems,’’ ,Journal of University of Baby-
lon, vol. 22, no. 4, 2014
131. H. Jidu, Z. Yongjun, T. Yu and W. Gang, ‘‘Research on vehicle
anti-braking system control algorithm based on fuzzy immune
adaptive PID control. In; 2012 Third International Conference
on Digital Manufacturing & Automation, pp. 723–726, 2012
132. Gambhire, S.J., Kishore, D.R., Londhe, P.S., Pawar, S.N.:
Review of sliding mode based control techniques for control
system applications. International Journal of Dynamics and
Control 9, 363–378 (2021)
133. Aghababa, M.P.: Design of a chatter-free terminal sliding mode
controller for nonlinear fractional-order dynamical systems. Int.
J. Control 86(10), 1744–1756 (2013)
134. Lochan, K., Singh, J.P., Roy, B.K., Subudhi, B.: Adaptive time-
varying super-twisting global SMC for projective synchronisa-
tion of flexible manipulator. Nonlinear Dyn. 93(4), 2071–2088
(2018)
135. Guo, J., Jian, X., Lin, G.: Performance evaluation of an anti-lock
braking system for electric vehicles with a fuzzy sliding mode
controller. Energies 7(10), 6459–6476 (2014)
136. Sun, J., Xue, X., Cheng, K.W.E.: Fuzzy sliding mode wheel slip
ratio control for smart vehicle anti-lock braking system. Ener-
gies 12(13), 2501 (2019)
137. Zhang, X., Lin, H.: Backstepping fuzzy sliding mode control for
the antiskid braking system of unmanned aerial vehicles. Elec-
tronics 9(10), 1731 (2020)
138. D. Mitic
´, D. Antic
´, S. Peric
´, M. Milojkovic
´and S. Nikolic
´,
’’Fuzzy sliding mode control for anti-lock braking systems. In;
2012 7th IEEE International Symposium on Applied Compu-
tational Intelligence and Informatics (SACI), pp. 217–222, 2012
139. J. Sun and K. W. E. Ceng, ‘‘Four-wheel anti-lock braking sys-
tem with road condition detection module. In; 2020 8th Inter-
national Conference on Power Electronics Systems and
Applications (PESA), pp. 1–5, 2020
140. Oudghiri, M.: Robust fuzzy sliding mode control for antilock
braking system. International Journal on Sciences and Tech-
niques of Automatic Control 1(1), 13–28 (2007)
123
A. Amirkhani, M. Molaie: Fuzzy Controllers of Antilock Braking System
141. W. Y. Wang, K. C. Hsu, T. T. Lee and G. M. Chen, ’’Robust
sliding mode-like fuzzy logic control for anti-lock braking
systems with uncertainties and disturbances. In; Proceedings of
the 2003 International Conference on Machine Learning and
Cybernetics (IEEE Cat. No. 03EX693), vol. 1, pp. 633–638,
2003
142. M. Khazaei and M. Rouhani, ‘‘Design and simulation of fuzzy-
sliding mode anti-lock braking system capable of identification
of different surfaces of road,’’ ,Majlesi Journal of Mechatronic
Systems, vol. 4, no. 1, 2015
143. Boopathi, A.M., Abudhahir, A.: Adaptive fuzzy sliding mode
controller for wheel slip control in antilock braking system.
Journal of Engineering Research 4(2), 1–19 (2016)
144. Latreche, S., Benaggoune, S.: Robust wheel slip for vehicle anti-
lock braking system with Fuzzy Sliding Mode Controller
(FSMC). Engineering, Technology & Applied Science Research
10(5), 6368–6373 (2020)
145. M. Habibi and A. Yazdizadeh, ‘‘A novel fuzzy-sliding mode
controller for antilock braking system. In; 2010 2nd Interna-
tional Conference on Advanced Computer Control, vol. 4,
pp. 110–114, 2010
146. Li, W., Du, H., Li, W.: A modified extreme seeking-based
adaptive fuzzy sliding mode control scheme for vehicle anti-
lock braking. Int. J. Veh. Auton. Syst. 15(1), 1–25 (2020)
147. Sun, J., Xue, X., Cheng, K.W.E.: Four-wheel anti-lock braking
system with robust adaptation under complex road conditions.
IEEE Trans. Veh. Technol. 70(1), 292–302 (2020)
148. M. R. Akbarzadeh-T, K. J. Emami and N. Pariz, ’’Adaptive
discrete-time fuzzy sliding mode control for anti-lock braking
systems. In; 2002 Annual Meeting of the North American Fuzzy
Information Processing Society Proceedings. NAFIPS-FLINT
2002 (Cat. No. 02TH8622), pp. 554–559, 2002
149. Wang, Z., Choi, S.B.: A fuzzy sliding mode control of anti-lock
system featured by magnetorheological brakes: performance
evaluation via the hardware-in-the-loop simulation. J. Intell.
Mater. Syst. Struct. 32(14), 1580–1590 (2021)
150. G. M. Chen, W. Y. Wang, T. T. Lee and C. W. Tao, ‘‘Observer-
based direct adaptive fuzzy-neural control for anti-lock braking
systems,’’ ,International Journal of Fuzzy Systems, vol. 8, no. 4,
2006
151. Y. Pan, Q. Li, H. Liang and H. K. Lam, ‘‘A novel mixed control
approach for fuzzy systems via membership functions online
learning policy,’’ ,IEEE Transactions on Fuzzy Systems, 2021
152. Pan, Y., Yang, G.H.: Event-triggered fault detection filter design
for nonlinear networked systems. IEEE Transactions on Sys-
tems, Man, and Cybernetics: Systems 48(11), 1851–1862 (2017)
153. Y. Pan, Y. Wu and H. K. Lam, ‘‘Security-based fuzzy control for
nonlinear networked control systems with DoS attacks via a
resilient event-triggered scheme,’’ IEEE Transactions on Fuzzy
Systems, 2022
154. Wang, W.Y., Li, I.H., Chen, M.C., Su, S.F., Hsu, S.B.: Dynamic
slip-ratio estimation and control of antilock braking systems
using an observer-based direct adaptive fuzzy–neural controller.
IEEE Trans. Industr. Electron. 56(5), 1746–1756 (2008)
155. Topalov, A.V., Oniz, Y., Kayacan, E., Kaynak, O.: Neuro-fuzzy
control of antilock braking system using sliding mode incre-
mental learning algorithm. Neurocomputing 74(11), 1883–1893
(2011)
156. Le, T.L.: Intelligent fuzzy controller design for antilock braking
systems. Journal of Intelligent & Fuzzy Systems 36(4),
3303–3315 (2019)
157. Wu, B.F., Chang, P.J., Chen, Y.S., Huang, C.W.: An intelligent
wheelchair anti-lock braking system design with friction coef-
ficient estimation. IEEE Access 6, 73686–73701 (2018)
158. Shih, M.C., Wu, M.C., Lee, L.C.: Neuro-fuzzy controller design
of anti-lock braking system. IFAC Proceedings Volumes 31(27),
97–102 (1998)
159. J. Pramudijanto, A. Ashfahani and R. Lukito, ‘‘Designing neuro-
fuzzy controller for electromagnetic anti-lock braking system
(ABS) on electric vehicle. In; Journal of Physics: Conference
Series, vol. 974, no. 1, pp. 12055, 2018
160. Zeng, X.H., Gao, Y.: An optimized algorithm for advanced
vehicle anti-lock braking system. Adv. Mater. Res. 791,
1489–1492 (2013)
161. Chen, M.-C., Wang, W.-Y., Li, I.-H., Su, S.-F.: Dynamic slip
ratio estimation and control of antilock braking systems con-
sidering wheel angular velocity. In: 2007 IEEE International
Conference on Systems, Man and Cybernetics, pp. 3282–3287,
2007
162. Topalov, A.V., Kayacan, E., Oniz, Y., Kaynak, O.: Neuro-fuzzy
control of antilock braking system using variable-structure-
systems-based learning algorithm. In: 2009 International Con-
ference on Adaptive and Intelligent Systems, pp. 166–171, 2009
163. Wang, W.Y., Chen, M.C., Su, S.F.: Hierarchical T-S fuzzy-
neural control of anti-lock braking system and active suspension
in a vehicle. Automatica 48(8), 1698–1706 (2012)
164. W. Y. Wang, G. M. Chen and C. W. Tao, ’’Stable anti-lock
braking system using output-feedback direct adaptive fuzzy
neural control. In; SMC’03 Conference Proceedings. 2003 IEEE
International Conference on Systems, Man and Cybernetics.
Conference Theme-System Security and Assurance (Cat. No.
03CH37483), vol. 4, p. , 3675–3680, 2003
165. W. Y. Wang, Y. H. Chien, M. C. Chen and T. T. Lee, Control of
uncertain active suspension system with anti-lock braking sys-
tem using fuzzy neural controllers. In: 2009 IEEE International
Conference on Systems, Man and Cybernetics, pp. 3371–3376,
2009
166. Hsu, C.F., Kuo, T.C.: Adaptive exponential-reaching sliding-
mode control for antilock braking systems. Nonlinear Dyn.
77(3), 993–1010 (2014)
167. A. V. Topalov, E. Kayacan, Y. Oniz and O. Kaynak, ‘‘Adaptive
neuro-fuzzy control with sliding mode learning algorithm:
Application to antilock braking system. In; 2009 7th Asian
Control Conference, pp. 784–789, 2009
168. Kueon, Y.S., Bedi, J.S.: Fuzzy-neural-sliding mode controller
and its applications to the vehicle anti-lock braking systems. In:
Proceedings IEEE Conference on Industrial Automation and
Control Emerging Technology Applications, pp. 391–398, 1995
169. Lin, C.M., Li, H.Y.: Intelligent hybrid control system design for
antilock braking systems using self-organizing function-link
fuzzy cerebellar model articulation controller. IEEE Trans.
Fuzzy Syst. 21(6), 1044–1055 (2013)
170. Hsu, C.F.: Intelligent exponential sliding-mode control with
uncertainty estimator for antilock braking systems. Neural
Comput. Appl. 27(6), 1463–1475 (2016)
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International Journal of Fuzzy Systems
Abdollah Amirkhani
(Senior Member, IEEE)
received the MSc and PhD
degrees (with honors) in elec-
trical engineering from Iran
University of Science and
Technology (IUST), Tehran, in
2012 and 2017, respectively. He
earned the Outstanding Student
Award (2015) form the First
Vice President of Iran. In 2016,
he was conferred award by the
Ministry of Science, Research
and Technology. He is an
Assistant Professor in the school
of automotive engineering at IUST. He is the Associate Editor of the
‘‘Engineering Science and Technology, an International Journal’’. He
has been actively involved in several National R&D projects, related
to the development of new methodologies and learning algorithms
based on AI techniques. His research interests are in machine vision,
fuzzy cognitive maps, autonomous vehicle, data mining and machine
learning.
Mahdi Molaie received the
B.Sc. degree in Electrical Engi-
neering from University of
Mazandaran, and he is currently
a master’s degree student in
digital electronics at Iran
University of Science and
Technology (IUST), Tehran,
Iran. His research interests
include autonomous vehicles,
type-2 fuzzy sets and systems,
intelligent systems, deep learn-
ing and machine learning.
123
A. Amirkhani, M. Molaie: Fuzzy Controllers of Antilock Braking System
