Proposed Fault Detection Algorithm with Optimized Hybrid Speed
Control
MARIEM AHMED BABA1,*, MOHAMED NAOUI2,*, AHMED ABBOU1,
MOHAMED CHERKAOUI1
1Engineering for Smart and Sustainable Systems Research Center,
Mohammadia School of Engineers, Mohammed V University,
BP: 765, Av. Ibn Sina, Agdal - Rabat,
MOROCCO
2Research Unit of Energy Processes Environment and Electrical Systems,
National Engineering School of Gabes,
University of Gabés, Gabés 6029,
TUNISIA
*Corresponding Author
Abstract: - The Brushless DC (BLDC) motor is a common choice for industrial applications, particularly in the
automotive sector, owing to its high efficiency and robust capabilities. To detect the position of the motor rotor,
hall-effect sensors can be used, but these sensors may prevent the system from operating if they fail.
Consequently, fault-tolerant control (FTC) has been proposed in several studies to ensure continuity of
operation in the event of sensor failure. This paper proposes an innovative method of fault detection in the hall
effect sensor for a BLDC motor using combinatorial functions. This paper proposes an innovative method of
hall-effect sensor fault detection for a BLDC motor using combinatorial functions. For the speed control of the
BLDC under study, a hybrid adaptive neuro-fuzzy inference control (ANFIS) is implemented. In addition, the
FTC signal reconstruction technique adopted has been improved to achieve motor start-up despite a fault in one
of the sensors, thanks to well-defined fault detection algorithms. Simulation results are presented for each
sensor failure case to test the effectiveness of the method used.
Key-Words: - BLDC motor, Hall position, PID controller, Fuzzy logic controller, fault-tolerant control
(FTC); hall effect sensors; artificial neural network (ANN); fuzzy logic (FL); intelligent
control; hybrid adaptive neuro-fuzzy inference control (ANFIS).
Received: March 9, 2023. Revised: December 23, 2023. Accepted: March 3, 2024. Published: April 11, 2024.
1 Introduction
Brushless DC (BLDC) motors are widely utilized
across various industries including industrial,
aerospace, household appliances, and automotive
sectors. These motors function similarly to DC
motors but without the presence of brushes. They
are distinguished by their electronic commutation
utilizing semiconductor electronic switches, [1]. The
BLDC motor is considered a type of permanent
synchronous machine, [2]. The rotor position can be
assured by several methods, with or without sensors.
In the case of sensors, optical or Hall-effect sensors
are used to detect rotor position. The wide use of
this motor is due to its considerable advantages,
such as high efficiency, low maintenance needs,
high torque-to-weight ratio, and low noise, thanks to
the absence of brushes, [3]. The automotive sector
has introduced the BLDC engine into their models
to a considerable extent, [4], [5]. For example,
Toyota and Honda, [6], have adopted these engines
in models that have become widespread.
In the literature, several papers have discussed
applications of the BLDC motor in electric vehicles.
For example, in [7], the authors used the
regenerative braking technique (RBS) applied to the
BLDC motor for electric vehicles. In the same
concept, the paper [8], deals with neural network
control of an electric vehicle drive train using the
brushless motor. In [9], a concrete study is presented
to define and discuss the important role of the
BLDC motor in promoting the performance of
electric vehicles. This work also presented the
different controllers widely used in the case of a
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BLDC motor, including neural network control and
fuzzy logic control.
Other researchers, [10], have adopted the BLDC
motor speed control system using the artificial
neural network (ANN) controller to apply it to
electric buses. As a result, the simulation results
obtained in this case demonstrated the effectiveness
of the technique employed. In addition, a
comparative study of different controllers aimed at
controlling a BLDC motor was carried out, [11].
Therefore, the authors proposed several types of
control based mainly on adaptive neuro-fuzzy
inference systems.
Faults during system operation are a serious
concern for vehicle manufacturers, who need to
ensure safety and high vehicle performance. Hence,
the focus on fault-tolerant control (FTC) is seen as a
strategy to ensure that a system continues operating
despite faults, [12]. Fault-tolerant control strategies
are generally divided into two main groups: active
tolerant control and passive tolerant control. In the
case of electric vehicle failures, faults can be located
either in the actuators or in the sensors. However,
many studies have treated the Hall sensor faults as
one of the most famous failures. Indeed, the
algorithms adopted in FTCs have recently been
widely used to improve the system's capabilities,
especially in industrial sectors where a small defect
in a product can affect its sales. Paper [13],
discussed an improved fault tolerant control (FTC)
method using a vector tracking observer. This
technique improved steady-state and transient
operating conditions despite the existence of hall-
effect sensor failures. As much research is based on
FTC control in the case of a single sensor failure,
the authors in [14] propose an innovative method
using fault-tolerant direct redundant control to limit
the failure effect in the case of multiple sensor
failures. Among the methods developed by the FTC,
is a technique adopting electronic logic gates that
aims to track the state of Hall effect signals to
translate them into binary language. Another
innovative FTC technique has been applied in [15],
using three main indices to detect reversal faults in a
brushless motor and another index to identify faulty
cases from normal ones. Despite the excessive use
of common FTC methods such as fault recovery
techniques and the vector tracking observer, it has
been observed that the system becomes less flexible
when used with different models. To avoid this
problem, the authors in [16] presented a new
method based on (CNN-LSTM) applied to a BLDC
motor for fault detection and signal reconstruction
of hall-effect sensors. The authors in [17] proposed
a hybrid approach between the genetic and binary
state transition algorithms to detect defective BLDC
motor bearings. In a comparative study, the
Adaptive Neuro Fuzzy Inference System controller
(ANFIS) was used to study the speed behavior of a
brushless DC motor, [18]. The results in this case
showed that the speed obtained by the ANFIS
controller was the closest to the reference speed
compared with other controllers applied. This
hybrid control has also been used in medical
applications, [19]. The process serves to improve
the speed performance of the BLDC motor using
(the ANFIS) controller to apply this strategy to
surgical robotic systems. This paper is organized as
follows. An overview of the BLDC motor is
presented, together with the overall mathematical
modeling of this motor. The second section studies
the speed control system used. The remaining part
uses the binary function method to deal with the
hall-effect sensor fault detection strategy. The final
section presents simulation results and a discussion
of each case.
2 Mathematical Modeling of the
Hybrid Vehicle
2.1 Mechanical Model
The mechanical model of a moving vehicle, as
shown in Figure 1, is determined by all the forces
acting on the direction of motion. To calculate the
power necessary for the vehicle to move forward
(Pm), we apply the fundamental principle of
dynamics (F.P.D):
(1)
Fig. 1: Balance of forces acting on the vehicle
The balance of external forces is summarized in
Figure 1.
(2)
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Where represents the air resistance on the
vehicle,
the wheel resistance, and the mechanical
traction force:
(3)
(4)
The projection of equation (2) onto the axis:
(5)
(6)
The mechanical power necessary for the
advancement of the vehicle can be expressed
through equation (7).
(7)
Based on equation (5) it is therefore possible to
express the mechanical power as in equation (8).
(8)
2.2 Modeling of the Electric Traction System
2.2.1 BLDC Motor Description
The threat of pollution caused by conventional
vehicles has prompted the world to use electric
vehicles as an alternative. The brushless DC motor
(BLDC) is one of the motors most widely used in
the drive train of EVs, and has been adopted by
several car manufacturers, including Toyota and
Honda, [20]. These motors are characterized by an
electronic commutation system, which makes them
different from DC motors. There are several
techniques for determining switching times in
electronic switching, the most common of which is
Hall-effect sensors. The BLDC motor structure does
not contain commutators or brushes and is
characterized by a rotating permanent magnet
located on the rotor, as well as other magnets
attached to the motor housing. The main
components of this motor are the stator, composed
of concentrated windings, and the rotor, which
comes in different types depending on the
performance required. The reason for introducing
BLDC motors in EVs is their exceptional
performance, which includes high efficiency, small
size, silent operation, and high power density, [21].
The efficiency of the BLDC motor is considered
among the highest in comparison with other types of
motor, and it also has a long service life when
subjected to normal conditions. On the other hand,
this motor is available at a high cost, especially as
its system requires electronic control, increasing the
total price of the motor and equipment system. This
engine has other disadvantages, such as sensitivity
to high temperatures, which can indirectly reduce
torque, [22]. The control study of a BLDC motor
first requires concrete mathematical modeling of the
machine. The following section focuses on the
mathematical equations of the overall system
adopted.
2.2.2 Mathematical Model of a Brushless DC
Motor
Modeling a BLDC motor requires the representation
of all the electrical and mechanical equations.
A. Electric model
Mathematical motor modeling presents fundamental
values such as voltages, currents, and speed. The
equations below examine the three-phase winding
voltages:
(9)
Equations (2), and (3) respectively represent the
voltage vector in the 3 phases and the corresponding
speed form.
By using the relationship between electromotive
force (EMF) and rotational speed, we obtain the
expression for EMF in the form:
(12)
The EMF equation is written as follows, where
ke is defined by the coefficient of the electromotive
force.
(13)
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The form of the currents is represented by the
equations below:
(14)
Where (Vab, Vbc) are the corresponding phase-
to-phase voltages and Ω represents the mechanical
rotational speed.
The motor studied is powered by a three-phase
inverter. The inverter part was realized from the
following equations:
(15)
B. Mechanical system of the BLDC motor
The rotor system of this motor type is generally
made of permanent magnet steel with several poles
determined according to each series. The following
system of equations shows respectively the
mechanical equation of motion in (8) and the second
equation defining electromagnetic torque (9):
Ω: Mechanical rotation speed and J represent the
moment of inertia
From equation (8) we can also obtain the speed
expression.
With Pe Represents electromagnetic power
which is expressed as follows:
(10)
The electromagnetic torque is defined as:
(11)
P: number of pairs of poles
2.3 Speed Control Techniques for BLDC
Motors
The BLDC motor is classified into two types
according to the structure of the electromotive force
(EMF), whether sinusoidal or trapezoidal. This fem
shape results from the interconnection of the coils in
the stator windings and also the pole structure of the
rotor magnets, [23]. There are several strategies for
controlling the speed of a BLDC motor, including
sensor-based control, sensorless control, and digital
control. In this work, the control method adopted is
based on hall-effect sensors. Despite the
development of control tools, traditional controllers
such as Proportional Integral (PI) and Proportional
Integral Derivative (PID) are still included in the list
of commonly used controllers. In addition, several
systems are based on robust controls such as sliding
mode control, [24] and others are based on artificial
intelligence such as fuzzy logic control and
Adaptive Neuro Fuzzy Inference System controller
(ANFIS), [25]. The following section describes the
different controllers used in this study.
2.3.1 PI Controller
The PI controller is present in various industrial
applications due to its ability to improve motor
speed. This controller type consists of correcting the
actual speed to approach or reach the desired speed.
Its architecture is simple and can be easily
implemented, [26].
The controller (PI) is available in several forms,
depending on whether it is connected in series or
parallel. It is generally presented by the following
transfer function:
(12)
Where
.
Kp: proportional gain
Ki:integral gain
2.3.2 PID Controller
The block diagram in Figure 2 show the PID
(Proportional, Integral, and Deferential) controller is
used to control and improve motor speed. In the
case of BLDC motor speed control, it offers
excellent performance thanks to its reliable and
stable system. The proportional action reduces the
error, while the integral term pushes the output
value to the same value as the setpoint. Derivative
action ensures the prediction of potential future
errors.
To optimize the adjustment of this controller,
several adjustment methods are applied, including
Zigler-Nichols, Modulus Optimum, and Åström-
Hägglund methods.
The following transfer function is expressed as
follows:
(13)
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The transfer function expression can be written
in a simpler way:
(14)
Fig. 2: Block diagram of a PID controller
2.3.3 Fuzzy Logic Controller
Fuzzy logic is derived from artificial intelligence
and used primarily to establish control systems that
imitate the human mind. The use of fuzzy logic (FL)
controllers in non-linear systems continues to grow
due to their advantages, including flexibility and
robustness. The FL controller also ensures plant
non-linearity management without the use of
mathematical models. This type of controller is
characterized by linguistic terms generally
expressed as logical implications based on the "if"
and "then" rules, [27]. To create and configure a
fuzzy logic controller, the following four phases
must be followed:
a. Fuzzification: This operation transforms
measured variables into fuzzy linguistic
variables using membership functions.
b. Fuzzy Inference: This step determines the
control rules needed to obtain the desired
results.
c. Defuzzification: It converts all fuzzy output
variables into the required net values.
The performance of the fuzzy logic controller
can be improved by hybridizing other controllers
with it, such as PID-Fuzzy logic and the Adaptive
Neuro-Fuzzy Inference System controllers. As
indicated in Table 1, the entire set of 49 rules was
justified after a thorough series of evaluations.
Table 1. Fuzzy Rule Look-Up Table
E/CE
NB
NM
NS
Z
PS
PM
PB
NB
NB
NB
NB
NB
NM
NS
Z
NM
NB
NB
NB
NM
NS
Z
PS
NS
NB
NB
NM
NS
Z
PS
PM
Z
NB
NM
NS
Z
PS
PM
PB
PS
NM
NS
Z
PS
PM
PB
PB
PM
NS
Z
PS
PM
PB
PB
PB
NB: negative big; NM: negative medium; NS: negative small;
Z: zero; PS: positive small; PM: positive medium; PB: positive
big.
2.3.4 Neuronal Networks Controller
In the field of artificial intelligence, the neural
network (ANN) is considered one of the most
recommended controllers. Its principle is to simulate
the behavior of a biological neural network, such as
the human one. This controller has been widely used
in BLDC motors for various roles, depending on the
desired objective, such as speed estimation or
control, [28], [29]. The neural network system
essentially comprises four parts: the layer, the
neurons, the weights, and the transfer functions.
The neural system depends on several main
criteria: the connection indicating the input-output
direction, and the weights of the relations, [30]. To
obtain the data needed to train the controller (ANN),
we first need to store the reference neural network
model and then apply it to the electrical system
under study.
2.3.5 ANFIS Controller
The ANFIS (Adaptive Neuro Fuzzy Inference
System) controller is considered to be a combination
of artificial neural networks and fuzzy logic in the
form of a well-defined algorithm. This control
technique has become very popular recently, thanks
to its performance features such as the simplicity of
its learning algorithms, [31] and the improved
robustness of the system. The structure of the
ANFIS controller consists of a network of linked
nodes with inputs and outputs that depend on the
learning system implemented to achieve the desired
goal of error minimization. The structure of the
ANFIS controller consists of a network of linked
nodes with inputs and outputs that depend on the
learning system implemented to achieve the desired
goal of error minimization. The system of this
controller is based on four blocks which are
respectfully fuzzification, knowledge base, neural
network, and defuzzification. Consequently, the
adopted fuzzy inference set has two inputs (x,y) and
one output z.
In the case of ANFIS controllers, the error is
expressed as follows:
e= Sr -Sa (15)
Where Sr represents the desired speed and Sa
represents the actual rotor speed. Despite the ANFIS
controller being used to control speed, it has also
been used in other innovative areas. For example, in
[32], a comparative study was carried out to test the
predictive ability of student performance, using both
hierarchical ANFIS and ANN systems, and the
results showed the success of the hierarchical
ANFIS model.
PID Corrector
+
-
P: G
I: 1/Ti
D: Td
1/S
S
+
+
+
Process
Sensor
E(s)
Set poit
e(s)
Error
U(s)
Control signal
C(s)
S(s)
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3 Proposed Hybrid Speed Control
The proposed system consists of applying hybrid
control (ANFIS) to a BLDC motor.
Fig. 3: Block of control system applied and Fault detection control
The control is realized by combining the fuzzy
logic controller and the neural network controller.
After determining the mathematical modeling of the
motor, a control study is carried out to produce a
single robust control system that combines the
performance of the two proposed controllers. The
second part of this work consists in studying the
fault of the hall effect sensors implemented.
Therefore, a fault-tolerant control was presented to
ensure system operation in the presence of faults.
Figure 3 shows the system studied for speed control
of a BLDC motor, with the different control
techniques applied. This diagram shows the general
structure of the system as it operates during
simulation in the MATLAB simulink environment.
It also includes a dedicated fault detection phase for
hall-effect sensors.
3.1 Proposed Fault Detection
The three hall-effect sensor signals (Ha, Hb, and
Hc) vary according to the rotor position of a BLDC
motor. These sensors provide six sequences for
360°, a process that results from phase current
switching according to the chosen direction of rotor
rotation. When a fault occurs, the six sectors
supplied by the three Habc signals become four
sectors only. This implies that there are two
erroneous commutations in two sectors, and the
phase is switched off in the case of the third sector
as show Figure 4.
Fig. 4: Normal operation (a) Hall signals. (b) Sector
3.2 The Strategy Adopted for Sector
Reconstruction
For BLDC motor control, a performance algorithm
is proposed to ensure correct operation if one or
both sensors fail. As a precautionary measure, three
circuits are available for signal reconstruction. In the
event of a sensor fault, one of these circuits
Three Phase
Six Step
Inverter
Commutation
Logic
Hall Effect
Sensor
Speed
Measurement
Fault
Detection
BLDC
Motor
Fault
Ha,Hb,Hc
Classic controllers
PID
ANN
FLC
Hybrid Speed Control
PID+ FLC
PID
FLC
ANN+ FLC
ANN
FLC
+
-
Reference
Speed
Actual
Speed
Ha
Hb
Hc
0
0
0
1
1
1
30°
90°
150°
210°
270°
330°
30°
90°
150°
210°
270°
330°
Sector
0
1
2
3
4
5
6
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reconstructs the sectors to ensure continuity of
operation.
Fig. 5: Proposed scheme for reconstructing the signal if Ha is faulty
In addition, a system for improving the
algorithm used to reconstruct sectors has been
applied during engine start-up. This initiative
guarantees safe starting in the event of sensor faults.
This technique enables the reconstruction algorithm
to distinguish between sectors 1 and 2, and also
between sectors 4 and 5.
If the BLDC motor rotates counter-clockwise,
the following circuit is obtained: sector 1 → sector 2
→ sector 3 → sector 4 → sector 5 → sector 6. As
the case studied consists of faulty Hall-effect
sensors, the sectors supplied become four instead of
the six sectors in the normal state. Therefore, the Ha
sensor is considered faulty if it persists in providing
a value of 1 or 0.
As a result, the scenarios presented in the
case of sensor fault Ha are summarized in
Figure 5, where the proposed signal
reconstruction method ensures immediate fault
detection.
4 Simulation Results
The results obtained from simulation in MATLAB
Simulink are based on a BLDC control system using
the following controllers: PI, PID, neural network,
fuzzy logic, and hybrid control (ANFIS). This
simulation aims to test the fault detection strategy
applied to hall-effect sensors and to discuss the
efficiency of the algorithm that ensures sector
reconstruction. The results presented consist of
observing the following parameters: Rotor speed
with and without fault, the signals from the three
sensors (Ha, Hb, and Hc), the sectors constructed by
the proposed algorithm, and the corresponding
currents.
(a)
Zoom A
==
=
6
3
Prev-Sec
Z-1
Z-1
t>Tprev
3
6
2
4
5
1
Ha
+
Sector
Hb
Hc
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Zoom B
(b)
Fig. 6: Rotor speed of the BLDC motor according to
controllers applied (PID, FLC, ANN, ANFIS) in
case of faults. (a): speed, (b) Zoom A, B
Figure 6 shows the different states of Speed in
each case for the controllers used. It can be seen that
the ANFIS or (ANN+FLC) controller shows a delay
at start-up, but in particular, has the most stable
curve, with a minimum peak compared with the
other controllers, which is equal to the instant
t=0.3s, as shown in Figure ZOOM A. Consequently,
Figure ZOOM B shows the disturbed phase at time
t=0.5s where the ANFIS controller curve gives the
fastest speed response.
Fig. 7: Structure of currents in each type of
controller applied (PID, FLC, (PID+FLC) ANN,
and ANFIS)
Figure 7 shows the different forms of phase
current using five controllers. The current curve for
neural network control showed limited disturbance,
but the current curve for hybrid ANFIS control was
the best, providing the most stable current.
Table 2 compares various operating
characteristics such as rising time, settling time, and
overshoot percentage.
Table 2. Speed response characteristics
Controller
Rise time
(sec)
Settling
time
(sec)
Overshoot
Percentage
(%)
PID
controller
0.03
0.06
40
ANN
controller
0.01
0.03
84
FLC+PID
0.06
0.054
87
ANN+FLC
0.012
0.023
98
5 Fault Tolerance Detection
This section discusses the failure states of the Ha,
Hb, and Hc sensors, and the results show the signal
reconstruction in each case.
Case 1: faults located in the Ha sensor
The Ha sensor fault occurs at t=0.7s in Figure 8
when Ha goes from 0 to 1. The sector then changes
after the fault and takes on a new phase between
[0,4] instead of the normal phase between [1,6].
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Fig. 8: Ha sensor results in the presence of a fault
Case 2: faults located in the Hb sensor
The Hb sensor fault occurs at t=0.7s as shown in
Figure 9, when Ha goes from 0 to 1. The sector then
changes after the fault and takes on a new phase
between [0,6] instead of the normal phase between
[1,6].
Fig. 9: Hb sensor results in the presence of a fault
Case 3: faults located in the HC sensor
The Hc sensor fault occurs at t=0.7s as shown in
Figure 10, when Ha goes from 0 to 1. The sector
then changes after the fault and goes from [0,6] to
[6,1] instead of the normal phase between [1,6].
Fig. 10: Hc sensor results in the presence of a fault
Case 4: Two or more faults Sensor
A problem with two or more malfunctions in the
BLDC motor sensor that results in the system
stopping or failing. In extreme cases, persistent
sensor malfunctions may lead to system shutdown
or complete motor failure. This can result in
downtime and the need for extensive
troubleshooting and repairs. Addressing sensor
malfunctions promptly through proper diagnostics
and troubleshooting is crucial to restoring the
reliable and efficient operation of BLDC motors.
6 Conclusion
This paper examines a developed fault detection
strategy adopted for a BLDC motor intended for
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electric vehicles. A study on speed control of the
BLDC motor was conducted using an ANFIS hybrid
controller, which yielded significant results
compared to other controllers. The fault detection
technique is applied to hall-effect sensors to identify
faults and ensure uninterrupted system operation.
This study examines both single-sensor fault and
dual-sensor fault scenarios, demonstrating the
effectiveness of the proposed method in maintaining
system functionality. In our future work, building
upon previous projects, we will introduce an
enhanced method for detecting and rectifying faults
in Ha, Hb, and Hc sensors using sector
reconstruction techniques. Additionally, we aim to
develop a detection strategy for mechanical or
electrical faults such as short circuits and winding
failures.
Acknowledgement:
This paper was completed thanks to the fellowship
the Organisation for Women in Science for the
Developing World (OWSD) and the Swedish
International Development Cooperation Agency
(SIDA) provided. The author would like to express
her warmest thanks for the support that contributed
to the success of this article.
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