Adaptive Controller PI-Fuzzy logic Speed for Brushless DC Motor
Drive Supplied by PEMFC Cell Optimized by P&O
YAMINA JOUILI, RADHIA GARRAOUI, MOUNA BEN HAMD, LASSAAD SBITA
Dept. Electric-Automatic, University of Gabes, Gabes, TUNISIA
National Engineering School of Gabes, Omar ibn elkatab Road, Gabes, 100190, TUNISIA
Abstract: - Brushless Direct Current (BLDC) motors have recently gained momentum. In this study, a fuel cell
stack, namely, a Proton-Exchange Membrane Fuel Cell (PEMFC), one of the promising renewable energy
technologies, is chosen for a brushless DC motor. To improve the performance of PEMFC, an efficient
maximum power point tracking (MPPT) algorithm was applied to the DC/DC boost converter. To this end, the
perturbation and observation (P&O) algorithm were developed. This work proposes an adaptive controller
proportional-integral (PI)-fuzzy logic speed for the BLDC. To evaluate its performance, the proposed controller
was simulated under several conditions: load disturbance and reference speed variation. This controller is
analyzed and compared with the classical PI controller. Therefore, the control performance parameters, such as
rise time, settling time, steady-state error, and overshoot, were determined and compared. This system is
analyzed and simulated using MATLAB/Simulink software.
Key-Words: - PEMFC, P&O, Adaptive PI-FL controller- PI - BLDC.
Received: September 22, 2022. Revised: May 23, 2023. Accepted: June 19, 2023. Published: July 17, 2023.
1 Introduction
Today, the world is becoming aware of the
problems associated with traditional energy sources
that have destructive impacts on the environment,
such as fossil fuels and non-renewable energy
sources.
Fuel cells are a potential alternative energy source to
fossil fuel-based power generators for clean
electricity production. Recently, this technology has
attracted much attention in electrical energy
generation, namely electric vehicles, mobile robots,
and unmanned aerial vehicles (UAVs) [1-3].In
addition, the fuel cell is not burned: the energy is
produced by an electrochemical reaction. It can
provide continuous energy in all seasons, providing
that fuel is available [4].
PEMFCs are the most popular and can operate at
low temperatures below 100°C. They are
commercially available, with high efficiency (up to
50%), fast start-up, as well as high reliability with
no pollution.
However, fuel cell systems have problems related to
harvesting electrical energy from the PEM FC stack.
FC systems have nonlinear output characteristics
because of their input variation, which causes a
significant loss in the overall system output.
So, an MPPT algorithm must be developed to
enhance and optimize the PEMFC system
efficiency. The problem of fuel starvation resulting
from sudden changes in load can cause severe
damage to the fuel cell membrane.
Many studies have addressed control problems
related to PEMFCs in the last few years, and diverse
control techniques have been used. During the last
few decades, many studies have addressed control
problems related to PEMFC. For instance, authors
of [1] proposed a smart MPPT algorithm based on
FLC.
Further, this type of fuel cell has been used as the
primary power source in rotary actuators. Many
studies have investigated the possibility of powering
electric motors with hydrogen technologies [2].
International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2023.2.9
Yamina Jouili, Radhia Garraoui,
Mouna Ben Hamd, Lassaad Sbita
E-ISSN: 2945-0489
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Hence, in this study, to improve power quality,
system performance, and design optimization, the
PEMFC system needs to be modeled and analyzed.
At present, electric rotary actuators play a crucial
role in commercial and residential applications. The
DC motor has been used mostly in actuators [1].
However, its main drawback remains the
mechanical commutator, which causes brush wear
and rotor losses, the susceptibility of the
commutator, the consequent need for maintenance,
lower robustness, and the need for more expensive
control electronics [4].
Due to their favorable electrical and mechanical
properties, Brushless Direct Current (BLDC) motors
are found in several segments, mainly in variable
speed operations, such as an unmanned aerial
vehicle (UAV), robotics, electric vehicles, and
electromechanical actuation systems [6].
BLDC motors belong to the synchronous motor type
with an electric commutation scheme. These drives
have become the best choice due to continuous
improvements in high-energy permanent magnet
materials, power semiconductors, and digital
integrated circuits [7, 8]. Thus, a BLDC motor has a
high power-to-mass ratio, less maintenance, and
high-speed capabilities [9-11]. Various control
schemes are created for speed regulation in a closed
loop, such as the Proportional Integral Derivative
(PID), optimization of PI coefficients using Genetic
Algorithm (GA), Fuzzy Logic Controller (FLC), and
Adaptive tuned Fuzzy Logic [12, 13].
PI controllers are widely used in industrial control
systems and several other applications that need
modulated control due to their simplicity of
adjustment and regulation. Conventional PID
controllers have become inefficient as they are non-
linear systems due to unstable conditions, higher
order, complexity, and having no mathematical
model.
To overcome these shortcomings, previous works
have focused on adaptive control; for example, an
adaptive PID neural network controller is developed
in [14-17]. Moreover, the particle swarm
optimization (PSO) algorithm was used for
controller design. However, it takes a higher time
delay to initialize the weight of the PID neural
network. An adaptive neuro-fuzzy inference System
(ANFIS) was developed in [18-20]. This controller
enhances the steady-state speed response but
degrades the transient response and is trained in
offline tuning. Besides, a self-adaptive PID-fuzzy
logic controller has been proposed for speed control
by several research works [21-23]. As such, fuzzy
logic control is used in online gains tuning.
Furthermore, the intelligent control techniques are
applied to dynamic systems guaranteeing high
robustness performance with a better steady-state
response, short rise and settling times, and low
overshoot.
In this study, all the performance factor parameters
of control are measured for the proposed controllers,
namely adaptive PI-FL, and compared with the
classical proportional-integral (PI) controller,
The remainder of the paper is organized as
follows: Section 2 describes the dynamics of the
PEMFC stack with the Maximum Power Point
Tracking (MPPT) strategy based on the Perturb and
Observe (P&O) method. Then, the mathematical
models of the BLDC engine are developed in
Section 3, and the proposed controllers are
explained in Section 4. The simulation results are
illustrated and discussed in the next section. Section
6 concludes the paper.
2 Modeling of PEMFC
A fuel cell is an electrochemical energy conversion
device capable of converting chemical energy into
electrical energy [24, 25]. The proposed system uses
a PEM fuel cell as a power supply source. This
device consists of an anode and a cathode supplied
with hydrogen and oxygen. These electrodes are
separated by an electrolyte and two catalysts,
usually made of platinum, as shown in Fig.1 [26-
28]. Hydrogen is the anodic reactant releasing two
electrons and the ion H+ according to equation (1).
Oxygen is the cathodic reactant or oxidant, as
indicated in equation (2). The working principle of
PEMFC is based on the anode oxidation of
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Mouna Ben Hamd, Lassaad Sbita
E-ISSN: 2945-0489
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hydrogen (fuel) to protons. This process generates
electrical energy and hot water, as in equation (3).
Fig.1. chemical reactions of the fuel cell.
The electrochemical reactions occurring at the
electrodes of the PEMFC are described by the
following equations:
Anode reaction
22
2
H H e
(1)
Cathode reaction
1
22
22
2
H O e H O
(2)
The full reaction in the PEM fuel cell produces
electricity, water, and heat as follows:
1
2 2 2
2
H O H O heat energy
(3)
According to [25] and [29], the PEM fuel cell is
calculated from the electrochemical reactions
expressed by the Nernst equation as follows:
act
cel
V =E -V -V -Vcon
Nernst
(4)
Where the first term is the thermodynamic potential
of the cell representing its reversible voltage
(without load) as:
22
Nernst -3 -5
E =1.229-0.85.10 T-289.15 +4.31.10 .T Ln(Ph )+0.5Ln(Po )
(5)
T represents the cell temperature, Ph2 is the partial
pressure of hydrogen, and Po2 is the partial pressure
of oxygen at the catalyst gas.
While the three last terms,
,
, and
,
represent the voltage losses; thus, voltage drops or
over potential caused by reaction activation, ohmic
resistances, and gas diffusion are given by equations
(6) to (8):
2
1 2 3 4
V=ξ +ξ .T+ξ .T.Ln(Co )+ξ .T.Ln(i)
act
(6)
ζi represents the parametric coefficients for each
cell, i is the cell operating current, and Co2 is the
concentration of oxygen gas in the catalytic cathode.
max
con
J
V =-B.Ln 1- J
(7)
Where B is the parameter influent by cell type,
is the maximum current density, and J
represents the actual current density of PEMFC.
mcV =i. R +R
(8)
Rc is proton resistance, taken as a constant value,
and Rm represents the equivalent membrane
resistance of the electron.
CO2, J, and Rm of the PEM fuel cell
mathematical model are presented in [4] and [10].
In an elementary cell, the nominal voltage is
about 0.8 V, and the current density can reach 1A
/cm^2. The output current is proportional to the
active area. Because the voltage is too low to
directly connect a power converter to achieve the
required voltage levels for larger-scale applications,
several cells must be connected in series to form a
stack.
The mathematical model of the PEM fuel cell
was simulated under (MATLAB/Simulink)
environment. Moreover, a step-up converter
(DC/DC) was used for voltage regulation. The
MPPT controller generator was used to drive the
Pulse Width Modulation (PWM) of the converter
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device, and the Simulink model for the fuel cell
stack is shown in Fig.2.
Therefore, the fuel cell stack voltage response is
given by:
act
= N. E -V -V -VVNernst con
PEMFC
(9)
Where N represents the number of fuel cells in
the stack
The mathematical model of the PEM fuel cell was
simulated under (MATLAB/Simulink) environment.
Moreover, a step-up converter (DC/DC) was used
for voltage regulation. The MPPT controller
generator was used to drive the Pulse Width
Modulation (PWM) of the converter device.
2.1 The boost converter
The circuit configuration of the boost converter
(DC/DC) is depicted in Fig. 2. It consists of a DC
source, an inductor L, a filter capacitor C, a load
resistor R, a transistor T, and a diode D [21]. The
gate pulses to control the switches S. The
converter’s operating modes are represented as
follows:
First, the inductor current increases when the switch
S is on (S=1). The voltage inductor is the voltage
input to the circuit as:
dI 1
=V
dt L
V1()
fc
out
in
dIout
dt C
(10)
Second, when S is off (S=0), the energy
accumulated is transferred into the capacitor. The
voltage of this state is calculated by (11):
dI 11
= .V - .Vout
dt L L
dV 1
out = ( )
fc in
II
fc out
dt C
(11)
According to the position of the switch S, the
dynamic system of the boost converter circuit can be
written as:
1
..
dI Vout
= - 1-
dt L L
dV = 1-
dt
in
V
fc
Ifc
out Iout
CC
(12)
Where
represents the output voltage of the
load,
is the input voltage from the cell stack, and
α is the signal control that defines the switch
position.
Fig.2: Schematic of the proposed system.
2.2 MPPT design
In the proposed scheme, the P&O algorithm of the
MPPT strategy is realized to maximize the PEMFC
outturn. The MPPT control strategy is based on
changing the converter’s duty cycle to force the cell
stack to operate at adequate power [29-30]. This
algorithm works by periodically perturbing the Ifc
and observing the resulting change in power output.
Indeed, the MPPT algorithm is started by
calculating the power at zero amperes. Then, the cell
stack (PEMFC) voltage and current are perturbed
slightly, and a new power value is calculated. The
P&O algorithm is illustrated in Fig.3.
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3 BLDC motor description and
modeling
Unlike the DC machine, the Brushless motor does
not use brushes for commutation. The BLDC
consists of a permanent magnet that replaces the coil
and does not require brushes; thus, noise,
interference, and graphite dust could be avoided. It
uses an electronic controller for switching DC
currents in the winding stator [31]. A DC/AC
inverter is used for this purpose. The phase current
of the BLDC motor, typically with a rectangular
waveform, is synchronized with the back-EMF to
produce a constant torque at a constant speed. Thus,
there are two strategies of control systems: sensored
and sensorless. The latter reduces the cost of the
BLDC; however, finding the Back-EMF for low-
speed applications is problematic.
A BLDC motor is usually modeled as a series
connection of a stator winding resistance, an
inductance, and a counter-electromotive force (CEF)
(Fig.4).
Fig.4. Equivalent circuit of BLDC
Mathematically, the brushless DC motor model is
similar to that of a conventional DC motor [31, 32].
The stator phase currents are a balanced system. The
output voltages of the BLDC motor can be
described by matrix equations (13).
0 0 0 0
0 0 . 0 0 . .
0 0 0 0
a a a a
b b b b
c c c c
V R i L M i e
d
V R i L M i e
dt
V R i L M i e
(13)
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Where
are the three-phase stator voltages of the
brushless dc motor drive, R, L, and M represent the
stator resistance, self-inductance, and mutual
inductance of winding, respectively. signifies
the three-phase currents of the BLDC motor, and the
back electromotive forces () are expressed by
equation (14).
(14)
represents the back-emf constant. Electrical and
mechanical angles are represented by θe and θm:
.mep
(15)
With p is the pairs of poles, and F(.) is the function
that gives the trapezoidal of the back EMF described
as follows:
2
10
3
2
62
1. 3
3
() 5
13
65
5
1. 2
33
e
e
e
e
e
ee
F
(16)
The mechanical movement equation can be
expressed as follows:
1. ( ) ( )
m
em m L
d
J dt
T t T t
(17)
Where J represents the moment of inertia, β is the
frictional constant, and TL is the load torque.
Since the electromagnetic torque of the three-phase
BLDC can be represented by the back emf, three-
phase current, and speed, the equation for
electromagnetic torque is modified and represented
as follows:
. . .
a a b b c c
em m
e i e i e i
T
(18)
Fig.5 depicts a Simulink model in the inner loop
[34].
Fig.5: BLDC motor in open loop.
4 Controller design of a BLDC motor
The overall control strategy for the brushless dc
motor is developed with MATLAB/Simulink
software. Fig.6 displays the considered Simulink
model blocks, such as the BLDC motor, dc bus,
inverter device, current control block (inner loop),
speed control block (outer loop), and motor
measurement block.
..
2
2
..
23
4
..
23
me
me
me
e
e
e
a
c
b
k
eF
k
eF
k
eF
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Fig.6: Simulink model blocks of the proposed controller for BLDC motor.
4.1 Current regulation
Duty-cycle controlled voltage PWM technique and
hysteresis current control technique are effective
methods in improving the performance of current
control strategies for a BLDC.
In the present work, the hysteresis current controller
is chosen to generate the necessary PWM signals for
the inverter and obtain fast dynamic responses
during transient states. This method is used to
replace the voltage control in BLDC. In this control
technique, the value of the controlled variable is
forced to stay within certain limits [33]. Therefore,
the reference current generator is determined by the
reference torque using the following expression:
,,abc ref
ref t
T
iK
(19)
with Kt is the torque constant.
Fig.7: Hysteresis current regulation block
Table. 1. Decoder Signals based on Hall Effect
sensor states
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4.2 Speed regulation
In what follows, we will study speed regulation. To
enhance the BLDC motor performance, two control
methods are developed. Firstly, a classical PI
controller is used. Secondly, a self-adaptive PI
approach is designed to control the speed of the
BLDC motor. On the one hand, it benefits from the
advantages of the PI controller, such as feasibility,
simplicity, easy implementation, and performance.
In particular, the performance of this technique is
significant in autonomous systems. On the other
hand, the gains of this controller are adjusted by an
online optimization method with a fuzzy logic
strategy.
Self-adaptive PI-Fuzzy logic control
Unfortunately, the PI gains must be balanced to
improve the transient response and, thus, the
performance parameters of the system, such as the
settling time, overshoot, oscillation, and steady-state
error, under various operating conditions. However,
in the event of poor estimation or constant gain
values, the control system parameters suffer due to
uncertainties and disturbances in the operating
conditions of the brushless dc motor. Practical
experiments have shown that the PI or PID
controller design could be optimized by the fuzzy
logic controller so that the control performance of
the controller could be enhanced with better stability
and high robustness.
In this paper, self-adaptive PI-fuzzy logic would
have to decide and allow changing the gains online.
On the one hand, the adaptive PI-FL controller
enjoys the advantages of the PI controller, such as
feasibility and easy implementation.
On the other hand, the fuzzy logic controller (FLC)
is known for its capability to handle different output
sets depending on the input, which is ideal for a
non-linear system without the requirement of its
mathematical model.
FLC mainly comprises fuzzification, inference
fuzzy rule base, and defuzzification as elemental
components. In this work, a fuzzy inference system
with the Sugeno model is proposed for the tuned PI
(adaptive PI-FL) controller. It depends mainly on
the value of update gains, speed error e, and its rate
of change ec as the fuzzy logic controller inputs.
Two output signals, kp, and ki are given to produce
the desired control The input variables are to be
fuzzy sets, such as PL (positive low), PH (positive
high), Z (zero), NL (negative low), and NH
(negative high). In addition, the output signals are
distributed with three membership functions that
describe the linguistic variables Z (zero), L (low),
and M (medium). The used membership functions
of FL control are described in the Figures below.
Fig.8: Proposed FLC controller.
Hall effect sensor
Decoded Signals
Ha
Hb
Hc
Ea
Eb
Ec
0
0
0
0
0
0
0
0
1
0
-1
+1
0
1
0
-1
+1
0
0
1
1
-1
0
+1
1
0
0
+1
0
-1
1
0
1
+1
-1
0
1
1
0
0
+1
-1
1
1
1
0
0
0
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Fig.9: Distribution of membership functions for of
error speed.
Fig.9: Distribution of membership functions for of
error speed.
Through fuzzification and fuzzy decision, overall,
the outputs are given in Table 2 and 3. Here, 25
fuzzy
Control rules are produced. Each of them is
obtained from the “IF-THEN” interference rules. In
control theory, the set of rules can be separated into
four groups to achieve the logic of the proposed
rules. In group 1: the velocity error and the rate of
change error of the velocity have zero, small
negative, or positive values. In this case, the
velocity output is slightly below or above the set
points. Therefore, small negative or positive control
values are applied.
As proposed, the kp update values are zero or low,
while the ki update values are zero or medium. In
group 2: the velocity error and the rate of change
error of the velocity have negative or positive
values. For this group, negative control values are
required for optimal operation, and the process
output is far below the set point. In this case, the
online kp fuzzy sets have medium, but the online ki
fuzzy sets have low, or zero values.
Table.2: The decision of the fuzzy inference rules of
kp
ΔE
E
Kp
NH NL Z PL PH
NH
NL
Z
PL
PH
M M L M M
M M M M M
Table.3: The decision of the fuzzy inference rules of
ki
ΔE
E
Kp
NH NL Z PL PH
NH
NL
Z
PL
PH
L L Z L L
L L M L L
Z Z Z Z Z
M M L M M
M M M M M
L L M L L
L L M L L
L L L L L
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Table.4: Parameters of bldc motor
5 Simulation Results
PI and adaptive PI-FL controllers were previously
developed for brushless DC motors. To achieve the
optimal control strategy, several states were
simulated from different load states and different set
point speed states. These controller designs were
then compared to obtain control performance
parameters, such as rise time, settling time, steady
state error, overshoot, and undershoot. The results
were obtained using MATLAB/Simulink software;
the global specification of the brushless DC motor is
shown in Table 4. Fig 10 shows the block diagram
for the identifier. The actual speed of the BLDC
motor will be compared with the reference speed to
obtain the error signal and rate of change of error.
Fig.10: Blocks of the proposed system
The operating performance of an individual cell is
shown in Fig.11. Thus, they depend on the three
main polarization losses: activation, ohmic, and
concentration losses. First, it starts from the
maximum voltage of the cell, then it behaves
linearly, and finally, a sudden drop occurs at a
higher current density. As can be seen from Fig 12,
the power received from the FC is 203.8 W, the
voltage is 24.23 V, and the current is 8.55 A. This
fuel cell consists of 40 cells. This stack runs at a
temperature of 298.15 K and pressure of (1.486 atm
and 0.98 atm).
Fig.11: Polarization curve of the PEM fuel cell
Fig.12: PEMFC generator characteristics.
The proposed MPPT technique works efficiently
and tracks the optimal performance of the fuel cell
stack, as shown in Fig.13 a, b, and c. The curves
show respectively, the PEMFC output of power, the
duty cycle signal, and boost converter output signals
(voltage and power). These curves show the
Name
Value
Value
viscous
damping
0.005
N.m.s
Inertia
0.089
Kg.m^2
pole pairs
8
-
static friction
0
N.m
Stator phase
resistance
0.2
Ω
Stator phase
inductance Ls
8.5e-3
H
Torque
constant
1.4
N.m/A_p
eak
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behavior of the MPPT strategy (P&O) to maintain
and track the optimal performance of the PEMFC
stack.
(a)
(b)
(c)
Fig.13: Responses for constant condition, (a) DC
link power and power of PEMFC generator, (b) duty
cycle response, (c) DC voltage response.
The phase currents, torque, and back EMF of the
BLDC motor are also shown in the following
figures. The observed ripple in the current
waveforms is due to the use of the PWM method for
the speed control of the BLDC motor. Acceptable
ripples occurred on the motor torque curves. The
current values change with the torque value. So, The
square waveforms of phase currents verify the good
control capability of the BLDC motor for all three
conditions.
(a)
(b)
(c)
Fig.14: Brushless dc motor response, a) phase
current waveforms, b) torque
waveform, c) stator back
Adaptative PI-FL (fuzzy-tuned PI) controller is
modeled using sugeno’s method with a constant
value, having two inputs and two outputs. The
Update values of online gains are multiplied by
velocity error. Then, the control signal (U) is
used to adjust the system. Simulation results of
the speed response of the BLDC motor with
classical PI and fuzzy-tuned PI controller are
shown in Fig.15.
Fig.15: speed response for constant variation
condition
The results were obtained by keeping the
reference speed at 50 rad/s and the load torque
constant at 0.5Nm. From the above speed plots,
the fuzzy-tuned PI and PI controllers reach the
reference set speed with a rise time equal to
0.237. The fuzzy-tuned PI manifests overshoot
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and undershoot speeds of 0.0934 (%) and 0(%),
respectively. The PI controller displays
overshoot and undershoots speeds of 0.3204
(%) and 0(%), respectively. For the same
variations, the fuzzy-tuned PI shows a settling
time and steady-state error of 0.3875 (s) and -
0.210(rad/s), respectively. The PI controller has
a settling time and steady-state error of 0.4035
(s) and -0.4808 (rad/s), respectively. In
addition, the performance parameter values of
the controllers are illustrated in Table 5.
Table 5: Comparison of performance parameters for constant condition
5.1 Results under load variation
The brushless DC motor must operate under varying
load conditions in most industrial applications. To
evaluate the performance of the proposed controller,
the closed-loop system of the brushless DC motor is
operated with load variation. The load increases
from 0.5 to 0.9Nm at t= 5s (Fig.16).
Fig.17,(a) and (b),(c), and (d) show the simulation
results obtained for varying load conditions. The
performance comparison of the proposed controllers
is shown in table 6. We consider control
performance parameters, such as rise time,
overshoot, settling time, peak time, peak value, and
undershoot, as comparison factors. Fig.17 (a) and
(b) illustrate the online gain value of the FL control
and Figure.17 (c) and (d) describe the duty cycle of
MPPT strategy and speed response of BLDC
behaviour under the same conditions.
Fig.16: Load variation
(a)
(b)
(c )
Controller
Control performance parameters
Rise time (s) Peak time (s) Peak value (rad/s) Overshoot value (%) Undershoot (%) Settling time (s) steady-state error(rpm)
PI-Fuzzy logic
0.1878 0.212 66.02 0.3204 0 0.4035 -0.4808
0.237 0.2989 54.67 0.0934 0 0.3875 -0.2100
PI
International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2023.2.9
Yamina Jouili, Radhia Garraoui,
Mouna Ben Hamd, Lassaad Sbita
E-ISSN: 2945-0489
87
Volume 2, 2023
(d)
Fig.17: Responses for load variation condition and
online control parameters, a) Kp, b) ki, c) Duty
cycle, d) speed of BLDC motor.
Consequently, the proposed Fuzzy-tuned PI
controller for the brushless dc motor drive is
perfectly tracked, and its oscillations are
effectively improved. When the load is
increased, the proposed controller restores the
system to the set value in the shortest possible
time and produces a low undershoot value.
Then, the comparison of the numerical
performance of the controllers is given in Table
6.
5.2 Results under speed variation
At the same time, the BLDC motor may be
required to operate at variable speed conditions.
To validate the effectiveness of the proposed
controller, the speed response is obtained under
varying speed conditions. In the first case, the
step reference speed is varied from 50 to 90
rad/s and then from 90 to 50 rad/s, applied at
time t= 4s and 7s (Fig.19). The proposed speed
operating conditions are simulated, and the
curves of speed responses are displayed in
figure 20,(d). In addition, the FL control online
value of gain for kp and ki under the same
conditions is shown in figure 20, (a) and (b).
Figure.21, (c) represents the duty cycle of the
MPPT algorithm. Then, the comparison of the
numerical performance of the controllers is
illustrated in table 7.
Fig.19: Speed variation
(a)
(b)
(c)
International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2023.2.9
Yamina Jouili, Radhia Garraoui,
Mouna Ben Hamd, Lassaad Sbita
E-ISSN: 2945-0489
88
Volume 2, 2023
Fig.20: System responses for speed variation and online control parameters, a) Kp, b) ki, c) Duty
cycle, d) speed of BLDC motor
Table 6: Comparison of performance parameters for load variation conditions
Table 7: Comparison of performance parameters for speed variation conditions
Simulation results and comparison tables show that
the proposed controller for BLDC performs very
well under speed and load variation conditions.
Small oscillations of the speed curve are observed
following the application of the Fuzzy tuned PI
controller in both cases. Moreover, the rotor speed
follows perfectly its speed reference but with some
differences depending on the type of controller
applied.
6 Conclusion
To achieve an accurate MPPT of the PEM fuel cell,
the P&O strategy was proposed by controlling the
DC/DC boost converter. Considering a more
reliable and simpler controller, a self-adaptive PI-
Fuzzy logic controller was used with the brushless
dc motor under load disturbance and reference
speed variation. To this end, the proposed controller
was compared with the classical PI controller. Thus,
the performance parameters of the controller, such
as rise time, peak time, peak value, overshoot,
undershoot, settling time, and steady-state error was
measured and presented. Based on the obtained
simulation results and analyses performed in this
work, the following conclusions can be
drawn:
• The proposed MPPT design technique works
efficiently, tracks the optimal performance of the
fuel cell stack, and maintains a constant current for
sudden external disturbance.
Controller
Control performance parameters
Rise time (s) Peak time (s) Peak value (rad/s) Overshoot value (%) Undershoot (%) Settling time (s) steady-state error(rpm)
PI-Fuzzy
logic
0.196 0.2119 67.08 0.3416 0.1404 0.3947 -1.0886
0.2289 0.2985 55.11 0.1022 0.1080 0.3392 0.3621
Controlle
r
Control performance parameters
Rise time (s) Peak time (s) Peak value (rad/s) Overshoot value (%) Undershoot (%) Settling time (s) steady-state error(rpm)
PI-Fuzzy
logic
0.191 0.2119 67.08 0.3416 0 0.427 -0.6578
0.209 0.3137 55.54 0.1108 0 0.3772 -0.6337
PI
PI
International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2023.2.9
Yamina Jouili, Radhia Garraoui,
Mouna Ben Hamd, Lassaad Sbita
E-ISSN: 2945-0489
89
Volume 2, 2023
• The proposed controller for the BLDC works
very well. It has a low oscillation of the speed curve
for varying conditions.
• The proposed controller improved the
performance of the controller parameters compared
to the conventional PI controllers in terms of
minimum rise time, settling time (s), and steady-
state error value under all operating conditions.
The proposed controller can eliminate the
uncertainty problem due to load and speed
variations. Since the controller has high
performance, it is ideal for the processing industries.
The selection of fuzzy logic parameters, such as
fuzzy membership functions, fuzzy rules, and inputs
and outputs, can limit the proposed controllers’
performance. Optimization algorithms that can be
applied for the selection and tuning of fuzzy logic
parameters to achieve efficient results under
different circumstances will represent avenues for
future research works.
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International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2023.2.9
Yamina Jouili, Radhia Garraoui,
Mouna Ben Hamd, Lassaad Sbita
E-ISSN: 2945-0489
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