Journal of Robotics and Control (JRC)

Volume 3, Issue 6, November 2022

ISSN: 2715-5072 DOI: 10.18196/jrc.v3i6.15974 762

Fuzzy Logic Control and PID Controller for

Brushless Permanent Magnetic Direct Current
Motor: A Comparative Study
Ahlam Luaibi Shuraiji 1, Salam Waley Shneen 2*
1
Electromechanical Engineering Department, University of Technology, Baghdad, Iraq
2
Nanotechnology and advanced material research Center, University of Technology, Baghdad, Iraq
Email: 1 50053@uotechnology.edu.iq, 2 salam.w.shneen@uotechnology.edu.iq
* Corresponding author

Abstract—Electrical machines based on permanent magnet Designing an efficient BLPMDC motor controller has
material excitations have been applied in many sectors since been of interest to many works of literature. Two-speed
they are distinguished by their high torque-to-size ratio and control methods, i.e., conventional and an optimal auto-
offer high efficiency. Brushless permanent magnetic direct tuning PID controller for BLPMDC motor, were
current (BLPMDC) motors are one type of these machines.
They are preferable over conventional DC motors. one of the
comprehensively compared in [21]. Seeking effective work,
main challengings of the BLPMDC motor drives is the the motor parameters were experimentally obtained and then
inherited feature of nonlinearity. Therefore, a conventional used in MATLAB simulation. It was shown that target
PID controller would not be an efficient choice for the speed speed could be efficiently achieved by the auto-tuning
control of such motors. The object of this paper is to design an controller, and the variation of both torque and current was
efficient speed control for the BLPMDC motor. The proposed reduced in the such controller. Using MATLAB/Simulink, a
controller is based on the Fuzzy logic technique. MATLAB/ censored closed-loop speed controller for both clockwise
Simulink has been employed to design and test the drive and anti-clockwise was discussed in [22]. The controller
system. Simulations were carried out for three cases, the first was tested at a different speed. The obtained results
without a controller, the other using conventional control, and
the third using expert systems. The results proved the
confirmed the validity of the suggested controller. Similarly,
possibility of improving the engine's working performance two-speed control techniques were adopted and compared in
using the control systems. They also proved that the adoption [23], which were self-tuned PID and modified model-
of expert systems is better than the traditional nonlinear reference adaptive control in which the control decision is
systems. The simulation response shows that the Rise Time(tr) established based on the compensation between the
at PID equals 66.306ms, while it equals 19.530ms for the Fuzzy modified model-reference adaptive and the PID. It was
logic controller. Moreover, Overshoot for PID and Fuzzy logic shown that the latter technique delivered better performance
controller are 6.989% and 1.531%, respectively. On the other than the former. A comparison between conventional PI and
hand, undershoot is equal to 1.788% and 11.924% for PID and digital controllers for BLPMDC motors was conducted in
Fuzzy logic controller, respectively.
[24]. Both methods were PWM-based controllers. The
Keywords—BLPMDC; PID Controller; FLC; Speed Control. simulation results were validated by experimental results. It
was concluded that the digital controller has instant
I. INTRODUCTION response speed, and its control algorithm is simple. Such
Brushless permanent magnet direct current (BLPMDC) features make the digital controller a good choice for
motors have gained considerable attention since they deliver applications in which the ripple of torque/speed profile is
high efficiency, have good reliability, and the need for not of considerable importance. Moreover, Ref. [25-28]
maintenance is low [1-5]. Such motors have been popular conducted a comparison between P and PI controllers for
and are being applied in different applications, including the BLPMDC motor. The mathematical model of the motor
industry, household, and aerospace fields. Generally, was driven, and MATLAB/SIMULINK was used to build
operations of these applications need a reliable with high the motor drive models. It was shown that the steady-state
efficiency and power density motor [6-10]. As the error could be overcome, and the overshoot could be
BLPMDC motors have no windings on their rotor, the reduced by the PI controller. Ref. [26 -30] introduced a
mechanical commutating process is replaced by electrical current controller for the BLPMDC motor based on a PID
commutating, and the motors can be fed by a power controller to control the switching sequences of the
electronic converter or inverter [11-15]. A proper speed MOSFET bridge, and by controlling the current, the speed
controller is required in order to obtain adequate motor would be controlled. In order to evaluate the introduced
performance. The speed controller of the BLPMDC motors controller, a comparison with the conventional PI and PID
can be categorized into three main types, including open speed controllers was conducted. It was revealed that the
loop speed control (constant load), variable load controller, introduced PID controller was the most efficient among the
and positioning controller [16-20]. other controllers.

Journal Web site: http://journal.umy.ac.id/index.php/jrc Journal Email: jrc@umy.ac.id

Journal of Robotics and Control (JRC) ISSN: 2715-5072 763

In order to obtain the desired performance of the motor, many applications due to the following advantages over the
its drive system must be efficient. Usually, the PI and PID conventional DC motor:
controllers are used in controlling the speed of the electrical
Simple rotor configuration, no windings, no
motor due to their uncomplex structures and simple
commutator. The absence of the brush allows for high-speed
implementations. However, such controllers deliver
performance at both no-load and load conditions.
insufficient performances with nonlinear systems and load
disturbances. Thereby, seeking an improvement in the  High efficiency, no copper loss in the rotor.
performance of such controllers, BLPMDC motor  Lower electromagnetic interference.
controllers based on intelligent techniques have emerged.
 No mechanical commutator and consequently all its
Ref. [25] compared conventional PID and self-tuning Fuzzy
PID controllers for BLPMDC motors. It was delivered that problems are eliminated.
the Fuzzy based tuning PID controller has the features of  Less maintenance, less noise.
robustness, efficiency, and simple construction. In this  Higher dynamic profile.
contest, Ref. [26] compared three BLPMDC motor  Its torque/weight ratio is higher.
controllers, including conventional PID, PID-based Genetic
 Better torque-speed curve.
Algorithm tuning, and PID-based Fuzzy Logic tuning
controllers. It was stated that the last controller delivered the Developed torque in the BLPMDC motor is affected by
best performance among the other controllers. In [27], ANN the shape of the motor back-EMF waveform. Generally, the
tuning PID and conventional manual tuning PID controllers BLPMDC motor delivers back-EMF with a trapezoidal
were compared. Both controllers were built using waveform, and the stator windings are usually fed by
MATLAB/ SIMULINK. It was delivered that using the rectangular current waveforms. Hence, theoretically, the
ANN for tuning the parameters of the PID controller would motor will deliver constant torque. However, due to the
enhance the controller performance piratical for nonlinear imperfection of the back-EMF waveform shape, the ripple
dynamic conditions. ANN controller based on model of the current, and the commutation of the phase current, the
reference adaptive control technique was introduced and torque ripple would be presented [37-42].
compared with the conventional PID controller in [29]. It
was confirmed that the ANN controller delivered a very The mathematical model of a three-phase BLPMDC
good performance for speed tracking, and it was able to motor can be represented by Equations (1-8).
minimize the parameter variations impact. 𝑑𝑖
𝑣 = 𝑅𝑖 + 𝐿 +𝑒 (1)
It can be observed that although the PI and PID 𝑑𝑡
controllers are not expensive as well as not complex, they 𝑑𝑖
are not good candidates for the cause of nonlinear system 𝑣 = 𝑅𝑖 + 𝐿 +𝑒 (2)
applications. On the other hand, such a problem would be 𝑑𝑡
overcome by adapting motor speed control based on 𝑑𝑖
𝑣 = 𝑅𝑖 + 𝐿 +𝑒 (3)
artificially intelligent systems. Therefore, in this paper, 𝑑𝑡
Fuzzy Logic will be adapted to design a speed controller for
the BLPMDC motor. Considering the evaluation of the where 𝑣 , 𝑣 , 𝑣 , 𝑖 , 𝑖 , and 𝑖 are terminal voltage and
proposed speed controller, a comparison of the PID input current of phases a, b, and c, receptivity, While 𝑅
conventional speed controller and the proposed counterpart represents the resistance of the stator windings, which is
is carried out. The rest of the paper is divided as follows. equal for all phases for a balanced windings motor.
Section 2 discusses the BLPMDC motor, and Section 3 is Furthermore, 𝐿 indicts induction of the stator windings,
for the speed control of the motor. Moreover, the simulation which is equal for all phases for a balanced windings motor.
model of both the motor and its drive is described in Section On the other hand, the back emf of phases a, b, and c is
4. represented by 𝑒 , 𝑒 and 𝑒 , respectively. The back-emf
equations are given by
II. BRUSHLESS PERMANENT MAGNET DIRECT CURRENT
𝑒 (𝑡) = 𝑘 ∗ ∅(𝜃) ∗ 𝜔(𝑡) (4)
(BLPMDC) MOTORS
BLPMDC motors have been of interest since the 𝑒 (𝑡) = 𝑘 ∗ ∅(𝜃 − 120 ) ∗ 𝜔(𝑡) (5)
introduction of high-energy rare earth permanent magnet 𝑒 (𝑡) = 𝑘 ∗ ∅(𝜃 + 120 ) ∗ 𝜔(𝑡) (6)
materials. This is because of the fact that such materials
offer high flux density. The BLPMDC motor is a where 𝑘 is the back-EMF constant, ∅ is the flux, 𝜃 is the
synchronous PM motor, which is driven by DC voltage rotor angle in electrical degrees, and ω is the motor speed.
through electrical power devices. It can be designed with a The developed electromagnetic torque (𝛵 ) is given by
single-phase, two-phase, or three-phase motor. The rotor of following
the BLPMDC motor has no windings on it, instated it has
permanent material on its surface (surface mounted (𝑖 ∗ 𝑒 ) + (𝑖 ∗ 𝑒 ) + (𝑖 ∗ 𝑒 )
𝛵 = (7)
permanent magnet motor) or buried inside its iron (interior 𝜔
permanent magnet motor), while the stator is being the same On the other hand, the shaft torque is
as that of the conventional Dc motor [31-36]. The BLPMDC
motor is being replaced by the conventional DC motor in 𝑑𝜔
𝑇 − 𝑇 = 𝐵𝜔 + 𝐽 (8)
𝑑𝑡

Ahlam Luaibi Shuraiji, Fuzzy Logic Control and PID Controller for Brushless Permanent Magnetic Direct Current Motor: A
Comparative Study
Journal of Robotics and Control (JRC) ISSN: 2715-5072 764

where 𝑇 represents load torque, 𝐵 is the constant of the

friction, and 𝐽 is the rotor shaft inertia [27-32].
III. SPEED CONTROL OF BLPMDC MOTOR
Developing motor drives having high performance has
become essential in all applications, from industrial to
household applications. The BLPMDC motors are Fig. 2. Model of BLPMDC motor with PID controller
preferable to the conventional DC motors, as they have an
electrical commentator and require less maintenance.
However, BLPMDC motor drive systems suffer from the
problem of high overshoot, which negatively affects drive
performance. Hence, in order to ensure the requirement of
all applications, the drive system of these motors must be
efficient and has the features of high response, minimum
overshoot as well as steady state error [33-35]. It was Fig. 3. Model of BLPMDC motor with FLC
confirmed that the drive system of the electric motor could
be enhanced by adopting the technique of Fuzzy Logic[36-
39]. It leads to improve dynamic performance of the drive
system and reduces the impact of load variations. It is
capable of dealing with the system's nonlinearity without the
needing for its mathematical model [40-42]. Due to its
individuality features, such a controller is becoming popular
and widely used in many sectors [43-47]. The structure of
the Fuzzy logic controller is comprised of the following
stages, Fuzzification, Knowledge, Fuzzy inference, and De-
Fuzzification.
IV. THE SIMULATION DRIVE SYSTEM OF THE BLPMDC
MOTOR
Fig. 4. Model of BLPMDC motor without a controller, with PID
In this section, a simulation model of the BLPMDC
controller, and with FLC
motor and its speed control is discussed. The transfer
function of the motor is given by Equation (9) [48]. The
simulation model of the BLPMDC motor shows in Fig. 1.
𝐾
𝑇. 𝐹 = (9)
𝐿 𝐽𝑠 + (𝑟 𝐽 + 𝐿 𝐵 )𝑠 + (𝑟 𝐵 + 𝐾 𝐾 )
4787
𝑇. 𝐹 = (10)
𝑠 + 132.8𝑠 + 1538
It should be mentioned that three models have been
simulated, including the BLPMDC motor without a
controller, the BLPMDC motor with a PID controller, and
BLPMDC with Fuzzy logic controller (FLC) [49, 50]. Fig. 1 Fig. 5. PID controller
shows the model of the BLPMDC motor without a
controller built by T. F. on the other hand, Fig. 2 shows the
model of the BLPMDC motor with PID controller, while the
BLPMDC motor with FLC controller is displayed in Fig. 3.
Fig. 4 shows the simulation models of BLPMDC motor
without a controller, BLPMDC motor with PID controller
and BLPMDC motor with FLC. On the other hand, Figs. 5
and 6 display the PID and the FL controller, respectively.
Figs. 7-11 is Fuzzy Design.

Fig. 1. Model of BLPMDC motor without controller

Fig. 6. FLC-Error-first input

Ahlam Luaibi Shuraiji, Fuzzy Logic Control and PID Controller for Brushless Permanent Magnetic Direct Current Motor: A
Comparative Study
Journal of Robotics and Control (JRC) ISSN: 2715-5072 765

Fig. 10. FLC-Rule viewer of input(e,de) &output(du)

Fig. 7. FLC-Change of Error-2nd input

Fig. 8. FLC-Change of Error-3rd output Fig. 11. The FLC-Surface viewer of input (e, de) & output (du)

V. RESULTS AND DISCUSSION

In order to evaluate the proposed Fuzzy logic controller,
three cases have been simulated, and the results were
obtained for both speed and error. Fig. 12 (a and b)
represent the response of speed and error, respectively, in
the case of the motor without a controller, while Fig. 13 (a
and b) display the simulation results for both speed and
error responses, respectively, in the case of the PID
controller. In addition, the response of both speed and error
in the case of the proposed Fuzzy controller are shown in
Fig. 14 (a and b), respectively. On the other hand, Fig. 15
(a) compares the speed responses for all three mentioned
cases, and their error responses are compared in Fig. 15 (b).
Apparently, less rise time, as well as overshoot, are
delivered by the Fuzzy logic controller compared to the
conventional (PID) counterpart. Table 1 summarizes the
performances of both proposed and conventional controllers
Fig. 9. FLC-Rule Editor of input (e, de) & output (du) in terms of rise time, overshoot, and undershoot. The
proposed controller offers about 70.5% less rise time and
about 78% less overshoot compared to the conventional
controller. However, in terms of undershooting, the

Ahlam Luaibi Shuraiji, Fuzzy Logic Control and PID Controller for Brushless Permanent Magnetic Direct Current Motor: A
Comparative Study
Journal of Robotics and Control (JRC) ISSN: 2715-5072 766

proposed controller has about 85% higher value than the

conventional one.

a. Speed
b. Error

Fig. 13. Simulation response of the motor with PID control

b. Error
Fig. 12. Simulation response of the motor without control

a. Speed

a. Speed

b. Error
Fig. 14. Simulation response of the motor with FLC

Ahlam Luaibi Shuraiji, Fuzzy Logic Control and PID Controller for Brushless Permanent Magnetic Direct Current Motor: A
Comparative Study
Journal of Robotics and Control (JRC) ISSN: 2715-5072 767

rising time and about 78% less overshooting for the FC

controller.
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