Optimized speed control with torque ripple reductions of BLDC motor based on SMC approach using LFD algorithm

International Journal of Power Electronics and Drive Systems (IJPEDS)
Vol. 13, No. 3, September 2022, pp. 1305~1314
ISSN: 2088-8694, DOI: 10.11591/ijpeds.v13.i3.pp1305-1314  1305
Journal homepage: http://ijpeds.iaescore.com
Optimized speed control with torque ripple reductions of BLDC
motor based on SMC approach using LFD algorithm
Quasy Shabib Kadhim1
, Abbas H. Abbas Dairawy1
, Mohammed Moanes Ezzaldean Ali2
1
Department of Electrical and Engineering, College of Engineering, Basrah University, Basrah, Iraq
2
Department of Electrical Engineering, University of Technology, Bagdad, Iraq
Article Info ABSTRACT
Article history:
Received Apr 10, 2022
Revised Jun 5, 2022
Accepted Jun 29, 2022
Brushless DC motors (BLDCM) are utilized in various applications,
including electric cars, medical and industrial equipment, where high-
efficiency speed control is necessary to meet load and tracking reference
fluctuations. In this study, the optimal parameters of proportional-integral
(PI) and sliding mode controller (SMC) for BLDC motor speed control are
determined using Lévy flight distribution (LFD) technique. The integral time
absolute error (ITAE) is used as a fitness function with the LFD algorithm
for tuning the PI and SMC parameters. The optimization algorithms'
performance is presented statistically and graphically. The simulation results
show the SMC based on the LFD technique has superiority over SMC
without optimization and PI controller in fast-tracking to the desired value
with zero overshoot with rising time (6 ms) and low-speed ripple up to
(± 9 RPM) under non-uniform conditions.
Keywords:
BLDC motor
LFD algorithm
PI Speed Controller
SMC speed controller
Torque ripple reductions
This is an open access article under the CC BY-SA license.
Corresponding Author:
Quasy Shabib Kadhim
Department of Electrical Engineering, Basrah University
PO Box 49, Ali Al-vine. B. 49, Basrah, Iraq
Email: qusay.eifaan@uobabylon.edu.iq
1. INTRODUCTION
Brushless DC motors (BLDCM) developed a new type of DC motor in response to the rapid
development of power electronic technology, control theory, and permanent magnetic materials. Its use was
also more extensive than traditional motor due to several benefits, including high-precision electronic
equipment, robots, aircraft, chemical mining, and many other sectors [1], [2]. For these purposes, various
electric motors have been proposed [1]. There are typical DC motors, which are well-known for their high-
performance characteristics. On the other hand, conventional DC motors have several drawbacks, requiring
frequent maintenance brushes to be replaced regularly, and commutators must be used. The original
investment [3]-[6]. Conventional DC motors are not suitable for use in a clean environment or a potentially
explosive setting. The squirrel cage induction motor is a type of induction motor. An alternative to the
standard DC motor, it has toughness. With a low price, its downsides, on the other hand, include a bad start,
common power factor and high torque ripple [1], [7]-[9].
Furthermore, neither standard DC motors nor induction motors are suitable for this application. The
application that runs at a high rate, the alternative machine to both traditional DC and AC power, is the DC
brushless motor, a combination of a DC motor and an induction motor. It can be regarded as an essential
electric motor in these applications. They're powered by dc voltage, but they're also powered by AC current.
Solid-state switches are used for commutation. Communication of the rotor position and the location of the
rotor determines instants. Position sensors or sensorless approaches detect the rotor speed or position.

 ISSN: 2088-8694
Int J Pow Elec & Dri Syst, Vol. 13, No. 3, September 2022: 1305-1314
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The control approach must be adaptable, resilient, accurate, and easy to apply to maintain the
BLDCM's stability under various conditions such as variable loads and parameters change [1], [7]-[11]. The
proportional-integral–differential (PID) controller is used in multiple technical domains because of its
simplicity, durability, reliability, and ease of parameter adjustment [1]. The Ziegler-Nichols rule is a well-
known approach for determining PID parameters, but it is not always the best. A genetic optimization
technique based on three alternative cost functions might identify the optimal PID control parameters. The
main challenges that the PID control technique faces are sudden changes in setpoint and parameter variation,
which causes PID control to have a poor response [4].
Advanced control techniques such as adaptive control, variable structure control, fuzzy control, and
neural networks can be used to solve this challenge [4], [9], [10]. The inability to perform trajectory control
in the presence of unexpected disruptions or big noises is one of the critical issues with implementing self-
tuning adaptive control approaches. This is because, in the case of rapid disturbances or huge sounds, the
parameter estimator may produce incorrect findings [6]. Although the variable structure controller is simple,
it is challenging to practice. This is due to the risk of a sudden shift in the control signal, which could disrupt
system operation [9]. The ability of a neural-network-based motor control system to address the structure
uncertainty and disturbance of the system is considerable. Still, it requires more computational power and
data storage space [4]. Nonlinear controllers based on fuzzy control theory can conduct various complicated
nonlinear control actions, even for uncertain nonlinear systems [4]-[10]. Unlike traditional control design, an
fullerene-like carbon (FLC) does not necessitate accurate knowledge of the system model, such as the system
transfer function's poles and zeroes [11]. Although a fuzzy-logic control system based on an expert knowledge
database requires fewer calculations, it does not have enough capacity to handle the new rules [7], [11], [12].
The sliding mode control (SMC) is used [13].
SMC is a control system that can keep a system stable in various models with different interference
and system parameters. As a result, it's frequently employed in nonlinear models. SMC has a working area in
the steady-state phase, which allows it to maintain system performance when disturbances and parameter
changes occur. SMC based on optimization algorithm is a new system that will enable you to arrange the
SMC sliding surface based on the best setting. This improves the system's transient response over the
previous SMC [14], [15].
With the advancement of artificial intelligence control technology, numerous authors have been
used intelligence algorithms for control of BLDCM, such as firefly algorithm [14], genetic algorithm [16],
fuzzy logic control [17], neural network [18], sine-cosine algorithm (SCA) [19], particle swarm optimization
(PSO) [19], moth swarm algorithm (MSA) [20], bat algorithm [21]. Bacterial foraging algorithms [22] have
increasingly been added to the traditional PID controller. In this paper, to the author's knowledge, a novel
algorithm is used for the first time for speed control of BLDCM for tuning the parameters of SMC, which is
called Lévy flight distribution (LFD). The proposed control scheme depends on two closed-loop outer and
inner loops. The outer loop is the speed control loop, and the inner loop is the current control loop. The
proposed control is robust and straightforward.
2. RESEARCH METHOD
2.1. BLDC motor modelling
To analyze the dynamic response and study the behavior of the BLDC motor, a mathematical model
is required. Figure 1 show the equivalent circuit of the BLD motor. According to the equivalent circuit, the
differential voltage equations can be deduced in (1) [1], [2], [5], [23].
�
𝑣𝑣𝑎𝑎
𝑣𝑣𝑏𝑏
𝑣𝑣𝑐𝑐
� = �
𝑅𝑅𝑎𝑎 0 0
0 𝑅𝑅𝑏𝑏 0
0 0 𝑅𝑅𝑐𝑐
� �
𝑖𝑖𝑎𝑎
𝑖𝑖𝑏𝑏
𝑖𝑖𝑐𝑐
� +
𝑑𝑑
𝑑𝑑𝑑𝑑
�
𝐿𝐿𝑎𝑎 𝐿𝐿𝑎𝑎𝑎𝑎 𝐿𝐿𝑐𝑐𝑐𝑐
𝐿𝐿𝑏𝑏𝑏𝑏 𝐿𝐿𝑏𝑏 𝐿𝐿𝑏𝑏𝑏𝑏
𝐿𝐿𝑐𝑐𝑐𝑐 𝐿𝐿𝑐𝑐𝑐𝑐 𝐿𝐿𝑐𝑐
� �
𝑖𝑖𝑎𝑎
𝑖𝑖𝑏𝑏
𝑖𝑖𝑐𝑐
� + �
𝑒𝑒𝑎𝑎
𝑒𝑒𝑏𝑏
𝑒𝑒𝑐𝑐
� (1)
BLDC motors typically use a surface-mounted salient-pole rotor. The winding inductance will not change
with time in this situation. Furthermore, because the three-phase stator windings are symmetrical, the self-
inductances and mutual inductances will be equal. The phase voltage equations of a BLDC motor can thus be
represented in matrix form as:
�
𝑣𝑣𝑎𝑎
𝑣𝑣𝑏𝑏
𝑣𝑣𝑐𝑐
� = �
𝑅𝑅 0 0
0 𝑅𝑅 0
0 0 𝑅𝑅
� �
𝑖𝑖𝑎𝑎
𝑖𝑖𝑏𝑏
𝑖𝑖𝑐𝑐
� +
𝑑𝑑
𝑑𝑑𝑑𝑑
�
𝐿𝐿 𝑀𝑀 𝑀𝑀
𝑀𝑀 𝐿𝐿 𝑀𝑀
𝑀𝑀 𝑀𝑀 𝐿𝐿
� �
𝑖𝑖𝑎𝑎
𝑖𝑖𝑏𝑏
𝑖𝑖𝑐𝑐
� + �
𝑒𝑒𝑎𝑎
𝑒𝑒𝑏𝑏
𝑒𝑒𝑐𝑐
� (2)
where,𝐿𝐿 = 𝐿𝐿𝑠𝑠 − 𝑀𝑀, and the developed torque equation can be expressed as below [24]-[27].

Int J Pow Elec & Dri Syst ISSN: 2088-8694 
Optimized speed control with torque ripple reductions of BLDC motor based on … (Quasy Shabib Kadhim)
1307
𝑇𝑇𝑒𝑒 = 𝐽𝐽
𝑑𝑑𝜔𝜔𝑟𝑟
𝑑𝑑𝑑𝑑
+ 𝐵𝐵𝜔𝜔𝑟𝑟 + 𝑇𝑇𝑙𝑙 (3)
Figure 1. Equivalent circuit of the BLDC motor
2.2. Control strategy
This paper focused on comparing of the traditional techniques and optimized PI and SMC based on
the Lévy flight distribution. The conventional control strategies considered in this paper are PI controller
without optimized gains, PI controller with optimized gains, and SM controller without optimized gains, SM
controller with optimized gains. To make a good comparison, the concept of PI and SMC are explained with
modeling in [27], [28]. The algorithm is used online with the modeling of the BLDC motor during the
running, and the controller error sends to the algorithm by the objective function. The proposed algorithm's
control and modeling are presented in sections (3).
2.3. Proposed control structure
The proposed control strategy includes the speed control loop and the current control loop,
presented in Figure 2. This paper used the SMC for the speed controller and compared it with the PI
controller to track the desired trajectory. At the same time, the PI controller regulates the stator current of
BLDCM. The LFD algorithm tunes the parameters of the two PI controllers to achieve excellent performance
under non-uniform conditions.
Figure 2. The structure of a BLDC motor with the proposed control approach
3. LÉVY FLIGHT DISTRIBUTION (LFD)
3.1. Inspiration
The suggested algorithm primarily focuses on the environment of wireless sensor networks
combined with Lévy flight (LF) motions. As seen in Figure 3, LF can be considered a random walk. The LF
shows that it can improve the efficiency of resource searches in uncertain contexts. In reality, numerous
natural-inspired or physical-inspired occurrences in the environment can inspire LFs. The pathways of LF
styles can be followed by natural animals such as spider monkeys, fruit flies, and humans.
Furthermore, albatross foraging practices have been discovered as an inspiration phase for the LFs.
Noise and cooling behaviors indicate the features of LFs under the right conditions, and diffusion of
fluorescent molecules might be considered a physically-inspired phenomenon for the inspiration of LFs.
Furthermore, LFs are more efficient than Brownian random walks exploring unknown significant search
areas. This efficiency is the primary justification for including LFs in the proposed optimization technique.
Figure 3. Lévy flights of fifty sequential steps starting from the origin marked with a bold point [29]
BLDC
Motor
inverter
𝜔𝜔
Vdc
𝜔𝜔ref i
PI cureent
controller
SM speed
controller
S1-S6
�
ew
Ddraganfiy Algorithhm
K C Kp Ki
Fitness
Function
Initial
parameters
ew+ei
PWM
BEMF
Ѳa,Ѳb,Ѳc
ha,hb,hc
i* ei

 ISSN: 2088-8694
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3.2. Mathematical model of LFD
The environment of wireless sensor networks is used for mathematical modeling. The algorithm
begins its mechanism by finding the Euclidean distance (ED) between the nodes of each neighboring sensor.
After that, the algorithm decides whether the node is in its original location depending on ED or moving it to
another position. Another location will be calculated using LFs model in which the new location will be in a
place that is close to a node with low neighboring nodes or in an area with no nodes in the search space to
decrease the chances of overlapping occurring among sensor nodes.
For random walks generation, it ought to assign two characteristics: the walk length step following
the selected Lévy distribution and the orientation that moves to the target location in the proposed algorithm,
which may be derived from the symmetric distribution. Many procedures may determine the mentioned
features, but the easiest and effective method is the Mantegna algorithm for a stable and uniform
distribution [29].
Concerning Mantegna's algorithm, the step length 𝑆𝑆 is:
𝑆𝑆 =
𝑈𝑈
|𝑉𝑉|1 𝛽𝛽
⁄ (4)
where β is the index of Lévy distribution limited as 0 < 𝛽𝛽 ≤ 2, U and V are such that
𝑈𝑈~𝑁𝑁(0, 𝜎𝜎𝑢𝑢
2), 𝑉𝑉~𝑁𝑁(0, 𝜎𝜎𝑉𝑉
2)
the standard deviation 𝜎𝜎𝜎𝜎 and 𝜎𝜎𝜎𝜎 are:
𝜎𝜎𝑢𝑢 = �
𝛤𝛤(1+𝛽𝛽)∗sin(𝜋𝜋𝜋𝜋 2
⁄ )
𝛤𝛤[(1+𝛽𝛽)/2]∗𝛽𝛽∗2(𝛽𝛽−1)/2
�
1 𝛽𝛽
⁄
, 𝜎𝜎𝑣𝑣 = 1 (5)
for an integer 𝑧𝑧 the Gamma function 𝛤𝛤 is:
𝛤𝛤(𝑧𝑧) = ∫ 𝑡𝑡𝑧𝑧−1
𝑒𝑒−𝑡𝑡
𝑑𝑑𝑑𝑑
∞
0
(6)
Euclidean distance 𝐸𝐸𝐸𝐸 between the first two adjacent. Agents (and 𝑋𝑋𝑋𝑋) positions:
𝐸𝐸𝐸𝐸�𝑋𝑋𝑖𝑖, 𝑋𝑋𝐽𝐽� = �(𝑋𝑋𝑖𝑖, 𝑋𝑋𝐽𝐽)2 + +(𝑦𝑦𝐽𝐽, 𝑌𝑌𝑖𝑖)2 (7)
xi, yi is the Xi position coordinate, 𝑥𝑥𝐽𝐽, 𝑦𝑦𝐽𝐽 is 𝑥𝑥𝐽𝐽 position coordinate. ED is compared with a specified threshold
till the agents are terminated after a defined iterations number. If the distance resulting is less than the
threshold, the mechanism of the algorithm begins by adjusting the agent's positions using:
𝑋𝑋𝐽𝐽(𝑡𝑡 + 1) = 𝐿𝐿𝑒𝑒′
𝑣𝑣𝑦𝑦𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹ℎ𝑡𝑡�𝑋𝑋𝐽𝐽(𝑡𝑡),𝑋𝑋𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿,𝐿𝐿𝐿𝐿,𝑈𝑈𝑈𝑈� (8)
where t is the iteration index, the function Levy flight accomplish the Levy flights work in terms of the
orientation a step length. LB and UB are the lowest and highest values in the search space 2D dimensions.
XLeader is the agent position with neighbors of the lowest number and will be used as the direction of the LF.
in (30) moves 𝑋𝑋𝐽𝐽 agent towards the agent's position, which has the lowest number of neighbors.
𝑋𝑋𝐽𝐽(𝑡𝑡 + 1) = 𝐿𝐿𝐿𝐿 + (𝑈𝑈𝑈𝑈 − 𝐿𝐿𝐿𝐿)𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟( ) (9)
The function rand ( ) produces R random numbers in uniform distribution [0, 1]. In (31) introduce
more opportunities for finding solutions of non-visited position in the search space and the suggested
algorithm exploration phase increasing. In (30) updates the 𝑋𝑋𝐽𝐽 position to a new area in the search space
where no other agents are there:
𝑅𝑅 = 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟( ), 𝐶𝐶𝐶𝐶𝐶𝐶 = 0.5 (10)
CSV is a scalar value for comparison with R in each update for the XJ position. For updating the node 𝑋𝑋𝐽𝐽
position, R is checked on at every iteration in (32). If R is less than CSV, execute in (30). If not, complete in
(31) to give more chances to find the search space. Altering the algorithm's solutions increase its exploration
capability and improve its performance. The suggested algorithm updates the Xi using:

1309
𝑋𝑋𝑖𝑖(𝑡𝑡 + 1) = 𝑇𝑇𝑇𝑇 + 𝛼𝛼1 ∗ 𝑇𝑇𝐹𝐹𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁ℎ𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 + 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟( ) ∗ 𝛼𝛼2 ∗ �𝑇𝑇𝑇𝑇 + 𝛼𝛼1𝐹𝐹𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁ℎ𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 2
⁄ − 𝑋𝑋𝑖𝑖(𝑡𝑡)� (11)
𝑋𝑋𝑖𝑖
𝑁𝑁𝑁𝑁𝑁𝑁(𝑡𝑡 + 1) = 𝐿𝐿𝑒𝑒′
𝑣𝑣𝑣𝑣_𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹ℎ𝑡𝑡(𝑋𝑋𝑖𝑖(𝑡𝑡 + 1), 𝑇𝑇𝑇𝑇, 𝐿𝐿𝐿𝐿, 𝑈𝑈 𝐵𝐵) (12)
New Xi is calculated by (33), while Xi final position is obtained by (34). T P is the solution achieving the
objective function best fitness value, named the target position. 𝛼𝛼1, 𝛼𝛼2 and 𝛼𝛼3 are random numbers, and their
values are such that 0 < 𝛼𝛼1, 𝛼𝛼2, 𝛼𝛼3 ≤ 10.
The total target fitness of neighbors around (𝑡𝑡) is:
𝑇𝑇𝐹𝐹𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁ℎ𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = ∑
𝐷𝐷(𝑘𝑘)∗𝑋𝑋𝑘𝑘
𝑁𝑁 𝑁𝑁
𝑁𝑁𝑁𝑁
𝐾𝐾=1 (13)
where Xk is the Xi(t) neighbor position, the neighbor’s index is k, the total no. of Xi(t) neighbors, and D(K) is
the degree of fitness for each neighbor obtained by:
𝐷𝐷(𝑘𝑘) =
𝜕𝜕1(𝑉𝑉−𝑀𝑀𝑀𝑀𝑀𝑀(𝑉𝑉))
𝑀𝑀𝑀𝑀𝑀𝑀(𝑉𝑉)−𝑀𝑀𝑀𝑀𝑀𝑀(𝑉𝑉)
+ 𝜕𝜕2 (14)
where
𝑉𝑉 =
𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹(𝑋𝑋𝐽𝐽(𝑡𝑡))
𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹(𝑋𝑋𝑖𝑖(𝑡𝑡))
, 𝑎𝑎𝑎𝑎𝑎𝑎 0 < 𝜕𝜕1, 𝜕𝜕2 ≤ 1 (15)
All mentioned equations are repeated at every iteration. Assuming t is iterations number and n is the agents
number, the LFD time complexity is (tnd), where d is each agent dimension
4. OBJECTIVE FUNCTION
This project aims to find more optimal values for PI controllers and SMC settings that control the
rotor speed of the BLDC motor. A target function must create an appropriate search space and find the best
PI parameters and SMC settings to solve the optimization problem. Different error parameters of the system's
dynamic response can be used to describe the objective function including: i) integrated absolute error (IAE),
ii) integrated squared error (ISE), iii) integrated time squared error (ITSE), and iv) integrated time absolute
error (ITAE). While these definitions are accurate, we propose in this paper to use the objective function
based on ITAE, which helps us to achieve better results:
𝐽𝐽 = 𝑚𝑚𝑚𝑚𝑚𝑚 �∫ 𝑡𝑡 ∗ [|𝑒𝑒𝑤𝑤| + |𝑒𝑒𝑖𝑖| ]
𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
0
𝑑𝑑𝑑𝑑� (16)
in (38) can describe the optimization problem in terms of the objective function: J should be as small as
possible.
Where Tsimulation is the final simulation time, the problem constraints are the parameter limit of the
controller; therefore, the parameters of two PI controllers are limited or SMC setting to help the optimization
algorithm achieve the best parameter as fast time. So, the constrained problem design can be formulated as
follows:
- For SMC
𝐾𝐾𝑚𝑚𝑚𝑚𝑚𝑚 ≤ 𝐾𝐾 ≤ 𝐾𝐾𝑚𝑚𝑚𝑚𝑚𝑚
𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 ≤ 𝐶𝐶 ≤ 𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚
� (17)
- For PI controller
𝐾𝐾𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 ≤ 𝐾𝐾𝑝𝑝 ≤ 𝐾𝐾𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
𝐾𝐾𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 𝐾𝐾𝑖𝑖 ≤ 𝐾𝐾𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖
� (18)
In (39) and (40) indicates the limited values of tune PI and SMC, which are used with the LFD algorithm to
tune the best parameters of the proposed controller. Figure 4 show the process of adjusting the gain values of
the PI controller and the setting coefficient of SMC with the control scheme.

 ISSN: 2088-8694
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Figure 4. Flowchart of LFD for tuning the parameters of SMC and PI parameters
5. SIMULATION RESULTS AND DISCUSSIONS
This section presents the comparative performance of the proposed optimizer SMC controller with
optimizer PI controller using the LFD algorithm with the same constraints (search agent=10, maximum
iteration=10 and threshold value equal to 1.3) under the non-uniform conditions. Table 1 lists the parameters
of the BLDC motor model utilized in the simulations. Table 2 depicts the optimum parameters of controllers
using the LFD algorithm. The fitness function tracking performance for SMC and PI controller based on LFD
is shown in Figure 5. It was evident from this figure the SMC with LFD has a minimum fitness value
compared with PI with the LFD approach. In order to show the superiority of the proposed system, the
simulation results are divided into two scenarios: dynamic response under rated conditions (w=4000 RPM
and load torque 0.32 Nm) and dynamic response under non-uniform conditions.
Table 1. Specification of BLDCM Type (LVT57BL-94-001-05)
Parameters Value Unit
DC voltage Vdc 36 V
Rated speed 𝜔𝜔 4000 RPM
Rated torque Te 0.32 Nm
maximum current Ia 16.5 A
Resistance R 0.45 Ω
Inductance L 1.4 mH
Torque constant Kt 0.063 Nm/A
Moment inertia J 0.0000173 Kg/m2
Number of poles P 4
Table 2. Parameters of controllers
Techniques SMC Speed controller Current controller
C K Kp Ki Kp Ki
Ziegler-Nichols 2000 5000 8 20 10 0.9
LFD 1088.941 2636.8221 0.6073 13.532 93.7725 64.102

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Scenario I: Dynamic responses of BLDC motor under rated conditions. In general, the Figures 6-11
the optimization SMC has a considerably better reaction than the optimization PI control. Figure 6 shows the
comparative dynamic speed response for PI, LFD-PI, SMC, and LFD-SMC. It can be seen that the speed
response is based on SMC and LFD SMC is better than PI controller and LFD-PI in terms of minor steady-
state error and no overshoot. Also, the chattering is mitigating with LFD-SMC as compared with SMC.
Figure 7 depicted the torque response, and we notice the SMC and LFD-SMC have notability over PI
and optimum PI controller in reducing the overshoot and torque ripple. While Figure 8 shows the speed error for
the four approaches, the LFD with SMC is continued as better performance in reducing error and tracking on
the zero, which implies no error at the steady-state region. On the other hand, Figure 9 shows the torque-speed
characteristic. We notice from this figure. The torque-speed feature quickly reached the desired value with
LFD-SMC without overshoot and less ripple than PI and SMC techniques. Finally, Figures 10 and 11
demonstrated the stator currents and trapezoidal back EMF voltage under rated conditions. It can be seen that
the stator current and back EMF voltage has an excellent steady state based on LFD –SMC as compared with
other techniques.
Figure 5. Fitness function of SMC and PI with LFD
Figure 6. Speed response of BLDCM Figure 7. Torque response of BLDCM
Figure 8. Speed error Figure 9. Torque-speed characteristic of BLDCM

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Scenario II: Dynamic responses of BLDC motor under non-uniform conditions. To show the
robustness of the proposed control strategy with the LFD algorithm, the proposed system is examined under
various speeds and step-change loads between (0.2 Nm to 0.32 Nm at t= 1s). Figure 12 demonstrated the
speed response. It is evident from this figure the actual speed is fast-tracking to desired value under variable
speed. Also, the speed response with LFD-SMC has accurate trajectory tracking with no overshoot and very
little chattering compared with traditional SMC.
The Figures 13, 14 and 15 have the same superiority based on LFD-SMC compared with SMC, PI,
and LFD-PI controllers in terms of no steady-state error, less overshoot, and fast-tracking to the desired
trajectory. While Figures 16 and 17 show that the stator current and back EMF voltage is fast change with
speed and torque with very short time are reaching the steady-state without overshoot.
To provide a fair comparison between the proposed SMC based on the LFD algorithm with another
traditional technique, the specification criteria are depicted in Table III. It can be evident from the results in
this table that the LFD-SMC has less rise time and less settling time, which implies its fast reach to steady-
state, and it has a high steady-state with no overshoot and very little ripple.
Figure 10. stator currents of BLDCM Figure 11. Back EMF response underrated
Figure 12. Speed response of BLDCM Figure 13. Torque response of BLDCM
Figure 14. Speed error Figure 15. Torque speed characteristic of BLDCM

1313
Figure 16. stator currents of BLDCM under
non-uniform conditions.
Figure 17. Back EMF response under
the non-uniform condition
Table 3. Performance criteria of output speed response
Technique ITAE Overshoot (RPM) Rise time Settling time Ripple (RPM)
LFD-PI 2.6255 78 20 ms 27 ms ± 50
LFD-SMC 2.2577 0 6 ms 8 ms ±9
6. CONCLUSION
This study uses the LFD algorithm to identify the best PI control and SMC settings. The BLDC motor
speed is chosen as the system to be controlled. The ITAE is used as a fitness function based on the summation
errors of comparisons between the actual speed with reference speed and reference currents with actual currents
to achieve excellent tracking for speed and reduction torque ripple of BLDC motor under various conditions.
The simulation results demonstrate the robust performance of the BLDC motor under variable speed and load
torque compared with optimization PI and traditional SMC. These optimization algorithms for BLDC motor
speed control can be enhanced in future studies by incorporating other system factors.
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BIOGRAPHIES OF AUTHORS
Quasy Shabib Kadhim was born in Babylon, Iraq in 1982. He received the B.Sc.
degree in electrical engineering from University of Babylon in 2007 and MSc in Power
Engineering from University of Technology in 2019. He is currently studying Ph.D degree in
Department of Electrical Power Engineering from university of AL-Basrah. His interest
includes intelligence techniques, control theory, power electronics and Machine drive. He can
be contacted at email: almhndsynn@gmail.com.
Abbas H. Abbas Dairawy was born in Basrah, Iraq. He received the B.Sc. degree
in Electrical Engineering from AL-Basrah University. He received the M.Sc. from the
University of Technology and Ph.D. in Electrical Engineering in Power Systems from
Technical University, Sofia, Bulgaria. His interest includes Power System Analysis, Power
System Protection, Power System Stability, Power System Control, Renewable Energy. He
can be contacted at email: abbas.hafis@uobasrah.edu.iq.
Mohammed Moanes Ezzaldean Ali was born in Baghdad, Iraq. He received
the B. Sc, M. Sc and Ph.D degrees in electrical engineering from University of Technology-
Iraq in 1994, 1997 and 2009, respectively. In 1997, he joined the Research and Development
Department - Al-Duha Electrical Industries Company Ltd. After that he was an Assistant
Lecturer at Poly-Technique Higher Institute-Surman, Libya from 2001 to 2004. Mohammed
Moanes was a consultant at the General Company for Electrical Industries-Baghdad from 2004
to 2006. Since May 2006, he has been with the Department of Electrical Engineering-
University of Technology, where he was an Assistant Lecturer, became a Lecturer in 2009,
and an Assistant Professor in 2018. His current research interests include Induction Heating,
Electrical Machines and Drives. He can be contacted at email: 30097@uotechnology.edu.iq.

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