A new design of fuzzy logic controller optimized by PSO-SCSO applied to SFO-DTC induction motor drive

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 10, No. 6, December 2020, pp. 5813~5823
ISSN: 2088-8708, DOI: 10.11591/ijece.v10i6.pp5813-5823  5813
Journal homepage: http://ijece.iaescore.com/index.php/IJECE
A new design of fuzzy logic controller optimized by PSO-SCSO
applied to SFO-DTC induction motor drive
Ali Taieb, Abdellaziz Ferdjouni
Department of Electonic, Laboratoire des Systèmes Electriques et Télécommande (LABSET),
Saad Dahlab University, Algeria
Article Info ABSTRACT
Article history:
Received Dec 7, 2019
Revised May 12, 2020
Accepted May 25, 2020
In this article, a new strategy for the design of fuzzy logic controllers (FLC)
is proposed. This strategy is based on the optimization of the FLC,
by the hybridization between the particle swarm optimization algorithm
(PSO) and the sine-cosine swarm optimization algorithm (SCSO), This new
strategy is called FLC-PSCSO. The input-output gains and the geometric
shapes of the triangular membership functions of the FLC are the objective
functions to be optimized. The optimization of the latter is obtained by
minimizing a cost function based on the combination of two criteria,
the integral time absolute error (ITAE) and the integral absolute error (IAE).
A comparison between the conventional FLC and the proposed FLC-PSCSO
is made. The FLC optimized by PSCSO shows a remarkable improvement in
the performance of the controlled induction motor.
Keywords:
Fuzzy logic controller
Integral absolute error
Integral time absolute error
Particle swarm optimization
Sine-cosine swarm optimization Copyright © 2020 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Ali Taieb,
Department of Electonic,
Laboratoire des Systèmes Electriques et Télécommande (LABSET),
Saad Dahlab University, Blida 1, Algeria.
E-mail: taiebali07@yahoo.fr
1. INTRODUCTION
Since the first appearance of fuzzy logic in the sixties by Zadeh [1], many other research works were
made such as those of Mamdani [2], Takagi and Sugeno [3] and then Yamakawa [4]. In recent years,
the phenomenal development of digital electronics has demonstrated the merit of using fuzzy logic
algorithms to control many complex systems. Nowadays, fuzzy logic controllers (FLCs) [5-7] have been
widely used successfully in industrial control system applications, such as: Electrical engineering [8, 9],
Medical field [10], Renewable energy [11-14], Robotics [15-17]. These complex applications are nonlinear
and do not require good knowledge of their exact mathematical models.
Nevertheless, an efficient design of FLC needs to be carried out by an expert with a very well
knowledge of the system. Furthermore, because of the large number of parameters of conventional FLC,
which are input-output gains in addition to the geometric shapes of membership functions, the use of
the trial-and-error method in order to find an optimal solution is a laborious work. In electrical engineering
for example, the conventional FLC gives acceptable performances but they are still insufficient. Indeed,
during changes in the operating point, the overshoot is important, involving a large consumption of stator
current that can be destructive for the inverter that controls the induction motor.
In order to overcome this problem, many approaches have been suggested [18], including the use of
heuristic methods inspired by nature [19-24], such as: particle swarm optimization (PSO), proposed by
Kennedy [25, 26], In order to improve the performance of the structure of the PSO algorithm, a contribution
was proposed in [27, 28]. On the other hand, the development of the SCSO and SCA algorithms [29-31] and
their contribution either by the optimization of the physical systems [32], or in the optimization of the FLC
controllers [33], gave satisfactory results. Both PSO and SCA [34] are random global optimization techniques.

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Int J Elec & Comp Eng, Vol. 10, No. 6, December 2020 : 5813 - 5823
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Combining PSO and SCA finds optimal areas for complex search spaces through the interaction of individuals
in a group of particles and has proven to be very powerful at solving persistent and non-linear complex
optimization problems [35]. Since SCSO is an improved version of SCA, hybridization between PSO and
SCSO techniques can generate an excellent-quality solution within an ideal computational time and a very
stable convergence characteristic compared to other random methods. The combination of PSO and SCSO is
called the PSCSO. As the PSCSO method is a perfect optimization methodology and a promising approach for
solving the optimal FLC controller parameters problem; therefore, this study develops the PSCSO-FLC
controller to search optimal FLC parameters. This FLC Controller is called the PSCSO-FLC controller.
In this paper, this new approach is applied to direct flux-oriented torque control (SFO-DTC) [36],
in order to be tested and subjected to a simulation using the MATLAB/Simulink process environment to
demonstrate its inherent capabilities. In the context of optimization, it is the performance index of the closed
loop system which becomes the fitness function. The goal is to have a short response time, a zero overshoot
and a steady state error close to zero. In this end, a multiple objective function that should be used depends
mainly on the ITAE and the IAE [37].
2. HEURISTIC ALGORITHMS
Induction motors (IM) are widely used in the industrial field, because they are robust, reliable,
compact and more efficient than other electrical motors. However, the main difficulties encountered in
controlling the induction motor reside in the coupling between flux and torque, as well as in the nonlinearity
of the mathematical model. The development in IM based electrical drive has manifested in the realization of
static converters, which respond to the speed of the fastest processors, as well as in the development of
efficient control algorithms. Among these, the Stator Flux Oriented Direct Torque Control (SFO-DTC) is
the most common method for variable frequency operation of IM. Nevertheless, an efficient design of fuzzy
logic controller (FLC) needs to be carried out by an expert with a very well knowledge of the system.
However, the inadequate performance provided by the traditional FLC to the SFO-DTC scheme is implicit in
its structure.
The idea suggested to solve this problem is to use heuristic algorithms such as PSO and SCSO.
The proposed new approach is based on the hybridization of these two algorithms to optimize the structure of
the membership functions with adequate normalization and denormalization gain values. This approach is
called PSCSO. In the following part, conventional FLC is briefly reviewed. The presentation of the two
algorithms, PSO and PSCO, is made with the development of this new PSCSO Algorithm.
2.1. Conventional fuzzy logic controller
A conventional fuzzy logic control includes three parts: fuzzification process, linguistic rule base, and
defuzzification process. The first input of the FLC is the error (e) between the controlled variable and its
reference value. The second is the error derivative (de). The integral of the increment control (U*
) is the output.
The input and output variables are replaced by their normalized values. Ke and Kde are the normalizing gains
which map the input variables into the range of [-1, 1]. KU is defined to map the de-normalized output value to
the actual output range.
The symmetric and equidistant triangular membership functions characterize the conventional FLC.
The membership functions are assigned with seven fuzzy sets which are NB (negative big), NM (negative
medium), NS (negative small), AZ (approximate zero), PS (positive small), PM (positive medium) and PB
(positive big), in ascending order as shown in Figures 2(a), 2(b) and 2(c). Table 1 represents the basic
linguistic rules which describe an FLC [9, 11, 14].
For the flux’s FLC, the input variables are the error between, the stator reference flux 𝜑𝑠
∗
, and the IM
estimated flux 𝜑̂ 𝑠 and its derivative. The output of this controller is the voltage vector 𝑣 𝑠𝑑
∗
. For the torque’s
FLC, the input variables are the error between the reference torque 𝑇𝑒
∗
, and the IM estimated electromagnetic
torque 𝑇̂𝑒 , and the error derivative. The output represents the voltage vector 𝑣𝑠𝑞
∗
. The speed’s FLC uses
the error between the reference speed 𝜔𝑟
∗
and the measured speed and its derivative, and its output represents
the reference torque vector 𝑇𝑒
∗
.
The fuzzy discourse universe is subdivided into seven zones involving 49 control rules [9].
The fuzzy rules are presented in Table 1. Mamdani’s min-max inference system has been selected for
the computation of the fuzzy decision. In the defuzzification step, the center of gravity method is used for
converting this decision into crisp value [2]. A trial-and-error method was used to determine
the normalization and denormalization gains of the three FLCs by numerical experiments. Table 2
summarizes the results obtained after several simulations.

Int J Elec & Comp Eng ISSN: 2088-8708 
A new design of fuzzy logic controller optimized by PSO-SCSO applied to SFO-DTC ... (Ali Taieb)
5815
Table 1. The fuzzy linguistic rule table for the three FLC’s (FLC-torque, FLC-flux and FLC-speed)
dU e
NB NM NS AZ PS PM PB
de
NB NB NB NB NB NM NS AZ
NM NB NB NB NM NS AZ PS
NS NB NB NM NS AZ PS PM
AZ NB NM NS AZ PS PM PB
PS NM NS AZ PS PM PB PB
PM NS AZ PS PM PB PB PB
PB AZ PS PM PB PB PB PB
Table 2. Normalization and denormalization gains found by trial and error method
Normalization and denormalization gains
𝑘 𝑝 𝑘 𝑑 𝑘 𝑢
FLC -Flux 0.95 0.021 3.15
FLC -Torque 0.15 0.015 1.5
FLC -Speed 156.08 0.857 0.2
2.2. PSO algorithm
Consider Swarm of Particles is flying through the parameter space and searching for optimum.
Each particle is characterized by its position vector or Pi (k) and its velocity vector vi (k). During the process
each particle will have its individual knowledge Pbest i.e. its own best –so- far in the position and social
knowledge gbest i.e., Pbest of its best neighbour. The velocity of each particle can be modified by the (1) [27]:
         1 2 31 . . . . .ii i best i best iv k C v k C rand P P k C rand g P k      (1)
where:
C1 : inertia weight
Rand : random number between 0 and 1
C2, C3 : acceleration constants
2.3. SCSO algorithm
While the structure of the sine-cosine based swarm optimization (SCSO) method, presented in [30],
calculates the velocity of each particle using the (2).
𝑣𝑖(𝑘 + 1) = {
Sin(2𝜋𝑟) ∗ (𝑃𝑏𝑒𝑠𝑡 𝑖
− 𝑝𝑖(𝑘)) , 𝑖𝑓 𝑟 < 0.5
Cos(2𝜋𝑟) ∗ (𝑃𝑏𝑒𝑠𝑡 𝑖
− 𝑝𝑖(𝑘)) , 𝑖𝑓 𝑟 > 0.5
(2)
where r is a random number in [0,1]. The current position (searching point in the solution space) can be
modified by the (3) [27, 30]:
𝑃𝑖(𝑘 + 1) = 𝑃𝑖(𝑘) + 𝑣𝑖(𝑘) (3)
2.4. Proposed FLC-PSCSO controller
During changes in the operating point, the conventional fuzzy logic controllers give acceptable
performance but are still insufficient. The fuzzy logic controllers, which have asymmetric and non-equidistant
membership functions, seem to provide improved performance. As infinity of structures with an asymmetric
membership functions exist, and the use of the trial-and-error method to find the optimal structure is laborious,
a new strategy based on a combination between the PSO algorithm and the SCSO algorithm is proposed to
overcome this problem. This approach is called PSCSO. The principle of FLC tuned by PSCSO algorithm is
shown in Figure 1.
The process takes place in two steps; first, the PSO algorithm begins to find the global optimum.
Then, to speed up the process, the SCSO algorithm takes over and ends the search process until the optimal
solution is obtained. The parameters of the algorithm with the iteration number are given in Table 3.
Here, ωref(k) is system input (the reference speed) , 𝑇𝑒
∗
(𝑘) is the output of FLC, which is used to control
the torque of SFO-DTC, ωr(k) is system output (the rotor speed).

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Linguisticrulebase
DEFUZZIFIER
FUZZIFIER
Ke
KdeS
KTe
SFO - DTC
IM
r
r *
eT*
edT
e
e

*
r
PSCSO
Algorithms
Multiple objective function
1
S
Figure 1. Proposed structure of the FLC-speed optimized by PSCSO algorithm for the SFO-DTC
Table 3. PSCSO algorithms parameters proposed
Swarm size particles 30
Neighborhood size for global 30
Nearest neighborhood 5
Coefficients of the algorithm C1=0.68, C2 = C3= 1.6
Number of iterations (Nmax) 300
2.4.1. Individual string definition
To apply the PSCSO method for searching the controller parameters, we defined ten controller
parameters 𝐾𝑒(𝑘) 𝐾𝑑𝑒(𝑘) 𝐾𝑢(𝑘) 𝑀1(𝑘) … 𝑀7(𝑘). Hence, there are ten members in an individual, which are
assigned as real values. If there are 30 individuals in a population, then the dimension of a population is
30x10. The matrix representation in a population is as follows.
𝑃𝑖(𝑘) = [ 𝐾𝑖_𝑒(𝑘) 𝐾𝑖_𝑑𝑒(𝑘) 𝐾𝑖_𝑢(𝑘) 𝑀𝑖_1(𝑘) … 𝑀𝑖_7(𝑘)] 𝑖 = 1,2, … ,30 (4)
According to equation (4), the vector Pi(k) regroups ten values and it subdivides into two essential
blocks. The first block is reserved for the normalization-denormalization gains for speed-FLC
(i.e. 𝐾𝑖_𝑒, 𝐾𝑖_𝑑𝑒 and 𝐾𝑖_𝑢); the second block is devoted to the parameters of the membership functions
speed-FLC (i.e. 𝑀𝑖_1,…, 𝑀𝑖_7). Figure 2 illustrates the general form of the Speed-FLC.
e
AZ PS PM PB
10
NB NM NS 1
1 1 212
Ge
de
AZ PS PM PB
10
NB NM NS 1
1 3 434
Gde
(a) (b)
ZE PS PM PB
0
1
1NSNMNB
5 6 7567
1
*
edT
*
edT

(c)
Figure 2. Parameters speed controller optimized by PSCSO algorithm,
(a) Error, (b) Derivative error, (c) Output membership functions

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2.4.2. Evaluation function definition
The multi-objective function (fitness) 𝐽𝑖 𝑜𝑏𝑗
(k) is the error function, which is defined as follows:
𝐽𝑖 𝑜𝑏𝑗
(k) = 𝐽𝑖 𝑜𝑏𝑗1
(𝑘) + 𝐽𝑖 𝑜𝑏𝑗2
(𝑘) (5)
𝐽𝑖 𝑜𝑏𝑗1
(𝑘) = 𝑁 𝜔 ∗ ∑ |𝜔𝑟
∗(𝑘) − 𝜔𝑟(𝑘)|𝑀
𝑘=1 = 𝑁 𝜔 ∑ |𝑒(𝑘)|𝑀
𝑘=1 (6)
(𝑘) = 𝑁 𝜔 ∗ ∑ 𝑘 ∗ |𝜔𝑟
∗(𝑘) − 𝜔𝑟(𝑘)|𝑀
𝑘=1 = 𝑁 𝜔 ∗ ∑ 𝑘 ∗ |𝑒(𝑘)|𝑀
𝑘=1 (7)
where:
(𝑘) : represent the Integral of absolute value of error (IAE).
(𝑘) : represent The Time Integral of absolute value of error (ITAE).
ωref(k)=f(k) represents second order function of zero overshoot with an imposed response time.
The function is applied to limit starting stator currents at full speed. While, Nω=p/(2*π*50) is
the normalization coefficient of the cost function. ITAE measures the steady state error [37], while IAE is
measure of a fast-dynamic response [37]. Each particle i represents a possible solution Pi(k). By minimizing
the multi-objective function Ji_obj by PSCSO algorithm, the optimal solution is found as well as
the performance of the speed FLC-PSCSO is improved. This paper presents a FLC-PSCSO controller for
searching the optimal or near optimal controller parameters 𝐾𝑒(𝑘) 𝐾𝑑𝑒(𝑘) 𝐾𝑢(𝑘) 𝑀1(𝑘) … 𝑀7(𝑘) with
the PSO algorithm, to speed up the process; the SCSO algorithm takes over and ends the search process until
the optimal solution is obtained. The searching procedures of the proposed PSCSO-FLC controller were
shown as follows:
- Step 1. Generate initial particles randomly in the search space.
𝑃𝑖(𝑘) = 𝑟𝑎𝑛𝑑(0,1) ∗ (𝑈𝐵𝑖(𝑘) − 𝐿𝐵𝑖(𝑘)) + 𝐿𝐵𝑖(𝑘) (8)
where 𝑈𝐵𝑖(𝑘) is upper bound, and 𝐿𝐵𝑖(𝑘) is lower bound.
Initialize inertia factor C1, weighting factors C2 and C3, max iteration Nmax=300, error (ɛ).
Evaluate Velocity 𝑣𝑖(𝑘) of each particle using (1). The current searching point is set to Pbest for each particle.
The best-evaluated value of Pbest is set to gbest and the particle number with the best value is stored.
- Step 2. Sample system input ωref(k) and system output ωr(k), comuting 𝐽𝑖 𝑜𝑏𝑗
(𝑘) in the moment of
sampling.
- Step 3. Evaluate searching points of each particle.
The multi-objective function value is calculated for each particle. If the value is better than
the current Pbest of the particle, the Pbest value is replaced by the current value. If the best value of Pbest is
better than the current gbest , then gbest is replaced by the best value and the particle number with the best value
is stored.
- Step 4. Modify each searching point.
The current searching point of each particle is changed using (1) and (3).
- Step 5. Check the exit condition.
The objective function (fitness) value is calculated for each particle according to (5-7).
𝑖𝑓 (( 𝐽𝑖 𝑜𝑏𝑗
(k) < ε ) 𝑜𝑟 (𝐽𝑖 𝑜𝑏𝑗
(k) − 𝐽𝑖 𝑜𝑏𝑗
(k − 1) < 0.001) 𝑜𝑟 iteration = 200),
then go to step 6, otherwise, continue iteration. Go to step 2.
The process starts with the PSO algorithm, when the search becomes slow, the SCSO algorithm is
automatically started to finalize the global optimization.
- Step 6. The near optimal values obtained by PSO are the initial values of the SCSO algorithm.
- Step 7. Generate r randomly. Range of r is [0, 1].
- Step 8. Modify each searching point.
The current searching point of each particle is changed using (2) and (3).
- Step 9. Evaluate all updated particles by using the multi-objective function.
- Step10. If particles exceed lower bound or upper bound, generate new particles in range of lower bound
and upper bound randomly.
- Step 11. Update Pbest.
- Step 12. Repeat steps 7 and 11 until the global optima is found or maximum iterations is reached.
(if fitness value of Pbest is gbest) or (reach the predetermined maximum iteration number iteration =Nmax).

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3. STATOR-FLUX-ORIENTED DIRECT TORQUE CONTROL STRATEGY (SFO-DTC)
For the Stator Flux Oriented Direct Torque Control (SFO-DTC), the stator flux vector is aligned
with d-axis and setting the stator flux to be constant equal to the rated flux, which means Φds=Φs and
Φqs=0. In a referential related to the rotating field, the dynamic model of the induction motor controlled by
SFO-DTC, as shown in Figure 3, is governed by the system of equations [36]:
𝑣 𝑠𝑑 =
𝐿 𝑠
𝑇0
(1 + 𝜎𝑇0 𝑠)𝑖 𝑠𝑑 − 𝜎𝐿 𝑠 𝜔 𝑠𝑙 𝑖 𝑠𝑞 −
𝜑 𝑠
𝑇𝑟
(9)
𝑣𝑠𝑞 =
𝐿 𝑠
𝑇0
(1 + 𝜎𝑇0 𝑠)𝑖 𝑠𝑞 + 𝜎𝐿 𝑠 𝜔 𝑠𝑙 𝑖 𝑠𝑑 + 𝜔𝑟 𝜑𝑠 (10)
𝜑𝑠 = 𝐿 𝑠
1+𝜎𝑇𝑟 𝑠
1+𝑇𝑟 𝑠
𝑖 𝑠𝑑 −
𝜎𝑇𝑟 𝐿 𝑠 𝜔 𝑠𝑙
1+𝑇𝑟 𝑠
𝑖 𝑠𝑞 (11)
𝜔 𝑠𝑙 =
𝐿 𝑠
𝑇𝑟
1+𝜎𝑇𝑟 𝑠
𝜑 𝑠−𝜎𝐿 𝑠 𝑖 𝑠𝑑
(12)
𝑇𝑒 =
3
2
𝑝𝜑𝑠
∗
𝑖 𝑠𝑑 (13)
The mechanical rotor speed equation is given by the following expression:
𝑑𝜔 𝑟
𝑑𝑡
=
1
𝐽 𝑚
(𝑇𝑒 − 𝑇𝑙) −
𝑓𝑣
𝐽 𝑚
𝜔𝑟 (14)
where: 𝜎 = (1 − 𝐿 𝑚
2
/𝐿 𝑠 𝐿 𝑟), 𝑇𝑠 = 𝐿 𝑠 𝑅 𝑠⁄ , 𝑇𝑟 = 𝐿 𝑟 𝑅 𝑟⁄ and 𝑇0 = 𝑇𝑠 𝑇𝑟/(𝑇𝑠 + 𝑇𝑟). From (11) and (13),
direct and quadrature stator currents are given by following expressions:
𝑖 𝑠𝑑 =
(1+𝑇𝑟 𝑠)
𝐿 𝑠(1+𝜎𝑇𝑟 𝑠)
𝜑𝑠 +
2𝜎𝑇𝑟 𝜔 𝑠𝑙
3𝑝𝜑 𝑠
∗(1+𝜎𝑇𝑟 𝑠)
𝑇𝑒 (15)
𝑖 𝑠𝑞 =
2
3𝑝𝜑 𝑠
∗ 𝑇𝑒 (16)
After some elementary calculation between (11) and (12) and under steady state conditions,
and by neglecting the term (𝜎𝑇𝑟 𝜔 𝑠𝑙)2
, slip speed obtained as:
𝜔 𝑠𝑙 ≈
𝐿 𝑠
(1−𝜎)𝜑 𝑠 𝑇𝑟
𝑖 𝑞𝑠 (17)
By considering equations (9), (10), (15) and (16), and by neglecting the same term (𝜎𝑇𝑟 𝜔 𝑠𝑙)2
, it can
be noticed that 𝑣 𝑠𝑑 and 𝑣𝑠𝑞 are coupled, where the coupling terms are (2σLsωsl Te)/3pφs
∗
and
−(𝜎𝜔 𝑠𝑙(1 + 𝑇𝑟 𝑠)/(1 + 𝜎𝑇𝑟 𝑠) + 𝜔𝑟)𝜑𝑠 respectively. The aforementioned two terms are considered to be
disruption; therefore, they can be eliminated by using a method known as decoupling by compensation term
which results in the following system of equations:
{
𝑣 𝑠𝑑1 = 𝑣 𝑠𝑑 + 𝐸 𝑑 = (
(1+𝜎𝑇0 𝑠)
𝑇0
(1+𝑇𝑟 𝑠)
(1+𝜎𝑇𝑟 𝑠)
−
1
𝑇𝑟
) 𝜑𝑠
𝑣 𝑠𝑞1 = 𝑣𝑠𝑞 + 𝐸 𝑞 ≈
(1+𝜎𝑇0 𝑠)
𝑇0
2𝐿 𝑠
3𝑝𝜑 𝑠
∗ 𝑇𝑒
(18)
where: Ed and Eq are the direct and quadrature back electromotive forces (EMF). Where:
{
𝐸 𝑑 =
2𝜎𝐿 𝑠 𝜔 𝑠𝑙
3𝑝𝜑 𝑠
∗ 𝑇𝑒
𝐸 𝑞 = (
𝜎𝜔 𝑠𝑙(1+𝑇𝑟 𝑠)
(1+𝜎𝑇𝑟 𝑠)
+ 𝜔𝑟) 𝜑𝑠
(19)
{
𝜃𝑠 = 𝜃𝑟 + 𝜃𝑠𝑙
𝜔𝑠 = 𝜔𝑟 + 𝜔 𝑠𝑙
𝜃𝑠 = 𝜔𝑠 𝑡
(20)
where, 𝜃𝑠 and 𝜔𝑠 are the position and stator angular velocity, and 𝜃𝑠𝑙 and 𝜔 𝑠𝑙 are the position and slip
angular velocity respectively.

5819
The block diagram of the SFO-DTC based on three controllers (hereafter, speed, flux and torque
controllers) is illustrated in Figure 4. From the system of (18), it can be seen that the voltage equations of
the d-axis and the q-axis are strongly coupled. It should be noted that the induction motor model is nonlinear
and its variables are interdependent. Therefore, the use of conventional fuzzy controllers can solve this
problem. Two conventional fuzzy controllers based on triangular membership functions are used for the three
control magnitudes (which are torque, flux, and speed).
axis 
axis
d
axis

q
axis

sl
axis
mechanical
s
r
sd
s


Figure 3. Vector diagram of SFO-DTC
PWM
generator



*
asV
*
bsV
*
csV
abi
*
s
*
eT
sˆ
eTˆ
1sdv
1sqv
sdv
sqv
sdi
sqi
Fe
Te
FLC
Flux
FLC
Torque
s
Equations11,13,17,18and19
Figure 4. Block diagram of the induction motor SFO-DTC
4. SIMULATION RESULTS
Simulations were carried out under the MATLAB/Simulink environment. The IM’s parameters are
illustrated in appendix. The PSCSO algorithm is applied to the control system under nominal conditions.
The initial setting parameters of PSCSO are given in Table 3. A full-speed startup of 157 rd/s is given to
the system drive. Full load of 10 Nm is applied at 1s, then; this load is completely removed at 2 s, while this
simulation is carried out till 3s.
As shown in Figure 5, the PSCSO algorithm is able to find a good optimal solution after only 267
iterations despite the high number of parameters to be optimized (ten parameters). Table 4 gives the optimal
values of Normalization gains and optimal values of membership functions parameters of the speed-FLC
found by PSCSO algorithm after 300 iterations. Figure 6 gives to the influence of the speed-FLC optimized
by PSCSO on the performance of the system in both transient and steady state conditions. The starting
transient performance of the induction motor under the different controllers’ types is shown in Figure 6.
FLC-PSCSO has the best transient response where the motor speed is approximately built up in less than 0.5
s without overshoot.

 ISSN: 2088-8708
5820
Table 4. Optimal values of normalization gains and membership functions parameters of the speed-FLC
Normalization-denormalization gains
Ke Kde Ku
146.000117 0.342356 0.20000
Parameters for each membership functions
Error (𝒆) Derivative of error (de) Output (𝑑𝑇𝑒)
M1 M2 M3 M4 M5 M6 M7
0.01 0.02 0.1639 0.3509 0.50000 0.7000 0.9500
Figure 5. Algorithm speed convergence Figure 6. FLC and FLC-PSCSO controller response
On the other hand, conventional FLC can provide the same response time but with a speed
overshoot of 10.2%. The FLC-PSCSO provide a robust control compared to conventional FLC when a load
of 10 Nm is applied to the induction motor at 1 s, since the induction motor’s speed controlled by these
controllers (FLC-PSCSO) drops initially to 141.6 rd/s at 1 s, then it has been adjusted back to the reference in
only 0.11s. While conventional FLC shows a speed drop to 120.8 rd/s and 0.5s to re-adjust the speed to
the reference. Table 5 gives more illustrations about the performance of FLC-PSCSO and conventional FLC.
According to Figure 7 and Table 5, it can be noticed that the ITAE and Jobj of conventional FLC is very high
compared to those of FLC-PSCSO. Moreover, FLC-PSCSO has very low values of speed overshoot, steady
state error and settling time compared to conventional FLC.
Table 5. Summary of results for FLC and FLC-PSCSO
Conventional FLC FLC-PSCSO
ITAE ϵ [0s, 1.5s] 0.052554 0.018940
Jobj ϵ [0s, 1.5s] 137.5475 19.1335
Speed overshoot (%) 9.26 0.64
Steady state error (%) 136.778 19.0348
Figure 7. ITAE with normal operating conditions
0 0.5 1 1.5
0
50
100
150
200
T ime ( s)
Speeds(rd/s)
FLC -PSCSO
Ref speed
FLC conventiona l
0 0.5 1 1.5
0
0.01
0.02
0.03
0.04
0.05
0.06
T i m e ( s )
ITAE
F L C - C o n v e n t i o n a l
FLC - P S C S O

5821
4.1. Robustness test
Various tests are conducted in this sub-section in order to evaluate the performance of FLC-PSCSO
when the parameters of the induction motor, such as the stator’s resistance and the moment of inertia,
varies because of drift in their magnitudes or because a bad identification of the induction motor. In the first
test, the parametric variation takes into consideration the stator’s resistance that up to 100% of its initial
value. While in the second test the moment of inertia Jm is up to 100% of its initial value. In both tests,
the induction motor is loaded and unloaded at 1s and 1.5s, respectively, by 50% of rated load, see Figure 8
and Figure 9.
Figure 8. Response FLC-PSCSO with variation
of Rs (Rs=2*Rsn)
Figure 9. Response FLC-PSCSO with variation
of Jm (Jm=2*Jmn)
In order to evaluate the tracking performance, a test is conducted by varying the speed reference with
a step of 50 rad/s at t=0, followed by a change of speed from 100 rad/s to 150 rad/s at 1s and 1.5s respectively as
shown in Figure 10. The observation of the obtained results permits making the following interpretations:
the most notable changes are those observed during changes in stator resistance. This is in accordance with
the fact that SFO-DTC control is mainly sensitive to the variations of this resistance at low speeds. A better
tracking is detected during the observation of the behavior changes of the optimized FLC-PSCSO, despite
the large variations applied. Indeed, the tracking error remains very low and the disruption are rejected very
quickly. It can therefore be said that the FLC-PSCSO is robust in controlling induction motors.
Figure 10. Speed change reference from 50 rd/s to 100 rd/s at 150 rd/s
5. CONCLUSION
In this paper, we have highlighted the improvement in the performance of FLC controllers
optimized by PSCSO algorithm, compared to other controllers, namely conventional FLC. Simulation results
showed a remarkable behavior of the FLC controller optimized by PSCSO in regulation and tracking, a much
better disturbance rejection than for conventional FLC controllers, and a very good performance with respect
to robustness. Thus, the use of such an optimization solution by PSCSO algorithm makes it possible to
exploit rationally the advantages of the conventional FLC controllers and to avoid their disadvantages.
0 0.5 1 1.5 2 2.5
-150
-100
-50
0
50
100
150
T i m e ( s )
Speed(rd/s)
R s = R s n
R s = 2 *R s n
R e f S p e e d
0 0.5 1 1.5 2 2.5
-150
-100
-50
0
50
100
150
T i m e ( s)
Speed(rd/s)
J = J n
J = 2 *J n
R e f sp e e d
0 0.5 1 1.5
0
50
100
150
T i m e ( s )
Speed(rd/s)
S p e e d F L C - P S C S O
R e f s p e e d

 ISSN: 2088-8708
5822
Generally, the PSCSO off-line tuning process is simple but may need a lot of time to converge to
the optimal solution, depending on the complexity of the drive system and as the choice of the PSCSO
parameters. To reduce the convergence time, the research domain and the particles number as well as
the stopping criterion must be carefully selected to form an adaptive algorithm.
APPENDIX
The parameters of the IM used in simulations are given in Table 6.
Table 6. Electrical and mechanical parameters
Rated power = 1.5Kw. Stator inductances Ls = 0.3312 H,
Rated frequency = 50Hz. Mutual inductance Lm = 0.3183 H,
Rated line voltage U = 380 V Moment of inertia Jmn = 0.0097 Kg.m2
,
Rated speed=1460 Tr/min. Viscous friction coefficient fv=0.00054085 Ns/rad.
Stator resistance Rs = 5.2177 Ω. Pole pairs p = 2
Rotor time constant Tr=0.1 sec.
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BIOGRAPHIES OF AUTHORS
Ali Taieb was born in Medea, Algeria, in 1969. He’s a member of ECME team working on
electrical machine control in the SET laboratory (LABSET) Saad Dahleb of Blida (USDB1).
He graduated as a communications engineer in 1996 from the Department of Electonic of
Saad Dahleb Blida University (USDB1). He has obtained a “Magister” degree in signals and
systems in 2009 at the USDB1. He is currently pursuing a doctorate in Sciences. His current
research focuses on the application of intelligent techniques (neural networks, fuzzy logic,
genetic algorithms, and Particle swarm optimization) in induction motor control.
Abdellaziz Ferdjouni is an Assistant Professor at University Saad Dahleb of Blida 1
(USDB1), Algeria. He is a member of ECME team working on electrical machine control
and diagnostic in the LABSET laboratory in USDB1. He received the “Ingénieur d’état”
degree from the “Ecole Nationale Polytechnique (ENP)” Algiers, Algeria in 1986, the
“Magister” and “doctorat d’état” degrees in Control from the USDB1 1994 and 2007. His
main research interests include Control and Diagnostic of electric machines, nonlinear
systems and chaos.

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