Control of a servo-hydraulic system utilizing an extended wavelet functional link neural network based on sine cosine algorithms

Indonesian Journal of Electrical Engineering and Computer Science
Vol. 25, No. 2, February 2022, pp. 847~856
ISSN: 2502-4752, DOI: 10.11591/ijeecs.v25.i2.pp847-856  847
Journal homepage: http://ijeecs.iaescore.com
Control of a servo-hydraulic system utilizing an extended
wavelet functional link neural network based on sine cosine
algorithms
Shaymaa Mahmood Mahdi, Omar Farouq Lutfy
Department of Control and Systems Engineering, University of Technology-Iraq, Baghdad, Iraq
Article Info ABSTRACT
Article history:
Received Sep 25, 2021
Revised Nov 30, 2021
Accepted Dec 9, 2021
Servo-hydraulic systems have been extensively employed in various industrial
applications. However, these systems are characterized by their highly
complex and nonlinear dynamics, which complicates the control design stage
of such systems. In this paper, an extended wavelet functional link neural
network (EWFLNN) is proposed to control the displacement response of the
servo-hydraulic system. To optimize the controller's parameters, a recently
developed optimization technique, which is called the modified sine cosine
algorithm (M-SCA), is exploited as the training method. The proposed
controller has achieved remarkable results in terms of tracking two different
displacement signals and handling external disturbances. From a comparative
study, the proposed EWFLNN controller has attained the best control precision
compared with those of other controllers, namely, a proportional-integral-
derivative (PID) controller, an artificial neural network (ANN) controller, a
wavelet neural network (WNN) controller, and the original wavelet functional
link neural network (WFLNN) controller. Moreover, compared to the genetic
algorithm (GA) and the original sine cosine algorithm (SCA), the M-SCA has
shown better optimization results in finding the optimal values of the
controller's parameters.
Keywords:
Functional link neural network
PID controller
Servo-hydraulic system
Sine cosine algorithm
Wavelet neural network
This is an open access article under the CC BY-SA license.
Corresponding Author:
Omar Farouq Lutfy
Department of Control and Systems Engineering, University of Technology
Baghdad, Iraq
Email: omar.f.lutfy@uotechnology.edu.iq
1. INTRODUCTION
Servo-hydraulic systems are essential operating units in many industrial applications due to their
high precision, low operating temperatures, low noise, and good repeatability. Moreover, servo-hydraulic
systems can attain energy savings of up to 70% compared to other conventional hydraulic systems [1].
However, these systems are characterized by their highly complex and nonlinear dynamics, and hence, they
require precise and powerful controllers to cope with the complexity and nonlinearity of such systems.
The proportional-integral-derivative (PID) controller is one of the most widely used controllers in
the industry due to its simple structure and satisfactory performance. Therefore, this controller was broadly
employed to control the servo-hydraulic systems. For instance, Wart et al. [2] utilized the PID controller for
the position control of an electro-hydraulic system. As the tuning method, the authors used the Ziegler-
Nichols approach to optimize the gains of the PID controller. In another work, Lin et al. [1] proposed a
method to control the velocity-pressure switchover point in a servo-hydraulic system using the PID
controller. As an intelligent tuning method, Mahdi [3] used the ant colony optimization to find the optimal
settings for the PID controller's gains to control a servo-hydraulic system whose model was linearized to

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Indonesian J Elec Eng & Comp Sci, Vol. 25, No. 2, February 2022: 847-856
848
simplify the control design procedure. Following the same control design, many researchers used different
tuning methods to find the optimal gains of the PID controller [4]-[11]. However, in the above-mentioned
works, it is worth noticing that controlling the highly complex and nonlinear hydraulic systems by the linear
PID controller might not give the best control results, especially when the complex and nonlinear system's
model is linearized around a specific operating condition, which means that the controller can perform well
only for certain operating conditions and not for other conditions.
To handle this limitation, many researchers employed various computational intelligence techniques
to directly control the complex and nonlinear models of the servo-hydraulic systems without the need to
make certain simplifications or linearization for the systems models. Among these intelligent techniques,
artificial neural networks (ANNs) have been successfully applied to control hydraulic systems. For example,
Gao et al. [12] exploited the radial basis function neural network (RBFNN) to control a servo-hydraulic
system. The gradient descent (GD) method was used to update the parameters of the RBFNN. Utilizing the
model reference adaptive control structure, Yao et al. [13] proposed a control strategy that employs an ANN
for the tracking control problem of a servo-hydraulic system. The ANN weights were optimized using a GD
procedure. In another work, Diontar et al. [14] proposed to use the nonlinear auto-regression moving average
(NARMA) network, which is a type of ANNs, for the position tracking of a hydraulic system using the GD
method to optimize the controller's parameters. However, GD techniques have certain limitations including
the slow convergence speed, the inclination to getting stuck in local minimum points, and the difficulty of
choosing a suitable learning rate [15]. These limitations can be avoided by adopting evolutionary algorithms
(EAs) for the optimization task. In particular, EAs can offer remarkable optimization results, as they can
escape local minima and find a global solution.
Among several ANN structures, wavelet neural networks (WNNs) that utilize wavelet transform
[16]-[18] and functional link neural networks (FLNNs) have distinctive approximation abilities that qualify
them to be effective tools for solving different modeling and control problems. To attain better performance,
the features of both the WNN and the FLNN can be combined to realize a more powerful structure with
better approximation ability [19]-[21].
This paper presents an extended wavelet functional link neural network (EWFLNN) controller to
control the servo-hydraulic system. A recently developed EA method, which is called the modified sine
cosine algorithm (M-SCA) was applied to optimize the parameters of the EWFLNN controller, which has
shown its superiority over other related controllers in controlling the servo-hydraulic systems. The rest of the
article is organized according to the following sections: section 2 describes the mathematical modeling of the
servo-hydraulic system. The structure of the proposed EWFLNN controller is highlighted in section 3.
Section 4 sheds some light on the M-SCA. The results of the control performance test along with those of
two comparative studies are presented and discussed in section 5. Finally, section 6 gives the main
conclusions of the present work.
2. MATHEMATICAL MODELLING OF THE SERVO-HYDRAULIC SYSTEM
A servo-hydraulic system has several components that are related to each other, as shown in
Figure 1. The main working principle is to use a pressurized liquid to control the displacement, velocity, and
acceleration of the system's cylinder that starts from tacking the oil from the tank and pressurizes it to control
its flow rate through the servo valve reaching the cylinder chambers, where the oil's pressure is transformed
into a mechanical force to implement the piston motion for a specific distance. This mechanism is explained
in the following sections.
Figure 1. The servo-hydraulic system schematic diagram

Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 
Control of a servo-hydraulic system utilizing an extended wavelet functional … (Shaymaa Mahmood Mahdi)
849
2.1. Dynamic equations of the hydraulic cylinder
The mathematical model of the hydraulic cylinder depends on Newton’s second law of moving a
mass load and taking into consideration the friction forces, as in the [4],
𝑦𝑎
̈ =
1
𝑀𝐿𝑜𝑎𝑑
( 𝑃𝑐ℎ1 𝐴𝑐ℎ1 − 𝑃𝑐ℎ2 𝐴𝑐ℎ2 − 𝐹𝑓𝑟), (1)
where (𝑦𝑎) is an unknown parameter representing the position of the cylinder piston's load, (𝑀𝐿𝑜𝑎𝑑)
represents the mass of the piston's load, and (𝑃𝑐ℎ1) and (𝑃𝑐ℎ2) denote the hydraulic cylinder's pressures of
Chamber 1 and Chamber 2, respectively. In this work, (𝐹𝑓𝑟), which represents the friction in the hydraulic
cylinder, is accounted for as an external force.
The LuGre model is used to represent the equations of the friction, as given in the [4],
dz
dt
= 𝑦𝑎
̇ −
|y𝑎
̇ |
g(y𝑎
̇ )
z (2)
𝑔(𝑦𝑎
̇ ) =
1
𝜎𝑠𝑡
(F𝑐𝑜𝑙 + (F𝑠𝑡 – F𝑐𝑜𝑙) 𝑒
− (
𝑦𝑎
̇
𝑉𝑠𝑡𝑟
)
2
) (3)
𝐹𝑓𝑟 = 𝜎𝑠𝑡 𝑧 + 𝜎𝑑𝑎𝑚𝑝
𝑑𝑧
𝑑𝑡
+ 𝑉
𝑓 𝑦𝑎
̇ (4)
where (𝑦𝑎
̇ ) signifies cylinder piston's velocity, Ffr represents the friction force that is defined by a linear
combination of (z), (
dz
dt
), and the viscous friction. In (4) is the friction's dynamics. The variable (z) represents
an internal state, 𝑔(𝑦𝑎
̇ ) defines part of the ‘‘steady-state” characteristics for motions of constant velocity,
𝑉𝑠𝑡𝑟 denotes the Stribeck velocity, 𝐹𝑠𝑡 denotes the static friction, 𝐹𝑐𝑜𝑙 is the Coloumb friction, and 𝑉
𝑓 is the
viscous friction. As a result, the final friction model is defined by four static parameters, two dynamic
parameters, the coefficient of stiffness (𝜎𝑠𝑡), and coefficient of damping (𝜎𝑑𝑎𝑚𝑝).
2.2. Calculations of pressure for the chambers within the cylinder
The equation of pressures in the cylinder chambers are calculated based on the equations of flow
continuity for the servo-valve in the volume between the orifices and their outlets, as given [4],
𝑃̇𝑐ℎ1 =
𝛽𝑒1
𝑣𝑐ℎ1
(− 𝑄𝑓𝑙1 + 𝐴𝑐ℎ1 𝑦𝑎
̇ − 𝑄𝐼𝐿 − 𝑄𝐸𝐿1) (5)
𝑃̇𝑐ℎ2 =
𝛽𝑒2
𝑣𝑐ℎ2
(− 𝑄𝑓𝑙2 + 𝐴𝑐ℎ2 𝑦𝑎
̇ − 𝑄𝐼𝐿 − 𝑄𝐸𝐿2) (6)
where (𝑄𝐼𝐿) is the internal leakage flow, (𝑄𝐸𝐿1) and (𝑄𝐸𝐿2) denote external leakage flows, (𝐴𝑐ℎ1) and (𝐴𝑐ℎ1)
signify areas of the cylinder's piston of Chamber 1 and Chamber 2, respectively, (𝑣𝑐ℎ1) and (𝑣𝑐ℎ2) represent
volumes between each side of the cylinder’s chambers, and (𝛽𝑒1) and (𝛽𝑒2) represent bulk modulus for the
hydraulic fluids in each side of the piston, respectively.
Volumes' calculations for each cylinder chamber are represented in the equations,
𝑣𝑐ℎ1 = 𝐴𝑐ℎ1 𝑦𝑎 + 𝑉𝑜1 (7)
𝑣𝑐ℎ2 = 𝐴𝑐ℎ2 (𝐿 − 𝑦𝑎) + 𝑉𝑜2 (8)
where (𝑉𝑜1) and (𝑉𝑜2) denote volumes of the pipeline at Ports 1 and 2, respectively, and L denotes the length
of the stroke.
2.3. Flow-pressure equations of the servo valve
The servo valve flow rate equations are considered nonlinear equations described by the relationship
between the servo valve spool displacement (𝑦𝑠) and the pressure drop, as given,
𝑄𝑓𝑙1 = {
𝐶𝑠 𝑦𝑠 √𝑃
𝑠𝑢𝑝 − 𝑃𝑐ℎ1 , 𝑉𝑖𝑛 ≥ 0
𝐶𝑠 𝑦𝑠 √𝑃𝑐ℎ1 − 𝑃𝑡𝑎𝑛𝑘 , 𝑉𝑖𝑛 < 0
(9)
𝑄𝑓𝑙2 = {
𝐶𝑠 𝑦𝑠 √𝑃𝑐ℎ2 − 𝑃𝑡𝑎𝑛𝑘 , 𝑉𝑖𝑛 ≥ 0
𝐶𝑠 𝑦𝑠 √𝑃
𝑠𝑢𝑝 − 𝑃𝑐ℎ2 , 𝑉𝑖𝑛 < 0
(10)

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where (𝑃𝑠𝑢𝑝) and (𝑃𝑡𝑎𝑛𝑘) represent the supply and the tank pressure, respectively, and (𝐶𝑠) represents a
parameter that includes the discharge coefficient and the fluid density.
Considering low frequencies of up to 50 Hz, a model of first-order representation can adequately
describe the spool dynamics. More precisely, the connection between the position of the spool (𝑦𝑠) and the
input voltage (𝑉𝑖𝑛) is described by the (11),
𝐺𝑠(𝑠) =
𝑦𝑠
𝑉𝑖𝑛
=
𝑥𝑠𝑑𝑣
𝑠+ 𝑥𝑡
, (11)
where (𝑥𝑠𝑑𝑣) denotes the gain's value, and (𝑥𝑡) denotes the time constant.
3. THE EXTENDED WAVELET FUNCTIONAL LINK NEURAL NETWORK (EWFLNN)
CONTROLLER
In this work, the servo-hydraulic system described above is controlled using the control structure
shown in Figure 2, in which the EWFLNN acts as a PID-like feedback controller whose parameters can be
adjusted by the M-SCA. In particular, the EWFLNN receives three input signals, namely; the control error
e(k), the rate of change in error Δe(k), and the summation of errors Σe(k). As the actuating signal, the
EWFLNN controller generates the control input u(k) to manipulate the displacement response of the servo-
hydraulic system. The controller's parameters are optimized by the M-SCA based on minimizing the integral
square of errors (ISE) criterion given in (12),
𝐼𝑆𝐸 =
1
2
∑ 𝑒2
𝑁
𝑘=1 (𝑘) (12)
where 𝑒(𝑘) = 𝑦𝑑(𝑘) − 𝑦𝑎(𝑘), N is the number of samples, 𝑦𝑑(𝑘) is the desired displacement, and 𝑦𝑎(𝑘), is
the actual system's displacement at time sample k.
To improve the approximation performance of a previously developed structure [21], a modification
was made in this work by adding the input variables together with a bias weight to the output node, as
illustrated in Figure 3, which depicts the proposed EWFLNN structure. Particularly, the input variables are
connected through the adjustable parameters 𝑎1, 𝑎2, . . . , 𝑎𝑁𝑖while the bias weight is connected through the
adjustable parameter b, as shown in Figure 3. This modification has significantly enhanced the approximation
accuracy of the resulting network compared to the original structure in controlling the servo-hydraulic
system, as will be seen in the comparative study of section 5.2.
Figure 2. A block diagram of the control structure to control the servo-hydraulic system
Figure 3. Structure of the EWFLNN controller

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Referring to Figure 3, the proposed EWFLNN structure is composed of three layers including a
functional expansion layer, a wavelet layer, and an output layer. Particularly, the functional expansion layer
is responsible for increasing the dimensions of the input space utilizing trigonometric function terms, as
described by (13),
𝜙 = [𝜙1, 𝜙2, . . . , 𝜙𝑁𝑤] = [𝑥1, cos(𝜋𝑥1), 𝑠𝑖𝑛(𝜋𝑥1), . . . , 𝑥𝑁𝑖, cos(𝜋𝑥𝑁𝑖) , 𝑠𝑖𝑛(𝜋𝑥𝑁𝑖1)], (13)
where 𝑁𝑤 and 𝑁𝑖 denote the number of functional expansion terms and the number of input variables,
respectively. Subsequently, each output from this layer enters a wavelet node in the wavelet layer, which
performs the following operator,
𝑧𝑗 = 𝑑𝑗 𝜙𝑗 − 𝑡𝑗 , (14)
where j = 1, 2, …, 𝑁𝑤, 𝑑𝑗and 𝑡𝑗 signify the dilation and the translation factors of the jth node in the wavelet
layer, respectively, and 𝜙𝑗 denotes the jth output resulting from the functional expansion layer. After that, the
RASP1 wavelet function was employed to compute the output of each node in the wavelet layer according to
the following expression,
𝜓𝑗(𝑧𝑗) =
𝑧𝑗
(𝑧𝑗
2+1)2 , (15)
where 𝑧𝑗 represents the result of (14). Next, the output of each wavelet node is connected to the output node
via a unity weight. Finally, the output node produces the network's output as given (16).
𝑦 = ∑ 𝜓𝑗
𝑁𝑤
𝑗=1 + ∑ 𝑎𝑖 𝑥𝑖 + 𝑏
𝑁𝑖
𝑖=1 , (16)
4. THE MODIFIED SINE COSINE ALGORITHM
The sine cosine algorithm (SCA) is a stochastic population-based technique that was developed by
Mirjalili in 2016 [22]. As an effective evolutionary search algorithm, the SCA has been successfully applied
for handling various optimization problems [23]-[25]. In this work, a modified version of the original SCA,
which was developed in [21], was exploited to train the EWFLNN controller. This algorithm was called the
M-SCA and it has shown superior optimization results compared with other algorithms, including the
original SCA. More specifically, the M-SCA was applied for optimizing the parameters of the EWFLNN
controller according to the following procedure:
- Step 1: Initialize the maximum number of iterations and the number of candidate solutions in the M-SCA.
- Step 2: Generate randomly the candidate solutions representing the modifiable parameters of the controller.
- Step 3: In this step, the cost function defined in (12) is calculated for each solution.
- Step 4: Find the best solution compared to other solutions. This solution is assigned as the destination point.
- Step 5: In this step, the values of four random parameters 𝑟1, 𝑟2, 𝑟3, and 𝑟4 are updated.
- Step 6: The position of each candidate solution is updated according to the following equation.
𝑋𝑖
𝑡+1
= {
𝑋𝑖
𝑡
+ 𝑟1 × 𝑠𝑖𝑛(𝑟2) × |𝑟3 𝑃𝑖
𝑡
− 𝑋𝑖
𝑡|, 𝑟4 < 0.5
𝑋𝑖
𝑡
+ 𝑟1 × 𝑐𝑜𝑠(𝑟2) × |𝑟3 𝑃𝑖
𝑡
− 𝑋𝑖
𝑡|, 𝑟4 ≥ 0.5
(17)
Where 𝑋𝑖
𝑡
denotes a solution position in the ith dimension at the t th iteration, 𝑟2, 𝑟3, and 𝑟4 represent random
variables, 𝑃𝑖 is the position of the destination point in the i th dimension, and | | is the absolute value. The
variable 𝑟1 decides the next movement's direction of each solution according to the position of the destination
point P. To achieve an appropriate balance between the exploration and the exploitation abilities of the
algorithm, 𝑟1 is computed adaptively using (18),
𝑟1 = 𝑎 − 𝑡
𝑎
𝑇
(18)
where a is a constant, t is the current iteration, and T is the maximum number of iterations. On the other
hand, the values of 𝑟2, 𝑟3, and 𝑟4 are generated randomly from the intervals [0, 2 π], [0, 2], and [0, 1],
respectively [22].
- Step 7: In this step, the solutions are ranked according to their cost function starting from the solution
with the best cost function to the solution with the worst cost function.
- Step 8: Substitute the worst n solutions by n new solutions, where n was set to 20 in this work, and the
solutions were produced according to the (19),

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𝑋𝑖,𝑗
𝑡+1
= 𝑃𝑗
𝑡
+ 𝜇𝑖,𝑗 (𝑋𝑚1,𝑗
𝑡
− 𝑋𝑚2,𝑗
𝑡
) (19)
where i indicates the position and j indicates the dimension of solution X, P is the best solution, 𝑚1 and 𝑚2
are two integer numbers randomly chosen between 1 and the maximum number of solutions and they should
also be different from the current solution's position, i, and 𝜇𝑖,𝑗 is a random number generated from [-1, 1].
- Step 9: A solution is randomly generated in this step and its cost function is calculated. If the cost
function is worse than that of the worst solution, the worst solution is substituted by the position of the
destination point. Otherwise, the newly generated solution replaces the worst solution.
- Step 10: If the maximum number of iterations is reached, the algorithm is stopped and the best solution
achieved so far is utilized as the optimized parameters of the EWFLNN controller. Otherwise, the above
procedure is repeated starting from Step 3.
5. SIMULATION RESULTS
This section aims at assessing the control accuracy of the proposed EWFLNN controller to control
the servo-hydraulic system described in section 2. As the training algorithm, the M-SCA was applied using
60 solutions and 30 iterations for all the controllers considered in this section. These settings were sufficient
to attain the required control performance.
5.1. Control performance tests
To evaluate the performance of the proposed EWFLNN controller, several simulation tests were
conducted using the mathematical model of the servo-hydraulic system described in section 2. For this
purpose, an M-file in the Matlab software was utilized to optimize the controller parameters, while the
nonlinear servo-hydraulic system's model with the servo valve was implemented using the Simulink
environment, as illustrated in Figure 4. Figure 5 depicts the open-loop response of the servo-hydraulic
system's model described in section 2 using the parameters' values listed in Table 1 [4].
Figure 4. A block diagram of the servo-hydraulic system in Simulink
Figure 5. The open-loop displacement response of the servo-hydraulic system

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Table 1. Parameters’ values of the servo-hydraulic system [4]
Parameter value
Area of Chamber 1 (𝐴𝑐ℎ1) 8.04 × 10−4
𝑚2
Area of Chamber 2 (𝐴𝑐ℎ2) 4.24 × 10−4
𝑚2
Mass load (𝑀𝐿𝑜𝑎𝑑) 210 kg
Piston's length (L) 1 m
Pressure of the supply (𝑃𝑠𝑢𝑝) 14 MPa
Pressure of the tank (𝑃𝑡𝑎𝑛𝑘) 0.9 MPa
Columbic friction (𝐹𝑐𝑜𝑙) 247.804 N
Static friction (𝐹𝑠𝑡) 7485.084 N
Viscous friction (𝑉𝑓) 376.613 Ns/m
Stribeck velocity (𝑉𝑠𝑡𝑟) 0.026318 m/s
Figure 5 clearly indicates that the system has an unstable open-loop response. Therefore, the
proposed EWFLNN controller was applied to control this system. In particular, two control performance tests
were conducted to assess the control result of the EWFLNN controller to make the output of the servo-
hydraulic system follow two different reference signals. Figure 6 demonstrates the system's response in
tracking the first reference signal, which is a changing step signal. As it is evident from Figure 6, the
EWFLNN controller has achieved remarkable control accuracy with zero steady-state error. Figure 7 shows
the output response of the servo-hydraulic system controlled by the EWFLNN controller to track another
reference signal. Figure 7 clearly demonstrates that the controller has done well in following the desired
signal with zero-steady state error.
Figure 6. The servo-hydraulic system response for the first reference input
Figure 7. The servo-hydraulic system response for the second reference input
In order to assess the controller's robustness ability, a disturbance test was performed by injecting an
external disturbance of (+0.4) for the period from 4 to 5 seconds and (-0.4) for the period from 5 to 6
seconds. Figure 8(a) depicts the result of this test. Moreover, Figure 8(b) shows the output response for the

 ISSN: 2502-4752
854
same disturbance of Figure 8(a) plus a uniform random disturbance that continues for the entire simulation
time. From both Figurs 8(a) and (b) it can be seen that the controller was able to suppress the effect of the
disturbance and it brought the system's response back to the desired reference signal.
(a)
(b)
Figure 8. The servo-hydraulic system response in handling: (a) the ∓ 0.4 external disturbance and
(b) both the ∓ 0.4 external disturbance and the ∓ 0.1 uniform random disturbance
5.2. A comparsion study with other types of controllers
In this section, the control performance of the EWFLNN controller was compared with those of
other controllers including, a proportional-integral-derivative (PID) controller, an artificial neural network
(ANN) controller, a wavelet neural network (WNN) controller, and the original wavelet functional link
neural network (WFLNN) controller. All the above controllers were trained by the M-SCA with the same
settings mentioned in section 5. In order to take the stochastic nature of the M-SCA into consideration, 10
runs were carried out for each controller and the average result was adopted. Table 2 displays the outcome of
the comparative study. From Table 2, it is obvious that the EWFLNN controller has resulted in the best
control accuracy in terms of achieving the least value for the ISE cost function. In this regard, it is worth
noticing that the proposed modification made in the EWFLNN has significantly improved the performance of
the original WFLNN controller.
Table 2. Comparison results of the PID, the ANN, the WNN, the original WFLNN, and the proposed
EWFLNN controller
Controller type ISE Criterion (average of 10 runs)
PID controller 7.27 × 10−5
ANN controller 64.22 × 10−5
WNN controller 33.13 × 10−5
WFLNN controller 121.21 × 10−5
EWFLNN controller 5.6 × 10−5

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5.3. A comparsion study with other optimization techniques
In this section, the optimization result of the M-SCA has been compared with those of the genetic
algorithm (GA), which is considered as one of the most powerful and widely used evolutionary algorithms
[26]-[28], and the original sine cosine algorithm (SCA). Using the same comparison analysis of the previous
section, 10 runs were made for each algorithm and the average of these runs was taken. Table 3 illustrates the
result of this test, where it is clear that the M-SCA has resulted in the fewest ISE value compared to those of
the GA and the SCA.
Table 3. Comparison results of the GA, the SCA, and the M-SCA acting as the training methods
Optimization Method ISE Criterion (average of 10 runs)
GA 10.4 × 10−5
SCA 27.6 × 10−5
M-SCA 5.62 × 10−5
6. CONCLUSION
In this paper, an extended wavelet functional link neural network structure was put forward to
control the highly complex and nonlinear servo-hydraulic system. A recently developed optimization method,
namely the M-SCA, was employed to find the optimal settings for the proposed controller, which has attained
remarkable control accuracy in tracking two different displacement signals. The results of a comparative
study involving other types of controllers revealed the superiority of the EWFLNN controller. In addition, M-
SCA has achieved better optimization results in finding the optimal values of the controller's parameters
compared to the GA and the SCA.
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BIOGRAPHIES OF AUTHORS
Shaymaa Mahmood Mahdi received her B.Sc. degree in Control and Systems
Engineering and the M.Sc. degree in Mechatronics Engineering from the University of
Technology-Iraq, in 2003 and 2008, respectively. She is currently a full-time Assistant Professor,
Head of the Quality Assurance & University Performance Unit, Department of Control and
Systems Engineering, University of Technology-Iraq. Her current research interests include
hydraulic and pneumatic systems, robotics and intelligent controllers. She can be contacted at
email: shaymaa.m.mahdi@uotechnology.edu.iq.
Omar Farouq Lutfy received the Ph.D. degree in Control and Automation
Engineering at the Department of Electrical and Electronic Engineering, University Putra
Malaysia (UPM), Malaysia in 2011. He received the B.Sc. degree in Computer Engineering
and the M.Sc. degree in Mechatronics Engineering at the Control and Systems Engineering
Department, University of Technology-Iraq in 2000 and 2003, respectively. He is currently
working as a professor at the Control and Systems Engineering Department, University of
Technology-Iraq. He is the author and co-author of more than thirty papers published in
international journals and conferences. His research interests include intelligent control,
artificial intelligence algorithms, and system identification techniques. He can be contacted at
email: omar.f.lutfy@uotechnology.edu.iq.

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