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Performance Evolution of Different Optimal Controllers for Controlling AVR System
Mohamed Jasim Mohamed , Layla H. Abood*
Control and Systems Engineering Department, University of Technology, Baghdad 10066, Iraq
Corresponding Author Email: 60066@uotechnology.edu.iq
Copyright: ©2023 IIETA. This article is published by IIETA and is licensed under the CC BY 4.0 license
(http://creativecommons.org/licenses/by/4.0/).
https://doi.org/10.18280/jesa.560608
ABSTRACT
Received: 14 August 2023
Revised: 28 October 2023
Accepted: 7 November 2023
Available online: 28 December 2023
The main issue in electrical system is providing a stable voltage values in order to obtain
best devices performance for this reason controlling the automatic voltage regulation
(AVR) system becoma more helpful to achieve this requirments, in this paper three
controllers are suggested for maintaining the terminal voltage level value of the generator
part in AVR system that supplied to custumers, these controllers are (Conventional PID,
ArcTan PID and Nonlinear PID), all gains of these controllers is tuned by using an
intelligent sun flower optimization (SFO) algorithm. The objective of the design is finding
suitable values of these gains that give a stable response based on minimizing error value
and testing it using the Integral Time Absolute Error (ITAE) fitness function, the numerical
results exhibited that the ArcTan PID controller give the best results values with a lower
settling time (0.698) and its faster than conventional PID 5.034 % and faster than nonlinear
PID by 5.163% for 5 second simulation time also its reach its peak value in 0.513 sec. and
an expectable overshoot value equal to 0.513 with a small error value (0.000645) at its
steady state case and then small error value when working at normal state without any
disturbance or any uncertainty cases applied but when a disturbances signal is applied
with a value equal to ± 0.3 to the system, the NLPID and the conventional PID presents a
best response by returning the system to its desired value in just 2 second in the two cases
applied and when change the gain values of two parts of AVR system( amplifier & sensor)
the NLPID behaves as a the more suitable one and give a superior robust performance in
facing this unwanted signals and then a desired response is achieved after small period
time with satisfied and acceptable values for woring in this enviroment.
Keywords:
AVR system, terminal voltage, PID, sun
flower optimization algorithm
1. INTRODUCTION
In power system, stability of the supplied voltage value is
regarded as a major and very important issue in order to
achieve quality of customer requirements and to protect any
equipments and devices from any fluctuations may happen
which is reflected on their performance an may be could not
work again, for this reason using automatic voltage regulator
(AVR) will increase the reliability of power system by
regulating the boundaries of the terminal voltage in the
generator to a suitable level. The major challenge of AVR
system will be facing the variations of costumer loads and
working with any complex power system. Therefore, various
controllers have been suggested to maintain AVR systems to
obtain a stable behavior with best evaluations parameters [1].
Different studies have suggested various controllers' types
for controlling AVR system and solving the terminal voltage
regulation issue like using the PID classical controller due to
its simple structure with the benefits of using the new
optimization algorithms, in Çelik and Öztürk [2], a
combination between simulated annealing algorithm and
symbiotic organisms algorithm is suggested for tune the PID
controller gains to enhance its performance while in Mosaad
et al. [3] two controllers are adopted PID and PID with
acceleration PIDA; these two types are tuned using different
algorithms like Local Unimodal Sampling (LUS),Teaching
Learned Based Optimization (TLBO) and Harmony search
Algorithm (HSA) and a robustness test is done to check system
performance based on changing its load as happen in any
regulator circuits. In the study [4], a Tree-Seed Algorithm
(TSA) is used for tuning PID gains and various tests are done
to verify system response and enhance system tracking until
reach to a stable level while in the study [5], a two optimization
method is hybridized together the Simulated Annealing (SA)
and Gorilla Troops Optimization (GTO) with a novel cost
function is adopted for best optimal values choice. Other
studies proposes the generalized form of PID controller which
is named the Fractional order PID (FOPID) controller in this
type of controller gains will be five parameters, two values are
added with a fractional values [6, 7], Ayas and Sahin [8]
suggest a novel FOPID controller combined with fractional
filter which increase controller gains to seven parameters
which are all tuned using Sine Cosine Algorithm(SCA) and its
compared with different classical controller then two analysis
is done one of them is done by changing AVR system
parameter and the other is done by applying external
disturbances while in Mok and Ahmad [9] a modified
smoothed function algorithm (MSFA) is proposed with the
FOPID controller to enhance system regulating facility based
on different objective functions.
Journal Européen des Systèmes Automatisés
Vol. 56, No. 6, December, 2023, pp. 973-979
Journal homepage: http://iieta.org/journals/jesa
973
In this paper a comparison analysis is utilized for three
optimal proposed controllers (PID, NLPID, Arc Tan PID) and
these three controllers are adopted to reflect the benefits
gained when adding a nonlinear function or changing the
structure of the conventional controller to modify system
performance then a comparison analysis is utilized to show the
suitable controller that can be used for maintain AVR system.
The smart and unique SFO algorithm is firstly and efficiently
used with AVR system which it enhances its performance,
then test AVR system robustness by adding external
disturbances in two different periods and changing the
parameter values for the two parts of AVR system to specify
the robust controller based on its response and its transient
analysis. The paper is organized as indicated: Section 2
indicates the AVR system model while section 3 describes the
suggested controllers. Section 4 explains the SFO method for
choosing the optimal controllers gains, section 5 analyzes the
simulation results for all controllers then the conclusions are
presented in section 6.
2. AVR SYSTEM MODELLING
The essential idea of an AVR system is to retain the level of
terminal voltage in the generator in a stable and constant value.
AVR system has four essential parts: an amplifier, an exciter,
a generator, and a sensor, it's a closed loop system in which
the voltage value of the synchronous generator is checked by
sensor. The sensor voltage is the feedback that is modified and
smoothed to be tested and then compared with the reference
voltage, and then the error is evaluated by taking the difference
between the sensor voltage value and input voltage value. This
value of error was amplified and sent to the exciter to maintain
the current of the excitation in the exciter part. The exciter
modifies the current of the rotor field save the terminal voltage
value to reach to its accepted value wanted. These parts are
represented by equations that represent the transfer function
equations which are adopted to simulate the dynamic behavior
of an AVR system parts using Matlab/Simulink. Each part has
its gain and time constant appeared together in a first-order
equation and regarded as the transfer function for each part as
indicted below in Table 1 and its block diagram without using
any controller is shown in Figure 1 [10, 11].
Table 1. AVR system main parts [10, 11]
AVR Part
Gain Value
Time Constant
Transfer Fun.
Amplifier
Ka=10
Ta=1sec.
Ka/sTa+1
Exciter
Ke=1
Te=0.4sec.
Ke/sTe+1
Generator
Kg=1
Tg=1sec.
Kg/sTg+1
Sensor
Ks=1
Ts=0.01sec.
Ks/sTs+1
Figure 1. Block diagram of AVR system
Eq. (1) below represents the AVR system transfer function
[11]:
(1)
3. PROPOSED CONTROLLER DESIGNS
This section discuss the scheme of three different
controllers was adopted for controlling the terminal voltage
value and keeping it in a stable level by minimizing error value
and achieve a robust response, the controllers suggested are
tested in normal enviroment and when there is unwanted signal
applied to the system to verify there performance when use
another structures like use nonlinear function or ading arc tan
function.
3.1 Conventional PID controller with filter
A conventional proportional–integral–derivative (PID)
controllers are commonly adopted in different engineering
applications due to its simplicity and can give efficient results
by reducing the system error and obtain stable response values
[12, 13], the first term named proportional will calculate the
controller output depending on the proportional error value,
with a high coefficient value, in this case the PID controller
will behave more fastly and give a faster target value. The
integral error will depend on the integral of the error value then
calculated for the error found and for its duration value, in this
case the integral appraises time, it can find the current error
and the past error values in which the proportional part alone
cannot find it. Higher integral value can to minimize error
levels in the steady state, the last term is the derivative that
depends on the slope of detected error as ist variation during
working over time, it is adopted for expect system response
then modify its performance by regulating the settling time and
system stability, the PID transfer function equation is shown
in Eq. (2) below and its block diagram in Figure 2.
(2)
Figure 2. PID controller block diagram
3.2 ArcTan PID controllers with filter
The use of different mathematic relations like trigonometric,
anti trigonometric and hyperbolic functions equations enhance
the system behavior and give accurate and stable response [14]
due to this many researcher adopts different types of these
equations, in this paper the second type was done by utilizing
the ARC Tan PID control law which is represented by
changing the integral for the error function in the conventional
PID control law with an integral for the arc tan relation to the
error, as shown in equation. When increasing system
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complexity the conventional PID controller is not sufficient
enough to save system dynamics stable and constant this will
make the control signal not able to track the desired value
needed efficiently and may attenuate system performance,
according to this adopted controller suggests to use the arc tan
of error value and the ARC Tan PID controller transfer
function is explained in Eq. (3) [15]:
(3)
where, γ is design parameter.
3.3 The nonlinear PID controller with filter
The Nonlinear PID controller has been developed to get a
best satisfied response [16] for the nonlinear system, where it
uses on each term of the linear PID controller a nonlinear
function f(.) which is a nonlinear formula of sign function in
which it will indicate whether the relation is positive, negative,
or zero. For the function f(x) on an period equal to 1 , the sign
is positive if f(x)>0 for all x in 1 , the sign is negative if f(x)<0
for all in 1, while the exponential function is as its name
suggests, involves exponents, it has a function with a constant
as its base and a variable as its exponent but not the other way
round, the exponention function of the error and its derivative
and its integral as given below:
(4)
(5)
(6)
for n=1, 2, 3.
where, β could bee ,, or ∫e dt, , the function kn(β) is
a positive term with variables . For
enhance the nonlinear controller sensitivity for small errors
values, the nonlinear variable kn(β) is utilized. For low error
values close to zero, the value of the nonlinear term kn(β)
approaches the upper bound kn1+kn2/2, and for large valuesof
error, the nonlinear gain term kn(β) approaches the lower
bound kn1, this explains the boundaries of nonlinear gain term
kn(β), it is laid in the region
. The equations
of nonlinear PID controller are shown below [17]:
(7)
Derivative term
(8)
(9)
Integral term
(10)
(11)
(12)
(13)
(14)
4. SUNFLOWER OPTIMIZATION ALGORITHM
The sunflower optimization method is regarded as a new
tuning algorithm, it is a population-based algorithm presented
in the study [18], it is used in this study due to its systematic
process and smart flow which can guarantee better
exploitation and exploration capability and this can be
reflected on enhance system efficiency and decreased
computational time process. SFO simulate the sunflowers
movement to the sunlight direction by using the pollination
between near sunflowers, if the space between them and sun
increases, the intensity of radiation will minimize and vice
versa based to equations below:
(15)
where, Spower is the sun power, and Srad depicts the sun
radiation intensity that depends on the solar intensity and the
square of distance (d) between sun and the palnt. Every
sunflower movement direction to the sun is expressed by:
(16)
i=1, 2, 3, 4, ……. n.
where, Xi and X* are the present and best sunflowers places, n
explains the size of population; every one sunflower is moved
by (di) distance to the sun path as indicated:
(17)
where, λ is the sunflowers' inertial displacement, (‖+-1‖)
represents the probability of pollination of two near flowers.
Each sunflower’s step is specific and it is as shown:
(18)
The places of the sunflower are being within the boundaries'
Xmin and Xmax, where Xmin and Xmax explain the lowest and
highest levels respectively. Npop represents the size of
population and the equation below indicates the next
population towards the sun:
(19)
The SFO algorithm like the other swarm intellegent
algorithms suffers from slow convergence and it can be
trapped easily in local minima. The SFO flow chart is shown
in Figure 3 below.
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Figure 3. The SFO algorithm flowchart
5. SIMULATION RESULTS
The simulation analysis of the AVR system based on
various optimal controllers is discussed in this section; the
three controllers are studied and investigated to obtain a stable
and robust system response based on SFO algorithm, Table 2
below lists the SFO algorithm parameter and the AVR system
block diagram is indicated in Figure 4.
Table 2. SFO algorithm parameter
Description
Value
Sunflower numbers
20
pollination rate
0.05
mortality rate
0.1
Maximum number of iteration
100
Figure 4. Block diagram of AVR based on SFO algorithm
For efficient monitoring and tracking to the desired
response and to achieve best controlling to the terminal voltage
value, an Integral Time Absolute Error (ITAE) function [19]
is adopted as a fitness function, it is represented by a
mathematical formula that depends on error value calculated
between desired and actual values wanted and the instanteous
time when running the algorithm to find the optimal prameters,
its variables are the error and the time as indicated in Eq. (19),
it is adopted as a cost function [20, 21] to test the error when
the SFO is run until reach to the most suitable gains values and
that make the sysetm give a stable wanted behavior, as
indicated in Figure 5 below.
(20)
Figure 5. AVR system response for the three different
controllers
The optimal gains of all controllers are listed in Table 3, its
arranged for each controller based on its structure indicated in
section 3 and all these gains are calcualted using the SFO
algorithm.
Table 3. Optimal gains of suggested controllers
Controller
Type
Kp
Ki
Kd
N
γ
Con_PID
0.20868
5.65316
0.25490
100.0
-
ArcTan_PID
0.26574
7.53114
0.29308
100.0
1
NL_PID
Kp1
0.106797
Kp2
3.31709
μp
0.5367
αp
0.77941
Ki1
0.00805
Ki2
9.0
μi
1.76899
αi
0.86079
Kd1
0.76485
Kd2
0.02617
μd
0.00284
αp
0.64616
100.0
-
The step response analysis in Table 4 is used to demonstrate
the evaluation parameters for the controllers used with AVR
system.
Table 4. Evaluation parameters for all controllers
Evaluation
Parameter
Con_PID
ArcTan_PID
NL_PID
Rise time
0.425
0.366
0.332
Over shoot /
Under shoot
%
3.25
4.808
3.16/8.24
Peak Time
0.589
0.513
0.4/0.598
Settling time
0.735
0.698
0.736
Steady state
Error
0.000727
0.000645
0.00130
ITAE
0.034456954
0.030291026
0.037403491
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As indicated in Table 4 the ArcTan PID controller have the
best performance when it is compared to the two other
controllers used, it is superior in its rise time but it has an
overshoot higher than others but it is faster in reaching to the
desired value with a lower settling time (0.698 sec.) even there
is an over shoot value with (4.808), with a smaller error value
and a low ITAE (0.030291026) while the NLPID controller
have a higher error value (0.00130) also a higher ITAE
(0.037403491) also its suffer from overshoot and undershot
value at its start working then reach to settling time at (0.736
sec.), finally the conventional PID will have a higher rise and
settling time with acceptable overshoot value (3.25), due to
this the ArcTan is considered as the best controller when the
simulation is done with normal environment without any
disturbances or any change in its parameters this in fact return
to the use of the mathematic anti trigonometric relation
(ArcTan) also to the best values tuned using the intelligent
SFO algorithm. Then to test the controllers robust response
two steps will done the first one is when the AVR system
terminal voltage generated from generator part is increased or
decreased during real working and this issue will translated by
applying an unexpected increase or decrease in its desired
value due to any reason may happen during real working of
the AVR system, two types of signals is applied as an external
disturbance in positive and negative values (± 0.3 volt) in two
different time periods as shown in Figure 6.
(a)
(b)
Figure 6. a) Add +0.3 volt at t=3 sec; b) Add -0.3 volt at t=2
sec
The second step is done by changing the gain value of the
sensor and the amplifier parts from the AVR system by a value
equal to ± 25% from its original values to see the behavior of
the controllers at this condition, the response of the controllers
is indicated in Figure 7.
(a)
(b)
(c)
(d)
Figure 7. a) - 25% in amplifier gain; b)+25% in amplifier
gain; c) - 25% in sensor gain; b) +25% in sensor gain
amplifier
It is obvious from Figure 6 the PID and nonlinear PID give
a robust response as shown, they are need 2 second to return
to their responses in the two cases of adding disturbances
signal(Positive ,Negative), this small value in not sensed when
the system is in continues supply for the terminal voltage in
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long time periods while in Figure 7 when changing the
amplitude of the gain of two parts of AVR system(amplifier
and sensor) the NLPID controller show the best robust
response when compared with Conventional PID and the
ArcTan PID controllers, it suffer from little fluctuation in its
value but it face this change and give a best response after
acceptable time period.
6. CONCLUSIONS
In this study, three types of controller's schemes are
presented for controlling AVR system with the benefits use of
a smart SFO algorithm to regulate the supplied voltage from
AVR system by adopting ITAE function for minimizing error
value during the whole simulation process. The comparison
between these controllers is utilized; ArcTan controller is
superior in different evaluation parameters with a small
settling time equal to 0. 698 as compared with other controllers
and an acceptable overshoot value equal to 0.408 also a small
eeror valu noticed at its steady state with a value equal to
0.000645, all these evaluation parameter is appeared on its
efficient system response. Then for check their performance
in facing different signal regarded as a disturbances signal and
the changing of its parameter value during supply voltage for
system distribution, a positive and negative disturbances
signals is given to the AVR system and their values are ± 0.3
v in two period (t=2 sec., t=3 sec.); the nonlinear PID
controller and the conventional PID give a best behavior in
solving these matter in 2 sec. and returning the system to its
wanted voltage level value and reflecting a stable desired
response, and when changing the gain of two of AVR system
parts (amplifier and sensor) with a value equal to ± 25% from
its original values, the NLPID controller fix this issue after a
small time duration. Finallly for future work different ideas
can be utilized to enhance system effeciency like using a
cascade controller structure or use an intelligent method
combined with convention controller or use another more
recent optimization algorithm which can give best tunable
gains values in which it can be reflected on system
performance.
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