Development of a 2 degree of freedom-proportional integral derivative controller using the hippopotamus algorithm

IAES International Journal of Artificial Intelligence (IJ-AI)
Vol. 14, No. 1, February 2025, pp. 780~787
ISSN: 2252-8938, DOI: 10.11591/ijai.v14.i1.pp780-787  780
Journal homepage: http://ijai.iaescore.com
Development of a 2 degree of freedom-proportional integral
derivative controller using the hippopotamus algorithm
Rattapon Dulyala1
, Worawat Sa-Ngiamvibool2
, Sitthisak Audomsi2
, Kittipong Ardhah3
,
Techatat Buranaaudsawakul4
1
Faculty of Industrial Technology, Uttaradit Rajabhat University, Uttaradit, Thailand
2
Faculty of Engineering, Mahasarakham University, Kantharawichai, Thailand
3
Faculty of Engineering and Industrial Technology, Kalasin University, Kalasin, Thailand
4
Faculty of Engineering, Pitchayabundit College, Nong Bua Lamphu, Thailand
Article Info ABSTRACT
Article history:
Received Jun 5, 2024
Revised Sep 2, 2024
Accepted Oct 8, 2024
This research project investigates the regulation of autonomous power
generation in two interconnected regions using two hydroelectric power
plants. It specifically addresses the challenges posed by significant electrical
system issues. The hippopotamus optimization algorithm (HOA) has
demonstrated enhanced gain value in research and designs of 2 degree of
freedom (2DOF)-proportional integral derivative (PID) controllers. The
objective is to provide efficient and uninterrupted functioning of the electrical
network in both areas. Contemporary technology and methods enable the
electrical system to efficiently and accurately fulfill user requirements,
resolving any problems related to system balance and stability. This
experiment evaluates the efficacy of several algorithms in accurately selecting
optimal values. We evaluate performance using the integral of absolute error
(IAE) and integral of time-weighted absolute error (ITAE) functions. This
experiment evaluates and contrasts different algorithms. Summarizing the
analysis using verifiable evidence. Optimization when evaluated using the
ITAE measurement, the HOA earned the lowest result of 0.08744 for ITAE.
Empirical research has demonstrated that this strategy is the most effective in
reducing the ITAE. The sine-cosine algorithm (SCA) and whale optimization
algorithm (WOA) have similar ITAE values, with SCA having an error of
0.08967 and WOA having an error of 0.08967. The numerical number is
0.08970.
Keywords:
2-DOF-PID control
A sine cosine algorithm
Hippopotamus optimization
algorithm
Load frquency control
Whale optimizatiom algorithm
This is an open access article under the CC BY-SA license.
Corresponding Author:
Techatat Buranaaudsawakul
Faculty of Engineering, Pitchayabundit College
Nong Bua Lamphun, 39000, Thailand
Email: techatat@gmail.com
1. INTRODUCTION
For the purpose of preserving the reliability and steadiness of power systems [1], it is of the highest
essential to guarantee that they will continue to provide energy without interruption, regardless of the varying
load needs [2], [3] load frequency control, often known as LFC, is a vital component of the functioning of
power systems. Its major function is to regulate the frequency of the system [4] within the parameters that have
been specified, and it also ensures that there is an equilibrium between the quantity of electricity produced and
the quantity consumed. LFC that is successful results in a reduction in frequency deviations, which in turn
decreases the likelihood of blackouts occurring and ensures that the power system remains stable [5].

Int J Artif Intell ISSN: 2252-8938 
Development of a 2 degree of freedom-proportional integral derivative controller … (Rattapon Dulyala)
781
As a result of its straightforward installation and dependable performance, proportional integral
derivative (PID) controllers [6] have discovered widespread use in the field of LFC. In spite of this, the problem
of fine-tuning the PID parameters (Kp, Ki, and Kd) continues to be a significant area of concern. Incorrectly
calibrated PID parameters may lead to insufficient frequency control, instability, and inefficiency in the power
system. These issues might be caused by the power system [7], [8].
When it comes to dealing with complex optimization problems [9], [10] such as the fine-tuning of
PID controllers, metaheuristic optimization approaches have grown more popular. There have been tremendous
accomplishments achieved via the use of algorithms such as the genetic algorithm (GA) [11], [12], the Bees
algorithm [13], [14], and the particle swarm optimization (PSO) [15], [16]. With that being said, the search for
optimization procedures that are both more efficient [17], [18] and effective continues, which has led to the
research of novel algorithms[19], [20] that are inspired by biological systems [21], [22].
Within the realm of bio-inspired optimization strategies, the hippopotamus optimization algorithm
(HOA) [23] is a recently established method that has recently come into existence. For the purpose of resolving
optimization challenges, HOA, which takes its cues from the social behavior, territorial instincts, and
cooperative hunting strategies of hippopotamuses, provides a highly promising approach. In order to enhance
the effectiveness and dependability of power systems, the purpose of this research is to investigate the
possibility of integrating a two degree of freedom (2DOF) PID control system [24] with HOA for LFC [25].
In this paper, the development of a PID control system [26] with 2DOF is described. For the purpose
of regulating the LFC in power systems, the system makes use of the HOA. There was an improvement in
system performance as a result of the introduction of HOA into the 2DOF-PID controller. This demonstrates
the power of bio-inspired algorithms to enhance complex control systems. By doing more research, it may be
possible to investigate the use of HOA in different control system domains and develop hybrid approaches that
combine HOA with other optimization techniques.
2. RESEARCH METHODOLOGY
2.1. Two degree of freedom proportional integral derivative control system
Due to the fact that they are uncomplicated and have the ability to deliver results that can be relied
upon, controllers have been utilized for a considerable amount of time currently. For the purpose of the study,
the LFC controller was a modified version of the PID controller that was referred to as the 2DOF-PID controller
[27]. As a result of its capacity to quickly reject disturbances without generating a large rise in overshoot during
set-point tracking, this option has been selected, in Figure 1 illustrates structure 2DOF PID control.
Figure 1. Structure 2DOF PID control [28]
2.2. Hippopotamus optimization algorithm
2.2.1. A mathematical representation of the hippopotamus optimization algorithm
The algorithm continuously monitors and saves the most optimal possible solution throughout its
operation. Once the process concludes, the hippopotamus plays a crucial role in revealing the final response,
also known as the prevailing solution to the dilemma. The flowchart in Figure 2 illustrates the procedural
components of the HOA.

 ISSN: 2252-8938
Int J Artif Intell, Vol. 14, No. 1, February 2025: 780-787
782
Figure 2. HOA flowchart [23]
2.3. Objective function
Consumer demands and system parameter disruptions have a significant impact on the frequency and
power variations of the linked electrical power system. These fluctuations deviate from the specified efficiency
values that are acceptable for a stable electrical system. A satisfactory level of stability, fast control response,
and reduced fluctuations is desired in the LFC system. These requirements enable the system to quickly restore
the frequency deviation (Δ𝑓) in each area and maintain the constant power deviation (Δ𝑃) at its original or
predetermined value [29].
The study work employs an integral performance index type as the fitness/objective function. The
fitness/objective functions of IAE and ITAE utilized in the literature are represented by (1) and (2):

783
𝐼𝐴𝐸 = ∫ [|Δf + ΔP|]
∞
0
⋅ 𝑑𝑡 (1)
𝐼𝑇𝐴𝐸 = ∫ [|Δf + ΔP|]
∞
0
∙ 𝑡 ⋅ 𝑑𝑡 (2)
Based on the literature study, it is preferred to use IAE and ITAE-optimized controllers in LFC systems.
Therefore, this study presents a new approach that utilizes the IAE and ITAE performance criterion to develop
and implement a weighted objective technique. This approach serves as the fitness function for optimizing the
2DOF-PID controller's settings.
3. METHOD
This research evaluates the efficacy of the HOA in finding the ideal configuration settings for the
2DOF PID control controller in a thermal power system that consists of two sections that are linked to one
another. Within the context of the simulation, each power plant has a load capacity of one thousand megawatts
and a production capacity of two thousand megawatts [28]. Currently, the system incorporates a governor-dead
band in order to further strengthen the realism of the system. Because of the enhancement, the system became
nonlinear, which enabled it possible to take use of it for the purpose of researching the dynamic response of
frequency in power plants [29]. To be more specific, it is able to conduct an analysis of the power response of
the tie line in response to a 0.01 p.u. Step load perturbation (SLP) disturbance at the thermal power plant located
at Figure 3 [30], the range of parameters will be set according to Table 1.
Figure 3. A thermal power system with two linked sections diagram [30]
Table 1. Minimum and maximum value of the control parameter [30]
Controller parameter Minimum Maximum
Kp 0 1
Ki 0 1
Kd 0 1
N 10 300
PW 0 2
DW 0 5
4. RESULTS AND DISCUSSION
The 2-DOF PID controller, which plays a crucial role in power system control, optimizes its
parameters using the HOA. The connection between two sources of information. We use the MATLAB
R2021A program to conduct tests and assess all operations. The program runs on a central processing unit
(CPU) that has a Core i5 processor operating at a clock speed of 2.50 GHz. In addition, it has a random-access
memory (RAM) capacity of 16 GB. Changing the settings for a 2DOF-PID controller yields different results.

 ISSN: 2252-8938
784
Table 2 shows that each function has just 6 parameter values, namely the parameters of the
2DOF-PID controller. Concerning the experimental power plant, the paramotor search operational simulation
produces an appropriate value for each method. The implementation has been carried out in two domains. A
link exists between the two thermal power plants.
Table 2. Optimization controller parameter
Parameter
HOA SCA WOA
IAE ITAE IAE ITAE IAE ITAE
Kp 1 0.3518 1 0.3132 1 0.3463
Ki 1 1 1 1 1 1
Kd 0.1215 0.2338 0.1714 0.1873 0.1188 0.2304
N 21.2966 282.3872 10 10 300 84.8399
PW 0.0123 1.3516 0.2124 0 0.5792 0.192
DW 4.3947 1.1593 0 0 3.2373 0.7401
The frequency response of areas 1-2 and 3 of the IAE was shown in Figure 4. The study revealed that
the HOA exhibited more responsiveness compared to the SCA and WOA in parameter search. The setting time
consideration value is 2%. Upon analyzing the function's graph, ITAE found that using the HOA yielded a
much superior response compared to the SCA and WOA. Additionally, Figure 5 demonstrates that the settling
time value at 2%, values of settling time, peak and values of error show in Tables 3 and 4.
Table 3. Values of settling time and peak
Values
HOA SCA WOA
Settling Time 2%
Area 1 605.928 242.4594 580.07 324.29 612.86 241.623
Area 2 579.732 302.578 442.86 267.22 469.46 301.951
Tie line 578.677 354.909 572.79 342.32 585.45 241.623
Peak
Area 1 0.0143 0.0149 0.0141 0.0159 0.0142 0.015
Area 2 0.0105 0.0096 0.0105 0.011 0.0102 0.0097
Tie line 0.0035 0.0031 0.0035 0.0036 0.0034 0.015
Table 4. Values of error
Algorithm HOA SCA WOA
Error 0.0348 0.0874 0.034 0.0896 0.0348 0.0897
Figure 4. Freqency deviation in area (IAE)

785
Figure 5. Freqency deviation in area (ITAE)
5. CONCLUSION
The aim of this experiment is to evaluate and compare the effectiveness of several algorithms in
determining the optimal values. The IAE and ITAE functions are used for quantifying the results. The
algorithms under comparison in this experiment are: According to the empirical data, the analysis may be stated
as follows. Effectiveness the SCA has exceptional efficiency in reducing the IAE when assessed using the IAE
metric, resulting in a minimum error of 0.034087693541846. SCA has higher optimization skills in comparison
to other approaches, particularly in terms of lowering the IAE. The HOA and WOA have similar IAE values,
with HOA showing an equal value. The error is 0.034848038938341, whereas WOA has an error value of
0.034846945292738, which exhibits a little disparity. Effectiveness when assessed utilizing ITAE
measurement, the HOA attained the minimum ITAE value of 0.087448913139503. Empirical research has
shown that this strategy is the most effective in reducing the ITAE. The SCA and WOA have similar ITAE
values, with SCA having an error of 0.089673119049235 and WOA having an error of 0.089673119049235.
The numerical number is 0.089705069065476.
ACKNOWLEDGEMENTS
The author expresses gratitude to all the Professors of Engineering at Mahasarakham University in
Thailand for their invaluable help in this endeavor.
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BIOGRAPHIES OF AUTHORS
Rattapon Dulyala, Ph.D. received his B.S.Tech. Ed. degree in electrical
engineering, from the Pathumwan Institute of Technology (PIT) and the M.S.Tech. Ed. degree
in electrical engineering, from the King Mongkut's University of Technology Thonburi
(KMUTT), Thailand. His research interests include power technology and power systems. Since
2007, he has been with Faculty of Industrial Technology, Uttaradit Rajabhat University (URU),
Thailand, where he is currently a lecturer of electrical engineering. He can be contacted at email:
rattapon.dul@live.uru.ac.th.

787
Worawat Sa-Ngiamvibool, Ph.D. received his B.Eng. degree in electrical
engineering, the M.Eng. degree in electrical engineering from the Khonkaen University (KKU),
Thailand and the Ph.D. degree in engineering from Sirindhorn International Institute of
Technology (SIIT), Thammasat University, Thailand. His research interests include analog
circuits and power systems. Since 2007, he has been with Faculty of Engineering,
Mahasarakham University (MSU), Thailand, where he is currently a Professor of Electrical
Engineering. He can be contacted at email: wor.nui@gmail.com.
Sitthisak Audomsi currently, he is pursuing a Ph.D. in the Department of Electrical
and Computer Engineering. He obtained a master's degree in electrical and computer
engineering in 2024, and a bachelor's degree in electrical engineering in 2023, Faculty of
Engineering at Mahasarakham University. His focused on doing research in the fields of control
systems, optimization methods, and artificial intelligence. He can be contacted at email:
65010353006@msu.ac.th.
Kittipong Ardhah received his B.Eng. degree in electrical engineering, from the
King Mongkut's University of Technology Thonburi (KMUTT), the M.Eng. and Ph.D. degree
in electrical and computer engineering from Maha Sarakham University (MSU), Thailand. His
research interests include interdigital capacitor and power systems. Since 2023, he has been with
Faculty of Engineering and Industrial Technology, Kalasin University (KSU), Thailand, where
he is currently a lecturer of electrical engineering. He can be contacted at email:
kittipong.ar@ksu.ac.th.
Techatat Buranaaudsawakul received his B.S.Tech. Ed. degree in electrical
engineering, from the King Mongkut's University of Technology Thonburi (KMUTT), the MBA
degree from the Bangkok University (BU) and the Ph.D. degree in electrical and computer
engineering from Maha Sarakham University (MSU), Thailand. His research interests include
power plant and power systems. Since 2023, he has been with Faculty of Engineering,
Pitchayabundit College (PCBU), Thailand, where he is currently a lecturer of electrical
engineering. He can be contacted at email: techatat@gmail.com.

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