i
DESIGNING AN OPTIMIZATION PID CONTROLLER FOR HEAT
EXCHANGER AND ELECTRO-HYDRAULIC SERVO SYSTEM:
SIMULATION STUDIES
NUR SHARLYANA BINTI MOHD ZAMRI
A thesis submitted in
fulfilment of the requirement for the award of the
Degree Bachelor of Mechanical Engineering with Honours
Faculty of Mechanical and Manufacturing Engineering
Universiti Tun Hussein Onn Malaysia
JULY 2020
ii
DECLARATION
I hereby declare that the work in this project report is my own except for quotations and summaries
which have been duly acknowledged
Student
:
NUR SHARLYANA BT MOHD ZAMRI
Date
:
Supervisor
:
06 AUGUST 2020
DR. NOORMAZIAH BT JAFFERI
iii
ACKNOWLEDGMENT
First and foremost, I would like to express gratitude to the Almighty God as with His
blessing, I was able to complete this project without any major difficulties. Next, I love
to express my appreciation and big thanks to my supervisor for my final year project,
Dr. Noormaziah bt Jafferi whom consistently guide and helping me from the beginning
and throughout the completion of this project despite her busy schedule and current
issues. Without her guide, I might not be able to complete this project even her guidance
only in virtual. She showed me her professionalism in not just educating but also in
spiritual and discipline.
Secondly, I would like to share this feeling and moment of success with my
friends. All thanks to them for the support and willingness to lend their ears and
shoulder during my tough time. I also able to create a good memories and friendship
even the process of completing this project does not happen face to face due to
unexpected event.
Most importantly, I should not forget the person behind my success, who are my
parents and family who always been my backbone since day one. The support that they
gave in various ways either directly or indirectly. The love, courage, sacrifice will
always will I treasured and be my inspiration in my life today, tomorrow and the future.
I hope to repay their support with success in my studies and life and most importantly
in becoming a better person.
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ABSTRACT
Heat exchanger (HE) and Electro hydraulic servo system (EHSS) are two systems that
widely used in industry to help with the production especially in refrigeration and blow
molding industry. HE has a system with third order transfer function while EHSS has
a system with fifth order transfer function. The order of the control system are depends
on the number of independent energy storage element in the system. ProportionalIntegral-Derivative (PID) is commonly used as a control device to help with the
control system. Yet, the PID controller has some defect which it remain stable even
some large changes happen to occur on the systems parameter. In this study, a design
for Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) of ProportionalIntegral-Derivative (PID) for the two systems were projected. For this two
optimization tools, it has been successfully applied in many areas in engineering and
also science field. The design of optimized PID help the systems to have a better
performance. The value of PID parameter which proportional gain (𝐾𝑝 ), integral gain
(𝐾𝑖 ) and derivative gain (𝐾𝑑 ) was determined based on previous research paper to be
used as reference to optimized both of the systems. Parameters that were used for
optimization were determined. Comparison between the results from the step response
of the HE and EHSS system with PID controller, system without PID controller and
system with optimized PID was done. Based on the results, PSO is the best
optimization tools for both systems with 90% improved overshoot percentage and less
than 0.01 second for rise time from the system without PID.
v
ABSTRAK
Heat exchanger dan Electro hydraulic servo system adalah antara dua sistem yang
biasa digunakan di industri terumatanya industri refrigeration dan blow molding.
Pengawal PID kebiasaannya menajadi satu peranti untuk mengawal sistem control.
Walaubagaimanapun, pengawal PID tidak memberi impak yang baik terhadap sistem
kerana pengawal PID tidak berubah walaupun ada perubahan yang besar terhadap
sistem–sistem tersebut. Di dalam kajian ini, satu reka bentuk optimasi algoritma
genetik dan optimasi zahrah gergasi untuk pengawal PID bagi sistem-sistem tersebut
telah dikemukakan. Reka bentuk optimasi PID membantu sistem-sistem tersebut
mempunyai prestasi yang baik. Nilai parameter PID di mana dapatan berkadar (𝐾𝑝 ),
dapatan integral (𝐾𝑖 ) dan dapatan derivative (𝐾𝑑 ) telah ditentukan dengan merujuk
kepada jurnal kajian terdahulu. Nilai yang diperolehi akan digunakan untuk
mengoptimasi pengawal PID. Parameter lain yang diperlukan untuk mengoptimasikan
pengawal PID telah ditentukan dalam kajian ini. Perbandingan di antara parameter
yang terhasil dari step response untuk sistem tanpa pengawal PID, sistem heat yang
menggunakan pengawal PID dan PID yang telah dioptimasikan dengan Algoritma
genetick dan optimasi zahrah gergasi telah dilaksanakan. Berdasarkan keputusan yang
diperolehi, optimasi zahrah gergasi adalah optimasi yang terbaik untuk kedua-dua
sistem dengan 90% penambahbaikkan peratusan overshoot dan kurang dari 0.01 saat
untuk rise time.
vi
CONTENTS
TITLE
i
DECLARATION
ii
ACKNOWLEDGEMENT
iii
ABSTRACT
iv
ABSTRAK
v
LIST OF TABLES
LIST OF FIGURES
CHAPTER 1
viii
x
INTRODUCTION
1
1.1 Background Study
1
1.2 Problem statement
2
1.3 Objectives
3
1.4 Scope of Study
3
1.5 Significant of study
3
CHAPTER 2
LITERATURE REVIEW
5
2.1 Introduction
5
2.2 Heat exchanger system
5
2.2.1 Shell and tube heat exchanger system
6
2.2.2 Counter and parallel flow heat exchanger system
7
2.2.3 Cross flow heat exchanger system
8
2.2.4 Plate heat exchanger system
8
2.3 Electro hydraulic servo system
9
2.4 Proportional-Integral-Derivative (PID) controller
9
2.4.1 Proportional controller
10
2.4.2 Intergral controller
10
2.4.3 Genetic Algorithm
10
vii
2.5 Artificial Intelligence
10
2.5.1 Genetic Algorithm
11
2.5.2 Particle Swarm Optimization
11
2.5.3 Whale optimization algorithm
12
2.5.4 Ant colony optimization
12
2.6 Proportional-Integrative-Derivative controller with GA and PSO for
CHAPTER 3
Heat exchanger and EHSS
13
METHODOLOGY
14
3.1 Introduction
14
3.2 Flow chart
15
3.3 Simulation studies
16
3.3.1 Heat exchanger system
16
3.3.1 Electro hydraulic servo system
17
3.4 Control algorithm
CHAPTER 4
19
3.4.1 Tuning with PID controller
19
3.4.2 PID tuning with GA
20
3.4.3 PID tuning with PSO
23
RESULTS AND DISCUSSION
24
4.1 Introduction
24
4.2 PID controller
24
4.3 PID optimized by GA
26
4.4 PID optimized by PSO
35
4.5 Discussion
42
CHAPTER 5
CONCUSSION AND RECOMMENDATIONS
46
5.1 Conclusion
46
5.2 Recommendation
47
REFERENCE
48
viii
LIST OF TABLES
3.1
Experimental process data for HE (Nandhini et al, 2018)
16
3.2
Experimental process data for EHSS (Sachin&Swankar, 2014)
18
3.3
PID values from Z-N tuning method for HE
19
3.4
PID values from Z-N tuning method for EHSS (Tandan & Swankar, 2015) 20
3.5
Range of PID values for HE system (Kumar & Garg, 2015)
21
3.6
Range of PID values for EHSS system (Nandhini et al, 2018)
22
3.7
Controller parameter for GA-PID (Nandhini et al, 2018)
23
3.8
Controller parameter for PSO (Jalilvand, 2011 and Aekarin & Wudhichai,
2016)
4.1
23
Comparison of step response result between with and without controller for
HE and EHSS systems
26
4.2
Table of experiment and its condition for GA
27
4.3
Data for Experiment 1
28
4.4
Data for Experiment 2
28
4.5
Data for Experiment 3
29
4.6
Data for Experiment 4
29
4.7
Data for Experiment 5
30
4.8
Data for Experiment 6
30
4.9
Data for Experiment 7
31
4.10 Data for Experiment 8
31
4.11 Step response result for GA-PID in HE system
32
4.12 Step response result for GA-PID in EHSS system
34
4.13 Table of experiment and its condition for PSO
35
4.14 Data for Experiment 1
36
4.15 Data for Experiment 2
36
4.16 Data for Experiment 3
37
ix
4.17 Data for Experiment 4
37
4.18 Data for Experiment 5
38
4.19 Data for Experiment 6
38
4.20 Data for Experiment 7
39
4.21 Data for Experiment 8
39
4.22 Step response result for PSO-PID in HE system
40
4.23 Step response result for PSO-PID in EHSS system
42
4.24 Comparison between step response result for HE and EHSS system
44
x
LIST OF FIGURES
2.2
Counter flow heat exchanger
7
2.3
Cross flow heat exchanger
7
2.1
Parallel flow heat exchanger
8
3.1
Flow chart
15
3.2
Block diagram of HE system (Sachin&Swankar, 2014)
17
3.3
Block diagram of EHSS system
18
3.4
Block diagram of classical PID controller
19
3.5
Block diagram of GA-PID controller
20
3.6
Flow chart of GA (Ravi et al, 2014)
22
4.1
Step response graph for HE system with and without PID cntroller
25
4.2
Step response graph for EHSS system with and without PID controller
25
4.3
Convergence graph for Experiment 1
28
4.4
Convergence graph for Experiment 2
28
4.5
Convergence graph for Experiment 3
29
4.6
Convergence graph for Experiment 4
29
4.7
Convergence graph for Experiment 5
30
4.8
Convergence graph for Experiment 6
30
4.9
Convergence graph for Experiment 7
31
4.10
Convergence graph for Experiment 8
31
4.11
Step response for GA-PID in HE system
32
4.12
Step response for GA-PID in EHSS system
33
4.13
Convergence graph for Experiment 1
36
4.14
Convergence graph for Experiment 2
36
4.15
Convergence graph for Experiment 3
37
4.16
Convergence graph for Experiment 4
37
4.17
Convergence graph for Experiment 5
38
xi
4.18
Convergence graph for Experiment 6
38
4.19
Convergence graph for Experiment 7
39
4.20
Convergence graph for Experiment 8
39
4.21
Step response for PSO-PID in HE system
40
4.22
Step response for PSO-PID in EHSS system
41
4.23
Step response graph for HE system
43
4.24
Step response graph for EHSS system
44
1
CHAPTER 1
INTRODUCTION
1.1
Background study
The engineering mechanical industry do have various division which focus on
different part such as design, manufacture, process, system, oil and gas and
engineering devices. Heat exchanger (HE) is one of the example of engineering
devices while electro hydraulic servo system (EHSS) is one of the system that are
widely used in engineering industry.
A heat exchanger (HE) is an engineering technology devices that work as a
heat transfer which exchange the heat between two or more fluids (Pandhee, 2014).
Bahman Zohuri (2017) stated that HE have widespread industrial and domestic
applications. Many types of HE have been developed for use in steam power plants,
chemical processing plants, building heat and air conditioning systems, transportation
power system and refrigeration units. The process fluid of the heat exchanger are need
to be heated to a certain temperature set points and the outlet temperature is the one
that are measured (Yehia, 2016). In order to control the outlet temperature of the heat
exchanger, PID controller is used as the medium to control it. Heat exchanger also a
third order transfer function control system.
Electro hydraulic servo system (EHSS) has a fifth order transfer function
control system. EHSS has a high power to weight ratio, high payload capability and
high stiffness also fast response and high degree of both accuracy and performance
which make the system widely used in many industrial application (Kumar Mishra
& Kumar Swarnkar, 2014). However, the behaviour of EHSS system is highly
nonlinear and time-varying with uncertainties parameters which make it difficult to
2
control (Jian Ming et al, 2013). Hence, PID controller is used to control the system
to gain the desired parameter.
Proportional, integral and derivative (PID) controller is a common form of
feedback (Ku Yusoff et al., 2015) which has been successfully adapted in industrial
engineering process since it is a simple and easy design controller (Sungthonga &
Assawinchaichote, 2016). According to Subhransu Pandhee (2014), even though
many other superior controller do exist, the ease of PID and proven track record of
PID controller makes it an evident choice for most of control problem. Yet,
Sungthonga and Assawinchaichote (2016) stated that, PID controller still has some
weaknesses such as difficulty to tuning the parameters and nonlinearity. Therefore,
many artificial intelligence techniques have been developed to gain the optimum
proportional, integral and derivative control parameter for PID controllers such as
Genetic Algorithm, Particle Swarm Optimization and Whale optimization.
Optimization technique optimally tune the three terms of classical PID controller to
regulate nonlinear process (Elbayomy et al., 2008). Since HE and EHSS are two
different system, this study propose to design a PID controller model for HE which
is a third order control system and EHSS, a fifth order control system using Genetic
Algorithm and Particle Swarm Optimization. For this two optimization tools, it has
been successfully applied in many areas in engineering and also science field (Jesus
& Barbosa, 2011). Also, to investigate which type of optimization will give the
optimal gain of step response result to both systems.
1.2
Problem Statement
In recent years, studies on performance of heat exchanger and electro hydraulic servo
system have been done extensively. However, for heat exchanger, it might be
challenging and difficult to control the outlet temperature at specific set points. Since
PID controller already used to control the system, it can help the system to get that
desired outlet temperature. However, classical PID controller cannot respond to major
disturbance, where it will effecting the controller and make the system instable (Yehia
et al, 2016).
Electro hydraulic servo system generate very high forces, exhibit fast
responses, and have high power. However, the system has the phenomenon such as
3
nonlinear servo valve flow-pressure characteristics, variations in trapped fluid which
make the performance of the system highly nonlinear and will make it difficult to
control the system (Tandan & Swankar, 2015). Since it is nonlinear dynamic system,
classical PID cannot give it best parameter when the controller is in a linear format.
(Samakwong & Assawinchaichote, 2016).
1.3
Research objective
This study achieved these following objectives:
1.
To optimized the performance of PID controller of HE and EHSS using
Genetic Algorithm (GA) and Particle Swarm Optimization (PSO).
2.
To compare the results of classical PID controller and optimization PID
controller.
1.4
Scope of study
The scope of this study are:
1.
Optimization are based on Genetic Algorithm (GA) and Particle Swarm
Optimization (PSO) only.
2.
Evaluating the optimized system and reduce the rise time and overshoot
percentage to threefold.
3.
1.5
The simulation were done by MATLAB software.
Significance of study
Heat Exchanger (HE) and Electro hydraulic servo system (EHSS) were two systems
that commonly used in engineering industry. There were many method used to make
the performance of the system better to gain its best value and achieve its objective of
using those systems.
4
Commonly, proportional-integral-derivative (PID) controller were used in
these systems. Though it is known to be a good controller, it can be better by using
some optimization tools. Genetic Algorithm (GA) and Particle Swarm Optimization
(PSO) are two example of optimization tools that can optimize the PID controller of
the HE and EHSS systems. The performance and result of optimized PID was
evaluated and analyse in step response.
In this project, the analysis was made by GA and PSO to optimize the PID
controller and were generated by using MATLAB software. This study is significance
to acknowledge the industry about the best method that they can use to have best
performance of a control system. They also can know which parameter suit best with
the systems.
5
CHAPTER 2
LITERATURE REVIEW
2.1
Introduction
In few years back, industrial engineering has used many type of system to ease the
work and complete the thing that need to be done in order to cope with people or
government needs. There are few engineering systems that very popular amongst
industry including Heat Exchanger (HE) and Electro Hydraulic Servo System (EHSS).
These two systems has common control system which both of it used PID controller.
In HE system, PID controller was used to regulate the outlet temperature of the system
according to desired needs while PID controller in EHSS was used to control and
improve the angular position response of the hydraulic rotary actuator. However, the
uses of PID controller does not give the best parameter gain for both HE and EHSS.
So, the artificial intelligence approach was suggested to improve the parameter gain
for both of the systems.
2.2
Heat exchanger system
Heat exchanger is very common engineering device. There are few types of heat
exchanger that have already created to fulfill the industrial needs. The basic principle
for all of heat exchanger is to change the output temperature of the fluid. Heat
exchanger are used in both heating and cooling process. Figure 2.1 shows the basic
principle of heat exchanger.
6
Figure 2.1: Principle of heat exchanger
2.2.1
Shell and tube heat exchanger system
For shell and tube heat exchanger, it is normal to have chemical reactor when there is
heating chemical process. The steam that comes from the boiler is the super-heated
one and it will flow through the tube. The output which is the fluid from the process
will be stored in the storage tank where it will then been supplied to heat exchanger
system. The heat exchanger will heat up the fluid which is supplied from the boiler to
a desired set point by using the super-heated steam. The fluid is supplied from the
storage tank by pump and non-returning valve. Also all the non-condensed steam will
go out from the heat exchanger by path to avoid a blocking in the system. (Kocher &
Dr. Kori, 2015).
In the heat exchanger system, the inlet fluid is at constant velocity. The
temperature of the inlet fluid and the steam is vary to some random functions of time.
The heat transfer coefficient which is steam side (ℎ𝑜 ) and water side (ℎ𝑖 ) is what the
heat transfer from the steam is depend on. Noted that the resistance of the metal wall
is deserted. (Sharma et al, 2011).
There are few factors that effects the dynamics of the heat exchanger which is
the difference between temperature, flow rate of fluid and the area of heat transfer.
Figure 1 shows, the basic principle of heat exchanger system (Pandhee, 2014).
7
2.2.2
Counter and parallel flow heat exchanger system
Counter and parallel flow heat exchanger is one of the simple heat exchanger system
which the fluid flow either in same or opposite direction. One fluid in counter flow
heat exchanger flow opposite direction to the other flow while parallel flow heat
exchanger is vice versa (Sridhar & Bicha, 2017). Figure 2.2 and figure 2.3 show the
illustrated diagram of the heat exchanger. The heat transfer for counter and parallel
flow heat exchanger involve conduction and convection. One of the fluid conductively
transferred the heat at the wall while another fluid convectively transfer heat to the
opposite wall. The temperature of the fluid inside the heat exchanger is not smoothly
constant along the heat exchanger but the rate of heat transfer is varies along the length
of the tubes due to some differences in temperature between the two fluids. (“Parallel
and Counter Flow Design”, n.d.)
Figure 2.2: Parallel flow heat exchanger
Figure 2.3: Counter flow heat exchanger
8
2.2.3
Cross flow heat exchanger system
Cross flow heat exchanger basically occurred when one fluid flows perpendicular to
the other flow of the fluid. The other fluid flow passes across the tube at 90 degree
angle (“Cross Flow Type Heat Exchange”, n.d.) as illustrated in figure 2.4. Most of
cross flow heat exchanger are gas to liquid heat exchanger where gas as the outside
fluid and liquid as the tube side fluid. (Mohammed et al., 2018). Fins addition and
corrugations to one or both of the directions might affect the heat exchanger’s
performance which then increase the surface area. This addition may cause fluid flow
or induce turbulence (Raju et al., 2014).
Figure 2.4: Cross flow heat exchanger
2.2.4
Plate heat exchanger system
A plate heat exchanger consists of a pack of thin rectangular plates where the fluid
flow through the portholes. The plate is place in parallel in series formation that placed
one above the other so that the formation will allow the fluid flow channel between
them. Inlet and outlet holes at the corners of the plate make both of the fluids (hot and
cold) alternatingly channels in the heat exchanger so the plate will always contacting
with hot fluid at one side, and cold fluid on the other side. (Golin, n.d.). In this heat
exchanger system, narrow channel flow make the system experienced high pressure
loss that occurred due to large turbulence.
9
2.3
Electro hydraulic servo system
The electro hydraulic servo system (EHSS) consists of a pressure vane pump, a two
stage servo valve, amplifier, and a fixed hydraulic motor with a mechanical feedback.
A part of motor is attached with a shaft for position measurement. Basically, this type
of hydraulic system applied to any machine that requires fast response and accurate
control also can handle the changes in load. The servo amplifier resulting the voltage
from the control signal. The valve in the system controlling the flow of the fluid with
the help of motor. Since the system very time varying make it difficult to control the
system so that, controller is designed to resolve the time varying behavior (Kumar
Mishra & Kumar Swarnkar, 2014).
2.4
Proportional-Integral-Derivative (PID) controller
The design of PID controller has been used for a long time also it is the common
controller in market. Convectional PID controller has widely used since its
introduction long time ago, 97% of the controllers has PID structure. Low cost,
inexpensive maintenance, and the simplicity of the controller might be the reason why
it is so famous in industry. As many used of controller in industry, many researcher
has done extensively research about PID to find the optimum value of the parameter
such as trial and error method and classical tuning (Hassan et al., 2012). This type of
controller is a linear control. Also, the difference between the actual output and the
desired output from the controller operates directly on the error signal (Jalilvand et al.,
2011).
The controller itself involve with three basic parameter which is proportional
gain (𝐾𝑃 ), integral gain (𝐾𝑖 ) and derivative gain (𝐾𝑑 ) that provide the closed loop
performance. The three parameter should be adjusted in order to design a controller
and from that value, the plant could accept the performance provide by the control
input (Jalilvand et al., 2011). Step response parameter can be gain from these value
that where the stability of the system can be satisfied.
10
2.4.1
Proportional controller
This type of controller which is proportional controller (𝐾𝑃 ) is really important in
control system. This controller can never eliminate the steady state error but it has the
effect of reducing the rise time value. If the value of 𝐾𝑃 increase, the response can go
faster but in fact it will create an oscillating output if the value is too large. (Aranza et
al, 2016)
2.4.2
Integral controller
The term integral in integral controller (𝐾𝑖 ) accelerate the movement process towards
the set point and eliminate the remaining error. The value of 𝐾𝑖 might cause high
transient response even if it can improve the response while eliminating the steady
state error and then cause the instability of the system (Aranza et al, 2016).
2.4.3
Derivative controller
Selection of the proper value of𝐾𝑑 , can help improve the stability of the system. If the
system parameter is rapidly increasing, the derivative factor will cause the output to
decrease. If the derivative time increase, the response of the control system will be
much stronger in the error term and speed of the control system (Aranza et al, 2016).
2.5
Artificial Intelligence
Artificial intelligence (AI) has been used in a while in various field such as gaming,
natural language system and expert system industry. AI help the system to gain its
desired output. It is a collection of concepts such as psychology, mathematics and
technologies combined. It is also act as a computer-controlled robot to perform any
task that usually related with intelligent human beings. It is also the advancement of
the machine which in integrative science.
11
Studying human brain thinks, decide, learning also work when trying to
complete and solve a problem is the accomplishment made by AI. Optimizations was
produce from the AI for existing practice. There are few optimization that are used for
heat exchanger and EHSS.
2.5.1
Genetic Algorithm
Genetic algorithm (GA) is a modern optimization technique that many researcher has
been studied to finding the best optimum value of PID parameter. For complex search
space and can give best approximately solution for any problem is what GA is good
for because it do not make any random assumption about the fitness function (Faris
Ku Yusoff et al, 2015). Also, the ideas of evolutionary is the base of natural selection
and genetics. According to Darwin’s principle, the GA is based on the survival of the
fittest, and how the competition produce better adapted generation in their problem
solution space (El-Telbany, 2007).
The GA has several parameters that need to take into account which is
crossover, mutation and population. It evolves the new generations individually by
using the previous knowledge of generations. The fundamental of GA is the
chromosomes that contained in the finest solution which included in the blocks of
genetic information. It is then increase the frequency if the opportunity of the
chromosomes is related to fit its fitness functions. Then, the crossover probability is
choose and the pair of each chosen chromosomes will have a random chosen position.
After that, it will subjected to that mutation operator (Jalilvand, 2011). The value of
mutation is important for GA to finally find the optimum solution to the given
problem.
2.5.2
Particle Swarm Optimization
Particle Swarm Optimization is inspired by the behavior and migrant of swarmintelligence and also the dynamic movements of birds. It is used for a controller to
find the parameters that give minimum value for the stated objective function. Also,
PSO is applied to bigger range of problem in order to find the best global solution.
The algorithm of PSO hold many solutions in one time and all the solution was
12
described as particle in its fitness search space. To reduce the objective function, each
of the particle will migrate through the search space (Nandhini et al., 2018).
Parameter that include in this algorithm is inertia weight, acceleration
coefficient and population. The inertia weight is important to help controlling the
previous velocities and its impact to the current velocity. In this way, the value of
inertia weight can help to regulate the exploration abilities between the global and
local of the swarm (El-Telbany, 2007).
2.5.3
Whale optimization algorithm
Whale optimization algorithm is a new heuristic algorithm. Whale can portray
emotions, judgement also the social behavior like a human because they have spindle
cells like a human. Bubble net feeding method is the special hunting method that the
humpback of the whale has. The parameter that need to have in this algorithm is the
value of population (search agent). To find the desired result, it first initialize the
population number, maximum iteration and design variable. Then calculate the value
of fitness function and the best value will pick up and other population will try to
update their best position (Mosaad, 2019).
2.5.4
Ant colony optimization
Ant colony optimization (ACO) is a population-based metaheuristic that can be used
to find the accurate solution for a difficult optimization problems. Artificial ants search
is the software agents to gain the best solution for the given optimization problem. To
give an applied to ACO, the optimization problem is then transformed into a problem
of finding the best solution in weighted graph. The moving on the graph is from the
solution that being built incrementally by the artificial ant (Dorigo, n.d.).
The application of ACO is from the behavior of ants searching for foods. The
ants wander at the first place and when the ant finds the source of food, it walks back
from the place and come to their colony and leaving the marks (pheromones) to show
that the path has food. The other ants will follow the path to find the food. When the
ants drop the pheromones, path that are shorter expected to be stronger hence,
13
optimizing the solution. Next, the ACO work well on a very dynamic system. (“Ant
Colony Algorithm”, n.d.)
2.6
Proportional-Integrative-Derivative controller with GA and PSO for Heat
exchanger and EHSS
According to Rajasekaran & Dr. Kannadasan (2012), control system performance
effect the total plant operation that is why controlling the system properly by controller
and optimization technique is important to have a good performance of the system.
Thus, PID controller became the approach to control the system. There are several
method that have been proposed to tuning a PID controller such as automatic tuning,
trial and error and Ziegler-Nichols method. From those methods, Zeigler-Nichols
might be the most famous method to tune PID controller (Tandan & Swankar, 2015).
Yet, Nandhini et al (2018) stated that traditional PID controller cannot give
satisfactory performance when it is used to control a non-linear system.
For heat exchanger, the using of PID in the system cannot give the desired
output parameter (Pandhee et al., 2011) and for EHSS, based on Samakwong &
Assawinchaichote (2016) since system is non-linear dynamic system, the PID
controller used, provides high overshoot response to the system. Hence, to improve
the performance of the convectional PID, many intelligent approach has been
introduced to improve the PID parameter such as GA and PSO. This GA-PID and
PSO-PID is proposed in order to find the optimal performance of the control
parameter. This optimized PID is expected to have minimum rise time, settling time
and overshoot (Tandan & Swarnkar, 2015).
14
CHAPTER 3
METHODOLOGY
3.1
Introduction
In this chapter, GA-PID and PSO-PID are discussed and were analyzed in step
response. The optimum value of optimized PID parameter for HE and EHSS were
gained and compared to the step response results of classical PID.
15
3.2
Flow chart
Figure 3.1: Flow chart
16
3.3
Simulation Studies
Simulation studies is a computer program and the other way to find the result for a
real-world problem system, event, or process.
3.3.1
Heat exchanger system
For HE system, counter flow heat exchanger was used in this study. The system
contain pump, control valves, pressure converter, heat exchanger and transmitter.
Other important part that act as a controlling equipment is the rota-meter, RTD sensor
and computer. The air regulator should always maintain at 20 psi.
The value of input and output data from the heat exchanger to gain the accurate
transfer function model. The tank is filled up with hot water and the temperature is
maintained at 70 ̊C. The inlet flow rate of the hot fluid is maintained constant at 50%
of the valve and another 40% for the cold fluid in order to get the variation in outlet
temperature. Based on the obtained result, transfer function for the heat exchanger is
calculated. Table 3.1 show the summarized experimental process data (Nandhini et
al., 2018).
Table 3.1: Experimental process data for HE system (Nandhini et al., 2018)
Variables
Values
Valve transfer function
0.13
s  52.06
Process transfer function
50
s  95.51
Gain current to pressure converter
0.743
Sensor transfer function
0.007522
45.242s  1
From the Table 3.1, a transfer function was created as shown in Equation (3.1)
(Nandhini et al., 2018).
17
Figure 3.2: Block diagram of HE system
C s  
3.3.2
48.29 s  1.0675
s  0.718 s 2  0.3916 s  0.007522
(3.1)
3
Electro hydraulic servo system
Electro hydraulic servo system consisted of a two stage electro hydraulic servo valve.
Other than that, it also consist of the hydraulic amplifier and armature flapper. Figure
3.3 shows the block diagram of the system. When the coil has been applied to the
electrical control signal, the resultant torque is proportional to the current, then the
torque make the flapper plate to move. The flapper then move to the jet area. The
movement of the jet make a difference in pressure at flapper valve. The pressure
difference that was produced by the flapper valve, move the spool valve hydraulically
(Elbayomy et al., 2008).
The standard values for the variable mentioned is vary to the system. In this
dissertation, the values is based on the bases of researcher (Kumar Mishra & Kumar
Swarnkar, 2014). Table 3.2 showed the experimental data for EHSS system while the
transfer function for the system was shown as in equation (3.2).
18
Table 3.2: Experimental process data for EHSS (Sachin and Swankar, 2014).
Variables
Armature Flapper
Values
1
Kr
 2   s 
1    s   
 n   n 
Spool
2
1
AS s
Torque of motor
𝐾1
Spool of gain
𝐾3
Feedback gain
𝐾𝑤
Figure 3.3: Block diagram of EHSS system (Mishra and Swankar, 2014)
The value in Table 3.2 shows the appropriate transfer function by the standard Moog
servo valve which will then produce a complete transfer function of the system. The
standard values of all the variables changes based on plant. In this project, standardize
value by an expert were used (Sachin and Swankar, 2014). Equation (3.2) shows the
transfer function of the electro hydraulic servo system:
25.28s 2  22.20s  3
Gs   5
s  16.60s 4  25.41s 3  17.20s 2  12s  1
(3.2)
19
3.4
Control algorithm
3.4.1
Tuning with PID controller
The block diagram of a closed loop feedback control for heat exchanger can be seen
in Figure 3.3 using the classical PID controller.
Figure 3.4: Block diagram of classical PID controller
A form of PID controller can be presented as (Sungthonga & Assawinchaichote,
2016):
G ( s)  K p 
(3.3)
Ki
 Kd s
s
Where 𝐾𝑃 is proportional gain, 𝐾𝑖 is integral gain and 𝐾𝑑 is derivative gain
There are various method to tuning the PID controller, some use frequency response
analysis and also there are method that use based on the performance analysis
minimization. Experiment also can be a method to tune a PID controller (Pandhee,
2014). Based on several research paper, Ziegler-Nichols (Z-N) method is commonly
used to obtain the PID parameters. Table 3.3 shows the values of PID parameter
through Z-N tuning method for heat exchanger system. (Nandhini et al, 2018)
Table 3.3: PID values from Z-N tuning method for HE system (Nandhini et al, 2018)
Parameters
Values
𝐾𝑃
0.5318
𝐾𝑖
0.8067
𝐾𝑑
0.0570
20
Based on the other journal, the best value for PID controller for EHSS is obtained from
the same method, which is Z-N method (Tandan & Swarnkar, 2015). Table 3.4 show
the value of PID parameter.
Table 3.4: PID values from Z-N tuning method for EHSS (Tandan & Swarnkar,
2015)
3.4.2
Parameters
Values
𝐾𝑝
3.9563
𝐾𝑖
4.1688
𝐾𝑑
0.9384
PID tuning with GA
Several different techniques have been developed over the past few years to obtain the
optimum proportional, integral and derivative control parameters for PID controllers
including GA. To tune the PID controller with GA, there are few thing that need to be
considered. Figure 3.5 show the block diagram of GA-PID.
Figure 3.5: Block diagram of GA-PID controller
For every optimization based PID, objective function plays a big role while tuning the
controller parameter. The feedback function is as shown at equation (3.4)
Error 1  feedback system
(3.4)
21
The optimization objective function is to minimize the following performance criteria
of PID controller that measure the response error which is Integral Time Absolute
Error (ITAE) as shown in equation (3.5)

(3.5)
ITAE   t e(t ) dt
0
A set of range of Kp, Ki and Kd, were decided before the simulation can be run in
MATLAB, alongside the other parameters that are crucial for GA optimized PID such
as mutation rate, crossover rate, number of population and number of iteration. Table
3.5 shows the range of the PID value for HE system (Kumar & Garg, 2015) while
Table 3.6 shows the range of PID values for EHSS system. (Nandhini et al, 2018)
Table 3.5: Range of PID values for HE system (Kumar & Garg, 2015)
PID parameter
Minimum
Maximum
Kp
0
10
Ki
0
10
Kd
0
10
Table 3.6: Range of PID values for EHSS system (Nandhini et al, 2018)
PID parameter
Minimum
Maximum
Kp
0
10
Ki
0
10
Kd
0
10
Table 3.7 shows the controller parameter that are needed before optimized PID can
run in MATLAB. Both heat exchanger and EHSS used the same controller parameter.
22
Table 3.7: Controller parameter for GA-PID (Nandhini et al, 2018)
Controller parameter
Values
No of population
30
Crossover probability
0.9-0.95
Mutation probability
0.05-0.2
No of iteration
50
The basic process of genetic algorithm that being used in MATLAB can be outlines
into 6 basic steps as Figure 3.5 (Ravi et al., 2014).
Figure 3.6: Flow chart of GA (Ravi et al., 2014)
23
3.4.3
PID tuning with PSO
Particle swarm optimization is one of the smart swarm techniques, each particle in the
swarm has the same characteristics and behaviors in the concept of PSO. But each
particle has a random variable of position and velocity. (Aekarin & Wudhichai, 2016)
The velocity is dependent on the global and particle’s best solution. If the i-th
particle of the swarm is represented by the D–dimensional vector Xi  xi1, xi 2 xiD 
and the best particle in the swarm is denoted by the gbest. The best previous position
of the i-th particle is recorded and represented as Pi   pi1, pi 2 piD  and the
location change (velocity) of the i-th particle is Vi  vi1, vi2viD . The particles are
manipulated according to the equations (3.8) (Mohammed El-Saied, 2007):
Vid  w.  Vid  c1  r1   pid  xid   c2  r 2 pid  vid 
(3.8)
xid  xid  vid
(3.9)
Where d  1, 2,and D  1, 2, N is the size of population; w is the inertia weight;
c1 and c2 are two positive constants and r1 and r2 are random values in the range [0,1].
Table 3.8 shows the controller parameter tuning PSO (Jalilvand, 2011 and Aekarin &
Wudhichai, 2016)
Table 3.8: Controller parameter for PSO (Jalilvand, 2011 and Aekarin & Wudhichai,
2016)
Controller parameter
Values
No of population
30-100
Weighting inertia
0.4,0.9
Acceleration coefficient, c1, c2
2.0
Maximum iteration
100
Problem dimension
3.0
24
CHAPTER 4
RESULT AND DISCUSSION
4.1
Introduction
This chapter discuss the result obtained from the simulation of MATLAB. The
discussion is referring to the objective which is the selection and optimization of PID
parameters using Genetic Algorithm (GA) and Particle Swarm Optimization (PSO)
for Heat Exchanger (HE) and Electro Hydraulic Servo System (EHSS). All the results
was recorded by using MATLAB software and all the graph also from the same
software.
4.2
PID Controller
The performance of a system can be enhance by the presence of PID controller. The
controller can decrease the percentage of overshoot in step response of the system.
Figure 4.1 and figure 4.2 shows the step response of HE and EHSS respectively.
25
Figure 4.1: Step Response Graph for HE system with and without PID Controller
From figure 4.1 shows the step response for HE system with and without
controller. The value of 𝐾𝑃 , 𝐾𝑖 and 𝐾𝑑 use in the controller is 𝐾𝑃 = 0.5218, 𝐾𝑖 = 0.8067
and 𝐾𝑑 = 0.0570.
Figure 4.2: Step Response Graph for EHSS System with and without PID Controller
26
From figure 4.1 shows the step response for EHSS system with and without
controller. The value of 𝐾𝑃 , 𝐾𝑖 and 𝐾𝑑 use in the controller is 𝐾𝑃 = 3.9563, 𝐾𝑖 = 4.1688
and 𝐾𝑑 = 0.9384. Table 4.1 shows the comparison of the step response specification
between with and without controller for both system.
Table 4.1: Comparison of step response result between with and without controller
for HE and EHSS systems
Heat Exchanger
Characteristic
EHSS
Without
With PID
Without
With PID
Controller
controller
Controller
controller
Overshoot, 𝑀𝑝 (%)
85.3
56.3
54.2
58.4
Peak time, 𝑇𝑝 (sec)
0.523
0.45
2.2
1.08
Rise time, 𝑇𝑟 (sec)
0.207
0.155
18.6
10.2
Settling time, 𝑇𝑠 (sec)
10.9
4.07
0.811
0.386
From table 4.1, we can clearly see the comparison for both systems between
with and without PID controller. For HE system, the step response result shows
improvement from system without controller and with controller. The value of
overshoot percentage was improved by 33% and other value were improved by more
than 10%. Meanwhile, for EHSS system, the step response result shows the system
with PID controller has lower value compared to the system without PID controller
except for the value for overshoot which has higher percentage for system without
controller. The value of peak time, rise time and settling time for system with
controller are 1.08, 10.2 and 0.386 respectively while the results for system without
controller are 2.2, 18.6 and 0.811 respectively.
4.3
PID Optimized by GA
Parameter for PID controller that optimized by GA is used to develop a better control
system for heat exchanger system and electro hydraulic servo system so it can improve
the performance of the systems. The objective is to achieve a desire step responses
which is low in values for step response result compared to the system without PID
controller.
27
In GA optimization, there are few conditions that were manipulated which is
the number of mutation probability and crossover probability. These manipulation
conditions was set to see the difference in step responses and also to determine which
parameter gives the best results. Eight different experiments were ran for each system.
Table 4.2 shows the conditions for GA where the iteration number, population number
and error criterion were kept the same for all experiments while mutation probability
and crossover probability were varied.
Table 4.2: Table of experiment and its condition for GA
Experiment No.
Error Criteria
1
2
3
4
5
6
7
8
ITAE
ITAE
ITAE
ITAE
ITAE
ITAE
ITAE
ITAE
Iteration
Number
50
50
50
50
50
50
50
50
Population
Number
30
30
30
30
30
30
30
30
Mutation
Probability
0.90
0.90
0.90
0.90
0.95
0.95
0.95
0.95
Crossover
Probability
0.05
0.10
0.15
0.20
0.05
0.10
0.15
0.20
The experiment for GA is run for 9 trial and the data is saved in matrix form
of A x (B x C), where matrix A shows the four optimizes result which is fitness
function, proportional gain ( 𝐾𝑃 ), integral gain (𝐾𝑖 ), and derivative gain (𝐾𝑑 ). Matrix
B represents the row of trial and matrix C represent the row of number of iteration for
each trial. Thus, the matrix form saved for all experiments produce 450 data. The best
trial is chosen from the convergence graph that also generated from MATLAB
software. Best convergence in GA is selected by choose the best fitness function which
is the lowest number of convergence.
28
Table 4.3: Data for Experiment 1
Fitness Solution
𝐾𝑃
𝐾𝑖
𝐾𝑑
0.0091
0.0233
0.0095
0.0091
0.0233
0.0233
0.0124
0.0091
0.0091
99.45
200
99.75
99.74
200
200
124.79
99.39
99.29
200
200
200
200
200
200
200
199.97
200
8.76
300
7.88
8.71
300
300
8.25
8.79
8.87
Figure 4.3: Convergence graph for Experiment 1
Table 4.4: Data for Experiment 2
Figure 4.4: Convergence graph for Experiment 2
Fitness Solution
𝐾𝑃
𝐾𝑖
𝐾𝑑
0.0091
0.0091
0.0094
0.0233
0.0141
0.0091
0.0091
0.0233
0.0091
99.46
99.31
101.07
200
93.03
99.35
99.82
200
99.22
200
200
200
200
188.95
200
200
200
200
8.70
8.59
8.05
300
5.18
8.68
8.73
300
8.63
29
Table 4.5: Data for Experiment 3
Fitness Solution
𝐾𝑃
𝐾𝑖
𝐾𝑑
0.0096
0.0091
0.0104
0.0091
0.0091
0.0091
0.0094
0.0160
0.0091
96.15
99.61
97.59
99.31
99.75
98.96
99.52
199.95
99.49
194.71
200
199.65
200
200
199.88
200
200
200
7.96
8.67
7.13
8.69
8.72
8.63
7.98
12.83
8.74
Figure 4.5: Convergence graph for Experiment 3
Table 4.6: Data for Experiment 4
Figure 4.6: Convergence graph for Experiment 4
Fitness Solution
𝐾𝑃
𝐾𝑖
𝐾𝑑
0.0233
0.0091
0.0091
0.0233
0.0091
0.0091
0.0233
0.0091
0.0091
200
99.67
99.51
200
99.47
99.68
200
99.59
99.59
200
200
200
200
200
200
200
200
200
300
8.52
8.72
300
8.75
8.73
300
8.41
8.74
30
Table 4.7: Data for Experiment 5
Fitness Solution
𝐾𝑃
𝐾𝑖
𝐾𝑑
0.0091
0.0091
0.0091
0.0091
0.0091
0.0233
0.0091
0.0091
0.0112
99.56
99.25
100.01
99.21
99.25
200
99.46
99.76
98.19
200
200
200
200
200
200
200
200
199.09
8.42
8.76
8.78
8.71
8.46
300
8.79
8.63
6.59
Figure 4.7: Convergence graph for Experiment 5
Table 4.8: Data for Experiment 6
Figure 4.8: Convergence graph for Experiment 6
Fitness Solution
𝐾𝑃
𝐾𝑖
𝐾𝑑
0.0106
0.0091
0.0091
0.0093
0.0091
0.0186
0.0091
0.0091
0.0185
97.04
99.35
99.37
99.13
99.55
91.42
99.53
99.53
74.83
197.63
200
200
200
200
185.30
200
200
148.86
7.01
8.76
8.69
8.16
8.73
3.68
8.57
8.50
6.57
31
Table 4.9: Data for Experiment 7
Fitness Solution
𝐾𝑃
𝐾𝑖
𝐾𝑑
0.0091
0.0091
0.0233
0.0091
0.0091
0.0100
0.0091
0.0091
0.0091
99.40
99.51
200
99.52
99.47
91.13
99.27
99.52
99.40
200
200
200
200
200
200
200
200
200
8.75
8.73
300
8.74
8.56
7.42
8.76
8.53
8.76
Figure 4.9: Convergence graph for Experiment 7
Table 4.10: Data for Experiment 8
Figure 4.10: Convergence graph for Experiment 8
Fitness Solution
𝐾𝑃
𝐾𝑖
𝐾𝑑
0.0091
0.0091
0.0103
0.0091
0.0091
0.0100
0.0091
0.0091
0.0091
99.53
99.45
98.88
99.13
99.41
91.51
99.38
99.61
99.68
200
200
200
200
200
200
200
200
200
8.68
8.74
7.18
8.84
8.74
8.74
8.75
8.65
8.43
32
Heat Exchanger
From each of the experiments, the best fitness were selected which is the lowest
number of fitness solution. Then, all the values were interpreted into step response
graph to see the difference in step response result of the system. Figure 4.11 shows the
step response graph of GA-PID for HE system while table 4.11 shows the step
response result.
Figure 4.11: Step response for GA-PID in Heat Exchanger system
Table 4.11: Step response result for GA-PID in Heat Exchanger system
Experiment
Characteristic
1
2
3
4
5
6
7
8
1
99.45
200
8.76
1
99.46
200
8.70
9
99.49
200
8.74
5
99.47
200
8.75
2
99.25
200
8.76
2
99.35
200
8.76
1
99.40
200
8.75
7
99.38
200
8.75
2.25
2.25
2.23
2.23
2.22
2.22
2.22
2.22
Peak time, 𝑇𝑝 (sec)
0.014
0.014
0.014
0.014
0.014
0.014
0.014
0.014
Rise time, 𝑇𝑟 (sec)
0.0049
0.0049
0.0049
0.0049
0.0049
0.0049
0.0049
0.0049
0.014
0.014
0.014
0.014
0.014
0.014
0.014
0.014
Best trial
𝐾𝑃
𝐾𝑖
𝐾𝑑
Overshoot, 𝑀𝑝 (%)
Settling time, 𝑇𝑠
(sec)
33
From figure 4.11, we can see that the plotting of graph for all the data is seemingly
same. While from table 4.11, the step response result shows that the value for peak
time, rise time and settling time were same for all experiments which is 0.014, 0.0049
and 0.014 respectively except for the overshoot value where there were different for
some of experiment. The overshoot values are 2.25, 2.23 and 2.22.
Electro Hydraulic Servo System
For EHSS system, the data were also interpreted into one graph. Figure 4.12 shows the
step response graph of GA-PID for EHSS system while table 4.12 shows the step
response result.
Figure 4.12: Step response for GA-PID in EHSS system
34
Table 4.12: Step response result for GA-PID in EHSS system
Experiment
Characteristic
1
2
3
4
5
6
7
8
1
99.45
200
8.76
1
99.46
200
8.70
9
99.49
200
8.74
5
99.47
200
8.75
2
99.25
200
8.76
2
99.35
200
8.76
1
99.40
200
8.75
7
99.38
200
8.75
91
91.3
91
90.9
90.7
90.8
90.9
90.9
Peak time, 𝑇𝑝 (sec)
0.227
0.226
0.227
0.228
0.228
0.228
0.228
0.228
Rise time, 𝑇𝑟 (sec)
0.0741
0.0742
0.0741
0.0741
0.0741
0.0741
0.0741
0.0741
4.27
4.29
4.27
4.26
4.05
4.25
4.26
4.26
Best trial
𝐾𝑃
𝐾𝑖
𝐾𝑑
Overshoot, 𝑀𝑝 (%)
Settling time, 𝑇𝑠
(sec)
From the graph, we can see that the data approached to the same place which make
the graph quiet same for all the experiments. From table 4.12, the result also shows
quiet same value for all experiment where only small difference between the results.
The value for overshoot are around 90.7% to 91.3%. Next, the value for peak time
and settling time are around 0.226 seconds to 0.228 seconds and 4.05 to 4.29
respectively. Meanwhile for rise time, the values for all the experiments is 0.0741
except for experiment 2 which is 0.226.
35
4.4
PID Optimized by PSO
Parameter for PID controller that optimized by PSO is also intended to improve the
performance of the system by develop a better control system for heat exchanger
system and electro hydraulic servo system. The objective is to minimize the step
response result by less than 1% for HE system and 5% for EHSS system overshoot
value and less than 1 second for rise time.
The conditions that were manipulated in PSO optimization was the number of
population while number of iteration, weighting inertia and the acceleration coefficient
were maintained the same. Eight different experiments were ran for each system. Table
4.13 shows the conditions for PSO where the population number are manipulated
while other conditions were same.
Table 4.13: Table of experiment and its condition for PSO
Experiment
No.
Error
Criteria
1
2
3
4
5
6
7
8
ITAE
ITAE
ITAE
ITAE
ITAE
ITAE
ITAE
ITAE
Acceleration
Coefficient,
c1,c2
2
2
2
2
2
2
2
2
Iteration
Number
100
100
100
100
100
100
100
100
Weighting
Inertia,
𝑊𝑚𝑖𝑛
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
Weighting
Inertia,
𝑊𝑚𝑎𝑥
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
Population
Number
30
40
50
60
70
80
90
100
For each configuration in PSO system, the configuration were run for 10 trial
separately. The files for each configuration is save manually. The result from the PSO
will show the best gain of the optimization. All the experiments produced a total of
1000 data (100 x 10). Since there are 10 trial in each experiment, the best gain in the
best run will form a convergence graph that is generated using MATLAB software
36
Table 4.14: Data for Experiment 1
Characteristic
Value
Fitness Function
10.1559
Best Run
2
𝐾𝑃
0.2834
𝐾𝑖
1.5418
𝐾𝑑
3.1655
Figure 4.13: Convergence graph for Experiment 1
Table 4.15: Data for Experiment 2
Figure 4.14: Convergence graph for Experiment 2
Characteristic
Value
Fitness Function
9.4080
Best Run
6
𝐾𝑃
0.4397
𝐾𝑖
1.4548
𝐾𝑑
3.1039
37
Table 4.16: Data for Experiment 3
Characteristic
Value
Fitness Function
9.3989
Best Run
4
𝐾𝑃
0.4417
𝐾𝑖
1.4542
𝐾𝑑
3.1038
Figure 4.15: Convergence graph for Experiment 3
Table 4.17: Data for Experiment 4
Figure 4.16: Convergence graph for Experiment 4
Characteristic
Value
Fitness Function
9.4118
Best Run
6
𝐾𝑃
0.4576
𝐾𝑖
1.4438
𝐾𝑑
3.0970
38
Table 4.18: Data for Experiment 5
Characteristic
Value
Fitness Function
9.3956
Best Run
1
𝐾𝑃
0.4381
𝐾𝑖
1.4565
𝐾𝑑
3.1051
Figure 4.17: Convergence graph for Experiment 5
Table 4.19: Data for Experiment 6
Figure 4.18: Convergence graph for Experiment 6
Characteristic
Value
Fitness Function
9.4068
Best Run
7
𝐾𝑃
0.4398
𝐾𝑖
1.4544
𝐾𝑑
3.1024
39
Table 4.20: Data for Experiment 7
Characteristic
Value
Fitness Function
9.4023
Best Run
3
𝐾𝑃
0.4491
𝐾𝑖
1.4495
𝐾𝑑
3.1010
Figure 4.19: Convergence graph for Experiment 7
Table 4.21: Data for Experiment 8
Figure 4.20: Convergence graph for Experiment 8
Characteristic
Value
Fitness Function
9.3961
Best Run
8
𝐾𝑃
0.4365
𝐾𝑖
1.4575
𝐾𝑑
3.1055
40
Heat Exchanger
The PSO results produced the best solution for each experiment. Next, all the values
were inferred into step response graph to see the difference in step response result of
the system. Figure 4.21 shows the step response graph of PSO-PID for HE system
while table 4.22 shows the step response result.
Figure 4.21: Step response for PSO-PID in HE system
Table 4.22: Step response result for PSO-PID in HE system
Experiment
Characteristic
1
2
3
4
5
6
7
8
2
0.2834
1.5418
3.1655
6
0.4397
1.4548
3.1039
4
0.4417
1.4542
3.1038
6
0.4576
1.4438
3.0970
1
0.4381
1.4565
3.1051
7
0.4398
1.4544
3.1024
3
0.4491
1.4495
3.1010
8
0.4365
1.4575
3.1055
Overshoot, 𝑀𝑝 (%)
0
0
0
0
0
0
0
0
Peak time, 𝑇𝑝 (sec)
0.0687
0.0701
0.0701
0.0703
0.0701
0.0701
0.0702
0.0701
Rise time, 𝑇𝑟 (sec)
0.0146
0.0148
0.0148
0.0149
0.0148
0.0148
0.0148
0.0148
0.0269
0.0273
0.0273
0.0274
0.0273
0.0273
0.0273
0.0273
Best Run
𝐾𝑃
𝐾𝑖
𝐾𝑑
Settling time, 𝑇𝑠
(sec)
41
From figure 4.21, the step response shows same plotting for all experiment. As for the
result, the value for overshoot percentage is zero for all experiment, and other
characteristic has slightly different value from each other with 0.001 seconds
difference. The value of rise time also less than 1 second.
Electro Hydraulic Servo System
For EHSS system, the data were also interpreted into one graph. Figure 4.22 shows the
step response graph of PSO-PID for EHSS system while table 4.23 shows the step
response result.
Figure 4.22: Step response for PSO-PID in EHSS system
42
Table 4.23: Step response result for PSO-PID in EHSS system
Experiment
Characteristic
1
2
3
4
5
6
7
8
2
0.2834
1.5418
3.1655
6
0.4397
1.4548
3.1039
4
0.4417
1.4542
3.1038
6
0.4576
1.4438
3.0970
1
0.4381
1.4565
3.1051
7
0.4398
1.4544
3.1024
3
0.4491
1.4495
3.1010
8
0.4365
1.4575
3.1055
5.1505
4.2157
4.2046
4.1310
4.2215
4.2140
4.1700
4.2289
Peak time, 𝑇𝑝 (sec)
5.8828
6.2666
6.2728
6.3279
6.2605
6.2666
6.2973
6.2544
Rise time, 𝑇𝑟 (sec)
0.4311
0.4199
0.4196
0.4189
0.4198
0.4204
0.4191
0.4200
16.2508
8.1973
8.2007
8.2230
8.1898
8.1962
8.2230
8.1847
Best trial
𝐾𝑃
𝐾𝑖
𝐾𝑑
Overshoot, 𝑀𝑝 (%)
Settling time, 𝑇𝑠
(sec)
From the graph, we can see that the data approached to the same place which make
the graph quiet same for all the experiments. From table 4.23, the result also shows
quiet same value for all experiment where only small difference between the results.
The value for overshoot are around 90.7% to 91.3%. Next, the value for peak time
and settling time are around 0.226 seconds to 0.228 seconds and 4.05 to 4.29
respectively. Meanwhile for rise time, the values for all the experiments is 0.0741
except for experiment 2 which is 0.226.
4.5
Discussion
The optimized PID intended to give best result and better performance for a control
system. The result from the experiments shows incredibly better result compared to
the system without PID.
For GA-PID, experiment 1 to 4 shows the value of 𝐾𝑝 are more than 99.45 while
other 4 experiments shows less than 99.45. This value may varied due to the difference
value of mutation probability used which was 0.9 for experiment 1 to 4 and 0.95 for
experiment 5 to 8. The value of 𝐾𝑖 are same for all experiments which was 200 while
𝐾𝑑 has the lowest value among all. In HE system, the step response results for all
experiment are same except for the overshoot percentage. The same result of step
response may occurred due to the PID value that quite same for all experiments.
Meanwhile, in EHSS system the result shows that the value of overshoot percentage
43
is high which is more that 90% but has lower value of peak time and rise which is less
than 1 second.
Next, for PSO-PID, the value of PID achieved is similar for every experiment
with the value of 𝐾𝑃 was lower compared to 𝐾𝑖 and 𝐾𝑑 value. The value of 𝐾𝑃 will
determined the speed of the control system where we can see by the result of overshoot
percentage. Lower value of 𝐾𝑃 will lead to lower value of overshoot percentage. In HE
system, the best fit for the system was the experiment 1 where all the result showed
lower value compared to other experiments. Experiment 1 showed no overshoot
percentage and 0.0146 seconds for rise time. Subsequently, for EHSS system, the best
fit for the system was experiment 5 which the result showed consistent lower value for
all the step response result.
Figure 4.23 shows the graph of comparison for HE system while figure 4.24 shows the
comparison step response for EHSS system.
Figure 4.23: Step response graph for HE system
44
Figure 4.24: Step response graph for EHSS system
Table 4.24: Comparison between step response result for HE and EHSS system
HE
Characteristic
Without
PID
Not
optimized
PID
EHSS
GA-
PSO-
Without
PID
PID
PID
Not
optimized
PID
GA-
PSO-
PID
PID
Overshoot, 𝑀𝑝 (%)
85.3
56.3
2.22
0
54.2
58.4
90.7
4.2215
Peak time, 𝑇𝑝 (sec)
0.523
0.45
0.014
0.0687
2.2
1.08
0.228
6.2605
Rise time, 𝑇𝑟 (sec)
0.207
0.155
0.0049
0.0146
18.6
10.2
0.0741
0.4198
10.9
4.07
0.014
0.0269
0.811
0.386
4.05
8.1898
Settling time, 𝑇𝑠
(sec)
From table 4.24, we can see the difference between the step response results for both
system. For HE system, the optimized PID improved the overshoot percentage close
to 90% also, the rise time improved by 87%. PSO-PID showed the best result between
the two optimization methods for HE system with no overshoot percentage and less
than 1 second for rise time. While for EHSS system, the optimized result showed the
overshoot percentage were improved by 92% for PSO but not improved in GA. For
GA-PID, despite from its high value of overshoot, its rise time managed to improve
45
by 90% same goes to PSO-PID. In this system, PSO-PID showed the consistent step
response result by means, PSO can give best performance for the control system in
EHSS.
46
CHAPTER 5
CONCLUSION AND RECOMMENDATION
5.1
Conclusion
This project is to design a PID controller for Heat Exchanger system (HE) and Electro
Hydraulic Servo System (EHSS) that has been optimized. There are two method of
optimization used in this project which is Genetic Algorithm (GA) and Particle Swarm
Optimization (PSO). Both optimization were planned to improve the performance for
both system. By applying the principle of GA and PSO to optimize the PID, 8
experiments were for each optimization for both system.
Based on analysis in previous chapter, we can see that PID value gained in all
experiment quite same for GA and also PSO. Similar value of PID resulting to similar
gain for step response result. In GA, high value of mutation probability give low value
of K_p. But, these slightly difference in value does not effecting the result of step
response in GA even the overshoot percentage different for some experiment, but it is
still small difference by 0.01. On the other hand, step response result for PSO showed
similar value, this also may due to alike of optimized PSO-PID.
From figure 4.23, figure 4.24 and figure 4.23, we can clearly see that PSO is
the best optimization method for both systems as it give the best step response result
and improved the step response compared to the system without PID and not optimized
PID using MATLAB software.
47
5.2
Recommendation
Throughout this project, there are few challenges were faced in terms of deciding the
parameter for the optimization method. There are some recommendation and
improvements that can be made for future work:
1.
Expanding the number of iteration and population for GA to see the variety
of step response result for the system.
2.
Include the Internal Model Based Controller which also help with
minimizing the overshoot percentage but in simpler way and see the
different with optimization method.
48
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