Ministry of Higher Education
& Scientific Research
University of Technology
Chemical Engineering Department
Comparative Study of
Temperature Control in a Heat
Exchanger Process
A Thesis
Submitted to the
Department of Chemical Engineering of the University of
Technology in Partial Fulfillment of the Requirements for the
Degree of Master of Science in Chemical Engineering / Unit
Operation
By
Afraa Hilal Kamel Al-Tae
(B.Sc. in Chemical Engineering 2005)
Supervised by
Prof. Dr. Safa A. Al-Naimi
March
2011
SUPERVISOR CERTIFICATION
I certify that this thesis entitled "Comparative Study of
Temperature Control in a Heat Exchanger Process" presented by Afraa
Hilal Kamel Al-Tae was prepared under my supervision in partial
fulfillment of the requirements for the degree of Master of Science in
Chemical Engineering at the Chemical Engineering Department,
University of Technology.
Signature:
Prof. Dr. Safa A. Al-Naimi
(Supervisor)
Date: / / 2011
In view of the available recommendations I forward this thesis for
debate by the Examination Committee.
Signature:
Asst. Prof. Dr. Mohammed I. Mohammed
Head of Post Graduate Committee
Department of Chemical Engineering
Date: / / 2011
CERTIFICATION
This
is
"Comparative
to
certify
Study
of
that
I
have
Temperature
read
the
Control
thesis
in
a
titled
Heat
Exchanger Process" and corrected any grammatical mistakes I
found. The thesis is therefore qualified for debate.
Signature:
Prof. Dr. Mumtaz A. Zablouk
University of Technology
Date: /
/ 2011
CERTIFICATE
We certify that we have read this thesis entitled "Comparative
Study of Temperature Control in a Heat Exchanger Process" by Afraa
Hilal Kamel Al-Tae and as an Examining Committee examined the
student in its contents and that in our opinion it meets the standard of a
thesis for the degree of Master of Science in Chemical Engineering.
Signature:
Prof. Dr. Safa A. Al-Naimi
(Supervisor)
Date:
/
/ 2011
Signature:
Signature:
Assist. Prof. Dr. Hassan W. Hilou
Dr. Zaidoon M. Shakoor
(Member)
Date:
/
(Member)
/ 2011
Date:
/
/ 2011
Signature:
Assist. Prof. Dr. Kutaeba J. Al-Khishali
(Chairman)
Date:
/
/ 2011
Approved for the University of Technology
Signature:
Prof. Dr. Mumtaz A. Zablouk
Head of Chemical Engineering Department
Date:
/
/ 2011
Acknowledgments
First of all, praise is to Allah for every thing. Without his great
assistance the work wouldn't have been finished.
I would like to express my sincere appreciation and thanks to my
supervisor Prof. Dr. Safa A. Al-Naimi, for his constant guidance and
valuable comments, without which, this thesis would not have been
successfully completed.
My grateful thanks to Prof. Dr. Mumtaz A. Zablouk, the Chairman
of the Department of Chemical Engineering at the University of
Technology for the provision of research facilities.
My deep thanks go to Assist. Prof. Dr. Mohammed I. Mohammed,
the head of post graduate committee for all the help and encouragement,
also I wish to express my sincere gratitude to Dr. Orooba N. Abdullah for
her support and helpful advice.
Special thanks to Assist. Prof. Dr. Amer Al-Dabagh, Mr. Basheer
Ahmed, Mr. Alaa Hussain and Mr. Khalid Mansoor for their help and
support.
Also I would like to convey my sincere appreciation to all staff of
Chemical Engineering Department in the University of Technology and the
workshops unit especially the welding workshop.
Finally, to all that helped me in one way or another, I wish to express
my thanks.
Afraa
Abstract
In this work the dynamic behavior of a plate heat exchanger (PHE)
(single pass counter current consists of 24 plates) both experimentally and
theoretically and the control of the system were studied. Different control
strategies; conventional feedback control, classical fuzzy logic control,
artificial neural network (NARMA-L2) control and PID fuzzy control were
used to control the outlet cold water temperature.
A step change is carried in the hot water flow rate which is
considered as a manipulated variable.
The experimental heat transfer measurements of the PHE show that
the overall heat transfer coefficient (U) is related to the hot water flow rate
(m h ) by a correlation having the form:
U = 11045 m
0.7158
h
In this work the PHE model is found dynamically as a first order lead
and second order overdamped lag while the experimental PHE represented
dynamically as a first order with negligible dead time value.
A comparison between the experimental and the theoretical model is
carried out and good agreement is obtained.
The response of 24 plates when justifying the design fitness of the
PHE, proved that the design is accurate and there are no losses in the
energy input.
The performance criteria used for different control modes are the
integral square error (ISE) and integral time-weighted absolute error
(ITAE) where the ITAE gave better performance. As well as the
parameters of the step performance of the system such as overshoot value,
settling time and rise time are used to evaluate the performance of different
control strategies.
The tuning of control parameters were determined for PI and PID
controllers by two different methods; Ziegler-Nichols (Bode diagram), and
Cohen-Coon (process reaction curve) to find the best values of proportional
gain (K c ), integral time (τ I ) and derivative time (τ D ).
Accurate results have been obtained using artificial neural network
over PI, PID and classical fuzzy logic controller. The PID fuzzy controller
gave better control results of temperature rather than PI, PID, classical
fuzzy logic and artificial neural network controller because PID fuzzy
controller combines the advantages of a fuzzy logic controller and a PID
controller.
The best value of settling time and overshoot were found of 0.432
and 1.0 respectively which represent the PID fuzzy controller, while the
best rise time found of 0.077 which represent the PID controller.
The lower value of ITAE of 0.0031 is obtained which represent the
PID fuzzy controller and to certain the best strategy of control among the
others.
MATLAB program version 7.10 was used as a tool of simulation for
all the studies mentioned in this work.
Contents
Contents
I
List of Abbreviations
V
Nomenclature
VI
Greek Symbols
VII
Symbol
VII
List of Tables
VIII
List of Figures
X
Chapter One: Introduction
1.1
Introduction
1
1.2
Control of Heat Exchangers
4
1.3
Aim of the Work
6
Chapter Two: Literature Survey
2.1
Introduction
8
2.2
Dynamic Modeling of Heat Exchanger
8
2.3
Control of Heat Exchangers
11
2.3.1
Conventional PI and PID Control
12
2.3.2
Computational Intelligence Techniques
13
2.3.2.1
Fuzzy Logic Control
13
2.3.2.2
Artificial Neural Network Control
15
Chapter Three: Experimental Work
3.1
Introduction
21
3.2
Description of the Experimental Rig
21
3.2.1
Plate Heat Exchanger
21
3.2.2
Sump Tank for Hot Water
22
3.2.3
Cooling Tower
26
3.2.4
Temperature Measurement
27
3.2.5
Water Flow rate Measurement
29
3.3
Description of the Computer Control System
29
3.4
Experimental Procedure
33
3.4.1
Steady - State Data
33
3.4.2
Dynamic Response Data
34
Chapter Four: Modeling and Theoretical Analysis
4.1
Introduction
36
4.2
Model Assumptions
37
4.3
Energy Balance
38
4.3.1
Energy Balance around Cold Plate
38
4.3.2
Energy Balance around Hot Plate
39
4.4
Control Strategies
41
4.4.1
Conventional Feedback Control
41
4.4.2
Controller Tuning
44
4.4.3
Fuzzy Logic Control
45
4.4.3.1
Introduction of Fuzzy Logic
45
4.4.3.2
Linguistic Variables
46
4.4.3.3
Fuzzy Logic Controller
47
4.4.3.3.1
Design of Fuzzy Logic Controller
48
4.4.4
Artificial Neural Network Control
51
4.4.4.1
Introduction of Artificial Neural Network
51
4.4.4.2
Biological Artificial Neural Network
51
4.4.4.3
Mathematical Model of a Neuron
52
4.4.4.4
Architecture of Artificial Neural Network
54
4.4.4.5
4.4.4.6
4.4.4.6.1
Back Propagation (BP) Algorithm Artificial
Neural Network
Artificial Neural Network Controller
Identification and Controller Stages of the
NARMA-L2 model
55
58
59
Chapter Five: Results and Discussion
5.1
Introduction
64
5.2
Open Loop System
64
5.2.1
Steady State Results
64
5.2.2
Dynamic Behavior
66
5.2.3
Justifying the Design Fitness of the PHE
68
5.3
Closed Loop System
70
5.3.1
Conventional Feedback Control
70
5.3.1.1
Control Behavior
72
5.3.2
Fuzzy Logic Controller
74
5.3.3
5.3.4
5.3.5
Artificial
Neural
Network
NARMA-L2
Controller
PID Fuzzy Controller
Comparison Among PID, Artificial Neural
Network and PID Fuzzy Controllers
78
82
86
Chapter Six: Conclusions and Future Work
6.1
Conclusions
89
6.2
Future Work
90
References
Appendices
Appendix A: Calibration Curves of Thermocouples
A.1
Appendix B: System and Operating Conditions
B.1
Appendix C: Controller Tuning Methods
C.1
C.1
Cohen-Coon Method
C.1
C.2
Ziegler-Nichols Method
C.2
Appendix D: MATLAB Program
D.1
D.1
D.1
Introduction
D.2
Open Loop Programs
D.3
D.3
Close Loop Programs
D.4
D.3.1
Ziegler-Nichols Method
D.4
D.3.2
Cohen-Coon Method
D.7
Appendix
E:
Experimental
Data
of
Dynamic
E.1
Behavior
Appendix F: Calculation of Overall Heat Transfer
Coefficient (U)
V
F.1
List of Abbreviations
Symbol
AC
AI
ANN
AO
APV
BP
CI
Definition
Alternating Current
Analog Input
Artificial Neural Network
Analog Output
Aluminum Plant and Vessel
Back-Propagation
Computational Intelligence
CPT
Crude Preheat Train
DAQ
de
DI
DO
e
Er
FL
GM
G PRC
GRNN
HE
ISE
ITAE
MLBP
MLP
MSE
N
NARMA-L2
NARX
NB
NN
NNPC
NS
P
PB
PHE
PI
PID
PS
RMSE
SISO
Data Acquisition Board
Change of Error
Digital Input
Digital Output
Error
Relative Error
Fuzzy Logic
Gain Margin
Process Reaction Curve Transfer Function
General Regression Neural Network
Heat Exchanger
Integral Square Error
Integral Time-weighted Absolute Error
Multi-Layer Back Propagation
Multi Layer Perceptron
Mean Square Error
Negative
Nonlinear Auto Regressive-Moving Average
Nonlinear Auto Regressive with eXogenous
Negative Big
Neural Network
Neural Network Predictive Control
Negative Small
Positive
Positive Big
Plate Heat Exchanger
Proportional-Integral
Proportional-Integral-Derivative
Positive Small
Root Mean Square Error
Single Input-Single Output
V
Symbol
V AC
V DC
Z
Definition
Alternating Current Voltage
Direct Current Voltage
Zero
Nomenclature
Symbol
A
CP
C Pc
C Ph
G
Gc
Gm
Gp
Gv
h
K
Kc
KD
KI
Ku
mc
Mc
mh
Mh
pu
s
S
t
T ci
T co
td
T hi
T ho
u
U
Definition
Area of heat transfer
Heat capacity
Cold heat capacity
Hot heat capacity
Transfer function
Transfer function of controller
Transfer function of measurment
Transfer function of process
Transfer function of control valve
Heat transfer coefficient
Steady-state gain of the process reaction
curve method
Proportional gain
Derivative gain
Integral gain
Ultimate gain
Cold water flow rate
Cold water mass
Hot water flow rate
Hot water mass
Ultimate period of sustained cycling
Laplacian variable
Slop of the tangent at the point of inflection
of the process reaction curve method
Time
Inlet cold water temperature
Outlet cold water temperature
Time delay
Inlet hot water temperature
Outlet hot water temperature
Control Action
Overall heat transfer coefficient
Units
m2
J/kg.oC
J/kg.oC
J/kg.oC
−
−
−
−
−
w/m2.oC
o
C
Volt/oC
Volt/oC
Volt/oC
decibels
Kg/sec
Kg
Kg/sec
Kg
sec/cycle
−
−
sec
o
C
o
C
sec
o
C
o
C
−
w/m2.oC
Greek Symbols
Symbol
µ
ΔT lm
τ
τa
τc
τD
τh
τI
τp
ψ
ω
Definition
Membership function
Logarithmic mean temperature difference
Time constant of the process reaction curve
method
Lead time constant
Cold time constant
Derivative time constant
Hot time constant
Integral time constant
Lag time constant
Damping coefficient
Crossover frequency
Symbol
Symbol
'
̅ ¯
°
Definition
Unsteady state
Deviation
Steady state
Units
−
o
C
sec
sec
sec
sec
sec
sec
sec
−
rad/sec
List of Tables
Table
Table (2.1) represents the articles of controlling the
HE.
Page
19
Table (3.1) Plate heat exchanger specifications
22
Table (3.2) Description of the experimental rig
25
Table (3.3) Standardized detail of the K-type
thermocouple
Table (4.1) IF-THEN rule base for fuzzy logic control
28
50
Table (5.1) The relative error (Er) and mean square
error (MSE) between experimental and theoretical
67
(T co ) response
Table (5.2) Control parameters of PI control
70
Table (5.3) Control parameters of PID control
71
Table (5.4) Comparison of different parameters of PI
and PID controllers
Table (5.5) IF-THEN rule base for classical FL control
Table (5.6) Comparison between the performance of
fuzzy logic controller and PID controller
Table (5.7) Different
performance indices and
different parameters of ANN NARMA-L2 controller
Table (5.8) The rule base of PID fuzzy controller
Table (5.9) Different
performance indices and
different parameters in PID fuzzy controller
Table (5.10) Comparison of different performance
indices and different parameters in controllers
71
76
77
82
84
85
87
Table (B.1) System and operating conditions
B.1
Table (D.1) Summary functions in MATLAB program
D.2
Table
Page
Table (E.1) ( ∆ T lm ) vs. (T hi - T ho ) at (m h =0.0497)
E.1
(kg/sec) and (m c =0.0414) (kg/sec)
Table (E.2) ( ∆ T lm ) vs. (T hi - T ho ) at (m h =0.0579)
(kg/sec) and (m c =0.0414) (kg/sec)
Table (E.3) ( ∆ T lm ) vs. (T hi - T ho ) at (m h =0.0662)
(kg/sec) and (m c =0.0414) (kg/sec)
Table (E.4) ( ∆ T lm ) vs. (T hi - T ho ) at (m h =0.0745)
(kg/sec) and (m c =0.0414) (kg/sec)
Table (E.5) ( ∆ T lm ) vs. (T hi - T ho ) at (m h =0.0828)
(kg/sec) and (m c =0.0414) (kg/sec)
Table (E.6) ( ∆ T lm ) vs. (T hi - T ho ) at (m h =0.091) (kg/sec)
and (m c =0.0414) (kg/sec)
Table (E.7) ( ∆ T lm ) vs. (T hi - T ho ) at (m h =0.0993)
(kg/sec) and (m c =0.0414) (kg/sec)
Table (E.8) ( ∆ T lm ) vs. (T hi - T ho ) at (m h =0.1076)
(kg/sec) and (m c =0.0414) (kg/sec)
Table (E.9) ( ∆ T lm ) vs. (T hi - T ho ) at (m h =0.1159)
(kg/sec) and (m c =0.0414) (kg/sec)
Table (E.10) The values of overall heat transfer
coefficient (U) as a function of hot water flow rate (m h )
Table (E.11) System parameters for different step
change
X
E.1
E.2
E.2
E.3
E.3
E.4
E.4
E.5
E.5
E.6
List of Figures
Figure
Page
Fig.(1.1) Gasketed plate-and-frame heat exchanger
3
Fig. (1.2) Flow of fluids through a PHE
4
Fig. (1.3) Schematic diagram of PHE
4
Fig. (3.1) Photographic picture of the experimental rig
23
Fig. (3.2) Schematic diagram of the experimental rig
24
Fig. (3.3) Schematic diagram of the cooling tower
27
Fig. (3.4) Schematic diagram of Signal conditioning
card (T 1 =T ci , T 2 =T co , T 3 =T hi , T 4 =T ho )
30
Fig. (3.5) Photographic picture of the interface unit
(A- DAQ board,
B- Signal conditioning card , C-
30
Relay , D- Power supply)
Fig. (3.6) MATLAB simulink used to operate the PHE
system (T 1 =T ci , T 2 =T co , T 3 =T hi , T 4 =T ho )
Fig. (4.1) Arrangement of cold and hot streams for
PHE (as lumped system)
33
36
Fig. (4.2) (a) Process, (b) Feedback control loop
42
Fig. (4.3) Fuzzy logic control system
48
Fig. (4.4) Biological neuron
52
Fig. (4.5) Basic model of neuron
54
Fig. (4.6) Error back propagation in MLP
58
Fig. (4.7) Neural network training with error backpropagation training algorithm
60
Fig. (4.8) General structure of neural network
62
Fig. (4.9) The block diagram of NARMA-L2
62
Fig. (4.10) The complete controller system with neural
network controller NARMA-L2
X
63
Figure
Fig. (4.11) NARMA-L2 controller simulink block
Fig. (5.1) The relation between overall heat transfer
coefficient (U) and hot water flow rate (m h )
Page
63
65
Fig. (5.2) Comparison between experimental and
theoretical (T co ) response for +ve different step
67
changes in (m h )
Fig. (5.3.a) The outlet cold water temperature
distributions for a counter flow of each plate on PHE
Fig. (5.3.b) The outlet hot water temperature
distributions for a counter flow of each plate on PHE
Fig. (5.4) The final outlet cold water temperature for
each plate vs. number of plates in PHE
Fig. (5.5) Bode diagram of the PHE
Fig. (5.6) Transient response of the PHE with PI
controller mode (unit step change)
Fig. (5.7) Transient response of the PHE with PID
controller mode (unit step change)
Fig. (5.8) The comparison between the transient
response for PI and PID controllers (unit step change)
Fig. (5.9) Simulation model of PHE with classical fuzzy
logic controller
Fig. (5.10) The comparison between the transient
response for PID and classical fuzzy logic controllers
Fig. (5.11) Plant identification window
Fig. (5.12) Simulation model of PHE with ANN
NARMA-L2 controller
68
69
69
72
72
73
73
75
77
79
80
Fig. (5.13) Training of ANN NARMA-L2 controller
80
Fig. (5.14) Testing of ANN NARMA-L2 controller
81
Figure
Fig. (5.15) The performance of ANN NARMA-L2
control
Fig. (5.16) Transient response of the PHE with ANN
NARMA-L2 controller
Fig. (5.17) Simulation model of PHE with PID fuzzy
controller
Fig. (5.18) Transient response of the PHE with PID
fuzzy controller
Fig. (5.19) The comparison among the transient
response for PID, ANN and PID fuzzy controllers
Fig. (A.1) Calibration curve of the thermocouple
Fig. (A.2) Calibration curve of cold water
rotameter
Fig. (A.3) Calibration curve of hot water
rotameter
Page
81
82
83
85
86
A.1
A.1
A.1
Fig. (C.1) (a) Temperature curve for Cohen-Coon
tuning. (b) Temperature curve approximation with a
C.2
first order dead-time system
Fig. (C.2) Definition of gain and phase margins
C.3
Fig. (E.1) Temperature difference (T hi - T ho ) as a
function of ( ∆ T lm ) for (m h =0.0497) (kg/sec) and
E.6
(m c =0.0414) (kg/sec)
Fig. (E.2) Temperature difference (T hi - T ho ) as a
function of ( ∆ T lm ) for (m h =0.0579) (kg/sec) and
E.7
(m c =0.0414) (kg/sec)
Fig. (E.3) Temperature difference (T hi - T ho ) as a
function of ( ∆ T lm ) for (m h =0.0662) (kg/sec) and
(m c =0.0414) (kg/sec)
E.7
Figure
Page
Fig. (E.4) Temperature difference (T hi - T ho ) as a
function of ( ∆ T lm ) for (m h =0.0745) (kg/sec) and
E.7
(m c =0.0414) (kg/sec)
Fig. (E.5) Temperature difference (T hi - T ho ) as a
function of ( ∆ T lm ) for (m h =0.0828) (kg/sec) and
E.8
(m c =0.0414) (kg/sec)
Fig. (E.6) Temperature difference (T hi - T ho ) as a
function of ( ∆ T lm ) for (m h =0.091) (kg/sec) and
E.8
(m c =0.0414) (kg/sec)
Fig. (E.7) Temperature difference (T hi - T ho ) as a
function of ( ∆ T lm ) for (m h =0.0993) (kg/sec) and
E.8
(m c =0.0414) (kg/sec)
Fig. (E.8) Temperature difference (T hi - T ho ) as a
function of ( ∆ T lm ) for (m h =0.1076) (kg/sec) and
E.9
(m c =0.0414) (kg/sec)
Fig. (E.9) Temperature difference (T hi - T ho ) as a
function of ( ∆ T lm ) for (m h =0.1159) (kg/sec) and
(m c =0.0414) (kg/sec)
E.9
Chapter One
Introduction
1.1 Introduction
Heat exchangers (HEs) are devices that are used to transfer thermal
energy between two fluid streams at different temperatures without mixing
the two streams.
They are one of the most important and frequently used processes in
engineering, and one of the thermal components that present nonlinear
behavior mainly due to complicated hydrodynamics and temperature
dependence of fluid properties. The heat exchange mechanism depends on
many other variables such as the heat transfer area, temperature difference,
flow rates of the fluids, flow pattern, etc [1-3].
P
P
HEs are key devices used in a wide variety of thermal applications in
the chemical process industries, including petroleum refining and
petrochemical processing; in the food industry, for example, for
0T
0T
pasteurization of milk and canning of processed foods; in the generation of
0T
0T
steam for production of power and electricity; nuclear reaction systems;
aircraft and space vehicles; and in the field of cryogenics for the low0T
0T
temperature separation of gases. HEs are the workhorses of the entire field
of heating, ventilating, air-conditioning, and refrigeration [4, 5].
0T
0T
0T
0T
P
P
There are several different types of HEs including shell-and-tube,
double pipe, plate type and spiral tube. This study is concerned with plate
heat exchanger (PHE), which is one of the most common type in
practice [6].
P
P
The first patent for a PHE was granted, in 1878, to Albretch Dracke,
a German inventor [7], but the first commercially successful plate-and-frame
P
P
heat exchanger in the world was introduced in 1923 by Dr. Richard
Seligman, the founder of the Aluminum Plant and Vessel Company Ltd.,
commonly known today as APV [8]. Around 1930, the company Alfa Laval,
P
P
Sweden, launched an analogous commercial PHE [7].
P
P
Chapter One
Introduction
An PHE is a unit which transfers heat continuously from one media
to another media without adding energy to the process
[8]
P
P
and the PHE is
widely recognized today as the most economical and efficient type of HE
on the market [9].
P
P
On the basis of their specific structure and how the plates are
attached together, several types of PHEs are available, the most common
type is gasketed PHE.
The PHEs consist of a pack of gaskets and corrugated metal plates
pressed together with a frame
[10, 11]
P
. A gasket that seals around the plate
P
prevents fluid mixing. It can also be used to create PHE flow
configurations such as series, parallel, and multi-pass arrangements by
closing and opening ports at the four plate corners [10].
P
P
The number of plates, their perforation, the type and position of the
gaskets and the location of the inlet and outlet connections at the covers
characterize the PHE configuration [11].
P
P
In the 1930’s PHEs were introduced to meet the hygienic demands
of the dairy industry. Today the PHE is universally used in many fields;
heating and ventilating, dairy, food processing, pharmaceuticals and fine
chemicals, petroleum and chemical industries, power generation, offshore
oil and gas production, onboard ships, pulp and paper production, etc [7, 12].
P
P
Nowadays they are finding increasing usage over wide variety of
applications because of the advantages such as flexibility, higher heat
transfer, ease of maintenance, compactness, lower rates of fouling, less
effect of flow induced vibration and better controllability [13], Plates can be
P
P
easily added or removed depending on the desired application and the
equipment is relatively low weight [14].
P
P
PHEs have been successfully used since the 1930s for single-phase
heat transfer from liquid-to-liquid in chemical and food processing
industries [15].
P
P
Chapter One
Introduction
A typical gasketed PHE is the plate-and-frame heat exchanger. The
PHE consists of a pack of corrugated metal plates pressed together into a
frame shown in Fig. (1.1). The gaskets between the plates form a series of
thin channels where the hot and cold fluids flow and exchange heat through
the metal plates. The flow distribution inside the plate pack is defined by
the design of the gaskets, the opened and closed ports of the plates and the
location of the feed connections at the covers [16, 17]. Appropriate design and
P
P
gasketing permit a stack of plates to be held together by compression bolts
joining the end plates. Gaskets prevent leakage to the outside and allow the
inter-plate channels to be sealed and to direct the fluids into alternate
channels, ensuring the two media never mix.
Fig. (1.1) Gasketed plate-and-frame heat exchanger [18].
P
P
The basic operation of a PHE is similar to any other heat exchanger,
in which heat is transferred between two fluid streams through a separating
wall. Here, in this case, the separating wall is a plate which is used for heat
transfer and to prevent mixing of the streams. As it can be seen from
Fig. (1.2) and Fig. (1.3) the hot and cold fluid streams flow into alternate
Chapter One
Introduction
channels between the corrugated plates, entering and leaving via ports at
the corner of the plates. Thus, heat transfer takes place from the warm fluid
through the separating plate to the colder fluid in a pure counter-current
flow arrangement [6].
P
P
Fig. (1.2) Flow of fluids through a PHE [14].
P
P
Fig. (1.3) Schematic diagram of PHE [12].
P
P
1.2 Control of Heat Exchangers
In recent years the performance requirements for process plants have
become increasingly difficult to satisfy. Stronger competition, tougher
Chapter One
Introduction
environmental and safety regulations, and rapidly changing economic
conditions have been key factors in tightening product quality
specifications. A further complication is that modern plants have become
more difficult to operate because of the trend toward complex and highly
integrated processes. For such plants, it is difficult to prevent disturbances
from propagating from one unit to other interconnected units.
In view of the increased emphasis placed on safe, efficient plant
operation, it is only natural that the subject of process control has become
increasingly important in recent years
P
[19]
. Without computer - based
P
process control systems it would be impossible to operate modern plants
safely and profitably while satisfying product quality and environmental
requirements. Thus, it is important for chemical engineers to have an
understanding of both the theory and practice of process control.
The two main subjects related are process dynamics and control. The
term process dynamics refers to unsteady-state (or transient) process
behavior. Transient operation occurs during important situations such as
start-ups and shutdowns, unusual process disturbances, and planned
transitions from one product grade to another.
The primary objective of process control is to maintain a process at
the desired operating conditions, safely and efficiently, while satisfying
environmental and product quality requirements. The subject of process
control is concerned with how to achieve these goals.
Two general approaches to control system design [19]:
P
P
 Traditional Approach. The control strategy and control system
hardware are selected based on knowledge of the process,
experience, and insight. After the control system is installed in the
plant, the controller settings are adjusted. This activity is referred to
as controller tuning.
Chapter One
Introduction
 Model-Based Approach. A dynamic model of the process is first
developed that can be helpful in at least three ways:
i.
It can be used as the basis for model-based controller design
methods.
ii.
The dynamic model can be incorporated directly in the control
law.
iii.
The model can be used in a computer simulation to evaluate
alternative control strategies and to determine preliminary
values of the controller settings.
Several specialized strategies that provide enhanced process control
beyond what can be obtained with conventional PID controllers. As
processing plants become more and more complex in order to increase
efficiency or reduce costs, there are incentives for using such
enhancements, which also fall under the general classification of advanced
control [19].
P
P
There are many different control strategies that have been used such
as conventional feedback control, cascade control, adaptive control, fuzzy
logic (FL) control and artificial neural network (ANN) control [20-24].
P
P
1.3 Aim of the Work
This work is concerned with dynamic behavior of a PHE and the
process control implemented using different control strategies through the
following steps:
1. Determining a correlation for the overall heat transfer coefficient of
the PHE by finding the effect of the hot water flow rate (m h ) on the
R
R
overall heat transfer coefficient (U) obtained from experimental
work.
2. Carrying out the experimental dynamic behavior by measuring the
response of the outlet cold water temperature (T co ) under different
R
R
Chapter One
Introduction
step changes in hot water flow rate (m h ) is compared with the
R
R
simulation results with MATLAB to implement the mathematical
model.
3. Justifying the design fitness of the PHE by determining the
temperature of the inlet and outlet of each plate using a matrix
solution method.
4. Selecting the best control parameters by carrying a tuning procedure
using two performance criteria; the integral of the square error (ISE)
and integral of the time-weighted absolute error (ITAE).
5. Applying different control strategies such as conventional feedback
control, fuzzy logic control and artificial neural network control as
well as a comparison among them.
Chapter Two
Literature Survey
2.1 Introduction
Heat exchangers are equipments which transfer the heat from a fluid
to another for thermal processes in which two fluids have different
temperatures. Plate type heat exchanger (PHE) is the most efficient HE [25].
P
P
PHEs are important components of process and power industry
today. Initially, use of the PHEs was limited to hygienic industries such as
food processing, pharmaceuticals and dairy industries primarily due to their
ease of clearing.
HEs are the subject of many dynamic and control studies. Although
considerable effort has been devoted for describing the dynamic behavior
of HE, little similar work has been done for PHE.
This chapter reviews the literature and studies that deal with
dynamics, different control strategies (conventional feedback, fuzzy logic
and artificial neural network).
2.2 Dynamic Modeling of Heat Exchanger
The objective of the dynamic analysis of the process is to observe
how conditions (variables) change with time. The first step in the analysis
of a dynamic system is to derive its model.
Dynamic process models can be used for simulation studies to get
information about the process behavior; the models can also be used for
control or optimization studies. Process knowledge may be available as
physical relationships or in the form of process data.
Dynamic analysis of HEs provides information about transient
responses subjected to various disturbances [13].
P
P
Modeling is the procedure to formulate the dynamic effects of the
system that will be considered into mathematical equations. The dynamic
behavior can be characterized by the dynamic responses of the system by
Chapter Two
Literature Survey
manipulated inputs and disturbances, taking into account the initial
conditions of the system [26].
P
P
Mathematical models are widely used to design, analyze and control
industrial processes. Steady state models are very useful, but for the
investigation of start-up and control strategies, the dynamic models are
needed.
Experimental measurements can be made only of inlet and outlet
global temperature of PHE, therefore the temperature profile along a PHE
is hardly ever known [27].
P
Alwan
[28]
P
P
studied the dynamic of PHE using step change technique
P
applied to cold water flow rate and other variables were maintained almost
constant. Recorded outlet cold water temperature analyzed by process
reaction curve which shows that the system can be represented as first
order with negligible time delay. Time constant was measured for various
flow rates and it was concluded that the time constant is inversely
proportional to the flow rate.
Baker
[29]
P
P
studied the dynamic characteristics of a PHE by
introducing a sinusoidal disturbance in flow of hot stream through
frequency generator, while inlet temperature of cold, hot streams and flow
rate of cold stream were maintained almost constant. A theoretical model
was proposed based on lumped parameter system. Basic equations were
obtained using energy balance and the analysis represented the system as
first order whereas considering convective mode of heat transfer resulted in
first order lead and second order overdamped lag system for lumped
parameter model expressed as:
G( ) =
S
T ( ) = H (τ s +1 )
m ( ) τ s + 2ψ τ s + 1
a
CO S
2
h S
P
2
p
Where:
G (s) : transfer function.
R
R
T co(s) : outlet cold water temperature.
R
R
……….. (2.1)
Chapter Two
Literature Survey
m h(s) : hot water flow rate.
R
R
H
τa
R
τp
R
: constant.
R
R
Ψ
: lead time constant.
: lag time constant.
: damping coefficient.
Various disturbances were introduced to suggest a model for
comparison with experimental results. They showed that the transfer
function from the final results of experimental and theoretical
investigations referred to PHE was of second order (overdamped) system
lag and first order system lead with dead time.
[30]
Khan, et al.
P
P
carried out theoretical and experimental analyses of
the dynamic of a counter current flow PHE. They have shown that the
transfer function relating the outlet temperature of the cold stream (T co ) and
R
R
the mass flow rate of the hot stream (m h ) were best represented by an
R
R
overdamped second order lag coupled with a first order lead with dead
time, namely:
G (S ) =
T
m
CO ( S )
=
h(S )
(
+1 )e t s
τ s + 2ψ τ s + 1
Hτas
2
−
……….. (2.2)
d
2
P
p
They found that the transfer function of theoretical model based on
lumped parameter system between (T co ) and (m h ) is a second order
R
R
R
R
(overdamped) lag combined with a first order lead.
Al-Zobai
P
[31]
P
conducted a simulation and experimental investigation
to study the dynamic of PHE. He used step change to predict the system
transient response and he found that the system can be represented by first
order lag with dead time. He concluded that the theoretical model based on
lumped parameter system is second order (overdamped) system lag with
first order system lead.
Scariot, et al.
P
[27]
P
studied the dynamic behavior of the temperature
response curves of the product along the PHE and found the best control
parameters by mean of fitting models. The response curves were obtained
Chapter Two
Literature Survey
after step disturbance in the product flow rate, different models were
evaluated to identify the dynamic behavior of the control parameters along
the PHE. The results were obtained using a simulation codified in
MATLAB 6.1 software. The results showed a clear non-linear behavior of
the response curves along the PHE.
Dwivedi and Das
[13]
P
investigated the transient performance of the
P
U-type PHE subjected to step flow disturbances. Experiments were
executed for various possibilities of step flow transients. They showed that
the step change was achieved by changing the hot or the cold flow rate
made a difference in response in the transient regime. They suggested the
scope of the control system required to regulate the outlet temperatures of
the PHEs subjected to dynamic state. Results also indicated the allowable
time duration required for the control system to bring back a PHE to a
steady state.
Thirumarimurugan and Kannadasan
P
[12]
P
studied the performance of
PHE with different systems. The experimental studies involved the
determination of the outlet temperature of both cold and hot fluid for
various flow rates for parallel and counter current flow patterns. The waterwater system and other systems were used to determine the performance of
type HE. They carried out the comparison between parallel flow and
counter current flow HEs.
Kapustenko, et al. [32] developed the simplified models for modeling
P
P
of PHE behavior and they improved the temperature control quality of the
regulator based on butterfly valve.
2.3 Control of Heat Exchangers
The control of HE is complex due to its nonlinear dynamics
[33, 34]
P
and complexity caused by many phenomena such as leakage, friction,
P
Chapter Two
Literature Survey
temperature dependent flow properties, contact resistance, unknown fluid
properties, etc.
2.3.1 Conventional PI and PID Control
The conventional proportional plus integral control (PI) is probably
the most commonly used technique
[35]
P
. The PI controller has received a
P
great deal of attention in the process control areas. It is used as a feed back
controller which drives the plant to be controlled with a weighted sum of
the error and the integral of that value [36].
P
P
PID control is one of the earlier control strategies
P
[37]
P
and it's the
most popular controller used in process control systems due to its
remarkable effectiveness and simplicity of implementation. The technique
is sufficient for the control of most industrial processes and widely used [38].
P
P
It needs very little knowledge about the process [39].
P
P
Many of the studies reported in literature on HE using conventional
PI control, can be found in the literature [40-43].
P
PID
control
of
HE
have
P
been
studied
by
several
researchers [34, 41, 44-55].
P
P
Alwan [28] studied the conventional controllers of PHE. He applied a
P
P
feedback control loop to the system and concluded that steady state offset
of the controlled variable tend to be smaller as the magnitude of flow
disturbance gets smaller for setting of proportional action. He applied
integral controller to eliminate the offset and getting stable operation.
Diaz, et al.
P
[56]
P
designed the PI and PID controllers of the HE to
observe the performance of the controller and to control the temperature of
air passing over it. Also the ANN controller was used for comparison. They
found that the PID controller showed better performance than PI and less
than neural network control in certain cases. They showed that PI and PID
controllers were significantly more oscillated and not able to bring the
Chapter Two
Literature Survey
system to a steady state, but keep the outlet air temperature by adjusting the
air speed.
Al-Zobai
[31]
P
P
conducted a simulation and experimental investigation
to study control of PHE. Temperature control had been investigated using
PI and PID controller implemented using analog and direct digital control
systems. He found the conventional strategy would not be the efficient one.
[57]
Berto and JR.
P
P
implemented and studied the efficiency of the
strategies PID feedback in controlling the pasteurization and the cooling
temperatures in a PHE. The controller was to keep those temperatures
within the range of ±0.5 oC after disturbances in the product inlet
P
P
temperature occurred.
2.3.2 Computational Intelligence Techniques
Traditional control methods have poor performances when applied to
industrial
processes
whose
models
are
strongly non-linear
and
multivariable -based. Better results can be obtained by applying modern
techniques [58].
control
P
P
The computational intelligence (CI) techniques, such as FL and
ANNs, have been successfully applied in many scientific researches and
engineering practices [59].
P
P
2.3.2.1 Fuzzy Logic Control
Fuzzy logic can be easily applied to most of applications in
industry
P
[60]
. Their great advantage is the possibility to introduce the
P
knowledge of human experts about proper and correct control of a plant in
the controller [61].
P
P
FL control provides a formal method of translating subjective and
imprecise human knowledge into control strategies, thus facilitating better
Chapter Two
Literature Survey
system performance through the exploitation and application of that
knowledge [62].
P
P
Many researches about HEs by means of FL were reported in
references [43, 54, 63-67].
P
P
Skrjanc and Matko
[68]
P
P
evaluated the proposed fuzzy predictive
control on HE plant, which exhibits a strong nonlinear behavior. It has been
shown that in the case of nonlinear processes, the approach using fuzzy
predictive control gave very promising results. The main advantage in
comparison to the other modern techniques was simplicity together with
excellent performance.
Al-Zobai
[31]
P
P
investigated temperature control using fuzzy control.
He obtained a good agreement by experimental responses when using
fuzzy control. The fuzzy control algorithm was implemented as a set of
rules expressed by conditional statements. He made comparisons among
different strategies and the results showed that the fuzzy control can be
preferable for control purposes.
Chen, et al. [69] designed an exclusive fuzzy control subsystem. They
P
P
studied the fuzzy control means for the supply air temperature of the HE,
and accomplished the fuzzy control performance test. According to the
their experimental results, the fuzzy control subsystem could not only
reduce the testing time for thermodynamic performances of finned-tube
heat exchanger; but also actualized easily the stable control of the supply
air temperature of the HE.
[25]
Mastacan, et al.
P
P
used soft computing techniques to control the
water temperature of the Alfa Laval type PHE. FL control was
implemented and the good performance of the fuzzy control proves that
this can be an alternative to the classic control.
Maidi, et al.
P
[42]
P
explained the proposed design procedure of an
optimal PID linear fuzzy controller in general and applied to design a linear
Chapter Two
Literature Survey
(PI-FL) controller that allowed the control of the temperature distribution
of the shell and tube heat exchanger. The performance of the fuzzy control
system was evaluated by simulation and compared to the conventional PI
controller designed optimization.
Habbi, et al. [70] first developed a non linear dynamic fuzzy model for
P
P
the HE using a set of input-output observations. The structure in the
collected data was determined by means of fuzzy clustering in the inputoutput product space. They designed an efficient fuzzy model-based leak
detection algorithm for a pilot heat exchanger. They had proven to be
efficient in detecting leaks of different magnitudes in the water circulation
pipe.
2.3.2.2 Artificial Neural Network Control
ANNs were developed a few decades ago and now widely used in
various application areas such as pattern recognition, system identification,
and dynamic control. ANN offers a new way to simulate nonlinear, or
uncertain, or unknown complex system without requiring any explicit
knowledge about input / output relationship [59].
P
P
Use of artificial intelligence is increasing day by day because of it's
adaptability to changes, and ruggedness in control [71].
P
P
A large number of papers dealing with the artificial neural network
for the HE, can be found in the literature [33, 59, 72-81].
P
Diaz
P
[44]
P
P
applied ANNs to the simulation of the steady and dynamic
behaviors of HEs, as well as to the control of fluid temperatures. The
experiments were carried out in a HE test facility. The ANN predications
were obtained using information about the flow rates and inlet temperatures
of both fluids in the HE. Numerical tests showed the feasibility of the
method and experimental comparison with standard control techniques
such as PID proved the ANN to be more accurate.
Chapter Two
Literature Survey
Diaz, et al. [56] extended the ANN technique to control the outlet air
P
P
temperature in HE by changing the air speed. They showed that the present
technique performed better than conventional PI and PID control in certain
cases when the results were compared with those of standard PI and PID
controller. ANN controller was less oscillatory behavior, which allowed the
system to reach steady state operating conditions in regions where the PI
and PID controllers are not able to perform as well.
Diaz, et al.
P
[2]
P
investigated the use of adaptive ANNs to control the
exit air temperature of HE. They showed that ANNs were a powerful
technique to control nonlinear systems. They can be trained to give small
errors in prediction and a stable closed-loop feedback control operation.
The neuro controller was able to control the experimental facility and adapt
to its new conditions for disturbances in the air and water flow rates. It was
also able to learn and control the plant behavior for a change in the set
point of the temperature. They suggested that ANNs were useful for the
control of thermal systems that may change over time.
Kharaajoo and Araabi [82] designed a NN based predictive controller
P
P
to govern the dynamics of a heat exchanger pilot plant. HE was a highly
non linear process. Advantages of NNs for the process modeling were
studied and a NN based predictor was designed, trained and tested as a part
of the predictive controller. The dynamics of the plant was identified using
a multi layer perceptron (MLP) neural network. The predictive control
strategy based on the NN model of the plant was applied then to achieve set
point tracking of the output temperature of the plant. Obtained results
demonstrated the effectiveness and superiority of the proposed approach.
Varshney and Panigrahi
P
[46]
P
implemented the NN based control in a
LABVIEW platform and compared with the PID control. They investigated
experimentally the control of HE in a closed flow air circuit. The
temperature inside the test section of the test facility was maintained at a
Chapter Two
Literature Survey
set value by variation of air flow rate over the heat exchanger tube surface
and the water flow inside the heat exchanger tubes. They showed that the
NN based control had higher speed of response and the steady state error
for NN control had a smaller average value than that of the PID control and
the control action based on the NN technique less oscillation in comparison
to that of the PID based control.
Hu, et al. [4] developed the two ANN-based models of a HE. One of
P
P
them was used to predict the steady-state performance of a HE that can be
used in practical situations. The other one was used to predict its dynamic
performance that can be used in air-conditioning control. They listed
experiences in using ANNs, especially those with back-propagation (BP)
structures. Also, the weights and biases of our trained-up ANN models.
That results showed that NN models were good alternatives to models
based on first principles and an actual ANN-based intelligent control will
be made possible.
Farahani, et al.
[83]
P
dealt with identification and control of a highly
P
nonlinear real world application and demonstrated the performance and
applicability of the proposed methods for an industrial HE. The main
difficulties for identification and control of that plant arise from the
strongly nonlinear center. ANN based predictive controller using multi
layer perceptron (MLP) was designed to govern the dynamics of a HE pilot
plant. Using the neuro predictive controller, the outlet liquid temperature of
the plant tracked the desired set points by applying the liquid flow rate as a
control signal.
Biyanto, et al.
P
[84]
P
proposed the NN model with nonlinear auto
regressive with exogenous input (NARX) structure type multi layer
perceptron and developed to describe the complex behavior of a HE in
crude preheat train (CPT) . They observed that the developed model had a
good predictive capability. The root mean square error (RMSE) between
Chapter Two
Literature Survey
the actual and predicted outlet temperature were found to be less than 0.3
o
P
C. A model with good predictive capabilities can be used as a tool to
P
assess the effect of changes in the operating conditions and feed stocks on
the performance of the HEs.
Selbas, et al.
[85]
P
P
applied NN to predict heat transfer rate for PHE.
The back-propagation algorithm was used to train and test the network.
They were obtained limited experimental data. They showed that the
predicted results by NN approach are close to experimental data. NN
approach was suitable and simple tool for use in the estimation of heat
transfer rates under different operating conditions. The procedure proposed
could help the manufacturer and engineers to model HE in engineering
applications.
Thirumarimurugan and Kannadasan
P
[12]
P
used experimental data to
develop NNs using general regression neural network (GRNN) model.
Those networks were tested with a set of testing data and then the
simulated results were compared with actual results of the testing data
.They showed that the predicted results are close to experimental data by
ANN approach.
Vasickaninova, et al.
P
[34]
P
studied possibility to use a NN predictive
control (NNPC) strategy for control of a HE. The control objective was to
keep the output temperature of the heated stream at a desired value and
minimize the energy consumption. The NNPC of the HE was compared
with classical PID control by simulations experiments. They demonstrated
from comparison of the simulation results obtained using NNPC and those
obtained by classical PID control the effectiveness and superiority of the
NNPC because of smaller consumption of heating medium.
Table (2.1) represents the articles of controlling the HE in general
and PHE in particular.
Chapter Two
Literature Survey
Table (2.1) represents the articles of controlling the HE.
Researchers
Year
Subject
Alwan
1982
Baker
1983
Dynamic behavior and model in PHE
Khan
1988
Dynamic behavior and model in PHE
Diaz
2000
Skrjanc and Matko
2000
Fuzzy control
Diaz and et al.
2001
Adaptive ANN control
Diaz and et al.
2001
Dynamic behavior and conventional
control in PHE
Conventional (PID) control and ANN
control
Conventional (PI, PID) control and
ANN control
Dynamic behavior, model,
Al-Zobai
2004
conventional (PI, PID) control and
fuzzy control in PHE
Berto and JR.
2004
PID feedback control
Kharaajoo and Araabi
2004
ANN control
Hu and et al.
2005
ANN model
Scariot and et al.
2005
Dynamic behavior in PHE
Varshney and Panigrahi
2005
Chen and et al.
2006
Fuzzy control
Farahani and et al.
2006
ANN control
Biyanto and et al.
2007
ANN model
Dwivedi and Das
2007
Dynamic behavior in PHE
Mastacan and et al.
2007
Fuzzy control in PHE
Maidi and et al.
2008
Conventional (PID) control and ANN
control
Conventional (PI) control and fuzzy
control
Chapter Two
Literature Survey
Researchers
Year
Subject
Habbi and et al.
2009
Fuzzy model
Kapustenko and et al.
2009
Model in PHE
Selbas and et al.
2009
ANN model
2009
Steady state and ANN model in PHE
Thirumarimurugan and
Kannadasan
Vasickaninova and et al.
2010
Conventional (PID) control and ANN
control
Chapter Three
Experimental Work
3.1 Introduction
This chapter explains and views in details the experimental part of
this work. It includes the description of experimental rig and the
instrumentation (i.e. computer control system and measuring devices) that
are used during this research and also the experimental procedure
necessary to generate the corresponding data sets.
3.2 Description of the Experimental Rig
The photographic picture and the schematic diagram of the
experimental rig used in the present work are appearing in Fig. (3.1) and
(3.2), respectively. The main items of the rig are discussed in the following
sections:
3.2.1 Plate Heat Exchanger
The main part of the experimental rig is a PHE. It was manufactured
by APV Company Ltd. England type (JHE) serial No. (1062) and the plates
are made of stainless steel with gaskets. It contains 24 corrugated stainless
steel plates assembled in counter-current configuration, single pass / single
pass for both hot and cold streams. The specifications of the PHE are given
in table (3.1) and a listing of experimental rig components appears in
table (3.2).
Chapter Three
Experimental Work
Table (3.1) Plate heat exchanger specifications [86].
P
Plate length (cm)
58
Plate width (cm)
7
Plate thickness (mm)
1
Equivalent diameter
4
of channel (mm)
Channel flow area (m2)
1.4*10-4
Plate pitch (mm)
3
Mean flow channel gap (mm)
2
P
P
P
P
The PHE is arranged as U-type flow configuration. Due to the
availability and high heat capacity of the water, it was employed in the
present work. The use of water as a cooler makes the universal cooling
media.
3.2.2 Sump Tank for Hot Water
The sump tank has a capacity of hot water (0.07) m3. The tank is
P
P
rectangular with the dimensions of (60*45*30) cm.
The sump tank outlet is kept as far away as possible from its inlet to
avoid short circuits in the flow.
Three immersion heaters were fixed in the sump tank, two
immersions heaters were used to achieve required hot stream temperature
having a power of 1.5 Kw and 3 Kw respectively and (220-240 V, AC,
single phase).
Thermostat range on either heater was (40-80) oC, all the pipes work
P
P
which carried hot water were insulated with glass wool.
Chapter Three
Experimental Work
Fig. (3.1) Photographic picture of the experimental rig.
Chapter Three
Experimental Work
Chapter Three
Experimental Work
Table (3.2) Description of the experimental rig.
Code
PHE
P1
Components
Description
Plate heat
APV plate heat exchanger type (JHE)
exchanger
serial No. (1062).
Cold water
1/2 inch size , 0.37 Kw , 0.3 HP , (0.6-
pump
2.4) m3/hr , 32.9 m , 220 V , 60 HZ.
P
P
1/2 inch size , 0.37 Kw , 0.5 HP , 45
P2
Hot water pump L/min , 35 m , (220~240) V , 50/60
HZ.
"GEC Elliot" rotameter , process
R1
Cold water
instruments Ltd , series 2000 , type
rotameter
(TM-24 FM-S 1804-V) , range (2-20)
L/min.
"GEC Elliot" rotameter , process
R2
Hot water
instruments Ltd , type (TM-14 FM-S
rotameter
1802-V) , range (0.5-5) L/min , this
rotameter not used in work.
R3
Hot water
"WDLL"
rotameter
,
Instrument
rotameter
company , range (2-18) L/min.
1/2 inch size , Siebe Environmental
Controls , Loves Park , IL 61111 , MF
FCV
Flow rate control – 22303 Valve actuator , 24 V, 50/60
valve
HZ , 1 watt class 2 , OP. AMB 40 to
140 oF , Temp. Ind. And Reg. Equip.
P
P
and Plenum Rated Cable.
Rectangular
CT
Cooling tower
tank
for
cold
water
(80*40*55) cm, duct (140*35*30) cm
and 12 inch fan.
Chapter Three
Experimental Work
Code
Components
V1,V7
Description
Cold water valve Gate valve , 1/2 inch size.
V2,V3,V4,
Hot water valve
V5,V6
Gate valve, 1/2 inch , the hot water
valve V2 not used in work (closed).
Rectangular tank (60*45*30) cm with
HWT
Hot water tank
three immersion heaters two in 1.5 Kw
and one in 3 Kw.
3.2.3 Cooling Tower
The cooling tower was supplied by a manufacturer with a capacity of
(0.160) m3. It consisted of a tank with dimensions (80*40*55) cm, duct
P
P
with dimensions (140*35*30) cm and a 12 inch fan.
Cold water circulated, and the outcoming (cold) stream from the
exchanger was cooled in the cooling tower and sent to the PHE.
A cooling tower was used in conjunction with the original rig to
ensure availability of the process fluid.
Hence a closed loop was established leading to a control over the
process fluid inlet temperature to desired levels compatible with the
specifications of the rig. The temperature drop obtainable from the cooling
tower was 3-9 oC.
P
P
The schematic diagram of the cooling tower and the main
dimensions are illustrated in the Fig. (3.3).
Chapter Three
Experimental Work
Fig. (3.3) Schematic diagram of the cooling tower.
3.2.4 Temperature Measurement
K-type thermocouples were connected at the entrance and exit pipe
lines of both cold and hot sides of the exchanger which able to measure the
exchanger temperature response every one second, the details of the K-type
thermocouple are illustrated in table (3.3).
The responses are recorded with the help of the data acquisition
system. All the thermocouples were calibrated before being used to
measure the temperatures of the experimental.
The apparatus consist of a glass beaker for water bath and a
calibrated thermometer.
All thermocouples to be calibrated were immersed in a constant
temperature bath (cooled water). The temperature in the bath was measured
Chapter Three
Experimental Work
using a precision thermometer. After this, thermocouples calibration can be
applicable using the digital multimeter type MASTECH (MS8217) for all
thermocouples. The calibration curves are shown in Fig. (A.1) in appendix
(A).Similar data were obtained for all the other three thermocouples.
Table (3.3) Standardized detail of the K-type thermocouple [87].
P
Temperature range
(°C)
P
–250 → 1100
40 from
Output (µV/°C)
250–1000°C
35@1300°C
Cost
Low
Stability over the
temperature range
Low
specified
Cable specification
K
Nickel–chromium
Common name
alloy (chromel)/
nickel–aluminium
alloy (alumel)
The type K thermocouple is commonly called
chromel alumel. It is the most commonly used
thermocouple and is designed for use in
oxidizing atmospheres. Maximum continuous
Brief description
use is limited to 1100°C although above 800°C
oxidation causes drift and decalibration. Note
that the type K thermocouple is unstable with
hysteresis between 300°C and 600°C which can
result in errors of several degrees.
Chapter Three
Experimental Work
3.2.5 Water Flow rate Measurement
Both hot and cold side rotameters were calibrated before being used
in this work to measure the water flow rate of the experiment with standard
calibration using calibrated cylinder.
The calibration curves are illustrated in Fig. (A.2) and (A.3) in
appendix (A).
3.3 Description of the Computer Control System
The computer control system required a computer and an interface
unit. The interface unit consisted of Data Acquisition Board (NI USB6009), signal conditioning card, relay, and power supply.
The computer used to control the system was a personal computer
(Pentium four, processor 3.42 GHZ).
The interface consisted of an electronic circuit which enables the
communication between the system under study and the computer to take
advantage of the computer software for generating reports, plots, etc.
The schematic diagram of signal conditioning card and photographic
picture appears in the Fig. (3.4) and (3.5) respectively.
Chapter Three
Experimental Work
1
14
1
14
13
2
13
2
13
3
12
3
12
3
12
3
12
4
11
4
11
4
11
4
11
10
5
10
5
10
5
9
6
9
6
9
6
7
8
7
8
7
8
7
8
x
x
x
x
x
x
x
x
6
1
out1
2
-
3
+
4
Vcc+
5
+
6
-
7
out4
LM324
5
out2
-
AD595
14
2
AD595
1
13
AD595
14
2
AD595
1
10
9
14
13
12
+
Vcc+
11
10
9
out3
8
T1
T1
T2
T2
T3
T3
T4
T4
Fig. (3.4) Schematic diagram of Signal conditioning card (T1 =T ci ,
R
R
R
R
T 2 =T co , T 3 =T hi , T 4 =T ho ).
R
R
R
R
R
R
R
R
R
R
R
R
C
A
B
D
Fig. (3.5) Photographic picture of the interface unit (A- DAQ board,
B- Signal conditioning card , C- Relay , D- Power supply).
Chapter Three
Experimental Work
The interface unit is consisting of many parts listed below:
1- Data Acquisition Board DAQ (NI USB-6009):
The NI USB-6009 is a USB based data acquisition (DAQ) and
control device with analog input and output and digital input and output.
The main features specifications of NI USB-6009 are as follows:
• Analog input (AI): 8 inputs with referenced single ended single
coupling. Software-configurable voltage ranges: ±20V, ±10V, ±5V,
±4V, ±2.5V, ±2V, ±1.25V, ±1V. Max sampling rate is 48KS/s
(48000 samples per second), and 14 bits AD converter.
•
Analog output (AO): 2 outputs with voltage range of 0-5V (fixed).
The output rate is 150 HZ (samples/second), with 12 bits DA
converter.
• Digital input (DI) and digital output (DO): 12 channels which can
be used as either DI or DO (configured individually). These 12
channels are organized in ports, with port 0 having lines 0,.., 7, and
port 1 having lines 0,..,3 . Low input is between -0.3V and +0.8V.
High input is between 2.0V and +5.8V. Low output is below 0.8V.
High output is above 2V.
• Counter: 32 bits. Counting on falling edge.
• On-board voltage sources (available at individual terminals):
2.5V and 5.0V.
• POWER: USB-6009 is powered via the USB cable.
• Application software: LABVIEW, C, or Visual Studio .Platforms:
Windows, Mac, or Linux.
In this work the DAQ board used with 4 channels analog inputs of
10V, sampling rate was 1000 kS/s and 2 bits digital outputs of 5V.
2- Signal Conditioning Card:
This card was built to convert the thermocouple signal to equivalent
to (10 mV/oC) by using thermocouple amplifier with cold junction
P
P
Chapter Three
Experimental Work
compensator. Then this signal was sent to a voltage follower amplifier to
increase its loading ability.
3- Relay:
The control relay was used to isolate control signal from the
loading circuit (AC motor).
4- Power Supply:
The power transformer was used to reduce the supplied voltage 220
V AC to 28 V AC . This voltage was supplied to a bridge (Full wave rectifier)
R
R
R
R
to convert it to DC voltage (i.e. 28 V DC ). Then voltage regulators were used
R
R
to get the required voltages +5V, +24V.
P
P
P
P
The temperature signal was sent as a voltage difference from a
thermocouple to the thermocouple amplifier with cold junction
compensator.
The process contained four thermocouples. These temperature
signals were received from the process by four analog channels in the DAQ
Board, which actually has eight channels. The DAQ Board sends these
signals as a 14-bit digital number to the computer, where the MATLAB
package was used to monitor these temperatures. A manual controller via
the MATLAB package was used to set different flow rates values, the
generated temperatures due to the different flow rates were read to get the
steady state and dynamic data.
The manual control action sent from the computer to the DAQ
Board. It was sent to two control relays via the DAQ board digital output
pins. Two bits were used in this control one to increase the flow rate and
the other to decrease it.
The control relay was used to isolate control signal from the
loading circuit (AC motor).
MATLAB simulink was used to operate the PHE system about the
DAQ board as illustrated in Fig. (3.6).
Chapter Three
Experimental Work
Fig. (3.6) MATLAB simulink used to operate the PHE system
(T 1 =T ci , T 2 =T co , T 3 =T hi , T 4 =T ho ).
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
3.4 Experimental Procedure
The system was calibrated before every experiment and the data
collected from the experiments were of two types:
• Steady - state data.
• Dynamic response data.
3.4.1 Steady - State Data
1. At the beginning of the experiments, valves V1, V3, V4 and V5
Fig. (3.2) were kept fully open, and V6 and V7 were opened
partially to drain the excess water to the tank.
2. The water was pumped by means of electrical pumps both for cold
and hot water.
3. After 10 minutes from water circulation in pipes, the valve V4 was
closed then the hot water flows in by pass line and back to the hot
water tank.
Chapter Three
Experimental Work
4. The control valve was adjusted to give different flow rates, the hot
water flow rate was varied from (0.0497 kg/sec - 0.1159 kg/sec) by
the controller via MATLAB package which used to set different
flow rates values.
5. The cold water flow rate remained fixed at a constant value of
(0.0414 kg/sec) by means of V1.
6. Two electrical heaters were switched on and the thermostat set to
50 oC.
P
P
7. Valve V5 was closed and the valve V4 was opened to allow the hot
water passing through the exchanger.
8. The inlet and the outlet temperatures of fluid streams were recorded
by the DAQ board via MATLAB package and the readings were
taken at intervals of twenty seconds until steady state readings was
reached .
9. The same procedure was repeated for different flow rates of hot
water.
3.4.2 Dynamic Response Data
1. Steps 1, 2, and 3 in the previous section were repeated.
2. The control valve was adjusted in order to get the desired flow rate
of hot water (0.0497 kg/sec) by means of DAC via MATLAB
package.
3. Setting the cold water flow rate to remain fixed at a constant value of
(0.0414 kg/sec).
4. The two electrical heaters were switched on and set the thermostat to
50 oC then waiting until the desired temperature was reached.
P
P
5. Valve V5 was closed then valve V4 was opened.
6. Waiting to reach the steady state by noting that the outlet cold water
temperature was fixed via MATLAB program.
Chapter Three
Experimental Work
7. A step change of (20%) was introduced in hot water flow rate after
steady state is reached.
8. The outlet cold water temperature was recorded each five seconds
until the new steady state was reached noting that the outlet cold
water temperature was fixed by DAQ Board via MATLAB package.
9. The same procedure was repeated for different step changes in hot
water flow rate (50%, 80%, 100%, 120%, and 135%).
Chapter Four
Modeling and Theoretical Analysis
4.1 Introduction
In this chapter, the mathematical model for the plate heat exchanger
is developed and the control strategies are presented.
The theoretical models of various process units are derived by the
fundamental principles of conservation of mass and/or energy balance.
In its most general form, the conservation state that:
Input - Output = Accumulation
In steady sate condition, the accumulation is equal to zero. For
dynamic simulation the accumulation term to the mass and/or energy
balance must be added.
Basic equations to present PHE are obtained based upon energy
balance. In Fig (4.1) it is considered that each plate operates independently
and the transfer function of one plate represents the over all transfer
function of the whole PHE. This plate can be considered as lumped system
if the theoretical analysis depends upon inlet and outlet temperatures, and
variation of temperature along the length is neglected [29, 31].
P
Thi
mh
Cold
plate
P
Tco
mc
Hot
plate
Hot
plate
Cold
plate
Tho
mh
Tci
mc
Fig. (4.1) Arrangement of cold and hot streams for PHE
(as lumped system).
Chapter Four
Modeling and Theoretical Analysis
4.2 Model Assumptions
In practice, application of this procedure introduces additional
complexity into the system equation, so it is sometimes necessary to make
simplifying assumptions of the dynamic behavior. To simplify this
complex problem, a few assumptions are made in order to set-up the
relevant differential equations.
The following assumptions are frequently made in the modeling of
PHEs:
1. The physical properties of the water are constant over the range of
temperatures employed [29-31].
P
P
2. The heat losses to the surroundings are negligible and the two end
plates of the exchanger serve as adiabatic walls [29-31].
P
P
3. The film coefficient for heat transfer is dependent principally upon
the fluid velocity and is proportional to an exponential function of
the flow rate [29-31].
P
P
4. The heat transfer within the water in any channel is by convection
only [29-31].
P
P
5. The temperature distributions in all channels belonging to the same
stream are identical [29-31].
P
P
6. The water will split equally between the parallel channels for each
stream [29-31].
P
P
7. The thermal capacity of the plate wall is negligible compared with
the thermal capacity of the water in the plate [29-31].
P
P
8. The plate can be considered as lumped system if the theoretical
analysis depends upon inlet and outlet temperatures [29, 31].
P
P
9. The variation of temperature along the length is neglected [29, 31].
P
P
These assumptions are incorporated in the development of a lumped
parameter model in which the system may be described by unsteady-state
energy balances across any specific plate.
Chapter Four
Modeling and Theoretical Analysis
On considering that the overall heat transfer coefficient (U) is a
function of the hot stream mass flow rate m h which in turn is a function of
R
R
time. Hence in the latter instance U is also a function of time, i.e. U (t).
4.3 Energy Balance
4.3.1 Energy Balance around Cold Plate
The steady state energy balance around cold plate gives:
o
o
o 
 o+ o
+
o
o
dT co =
T
T
hi T ho
ci T co 

−
=
+
−
mc C p T ci UA 
mc C p T co M c C p
0
dt
2
2 

o
……….. (4.1)
o
For dynamic studies the flow rate of hot water is chosen as an input
variable while the inlet-temperature of cold and hot streams and flow rate
of cold water are maintained constants. The overall heat transfer coefficient
is a function of thermal resistance offered by hot and cold stream. As the
flow rate of cold stream is considered constant, the overall heat transfer
expression is given as:
U =α m
……….. (4.2)
w
h
Substituting equation (4.2) into equation (4.1) and simplification
takes the shape as:
o
mc C pT ci − mc C pT co + Z
o
o
o
o
ow
m
h
T hi + Z
o
ow
m
h
T ho − Z
o
ow
m
h
T ci − Z
o
ow
m
h
dT
T co = M c C p co = 0
o
dt
……….. (4.3)
Where:
α Α 

Z = 
 2 
……….. (4.4)
The unsteady state energy balance around the cold plate gives:
m C T − m C T ′ + Z m′ T
o
c
p
o
o
ci
c
p
co
w
o
h
hi
+Z
m′ T ′ − Z m′ T − Z m′ T ′
w
h
ho
w
o
w
h
ci
h
co
= M c C p dT
′
co
dt
……….. (4.5)
The non linear terms in equation (4.5) are linearized using Taylor
series:
Chapter Four
m′ T
w
o
h
hi
Modeling and Theoretical Analysis
= mh
ow
T + T ∗ w m (m′ − m )
o
o
w−1
hi
hi
h
……….. (4.6)
o
h
h
Similarly:
m′ T ′
w
m′ T
w
o
h
ci
w
w−1
o
ho
h
h
o
ow
h
h
ho
T + T ∗ w m (m′ − m )
= mh
T + T ∗ w m (m′ − m )+ m (T ′ − T
ow
co
m (m′ − m )+ m (T ′ − T
+ T ho ∗ w
o
T
= mh
ow
m′ T ′
h
= mh
ow
ho
h
o
o
w−1
ci
ci
h
o
o
w−1
co
co
h
o
ho
)
……….. (4.8)
o
h
h
……….. (4.7)
h
o
ow
h
h
co
o
co
)
……….. (4.9)
Substituting equations (4.6)-(4.9) into equation (4.5) and subtracting
the steady-state equation (4.3) from equation (4.5) and introducing
deviation variables lead to:
τ
dT
dt
c
co
+T
=
co
K m +K T
1
2
h
……….. (4.10)
ho
Where:
T
co
m
o
……….. (4.11)
= m′h − mh
……….. (4.12)
= T ′ho − T ho
……….. (4.13)
o
h
o
T
ho
τ
=
c
= T ′co − T co
MC
m C +Z m
c
ow
c
K1 =
……….. (4.14)
p
o
p
h
Z w m (T + T − T − T
m C +Z m
w−1
o
o
o
o
h
hi
ho
ci
co
o
c
)
……….. (4.15)
ow
p
h
ow
K2 =
Zm
m C +Z m
……….. (4.16)
h
o
c
ow
p
h
Applying the Laplace transformation:
T
co ( s )
=
K
K
(1 +τ s ) m ( ) + (1 +τ s )T
1
2
h s
c
ho ( s )
……….. (4.17)
c
The same procedure is repeated around the hot plate.
The initial conditions used are listed in table (B.1) in Appendix (B).
4.3.2 Energy Balance around Hot Plate
The steady state energy balance around hot plate gives:
Chapter Four
Modeling and Theoretical Analysis

o
o
−
mh C p T hi mh C p T ho + UA

o
o
o
o
o 
 o+ o
+
T hi T ho − T ci T co   = M C dT ho = 0
h
p

2
2  
dt

……….. (4.18)
Substituting equation (4.2) into equation (4.18) and simplification
takes the shape as:
o
mC T
h
p
− mh C p T ho − Z
o
o
hi
o
ow
o
h
hi
m T
−Z
ow
o
h
ho
m T
+Z
ow
o
h
ci
m T
+Z
ow
o
h
co
m T
= M h C p dT
ho
dt
=0
……….. (4.19)
The unsteady state energy balance around hot plate gives:
m′ C T
h
o
hi
p
− m′h C p T ′ho − Z
m′ T
w
o
h
hi
−Z
m′ T ′ + Z m′ T
w
ho
h
w
o
h
ci
+Z
m′ T ′
w
h
co
= M h C p dT ho
dt
……….. (4.20)
The non linear terms in equation (4.20) are linearized using the
Taylor series:
m′ T ′
(
)
= mh T ho + mh T ′ho − T ho + T ho
o
ho
h
o
o
o
o
(m′ − m )
o
h
h
……….. (4.21)
Substituting equation (4.21) and equations (4.6)-(4.9) into equation
(4.20) and subtracting the steady state equation (4.19) from of equation
(4.20) and introducing deviation variables lead to:
dT
τ dt
ho
h
+T
ho
=
K m +K T
3
4
h
……….. (4.22)
co
Where:
τ
h
=
M C
m C +Z m
h
ow
h
K3 =
……….. (4.23)
p
o
p
[C (T
p
o
hi
h
)
w m (T + T
m C +Z m
− T ho − Z
o
w−1
o
o
h
hi
ow
ho
o
h
p
− T ci − T co
o
o
)]
h
ow
K4 =
Zm
m C +Z m
……….. (4.25)
h
o
h
……….. (4.24)
ow
p
h
Applying the Laplace transformation:
T
ho ( s )
=
K
K
(1 +τ s ) m ( ) + (1 +τ s )T
3
4
h s
h
co ( s )
……….. (4.26)
h
Substituting T ho(s ) in equation (4.17) into equation (4.26) leads to:
Chapter Four
G( ) =
s
T
m
Modeling and Theoretical Analysis
co ( s )
=
h(s )
H (1 +τ s )
τ s + 2 ψ τ s +1
……….. (4.27)
a
2
2
p
p
Where:
K +K K
3
K =1 − K K
4
K
=
5
1
2
6
=
H
τ
a
2
=
K
K
ψ
p
……….. (4.30)
6
K
K
……….. (4.31)
1
5
(τ τ )
= c h
K
=
……….. (4.29)
5
1
τ
……….. (4.28)
1
2
……….. (4.32)
2
6
(τ +τ )
2 (τ cτ h)
c
……….. (4.33)
h
1
2
Thus if U is considered to be a function of t then the resulting
transfer function G (S) between T
R
R
co ( s )
and m h(s ) represents a second-order lag
with time constant τ p and damping coefficient ψ combined with a first
R
R
order lead element having a time constant τ a .
R
R
4.4 Control Strategies
The main aim of this work is to develop a mathematical model to
control the PHE. In this section, the application of conventional feedback
control to the PHE is described and discussed. The FL control and ANN
control are also described and employed to improve the PHE response. In
the present work, MATLAB version 7.10 was used as the simulation
software.
4.4.1 Conventional Feedback Control
Conventional feedback control in general is the achievement and
maintenance of a desired condition by using an actual value of this
Chapter Four
Modeling and Theoretical Analysis
condition and comparing it to a reference value (set point) and using
difference between these to eliminate any difference between them.
The controller receives a continuous signal of the temperature
measurement, which is compared with the set point to produce the
actuating signal. The controller thus produces an error signal, which can be
used to regulate the control valve. However, the characteristics of the signal
produced can be varied to a large extent according to the internal settings of
the controller. Fig. (4.2) shows the block diagram of feedback control
system.
d
m
process
T
(a)
Controller mechanism
d
comparator
Tsp
e(t)
+
(set point
variable)
-
(error)
controller
c(t)
Tm
(measured variable)
Final control
element
m(t)
Tout
process
(Controlled
variable)
T measuring
device
(b)
Fig. (4.2) (a) Process, (b) Feedback control loop [88].
P
P
There are three basic types of feedback controllers which described
briefly as follow:
A- Proportional Controller
The output of a proportional controller changes only if the error
signals changes. Since a load change requires a new control valve position,
the controller must end up with a new error signal. This means that a
proportional controller usually gives a steady-state error or offset
P
[89]
. A
P
proportional controller will have the effect of reducing the rise time but
never eliminate the steady-state error [90].
P
P
Chapter Four
Modeling and Theoretical Analysis
Since this controller uses the value of error to adjust the input to the
process, this type of controller can never fully return the output variable to
its set point. This is a disadvantage of proportional action [89].
P
P
The proportional control action may be described mathematically
as [88]:
P
P
C (t ) = K E (t ) + C
C
……….. (4.34)
S
Where:
C(t) : controller output.
K c : proportional gain of the controller.
R
R
C s : initial value of controller.
R
R
E(t) : error (difference between measured signal and set point).
The transfer function for the proportional controller has the form:
G (s ) = K
C
……….. (4.35)
C
B- Proportional-Integral (PI) Controller
Most control loops use PI controllers. The integral action eliminates
steady-state error in temperature. The measured variable can be returned to
the set point without excessive oscillation. The smaller the integral time τ I ,
R
R
the faster the error is reduced. But the system becomes more underdamped
as τ I is reduced. If it is made too small, the loop becomes unstable [89].
R
R
P
P
Its actual signal is related to the error by the equation [88]:
P
C (t ) = K E(t ) + K ∫ E(t ) dt + C
t
τ
C
……….. (4.36)
C
I
P
S
0
Where:
τ I : integral time constant.
R
R
The PI controller transfer function is:

1
G (s ) = K 1 +
τ s

C
C
I




……….. (4.37)
The response of the PI controller will be slower than the proportional
controller. Thus, the response period of the loop under PI control is 50%
Chapter Four
Modeling and Theoretical Analysis
longer than that for a loop under proportional only control. In order to
increase the speed of the response it may be necessary to add an additional
control mode [20].
P
P
C- Proportional-Integral-Derivative (PID) Controller
PID controllers are widely used in industrial control systems. The
primary purpose of a PID is to provide a fast response that is much the
same as with proportional only controller but which has no offset. The
derivative action adds the additional response speed required to overcome
the lag in the response from the integral action [20].
P
P
The output of this controller is given by [88]:
P
t
C (t ) = K E (t ) + K ∫ E (t ) dt + K τ dE + C
dt
τ 0
P
……….. (4.38)
C
C
C
D
S
I
Where:
τ D : derivative time constant.
R
R
The PID transfer function is given by:


1 +
G (s ) = K 1 +
τ s 
τ s


C
C
……….. (4.39)
D
I
4.4.2 Controller Tuning
Performance of feedback controllers depends on the values of their
chosen parameters. If these parameters are properly chosen, they offer the
highest flexibility to achieving the desired controlled response and stability.
The process of choosing these parameters is known as controller tuning.
Also controller tuning can be defined as an optimization process that
involves a performance criterion to the form of the controller response and
to the error between the process variable and the set point [20].
P
P
The following two methods are preferred here those of Cohen-Coon
method also known as process reaction curve derived from open-loop
systems
P
[91]
. The other is Ziegler-Nichols method based on frequency
P
Chapter Four
Modeling and Theoretical Analysis
response analysis (bode diagram)
[92]
P
P
that it derived mainly from closed-
loop systems. The two methods are described in appendix (C).
The main two methods of the time integral performance criteria used
in the proposed work evaluated in terms of:
 Integrated Square Error (ISE)
This error uses the square of the error, thereby penalizing large errors
more than small errors. This gives more conservative response (faster
return to set point) [20].
P
P
∞
……….. (4.40)
ISE = ∫ e dt
2
0
 Integrated Time-Weighted Absolute Error (ITAE)
This criterion is based on the integral of the absolute value of the
error multiplied by time. It results in errors existing over time being
penalized even though may be small, which results in a more heavily
damped response [20].
P
P
∞
ITAE
= ∫t
……….. (4.41)
e dt
0
If the performance indices increases, control system can perform
poorly and even become unstable. So it needs to tune the controller
parameters to achieve good control performance with the proper choice of
tuning constants [90].
P
P
4.4.3 Fuzzy Logic Control
4.4.3.1 Introduction of Fuzzy Logic
FL is one of the tools of what is commonly known as computational
intelligence (CI) and it's a logical system, which is an extension and
generalization of multi valued logic systems [93].
P
P
FL is much closed in spirit to human thinking and natural language
than classical logical systems. Nowadays FL is used in almost all sectors of
industry and science [35, 94, 95].
P
P
Chapter Four
Modeling and Theoretical Analysis
FL is one of the successful applications of fuzzy set in which the
variables are linguistic rather than the numeric variables [96].
P
P
In FL theory, the range of values for a given input or output space is
often called the universe of discourse. For greater flexibility in fuzzy
controller implementation, the universes of discourse are “normalized” to a
certain interval (e.g., [-1, 1] or [0, 1]) by means of constant scaling
factors [93].
P
P
FL starts with the concept of a fuzzy set. The concept of fuzzy set
theory was introduced by Zadeh in 1965. Fuzzy set theory can be
considered as a generalization of the classical set theory. In classical set
theory an element of the universe either belongs to or does not belong to
the set. Thus the degree of association of an element is crisp. In a fuzzy set
theory the association of an element can be continuously varying.
Mathematically, a fuzzy set is a mapping (known as membership function)
from the universe of discourse to the closed interval [0, 1]. The
membership function is usually designed by taking into consideration the
requirement and constraints of the problem. FL implements human
experiences and preferences via membership functions and fuzzy rules.
Due to the use of fuzzy variables, the system can be made understandable
to a non-expert operator. In this way, FL can be used as a general
methodology to incorporate knowledge, heuristics or theory into controllers
and decision makers [95, 97].
P
P
4.4.3.2 Linguistic Variables
The concept of a linguistic variable, a term which is used to describe
the inputs and outputs of the FL control, is the foundation of FL control
systems. A conventional variable is numerical and precise. It is not capable
of supporting the vagueness in fuzzy set theory. By definition, a linguistic
variable is made up of words, sentences or artificial language which is less
Chapter Four
precise
than
Modeling and Theoretical Analysis
numbers.
It
provides
the
means
of
approximate
characterisation of complex or ill-defined phenomena. A more common
example in fuzzy control would be the linguistic variable ‘ERROR’, which
may have linguistic values such as ‘POSITIVE’, ‘ZERO’ and
‘NEGATIVE’. The following conventions are used to define linguistic
variables
P
[98]
. If X i is a linguistic variable defined over the universe of
P
R
R
discourse U where x ∈ U then
LX i k
(for k = 1, . . . n) are the linguistic values X i can take.
n
is the number of linguistic values X i have.
R
RP
P
R
R
R
R
μ LXi,k (x)
is the LX i k membership function for the value x.
LX i
is the set containing LX i k , where LX i = { LX i 1, LX i 2 … LX i n }.
R
R
R
R
R
RP
P
R
RP
P
R
R
R
RP
P
R
RP
P
R
RP
P
In the example above:
X1
is ‘ERROR’
n=3
is the number of linguistic values in X 1
LX 1 1
is ‘POSITIVE’
R
RP
P
LX 1 2
R
R
is ‘ZERO’
RP
LX 1 3
RP
R
P
is ‘NEGATIVE’
P
And, for x = {–1, 0, 1}:
μ LX1,1 (–1) = 0;
μ LX1,1 (0) = 0;
μ LX1,1 (1) = 1
μ LX1,2 (–1) = 0;
μ LX1,2 (0) = 1;
μ LX1,2 (1) = 0
μ LX1,3 (–1) = 1;
μ LX1,3 (0) = 0;
μ LX1,3 (1) = 0
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
4.4.3.3 Fuzzy Logic Controller
The idea of FL controller was initially introduced by Zadeh (1973)
and first applied by Mamdani (1974) in an attempt to control systems that
are difficult to model mathematically [93].
P
P
The Mamdani fuzzy model is the first working model of fuzzy
control systems. It constructs a bridge between the operator's knowledge
Chapter Four
Modeling and Theoretical Analysis
and IF-THEN rules by fuzzy logic. The Mamdani fuzzy model provides a
basic procedure for fuzzy controller design [99].
P
P
4.4.3.3.1 Design of Fuzzy Logic Controller
An alternative approach to design a controller as compared to
transfer function based controller is to use linguistic control protocol
employed by a human operator as used in FL controller. A block diagram
of FL control system is shown in Fig. (4.3), which comprises of a
fuzzification interface, data base, rule base, inference mechanism and a
defuzzification interface
[94, 100-103]
P
. Sometimes both data and rule base can
P
be called as knowledge base [94, 100].
P
P
Fig. (4.3) Fuzzy logic control system [104].
P
P
 The fuzzification interface measures the values of input variables,
performs a scale mapping that transfers the range of values of input
variables, and converts input data into suitable linguistic values [94].
P
P
This transformation is performed using membership functions. In a
FL controller, the number of membership functions and the shapes of these
Chapter Four
Modeling and Theoretical Analysis
are initially determined by the user. The membership functions can take
many forms including triangular, gaussian, trapezoidal, etc [105].
P
P
 The data base provides necessary definitions, which are used to
define linguistic control rules and fuzzy data manipulation in an FL
control [94].
P
P
 The rule base characterizes the control goals and control policy of
the domain experts by means of a set of linguistic control
rules
P
[94]
. The relationship between input and output variables are
P
described in a rule base composed of IF-THEN form rules. Usually
fuzzy systems are synthesized using two types of rules that differ in
the consequent (Then part) proposition form: Mamdani, or standard
and Takagi-Sugeno, or functional [54].
P
P
The main part of the FL controller is the rule base and the inference
mechanism. The rule base is normally expressed in a set of fuzzy linguistic
rules, with each rule triggered with varying belief for support. The ith
linguistic control rule can be expressed as:
R i : IF e is A i and de is B i THEN u is C i ,
R
R
R
R
R
R
R
R
Where A i and B i (antecedent), C i (consequent) are fuzzy variables
R
R
R
R
R
R
characterized by fuzzy membership functions [100].
P
P
For FL controller the error (e) and the change of error (de) as input
linguistic variables are taking and the control action (u) taken as output
linguistic variable.
For example, the membership function for error, change of error
and control action consist of negative (N), zero (Z), positive (P).
The set of fuzzy rule for FL control can be written in a table as
shown in table (4.1).
Chapter Four
Modeling and Theoretical Analysis
Table (4.1) IF-THEN rule base for fuzzy logic control.
de
N
Z
P
N
P
P
Z
Z
P
Z
N
P
Z
N
N
e
 The inference mechanism (also called an “inference engine” or
“fuzzy inference” module), which emulates the expert’s decision
making in interpreting and applying knowledge about how best to
control the plant [104].
P
P
The decision making logic is the kernel of an FL controller, and has
the capability of simulating human decision-making based on fuzzy
concepts [94].
P
P
 The defuzzification interface converts the range of values of output
variables into corresponding universe of discourse, and yields a nonfuzzy control action from a fuzzy control action [94].
P
P
The performance of the FL control depends very much on the
defuzzification process. This is because the overall performance of the
system under control is determined by the controlling signal (the
defuzzified output of the FL controller) that the system universe [100].
P
P
The design of a fuzzy controller remains a difficult task due to the
fact that there is insufficient analytical design technique in contrast with the
well-developed linear control theories. Although the fuzzy controller has
the advantage of being relatively easy to understand, the controller tuning
is complex or nontransparent due to many involved design parameters, and
in most cases the fuzzy controller design is accomplished by trial and error
methods using computer simulations. It is an attempt to undertake the
Chapter Four
Modeling and Theoretical Analysis
development of an approach to the optimal design of linear PID fuzzy
controller [42].
P
P
4.4.4 Artificial Neural Network Control
4.4.4.1 Introduction of Artificial Neural Network
An ANN takes their name from the network of nerve cells in the
brain [106] and it's a flexible mathematical structure, having strong similarity
P
P
to the biological brain and therefore a great deal of the terminology is
borrowed from neuroscience [107].
P
P
An ANN is an information-processing paradigm that is inspired by
the way biological nervous systems, such as the brain, process information.
It is composed of a large number of highly interconnected processing
elements (neurons) working in unison to solve specific problems [33, 108, 109]
P
P
and they are powerful tools that can learn to solve problems in a way
similar to the human brain. ANNs gather knowledge by detecting the
patterns and relationships in data and learn (or: are trained) through
experience, not from programming [110] especially when the underlying data
P
P
relationship is unknown [111].
P
P
4.4.4.2 Biological Artificial Neural Network
An ANN is an information processing system that has been
developed as a generalization of the mathematical model of human
cognition.
A biological neuron has three types of components, namely, the
dendrites, soma and axon. Dendrites are bunched into highly complex
“dendritic tree”, which has an enormous total surface area. The dendrites
receive signals from other neurons. Dentritic trees are connected with the
main body of the neuron called the soma. The soma has a pyramidal or
cylindrical shape. The soma sums the incoming signals. The cell fires when
Chapter Four
Modeling and Theoretical Analysis
sufficient input is received. The output area of the neuron is a long fibre
called the axon. The impulse signal triggered by the cell is transmitted over
the axon to other cells. The connecting point between a neuron’s axon and
another neuron’s dendrite is called a synapse. The impulse signals are
transmitted across a synaptic gap by means of a chemical process. A single
neuron may have 1000 to 10000 synapses and may be connected with 1000
neurons. There are 100 billion neurons in the brain and each neuron has
1000 dendrites [112, 113]. Fig. (4.4) shows the biological neuron.
P
P
Fig. (4.4) Biological neuron [112].
P
P
4.4.4.3 Mathematical Model of a Neuron
A first wave of interest in ANNs (also known as connectionist
models or parallel distributed processing) emerged after the introduction of
simplified neurons by McCulloch and Pitts (1943) [114].
P
P
ANNs are inspired by the early models of sensory processing by the
brain. An ANN can be created by simulating a network of model neurons
in a computer. By applying algorithms that mimic the processes of real
neurons, we can make the network ‘learn’ to solve many types of
problems [115].
P
P
Chapter Four
Modeling and Theoretical Analysis
The artificial neuron imitates the characteristics of the biological
neuron. A processing element possesses a local memory and carries out
localized information processing operations. The artificial neuron has a set
of ‘p’ inputs x i , each representing the output of another neuron (the
R
R
subscript i takes values between 0 and p and indicates the source of the
vector input signal). The inputs are collectively referred to as X. Each input
is weighted before it reaches the main body of the processing element by
the connection strength or the weight factor analogous to the synaptic
strength. The amount of information about the input that is required to
solve a problem is stored in the form of weights. Each signal is multiplied
with an associated weight wk 1 , wk 2 ,…, wk p before it is applied to the
R
R
R
R
R
R
summing block. Equation (4.42) and (4.43) show how the sum of the
weights is calculated. In addition, the artificial neuron has a bias term, wk 0 ,
R
R
a threshold value that has to be reached for the neuron to produce a signal.
Activation function is needed to produce the output, y k as shown in
R
R
equation (4.44). The basic model of a neuron is shown in Fig. (4.5). It
should be noted that the input to the bias neuron is assumed to be 1.The
main task of the activation function is to map the outlying values of the
obtained neural input back to a bounded interval such as [0, 1] or [-1, 1].
The transfer function of the basic neuron model is described [112].
P
v = x wk + x wk + x wk + x wk + ........ + x wk
k
o
o
1
1
v = wk + ∑ x wk
2
p
k
o
y = F (v k )
k
i =0
i
i
2
3
3
p
p
P
…….... (4.42)
.…..…. (4.43)
………. (4.44)
Chapter Four
Modeling and Theoretical Analysis
Fixed
Fixed
Input X o = ± 1
X o= ± 1
Input
XX
o
wk =
wk o wk
o = b(bias)
b k (bias)
wk
o
o
XX
o
k
wk 1
wk
11
1
Activation
Activation
Function
Function
XX
2
wk
wk 2
2
2
∑∑
v vk
k
Output
Output
ϕ( ϕ
)
( )
o
y y
k
o
k
Summing
Summing
Junction
Junction
X
X
Input
wk
P
P
wk
P
P
Synaptic
Synaptic
Weight
Weight
Input
signals
signals
Fig. (4.5) Basic model of neuron.
A common choice for the threshold function is the sigmoid
activation function:
ϕ (x ) =
1
1 + e cv
−
………. (4.45)
k
Where c is a constant parameter that determines the shape of the
sigmoid [116].
P
P
Sigmoid function is used for the activation function due to some of
its advantages [117]:
P
P
1. Nonlinearity makes the learning powerful.
2. Differential is possible and easy with simple equations.
3. Negative and positive value makes learning fast.
4.4.4.4 Architecture of Artificial Neural Network
There are several types of ANNs according to their structure (or
Architecture) and learning algorithms. According to their structure, ANNs
can be classified as feed forward networks and recurrent networks [110].
P
P
Chapter Four
Modeling and Theoretical Analysis
The most common for chemical engineering application is Multi
Layer Perceptron (MLP), which is a feed forward neural network. An MLP
is a powerful system, often capable of modeling complex, relationships
between variables. It allows prediction of an output object for a given input
object. It consists of multilayer structure, which a part from input and
output layers, has at least one layer of processing units in between them.
The layers between the input and output layers are termed "hidden" since
they do not converse with the outside world directly. The nodes between
the two successive layers are fully connected by means of weights. That is
outputs from the input layer are fed to the hidden layer units, which in turn,
feed their outputs to the next hidden nodes. The hidden node passes the net
activation through a nonlinear transformation of a linear function, such as
the logistic sigmoidal to compute their outputs [33].
P
P
4.4.4.5 Back Propagation (BP) Algorithm Artificial Neural Network
An ANN starts with a set of initial weights and then gradually
modifies the weights during the training cycle to settle down to a set of
weights capable of realizing the input-output mapping with either no error
or a minimum error set by the user [118].
P
P
For many years, there was no theoretically sound algorithm for
training multilayer ANNs. The invention of the BP algorithm has played a
large part in the resurgence of interest in ANNs. BP is a systematic method
for training multilayer ANNs (Perceptrons).
The BP learning algorithm is currently the most popular learning rule
for performing supervised learning tasks [119].
P
P
A learning algorithm of an MLP is called a Multi-Layer Back
Propagation (MLBP).
Chapter Four
Modeling and Theoretical Analysis
The main idea of this algorithm is to minimize cost function by
steepest descent method to add small changes in the direction of
minimization [59].
P
P
The feed forward back propagation network is a very popular model
in neural networks. It does not have feedback connections, but errors
propagate backward from the output layer during training. BP is a gradient
descent method to minimize the total squared error of the output computed
by the NN [120].
P
P
It has been proven that BP learning with sufficient hidden layers can
approximate any nonlinear function to arbitrary accuracy. This makes back
propagation learning neural network a good candidate for signal prediction
and system modeling [114].
P
P
The back propagation learning algorithm is performed in the
following steps [114,117]:
P
P
1. Initialize network weight values.
2. Repeat the following steps until some criterion is reached: (for each
training pair).
3. Sums weighted input and apply activation function to compute
output of hidden layer.
h
i
=
f (∑ X W
i
i
ij
)
………. (4.46)
4. Sums weighted output of hidden layer and apply activation function
to compute output of output layer.
y
K
=
f (∑ h W
j
j
jK
)
………. (4.47)
5. Compute back propagation error.
δ
K
=
(d
K
−
y ) f ′ (∑ h W
j
K
j
jK
)
………. (4.48)
6. Calculate weight correction term.
∆W (n) = η δ h + α ∆W (n −1)
jK
K
j
jK
………. (4.49)
7. Sums delta input for each hidden unit and calculate error term.
Chapter Four
Modeling and Theoretical Analysis
δ = ∑ δ W f ′ (∑ X W )
j
K
K
jK
i
i
ij
………. (4.50)
8. Calculate weight correction term.
∆W (n) = η δ X + α ∆W (n −1)
ij
j
i
………. (4.51)
ij
9. Update weights.
W (new) = W (old ) + ∆W
jK
jK
W (new) = W (old ) + ∆W
ij
ij
………. (4.52)
jK
………. (4.53)
ij
10. End.
These steps are illustrated in Fig. (4.6).
Where:
ΔWij : Amount of Change Added to The Weight Connection W ij .
R
R
y K : Output Signal of an Output Neuron (K) at Time (n).
R
R
d K : Desired (Target) Output Neuron (K) at Time (n).
R
R
η : Learning Rate Coefficient.
h j : Output Signal of Hidden Neuron (j) at Time (n).
R
R
δ j : Delta Quantity for Hidden Neuron (j).
R
R
δ K : Delta Quantity for Output Neuron (K).
R
R
α : Momentum Constant.
R
R
Chapter Four
Modeling and Theoretical Analysis
Inputs
X
X
1
X
2
X
3
Forward Pass
Back Pass
X
i
W (n) = W (n−1) + ∆W (n)
W
ij
i
ij
h
h
1
h
2
ij
y
1
ij
)
j
Y
y
j
i
W
K
j
i
j
ij
δ = ∑ δ W f ′ (∑ X W
j
K
K
jK
i
i
ij
)
W (n) = W (n−1) + ∆W (n)
jK
jK
f (∑ h W
=
ij
∆W (n) =η δ X + α ∆W (n−1)
h = f (∑ X W
j
ij
j
jK
)
jK
jK
∆W (n) =η δ h + α ∆W (n−1)
jK
K
j
jK
δ = (d − Y ) f ′ (∑ h W
K
K
K
K
j
j
jK
)
Outputs
Fig. (4.6) Error back propagation in MLP.
4.4.4.6 Artificial Neural Network Controller
As in real world of control engineering the nonlinearities are an
unavoidable problem that necessitates the development of controllers with
special capabilities in solving the nonlinearity problems. ANNs have been
proved a successful method in identification and control of dynamic
systems. Their approximation capabilities of MLP made them a popular
choice for modeling nonlinear systems and for implementing general –
purpose nonlinear controllers [121].
P
P
Different control algorithms and architectures are implemented. One
of them, among others, for prediction and control is the NARMA–L2 (or
feedback linearization) controller.
NARMA-L2 control is one of the three popular ANN architectures
that have been implemented in the neural network toolbox of MATLAB
software. Nonlinear auto regressive-moving average (NARMA-L2)
Chapter Four
Modeling and Theoretical Analysis
controller is simply a rearrangement of the ANN plant model, which is
trained offline in batch form, so it is the best technique to be presented in
this work [122-124]. This ANN controller is referred as feedback linearization
P
P
when the plant model has a particular form (companion form) and it is
referred to as NARMA-L2 control when the plant model can be
approximated by the same form. The central idea of this type of control is
to transform nonlinear system dynamics into linear dynamics by canceling
the nonlinearities
P
[125]
. The drawback of this method is that the plant must
P
either be in companion form, or be capable of approximation by a
companion form model. NARMA-L2 controller is implemented as
simulink block, which is contained in the neural network toolbox blockset.
4.4.4.6.1 Identification and Controller Stages of the NARMA-L2 model
NARMA-L2 controller, a multilayer neural network has been
successfully applied in the identification and control of dynamic systems.
System identification and control design are the two steps involved in using
NARMA-L2 controller. The identification of the system by this controller
can be summarized by the following steps [122, 125, 126]:
P
P
 Identify the system to be controlled. A neural network of the plant
that needs to be controlled is developed. One standard model that has
been used to represent general discrete-time nonlinear systems is the
NARMA-L2 model:
y (k + d ) = N [ y (k ), y (k − 1),...., y (k − n + 1), u (k ), u (k − 1),...., u (k − n + 1)]
………. (4.54)
Where u(k) is the system input, y(k) is the system output and k,d,n
are integral number. Fig. (4.7) shows the block diagram representation of
the system identification stage, where the NN training with error backpropagation training algorithm.
Chapter Four
Modeling and Theoretical Analysis
Fig. (4.7) Neural network training with error back-propagation
training algorithm.
 Make the output system follows some reference trajectory by
developing a nonlinear controller of the form
y(k + d ) = y (k + d )
………. (4.55)
r
u(k ) = G  y(k ), y(k −1),...., y(k −n +1), y (k + d ) ,u(k −1),...,u(k −m+1) 
r
………. (4.56)
To implement the controller model with NARMA-L2, one solution is
to use approximate models to represent the system:
yˆ (k + d ) = f [ y (k ), y (k − 1),...., y (k − n + 1), u (k − 1),...., u (k − m + 1)]
+ g [ y (k ), y (k − 1),...., y (k − n + 1), u (k − 1),...., u (k − m + 1)].u (k )
………. (4.57)
Where f(.) and g(.) are approximated using NNs. The advantage of
this form is that one can obtain the controlled input that makes the system
output follows the reference in equation (4.55). Using this NARMA-L2
model, the resulting controller has the form:
Chapter Four
u(k ) =
Modeling and Theoretical Analysis
y (k + d ) − f [y(k ), y(k −1),..., y(k − n +1),u(k −1),....,u(k − n +1)]
g[y(k ),..., y(k − n +1),u(k −1),....,u(k − n +1)]
r
………. (4.58)
Using this equation directly can cause realization problems, because
must determine the control input based on the output at the same time ,
i.e.
y (k + d ) = f [ y (k ), y (k − 1),...., y (k − n + 1), u (k ), u (k − 1),...., u (k − n + 1)]
+ g [ y (k ),..., y (k − n + 1), u (k ),..., u (k − n + 1)]u (k + 1)
.………. (4.59)
Fig. (4.8) shows the structure of NN representation of equation
(4.59). The block diagram of NARMA-L2 controller together with the
reference model and the plant is shown in Fig. (4.9) and the controller
which make (e c ) [the difference between plant output (y) and the reference
R
R
y(r)] very small by evaluated input plant (u). The controller system that can
be implemented with the previously identified NARMA-L2 plant model is
shown in Fig. (4.10). The NARMA-L2 controller simulink block which is
contained in the neural network toolbox blockset is shown in Fig. (4.11).
Chapter Four
Modeling and Theoretical Analysis
Fig. (4.8) General structure of neural network.
Fig. (4.9) The block diagram of NARMA-L2.
Chapter Four
Modeling and Theoretical Analysis
Fig. (4.10) The complete controller system with neural network
controller NARMA-L2.
Fig. (4.11) NARMA-L2 controller simulink block.
Chapter Five
Results and Discussion
5.1 Introduction
This chapter presents the results obtained from the computer
programs using MATLAB program version 7.10 cited in appendix (D) for
dynamic model and control.
The first part of this chapter shows the results of the open loop
experimental and theoretical response for different magnitudes of step
change in hot water flow rate.
The second part shows the results of the control system using
different control strategies.
5.2 Open Loop System
5.2.1 Steady State Results
Tables (E.1) to (E.9) in appendix (E) include the data of ( ∆ T lm ) and
R
R
temperature difference (T hi - T ho ) obtained from steady state data to
R
R
R
R
calculate the overall heat transfer coefficient for the conditions of counter
current flow for different vales of hot water flow rate (0.04970.1159)(kg/sec) while the cold water flow rate remained constant at
(0.0414)(kg/sec), using equation (F.7) in appendix (F).
Figs. (E.1) to (E.9) in appendix (E) show the relations between
( ∆ T lm ) vs. (T hi - T ho ). The results show the linear fitting represented by
R
R
R
R
R
R
equation (F.7) of the experimental data which show a good fitting with
little deviations according to the heat losses to the surrounding although
efforts had been spent to insulate the exchanger system. From these figures
the values of the overall heat transfer coefficient were determined and
presented in table (E.10) in appendix (E). In Fig. (5.1) the values of overall
heat transfer coefficient (U) are plotted against hot water flow rate (m h ),
R
R
from which the following correlation has been obtained using the method
explained in appendix (F).
U = 11045 m
0.7158
h
……….. (5.1)
Chapter Five
Results and Discussion
Since the change in the physical properties of water is negligibly
small for the same flow rate, the above correlation can be applied for both
cold and hot streams and can be written as:
……….. (5.2)
U = 11045 m
0.7158
The above correlation appears to be in good agreement with those
reported by literature [128,129].
P
P
Previous reports show that the correlation has the form:
h∝m
……….. (5.3)
w
Where w ranges between (0.697-0.864).
In order to present a comparison between the present model
equation (5.2) and the above model, equation (5.3) may be written as:
h =α m
……….. (5.4)
w
Since:
U
=
f (h)
……….. (5.5)
∴U = α m
……….. (5.6)
w
Or:
……….. (5.7)
U =α m
0.697 − 0.864
Comparing equation (5.7) with equation (5.2), the agreement
between the two models is quite apparent.
Fig. (5.1) The relation between overall heat transfer coefficient (U) and
hot water flow rate (m h ).
R
R
Chapter Five
Results and Discussion
5.2.2 Dynamic Behavior
The dynamic responses were studied for different step changes in the
manipulated variable (m h ) in order to study the effect of each change on
R
R
the controlled variable (T co ). These changes are:
R
R
+Ve (20%, 50%, 80%, 100%, 120% and 135%) step changes in the
hot water flow rate (m h ).
R
R
The theoretical results are obtained by using computer simulation
programs given in (D.2) in appendix (D).
The theoretical results are compared with experimental results for
different step changes. Fig. (5.2) represents the comparison between
experimental and theoretical outlet cold water temperature response. Table
(5.1) illustrates the relative error (Er) and mean square error (MSE)
between experimental and theoretical responses.
Fig. (5.2) shows the relation between controlled variable (T co ) and
R
R
time. It can be seen that the increase in hot water flow rate (m h ) is directly
R
R
proportional to outlet cold water temperature (T co ) for different steps in the
R
R
hot water flow rate (m h ) for theoretical and experimental work.
R
R
Table (5.1) Shows that the theoretical results are in good agreement
with experimental results.
The determined values of the steady-state gain (K) and the time
constant (τ) experimentally by using process reaction curve are tabulated in
table (E.11) in appendix (E).
The analysis indicated that the process can be experimentally
represented by first order.
Chapter Five
Results and Discussion
20
50
80
33
Outlet Cold Water Temperature (C)
100
120
32
135
exp
31
30
29
28
27
0
20
40
60
80
100
Time (sec)
120
140
160
180
Fig. (5.2) Comparison between experimental and theoretical (T co )
R
response for +ve different step changes in (m h ).
R
R
Table (5.1) The relative error (Er) and mean square error (MSE)
between experimental and theoretical (T co ) response.
R
R
mh
Er
MSE
20%
0.1110
3.3329e-004
50%
5.2986
0.7588
80%
0.9694
0.0254
100%
0.8960
0.0217
120%
5.8441
0.9231
135%
1.8257
0.0901
R
R
Chapter Five
Results and Discussion
5.2.3 Justifying the Design Fitness of the PHE
The design fitness of the PHE has been justified by determining the
inlet and outlet temperature of each plate using a matrix solution method
(Gaussian-Elimination) [130].
P
P
The value of hot water flow rate (m h ) used in the design is
R
R
(0.0993)(kg/sec) and the value of cold water flow rate (m c ) is
R
R
(0.0414)(kg/sec).
Figs. (5.3.a) and (5.3.b) represents the outlet cold and hot water
temperature distributions for a counter flow of each plate on PHE
respectively and Fig. (5.4) represents the final outlet cold water
temperature for each plate vs. number of plates in PHE.
Figs. (5.3) and (5.4) show the response of 24 plates which prove that
the design is accurate and there is no losses in the energy input. This is
clear through the exponential shape of Fig. (5.4) which proves the
reasonable number of plates and accurate geometric design of each plate.
34
Outlet Cold Water Temperatures (C)
32
30
28
26
24
22
20
0
Plate 1
Plate 24
10
20
30
40
50
60
Time (sec)
70
80
90
100
Fig. (5.3.a) The outlet cold water temperature distributions for a
counter flow of each plate on PHE.
Chapter Five
Results and Discussion
50
Plate 1
Plate 24
Outlet Hot Water Temperatures (C)
48
46
44
42
40
38
0
10
20
30
40
50
60
Time (sec)
70
80
90
100
Fig. (5.3.b) The outlet hot water temperature distributions for a
counter flow of each plate on PHE.
Outlet Cold Water Temperature (C)
34
33
32
31
30
29
Plate
0
5
10
15
Number of Plates
20
25
Fig. (5.4) The final outlet cold water temperature for each plate vs.
number of plates in PHE.
Chapter Five
Results and Discussion
5.3 Closed Loop System
In this section, different control strategies are used: conventional
feedback control, classical FL control, ANN control and PID fuzzy control.
The Value of hot water flow rate used in the control system is (0.0993)
(kg/sec) and the value of cold water flow rate is (0.0414) (kg/sec).
5.3.1 Conventional Feedback Control
Conventional feedback control was applied using PI and PID modes
to control the outlet cold water temperature. The tuning of the control
parameters (proportional gain (k c ), time integral (τ I ) and time derivative
R
R
R
R
(τ D )) were applied.
R
R
The optimum values of the controller parameters (k c , τ I , τ D ) were
R
R
R
R
R
R
tuned by using computer simulation programs based on minimum integral
of square error (ISE) and minimum integral of the time-weighted absolute
error (ITAE). These programs are shown in programs (D.3.1) and (D.3.2)
in appendix (D).
The results of the control tuning parameters are given in tables (5.2)
and (5.3).
To evaluate the performance of the PI and PID controllers we have
considered three parameters of the step response and the parameters
(overshoot, settling time and rise time) have been given in the table (5.4).
Table (5.2) Control parameters of PI control.
Control tuning
0B
methods
Controller parameters
Kc
τI
τD
ITAE
ISE
10.6614
0.1587
‫ــــ‬
0.2163
0.2517
10.8959
0.1596
‫ــــ‬
0.2795
0.2804
R
R
Ziegler-Nichols
tuning
Cohen-Coon
tuning
R
Chapter Five
Results and Discussion
Table (5.3) Control parameters of PID control.
Control tuning
1B
methods
Controller parameters
Kc
τI
τD
ITAE
ISE
13.7972
0.0952
0.0238
0.0298
0.1236
16.1441
0.1181
0.0175
0.1871
0.2705
R
R
R
Ziegler-Nichols
tuning
Cohen-Coon
tuning
Table (5.4) Comparison of different parameters of PI and PID
controllers.
Parameters
PI controller
PID controller
Overshoot
2.177
2.12
Settling time
1.61
0.73
Rise time
0.086
0.077
As shown in the tables (5.2) and (5.3) the control tuning was found
in two different methods therefore; it can be seen that the tuning by using
the Ziegler-Nichols method is better than that of Cohen-Coon method
because Ziegler-Nichols method depends on closed loop system while
Cohen-Coon method depends on open loop system, also the ISE values and
ITAE values of first method are less than that of the second method.
In this work the ITAE is implemented because it uses the time to
determine its value which states the faster criteria to reach the new steadystate value.
As shown in table (5.4) it is clear that PID controller is better than PI
controller because it gives smaller overshoot, settling time, and rise time
values than that of PI controller.
Chapter Five
Results and Discussion
5.3.1.1 Control Behavior
Bode Diagram
40
Magnitude (dB)
20
0
-20
-40
-60
360
Phase (deg)
270
180
90
0
-90
-3
10
-1
-2
10
10
0
10
2
1
10
10
3
10
Frequency (rad/sec)
Fig. (5.5) Bode diagram of the PHE.
Ziegler-Nichols Method
Cohen-Coon Method
Outlet Cold Water Temperature (C)
2
1.5
1
0.5
0
0
0.5
1
1.5
2
Time (sec)
2.5
3
3.5
Fig. (5.6) Transient response of the PHE with PI controller mode
(unit step change).
Chapter Five
Results and Discussion
Ziegler-Nichols Method
Cohen-Coon Method
Outlet Cold Water Temperature (C)
2
1.5
1
0.5
0
0
0.5
1
2
1.5
Time (sec)
2.5
3
3.5
Fig. (5.7) Transient response of the PHE with PID controller mode
(unit step change).
PID Controller
PI Controller
Outlet Cold Water Temperature (C)
2
1.5
1
0.5
0
0
0.5
1
1.5
2
Time (sec)
2.5
3
3.5
Fig. (5.8) The comparison between the transient response for PI and
PID controllers (unit step change).
Chapter Five
Results and Discussion
Fig. (5.5) shows the bode diagram of the closed loop system which
implemented to determine the value of ultimate gain (k u ) and ultimate
R
R
period of sustained cycling (P u ) in order to tune the adjusted parameters
R
R
values of both PI and PID modes as in the section (D.3.1) in appendix (D).
Figs. (5.6) and (5.7) show the control responses for PI and PID
modes for two different criteria. As shown in the figures, it is clear that the
overshoot and setting time of Ziegler-Nichols method are less than of the
Cohen-Coon method for both PI and PID modes.
Fig. (5.8), shows the comparison between two control modes. It is
clear that PID mode gave better response that is clear through the lower
values of the overshoot and response time. So PID controller is used in this
work as a feedback mode of comparison with the other modes of a classical
FL, ANN and PID fuzzy controllers.
5.3.2 Fuzzy Logic Controller
In this section, classical FL controller is discussed and studied.
The control tuning of the FL controller depends on the trial and
error to find the scaled factors for each variable. The main difficulty of
implementing this FL controller is the number of tuning parameters: the
scaled factors for each variable, the membership functions and the rules.
The best values of the scaled factors were tuned using simulink program.
The simulation model of PHE with classical FL controller is illustrated in
Fig. (5.9).
Chapter Five
Results and Discussion
+
-
step
+
Mux
G
Mux
Transfer
Fcn Valve
-
Fuzzy Controller
with Ruleviewer
v
G
p
Transfer
Fcn Process
Transport
Delay
Scope
-1
Z
Integer Delay
G
m
Transfer Fcn
measuring
Fig. (5.9) Simulation model of PHE with classical FL controller.
For the classical FL controller the input variable are error (e) and
change of error (de), the output variable is the control action (u).
Gaussian membership functions are used for input variables
simulations while for the output variable the triangular membership
function was used. The universe of discourse of error, delta error and
output are [-1, 1], [-0.15, 0.15] and [-1, 1] respectively. The rule base that
have been taken proposed by Mamdani fuzzy system.
The membership function for error and change of error consist of
negative big (NB), negative (N), zero (Z), positive (P) and positive big
(PB). Meanwhile, membership function for control action consist of
negative big (NB), negative (N), negative small (NS), zero (Z), positive
small (PS), positive (P) and positive big (PB). The complete set of classical
FL control rules given in table (5.5).
The value of membership function for control action is:
PB : [0.8 0.9 1] , P : [0.4 0.6 0.7] , PS : [0.1 0.3 0.5] , Z : [-0.2 0 0.2] ,
NS : [-0.5 -0.3 -0.1] , N : [-0.7 -0.6 -0.4] , NB : [-1 -0.9 -0.8].
Chapter Five
Results and Discussion
Table (5.5) IF-THEN rule base for classical FL control.
de
e
NB
NB
N
Z
P
PB
PB
PB
P
PS
Z
N
PB
P
PS
Z
NS
Z
P
PS
Z
NS
N
P
PS
Z
NS
N
NB
PB
Z
NS
N
NB
NB
The table is read in the following way:
IF e is NB AND de is NB THEN u is PB.
The comparison between the transient response for PID and classical
FL controller is shown in Fig. (5.10).
Table (5.6) shows the performance criteria for classical FL and PID
controllers.
As shown in Fig. (5.10) and table (5.6), it's clear that the classical FL
controller performs better compared to PID controller in terms of
overshoot. But, on comparing the ISE, ITAE, settling time and rise time of
both controller, the PID controller performs better because of the trial and
error depending of FL controller tuning process.
Also there are several reasons that make the PID controller better
than classical FL controller [131]:
P
P
• The PID controller is well understood, easy to implement – both in its
digital and analog forms – and it is widely used. By contrast, the fuzzy
controller requires some knowledge of FL. It also involves building
arbitrary membership functions.
• The fuzzy controller is generally nonlinear. It does not have a simple
equation like the PID, and it is more difficult to analyze mathematically;
approximations are required.
Chapter Five
Results and Discussion
• The fuzzy controller has more tuning parameters than the PID controller.
Furthermore, it is difficult to trace the data flow during execution, which
makes error correction more difficult.
The results obtained agreed with the findings of Erenoglu [132].
P
PID Controller
Classical Fuzzy Controller
2
Outlet Cold Water Temperature (C)
P
1.5
1
0.5
0
0
0.5
1
1.5
Time (sec)
2
2.5
3
Fig. (5.10) The comparison between the transient response for PID and
classical FL controllers.
Table (5.6) Comparison between the performance of classical FL
controller and PID controller.
Parameters
Classical FL controller
PID controller
ISE
0.4655
0.1236
ITAE
0.2187
0.0298
Overshoot
1.006
2.12
Settling time
2.575
0.73
Rise time
2.715
0.077
Chapter Five
Results and Discussion
5.3.3 Artificial Neural Network NARMA-L2 Controller
In order to evaluate the effectiveness of the NARMA-L2 control, the
controller is implemented and applied to control PHE.
NARMA-L2 control is one of the popular neural network
architectures that have been implemented as simulink block in MATLAB
software version 7.10 which contained in the neural network toolbox
blockset.
The plant model neural network has one hidden layer of seven
neuron which was found as a best neuron number in this work and an
output layer of one neuron. The size of hidden layer, the number of delayed
inputs and outputs, and the training function are selected in window as
shown in Fig. (5.11). This window enable to train and control the plant
model. The training function is trainlm and MATLAB simulink used to
design the model for the PHE. ANN NARMA-L2 controller simulink block
is added to the plant by MATLAB simulink. Fig. (5.12) illustrates the
simulation model of PHE with ANN NARMA-L2 controller.
Figs. (5.13) and (5.14) show the training and testing of ANN
NARMA-L2 controller respectively. These figures contain the input and
output of the plant, also it's seen that the NN trained to identify the
response of the plant.
Fig. (5.15) shows the performance of ANN NARMA-L2 control.
The training reached the specified performance of mean square error of
(4.654 * 10-9) with 463 epoch. Also the validation and test show the same
P
P
as or close to the training performance.
Fig. (5.16) shows the transient response of the PHE with ANN
NARMA-L2 controller that shows the outlet cold water temperature (T co )
R
R
response. This figure shows that the NARMA-L2 gave a good control
performance with low values of ISE and ITAE as well as low rise time and
settling time as given in table (5.7).
Chapter Five
Results and Discussion
It is clear in Fig. (5.16) and table (5.7) that the ANN NARMA-L2
controller is better than feedback and classical FL controllers because of
the good tuning of adjusted parameters values that give smaller ISE, ITAE,
and faster to reach the steady state in lower time, lower oscillatory
compared with feedback and classical FL controllers but the classical FL
controller is better in lower overshoot compared with ANN NARMA-L2
controller.
Fig. (5.11) Plant identification window.
Chapter Five
Results and Discussion
Fig. (5.12) Simulation model of PHE with ANN NARMA-L2 controller.
Fig. (5.13) Training of ANN NARMA-L2 controller.
Chapter Five
Results and Discussion
Fig. (5.14) Testing of ANN NARMA-L2 controller.
Fig. (5.15) The performance of ANN NARMA-L2 control.
Chapter Five
Results and Discussion
ANN NARMA-L2 Controller
Outlet Cold Water Temperature (C)
1
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
Time (sec)
2
2.5
3
Fig. (5.16) Transient response of the PHE with ANN NARMA-L2
controller.
Table (5.7) Different performance indices and different parameters of
ANN NARMA-L2 controller.
Parameters
ANN NARMA-L2 controller
ISE
0.0601
ITAE
0.0091
Overshoot
1.049
Settling time
0.462
Rise time
0.5
5.3.4 PID Fuzzy Controller
The design for classical FL controllers is still considered premature
in general, significant progress has been gained recently in the pursuit of
Chapter Five
Results and Discussion
this technology and it remains a difficult task due to the fact that there is
insufficient analytical design technique in contrast with the well-developed
linear control theories .The FL controller structure can be classified into
different types, and the most popular one is PID fuzzy controller.
The control tuning of the PID fuzzy controller depends on the trial
and error to find the scaled factors for each variable
P
[133]
. The best values
P
of the scaled factors were tuned using simulink program. The simulation
model of PHE with PID fuzzy controller is illustrated in Fig. (5.17).
+
Gain1
step
1
S
G
Integrator
Gain2
Gain
Fuzzy Logic
Controller
v
Transfer
Fcn Valve
G
p
Transfer
Fcn Process
Transport
Delay
Scope
du dt
Gain3
G
m
Transfer Fcn
measuring
Fig. (5.17) Simulation model of PHE with PID fuzzy controller.
The inputs of PID fuzzy control are defined as the proportional gain
(K c ), integral gain (K I ) and derivative gain (K D ). The output variable, is
R
R
R
R
R
R
called the control action (u). Fuzzy sets are defined for each input and
output variable. There are three fuzzy levels (negative (N), zero (Z) and
positive (P)). The membership functions for inputs are triangular and the
membership function for output variable is linear. By trial and error the
proportional gain has a range of [0, 1.25], integral gain has a range of [-2,
2], derivative gain has a range of [0.1, 1.25] and control action has a range
of [0, 1.25]. The system is a Sugeno fuzzy system and the rule base of PID
fuzzy controller is shown in table (5.8).
Chapter Five
Results and Discussion
Table (5.8) The rule base of PID fuzzy controller.
27 PID fuzzy rules are used for this case because of using three
dimensional rule set. For example, one of the rules for PID fuzzy
controller:
IF K c is N AND K I is N AND K D is N THEN u is P.
R
R
R
R
R
R
The transient response of the PHE with PID fuzzy controller is
shown in Fig. (5.18) and the performance indices used of PID fuzzy
controller are the ISE and ITAE as well as the performance of the PID
fuzzy controller of the step response of the system are given in table (5.9).
As shown in Fig. (5.18) and table (5.9), it's clear that the PID fuzzy
controller is improved over to other controllers used in this work.
Chapter Five
Results and Discussion
PID Fuzzy Controller
Outlet Cold Water Temperature (C)
1
0.8
0.6
0.4
0.2
0
0
1
0.5
2
1.5
Time (sec)
2.5
3
Fig. (5.18) Transient response of the PHE with PID fuzzy controller.
Table (5.9) Different performance indices and different parameters in
PID fuzzy controller.
Parameters
PID fuzzy controller
ISE
0.0547
ITAE
0.0031
Overshoot
1
Settling time
0.432
Rise time
0.599
Chapter Five
Results and Discussion
5.3.5 Comparison Among PID, Artificial Neural Network and PID
Fuzzy Controllers
This section shows a comparison among different control strategies
of the transient response for the PHE with PID, ANN and PID fuzzy
controllers as shown in Fig. (5.19).
To evaluate the performance of different controllers parameters of
the step response of the system have been considered. In all the three
controllers the performance indices of different controllers are the ISE and
ITAE as well as the parameters are evaluated and comparative studies of
their performance are tabulated in the table (5.10).
PID Fuzzy Controller
ANN Controller
PID Controller
Outlet Cold Water Temperature (C)
2
1.5
1
0.5
0
0
0.5
1
1.5
Time (sec)
2
2.5
3
Fig. (5.19) The comparison among the transient response for PID,
ANN and PID fuzzy controllers.
Chapter Five
Results and Discussion
Table (5.10) Comparison of different performance indices and
different parameters in controllers.
PID
ANN
PID fuzzy
controller
controller
controller
ISE
0.1236
0.0601
0.0547
ITAE
0.0298
0.0091
0.0031
Overshoot
2.12
1.049
1
Settling time
0.73
0.462
0.432
Rise time
0.077
0.5
0.599
Parameters
From Fig. (5.19) and table (5.10), the simulation results clearly show
that the PID fuzzy controller gives better control of temperature rather than
PID controller and ANN controller. It has been seen that more accurate
results were obtained using ANN controller over PID controller, further
better results obtained by using PID fuzzy controller.
From the above observations it is clear that the PID controller
produces high values of overshoot and settling time. To compensate this
kind of high values, ANN controller has been implemented. By
implementing this method the system overshoot and settling time were
reduced. For further reduction requirements, the PID fuzzy controller was
suggested. ISE and ITAE of PID fuzzy controller show lower values
compared to other modes which indicates the robust control of this
controller. Although PID fuzzy mode gave better performance, but the high
value of the rise time shows one of its disadvantages. The reason for that
high value is the significant time investment needed to correctly tune
membership functions and adjust rules to obtain a good solution. The more
rules suggested, the increasing difficulty obtained. The results required
more system memory and processing time [133].
P
P
Chapter Five
Results and Discussion
The results showed that the PID fuzzy controller is slightly better
than ANN controller.
From these observations it is clear that PID fuzzy controller is a
much better option for control rather than PID and ANN controller because
PID fuzzy controller combines the advantages of a fuzzy logic controller
and a PID mode. Also PID fuzzy controller is decreasing the number of
rules, decomposition of multivariable control rules into three sets of one
dimensional rules for each input variable, simplified the evolution of the
rule base, conventional control and easy connection between fuzzy
parameters and operation of the controller and membership functions are
simple triangular with fuzzy logic rules. A major problem with neural nets
is the “Black Box” nature, or rather, the relationships of the weight changes
with the input-output behavior during training and use of trained system to
generate correct outputs using the weights.
Chapter Six
Conclusions and Future Work
6.1 Conclusions
Based on this study of dynamics and control of a PHE, the following
conclusions can be derived:
1. The experimental heat transfer measurements of the PHE show that
the overall heat transfer coefficient (U) is related to the hot water
flow rate (m h ) by a correlation having the form:
R
R
U = 11045 m
0.7158
h
……….. (6.1)
2. The PHE model is found dynamically as a first order lead and second
order overdamped lag while the experimental PHE represented
dynamically as first order with a negligible dead time value.
3. The assumptions used to establish the mathematical model of present
process give good agreement when the theoretical and experimental
results are compared with each other.
4. The response of 24 plates when justifying the design fitness of the
PHE prove that the design is accurate and there is no losses in the
energy input.
5. An important step in implementing the mathematical model of the
PHE is the selection of the controller parameters. Different methods
were used in the computer simulation to optimize the numerical
value of controller parameters, the ITAE gives a good comparison
and clearance of the error.
6. PID feedback controller is better than PI feedback controller because
it gives smaller ITAE, ISE, overshoot, settling time and rise time
values.
7. PID controller performs better when it is compared to classical fuzzy
logic controller because of the trial and error depending of fuzzy
logic controller tuning process.
Chapter Six
Conclusions and Future Work
8. Artificial neural network controller is better than feedback and
classical fuzzy logic controllers because the artificial neural network
controller learns system and it has got generalization capabilities.
9. The PID fuzzy controller gives a much better control performance of
temperature rather than PID controller and artificial neural network
controller because PID fuzzy controller combines the advantages of
fuzzy logic controller and a PID controller.
6.2 Future Work
The following suggestions for future work can be considered:
1. The same procedure of this work is useful for another type of heat
exchanger with different specifications or using the same procedure
for other controlled and manipulated variables.
2. Adding other control strategies like cascade control, adaptive
control, neuro-fuzzy control and genetic algorithms control.
3. Application of on-line control is recommended.
References
1. Bayazit, S., Bicer, K. H., Kulali, G., Müminoglu, M., and Torres, J.
J. J., "Automatic Control of a Heat Exchanger with Changing
Operation Conditions", http://www.mathematik.uniU
dortmund.de/papers/BayazitBicerKulaliMueminogluTorres2008.pd
f, 2008.
U
2. Diaz, G., Sen, M., Yang, K. T., and McClain, R. L., "Adaptive
Neurocontrol of Heat Exchangers", Transactions of the ASME,
Journal of Heat Transfer, Vol.123, PP.556-562, June, 2001.
3. Patel, A. M., "Dynamic Mathematical Model of a Heat
Exchanger", PhD Thesis, Chemical Engineering, University of
Tennessee at Chattanooga, March, 2003.
4. Hu, Q., So, A. T. P., Tse, W. L., and Ren, Q., "Development of
ANN-Based Models to Predict The Static Response and
Dynamic Response of a Heat Exchanger in a Real MVAC
System", International Conference on Control and Synchronization
of Dynamical Systems, China, Journal of Physics, Vol.23, PP.110121, 2005.
5. "Heat
Exchanger",
http://www.answers.com/topic/heatU
U0T
U0T
exchanger, November 2010.
U
6. Haile, G. T., "Heat Transfer in Plate Heat Exchangers", M.Sc.,
Thesis, Chemical and Process Engineering, Lappeenrata University
of Technology, June 2009.
7. Fernandes, C. S., Dias, R. P., and Maia, J. M., "New Plates for
Different Types of Plate Heat Exchangers", Recent Patents on
Mechanical Engineering, Vol.1, No.3, PP.198-205, 2008.
8. "APV Plate Heat Exchangers", APV ANSPX BRAND,
http://www.apv.com , 2010.
0TU
U0T
References
9. "Plate Heat Exchangers", WCR Sweden Specialist in Plate Heat
Exchangers, http://wcrbenelux.nl/site/content/view/12/13/lang ,en,
0TU
U0T
U
2009.
10. Narataruksa, P., Triratana, P., Suppamassadu, K. P., Heggs, P. J.,
and Tia, S., "Dynamic Simulation of Plate and Frame Heat
Exchanger Undergoing Food Fouling: Coconut Milk Fouling
Case Study", www.scienceasia.org, Jan 2008.
0TU
U0T
11. Gut, J. A. W., and Pinto, J. M., "Modeling of Plate Heat
Exchangers with Generalized Configurations", International
Journal of Heat and Mass Transfer, Vol.46, PP.2571-2585, 2003.
12. Thirumarimurugan, M., and Kannadasan, T., "Simulation Studies
on Plate Type Heat Exchanger Using ANN", International
Journal of Chem. Tech. Research, Vol.1, No.2, PP.349-354, AprilJune, 2009.
13. Dwivedi, A. k., and Das, S. K., "Dynamics of Plate Heat
Exchangers Subject to Flow Variations", International Journal of
Heat and Mass Transfer, Vol.50, PP.2733-2743, 2007.
14. Williams, D., "Plate Heat Exchangers", Canada Composting Inc.
(CCI), State of the Art Engineering Report-MME 499, October,
2002.
15. Longo, G. A., and Gasparella, A., "Refrigerant R134a
Vaporization Heat Transfer and Pressure Drop Inside A Small
Brazed Plate Heat Exchanger", International Journal of
Refrigeration, Vol.30, PP.821-830, 2007.
16. Gut, J. A. W., Fernandes, R., Pinto, J. M., and Tadini, C. C.,
"Thermal Model Validation of Plate Heat Exchangers with
Generalized Configurations", Chemical Engineering Science ,
Vol.59, PP.4591-4600 , 2004.
References
17. Galeazzo, F. C. C., Miura, R. Y., Gut, J. A. W. and Tadini, C. C.,
"Experimantal and Numerical Heat Transfer in a Plate Heat
Exchanger", Chemical Engineering Science, Vol.61, PP.71337138, 2006.
18. Alfa Laval, Product Catalogue, Sweden, http://www.alfalaval.com.
0TU
U0T
19. Seborg, D. E., Edgar, T. F., and Mellichamp, D. A., "Process
Dynamics and Control", 2nd Edition, John Wiley and Sons, Inc.,
P
P
2004.
20. Ali, E. M., "Process Control in The Chemical Industries",
http://ksu.edu.sa/Pages/default.aspx, 2002.
0TU
U0T
21. Kaya, I., Tan, N., and Atherton, D. P., "Improved Cascade
Control
Structure
and
Controller
Design",
44th
P
P
IEEE
Conference on Decision and Control and the European Control
Conference, Seville, Spain, December, 2005.
22. You, K., "Adaptive Control", In-Tech, www.intechopen.com,
U
U
January, 2009.
23. Grigorie, T. L., "Fuzzy Controllers, Theory and Applications",
In-Tech, www.intechopen.com, February, 2011.
U
U
24. Luebbers, P. G., "Process-Industrial Instruments and Control
Handbook", Iocalhost, http://localhost.com, 2004.
0TU
U0T
25. Mastacan, L., Olah, I., and Dosoftie, C. C., "District Heating
Substations Water Temperature Control Based on Soft
Computing Technology", 6th International Conference on
P
P
Electromechanical and Power System, Chisinau, Rep.Moldova,
October, 2007.
26. Roffel, B., and Betlem, B., "Process Dynamics and Control",
John Wiley and Sons, Ltd, 2006.
27. Scariot, M. R., Berto, M. I., and Silveira, V., "Simulation of The
Temperature Profile of a Pectin Solution in a Plate Heat
References
Exchanger: a Non-Linear System Approach for Control",
Thermal Engineering, Vol.4, No.1, PP.30-34, June, 2005.
28. Alwan, G. M., "Study of Dynamics and Control of a Plate Heat
Exchanger", Msc Thesis, Chemical Engineering, University of
Baghdad, November, 1982.
29. Baker, N. S., "Dynamic Characteristics of Plate Heat
Exchanger", Msc Thesis, Chemical Engineering, University of
Technology, December, 1983.
30. Khan, A. R., Baker, N. S., and Wardle, A. P., "The Dynamic
Characteristics of a Counter Current Plate Heat Exchanger",
Int. J. Heat Mass Transfer, Vol.31, No.6, PP.1269-1278, 1988.
31. AL-Zobai, K. M. M., "Computer Control on Plate Heat
Exchanger", PhD Thesis, Chemical Engineering, University of
Baghdad, 2004.
32. Kapustenko,
P.,
Dobromyslova,
O.,
Dobromyslov,
O.,
Perevertaylenko, O., Arsenyeva, O., Ilyunin, O., and Shabanov, E.,
"Control of Plate Heat Exchanger Outlet Temperature Using
Butterfly Valve and Parametric Model Predictive Control
Technique", Chemical Engineering Transactions, Vol.18, 2009.
33. Mandavgane, S. A., and Pandharipande, S. L., "Application of
Optimum ANN Architecture for Heat Exchanger Modeling",
Indian Journal of Chemical Technology, Vol.13, PP.634-639,
November, 2006.
34. Vasickaninova, A., Bakosova, M., Meszaros, A., and Klemes, J.,
"Neural Network Predictive Control of a Heat Exchanger",
Chemical Engineering Transactions, Vol.21, 2010.
35. Prasanth, B. V., and Kumar, D. S. V. J., "New Control Strategy
for Load Frequency Problem of a Single Area Power System
References
Using Fuzzy Logic Control", Journal of Theoretical and Applied
Information Technology, 2008.
36. Anand, B., and Jeyakumar, A. E., "Load Frequency Control with
Fuzzy Logic Controller Considering Non-Linearities and Boiler
Dynamics", ICGST-ACSE Journal, Vol.8, Issue III, January,
2009.
37. Xue, D., Chen, Y. Q., and Atherton, D. P., "Linear Feedback
Control", The Society for Industrial and Applied Mathematics,
2007.
38. Imal, E., "CDM Based Controller Design for Nonlinear Heat
Exchanger Process", Turkey Journal Electrical Engineering and
Computer Science, Vol.17, No.2, 2009.
39. Henriques, J., Gil, P., Cardoso, A., and Dourado, A., "Scheduling
of PID Controllers by Means of a Neural Network with
Application to a Solar Power Plant", The World's Largest
Professional Association for the Advancement of Technology,
IEEE, 2002.
40. Delnero, C., "Neural Networks and PI Control Using Steady
State Prediction Applied to a Heating Coil", Msc Thesis,
Mechanical Engineering, Colorado State University, October,
2000.
41. Fink, A., Nelles, O., and Isermann, R., "Nonlinear Internal
Model Control for Miso Systems Based on Local Linear NeuroFuzzy Models", IFAC, 15th Triennial World Congress Barcelona,
P
P
Spain, 2002.
42. Maidi, A., Diaf, M., and Corriou, J. P., "Optimal Linear PI Fuzzy
Controller Design of a Heat Exchanger", Chemical Engineering
and Processing, Vol.47, PP.938-945, 2008.
References
43. Dale, S., Gabor, G., and Bara, A., "Reduced Complexity
Interpolative
Control
System
for
a
Geothermal
Heat
Exchanger", World Geothermal Congress, Bali, Indonesia, April,
2010.
44. Diaz, G. C., "Simulation and Control of Heat Exchangers Using
Artificial Neural Networks", PhD Thesis, Aerospace and
Mechanical Engineering, University of Notre Dame, March, 2000.
45. Rouhani, H., Kharaajoo, M. J., Araabi, B. N., and Lucas, C.,
"Intelligent Control of Electrically Heated Micro Heat
Exchanger with Locally Linear Neurofuzzy Identifier and
Emotional Based Learning Controller", The World Scientific
and Engineering Academy and Society (WSEAS), Conferences,
Austria, 2004.
46. Varshney, K., and Panigrahi, P. K., "Artificial Neural Network
Control of a Heat Exchanger in a Closed Flow Air Circuit",
Applied Soft Computing, Vol.5, PP.441-465, 2005.
47. Qu, Y., Xu, L., Fang, X., Wang, J., and Gu, S., "A New Approach
to Heat Exchanger Control Based on Model Control",
International Journal of Information and Systems Sciences, Vol.2,
No.1, PP.31-41, 2006.
48. Jan, M., and Jaroslava, K., "Control of Laboratory Pilot Plant
with Dead Time", Instruments and Control, ASR, Babiuch,
Ostrava, 2009.
49. Mulyana, T., Than, M. N. M., and Hanafi, D., "A Discrete Time
Model of Boiler Drum and Heat Exchanger QAD Model BDT
921", International Conference on Instrumentation, Control and
Automation, Bandung, Indonesia, October, 2009.
50. Homod, R. Z., Sahari, K. S. M., Mohamed, H. A. F., and Nagi, F.,
"Hybrid
PID-Cascade
Control
for
HVAC
System",
References
International Journal of Systems Control, Vol.1, Iss.4, PP.170-175,
2010.
51. Khare, Y. B., and Singh, Y., "PID Control of Heat Exchanger
System", International Journal of Computer Applications, Vol.8,
No.6, October, 2010.
52. Padhee, S., and Singh, Y., "A Comparative Analysis of Various
Control Strategies Implemented on Heat Exchanger System: A
Case Study", World Congress on Engineering (WCE), London,
U.K., Vol.II, 2010.
53. Rajasekaran, R., and Kannadasan, T., "A Simplified Predictive
Control for a Shell and Tube Heat Exchanger", International
Journal of Engineering Science and Technology, Vol.2, No.12,
PP.7245-7251, 2010.
54. Vasickaninova, A., and Bakosova, M., "Locally Optimal Fuzzy
Control of a Heat Exchanger", The World Scientific and
Engineering Academy and Society (WSEAS), Transactions on
Systems, Vol.9, Issue 9, September, 2010.
55. Riverol, C., and Naplitano, V., "Use of Neural Networks as a
Tuning Method for an Adaptive PID Application in a Heat
Exchanger", Transactions Institution of Chemical Engineers,
Vol.78, Part A, November, 2000.
56. Diaz, G., Sen, M., Yang, K. T., and McClain, R. L., "Dynamic
Prediction and Control of Heat Exchangers Using Artificial
Neural Networks", International Journal of Heat and Mass
Transfer, Vol.44, PP.1671-1679, 2001.
57. Berto, M. I., and JR, V. S., "Configuration of PID / Feed Back
and PID / Feed Back / Feed Forward Controllers in
Temperature Control of a HTST Heat Exchanger", 2th
P
Mercosur Congress on Chemical Engineering and 4th Mercosur
P
P
P
References
Congress on Process Systems Engineering, Sao Paulo, Brazil,
2004.
58. Juneja, P. K., Ray, A. K., and Mitra, R., "Fuzzy Control and
Neural Network Control of Limekiln Process", International
Journal of Electronics Engineering, Vol.2, No.2, PP.305-306, 2010.
59. Xie, G. N., Wang, Q. W., Zeng, M., and Lou, L. Q., "Heat
Transfer Analysis for Shell-and-Tube Heat Exchangers with
Experimental Data by Artificial Neural Networks Approach",
Applied Thermal Engineering, Vol.27, PP.1096-1104, 2007.
60. Cam, E., and Kocaarslan, I., "Load-Frequency Control in Two
Area Power System", Teknoloji, Vol.7, Issue 2, PP.197-203,
2004.
61. Piegat, A., "What is Not Clear in Fuzzy Control Systems?",
International Journal Applied Mathematic Computer Science,
Vol.16, No.1, PP.37-49, 2006.
62. Malhotra, R., Singh, N., and Singh, Y., "An Efficient Fuzzy-GA
Flow Control of Turbine Compressor System: A Process
Control Case Study", International Journal of Advancements in
Computing Technology, Vol.2, No.4, October, 2010.
63. Skrjance, I., Blazic, S., and Matko, D., "Model-Reference Fuzzy
Adaptive Control as a Framework for Nonlinear System
Control", Journal of Intelligent and Robotic Systems, Vol.36,
PP.331-347, 2003.
64. Dale, S., Bara, A., and Gabor, G., "Interpolative Control
Structure Design for a Heat Exchanger in a Geothermal Power
Plant", Journal of Computer Science and Control Systems, Vol.1,
Issue.1, PP.131-134, 2008.
65. Auttawaitkul, Y., Monyakul, V., and Therdyothin, A., "A new
Model of Variable Air Volume Diffuser for Thermal Comfort
References
Based on Fuzzy Logic Control", ECTI International Conference,
Thailand, 2007.
66. Kolek, L., and Harmati, I., "Model Based Simulation and Fuzzy
Control of Solar Heating Systems", 13th IEEE IFAC International
P
P
Conference on Methods and Models in Automation and Robotics,
Szczecin, Poland, August, 2007.
67. Mazinan, A. H., and Sadati, N., "Multiple Modeling and Fuzzy
Predictive Control of a Tubular Heat Exchanger System", The
World Scientific and Engineering Academy and Society (WSEAS),
Transactions on Systems and Control, Vol.3, Issue 4, April, 2008.
68. Skrjanc, I., and Matko, D., "Predictive Functional Control Based
on Fuzzy Model for Heat-Exchanger Pilot Plant", IEEE
Transactions on Fuzzy Systems, Vol.8, No.6, December, 2000.
69. Chen, Y., Zhang, J., Zhang, B., and Gao, F., "Development of
Monitoring Control and Fuzzy Control Test of Finned-Tube
Heat-Exchanger Test-Board", Sixth International Conference for
Enhanced Building Operations, Shenzhen, China, Vol.VI-6-1,
November, 2006.
70. Habbi, H., Kinnaert, M., and Zelmat, M., "A Complete Procedure
for Leak Detection and Diagnosis in a Complex Heat
Exchanger
Using
Data-Driven
Fuzzy
Models",
ISA
Transactions, Vol.48, PP.354-361, 2009.
71. Agashe, S., Ghatol, A., and Agashe, S., "Automation of Heat
Exchanger Using Neural Network", World Academy of Science,
Engineering and Technology, Vol.15, 2006.
72. Renotte, C., Wouwer, A. V., and Remy, M., "Neural Modeling
and Control of a Heat Exchanger Based on SPSA Techniques",
American Control Conference, Chicago, Illinois, PP.3299-3303,
June, 2000.
References
73. Babu, B. V., and Shailesh, M., "Adaptive Networks for Fault
Diagnosis and Process Control", Birla Institute of Technology
and Science, India, www.bits-pilani.ac.in, 2002.
U
U
74. Kharaajoo, M. J., "Neural Network Control of a Heat
Exchanger Pilot Plant", The World Scientific and Engineering
Academy and Society (WSEAS), 2003.
75. Riverol, C., and Napolitano, V., "Estimation of Fouling in a Plate
Heat
Exchanger
Through
The
Application
of
Neural
Networks", Journal of Chemical Technology and Biotechnology,
Vol.80, PP.594-600, 2005.
76. Ramasamy, M., Zabiri, H., Ha, N. T. T., and Ramli, N. M., "Heat
Exchanger Performance Prediction Modeling Using NARXType Neural Networks", The World Scientific and Engineering
Academy and Society (WSEAS), International Conference on
Waste, Management, Water Pollution, Air Pollution, Indoor
Climate, Arcachon, France, October, 2007.
77. Dudzik, S., "Calculation of The Heat Power Consumption in
The Heat Exchanger Using Artificial Neural Network", 9th
P
P
International Conference on Quantitative Infrared Thermography,
Krakow, Poland, July, 2008.
78. Fadare, D. A., and Fatona, A. S., "Artificial Neural Network
Modeling of Heat Transfer in a Staggered Cross-Flow TubeType Heat Exchanger", Pacific Journal of Science and
Technology, Vol.9, No.2, November, 2008.
79. Ramasamy, M., Shahid, A. and Zabiri, H., "Drift Analysis on
Neural Network Model of Heat Exchanger Fouling", Journal of
Engineering Science and Technology, Vol.3, No.1, PP.40-47, 2008.
80. Bonala, S. Y., "A Study on Neural Network Based System
Identification with Application to Heating Ventilating and Air
References
Conditioning
(HVAC)
System",
Msc
Thesis,
Electrical
Engineering, National Institute of Technology, Rourkela, May,
2009.
81. Martinez, J. C. T., Menendez, R. M., and Castanon, L. E. G.,
"Fault Diagnosis in a Heat Exchanger Using Process History
Based-Methods", 20th European Symposium on Computer Aided
P
P
Process Engineering-ESCAPE20, Monterrey, Mexico, 2010.
82. Kharaajoo, M. J., Araabi, B. N., "Neural Network Based
Predictive Control of a Heat Exchanger Nonlinear Process",
Journal of Electrical and Electronics Engineering, Vol.4, No.2,
PP.1219-1226, 2004.
83. Farahani, S. S. A., Nekoui, M. A. and Goharrizi, A. Y.,
"Predictive Control of a Heat Exchanger Based on Local Fuzzy
Models and Neural Networks", Journal of Electrical and
Electronics Engineering, Vol.6, No.2, PP.129-138, 2006.
84. Biyanto, T. R., Ramasamy, M., and Zabiri, H., "Modeling Heat
Exchanger Using Neural Networks", International Conference on
Intelligent and Advanced Systems, Perak, Malaysia, 2007.
85. Selbas, R., Sencan, A., and Kilic, B., "Alternative Approach in
Thermal Analysis of Plate Heat Exchanger", Heat Mass
Transfer, Vol.45, PP.323-329, 2009.
86. APV Company Ltd. England type (JHE) serial No. (1062), 1972.
87. Peter, R. N. C., "Practical Temperature Measurement",
Butterworth-Heinemann, 2001.
88. Stephanopoulos,
Introduction
G.,
to
"Chemical
Theory
and
Process
Practice",
Control
An
Prentice-Hall
International Inc., London, 1984.
89. Luyben, M. L., and Luyben, W. L., "Essential of Process
Control", McGraw-Hill Companies Inc., 1997.
References
90. Nagaraj, B. ,Muthusamy, P., Murali, B., Shahulhammed, M., and
Murugananth, N., "Optimum Tuning Algorithms for PID
Controller A Soft Compuing Approach", IPPTA Journal,
Vol.22, No.2, June, 2010.
91. Cohen, G. H., and Coon, G. A., "Theoretical Considerations of
Retarded Control", Trans. ASME, Vol.75, PP.827, 1953.
92. Ziegler, J. G., and Nichols, N. B., "Optimum Settings for
Automatic Controllers", Trans. ASME, Vol.64, PP.759, 1942.
93. Chrysostomou, C., "Fuzzy Logic Based AQM Congestion
Control in TCP/IP Networks", PhD Thesis, Computer Science,
University of Cyprus, September, 2006.
94. Srivastava, A. K., Kamalasadan, S., and Hande, A., "Comparative
Performance of Improved Shrinking Span Fuzzy Logic
Controller", The World's Largest Professional Association for the
Advancement of Technology, IEEE, 2006.
95. Mathur, H. D., and Manjunath, H. V., "Frequency Stabilization
Using Fuzzy Logic Based Controller for Multi-Area Power
System", The South Pacific Journal of Natural Science, Vol.4,
PP.22-30, 2007.
96. Pundaleek, B. H., Rathi, M. G., and Vijay, K. M. G., "Speed
Control of Induction Motor: Fuzzy Logic Controller v/s PI
Controller", International Journal of Computer Science and
Network Security, Vol.10, No.10, October, 2010.
97. Monga, H., Kaur, G., Kaur, A., and Soni, K., "Fuzzy Logic
Controller for Analysis of AGC", International Journal of
Advanced Engineering and Applications, January, 2010.
98. Cirstea, M. N., Dinu, A., Khor, J. G., and Cormick, M. M.,
"Neural and Fuzzy Logic Control of Drives and Power
Systems", Newnes, www.newnespress.com, 2002.
U
U
References
99. Zhang, H., and Liu, D., "Fuzzy Modeling and Fuzzy Control",
Birkhauser Boston, www.birkhauser.com, 2006.
U
U
100. Corcau, J. I., and Stoenescu, E., "Fuzzy Logic Controller as a
Power System Stabilizer", International Journal of Circuits,
Systems and Signal Processing, Vol.1, Issue 3, 2007.
101. Gayakwad, R., "Optimized Fuzzy Logic for Motion Control",
Acta Polytechnica Hungarica, Vol.7, No.5, 2010.
102. Mortazavi, S. S., Razaz, M., and Khavari, E., "Power Quality
Improvement Using a Fuzzy Logic Control of a Series Active
Filter", Journal
of
Theoretical
and
Applied
Information
Technology, 2010.
103. Sakthivel, G., Anandhi, T. S., and Natarajan, S. P., "Real Time
Implementation of a Fuzzy Logic Controller on FPGA Using
VHDL for DC Motor Speed Control", International Journal of
Engineering Science and Technology, Vol.2, No.9, PP.4511-4519,
2010.
104. Wahyudi, and Jalani, J., "Design and Implementation of Fuzzy
Logic Controller for Intelligent Gantry Crane System", 2nd
P
P
International Conference of Mechatronics, Kuala Lumpur,
Malaysia, May, 2005.
105. Peri, V. M., "Fuzzy Logic Controller for an Autonomous
Mobile Robot", Msc Thesis, Electrical Engineering, Cleveland
State University, May, 2005.
106. Jha, P., "Novel Artificial Neural Network Application for
Prediction of Inverse Kinematics of Manipulator", Msc Thesis,
Mechanical Engineering, National Institute of Technology, 2009.
107. Haghizadeh, A., Shui, I. T., and Goudarzi, E., "Estimation of
Yield Sediment Using Artificial Neural Network at Basin
References
Scale", Australian Journal of Basic and Applied Sciences, Vol.4,
No.7, PP.1668-1675, 2010.
108. Dase, R. K., and Pawar, D. D., "Application of Artificial Neural
Network for Stock Market Predictions: A Review of
Literature", International Journal of Machine Intelligence, Vol.2,
Issue 2, PP.14-17, 2010.
109. Basu, J. K., Bhattacharyya, D., and Kim, T. H., "Use of Artificial
Neural Network in Pattern Recognition", International Journal
of Software Engineering and Its Applications, Vol.4, No.2, April,
2010.
110. Almhdi, K. M., Valigi, P., Gulbinas, V., Westphal, R., and Reuter,
R., "Classification with Artificial Neural Networks and
Support Vector Machines : Application to Oil Fluorescence
Spectra", European Association of Remote Sensing Laboratories
(EARSEL), www.eproceedings.org, 2007.
U
U
111. Jha, G. K., "Artificial Neural Networks", Indian Agricultural
Research Institute, PUSA, New Delhi, 2004.
112. Paulraj, M. P., Yaacob, S., and Andrew, A. M., "Vehicle Noise
Comfort Level Indication Using Artificial Neural Network", 3rd
P
Regional Conference on Noise, Vibration and Comfort (NVC),
Putrajaya, Malaysia, June, 2010.
113. Jena, G., and Baliarsingh, R., "An Introductory Course on
Artificial Neural Network and Fuzzy Logic, The World's Largest
Professional Association for the Advancement of Technology,
IEEE, http://www.drgjena.co.cc, 2009.
U
U
114. Abraham, A., "Handbook of Measuring System Design", John
Wiely and Sons, Ltd., 2005.
115. Krogh, A., "What are Artificial Neural Networks?", Nature
Biotechnology, Vol.26, No.2, February, 2008.
P
References
116. Messa, V., "Neural Networks for Diagnosis of Infarct and
Ischemia", Msc Thesis, IT-University of Goteborg, May, 2006.
117. Lee, Y., "A Neural Network Face Detector Design Using BitWidth Reduced FPU in FPGA", Msc Thesis, Electrical and
Computer Engineering, University of Saskatchewan Saskatoon,
January, 2007.
118. Kamruzzaman, J., Begg, R. K., and Sarker, R. A., "Artificial
Neural Networks in Finance and Manufacturing", Idea Group
Inc., http://www.idea-group.com, 2006.
U
U
119. Du, K. L., and Swamy, M. N. S., "Neural Networks in a Soft
Computing Framework", Springer-Verlag London Limited,
2006.
120. Bomma, P., "Computer-Aided Diagnosis Tool for the Detection
of Cancerous Nodules in X-Ray Images", Msc Thesis, Electrical
and Computer Engineering, Louisiana State University, May, 2005.
121. Georgios, T., Dimitrios, B., Dimitrios, P., and Luis, L. J.,
"Comparative Control of a Nonlinear First Order Velocity
System
by
a
Neural
Network
NARMA-L2
Method",
Elektronika IR Elektrotechnika, Vol.55, No.6, 2004.
122. Oliveira, J. C. P. D., and Bauchspiess, A., "Neural Control of a
4rd Order Level Process", ABCM Symposium Series in
Mechatronics, Vol.3, PP.197-206, 2008.
123. Mokri, S. S., Husain, H., Martono, W., and Shafie, A., "Real Time
Implementation of NARMA-L2 Control of a Single Link
Mainipulator", American Journal of Applied Sciences, Vol.5,
No.12, PP.1642-1649, 2008.
124. Atasoy, I., Yuceer, M., and Berber, R., "Molecular Weight
Control in Acrylonitrile Polymerization with Neural Network
Based Controllers", 16th European Symposium on Computer
P
P
References
Aided Process Engineering and 9th International Symposium on
P
P
Process Systems Engineering, Ankara, Turkey, 2006.
125. Beale, M. H., Hagan, M. T., and Demuth, H. B., "Neural Network
ToolboxTM 7", The Math Works, Inc., 2010.
P
P
126. Araghi, L. F., and Koorayme, M. H., "Neural Network
Controller for Two Links-Robotic Manipulator Control with
Different Load", International Multi Conference of Engineers and
Computer Scientists, Hong Kong, Vol II, March, 2009.
127. Chapman, S. J., "Matlab Programming for Engineers",
Bookwave Companion Series, Second Edition, 2004.
128. Ayub, Z. H., "Plate Heat Exchanger Literature Survey and New
Heat Transfer and Pressure Drop Correlations for Refrigerant
Evaporators", Heat Transfer Engineering, Vol.24, No.5, PP.3-16,
2003.
129. Durmus, A., Benli, H., Kurtbas, I., And Gul, H., "Investigation of
Heat Transfer and Pressure Drop in Plate Heat Exchangers
Having Different Surface Profiles", International Journal of Heat
and Mass Transfer, Vol.52, PP.1451-1457, 2009.
130. Chapra, S. C., and Canale, R. P., "Numerical Methods for
Engineers with Personal Computer Applications", McGraw-Hill,
Inc., 1985.
131. Jantzen, J., "Foundations of Fuzzy Control", John Wiley and
Sons, Ltd, 2007.
132. Erenoglu, I., Eksin, I., Yesil, E., and Guzelkaya, M., "An
Intelligent Hybrid Fuzzy PID Controller", 20th European
P
P
Conference on Modelling and Simulation Wolfgang Borutzky,
Alessandra Orsoni, Richard Zobel, 2006.
References
133. Jain, L. C., and Martin, N. M., "Fusion of Neural Networks,
Fuzzy
Systems
and
Genetic
Algorithms:
Applications", www.itknowledge.com, 1998.
0TU
U0T
Industrial
Appendix A
Calibration Curves of Thermocouples
4.5
4
3.5
mVolt
3
2.5
mV experimental
Linear (fit)
2
1.5
1
0.5
0
0
50
100
150
Temperature (°C)
Fig. (A.1) Calibration curve of the thermocouple.
volume flowrate (lit/min)
12
10
8
Series1
6
Linear (Series1)
4
2
0
0
2
4
6
8
10
Rotameter reading (lit/min)
Fig. (A.2) Calibration curve of cold water rotameter.
volume flowrate (lit/min)
9
8
7
6
5
Series1
4
Linear (Series1)
3
2
1
0
0
2
4
6
8
Rotameter reading (lit/min)
Fig. (A.3) Calibration curve of hot water rotameter.
Appendix B
System and Operating Conditions
Table (B.1) System and operating conditions.
Cold water flow rate
mc
0.0414 (kg/sec)
Hot water flow rate
mh
0.0497 (kg/sec)
Temperature of initial cold water
T ci
20 (oC)
Temperature of initial hot water
T hi
50 (oC)
Specific heat capacity
Cp
4174 (J/kg.oC)
Water density
Ro
993 (kg/m3)
Length of plate heat exchanger
L
0.58 (m)
Width of plate heat exchanger
E
0.07 (m)
Thickness of one plate heat exchanger
S
0.001 (m)
Length of fluid in plate heat exchanger
L_ fluid
0.50 (m)
Width of fluid in plate heat exchanger
E_ fluid
0.065 (m)
Thickness of fluid in plate heat exchanger
S_ fluid
0.046 (m)
B.1
Appendix C
Controller Tuning Methods
C.1) Cohen-Coon Method [91]
Cohen-Coon used process reaction curve, that it is a response of the
process to a step change in the manipulated variable. Cohen and Coon
observed that the response of most processing units to a step change in
input variable can be adequately approximated by the response of first
order system with dead time, and the transfer function is:
G
PRC
(s)
−
K ets
τ s +1
=
……….. (C.1)
d
The values of K, τ and t d are calculated from the process reaction
curve which is shown in Fig. (C.1). A tangent is drawn to the curve at the
point of maximum rate or ascent, and then t d is the intercept of this tangent
with x-axis, and is defined as the time elapsed until the system responds.
K =
B Output (at steady state)
=
A Input (at steady state)
B Output (at steady state)
=
S
Slope
τ =
……….. (C.2)
……….. (C.3)
1) For Proportional controller:
K
C
=
1 τ  + t
1
K t  3τ
d
d




……….. (C.4)
2) For Proportional-Integral controller:
K
C
=
1 τ 
t
0.9 +
12τ
K t 
d
d




……….. (C.5)
30 + 3t τ
τ = t 9 + 20t τ
……….. (C.6)
d
I
d
d
3) For Proportional-Integral-Derivative controller:
K
C
=
1 τ  4 + t
K t  3 4τ
d
d




……….. (C.7)
32 + 6t τ
τ = t 13 + 8t τ
……….. (C.8)
d
I
d
d
C.1
Appendix C
τ
= td
D
Controller Tuning Methods
4
11 + 2t τ
……….. (C.9)
d
Actual
response
ym
ym
B
B
Approximate
response
S
Slop = S
t
td
t
td
(b)
(a)
Fig. (C.1) (a) Temperature curve for Cohen-Coon tuning.
(b) Temperature curve approximation with a first order dead-time
system.
C.2) Ziegler-Nichols Method [92]
Ziegler-Nichols used bode diagram of two graphs: one is a plot of
the logarithm of the magnitude of sinusoidal transfer function; the other is a
plot of phase angle; both are plotted against the frequency on a logarithm
scale as shown in Fig. (C.2).
Gain margin (GM) and crossover frequency ( ω ) can be found from
two plots therefore, the ultimate gain and period of oscillation are
calculated from following:
K = 20 log(GM )
……….. (C.10)
u
P
u
=
2×3.1428
……….. (C.11)
ω
C.2
Appendix C
Controller Tuning Methods
1) For Proportional controller:
K
K
2
=
C
……….. (C.12)
u
2) For Proportional-Integral controller:
K
2.2
……….. (C.13)
τ = 1P.2
……….. (C.14)
K
C
=
u
u
I
3) For Proportional-Integral-Derivative controller:
K
K
1.7
……….. (C.15)
=
P
2
……….. (C.16)
=
P
8
C
τ
I
τ
D
=
u
u
……….. (C.17)
u
1.0
Gain
margin
A.R
M
0o
Ø(I)
Phase
margin
Ø
-180o
ω
ωCO
Figure (C.2): Definition of gain and phase margins.
C.3
Appendix D
MATLAB Program
D.1 Introduction
This appendix discusses the computer program developed for the
dynamic model and control for both open loop and closed loop of system.
All programs were developed using MATLAB program version
7.10. The use of friendly, easy to use interfaces for these programs were
efficient in the implementation of the model procedure that gave dynamic
results obtained from the computer programs.
Each program was executed and the results were checked to meet the
model requirements, then–if necessary– the design data was modified to
meet the requirements of the model.
Table (D.1) lists some functions and commands and their
description that were used in computer simulation for dynamic behavior
and controller design [127].
P
P
D.1
Appendix D
MATLAB Program
Table (D.1) Summary functions in MATLAB program.
Function Name
Function Description
Pade
Computes the an nth-order approximation to a
time delay
Series
Computes a series system connection
Tf
Creates a transfer function model object
Step
Calculates a unit step response of a system
Figure
Creates new figure window
Plot
Generates a linear plot
Xlabel
Add the label to the x-axis of the current graph
Ylabel
Add the label to the y-axis of the current graph
Axis
Specific the manual axis scaling on plot
Title
Add a title to the current graph
Hold on
Holds the current graph on the screen
Legend
Puts a legend on the current screen
Margin
Computes the gain margin, phase margin , and
associated crossover frequencies from frequency
response data
Bode
Generates bode frequency response plots
Feedback
Computes the feedback interconnection of two
systems
Trapz
Computes the integration value
For
Generate loop structure
End
End of loop generated
D.2
Appendix D
MATLAB Program
D.2 Open Loop Programs
% Matlab program
% for dynamic behavior of open loop with plotting
% dynamic behavior of open loop between Tco vs. mh
% define hot water flow rate (mh) (kg/sec) at steady state
mh=[ value of hot water flow rate at steady state];
% define the transfer function between input mh with outputs Tco with
% delay time by using pade function
num=[value of nominator];
den=[value of denominator];
[numdt,dendt]=pade (value of delay time, number of approximation);
% apply series function
[nump,denp]=series (num,den,numdt,dendt);
Gp=tf(nump,denp);
% where Gp is transfer function between Tco & mh
% define outlet cold temperature(C) at steady state (Tco_ss)
Tco_ss= value of outlet cold water Temperature(C) at steady state
[Tco, x, t]=step (nump,denp);
% plotting Tco vs. mh at step response
figure (1)
plot (t,Tco+Tco_ss ,'k')
ylabel ('Outlet Cold Water Temperature (C)')
xlabel ('Time(sec)')
hold on
% or plotting Tco vs. mh at multi-step response
[Tco, x, t]=step (value of step1*manuipulated variable*nump,denp);
plot (t,Tco+Tco_ss ,'m')
[Tco, x, t]=step (value of step2*manuipulated variable*nump,denp);
plot (t,Tco+Tco_ss ,'g')
D.3
Appendix D
MATLAB Program
[Tco, x, t]=step (value of step3*manuipulated variable*nump,denp);
plot (t,Tco+Tco_ss ,'r')
[Tco, x, t]=step (value of step4*manuipulated variable*nump,denp);
plot (t,Tco+Tco_ss ,'c')
[Tco, x, t]=step (value of step5*manuipulated variable*nump,denp);
plot (t,Tco+Tco_ss ,'y')
[Tco, x, t]=step (value of step6*manuipulated variable*nump,denp);
plot (t,Tco+Tco_ss ,'b')
legend(' value of step1',' value of step2',' value of step3',' value of step4', '
value of step5', ' value of step6',2)
D.3 Close Loop Programs
D.3.1 Ziegler-Nichols Method
% Control tuning in the PHE.
% by using Ziegler-Nichols method (bode diagram).
% define the transfer function of process (PHE) with delay time
num=[value of nominator];
den=[value of denominator];
[numdt,dendt]=pade (value of delay time, number of approximation);
% apply series function
[nump,denp]=series (num,den,numdt,dendt);
Gp=tf(nump,denp);
% where Gp is transfer function of process with delay time
% define the transfer function of measurment
numm=[ value of nominator];
denm=[ value of denominator];
Gm=tf(numm,denm)
% define the transfer function of control valve
numv=[ value of nominator];
D.4
Appendix D
MATLAB Program
denv=[ value of denominator];
Gv=tf(numv,denv)
% apply series function
[numvp,denvp]=series(numv,denv,nump,denp)
Gvp=tf(numvp,denvp)
% where the Gvp=GvGp
% specify the frequency range
w=logspace(-3, 4,100);
[Gm,pm,w]= margin (Gp);
% where Gm is the gain margin, pm is the phase margin, w is the
frequency.
Gmdb=20*log10(Gm)
figure(1)
bode(Gp,'b-')
%
% calculation the adjusted parameter of controller (PI)
Ku=Gmdb;
% where ku is ultimate gain
Pu=(2*pi)/w;
% where Pu is ultimate period of sustained cycling (sec/cycle)
kc=Ku/2.2
ti=Pu/1.2
numc=[kc*ti kc];
denc=[ti 0];
Gc=tf(numc,denc)
%or
% calculation the adjusted parameter of controller (PID)
Ku=Gmdb;
%where ku is ultimate gain
D.5
Appendix D
MATLAB Program
Pu=(2*pi)/w;
% where Pu is ultimate period of sustained cycling (sec/cycle)
kc=Ku/1.7
ti=Pu/2
td=Pu/8
numc=[kc*ti*td kc*ti kc];
denc=[0 ti 0];
Gc=tf(numc,denc)
% apply series function
[numol,denol]=series(numc,denc,numvp,denvp);
GoL=tf(numol,denol)
% where the GOL=GpGcGv
% apply feedback function
[numcl,dencl]=feedback(numol,denol,numm,denm);
TFCL=tf(numcl,dencl)
% where the TFCL is T.F. of close loop
[y,x,t]=step(numcl,dencl);
figure(2)
% plotting the step respone of close loop
plot(t,y,'k-')
xlabel('Time (sec)')
ylabel(' Outlet Cold Water Temperature (c)')
%
% find ISE (integral square error)
a=y';
% where a is response values
% E=set point value- measured value
% where E is the error
E=1-a;
D.6
Appendix D
MATLAB Program
SE=E.*E;
% where SE is square of the error
% use trapz function to calculate the area under the curve
ISE= trapz(t,SE)
figure(3)
plot(t,SE,'r-')
xlabel('Time (sec)')
ylabel('Square of Error')
% or
% find ITAE (integral time-weighted absolute error)
a=y';
% where a is response values
% e=set point value- measured value
% where e is the error
e=1-a ;
E=abs(e);
TE=t.*E;
% where TE is the time* absolute error
% use trapz function to calculate the area under the curve
ITAE= trapz(t,TE)
figure (3)
plot (t,TE,'r-')
xlabel('Time (sec)')
ylabel('Time* absolute error')
D.3.2 Cohen-Coon Method
% Control tuning in the PHE.
% by using Cohen-Coon method (process reaction curve).
% define the transfer function of process (PHE) with delay time
D.7
Appendix D
MATLAB Program
num=[value of nominator];
den=[value of denominator];
[numdt,dendt]=pade (value of delay time, number of approximation);
% apply series function
[nump,denp]=series (num,den,numdt,dendt);
Gp=tf(nump,denp);
% where Gp is transfer function of process with delay time
% define the transfer function of measurment
numm=[ value of nominator];
denm=[ value of denominator];
Gm=tf(numm,denm)
% define the transfer function of control valve
numv=[ value of nominator];
denv=[ value of denominator];
Gv=tf(numv,denv)
% apply series function
[numvp,denvp]=series(numv,denv,nump,denp)
Gvp=tf(numvp,denvp)
%where the Gvp=GvGp
[Tco,x,t]=step(nump,denp);
figure (1)
plot(t,Tco,'r')
xlabel('Time(sec')
ylabel(' Outlet Cold Water Temperature (c)')
hold on
% finding the values of k,Tau and td from figure (1)
k=[ values of k];
Tau=[ values of Tau 1];
td= values of td;
D.8
Appendix D
MATLAB Program
[Tco,x,t]=step(k,Tau);
plot(t+td,Tco,'b')
hold off
% from figure (1)
k= values of k;
Tau= values of Tau;
td= values of td;
% calculation the adjusted parameter of controller(PI)
kc=(Tau/(k*td))*(0.9+(td/(12*Tau)))
ti=td*((30+((3*td)/Tau))/(9+((20*td)/Tau)))
numc=[kc*ti kc];
denc=[ti 0];
Gc=tf(numc,denc)
% or
% calculation the adjusted parameter of controller(PID)
kc=(Tau/(k*td))*((4/3)+(td/(4*Tau)))
ti=td*((32+((6*td)/Tau))/(13+((8*td)/Tau)))
td=td*((4)/(11+((2*td)/Tau)))
numc=[kc*ti*td kc*ti kc];
denc=[0 ti 0];
Gc=tf(numc,denc)
% apply series function
[numol,denol]=series(numc,denc,numvp,denvp);
GoL=tf(numol,denol)
% where the GOL=GpGcGv
% apply feedback function
[numcl,dencl]=feedback(numol,denol,numm,denm);
TFCL=tf(numcl,dencl)
% where the TFCL is T.F. of close loop
D.9
Appendix D
MATLAB Program
[y,x,t]=step(numcl,dencl);
figure(2)
% plotting the step respone of close loop
plot(t,y,'k-')
xlabel('Time (sec)')
ylabel(' Outlet Cold Water Temperature (c)')
%
% find ISE (integral square error)
a=y';
% where a is response values
% E=set point value- measured value
% where E is the error
E=1-a;
SE=E.*E;
% where SE is square of the error
% use trapz function to calculate the area under the curve
ISE= trapz(t,SE)
figure(3)
plot(t,SE,'r-')
xlabel('Time (sec)')
ylabel('Square of Error')
% or
% find ITAE (integral time-weighted absolute error)
a=y';
% where a is response values
% e=set point value- measured value
% where e is the error
e=1-a ;
E=abs(e);
D.10
Appendix D
MATLAB Program
TE=t.*E;
% where TE is the time* absolute error
% use trapz function to calculate the area under the curve
ITAE= trapz(t,TE)
figure (3)
plot (t,TE,'r-')
xlabel('Time (sec)')
ylabel('Time* absolute error')
D.11
Appendix E
Experimental Data of Dynamic Behavior
Table (E.1) ( ∆ T lm ) vs. (T hi - T ho ) at (m h =0.0497) (kg/sec) and
(m c =0.0414) (kg/sec).
( ∆ T lm ) oC
(T hi - T ho ) oC
11.7124
2.1000
12.4615
2.3000
13.1504
2.4000
13.8594
2.8000
14.0808
3.0000
14.7251
3.2000
15.4305
3.6000
15.6436
3.8000
Table (E.2) ( ∆ T lm ) vs. (T hi - T ho ) at (m h =0.0579) (kg/sec) and
R
R
R
R
R
R
R
R
(m c =0.0414) (kg/sec).
R
R
( ∆ T lm ) oC
(T hi - T ho ) oC
11.5974
3.1000
12.2385
3.1000
13.0315
3.1000
14.2453
4.3000
14.9433
4.5000
15.1998
4.7000
15.3922
4.0000
15.9925
4.4000
16.6902
4.6000
R
R
P
P
R
E.1
R
R
R
P
P
Appendix E
Experimental Data of Dynamic Behavior
Table (E.3) ( ∆ T lm ) vs. (T hi - T ho ) at (m h =0.0662) (kg/sec) and
(m c =0.0414) (kg/sec).
( ∆ T lm ) oC
(T hi - T ho ) oC
13.2424
3.2000
13.7804
3.3000
14.5815
3.5000
15.2736
3.6000
15.5923
3.8000
16.2926
4.1000
16.8903
4.4000
17.5907
4.7000
Table (E.4) ( ∆ T lm ) vs. (T hi - T ho ) at (m h =0.0745) (kg/sec) and
R
R
R
R
R
R
R
R
(m c =0.0414) (kg/sec).
R
R
( ∆ T lm ) oC
(T hi - T ho ) oC
11.6929
2.8000
12.3348
2.9000
13.0269
3.0000
13.7758
3.2000
14.4721
3.4000
15.2158
3.5000
15.4379
3.8000
16.1351
4.0000
15.8527
3.6000
R
R
P
P
R
E.2
R
R
R
P
P
Appendix E
Experimental Data of Dynamic Behavior
Table (E.5) ( ∆ T lm ) vs. (T hi - T ho ) at (m h =0.0828) (kg/sec) and
(m c =0.0414) (kg/sec).
( ∆ T lm ) oC
(T hi - T ho ) oC
11.9372
2.5000
12.7244
2.5000
13.5202
2.6000
14.2242
2.9000
14.4548
3.1000
15.1036
3.4000
15.8057
3.7000
16.4544
4.0000
16.0533
3.4000
Table (E.6) ( ∆ T lm ) vs. (T hi - T ho ) at (m h =0.091) (kg/sec) and
R
R
R
R
R
R
R
R
(m c =0.0414) (kg/sec).
R
R
( ∆ T lm ) oC
(T hi - T ho ) oC
11.3707
2.6000
12.2729
2.7000
12.7022
2.9000
12.4935
2.4000
13.2999
2.6000
13.9951
2.8000
14.2865
3.0000
14.9194
3.1000
15.7458
3.6000
R
R
P
P
R
E.3
R
R
R
P
P
Appendix E
Experimental Data of Dynamic Behavior
Table (E.7) ( ∆ T lm ) vs. (T hi - T ho ) at (m h =0.0993) (kg/sec) and
(m c =0.0414) (kg/sec).
( ∆ T lm ) oC
(T hi - T ho ) oC
12.7090
3.0000
12.8708
2.3000
13.6666
2.4000
14.4713
2.6000
14.6020
2.9000
15.3575
3.2000
16.1065
3.4000
16.8083
3.7000
Table (E.8) ( ∆ T lm ) vs. (T hi - T ho ) at (m h =0.1076) (kg/sec) and
R
R
R
R
R
R
R
R
(m c =0.0414) (kg/sec).
R
R
( ∆ T lm ) oC
(T hi - T ho ) oC
11.5651
2.3000
12.1537
2.5000
12.8094
2.9000
12.9714
2.2000
13.7299
2.5000
14.0129
2.7000
14.6616
3.0000
15.3575
3.2000
R
R
P
P
R
E.4
R
R
R
P
P
Appendix E
Experimental Data of Dynamic Behavior
Table (E.9) ( ∆ T lm ) vs. (T hi - T ho ) at (m h =0.1159) (kg/sec) and
(m c =0.0414) (kg/sec).
( ∆ T lm ) oC
(T hi - T ho ) oC
12.1383
2.3000
13.0425
2.4000
13.7379
2.6000
14.5414
2.8000
15.2441
3.1000
16.0791
3.0000
16.1652
3.5000
16.3878
2.8000
Table (E.10) The values of overall heat transfer coefficient (U) as a
function of hot water flow rate (m h ).
R
m h (kg/sec)
U (w/m2.oC)
0.0497
1077.605
0.0579
1653.626
0.0662
1695.345
0.0745
1809.100
0.0828
1846.360
0.0910
1985.241
0.0993
2064.224
0.1076
2198.045
0.1159
2286.572
R
R
P
E.5
P
P
P
R
Appendix E
Experimental Data of Dynamic Behavior
Table (E.11) System parameters for different step change.
Step size %
k
τ (sec)
20%
103.62
36.45
50%
96.58
35.71
80%
95.82
32.78
100%
94.96
30.53
120%
93.9
30
135%
93.3
29.2
Fig. (E.1) Temperature difference (T hi - T ho ) as a function of ( ∆ T lm ) for
(m h =0.0497) (kg/sec) and (m c =0.0414) (kg/sec).
E.6
Appendix E
Experimental Data of Dynamic Behavior
Fig. (E.2) Temperature difference (T hi - T ho ) as a function of ( ∆ T lm ) for
(m h =0.0579) (kg/sec) and (m c =0.0414) (kg/sec).
Fig. (E.3) Temperature difference (T hi - T ho ) as a function of ( ∆ T lm ) for
(m h =0.0662) (kg/sec) and (m c =0.0414) (kg/sec).
Fig. (E.4) Temperature difference (T hi - T ho ) as a function of ( ∆ T lm ) for
(m h =0.0745) (kg/sec) and (m c =0.0414) (kg/sec).
E.7
Appendix E
Experimental Data of Dynamic Behavior
Fig. (E.5) Temperature difference (T hi - T ho ) as a function of ( ∆ T lm ) for
(m h =0.0828) (kg/sec) and (m c =0.0414) (kg/sec).
Fig. (E.6) Temperature difference (T hi - T ho ) as a function of ( ∆ T lm ) for
(m h =0.091) (kg/sec) and (m c =0.0414) (kg/sec).
Fig. (E.7) Temperature difference (T hi - T ho ) as a function of ( ∆ T lm ) for
(m h =0.0993) (kg/sec) and (m c =0.0414) (kg/sec).
E.8
Appendix E
Experimental Data of Dynamic Behavior
Fig. (E.8) Temperature difference (T hi - T ho ) as a function of ( ∆ T lm ) for
(m h =0.1076) (kg/sec) and (m c =0.0414) (kg/sec).
Fig. (E.9) Temperature difference (T hi - T ho ) as a function of ( ∆ T lm ) for
(m h =0.1159) (kg/sec) and (m c =0.0414) (kg/sec).
E.9
Appendix F
Calculation of Overall Heat Transfer Coefficient (U)
Calculation of Overall Heat Transfer Coefficient (U)
The rate of heat transferred through the exchanger Q is given by:
……….. (F.1)
Q = U A ∆Τ
lm
Where:
A: Area of heat transfer (m2).
P
P
o
∆ T lm : Logarithmic mean temperature difference ( C).
R
R
P

(∆Τ ) = (Τ − Τ ) − (Τ − Τ ) ln  Τ − Τ
Τ −Τ



ci 
hi
lm
hi
co
ho
co
ci
ho
P
……….. (F.2)
Then equation (F.1) become:
( − )− ( − )
Q = UA Τ Τ −Τ Τ
Τ Τ
ln  − 
Τ Τ 
hi
co
ho
……….. (F.3)
ci
hi
co
ho
ci
This amount of heat is equal to the enthalpy lost by the heating fluid,
which is the same as the enthalpy gained by the process fluid providing that
there are negligible heat losses. Therefore,
Q = m C (Τ − Τ ) = m C (Τ − Τ )
h
hi
ph
ho
c
co
pc
……….. (F.4)
ci
Since both fluids are water, it is reasonable to assume that the
specific heat C
ph
.
= C pc = C p
Thus:
m (Τ − Τ ) = m (Τ − Τ ) =
hi
h
ho
c
co
ci
hi
……….. (F.5)
p
(Τ − Τ ) − (Τ − Τ )


−
ln  Τ − Τ 
Τ Τ
UA
∴ m (Τ − Τ ) =
C
h
Q
C
hi
ho
p
co

ho
ci
hi
co
ho
ci
……….. (F.6)

Or:
……….. (F.7)
(Τ − Τ ) = UA ∆Τ
mC
hi
ho
lm
h
p
The above equation shows a linear relationship between (T hi - T ho )
R
R
R
R
and ∆ T lm with slop UA from which U can be determined. From each
R
R
mC
h
p
figure a single value of the overall heat transfer coefficient (U) was
F.1
Appendix F
Calculation of Overall Heat Transfer Coefficient (U)
determine for each hot water flow rate (m h ) and the complete set values can
R
be found in table (E.10) in appendix (E).
F.2
R
Fig. (3.2) Schematic diagram of the experimental rig.