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FUZZY MODELLING AND CONTROL FOR A NONLINEAR REBOILER
SYSTEM OF A DISTILLATION COLUMN
MOHD FAISAL BIN IBRAHIM
A thesis submitted in fulfilment of the
requirements for the award of the degree of
Master of Electrical Engineering
Faculty of Electrical Engineering
Universiti Teknologi Malaysia
MAY 2006
iii
In The Name of Allah, Most Gracious and Most Merciful
To my beloved
Abah and Mama;
Ibrahim bin Md Saleh & Jahani binti Ali
and
brothers and sister;
Mohd Hafiz Ikhwan, Mohd Farhan Fitri & Nurul Fathiah
iv
ACKNOWLEDGEMENTS
First of all, I wish to express my sincere appreciation to my supervisor, Prof.
Madya Dr. Rubiyah Yusof and also my co-supervisor, Prof. Dr. Marzuki Khalid for
their constant guidance, advices and all those beneficial discussions during the whole
period of research. I also would like to thank Prof. Madya Dr. Azian Morad and Prof.
Madya Mustafa Kamal for their assistance and permission of using facilities at
CLEAR laboratory.
This work was supported by Ministry of Science, Technology and
Innovation, Malaysia through an Intensified Research Grant Allocation (IRPA).
Last but not least, my extended appreciation goes to all my colleagues and
staffs at CAIRO and CLEAR of UTM who have provided assistance at various
occasions. Their views and supports are useful indeed. Unfortunately, it is not
possible to list all of them in this limited space. The days with all of you were
enjoyable.
v
ABSTRACT
Most process control systems are complex and nonlinear in nature. To design
a good controller for these systems, accurate models are needed. Most of the
available conventional plant modelling techniques cater linear plants and therefore in
most cases, inaccurate nonlinear plant models are obtained which in turn resulted in
poor control performance. In view of this, the thesis explored the Fuzzy modelling
technique based on Takagi-Sugeno (TS) method for modelling a reboiler system of a
distillation column. Model parameters are tuned using Genetic algorithm (GA) and
Recursive least square (RLS). The Unbiasedness criterion (UC) is applied for
structure identification. Data from simulation system that represents the actual plant
is used in model development. Fuzzy model obtained using the proposed technique is
compared with various other modelling techniques such as the conventional Fuzzy
model and linear model. The result shows that the technique proposed gives a more
accurate model as compared to the other methods. The optimized Fuzzy model
obtained is used to design a Fuzzy controller for the temperature control of the vessel
of the distillation column. Manipulated variables for the Fuzzy controller are heat
from electrical heater and flowrate of silicon oil in the reboiler system. Genetic
algorithm (GA) is used to tune the parameters of the Fuzzy controller. The
performance of the Fuzzy controller using the optimized Fuzzy model is better than
using the linear model.
vi
ABSTRAK
Kebanyakan sistem kawalan proses adalah kompleks dan tidak lurus. Bagi
merekabentuk pengawal yang baik untuk proses tersebut, model yang tepat adalah
diperlukan. Kebanyakan teknik permodelan konvensional yang sedia ada hanya
sesuai untuk sistem lurus. Oleh itu, dalam kebanyakan kes, model sistem tidak lurus
yang tidak tepat diperolehi di mana ia akan menghasilkan prestasi pengawal yang
buruk. Berasaskan fakta ini, tesis ini menyelidik teknik permodelan Fuzzy
berdasarkan metod Takagi-Sugeno (TS) bagi memodelkan sebuah sistem pemanas
kolum penyejatan. Parameter-parameter model diselaras menggunakan teknik
Genetic algorithm (GA) dan Recursive least square (RLS). Teknik Unbiasedness
criterion (UC) diaplikasikan untuk pengenalpastian struktur model. Data daripada
sistem simulasi yang mewakili loji sebenar digunakan dalam proses pembinaan
model. Model Fuzzy yang diperolehi kemudiannya dibandingkan dengan pelbagai
teknik permodelan yang lain seperti model Fuzzy konvensional dan model lelurus.
Keputusan menunjukkan teknik yang dicadangkan dapat menghasilkan model yang
lebih tepat berbanding teknik-teknik lain. Model Fuzzy yang optimum ini juga
digunakan untuk merekabentuk pengawal Fuzzy bagi mengawal suhu tangki di dalam
kolum penyejatan. Pembolehubah yang dimanipulasi bagi pengawal Fuzzy adalah
haba daripada pemanas elektrik dan kadar aliran minyak silikon di dalam sistem
pemanas. Genetic algorithm (GA) digunakan untuk melaraskan parameter-parameter
pengawal Fuzzy. Prestasi yang ditunjukkan oleh pengawal Fuzzy yang dibina
berdasarkan model Fuzzy yang optimum adalah lebih baik daripada model lurus.
vii
TABLES OF CONTENTS
CHAPTER TITLE PAGE
DECLARATION ii
DEDICATION iii
ACKNOWLEDGEMENTS iv
ABSTRACT v
ABSTRAK vi
TABLES OF CONTENTS vii
LIST OF TABLES xii
LIST OF FIGURES xiii
LIST OF SYMBOLS AND ABBREVIATIONS xviii
LIST OF APPENDICES xix
1 INTRODUCTION
1.1 Overview 1
1.2 Problem statement 2
1.3 Objective of the thesis 5
1.4 Scope of the thesis 6
1.5 Contribution of the thesis 7
1.6 Thesis layout 8
viii
2 LITERATURE REVIEW
2.1 Literature review on techniques for modelling 9
distillation column.
2.2 Literature review on Fuzzy modelling and control 11
2.2.1 Fuzzy modelling 11
2.2.2 Fuzzy control 14
3 DEVELOPMENT OF FUZZY MODELLING
3.1 Takagi-Sugeno (TS) Fuzzy model 16
3.2 Identification of TS Fuzzy model 20
3.3 Identification of TS Fuzzy model using 22
Recursive least square (RLS) method
3.3.1 Recursive least square (RLS) method 22
3.4 Identification of TS Fuzzy model using 24
Recursive least square (RLS) method and
Genetic algorithm (GA)
3.4.1 Genetic algorithm (GA) 25
3.4.1.1 Operation of GA 26
3.4.1.2 Tuning membership function 29
with GA
3.4.1.3 GA-RLS algorithms for 33
Fuzzy model parameter tuning
3.5 Identification of TS Fuzzy model using 35
Recursive least square (RLS) method, Genetic
algorithm (GA) and Unbiasedness criterion (UC)
3.5.1 Structure identification and Unbiasedness 35
criterion (UC)
3.6 Summary 40
ix
4 DEVELOPMENT OF FUZZY CONTROL
4.1 The standard Fuzzy control (Mamdani type) 41
4.2 Tuning Mamdani Fuzzy control with Genetic 47
algorithm (GA)
4.2.1 Chromosome representation 48
4.2.2 Performance index for evaluation 50
4.3 Summary 52
5 MATHEMATICAL MODEL FOR THE REBOILER
SYSTEM OF THE DISTILLATION COLUMN
5.1 Background of the pilot plant distillation column 53
5.2 Components of the distillation column 54
5.3 Structure of the reboiler system model 56
5.4 Mathematical model derivation 57
5.4.1 Energy balance equation 58
5.4.2 Differential equation for silicon oil tank 59
sub-model
5.4.3 Differential equation for jacket tank 62
sub-model
5.4.4 Differential equation for vessel sub-model 65
5.5 Discrete time dependent model 68
6 IMPLEMENTATION OF FUZZY MODELLING
TECHNIQUE TO THE REBOILER SYSTEM OF
THE DISTILLATION COLUMN
6.1 Procedures 71
6.1.1 Procedures for obtaining data 72
6.1.2 Procedures for training phase 73
6.1.2.1 Proposed Fuzzy model with structure 73
and parameter optimization (FM-SPO)
6.1.2.2 Fuzzy model with parameter 74
optimization (FM-PO)
6.1.2.3 Conventional Fuzzy model (FM-C) 75
6.1.2.4 Linear model (LM) 75
x
6.1.3 Procedures for testing phase 76
6.2 Obtaining data 77
6.3 Identification of silicon oil tank sub-model 81
6.3.1 Training phase 81
6.3.1.1 Training phase of Fuzzy model 81
FM-SPO of silicon oil tank sub-model
6.3.1.2 Training phase of Fuzzy model 86
FM-PO of silicon oil tank sub-model
6.3.1.3 Training phase of Fuzzy model 88
FM-C of silicon oil tank sub-model
6.3.1.4 Training phase of linear model 89
of silicon oil tank sub-model
6.3.2 Testing phase 89
6.4 Identification of jacket tank sub-model 90
6.4.1 Training phase 90
6.4.1.1 Training phase of Fuzzy model 91
FM-SPO of jacket tank sub-model
6.4.1.2 Training phase of Fuzzy model 93
FM-PO of jacket tank sub-model
6.4.1.3 Training phase of Fuzzy model 95
FM-C of jacket tank sub-model
6.4.1.4 Training phase of linear model 96
of jacket tank sub-model
6.4.2 Testing phase 96
6.5 Identification of vessel sub-model 97
6.5.1 Training phase 97
6.5.1.1 Training phase of Fuzzy model 98
FM-SPO of vessel sub-model
6.5.1.2 Training phase of Fuzzy model 100
FM-PO of vessel sub-model
xi
6.5.1.3 Training phase of Fuzzy model 100
FM-C of vessel sub-model
6.5.1.4 Training phase of linear model 100
of vessel sub-model
6.5.2 Testing phase 103
6.6 Discussion 104
7 IMPLEMENTATION OF FUZZY CONTROL
TECHNIQUE TO THE REBOILER SYSTEM OF
THE DISTILLATION COLUMN
7.1 Control strategy 107
7.2 Selecting Fuzzy control structure 109
7.3 Configuring GA-based parameter tuning program 110
7.4 Procedures 113
7.4.1 Training phase procedures 113
7.4.2 Testing phase procedures 115
7.5 Results 117
7.5.1 Training phase results 117
7.5.2 Testing phase results 121
7.6 Discussion 125
8 CONCLUSION AND RECOMMENDATION
8.1 Conclusion 128
8.2 Recommendation 130
REFERENCES 132
APPENDIX A 136
xii
LIST OF TABLES
TABLE NO. TITLE PAGE
6.1 Configuration of FM-SPO of silicon oil tank 82
6.2 Comparison of UC values of models in 84
stage 0 and 1 (silicon oil tank model)
6.3 Configuration of FM-PO of silicon oil tank 86
6.4 Value of mean squared error (MSE) for all 89
models of silicon oil tank system
6.5 Comparison of UC values of models in stage 0 91
and 1 (jacket tank model)
6.6 Configuration of FM-PO of jacket tank 93
6.7 Value of mean squared error (MSE) for all 96
models of jacket tank system
6.8 Comparison of UC values of models in stage 0 98
and 1 (vessel model)
6.9 Value of mean squared error (MSE) for all 103
models of vessel system
7.1 Structure configuration of Fuzzy controller for 110
the reboiler system of the distillation column
7.2 Performance comparison for FM – SPO Fuzzy 126
model-based Fuzzy controller when trained on
Fuzzy model and tested on the plant
7.3 Performance comparison for linear model-based 126
Fuzzy controller when trained on Fuzzy model and
tested on the plant
xiii
LIST OF FIGURES
FIGURE NO. TITLE PAGE
1.1 A schematic diagram of distillation column plant 4
3.1 Block diagram of TS Fuzzy model 17
3.2 The symmetrical Gaussian membership function 17
3.3 Block diagram of system model identification 20
3.4 Flowchart of a binary GA operation 26
3.5 Dynamic probability of crossover and mutation 29
3.6 An arrangement of membership functions of 30
inputs in a chromosome for TS Fuzzy model
3.7 Three symmetrical Gaussian membership functions 30
3.8 Sub-chromosome contains information of 31
three membership functions
3.9 Chromosome contains information of membership 31
functions of all input variables
3.10 A graphical view of the GA-RLS algorithms 34
3.11 Flowchart of structure and parameter identification 39
of Fuzzy model
4.1 A closed-loop Fuzzy controller 42
4.2 Graphical view of rule base of two input 43
one output Fuzzy control
4.3 MAX-MIN Fuzzy reasoning 45
4.4 Three symmetrical triangular membership 46
functions with desired membership value
4.5 Training phase of model based Fuzzy control 47
4.6 Chromosome for two input one output 48
Fuzzy control
xiv
4.7 Sub-chromosome of membership functions 49
information
4.8 Sub-chromosome of consequent of rule 50
4.9 A graphical view of the GA based parameter 51
tuning for Fuzzy control
5.1 Process of extraction and distillation of ginger 54
oleoresin from solid ginger using ethanol as the
solvent
5.2 Block diagram of the reboiler system 56
5.3 Sub-systems for the reboiler system 57
5.4 Diagram of silicon oil tank 59
5.5 Heat transfer direction in silicon oil tank system 61
5.6 Diagram of jacket tank 62
5.7 Heat transfer direction in jacket tank system 63
5.8 Diagram of vessel tank 65
5.9 Heat transfer direction in vessel system 67
5.10 Flow of calculation for the reboiler system’s 69
model for every integration step time.
6.1 Inputs data of the reboiler system from 77
the first simulation.
6.2 Outputs data of the reboiler system 78
from the first simulation.
6.3 Inputs data of the reboiler system from 79
the second simulation.
6.4 Outputs data of the reboiler system 80
from the second simulation.
6.5 Input-output of silicon oil tank discrete model 81
6.6 Program interface of GA-RLS algorithm for 83
Fuzzy model tuning
6.7 Convergence of the best Fuzzy model 84
performance in every generation
xv
6.8 The best configuration of Fuzzy model FM-SPO 85
for silicon oil tank system
6.9 The best configuration of Fuzzy model FM-PO 87
for silicon oil tank system
6.10 The configuration of Fuzzy model FM-C 88
for silicon oil tank system
6.11 Input-output of jacket tank discrete model 90
6.12 The best configuration of Fuzzy model FM-SPO 92
for jacket tank system
6.13 The best configuration of Fuzzy model FM-PO 94
for jacket tank system
6.14 The configuration of Fuzzy model FM-C 95
for jacket tank system
6.15 Input-output of vessel discrete model 97
6.16 The best configuration of Fuzzy model FM-SPO 99
for vessel system
6.17 The best configuration of Fuzzy model FM-PO 101
for vessel system
6.18 The configuration of Fuzzy model FM-C 102
for vessel system
6.19 Performance comparison through simulation from 105
various models of the reboiler system. (a) Input
variables signal: pulse width modulation (PWM)
of heater and flowrate of silicon oil (b) Output
variable signal of silicon oil tank temperature
(c) Output variable signal of jacket tank temperature
(d) Output variable signal of vessel temperature
7.1 Block diagram of closed-loop Fuzzy control 108
7.2 Membership functions of input and output for 109
Fuzzy controller
7.3 Chromosome for DIDO Fuzzy controller of 111
the plant
xvi
7.4 Program interface of GA algorithm for Fuzzy 112
controller tuning
7.5 Block diagram of training phase of Fuzzy 114
controller based on Fuzzy model (FM – SPO)
of reboiler system for distillation column
7.6 Block diagram of training phase of Fuzzy 114
controller based on linear model of
reboiler system for distillation column
7.7 Block diagram of Fuzzy model-based Fuzzy 115
controller tested on the simulated plant
7.8 Block diagram of linear model-based Fuzzy 116
controller tested on the simulated plant
7.9 Convergence of the best performance of 117
FM – SPO Fuzzy model based Fuzzy controller
in every generation
7.10 Configuration of FM – SPO Fuzzy model-based 118
Fuzzy controller
7.11 Convergence of the best performance of linear 119
model-based Fuzzy controller in every generation
7.12 Configuration of linear model-based Fuzzy 120
controller
7.13 (a): Performance of FM – SPO Fuzzy model- 122
based Fuzzy controller trained on Fuzzy
model (training process). (b) Performance of
FM – SPO Fuzzy model-based Fuzzy controller
applied on the mathematical model representing
actual plant (testing process).
7.14 (a): Performance of linear model-based 123
Fuzzy controller trained on linear model
(training process). (b) Performance of linear
model-based Fuzzy controller applied on the
mathematical model representing actual plant.
(testing process).
xvii
7.15 (a) Temperature different between Ts and Tv 125
for FM – SPO Fuzzy model-based Fuzzy controller.
(b) Temperature different between Ts and Tv for
linear model-based Fuzzy controller.
xviii
LIST OF SYMBOLS AND ABBREVIATIONS
GA - Genetic algorithm
MIMO - Multi input multi output
MISO - Multi input single output
MSE - Mean squared error
RLS - Recursive least square
BLS - Batch least square
UC - Unbiasedness criterion
FM – SPO - Fuzzy model with structure and parameter optimization
FM – PO - Fuzzy model with parameter optimization
FM – C - Conventional Fuzzy model
LM - Linear model
c - Center of membership function
σ - Width of membership function
µ - membership value
ρc - probability of crossover
ρm - probability of mutation
CHAPTER 1
INTRODUCTION
1.1 Overview
Modelling of process plant is a challenging task as most process plants are
nonlinear, time varying and complex in nature. Accurate plant models are necessary
in order to develop good control system. In most industrial applications, linear
models are more popularly used for control system development. This is because the
linear approach for modelling and control is easier to develop. However, since most
industrial plants are complex and nonlinear, the linear model is usually over
simplistic and therefore a good performance controller is non-achievable. This
resulted in a non-optimized plant control.
With the establishment of artificial intelligence techniques, alternative
strategies have been introduced, developed and applied to overcome the problems of
nonlinear and complex plant system modelling and control. The techniques make use
of deductive process with learning capabilities by adapting or combining several
intelligence techniques such as Fuzzy logic, Genetic algorithm or Neural network.
This thesis presents such study that implements the principle and concept of
artificial intelligence especially Fuzzy logic to solve the problems of modelling and
control of a reboiler system for a distillation column. The nonlinearity nature of a
distillation column makes it difficult for an accurate model to be obtained. There are
many variables to be manipulated and controlled in a distillation column control
2
system. These variables are interacting and therefore to achieve control objective of
each variable is not an easy task. This thesis attempts to develop an accurate model
of a reboiler system for a distillation column using artificial intelligence techniques
such than a good controller can be designed to improve the performance of the
system.
1.2 Problem statement
The process of separating mixture of liquids is probably the most common
and important process in process control industries. The example of the process can
be found in petroleum industry where crude oil is separated into several components
such as petrol, diesel, tar and bitumen. The process plant used for this purpose is a
distillation column.
The objective of a distillation column process is to separate mixture
substances into several components in order to acquire useful component. The basic
idea behind the process lies on the concept of different component has different
boiling point. To separate a mixture, the liquid in the column can be heated at certain
temperature to force components transform into the gas phase. The gas is then
condensed back into liquid form and after a certain period, an amount of desired pure
component can be collected.
There are many types of distillation columns where each plant is designed to
perform specific types of separation and also depends on the complexity of the
process. Commonly, the distillation column type is classified by looking at how the
plant is operated. There are two types of distillation column operation namely:-
1) Batch distillation column.
2) Continuous distillation column.
Obviously, the difference between these two types of distillation column lies
on the volume of the mixture that going to be separated. In batch operation, the
mixture is introduced batch-wise where there will be no more mixture to be added
3
during distillation or extraction process. The next batch of mixture will only be
introduced when the desired distillation task is achieved. Batch distillation column is
frequently used for small-volume products.
In contrast, continuous distillation column processes a continuous feed stream
of mixture. A certain amount of mixture is continuously fed into the column during
the distillation process. Continuous distillation column is capable of handling high
throughputs.
In this research, the process plant used as the reference system is the pilot
plant distillation column located at Centre of Lipids Engineering and Applied
Research (CLEAR), Universiti Teknologi Malaysia (UTM), Kuala Lumpur. This
plant is a batch type of distillation column. Thus, based on this plant, a simulation
system is developed in this thesis.
The plant is mainly used to extract and distillate ginger oleoresin from
Zingiber officinale Roscoe or commonly known as solid ginger using ethanol as the
solvent. Ginger oleoresin is the final product to be collected for further application.
Generally, in industry, the oleoresin is gaining popularity as a component which is
widely used in herbal-based medicine product. The ginger oleoresin also has
widespread uses as a flavouring agent in food and odour in perfume. A schematic
diagram of the distillation column is as shown in figure 1.1.
4
Figure 1.1 A schematic diagram of distillation column plant
From the control perspective of the pilot plant distillation column, the
temperature of the vessel that contains extraction mixture needs to be controlled and
maintained at certain setpoint. The heat which causes the temperature to increase is
supplied from the reboiler part of the distillation column. There are two elements that
can be controlled in the reboiler part: electrical heater and pump.
The main objective is to control these elements so that the temperature in the
vessel that contained mixture to be separated can reach the setpoint value and at the
same time the power consumption and heat loss can be reduced. In order to achieve
these objectives, it is very important to make sure that heat from the heater and
flowrate of silicon oil controlled by the pump have a balance relationship. Incorrect
values of the output from one of these elements can affect the temperature behaviour
which finally will give poor result. For example, if the maximum heater power is set
and minimum flowrate is selected, the temperature inside the vessel increases very
slowly meanwhile temperature at other part increases quickly. This causes a power
5
waste whereby heat is used to increase the temperature of different part of the
reboiler.
To optimally control two interacting variables is not an easy task in the
absence of accurate plant model. Therefore, it is essential that a good and accurate
plant model is obtained for the pilot plant distillation column in order for a good
performance controller to be designed.
1.3 Objective of the thesis
The objectives of the thesis can be divided into two main parts:-
Part 1: Fuzzy modelling for reboiler system of distillation column.
1) To develop models for nonlinear system namely reboiler system of
distillation column using Fuzzy modelling technique.
2) To develop an algorithm for tuning Takagi-Sugeno (TS) Fuzzy model
structure and parameter using numerical data.
3) To compare the performance of the optimized Fuzzy model with
conventional Fuzzy models and linear model as well.
Part 2: Designing Fuzzy controller of distillation column based on Fuzzy model.
1) To design Fuzzy controller for the distillation column plant based on its
Fuzzy model.
2) To apply an algorithm for tuning Fuzzy control parameter.
3) To compare the performance index of the Fuzzy model-based Fuzzy control
with the linear model-based Fuzzy control.
6
1.4 Scope of the thesis
In order to ensure the objectives of the thesis can be achieved, scope of the
research has been determined so that the work done in this research will be clearly
understood. The scope of this thesis covers:-
1) To focus on a part of distillation column called reboiler system as the
reference system for model development. The reboiler system is the critical
part in the distillation column plant that will determine the performance of the
extraction process.
2) To use the mathematical model based on energy balance principle to
represent the reboiler system of distillation column plant. This simulation
plant will be stated as the reference plant.
3) Implementation of artificial intelligence concept and principle especially
Fuzzy logic as the core subject in the development of intelligence model and
control of the plant.
4) Application of software namely LabView as the computational platform for
developing plant’s simulation, data acquisition and training of Fuzzy model
and control.
7
1.5 Contribution of the thesis
Previous work on Fuzzy modelling concentrates on using Genetic algorithm
(GA) for tuning the parameters of the model (Setnes and Roubus, 2000; Wong et al.,
2000; Teng et al.,2002). However, studies have shown that by modifying the model
structure of Takagi-Sugeno Fuzzy model, some improvement of the accuracy of the
model can be achieved (Sugeno and Kang, 1988).
In this thesis, we proposed to combine the use of GA for optimizing the
parameters of the antecedent part, Recursive least square (RLS) method for obtaining
the consequent part of the Fuzzy model and Unbiasedness criterion (UC) steps, as
such forming a hybrid method of optimizing the structure and parameter of Fuzzy
model.
The method is used to have accurate model of the distillation column. A
Fuzzy logic controller is designed offline using GA to optimize the tuning of its
parameters. Through the comparisons with several methods, namely conventional
Fuzzy model, Fuzzy model with optimum parameter and linear model, the results
show that the proposed method gives a more accurate model.
Below are some of the expected contributions of this thesis:-
i) Fuzzy model for the reboiler system of distillation column plant that is more
accurate to represent the plant.
ii) Based on Fuzzy model, Fuzzy controller for the distillation column plant is
developed which is well-performed when being applied to the model and the
plant.
iii) Provide reliable method to optimize the structure and parameter of Fuzzy
model which will improve the accuracy and exactness of the model compared
to the reference system.
iv) Provide method to tune parameter of Fuzzy control that will guide the
controller to be set up so that it can meet the control specification.
8
1.6 Thesis layout
This thesis is organized with eight chapters. Chapter 1 describes the general
introduction of this thesis, objective, scope and contribution of the research.
Followed by chapter 2 with literature review on modelling of distillation column
system, Fuzzy modelling technique and Fuzzy control technique. In chapter 3 and 4,
a detail explanation on Fuzzy modelling and Fuzzy control will be presented,
separately. Starting with general overview on Takagi-Sugeno Fuzzy model, then the
tuning algorithm to find optimum structure and parameter will be discussed. This
includes the explanation on Genetic algorithm (GA), recursive least square (RLS)
method and Unbiasedness criterion (UC). Comprehensive description on Fuzzy
control is then presented including overview on standard Fuzzy control and
parameter tuning using Genetic algorithm (GA).
Chapter 5 will give detail explanation on the reboiler system of distillation
column plant. The derivation on differential equation mathematical model of the
system will first been described. Next, the discrete time variant model will be
expressed. The implementation of Fuzzy modelling technique and Fuzzy control
technique on the distillation column are then illustrated in chapter 6 and 7
respectively. Procedures, results and discussion will be explained in both chapters.
Finally the conclusion and further development will be given in chapter 8.
REFERENCES
Babuska R., Roubus J.A. and Verbruggen H.B. (1998). Identification of MIMO
systems by input-output TS fuzzy models. Proceedings of the IEEE World
Congress on computational intelligence. May 4-9. Alaska: IEEE, 657-662.
Faraq W.A., Quintana V.H. and Lambert-Torres G. (1998). A genetic-based neuro-
fuzzy approach for modeling and control of dynamical systems. IEEE
Transactions on Neural Networks. 9(5): 756-767.
Geankoplis C.J. (1995). Transport Processes and Unit Operations. Singapore:
Prentice Hall.
Goldberg D.E. (1989). Genetic Algorithms in Search, Optimization and Machine
Learning. Reading, MA: Addison-Wesley.
Hadjili M., Lendasse A., Wertz V. and Yurkovich S. (1998). Identification of Fuzzy
Models for A Glass Furnace Process. Proceedings of IEEE International
Conference on Control Applications. September 1-4. Trieste, Italy: IEEE, 963-
968.
Holland J.H. (1975). Adaptation in Natural and Artificial Systems. An Arbor, MI:
University of Michigan Press.
Huang R.P. (1996). Adaptive fuzzy control: a GA approach. Proceedings of the 5th
IEEE International Conference Fuzzy Systems. September 8-11. New Orleans,
LA: IEEE, 1266-1272.
Hwang H.S. and Woo K.B. (1995). Linguistic fuzzy model identification. IEE
Proceedings on Control Theory and Applications. 142(6): 537-544.
Hwang W.R. and Thompson W.E. (1993). An intelligent controller design based on
genetic algorithms. Proceedings of the 32nd IEEE Conference on Decision and
Control. December 15-17. San Antonio: IEEE, 1266-1267.
133
Iwata T., Machida K. and Toda Y. (1990). Fuzzy control using neural network
techniques. Proceedings of IJCNN International Joint Conference on Neural
Networks. June 17-21. San Diego, USA: IEEE, 365-370.
Karacan S., Hapoglu H. and Alpbaz M. (1998). Generalized predictive control to a
packed distillation column for regulatory problems. Computer Chemical
Engineering. 22: 629-632.
Kelkar B. and Postlethwaite B. (1994). Fuzzy-model based pH control. Proceedings
of the 3rd IEEE Conference on Fuzzy Systems. June 26-29. Orlando, Florida:
IEEE, 661-666.
Koskinen J., Yliniemi L. and Leiviskii K. (1998). Fuzzy modelling of pilot plant
rotary dryer. Proceedings of UKACC International Conference on
Control.September 1-4. Swansee, UK: IEEE, 515-518.
Luyben W.L. (1990). Process Modeling, Simulation and Control for Chemical
Engineers. Singapore: McGraw-Hill.
Mamdani E.H. and Assilian S. (1975). An experiment in Linguistic Synthesis with a
Fuzzy Logic controller. International Journal Man-machine studies. 7: 1-13.
Mannle M. (2001). Parameter optimization for Takagi-Sugeno fuzzy models-lessons
learnt. IEEE Transactions on Systems, Man and Cybernetics. 1: 111-116.
Mantawy A.H. (2000). A genetic-based algorithms for fuzzy unit commitment
model. Proceedings of IEEE Power Engineering Society summer meeting. July
16-20. Seattle, Washington: IEEE, 250-254.
Melin P. and Castillo O. (2003). A new method for adaptive model-based control of
nonlinear plants using type-2 fuzzy logic and neural networks. Proceedings of
the 12th IEEE International Conference on Fuzzy Systems 2003. May 25-28. St.
Louis, MO, USA: IEEE, 420-425.
Ng K.C. and Li Y. (1994). Design of sophisticated Fuzzy logic controllers using
Genetic algorithms. Proceedings of the 3rd IEEE Conference on Fuzzy Systems.
June 26-29. Orlando, Florida: IEEE, 1708-1712.
Nie J., Loh A.P. and Hang C.C. (1994). Fuzzy modelling of nonlinear pH processes
through neural approach. Proceedings of the IEEE World Congress on
computational intelligence. June 26 – July 2. Orlando, Florida: IEEE, 1224-
1229.
Passino K.M. and Yurkovich S. (1998). Fuzzy control. Menlo Park, California:
Addison Wesley Longman Inc.
134
Pavel O. and Radomil M. (1997). Automatic optimal design of fuzzy controllers
based on genetic algorithms. Proceedings of the 2nd International Conference
on Genetic Algorithms In Engineering Systems: Innovations and Applications.
September 2-4. Strathclyde: IEEE, 439-443.
Ren L., Ding Y and Shao S. (2000). DNA genetic algorithms for design of fuzzy
systems. Proceedings of the 9th IEEE International Conference on Fuzzy
Systems.May 7-10. San Antonio, Texas: IEEE, 1005-1008.
Salimi F. and Depeyre D. (1998). Comparison between dynamic behaviour of a batch
packed and plate column. Computer Chemical Engineering. 22(3): 343-349.
Satyadas A. and Krishnakumar K. (1994). GA-optimized fuzzy controller for space
craft attitude control. Proceedings of the 3rd IEEE Conference on Fuzzy
Systems. June 26-29. Orlando, Florida: IEEE, 1979-1984.
Seng T.L., Khalid M. and Yusof R. (1999). Tuning of a Neuro-Fuzzy Controller by
Genetic Algorithms. IEEE Transactions on Systems, Man and
Cybernetics.29(2): 226-236.
Setnes M. and Roubos H. (2000). GA-Fuzzy modelling & classification: complexity
and performance. IEEE Transactions on Fuzzy System.8(5): 509-522.
Shieh M.Y., Huang C.W. and Li T.H.S. (1997). A GA-based Sugeno-type fuzzy
logic controller for the cart-pole system. Proceedings of 23rd International
Conference on Industrial Electronics, Control and Instrumentation. November
9-14. New Orleans, LA: IEEE, 1028-1033.
Siddique M.N.H., Tokhi M.O. (2002). GA-based neuro-fuzzy controller for flexible-
link manipulator. Proceedings of the 2002 International Conference on Control
Applications. September 18-20. Glasgow, Scotland: IEEE, 471-476.
Steck J., Krishnamurthy K., McMillin B. and Leininger G. (1991). Neural modelling
and control of a distillation column. Proceedings of the IJCNN 91
International Joint Conference on Neural Networks. July 8-14. Seattle: IEEE
771-774.
Sugeno M. and Kang G.T. (1985). Fuzzy Modeling and Control of Multilayer
Incinerator. In: Nguyen H.T. and Prasad N.R. Fuzzy Modeling and Control,
Selected works of M.Sugeno. Florida: CRC Press. 113 – 128.
Sugeno M. and Kang G.T. (1988). Structure Identification of Fuzzy Model. In:
Nguyen H.T. and Prasad N.R. Fuzzy Modeling and Control, Selected works of
M.Sugeno. Florida: CRC Press. 161 – 178.
135
Suzuki T., Furuhashi T. and Tsutsui H. (2000). A framework of fuzzy modelling
using genetic algorithms with appropriate combination of evaluation criteria.
Proceedings of the 2000 Congress on Evolutionary Computation.July 16-19.
San Diego, California: IEEE, 1252-1259.
Takagi T. and Sugeno M. (1985). Fuzzy identification of systems and its application
to modelling and control. IEEE Transactions on Systems, Man and
Cybernetics. 15(1): 116-132.
Teng Y.W. and Wang W.J. (2002). System approximation via GA-based fuzzy
model. Proceedings of APCCAS ’02 Conference on Circuits and Systems.
October 28-31. Bandung, Indonesia: IEEE, 547-550.
Wang B., Wang S.A., Du H.F. and Qu P.G. (2003). Parameter Optimization in
complex industrial process control based on improved Fuzzy-GA. Proceedings
of 2nd International Conference on Machine Learning and Cybernatics.
November 2-5. Xi’an: IEEE, 2512-2515.
Wei W., Wang M.J. (2003). Fuzzy-GA-based traffic signal control. Proceedings of
2nd International Conference on Machine Learning and Cybernatics.
November 2-5. Xi’an: IEEE, 645-650.
Wong C.C. and Chen C.C. (2000). A GA-based method for constructing fuzzy
systems directly from numerical data. IEEE Transactions on Systems, Man and
Cybernetics. 30(6): 904-911.
Xu C.W. (1989). Fuzzy systems identification. IEE Proceedings Part D. 136(4):
146-150.
Yamazaki T. (1996). An application of Fuzzy modelling to distillation control.
Proceedings of the 5th IEEE Conference on Fuzzy Systems. September 8-11.
New Orleans, LA: IEEE, 654-659.
Yi Y. (1998). On Fuzzy Modeling of Nonlinear Dynamical Systems. National
University of Singapore: Ph.D. Thesis.
Zadeh L.A. (1968). Fuzzy algorithm. Information and Control. 12(2): 94-102.