fuzzy modelling and control for a nonlinear reboiler...

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

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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.

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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.

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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

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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


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


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

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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


FM-PO of silicon oil tank sub-model


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



FM-SPO of jacket tank sub-model


FM-PO of jacket tank sub-model


FM-C of jacket tank sub-model


of jacket tank sub-model


6.5 Identification of vessel sub-model 97



FM-SPO of vessel sub-model


FM-PO of vessel sub-model

xi


FM-C of vessel sub-model


of vessel sub-model


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


models of jacket tank system

6.8 Comparison of UC values of models in stage 0 98

and 1 (vessel model)


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

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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


6.10 The configuration of Fuzzy model FM-C 88


6.11 Input-output of jacket tank discrete model 90


for jacket tank system





6.15 Input-output of vessel discrete model 97


for vessel system


for vessel system


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

xix

LIST OF APPENDICES

APPENDIX TITLE PAGE

A Related publication 136

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.

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