Shoaib Thesis Final 2011-12-15

Development of a Fuzzy Logic Controller for a Distillation Column Using Rockwell Software

by

Muhammad Shoaib Nizami

A Thesis

presented to The University of Guelph

In partial fulfilment of requirements

for the degree of Master of Applied Science

in Engineering

Guelph, Ontario, Canada

© Muhammad Shoaib Nizami, September, 2011

ABSTRACT

Development of a Fuzzy Logic Controller for a Distillation Column using Rockwell

Software

Muhammad Shoaib Nizami Advisor:

University of Guelph, 2011 Professor Simon X. Yang

In this thesis, an alternative control method based on Fuzzy Inference System (FIS)

is proposed to keep the product composition of a distillation column constant. This

study compares a proposed FIS with traditional PID (proportional, integral, deriva-

tive) control technique and analyzes the results. The FIS is applied to the control

of the tray temperature of the distillation column by using indirect feed split control

structure to modulate the steam flow with management of the tray temperature. In

turn, this modulation maintains the composition of product at specified levels.

Rockwell fuzzy designer is used to develop the fuzzy logic controller. Both a fuzzy

logic controller and a PID controller are downloaded in the Rockwell ControlLogix

L62 process controller. Chemstations Chemcad simulation software is used to run

the distillation column simulations. Simulation results are programmed into L62

process controller to behave as a dynamic distillation column. Results show that the

proposed fuzzy logic controller is more tolerant to disturbances in the feed flow and

feed composition of the distillation column than the PID controller.

Dedication

To my grandfather, Hafiz Nizamuddin, and

to my parents, Siddique Ahmed Nizami and Ashraf Jahan Aara, whose

encouragement was great source of inspiration for me

to my wife, Andleeb, for her patience and steadfastness support

and to my kids Tooba, Taha, and Tabish in whom glittering eyes I can

see my own unfulfilled dreams

iii

Acknowledgements

First of all thanks to my advisor, Professor Simon Yang, who supported me in

every step of my studies at the University of Guelph and whose valuable suggestions

during the completion of this thesis were unparalleled. I will remember him in my

heart throughout out my life along with the University itself who gave me the chance

to complete my dream of doing master’s in control systems engineering. A well deserve

thanks to my advisory committee member, Professor Gordon Hayward, for his out of

the way cooperation in completing this thesis.

Completion of this thesis was almost impossible without the support of my man-

ager, Sean Murray, at Zeton Incorporated. He facilitated me in every manner and did

let me to utilize every resource available at Zeton from control system equipment to

all kind of control and simulation software. I am also thankful to my colleagues, Leisl

Dukhedin-Lalla, Majid Kazi, and Asif Raza, at Zeton who helped me run chemical

engineering simulations and gave me very valuable insight into the distillation column

process and operation. I will certainly mention Jim Thomson who finally came up

with the solution of my idea.

At the end I must thank Rockwell Automation and their local representative

at Burlington, Gerrie Electric, for providing me the Fuzzy Designer software free of

cost.

iv

Contents

List of Figures viii

List of Tables xiii

List of Symbols and Abbreviations xiv

1 Introduction 1

1.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Objective of This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Contribution of This Thesis . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Organization of This Thesis . . . . . . . . . . . . . . . . . . . . . . . 3

2 Background and Literature Survey 5

2.1 Distillation Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Traditional Approaches to the Problem . . . . . . . . . . . . . . . . . 8

2.3 New Approaches to the Problem . . . . . . . . . . . . . . . . . . . . . 15

2.3.1 Basic Components of a Fuzzy System . . . . . . . . . . . . . . 15

2.3.2 Fuzzy Control Systems . . . . . . . . . . . . . . . . . . . . . . 20

3 The Proposed Method 31

3.1 The Fuzzy Inference System Design . . . . . . . . . . . . . . . . . . . 31

3.2 The Controller Software . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.3 The Controller Hardware . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.4 Experiment Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

v

3.5 Distillation Column under Study . . . . . . . . . . . . . . . . . . . . 44

3.5.1 Salient Features of the Distillation Column . . . . . . . . . . . 45

3.5.2 Feed Stage Base Conditions . . . . . . . . . . . . . . . . . . . 46

3.5.3 Control Stage Base Conditions . . . . . . . . . . . . . . . . . . 47

3.5.4 Feed Stream Base Conditions . . . . . . . . . . . . . . . . . . 47

3.5.5 Distillate Stream Base Conditions . . . . . . . . . . . . . . . . 47

3.5.6 Bottoms Stream Base Conditions . . . . . . . . . . . . . . . . 47

4 Results and Discussion 51

4.1 Function Block Diagram Arrangement . . . . . . . . . . . . . . . . . 52

4.2 Chart Arrangement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.3 Tuning of Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.3.1 Tuning of Fuzzy Controller . . . . . . . . . . . . . . . . . . . . 55

4.3.2 Tuning of PID Controller . . . . . . . . . . . . . . . . . . . . . 63

4.4 Experiments and Results . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.5 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5 Conclusion and Future Work 91

5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

References 93

A Appendix: Distillation Column Temperature Profiles 98

A.1 Distillation Column Temperature Profile at 950 pph flow and 26 per-

cent of Methanol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98


cent of Methanol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101


cent of Methanol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104


cent of Methanol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

vi


cent of Methanol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110


cent of Methanol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113


cent of Methanol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116


cent of Methanol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

B Appendix: Distillation Column Tray50 Temperature Profiles 122

B.1 Tray50 Temperature Profile versus Reboiler Duty at various flow and

composition of feed and Methanol . . . . . . . . . . . . . . . . . . . . 122

B.2 Tray50 Temperature Profile versus Reboiler Duty at 900 pph flow and

26 percent composition of feed and Methanol respectively . . . . . . . 129







C Appendix: FLC and PID Controllers Code 141

C.1 FLC and PID Controllers Code, exported from RSLogix5000 in L5X/XML

format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

vii

List of Figures

2.1 A typical distillation column with controllers. . . . . . . . . . . . . . 6

2.2 Error calculation in reverse acting mode. . . . . . . . . . . . . . . . . 10

2.3 Error calculation in direct acting mode. . . . . . . . . . . . . . . . . . 10

2.4 Process variable (PV) tightly following setpoint (SP). . . . . . . . . . 12

2.5 Process variable (PV) overshooting due to high gain and reset value. 14

2.6 Basic formulation of PID controller. . . . . . . . . . . . . . . . . . . . 14

2.7 Standard membership function shapes. . . . . . . . . . . . . . . . . . 17

2.8 Trapezoidal and Triangular membership functions. . . . . . . . . . . . 17

2.9 Defuzzification methods (a) Centre of Gravity; (b) Maxima . . . . . . 19

2.10 Structure of a conventional fuzzy inference system. . . . . . . . . . . 23

2.11 A supervised learning fuzzy controller. . . . . . . . . . . . . . . . . . 26

2.12 A self-learning layer added to a fixed rule base fuzzy controller. . . . 30

3.1 General overview of the experiment concept. . . . . . . . . . . . . . . 32

3.2 General overview of the proposed fuzzy system. . . . . . . . . . . . . 33

3.3 Equivalent fuzzy system in Rockwell software (FuzzyDesigner). . . . . 33

3.4 Error variable Input Membership functions in Rockwell software (Fuzzy-

Designer). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.5 Delta error variable Input Membership functions in Rockwell software

(FuzzyDesigner). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.6 Non-Linear variable Input Membership functions in Rockwell software

(FuzzyDesigner). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

viii

3.7 Non-Linear Low variable Input Membership functions in Rockwell soft-

ware (FuzzyDesigner). . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.8 Rule base in Rockwell software (FuzzyDesigner). . . . . . . . . . . . . 38

3.9 Output Membership functions in Rockwell software (FuzzyDesigner). 40

3.10 The diagram of experiment setup. . . . . . . . . . . . . . . . . . . . . 44

3.11 Proposed distillation column and control structure. . . . . . . . . . . 45

3.12 Equivalent Distillation column in Chemcad simulation environment. . 46

4.1 Physical setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.2 Function block arrangement for the experiment in Rockwell RSLogix5000

software. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.3 Chart arrangement for the experiment in Rockwell RSLogix5000 soft-

ware. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.4 Fuzzy Designer on-line tuning. . . . . . . . . . . . . . . . . . . . . . . 55

4.5 Fuzzy Designer on-line tuning, Membership functions. . . . . . . . . . 56

4.6 Fuzzy Designer on-line tuning, Rule base. . . . . . . . . . . . . . . . . 56

4.7 Response of FLC controller after loading initial tuning parameters. . 57

4.8 Response of FLC controller after reducing TempError to 50 and Er-

rorDelta to 5 tuning parameters. . . . . . . . . . . . . . . . . . . . . . 58

4.9 Response of FLC controller after reducing ErrorDelta to 0.01 while

keeping TempError at 50. . . . . . . . . . . . . . . . . . . . . . . . . 59

4.10 Response of FLC controller after reverting ErrorDelta back to 5 while

reducing TempError to 10. . . . . . . . . . . . . . . . . . . . . . . . . 59

4.11 Response of FLC controller after reducing TempError further to 5 while

keeping ErrorDelta back at 5. . . . . . . . . . . . . . . . . . . . . . . 60

4.12 Response of FLC controller after keeping TempError at 5 while reduc-

ing ErrorDelta to 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.13 Response of FLC controller after reducing TempError to 1 while re-

verting ErrorDelta back to 5. . . . . . . . . . . . . . . . . . . . . . . 61

ix

4.14 Response of FLC controller after reverting TempError back to its best

value of 5, ErrorDelta back at its best value of 5, and reducing Rule 3

weight from initial weight of 1 to 0.1. . . . . . . . . . . . . . . . . . . 62

4.15 Response of FLC controller at the best and final values, TempError at

5, ErrorDelta at 5, and Rule 3 weight at 0.3. . . . . . . . . . . . . . . 63

4.16 Auto-Tuning results in Rockwell RSLogix5000 software. . . . . . . . . 64

4.17 Response of PID controller after loading auto-tune parameters in Rock-

well RSLogix5000 software. . . . . . . . . . . . . . . . . . . . . . . . . 65

4.18 PID controller in oscillation when P was increased to 1600 while keep-

ing other parameters at auto-tune values. . . . . . . . . . . . . . . . . 66

4.19 PID controller in oscillation when P was decreased to 800 while keeping

other parameters at auto-tune values. . . . . . . . . . . . . . . . . . . 67

4.20 PID controller with P set to 400 while keeping other parameters at

auto-tune values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.21 PID controller with P set to 400 and I set to 12800 while keeping D

parameter at auto-tune value. . . . . . . . . . . . . . . . . . . . . . . 68

4.22 PID controller with P set to 400 and I set to 6400 while keeping D

parameter at auto-tune value. . . . . . . . . . . . . . . . . . . . . . . 68

4.23 PID controller with P and D set to 400 and 6400 respectively and D

set to16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.24 PID controller with P and D set to 400 and 6400 respectively and D

reduced from 16 to 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.25 PID controller with P set to 400, I set to 6400, and D set to 8. . . . . 70

4.26 Effect of flow change from 950 to 900 lb/hr at constant composition . 71

4.27 Effect of flow change from 900 to 950 lb/hr at constant composition . 72

4.28 Effect of flow change from 950 to 1000 lb/hr at constant composition 73

4.29 Effect of flow change from 1000 to 950 lb/hr at constant composition 73

4.30 Effect of composition change from 26 to 31 percent of MeOH at con-

stant flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

x


stant flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75


stant flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76


stant flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.34 Effect of flow change from 950 to 1100 lb/hr and composition change

from 26 percent methanol to 36 percent methanol. . . . . . . . . . . . 77









4.39 Figure 4.38 with different zoom on a different day to check whether

FLC fell into saturation. . . . . . . . . . . . . . . . . . . . . . . . . . 81



4.41 Figure 4.40 with different zoom on a different day to check whether

FLC fell into saturation. . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.42 Effect of setpoint change from 101.0 to 104.0 degree at the base con-

ditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.43 Effect of setpoint change from 101.0 to 97.8 degree and vice versa at

36 percent methanol composition and 1100 pph flow. . . . . . . . . . 84

4.44 Effect of setpoint change from 101.0 to 98.5 degree and vice versa at

33 percent methanol composition and 1050 pph flow. . . . . . . . . . 85

4.45 Effect of setpoint change from 101.0 to 102.8 to 99.8 degree and back

to 101.0 at 30 percent methanol composition and 1000 pph flow. . . . 86

xi

4.46 Effect of randomly selected setpoint change and disturbances. . . . . 87

4.47 Effect of falling into extremely non-linear region of temperature profile. 88

4.48 Temperature profile of Distillation column under study at 950 l/hr of

flow and 26 percent of methanol. . . . . . . . . . . . . . . . . . . . . 90

4.49 Temperature profile of Tray 50 of Distillation column under study at

950 l/hr of flow and 26 percent of methanol. . . . . . . . . . . . . . . 90

xii

List of Tables

2.1 RuleBaseExample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.1 Rockwell RuleBase Text . . . . . . . . . . . . . . . . . . . . . . . . . 39

xiii

List of Symbols and Abbreviations

Symbols in This Thesis

ai Weight of rule i

lb/hr Engineering unit for flow measurement pounds per hour

CO Controller Output also called manipulated variable is the output of

the process controller

D Derivative is the rate of change of error between SP and PV of the

PID controller

e Error between the values of SP and PV of the process controller

I Integral also called reset defines the integral of the error between SP

and PV of the PID controller

MeOH Chemical formula of Methanol

N Number of rules

OP Output also called manipulated variable is the output of the process

controller

P Proportional band also symbolized as PB defines the proportional

gain of the PID controller

PV Process variable also called controlled variable is the output of the

plant

SP Set point also called referenced point in a typical process controller

is the threshold point at which plant process has to be maintained

Y Output of the FIS system

xiv

Abbreviations in This Thesis

AI Artificial Intelligence

ANFIS Adaptive Neuro Fuzzy Inference System

ANN Artificial Neural Network

DC Distillation Column

DDC Direct Digital Control

DFQL Dynamical Fuzzy Q-Learning

FACL Fuzzy Actor-Critic Learning

FBD Function Block Diagram

FIS Fuzzy Inference System

FLC Fuzzy Logic Controller

FQL Fuzzy Q-Learning

GA Genetic Algorithm

GLC Globally Linearizing Control

MMBtu/hr Engineering unit for heat measurement

Million British thermal unit per hour

MP Matching Pursuit

NN Neural Network

OLE Object Linking and Embedding

OMP Orthogonal Matching Pursuit

OPC Object Linking and Embedding for Process Control

PID Proportional Integral Derivative algorithm is the most popular

type of control technique in control engineering

PLC Programmable Logic Controller

PMBE Process Model Based Engineering

PMC Model Predictive Control

pph pounds per hour, equivalent to lb/hr

PSIG Engineering unit for pressure measurement

Pounds per Square Inch (Gauge)

xv

RL Reinforcement Learning

SFC Sequence Function Chart

SL Supervised Learning

SLFC Self Learning Fuzzy Logic Control

xvi

Chapter 1

Introduction

Petroleum refining and extraction is one of the complex processes of raw ma-

terials. Normally it is divided into two stages; upstream and downstream. In the

upstream stage oil is drilled and/or mined to extract it out of the subsurface and in

the downstream stage it is refined to usable levels in the form of different products

namely benzene, gasoline, kerosene, and tar.

Different products are separated by using the phenomenon of different boiling

temperatures of different components of the crude oil feed, and this process is called

distillation. This process becomes challenging due to the presence of dynamic vari-

ables such as feed flow, temperature, pressure, level, and composition.

The focus of this research thesis is a binary distillation column; a binary dis-

tillation column is where two products are separated from the feed. Typically the

lighter product is collected from the top and heavier product is collected from the

bottom of the column. Traditionally one or two control loops are constructed to

control the composition of the top and bottom product. In two loop architecture,

the top loop monitors the composition of the distilled product and controls the reflux

into the column, while bottom loop monitors the composition of the bottom product

and controls the heating of the bottom section of the distillation column. In one

loop architecture only one loop controls the heating or the reflux into the distillation

column to maintain the composition of both top and bottom product. The controller

of this single loop architecture is the topic of this thesis.

1

1.1 Problem Statement

Controlling the composition of the product of the distillation column is one of

the challenges engineers face during the operation of the distillation of the raw feed

into the refinery. The steady-state operation of the column is disturbed by the sud-

den change in the feed flow, composition of the feed, feed pressure, and ambient

temperature.

PID (proportional, integral, derivative) controllers are used to control the differ-

ent variables of the process. Distillation column is a highly complex and non-linear

process where variables do not follow each other linearly and that is why this type of

control often requires a lot of tuning when variables change at different rates then at

which the controller was originally tuned. The control parameters are usually selected

by trial and error method, which is difficult to systematically incorporate human ex-

pert knowledge. In many situations, one fixed set of PID control parameters may not

be suitable for some cases that require a range of control rules.

1.2 Objective of This Thesis

The objective of this research is to highlight the applicability of fuzzy control to

a non-linear process from an industrial view point. The proposed fuzzy controller will

directly address the problems encountered in distillation operation and can also be

used in other applications where more than one variable affect the operation of the

process and the nature of the control is non-linear such as boiler level control, waste

water pumps speed, and food processing.

The procedure developed for collecting distillation column data and program-

ming this data into RSLogix 5000 software can also be used in pilot and commercial

production plants for testing and developing new fuzzy controllers and comparing

their performance with existing operational PID controllers.

2

1.3 Contribution of This Thesis

There are three novel techniques being used in this thesis,

• Industrial software, Rockwell Fuzzy Designer is used to develop the fuzzy con-

troller

• By using the sensitivity analysis simulation results of the CHEMCAD distilla-

tion column software, a real-time distillation column function is generated in

the Allen Bradley RSLogix5000 control software

• Both Fuzzy Controller and distillation column function are running in Rockwell

ControlLogix L62 PLC

By applying the fuzzy control it is proved that fuzzy logic controller can be a

better alternative to the PID controller for the control of distillation column control

loops by utilizing the human experience and inherent fuzzy characteristics of the fuzzy

logic. In a normal setup at the petroleum plant operators are the ones who operate

the distillation column and control engineers are the ones who tune the control loops.

By employing the fuzzy technique, the experience of operators can be incorporated

in the configuration of fuzzy controllers that will result in a more stable and efficient

control loops. In this thesis the experience of the people who have worked in the

refinery is utilized to prove that human experience in controlling the plant can be an

asset while developing control loops.

1.4 Organization of This Thesis

This thesis is divided into chapters, sections and subsections. Chapter 1 includes

the introduction where problem statement, objective and contribution of this thesis

are briefly described.

Chapter 2 is a literature survey and background of the topic of this thesis. Some

very basic information of the operation of distillation column is given along with

the brief history of development of control techniques for the distillation column.

3

A detailed discussion is provided for traditional approach and its weaknesses. An

introduction to the basic functioning of FLC is provided along with the different

learning techniques of FIS. A detailed literature survey of the fuzzy control approach

in the last four decades is presented at the end of the chapter. A discussion is also

provided between the differences found in the design of academic versus industrial

fuzzy controllers in today’s world.

Chapter 3 presents the basic idea behind the methodology of the experiment. It

gives details about the components of the system which includes fuzzy logic controller,

PID controller, selection of controller software, selection of control hardware, and

selection of control structure of the distillation column. This chapter also introduces

the reader to the hypothetical distillation column used for this experiment along with

the its base conditions. The reader is also introduced to the CHEMCAD software

used in this experiment for the simulation of distillation column sensitivity analysis.

In Chapter 4, results are presented, analyzed, and summarized. Arrangement

for the theorem in terms of function blocks and arrangement for the results in charts

are presented. Comparative analysis between the two type of controllers, FLC and

PID, is given for each type of experiment. Figures are provided to depict not only the

experiment results but also to show the basic setup of the experiment, and nonlinear

behaviour of the temperature profile of the distillation column.

Chapter 5 concludes the research and suggests possible future work. Based on

the results presented in chapter 4, it is explained why FLC performed better than

PID controller in controlling the distillation column. Suggestions for future work are

based not only on the results of this thesis but also on the contemporary control

practises and trends in the industrial control world.

4

Chapter 2

Background and Literature Survey

This chapter is about the background information underlying the project, start-

ing with the introduction of the distillation column, distillation column control struc-

ture problem and traditional approach to the problem. It reviews new approaches,

and provides survey of current literature. Details of the functioning of a traditional

PID control and of new FLC controls are discussed. How control and PID technique

have been developed and applied to distillation column is explained and the survey

of the new approaches investigates how deficiencies of PID control are addressed in

the new approach.

2.1 Distillation Column

Distillation Columns are used in the chemical and petroleum industry to separate

the multiple liquids by using their physical and chemical properties. They are one of

the most common plant units along with the utilities in the petrochemical industry.

Feed enters from one side of the column while exact height of the location of

the inlet stream into the column vary by application. By heating the feed, one

liquid boils earlier than the other due to its lower boiling point and transforms into

vapours. This vapour liquid is referred to as light product and is collected from top

of the distillation column and is condensed to convert it back to liquid distillate,

before storing or feeding it into other downstream units for further process. The

5

Figure 2.1: A typical distillation column with controllers.

other component of the feed, which remains in the liquid state, is heavier component

and is collected from the bottom of the distillation column and is termed as bottoms.

The control of distillation column becomes difficult because of the following reasons:

• Presence of number of interacting variables

• Extreme process interactions

• Process non-linearity and dead times

• Difficult to measure process variables

Due to all the above reasons and other industrial plants challenging situations,

the control strategies of distillation column have been a topic of choice for researchers

both in the academic and industrial world for a long time.

The most important issue in Distillation Column (DC) control is to keep the

product quality at constant parameters. Traditionally, PID control techniques have

6

been employed to control these parameters. Since the DC is quite complex, highly

nonlinear, multivariable process it has remained a challenge for engineers to control

and for operators to operate. This is the reason that alternative control techniques

have been tried to overcome this complex control. Adaptive control, model predictive

control, and fuzzy control are the few techniques that stand out among hundreds of

others like Globally Linearizing Control (GLC) by Trotta and Barolo (1995), Process

Model-Based Engineering (PMBE) by Cott et al. (1989) based on original Generic

Model Control, NN model-based controller by Monsanto (1997), and multiple control

techniques by Vester et al. (1993).

A fine example of an adaptive control technique is the experiment done by Barolo

et al. (1994), although approach was limited to only one distillation loop the author

believes that the second loop for bottoms control could be implemented in the same

way though further research is needed. Barolo method was based on GLC, Globally

Linearizing Control. The controller model was developed by grouping a number of

component dynamic balance equations into one dynamic equation. The developed

controller need not to be tuned separately for start-up and steady state operation

of the distillation column unlike a legacy PI controller that needs a separate tuning

parameters for varying operating scenarios.

It is often questioned why to use fuzzy control while well established PID control

can handle most of the situations in the operating range of the processes. PID control

can be further enhanced by the use of adaptive techniques. The answer is that each

type of control has its strengths and weaknesses and now fuzzy control is finding its

applications in multivariable control problems like dairy, traffic control, and process

control.

Fuzzy logic is one of the strongest contenders of alternate solutions for non-linear

controls among other new approaches because of its ease of use and its exploitation of

human experience. Still some prefer to use fuzzy control to only tune the parameters

of traditional PID controller (Karray and Desilva, 2004). In the operation of DC,

the operators role at the front line of the operation is very important. To use this

knowledge as a way to automate the control of DC fuzzy logic has been proposed

7

as fuzzy logic inherently has the ability to convert this human knowledge into rule

based control. The other great advantage of fuzzy logic control is that it does not

need an analytic model of the process for the development of fuzzy controller, so their

conception is greatly simplified (Margaglio et al., 1997).

An other aspect that has been noted in the control applications is that fuzzy

control has the edge over PID control in the recovery of the process from OFF position.

Fuzzy systems have less overshoot than their counterpart PID controllers and that

is why fuzzy overshoot suppression phenomenon is being implemented by leading

control software developers.

Most of the earlier fuzzy models were based on the trial and error methods, as

humans do most of the time. A system is developed by the knowledge of human

experts and applied to the particular system. If the results are not according to the

expectations then further tuning is done and the model is reapplied. The procedure

goes on until perfection is attained and thus sometimes require a lot of resources. To

overcome this difficulty an on line tuning of the system has been developed by using

different learning methods, namely Supervised and Reinforcement Learning.

As fuzzy control is part of the bigger family of Artificial Intelligence (AI) so it

can tremendously increase its efficiency by easily incorporating the advancements in

this growing field of AI. At the same time, cognitive sciences are making use of fuzzy

logic in a number of ways such as pattern recognition and data modelling (Wang and

Lai, 2000).

2.2 Traditional Approaches to the Problem

Since James Watt used a mechanical governor to control the speed of his im-

proved steam engine in 1788, control engineering has been part and parcel of the

industrial world. During this time, different mechanical control techniques were used

to control the machinery and this was true when the oil industry developed in the late

18th century. Mechanical pneumatic instrumentation evolved for the control of the

process in the early 20th century and became mature in 1950s and 1960s. The PID

8

controller was the most popular method of employing closed loop control although

adaptive control found applications in niche markets like in the aerospace industry.

As electronic equipment became more and more available, the electronic controllers

started to replace the pneumatic controllers, although pneumatic controllers are still

used in the petrochemical industry in particular cases. The evolution goes on with

the growth of digital computing and advent of new intelligent control theories like

fuzzy and neural networks. Scientists and engineers started looking into these new

theories for better solution to their problems.

This section describes in detail how PID control works, its basic components,

and why it become so popular.

Reverse Action vs Direct Action in PID controller

PID control evolved from the need of controlling the process without human

intervention. The basic objective is to keep the actual condition of the process as

close to the desired condition as possible without unsettling the whole system. So

the simple method of subtracting the actual condition of the process, process variable

PV , from the desired process condition, set point SP , used to find the error e.

e = SP − PV (2.1)

The above approach is also termed as reverse acting. A variant of the above approach

is direct acting which is as follows;

e = PV − SP (2.2)

Reverse acting implies that controller output will move in opposite direction to

that of the process variable to maintain the process variable at the referenced point

where as direct acting implies that controller output will move in the same direction

to that of process variable to maintain the process variable at the referenced point.

Reverse acting is the generic form of control and for sake of simplicity this form of

control is used for further discussion in this chapter.

9

Figure 2.2: Error calculation in reverse acting mode.

Figure 2.3: Error calculation in direct acting mode.

10

Closed Loop versus Open Loop in PID controller

Before going further, difference between open loop control and close loop control

has to be defined clearly. In open loop control the controller does not have feed back

from the process and it is not aware of the consequences of its action and hence cannot

control precisely. It is like driving a car with closed eyes. Whereas in close loop control

the controller gets the instantaneous feedback from the process and hence modulates

its output accordingly. In this study only the close loop control is discussed further.

This type of feedback in the close loop control is also called negative feedback because

controller counteract basis on this feedback.

Basic Components of PID Control

As the name implies, the PID controller is made up of following three compo-

nents;

1. Proportional Band

2. Integral

3. Derivative

1. Proportional band function in PID controller

As seen from Eq. (2.1), the controller generates a proportional control output,

called CO. An important point to emphasize is that proportionate change in CO

depends on the proportionate change in the error. The earlier controllers were only

proportional controllers or P controllers. They worked fine and kept the process

close to their set point. However, there was one issue that they introduce offset after

sometime or when there was disturbance in the process.

First component of PID controller is in the following form;

CO = eP (2.3)

where CO is the controller output, e is the error and P is the proportional factor.

11

Figure 2.4: Process variable (PV) tightly following setpoint (SP).

2. Integral (Reset) function in PID controller

In the real world of process control there is a parameter which is disliked by

all, control engineers, chemical engineers etc. It is called disturbance. Disturbance

is anything which causes the normal setup of control out of its set parameters. For

the sake of simplicity it can be supposed that a sudden drop of ambient temperature

is the disturbance in a heater control loop. The offset created by the disturbances

used to be reset by the operators by themselves by manually increasing the output

of the controllers. To make this manual reset automatic, integral phenomenon was

introduced into the Eq. (2.3) which results in the following equation;

CO = Pe + I

∫edt (2.4)

where CO is the controller output, e is the error, P is the proportional factor, and I

is the integral.

Integral of a control loop will work in parallel with proportional gain and will

keep adding up the error signal and hence boost the controller output until error e

becomes 0. Thus deficiency in the P only controller can be accommodated by the

integral I factor. A vast majority of the PID controllers used in the petrochemical

12

industry today are of PI type.

3. Derivative (Rate) function in PID controller

There are numerous processes in the industry which are too slow to change and

hence difficult to control efficiently with PI controllers; temperature is one of them.

Because of their slowness in change they (slow process) introduce large amounts of

time lag between the controller action and the response generated by the process that

the PI controller cannot handle it efficiently and in turn controller action becomes

sluggish. To overcome this sluggishness controller P and I parameters are increased

which give a fast response but ultimately introduce the overshoot problem. Over-

shooting is the phenomenon in which controller action causes the PV to go beyond

the desired value. This is the scenario where the third term of the PID controller,

derivative D, comes into action. Derivative is nothing but a rate of change of error e.

Derivative will continuously check the rate of change of error e and based on this

rate will determine how much negative gain it should introduce into the controller

output CO to prevent it causing the PV to overshoot the SP . Now the Eq. (2.4)

becomes;

CO = Pe + I

∫edt + Dde/dt (2.5)

where CO is the controller output, e is the error, P is the proportional factor, I is

the integral, and D is the derivative.

There are a lot of variations of the above PID controllers such as interactive and

non-interactive algorithms and then each controller manufacturer has its own unique

algorithm but the basic idea behind all of these is the same as have been presented

above.

Along with PID control there are other control techniques which found applica-

tions in the industry. All of these techniques can be broadly categorized as classical

and modern. Classical control technique deals with single input single output systems

and the PID technique is one of them. On the other hand, modern control technique

can deal with the multivariable systems and model predictive control (MPC), adap-

tive control, and robust control are some of the examples. Other advanced control

13

Figure 2.5: Process variable (PV) overshooting due to high gain and reset value.

Figure 2.6: Basic formulation of PID controller.

14

techniques like cascade control, split control, and feed forward control can be used

with both types of categories.

2.3 New Approaches to the Problem

With the advent of the micro computer chip, soft computing has gained a lot

of attention. As this technique relies heavily on computing power it got greater

acceptance with the availability of cheap and powerful computing chips.

Collectively soft computing is a part of Artificial Intelligence which includes fuzzy

logic, neural networks, genetic algorithm, and Bayesian control. There is further

combination of these techniques like neuro-fuzzy control, fuzzy-genetic control, to

name a few. Among all of these intelligent control methods fuzzy control has better

acceptance in the petrochemical industry and commercial control applications can be

spotted which are discussed later. In this section, basic components of FLC structure

are described and literature survey of fuzzy control in the petrochemical industry and

around its application to distillation column control is presented.

2.3.1 Basic Components of a Fuzzy System

Fuzzy Control System is based on the Fuzzy Set Theory and Fuzzy Logic pre-

sented by Lotfi Zadeh in 1965 and 1973 respectively (Zadeh, 1965), (Zadeh, 1973).

Zadeh is considered to be the father of fuzzy logic and wrote every aspect of this new

theory up to now (Bellman and Zadeh, 1970), (Zadeh, 1975), (Zadeh et al., 1975),

(Gaines et al., 1984), (Zadeh, 1978), (Zadeh, 1979), (Zimmermann et al., 1984), and

(Zadeh, 1999). FIS (Fuzzy Inference System) system is generally consists of following

5 components:

1. Input variables

2. Method of fuzzification through membership functions for input variables

3. Rule-base (if-then rules)

15

4. Method of defuzzification through membership functions for output variables

5. Output variables

Input Variables

An input variable to the FIS is the variable to be controlled. This variable has

to be kept at a certain value called set point or reference signal to keep the system

stable and free of oscillation. In most of the FIS systems, single input variable is

used but it can be increased to any number. The rule of thumb is that increasing

the number of input variables increases the complexity of the system. In most of the

process control applications of fuzzy control two input variables namely “error” and

“rate of change of error” are used (Mamdani and Assilian, 1975).

Fuzzification

Membership functions describe how the input variable is fuzzified. Popular mem-

bership functions are; triangular, trapezoidal, Gaussian, Bell-shaped, Z-type, S-type,

and pi. Triangular membership functions are the most commonly used membership

functions. Membership functions for a variable can be of any number and they can be

different to each other. Shape and number of the output membership functions could

be different than those of input membership functions. Generally there are three ways

to decide the shape and number of input and output membership functions:

• Experts knowledge

• Simulation and experiments

• From examples

Some of the standard membership functions shapes are given in Figure 2.7

(Altrock, 1995) and Figure 2.8.

16

Figure 2.7: Standard membership function shapes. (Redrawn from Altrock (1995))

Figure 2.8: Trapezoidal and Triangular membership functions.

17

Rule-base

Fuzzy if-then rules are the heart of FIS. These rules relate the antecedent part of

the FIS to the consequent part of the FIS, input variables and membership functions

are called antecedent part of FIS and output variables and output membership func-

tions are called consequent part of FIS. The efficiency of the system largely depends

on how these rules are developed and how many are developed. In the FIS systems

where learning agents are used, rules can be generated, modified and or deleted.

Generally there are three ways to develop these rules:

• Experts knowledge

• Simulation and experiments

• From examples

A simple rule base is shown in Table 2.1

Table 2.1: RuleBaseExample

No Rule Weight

1 IF Error is negative AND DeltaError is negative THEN Output is

positive

1.00

2 IF Error is negative AND DeltaError is positive THEN Output is

zero

1.00

3 IF Error is positive AND DeltaError is negative THEN Output is

zero

1.00

4 IF Error is positive AND DeltaError is positive THEN Output is

negative

1.00

18

Defuzzification

The aggregate of the output membership functions is a fuzzy set and to use it

in the real world it should be de-fuzzified with a single number. The most popular

method of defuzzification is centroid, in which the centre of the area under the ag-

gregate curve is calculated. Some other methods which are also used are smallest

of maximum, largest of maximum. Popular defuzzification methods are shown in

Figure 2.9 (Wang, 1997).

Figure 2.9: Defuzzification methods, (a) Centre of Gravity; (b) Maxima. (Redrawn

from Wang (1997))

19

Mamdani versus Sugeno Type FLC

The two most commonly used FIS types, Mamdani and Sugeno, differ in de-

fuzzifying output variable. The two methods are same except for the evaluation of

output value of the output variable. The Mamdani method uses the fuzzy output

membership functions, whereas Sugeno type (Sugeno and Takagi, 1985) uses a single

spike as the output membership function. In many cases Sugeno is more efficient and

the output membership function is called a singleton output membership function.

Sugeno method can be thought of as pre-defuzzified fuzzy set. Mamdani type is the

most commonly used and is largely depends on human experience where as Sugeno is

easy to use where computation is involved as in ANFIS (Adaptive Neuro Fuzzy Infer-

ence System). Although Mamdani method has more acceptance and is intuitive but

Sugeno is more suitable for the processes where control is closed to linear techniques

like PID control (Sivanandam et al., 2007).

2.3.2 Fuzzy Control Systems

The use of fuzzy logic as a tool for the development of control systems was first

projected in development of a fuzzy control system for a laboratory-scale steam engine

boiler (Mamdani and Assilian, 1975). Although the system was successful and many

commercial and industrial applications still use the same principles of fuzzy logic

control (FLC) developed by Mamdani, the control system had no online learning

technique associated with it. To tune the parameters of the controller or change the

rule base, one has to take the controller offline, change the parameters, and then

observe the results. This process goes on and on until the perfect, or near-perfect,

controller is formed. Mamdani used pressure and speed as the input variables and

heat and throttle as the output variables of the Fuzzy logic controller, and compared

its results with the fixed Digital controller. The FLC performed better than the Direct

Digital Controller (DDC) (Mamdani and Assilian, 1975). From this point, fuzzy logic

control started to appear in the literature as an alternate method of control in a

number of different disciplines.

20

Application of Fuzzy technique to petrochemical processes, especially the control

of a distillation column, grew slowly throughout the 1980s and 1990s, on the other

hand the application of fuzzy controls in the manufacturing, electronics, and robotics

was quickly accepted. The highly complex nature of petrochemical plants and the

high cost of investment associated with the stable operation of a control system, have

forced the petrochemical industry to wait for the fuzzy technology to mature before

applying it to process control systems.

Although practical FLC system have been in industrial use since 1980 (Mukaidono,

2001), a great difference can be found between the industrial and academic fuzzy sys-

tems. There are three main reasons behind this attitude, firstly the difference of

level of skill and knowledge of fuzzy systems is far greater in academic circle than

that of industrial end users, secondly industrial control system manufacturers are still

waiting for fuzzy technologies to become bit easier to implement on the shop floor,

and thirdly government rules and regulations prohibit industry to use some of the

technologies, like pharmaceutical industry.

During the literature survey, it is found that almost all of the fuzzy systems

proposed by the academics had learning algorithms which tuned the rule base or even

tuned the membership functions parameters too. These fuzzy systems were mostly

developed in the very controlled atmosphere of university labs. But when looking

into the industrial level fuzzy softwares it was found out that no one has this type of

elaborate learning algorithm in their software suite. The fuzzy system software used

for this research didn’t have any learning algorithm. However one of the industrial

software products for fuzzy control, DeltaV from Emerson Process Management, has

an online tuning of the system which adjusts scaling of the membership functions but

not more than that. However it must be noted that even if learning is not taking place

in the computing machine it is still going on human brain which modifies the rules

and shape of the membership functions as per his/her observations. It means learning

is an important part of fuzzy controller development though it may not part of fuzzy

controller algorithm. As explained in the above paragraph there are reasons behind

this attitude. In the process control world, systems are huge but not as complex

21

and integrated as could be found in aerospace, machine control, or robotics so it

means that there are less variables involved and need for modifying the rule base and

membership functions does not exist. In the same way, code issues and regulations

do not allow some industrial plants like those of food processing and pharmaceutical

to change and test control parameters randomly.

The other major difference found during the survey was the type of member-

ship function. In academic world dozens of membership function types, shapes, are

being explored and suggested but in the industrial world one or maximum of two

were available for the development of the system. DeltaV offers none to select from

and uses only Triangular type membership functions. Rockwell offers the option of

choosing between S − type and Trapezoids only. The explanation could be principle

of incompatibility (Zadeh, 1973)

“As the complexity of a system increases, human ability to make precise and

relevant (meaningful) statements about its behaviour diminishes until a threshold

is reached beyond which the precision and the relevance become mutually exclusive

characteristics. It is then that fuzzy statements are the only bearers of meaning.”

At the end it can be safely said that both sectors are doing what they are sup-

posed to do.

The research articles can be categorized broadly into the following three cate-

gories:

1. Fuzzy systems without online learning

2. Fuzzy Systems with Supervised Learning (SL)

3. Fuzzy Systems with Reinforcement Learning (RL)

1. Fuzzy Systems without Online Learning

As obvious from their category name, fuzzy systems falling in this category do

not have any kind of learning system means once they are developed and applied they

will use their fixed rule base that is stored into them. While on the other hand fuzzy

systems, which use some kind of learning method can constantly develop new rules

22

Figure 2.10: Structure of a conventional fuzzy inference system.

and can also delete some obsolete ones as a way to update the rules as required by

the changing environment. Fuzzy systems without learning are simpler and easier to

develop and are more popular in the process industry. They find applications where

variables are not changing much and parameters are relatively constant but they have

the drawback that tuning them for a changed environment takes a lot of time and

effort.

Klett (1993) formulated this kind of model in 1993. His proposed model was very

successful to a small-scale laboratory type experimental batch distillation application

where there is not any problem of continues feed flow. Another article by Fileti et al.

(2002) also presented the application of fuzzy control to a batch distillation process

and although they have reported a success but at the same time they have admitted

that some of the conditions of the column were considered as constant. Glankwamdee

et al. (1999) presented the idea of fuzzy control as supervisory control to the legacy

PID controller and they had success up to a certain limit but as they rightly admit

that rule changing is a time consuming process.

Aliev and Mamedova (1990) discussed and presented the following theorems to

construct a fuzzy model as follows:

“DEFINITION: Let Ri = ∪ni=1Xi × Yi. If for each Xi,

Yi = Xi ◦ R, (2.6)

23

then the compositional rule of inference is executed strictly; otherwise it is done ap-

proximately. Below, theorems about the strict execution of the compositional rule of

inference are formulated, defining the conditions of minimizing the adequacy crite-

rion.

THEOREM 1: Let R be a regular fuzzy relation matrix:

R = X × Y (n = 1)

If fuzzy sets X and Y are normal, then the Eq.(2.6) is executed strictly.

THEOREM 2: Let non-regular fuzzy relation matrix R = ∪ni=1Ri be given. Here

Ri = Xi × Yi are regular relation matrices. If fuzzy sets Xi and Yi(i = 1, ...., n) are

normal and satisfy the conditions

∪ni=1Xi = φ ∪n

i=1 Yi = φ

then the Eq.(2.6) is executed strictly.”

It implies that the Eq.(2.6) is fully applied when fuzzy input and output mem-

bership function values are normal, meaning their values are 1, and if individual value

is not normal but the whole set value is normal and the set is not empty then Eq.(2.6)

is also fully applied otherwise it applies approximately.

Neves-Jr et al. (1997) presented the idea of Orthogonal Matching Pursuit (OMP)

for constructing fuzzy models. OMP is an extension of matching Pursuit (MP), which

works on a greedy mechanism for finding the optimal solution from a directory of

possible solutions. Here “greedy” implies that algorithm aggressively search for the

best solution.

“In the OMP algorithm, a model is developed for the dependence of an addi-

tionally selected vector on the previously selected vector. Using this dependency

model, the model is extended such that the new residual error is orthogonal to all the

previously selected error” (Neves-Jr et al., 1997). The method results show it was

successful but author agrees that it failed on some occasions.

24

2. Fuzzy Systems with Supervised Learning

Supervised learning approach needs a teacher to tell the learner what actions

to take (Er and Zhou, 2006). Supervised learning is most commonly used in pat-

tern recognition among other applications. The most popular techniques are Genetic

Algorithm (GA) and Artificial Neuro-Network (ANN).

Fernandez et al. (2000) presented an application of Adaptive Neuro-Fuzzy ap-

proach to control a distillation column but only up to the level of simulation hence

its practical implementation is still a question. Luo et al. (1995) used Fuzzy-Neural-

Net based inferential control for a distillation column and the author claims that the

algorithm is running successfully for more than two years but still the results are

reasonable and not perfect.

Figure 2.11 describes how a supervised learning works, it shows a Self-learning

Fuzzy Logic Control (SLFLC). The basic level is a simple fuzzy logic controller, the

second level is the self-organizing or self-learning which supervises the basic level by

monitoring its performance, subsequently generating and modifying the fuzzy control

rules in an online manner (?).

3. Fuzzy Systems with Reinforcement Learning

Reinforcement learning (RL) is also called unsupervised learning as it does not

need teacher to teach it which actions to take in a given situation. Reinforcement

approach is that the learner must discover itself which actions will yield the most

reward by trying all the possible actions in the action set(Sutton and Barto, 1998).

Fuzzy Q Learning is one of the most favourite method of RL.

The theory of Q-Learning convergence was proved by Christopher Watkins in

1989. Watkins and Dayan (1992) proved that Q-learning is a form of model-free

reinforcement learning. The greatest advantage of this method is that there is no

need to remember situations or actions for more than a short period of time (Watkins,

1989).

Q-learning dose not need model to check that which of the available action is

25

Figure 2.11: A supervised learning fuzzy controller. (Redrawn from Szczepaniak

(2000))

suitable for the environment. Lately Q-learning has been enhanced by a new technique

called delayed-Q learning.

Glorennec (1994) was one of the first who proposed the fuzzy version of Q-

Learning called Fuzzy Q-Learning (FQL) and Dynamic Fuzzy Q-Learning (DFQL).

Glorennec and Jouffe (1997) proposed an adaptation of Watkins Q-Learning for

Fuzzy inference systems where both the actions and the Q-functions are inferred from

fuzzy rules. They compared this learning technique with Genetic Algorithm approach

and proved that Q-Learning is more effective than GA.

Margaglio et al. (1997) applied the Q-learning technique for on-line tuning of the

fuzzy controller to control the composition of a distillation column. The technique

was successful in some respect although not perfect and it was applied with only two

inputs, product composition (Xb) and its set point (Xbr), of a distillation column

where as practically there are more than one variable affecting the process. The main

limitation of that model was not addressing the dynamics of the feed into the DC,

which was duly admitted by the team that work is required to make it a real world

26

application.

Jouffe (1998) used Fuzzy Actor-Critic Learning (FACL) and Fuzzy Q-Learning

(FQL) to tune online the conclusion part of Fuzzy Inference System (FIS). He used

these techniques on number of real world problems and reported the success.

Gaskett (2002) used Q-Learning to reduce the programming for the robot and

to increase its abilities. Er and Deng (2004) used Fuzzy Dynamic Q-Learning to tune

the Fuzzy Inference System online of the wall-following mobile robot. Er and Zhou

(2006) used the Q-Learning to generate not only the consequent part but also the

preconditioning parts of the Fuzzy Inference System.

All above scholars have been attracted to Q-Learning due to its many features

including simple structure as it mainly depends upon the feedback of the system but

it has the drawback that its response time is large enough to produce instability in

fast dynamic system. As Q-Learning have been chosen by majority of the above

researchers as a method of learning so it is appropriate to review the working of this

algorithm in detail.

Q-Learning

Q-learning comes from Q-Function and that function can be defined as optimal

action-value function. Q-Learning basically is one of learning algorithm from a long

list of learning algorithms which reward their agent based on their previous action.

Q-learning has been widely used for the reinforcement learning and especially

for fuzzy systems developed for chemical process. Q-Learning belongs to a family

called Temporal Difference Method and has been explained by Glorennec (1994) as

an environment in which agents learn themselves by comparing their actions and the

results of those actions. Q-learning tries to predict the future reinforcement from the

set of already established state-action pairs.

Advantages of Q-Learning are:

• No model is needed

• No separate (supervised) learning of an agent

27

• Can be applied on complex systems where it is difficult to obtain a dynamic

behaviour of the process

• Inexpensive, less computing power is needed

• Simple to apply

Disadvantage of Q-Learning is that it is slow because it waits for the result to

be available of its previous action.

To understand how Q-Learning works suppose there are two input variables and

one output variable and as per generic fuzzy logic principle they can be expressed as

follows:

If A1 is A1i and B1 is B1i Then Y is Yi. (2.7)

It can be explained that change in input variables result in corresponding change

in output variable depending upon the type of membership functions. The relation

between input and output variables can be linear and non-linear depending upon the

membership functions and this is one of the strength of FLC over PID controller that

in contrast to the PID controller whose behaviour is linear across the board the FLC

changes its behaviour from linear to non-linear across the profile depending upon the

process dynamics.

The output of the FIS is the aggregation of all rules which can be given as:

Y =N∑

i=1

aiYi, (2.8)

where ai is the weight of the rule i and N is the number of rules.

By introducing Q-learning into the fuzzy controller the controller is forced to

choose the action based on not only input variable values but also the result of the

previous action of the controller. In this way the controller will have more knowledge

in selecting action for a given input variables.

It means that the output part of the rule-base has to carry number of different

values J against the same set of input parameters. The rule-base is now modified in

the following way;

28

If A1 is A1i and B1 is B1i

Then Y is Yi1 with attributes q[i, 1]

or Y is Yi2 with attributes q[i, 2]

.

.

.

or Y is YiJ with attributes q[i, J ]

The above expression shows that learner has to choose between the different rules

for the same set of input variables each time when the feedback shows that controller

is not performing well.

As Figure 2.12 shows, the Reinforcement learning is an unsupervised learning and

does not need teacher to learn what to do and how to do. Reinforcement learning

depends on feedback of the controller and modifies the rules basis on the performance

of the previous state of the manipulated (output) variable. Reinforcement learning is

successful where process is difficult to model and the plant behaviour is highly non

linear. It works by rewarding the FIS by comparing the current state of the output

variable against the previous state.

Latest literature on the topic of fuzzy controller application to distillation column

control can be found in Khazraee et al. (2011) that applied a Adaptive Neuro-Fuzzy

Inference System (ANFIS) on a reactive batch distillation column, Kapoor et al.

(2011) that experimented by applying classical PID controller and intelligent Fuzzy

controller to control the composition of a reactive distillation column and reported

that fuzzy performed better than the classical PID controller, Lima et al. (2011) ex-

perimented with a high boiling point crude oil in a molecular distillation process and

compared the results of mathematical model to that of fuzzy model and claimed that

results were comparable and fuzzy models took less time and effort to develop than

their mathematical models, Baloch et al. (2010) concluded in their experiment that

29

Figure 2.12: A self-learning layer added to a fixed rule base fuzzy controller. (Redrawn

from Szczepaniak (2000))

building a conventional model for a non-linear process is difficult than the model de-

veloped in ANFIS and even that ANFIS model whose data was taken from the actual

distillation column was not successful which shows error in their model, Salahshoor

and Hamzehnejad (2010) developed a novel method of modelling a non-linear process

by using ANFIS, and Sun et al. (2010) applied a self-adaptive intelligent fuzzy-Smith

control strategy to control a continuous process for refining high purity acetonitrile

synthesized by dimethyl sulphate and sodium cyanide.

30

Chapter 3

The Proposed Method

The proposed fuzzy inference system is a classic fuzzy logic controller details

of which are presented in this chapter. Also presented are the details of distillation

column and the selection of control structure. Fuzzy control system is often referred

to as Fuzzy Inference System (FIS) or Fuzzy Logic Controller (FLC) so now all three

terms will be used alternatively.

The basic concept of this thesis was to develop a fuzzy logic controller, preferably

by using a industrial control system software, for a binary distillation column that can

be used later in a full commercial scale plant or on a pilot plant in the petrochemical

industry. Further a comparison between the performance of FLC and PID controller

is added to have a better understanding of their weaknesses and strengths. The

comparison will help in future while selecting a type of controller for a particular

application. A general overview of the concept is presented in Figure 3.1.

3.1 The Fuzzy Inference System Design

The most important aspect of the design of the fuzzy controller is the application

itself. For example the FLC designed for a discrete process control will be different

from the one for a continuous process control application. Similarly even within the

continuous process control one fuzzy system could be different from the other fuzzy

system. One fuzzy system may need only one input variable while the other need two

31

Figure 3.1: General overview of the experiment concept.

or three input variable to function properly and this is the beauty of fuzzy control

that it can be easily modified to the requirement of the particular application.

The fuzzy controller developed for the application of this thesis is a Takagi-

Sugeno type fuzzy controller. Sugeno type fuzzy systems use defuzzified outputs

called singletons which make the system simpler. As this thesis focus more on the

industrial application and environment in contrast to most other scholars research

which deal with the academic setup that is why simpler option is selected. In the

same way only two major input variables are used as 95 percent of the process control

applications falls in this category. Input membership function chosen are Trapezoids,

again selection was influenced by the application as these type of membership func-

tions are easy to understand. Number of rules are also kept to minimum, only thirteen.

Output membership function are singletons and the number of output variable is one,

again 95 percent of the process control applications falls in this category. Number of

membership functions for input and output varies from two to nine.

FIS system for this experiment is consist of following 5 components that are

shown in block diagram in Figure 3.2 and an equivalent FIS in Rockwell fuzzy designer

software environment in Figure 3.3;

32

Figure 3.2: General overview of the proposed fuzzy system.

Figure 3.3: Equivalent fuzzy system in Rockwell software (FuzzyDesigner).

33

1. Input variables

2. Method of fuzzification through membership functions for input variables

3. Rule-base (if-then rules)

4. Method of defuzzification through membership functions for output variables

5. Output variables

Input Variables

Input variables for this experiment are derived from the process variable of the

control loop. In this case it is the temperature of the tray 50 of the distillation col-

umn. Four input variables are being used, TempError, DeltaError, NLTemp, and

NLLTemp. TempError determines the offset between the set point and the process

variable and DeltaError calculates how fast or slow the offset is increasing or decreas-

ing while the remaining two input variables are specialized input variables only active

in particular situations. NLTemp helps in bringing out controller when controller

falls into extreme non-linear high temperature region of distillation column whereas

NLLTemp does the same thing when controller falls into the extreme non-linear low

temperature region of distillation column. In most of the process control applications

of fuzzy control two major input variables namely error and rateofchangeoferror

are used and this is also true for this experiment.

Fuzzification

Rockwell fuzzy designer offers only S − type and Trapezoids shapes of member-

ship functions. As Trapezoids are the most common form so they were picked for

this experiment. Also during Matlab experiments some results were available that

helped in selecting the membership functions. Nine terms, labels, for TempError

input variable were used, namely BigBigNegative, BigBigPositive, BigNegative,

BigPositive, BigNegative1, BigPositive1, SmallNegative, SmallPositive, and Medium.

See Figure 3.4. Five terms, labels, for DeltaError input variable were used, namely

34

Figure 3.4: Error variable Input Membership functions in Rockwell software (Fuzzy-

Designer).

BigNegative, BigPositive, SmallNegative, SmallPositive, and Medium, see Fig-

ure 3.5. Two terms, labels, for NonLinearTemp input variable were configured

namely high and low but only one, high, was used, see Figure 3.7. Two terms, la-

bels, for NonLinearlowTemp input variable were configured namely high and low

but none of them was used, see Figure 3.7.

With reference to Figure 3.4 and Figure 3.5 a point is worth mentioning that

membership functions do not always add up to 1 as generally is assumed. From

the results in chapter 4 we have observed that this has not any bad effect on the

performance of the fuzzy controller.

Rule-base

Total 13 rules, Figure 3.8, were developed to capture all the possible scenarios

of relationship among the input and output membership functions but one was made

passive as it had no significance in the current set of data for this study, however it

35

Figure 3.5: Delta error variable Input Membership functions in Rockwell software

(FuzzyDesigner).

Figure 3.6: Non-Linear variable Input Membership functions in Rockwell software

(FuzzyDesigner).

36

Figure 3.7: Non-Linear Low variable Input Membership functions in Rockwell soft-

ware (FuzzyDesigner).

37

could be used wherever a low temperature nonlinear region is present in the distillation

column temperature profile. It was later felt that number of rules were still high for

a common application in process control and could be minimized further but time

constraints did not allow further experimentation in this regard. The rule base in

Figure 3.8 in text format is shown in Table 3.1.

Figure 3.8: Rule base in Rockwell software (FuzzyDesigner).

38

Table 3.1: Rockwell RuleBase Text

No Rule Weight

1 IF TempError is Big Big Negative THEN Output is Big Positive 1.00

2 IF TempError is Big Big Positive THEN Output is Big Negative 1.00

3 IF TempError is Medium AND DeltaError is medium THEN Out-

put is Medium

0.3

4 IF DeltaError is Big Negative THEN Output is Big Positive 1.00

5 IF DeltaError is Big Positive THEN Output is Big Negative 1.00

6 IF TempError is Big Big Negative AND DeltaError is Small Nega-

tive THEN Output is Small Positive

1.00

7 IF TempError is Big Big Positive AND DeltaError is Small Positive

THEN Output is Small Negative

1.00

8 IF TempError is Small Negative OR Big Negative THEN Output

is Big Positive

1.00

9 IF TempError is Small Positive OR Big Positive THEN Output is

Big Negative

1.00

10 IF NonLinearTemp is High THEN Output is Big Negative 1.00

11 IF TempError is Big Negative 1 THEN Output is Big Positive 1.00

12 IF TempError is Big Positive 1 THEN Output is Big Negative 1.00

13 IF NonLinearLowTemp is Low THEN Output is Big Positive 1.00

39

Defuzzification

As the chosen FIS is Takagi-Sugeno type fuzzy controller so the defuzzifica-

tion membership function are Singleton. Five terms, labels, namely, BigPositive,

BigNegative, Positive, Negative, and Medium were used. Singleton membership

functions are simple, use less computing resources, easy to work with, and better

suited for process control applications. Output Membership functions in Rockwell

software are shown in Figure 3.9.

Figure 3.9: Output Membership functions in Rockwell software (FuzzyDesigner).

3.2 The Controller Software

Matlab software for the development and execution of fuzzy controller has been

the favourite choice of the scholars for distillation column control. Being practising

control engineer the author had the wish to develop a fuzzy controller in the real in-

dustrial software like Honeywell Experion, Rockwell PlantPAX/AllenBradley, Emer-

son DeltaV, Yokogawa CentumVP, to name a few, being used by the petrochemical

40

industry .

While exploring the possibility it was found out that at least two of control sys-

tem manufacturers, Emerson DeltaV and Rockwell AllenBradely, has now introduced

fuzzy logic controller in their suite of applications. Further investigations revealed

that DeltaV software is a kind of black box and has no flexibility in choosing and

developing of the fuzzy controller components like membership functions and rule

base while on the other hand Rockwell software offers the flexibility of developing

the fuzzy controller right from selecting membership functions, developing rule base,

selecting number of variables and the type of defuzzification. So decision was made

to use the Rockwell software for the development of fuzzy controller.

3.3 The Controller Hardware

While it was quite possible to run the fuzzy controller entirely in a simulation

environment of Rockwell RSLogix Emulate5000 environment and have the results

close to real controller but as the Rockwell AllenBradley ControlLogix L62 PLC

(programmable logic controller) was available in the facility, courtesy of Zeton incor-

porated, Burlington Ontario, where the author works as a full time control system

engineer. It was a good opportunity to use the actual industrial grade PLC in the

study. After development the fuzzy controller software was downloaded into the PLC

and ran it as it run normally in a typical industrial process plant.

Controllogix L60 series of PLC’s are the premium brand of Rockwell/AllenBradley

and are used in the entire spectrum of industrial applications right from nuclear power

plants, oil refineries, auto manufacturing to food processing and waste water treat-

ment facilities. The application of fuzzy controller in this specific PLC brand will

surely boost the level of confidence of the fuzzy logic technology among practising

process control community.

41

3.4 Experiment Setup

Initial proposal was to develop distillation column in a simulation environment

and later use the final controller design on the real distillation column but due to

number of constraints real distillation column option was dropped for future work

and study was limited to simulation only.

As Rockwell fuzzy designer was preferred over Matlab for the development of

fuzzy system so at the end there were following three options available for the setup

of the experiment in which distillation column could be dynamically mimic in real

time:

1. Rockwell fuzzy controller in L62 PLC and Chemcad distillation column simu-

lator in a PC using OPC (OLE for process control) link

2. Rockwell fuzzy controller in L62 PLC and Myanah Mimic simulation software

for distillation column in a PC using OPC link

3. Rockwell fuzzy controller and distillation column simulation downloaded into

L62 PLC. (Chemcad distillation column simulation results programmed into

Rockwell ControlLogix software and then link them internally to fuzzy con-

troller)

CHEMCAD from Chemstations Inc. is one of the leading simulation software

for the petrochemical industry. The software was available in the facility, courtesy of

Zeton incorporated, Burlington, Ontario, but detailed study revealed that linking the

CHEMCAD simulation running in a separate PC with the fuzzy controller running

in a PLC will be a daunting task which at the end will not even possible because

CHEMCAD is not inherently build for this purpose.

In second option Myanah local representative was contacted that if the soft-

ware could be temporarily licensed for academic purpose but certain limitations and

corporate restrictions prevented Myanah from issuing the license. Myanah Mimic

simulation software would have been a perfect combination for this type of control

42

setup as this software has been designed to work directly with Emerson DeltaV con-

trol software and hardware running on the same PC and work with other PLCs and

process controllers through industry standard OPC link.

At the end decision was made to use the third option, run the distillation col-

umn simulation in the CHEMCAD and then programme the results into Rockwell

RSLogix5000 software and to link them to fuzzy controller internally to have the real-

time setup and finally download this programme into L62 PLC. Figure 3.10 shows

the experiment setup.

Sensitivity analysis was carried out in Chemcad to establish the relationship

between variation in steam flow and corresponding change in tray 50 temperature

around the base condition of reboiler duty and tray 50 temperature, tray 50 temper-

ature was selected as the point of control of composition. The exercise was repeated

for all the eight cases of feed flow and feed composition. Steady state models for de-

termining the best control structure have been in use for a long time and if used with

experience and general knowledge of distillation columns are adequate for addressing

most of the problems and proves to be better than dynamic models (Fruehauf and

Mahoney, 1993) as dynamic models need more resources than steady state models. A

point of caution however is steady state models have their limitations too and should

be used intelligently (Mahoney and Fruehauf, 1999). The two stand out limitations of

steady state models are their inability of responding to initial startup of the operation

of the column when there is maximum control action taking place and ignoring the

effect of liquid holdup on column trays. In applications where prior knowledge of the

process is unknown dynamic simulation models will be must but in other applications

where enough information is at hand then steady state models can be used along with

the experience and general knowledge of the operation of distillation column. Steady-

state models could also helpful in determining optimal tray locations for inferential

control by finding the trays whose temperatures show the strongest correlation with

product composition (Riggs, 2008). In the current study steady state model was used

to have a control relationship between the reboiler duty and the tray 50 temperature

response so that this relationship can be used to highlight the nonlinearity in the

43

distillation column variables but at the same time the importance of dynamic models

can not be ignored as dynamic models give the complete picture of the operation of

the distillation column.

Refer to Figure 4.2, a dead time block and a lead-lag block was added to the

control routine between the controllers and their respective distillation columns to

introduce the process dead time and the process lag time which is the characteristic

of the actual distillation column. The values used for those blocks were in the order

of seconds and were identical for both controller routines. The values for this partic-

ular application came from the experience of the people who are involved with the

designing of distillation columns in their day to day job.

Figure 3.10: The diagram of experiment setup.

3.5 Distillation Column under Study

The theoretical distillation column chosen for this study is a binary distilla-

tion column, binary distillation column is one which separates two products from

the mixture of feed coming into the column. The top product will be one with

lighter molecular weight (lower boiling point) and bottom product will be one with

the heavier molecular weight (higher boiling point). A mixture considered in this

44

Figure 3.11: Proposed distillation column and control structure.

study is makeup of methanol and water. Methanol has lower boiling point, 65 degree

Celsius, than water, 100 degree Celsius, so it will be converted into vapours earlier

than water and will be collected from the top draw and water will be collected from

the bottom draw. Figure 3.11 shows the hypothetical distillation column and con-

trol structure. Figure 3.12 shows the hypothetical distillation column in Chemcad

simulation environment.

3.5.1 Salient Features of the Distillation Column

Salient features of the selected distillation column at the base conditions are as

follows;

Number of trays = 70

Pressure drop across column = 5 psig

Mass reflux ratio = 2.85

Reboiler duty = 0.5347 MMBtu/hr

45

Figure 3.12: Equivalent Distillation column in Chemcad simulation environment.

Condenser duty = -0.3920 MMBtu/hr

Feed stream stage = 35

Feed mixture = Water and methanol

Feed temperature = 25.00 degree Celsius

Feed pressure = 15.30 psig

Feed flowrate = 950.00 lb/hr

Feed (water) flowrate = 700.00 lb/hr

Feed (methanol) flowrate = 250.00 lb/hr

Methanol percentage = 26 percent

3.5.2 Feed Stage Base Conditions

Feed stage, tray 35 base conditions are as follows;

Temperature = 100.00 degree Celsius

Pressure = 17.73 psig

Liquid flowrate = 1625.59 lb/hr

46

Vapor flowrate = 684.15 lb/hr

3.5.3 Control Stage Base Conditions

Control stage, tray 50 base conditions are as follows;



Liquid flowrate = 1628.48 lb/hr

Vapor flowrate = 903.03 lb/hr

3.5.4 Feed Stream Base Conditions

Feed stream, inlet product, base conditions are as follows;



Methanol flowrate = 250.00 lb/hr

Water flowrate = 700.00 lb/hr

3.5.5 Distillate Stream Base Conditions

Distillate, top product, base conditions are as follows;





3.5.6 Bottoms Stream Base Conditions

Bottoms, bottom product, base conditions are as follows;




47


Detailed reports of column and reboiler profiles are attached at the end as ap-

pendixes.

In the study mass flows are considered instead of molar flows because most

industrial distillation columns use mass flow or equivalent but not the molar flows.

Also instead of using a two point control, the single point control is used (in two

point control two separate control loops are used for top and bottom products while

in single point control only one loop is used to control the composition of top and

bottom products). Two point controls can result in saving energy but the control

become so complex that advantages are not as great so single point control is mostly

used in the industry (Fruehauf and Mahoney, 1993). In single point control a normal

practice is to set the reflux to maximum disturbance rejection condition and control

the composition of the column by maintaining the tray temperature by modulating

steam flow and this results in consumption of more energy than if reflux were also

controlled in parallel to the steam flow in two point control structure.

In the design of this study the feed stream is the demand stream which means

that feed entering into the column has to be stay constant. Following are the expected

disturbances that are being considered for the study of the control of the distillation

column:

1. Feed rate flow changes

2. Feed composition changes

Pressure control is not being considered in the control structure as pressure can

be kept constant by different means, like a vent in the condenser, designed control

structure is independent of pressure control parameters.

For the inventory (level) control of the holdup tank and boiler a decision has

to be taken between the reflux versus distillate and boilup versus bottoms flow. If

the ratio is greater than 10:1 then the stream with larger flow has to be selected as

controlling the level (Mahoney and Fruehauf, 1999). The column under study does

not fall in this category. In the selected control structure mass flow reflux ratio has

48

to be kept constant so distillate flow is used for controlling the level of holdup tank.

The bottoms stream flow has to be used for controlling the level of boiler as boilup

flow is already being taken for keeping the temperature at tray 50 constant. One of

the advantage of controlling bigger stream is that it can be used to offset the bigger

disturbances in the system.

Choosing the composition control scheme is one of the greatest challenges in the

design of distillation column control. Usually typical distillation column has 5 degree

of freedom with the following valves available as manipulated variables:

1. Feed valve

2. Distillate valve

3. Reflux valve

4. Bottoms valve

5. Heat input valve

Three out of the above five valves are already tied to the controlled variables like

feed flow, holdup and boiler tank level, so it comes to remaining two valves namely

reflux and heat input valve. If the composition is controlled by using the reflux valve

it is called direct feed-split control and if heat input valve is used to control the

composition then it is called indirect feed-split control. Indirect feed-split control is

used as it has two advantages over the former(Mahoney and Fruehauf, 1999):

1. Temperature-boilup loop response time is faster

2. Due to inventory in the holdup tank a smooth downstream flow is guaranteed

Although independent online analyzer can be used to control the composition

of distillate and bottoms but this will result in a complex control due to process

interactions between the two independent loops, will be costly, and with larger lag

time. The author used temperature control of the tray 50 in the distillation column

to control the composition. By interactive open loop testing a sensor location can be

49

determined where the effect of manipulated variable in either direction results in a

approximate linear response by the temperature sensor. In this study sensor location

was chosen after analyzing the column profile and reboiler duty profile where stable

temperature region is between tray 40 and tray 60 and between tray 20 and tray

30. Experimentation showed that tray temperatures in the region of tray 20 to tray

30 are less sensitive to the change in steam flow than the tray temperatures in the

region of tray 40 and tray 60. Consequently tray 50 temperature was chosen for the

control. Further by using the worst case scenarios of feed flow rate and composition

change a fixed reflux can be determined that will satisfy the full range of operating

condition and required composition of the final draws both from top as distillate and

from bottom. The temperature measured at that point will be the setpoint of the

operating conditions. In this study reflux flow rate was fixed at 2.85 to determine

the operating parameters and temperature measured at tray 50, 101.0 degree Celsius,

was used later as setpoint for control of the composition of top and bottom products.

Some readers might wonder that the chosen setpoint is already higher than the water

boiling point of 100 degree Celsius, but keep in mind that the column under study

is a pressurized column where boiling points of components move upward than what

they have normally under normal atmospheric pressure.

50

Chapter 4

Results and Discussion

In this chapter results are presented, discussed, analyzed, and summarized. The

RsLogix5000 software setup is presented to show how the different segments of the

software were arranged for both function block diagram and chart. Step by step tuning

procedure is laidout for both FLC and PID controllers. Total of 13 experiments are

run to show the performance of the FLC and PID controllers in the form of charts.

Physical setup of the experiment is shown in Figure 4.1.

Figure 4.1: Physical setup.

51

Experiments were conducted with different feed flow and feed mixture combi-

nations. Results were compared after tuning the controllers with their optimum

parameters i.e. FLC controllers membership functions shapes were adjusted, rule-

base was trimmed and weights were adjusted and in the same way PID controllers

proportional band, reset, and rate were also tuned aggressively to have the best re-

sults at the base condition of distillation column operation. It is admitted that FLC

controller took more time to adjust its parameters than its counterpart. When both

controllers started performing optimally at the base conditions then actual tests were

conducted to see their behaviour at different disturbances.

Overall results showed that FLC is more stable than PID and is less susceptible

to disturbances. It dealt both flow changes and composition changes efficiently than

PID controller. It is also admitted that PID was more precise to the level of decimals

in some of the experiments than FLC although both controllers performance were

within acceptable threshold.

4.1 Function Block Diagram Arrangement

As explained earlier two identical distillation column functions are created and

are connected to the output of the FLC and PID controllers. In this arrangement

both distillation columns are facing exactly the same disturbances but are operating

independently and are controlled by their respective controllers without affecting

other. At the top left of the diagram is the PID controller and at the bottom left is

the FLC controller where their respective distillation columns are on the right side. A

subtraction block is used to generate the error and an alarm block is used to generate

the rate of change of error. PID controllers function block do not need these blocks as

they have been developed to have these functions integrated to their function blocks.

A set point tag is created which feeds both controllers at the same time. A fuzzy PV

tag and a PID PV tag are created to map it into charts, please note mapping of PV

by this arrangement had no effect on the results. Different make-up of the function

blocks for the two controllers also had no effect on the results, this was done only

52

Figure 4.2: Function block arrangement for the experiment in Rockwell RSLogix5000

software.

because the way function blocks created by the Rockwell automation are not exactly

same. Functional block arrangement of the experiment is shown in Figure 4.2.

4.2 Chart Arrangement

Only necessary markers were used to clarify and emphasis the behaviour of con-

trollers. Red pen was used for the set point which is of course is constant for the

experiment of disturbances when flow and composition changes the tray 50 tempera-

ture has to be remain constant and it is the function of the controllers to adjust their

outputs, by modulating steam flow, so that temperature at tray 50 remains constant

which in turn guarantees the designed specifications of the top and bottom products

at the base conditions. This red pen will always be at 101.0 degree Celsius except

for experiments where set point was changed too drastically to see the behaviour of

controllers in worst out of design conditions. Blue pen is the process variable of the

53

Figure 4.3: Chart arrangement for the experiment in Rockwell RSLogix5000 software.

distillation column, temperature at tray 50, controlled by PID controller; it has to

be close to 101.0 degree. Light green pen is the process variable of the distillation

column, temperature at tray 50, controlled by FLC controller; it also has to be close

to 101.0 degree. Chart arrangement of the experiment is shown in Figure 4.3

4.3 Tuning of Controllers

Before taking on experiments to observe the performance of both controllers;

they were tuned optimally. The factors considered for the optimal tuning were;

• Rise time

• Settling time

• Overshoot

The procedure for tuning can best be described as manual tuning. Both con-

trollers were tuned intuitively although for PID controller the built-in auto-tune func-

54

Figure 4.4: Fuzzy Designer on-line tuning.

tionality was also used for initial parameters. The controllers were tuned for the spe-

cific narrow band of near-linear band of temperature profile. Tuning was done on-line

as Rockwell software allows to change the parameters of PID and FLC controllers

while they are in run mode.

4.3.1 Tuning of Fuzzy Controller

FLC for the experiment evolved from a simple controller with default parameters

in the Fuzzy designer software to the final controller in a very slow and step by step

procedure. On-line tuning functionality was used extensively for tuning different

parameters of the FLC, refer to Figures 4.4, Figure 4.5, and Figure 4.6. Placement of

membership functions were initially determine by making a change and then observing

the behaviour for both input and output variables. The same procedure was adopted

for the rule base. When a workable solution evolved from the default setup, it had

the following parameters which can be termed as initial parameters;

• TempError range = -100 to 100

55

Figure 4.5: Fuzzy Designer on-line tuning, Membership functions.

Figure 4.6: Fuzzy Designer on-line tuning, Rule base.

56

• ErrorDelta range = -10 to 10

• NLTemp range = 105 to 107

• NLLTemp range = 90 to 97

• Output range = 0 to 800

• Rule weight, for all rules = 1

Further in the discussion only one number will be mentioned which automatically

implies that positive and negative, like 50 will be actually +50 and -50. The above

parameters were the initial parameters and when put to test the result was as shown

in Figure 4.7. Figure 4.7 shows that when setpoint changes from 101.0 to 103.0 degree

centigrade the offset follows the FLC at the new setpoint value by 0.4 degree.

Figure 4.7: Response of FLC controller after loading initial tuning parameters.

During first stage of tuning which resulted into the initial set of parameters it

was observed that single biggest effect was from the input variable of TempError. To

reduce the offset observed in Figure 4.7 the range of the input variable TempError

was reduced from 100 to 50. After observing the result it was seen that offset was

still there. By keeping TempError at 50, ErrorDelta range was reduced from initial

57

Figure 4.8: Response of FLC controller after reducing TempError to 50 and Er-

rorDelta to 5 tuning parameters.

value of 10 to 5. The response of the controller from Figure 4.8 showed that offset

has reduced though not to a great extent but surely it has decreased.

Encouraged by the result in Figure 4.8, DeltaError was further reduced but it

did not result in further success. To see the full impact of minimized DeltaError

it was reduced to very meagre number of 0.01. From Figure 4.9 it can be observed

that when DeltaError was set to 0.01 and TempError was set to 50, system became

unstable with a wide offset.

Results obtained from Figure 4.9 suggested the best value of DeltaError was

around 5, so the value for DeltaError was reverted back to 5. In the next step

TempError which was up to now was fixed at 50 was reduced to 10, while keeping

DeltaError at 5, and all other parameters at their initial value. Results from this

arrangement were encouraging as shown in Figure 4.10.

From Figure 4.10 it was observed that offset was reduced dramatically but it

was not or near perfect. In the next step TempError was further reduced while

keeping DeltaError at 5 and all other parameters at their initial positions. Result

from Figure 4.11 showed that offset has further shrank to very small number. Further

58

Figure 4.9: Response of FLC controller after reducing ErrorDelta to 0.01 while

keeping TempError at 50.

Figure 4.10: Response of FLC controller after reverting ErrorDelta back to 5 while

reducing TempError to 10.

59

Figure 4.11: Response of FLC controller after reducing TempError further to 5 while

keeping ErrorDelta back at 5.

Figure 4.12: Response of FLC controller after keeping TempError at 5 while reducing

ErrorDelta to 0.5.

reducing TempError did not have any significant effect so the value of 5 was fixed

as new fixed value for TempError

60

In the next step it was decided to reduce the value of deltaError from its fixed

value of 5 to 0.5 while keeping TempError at its new fixed value of 5 and keeping all

other parameters at their initial values. From the response in Figure 4.12 it can be

observed that controller became slow without having any improvement in the offset.

So the deltaError value reverted to 5. Again attention was given to TempError

and it was reduced to 1, which is of course impractical, to see the effect of such a

aggressive value.

Figure 4.13 confirms that TempError value of 1 is too aggressive and it intro-

duced chattering into output of the controller. Responses from the controller sug-

gested that the value of 5 for both TempError and DeltaError is the optimal value.

But we still have the offset that can be seen from Figure 4.11.

Figure 4.13: Response of FLC controller after reducing TempError to 1 while revert-

ing ErrorDelta back to 5.

From first stage of tuning it was observed that the effect of placement of output

membership function is not as sensitive to compensate the current offset. Input

variables TempError and DeltaError were already tuned to their optimal values.

Input variable of NLTemp and NLLTemp were not designed to reduce the offset and

to fine tune the controller performance. The last thing that could be done without

61

disturbing the whole setup was to tweak the weights of rules which were up to now

not touched upon. Further analysis revealed that it is the Rule3 which has the effect

on the FLC output in this region where PV is very close to SP . Rule 3 purpose

is to introduce the medium response from the controller. This medium response

then introduced the offset. To see the effect of Rule3, it was reduced from 1 to 0.1

while keeping TempError and DeltaError at their optimal values of 5 and all other

parameters to their initial setup values.

Figure 4.14: Response of FLC controller after reverting TempError back to its best

value of 5, ErrorDelta back at its best value of 5, and reducing Rule 3 weight from

initial weight of 1 to 0.1.

Figure 4.14 revealed that although offset has reduced to minimum of 0.02 but

at the same time new value of Rule3 had introduced chattering. Further tweaking

the value of Rule3 and observing the results suggested the optimal value of 0.3. This

new value of 0.3 for Rule3 did not cause chattering and minimized the offset to 0.02

as shown in Figure 4.15.

During tuning sometimes it happened that due to aggressive gain controller fell

into the extremely nonlinear temperature region. In this region rules for controls are

reverse. In normal operating region increasing steam flow reduces the temperature

62

Figure 4.15: Response of FLC controller at the best and final values, TempError at

5, ErrorDelta at 5, and Rule 3 weight at 0.3.

whereas in extremely nonlinear region increasing steam flow causes temperature to rise

rapidly. To arm the controller to cope with this situation two rules were added. One

rule takes care of the controller when controller falls into high temperature nonlinear

region and tries to bring it back to normal operating region. The other rule takes

care of the controller when it falls into low temperature nonlinear region and tries

to bring it back to the normal operating region. The effectiveness of the first rule is

demonstrated in the results section. However second rule never used in this particular

application as the current study is not exposed to that low temperature nonlinear

region. The second rule was kept in the controller instead of deleting altogether but

had made it passive so that in future it could be used if situation demands.

4.3.2 Tuning of PID Controller

After FLC controller had been tuned optimally and the results were satisfactory,

PID controller was taken up for tuning and the challenge was to tune the PID con-

troller so that it can perform better than the FLC controller or at least equivalent to

that. As mentioned earlier the starting point for PID controller tuning was to have

63

the auto-tune results. Rockwell software does allow auto-tuning for PID controller

in contrast to FLC controller where this type of luxury is not available. However an

other control software Emerson DeltaV have the auto-tune functionality for both PID

and FLC controllers. Anyhow the PID controller was put into auto-tune and the re-

sults are shown in Figure 4.16. Parameters obtained in this procedure were deployed

in the PID controller. To see the effectiveness of these parameters, the setpoint was

changed from 101.0 to 103.5, keep in mind that the near-linear band is only available

in the range of 100.63 to 104.19 at the base conditions of 26 percent Methanol solution

and the flow rate of 950 pph. Response of the controller after deploying auto-tune

parameters are shown in Figure 4.17.

Figure 4.16: Auto-Tuning results in Rockwell RSLogix5000 software.

64

Figure 4.17: Response of PID controller after loading auto-tune parameters in Rock-

well RSLogix5000 software.

Figure 4.17 shows that the newly formed PID controller have overshoot, have

larger settling time, and less rise time than the optimally tuned FLC. To optimally

tune the PID controller a step by step procedure of changing one parameter while

keeping all other constant was started. After each step response of the controller

was observed in the light of above mentioned three performance categories namely

rise time, settling time, and overshoot and further change was made to improve the

response.

In the first step to improve the rise time of the controller Proportional gain (P)

was slowly increased from its auto-tune value of 132.7 while keeping Integral (I) and

Derivative (D) at their auto-tune values of 814.1 repeats per minute and 2.35 minutes

respectively. Response of the controller is shown in Figure 4.18.

Figure 4.18 shows that although rise time have become faster but the controller

started oscillating. To reduce or to eliminate the oscillation P was decreased to 800

while keeping I and D at their auto-tune values. Figure 4.19 shows that the controller

is still in oscillation. From here P was further reduced slowly and the best response

was obtained at P = 400, which is shown in Figure 4.20. By having this new P value

65

Figure 4.18: PID controller in oscillation when P was increased to 1600 while keeping

other parameters at auto-tune values.

the overshoot was decreased from 103.60 to 103.56 degree.

In the next step I was slowly increased from its auto-tune value of 814.1 to reduce

the area under offset curve. It was observed that controller started oscillating after a

certain threshold and went into sustained oscillation at I = 12800, P was kept at its

new value of 400 and D was set to its auto-tune value of 2.35, refer to Figure 4.21.

To eliminate the oscillation different values if I was checked while keeping P and D

constant and found the optimal value of D at 6400 repeats per minute as shown in

Figure 4.22.

At this stage the performance of PID controller was comparable to that of the

FLC controller. But certainly by just viewing the chart it was easy to judge that

FLC was performing better in all three categories mentioned above. Up to this

point parameter D of the PID controller was not touched and it was sitting on its

auto-tune value. To reduce the little overshoot still present in the PID response

curve the parameter D was slowly increased from its auto-tune value of 2.35 minutes

while keeping all other parameters at their new explored best values of 400 and 6400

for P and I respectively. It was observed that when the value of D approached 16

66

Figure 4.19: PID controller in oscillation when P was decreased to 800 while keeping

other parameters at auto-tune values.

Figure 4.20: PID controller with P set to 400 while keeping other parameters at

auto-tune values.

67

Figure 4.21: PID controller with P set to 400 and I set to 12800 while keeping D

parameter at auto-tune value.

Figure 4.22: PID controller with P set to 400 and I set to 6400 while keeping D

parameter at auto-tune value.

68

the response curve bounced without any improvement, refer to Figure 4.23. It was

concluded that the optimal value of D is somewhere between 2.35 and 16. The value

of D was slowly decreased and observed the response. The best response was achieved

at 8, refer to Figure 4.24. Comparing both figures it can be observed that bounce has

reduced and settling time is relatively shorter. To have one more closer look at the

optimal values of PID controllers an other snapshot was taken, refer to Figure 4.25

with the parameter P set to 400, I set to 6400, and D set to 8. Comparing this figure

with Figure 4.22, it is hard to judge any improvement except the fact that with higher

values of P and I it is possible that PID might fell into sustained oscillation region in

some scenario so the new higher value of D is justified, that will help in preventing

the PID controller from falling into oscillation by keeping check on P and I.

Figure 4.23: PID controller with P and D set to 400 and 6400 respectively and D set

to16.

69

Figure 4.24: PID controller with P and D set to 400 and 6400 respectively and D

reduced from 16 to 8.

Figure 4.25: PID controller with P set to 400, I set to 6400, and D set to 8.

70

Figure 4.26: Effect of flow change from 950 to 900 lb/hr at constant composition

4.4 Experiments and Results

Experiment 1: Change of rate of flow from 950 to 900 lb/hr and vice versa

while keeping composition constant at 26 percent MeOH

Figure 4.26 shows that both controllers responded well to the disturbance of flow

change. In Figure 4.27 disturbance was reversed, flow increased from 900 to 950.

Although PID is more precise but FLC is better in rise time and settling time in both

cases.

71


Experiment 2: Change of rate of flow from 950 to 1000 lb/hr and vice

versa while keeping composition constant at 26 percent MeOH

Figure 4.28 shows that both controllers responded well to the disturbance of flow

change. In Figure 4.29 disturbance was reversed, flow decreased from 1000 to 950. A

moderate overshoot in the PID response is well noticed.

72



73

Figure 4.30: Effect of composition change from 26 to 31 percent of MeOH at constant

flow

Experiment 3: Change of composition from 26 to 31 percent of MeOH

and vice versa while keeping flow constant at 950 lb/hr

Figure 4.30 shows that PID controller fell into sustained oscillation while FLC is

within acceptable limits.

74


flow

Experiment 4: Change of composition from 26 to 36 percent of MeOH

and vice versa while keeping flow constant at 950 lb/hr

From Figure 4.32 and Figure 4.33 FLC superiority is very evident and even it

recovered quickly from the bump than PID controller in the former figure.

In the next three experiments composition and flow rate are being changed si-

multaneously.

75


flow


flow

76

Figure 4.34: Effect of flow change from 950 to 1100 lb/hr and composition change

from 26 percent methanol to 36 percent methanol.

Experiment 5: Change of rate of flow from 950 to 1100 lb/hr and change

of composition of feed from 26 percent methanol to 36 percent methanol,

and vice versa

Figure 4.34 shows that both controllers responded well to the disturbances of

flow and composition change. In Figure 4.35 disturbances were reversed, flow and

methanol composition decreased from 1100 to 950 and 36 percent to 26 percent re-

spectively. Although PID is more precise but FLC is better in rise time and settling

time in both cases.

77





and vice versa

Results from Figure 4.36 and Figure 4.37 suggested that both controllers are

properly tuned as both have responded well to the disturbances in the feed flow and

composition. In both cases controllers have repeated their performance that was

observed in experiment 5 although a slight overshoot in the PID controller curve was

well noticed.

78





79



and vice versa

From Figure 4.38 it is very clear that PID controller totally failed in this sit-

uation and went into sustained oscillation. FLC had also some oscillation but to a

very minute level within acceptable range. Oscillation in the PID controller can be

attributed to the fact that steam flow and tray 50 temperature relationship did not

have same linearity as it can be found in other profiles of feed flow and composition

at this very specific point. On the other hand FLC showed its superiority by perform-

ing within acceptable limits even in this different environment. In normal operation

of the plant PID controllers are tuned to the normal operating conditions or within

a specific operating band and if the disturbance hit the plant then PID controller

usually unable to handle the situation and operator put the controller into manual

mode till the time disturbances are gone or the controller is tuned to the new set

of conditions. However when feed conditions were back to normal both controller

performed within acceptable limits.

Concern was raised about the sharp termination of FLC curve at the very set-

point value. One suspicion was that FLC controller might reached it’s limit, fell into

saturation. To check that experiment was repeated and snapshot were taken at higher

resolution and at the same time FLC controller output was observed while it travelled

from its start journey to its destination. It was observed that FLC was dynamic and

was far away from its lower limit of of output when it reached the desired setpoint

value. Sharp curves of the FLC controller can be attributed to the combination of

factors including tighter tuning, large number of membership functions centred at the

profile centre of input variables, and the rule base.

From results of the preceding seven experiments it can be concluded that FLC

performed well in all the three categories of rise time, settling time and overshoot.

PID was better than FLC in precision, close to setpoint up to second decimal, at

some occasions but it failed at two occasions and went into sustained oscillation.

80



Figure 4.39: Figure 4.38 with different zoom on a different day to check whether FLC

fell into saturation.

81



Figure 4.41: Figure 4.40 with different zoom on a different day to check whether FLC

fell into saturation.

82

Figure 4.42: Effect of setpoint change from 101.0 to 104.0 degree at the base condi-

tions.

Experiment 8: Change of setpoint at the base conditions of 950 lb/hr flow

and 26 percent methanol composition of feed

Experiments from 8 to 11 show that how a set point change could affect the

controller’s performance. Refer to Figure 4.42, the controllers were originally tuned

for the step change at the base conditions from 101.0 to 103.5 degree. The response

in this experiment was as expected. It was the same region for which both controllers

had been tuned.

83

Figure 4.43: Effect of setpoint change from 101.0 to 97.8 degree and vice versa at 36

percent methanol composition and 1100 pph flow.

Experiment 9: Change of setpoint at 1100 lb/hr flow and 36 percent

methanol composition of feed

Refer to Figure 4.43, both controllers performed well, due to tighter tuning results

were astonishing. The offset in the response curves of both controllers at the setpoint

of 97.8 degree is unexplained. The only explanation could be the fact that 97.8 degree

temperature needs a steam flow of 784.3 pph which is very close to the maximum

available steam flow of 800. Both controllers might have pushed the maximum steam

flow portion of which might have lost in the dynamics of distillation column.

84

Figure 4.44: Effect of setpoint change from 101.0 to 98.5 degree and vice versa at 33

percent methanol composition and 1050 pph flow.



Refer to Figure 4.44, both controllers performed optimally. A little bump in the

curve of both controllers can be attributed to the fact that temperature drops rapidly

when steam flow increases from 404.0 to 448.0 pph. Both controllers responded to

this sudden drop and remained stable and on course to their ultimate destination of

new setpoint 98.5 degree.

85

Figure 4.45: Effect of setpoint change from 101.0 to 102.8 to 99.8 degree and back

to 101.0 at 30 percent methanol composition and 1000 pph flow.



Refer to Figure 4.45, this is the particular region where PID controller failed

earlier too. It showed that even optimally tuned PID controller is prone to oscillation.

It also proves that if PID failed at this randomly selected operational condition there

must be other scenarios in the whole profile of 26 percent to 36 percent of methanol

composition and 950 pph flow to 1100 pph flow where PID could potentially fail. In

contrast FLC performance was better and it remained within acceptable limits.

86

Figure 4.46: Effect of randomly selected setpoint change and disturbances.

Experiment 12: Change of setpoint and disturbances randomly

Refer to Figure 4.46, both controllers repeated their earlier performance well.

PID controller went into oscillation in the specific region whereas FLC did not. FLC

was also more agile in responding to quick changes. In a way this was the true test

as it almost mimic the rapidly changing conditions at the distillation column.

87

Figure 4.47: Effect of falling into extremely non-linear region of temperature profile.

Experiment 13: Falling into extremely non-linear region

Refer to Figure 4.47, it is likely that due to some operational problems tem-

perature measurement could fall into non-linear region. FLC could use its inherent

characteristic of rules to ward off this problem whereas PID could not. These type of

troubles are faced by operation staff at distillation column sites that once PID gets

affected by the disturbance then they have to take the controller into manual mode

adjust its output and put it back to automatic mode. During experimentation it

happened that both controllers fell into this non-linear region where increasing steam

flow causes temperature to increase rapidly in contrast to near-linear region where

increasing steam flow causes temperature to drop. Two rules were developed for FLC,

one for high temperature non-linear region and other for low temperature non-linear

region. In this particular case there is only high non-linear region so the rule for low

temperature non-linear region was made passive. This shows the power and flexibility

of FLC where certain rules can be developed to tackle certain issues.

88

4.5 Summary of Results

Results in section 4.4 showed that both FLC and PID controllers performed neck

to neck except at couple of occasions where PID fell into oscillation. PID controller

fell into oscillation because the distillation column temperature profile is not linear

and one set of PID parameters was not able to handle a different profile for which it

was not tuned. Also FLC used well its power of deploying situation specific rules to

counter the disturbances. PID controller was better at some occasions in precision,

closer to setpoint value up to second decimal.

Tuning wise FLC is harder to tune as it has more parameters to tune whereas

PID has only three parameters to be taken care of. Interestingly enough both con-

trollers are prone to disturbances although FLC performed better than PID in those

disturbances. Results also prove that FLC is not the solution for all the evils associ-

ated with controllers although it did performed better in the design range than PID

controller for this non-linear application.

From experiment number 1 to experiment number 7 set point was kept at 101.0

and never changed although control set point for the 30 to 36 percent methanol and

70 to 64 percent water mixture was not at 101.0. This was done to see the effect

of load disturbance change, both in terms of rate of flow and composition, at a one

given set point. From the results it is safe to say that collectively FLC performed

better than PID and more importantly it was more stable than its counterpart.

Changing set point along with the disturbances is a complete another study.

Experiments from experiment number 8 to experiment number 11 showed the phe-

nomenon that how a set point change in a distillation column could affect the perfor-

mance of the controller.

Figure 4.48 and Figure 4.49 of temperature profiles of distillation column show

that how temperature varies non-linearly in the distillation column from one tray to

other tray and that makes it difficult to control with traditional PID controllers.

89

Figure 4.48: Temperature profile of Distillation column under study at 950 l/hr of

flow and 26 percent of methanol.

Figure 4.49: Temperature profile of Tray 50 of Distillation column under study at

950 l/hr of flow and 26 percent of methanol.

90

Chapter 5

Conclusion and Future Work

5.1 Conclusion

Results presented in the chapter 4 prove that FLC could perform better than

PID controller for a distillation column control and reason behind this is the inherent

structure of both controllers. PID is based on linear philosophy and it fails whenever

the object that it is controlling deviate from the linear curve. Distillation column

temperature curve is one of the finest example of this nonlinearity as the Figure 4.48

and Figure 4.49 show. On the other hand FLC is built on non-linear structure so

it adapts to any control structure easily. Non-linearity can be developed easily by

defining the membership functions scaling and their shapes, it can be introduces

into the rule base and in the output membership functions. So right from input

components to output components, FLC is a non-linear controller and that is why it

performed so well. It is also concluded that exceptional situations can be tackled in

FLC but not in PID control.

91

5.2 Future Work

It is surprising to know that process control design engineers do not give FLC

controller a serious thought and the ultimate choice is PID controller. Although fuzzy

systems are starting to appear in the software suites of control system manufacturers

but the end user still hesitate to use it and even to discuss about it.

Future work would include following topics.

1. Application of Rockwell FLC to a real industrial distillation column

2. Trimming of number of rules in this thesis

3. A survey of end user and control system integrator about their hesitation of

using FLC in their plants and facilities

4. A simple mechanism, could be genetic algorithm, that will suggest appropriate

parameters for a fuzzy controller for a particular applications

92

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Appendix A

Appendix: Distillation Column

Temperature Profiles

A.1 Distillation Column Temperature Profile at

950 pph flow and 26 percent of Methanol

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Appendix B

Appendix: Distillation Column

Tray50 Temperature Profiles

B.1 Tray50 Temperature Profile versus Reboiler

Duty at various flow and composition of feed

and Methanol

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Duty at 900 pph flow and 26 percent compo-

sition of feed and Methanol respectively

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Appendix C

Appendix: FLC and PID

Controllers Code

C.1 FLC and PID Controllers Code, exported from

RSLogix5000 in L5X/XML format

This code is less than one sixth of the original code. The intention was to make

full code as part of the thesis but after realizing that it will add-up more than 100

pages in addition to the existing 18, it was restricted to a sample only, to let the

reader feel for it.

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Documents

Shoaib Thesis Final 2011-12-15