ASTUDYOF PLANTWIDE DISTURBANCE DIAGNOSIS

A STUDY OFPLANTWIDE DISTURBANCE DIAGNOSIS

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A THESISSUBMITTED TO THE DEPARTMENT OF CHEMICAL ENGINEERINGIN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE

DEGREEOF

MASTER OF SCIENCE IN CHEMICAL ENGINEERING

BY

NAHID SANZIDA (l00602001P)

SUPERVISED BY

Dr. Md. ALI AHAMMAD SHOUKA T CHOUDHURY"

ASSISTANT PROFESSOR

DEPARTMENT OF CHEMICAL ENGINEERING

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY

DHAKA,BANGLADESH

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CERTIFICA nON OF THESIS WORK

We the undersigned, glad to certify that Nahid Sanzida candidate for the degree of Master

of Science in Engineering (Chemical) has presented her thesis work on the subject "A

Study of Plantwide Disturbance Diagnosis". The thesis is acceptable in form and content.

The student demonstrated a satisfactory knowledge of the field covered by this thesis in an

oral examination held on December 22, 2009.

""~/v!6.JDr. Md. Ali Ahammad Shoukat ChoudhuryAssistant ProfessorDepartment of Chemical EngineeringBUET, Dhaka-IOOO

Dr. DilProfess' eadDepartment of Chemical EngineeringBUET, Dhaka-IOOO

~"'?<.b.JQJ;>~Dr. A.K.M.A. QuaderProfessor. Department of Chemical EngineeringBUET, Dhaka-IOOO .

Dr. M. SerajullslamAssociate Professor RetiredHouse-33, Road-4, Block-BBanasree, Rampura, Dhaka-1219

Chairman

Member(Ex -Officio)

Member

Member(External)

ABSTRACT

In the highly complex and integrated chemical process plants, it is a challenge to prevent

disturbances from propagating from one unit to other interconnected un'its. Moreover, in

today's world chemical process plant operation is relying highly on automated control

systems, Automation tends to make the plant vulnerable to disturbances if the fault is not

detected and diagnosed within the appropriate time scale in the context of process dynamics.

Disturbances that propagate throughout the plant and create plantwide oscillations are

originated due to various faults such as sensor faults, valve faults, process faults and

controller tuning faults. One important characteristic of this kind of nonlinear faults is that

they can create oscillation with a fundamental frequency and its harmonics. Once the

frequencies, amplitudes and phases of the fundamental oscillation and its harmonics are

estimated, these information can be utilized to diagnose the root-cause of plantwide or unit-

wide disturbances.

For this thesis work, at first the Three Tank Level plus Temperature Control pilot plant set up

of the Department of Chemical Engineering, BUET was brought under complete working

condition, The utility section was serviced and several defective transmitters of the set up

were repaired and replaced, A data acquisition system using ADAM 5000 TCPIIP Module

was developed for the pilot plant set up to measure and log variables for the purpose of

running the experiment and analyzing the logged data. A Human Machine Interface (HMI)

was developed for the entire pilot plant set up using MatLab OPC toolbox and Simulink to

control and monitor the pilot plant system. Models of the various part of the system were

identified and PI controllers were designed accordingly. Both feedback controllers and

cascade controllers were designed for the system.

After preparing the laboratory set up for experimental work, fault in the form of valve stiction

was introduced to create plantwide oscillation(s), Experiments were performed for varying

amount of stiction and data were collected for plantwide oscillation diagnosis.

In this study, a novel data driven off-line time domain method was developed to troubleshoot

plantwide disturbances using harmonic analysis, Simple linear least square regression

techniques and Fernando Quinn's technique were used to determine the amplitude, frequency

and phase information of the time series data, Harmonically related components were then

used to define a new index called Total Harmonic Contcnt (THC), which was used to

quantify the harmonic information.

The proposed THC index was evaluated usmg experimental data, simulated Nonlinear

Dynamic Vinyl Acetate Process data and South East Asia Refinery industrial data. The

proposed methodology was successful in identifying root-cause of plantwide oscillation for

all cases of experimental, simulated and industrial data

ii

ACKNOWLEDGEMENT

First, I would like to pay my gratitude to Almighty Allah for His loving care and guidance

throughout my life.

Then my thanks go to my Supervisor, Dr. Md. Ali Ahammad Shoukat Choudhury for his

wonderful guidance, encouragement and support from the beginning to end of the thesis. I

have thoroughly enjoyed our work together and consider myself very fOl1unate to have been

under his supervision. Our interaction has been an invaluable learning experience.

Very special thanks go to my Colleagues Anisur Rahman and Monir Ahammad whose

comments and help from time to time are appreciated.

Most importantly, I would like to thank my Husband and my Daughter for being the

enormous source of inspiration for my war!"..

Last, but not the least, I want to thank my Parents for their love, support, encouragement and

prayer.

iii

TABLE OF CONTENTS

ABSTRACT

ACKNOWLEDGEMENT

LIST OF FIGURES

LIST OF TABLES

CHAPTER I

INTRODUCTION

I.I Motivation

1.2 Background and Present State of the Problem

1.3 Objectives

1.4 Thesis Outline

CHAPTER 2

LITERATURE REVIEW

2.1 Description of Terms

2.2 Classification of Disturbances

2.3 Detection of Plantwide Disturbance

2.4 Diagnosis of Plantwide Disturbance

2.5 Chapter Summary

CHAPTER 3

THEORY OF TIME DOMAIN APPROACH FOR PLANTWlDE OSCILLATION

iii

VII

x

2

2

4

5

6

9

9

II

12

17

23

DIAGNOSIS25

3.1 The Fourier Series 25

3.2 Frequency Estimation 31

3.3 Harm<;>nicsAnalysis and Plantwide Oscillation 33

3.4 Total Harmonic Content 36

3.5 Summary of the Proposed Techni~.,'e. 37

3.6 Chapter Summary 37

IV

CHAPTER 4

EVALUATION OF THC IN SIMULATION AND INDUSTRIAL ENVIRONMENT 39

4.1 THC Index Evaluation in Simulated VAc Process Data Sets 39

4.2 THC Index Evaluation in South East Asia Refinery (Sear) Data Sets 49


CHAPTER 5

EXPERIMENTAL SET UP 54

5.1 Three Tank Level plus Temperature Control Pilot Plant Set up 54

5.2 Schematic Diagrams 55

5.3 Detailed Description of the Plant 58

5.4 Operating Procedure 61


CHAPTER 6

HUMAN-MACHINE INTERFACE (HMI) DEVELOPMENT AND CONTROLLER

DESIGN 64

6. I Human Machine Interface (I-IMI) Development 64

6.2 Feedback Controller Design and Tuning 66

6.3 Model Identification and Controller Design for FCVO 1 and FTO1 System 66

6.4 Model Identification and Controller Design for FCV02 and FT02 System 69

6.5 Model Identification, Controller Design and Tuning of PI Controller

for Water Level Control in Tank 1 72


for Water Level Control in Tank 2 79


for Water Level Control in Tank3 83

6.8 Cascade Controller Design and Tuning 87


CHAPTER 7

PLANTWIDE OSCILLATION EXPERIMENTS AND RESULTS 99

7.1 Introduction of Fault to the System 99

7.2 Troubleshooting of Plant wide Oscillation 106

v

7.3 Chapter Summary

CHAPTER 8

CONCLUSION AND FUTURE WORK

8.1 Contribution of the thesis work

8.2 Future Work

REFERENCES

116

I 18

118

119

121

APPENDICES

APPENDIX A

APPENDlXB

APPENDlXC

APPENDlXD

APPENDIXE

VINYL ACETATE PROCESS DESCRIPTION A-I

HARMONICS ANALYSIS RESULTS FOR VAc PROCESS A-S

HUMAN MACHINE INTERFACE (HMl) A-17

OPC TOOLBOX-READ, WRITE, AND LOG DATA FROM

OPC SERVERS A-19,PRELIMINARIES OF VALVE STICTION A.21

VI

LIST OF FIGURES

Figure 1.1 Oscillations in product quality with smaller deviation from the set point 3

Figure 1.2 Oscillations in product quality with larger deviation from the set poin!.. 3

Figure 2.1 A sinusoidal signal 9

Figure 2.2 Frequency domain representation of signal. 10

Figure 2.3 Time trends and their power spectra for the VAc Process data set.. 11

Figure 2.4 Family tree of methods for data-driven plantwide disturbance detection(Thornhill and Horch, 2007) 13

Figure 2.5 Time trends and their power spectra , 15

Figure 2.6 PSCMAP 16

Figure 2.7 Family tree of methods for data-driven plantwide root cause diagnosis

(Thornhill and Horch, 2007) 17Figure 3.1 A square wave with a period of2L 27

Figure 3.2 Harmonic relations of different types of error signals 33

Figure 3.3 Time series data and the power spectra for a sticky valve .34

Figure 3.4 Bode plot for a low pass filter (http://en.wikipedia.org/wiki/Bodeylot) 35

Figure 4.1 VAc process flowsheet (Chen et aI., 2003) .40

Figure 4.2 Time trends and power spectra for the VAc Process Variables,

applied stiction in loop 9 is 5% .41

Figure 4.3 PSCMAP for the VAc Process Variables, applied stiction in loop 9 is 5% 42

Figure 4.4 THC values for the VAc Process Variables for stiction applied in loop 9 .44

Figure 4.5 Time trends and power spectra for the Vac Process Variables,

applied stiction in loop 14 is 5% , .45

Figure 4.6 PSCMAP for the VAc Process Variables, applied stiction in loop 14 is 5% .46

Figure 4.7 THC values for the Vac Process Variables for stiction applied in loop 14 .48

Figure 4.8 Schematic of the SEA Refinery Process (Tangirala et aI., 2007) .49

Figure 4.9 Time trends and power spectra for the South-East Asia Refinery data set 50

Figure 4.10 PSCMAP for the South-East Asia Refinery data set... 51

Figure 4.11 Total Harmonic Contents (THC) Results for SEA refinery data set.. 51

Figure 5.1 Schematic Diagram of the Three Tank Level plus Temperature

Control set up 55

Figure 5.2 P&ID of the Three Tank Level plus Temperature Control set up 56

.: )

VII

http://en.wikipedia.org/wiki/Bodeylot

Figure 5.3 The Three Tank Level plus Tcmperature Control pilot plant set up

at the Proccss Control Laboratory 57

Figure 6.! The Human Maehine Interface (HMI) for thc laboratory pilot plant set up of til':

Department of Chcmical Enginccring, 13UET 65

Figure 6.2 The Simulink diagram for controllcr dcsign for the FCY 01

and FT 01 system 67

Figure 6.3 (a)Flow Transmitter (FTO!) reading Ys. Time 68

(b) Valve (FCYOl) opening Ys. Time 68

Figure 6.4 The Simulink diagram for Controller design for the FCY 02

and FT 02 System 70

Figure 6.5 (a) Flow Transmitter (FT02) reading Vs. Time 7]

(b) Valve (FCY02) opening Vs. Time 71

Figure 6.6 Open loop block diagram for,le.vel control system 72

Figure 6.7 Closed loop block diagram for level control system 73

Figure 6.8 The Simulink Model for Controller Design for Tank 1 75

Figure 6.9 Set point tracking of Level in Tank I 78


Figure 6.11 Set point tracking of Level in Tank 2 82


Figure 6.13 Set point tracking of Level in Tank 3 86

Figure 6.14 The Simulink Model for Cascade Controller Design for Tank I 89

Figure 6.] 5 Tank 1 level control system's response at trial no.] 2 90

Figure 6.16 Tank 1 level control system's response at trial no.16 90

Figure 6.17 Tank 1 level control system's response at trial no. 19 91


Figure 6.19 Tank 2 leveleontrol system's response at trial no.7 93

Figure 6.20 The Simulink Model for Cascade Controller Design for Tank 2 94


Figure 6.22 The Simulink Model for Cascade Controller Design for Tank 3 96

Figure 7.1 The Simulink model for Tank 1 level control system where fault

is introduced to FCVO] 10 I

Figure 7.2 The Simulink model for Tank 2 level control system 102

Figure 7.3 The Simulink model for Tank 1 heating system I03

Figure 7.4 The Simulink model for Tank 2 heating system I03

VIII

Figure A-I

Figure D-I

Figure D-2

Figure D-3

]

Figure 7.5. The response of the Tank 1 and Tank 2 cascade control systcm

for 20% stiction in FCYO I , I05

Figure 7.6 The time series data with thcir power spectra for 7 % stiction at FCYO I I06

Figure 7.7 PSCMAP for 7% stiction at FCYO1 107

Figure 7.8 The time series data with their power spectra for 20% stiction at FCYO 1 108

Figure 7.9 PSCMAP for 20% stiction at FCYO1 108

Figure 7.10 THC values for the pilot plant variables when 20% stiction was introduced and

heating of water by saturated steam 110

Figure 7.11: High density plot for the pilot plant variables for 2% stiction at FCYOI(without heating) .........................................•.............................. I I0

Figure 7.12 High density plot for the pilot plant variables when for 20% stiction at FCYOl

(without heating) III

Figure 7.13 High density plot for the pilot plant variables for 30% stiction at FCYOI

(with heating) 111

Figure 7.14 THC values for the pilot plant variables for 2% stiction at FCYO I

(without heating) 114

Figure 7.15 THC values for the pilot plant variables for 7% stiction at FCYOI


Figure 7.16 THC values for the pilot plant variables for 20% stiction at FCYO 1


. Figure 7.17 THC values for the pilot plant variables for 30% stiction at FCYO 1

(with heating) 115

SISO plantwide control system for the YAC process (Chcn et a\., 2003) A-I

A simulink model file built using the OPC read-write blocks A-19

Properties of OPC Read block A-20

Properties of OPC Write block A-20

Figure E-I

Figure E-2

Typical input-{)utput behavior of a sticky valve

(Choudhuryet a\., 2005) A-22

Signal and logic flow chart for the data-driven stiction model

(Choudhury et a\., 2004) A-25

IX

LIST OF TABLES

Table A-I

Table 7.6

Table B-1

Table B-2

The IMC based PID Controller Scttings for a first ordcr system 69

Trial values of Primary and Sccondary Controller Paramcters 88

Trial values of Primary and Secondary Controller Parameters 92

Trial values of Primary and Secondary Controller Parameters 95

.Description of the Variables : 104

Harmonic analysis results for simple oscillation propagation example

(for 20%) stiction at FCVOI with heating water by saturated steam) 109


(2% stiction was introduced and no heating of water was done) 112






(30% stiction was introduced and heating of water was done) 113

Steady State Values of Manipulated Variables (Chen et aI., 2003) A-2

Control Structure and Controller Parameters (Chen et aI., 2003) A-3

Measurements at Steady State (Chen et aI., 2003) A-4

Harmonic analysis results of the manipulated variables (MV) for

1% stiction in Loop 9 of the VAc Process A-5





Table B-4 Harmonic analysis results of the manipulated variables (MV) for

Table B-3

Table A-3

Table A-2

Table 6.1

Table 6.2

Table 6.3

Table 6.4

Table 7.1

Table 7.2

Table 7.3

.tTable 7.4

Table 7.5



5 % stiction in Loop 9 of the VAc Process.. A-9


I % stiction in Loop 14 of the VAc Process A-] 0


2 % stiction in Loop]4 of the VAc Process A-11

x

Table B.8 Harmonic analysis results ofthe manipulated variables (MY) for

3 % stietion in Loop 14 of the YAe Proeess A.12

Table B-9 Harmonic analysis results of the manipulated variables (MY) for

4 % stietion in Loop 14 of the YAe Process A.13

Table B.1O Harmonic analysis results of the manipulated variables (MY) for

5 % stietion in Loop 14 ofthe YAe Proeess A-14

Table B.II Harmonic analysis results of the South East Asia Refinery data sets A.15

XI

CHAPTER 1

INTRODUCTION

1.1 MOTIVATION

1.2 BACKGROUND AND PRESENT STATE OF THE PROBLEM

1.3 OBJECTIVES

1.4 THESIS OUTLINE

CHAPTER 1

INTRODUCTION

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This chapter discusses the motivation for the thesis work from the vie~~£'d~;~(~

commercial aspects. The background along with the present state of the problem has been

presented. Finally, the objectives and the scopes ofthe work have been discussed.

1.1 Motivation

Plantwide oscillations are common in many processes. Their effects propagate to many units

and may impact the overall process performance. It is important to detect and diagnose the

oscillations early in order to rectify the situation. Increasing emphasis on plant safety and

profitability strongly motivates the search for techniques to detect and diagnose plantwide

oscillations (Jiang et aI., 2006). The motivc for the detection of plantwide oscillation and

root-cause diagnosis is cxplained with the cxample of the control of a distillation column.

Distillation is one of the most common separation techniques in chemical manufacturing.

This multi-input, multi-output staged separation process is strongly interactive (Rivera et aI.,

2007). Distillatioil operation directly affects product quality, process production rates and

utility usage; hence, the economic importance of distillation control is clear. It is a

challenging problem because of the following factors:

• Process nonlinearity

• Multivariable coupling

• Severe disturbances

• Nonstationary behavior

Distillation columns exhibit static nonlinearity because impurity levels asymptotically

approach zero. Coupling is significant when the composition of both overhead and bottoms

products are being controlled. Columns are :.ffected by a variety of disturbances, particularly

feed composition and flow upsets. Nonstationary bchavior stems from changes in tray

efficiencies caused by entrainment or fouling.

2

Improved distillation control is characterized by a reduction in the variability of the

impurities in the products. Let us consider the following two situations where the oscillation

in final ~roduct quality leads to two different types of distribution as shown in Figure 1.1 and

Figure 1.2. Clearly, product quality represented by Figure 1.1 is better than that of Figurc 1.2.

Figure 1.1: Oscillations in product quality with smaller deviation from the set point.

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Figure 1.2: Oscillations in product quality with larger deviation from the set point.

Meeting the specification requirements on the variability of final products can make the

difference between the product being a high value-added product with large market demand

and being a low-valued product with a small market demand.

For customers who purchase the products produccd by distillation columns as feedstock for

their processes, the variability of the feedstock can directly affect the quality of the products

they produce, e.g., the variability in the monomer feed to a polymerization process can

directly affect the mechanical properties of the resulting polymer produced.

In addition, control performance can affect plant processing rates and utility usage.

Therefore, from the above example it is clear that any disturbance generated in the distillation

column will affect product quality, production rate, utility usage etc. Each of these factors is

economically important for large-scale precesses.

A distillation column consists of several sections like the feed inlet, condenser, reboiler etc

and the operation depends on many factors like feed composition, cooling water temperature,

3

cooling water flow rate, steam flow rate and temperature, gradually changing plate efficiency

etc. These factors are highly interactivc and an error caused by any of the factors results in

faulty behavior of others. This is the case when plantwide disturbances arise. So, first it is

necessary to detect whether the disturbances that have spread all over thc plant is due to somc

malfunctioning of any of the control loop associated with the tower and the next step is to

isolate the exact loop where the disturbance has been originatcd. After the root-cause is

diagnosed, maintenance effort can be directed efficiently.

1.2 Background and Present State of the Problem

Modern industrial process plants are utilizing recycle streams and hcat integration in the drive

towards efficiency. The mass and energy integration complicates the process control because

variations can propagate through the plant in complex ways, often turning a single source of

variation into a widely distributed disturbance. Disturbances and oscillations in production

process usually have a large impact on product quality, running cost and profitability because

production and throughput may have to back away from their optimum settings to

accommodate process variability (Horch et aI., 2008). Thus, it is important for process

control engineers to detect and diagnose the causes of oscillations or disturbances III a

chemical process operation as soon as possible (Paulonis et aI., 2003; Qin, 1998).

Over the last few years, some studies were carried out to detect plantwide oscillations

(Choudhury et aI., 2007; Jiang et aI., 2007; Zang et aI., 2005; Thornhill et aI., 200 I). To

detect oscillations in process measurements and identify signals with common oscillatory

behavior, the use of spectral principal component analysis (PCA) (Thornhill et aI., 2002) or

autocorrelation function (act) (Thornhill et aI., 2003) w.as suggested. Xia and Howell (2003)

have proposed a tcchnique that takes into account the intcraction between the control loops.

Xia et al. (2005) described a method based on the spectral independent component analysis.

Zang et a!. (2007) described a method to isolate thc source of whole plant oscillation through

bi-amplitude ratio analysis. Xia et a!. (2007) described a plantwide oscillation detection

method using nonnegative spectral decomposition method. Tangirala et al. (2007) proposed

the use of nonnegative matrix factorization (NMF) of multivariate spectra. Most of the works

mentioned above are devoted to the detection of plantwide oscillation only. A few papers

(Zang et aI., 2007; Thornhill et aI., 2003; i'h0rnhill et a!., 2001) described some techniques to

perform root-cause diagnosis of plantwide oscillation. However, those methods involve

4

complicated mathematics leaving root-cause diagnosis cspccially the effcct of multi loop

interaction and linear causes of plantwide oscillation still an open area for research (Thornhill

and Horch, 2007). This thesis work aims to detect plantwide disturbances and diagnose the

root-cause of such disturbances using simple Fourier based signal processing technique and

least square estimation method.

1.3 Objectives

The main goal of the thesis project is to dcvelop an algorithm that can succcssfully identify

plantwide disturbance and its root-causes so that operational and maintenance efforts can be

directed effectively. The study has two parts,:

Part 1: Development of human machine interface (HMl) based data acquisition system for

the Three Tank Level plus Temperature Control pilot plant set up located in the Process

Control Laboratory of the Department of Chemical Engineering, BUET.

Part 2: Development of a methodology that can efficiently and economically troubleshooL

plantwide disturbance.

To fulfill the above stated objectives the following methodology has been used. The pilot

plant set up of the laboratory has been brought under completc working condition. The

electric boiler (capacity 75 psig) used for steam supply has been repaired and serviced by

Modern Erection Limited. The centrifugal compressor used for supplying instrument air has

been serViced. Several transmitters (Level, flow and temperature transmitters) were not

working properly. They have been calibrated. Two water flow control valves and two steam

flow control valves that are pneumatic in nature have also been calibrated.

A data acquisition system using ADAM 5000 TCP/IP Data Acquisition Module to measure

and log variables for the purpose of running the experiment and analyzing the logged data has

been developed. The data acquisition system is electronics based, and it is made of hardware

and software. The hardware part is made' "f sensors, cables and electronic components. The

software part is made of data acquisition logic and analysis software. ADAM utilities have

also been used to configure the logic or to move data from data acquisition memory to a

computer.

5

An HMI for the laboratory pilot piantsct up has been developed to control, monitor and

manage the system using OPC toolbox and Simulink in MatLab environment.

A statistical signal-processing algorithm has been developcd to troubleshoot plantwide

disturbances. Simple linear least square regression techniques and Fernando Quinn's

technique have been used to determine the amplitude, frequency and phase information of the

time series data. Harmonically related components are then used to define a new index called

Total harmonic content (THC) which is used to quantify the harmonic information. The

potential of the proposed THC index to detect and diagnose plantwide oscillation has been

tested using simulated VAc process data, industrial data and laboratory experimental data.

1.4 Thesis Outline

This thesis is outlined as follows,

Chapter One provides motivation and introductory background of this study.

Chapter Two reviews past works in the ficld of plantwide oscillation dctcction and diagnosis.

It gives an overview of the tcchniques that are available for detection of plantwide oscillation

and diagnosis of its root-cause. This chapter also pinpoints the limitations associated with

those techniques.

Chapter Three describes decomposition of time series data into sinusoidal components using

Fourier Series. It also describes how simple linear least square regression techniques and

Fernando Quinn's technique are used to determine the amplitude, frequency and phase

information. Finally, harmonically related components are used to define a new index called

Total harmonic content (THC).

Chapter Four describes two case study examples for the assessment of the proposed THC

index. Simulated nonlinear dynamic model of Vinyl Acetate process data and South East

Asia Refinery industrial data were analyzed where the root-cause ofplantwide oscillation was

known.

Chapter Five provides a detailed description of the Three Tank Level plus Temperature

Control pilot plant set up located at thc Process Control laboratory of the Department of

6

Chemical Engineering, BUET. Simplified schematic diagram and P&lD arc included for the

set up. The operating procedure for the system is provided at the last section of this chapter.

Chapter Six describes the experimental work performed under this thcsis work. All works

including the design of Human Machine Interface (HMI), development of the data acquisition

system, system identification and controller design have been described in detail.

Chapter Seven describes the evaluation of the proposed THC index using laboratory

experimental data. It also includes the design of cascade controllers for the pilot plant set up

and troubleshooting of plant wide oscillation after introducing fault to the system.

Chapter Eight concludes the thesis by discussing what has been achieved in this work and

making recommendations for future work.

7

..

CHAPTER 2

LITERATURE REVIEW

2.1 DESCRIPTION OF TERMS

2.2 CLASSIFICATION OF DISTURBANCES

2.3 DETECTION OF PLANTWIDE DISTURBANCE

2.4 DIAGNOSIS OF PLANTWIDE DISTURBANCE

2.5 CHAPTER SUMMARY

CHArTER 2

LITERA TURE REVIEW

A propagated disturbance may affect key process variables such as feed, product and recycle

flows, column temperature and product composition. It may upset from a single unit to the

complete production process. When tltere are many osci Ilating measurements, finding tlte

root-cause of the disturbance is like looking for .a needle in a Itaystack. However, a few

techniques based on different approaches have been developed for the detection and

diagnosis of plantwide disturbances. This chapter gives an overview of the techniques that are

available for root-cause detection and diagnosis ofplantwide oscillation or disturbance.

2.1 Description of Terms

2.1.1 Time domain

Time domain is a term used to describe the analysis of mathematical functions, or physical

signals, with respect to time. In the time domain, the signal or function's value is known for

all real numbers for the case of continuous time, or at various separate instants in the case of

discrete time. Figure 2.1 shows a time domain signal which is a simple sinusoid.

Figure 2.1: A sinusoidal signai.

2.1.2 Frequency domain

In electronics and control systems engineering, frequency domain is a term used to describe

the analysis of mathematical functions or signals with respect to frequency, rather than time.

A time domain can be represented in the frequency domain using Fourier transform. For any

time series signal, y (/), the Fourier Transform is defined as,

9

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Y(f) =L>(t)e-2~fI1=0

where, Y(f) is the Fourier Transform of y(t). It is a complcx numbcr having both magnitude

and phase. When magnitude of Y(f) is plotted against the frequency, f, the resulted plot is

called power spectrum. Power spectrum is the frequency domain reprcsentation of time

domain signal and is defined by I"(f) = IY(f)I'- Figure 2.2 shows the equivalent frequency

domain representation of the signal described in Figure 2.1.

'---'A'------0.0 I 0.1

Frequency ---,~

Figure 2.2: Frequency domain representation of signal.

Since the time domain signal has one oscillation, the power spcctrum shows only one peak at

the frequency of this oscillation. Therefore, power spectrum shows the power of the signal at .

various frequency channels.

A time domain graph shows how a signal changes over time, whereas a frequency-domain

graph shows how much of the signal lies within each given frequency band over a range of

frequencies.

2.1.3 Plantwidc Oscillation(s)

When an oscillation generated in a particular part of the plant propagates throughout the

whole plant or a group of units such oscillations are termed as plantwide or unitwide

oscillation(s). In today's highly complex and integrated chemical process plants it is a

challenge to prevent disturbances to propagate from one unit to other interconnected units

due to the tight heat and mass integration in the plant as well as the presence of recyclc

streams in the plant. Figure 2.3 shows an example of a plantwide oscillation problem. The left

panel shows the time trends of22 variables representing.a plantwide oscillation problem in a

10

Vinyl Acetate Monomer (VAc) manufacturing process. The right panel shows the power

spectrum ofthese variables. This clearly shows the presence of a common oscillation with a

frequency of 0.05 or approximately 20 sa":lples/cycle in many ofthese variables.

Samples

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1

Power Spectra

22 ,,'": : : : "'" : : : l;::: : : :21 .. : : : : : : : : :20 ""'" .....: : : : : : : :19 " '"''

...18 .. : '''''' : : : : .. : : :

17 : ,,'" : : : : ... : : :..,16 --,- : : : ",,' : : : ::1::: : : :14 : : : : "". : : :'1" : :1211 : : : : .,,,. : : : "n, : : :

9 : : : : .'". : : : ::1::: : : :

8 "I'": : : : '"'' : : "n, : : :

7 : : : : '"'' : : : ... : : :6S

: : : : ., ... : : : .. : : :

4 : : : : " .., : : : .. : : :

3 ,," : : : : .. : : :: : .,,"2 : : 0>'" : : ~::::1 : : : : '"'' : : :~,,"

0.001 0.01 0.1Frequency II I,

Figure 2.3: Time trends and their power spectra for the VAe Process data set.

2.2 Classification of Disturbances

The disturbances that propagate throughout the whole plant are classified considering

timescales (Thornhill and Horch, 2007). Fr.~m the viewpoint of time scale, disturbances may

be

(a) Slowly developing, e.g., catalyst degradation or fouling of a heat exchanger

(b) Persistent and dynamic, e.g., valve limit cycle, hydrodynamic instability,

tuning problems, controller interaction, recycles

(c) Abrupt, e.g., a compressor trip

The dynamic disturbances that persist over a time horizon of hours to days are again

classified based on the presence of oscillation(s).

The most common situation in case of plantwide disturbance propagation is the oscillation of

the variables. This often causes severe deterioration of performance in process control loops.

I 1

A very common cause for oscillation is the presence of nonlinearity such as a valve stiction

or a faulty instrument which sets up a limit cycle in a control loop. Another possible cause is

bad tuning, which can destabilize the system. Sometimes there may be an external oscillatory

disturbance acting as the third possible reason (Zang et aI., 2005).

Non-oscillating disturbances include non-periodic disturbances like controller interaction etc.

This thesis work is focused on the oscillating disturbances that arc spread all over the plant.

In this work, historical data set is analyzed off-line. The off-line approach gives opportunitie,

for advanced signal analysis methods.

2.3 Detection ofPlantwide Disturbance

Mathematical model of a system was the heart of process monitoring as the fiaditional fault

detection and identification methods wcre bascd on it. Since 1980s, the process control

community began to investigate the use of multivariate statistics for process monitoring.

Statistical process monitoring (SPM) has become one of the most active research areas in the

last decade. As the SPM methods are data-based in nature, it is relatively easy to apply to

large scale processes as compared to other mcthods bascd on systcms theory or rigorous

process models. Today, SPM has found wide applications in differcnt industrial proccsses,

especially for fault detection (Qinghua, 2005).

It is relatively easy to detect the preser;ce of plantwide oscillations by analyzing routine

operation data. After the plant operators notice some oscillations in the plant, the problem is

deeply investigated and sometimes this revcals the existence of a plantwide oscillation of a

larger nature. Over the last few ycars, some studies were carried out to detect plantwidc

oscillations and to group the. similar oscillations togcther (Choudhury et aI., 2006; Jiang et aI.,

2006; Tangirala et aI., 2005).

2.3.1. Detection of oscillating disturbances

Thornhill and Horch (2007) organized a family trec of methods for the detection of plant wide

disturbilnces and cite the references. The main sub-division is between oscillating and non-

oscillating behaviors as shown in Figure 2.4.

12

Itime-domain mettlods

Wfl\'clcl

Matsuof'ltnl" 7.GO:l

no,.-.,..s:n!ionary

1

I

I5;:lOl':lml(~llVdo[?c

Jiang I;?I iJi ..

2006

spectml melhodsI

curreli:ltio~'

i iJ.ngiraln01,1;.,2005

PLANT-WIDE DISTURBANCE DETECTIONI

oscillating anrlI l!J( I-(J s~-.iI h:lt~r1~j

lieF rne\h()o~ ~pe(:[alpeaki-----~ detection

lew r.rl)!';sirY,s ,:1<l:1lPll1q {tcl,lbookiTho:nhill. Mii.:lO & Se:.HJrq.Huang & ~,99 dec8mpos'lio')Zhiln~ 20a] Thornhill ci .1'".LOO~

Xin 1'. r.(!'.'mll. 2005

Xia ~I al" :?O05Xi;;! el i:li" 20C?fanql;:.Jl<:l c! .11._ 200"',

oscillnhng

ll'!fO cross1r.q$

Thorntlill & H;j~EJlulld.191:;1"/For5mnn& Stnttin.1999

poles alARM" mode!Snlsbury & Singhnl, 2005,

lAE deviationsHagglund. 1995, 2005Forsman & Slaitin,1999

Figure 2.4: Family tree of methods for data-driven plantwide disturbance detection

(Thornhill and Horch, 2007).

Methods for detection of oscillation can be broadly classified as,

• Time domain techniques: Time domain techniques capture and explore the

temporal aspects of the measurements. This includes Integral Absolute Error

(IAE) deviation method, Zero Crossing method and Auto-correlation (ad) based

method.

• Freqneney domain or spectral techniques: Frequency domain techniques

extract the frequency and amplitude information from the raw measurements. This

include spectral decomposition method, spectral envelop method and power

spectrum method.

There is another method called Wavelet method which combines the time domain and

spectral techniques.

Advantagcs of Frcqueney Domain techniques over the Time Domain teehniqncs

1. Time domain techniques arc limited in their applicability to the oscillation detection

problem because they require the knowledge of process order and time .delays. On the

other hand, spectral techniques do not require any knowledge of process order and

time delays.

2. The oscillating disturbance can be visualized as a wave in the time domain and as a

peak in the frequency domain. On the other hand, for non-oscillating disturbances the

trends of the measurements may not look similar in the time domain. However, their

13

power spectra In the frequency domain arc capablc of revcaling their common

features.

Most of the methods mentioned abovc arc off-line thcrcfore cxploit thc off-line advantages,

like the use of the whole data history to determine a spectrum or autocovariance function.

The oscillation monitor of Hagglund (1995) is an on-line method. The methods in Hagglund

(1995,2005), Thornhill and Hagglund (1997), Forsman and Stattin (1999), Miao and Seborg

(1999) and Salsbury and Singhal (2005) achieve the detection of an oscillation using onc

measurement at a time. But more is needed for plantwide detection than the detection of

oscillations in individual control loops. It is important for the process control engineers to

recognize that an oscillation in one measurement is the same as the oscillation in another,measurement, even though the shape of the waveform may differ and interferences such as

other oscillations are present. Characterization and clustering is needed in addition to

oscillation detection. Thornhill et al. (2003) automated the detection of clusters of similar

oscillations.

2.3.2. Detection of multiple oscillations and non-oscillating disturbances

Spectra having broad-band features or multiple spectral peaks are the general characteristics

of persistent non-oscillatory disturbances. The plantwide detection problem requires:

(a) a suitable distance measure for the detection of similarity and

(b) determination and visualization of clusters of measurements with similar spectra.

Spectral decomposition methods have been used to distinguish significant spectral features

from broad-band noise that spreads all across the spectrum. Decomposition methods include

principal component analysis (PCA), independcnt component analysis (ICA) and non-

negative matrix factorization (NNMF).

2.3.3. Techniques for Detection of Plantwide Oscillations

Some of the techniques that can be used for detecting plantwide oscillation(s) have been

briefly described as below.

A. High density plot

B. PSCMAP

14

A. High Density Plot

In the high density plot both the time series data and their spectra arc described m a l1Iee

compact form in one plot. This is an excellent visualization tool that reveals the nature of the

data and the presence of common oscillation(s) in the data. The main drawback of this

method is that it is not automated to provide a list of the variables that oscillate together

(Choudhury et aI., 2006). Figure 2.5 is an example of a high-density plot.

"'" ''''

: : : : '"'' : : : : f"" : : :..

: : : : : : : : : : :"." ."..: : : : : : : : : :"n, '"

: : : ",,' : : : : ". : : :'\ : ,"" : : : : ". : : :

,,,.. '"~-;- : : : n,,, : : : '" : : :

: : : : .,," : : :1'" : : :: : : ..... : : ,n" : : :

: : : : 'H" : : : ::1::: : : :"'" '~'"

: : : : "'" : : : :"::: : :

: : : : "'" : : '" : : :: : : : "'" : : I : '" : : :: : : : .,'" : : : ."

--,- "" : : ...: :" ... ,..

: : : : "'" : : :11 ~: ::: : : :: : : : ..." : : :i: I:::: : : :

Time Trends

Samples

Time Trends

Power Spectra

222120191817161412119876543210.001 0.Q1 ..0.1

Frequency f I f5

Power Spectra

Figure 2.5: Time trends and their power spectra.

The left panel shows the time trends of the 22 process variables plotted in a nice compact

fashion. The right panel shows the power spectrum of the variables. It is hard to find the

variables with similar oscillations from the time trend shown in the left panel. The power

spectrum in the right panel clearly indicates the variables with similar oscillation because the

common oscillation has been showed up as a peak in a particular frequency, e.g., at the

frequency of 0.05 approximately.

B. Power Spectral Correlation Map (PSCMAP)

Another visualization tool termed as the power spectral correlation map (PSCMAP) can be

used for the detection of plantwide oscillations. This color map is based on a measure called

power spectral correlation index (PSCl). The power spectral correlation index (PSCl) is

15

defined as the correlation between the power spectra of two different measurements. It is a

nieasure of the similarity of spectral shapes, i.e., measure of the commonness of frequencies

of oscillations (Tangirala et a1., 2005). The PSCI for any two spectra IXi (co) 12 and IAj (co) 12

is calculated as,

2.1

Equation 2.1 ensures that PSCI always lies between 0 and 1.

For multivariate processes, the PSCI is a matrix of size m x m, where m is the number of

measured variables. An effective interpretation of the PSCI is provided by plotting the matrix

as a color map termed as Power Spectral Correlation Map (pSCMAP). The intensity as well

as the type of color in the map is assigned in proportion to the value of the correlation index

i.e., the correlation between the measurements decreases With the decrease of the intensity of

color. This mapping is performed according to the choice of color and the number of shades

in that color. The important aspect of PSCMAP is its ability to automatically re-arrange and

group variables which oscillate at a common frequency. Figure 2.6 is an example of

PSCMAP. From this map it is clear that the tags 1,2,4,5,6,7,8,9, II, 12, 14,21 and 22 are

oscillating together at a common frequency. In fact, in this PSCMAP the variables of Figure

2.5 have been grouped together according to the commonness of frequency.

Power Spectral Correlation Map20,.22

21

••12

'"CD 11:a•• 9'l: •~ 7

•5

•2

-

,,

1 2 4 5 6 7 B 9 11 12 14 ~ ~ 16 ~Variables

Figure 2.6: PSCMAP.

0.9

0.8

0.7

0.6

0.5

0.'

0.3

0.2

0.1

o

16

2.4 Diagnosis of Plantwide Disturbance

After the detection of the prcsence of plantwidc oscillation the next step is to identify its

root-cause. Plantwide disturbances are problematic for maintenance staff because it is

difficult to locate their sources whcn they are observed simultancously in measurements

recorded all around a plant. The testing of each control loop in turn until the root-cause is

found is time consuming and in any case is not guaranteed to succeed if the root-cause is a

process effect or due to plant structure (e.g., a recycle) rather than due to a control problem.

Plantwide diagnosis maps out the distribution of a disturbance across the plant and isolates

the location and nature of the root-cause of the disturbance. Recently there appeared a few

techniques in literature to perform root-cause diagnosis of plantwide oscillation (Zang and

Howell, 2006; Thornhill ct aI., 2003; Thornhillet aI., 2001). Figure 2.7 is a family tree of

.methods for the diagnosis of the root-cause of a plantwide disturbance. It focuses on the data

driven methods using signal analysis on the measurements from routine operation (Thornhill

and Horch, 2007).

ROOT CAUSE DIAGNOSIS

variance indexXi;) &. Ho••••'eli. 2003c<:Iusalily13alJer et ai,2004.2007mllitivan;'lltJ analYSISRossi et ai" 2006

Xi<l &. Howell,2003lang & Howell.700:lSI50 lllel!1{)ds

Vendor lools

Iil1l:i1r Cil,lSI)S1----' ----1

lunirlg dia£lnol;is inlcractionl1 structural

va~iance ir~de-x dragnosisintervontioncontroller (lain changeThornhill, Cox andPaulonis, 2003Rossi and Scali, 2005

CI"'.Oudhury, r<anwalaet ai, 2005

no interventioncross correlationHorch, H199Horch 01 01,. 200?sipnal probability denSity

Horch, 2002Yarnasllila,2006bwaveform ShaDE'

Rcn9<1~w<lrni 01 iJ"" 200',Stcnrnan ;Jl aL, 2003Kana I'll ill., 2004

Yamashita, 2004, 2006(/

Sin~Jhal and Salsbury,2005,Srinivasan, Rengaswamy& Millor, 200GRossi and Sc.ah, 20D5

Owen et ai, 1996Thornhill &Htlgglund.1997Ruel & Gerry,',998

. Z<Jng & Howell.2006

non-linem CUU5C!)i"------.--,------~-----.-.l

non-lineartimt: st:ries lImit cydt: methods v"lve dingllo~'s nll1\hudson,iys;s I ,--- ._._ .. _..-- .. _-_.. ,I hnrrnonics

LJicoherenceEmara.Shabaik et al"1996ChoUdhury af /)1"

2004surrogate testing

Thornhill. Cox &Paulonis. 2003Thoron & Aldrich, 200 ••Thorntlill, 2005correlation dimensionZang & Howell. .2004Hammcrsioin model,Srinivasan.Rengaswamy,Narasimhan & Millar.2005.

Figure 2.7: Family tree of methods for data-driven plantwide root-cause diagnosis

(Thornhill and Horch, 2007).

The root-causes are classified mainly as nonlinear and linear. The diagnosis consists of two

stages. Firstly, the root-cause of each plantwide disturbance should be identified. The second

stage istesting of the candidate root-cause loop to confirm the diagnosis.

17

2.4.1. Nonlincar root-causcs of a plantwidc disturbancc

There are different types of nonlincar root-causes of plantwide disturbances as follows,

• control valves with excessive static friction

• on-off and split-range control

• sensors faults

• process nonlinearities

• hydrodynamic instabilities such as slugging flows

Control loops having nonlinearities exhibit sustained limit cycles. Examples include the stop-

start nature of flow from a funnel feeding molten steel into a rolling mill (Graebe et aI., 1995)

and variations in consistency of pulp in a mixing process (Ruel and Gerry, 1998). A

hydrodynamic instability caused by foaming in an absorber column was described by

Thornhill (2005). These exemplify the presence of disturbances due to nonlinearity other than

control valve problems.

2.4.2. Linear root-causc of a plantwidc disturbancc

The most common root-causes after nonlinearity are poor controller tuning, control Ie:'

interaction and structural problems involving recycles. The detection of poorly tuned SISO

loops is now a routine work using commercial Control Loop Performance Assessment

(CLPA) tools. However, the use of signal analysis of routine operating data could not found

the solution of the problem whether an oscillation is generated within the control loop or

external. Promising approaches still require some knowledge of the process modcl (Xia and

Howell, 2003).

2.4.3. Diagnosis Tcchniqncs for Plantwidc Oscillations

Since oscillation can be conveniently characterized in the frequency domain, spectrum based

methods have emerged as popular tools in this area. Some of these methods are discussed

below.

18

2.4.3.1. Bicoherence Based Total Nonlinearity Measnre

For the analysis of nonlinearity in communication signals and mechanical machine condition

monitoring the third and fourth ordcr moments and thcir frcqucncy domain countcrparts

(bispectrum and trispcctrum) are found to bc uscful (Nikias and Pctropulu, 1993; Collis ct ai.,

1998). Currently, these highcr order statistical techniques have also found considerable

application in detection and diagnosis of nonlinearities in control valves used in process

industries (Choudhury etal., 2004; Choudhury, 2004).

Choudhury et al. (2006) defined an index called Total Nonlinearity Index (TNU) to quantify

time series nonlinearity,

2.2

where, TNLI is Total 'Nonlinearity Index, bic',;gniflcan, are determined using statistical

hypothesis test. The TNLI is bounded between 0 and L, where L is the number of biC2,;gniflmn,.

The loop with the maximum TNU is identified as the root-cause of plantwide disturbances.

The limitation of this approach is that it is applicable if the source of disturbances is

nonlinear. In case of a linear root-cause this index cannot hclp.

2.4.3.2. Bi-amplitude ratio analysis

Derived from bi-spectral analysis, a new diagnostic index called the bi-amplitude ratio is

._proposed as an aid to the isolation of the source of nonlinearity induced oscillations that can

propagate throughout a process plant. This ratio ,relates the power pertaining to the

fundamental, to the power pertaining to its third harmonic, and hencc it can quantify

harmonic attenuation or amplification with respcct to the fundamcntal as thc oscillation

propagates through the process plants. An oscillatory source can then be isolated provided

that low-pass filtering is inherent (Zang et aI., 2007).

However, the method has some limitations. If harmonics are hidden by this noise they will be

indistinguishable in the bispectrum. As a result, the dominant peak in the magnitude bi-

spectrum plot is not due to the bi-amplitude at the fundamental bi-frequency. Low-frequency

noise might also result in. the presence of a dominant peak at the corresponding low bi-

19

frequency in the bi-amplitude plot, i.e., at a location other than at the fundamental

bifrequency. The power of the harmonics may be disproportionately affectcd by noise.

2.4.3.3. Spectral Envelope Method

Jiang et al. (2006) proposed a new procedure based on thc spectral envelope method for

detection and diagnosis of common oscillation(s).

Let X (I) is a data matrix, if the covariance matrix and the power spectral density matrix.of X

(I) are denoted as Vxand Px(w) respectively, then the spectral envelope of X(t) is defined as,

2.3

where, A(W) is the spectral envelope and fJ is the loading vector. This method involves

complicated mathematical analysis and matrix operation.

2.4.3.4. Non-Negative Matrix Factorization

Tangirala et al. (2007) proposed the use of Non-negative Matrix factorization (NMF) of

multivariate spectra for plantwide oscillation detcction. A measure callcd Strength Factor

(SF) was defined to assess the strength of the localized features in the variables. The Strength

Factor (SF) always lies between 0 and I. The maximum value of SF indicates the root-cause.

However, this method has some limitations. Initialization of NMF algorithm is not

straightforward. Choosing the size of thc basis space required in NMF algorithm remains an

unresolved issue to date.

2.4.3.5. Distortion Factor Calcnlation

The presence ofa limit cycle infers the presence ofnonlincarity. Although thc limit cycles are

periodic, these are generally non sinusoidal and therefore have harmonics at multiples of the

fundamental frequency. When limit cycle is the cause of plantwide oscillation a candidate for

the root-cause is the time series with the maximum nonlinearity.

20

In their work, Thornhill et al. (2001) focused on the case where the root-cause was a

nonlinear element in a control loop. The~ proposed the use of distortion factor to aid the

diagnosis of oscillations. The distortion factor D is calculated as,

Plot - Prund

where, Ptot is the total power in the fundamental and harmonics and Pfuod is the power at the

fundamental frequency. The measurement having the highest distortion factor has more

power in the harmonics and is thus a candidate for the root-cause.

However, in the absence of well defined oscillation and spectral peak, D cannot be

determined. This method provides poor results in the presence of excessive noise in the data.

2.4.4. Use of Process Insights and Knowledge

Data driven and signal based methods have been developed in the past few years for finding

root-causes of plantwide disturbances using measurements from routine process operations

(Ruel and Gerry, 1998; Thornhill 2005; Xia and Howell, 2003). It has been observed,

however, that data driven analysis is enhanced if a qualitative model of the process is used as

well to capture the fundamental causal relationships of a process in a nonnumeric way

(Chiang and Braatz, 2003; Lee et aI., 2003;.

It is hard to find a good quantitative model representing the actual process. Also, the

multivariate connectivity of the process is ignored. Vim et al. (2006) attempted to capture

multivariate nature of the process plant topology.

The term topology has been used in its definition as the physical structure of a network.

When an electronic schematic of the plant and the results from a data driven analysis are

available, the users can use a prototype software to find root-causes of plantwide

disturbances. This software uses two new technologies,

i) the plant topology information written in XML according to the computer aided

exchange (CAEX) scheme and

ii) the results of a signal analysis tool called plantwide disturbance analysis (PDA)

21

The CAEX file describes items of equipment in thc plant such as tanks, pipes, valvcs and

instruments and how they are linkcd together physically and/or through electronic control

signals.

Information about the plant disturbances such as the pcriod, intcnsity and regularity of an

oscillation, the measurement points where it was detected and any nonlincarity detected in the

time trends are given by the PDA report file.

A reasoning engine finds physical paths and control paths in the plant and the connections

between items of equipment and determines the root-causes for plantwide disturbances. It can

also verify that there is a feasible propag~ti;'n path between a candidate root-cause and the

other locations in the plant where secondary disturbances have been detected.

Limitations of CAEX Plant Analyzer in identifying the correct root-cause stem from two

sources. Firstly, the rule base is incomplete because the science of root-cause diagnosis is not

yet complete. If the root-cause is a nonlinear effect the reasoning using signal nonlinearity as

described here is effective. Till now there remain other causes of plant wide disturbances such

as controller interaction and structural effects such as the dynamics caused by recycle. These

do not have nonlinear signatures, therefore enhanced signal analysis in PDA and rules to

operate on the PDA results arc needed for these cases.

Another limitation is that, even for a nonlinear root-cause, there may be no measurement

available at the exact source of the root-cause. In this case, a proxy measurement is used for

that unmeasured variable. If no proxy is available, then an outcome of a session with CAEX

Plant Analyzer might be to collect a new data set for analysis with more measurements

included from the region close to the suspected root-cause.

22

2.5 Chapter Summary

This chapter described various methods available for plantwide oscillation detection and

diagnosis. High density plot and PSCMAP are two tools to detect and group plantwide

oscillation(s). Upon detection of plantwide oscillation and finding the group of variables

oscillating with a common frequency, several techniques such as TNLI, bi-amplitude ratio,

NMF and distortion factor can be used to .isolate the root-cause of such plantwide disturbance

or diagnosis. All these diagnosis methods are frequency domain methods. This study focuses

on a time domain method based on Fourier series. The next chapter describes the theory of

the time domain approach proposed in this study.

23

CHAPTER 3

THEORY OF TIME DOMAIN APPROACH FOR PLANTWIDE

OSCILLATION DIAGNOSIS

3.1 THE FOURIER SERIES

3.2 FREQUENCY ESTIMATION

3.3 HARMONICS ANALYSIS AND PLANTWIDE OSCILLA nON

3.4 TOTAL HARMONIC CONTENT(TI-lC)

3.5 SUMMARY OF THE PROPOSED TECHNIQUE

3.6 CHAPTER SUMMARY

CHAPTER 3

THEORY OF TIME DOMAIN APPROACH FOR PLANTWIDE

OSCILLATION DIAGNOSIS

Industrial data is generally available in the time series format. As described in the previous

chapter, all methods available so far for plantwide oscillation diagnosis are frequency domain

methods. This chapter introduces a new time domain method to identify root-cause of

plantwide oscillation. The proposed approach uses Fourier Series to decompose the time

series data into sinusoidal components. Every sinusoidal component has an amplitude,

frequency and phase information, which are estimated using least square regresSIOn

techniques. Finally, harmonically related components arc used to define a new indcx called

Total Harmonic Content (THC). It is proposed to usc THC to troubleshoot plantwide

oseillation(s).

3. I The Fourier Series

Fourier analysis is a family of mathematical techniques, all based on decomposing signals

into sinusoids. All continuous periodic signals can be represented as a summation of

sinusoids. The Fourier series is an expansion of a periodic function j(x) in terms of an infinite

sum of sins and cosines. If j(x) denotes a periodic function of the real variable x with a period

of 27r, so that j(x+2n) = j(x), for all real numbers x, the Fourier series of the function j(x)

over [-n, nJ is given by,

where,

f(x) = ~ao + L-'; = 1an eos(nx) + L-'; = ibn sin(nx)

1 f' .ao =- f(x)dxn -,

1 f'an = - jCx)eos(nx)dxJr -,

3.1

25

1 f'b" = - f(x)sin(nx)dxTr -,

For an even function (where fix) = f (-x», fix) sin(nx) is odd. Therefore, b,,= 0 for all n.

Similarly, for an odd function (wherefix)-' fe-x»~, j(x) cos(nx) is odd. Therefore, a,,~ 0 for

all n. If the function is periodic on an interval [0 2L] instead of [-Tr Jil the coefficients can be

written as,

IfUao = - f(x')dx'L 0

I I2L e'lan = - f(x')cos(nllXl L)dx'L Il

1 f2L e'lbn =L 0 f(x') sin(nllXIL)dx'

where,

If the signal is odd, all of the even harmonics will have a value of zero. This can be shown

with the help of a square wave. Figure 3.1 shows an example square wave with a period of

2L. This is an odd function because it is not symmetric around y-axis. Mathematically,

fix) = 1, x .5"L

= -1, L.5"x .5"2L

Since the function is odd, so aD ~ an ~O and b" =~ L'J. f(x)sin(n"li)dx ,which reduces to,

bn = 3- f L f(x) sin(nJ'7i:)dxL 0

26

=~sin2(nJrI)/ll[ 12

=~[H-In/ll[

The Fourier series is therefore,

_4/ {o....,/nff 1

II evcn

11 odd

f(x) = i I _"I sii /lLTrX)n lI'O'I,J,5 l

4 { . (TrX) I . (3TrX) 1 . (5TrX)= l[ Sln~L + ]S1l1 L + SSin L + }

y

1

L L

- -1

2L

Figure 3.1: A square wave with a period of2L

In order to use Equation 3.1, one requires the analytical function for f(x). However, for a

chemical plant this is not available. Only routine operating data arc available from the plant.

These are time series data. They can be used to estimate the coefficients ao, a" and b".

However, it requires to rewrite Equation 3.1 in the following form so that least square

regression technique can be used.

27

Any time series, y(I), where I E: R can be reprcsented as,

~yet) = L: A; cos(A; 1+ 'M

1=0

For Mterms Equation 3.2 can be rewritten as,

y(t) = AI cos(}'11+M +A2 cos(A21+rh) + +AM COS(AMI+r/JM)+ e{l)

3.2

3.3

or,M

y(t) = L.: A, cos(A, I +r/J,)+ c{1)1=0

3.4

This equation with a finite number of terms is used in the calculation, since an infinitc

number of parameters would be impossible to estimate. Here, A is the fundamental frequency.

The error term c{t), is introduced because we are using M terms instead of infinite terms.

Each component in the right hand side of the above equation contains three unknowns

namely, amplitude (A), frequency (A) and phase (r/J).

Least square regression technique will be used to estimate each component at a time. For

example, if y is the time series data, YI = A, cos(A, I + r/J,) will be first estimated. Then from (y

_ y,) data, Y2= A2 cos(A2t +t/J,.)will be estimated. Subsequently from (y - y, - Y2), Y3 = A3

cos(A3t +rh) will be estimated. In this way all M terms will be estimated. Therefore, let us

write,

y, =Ao +A, cos(A,1 +r/J,)+ ",

=Ao+ acos(A,t) + flsin(A,t) + ",

where, a = A,cosr/J, and fl= A,sinr/J,

3.5

Equation 3.5 contains four unknowns namely Ao, a, A, and fl. The frequency A, will be

estimated first using Fernando-Quinn's technique which will be described in section 3.2. If A,

is known, parameters of Equation 3.5 can be estimatcd using simple linear least square

regression tcchniques. Predictions of y can bc made from the regression model,

y = AD + IX cos(..1,I)+ /J sin(..1,I) 3.6

28

WhereAo' a and 13 denote the estimated values of Ao, a and 13, 51denotes the predicted

value ofy. If Y denote the measured valuc ofy, cach observation ofy satislics,

The least square mcthod calculates valucs of Ao, ,a and 13, that minimizcs the sum of thc

squares of the errors S for an arbitrary numbcr of data points N,

N'\- ,s== LJEt1'=1

N~L {Yj - Au - aCOS(Ajl)- fi sin(A;I)) 2

i=l

If we replace the unknown values of A", a and fJ by their estimates, then using Equation 3,6, S

can be written as,

N N'" ,,,,' ,S = L. C; ~ L. {Y; - Ao - a cOS(AJ) - fi sin(AJ)}'i""l 1",,1

where the i-th residual, Cj, is defined as,

Generally, y(t) is available as time series data at equidistant time points, It may be assumcci

without the loss of generality that the data are observed at f ~ 0, I, 2, """ T - J, Let us

consider we have T set of available time series data, which can be written as,

YI =Ao+ acos(Alfl) + fisin(AI II)

Y3 = Ao + a eos(AI f3) + 13 sin (AI f3)

YT =Ao + a eos(AI fT) + fJ sin(AI f,)

29

These equations can bc writtcn in matrix form as,.

y,

X [icostA,!, ) ;;"",<,) 1

[;]y= Y2 costA,',) sin(A,',)and G=

YrcostA,')~ ~in(A,,) )

So that,

Y = XxG

The least-squares regression estimators of Ao, a and fJ are given by,

where,

D(A,) = XiX

3.7

[

1 COS(A1'1)1 COS(Al'Z)

- ; ~OS(Ah)

Sin(AlI1).1"[1 COS(A,11) Sin(AlI1)]sin(A1'z) 1 cos(Ah) sin(A,lz)

~in(Ah) ; ~os(}'h) ~il1(AI'.,)_

[

1+1+ ... +1= COS(,1,I,)+COS(,1,I,)+ +COS(,1,I,)

sin(,1,I,) + sin(,1,I,) + + sin(,1,I,)

COS(,1,I,)+ COS(}"I,)+ + COS(A,I,) sin(A,I, ) + sil1(,1,I,) + ... + sin(,1,I) Jcos' (,1,1,)+ cos' (A,I,) + + cos' (,1,1,) cos(A,I, )sil1(,1,I,) + ... + cas(,1,I) sin(A,I)COS(A,I,)sin(A,I,) + ... + COS(,1,I,)sin(A,Ir) sin' (,1,1,)+ sin' (A,I,) + ... + sin '(,1,1,)

T1"-1

D(AI) = L,=o COS(AI)

"T-'L.,=o sin(AI)

'\'T-'L.,=o COS(AI)

""T-l 'J

L.,=o cos-(AI)

'\'T-IL.,=o sin(At)coS(AI)

T-lL,=o sin(AI)1"-1

L,=o sin(AI) cos(AI)

"""T -I ..,L.,=osin-(At)

3.8

30

and

cos(Aj[l)cos(Ah)

sin(Al[l) T YIsin(Al (2) Y2

YT

1

cos (AI(2)

sin(AI[2)

Therefore,

L:T -ly(t)[=0

E(2,) = L:;=6 y(t) costA/)

L:J:r}Y([) sin(A[)

y, ~ AD +a, COS(A,I)+iJ, sin(A,I)

3.9

Now, from y - y, data, we can estimate the second term, I.e., Yl

=Al + el2COS(A

2/)+ iJ2 sin(A2[). In this way, all Mterms can bc estimatcd.

3.2 Frequency Estimation

Fernando and Quinn (1991) proposed a least square technique to estimate frequency of a time

series data. According to this when there is a second order filter which annihilates a (discrete-

time) sinusoid at a given frequency, ify(t) satisfies,

y(t) = A COS(A[+t/J) + x(t)

Then it also satisfies,

y(t) - 2 cosAy(t-l) + y(t-2) = x(t) - 2 COSAx(t-l) + x(t-2)

Now, Equation 3.11 can be written in the following form as,

3.10

3. II

31

y(l) - .8y(l- I) +y(I-2) =X(I) - a x(I-l) + x(I-2) 3.12

where, a = .8 = 2cosA. If a is known and the x(l) arc independent and identically distributed

then.8 can be estimated by Gaussian maximum likelihood, that is by minimizing,

1'-1 7"-1

2>~.p(l)=L {W) - .81;(1-I) + 1;(1- 2))2("'O 1=0

3.13

with respect to .8, where I; (I) = y(l) + a I; (1-1) - I; (1-2) and i;(t) = 0, 1< O. As Equation 3.13

is quadratic in .8, the minimizing value is the regression coefficient of I; (I)+ I; (1-2) on I; (I-

I), viz.

7"-1L {W) + 1;(1- 2)g(l -I)1=0

1'-1Le(l -I)1==0

1"-1

Ly(l)I;(1 -I)1==0- a -I- ~'-_I----

LI;2(1-I)

=a+h,(a) 3.14

It can be taken as a and.8 can be re-estimated using Equation 3.14. The iteration is continued

until a and .8 is sufficiently close. A is estimated from the equation a = 2cos A. However, in

order to accelerate the convergence the correction term h,(a) is replaced by twice that value.

The complete algorithm can be writtcn as follows,

i) Calculate a = 2 cos ~ , where ~ is an initial estimator of the true value An. ~ can

be estimated from the maximum value or power spectra.

ii) For j;:' I, calculate I; (I) = y(l) + a, I; (I-I) - I; (1-2), 1= 0, ... , T-I, where 1;(1)= 0, 1

<0.

T-1

Ly(I)W-I)

iii) Calculate.8j = a) + 2 f~;_1Lq2(t-I)1",0

iv) Ifl.8r !.1j1 is suitably small, estimatei = eos-' (.8) /2). Otherwise, let !.1j+1 = ,0 and

repeat from step (ii).

32

3.3 Harmonics Analysis and Plantwide Oscillation

Figure 3.2 shows 'different representative forms of oscillating time series data and their

corresponding power spectra. At first, we consider the last row showing a simple sinusoidal

time trend. For this signal, the corresponding power spectrum gives a single sharp peak at the

normalized frequency of 0.0 1. Since this was a single sinusoid, the power spectrum produces

a single frequency. On the other hand, for the multiple sinusoids there are two peaks at the

power spectra having normalized frequency of 0.0 I and 0.02. This simply reveals the

overlapping of two sinusoids of two different frequencies in the time series data. Now we

consider the second row, it shows that for the rectangular time trend of the error signal the

power spectra produces gradually decreasing peaks at normalized frequency of 0.01, 0.03,

. 0.05 and 0.07. This indicates that only odd harmonics are resulted in the power spectra of

rectangular signal. In addition, the fundamental frequency of 0.01 samples/cycle corresponds

to lOa samples/cycle. For the saw-toothed nature of the time-trend, power spectra produces

gradually decreasing peak at normalized frequency of 0.01, 0.02, 0.03, 0.04 and so on.

Therefore, a saw toothed signal has both odd and even harmonics.

Time Trends

I !I I, I~ ~ ~"Ni'... !

••.• -loolh f""! "'! " i ,,! s.w-toolhI" ,,"1 ~, I

I ,.----, ,.------" In ,-!~cIang(j.LJ L.J \_'_! u LJ 1 rectangular

I II ,ilC.. r.. r', 1\ li\ I

,uIlp. ''''1 V\, j "of\ ! V\ i \/\, V\, j sumoisoes\j Ii J V VI

, I,ro" r., 1\ f\ j' I

SinfClm:

I

' '\ / \ ./ \. / \ I \ i. sine curve,-.j \j \/ \j Vi,

II II soo

Sa••

Po•• , Spectra

0.01 0.1Frequency f I f•

Figure 3.2: Harmonic relations of different types of error signals.

It was confirmed earl ier by Xia and Howell (2005), that the rectangular error signal was

resulted in a sticky control loop. Thus for a sticky control loops odd harmonics can be found.

33

Even harnionies might be found due to the presence of nonlinearities in the loop other than

stietion.

Let us consider the time series data and the corresponding power spectra for a sticky valve as

shown in Figure 3.3. The time trend is almost rectangular and the power spectra give peaks at

the normalized frequency of 0.0078, 0.024 and 0.039. Here, 0.0078 is the fundamental

frequency and 0.024 and 0.039 are the third and fifth harmonics respectively.

1

Time Trends

Samples

Power Spectra

1024 0.001 0.01 0.1Frequency f If. ,

Figure 3.3: Time series data and the power spectra for a sticky valve.

Sinusoidal fidelity states that if a sinusoidal input passes through a linear system, the output

of the linear system is a sinusoid with the same frequency, but with a different magnitude and

phase (Choudhury et aI., 2008). A linear system does not produce any new frequency. On the

other hand, when a sinusoidal signal with a certain Irequency passes through various types of

nonlinear systems or functions such as a square function, an exponential function, a

logarithmic function and a square-root function, nonlinear systems may generate harmonics

in addition to the original fundamental frequency of the input sinusoid. Thercfore,

nonlinearity induced oscillatory signals generally contain a fundamental frequency and its

harmonics. Harmonics are oscillations whose frequencies are integcr multiples of the

fundamental frequency.

A common cause of the plantwide oscillations is a nonlinearity in a control valve (Astrom,

1991; Cook, 1996). As it is said, such nonlinearity induced oscillations contain harmonics,

asymmetric triangular waves arc often observed in controller outputs (Hagglund, 2002;

34

Rengaswamy et aI., 2001), whilst valve stiction often produces squarc-like waves in the

controlled variable (Xia and Howell, 2006). Although both symmetric triangular and purc

square waves contain solely odd harmonics, in practice the time series records may contain

even harmonics too.

It is well known that chemical process plants act as low pass filters, i.e., they allow low-

frequency signals to pass but attenuates signals with higher frequcncies. This can be

discussed with the help of the bode plots which are widely used means of displaying the

frequency response information of a system. If we consider the bode plot for the low pass

filter as shown in Figure 3.4.

10I'C< 0-=~" -10-=" -~O~.~Sj, -30'"•••'" -40

1 10 100Fl"f'PlfIH'Y

-&- Low Pn."."- BodE" Pole-

FrfllUtlH)'

Figure 3.4: Bode plot for a low pass filter (http://en.wikipedia.org/wiki/Bode plot).

In the gain plot (the upper plot) the two lines meet at the corner frequency. From this plot, it

can be seen that for frequencies well below the corner frequency, there is no attenuation, i.e.,

the amplitude of the output equals the amplitude of the input. Frequencies above the corner

frequency are attenuated. The higher the frequency, the higher.the attenuation.

In the phase plot (the lower plot) for input frequencies much lower than corner, the ratio w/we

is small and therefore the phasc angle is close to zero. As the ratio increases the absolute

value of the phase increases and becomes - 45 degrees when W = We. As the ratio increases

for input frequencies much greater than the corner frequency, the phase angle asymptotically

approaches - 90 degrees.

35

http://en.wikipedia.org/wiki/Bode

The above-discussed behavior is the characteristic of most of the chem ical process plants. It

is observed that the process gain typically decreases as the frequency increases in most Bode

plots no matter if it is a first, second or third order process.

3.4 Total Harmonic Content (THe)

This study focuses on the nonlinearity induced plantwide oscillation. It has been already

discovered that nonlinearity produces oscillation with fundamental frequency and its

harmonics. Power spectrum can reveal the fundamental frequency and its harmonics.

However, for a large number of variables in a process plant, it is inconvenient to look at so

many figures. Therefore, it is desirable to quantify this harmonic information u'sing a single

index. This will not only help quantifying information but also facilitate automation of

diagnosis procedure. For this purpose, a new index called the Total Harmonic Content (THe)

has been defined as,

THC = nx WI-1M 3.15

Where, n is the number of harmonics found and WHM is the Weighted Harmonic Mean.

WHM is defined as,

WHM 3.16

where, w; is the weights and is defined as, w, =i/I:,i so that the summation of the weights

is equal to 1. More weights are given to the higher harmonics because due to the low-pass

filtering effect of the chemical processes the higher harmonics get filtered out gradually as

the signal propagates away from the source or the root-cause.

For plantwide oscillations, the amplitudes, frequencies and phases of first five term of

Equation 3.4 are estimated. Tags or variable, having the same fundamental frequency and

harmonics (if any) are identified. Weighted harmonic mean is calculated using amplitudes

whose frequencies are in harmonics and multiplied by number of harmonics present. After

calculating the THCs using Equation 3.15, the variables are ranked according to the

descending order ofTHC. The possibility of being the root-cause increases with the increase

of the value ofTHC.

36

Plant information such as Piping and Instrumentation (P&I) diagrams, Process Flow

Diagrams (PFD) and operators' knowlcdge should bc utilized in conjunction with the

information provided by THC to confirm the root-cause (Choudhury et aI., 2009). The chance

of being right first time is high. However, if the variable with the maximum value ofTHC is

not the root-cause, the variable with the second highest value of THC should be investigated

as a root-cause. Thus, maintenance effort should be started from variable with the maximum

value ofTHC to the variables in the descending order of THe.

3.5 Summary of the Proposed Technique

1. Detection of plantwide oscillation using High Density Plot and PSCMAP

2. Get the group of variables for plantwide oscillation diagnosis

3. Estimate amplitudes, frequencies and phases for all variables

4. Estimate THC for all these variables

5. Rank the variables according to thc magnitudc of THe. Thc variable with thc

highest THC is most likely the root-cause

3.6 Chapter Summary

This chapter describes how time scries data can be decomposed into sinusoidal components

using Fourier Series. Simple linear least square regression techniques and Fernando Quinn's

technique have been used to determine the amplitude, frequency and phase information.

Finally, harmonically related components are used to define a new index called Total

Harmonic Content (THC). This new time domain method is proposed to apply to identify

root-cause of plant wide oscillation. In the next chapters, the proposed THC index is evaluated

in simulated, laboratory and industrial data. sets.

37

CHAPTER 4

EVALUATION OF THC IN SIMULATION AND INDUSTRIAL

ENVIRONMENT

4.1 THC INDEX EVALUATION IN SIMULATED VAc PROCESS

DATA SETS

4.2 THC INDEX EVALUA nON IN INDUSTRIAL DATA SETS

4.3 CHAPTER SUMMARY

CHAPTER 4

EVALUATION OF THC IN SIMULATION AND INDUSTRIAL

ENVIRONMENT

This chaptcr describcs the evaluation of the proposed index called Total Harmonic Content

(THC). For the assessment of new technologies, researchers arc always interested in

obtaining realistic test problems for plantwide design, optimization, and control. In this thcsis

work, the efficacy of the proposed methodology for root-cause diagnosis of plantwide

oscillations has been evaluated using both simulated and industrial data sets. Since it is not

possible to say the identified root-cause is the right one without any verification, at first data

were analyzed where the root-causes of plantwide oscillations were known. This evaluation

work is discussed in detail in the following sections.

4.1 THC Index Evaluation in Simulated VAc Process Data Sets

In 1998, Luyben and Tyreus published a model of a large, industrially rclevant system of

vinyl acetate monomer (VAc) manufacturing process. The VAc process contains sevcral

standard unit operations that are typical of many chemical plants. Both gas and liquid recycle

streams are present, as well as process to process heat integration. Chen et al. (2003),

published the Nonlinear Dynamic Model of the Vinyl Acetate process developed in the

MatLab. Both the steady state and dynamic behavior were modeled using MatLab. This

model is freely available from the authors' website. Because the MatLab model does not

depend on commercial simulation softwarc and the source code is open to the public, the

model can be modified for use in a wide variety of process control research areas. Figure 4. I

shows a simplified schematic of the Vinyl Acetatc Proccss with the locations of the

manipulated variables.

In the VAc process, there are 10 basic unit operations, which include a vaporizer, a catalytic

plug flow reactor, a feed-effluent heat exchanger (FEHE), a separator, a gas compressor, an

absorber, a carbon dioxidc (C02) removal systcm, a gas rcmoval systcm, a tank for the liquid

recycle stream and an. azcotropic distillation column with a decanter. There arc seven

chemical components in the VAc process. Ethylene (C2H4), pure oxygen (02), and acetic acid

(HAc) are converted into the vinyl acetate (VAc) product, and water (H20) and carbon

39

dioxide (C02) are by-products. An inert, ethane (C21-I6), enters with the fresh C21-I. feed

stream. The following reactions take place,

4.1

4.2

The process model contains 246 state variables, 26 manipulated variables and 43

measurements. The process takes approximately 300 minutes time to reach steady state. For

details, refer to Chen et aI., 2003. This section describes a simulation case study for root-

cause diagnosis of plantwide oscillations using the nonlinear dynamic model of the Vinyl

Acetate process.

Recycle Gas

Vaporizer

Scrub Stream

~ AqueousProduct

CO2 Purge

Purgeo

()

2.c3~

HAC Tank

'-' @~Acetic Acid

Feed

Steam

Reactor

0)

Acotic AcidRecycle

O_x_y_ge_n_F_ee_d_~.. I@

@~EthyleneFeed

Figure 4.1: VAc process tlowsheet (Chen et aI., 2003).

In order to create plantwide oscillations disturbance, valve stiction was introduced to control

loops 9 and 14, independently. Valve stiction was introduced using Choudhury's stiction

model (Choudhury et aI., 2005). The summary of the model is provided in Appendix-E.

40

Introduction of valve stiction in a control valve causcs limit cyclc oscillations. Thc oscillation

generated in the loop containing sticky valve may propagate to other control loops and

eventually to the whole plant or some part of the plant. Different extent of stiction as 1%,2%,

3%, 4% and 5% was introduccd so that both thc systems sensitivity to disturbance and the

THC's compatibility can be studied.

In loop 9, the controlled variable is the separator temperature and the manipulated variable is

the scparator coolant valve corresponding to the cooling water Ilow rate for thc scparator

jacket. After the process reached steady state, different extcnts of stiction (I %, 2%, 3%, 4%

and 5%, where S = J) was introduccd in the manipulated variable coolant valve. Simulation

data set consisted of 2000 minutes of data with a sampling time of 15 seconds; therefore,

each variable has 8000 observations. The last 1024 data points were uscd in this analysis in

order to avoid transient behavior due to the sudden introduction of stiction. Figure 4.2 shows

the time trends and power spectra and Figurc 4.3 shows the PSCMAP of thc manipulated

variables of the Vinyl Acetate process for 5% stiction. Both PSCMAP and power spectra

show that the variables 1,2,4, 5, 6, 7, 8,9, II, 12, 14,21 and 22 are oscillating togethcr. The

high density plot reveals that they are oscillating at a normalized frequency of 0.0505. The

same results wcre obscrved while 1,2,3 and 4% of stiction was introduced.

Time Trends,

22 __ WI,YIIiIIII;YIM~~21 - !jl)NJWJ'I:JNM~WN(JM'/tNyrf.!"Y;"'V,wrJ(~

~~~-;~':O-.-"'~.:~~~_~:•..~''-~.Ii14 ~Wll\'ill\\WINIII!12 1IINIIIl!lllllllllMllllllIiIWlII/IIMYilllllil11 MIIIII.'(IIIMIWI~'fWNN{iIMW"YII,,\'llil9 ml'lNL~LlJilIllIllNl1.rv~WI/Uf!NlliUlWIlJllWl1r~JI'lM!'i!lPi

8 !IIIIIIIIIIIIIN/IfIIIINIIMWlIllI/NIIl/!IH\7 ~'IN,'/mI/IlIiIIIIWNIIIINNIWIMWII,1

6 !E-\'I~f:I~y~:~,r[:\Il\~~INJ)"),~5 ~!,11M\iiif1,y«,'4 w \W,W,t(MWIiI"YJ(;~WNilllC2 ;II/IIIN"YIi\\IIj\lil\~Wi\llilh\Yh\\\l\WIM~

1 '_M~WlHlkNl~fINIIliII'1

Samples1024

Power Spectra

b",-c ":::,::~22--"" "."'.r ., :: ' :,:: I

21 1".:' ..'1'- ... :::::::1~~ l"'t i' ;; r I141"" 'T::'~I..••••••Iil

I " ''1',',1~ ! ,...1151 .....1"'141 ......TiIHi

~L~:L~~..jJL.L:0.001 0.01 0.1

Frequency f I fs

Figure 4.2: Time trends and power spectra for the VAc Process Variables, appl ied stiction inloop 9 is 5%.

41

Power Spectral Correlation Map20

16

22

21

14

12IIIGl 11:c 9III;:

8ca> 7

6

5

4

2

1

-

-

1 2 4 5 6 7 8 9 11 12 14 21 22 16 20

Variables

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

o

Figure 4.3: PSCMAP for the VAc Process Variables, applied stiction in loop 9 is 5%.

Total Harmonic Content (THC) was calculated for these variables. Figure 4.4 (a, b, c, d and

e) show the calculated THC values against the variable or tag number. The maximum THC

corresponds to the tag 9 correctly indicating the root-cause of the plantwide oscillation

because stiction was introduced in this variable during simulation.

@

'"G

@

0",@)

'" 66 @) Q

0.700-:E:I- 0.60-••i 050••Co(J 0.40

.~C 0.30oE:a 0.20:E:S 0.10

~0.00

o 5 10 15 20 25

Manipulated Variables

(a) Applied Stiction is 1%.

42

302520

.----- -to. - _.

15105

i

----.~GT-~.--~----~---~---.---~-~----.-------.

I, i ° i

I -I_______ :_._~ __,I. _0_"'_- _G>_ .. ,. . ! I

II '" --1-----0 r~O0(;} i I

I LI Ii 0 I---_ ...--()..--_ ..._ ...~-_.~--- -

i '____ .• .~~~~~.~ __ c_1III

II

1 i~--J0.00o

0.20

0.30

0040

19 0.10oI-

0.70ITJ:I- 0.60-•..c.s 0.50CoUocoEL.IIIJ:

Manipulated Variables.

(b) Applied Stiction is 2%.

0.70~ (1)UJ: 0.60 -- ----I- i- I.•.. ,

C 0.50 ICllI.•.. @>c __.-10 OAOU I

.!:! !c 0.30 ---eo' --c+0E iL.III 0.20 IJ:

@ i 0 @III @.•.. :::1"--- . !0

,I- !

,II

0 5

t,

10 15 20 25


(c) Applied Stiction is 3%.

43

252015105

III

I.

e--

'". III

ee III

e •e III ••III

0.00o

0.20

0.30

0.40

.l! 0.10oI-

-c2 0.50CooCJCoE••l'G:x:

0.70IT:x:I- 0.60-


(d) Applied Stiction is 4%.

252015105

III

.

"...-

III

e,Ill. •

•• •• • ••0.00o

0.20

0.30

OAO

-5 010

I-

-c2 0.50Coo.~coEl'G:x:

0.70-o:x:I- 0.60-


(e) Applied Stiction is 5%.

Figure 4.4: THe value~'for the VAc Process Variables for stiction applied in loop 9.

44

In loop 14, the controlled variable is the circulation stream temperature and the manipulated

variable is the absorber scrub heater valve corresponding to the scrub stream flowrate for the

absorber. After the process reached steady state, different extents of stiction (1%, 2%, 3%,

4% and 5%) was introduced in the manipulatcd variable heater valve. Simulation data set

consisted of 2000 minutes of data with a sampling time of 15 sceonds containing a total of

8000 observations for each variable. Again, the last 1024 data points were used in this

analysis in order to avoid transient behavior due to the sudden introduction of stiction. For

this loop introduction of 1% stietion did not produce any plantwide oscillation.

Figure 4.5 shows the time trends and power spectra and Figure 4.6 shows the PSCMAP of the

manipulated variables of the Vinyl Acetate process for 5% stiction. Both PSCMAP and

power spectra show that the variables 5, 6 and 14 arc oscillating together. The high density

plot reveals that they are oscillating at a normalized frequency of 0.0625. The same results

were observed while 2, 3 and 4% of stiction was introduced. The first group in the PSCMAP

containing variables 7, 9, 11, 16, 20 and 21 corresponds to the very low frequency variations

in the data.

Power Spectra~~-''''-'~~~'''.'~'-']N-/~! '.H • U22,",;: ::; ::,1""-'-....... •..... .1

21 i""' ••• • I Ii"- II.... • .1

::@::r . ,:;11~~. ..+; '19Mi' :'.:"N-'::' .... "\7[""":. -. :;:; .. '1: : ..- : ::::: ::: : :: : ::: :;:

6u

'; > "1. ::: :;::: : :: ,.:::: :::

5 iliJB1~~'~.~_U0.001 0.01 0.1

Frequency f I f5

I.~::,,:,,:,,:,:,,----'l--,

I-_._-~~

,

Time Trends

Samples1024

___ __J

iWlitiNmm~t\\Wlli~.1I!~/IIIII!WIlllNllilt'tllNl/llli%Wllllm~~l~~,

I

1

7

6

5

9

2221

14

----:-:.JI

--~'-=~:~:'::I

lIIIlilllllllllllllllllJJlllllllrul\llllllllll:

11---.------ ---------_."--.v.w,,~iW;~~i

2016 --

Figure 4.5: Time trends and power spectra for the Vac Process Variables, applied stietion inloop 14 is 5%.

45

Power Spectral Correlation Map

14

6

5

22UI.!! 21;Cas-i: 20

~16

11

9

7

,I

,

I

7 9 11 16 20 21 22 5 6 14

Variables

0.9

0.8

0.7

0.6

0.3

0.2

0.1

o

Figure 4.6: PSCMAP for the VAc Process Variables, applied stiction in loop 14 is 5%.

Total Harmonic Content (THC) was calculated for these variables. Figure 4.7 (a, b, c and d)

show the calculated THC values against the variable or tag number. The maximum THC

corresponds to tag 14 correctly indicating the root-cause of the plantwide oscillation because

stiction was introduced in this variable during simulation.

Gl

Gl

Gl Gl Gl

0.70U:J:I- 0.60--c:Gl 0.50-c:oo 0.40U'2 0.30oE:ii 0.20:J:S 0.10oI- 0.00

o 5 10 15 20 25


(a) Applied Stiction is 2%.

46

_ 0.70

"'Il.lJ:I- 0.60

I-•..<: 0.50

,C1l I•..<: I0 0.40l.l It.l"c 0.300E.. 0.20l'GJ: @

iii 0.10 ----•.. @ "0 "I-0.00

o . 5 10 15 20 25 30


(b) Applied Stiction is 3%.

30252015105

OIl

.

.

--

--- --

••" " •• ••

0.00o

0.30

0.40

0.20

]i 010oI-

•..<:S 0.50<:ol.l.!:!<:oEl'GJ:

_ 0.70l.lJ:I- 0.60-


(c) Applied Stiction is 4%.

47

Ii>

1-------I

IIi

i i ,-_._- I I, , I

r I I! !

i I,

I I I JI I

C!> <b I

G E> Ii>

0.70

uE. 0.60•..~ 0.50•..Co() DAD

.!:1c: 0.30oECO 0.20::t:'E! 0.10ot-

0.00o 5 10. 15 20 25


(d) Applied Stiction is 5%.

Figure 4.7: THe values for the Vac Process Variables for stiction applied in loop 14.

The harmonic analysis results of the simulated VAc process are given in Appendix-B.

48

4.2 THe Index Evaluation in South East Asia Refinery (Sear) Data Sets

The proposed method was applied to a benchmark industrial data set for plantwide

oscillations study appeared in the literature such as (Tangirala et aI., 2007; Tangirala et aI.,

2005; Thornhill et aI., 2001). The data set, courtesy of a South East Asia Refinery, consists of

512 samples of 37 measurements sampled at I min interval. It comprises measurements of

temperature, flow, pressure and level loop along with some composition measurements. A

simplified schematic of the refinery proqes5 is shown in Figure 4.8. The process contains a

recycle loop from the PSA unit to the reformer unit. Controller errors are analyzed for control

loop measurements.

f'I':O"_"'~ ';1,1'.

illl,,1 \<'lIlI>,'I,lIUl":'

Fu~ 0;:1(''1' fkr\~' (ZO:;,1o Dr>f\sity (3S)o Tt'mp<.'lolfurQ f:;(.ja Prl'~Slllo(371

o

o Cl) t.n{jl','t(>f It 9)

D GHJ :'nhly:N q(+;

Figure 4.8: Schematic of the SEA Refinery Process (Tangirala et aI., 2007).

The time trends of the controller errors and the corresponding power spectra are shown 111

Figure 4.9. Power spectral correlation map (PSCMAP) shown in Figure 4.10 indicates that

the tags 2, 3, 4, 8, 9, 10, II, 13, 15, 16, 17, 19,20,24,25,28,33 and 34 are oscillating

together with a common frequency of 0.0605 or 17 samples/cycle approximately. All data

corresponding to the variables with the common frequency were first normalized so that they

had zero mean and unit variance. Then the amplitudes, frequencies and phases for first five

49

sinusoids were estimated and THCs wcrc calculatcd for thcsc variablcs. Thc calculatcd THC

values are plotted against thc tag number in Figure 4.11. The highest THC value corresponds

to the tag no. 34, which is the first candidate for the possiblc root-cause of this plantwide

oscillation. In real plant investigation if this tag is not found to be the root-cause, then the tag

corresponding to next highest value of THC should be investigated. For this case, earlier

studies (Thornhill et aI., 2001; Tangirala et aI., 2005; Tangirala et aI., 2007) found tag 34 as

the root-cause. Therefore, the proposed THC index correctly detected the root-causc of these

plantwide oscillations. The harmonic analysis rcsults ofthe SEA refinery data set are given iri

Appendix-B, Table B-16.

Power Spectra

v•••

,,V , . •• .','V .. ' ... . " ,V . . ; .V

. , ," ,

V,

. ',

V••

V•••

,•V

. "

,V

V

V

V , , , ;,V ,

•••V••, , ,

V ~ .. , , ,

...~- : ~: ,• i'

, ,

,•

.~, .-, . , ,!

•••

,,

-' , , ,

• • ••I•• I' , ,•!••••

••,

PCJ8003B.P

TIJ8001.P

AIJ8002,P

F176304.P

FC76301S.P

FC76022.P

FC76018.P

FeT6017.?

FC76012.P

Fe7G01'.?

FC76009.P

FC76008.P

FC76004.P

FC76002,P

FC76001.P

A176302.P

AI76009,PV

Ar76007,PY

A176006.PV

LC76028,PV

LC76026.PV

LC76022.PV

LC76020.PV

LC7G019.PV

LC76011,PV

LC76001,PV

P176055.PV

PC76064.PV

PC760J9.PV

PC76036.PV

PC76020.PV

PC7601'.PVTC76095.PV

TC76058,PV

TC76054.PV

TC76025.PV

TC76013.PV

Time Trends

3736

J534

3332~,mIlM'IIII<'~,~1Ii!"~~i,IIii\I,\~~\~I~III~liIMJ.""(,I/o\W~

"3029

28

27 ~/II-li'I'#~\/I'!I>V"''I'I'MV~26 If'25 - ~

24 !'t'rA~23 iI\I~~\11lr1k!!N\f'lit"'<\'!\Iti'f'I"'J~il'i"wWlN2221

5\2Samples

0.01Frequencyf/f.

0.1

Figure 4.9: Time trends and power spectra for the South-East Asia Refincry data set.

50

;. - ,- ,-

,-

.. _ . , ; I. ,,

, ,, -

,

,, ,

,, - -

I,- - -I,-

I --I

II I

- i ;

-I; , ,

- _. ,I

323027261.•129231817312221537

'" 38.!! 35~ 12'l: 7Ill ••> ••

2825242019,.151311109••32

Power Spectral Correlation Map

234 B 9 101113151619202425283334712353637521223117182329161426273032

Variables

Figure 4.10: PSCMAP for the South-East Asia Refinery data set.

0.9

o.a

0.7

0.6

0.5

0.'

0.3

0.2

0.1

o

III

II

8

8 IIG>

G>

1.2

~1: 0.8

!." 0.6C

~~ 0.4

~0.2

oo 5 10 15 20

Tags

25 30 35 40

Figure 4.11: Total Harmonic Contents (THC) Results for SEA refinery data set.

51

4.3 Chapter Summary

This chapter describes two case study examples for the assessment of the proposed

methodology. At first data were generated using a simulated nonlinear dynamic model of

Vinyl Acetate process where fault was introduced to particular control loops ofthc system. In

addition, an industrial data set of a Sf Asia Rcfinery was analyzcd where the root-cause or

plantwide oscillation was known. In order to establish the potcntial of the methodology to

identify the root-cause at the first chance thcse simulated and industrial data were then

analyzed. The methodology correctly identifies the variables causing the plantwide

oscillations for both data sets.

52

CHAPTERS

EXPERIMENTAL SET UP

5.1 THREE TANK LEVEL PLUS TEMPERATURE CONTROL PILOT

PLANT SETUP

5.2 SCHEMATIC DIAGRAMS

5.3 DETAILED DESCRIPTION OF THE PLANT

5.4 OPERATING PROCEDURE

5.5 CHAPTER SUMMARY

CHAPTER 5

EXPERIMENTAL SET UP

As said in the previous chapter, laboratory based experiments were also carried out under this

thesis work. This chapter gives a complete description of the experimental set up along with

diagrams. In addition, the operating procedure for the set up has been described here.

5.1 Three Tank Level plus Temperature Control Pilot Plant Set up

There is a pilot plant set up called Three Tank Level plus Temperature Control in Chemical

Engineering Department, BUET. It is used to control water level and temperature for Process

Control study at undergraduate and graduate level course work. This setup has seventeen

variables - three levels, six temperatures, four flows and four controller output. Figure 5.1

shows a simplified schematic diagram of the pilot plant set up. Figure 5.2 shows a detailed P

& ID diagram of the set up.

54

5.2 Schematic Diagrams

Water Inlet FT 01 FCV 01 TT 01

Stearn

I r fl to•• 11<l"

TCV 01

LT0191 @!Illj__ '-/I~1-l -- I--

~ I:::=; ~ TT OSTCV 02

~

T 11 I ~FC; 02 ~.

E-o

TT 061 __

Dram

FT 02

FT 03

FT04

/'I '"I ,

/ ''-

~~C3

~LT03

<~

Drain

Water Inlet

.Pressure Gauge

Boiler

Figure 5.1: Schematic Diagram of the Three Tank Level plus Temperature Control set up.

55

... 1 TT - c.:;

_,--J LT. (Ii

,L iTT. (14

--:::1IT.O:

- -:~:JLT - (t-,:

-,L ~ TT. (I:'

- -,

,L_

_ HC"'i4.~,

- -',,,,,,It - - -

To dnm

,.-Onir, H'!3,j':r

HOT WATER

•••

~,5

MP---- -------, Un-",---------~~.:iCV01 -----------------------~~~~L---}_~~~~~~~~g~~~,01Hc;jL---:""-;-;- ! -_-_- ===::-_==~:T:::;

COLO WATER --,--:;;;--------:::=-=- :......oJT!.:· I,~OO"'''OO __ : __~24 ------- , '-:JFT-O_'STE"', : 3. .<->.-. LTo, _ _ _ " __

I --- 'l,,{J'YtJ.L_--, 0'--- - , L -':-J'CV- •

'"~,,, " " L __ , ~

--" "~ " C.J ""." - -- -- - -, -,

--- L --~ FT-(\";~---, -- 1

----- , -'-J FT-O'

ToTCVO' ,,"

.-H, ,~. J TI"

Figure 5,2: P&ID of the Three Tank Level plus Temperature Control set up.

56

,0"

....J .• '~••. , •• ! •

,

Figure 5.3: The Three Tank Level plus Temperature Control pilot plant set up at the Process Control Laboratory.

57

5.3 Detailed Description of the Plant

The Pilot Plant set up of three Tank Level plus Temperature Control consists of the following

major parts,

•••

•••••

••

Tanks

Pneumatic Control Valves

Transmitters (Flow,.Levcl and Temperature Transmitters)

Manual Valves

Heating Coils

Steam Traps

Boiler

Compressor

Water Supply Line

Instrument air supply

Detailed description of these items and other associated items is given below,

5.3.1 Tanks

There are three tanks in the setup. Material of construction of these tanks is SS, Grade

_ 304. Size of each tank is 28"x 28"L. Two tanks (Tank 1 and Tank 2) are of simple

cylindrical shape. Tank 3 has conical shape at the bottom, and there is an inverted

cone inside this tank ..

5.3.2 Pneumatic Control Valves

There are four pneumatic control valves of fail to closed type. Two valves named

FCVOI and FCV02 control the flow of water to the tanks. The other two valves

named TCVO I and TCV02 control the flow of steam through the coils. Material of

Construction of each valve is SS, internal threaded. Size of each valve is y," in

diameter.

58

5.3.3 Transmitters (Flow, Level and Temperature Transmitters)

There are three types of transmitters in the setup. Level, Temperature and Flow

transmitters. The flow, level and temperature transmitters are designated as FT, LT

and IT respectively. The flow and level transmitters arc of Model 1151 Smart

Pressnre Transmitters. The temperature transmitters arc of Model 644H and 644R

Smart Temperature Transmitters. All are manufactured by Fisher-Rosemount Inc.

5.3.4 Manual Valves

There arc two types of manual valves (HCYs) through out the set up. These are ball

valves and needle valves. Material of construction for all types of valves is SS,

internal threaded. Size of the needle valves is 1," and ball valves are of I", 1, " and

1,4" .

5.3.5 Pipe Line

All pipelines for transpOlting water and steam arc made of SS, grade-304. The size of

main pipeline is 1," diameter, Schedule 10 and the size of the lines that goes to the

transmitters is y.." diameter, Schedule 10.

5.3.6 Heat Exehanger/ Time delay study coil

There is a heat exchanger in between Tank I and Tank 2 made up of SS, Grade -304.

~ize is 1," diameter, Schedule 10.

5.3.7 Steam Traps

There are two steam traps in the sys,em. Material of construction is SS and their size

is 1;2/1.

5.3.8 Boiler

An electric boiler is used to supply saturated steam to the system. The capacity of the

boiler is 75 psig. It was fabricated by Modern Erection, Co. Ltd.

59

5.3.9 Compressor

A centrifugal compressor is used to supply instrument air to the pilot plant.

5.3.10 Level Glass

There is a level indicator along with each tank. This celluloid made glasses have a

sizc of 14 mmX 28" L.

5.3.11 Pressure Regulator

A pressure regulator ofSS is used to regulate the pressure of steam. Its size is \12 ".

5.3.12 Pressure Indicator

An oil filled pressure indicator of SS is used to indicate the pressure of steam. Its size

is Y, " and range is 0 -10 bars.

5.3.13 Instrnment Air Supply

From the instrument air header, air is supplied to operate the pneumatic control

valves. Minimum air pressure required for the system is 4 bars. The material of

construction of the header is SS. Size is I ", Schedule 1O. 6 mm PVC tubes are used as

pneumatic cables.

5.3.14 Flow Element and Condensate Pot

There are four SS made Flow Element (FE) and' four MS made Condensate Pot (CP)

in the system.

60

5.4 Operating Procedure

The following is the operating procedure of the pilot plant,

1. The computer connected to the setup was. turned on

2. Power was supplied to the Adam 5000TCP/IP data acquisition module

3. The computer and the module were connected by launching the Adam software

4. The HCYs along the by-pass lines were opened and the water flowed to Tank 1 and

Tank 2. The tanks were filled up to a level of 50%

5. The instrument air supply line was kept closed

6. The compressor was turned on. The accumulated water from the resin pack column of

the compressor system was drained

7. The instrument air supply line was opened

8. The boiler was turned on and it was set in auto mode. During operating the boiler the

following things were made sure

./ The water storage tank is full

./ Natural gas supply line is open

./ The furnace switch is on

9. The by-pass lines to the steam traps were opened and condensate from all the lines

was drained10. The HCYs along the bypass line were opened and steam was allowed to flow through

the coils in Tank 1 and Tank 211. After steam started to flow through the tanks theby pass lines of the steam traps were

closed

12. All the by pass lines for water and steam flow were closed

13. All the HCYs along the pneumatic control valves were opened

14. The Modbus_TCP-Server_ Y2_1_ 4_001 software was launched. The software reads

and displays the values of the level, 11ow,valve opening etc

15. A library of simulink files was prepared for this work. This can be used to build new

simulink files for running the experiments

61

5.5 Chapter Summary

This chapter provides a detailed description of the Three Tank Level plus Temperature

Control pilot plant set up located at the Process Control laboratory of the Depal1mcnt of

Chemical Engineering, BUET. Simplified schematic diagram, P&ID are shown for the set up.

The operating procedure for the system is provided at the last section ofthe chapter. Different

experimental works that were performed during the thesis work using this set up has been

described in the next chapter.

62

CHAPTER 6

HUMAN MACHINE INTERFACE (HMI) DEVELOPMENT AND

CONTROLLER DESIGN

6.1 HUMAN MACHINE INTERFACE (HMI) DEVELOPMENT

6.2 FEEDBACK CONTROLLER DESIGN AND TUNING

6.3 MODEL IDENTIFICATION AND CONTROLLER DESIGN FOR

FCV01 AND FT01 SYSTEM

6.4 MODEL IDENTIFICATION AND CONTROLLER DESIGN FOR

FCV02 AND FT02 SYSTEM '

6.5 MODEL IDENTIFICATION, CONTROLLER DESIGN AND

TUNING OF PI CONTROLLER FOR WATER LEVEL CONTROL IN

TANK 1



TANK 2



TANK 3

6.8 CASCADE CONTROLLER DESIGN AND TUNING

6.9 CHAPTER SUMMARY

0\0;1\£\

"r0

f

CHAPTER 6

HUMAN MACHINE INTERFACE (HMI) DEVELOPMENT AND

CONTROLLER DESIGN

This chapter describes the experimental works performcd under this thesis work. A Human

Machine Interface (HMI) was designed and developed for running, opcrating and controlling

the system using desktop personal eomputcr (PC). This also cnablcs to acquire the operating

data in the computer. After the system was identified, thc controllers wcre designcd and

tuned. Conventional feedback controllers and cascade controllers both were designed for this

system.

6.1 Human Machine Interface (HMI) Development

The human machine interface (HMI) is a place where people and technology meet. Human

Machine Interface (HMI) provides a control and visualization interface between a human and

a process, a machine or an application. For the thesis work a HMI was dcveloped for the

three tank level plus temperature control pilo' plant set up to control, monitor and manage the

system using MatLab OPC toolbox and Simulink. The HMI is shown in Figure 6. I.

A data acquisition system was developed using ADAM 5000 TCPIIP Data Acquisition

Module to measure and log variables for the purpose of running the experiment and analyzing

the logged data. The data acquisition system is electronics based, and it is made of hardware

and software. The hardware part is made of sensors, cables and electronic components. The

software part is made of the data acquisition logic and th.e analysis s~ftware. ADAM utilities

had also been used to configureure the logic or to move data from datq acquisition memory to

a computer. The ADAM 5000 TCP/IP Data Acquisition Module that was used consists of

eight siots for 1/0 modules and there were five I/O modules available in the' system. The

input modules read the data from the system, i.e., the transmitter readings and the output

modules were used to write data to the system, i.e., controller output signal for the final

control elements (control valves). In this way, data were communicated throughout the

system. The Modbus_TCP-Server_V2_1_4_001 software was used to read and display the

values of the variables namely water level, flow of water, valve opening and water

temperature in tanks. This was used in conjunction with the HMI developed in Simulink.

64

Water in

TIO! FrO!

FCV 01

,p,~COI'!):lF:tal-Tln~+

':'P'~~I

',III tl'17.•~,I ~

LIOI TI01

Tank !1-'3

Condensate OuiFr03

TIO.

\Vaterout

L'IOZ

Condensate Out

L..~Tank 2Coil

i J~l~

lev 01

ICV 01

':'''"

Boiler

FCllOZFIOZ

Water in

LT03

\ilater out

Tank 3

Figure 6,1: The Human Machine Interface (HMl) for the laboratory pilot plant set up of the Department of Chemical Engineering, BUET

65

6.2 Feedback Controller Design and Tuning

In order to run the whole plant effectively, controllers must be designed properly. Controller

design involves finding the controller gain, reset time and derivative time constant for a

Proportional Integral Derivative (PID) controller. The values of these parameters can be

found from the model of the system. Therefore, controller design requires identification of a

model of the system.

For this study experimental works were performed using the three tank level plus temperature

control pilot plant set up of the Department ofChcmical Enginecring, BUET. There arc total

seventeen variables of which seven arc controlled variables, four are manipulated variables.

Seven controlled variables are three level, two flow rate and two temperatures. Due to the

physical limitations, Tank 3 cannot be operated simultaneously with Tank I and Tank 2.

Therefore, Tank I and Tank 2 including the steam heating system were used for plantwide

oscillation study. In order to run the plant effectivcly, the following system identification and

controller design were performed.

6.3 Model Identification and Controller Design for FCYO I and FTOI System

6.3.1 Development of a model for the FCV01 and FTOI System

For the development of a model for the FTOI and FCVO1 system, a simulink model shown in

Figure 6.2 was developed. MatLab Simulink and OPC toolbox were used to build it. During

the experiment, at first the system was allowed to come to the stcady state with respect to the

flow of water for a valve (FCV01) opening of 40% (10..4 mAl. The FTOI was transmitting

the flow as percent of total flow and il was monitored in a display. Aller steady state was

reached the valve position was changed 1rom40% (10.4 mA) to 60% (13.6 mAl. As a result,

Flow was changed from the steady state flow of 44.5677% to 90.4558%. The system then

again allowed to attain steady state for 60% of valve opening. The responses are shown in

Figure 6.3(a) and (b). Since the response of this systcm was very fast, the sampling time for

this experiment was selected as 0.2 second, which mcans data were collected at every 0.2

second.

66

OPC Configuration

OPC Read (Cache):Heatin ... k1.FT01 V

FT01

oScope

Vallie openig (%)

OPC Write (Sync):Heatin .... FCV01

FCV01

Figure 6.2: The Simulink diagram for controller design for the FCVOI 01 and FTO! system.

Figure 6.3(a) and (b) show that there was no time lag in this system and it was a first order

process. The general Transfer function for this kind of process is,

KGp(s)~ --

v; + 1

The model parameters can be calculated as follows,

6.1

Process gain, K =

From Figure 6.3(a) and (b),

Change in OutputChange in Input

K ~ (90.4558 - 44.5677) ~ 2.2944(60-40)

6.2

For a first order process, time constant T, is the time when the system reaches 63.2% of its

ultimate value. The 63.2% of the ultimate response is 44.5677 + (90.4558 - 44.5677) x 0.632

~ 73.5689% of flow for this system. This point has been indicated in Figure 6.3(a).

So, for this system,

r= (1077.93 - 1077.8) ~ 0.13

Hence the Process Transfer Function is,

6.3

67

G(s) = 2.29440.13s+ I

6.4

9792878277

~ 720u: 67

62575247421077.5 1077.6

63.2 % of L\y

I!.y

-------,---~,--_._-,-----j

1077.7 1077.8 1077,9 1078 1078,1 1078.2 1078,3 1078.4 1078.5

t

Time (s)

Figure 6.3(a): Flow Transmitter (FTO!) reading Vs. Time

0._.__ .-----_.~-~ - -_._--,----- ------

0

6u

II

~---.--~

9

201077.5 1077.6 1077.7 1077.8 1077,9 1076 1078.1 1078.2 1078,3 1078.4 1076.5

Time(s)

30

40

10

80

C 70Olc'c8. 60o

">iU 50>

Figure 6.3(b): Valve (FCV01) opening Vs. Time

68

6.3.2 Design of a PI Controller

The controller parametcrs K and T wcre calculated according to the Internal Model Control

(lMC) method. The IMC based PID Controllcr Scttings for first ordcr systcms are given by

Seborg, D.E., 2004 and they are shown in Table 6.1 .

Table 6.1: The IMC based PID Controller Settings for a first order system.

Model KcK r, TV

K T T -Gp(s) = -- -

70 + 1 'cAccording to Chien and Fruehauf (1990), the IMC guideline for selccting T,< is,

r> rc >()

Using the formulae in Equation 6.4 and in Table 6.1, thc controller parameters are calculated

as,

TC = 0.1 (assumed)

Kc= 0.5666

T,=0.13

6.4 Model Identification and Controller Design for FCV02 and FT02 System

6.4.1 Development of a model for the FCV02 and FT02 System

The entire procedure followed for the development of a model lar the FT02 and FCV02

system was the same as described in the previous section. The simulink model file to run the

experiment is shown in Figure 6.4. At first the system was allowed to come to the steady state

with respect to the flow of water for a valve (FCY02) opening of 40% (10.4 mAl. The FT02

was transmitting the flow as percent of total flow. After steady state was reached the valve

position< was changed from 40% (10.4 mAl to 60% (13.6 mAl. As a result, Flow was

changed from the steady state flow of 14.8097% to 53.2027. The system then again allowed

to attain steady state for 60% ofvalvc opening. The responses arc shown in Figure 6.5(a) and

(b).

69

OPC Configuration

\fl(aterflowto Tank2

OPC Read (Cache)'Heatin .. ,k3,FT02 V

FT02

DScope

Valve Opening %

OPC Write (Sync)'Heatio .. ..FCV02

FCV02

Figure 6.4: The Simulink diagram for Controller design for the FCY 02 and FT 02 System.

Figure 6.5(a) and (b) show that there was no time lag in this system and it was a first order

process. The model parameters are calculated using Equations 6.2 and 6.3 as follows,

Using Figure 6.5(a) and (b),

Process gain,K= (53.2027 -14.8097)

(60 - 40)=1.92 6.5

The 63.2% of the ultimate response is 14.8097 + (53.2027 - 14.8097) x 0.632 = 39.07% of

flow for this system. This point has been indicated in Figure 6.5(a).

So, for this system, r= (435.57 -435.5) = 0.07 6.6

Hence the Process Transfcr Function is,

G(.I')= 1.920.07" + 1

6.7

70

18

13435.3 435.35 435.4 435.45 435.65 435,7 435,75 435.8 435.85 435.9431~5 'l:435.5~ 435.6

Time(S)

63.2 % ofl'l.y

58534843

~38

~ 33u.

28 "y

23

Figure 6.5(a): Flow Transmitter (FT02) reading Ys. Time

435.9435.8435.7435.6

Time (s)435.5435.4

---~---------_.--_._._---

"" IIIIII

~----_. I20435.3

30

90

40

100

80

~ 70

'"o..,~ 60o~~ 50

Figure 6.5(b): Valve (FCY02) opening Ys. Time

6.4.2 Design of a PI Controller

Using the formula in Equation 6.7 and in Table 6.1, the controller parameters arc calculated.

The calculated controller parameters are,

71

TC = 0.05 (assumed)

Kc = 1.042

TI = 0.07

6.5 Model Identification, Controller Design and Tuning of PI Controller for

Water Level Control in Tank 1

6.5.1 Theory

In this study, the level control system of the tanks consists of water inlet and outlet, a

pneumatic flow control valve, tank and leveitransmitter. The open loop block diagram of the

system is shown in Figure 6.6.

u ~i\' .C=l •

Yal\.~ P!'('Ct5~

Figure 6.6: Open loop block diagram for level control system

The open loop transfer function is,

The process transfer function is,

6.8

6.9

and

The transfer function of the valve is taken as.

Gv(s)=Kv

So, the open loop transfer function for the system becomes,

G(s) =Kv JiLr.s+l

72

During the study, at first experiments were started in opcn loop cond ition for developing a

model for the tanks with respect to level. For this, the level in tank was made to come to a

s'teady state so that the level remained fixed with respect to a particular position of the valve

opening. Then the level sct point was changed and the set point tracking of the system was

studied. However, it was observcd during the experiments that the residence time or the time

constants of the tanks are very large, i.e., 100 minutes and 84 minutcs for the Tank 1 and

Tank 2 respectively. As a result, it was difficult to run the experiments in the open loop. It

took too long to rcspond to a step change in input for the system to reach the steady state.

For these reasons, a closed loop approach was followed to develop thc model for the tanks. A

proportional controller was used to make a closed loop systcm. Aftcr the introduction of a

proportional controller the response of the system was quite faster. The model or the transfer

function for the tanks with respect to the level was then developed by trial and error.

The closed loop block diagram for this system is shown in Figure 6.7.

COlltroll er

p

Process

L

Figure 6.7: Closed loop block diagranl for levcl control systcm

The closed loop transfer function for sct point change is given by,

Where,

The transfer function of the controller is, Gc (;) =K c

The transfer function of the valve is, Gv (s) = Kv

and, the process transfer function is, G,,(s) = ,~T.I'+I

6.10

73

So, Equation 6.9 can be rewritten as,

K"KvK,.T.\'+I+K"KvK,.

6.11

Now, as we know the open loop gain is given by,

Now, from Equation 6.3,

L(s) = Ko"Lw'(s) T.\' + 1 + Km.

K(n1+ Km,

rs+ 1+ K'N.1 + Km

6.12

Let, Kl =

L(s) =

L", (s)

K(Jf.----I+ Kill,

r---s+11+ Km,

6.13

6.14

rand, 'I = ---

I+ Kill.

6.15

Now, from Equations 6.12, 6.13 and 6.14 the relation can be rearranged in the standard form

for a first order transfer function,

L(s) =~L",(s) r,s+1

6.16

74

At first, the closed loop system was identified and then the model for the tank with respect to

level was developed using the responsc of the closed loop systcm.

6.5.2 Model Identification

The Simulink model developed for the determination of transfcr function is shown in Figure

6.8. MatLab Simulink and'OPC toolbox werc used to gencratc the file.

It was a conventional feedback control system having onc controlled variable (the water

levcl), one sensor (flow transmitter FT01) and one manipulated variable (flow of water). At

first, the level transmitter LTOI transmitted the water Icvel or the tank, this transmitter signal

was read by OPC read block and it was conipared to the level set point, the error was then

sent to the PI controller The controller output was then written to the flow control valve

FCVOI using OPC write block. The responses of the system were monitored by the scope

block. Here, another point to be noted that a gain of 0.5 was used in the model.

~ .~ 'IFCVl)1 op.n;nq (mA.)

ope R•• d(C.~".)11•• ,," ~1 ,LTOl

fCVOl

OPC W,;!. (5)"00)H •• lon .. ,rCVIJ1

~PID

PI CO"hollo,

Figure 6.8: The Simulink Model for Controller Design for Tank 1.

Several trials were made to finalize the model of the system. The last two trials are discussed

here,

For, Kc= 5

Level set point was changed from 52% to 57%

75

The corresponding change in level was from 48.71% tei 53.58%

So, for this system the closed loop gain is,

Change in OutputChange in Input

6y = 53.58-48.716u 57-52

0.97 6. I 7

and, Time constant, ,,= (108.8 - 61) = 47.8 6. I 8

Hence, the following parameters are calculated using Equations 6.12, 6. I4, 6.15, 6. I 7 and

6.18 as follows,

K,K01 = -- = 36.65

. I-K,

, = ,,(I + Kill.) = 1798.24

The process time constant ,obtained was 1798.24 seconds that is too large; therefore, the

next trial was made reducing the value of proportional controller gain K(.'. It is to be noted

that, other trials were made by increasing the value of proportional controller gain Kc over 5

but in those cases the process time constant, obtained was even higher than it was obtained

for Kc= 5.

For, Kc = 1


The corresponding change in level was from 52.5% to 55.03%

So, for this system the closed loop gain was,

K,Change in Output = 6yChange in Input 6u

55.03 - 52.5 = 0.50660 - 55

6.19

76

and, Time constant, T, = (280.7 - 46) = 234.7 6.20

Hence, the following parameters are calculated using Equations 6.12, 6.14, 6.15, 6.19 and

6.20 as follows,

K,KOL =--=1.024

I-K,

T = T, (l + Km.J = 475.1

This was taken as the final trial as the time constant for the system is considerably small

which means a faster process. So, The Process Transfer Function from Equation 6.9 is,

6.5.3 PI Controller Design

G(P)= ~= 1.024<:5+1 475.ls+1

6.21

Using the formula in Equation 6.21 and in Table 6.1, the controller parameters are calculated.


TC = 100 (assumed)

Kc= 10.642

T,=475.1

6.5.4 Tuning of the PI Controller

As a high value of Kc makes the system unstaJIe, the gain (Ke) of the PI controller was set to

7 and for a set point change from 55 to 65% of level the following response was observed

which is shown in Figure 6.9.

77

500400300200

--+- Level in Tank 1 (%)-D- Level set point (%)...•...Valve Opening (rnA)

100

706560555045

Ul 400>:c 35.III';::III 30>

25201510500

Time (sec)

Figure 6.9: Set point tracking of Level in Tank I.

The response is satisfactory since the level reached the set-point within 350 seconds which is

quite faster and the response is stable.

So, the ultimate PI controller paramcters arc,

Kc= 7

'c = 100 (assumed)

n=475

78




The entire procedure that was followed for Tank 1 level control system was repeated for

Tank 2. The Simulink model file developed for the determination of transfer function is

shown in Figure 6.10. MatLab Simulink tool and OPC toolbox werc uscd to gencrate the file.

It was a conventional feedback control system having onc controlled variablc (the water

level), one sensor (flow transmitter FT02) and one manipulated variablc (flow of water). At

first, the level transmitter LT02 transmitted the level in tank, this transmitter signal was read

by OPC read block and it was compared to the level set point, the error is then sent to the PI

controller The controller output was then written to the flow control valve FCY02 using

OPC write block. The responses of the system were monitored.

1c=J1L••• II. T.oI<2 ('li)

o



here,

For,Kc= 10

Level ,set point was changed from 50 % to 55%

The corresponding change in lcvel was from 48.03 % to 52.97%

79 .

So, for this system the closed loop gain was,

K, = Change in OutputChange in Input

L'iy 52.97 - 48.03=

L'iu 55-500.988 6.22



6.23 as follows,

T = T, (l + K()fJ = 3450

K" = K()f. = 8.19Kc

For, Kc=5


The corresponding change in level was from 43.08% to 48.04%


K_ Change in Output,- Change in Input

L'iy = 48.04 - 4308L'iu 53 ~ 48

0.994 6.24



6.25 as follows,

K,KOl =--=172.91, 1-K,

T = T, (l + K()fJ = 8643

80

The second trial gives a very high value for both the process time constant and gain. A large

time constant indicates a slower process and a high value for gain makes the process unstable,

hence the second trial was rejected. Other trials were made making the value of Kc higher

than 10 but in those cases the corresponding K1 values obtained was greater than 1 which is

not possible in real life. Therefore, those trials are not shown here. The first trial is taken as

the final trial as the time constant for the system is considerably small which means a faster

process and also a small process gain indicates stability.

So, The Process Transfer Function is,

G(P)= JS.L= 8.19TS + 1 3450.--+ 1


6.26

Using the formula in Equation 6.26 and in Table 6.1, the controller parameters are calculated.


TC = 100 (assumed)

Kc= 8.0837

TI = 3450


As a high value of TI makes the system ver~ slow the integral time constant of the PI

controller was set to 350 and for a set point change Irom 50 to 60 'Yc, of level the following

response as shown in Figure 6.11 was observed.

81

70.00

60.00

50.00

II) 40.00Ql:cIII

';:III 30.00>

20.00

10.00

--+- Level in Tank 2 (%)-'I>- Level set point (%)-tr- Valve Opening (mA)

0.00o 50 100 150 200 250 300 350 400 450 500 550

Time (sec)

Figure 6.11: Set point tracking of Level in Tank 2.


quite faster and the response is stable. So, the PI Controller Parameters arc chosen as,

fC = 100 (assumed)

Kc=8

f[ = 350

82

I

J




The entire procedure that was followed for Tank I and Tank 2 level control system

development was repeated for Tank 3. The Simulink model file developed for the

determination of transfer function is shown in Figure 6.11. MatLab Simulink and OPC

toolbox were used to generate the file.

It was a conventional feedback control system having one controlled variable (the water

level), one sensor (flow transmitter FT02) and one manipulated variable (flow of water). At

first, the level transmitter LT03 transmitted the water level in tank, this transmitter signal

was read by OPC read block and it was compared to the level set point, the error was then

sent to the PI controller The controller output was then written to the flow control valve

FCV02 using OPC write block. The responses ofthe system were monitored.

PI Con1roll.,

ope Wrlll (Syno),H•• tln .. ..FCV02

fCW2

V~lv@ oponlng(mA)

ope Rud (Coeh.)Hulin ...k3.LT03 \,/

LT03

o



here.

For, Kc =1

Level set point was changed from 49 % to 54%

83

The corresponding change in level was from 46% to 51.65%


K1= Change in Output _ ~y = 51.65 - 46 -1.13

Change in Input ~u 54 - 49

and, Time constant, 'I = 118.7

6.27

6.28

Hence, the following parameters are calculated using Equations 6.1.12, 6.1.14, 6.1.15, 6.1.27

and 6.28 as follows.

KjKOL = -- = -8.44I-Kj

, = '1 (I + KOiJ = -883.6

KKp = ~ = --4.39

KcThis trial was rejected since in real life it is not possible to have a closed loop gain that is

greater than one. This abnormal value of closed loop gain resulted in negative process gain

and negative time constant of the process which are in no way acceptable. Attempts were

made to decrease the proportional controller gain below one but there was not any

improvement in result and then trials were made by increasing the proportional controller

gain above one. The results indicated that there was no significant improvement until the

proportional gain was sufficiently increased.

Trial 2

For,Kc=15


The corresponding change in level was from 41.71 % to 46.66%


84

K1= Change in Output = L'.y _ 46.66 - 41.71 = 0.99Change in Input L'.u 53 - 47

and, Time constant, TI = 70.2

6.29

6.30


6.30 as follows,

K1KOL =--=185.34I-K1

T = TI(l +KOIJ = 13081

KI' = KOL = 6.44Kc

This is taken as the final trial though the time constant for thc system is large which means a

slower process but further incrcase of controller gain Kc makcs the process unstable.

So, The Process Transfer Function is,

G(P) = l5L _ 6.44Ts+1 13081.1"+1


6.31

Using the formula in Equation 6.31 and in Table 6.1, the controllcr parameters are calculated.

The calculated controller paramcters are,

Te = 100 (assumed)

Ke = 20.323

T{ = 13081

85


As a very high value of T{ makes the system response sluggish, the integral time constant T{ of

the PI controller was set to 200. For a set-point change from 50 to 55% of level, the following

response was observed as shown in Figure 6.13.

60 .-----.--.----------

50

40IIIQl

~ 30.;:n:I>

20

10

--+- Level in Tank 3 (%)~ Level set point (%)--lr- Valve Opening (rnA)

oo 100 200 300 400 500

Time (sec)600 700 800

Figure 6.13: Set point tracking of Level in Tank 3.


quite faster and the response is stable. So, the ultimate PI controller par~meters are,

Kc= 20.323

1C = 100 (assumed)

T{ = 200

86

6.8 Cascade Controller Design and Tuning

In case of the conventional feedback control the corrcctivc action for disturbances does not

begin until after the controlled variable deviatcs from the set point. Although feed forward

control offers large improvements over feedback control for processes having large time

constants or time delays. Howevcr, fecdforward controllcrs require cxact measurement of all

the disturbances and a process model must be available to calculate the controller output. An

alternative approach that significantly improvcs the dynamic response to disturbances is

known as the cascade control. It employs a secondary measurement point and a secondary

feedback controller. The function of the secondary measurcment point is to recognize the

upset condition sooner than the controlled variable, but the disturbance is not necessarily

measured. Cascade controller is widely used where the disturbances are associated with

manipulated variables or when the final control clement exhibits nonlinear behavior

(Shinskey, 1996).

The cascade control loop structure has two distinguishing features:

I. The output signal of the master controller serves as the sct point for the slave controller.

2. The two feedback control loops are nested, with the secondary control loop (for the slavc

controller) located inside the primary control loop (for the master controller).

Thus, there are two controlled variables, two scnsors and one manipulated variable. The

principal advantage of the cascade control strategy is that a second measured variablc IS

located close to a potential disturbance and its associatc feedback loop can react quickly.

6.8.1 Design and Tuning of Cascade Controller for Tank 1

The Simulink model developed for the design and tuning of cascade controller for Tank I IS

shown in Figure 6.14. In this cascade control system water level in tank was controlled by

controlling the flow of water to the tank. The controller that controls water level in Tank I

was selected as the master or primary con(roller and the controller that controls water flow

was the slave or secondary controller. The cascade controllers were designed by tuning the

controllers designed previously in section 6.6.3 and 6.7.3. It (ook nineteen trials to design

cascade controller for Tank I. As for example, here the rcsponses of the Iih, 16thand 19

th

87

trials are shown in Figure 6.15, figure 6.16 and Figure 6.17 respectively. The controller

parameters at different trials are given in Table 6.2.

Table 6.2: Trial values of Primary and Secondary Controller Parameters

Trial No. Master Controller Parameters Secondary Controller Parameters

Trial 1 Kc ~ 10, T[= 300, gain = 0.6 K( ~ 0.7, T[= 1.5, gain ~ 0.065

Trial 2 Kc = 10, T, ~ 300, gain = 0.6 K( = 0.7, T,= 2, gain = 0.065

Trial 3 Kc ~ 10, T[= 300, gain = 0.6 K(' = ], T,~ 3, gain = 0.065

Trial 4 Kc = 10, T[= 300, gain = 0.5 Kc ~ 1.5, T,= 3, gain ~ 0.065

TrialS Kc= 10, T[~300,gain=0.5: Kc = ].5, T, = 4, gain ~ 0.05

Tria16 Kc ~ 10, T,~ 300, gain ~ 0.4 Kc = 1.5, T, ~ 4.5, gain = 0.05

Trial 7 Kc = 10, T, ~ 300, gain = 0.4 Kc ~ I. T,~ 3.5, gain ~ 0.05

Trial 8 Kc = 10, T, ~ 300, gain = 0.6 K(~ I, T,~3.5,gain~0.05

Trial 9 Kc = 10, T[~ 250, gain ~ 0.6 Kc ~ I, T,~ 3.5, gain = 0.05

Trial 10 Xc.' = 10, T, = 200, gain = 0.6 K(, = I, T,= 3.5, gain ~ 0.05

Trial I I Kc = 10, T, ~ ]80, gain ~ 0.6 K(,= I, T,= 3,5, gain = 0.05

Trial 12 Kc ~ 10, T[~ 180, gain ~ 0.5 Xc.' ~ I, T,~ 3, gain~' 0.05

Trial 13 Kc ~ 9, T, ~ ]70, gain = 0.5 Kc = I, <, = 2.5, gain ~ 0.05

Trial 14 Kc = 10, T, = ]70, gain = 0.5 K(, ~ I, T, ~ 2.5, gain ~ 0.05

Trial 15 Ki, = 10, T, ~ 150, gain = 0.5 K(, ~ I, T[~ 2.5, gain ~ 0.05

Trial 16 Kc ~ 9, T,= 135, gain ~ 0.45 K, ~ I, "~ 2.5, gain = 0.045

Trial 17 Kc = 9, T[= 100, gain = 0.4 K(. ~ I, T,~ 2.5, gain = 0.03

Trial] 8 Kc = 10, T, ~ 200, gain = 0.6 Kc = I, T,= 3.5, gain ~ 0.05

Trial 19 Kc = 10, T[= 250, gain = 0.6 K(, = I, T,= 3.5, gain ~ 0.05

88

0-00

.s :(i

~~

;'; w;':;~I:> p ~ "() D ."". 1: •• j " ..." ". "'"' " :r 'I; ."> "" -'/.~

~ ~

:':.. :.:i :;,>,. ."." < ,.<. ". ,",

;0 ,,_ f-

+ , " "" ". t;:

" .""

.,

~

""",.",.';

;0

".. "'"<

.,. ."",

~n.. i7" ~" "". ." "'.) " " iIi" I." '"0 ";i,

'1:

o~-<:oU"-0'"'Q'"'"'u

-11- Level set - point ("!o)

I I I I , I I I • I I "'_u-a-a-cl_I1-/oI.D-IIl_lJH.'1_G-n_~.D_l;Hi':'.z'I_II111.nn_IOl,.g_lii '"

__ Water level in Tank1 (%)

Master Controller:

K(' = 10, f, = 180, gain = 0.5Secondary Controller:

K(' = I, f, ~ 3, gain = 0.05

Controller Parameters are-?I(- Flow set - point (%. secondary

controller out- pull

0- Valve opening (mA)

6. Water flow in line (%)

Time (sec)

e-e-e-e-e-e-&&e-e-e-e-ee-ef)Be . t.

BG"...,>~~E:)H':JU~)(::'D

~ ~ ~_~ ---;K-~Q_~_~_~4:1200 400 600 800 1000

Trial 12

70

60

50

'"40

Q)

jj30••';:••> 20

10

.,:;

Figure 6.15: Tank 1 level control system's response at trial no. 12.

In this trial, the level first tracked the set point at 330 seconds that was quite faster but the

overshoot was high, the level set point was 45% and the maximum level reached was

48.44%. In case of the secondary controller performance, there were fluctuations in the flow

of water to the tank, which is quite unacceptable.

Trial 16

70

Kc ~ 9, f,= 135, gain ~ 0.45

Secondary Controller:

K('~ I, T,= 2.5, gain ~ 0.045

Controller Parameters arc

Master Controller:

&&&&&f:"

':'OOQ 1000

.. ~;t;'~-:).;~:f."''''_~;o'K_:t~

-I!:r Water flow in line (%)

r::I Level sel- point (%)

--Water level in Tank1(%)

600

-+-+-+-+ .•..•.. ..--.....-.-..1I_Q_il_Q_i:J'Il_C!l_J:\_".p_O_Il_elll IIIG.C!I-fI D'" IH!j II Ii tJ

400200

...,(- Flow set. point (%, secondarycontroller oul- pull

, -'2'--Valve opening (rnA)

r~G":'J €;LJ-eB-e-0"~)";;'-t:H.".t=}-o3_E:' t'-~'7_'-9-:;,";~;".:-",~"."" ...' '-J'.'"-c-7" ' •..• ,.- ..

60

o

40

50

-10

"'~30-"~0:i 20>

10

-20Time (sec)

Figure 6.16: Tank I level control system's response at trial no. 16.

90

In this trial, the level first tracked the set point at 300 scconds which was quite fastcr but the

overshoot was high, thc lcvel set point was 60% and the maximum lcvel rcached was 64%. In

case of the secondary controller performance, therc were fluctuations in the flow of water to

the tank which is quite unacceptablc.

Trial 19

80

__ Water level in Tank1(%)

-Il- Level set - point (%)

t::,. Water flow in line (%)

K, ~ 10, ,,= 250, gain ~ 0.6


K,. ~ I, f, = 3.5, gain = 0.05

Controller Paramcters are

Master Controller:

1000800600

---;:1(-Flow set - point (%. secondary controlleroul- pull

-e- Valve opening (rnA)

400200a

o

10

20

60

Ul 50

'" {,:ccu, 40.;:'"> 30

Time (sec)


In .this trial, the level first trackcd the set point at 390 scconds which was slowcr than the

earlier trials but the overshoot was much lowcr, thc Icvel set point was 7 I% and the

maximum level reached was 73%. In case of the secondary controller performance, there was

considerably less fluctuations in the flow of watcr to the tank. Thercfore, for Tank 1 trial 19

was taken as the final trial.

91

6.8.2 Design and Tuning of Cascade Coillrollcr for Tank 2

The Simulink model developed for Ihe design and luning of cascade conlrollcr for Tank 2 is

shown in Figure 6.20. It took seven trials to design and tunc the cascade controller for Tank

2. The procedure followed for designing and tuning cascade controller for Tank I was

repeated for Tank 2. Here, the responses of the variables at trial no. 4 and trial nO.7 are shown

in Figure 6.18 and Figure 6.19 respectively. The controller parameters at different trials are

given in Table 6.3.



Trial 1 Kc = 8, ,,= 350, gain = 0.6 Kc = I, Tf = I, gain = 0.05

Trial 2 Kc ~ 8, ,,= 350, gain ~ 0.6 K,. = 0.5, ,,= I, gain = 0.05Trial 3 Kc = 8, ,,= 300, gain = 0.6 Kc = 0.5, ,,= 1, gain = 0.05Trial 4 Kc = 8, ,,= 280, gain = 0.5 K,.=0.5, T, = 1.5, gain = 0.05

TrialS Kc = 8, ,,= 250, gain = 0.5 K, = 0.5, "~ 1.5, gain = 0.05Trial 6 Kc = 9, 'I = 250, gain = 0.5 K,. ~ 0.5, ,,= 1.5, gain - 0.05

Trial 7 Kc = 8, ,,= 250, gain = 0.5 Kc ~ 0.5, ,,= 1.5, gain = 0.05

Trial 4

80

70

60

Ul 50

":c'" 40."'"> 30

20

10

,~~~2~*_?:_~~~-t:!-i.-{'",; ••-",,:,~:,~~t~'"b'M

66.?;~.);",-- Water level in Tank 2(%) ~~t:~.-0- Level 501- point (%) '6"1:1~4'I

-6-'Waler flow in line (%)

-::1(-Flow set - point (%. secondarycontroller cui. pull

-e- Valve opening (rnA)

Controller Parameters are

Master Controller:

Kc ~ 8, "~ 300, gain ~ 0.6


K,. ~ 0.5, "~ I, gain = 0.05

oo 200 400 600 800 1000

Time (sec)


92

This trial was rejected as the water level in the tank first tracked the set point at about 700

seconds that was much slower and thcrc werc considcrablc Iluctuations in the !low of water

in line. Moreover, it was observed that there were !luctuat;ons in the FCY02, which is not

acceptable.

Trial 7

80

70

60

50g::0'" 40."'"> 30

20

10

...•.... Water I~vcl in Tank 2(%)

-.- Level sel- point {%}

6. Water now in line (%)

~ Flow set - point (%, secondary controllerout- pUI)


Master Controller:

K" = 8, T, ~ 250, gain ~ 0.5Secondary Controller:

K, = 0.5, T, = 1.5,gain ~ 0.05

oo 500 1000

Time (sec)

1500 2000

Figure 6.19: Tank 2 levcl control systcm's rcsponse at trial no. 7.

Trial 7 was selected as the final trial as the level trackcd the sct point at about 600 seconds

which was faster than other trials. The overshoot was not so high (Icvel set point was 62%

and maximum level reached was 64.6%) and there were occasional !luctuations in the !low of

water in line, which can be considered as due to external flisturbances. Controller parameters

are acceptable and the response of the system was quite satisfactory.

93

OPC Configuration I -I% Valve Opening

Flow Set Point flow errorope Write (Sync):

Hea ... V02

FCV01

Loavoalin Tank2

I I

Slave Controller

LT01

ope Read (Cache):Hea ... LT02 V

+

FTO'1

,OPC Read (Caohe):Hea.,.FT02 \/

Marlo!.[ Controtler

,- I

r--- I

e.vel Se.t Point

oScope2

Figure 6.20: The Simulink Model for Cascade Controller Design for Tank 2.

94

6.8.3 Design and Tnning of Cascade Controllcr for Tank 3

The Simulink model developcd for the dcsign and tuning of cascadc controller for Tank 3 is

shown in Figure 6.22. It took three trials to design and tune the cascade controller for Tank 3.

The procedure followed for designing and tuning cascade controller for Tank I and Tank 2

was repeated for Tank 3. Here, the response of the variables at trial 3 is shown in Figure 6.21.

The controller parameters at different trials are given in Table 6.4.



Trial 1 Kc ~ 2.032, '[ ~ 200, gain ~ 1 Kc ~ 0.5, '[ ~ 3, gain ~ 0.2

Trial 2 Kc ~ 2.032, '[ ~ 200, gain ~ 1 Kc ~ 0.2, '[ ~ 3, gain ~ 0.2

Trial 3 Kc ~ 2, '[- 210, gain ~ I K ~ 0.2, '[ ~ 3, gain ~ 0.2

Trial 3

70

K,.~ 2, 'I~210, gain = I


Kc = 0.2, '[ = 3, gain ~ 0.2


Master Controller:

200015001000

Time (sec)500

I!I,.

~Wa'" ,,,,, '0 Taok ~...• -level set - point ("!o) 1.11.

8' Waterll~winlinc(%) ~~lS ,,' :'l!;"""'*- Flow set _point (%, secondary controller oul pul) i$lli:'t1.alKlKit.i~_~_i!fO-lI'~tt

--e- Valve opening (rnA)

, ~eeeeeeee8(-)o*\e0ee()r'K).i':-)8<.;)c-:lk8,o,,~,e

20

oo

'0

50

60

<IIQ) 40:c••'C•• 30>


Trial was taken as the final one as the response was quite faster and stable than other trials.

Overshoot was considerable as the maximum level reached was 61.5% for a level set point of

58%. Controller parameters were acceptable and the response of the system was quite

satisfactory.

95

OPC ConfigurationI I% Valvl! Opening

I I C IFlow Set Point Flow errOl

OPC Write (Sync):HU ... VD2

I I

FCV01

r==--]OPC Read (C.;;che):Hea. __LT03 V

•

ope Read (Ca.:-he)He~, __FT02 V

r- I

el/e! Set Point

M~rter ControllerFTOl LTO-1

Level In Tank3

J

SCQpe2

Figure 6.22: The Simulink Model for Cascade Controller Design for Tank 3.

96

6.9 Chapter Summary

In this chapter, all works including the design of Human Mach inc Interface (HMI),

dcvelopment of the data acquisition system, systcm idcntification and controller design have

been described in dctail. The HMI was built using the Matl.ab simulink and OPC toolbox.

The data acquisition system was developed using ADAM 5000 TCP/II' Data Acquisition

Module and the Modbus_TCP-Server_ V2_1_ 4_001 software was used to establish data

communication with the HMI. Both conventional feedback and cascade controllers were

designed and tuned. These works were required to run the cntire pilot plant set up so that

plantwide experimcnts can be performed. The next chapter dcscribcs in dctail thc plantwide

oscillation experiments.

97

CHAPTER 7

PLANTWIDE OSCILLA nON EXPERIMENTS AND RESULTS

7.1 INTRODUCTION OF FAULT TO THE SYSTEM

7.2 TROUBLESHOOTING PLANTWIDE OSCILLATION

7.3 CHAPTER SUMMARY

CHAPTER 7

PLANTWIDE OSCILLATION EXPERIMENTS AND RESULTS

In addition to simulated and industrial data, THC index has bcen also cvaluated uSlI1g

experimental data. The Three Tank Level plus Tcmpcrature Control pilot plant set up in the

Control Laboratory, Chemical Engineering Department, BUET, was used to examine the

efficacy of THC to identify the root-cause of plantwide oscillations. After the systems were

identified and PI controllers were designed for different sections of the pilot plant set up, fault

was introduced in the system in the form of valve stiction. High density plot and PSCMAP

were used to group all variables oscillating togethcr. Then harmonics analysis of the

experimcntal data was carried out to examine if the proposed indcx can idcntify the root-

cause correctly.

7.1 Introduction of Fault to the System

For these experiments a cascade of Tank 1 and Tank 2 level control loops were built, where

outlet flow from Tank 1 acted as the disturbance to Tank 2. Saturated steam was used to heat

water in both tanks. The models of the cascade control system are shown in Figure 7.1 to 7.4.

The models were developed using MatLab Simulink and OPC toolbox.

Figure 7.1 shows thc Simulink model for the Tank I Icvcl control systcm. This was a cascade

control system where the level in the tank was controlled by controlling flow of water to the

tank. There were two controllers namely the master controller and the slave controller. The

master controller was controlling the level of water in Tank I and the slave controller was

controlling the water flow to Tank 1. At first, the level transmitlerLTO I transmittcd the level

in Tank 1 that was read by OPC Read block. The level was then compared to the level set

point and the level control error was sent to the master PI controller. The master controller

output was the set point for the water flow to Tank I. The flow transmitter 1'1'0 I transmits the

flow in the line and this was compared to the flow set point. The error in flow was sent to the

slave PI controller. The slave controller changes thc opening of flow control valve FCYO I by

writing the slave controller output to the valve using OPC Write block. In this way, the level

in Tank 1 was controlled by manipulating the water flow to the tank.

99

Figure 7. 2 shows the model for the Talik 2 k',c1 control systClil. This is similar to thc Tank 1

system. The master controller was controlling the level of water in Tank 2 and the slave

controller was controlling the water flow to the Tank 2, At first, the level transmitter LT02

transmitted the level in Tank 2 that was read by OPC Read block. The level was then

compared to the level set point and the level error was sent to the master PI controller. The

master controller output was the set point for the waleI' now to Tank 2. The now tran5m itter

1''1'02 transmitted the flow in the line and this was compared to the flow set point. The error

in flow was sent to the slave PI controller. The slave controller changed the opening of flow

control valve FCV02 by writing the slave controller output to the valve using OPC Write

block. In this way, the level in Tank 2 was controlled by manipulating the water flow to the

tank.

Figure 7.3 shows the model for the Tank I temperature control system. This was a

conventional feedback control system where the temperature of watcr in Tank 1 was

controlled by manipulating the flow of saturated steam through the valve TCVO I. At first, the

tcmperature transmitter TT02 transmitted thc temperature of water in Tank I using the OPC

Read block and this was compared to thc temperature set point of water J()r this tank. The

error was then sent to the PI controller. The controller then manipulated the now of saturated

steam to the Tank 1 by changing the steam flow control valve TCVO 1 opening using OPC

Write block.

Figure 7.4 shows the model for the Tank 2 temperature control system. This is similar to the

Tank 1 temperature control system. In this system, the temperature of water in Tank 2 was

controlled by manipulating the flow of saturated steam through the valve TCV02, At firsl, the

temperature transmitter '1''1'06 transmitted the temperature'of water in Tank 2 using the OPC

Read block and this was compared to the temperature set point of water for this tank. The

error was then sent to the 1'1controller. The controller then manipulated the flow of saturated

steam to the'Tank 2 by changing the sleam flow control valve TCV02 opening using OPC

Write block.

100

OPC Con1igIJration I . IValve Opening in mA

I I

MastoH COfltroller

J!

loPC Read (CAche}Hea ... FT01 V

FT01

OPC Read (Cache):H~a...lT01 V

LT01

--- -

O~l

Stlction Block

-----

OPC Write (Sync):Hea .. ,V01

FCV01

Stiction Block

\/1,,,

1m

I

level in T anI< 1

D

Figure 7.1: The Simulink model for Tank 1 level control system where fault is introduced to FCVO I.

101

C IValu-e Opening in rnA

I 1 C IFlow Set Point 1 Flowerror1

OPC Write (Sync):Hea...V02

+FCV1

ope Read (Ca"h ••):Hea ... FT02 \/ C=.. Iope R~ad (Cache.):

Ho::a...LT02 \/

11Flow in the Line1

~. I

+

Leu-el Set Point1

Master Controli ••r1'TI LT1

Leu-el in Tartl<2

o

J

Figure 7.2: The Simulink model for Tank 2 level control system.

102

PI Controller

Saturation9

OPC Writ~(Sync):Ho;!,alin.... TC\I01

TC\I01

-11 IIDisplay3

OPC R~ad (Cach~):Heatin ...k1. TT02 V

TT02

[_ ..... J

Temp if'l Taf'lk1 (%)

o

Figure 7.3: The Simulink model for Tank 1 heating system.

../

SattJfation7

c=- HIDisplaye

PID

PI COf'llrol1el1

../

ope \lVrit~(Sync):H",atin TCV02

TCV02

OPC Read (Ca.::he):Heatin ...\.2.TT06 V

TT06

I ITemp in Tank2(O,l))

o

Figure 7.4: The Simulink model for Tank 2 heating system.

103

After the system reached steady state, a fault in the form of sticiion was introduccd to thc

valve FCVO 1, controlling the flow of watcr to Tank 1. Thc stiction block is highlighted in.

Figure 7.1. The stiction model developed in (Choudhury et aI., 2005) was used to introducc

stiction. The introduced stiction was varied as 2%, 7%, 20% and 30% (8 = J). Experiments

were performed with or without heating water by saturated stcam. The responses of the

system arc shown in Figure 7.5. Table 7.1 describes all variables of this pilot plant set up.

Table 7.1: Description ofthe Variables

Tag No. Variable Name. Description

1 LTOI.PV Level in Tank I

2 LTOI.SP Level Set point for Tank I

3 FTOI.SP Flow set point for Tank 1.

4 FTOl.PV Flow of water to Tank I

5 FTOl.OI' Flow control valve FCVO I opening

6 LT02.PV Level in Tank 2

7 LT02.SP . Level Set point for Tank 2

8 FT02.SP Flow set point for Tank 2.

9 FT02.PV Flow of water to Tank 2

10 FT02.0P Flow control valve FCY02 opening

I I TT02.PV Temperature ofwa!er;n Tank I.-

12 TT02.SP Temperature set point for Tank I

13 TT02.0P Temperature control valve TCVOI opening

14 TT06.PV Temperature of water in Tank 2

15 Tf06.SP Te;nperature set point for Tank 2

16 TT06.0P Temperature control valve TCY02 opening

104

noo.oP

TT06.SP

n06.PV

TT02.0P

TT02.SP

n02.PV

FTOZ.oP

FT02.PV

FT02.SPLT02.SP

LT02.PV

FT01.0P

FT01.PV

FT01.SP

LT01.SP

LT01.PV

-------- --------------

~~"= .._ .... ~~~~'~ ...

r=",===,,==:r= .....~.

1024

Figure 7.5: The response of the Tank 1 and Tank 2 cascade control systcm for 20% stiction inFCYO I (SU=20, SD=20, jump=20).

105

7.2 Troubleshooting of Plant wide Oscillation

The experimental data set consisted of 58 minutes of data with a sampling time of 0.5

seconds containing a total of 7000 observations for each variable. The last 1024 data points

were used in this analysis in order to avoid transient behavior due to the sudden introduction

of stietion. Let us denote each variable with a tag number as indicated in Table 7.1. It was

observed that since the tanks are large and have time constants of 100 min and 84 min for

Tank I and Tank 2 respectively, the oscillation was damped out if the stiction was below

20%. In those cases, the disturbance did not propagate plantwide. For example, the response

ofthe system for introduction of7% stiction in FCYOI is shown in Figure 7.6 and Figure 7.7.

Time Trends

10 --.. ---.--

9 -----------

6 --------

Power Spectra

: ::

10 ..... ,,,'"

<)"',,'

6 """

5. , .. ''''''

.. "''''4

3.. ."n,

:

1 "" """

.. " ....";~:;L...:........:.":

Samples1024 0.001 0.01 0.1

Frequency f I fs

Figure 7.6: The time series data with their power spectra for 7% stiction at FCYO I.

The power spectra show that only tags I, 3, 4 and 5 arc oscillating with a common

normalized frequency of 0.058 and variables 6, 9 and 10 eorrespondii1g to Tank 2 arc not

affected at all.

106

0.1

0.3

0.8

0.5

o

0.9

0.2

0.6

0.4

0.7

6 9 10Variables

31

I

. - . ... _ .. ..

,

II11

I

I:II;II ..

3

1

Figure 7.7: PSCMAP for 7% stiction at FCVOl.

Therefore, stiction was increased to 20% for introducing a large fault so that the whole

system is affected. The time series data with their power spectra are shown in Figure 7.8 for

20% stiction in FCVOI. For this experiment, steam was used to heat water in both tanks. In

this case, both PSCMAP (Figure 7.9) and the power spectra (Figure 7.8) show that the

variables 1, 3, 4, 5, 9 and 10 are oscillating with a common oscillation at a normalized

frequency of 0.007 approximately.

Table 7.2 shows the harmonic analysis results of this experimental data. Five components of

Fourier Series expansion of each variable have been estimated for each signal. The dominant

frequency of the main sinusoid was estimated as 0.045 rad/sec or 0.007 in a normalized scale.

The Total Harmonic Content (THC) was calculated for each tag where oscillation with

fundamental frequency and its harmonic are found. The maximum THC corresponds to tag 5

which is the controller signal to valve FCV01, correctly indicating the source or root-cause of

the propagated oscillation because stiction was introduced in this variable during the

experiment.

107

Time Trends Power Spectra

1614 -..

1311

10

9

6

54

31

1614

131110

9

6

54

31

I •• , '"'' • '" •• ,n .,I ,., "'" .,.. ••••• , •. ,....... .., """ ,.--;--:-::-:::;---:-t~-:::::--t -;-'\i~""'" ..."".. "....... ... ...... ,...• .- ••••••••••••••• '0 •0""'''' •••••••••• 0'

I • ••••••• ., ••• ".. ..,~~~~:~:.:~::::...:.::~::~:..:.~~x.tI'"" ••..• 11.. '"•• '11"" ••••• ".. , ••I'""" ., I••".. • ••--,-- . '1~;1 . ..".. : : :. . '0 •• . : ::,.. .".".--.L: :: it:: . '10'" : ::. . '''.<1 : ::'~~:'I' . ,, '01'" . . .\.: , ....... : : :. ,.."". ._. ..., , .. .. . . . ''''n. . . .. .. of"•, , .. .. . , , ,..... . . .. , .. . " . . , ,...... . . . .• ... " . . , ,...., , . ., . .. " . ::...,... " , ,. . .. ... . , . ..".., . .. ...... , ,, .. , .,"". . , ,u, •.. . .,,,.... , .,"". . . ,,,,.., . •,"'Ii .."..

1Samples

1024 0.001 0.01 0.1Frequency f Ifs

Figure 7.8: The time series data with their power spectra for 20% stiction at FCVOl.

11

14

6

<It 10GO

-= 9'C

~ 5

4

3

1

I

I.

I

. ..

II:I

,I

II .. .. .. ..

1 3 4 5 9 10 6 11 14Variables

Figure 7.9: PSCMAP for 20% stiction at FCVOl.

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

o

Figure 7.10 shows the calculated ruc values against the variable or tag nwnber. The

maximwn THC corresponds to the tag 5 correctly indicating the root-cause of the plantwide

oscillation.

108

Table 7.2: Harmonic analysis results for simple oscillation propagation example (for 20% stiction at FCVO I with heating water by saturated

steam)

Tags Al A, A) A, "5 Al A, A) A, As 01 0, 0) 0' 05 RESS At/At 'AlAI AJO"l A/Al ) ..-sFA\ THe1 0.0~5 0.14 0.01 0.05 0.23 1.40 0.14 0.11 0.06 O.O~ 2.86 2.26 0.80 -1.29 1.84 19.21 1.00 3.00 0.15 U6 4.99 0.20

3 0.0~5 0.01 0.14 0.05 0.23 1.39 0.14 0.14 0.06 0.04 -0.32 -2.71 -0.92 2.40 -1.29 19.51 1.00 0.15 3.00 1.13 4.99 0.20

4 O.O-t5 0.14 0.23 0.09 0.3" 1.31 0.38 0.19 0.11 0.11 -1.83 -2.42 -2.92 -0.59 3.13 47.9~ 1.00 3.00 5.01 2.00 7.00 0.665 0.0-15 0.14 0.23 0.32 0.05 l.78 0.40 0.22 0.14 0.08 -1.48 -1.50 -1.47 -1.39 1.65 50.26 1.00 3.01 5.02 7.02 1.12 0.986 0.006 0.01 0.02 0.03 0.04 0.89 0.47 0.24 0.22 0.19 -3.03 2.68 2.46 -0.52 1.86 413.2 1.00 1.85 3.22 4.49 6.719 0.0~5 0.06 0.01 0.05 0.03 1.19 0.27 0.23 0.20 0.15 2.06 -2.83 0.00 2.70 1.63 231.3 1.00 1.38 0.14 U8 0.68 0.010 0.0-15 0.01 0.06 0.02 0.05 1.34 0.20 0.24 0.17 0.'0 -2.70 0.28 -1.20 0.44 -2.07 51.3 ? 1.00 0.14 1.37 0.43 1.17 0.0II 0.037 0.01 0.06 0.09 0.11 0.77 0.56 0.51 0.34 0.33 1.56 -0.17 0.67 -2.07 1.81 321.4 1.00 0.17 1.48 2.45 2.9813 o.oo~ 0.01 0.09 0.01 0.18 1.29 0.27 0.08 0.09 0.04 '.76 3.13 1.68 -2.86 -1.22 37.5" 1.00 2.42 23.83 3.89 47.5114 0.012 0.02 0.05 0.03 0.02 0.86 0.45 0.39 0.29 0.31 1.50 -0.52 2.59 ~1.35 -0.92 373.2 1.00 1.58 4.65 2.50 2.01 .~-16 0.004 0.01 0.01 0.18 0.02 1.30 0.27 0.10 0.04 0.04 '.76 3.12 -2.91 1.88 -2.91 37.52 1.00 2.43 3.90 46.61 5.51

109

. --

I i ...~0 I ,...-------

i .

.

-0 -0 -~

1.00

0" 0.90E. 0.80~ 070S .g 0.60ou 0.50'c~ 040

:l!! 030]i 020{3. 0.10

0.00o 5

Tags

10 15

Figure 7.10; THC values for the pilot plant variables when 20% stiction was introduced andheating of water by saturated steam.

During the experiments, differentextent of stiction (2%, 7%, 20% and 30%) was introduced

in FCVOL The responses of the system for 7% and 20% stictionhave been described already.

The high density plots for other experiments with different extent of valve stiction have been

shown in Figure 7.11 to Figure 7.13. These figures clearly indicate that tag no. 1,3,4 and 5

are oscillating together at a common normalized frequency of 0.007 when there is no steam

heating of water and tag no. I, 3, 4, 5, 9 and 10 are oscillating together at a common

normalized frequency of 0.007 when water was being heated by steam.

1

Time Trends

Samples1024

POWerSI)ectm

""" ""

'"'''' "

,,,,,,,"6 ' "" In

, ", ",'"''''5

"",,"4 '" '", "'"'"

""'''' """"3

.,,"'"1 .,,","

: ",","",,,,,,: ", ..",

0.001 0.D1 0.1Fre(IUencyfjfs

Figure 7.11; High density plot for the pilot plant variables for 2% stiction at FCVOI(without heating).

110

TIme Tlends

10 p.c-d: . 10o

3

"""",,' ",,",: " :

. " ."""

\(.: """"""" '"''

\;.: " '"'' "'''',''''''

" : : : : ::: ''''''

"'''''::~: """"" '" ,

'::i ""","''''''

: """: ''''''

"

'ISamples

1024 0.00'1 0,0'1 0.1Fl'eqllellcy f :'f:::

Figure 7.12: High density plot for the pilot plant variables when for 20% stietion at FCYOI(without heating).

Time Trends Powel SpeCtl,1

"",,' II , " ••-. - •••.••,••••• +., .•••• -- -+~ .•

~ :'"'''' , """_,_r

, ,""'" ",'"'' '", '" ,,'" ,'" "" ,,,, ' ,,,'"'' ,"',," ,,'- 1 -(" ••••TIT"- - T -, •••, "r.- - T •••-,

'" : ","" , '"'''' ",,"'" .. ",

. '::~:' " , " .." "".4~:II "'"

, ," " ,,'"''~: ...'..: ........ " ",..':': :: X::: : " , ""~::-,::: :: : .. '" ,,'"''.. '" " "" . : : :.. " ",,, ..

'"'''' : :~,:,::

: : " "". :,""" " "',,

1014

F11

10

G G5 5

4 43 \/\/'1/\/\;/\/' 3

I .,l-\Ah/-\-Af\'

9 9

16

1024 0.001 0.01 0.1FIe-queue)' f .'f5

Figure 7.13: High density plot for the pilot plant variables for 30% stietion at FCYO1

(with heating).

The harmonics analysis results obtained for these experimental data have been given as Table 7.3

to Table 7.6.

111

Table 7.3: Harmonic analysis results for simple oscillation propagation example (2% stiction was introduced and no heating of water was done)

Tags A, A, A, A, l., A, A, A, A, A, $, ., I"" $, ., AlAI AzlA, A,fl., A4n..\ l.,/l., THe1 0.044 0.089 0.012 0.055 0.036 1.01 0.35 0.28 0.26 0.23 1.47 -0.65 -0.26 -1.93 -1.33 1.00 2.01 0.27 1.25 0.82 0.893 0.044 0.089 0.012 0.055 0.007 0.99 0.34 0.30 0.27 0.25 .1.68 2.50 3.01 1.15 -2.86 1.00 2.01 0.26 1.25 0.15 0.874 0.044 0.133 0.221 0.309 0.397 1.29 0.40 0.21 0.13 0.09 3.03 -0.39 2.50 -0.90 2.30 1.00 3.00 5.01 7.01 9.00 0.975 O.OH 0.132 0.221 0.309 0.397 1.28 0.41 0.22 0.14 0.10 -2.97 0.59 .2.16 1.46 .1.17 1.00 3.00 5.01 7.01 9.01 0.986 0.007 0.017 0.032 0.017 0.044 1.04 0.30 0.29 0.25 0.19 -3.13 2.06 2.66 2.59 -3.13 1.00 2.63 4.86 1.77 6.759 I 0.007 0.016 I 0.115 0.191 I 0.079 I 1.09 0.36 016 I 0.13 0.17 I .0.76 I .1.11 .3.12 I -1.53 I 1.39 1.00 2.46 17.30 28.57 11.7810 I 0.009 I 0.0]8 I 0.032 0.036 I 0.048 I 1.23 I 0.61 0.26 0.16 0.13 I .0.79 0.02 .1.42 I 0.61l 2.03 1.00 2.08 3.76 4.25 5.65


Tags A, A, A, A, A, A, A, A, A, A, ., ., ., ., ., ),I)..., AzlAt "AIA.] 1..4/A\ "AI).l TllC1 . 0.04 0.01 0.12 0.09 0.20 1.30 0.18 0.15 0.10 0.11 0.37 1.03 1.30 -1.?3 0.73 1.00 0.19 2.98 2.]0 5.0' 0.383 0.04 0.01 0.01 0.12 0.0' 1.11 0.82 0.23 0.12 0.11 .2.80 -3.08 3.10 .2.04 2.67 1.00 0.16 0.30 2.99 0.45 OJ)4 0.04 0.12 0.20 0.28 0.08 1.28 0.38 0.19 0.13 0.09 2.06 2.76 3.04 -3.09 1.11 1.00 3.01 5.04 7.07 l. 98 0.585 0.04 0.12 0.20 0.28 0.08 1.27 0.37 0.19 0.13 0.10 2.25 .7.87 .2.18 .1.61 1.54 1.00 3.01 5.03 7.06 1.97 0.636 0.01 I 0.01 0.02 0.07 0.01 I 18'.67 I 0.11 0.03 0.02 20.25 2.99 2.85 1.93 3.08 .0.04 1.00 1.89 2.87 3.79 0.979 0.01 I 0.04 0.01 0.00 0.01 I 16.35 I 0.27 12.93 VI 1.31 I ' .87 -0.51 .0.67 1.38 1.26 1.00 6.12 1.14 0.50 I 1.54

10 0.01 I 0.01 0,03 0.04 0.02 I 1.35 0.22 0.10 0.17 0.17 I 2.96 .2.96 -2.04 2.16 -2.29 1.00 1.89 4.88 6.14 I '.76

112


Tags A, A, A, A, A; A, A, A, A, A, ., cb, ., ., ., AlA, A2IA, AiA, A4fJ..., AsiA, TIIC1 0.05 0.01 0.01 0.15 0.05 1.31 0.35 0.18 0.15 0.10 0.38 -3.08 -3.05 0.83 -2.01 1.00 0.13 0.26 3.01 1.11 0.38

3 0.05 0.15 0.01 0.05 0.04 1.38 0.15 0.12 0.06 0.05 M2.93 .2.36 0.38 1.35 0.69 1.00 3.00 0.25 1.12 0.74 DAD

4 0.05 0.15 0.24 0.00 0.10 1.30 0.38 0.19 0.13 0.11 1.93 2.42 3.07 -0.51 0.34 1.00 3.01 5.02 0.08 2.01 0.65

5 0.05 0.15 0.25 0.34 OA4 1.28 DAD 0.22 0.14 0.09 2.20 -2.98 -1.77 -0.57 0.67 1.00 3.01 5.01 7.01 9.02 0.97

6 0.01 0.01 0.05 0.04 0.03 1.32 0.37 0.12 0.10 0.1' 0.03 0.06 -1.70 -1.00 -0.35 1.00 1.85 7.55 6.60 4.68

9 I 0.01 I 005 0.0\ 0.05 0.04 1.07 070 I 0.29 0.27 I 0.18 I 3.09 -OA6 -1.87 ').28 , .60 1.00 I 7.87 I 1.90 8.65 6.02

10 I 0.05 0.01 0.05 0.04 0.01 1.01 0.83 I 033 0.18 I 0.18 1.31 3.02 -2.57 -!.SO -2.13 1.00 I 0.13 1.12 0.74 0.24

Table 7.6: Harmonic analysis results for simple oscillation propagation example (30% stiction was introduced and heating of water was done)

Tags A, A, A, A, A, A, A, A, A~ A5 ., m, ., $, ., A/A.( ').,1A.1 A3/')..( A4f)..1 I A5!A1 TIICI 0.04 0.12 0.08 0.16 0.01 1A2 0.12 0.11 0.05 0.03 -2.29 -0.55 3.12 -1.17 -3.12 1.00 3.00 2.00 3.99 I 015 0.29

3 0.04 0.12 008 0.16 0.03 1AI 0.12 0.11 0.05 0.04 0.81 2.54 -0.02 1.95 1.28 1.00 3.00 2.00 3.99 0.84 0.29

4 0.04 0.12 0.17 0.21 0.08 1.28 0.38 0.\7 0.18 0.20 -0.76 0.83 -0.14 2.37 -U9 1.00 3.00 4.01 5.01 2.00 0.99

5 0.04 I 0.12 017 0.21 0.08 1.28 0.39 0.17 I 0.\8 i 0.19 -OA4 1.76 1.17 I -236 -0.87 1.00 3.00 4.01 I 5.01 2.00 I 1.00

6 0.02 0.01 0.02 0.04 0.03 0.37 0.43 0.51 0.47 I 0.26 1.88 I -1.86 -1.02 I 2.04 -0.22 1.00 0.33 0.64 I 1.66 I 1.13 I9 0.04 0.12 0.08 0.01 om 1.19 0.25 0.24 0.23 I 0.20 I -215 -I A 7 -0 19 I 2.99 0.07 1.00 3.05 210 I 0.16 1.69 I OA7 I10 0.04 007 0.08 0.12 0.01 1.38 016 0.15 0.10 i 0.09 -0.51 !.S6 1.60 I 0.84 2.96 1.00 1.68 2.10 3.03 I 0.16 0.20 III 001 I 0.02 i 0.04 I 0.03 0.07 0.80 0.82 I 052 I 0.50 i 023 I 1.13 2.10 -1.67 I -313 -1.96 1.00 1.45 2.86 I 2.00 I 4.58 I I13 0.00 I 0.0 I 0.09 I 0.01 0.18 1.29 0.27 0.08 I 009 I 004 I 2.76 3.13 1.68 I -2.86 I -1.22 1.00 I 2A2 ,- 8- I 3.89 i 47.51 I I_j . .J

I 14 0.0 I I 004 I 0.02 I 003 0.11 0.62 051 I 0.36 I OJ 7 i 0.33 I -0.14 -1.85 I 2.99 ! 0.80 I 0.24, 1.00 I 5.69 2.71 i 3.71 I 15.98 I ,

II 16 I 0.00 I 001 I 009 I 00\ I 018 1.29 0.27 I 0.08 I 0.09 I 0.04 I 276 3.13 i 1.68 ! -2.86 I -1.22 I 1.00 I 2.42 I 23.83 I 3891~

113

Figure 7.14 to 7.17 show the calculated THC values against the variable or tag number for

different percentage of stiction introduced. The maximum THC corresponds to the tag 5 for

all cases correctly identifying the root-cause of plantwide oscillation.

-0 y I Iu , ! t --

H------. .

~----

.-

---

l--_----

1~~ 0.9

!::. 0.8••c~ 0.7co 0,6U.!:! 0.5co 0.4E:; 0.3J:]j 02o 0.1I-

oo 2 4 6

Tags

8 10 12

Figure 7-1.4: THC values for the pilot plant variables for 2% stiction at FCVOI

(without heating).

-------

--.

n .

---_._--

--Un J----

1

1l 0.9!::. 0.8••cGl 0.7••co 0.6U.!:! 0.5co 0.4E:a 0.3J: 0.2

~ 0.1oo 2 4 6

Tags

8 10 12

Figure 7.15: THC values for the pilot plant variables for 7% stiction at FCVOI

(without heating).

114

v -+-----I, -----

i II

( i L_-~__III

I --- - ._------

--- U! ----~-I~----------

I L____ .. 1-------

1

0' 0.9:I:!::. 0.8~ 0.7.-5 0.6u.~ 0.5c~ 04

~ 03

~ 02I- 0.1

oo 2 4

Tags

6 8 10


(without heating) .

1.00

0' 0.90:I:!::. 0.80~ 0.70g 060uu 0.50'2~ 040~ 0.30

0; 0.20"0. I- 010

0.00o 5

.

.

Tags

o

-(

10

.

--

.-

--

--

15


(with heating).

115

7.3 Chapter Summary

This chapter describes the evaluation of the proposed indcx called TIIC uSll1g laboratory

cxperimental data sets. All experiments wcre carried out using the three tank level plus

temperature control pilot plant set up of the Department of Chemical Engineering, BUET.

Fault was introduced to the system and at first the high density plot and PSCMAP have been

used to detect and group variables oscillating together. Finally, THCs of thcse variables have

been calculated and ranked according to the magnitudc. It has been dcmonstrated that the

proposed THe index can successfully identify the root-cause of plantwide oscillations.

116

CHAPTER 8


8.1 CONTRIBUTION OF THE THESIS WORK

8.2 FUTURE WORK

CHAPTER 8


8.1 Contribution of the thesis work

This thesis work has two major parts, namely,

1. Fixing the Process control laboratory, development of Human Machinc Interface

(HMI) and configure data acquisition system.

2. Development of a statistical signal-processing tool to troublcshoot plantwide

disturbances.

All experiments were conducted using the Three Tank Level plus Tempcrature Control Loops

pilot plant set up in the Process Control Laboratory of Chemical Engineering Department,

BUET. At first, the laboratory set up was prepared to be in full working condition for

performing experiments as some paJ1s of the set up were not functioning properly. Thc

arrangement was madc for fixing the boilcr used for stcam supply. Thc centrifugal

compressor used for supplying instrumcnt air has also becn serviced. There arc sevcral

transmitters (level, flow and temperature transmittcrs) which were not working properly.

These have been calibrated and two transmitters were changed. Two water flow control

valves and two steam flow control valves that are pneumatic in naturc have been calibrated.

In addition, there were some problems in the power supply and thcy were corrcctcd. All these

works were carried out with the assistance of engineers from TlCl, Ghorashal.

The ADAM 5000 TCP/IP Data Acquisition Module 'was installed and configured for

measuring and logging the variablcs. This device was purchascd dircctly from Advantech

Co., Ltd. A Human Machine Intcrfacc (HMl) has been developed for the pilot plant sct up to

control, monitor and manage the system using MatLab software. Thc OPC toolbox and

Simulink in the MatLab environment were used for this purpose. The HMI has been uscd to

perform all experiments requircd for this study. This is also available for performing

experiments in futurc. Currently, undergraduate Level 4, Term I students arc using the HMI

for performing their control experiments.

1 18

The second part of the thesis work was based on both theory and experimental works. The

experimental works include system identification or determination of process models for

different section of the set up. Then PI controllers were designed and tuned for controlling the

flow of water, water levels in the tanks and temperature of water in the tanks. Both

conventional feedback and cascade control systems were designed for controlling the level of

water in the tanks. Finally, a cascade of Ta.nk 1 and Tank 2 level control loops were built,

where outlet flow from Tank 1 acted as the disturbance to Tank 2. This cascade control set up

was used for the plantwide oscillation diagnosis experiments.

The amplitudes, frequencies and phases of the time series data were estimated uS1l1gleast

square regression techniques. An Index called Total Harmonic Content (THC) based on

harmonic analysis has been developed to diagnose root-cause. of plantwide oscillation.

Disturbance in the form of different extent of valve stiction was introduced to the pilot plant

set up to examine the performance of the index. Siinulated and industrial data sets were also

analyzed to evaluate the competence of the proposed index. In order to generate plantwide

oscillation data, stietion was introduced to two control loops namely Loop 9 and Loop] 4 of a

simulated Nonlinear Dynamic Model of the Vinyl Acetate process. Industrial data from the

South East Asia refinery were also used for the evaluation ofTHC.

It has been shown that THC was capable of isolating the root-cause of plantwide oscillations

for all cases of experimental, simulated and industrial data.

8.2 Future Work

Some recommendations for future work can be listed as below:

• During the system identification and controller designing work. all sections were

assumed to be first order processes without time delay. The system was taken as

linear. While conducting experiments in future the system order can be increased.

• Tank 3, which have an inverted cone inside the tank and conical outlet can be used

for studying process nonlinearity.

• In this work, different extent of valve stietion was introduced as the source of

plantwide disturbance but there may be other reasons for disturbances like an

oscillatory external disturbance or a poorly tuned controller. The potential ofTHC can

be. examined for those cases.

119

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126

APPENDICES

APPENDIX A - VINYL ACETATE PROCESS DESCRIPTION

APPENDIX B - HARMONICS ANALYSIS RESULTS FOR VAc PROCESS

APPENDIX C - HUMAN MACHINE INTERFACE (HMI)

APPENDIX D - OPC TOOLBOX-READ, WRITE, AND LOG DATA FROM

OPC SERVERS

APPENDIX E - PRELIMINARIES OF VALVE STICTION

APPENDIX A - VINYL ACETATE PROCESS DESCRIPTION

CO, Purge

Purge

Scrub Stream

o. °P"

J~·,,"--+ J ~'B.

Scpo (---to .., : ~ ~

4-~-", ~;;~:~~

: • : ..+T F1"d () ~, ,rb 0 :0H~O~ - C 1'--,

'---~B 3 : ',.y~..:J l, ~>'::;f " I.: " - Aqueous: Get; I( •••••• ,',

.> , . ]_ ~,,~:~dUCI

; ... ~ .. ~.( I -- 1~~ :, '

, '~--------------------_!c.Acetic acid

feed

HI. Ex, .

T Manlp.

Steam

Reactor

TC-~-----'

>,<

Filted

t" ~ PC,

Oxygen feed

Ethylenefeed

Figure A.I, S1S0 plantwide control system for the VAc process (Chen et aI., 2003),

A.l

Table A-I: Steady State Values of Manipulated Variables (Chen et aI., 2003)

MV Description Steadv Stale RnllzE' Vnit

I Fresh 02 Feed 0~2343 (} - 2.26S Kmohnin

2 Fresh C,H. Feed 0,83522 o - 7~(j Kmohnin

3 Fresh R",.c Feed 0.79003 o - ..1~36 Knwlimill

4 Vaporizer Stemn Dmy 21877 0-1433400 Kcal'tnin

~ Vaporizer Vapor Exit 18 728 o - ~o Kmohnin

(j Vaporizer Heater Dntv 9008.~4 o - I~OOO Kcalimin

7 Reactor Shell Temp. IF02 110- J ~O °C

8 Separator Liquid Exit 2.7~44 0-4.536 KmoVmill

9 Separator Jacket Temo. 36001 0-80 °c10 Seoarator Vapor Exit I(j 1026 0- 30 Kmohnin

11 Compressor Heater Duty 27192 o - ~OOOO Kcal'tnin

12 Absorber Liquicl Exit 1.2137 0-4~3(j Kmolimin

13 Absorber Circulation Flow I~ 1198 o - ~O Kmolilllill

14 Circulation Cooler Duty 10730 0-30000 Kcal'tuin

IS Absorber SCl11bFlow 0.7~6 0-7.560 Km,>lilllin

16 SCl11bCooler Dutv 2018.-:13 o - ~OOO Kcalimlll

17 C02 Removal Inlet "6.5531 0-22.68 Klllolilnin

18 Purge 0.O031~7 0-0.02268 K.1ll(IIimin

19 FEHE BV1)aS'Ratio 0.31303 0-1

20 Column Ret1ux 4.9849 o - 7.~6 KnlOl/mill

21 Cohunn Reboiler Duty 67179 0- 100000 Kcal'tnin

00 ColunUl Conclenser Duty 60367 o - I~OOOO Kcal'tnin~-23 ColUllln Onwnic Exit 0.8290 0-2.4 Knwlimin

24 ColunUl Aoueous Exit 08361 0-2.-:1 K11101/Ulill

25 COhUlUlBottom Exit 2.1584 0-4536 Kmohnin

26 Vaoorizer Liouid Inlet 2.1914 0-.'\)36 Kmo 1/min

A - 2

Table A-2: Control Structure and Controller Parameters (Chell et aI., 2003)

LOOP ConfJ:ollffi Vnriable Manipulaled Variable eY. Value I've '" T,.(miu)

1 0/002 in t11e-Reador Wet 02 fre.Jlfm sp 1.:;°0 PI 10 10

l'O-::.0}

2 GAS Recycle Strco,\lll C2H4 fre~hf~d \"(\1\'," 12S p~ia PI 0,' CO

Pre~5111"e«(1-'::00>

3 HAcTank~\"('l H.~ £•..e~h few valve :';0°0 P,-

(0 100)

4 Vapot1Zer uyel Vl\pofiZer He-Mer VJ.ln' 7if, PI 0.1 30

(0 - II)O'~, Vllporiur Pr~M\fe V<l.porJ,zerVapor ElUI \'(\1-, •• 1~S Jl'>lil PI :; 10

,0- :(0)

• fuaterUirTemp . ReilCIOf Preheafe1' Val\"(', PI 1 ;

l~O <:(] '::0 ]70)

7 Reactor,Exit Telllp. STealll Dnlln Pre,,>,>lIre'>[), PI .' 10

j5Y.17 (10 - ~O(,\

S Sq>aIator Level Sqh1rator Llqllid EXlI \'ah"(' :'Oo~ p(I) - 1(0)

9 Sq>arator Temp. SqJ<uiltor Coolant Va1-,'•• 40o( PI CO

,0 SI)'I

10 Separator Vapor Flo","ate S(J><mllOrVnpOrEJ\.I1 Vah-e Fi~ed

11 COlllpr~rE:cit Teulp. C011lpre-<.wfHeater Vi\ln~ SO °c PI l,

(70-90)

12 A~le,.el Ab,>cr~ Liquid Exir Val\"(' :,0"0 P ;

(0-100)

J3 Absorlx-r Scrub Flowr.l1C' HAc T.'I11kE.-::itV,l1YC'l Fixed

14 Circulation StrC';\lll TC'llJp. Absonxr Scnlb He<1terV~h.e '::5°C- PI 1 ;

(IO-~O\

IS Absorber CircuL,tiou Absorl.=" Cir.:ulnlioll V;lh-t" Fixed

Flo\\Tnle16 Scnlb StrC'anl T erop. Circulation Cooler V;tl';e ~) o( PI 1

,1I0 - .to)

11 ~/cC02 in die Gil~ RecyclC' C02 Ptlfge FlO\\TiltC' ~p o j().IC," P l

(0 - 50~oi

IS ~'<tC2H6 in the G<I~ PurgC' FlowrntC' sp .25"" P l

RC'cvcle(0 - 100(0)

19 FEHE HoI Exit Temp., 8yp,w; ValvC' 13.t 0c- PI ; 10

(0- '00)

" %ffiO III the Column COIWlIll RC'fltl~ FlO\\Tatt" '>P 9.3-4"0 PI 0.5 60

BoUomro - ~O)

'1, tray TC'UlpmJlure Rttxlller $teil1ll \ ""I;-e iiOoC PI '0 30

(0-1.20)

22 ~caute"l T(11lper.llUIe CohulDl COlldell~e-r Du~ .t:i.S~5 o( PI 1,

(-10 :'0)

,. DeClllltef OrgMic w.C'1 Org<llll': Prodll.:! FlO\\T;lte :'O~" P l .

"' (0 -100)

'4 ~anlff AqUC'Ou'>u\.d AqlleOlI'> Product FlouT.lte ':'0"0 P l(Q il)(ll

" Colulr&I BOn01I1 Lewl ('ollllnn Bonom FIO\\T;ll(' 50"0 P 1

10-100;0,. Lqnid RecyclC' Flowrnte HAc Tank Btlt V.,h.e I Fixed

A - 3

Table A-3: Measurements at Steady State (Chcn ct aI., 2003)

M~a!>\unllellt D~.<.criptioll V"lnC' Umt

1 Val)onzer Pres<'\1f~ 12S P"i"

2 V.,porizer uyel 0.7

3 V"porizer TeUlperature 119.1-\5 °c4 Heater EXJt T~llpel.'<lnu'e 1:;0 0'('

; Reactor Exil Tempernuu-e 1:'9.17 °c6 Reactor E.xit Flowfille 18.8:'7 Kmohnin

7 FEHE Cold Exit Telllpewnue 97.1 °cS FEHE Hot E"U.tTemperilfl.1re 13-\ °c9 Sep..1CtltorUH'} OJ10 $~'U'<ltor Tempemmu -\0 °c11 ('ompre,ssof Exit Temperature SO °c12 Ab"oroer Pres.!>\u-e 128 P"ia

13 Ab':>oroeruwl 0,"'

14 Circulation Cooler Exit T~nperamre 25 °c1; Scrub Cooler Exit T~llperamre 25 °c .

16 G<!.!)Recycle Flo\\Hlte 16.5359 KmQlilllll1

17 Org<UlicProduct Flowrale 0,829 K.1l1olimin

18 Decanter uyel (Organic 1 0.5

19 Decanter Le\"d (Aqu('ou<;) 0.5

20 Dc-canter Tempemnue 45.845 °c21 COhU1Ul Bottom Leyd 0'

22 SillTray Telllper.1mre 110 °c23 HAc Tnllkuwl 0.5

24 Organic Product Compo<,ItIOIl 0.949786 o'omol

01Ac. H,O. Hi>.c)

25 0.049862 °omol

26 0.00035:!. ~'omol

27 COllUIUlBottom COlllpo~itioll 0.000010 %11101

(VAc. H,O. HAc)

280,09:;4-1-0 ooillol

29 0.906550 ~'o1ll01

30 Gil!>Recycle 0.05566-1- ~'011101

Composition(0,. CO,. C,Ii,. C,ll,. VA, H,O HAc)

31 0.007304 O:'-olUoi

32 0.681'08 O:'omol

33 . O.~-I-9191 ,0'olUol

34 0.001:'97 0'':'11101

3; 0000894 ootllol

36 0.fJ04142 %mol

37 Reactor Feed 0.07:,000 o,'omol

Compos-ition(0,. CO,. C,li" C,ll,. VA, H,O. HAc)

38 0.006"73 O'otuol

39 0.585110 o'olliol

40 0.114038 °"Omol

41 0,001373 0:011101

42 0.008558 ~'011l01

43 0.1096-1-8 ~'01l101

A -4

APPENDIX B - HARMONICS ANALYSIS RESULTS FOR VAc PROCESS

Table B-1: Harmonic analysis results of the manipulated variables (MV) for 1% stiction in Loop 9 of the VAc Process

MV A, A, A, A, As A, A, A, A, As Ii" "'- <b.. cb, cbs A,IA, J..2n.., A,tA, AJA, AsIA, RESS THe1 0.317 0.950 1.584 2.2\7 0.633 1.335 0.300 0.\56 0.097 0.069 -0.08 -1.60 -2.30 -2.78 -2.47 \ 3.000 5.000 7.000 1.999 40.73 0.460

2 0.317 0.950 1.584 0.633 2.217 1.38\ 0.260 0.094 0.072 0.044 -1.82 -3.07 2.550 2.228 2.012 1 3.000 5.000 2.000 7.00\ 5.173 0.354

3 0.006 0.317 0.012 0.017 0.023 1.207 0.749 0.286 0.138 0.069 -0.03 -2.92 0.134 0.070 -0.06 1 50.16 1.846 2.753 3.670 4.290

4 0.317 0.950 1.584 0.633 0.325 1.394 0.157 0.054 0.049 0.036 0.748 -0.28 -0.84 -1.34 -0.90 1 3.000 5.000 1.999 1.026 2.742 0.198

5 0.317 0.950 1.584 2.217 1.994 1.211 0.376 0.213 0.\42 0.086 -0.39 -1.47 -2.06 -2.39 2.59\ \ 3.000 5.000 7.000 6.296 158.6 0.558

6 0.317 0.950 1.584 0.633 0.325 1.392 0.179 0.062 0.054 0.036 -1.97 3.072 2.394 2.091 2.576 1 3.000 5.000 2.000 1.027 3.082 0.22\

7 0.317 0.950 0.633 1.584 0.325 1.393 0.177 0.064 0.054 0.037 -I. 74 2.562 1.782 1.713 2.800 1 3.000 1.999 5.000 1.0'6 2.433 0.212

8 0.317 0.950 1.584 0.633 0.325 1.394 0.\47 0.049 0.047 0.035 -0.15 -0.59 -1.03 -1.85 -1.62 I 3.000 5.000 1.999 1.025 '.200 I 0.184

9 0.317 0.950 1.584 2.217 0.633 1.270 0.414 0.236 0.\56 0.085 -1.69 -1.99 -2.28 -2.58 2.980 \ 3.000 5.000 7.001 1.999 65.67 I O.62~

\0 0.004 0.012 0.021 0.029 0.038 1.316 0.445 0.264 0.177 0.137 ~3.08 0.600 -2.44 , 0.951 -1.99 I 2.854 4.858 6.838 8.735 36.0-l

1\ 0.317 0.950 1.584 0.633 0.325 1.379 0.240 0.079 0.070 0.036 -2.39 2.647 1.795 . 1.710 2.238 1 3.000 5.000 1.999 1.026 3.800 I 0.270

12 0.317 0.950 0.325 0.308 0.633 1.41, 0.066 0.036 0.036 0.033 1.243 -1,03 -0.45 .0.23 -1.5\ 1 3.000 1.026 0.974 1.999 0.585 I 0.098

13 0.004 0.030 0.009 0.063 0.093 1. 75-1- 0.231 0.242 0.\01 0.07\ 2.791 2.051 -3.04 .1.73 1.769 \ 7.966 2.402 16.54 24.55 10.51

\4 0.317 0.325 0.308 0.950 0.633 1A13 0.036 0.038 0.018 0.015 0.687 -0.88 -0.85 -1.10 -1.81 I 1.0'6 0.974 3.000 1.999 0.720 I 0.044

15 0.004 0.025 0.009 0.078 0.052 I. '41 '0.236 0.238 0.086 0.\27 2.823 2.336 -2.96 2.133 -1.10 1 6.474 2.399 20.46 1355 14.75 I16 0.006 0.01\ 0.0\7 0.006 0.023 5.296 0.302 0.047 7.092 0.028 -0.30 0.729 1.365 -2.94 2.079 1 1.806 2.691 0.869 3.576 1.771

17 0.008 0.013 0.018 0.025 0.005 1.5 J3 I l.O4:l 0.522 0.215 1.002 2.973 2.720 2.417 1.140 0.86\ 1 1.699 2.390 3.252 0.614 104.8

18 0.010 0.006 0.015 0.157 0.02\ 1.09' I 0.430 0.649 0.252 0.175 -2.98 -2.00 2.854 -1.59 2.236 \ 0.582 1.488 15.10 2.003 -1-8.33

19 0.317 0.950 0.633 0.324 0.309 1.408 0.083 0.038 0.037 0.037 2.958 0.541 -0,03 1.569 1.316 I 3.000 1.999 1.0'4 0.975 0.800 0.\1'

20 0.157 0.314 0.006 0.471 0.785 1.069 0.539 0.347 0.359 0.220 1.515 1.439 0.021 1.333 1.178 1 2.000 0.040 3.001 5.001 148.0

21 0.317 0.157 0.006 0.950 0.324 1.395 0.171 0.071 0.043 0.040 -0.96 -0.11 0.173 0.504 -2.16 1 0.496 0.020 3.000 1.0" 2.018 I 0.052

22 0.317 0.950 0.157 0.006 0.324 1.397 0.097 0.\00 0.049 0.037 -0.55 -0.44 0.053 0.268 -1.86 I 3.000 0.496 0.019 1.023 1.855 0.085

23 0.3\7 0.157 0.006 0.324 0.950 1.376 0.298 0.042 0.041 0.031 -2.07 -2.21 -0.06 3.073 -2.02 I 0.496 0.020 1.0" 2.999 1.766 0.041

24 0.006 0.317 0.012 0.018 0.157 1.278 0.578 0.322 0.\23 0.091 -0.01 -2.\3 0.\07 0.\08 -\.48 I 50.45 1.862 2.804 24.98 4.013

25 0.317 0.006 0.012 0.308 0.\57 1.379 0.311 0.068 0.035 0.045 1.704 3.130 -3.04 0.5\5 2.096 1 0.0'0 0.037 0.972 0496 2.452

26 0.004 0.012 0.021 0.029 0.038 1.316 0.445 0.264 0.177 0.137 0.060 -2.54 0.70\ -2.\9 1.148 I 2.854 4.858 6.838 &.735 36.04

A - 5


MY'" '" '" ••• l.s AI A, A, A. As ~. d>, d>, ~.~ A.tfJ...1 •.,n. •.,Il., •..n., l.sf!.. RESS THe

1 0.317 0.952 1.587 2.221 2.793 1.336 0.308 0.169 0.112 0.058 -0.30 -2.25 2.875 1.859 -0.10 1.000 3.000 5.000 7.000 8.800 33.788 0.449

2 0.317 0.952 1.587 2.221 2.856 1.384 0.266 0.101 0.051 0.030 -2.05 2.547 1.466 0.522 -0.35 1.000 3.000 5.000 7.000 9.000 1.740 0.293

3 0.006 0.317 0.012 0.018 0.030 1.121 0.805 0.255 0.161 0.060 -0.Q7 3.137 -0.14 0.765 -0.25 1.000 50.44 1.916 2.907 4.815 3.259

4 0.317 0.952 1.587 2.221 0.324 1.402 0.161 0.058 0.030 0.018 0.520 -0.94 -1.94 -2.85 -1.14 1.000 3.000 5.000 7.000 1.020 1.147 0.125

5 0.317 0.952 1.587 2.221 2.031 1.210 0.387 0.234 0.169 0.109 -0.60 -2.10 -3.08 2.316 3.040 1.000 3.000 5.000 7.000 6.400 144.68 0.601

6 0.317 0.952 1.587 2.221 0.324 1.400 0.184 0.067 0.033 0.018 -2.20 2.412 1.306 0.331 2.407 1.000 3.000 5.000 7.000 1.020 1.198 0.137

7 0.317 0.952 1.587 2.221 0.324 1.402 0.180 0.057 0.024 0.019 -1.97 1.899 0.610 -0.54 2.653 1.000 3.000 5.000 7.000 1.020 0.857 0.127

8 0.317 0.952 1.587 2.221 0.324 1.401 0.\50 0.052 0.025 0.018 -0.36 -1.25 -2.12 -2.96 -2.02 1.000 3.000 5.000 7.000 1.020 0.912 0.117

9 0.317 0.952 1.587 2.221 2.793 1.272 0.420 0.248 0.172 0.101 -1.92 -2.63 2.941 2.241 -0.93 1.000 3.000 5.000 7.000 8.801 52.989 0.640

10 0.004 0.012 0.021 0.029 0.038 1.316 0.445 0.264 0.177 0.137 -3.08 0.600 -2.44 0.95\ -1.99 1.000 2.854 4.858 6.838 8.735 36.044

II 0.317 0.952 1.587 2.22\ 0.635 1.388 0.245 0.084 0.037 0.026 -2.62 1.981 0.695 -0.44 1.230 1.000 3.000 5.000 7.000 2.000 1.183 0.221

12 0.317 0.952 0.324 0.312 0.018 1.414 0.067 0.019 0.018 0.011 1.008 -1.70 -0.67 -0.69 1.156 1.000 3.000 1.020 0.982 0.058 0.313 0,039

iJ 0.004 0.030 0.009 0.063 0.093 1.254 0.231 0.242 0.101 0.071 I 2.791 .2051 -3.04 -1.73 1.769 1.000 7.966 2.402 16.54 24.55 10.5II

14 0.317 0.018 0.952 0.324 0.312 IA13 0.026 0.018 0.018 0.019 I 0.456 1.226 -1.76 -1.18 -1.22 1.000 0,058 3.000 1.020 0.982 0.531 0.0'2

15 0.004 0.025 0.009 0.078 0.052 1.241 0.236 0.238 0.086 0.127 I 2.823 2.336 -2.96 2.133 -1.10 1.000 6.474 2.399 20.46 13.55 14.755

16 0.006 0.012 0.029 0.023 0.018 1.411 0.403 0.\02 0.148 0118 I -313 3.056 -3. t 1 3.067 -3.11 1.000 1.818 4.604 3.584 2.892 4.556

17 0.008 0.013 0.019 0.027 0.042 0.987 .0.741 0.438 0.216 0.207 -3.03 2.351 1.439 -0.75 2.434 1.000 1.697 2.440 3.443 5.388 82.250

18 0.010 0.006 0.015 0.025 0.003 0.87' 2.733 0.626 0.178 5.519 I 2.690 -0.11 2.885 -0.71 -1.69 1.000 0.580 1.465 2.460 0.314 )4.923

19 0.317 0.952 0.324 1.587 0.31\ 1.408 0.085 0.0\9 0.022 0.017 I 2.733 -0.12 1.119 -1.53 1.040 1.000 3.000 1.020 5.000 0.981 0.428 0.059

20 0.157 0.006 0.314 0.471 0.785 0.964 0.663 0.487 0.325 0.199 I 1.516 -0.03 1.428 1.329 1.176 1.000 0.040 2.000 3.001 5.001 140.20

21 0.317 0.006 0.157 0.952 0.323 1.407 0.067 0.086 0.044 0.025 I -1.17 0.183 -0.11 -0.17 -2.24 1.000 0.020 0.495 3.000 1.017 0.526 0.046

22 0.317 0.952 0.006 0.157 1.587 1.405 0.099 0.049 0.050 0028 I -0.76 -1.08 0.314 0.070 -2.20 1.000 3.000 0.019 0.495 5.000 0.783 0.087

23 0.317 0.\57 0.952 0.323 0.006 1.407 0.15\ 0.032 0.026 00\6 I -2.27 -2.21 -2.71 3.101 -0.04 1.000 0.495 3.000 1.017 0.020 0.468 0.038

24 0.006 0.317 0.012 0.018 0.024 1.225 0.673 0.291 0.123 0.047 I -0.05 -2.34 0.080 0.409 0.237 1.000 50.54 1.884 2.863 3.8'0 2.490

25 0.317 0.006 0.012 0.018 0.952 1.381 0.279 0.067 0.035 0.019 I 1.474 3.103 2.933 -2.21 1.594 1.000 0.020 0.038 0.058 3.000 1.234 0.0'6

26 0.004 0.012 0.021 0.029 0.038 1.316 0.445 0.264 0.177 0.137 I 0.060 -2.54 0.701 -2.19 1.148 1.000 2.854 4.858 6.838 8.735 36.044

A - 6


MV Al A, A, A. '" Al A, A, A, As <1>1 d>. d>. ~, cis 1..11A.. )./A. A,fl.1 AAI ",fl.1 RESS THe1 0.317 0.952 1.586 2.221 2.856 1.339 0.309 0.170 0.113 0.081 -2.67 -3.07 -2.65 -2.07 -1.42 1.000 3.000 5.000 7.000 9.000 31.919 0.452

2 0.317 0.952 1.586 2.221 2.856 1.382 0.266 0.101 0.051 0.030 1.862 1.725 2.183 2.784 -2.83 1.000 3.000 5.000 7.000 9.000 1.589 0.293

3 0.317 0.007 0.011 0.004 0.035 1.275 0.960 0.217 0.484 0.053 0.778 -2.88 -1.86 2.064 1.755 1.000 0.022 0.034 0.012 0.111 4.712

4 0.317 0.952 1.586 2.221 0.324 1.404 0.162 0.058 0.030 0.024 -1.84 -1.77 -1.21 -0.57 2.606 1.000 3.000 5.000 7.000 1.020 1.051 0.136

5 0.317 0.952 2.221 1.587 1.717 1.217 0.391 0.171 0.236 0.104 -2.97 -2.96 -1.67 -2.39 -2.38 1.000 3.000 7.000 5.000 5.413 135.84 0.607

6 0.317 0.952 1.587 2.221 0.324 1.399 0.184 0.067 0.033 0.023 1.708 1.589 2.022 2.588 -0.10 1.000 3.000 5.000 7.000 1.020 1.062 0.149

7 0.317 0.952 1.587 2.221 0.324 1.399 0.180 0.057 0.025 0.024 1.933 1.067 1.311 1.701 0.186 1.000 3.000 5.000 7.000 1.020 0.753 0.137

8 0.317 0.952 1.587 2.221 0.324 1.404 0.151 0.053 0.026 0.023 -2.73 -2.08 -1.40 -0.70 1.766 1.000 3.000 5.000 7.000 1.020 0.739 0.126

9 0.317 0.952 1.587 2.221 2.793 1.273 0.424 0.254 0.181 0.115 1.981 2.786 -2.68 -1.87 0.191 1.000 3.000 5.000 7.000 8.802 45.094 0.653

10 0.004 0.012 0.021 0.029 0.038 1.316 0.445 0.264 0.177 0.137 -3.08 0.600 -2.44 0.951 -1.99 1.000 2.854 4.858 6.838 8.735 36.044

11 0.J17 0.952 1.587 2.221 0.324 1.390 0.246 0.085 0.037 0.023 1.293 1.152 1.405 1.801 -0.51 1.000 3.000 5.000 7.000 1.020 1.001 0.175

12 0.317 0.952 0.324 0.311 0.005 1.412 0.067 0.024 0.023 0.011 -1.36 -2.54 -3.12 -2.91 1.613 1.000 3.000 1.020 0.98' 0.0\5 0.2\8 OM6

13 0.004 0.030 0.009 0.063 0.093 1.254 0.231 0.24' 0.\01 0.071 2.791 2.051 -3.04 -1.73 1.769 1.000 7.966 2.402 16.54 24.55 10.511

14 0.317 0.323 0.3\1 0.952 0.036 1.415 0.023 0.024 0.018 0.0\3 -1.91 2.6'7 2.868 -2.60 1.447 1.000 1.019 0.982 3.000 0.115 0.489 0.024

15 0.004 0.025 0.009 0.078 0.052 1.241 0.236 0.238 0.086 0.127 2.823 2.336 -2.96 2.133 -1.10 1.000 6.474 2.399 20.46 13.55 14.755

16 0.007 0.009 0.003 0.012 0.017 1.934 0.351 6.569 0.132 0.030 0.492 1.995 ~1.13 0.730 0.450 1.000 1.351 0.359 1.775 2.446 6.541

17 0.008 0.016 0.021 0.026 0.033 1.098 0.589 0.489 0.295 0.171 3.003 2.708 -2.41 -1.11 -0.74 1.000 1.972 2.575 3.177 4.010 9. - -1 I'.J)

18 0.006 0.012 0.157 0.017 0.314 1.361 0.472 0.240 0.195 0.1\9 -3.09 3.088 -1.68 2.909 -1.60 1.000 1.855 24.96 2.759 49.87 25.786

19 0.317 0.952 0.323 0.311 1.586 1.410 0.085 0.024 0.023 0.022 0.363 -0.94 -1.33 -1.11 -0.82 1.000 3.000 1.019 0.981 5.000 0.295 0.063

20 0.157 0.314 0.471 0.007 0.785 1.059 0.533 0.355 0.345 0.217 1.535 1.447 1.374 -2.90 1.211 1.000 2.001 3.001 0.045 5.002 149.77

21 0.317 0.157 0.952 0.324 0.312 1.410 0.060 0.043 0.023 0.026 2.772 -0.09 -0.98 0.875 0.982 1.000 0.495 3.000 1.020 0.982 0.351 0.040

22 0.317 0.952 0.157 0.324 1.587 \.408 0.099 0.035 0.023 0.028 -3.11 -1.91 0.074 1.361 -1.49 1.000 3.000 0.495 1.020 5.000 0.728 0.080

23 0.317 0.157 0.952 0.006 0.324 1.409 0.106 0.032 0.030 0.024 1.711 ~2.23 2.808 -0.15 -0.30 1.000 0.495 3.000 0.019 1.0'0 0.527 0.037

24 0.317 0.007 0.011 0.004 0.015 1.263 0.788 0.171 0.863 0.027 1.570 -2.0\ -0.52 -2.52 1.407 1.000 0.022 0.034 0.012 0.047 3.501

25 0.317 0.007 0.311 . 0.952 0.323 1.408 0.088 0.027 0.020 0.021 -0.90 0.355 -2.30 0.761 -2.40 1.000 0.022 0.980 3.000 1.018 0.998 0.025

26 0.004 0.012 0.02\ 0.029 0.038 1.316 0.445 0.264 0.177 0.137 0.060 -2.54 0.701 -2.19 1.148 1.000 2.854 4.858 6.838 8.735 36.044

A - 7


MV ),., ),., ),., )., ),., A, A, A, A, As dl. c!h c!h dl, dl, ),..().., /..zfl\ ),.,n.., ),.J1,., ),.,11., RESS THet . 0.317 0.952 1.586 2.220 2.855 1.338 0.310 0.171 0.113 0.081 2.855 0.925 -0.18 -l.l7 -2.12 1.000 3.000 5.000 7.000 9.001 28.8 0.453

2 0.317 0.952 1.586 2.220 2.855 1.384 0.267 0.102 0.052 0.030 l.l06 -0.54 -1.59 -2.50 2.941 1.000 3.000 5.000 7.000 9.000 1.1 0.295

3 0.317 0.006 0.012 0.023 0.018 1.154 0.802 0.129 0.076 0.060 0.020 3.043 -3.06 2.821 2.988 1.000 0.020 0.037 0.073 0.056 2.4

4 0.317 0.952 1.586 2.220 2.855 1.402 0.162 0.059 0.030 0.018 -2.60 2.243 1.290 0.422 -0.40 1.000 3.000 5.000 7.000 9.000 0.8 0.172

5 0.317 0.952 2.220 1.586 1.711 1.207 0.390 0.173 0.240 0.133 2.548 1.053 -0.69 0.119 1.995 1.000 3.000 7.000 5.000 5.393 141.7 0.614

6 0.317 0.952 1.586 2.220 2.855 1.400 0.184 0.067 0.034 0.020 0.952 -0.68 -1.75 -2.68 2.733 1.000 3.000 5.000 7.000 9.000 0.7 0.197

7 0.317 0.952 1.586 2.220 0.323 1.402 0.181 0.058 0.025 0.018 l.l80 -1.19 -2.45 2.718 -0.50 1.000 3.000 5.000 7.000 1.019 0.5 0.125

8 0.317 0.952 1.586 2.220 0.323 1.40 I 0.151 0.053 0.026 0.017 2.786 1.932 1.101 0.302 l.l21 1.000 3.000 5.000 7.000 1.020 0.6 0.115

9 0.317 0.952 2.220 1.586 2.855 1.273 0.424 0.180 0.253 0.140 1.244 0.571 -0.74 -0.09 -1.38 1.000 3.000 7.000 5.000 9.000 42.7 0.652

10 0.004 0.012 0.021 0.029 0.038 1.316 0.445 0.264 0.177 0.137 .3.08 0.600 -2.44 0.951 -1.99 1.000 2.854 4.858 6.838 8.735 36.0

11 0.317 0.952 1.586 2.220 2.855 1.388 0.246 0.085 0.038 0.019 0.537 -1.11 -2.36 2.817 1.805 1.000 3.000 5.000 7.000 9.000 0.7 0.251

12 0.317 0.952 0.323 0.312 0.006 1.41~ 0.068 0.018 0.017 0.007 -2.11 1.480 2.433 2.527 -0.83 1.000 3.000 1.019 0.982 0.070 0.2 0.038

13 O.OO~ 0.030 0.009 0.063 0.093 1.25~ 0.231 0.242 0.101 0.071 2.791 2.051 -3.04 -1.73 1.769 1.000 7.966 2.402 16.54 24.55 10.5

14 0.317 0.952 0.006 0.323 0.311 1.413 0.0\8 0.018 0.0\7 0.017 -2.66 1.408 -0.67 1.900 1.968 1.000 3.000 0.019 1.020 0.982 0.3 0.021

15 0.004 0.025 0.009 0.D78 0.052 1.241 0.236 0.238 0.086 0.127 2.823 2.336 -2.96 2.133 -1.10 1.000 6.474 2.399 20.46 13.55 14.8

16 0.007 0.022 0.017 0.011 0.004 2.35) 0.068 0.\40 0.713 3.986 1.9~\ -0.40 -2.21 -3.01 0.752 1.000 3.?49 2.414 1.600 0.603 4.3

17 0.008 0.013 0.018 0.026 0.005 0.952 0.611 0.371 0.220 0.509 0.519 -0.67 -1.51 2.906 0.561 1.000 1.687 2.394 3.3/4 0.595 69.7

18 0.0\0 0.006 0.015 0.157 0.314 1.251 0.368 0.590 0.220 0.111 0.213 0.924 0.052 -1.62 -1.43 1.000 0.593 1.476 \5.96 31.87 41.3

19 0.317 0.952 0.323 1.586 0.311 1.408 0.085 0.018 0.022 0.016 -0.39 3.06\ -2.02 1.685 -2.08 1.000 3.000 1.020 5.000 0.98\ 0.3 0.058

20 0.006 0.157 0.314 0.471 0.785 0.689 0.940 0.470 0.314 0.\91 -3.09 1.532 1.436 1.367 1.224 1.000 2~.94 49.91 74.86 124.7 124.0

21 0.317 0.952 0.006 0.157 0.31\ 1.411 0.043 0.035 0.046 0.024 2.013 3.030 -2.76 -0.05 0.329 1.000 3.000 0.019 0.495 0.982 0.3 0.0~5

22 0.317 0.952 0.006 0.157 1.586 1.407 0.098 0.0'7 0.027 0.028 2.408 2.091 -2.53 0.138 1.007 1.000 3.000 0.019 0.495 5.000 0.6 0.087

23 0.317 0.157 0.952 0.3\ I 0.006 1.41' 0.080 0.032 0.027 0.021 0.955 -2.20 0.510 -0.80 -0.06 1.000 0.495 3.000 0.982 0.020 0.4 0.Q38

24 0.317 0.006 0.012 0.018 0.157 1.106 0.861 0.162 0.057 0.041 0.8~1 3.062 3.1\6 -3.13 -1.50 1.000 0.020 0.037 0.057 0.495 1.7

25 0.317 0.006 0.952 0.012 0.311 1.406 0.141 0.020 0.021 0.020 -1.65 -0.D2 -1.50 0.110 -3.11 1.000 0.020 3.000 0.037 0.981 0.6 0.025

26 0.004 0.012 0.021 0.029 0.Q38 1.316 0.445 0.264 0.177 0.137 0.060 -2.54 0.701 -2.19 1.148 1.000 2.854 4.858 6.838 8.735 36.0

A - 8

Table B-5: Harmonic analysis results of the manipulated variables (MV) for 5 % stiction in Loop 9 of the VAc Process

MV )" )", )", )",""

A, A, A, A, As d>, d>, d>, d>, cb. ')..1'1)"1 )",f1.., A.Jn.., )",1)", J..,f)", RESS THet 0.3t7 0.951 1.585 2.219 2.853 1.339 0.309 0.169 0.114 0.083 -0.69 2.812 0.856 -0.91 -2.63 1.000 3.000 5.000 7.000 9.000 30.8 0.450

2 0.317 0.951 1.585 2.219 2.853 1.383 0.266 0.101 0.051 0.029 -2.44 1.366 -0.50 -2.24 2.397 1.000 3.000 5.000 7.000 9.000 1.8 0.293

3 0.006 0.317 0.012 0.018 0.043 1.004 0.968 0.237 0.073 0.033 -0.17 2.731 0.479 0.874 1.374 1.000 50.00 1.891 2.846 6.711 2.7

4 0.317 0.951 1.585 2.219 0.323 1.401 0.161 0.058 0.029 0.024 0.123 -2.13 2.376 0.692 -1.61 1.000 3.000 5.000 7.000 1.019 1.2 0.136

5 0.317 0.951 1.585 2.219 2.853 1.218 0.389 0.235 0.168 0.130 -1.00 2.952 1.142 -0.46 -2.01 1.000 3.000 5.000 7.000 9.000 135.4 0.603

6 0.317 0.951 1.585 2.219 0.323 1.399 0.184 0.067 0.033 0.025 -2.60 1.229 -0.66 -2.43 1.934 1.000 3.000 5.000 7.000 1.019 1.2 0.151

7 0.317 0.951 1.585 2.219 0.323 1.401 0.181 0.057 0.025 0.026 -2.37 0.709 -1.38 2.947 2.175 1.000 3.000 5.000 7.000 1.019 0.9 0.140

8 0.317 0.951 1.585 2.219 0.323 1.402 0.150 0.052 0.025 0.026 -0.76 -2.44 2.196 0.567 -2.50 1.000 3.000 5.000 7.000 1.019 0.9 0.129

9 0.317 0.951 1.585 2.220 2.854 1.272 0.423 0.252 0.178 0.137 -2.33 2.400 0.848 -0.69 -2.22 1.000 3.000 5.000 7.000 9.000 45.0 0.649

10 0.004 0.012 0.021 0.029 0.038 1.316 0.445 0.264 0.177 0.137 -3.08 0.600 -2.44 0.951 -1.99 1.000 2.854 4.858 6.838 8.735 36.0

11 0.317 0.951 1.585 2.219 0.323 1.387 0.245 0.085 0.037 0.024 -3.01 0.791 -1.28 3.055 1.558 1.000 3.000 5.000 7.000 1.019 1.2 0.177

12 0.317 0.951 0.323 0.311 1.585 1.412 0.067 0.026 0.025 0.009 0.613 -2.90 -1.14 -0.98 1.160 1.000 3.000 1.019 I 0.982 5.000 0.3 0.033

13 0.004 0.030 0.009 0.063 0.093 1.254 0.231 0.242 0.101 0.071 2.791 2.051 -3.04 -1.73 1.769 1.000 7.966 2.402 i 16.54 24.55 10.5

14 0.317 0.323 0.311 0.951 0.029 1.411 0.025 0.025 0.018 0.015 0.059 -1.68 -1.61 -2.98 -0.75 1.000 1.020 0.982 3.000 0.090 0.5 0.024

IS 0.004 0.025 0.009 0.078 0.052 1.241 0.236 0.238 0.086 0.127 2.823 2.336 -2.96 2.133 -1.10 1.000 6.474 2.399 20.46 13.55 14.8

16 0.006 0.012 0.017 0.029 0.023 10404 0.346 0.134 0.091 0.093 3.104 -3.09 -3.03 2.895 3.065 1.000 1.902 2.719 4.547 3.630 3.0

17 0.007 0.014 0.024 0.030 0.042 1.245 .0.516 0.299 0.203 0.140 2.886 0.549 2.713 1.675 -3.12 1.000 1.971 3.407 4.190 5.909 31.6

18 0.007 0.011 0.004 0.020 0.025 0.927 0.382 0.798 0.181 0.082 -2.71 2.195 -2.50 -2048 2.587 1.000 1.581 0.611 2.840 3.556 10.7

19 0.317 0.951 0.323 0.311 1.585 1.409 0.085 0.026 0.024 0.022 2.335 -1.29 0.610 0.687 2.766 1.000 3.000 1.019 0.982 5.000 004 0.064

20 0.006 0.157 0.314 0.471 0.012 0.944 0.807 00407 0.272 0.168 -0.14 1.508 1.434 1.323 0.049 1.000 24.41 48.87 73.25 1.926 10204

21 0.317 0.006 0.951 0.157 0.323 1.411 0.052 0.043 0.039 0.028 -1.55 -0.02 -1.33 -0.14 3.088 1.000 0.020 3.000 0.496 1.018 0.5

22 0.317 0.951 0.006 1.585 0.323 10408 0.099 0.037 0.028 0.026 -1.15 -2.27 0.144 2.112 -2.80 1.000 3.000 0.020 5.000 1.019 1.0

23 0.317 0.157 0.951 0.323 0.311 1.411 0.069 0,033 0.028 0.017 -2.63 -2.19 2.428 2.162 2.553 1.000 0.495 3.000 1.018 0.980 0.3

24 0.006 0.317 0.012 0.018 0.024 1.110 0.853 0.241 0.091 0.046 -0.14 -2.75 0.449 0.587 00446 1.000 50.19 1.870 2.831 3.842 2.1

25 0.317 0.006 0.012 0.323 0.311 1.395 0.214 0.046 0.027 0.024 1.083 2.980 -2.69 -0.70 -0.34 1.000 0.020 0.038 1.019 0.982 0.7

26 0.004 0.012 0.021 0.029 0.038 1.316 0.445 0.264 0.177 0.137 0.060 -2.54 0.701 -2.19 1.148 1.000 2.854 4.858 6.838 8.735 36.0

A - 9

Table B-6: Harmonic analysis results of the manipulated variables (MV) for 1% stictionin Loop 14 of the VAc Process

MV AI A, A, ••• As AI A, A, A, As •• m. m. ., • s AlIA. A,n.. A.n. • A.Il.. A.,Il.I RESS THe1 0.006 0.012 0.018 0.024 0.006 25.64 0.128 0.0\6 0.003 27.32 3.088 -2.94 -2.88 -2.88 0.029 1.00 1.901 2.863 3.848 0.974 0.Q28

2 0.006 0.012 0.0\8 0.024 0.006 25.57 0.\23 0.015 0.003 27.25 3.088 -2.94 .2.89 .2.88 0.Q28 1.00 1.90\ 2.863 3.848 0.974 0.010

3 0.006 0.012 0.018 0.157 0.024 1.394 0.387 0.153 0.103 0.077 .0.04 0.214 0.284 -2.2\ 0.3\2 1.00 1.901 2.862 25.\6 3.836 2.283

4 0.006 0.0\2 0.0\8 0.024 0.006 26.14 0.\49 0.023 0.006 27.84 3.088 -2.95 .2.87 -2.90 0.032 1.00 1.901 2.862 3.847 0.973 1.134

5 0.006 0.012 0.157 0.3\4 0.0\8 1.349 0.369 0.26\ 0.\56 0.144 .0.05 0.179 1.833 1.483 0.225 1.00 1.906 25.14 50.30 2.878 25.072

6 0.006 0.012 0.018 0.024 0.006 27.04 0.\50 0.024 0.008 28.73 .0.05 0.187 0.422 0.303 -3.11 1.00 1.902 2.863 3.847 0.974 1.460

7 0.006 0.0\2 0.018 0.024 0.006 25.58 0.124 0.015 0.003 27.25 .0.05 0.\89 0.241 0.187 -3.\1 1.00 1.901 2.863 3.848 0.974 0.0\2

8 0.006 0.012 0.018 0.024 0.006 25.3\ 0.112 0.0\2 0.000 26.98 3.087 -2.94 .3.00 2.5\4 0.027 1.00 1.90\ 2.863 3.850 0.974 0.049

9 0.006 0.0\2 0.Ql8 0.024 0.006 25.70 0.\\8 0.013 0.002 27.37 3.088 -2.94 -2.87 -2.82 0.027 1.00 1.901 2.863 3.849 0.974 0.08\

10 0.004 0.012 0.02\ 0.029 0.038 1.3\6 0.445 0.264 0.\77 0.\37 .3.08 0.600 .2.44 0.95\ .1.99 1.00 2.854 4.857 6.838 8.735 36.044

11 0.006 0.012 0.018 0.024 0.006 25.62 0.1l9 0.013 0.002 27.29 3.088 .2.94 -2.90 -2.9\ 0.027 1.00 1.90\ 2.863 3.849 0.974 0.054 I12 0.006 0.0\2 0.Ql8 0.024 0.OQ6 25.6\ 0.125 0.0\5 0.003 27.29 3.087 -2.95 .2.89 .2.92 0.028 1.00 1.901 2.863 3.848 0.974 0.005 I13 0.004 0.030 0.009 0.063 0.0"3 1.254 0.23\ 0.242 0.101 0.071 2.79\ 2.051 -3.04 -1.73 1.769 1.00 7 %6 2.40\ 16.54 24.55 \0.5\1 I14 0.006 0.0\2 0.018 0.024 0.006 25.63 0.126 0.016 0.003 27.3\ 3.087 -2.95 -2.88 -2.91 0.028 1.00 1.901 2.863 3.848 0.974 0.00\ i

15 0.004 0.025 0.009 0.078 0.052 1.241 0.236 0.238 0.086 0.\27 2.823 2.336 .2.96 2.133 .1.l0 1.00 6.474 2.399 20.46 13.55 \4.755

16 0.006 0.012 0.018 0.024 0.006 26.01 0.\\2 0.012 0.002 27.67 .0.05 0.152 0.049 .0.59 -3.12 1.00 1.902 2.863 3.850 0.975 1.867 i17 0.\57 0.3\4 0.471 0.785 0.628 1.l04 0.554 0.371 0.227 0.281 1.523 1.425 1.333 1.204 1.258 1.00 2.000 3.00\ 5.001 4.001 107.80 1.2286

18 0.157 0.314 0.47\ 0.006 0.785 1.082 0.546 0.364 0.282 0.222 .1.62 .1. 70 .1.8\ 3.061 .1.96 1.00 2.000 3.001 0.039 5.00\ \47.\5 0.9346

19 0.006 0.0\2 0.018 0.024 0.006 25.98 0.\40 0.018 0.005 27.67 .0.05 0.183 0.'66 0.224 -3.11 1.00 1.900 2.862 3.846 0.974 0.206

20 0.157 0.314 0.47\ 0.785 0.628 1.092 0.55\ 0.368 0.226 0.279 1.5\9 1.428 1.325 1.196 1.260 1.00 2.000 3.00\ 5.001 4.001 124.35 1.2'07 I21 0.157 0.314 0.006 0.47\ 0.012 1.312 0.373 0.293 0.\50 0.079 .0.\0 .1.62 0.007 .2.69 0.308 1.00 1.999 0.039 2.999 0.075 5.\47 0.4595

22 0.\57 0.006 0.314 0.47\ 0.012 1.320 0.365 0.253 0.123 0.098 0.054 .0.0\ -1.63 2.952 0.279 1.00 0.039 2.000 2.999 0.075 \7.\39 0.36'6

23 0.157 0.314 0.006 0.47\ 0.012 1.333 0.364 0.2'\ 0.\24 0.059 -2.23 -3.07 .0.06 2.889 0.167 1.00 2.000 0.039 3.000 0.075 3.577 O.395~

24 0.006 0.0\2 0.018 0.\57 0.024 1.387 0.386 0.153 0.169 0.077 -0.04 0.220 0.293 -1.52 0.357 1.00 1.900 2.860 25.17 3.823 2.\63

25 0.006 0.0\2 0.157 0.0\8 0.314 1.342 0.372 0.337 0.145 0.133 3.103 .2.9\ 2.120 .2.78 1.808 1.00 1.899 25.21 2.844 50.47 \0.213

26 0.004 0.012 0.021 0.029 0.038 1.316 0.445 0.264 0.\77 0.137 0.060 .2.54 0.70\ .2.19 1.148 1.00 2.854 4.857 6.838 8.735 36.044

A. 10

Table B-7:Harmonic analysis results of the manipulated variables (MV) for 2 % stictionin Loop 14 of the VAc Process

MV A, A, A, A. 1.. AI A, A, A. As ~. •.. •.. ~. "'- A,1A.1 A,n... A,n... A,n.. l.,n.. RESS THe1 0.400 1.199 0.006 1.998 2.798 1.40 I 0.165 o.on 0.055 0.025 -1.65 -0.93 0.150 0.310 1.606 1.000 3.000 0.015 5.000 7.000 0.90 0.1637

2 0.400 0.006 0.012 0.025 Ll99 1.363 0.339 0.098 0.056 0.056 -0.44 .0.06 0.124 0.835 0.753 1.000 0.016 0.030 0.062 3.000 1.49 0.0733

3 0.006 0.025 0.031 0.012 0.047 1.211 0.428 0.391 0.297 0.131 -0.07 -1.06 0.277 -0.14 1.041 1.000 4.094 4.957 1.994 7.517 24.00

4 0.400 0.025 0.030 0.006 0.046 1.053 0.662 0.571 0.247 0.284 -0.42 0.274 2.109 .0.91 .3.13 1.000 0.063 0.075 0.016 0.1l6 28.23

5 0.400 1.199 1.998 2.798 2.686 1.405 0.151 0.052 0.026 0.016 -1.79 -0.60 0.961 2.57 2.108 1.000 3.000 5.000 7.000 6.nO 0.61 0.1552

6 0.400 0.025 0.031 0.046 0.062 1.380 0.190 0.176 0.1l5 0.045 3.071 0.923 2.628 -2.17 -2.96 1.000 0.063 0.077 0.1l6 0.155 5.95

7 0.400 0.006 0.012 Ll99 0.025 1.389 0.257 0.066 0.047 0.034 -1.43 3.043 .2.97 -1.74 2.194 1.000 0.016 0.030 3.000 0.062 1.03 0.0614

8 0.400 0.025 0.031 0.047 0.006 1.320 0.303 0.303 0.222 0.146 -2.14 -2.12 -0.67 0.81 0.522 1.000 0.064 0.079 0.117 0.015 17.78

9 0.400 0.025 0.031 0.047 0.004 1.389 0.168 0.156 0.109 0.054 -2.67 .2.10 .0.55 1.01 1.986 1.000 0.063 0.078 0.1l7 0.010 5.91

10 0.004 0.012 0.021 0.029 0.038 1.316 0.445 0.264 0.177 0.137 -3.08 0.600 -2.44 0.95 -1.99 1.000 2.854 4.858 6.838 8.735 36.04

11 0.400 0.025 0.031 0.047 0.065 1.383 0.187 0.174 0.122 0.063 2.512 -2.10 -0.55 0.96 -0.73 1.000 0.063 0.D78 0.117 0.162 4.52

12 0.400 0.006 1.199 0.031 0.046 . 1.410 0.039 0.036 0.020 0.022 .0.60 -0.01 -0.25 -1.26 0.067 1.000 0.016 3.000 0.077 0.116 0.61 0.0471

13 0.004 0.030 0.009 0.063 0.093 '1. 1.254 0.231 0.242 0.101 0.071 2.791 2.051 -3.04 -1.73 I. 769 1.000 7.966 2.402 16.54 24.55 10.51

14 0.400 1.199 1.998 2.798 2.686 1.273 0.424 0.255 0.181 0.140 2.436 -2.11 -0.38 1.34 -3.08 1.000 3.000 5.000 7.000 6.no 41.32 0.6544

15 0.004 0.025 0.009 0.078 0.052 1.241 0.236 0.238 0.086 0.127 2.823 2.336 -2.96 2.13 -LIO 1.000 6.474 2.399 20.46 13.55 14.76

16 0.006 0.012 0.024 0.031 0.018 1.324 0.333 0.255 0.238 0.146 3.074 -3.05 2.097 2.92 -1.92 1.000 1.941 3.800 4.897 2.807 17.35

17 0.157 o.on 0.086 0.314 0.471 0.845 .0.597 0.493 0.422 0.283 1.565 2.857 -0.27 1.45 1.387 1.000 0.461 0.546 2.001 3.002 240.n18 0.157 0.314 o.on 0.085 0.471 0.985 0.500 0.381 0.327 0.333 -1.60 .1.70 2.584 0.332 .1.80 1.000 2.001 0.460 0.542 3.002 209.41

19 0.025 0.030 0.400 0.006 0.046 0.868 0.718 0.667 0.359 0.322 0.652 2.493 -2.37 -1.43 -2.61 1.000 1.206 16.19 0.258 1.883 48.50

20 0.157 0.314 0.471 0.785 0.628 1.091 0.550 0.368 0.226 0.279 1.519 1.428 1.326 1.19 1.259 1.000 2.000 3.001 5.002 4.001 126.D721 0.157 0.400 0.314 0.006 0.471 1.141 0.684 0.324 0.260 0.131 -0.11 -2.88 .1.62 -0.02 .2.68 1.000 2.544 2.000 0.040 2.999 12.19

22 0.157 0.400 0.006 0.314 0.471 1.232 0.497 0.336 0.236 0.115 0.052 2.926 -0.02 -1.63 2.971 1.000 2.544 0.040 2.000 3.000 23.33

23 0.157 0.314 0.006 0.400 I 0.471 1.323 0.360 0.219 0.146 0.124 -2.23 -3.09 -0.13 1.40 2.897 1.000 2.000 0.040 2.545 3.000 9.83

24 0.006 0.012 0.018 0.157 0.024 1.385 0.386 0.145 0.169 0.1l6 -0.04 0.229 0.264 -1.50 0.235 1.000 1.899 2.866 25.20 3.870 3.68

25 0.006 0.400 0.025 0.030 0.012 1.040 0.617 0.426 0.349 0.287 3.063 -0.12 2.748 .2.09 2.993 1.000 64.59 4.047 4.918 1.995 63.54

26 0.004 0.012 0.021 0.029 0.038 1.316 0.445 0.264 0.177 0.137 0.060 -2.54 0.701 -2.19 1.148 1.000 2.854 4.858 6.838 8.735 36.04

A - II

Table B-8: Harmonic analysis results of the manipulated variables (MV) for 3 % stiction in Loop 14 of the VAc Process

MY A, A, A, A. A., A, A, A, A. A, m. d>. d>. m. cb. A,Il.. ')."Il. A,Il.. loA A.,1l., RESS THe1 0.400 1.199 0.006 1.999 2.798 1.402 0.165 0.052 0.055 0.025 -2.22 -2.62 0.24 -2.48 .2.28 1.000 3.000 0.015 5.000 7.000 0.58 0.164

2 0.400 0.006 0.012 1.199 0.018 1.395 0.196 0.042 0.057 0.034 -1.00 0.03 0.29 .0.93 .0.27 1.000 0.016 0.031 3.000 0.046 1.37 0.075

3 0.013 0.041 0.021 0.030 1.132 0.350 0.327 0.342 0.231 0.00 0.02 -1.66 -2.31 -0.81 1.000 2.050 6.601 3.326 4.822 65.17

4 0.400 0.041 0.025 0.036 0.016 1.119 0.432 0.414 0.316 0.333 -0.96 0.16 2.97 -1.67 -0.01 1.000 0.102 0.062 0.090 0.040 77.30

5 0.400 1.199 1.999 2.798 2.686 1.404 0.151 0.053 0.026 0.016 -2.36 -2.29 -1.84 -1.35 0.85 1.000 3.000 5.000 7.000 6.719 0.49 0.156

6 0.400 0.041 0.024 0.036 0.049 1.384 0.173 0.113 0.116 0.101 2.51 0.64 -2.02 -1.00 1.98 1.000 0.104 0.061 0.091 0.122 10.18

7 0.400 0.006 0.012 1.199 0.025 1.401 0.179 0.054 0.047 0.016 .2.00 3.04 3.11 2.85 -2.68 1.000 0.016 0.030 3.000 0.064 0.51 0.062

8 0.400 0.042 0.036 0.048 0.024 1.305 0.333 0.199 0.199 0.172 -2.71 -2.32 2.49 -0:84 1.65 1.000 0.104 0.090 0.121 0.060 41.66

9 0.400 0.041 0.036 0.024 0.049 1.384 0.161 0.111 0.099 0.102 3.04 -2.05 2.85 1.36 -0.89 1.000 0.103 0.089 0.061 0.122 12.20

10 0.004 0.012 0.021 0.029 0.038 1.316 0.445 0.264 0.177 0.137 -3.08 0.60 -2.44 0.95 -1.99 1.000 2.854 4.858 6.838 8.735 36.04

11 0.400 0.041 0.036 0.048 0.024 1.379 0.183 0.115 0.115 0.103 1.95 -2.12 2.76 -0.72 1.59 1.000 0.104 0.090 0.121 0.059 14.43

~. 0.400 0.042 1.199 0.006 0.048 1.412 0.032 0.036 0.023 0.023 -1.16 2.50 -1.95 0.51 -1.84 1.000 0.106 3.000 0.015 0.120 0.58 0.047

13 I 0.004 0.030 0.009 0.063 0.093 1.254 0.231 0.242 0.101 0.07\ 2.79 2.05 -3.04 -I. 73 1.77 1.000 7.966 2.402 16.54 24.55 10.5\

14 0.400 1.199 1.999 2.798 2.686 1.272 0.423 0.253 0.181 0.141 1.88 2.49 3.09 -2.57 2.00 1.000 3.000 5.000 7.000 6.719 I 42.61 0.651

15 0.004 0.025 0.009 0.078 0.052 1.241 0.236 0.238 0.086 0.127 2.82 2.34 -2.96 2.13 -1.10 1.000 6.474 2.399 20.4 13.55 14.76

16 0.006 0.012 0.024 0.041 0.035 1.281 0.429 0.273 0.165 0.137 3.09 3.05 -1.79 0.25 -0.76 1.000 2.002 3.781 6.608 5.539 16.65

17 0.072 0.086 0.157 0.314 0.057 0.722 0.618 0.654 0.332 0.293 -2.65 -0.93 1.48 1.53 -1.77 1.000 1.189 2.\79 4.355 0.790 261.56

18 0.157 0.073 0.086 0.314 0.471 0.914 0.515 0.432 0.467 0.308 -1.60 2.98 -0.47 - 1.71 -1.80 1.000 0.462 0.545 2.00\ 3.002 ,220.18

19 Q.400 0.025 0.040 0.007 0.036 0.721 0.55\ 0.525 0.455 0.459 -2.93 -3.03 1.17 1.84 -0.80 1.000 0.062 0.100 0.018 0.089 218.24 I20 0.157 0.314 0.471 .0.785 0.628 1.090 0.551 0.368 0.226 0.279 1.52 1.43 \.32 1.19 1.26 1.000 2.000 3.001 5.001 4.001 126.99

21 Q.400 0.157 0.314 0.006 0.471 0.908 1.010 0.286 0.194 0.116 2.86 -0.11 -1.63 0.02 -2.65 1.000 0.393 0.786 0.016 1.179 8.54

22 0.157 Q.400 0.006 0.314 0.471 1.152 0.698 0.297 0.221 0.107 0.05 2.35 -0.02 -1.63 3.00 1.000 2.544 0.040 2.000 2.999 20.59

23 0.157 0.314 Q.400 0.006 0.471 1.317 0.361 0.216 0.195 0.122 -2.23 -3.13 0.83 0.00 2.90 1.000 2.001 2.545 0.040 3.000 10.96

24 0006 0.012 0.018 0.157 0.031 1.374 0.379 0.156 0.169 0.062 -0.03 0.23 0.13 -1.53 -0.37 1.000 1.904 2.883 25.19 4.974 3.17

25 0.006 0.400 0.042 0.013 0.021 0.805 0.853 0.35\ 0.244 0.250 -3.13 -0.73 1.80 -3.10 1.30 1.000 63.39 6.605 2.100 3.291 111.17

26 0.004 0.012 0.021 0.029 0.038 1.316 0.445 0.264 0.177 0.137 0.06 -2.54 0.70 -2.19 1.15 1.000 2.854 4.858 6.838 8.735 36.04

A - 12

Table 8-9: Harmonic analysis results of the manipulated variables (MV) for 4% stictionin Loop 14 of the VAc Process

MV A.. A., A., •••• ••• AI A, A, A. As ~I d>. d>. m. d>. A. /1.., ••• /1.. A.,fl... A..n... ••• /1.. RESS THe1 OAOO 1.199 1.998 0.006 2.798 1.401 0.164 0.055 0.042 0.025 -2.93 1.54 0.25 0.07 -0.97 1.00 3.00 5.00 0.Q2 7.00 0.5 0.163

2 OAOO 0.006 1.199 0.019 0.012 1.401 0.171 0.057 0.041 0.036 -1.70 0.08 -3.06 0.30 -0.47 1.00 0.02 3.00 0.05 0.03 1.0 0.075

3 0.006 0.019 0.027 0.036 0.400 1.202 0.386 0.325 0.197 0.138 -0.08 .1.07 -1.16 -0.52 0.21 1.00 2.97 4.24 5.69 62.34 12.4

4 0.400 0.008 0.018 0.029 0.036 1.151 0.568 0.467 0.303 0.228 -1.68 -0.39 0.23 -0.57 1.14 1.00 0.02 0.04 0.07 0.09 33.1

5 OAOO 1.199 1.998 2.798 2.686 1.402 0.151 0.052 0.026 0.016 .3.08 1.86 0.89 .0.03 0.92 1.00 3.00 5.00 7.00 6.72 0.5 0.155

6 OAOO 0.029 0.017 0.038 0.010 1.402 0.105 0.091 0.080 0.069 1.81 0.03 1.33 1.52 -0.64 1.00 0.07 0.04 0.09 0.03 6.3

7 0.400 0.006 1.199 0.012 0.018 1.403 0.149 0.047 0.030 0.023 -2.72 2.98 0.74 -2.94 2.55 1.00 0.Q2 3.00 0.03 0.04 0.5 0.062

8 0.400 0.029 0.038 0.018 0.056 1.375 0.195 0.164 0.113 0.098 2.85 -2.97 -1.65 -2.15 -2.28 1.00 0.07 0.09 0.05 0.14 14.3

9 OAOO 0.029 0.017 0.038 1.199 1.402 0.095 0.075 0.073 0.059 2.33 -2.68 .1.49 -1.26 0.45 1.00 0.07 0.04 0.09 3.00 6.0 0.077

10 0.004 0.012 0.021 0.029 0.038 1.316 0.445 0.264 0.177 0.137 .3.08 0.60 .2.44 0.95 .1.99 1.00 2.85 4.86 6.84 8.74 36.0

11 0.400 0.029 0.017 0.038 0.074 1.40\ 0.107 0.083 0.084 0.056 1.25 -2.82 -1.59 -1.36 -2.56 1.00 0.07 0.04 0.09 0.19 6.8

12 0.400 0.006 1.199 0.075 0.030 1.414 0.035 0.036 0.016 0.013 -1.87 0.32 2.21 2.94 1.81 1.00 0.02 3.00 0.19 0.08 0.4 0.047

13 0.004 0.030 0.009 0.063 0.093 1.254 0.231 0.242 0.101 0.071 2.79 2.05 .-3.04 -t.73 1.77 1.00 7.97 2.40 16.55 24.55 10.5

14 0.400 1.199 1.998 2.798 2.686 1.272 0.423 0.253 0.180 0.139 1.17 0.34 -0.48 -1.29 2.16 1.00 3.00 5.00 7.00 6.72 44.1 0.650

15 0.004 0.025 0.009 0.078 0.052 1.24\ 0.236 0.238 0.086 0.127 2.82 2.34 -2.96 2.13 -1.10 1.00 6.47 2.40 20.46 . 13.55 \4.8

16 0.006 0.0\9 0.027 0.011 0,032 1.316 0.297 0.216 0.168 0.130 2.99 1.61 1.46 -1.8\ -2.53 1.00 2.88 4.19 1.74 4.98 8.8

17 0.085 0.072 0.157 0.314 0.229 0.67\ ,0.778 0.523 0.263 0.260 -1.47 -1.76 1.46 1.52 -1.60 1.00 0.84 1.84 3.68 2.68 235.3

18 0.157 0.085 0.072 0.314 0.471 0.8\0 0.532 0.635 0.407 0.272 -1.58 -0.68 -1.95 -1.71 -1.80 1.00 0.54 0.46 2.00 3.00 219.8

19 0.008 0.400 0.017 0.028 0.036 1.037 0.687 0.663 0.369 0.259 -0.51 2.66 0.58 -0.1\ 1.74 1.00 52.46 2.23 3.72 4.73 43.4

20 0.157 0.314 0.471 0.785 0.628 1.092 0.551 0.368 0.226 0.279 1.52 1.43 1.33 1.20 1.26 1.00 2.00 3.00 5.00 4.00 125.4

21 0.400 0.157 0.3\4 0.006 0.471 1.052 0.879 0.249 0.\90 0.100 2.14 -0.1\ .1.62 -0.02 -2.65 1.00 0.39 0.79 0.02 1.18 9.3

22 0.400 0.157 0.006 0.314 0.471 0.853 1.057 0.280 0.202 0.098 1.64 0.05 -0.04 -1.63 3.0\ 1.00 0.39 0.02 0.79 1.18 20.5

23 0.157 0.314 0.007 0.400 0.471 1.283 0.350 0.303 0.283 0.119 -2.22 -3.13 -0.14 0.08 2.91 1.00 2.00 0.04 2.55 3.00 12.3

24 0.006 0.012 0.0\8 0.157 0.025 1.382 0.355 0.173 0.164 0.075 -0.05 0.25 0.20 -1.52 0.26 1.00 1.89 2.88 25.14 3.93 3.3

25 0.006 0.400 0.019 0.028 0.037 0.903 0.877 0.327 0.281 0.209 3.10 -1.44 2.38 1.87 2.75 1.00 62.74 2.98 4.46 5.85 32.4 I26 0.004 0.012 0.021 0.029 0.038 1.316 0.445 0.264 0.177 0.137 0.06 -2.54 0.70 -2.19 1.15 1.00 2.85 4.86 6.84 8.74 36.0 I

A-13

Table B-I0: Harmonic analysis results ofthe manipulated variables (MV) for 5% stiction in Loop 14 of the VAc Process

MV 1.., 1.., 1.., l... As A, A, A, A, As ~. cb, cb, ~, ~. 1..,1l. 1..,Il., 1..,fl., 1..,1l. ),JI.. RESS THeI OAOO 1.199 1.998 0.006 2.798 1.403 0.165 0.055 0.035 0.025 -1.83 -1.44 -0.53 0.24 0.45 1.00 3.00 5.00 0.Q2 7.00 0.8 0.164

2 0.400 0.006 0.014 1.199 0.022 1.400 0.142 0.065 0.057 0.046 -0.61 -0.12 -0.34 0.23 0.59 1.00 0.02 0.04 3.00 0.06 0.6 0.075

3 0.006 0.013 0.019 0.025 0.043 1.002 0.621 0.485 0.300 0.146 -0.3 1 -0.39 0.88 2.87 1.46 1.00 2.09 3.02 4.00 6.81 34.7

4 OAOO 0.015 0.021 0.009 0.044 0.970 0.724 0.591 0.369 0.171 -0.56 -1.31 0.27 -2.\0 2.73 1.00 0.04 0.05 0.Q2 0.11 32.6

S OAOO 1.199 1.998 2.798 2.686 1.405 0.151 0.052 0.026 0.016 -1.97 -1.12 0.12 1.40 -2.71 1.00 3.00 5.00 7.00 6.72 0.6 0.155

6 OAOO 0.018 0.022 0.014 0.044 1.381 0.145 0.145 0.096 0.072 2.90 -2.43 0.03 1.00 -2.26 1.00 0.04 0.06 0.03 0.11 8.7

7 0.400 0.006 0.013 0.018 1.199 1.408 0.114 0.048 0.037 0.047 -1.61 2.95 2.68 -2.50 -2.26 1.00 0.02 0.03 0.05 3.00 0.5 0.063

8 0.400 0.021 0.043 0.056 0.016 1.350 0.262 0.139 0.144 0.190 -2.32 -1.68 1.04 1.23 2.94 1.00 0.05 0.11 0.14 0.04 16.5

9 OAOO 0.019 0.023 0.015 0.057 1.389 0.117 0.087 0.131 0.077 -2.85 -0.47 3.08 -3.08 1.14 1.00 0.05 006 0.04 0.14 7.4

10 0.004 0.012 0.021 0.029 0.038 1.316 0.445 0.264 0.177 0.137 -3.08 0.60 -2.44 0.95 -1.99 1.00 2.85 4.86 6.84 8.74 36.0

II 0.400 0.019 0.022 0.015 0.057 1.382 0.129 0.102 0.144 0.090 2.34 -0.32 3.11 -2.91 1.02 1.00 0.05 0.06 ON 0.14 8.0

12 OAOO 1.199 0.006 0.056 0.044 1.411 0.036 0.024 0.021 0.018 -0.78 -0.77 -0.09 0.13 -0.42 1.00 3.00 0.02 0.14 0.11 0.5 0.047

13 0.004 0.030 0.009 0.063 0.093 1.254 0.231 0.242 0.\01 0.071 2.79 2.05 -3.04 ~1.73 1.77 1.00 7.97 2.40 16.55 24.55 10.5

14 OAOO 1.199 1.998 2.798 2.686 1.273 0.423 0.253 0.181 0.140 2.27 -2.61 -I.21 0.21 -1.57 1.00 3.00 5.00 7.00 6.72 42.8 0.652

15 0.004 0.Q25 0.009 0.078 0.052 1.241 0.236 0.238 0.086 0.127 2.82 2.34 -2.96 2.13 -1.10 1.00 6.47 2.40 20.46 13.55 14.8

16 0.006 0.013 0.018 0.024 0.010 1.873 0.646 0.208 0.402 1.437 3.07 0.25 -1.43 -0.01 -1.79 1.00 2.14 2.94 3.81 1.64 8.0

17 0.073 0.086 0.157 0.044 0.058 0.839 .0.675 0.449 0.203 0.3 18 3.02 -0.53 1.55 2.85 2.78 1.00 1.18 2.16 0.61 0.80 284.3

18 0.072 0.086 0.157 0.314 0.471 0.711 0.596 0.734 0.374 0.'49 2.70 -0.10 -1.64 -1.69 -1.78 1.00 1.18 2.17 4.34 6.51 215.2

19 0.015 0.020 Q.400 0.008 0.024 0.838 0.697 0.518 0.543 0.200 -0.99 0.99 -2.55 -1.6 , -2.28 1.00 1.34 26.94 0.5' 1.64 40.2

20 0.157 0.3 14 0.471 0.785 0.628 1.091 0.551 0.368 0.226 0.279 1.52 1.43 1.32 1.19 1.26 1.00 2.00 3.00 5.00 4.00 126.3

21 Q.400 0.157 0.314 0.007 0.471 1.143 0.762 0.217 0.167 0.088 -3.06 -0.11 -1.62 -0.02 -2.64 1.00 0.39 0.79 0.0' 1.18 10.3

22 Q.400 0.157 0.006 0.314 0.471 0.971 0.961 0.241 0.184 0.090 2.73 0.05 -0.03 -1.6-1 3.00 1.00 0.39 0.02 0.79 1.18 17.6

23 0.157 0.399 0.006 0.314 0013 1.243 0.340 0.299 0.341 0.177 -2.23 1.32 -0.32 ~3.10 -0.33 1.00 2.54 0.04 2.00 0.08 28.8

H 0.006 0.012 0.019 0.157 0.024 1.351 0.384 0.118 0.165 0.071 -0.06 0.20 0.31 -1.53 -0.53 1.00 1.93 2.98 25.16 3.82 4.4

25 0.400 0.006 0.014 0.020 0.026 0.873 0.722 0.482 0.393 0.176 -0.32 2.79 2.50 -2.8-1 -0.27 1.00 0.02 0.03 0.05 0.06 58.0

26 0.004 0.012 0.021 0.029 0.038 1.316 0.445 0.264 0.177 0.137 0.06 -2.54 0.70 -2.19 1.15 1.00 2.85 4.86 6.8-1 8.74 36.0

A - 14

Table B-ll: Harmonic analysis results of the South East Asia Refinery data sets

PV 1.., 1.., 1.., 1.., •• A, A, A, A, A, ~, lb, lb, ~, ~, 1.. n.., 1..,n.. 1..,1)., 1..,11.., ).,11.., THe1 0.075 0.377 0.284 0.297 0.087 0.433 0.383 0.399 0.376 0.327 0.756 2.860 -0.54 -2.33 -0.32 1.000 5.019 3.775 3.947 1.156

2 0.380 0.760 0.366 0.083 0.\23 1.367 0.157 0.110 0.108 0.084 0.248 -0.45 -0.54 1.556 0.996 1.000 1.999 0.964 0.218 0.324 0.177

3 0.380 0.073 0.051 0.128 0.096 1.318 0.30 I 0.152 0.208 0.160 -0.96 2.816 -\.52 -1.43 -2.20 1.000 0.192 0.135 0.336 0.254

4 0.380 0.073 0.014 0.057 0.125 1.138 0.390 0.321 0.37\ 0.235 -0.91 2.677 -0.11 3.045 -0.93 1.000 0.\91 0.037 0.149 0.330

5 0.017 0.027 0.039 0.060 0.013 1.942 0.138 0.393 0.135 0.733 1.974 . -0.78 0.76 0.049 -0.22 1.000 1.603 2.337 3.6\6 0.760

6 0.157 0.474 0.722 0.708 0.574 0.395 0.394 0.245 0.289 0.259 1.756 .2.70 -0.46 0.368 2.097 1.000 3.007 4.586 4.497 3.647

7 0.073 0.035 0.378 0.145 0.197 0.550 0.299 0.263 0.275 0.240 -1.17 -3.02 0.140 1.559 2.617 1.000 0.472 5.154 1.970 2.686

8 0.380 0.072 0.054 0.032 0.090 0.736 0.458 0.415 0.310 0.235 1.832 -1.31 -0.59 3.062 0.539 1.000 0.188 0.14\ 0.085 0.237

9 0.378 0.759 0.084 0.182 0.148 0.652 0.313 0.263 0.211 0.223 2.311 2.963 0.334 0.905 -0.79 1.000 2.005 0.221 0.48\ 0.392 0.379

10 0.380 0.368 1.140 0.355 0.458 1.394 0.103 0.085 0.065 0.071 -1.63 3.086 -2.09 2.254 -0.44 1.000 0.970 3.001 0.933 1.204 0.\09

11 0.380 0.071 0.052 1.140 0.061 1.082 0.527 0.352 0.291 0.249 -1.15 0.383 0.082 1.216 -0.87 1.000 0.188 0.138 3.001 0.160 0.356

12 0.074 0.140 0.159 0.089 0.378 1.044 0.731 0.280 0.278 0.219 -1.18 -1.2\ 0.5\5 0.191 -2.18 1.000 1.896 2.158 1.206 5.124

13 0.380 0.760 1.756 1.777 1.897 1.095 0.373 0.349 0.302 0.\81 2.673 1.953 -0.78 -0.31 1.949 1.000 2.001 4.620 4.676 4.992 0.472

14 0.125 0.100 0.135 0.113 0.080 0.972 0.451 0.398 0.306 0.249 0.556 2.871 -0.81 1.834 1.793 1.000 0.799 1.073 0.901 0.641

15 0.381 0.095 0.11\ 0.204 0.166 0.617 0.500 0.397 0.311 O.34~ 2.574 2.737 0.487 I. 788 2.484 1.000 0.249 0.291 0.536 0.435

16 0.380 0.074 1.755 0.060 1.775 0.597 0.384 0.361 0.267 0.282 1.707 -1.94 2.979 -0.98 -2.11 1.000 0.194 4.618 0.157 4.668

17 0.379 0.162 0.207 0.234 0.\80 0.560 0.597 0.579 0.503 0.517 1.845 -1.65 1.745 -2.47 -0.58 1.000 0.428 0.546 0.618 0.476

18 0.162 0.233 0.382 0.205 0.221 0.504 0.542 0.500 0.558 0.373 1.570 1.154 -0.47 -0.79 1.789 1.000 1.441 2.360 1.270 1.365

19 0.380 0.076 0.759 0.063 0.090 0.984 0.352 0.234 0.207 0.264 -1.27 1.050 2.316 .0.93 -0.75 1.000 0.200 1.998 0.167 0.237 0.314

20 0.380 0.073 0.760 0.128 0.054 1.324 0.235 0.164 0.183 0.156 1.522 -0.19 -0.17 1.603 0.772 1.000 0.192 2.000 0.336 0.142 0.232

21 0.017 0.033 0.071 0.053 0.101 1.121 0.531 0.400 0.405 0.152 0.770 -0.75 1.017 0.863 -0.53 1.000 1.945 4.214 3.153 5.956

22 0.514 0.220 0.369 0.135 0.235 0.298 0.274 0.227 0.207 0.221 -2.53 0.504 -2.94 -2.59 2.402 1.000 0.428 0.718 0.263 0.456

23 2.370 1.312 1.276 2.500 1.231 0.297 0.260 0.250 0.272 0.292 1.573 -0.38 -0.87 2.395 0.507 1.000 0.554 0.538 1.05.5 0.520

24 0.380 0.812 0.702 0.663 0.501 0.901 0.266 0.251 0.199 0.189 0.428 1.447 0.004 1.933 2.723 1.000 2.137 1.847 1.745 1.320

25 0.379 0.761 1.138 1.116 0.702 0.787 0.281 0.233 0.175 0.178 -0.51 1.898 1.263 -1.13 2.917 1.000 2.007 3.002 2.944 1.850 0.564

26 0.4\5 0.212 0.268 0.129 0.226 0.264 0.243 0.240 0.347 0.315 2.463 1.642 2.321 2274 2.063 1.000 0.511 0.645 0.311 0.545

27 0.614 2.368 1.291 1.471 2.401 0.263 0.254 0.259 0.244 0.234 0.199 -0.94 2.873 1.572 1.358 1.000 3.854 2.102 2.394 3.907

28 0.377 0.258 0.3 15 0.564 0.275 0.678 0.376 0.367 0.272 G.lD 2.654 ~2.83 1.797 -3.01 1.155 1.000 0.685 0.835 1.495 0.728

29 1.309 2.500 1.277 1.181 0.243 0.309 0.257 0.220 0.247 0.211 2.894 -0.56 1.678 .1.29 -0.24 1.000 1.909 0.975 0.902 0.\86

30 0.380 0.721 0.430 0.222 0.474 0.358 0.289 0.219 0.251 0.265 -0.10 -1.18 -2.39 1.723 2.349 1.000 1.895 1.131 0.585 1.246

A - 15

31 0.017 0.380 0.078 0.056 0.100 0.587 0.395. 0.584 0.508 0.375 0.654 -1.11 1.512 0.126 2.221 1.000 22.56 4.603 3.338 5.954

32 1.756 1.777 1.828 1.732 1.767 0.614 0.556 0.300 0.336 0.301 0.761 1.099 1.919 .1.93 .0.99 1.000 1.012 1.041 0.987 1.006

33 0.381 0.761 1.140 0.299 0.293 0.957 0.642 0.311 0.375 0.372 -0.52 0.484 -0.69 -1.44 3.048 1.000 1.998 2.995 0.787 0.770 0.869

34 0.380 0.760 1.901 1.140 1.521 1.171 0.584 0.403 0.168 0.143 2.231 2.156 2.787 -0.11 1.505 1.000 2.001 5.002 3.000 4.001 0.961

35 0.073 0.053 0.086 0.025 0.035 0.818 0.558 0.357 0.339 0.347 2.168 -3.01 -0.64 1.310 -0.03 1.000 0.728 1.185 0.342 0.476

36 0.072 0.052 0.018 0.085 0.035 0.785 0.721 0.557 0.347 0.380 -0.79 0.000 -0.63 2.446 3.016 1.000 0.729 0.245 1.182 0.490

37 0.075 1.885 0.055 0.125 0.376 0.697 0.568 0.435 0.324 0.355 -0.20 -2.35 0.925 -2.94 2.128 1.000 25.24 0.735 1.674 5.039

A - 16

APPENDIX C - HUMAN MACHINE INTERFACE (HMI)

Industrial processes, such as petroleum rcfining, water treatmcnt, materials manufacturing,

and the like, are increasingly automated and often require constant monitoring of one or more

process variables to ensure the process is performing as expected or desired. Often these

process variables are monitored from a location remote from the machines controlling the

process.

The human-machine interface is where people and technology meet. I'(uman Machine

Interface (HMI) equipment provides a control and visualization interface between a human

and a process; machine, application or appliance. HMIs allow controlling, monitoring,

diagnosing and managing the respective application. Interaction can include touch, sight,

sound, heat transference or any other physical or cognitive function

HMI effectiveness is measured by a number of components, such as learnability and

productivity. These components are sometimes brought together under the titlc of "usability,"

also known as quality of use. Thc design of a uscr interface affccts thc amount of effort the

user must expend to provide input for the system and to interprct thc output of the system,

and how much effort it takes to learn how to do this. Usability is the degree to which the

design of a particular user interface takes into account the human psychology and physiology

of the users, and makes the process of using the system effective, efficient and satisfying.

Usability is mainly a characteristic of the user interface, but is also associated with the

functionalities of the product and the process to design it. It describes how well a product can

be used for its intended purpose by its target users 'with efficiency, effcctiveness, and

satisfaction, also taking into account the requirements from its context of use.

ISO Definition of Quality of Use

The ISO 9241 standard defines three components of quality of use applicable to the design of

HMIs:

EffectivenesS - Does the product do what the users require? Does it do the right thing?

A-17

Efficiency - Can the users learn the HMI quickly? Can they carry out their tasks with

minimum expended effort, including a minimum of errors? Does it improve the

productivity/effort ratio? Does it do things right?

Satisfaction _ Do users express satisfaction with the product? Does the new product reduce

stress? Do the end users now have a more satisfying job?

Types

Currently the following types of user interface are the most common:

Graphical user interfaces (GUI) accept input via devices such as computer keyboard and

mouse and provide articulated graphical output on the computcr monitor.

Web-based user interfaces or web user interfaces (WUl) accept input and provide output by

generating web pages which are transmitted via the Internet and viewed by the user using a

web browser program.

HMI Design guidelines

Make sure the design is simple, logically organizcd and welliabcled.

Avoid cluttering the screen with data that is irrelcvant to the operator.

Where appropriate present information graphically, such as with analogue meters or moving

bars, rather than alpha-numerically.

Line up numeric values and always show clcar labels with units.

Do not use all uppercase and keep the number of fonts to a minimum.

Use changing icons for digital states

Outline objects in black

Group related items, perhaps by drawing a box around them.

Make sure the results of pressing a control button are absolutely clear.

Give feedback on all operator actions.

Use color conservatively, conventionally and consistently.

Use a muted, neutral color for the background, such as grey or blue.

Use dark characters on a lighter background.

Minimize the number of colors and make these as distinct as possible.

Do not make color the sole source of information - use labels or position to clarify.

A - 18

APPENDIX D - OPC TOOLBOX-READ, WRITE, AND LOG DATA FROM

OPCSERVERS

The OPC Toolbox™ extends MatLab@ and Simuiink@ with tools for interacting with OPC

servers. One can read, write, and log OPC data from devices that conform to the OPC

Foundation Data Access standard, such as distributed control systems (DCS), supervisory

control and data acquisition systems (SCADA), and programmable logic controllers (PLCs).

The toolbox enables MatLab and Simulink products to respond to an OPC server or OPC

Toolbox software initiated event, such as a shutdown, server error, or item value change.

Engineers in chemical, pharmaceutical, power generation and other continuous process

industries can use the toolbox to import plant data into MatLab for analysis, visualization,

simulation, and rapid prototyping of algorithms. It lets one to use Simulink models in online

supervisory control and controller testing (hardware-in-the-Ioop) applications.

Working with the ope Toolbox

The OPC Toolbox provides three ways to implement an OPC Data Access Client. One can:

Execute all OPC Toolbox functions dircctly from thc MatLab command linc or incorporatc

them into your own MatLab applications

Use the graphical user interface (GUI) to rapidly connect to OPC servers, creatc and

configure OPC Toolbox objects, and read, write, and log data

Use the Simulink Block set library to read and write data to and from an OPC server while

simulating a system.

ope Configuration

Walel flow to Tank2

ope Read (Cache):Heatin ...k3.FT02 V

H02

oScope

Valve Opening %

ope Write (Sync):Heatin .... FCV02

FCV02

Figure 0-1: A simulink model file built using the OPC rcad-writc blocks.

A - 19

Reading and Writing OPC Data

In Simulink, read and write blocks retrieve and transmit data synchronously or

asynchronously to and from the ope server. The blocks contain a client manager that lets

you specify and manage the ope server, select items, and define block sample times.

OK I l C~ncel I 1 Help

------------ - -------_.

V03lueport d03t03type: ldouble

o Soow qU.,]lty port

o Show timest~mp port lIS:

Sample time: I

Re.lId mode: Synchronous (c~che)

,,I,+

[Add Items .• 1 I Delete II,.._ ._, I

_ P~r.ometers---

cbent: !loc03_lhos~dv03nte(h.ModbusTCP yer2.0 ~JiCConfigureOPCOents .• , 1 i

,ItemJDs--------- ---:-:- _=-_-=-_~~~'_:l:"He.otk'lijT.on!ISystem.T"nkLFTOI :•.••j !

_ope Read block - ---------,; Reed deta from an ope server. Reeds cen ~ synchronous (from: the ceche or device) or llsynchtonOUS (from the device).

. The output ~ts IIrll vectors the scme size es the rKJmber d Items; specified in the block. y<!!lueIs output as II vector of the specified. date type. The optional Quality port Is a UINTl6 vector. The: optioMl Timest~ port is e double vector.__ ._. __ ~_._ ___. -.J

C?X'" •• 1 I ~C.oncel 1 1 H~p

P¥,vneteN---------------,~; [r~~t(~~_;ch.~u~T(pjerz~o~_..-_ ~ i

IL C;onfl9tl:e OPe Oents... I r. ItemlOS 1[""_Y." ,,=,,', -------"R II

~I i

il:----- ~!I

~l:' .."'_J,' j.))'."dc':-', ~IAdd-'-t~-,~1I Oelete III~d mode:Ft;;~d;)~-~--.--- _~=-~~I54rnp1e'tme:- L '. _j t;.:~:~t:;1;;;;"--- __n==- __~ Io7;::::::(t:~: Ii

~,I~l cJal:e numbe..,. __ .~__I

OPCReaclbIock---------------

[

Reed dale from an oPe server. Reem CHl be syndYonous (from .,1'

the ClIChe or device) or asyndYCIl1OU5 (from the device).

The 0ttpJt ports Me vectors the 581'1"lelsize as the ntmbet of ll:ems

.specfied h the b/ock. value Is outpUt liS e vector of the specified IdIIU1 type. The optloMl QuMty port Is a U1NTI6 vector. The Joption/ll Tlnlestamp port Is II dolbIlI vector. I__________________ J

Figure D-2 Properties of ope Read block Figure D-3 Properties of ope Write block

Logging OPC Data

The toolbox enables one to log data as it changes over time. Data can be logged to memory ordisk. One can use MatLab and add-on toolboxes to analyze and visualize the time series data

to design control systems and optimize plant performance.

A -20

APPENDIX E - PRELIMINARIES OF VALVE STICTION

The most common final control element in the process control industries is the control valve.

The control valve manipulates a flowing fluid, such as gas, steam, water, or chemical

compounds, to compensate for the load disturbance and keep the regulated process variable

as close as possible to the desired set point.

The control valve is a critical part of the control loop. A control valve static friction is the

force that must be overcome before there is any relative motion between the two surfaces.

Once relative movement has begun, dynamic friction is the force that must be overcome to

maintain the relative motion. Running or sliding friction is colloquial terms that are

sometimes used to describe dynamic friction. Stick/slip or "stiction" are colloquial terms that

are sometimes used to describe static friction.

Different people or organizations have defined stiction in different ways. According to the

Instrument Society of America (ISA) "Stiction is the resistance to the start of motion usually

measured as the difference between the driving values required to overcome static friction

upscale and downscale". Based on careful investigation of real process data, a new definition

of stiction has been proposed by Choudhury et al. (2005) and is summarized as follows.

The input-output behavior of a sticky valve can be described with the help of a phase plot as

shown in Figure E-!. The plot consists of four components: deadband, stickband, slip-jump

and the moving phase. Let us consider the valve position at point A as if it comes to a rest or

changes the direction. In case of an input is introduced, the valve position remains fixed as it

cannot overcome the force due to static friction immediately. After the controller output

overcomes the deadband (AB) plus the stickband (BC) of the valve, the valve jumps to a new

position (point D) and continues to move. Due to very low or zero velocity, there may be

occasional sticky responses in-between points 0 and E in Figure E-I, while traveling in the

same direction. In such a case, the magnitude of the deadband is zero and only the stickband

is present. The deadband and stickband represent the behavior of the valve when it is not

moving though the input to the valve keeps changing. The jumping movement of the valve

along the line CD is termed as slip jump. As the valve starts to move there is an abrupt

conversion of potential energy stored in the actuator due to high static friction into kinetic

energy and the slip jump occurs. The magnitude of the slip-jump is very crucial in

determining the limit cyclic behavior introduced by stiction. Once the valve jumps or slips, it

A - 21

continues to move until it sticks again (point E in Figure E-I), Naturally In the moving phase

dynamic friction is present, but that is much lower than the static 1"iction, The whole

phenomenon is repeated with the reversal of valve direction, Therefore according to

Choudhury et al. (2005) valve stiction is defined as follows,

"Stiction is a property of an element such that its smooth movement in response to a varying

input is preceded by a static part (dead band + stickband) followed by a sudden abrupt jump

called 'slip-jump', Slip-jump is expressed as a percentage of the output span, Its origin in a

mechanical system is static friction, which exceeds the dynamic friction"

stickband + deadband~, , ,..""' .." , ..,~

F' 'E.,q,;

~~~~$I

,.,/,1J, ..., "....

;~~;J

/};~J.

,./,' :slip jump, JA~ , .., , ,~"'tC"'"~ deadband r.....stickband, 5

valve input(controller output, op)

Figure E-l: Typical input-{)utput behavior of a sticky valve (Choudhury ct aI., 2005),

A - 22

VALVE STICTION MODEL FORMULATION

The valve stiction model was developed by Choudhury et aI., 2004. The model consists of two

parameters namely the size of dead band plus stickband 8 (specified in the input axis) and the slip

jump.J (specified on the output axis). Note that the term '8' contains both the deadband and

stickband. Figure E-2 summarizes the model algorithm, which can be described as:

• First, the controller output (rnA) is provided to the look-up table where it is converted

to valve travel %.

• If this is less then 0 or more than 100, the valve is saturated (i.e., fully close or fully

open).

• If the signal is within 0 to 100% range, the algorithm calculates the slope of the

controller output signal.

• Then the change of the direction of the slope of the input signal is taken into

consideration. If the 'sign' of the slope changes or remains zero for two consecutive

instants, the valve is assumed to be stuck and does not move. The 'sign' function of

the slope gives the following

-If the slope of input signal is positive, the sign (slope) returns '+1'

_ If the slope of input signal is negative, the sign (slope) returns '-I' and

.Ifthe slope of input signal is zero, the sign (slope) returns '0'.

Therefore, when sign (slope) changes from '+1' to '.1' or vice-versa it means the direction of

the input signal has been changed and the valve is in. the beginning of its stick position

(points A and E in Figure E-I). The algorithm detects stick position of the valve at this point.

Now, the valve may stick again while traveling in the same direction (opening or closing

direction) only if the input signal to the valve does not change or remains constant for two

consecutive instants, which is usually uncommon in practice. For this situation, the sign

(slope) changes to '0' from '+ l' or '-1' and vice versa. The algorithm again detects here the

stick position of the valve in the moving phase and this stuck condition is denoted with the

indicator variable I = 1. The value of the input signal when the valve gets stuck is denoted as

xss. This value of xss is kept in memory and does not change until valve gets stuck again. The

A - 23

cumulative change of input signal to the model is calculated from the deviation of the input

signal from xss.

• For the case when the input signal changes its direction (i.e., the sign(slope) changes

from '+1' to '-)' or vice versa), if the cumulative change of the input signal is more

than the amount of the dead band plus stickband (S), the valve slips and starts moving.

• For the case when the input signal does not change the direction (i.e., the sign (slope)

changes from '+1' or '.1' to zero, or vice versa), if the cumulative changes of the

input signal is more than the amount of the stickband (J), the valve slips and starts

moving. Note that this takes care of the case when valve sticks again while travelling

in the same direction (EnTech, 1998; Kano ct aI., 2004).

• The output is calculated using the equation:

output = input - sign( slope) • (S - J)/2

'and depends on the type of stiction present in the valve. It can be described as follows:

_Deadband: If J= 0, it represents pure dead band case without any slip jump.

_ Stiction (undershoot): If J < S, the valve output can never reach the valve input. There is

always some offset. This represents the undershoot case of stiction.

_ Stiction (no offset): If J = S, the algorithm produces pure stick-slip behavior. There is no

offset between the input and output. Once the valve overcomes stiction, valve output tracks

the valve input exactly. This is the well-known "stick-slip case".

_ Stiction (overshoot): If J > S, the valve output overshoots the valve input due to excessive

stiction. This is termed as overshoot case ofstiction.

Recall that J is an output (y-axis) quantity. Also, the magnitude of the slope between input

and output is 1.

• The parameter, J signifies the slip jump start of the control valve immediately after it

overcomes the deadband plus stickband. It accounts for the offset between the valve

input and output signals.

A - 24

• Finally, the output is again convcrted back to a mA signal using a look-up table

based on the valve characteristics such as lincar, equal percentage or square root, and

the new valve position is reported.

xss=xss)"(1<)=0 no

Look up tllbl('(C{lUHI1~ InA 10 ,'~IH'~1I)

~'E'S

no

J,'aI1't! saps (lnd mow's

no

no

)(k)~'(k-l)

x(k)<100

remain stllckxss=x(k-l))"(I<M"(I<-1

XS5=x5S

)"(1<)=100

Vain" sticks

Vain cbanl.ctelistirs(r.g., linear, square I'oot, ftC.) I ./(Com'forts nh"f' ¥. to m4.) L!:--

Figure E-2: Signal and logie flow ehart for the data-driven stietion model

(Choudhury et aI., 2004)

A - 25

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