Simulation of Boiler Drum Process Dynamics and Controldigitool.library.mcgill.ca/thesisfile61104.pdf · 1 1 Simulation of Boiler Drum Process Dynamics and Control Jian Zhao B. En,

1

1

Simulation of Boiler Drum Process Dynamics and Control

Jian Zhao

B. En,.

Department of Mechanical Engineering

McGill University

Montréal, Canada

A thesis submitted to the Faculty of Graduate Studies and Research

in partial fulfillment of the requirements f >r the aegree of

Master of Engineering

January 1992

@ Jian Zhao

1

1

Abstract

This thesis presents a mathematical process model for the dynamic analysis

of a vertical reheat boiler and the application of this model to the optimal design of a

drum water level controller. A numerical finite difference technique is used to formulate

this model.

The control system contains two loops, a feedforward loop using the steam

flow and drum pressure signais as the input and a feedback loop using the deviation of

the measured drum water level from its set point as an input. The feedback loop is an

incremental PlO controller with an adjustable proportion a 1 gain. The feedforward loop is

designed to directly actuolte the control devices before the "swell" and "shrinkage" in the

boiler water level occur. The feedforward controller output signal is summed along with

the output of the PlO controller to establish the set point for the c.ontrol actuator ThiS

scheme is effective because steam flow changes are immediately fed forward to change

the final feedwater set point for the control actuator. In this way, feedwater flow tracks

steam flow and any disturbances in the feedwater system will be arrested quickly

It is shawn that an incremental PlO controller plus adapt feedforward com

pensator can be successfully employed for the control of water level in such a plant.

Il

1 1

1

Résumeé

La thè~e présente un modèle mathématique de processus qUi peut servir dans

l'analyse dynamique d'une chaudière verticale à postcombustioh, et dans la conception

optimale d'un contrôleur de niveau d'eau du tambour. Pour l'élaboration de ce modèle,

on a utilisé UfI" tc-rttnique numérique différentielle.

le système de commande comporte deux boucles' une à commande directe

utilisant l'échappement de la vapeur et les indicateurs de pression du tambour, comme

donnée d'entrée, et l'autre, rétroactive, utilisant la déviation dans la mesure du niveau

d'eau du tambour, à partir de son ~oint de réglage. la boucle de commande rétroactive est

un régulateur proportionnel, intégral et différelltiel (PID) avec gam proportionnel ajustable

la boucle de commande directe tst conçue afin que l'organe de commande réagisse directe-

ment avant que ne surviennent le "gonflement" et la "diminution" du niveau d'eau dans la

chaudière. Les indications données par le contrôleur du niveau d'eau ajoutées aux résultats

obtenus par le régulateur PlO permettent d'établir le point de réglage du mécanisme de

commande. Ce procédé est efficace parce que les variations dans l'échappement de la

vapeur sont immédiatement et directement transmises et modifient le point de réglage

final du mécanisme d'alimentation d'eau. De cette façon le mécanisme d'alimentation

d'eau s'active dès qu'il y a échappement de vapeur le tambour se trouvant au niveau

du mécanisme d'alimentation d'eau arrêtera immédiatement toute pE'fturbatlon dans le

système d'alimentation d'eau.

On démontre ainsi qu'un régulateur PlO, utilisé avec un compensateur à cam-

J mande directe adaptable, peut-être employé avec succès comme contrôleur de niveau

d'eau dans les usines visées.

III

1 Acknowledgements

The author wishes to express his deep gratitude to Prof. louis J. Vroomen

and Dr. Paul J. Zsombor-Murray for their supervision of the research project and their

guidance, encouragement and patience during the course of this study.

Special acknowledgements are due to fellow members of the simulation and

modeling group: David Vaitekunas. Chen Huan-Wei and Eric VanWalsum.

A note of thanks is also extended to ail McRClM technicians and system

management persons who helped in the study of this project.

IV

1

J

Contents

List of Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. '"

List of Tables . ........................................ .

Nomenclature . .................................. .

Chapter 1 Introduction ..................... .

1.1 Description of the Boiler .................. .

1.2 The Control of Modeled Boiler System by Simulation

1 2.1 Model Development Strategy ......... .

1 2.2 Control Simulator Development Strategy

Chapter 2 Process Model of the Drum Water level

System ............................ .

2.1 The Structure of the Drum Water level System ...

2.2 The Method to Develop the Model .. .... . ..

2.3 Process Model of the Feedwater Valve ....... .

2.4 Process Model of Recirculation loop

24.1 Downcomer Model ...

2.4.2 Riser Model . .

2.5 Process Model of the Feedwater line .. . .....

2.6 Process Model of the Drum ............... .

2.7 Steam Flow line Model . . . . . . . . . .. ..... . ....

VIII

XII

XIII

1

2

5

5

9

12

12

15

18

19

19

20

21

2?

25

v

1 Chapter 3 Oynamic Analysis of the Process Model . . . . . .. . 30

3.1 Solution of the Process Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 30

J.l.1 Runge-Kutta method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 31

3 1.2 The Application of Runge-K\Jtta Methods on the Model . . . . . . . . 33

3.2 Simulation Methods ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. 35

3.2.1 Variable Step-Size Multistep Aigorithm .. . . . . . . . . . . . . . . . . .. .. 35

3.2.2 Simulation Program Structurf' ... . . . . . . . . . . . . . . . . . . . . . . . . . .. 44

3.3 Oynamic Behavior of the Process Model .. . . . . . . . . . . . . . . . . . . . . . . . .. 46

3.3.1 Time-Domain Dynamics of the Process Model . . . . . . . . . . . . . . . .. 47

3 32 Time-to-Frequency-Oomain Transformation Method . . . . . . . . . . 52

3.3.3 Frequency-Domain Oynamics tIf thp. Process Model. . . . . 55

Chapter 4 Control System Structure ............. . 65

4.1 The Outline of the Controlled Plant. . . . . . . . . .. ...... ............ 65

4 2 Drum W~ter Levet Control System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

Chapter 5 <Control Strategy . . . . . . . . . . . . . . . . . . . . .. ......... .... 71

5.1 Control Aigorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ..... 71

5.1.1 Digital PlO Control Technique. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 71

5.1 2 Feedforward Control Aigorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 74

5.1.3 Combined PID-feed1orward Control Algorithm ................. 77

5.2 Refinements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. 78

5.2.1 Data Sampling and Filtering . . . . . . . . . . . . . . . . . .. ............ 79

5 22 Improving the Differentiai Character of Output Response . . .. . . 80

~I

r 5.2.3 Antireset Windup ........................... .

5.3 The Control Program Structure. . . . . . . . . . . . .. . .. .

Chapter 6 Selection of Design Param<C!ters .

6.1 Ziegler-Nichols Method. . . . . . . . . . . . . . . .. . ...... .

6.2 The Feedback Controller Parameters Sett,"g ..... .

6.3 Influence of the Sampling Time At . ................ .

Chapter 7 Presentation of the Results ..

7.1 Closed-Ioop Behavior of the Process . . .. ..

7.1.1 Specification of Closed·loop Response ... .

7.1.2 Closed-Ioop 8ehavior Us,"g Feedback Control ..

7.1.3 Feedback-Feedforward Control 8ehavior ..

7.2 The Simulation Results ....

Chapter 8 Conclusions ......... .

8 1 Drum Water level System Model .. ..

8 2 Simulation Methods ............... .

8.3 Control Aigorithm .............. .

8.4 Future Work

References. . . .. ............. .. ....... . .. .

Appendix A. Sample Values of Frequency w ....

81

82

85

85

86

89

98

98

", 99

100

102

103

113

113

114

115

117

120

123

VII

1

List of Figures

1.1 Typical industrial boiler unit. . . . . . . . . . . . . . . . . . . . . . . . .. ........ .. 3

1.2 Boiler plant component models . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . .. 6

2.1 Schematic diagram of boiler drum system . . . . . . . . . . . . . . . . . . . . . . . . .. 13

2.2 The drum model - block diagram ................................. 15

2.3

2.4

31

3.2

Simplified recirculation loop diagram

Srmplified drum diagram.. ................... .

Flow chart of the programming procedure ....... .

The structure of the simulation program ., ............. .

19

23

36

45

3.3 Change in drum water level for 10 percent step increase ..... . . . . . . . .. 48

in feedwater flow n.' !

3.4 Change in steam discharge for 10 percent step increase .. . 48

in feedwater flC'w rate

3.5 Change in drum water level for 10 percent step increase ..... . . .. .... 49

in fuel flow rate

3.6 Change in stearn discharge for 10 percent step increase . . . . . . .. . .... 49

in fuel flow rate

3.7 Change in drum water level for a 50-psi step decrease ....... .... ... 50

in system pressure

3.8 Chang~ in steam discharge for a 50-psi step decrease . . . . . . . . . . . . . 50

in system pressure

3.9 Change in drum water level for 10 percent increase . . . . . . . . . . . . . . .. . 51

in steam flow rate

\/111

1 3.10 Frequency response of drum water level for 10 percent 59

step increase in feedwaler flow rate

3.11 Frequency response of steam discharge for 10 percent 60

step increase in feedwater flow rate

3.12 Frequency response of drum water level for 10 percent 61

step increase in fuel flow rate

3.13 Frequency response of steam dischetrge for 10 percent 62

step increase in fuel flow rate

3.14 Frequency response of drum water level for a 50-psI ..... 63

~tep decrease in system pressure

3.15 Frequency response of steam discharge for a 50-psI 64

step decrease in system pressure

4.1 Feedback control loop for drum water level system 67

42 General drum water level control system .. 69

5.1 PlO control with derivative on Pl :cess measurement 72

5.2 The feedforward control alg0f1thm 75

5.3 The adjustment of the gain Kc ........ . 82

5.4 The control program structure .......... . 83

6.1 The closed-Ioop responses from the initi'il and final controller

parameters .... .................. . ... . 90

6.2 Trall~ient response of the process for 10% increase ln steam flow

wlth sample interval ~t=l second ..... . 94

6.3 Transient response of the process for 10% increase ln steam flow

with sample interval ~t=2 second 95

J 6.4 Transient response of the process for 10% increase ln steam flow

wlth sample interval ~t=4 second. '" ... .. 96

1,1(

1 6.5 Transient response ct the process for 10% increase in steam flow

with sam pie interval At==8 second. . . . . . . . . . . . . . . . . .. .. ..

7.1 Step response of water level change for a 10 percent step in<.rease

97

in turbine governor valve area for difTerent values of Kc .. . . . . . . . . . . .. 105

7.2 Step response of water level change for a 10 percent step i nCiease

in turbine governor valve area for difTerent values of J(c

(Cont'd) ....................................... .

7.3 Step response of water level change for a 10 percent step i ncrease

in turbine governor valve area for difTerent values of TI

7.4 Step response of water level change for a 10 percent step Increase

in turbine governor valve Jrea for difTerent values of Tl

!Cont'd) ....................... " ............. .


106

.. 106

107

in turbine govt:rnor valve area for difTerent values of TD 108


in turbine governor valve area for dlfTerellt values of TD

(Cont'd) 109

7.7 Response of water lev el for a step change of 5 inches in set

point.. .. ............. " .......... .. . . ......... .. .. 109

7.8 Closed·loop response of drum water level change to a 10 per cent

step increase in governor valve area (feedback control) 110

7.9 Closed-Ioop response of drum water level change to a 10 per cent

step increase in governor valve area (feedforward-feedback

control) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. ........ . ... 110

7.10 Step response of boiler's four most important variables for a 10

percent step increase in turbine governor valve area for optimum

controller settings ........................ . 111

x

1 7.11 Step response of boiler's four most important variables for a 10

percent step increase in turbine governor valve area for o~timum

controller settings (Cont'd) . . . . . . . . . . .. ....... .... .... 112

XI

..

1 List of Tables

2.1 Feedwater valve positioner characteristics ........................... 18

2.2 Values of constants Cl to C7 ...................................... 29

3.1 Sorne physical dimensions of the sample boiler. and the values

of its variables at steady-state 44 per cent full load .................. 34

:1

XII

Nomenclature

Symboll

A : flow cross-sectional area [ft2]

a: reset windup boundary

Cl to C7: tonstants

D : hydraulic diameter (ft)

e: error

f: friction factor

G: transfer function

g: acceleration of gravit y (ftjsec2]

Hl : pump head-flow characteristic

H2 : feedwater valve loss-coefficient lift characteristic

H3: specifie-volume-pressure relationship for saturdted vapor

H4: specifie-volume-pressure relationship for critical flow

T i

h: fluid enthalpy [Btu/lb]

)'111

1 i : number of simulat:on steps

./: 778 (ft-Ib/Btu)

/(: feedwater valve positioner gain

/(c : feedback controller gain

/(,: feedforward controller gain

L: feedwater valve lift (ft)

1 : pipe equivalent length [ft)

P: Controller output

PB: proportional band

p: steam generator pressure [psi]

Pl : feedwater pump discharge pressure (psi]

Q: heat transfer rate (Btu/ft3 - sec]

s : Laplace transform variable

T: steam temperature[ OF)

'l'OL: simulation tolerance

t : time (sec]

l v: steam drum volume [ft3]

XIV

~----------- ~-

1 v: specifie volume [ft3/lb)

W: fluid mass flow rate [lb/sec)

>[ . .J • quality of steam-water mixture leaving riser

Y: sampling value

y: water level [ft]

.,. . .. . z transform variable

f3: filtering coefficient

p: fluid density [lb/ft3)

(: feedwater valve positioner damping factor

f : coefficient of simulation algorithm

TD: differential period [sec]

TI : integral period [sec)

w: feedwater valve positioner natural frequency [sec- 1)

h.t : time increment [sec)

Subscripts

o : initial condition

cr : critical flow

xv

1 d: steam flow li ne

D: circulatin, flow li ne

dw: steam-water drum

e: feedwater line

f: saturated liquid

9: saturated vapor

m,: governor valve openin,

n' governor valve inlet

0: steady-state value

v: feedwater valve

w: steam-water mixture leaving the riser

Superscript

average

XVI

1

Chapter 1 Introduction

Although boiler controls have progressed to a certain extent, the role of the

boiler room operator has essentially remained the same durtng the last twenty years Even

today, boiler operators still physically check water levels at gauge glasses and vlsually

verify the pressure and temperature controls [6].

Thus safe and efficient operation of an industrial process depends on the

human operator as weil as the real-time process control system 80th elements must

perform weil together. The operator, in order to make decisions, depends upon the

availabillty, the timeliness, and the quality of the information presented to hlm by the

process control system. If the control system does not perfoim weil, the operator, no

matter how capable, will experience great difficulty ln ma king the nght decision On

the other hand, even if the control system does perform weil, the operator may not be

psychologically or technically prepared to make the nght deCISlon

Due to the infrequent occurrence of upset conditions ln the process, the abliity

of the operator and the control system to cope with these situations rernains untested

It is therefore quite clear that in order to efficiently train the operator and program the

control system, it is necessary to use simulation of both normal and abnorrnal operatlng

conditions, in real-time situations.

1 Introduction

Early studies of boiler process and control simulation tended towards the de~

velopment of complete transfer functions for the process and the controller. Then the

parameters of the controller were determined with convention al control techniques Even

when the process models are quite simple, this approach leads to controller transfer func-

tions which are either physically unfeasible or, at best, extremely complicated [2] With

the availability of modern high speed computers, it is now feasible to use direct digital

control (DOC) simulation of an entire plant.

This thesis discusses a method of using direct digital control and modern

computer techniques to combine the conventional PlO and feedforward control algorithms

Into a control simulator for a boiler drum system. In this project, a dynamic model of

a boiles drum syst~m will be presented first. Then the application of this model to

the optimal des;gn of a water level digital control simulator will be demonstrated The

performance of this control slmulator applied to this model will also be discussed It is part

of ongoing research at the McGill Research Centre for Intelligent Machines (McRClM) to

develop a boiler plant control simulator.

1.1 Description of the Boiler

The purpose of a boiler is to generate process steam, whether it be part of

a pulp and paper mill, a power station or on a marine vesse!. The system under study

is limited to a particular class of boilers: large-scale natural circulation fossil-fuel boilers

which opera te on any combination of oil, coal, natural gas, or wood. A dlagram of the

bOlier unit considered in this project is shown in Figure 1.1.

Fuel and air are delivered into the mill at a controlled rate. The mil! exhaust

fan blows the fuel-air mixture to burners in the combustion chamber or furnace. At the

2

t .~.

L

1

J

1 Introduction

Figure 1.1 Typical industrial builer unit

burners, the iir required for efficient combustion is supplied as secondary air, and the

fuel-air mixture is burned in suspension in the furnace. The combustion gases are wlth-

drawn from the furnace zone and pass, in succession, through the furnace eXit tubes, the

secondary-superheater tube bank, the pflmary-superheater tube bank and the economlzer

The flue gases finally pass through a heat exchanger, before belng reJected to the stack

at a temperature just in excess of the dew point of the sulphurous gas present

3

1 1 Introduction

Air is drawn from the top of the boilerhouse, where it is warm. It is then

passed through the heat exchanger, where it absorbs heat from the flue gas. By means

of ducts and dampers, a proportion of this air is used as primary air, the remainder is

distributed to the burner as secondary air.

Feedwater from the br;:er feedpump enters the boiler via the economizer,

where it absorbs sufficient heat to raise it to almost the saturation temperature corre

sponding to the boiler pressure. From the economizer, the feedwater flows through the

downcomers to horizontal headers at the bottom of the furnclce waterwalls. Water from

these headers is discharged into the waterwall tubes lining the furnace; heat is absorbed,

and partial evaporation takes place. The mixture of steam and water from the waterwalls

enter into the steam drum. In the drum, the saturated steam is separated from the water,

whlCh is recirculated via the downcomer-waterwall loop either by the difTerence between

flUld density, and/or a pump. The steam passes, in sequence, through the prlmary and

secondary superheater-tube banks and then to the plant, e.g., a turbine

From the control point of view, a boiler can be functionally dlvided into three

main loops comprising:

(a) the combustion loop

(b) the drum-feedwater loop

(c) the steam-temperature loop.

This thesis is limited to a study of the drum-feedwater loop.

To better understand the role of the individual elements of a boiler, consider

the component model diagram, Figure l.2. The inputs to the plant are air, fuel and

4

1

J

Introduction

water which ire converted using various energy processes to generate steam, the pJlnClpal

output, and combustion giS, ~ waste by-product. The diagram only illustrates the physlCal

processes which must be interfaced with the plant control system via control signal Inputs

Four elements of the boiler system are involved with the control of the drum water level

ln this project, the dynamic mathematical model of these elements was establsshed flrst,

then the direct digital control schemes were applled to these models

1.2 The Control of Modeled Boiler System by Sinll.lation

1.2.1 Model Development StratelY

Earlier water-Ievel control studies used "Iumped- parameter" 'frlresentation of

flow behavior in various system flow segments. The mathematical model was then slmu

lated on a real-time computer for the optlmization of the water-Ievel controller parameters

[1). In a lumped·parameter model, restrictive assumptlons pertalning to the spatial dlstJl

bution of the dependent variables within each segment must be made, thereby reduclng

the accuracy of the solution. Rigorous water-Ievel control studies must Include the slmul

taneous solution of the space-dependent and time-dependent conservation equatlons of

mass, momentum, and energy for the coolant flow through the steam plant. Dynamlc

models of this type will be discussed in this thesis.

For the purpose of digital-computer simulation, the boiler was subdlvided into

a number of sections, comprising:

1) feedwater valve/boiler t'eed pumps

2) recirculation loop

•

! • LI ..

1

1"" " "------..1; :i i e :. III • ....... Q

!~---~ i

DOWJiICOM8 MODIL

Figure 1.2 Boiler plant component models

1. Introduction

PUlLHIA'I'D MODIL

6

Introduction

1 3) drum

4) primary superheater

5) superheater spray

6) second.uy superheater

7) turbine governing stage

8) turbine

9) reheater spray

10) reheater

11) mills

12) combustion

13) superheater furnace

14) reheater furnace

Only those processes involved in item 1), 2), 3) and 7) will be dlscussed ln

this thesis.

By use of appropria te laws governing fluid dynamlcs, the empmcal. steady-

state heat-transfer relationships and the equations of state (nonllnear dlfferentlal and

algebraic) were written to describe the dynamic behavior of the above-listed four sections

of the boiler. These equations were then Ilnearized by consldenng only srnall variations

1 Introduction

• about a steady-state operating level. The resulting equations were used as the process

",odel by the simulated controller on the computer.

The major difficulty in the boiler's dynamic behavior analysis is the fact that

the whole system is very complex and contains n!Jmerous variables which are extremely

unwieldy to manipulate. The solution of the set of equations is as difticult to obtaln as the

synthesis of the actual mathematical description. large number of variables, nonlinearities,

and uncertainties in many phenomena ail contribute to the complexity of the problem.

One is then faced with the necessity of ma king some simpllfying assumptions ln order

to facilitate a solution. Oversimplification results in solutions which do not deswbe the

character of dynamic behavior properly, but too little or no simplification might Involve

unreasonable time and expense in obtaining a solution. Necessar, slmphfying assumptlons

may be classified under two types depending on the nature of simplification'

(a) certain physical phenomena are too complex to admit an exact mathematical

description, and some empirlcal or approximate formulation is required.

(h) the need to obtain a solution within a reasonable time for the set of equations

derived from analysis.

The simplifications may be made in the nature of flow or in the equations

themselves by eliminating nonlinearities, partial differentiation through appropriate tech-

niques (numerical analysis methods were used in this thesis). In the present study these

simplificatIons are combined in such a way that a set of linear ordinary differential equa-

tlons describes the dynamic behavior of the boiler drum system. Even after simplIficatIon,

the set of equations obtained in the following chapter is not tractable for hand so!ntion

and It is necessary to use machine computation.

8

1

. ...,

1 Introduction

Both the process model and the control simulatcr were written in the C

language on a SUN SPARCTM work station.

1.2.2 Control Simulator Development Strate~y

The control of the water level in the boiler drum and the feedwater flow is

extremely important to the operation of conventional steam generatll1g plants large

level variations can affert system power and hydrodynamic stabi!ity. Translent changes

in feedwater flow can also affect the plant power output and even create thermal shock

problems. In order to minimize these adverse efTects, it is deSifable even dunng large

fluctuations in steam demand to maintarn the water level close to a predetermmed set

point. The feedwater flow rate, should be adjusted in re~l-tlme to compensa te for the

level changes [21].

Boiler controls were essentially designed to control actlvity w,th,n a boder and

ensure its safe operation. Each boiler cons:sts of a pressure vessel, furnace a'ld burner,

working a~ an integral unit within a specific capacity If operated improperly. the bolier

experiences serious problems. Controls were developed to minlmlze these nsks

Separated by function, these devices fall into two areas of control, tlreslde

and waterside. Fireside devices monitor the burner and its operation They sense the

existence and strength of the f1ame using, in most cases, electronic, ultraviolet or mfrared

sensors. Fireside controls also check fuel pressure and temperature Waterside devices

control the water temperature, pressure and level in order to ersure safe operation The

control simulator developed in this thesis is only used to manlpulate the waterslde devlces

Pneumatic, analog, PlO control developed in the 1930'5 15 consldered to be

the first gener.:-tion of process control. Electronic, analog, PlO controllers, wh,ch appeared

9

-

1 1 Introduction

in the 1950'5, may be regarded u the second generation. In the 1970'5, direct digital

control (DOC) wu developed. But single loop PlO controllers are still in use where DOC

cannot be justified because of insufficient computing needs [20]. With the rapid growth in

high speed computers, particularly microcomputers, it has now become feasible to develop

a digital control simulator for an entire plant.

This project discusses a digital PlO combined with a feedforward scheme as

a control algorithm for a single loop digital control simulator. This digital control sim

ulator will be applied to a boiler drum. An attractive aspect of digital control is its

flexibility in implementing various algorithms. This has be reenforced by rapid growth

in software technology. Theoretically, because of time sampling and signal quantization,

digital PlO control cannot attain the same quatity as analog PlO control. But practically,

with powerful computers and modern software tools, it is possible to ma~e digital PlO

control perform as weil as or even better than its analog counterpart. The digital control

simulator includes five distinct blocks:

(a) feedwater valve

(b) recirculation loop

(c) feedwater line

(d) steam drum

(e) steam flow line

The first step to be taken in the control-system analysis is obvious from these

considerations. It consists of acquiring a complete understanding of the process to be con

trolled. The understanding begins with the formulation of a phenomenological description

10

IntroductIon

of the process. i.e., by following the physical ind chemical changes that occur along the

process path, and t:nds when transfer functions, that is, time-dependent functional re

lations between input (controlling) and output (controlled) variables of the process, are

obtained. This first step, which may be ca"ed "dynamic analysis", leads to the mathemati

cal description of the system so that an intelligent choice of the basic design configurations

for the cOlltroller becomes possible. The second step is to develop a real-time controller

based upon the results of the mathematical description of the boiler's dynam;c response

to various disturbances.

From this point of view, ,his digital water-Ievel controller study consists of

two parts. The first is a digital computer program simulating the dynamlC behavior of

the steam drum plant with length along the flow path and time as system independent

variables. This dynamic boiler drum plant model will be established in Chapter 2 Chapter

3 will present the dynamic behavior of this model both in the time-domain and frequency

domain. The time-to-freqllency domain transformation technique will also be shown

Then the drum model will be simulated using this technique. The second part 15 a digital

simulator for controller parameter optimization studies. The structure of the control

system will be described in detail in Chapter 4. In Chapter 5, the digital PID combined

with ;a feedforward control algorithm will be presented A filter which is used to Irnprove

the sampling quality will also be discussed. Chapter 6 will analyze the stabillty of the

control system. The controller parameter tuning technique will also be dlscu5sed The

performance of the model and the control algorithm used to simulate It Will be analyzed

in Chapter 7. Finally in Chapter 8. a summary of the flOdlOgs will provlde a baSIS for

further research into other aspects of process control.

11

1

Chapter 2 Process Model of the Drum Water Level System

The primary objective of this ch~pter is ta generate a drum water level system

model th~t beh~ves with reasonable accur~cy in representing the dynamic relationships

which exist between the gtnerated outputs, including: steam flow and water level, and

the manipulated input variable: feedwater v~lve position.

To be useful for analysis, the model is kept simple, but is still consistent with

the above requirements. Furthermore, the model must reflect the specifie values of ail

plant parameters ~t any ,iven operating level. This model can then be used to subject any

proposed control scheme ta a sensitivity an~lysis with respect ta certain variable boiler

pilrameters.

2.1 The Structure of the Drum Water Level System

The system under study is a typical industrial steam generator, and its drum

subsystem was modeled as the five sections shown in Figure 2.1.

1) Feedwater Valve - The feedwater valve regulates the feedwater flow from the

pumps. It consists of the feedwater valve itself and an electric-to-pneumatic

converter.

2. Protess Model of the Drum Waler level System

1

Figure 2.1 Schematic dialram of boiler drum system

13

1

1

2. Process Model of the Drum Water level System

2) Recirculation loop - The recirculation lûop includes a heating zone, riser, steam

separator and downcomer.

3) Feedwater Line - The cold water from the feed pumps go through the feedwater

line into the downcomer of the recirculation loop.

4) The Drum - The steam drum coUects the steam when it leaves the recirculation

loop.

5) Steam Flow Line - This is the steam outlet line from the drum. A governor

valve controls the mass f1ow.

Boilers operating below the critical point, except for once-through types, are

customarily provided with a steam drum in which saturated steam is separated from the

steam-water mixture discharged by the boiler tubes. Saturated liquid leaves the drum and

enters the downcomer while a saturated liquid vapor mixture enters the drum from the

risers. Saturated steam leaves the drum and enters the primary superheater. The drum

may also serve as a vessel for chemical boiler water treatment. However, the primary

functions of this drum are to provide a free, controllable, surface for the separation of

saturated steam from water and a housing for any mechanical separating devices.

Mass balance equations for water, steam and a liquid/vapor mixture have been

established for the drum water level system, from feedwater valve to primary superheater.

The controlled plant is shown in Figure 2.2.

The following basic assumptions have been adopted:

• 80th steam and liquid in the drum are at saturation temperature.

14

2. Proeess Model of the Drum Waler level System

1

Plll!DWA1D DaUM DOWNCOMEl IUSlll

VALVII

Filure 2.2 The drum model - block diagram

• This temperature is a function of drum pressure.

• There is negligible heat transfer along the length of the downcomer.

• There is no mass or energy storage in the downcomer and rlSer.

• The total circulating flow rate is constant.

2.2 The Method to Develop the Model

The model of the drum water level system was developed based upon the

mass, energy balance and the state equation of the system:

(a) Mass Balance: These are the well-known Navier-Strokes-type equations for

one-dimensional nonturbulent flow. Viscous friction is neglected 50 that the

15

1 2. Process Model of the Drum Water level System

velocity profile icross the flow is constant. However, a frictional-Ioss propor

tion~1 to the square of the lelocity is included in the momentum equation.

Continuity. momentum, and energy equations are applied with certain sim pli-

fyin, assumptions, mentioned later.

(h) Energy Balance: Empirical equations are used to determine the rate of heat

trinsfer from hot gas to superheated steam and to boiling liquid.

(c) State Equations: These are approximated from steam tables for saturated and

superheated steam about the steady-state operating conditions. The relations

are iSsumed to be linear for a given range of values of the variables.

It was mentioned in Chapter 1 that the first two types of equations involve

partial diff'erentiition as weil as nonlinearities. In order to facilitate a solution of these

complicated equations, it is necessary to reduce these equations to an ordinary linear-

equation form by applying small perturbations and diff'erence equation techniques.

Suppose an equation of the form:

(2 -1)

is to be reduced to linear ordinary differential equation form. In Equation (2 - 1) ft indicates time derivative and lm is the derivative with respect to the spa ce variable m.

ft is assumed that for small space intervals AI. the variables x, y, z, ... may be written as

linear functions of the variable m such that:

X2 - Xl ay Y2 - YI az z2 - z1 -ôm-= M 'am= M 'am= M ôx , ...

16

1 2. Process Model of the Drum Water Level System

where X2. !l2. '2 •... and Zl. YI. Zl. '" denote the value of the variables x. y. z . ...

Olt the end and at the beginning. respectively. of the space interval AI. Even though Tt,

YI. zb ... and X2. Y2, Z2 • ... are no longer functions of m, they are still functions of

time. x. y. z, ... ~. ~. ~ •... are now assumed to be thfl value of the variables at

the beginning of the space interval }.·f; hence Equation (2 - 1) can be written as

(2 - 2)

The Equation (2 - 2) is then perturbed about its steady-state operating con-

dition in order to eliminate the nonlinearities.

Hence it cOIn be written as:

(2 - 3)

where il dâ,t, ... cOIn be replaced by 1,(ll.xll . ... for sma" perturbations.

It is seen from Equation (2 - 3) that time derivative terms d;i, c!p" (~l, .. are treated as independent variables. and second or higher-order terms in perturbed vari

ables are neglected. The partial difTerentials i~ ./k. 3ft .... that form the coefficients

of the perturbed variables are evaluated at the initial steady-state operating condition

about which the dynamic behavior of the drum water level system is to be analyzed. As

a result of these simplifications, Equation (2 - 3) becomes a linear, first-order, ordinary

difTerential equation with constant coefficients in perturbed variables llXt, ll.T2. llYl.

17

1 2. Process Mode! of the Orum Water level System

2.3 Process Model of the Feedwater Valve

Condens~te is delivered to the inlet of the boiler feed pumps from the feedwater

heater. The feedwater flow from the pumps is regulated by the feedwater valve. The valve

positioner has built-in position feedb"k to eliminate drift in valve position. After analysis

and consultation with control equipment manufacturers, il simple second-order transfer

function was selected to ~pproximate the positioner's behavior [8).

L K

P = (w'n)2 + 2({w'n) + 1 (2 - 4)

The characteristics of the selected feedwater valve positioner are shown ln

Table 2.2.

Time for Full Valve Stroke Natural Frequency ColIn Dampins Coefficient' Seconds Radians/seconds

2 2.0 10 10 0.9 224 20 0.63 3.18 40 0.45 446

Table 2.1 Feedwater valve positioner characteristics

The electric-to-pneumatic converter can also be represented by a second-order

system having a natural frequency of 20 radians/second and an approximate damping

coefficient of 1.0. Consequently, the dyna mic characteristics of the converter are neglected

and the gain factor is incorporated in that of the valve positioner. A nominal valve speed

of 10% of full range per second was assumed.

18

2. Pro cess Model of the Drum Water Level System

2.4 Process Model of Recirculation Loop

A mathematical model of the recirculation loop was developed based upon tha t

of MacDonald (19). using several of his assumptions. For example. the system pressure,

feedwater f10w rate and the heat transfer from the combustion system are assumed con

stant during one control step. Figure 2.3 shows the simplified diagram of the recirculation

loop with the variables indicated along the path.

RIS ER DOWNCOMER.

Figure 2.3 Simplified recirculation loop diagram

2.4.1 Downcomer Model

As mentioned before. the downcamer is assumed ta have simple fluid-flow

19

1

(

2. Process Model of the Drum Waler level System

characteristics with no heat input or temperature difference between the top and the

bottom.

Usina acceptance test data (19) variations of downcomer out/et enthalpy he

with changes in feedwater flow, are approximated by the following quadratic:

he = -499.7251 We 2 + 655.7251 We + 365.0398

(-1162.3606We2 + 1525.2166We + 849.0826)

Btu/lb

kJ/kg (2 - 5)

An energy relationship between feedwater flow and circulating flow based on

adiabatic mixin, of two streams, is given by:

(2 - 6)

2 ••• 2 Riser Model

Feedwater discharging from the circulating pumps enters distribution headers

beneath the furnace sections. The water rises in the furnace riser tubes where boiling

takes place and the water-steam mixture enters the drum from the riser.

The enthalpy of the steam-water mixture leaving the risers is:

(2 -7)

The energy balance equation is given as:

Qw = Qws + Qwr = WD(h w - hD) (2 - 8)

20

1

J 2 Process Model of the Drum Ww~tr level System

2.5 Process Model of the Feedwater li ne

The feedwater line model is derived by application of the momentum equation

to the feedwater flow throulh the feedpump, feedwater valve and interconnectlng pIpes

The momentum equation for the feedwater flow is liven by,

(2 - 9)

ln the above equation. the contribution of momentum change, wh,ch 15 smalt,

i5 neglected. The pump di5charge pressure Pl is a glven function of mass flow rate and IS

obtained from the pump head-f1ow characteristic:

(2 - 10)

The feedwater valve 1055 coefficient Iv is a function of feedwater valve lift and

i5 obtained from the valve spec.:ification:

(2 - 11)

Introducing small perturbations around steady state for We. 1), ]JI. Iv and l"

expanding Equations (2 - 10) and (2 - 11) usÎng Taylor-Series about the steady state

point and neglectinl second and higher order terms, Equation (2 - 9) can be linearized.

It can be easily shown that this linearization pro cess gives:

21

2 Proeess Model of the Orum Water Level System

1 llWe(( dPI) _ 2(PI - plo) ~ IIp + AL (df tJ ) (6p)tJo

dWe 0 Weo dL 0 fvo (2 - 12)

Reuranging Equation (2 - 12) and deflning constants Cl and C2 as:

results in:

(2 - 13)

2.6 Process Model of the Drum

Figure 2.4 is the diagram of the drum showing various input and output vari-

ables. Two types of equations, mass-balance and energy-balance determine the behavior

of the drum sinee it is basically a eapacitance. In this study the efTect of the mass-transport

phenomena between the two phases is taken into consideration, but the water-Ievel varia-

tion due to bubble formation is neglected. In other words, it is assumed that evaporation

and condensation take place at the surface of the liquid phase. Henee the mathematieal

model of the drum dynamics takes the form of:

Mass balance:

22

1

f

2 Process Model of the Drum Water level System

RISBR:

Energy balance:

WDh w - (WD - We)hdw - Wdhd =

d dt«Vd - Vdw)Pdhd + VdwPdwhdw)

V APOR PHASE:

TO SUPERHEATERS:

ST'EAM FLOW RA'm TEMPERATURE DENSITY

MASS FLOW RATE _-..,.

PRESSURE TEMPERA1UIlE

DENSrrY VOLUME

(2 - 14)

(2 - 15)

QUALn'Y TEMPERATURE DENSrrY / ---. UQUlDPHASE: ~

,------ MASS fVV'v

-------r UQlllDLEVEL

DOWNCOMER: MASS PLOW RATE TEMPERATUR.E DENSITY

~ VOLUME 1'\.1'\./". FEEDWATER' DENSrrY --+--

TEMPERAruRE MASS FLOW RATE ~ TEMPERATURE

Figure 2.4 Simplified drum diagram

1

1

'l'·

2. Process Model of the Drum Water Level System

The following linear approximation of thermodynamic state relations are sat-

isfactory for conditions in the drum:

Pdw = -2.0132Pd + 49.7224 Ib/ Jt'; (-32.2483Pd + 796.4759 kg/m3)

Td = 20.5097Pd + 525.9288 oF (-6.3835Pd + 214.4049 OC)

Pd = 273.5046Pd + 539.5794 psi (1885.8142Pd + 3720.4000 kPa)

hdw = 32.5179Pd + 49&.3699 Btu/lb (75.6366pd + 1l59.2084 kJ/kg)

hd = -18.9583Pd + 1238.9003 Btu/lb (-44.0970Pd + 2881.6821 kJ / kg) (2 - 16)

They were calculated for saturated steam temperatures between 600 and

6500 F using data from Keenan and Keyes steam tables[5J.

It is convenient to define the funetion:

(2 -17)

where:

o.hd = (~hd) = _18.9583Btu I..!!!-. (_2.7530

kJ / kg)

8Pd sat lb ft 3 kg m3 (2 - 18)

o.hdw:= (8hdw ) = 32.5179Btu /~ (4.7220

kJ / kg)

8Pd sat lb Jt 3 kg ml (2 - 19)

24

1 2. Process Model of the Drum Water Level System

(ÔPdW) apdw = -ô = -2.0132

Pd .at (2 - 20)

The mass and energy balance equations (2 - 14) and (2 - 15) can now be

transformed to obtain:

(2 - 21)

1+ X d .!.tlU'e - -LWd - -WD Il' Pdw Pdw Pdw

-"dw = dt 1 + g(l-..eL)

Pdw

(2 - 22)

2.7 Steam Flow Line Model

The steam-f1ow li ne model consists of a steam f1o~,1 model and a governor

valve model. In the development of the steam f10w model, the steam flow rate IS lumped

with the steam generator drum volume. The steam f10w model is derived by application

of the momentum equation to the steam f10w from steam generator discharge nozzle to

governor valve.

(2 - 23)

ln the development of the above equations, the steam discharge through the

steam flow line is assumed to be 100% dry, therefore the contribution of momentum

change may be neglected. Moreover, the steam f10w volume is lumped with the steam

25

1 2 Process Model of the Drum Water level System

generator drum volume. Consequently, the time-dependent term in the momentum equa

tion can be ignored. The siturited vapor specifie volume Vg is a function of main pressure.

Since the steim flow pressure is viriable, it is issumed that Vg is calculated from steam

tables on the basis of average main pressure,

where

_ P+Pn P= 2

(2 - 24)

(2 - 26)

8y introducing small perturbations around steady state for p, pn, Vg and

Wd' expanding Equation (2 - 24) using Taylor-Series about the steady state point and

neglecting second and higher order terms, Equation (2 - 23) can be linearized as follows:

~ _ A = f.l.W:o ((dvg) ~- 2vgo At-I' ) P Pn 2 D A2 .r.= p + u! d 9 •• up 0 t'Ji 80

(2 - 26)

Rearringing Equation (2 - 26) and defining constants C3 and 04 as:

results in:

26

r 2. Process Model of the Drum Water Level Sy$tem

1 (2 - 27)

The steam velocity at the valve opening is related to stagnation conditions by

the steady state energy equation:

Uer = J2gJ(hg - hcr } (2 - 28)

The enthalpy hcr is found by maximizing. under isentropic condition. the mass

velocity given by the following equation:

(2 - 29)

Where p and h are function of pressure at the valve opening. The steam flow

rate through the governor valve is then given by:

(2 - 30)

where:

(2 - 31)

l and:

27


Per = CSPn (2 - 32)

Introducin, 5mall perturbition5 iround steady stite for Wd. Am and Per,

expandin, Equation (2 - 31) usin, Tiylor-Series about the steady state and neglecting

second and higher order ter ms. one obtiin:

Definin, constants C6 and C7 u:

results in:

rt _ W,o (dper) '-'6 - - -

Pero dpn 0

(2 - 33)

(2 - 34)

28

1 1


(onstants Values

Cl 4.103 C2 -0.5215 C3 1.038 C4 -0.1109 Cs 0.58 C6 0.11 C1 452.2

Table 2.2 Values of constants Cl to C7

.'.

29

1

1

Chapter 3 Oynamic Analysis of the Process Model

Once i dynamic process model has been developed, methods to solve this

model should be selected ind i dynamic analysis of this model should be done in order

to be able to design the suitable controller for this mode!. By solve, we mean thctt the

transient responses of the dependent variables can be found to sorne degree of accuracy by

numerically integriting the difTerential equations, given that appropriate initial values for

the dependent variables have been specified and that the inputs also have been specified

as functions of time. Oynamic analysis of the model will be based on time ana Irequency

response of the model.

ln this chapter, the method to solve the process model will be discussed first

then the simulation methods and simulating software will be described, finally the dynamic

behavior of the pro cess model will be presented.

3.1 Solution of the Process Model

Over the years applied mathematicians have developed a large number of nu

merical integration techniques from the simple (e.g., the Euler method) to the complicated

(e.g., the Runge-Kutta method) (13). Ali of these techniques represent sorne compromise

1 3. Oynamic Analysis of the Process Model

between computational effort (computing time) and accuracy. While a dynamic model

can always be 5OIved, there may be difficulties in obtaining useful numerical solutions

in some cases. A repertoire of modern computer programs for integrating ordinary dif·

ferential equations is available on most computer systems. Since most programs were

designed for general simulation, obtaining dynamic model solutions to systems composed

of a number of simulation equations may not be simply a straight forward process of using

standard integration routines. There will be a much larger expenditure of computer time

and cost. Secondly the cost of selecting, integrating and perfecting an extensive numerical

procedure is also high.

After a careful comparison and study of the available numencal techniques.

standard simulating programs and the entire process model, the Runge-Kutta method was

selected and it was decided to develop customized simulation software.

3,1.1 Runge-Kutta method

ln analyzing engineering systems, it is frequently necessary to solve sets of

simultaneous first-order differential equations. Such systems of equations are often used

to solve higher order difTerential equations which can be validly transformed into a set

of first-order difTerential equations. The process model in this project can be formulated

as a set of simultaneous first-order differential equations. Runge-Kutta methods are weil

suited to their solution. The application of these methods will be discussed.

Runge-Kutta formulas can be used to solve a pair of simultaneous first·order

differential equations of the form:

31

1 3. Dyn.mic Analysis of the Proeess Model

dy dz = J[z,y(x), u(z»)

du dz = F[z,y(x),u(z»)

(3 - 1)

where the initial values (y = YO, u = uo, when x = Zo) are known. Using the classical

fourth-order method described in (13). the following sets of equations are required:

where

where

kl = h[J(Zi' Yi, uïl)

k2 = h [J ( zi + ~, Yi + ~, ui + Y) ] k3 = h [J( xi + g, Yi +~, ui +~)]

k4 = h[J(Zi + h, Yi + k3, ui + q3»)

ql = h[F(Zi, Yi, Ui»)

q2 = ... [ F (Xi + g, Yi + ~, ui + y) ] q3 = h [F(Xi + g,Ui +~, ui +~)]

q4 = h[F(Xi + h, Yi + k:}, ui + q3»)

(3 - 2)

(3 -3)

(3 -4)

(3 - 5)

32

1 3. Dynamic Analysis of the Process Model

The function I(z, y, u) is used for calculating k values, sinee it is equal to

~,and k's are used in the recurrenceformula for 11. The funetion F(Z,lI,z' is used to

caleulate q values, since it is equal to ~, and q' 8 are used in the reeurrenee formula for

u values.

Runge-Kutta methods could be called single-step methods, sinee they require

only that Yi to be known in order to determine Yi+l' Thus th(~e methods are selfstarting.

Runge-Kutta methods were among the earliest methods employed in the numerical solution

of difTerential equations, and they are still widely used. As with any methods, they

possess certain advantages and disadvantages which must be weighed in considering thelr

suitability for a particular application. The principal advantage of Runge-Kutta methods

is their selfstarting feature and consequent ease of programming. One disadvantage IS the

req uirement that the function I( z, 11) must be evaluated for sever al sllghtly dlfTerent values

of x and 11 in every step of the solution (in every inerement of x by h) This repeated

determination of l(z,lI) may result in a less efficient method with respect to computing

time than other methods. But with today's high speed computers, this problem can be

easily solved and real-time simulation still can be obtained using the approach developed

in this thesis.

3.1.2 The Application of Runae-Kutta Methods on the Model

To be able to simulate the proeess model, sorne physical dimensions and

parameters of the sample boiler were adapted from Chien (4). These values are listed in

Table 3.1.

The solution of Equation (3 - 1) begins by substitut,"g the initial values of y

33

1

3. Oynamic Analysis of the Pro cess Model

Orum pressure Superh.at.r out let pressure Steam fIow rat. Feedwater rat, Quality of mixture leavin, riser Circulation rat,

Orum diameter Orum len,th

Variabl. values

Physical dimensions

1218 psi (8398.11 kPa) 1200 psi (8214 kPa)

32.6 lb/sec (14.1815 ki/sec) 32.6 lb/sec (14.1814 ki/sec)

4.3 per cent dry 990 lb/sec (449.064 ki/sec)

42ft (1 2802 m) 17 ft (5 1816 m)

Table 3.1 Some physical dimensions of the sample boiler, and the values of its variables at steady-state 44 per cent full load

and u, which must be known, into the given difTerential equations to obtain initial values

of the funetions 1 and F. Values of k1 and q1 are next obtained by multiplying the initial

values of 1 and F by h as indicated in Equtltion (3 - 3) and (3 - 5) and where h = tJ.x,

the step increment. When values of k1 and q1 are known, k2 and q2 are evaluated next,

then k3 and q), and finally k4 and q4. Then the recurrence formulas (Equation (3 - 2)

and (3 - 4)) are used to obtain values of y and u at x = Xi + h (Yi+1 and ui+d. These

new values of y and u are then used as starting values in the next iteration, to obtain

values of Yi+2 and Ui+2 at Xi + 2h, and so on, until the desired range of integration has

been reached.

ln this projeet, !(x, y, u) = Pd and F(x, y, u) = Vdw' By substituting the

initial values of We and Wd into Equation (2 - 21) and (2 - 22), the values of Pd and

Vdw ' required to determine k1 and ql, expressed in Equation (3 - 3) and (3 - 5), are

obtained. The other 3 k and q values are then determined. Ali four k and q are used

in the recurrence formulas, (3 - 2) and (3 - 4), to obtain values of Wei+l and Wdi+l'

34

J 3. Dynamic Analysis of the Process Model

These are then used in Equation (3-3) and (3-5) to recalculate k and q for substitution

into Equation (3 - 2) and (3 - 4) to obtain values of Wei+2 and Wdi+2' and 50 on An

outline of the procedure is shown in the flow chart of Figure 3.1. The initial values used

are:

t - 0 {We = 32.61b/sec (14.7874kg/sec) - Wd = 32.61b/sec (14.7874kg/sec)

3.2 Simulation Methods

The main problem in simulation is the solution of the modeling equations. If

these equations are complex or nonlinear or contain transcendental funetions, analytical

solutions are impossible. Therefore an iterative trial-and-error procedure must be devised

Based on the given initial conditions, a next step value is estimated by employing numerical

methods (Runge-Kutta in this thesis). Then this approximation is cheeked by predefined

convergent conditions to see if it satisfies them. If not, a new estimate 15 made and the

whole process is repeated until the iteration converges withlO the required "mits ln thls

trial-and-error procedure, the tolerance must be specified first and the step-slze must be

determined at each iteration to optimize the speed and aeeuraey of the simulation. The

details of the algorithm designed to meet the speed and aeeuraey requirements will be

described in this section. This is followed by a description of the simulation software in

which this algorithm is applied.

3.2.1 Variable Slep-Size Mullislep Aigorithm

ln the simulation of a difTerential equation:

35

•

f

DEFINI! STATEMBNT FUNCI10N

ItEADDATA

1. INmAL VALUE OPTIMB 2. TIMB INCRBMENT 3. PROO' INCRBMENT

.1NI11AL FBED WA TER FLO 5. lNJ11AL S"ŒAM FLOW

6. MAXIMUM 11MB

lNI'J1AlJZB PRINT 11MB

CALaJLAm"l AND RHO

CALCULATE tl,t2,k3 AND t4

3. Oynamic Analysis of the Pro cess Model

INCREMENT 11MB

N

INCllEMENT PRlNT11MB

Figure 3.1 Flow chart of the prolramminl procedure

36

1

T

3. Oynamic Analysis of the Process Model

y' = J(t,y) (3 - 6)

whenever a tolerance TOL > 0 is given, a minimum number of steps should be used to

ensure that the Ilobai error:

(3 - 7)

where:

yeti) - the exact value of the solution of the difTerentiai equation

Wi - the approximation obtained at the i-th step.

Generally speaking, integration step size must be varied during the procedure

in order to minimize the number of steps while controlling the global error. In this section

we examine a variable step-size multistep algorithmic technique that controls the error

efficiently through appropriate choice of step size. This algorithm is designed to avoid

waiting time with very smalt step sizes in regions of derivatives, and to avoid large step

sizes in analytic regions with higher order derivatives of great magnitude.

ln the study of the variable step-size multistep algorithm, the four-step Adams

Bashforth method was employed as predictor and the three-step Adams-Moulton method

as corrector in the error control procedure[13]. These methods are multistep methods

which use the approximation at more than one previous step to d~termine the approxi-

mation at the next step. Because of the 'multistep', these methods will generate a more

accu rate result than the 'single-step' method. The algorithm can be described as follows:

• Definitions:

37

1 3 Oynamic Analysis of the Process Modet

WPi: the predicted variable at i-th step.

WCi: the corrected variable at i-th step.

hi: the interval variable at i-th step.

q: the current step coefficient of hi

• Aigorithm:

h WPi = Wi-l + 24 (55f(ti-l! wi-d - 59f{ti-2! Wi-2)

+37/(ti-3! Wi-3) - 9f(I.-4, Wi-4»

h WCi = Wi-l + 24 (9f(ti! WPi) + 19f{ti-b Wi-l)

-5f{ti-2! Wi-2) + f(ti-3, Wi-3»

191WCi - wPil t: = 270hi

(3 - 8)

A difTerence equation method is said to be convergent with respect to the

differential equation it approximates if:

38

1 3 Dynamic Analysis of the Procm Model

(3 - 9)

Otherwise it is divergent. To better understand the local truncation error, we define that

the estimation at the next step is convergent when the error between the exact value and

the approximation is within the defined to/erance. Otherwise, we say the estimation is

divergent at this step. Under most conditions, the results will either converge or diverge

at the current step. In case of convergence, the local truncation error can be tolerated,

but perhaps at the cost of computation time. In this case, since the multistep method is

used in the algorithm and the new equally spaced starting values must be computed, a

change in step size for this method is much more costly in terms of functional evaluations

than single-step method. As a consequence, it is common practice to ignore the step-size

change whenever the local truncation error is between TOL/lO and TOL. The deflnltion

of TOL/lO rather than 0 is to avoid large computing cost. On the other hand, large

divergence cannot be permitted. In su ch a case, the algorithm follows a back-up procedure

as described as follows:

if: ERROR> TOL

then:

hi = qh j

tj = ti-l + qhi

If the local error exceeds the tolerance. the previous caleulalion 15 repeated

but with an estimated step size as a funetion of this error.

8ased on the algorithm discussed above, thl! following iterative procedure was

developed for the simulation program.

39

1 3. Oyn.mie Analysis o( the Protus Model

• Definitions:

Input:

a: start point

b: end point

Q: initial condition, y(o) = Q

hmox: maximum step size

hmin: minimum step size

Output:

Wi: the approximation of lI(tï) at i-th step

h: the step size at ;-th step

• Procedure:

(1) Set up a subalgorithm for the Runge-Kutu fourth-order method to be ca lied

RK4 which ICcepts as input a step size h and starting values Vo = y(XO,UO)

and returns (Zj, vj)lj = 1,2,3 defined by the following:

for j = 1,2,3

set:

40

1 3. Dynamic Analysis of the Process Model

kl = (h)f(Xj,Yi,"i)

k2 = (h)f( xi +~,Yi + ~,Ui + '1) k3 = (h)f(Xi +~,Yj + ~,Ui + 9f) k4 = (h)f(Xi + h,Yi + k3,Ui + 93)

91 = (h)F(Xi, Yi, ",)

92 = (h)F( xi +~,Yi + ~,Ui +~)

93 =(h)F(Xi+~,Yi +~,Ui+9f)

94 = (h)F(Xi + h, Yi + k3. ui + q3) 1

Yi+l = Yi + 6(k1 + 2k2 + 2k3 + k4)

1 ui+l = "i + 6(ql + 2q2 + 2q3 + q4)

(2) Input the initial conditions, by setting:

to = a;

wo = 0;

h = hmax;

Output (to, Wo)

[3] BiSed on the initial conditions, calculate the first, second and third estima-

tions. Cali RK4;

Set

N FLAG = 1; (Indicates computation (rom RK4)

M FLAG = 1; (MFLAG=O indicates acceptable computation)

i = 4;

t = t3 + h;

41

1 3 Oynlmic Analysis of the Process Model

[4] 8ased on the input functions, iterate ail the solutions until the final condition

is reached. While (ti-l ~ b or MFLAG = 1) do (5) to (9).

(5) 8ased on the startins values, calculate the values of predictor and corrector.

Set:

w P = Wi-l + 2~ (55J(ti-lt Wi-t> - 59J(ti-2, Wi-2)

+37/(ti-3, Wi-3) - 9/(ti-4, Wi-4»)

wc = Wi-l + ;. (9f(ti, WPi) + 19J(ti-b wi-d

-5/(ti-2,Wi-2) + !(ti-3,Wi-3»)

191WC- WPI t = 270hi

(6] Test the new estimation for convergence:

a) If ( ~ TOL, the solution has converged:

Set Wi = WC; (Result accepted)

MFLAG= 0;

and proceed to step (7).

b) Else, continue executing step (5] using the following transfer of

variables:

42

1 3 Oynamie Analysis of the Process Model

[7J The solution has now converled at the ,iven time step. The next estimation

should be set up:

i = i + 1;

NFLAG = O.

18J Before executing the next iter~tion, the local truncation error needs to be

further analyzed in order to optimize the step size.

a) If f ~ O.1TOL, the step size h should be increased.

Set HOLD = hi;

q = (T~L) 1/4

If q > 4 (given upper bound)

then set hi = 4hi

If hi > hmax then set hl = hmax.

If ti-l + 3h ~ b then set h = HOLD (Avoiâ terminating with

changes in step size)

b) If h f:. BOLD, the step size has been changed. The new starting

values at the current point need to be recalculated

Set NFLAG = 1;

Cali RJ(4; (recalcula te the new starting vdlues)

43

..

1

1

3. Dynamic Analysis of the Pro cess Model

Set i = i + 3; and proceed with step (9).

c) Else the result is rejected ind set up a new step size:

Set: MFLAG = 1;

( )1/4

Set: q = TgL

If q < 0.1 then set h. = O.lh.;

If hi < hm in then set hi = hmin.

(9) Set li = ti-l + hi return to step (5).

It should be emphasized that since the multistep methods require equal step

sizes for the stirting values, any change in step size necessitates recalculating new starting

values at that point. This is done by ca iii ni a Runge·Kutta subalgorithm (see Section

3.1.1). In addition, the coefficient q is generally given an upper bound to ensure that

a single unusually accurate approximation does not result in too large a step size. The

algorithm presented incorporates this safeguud with an upper bound of 4.

3.2.2 Simulation Prolram Structure

The simulation program was designed to carry out a simulation of the boiler

drum water level system as an initial dynamic analysis of its process model. Furthermore,

this simulation program will be employed as a control plant for the drum water level

44

1 3 Dynamic Analysis of the Process Model

soumON ALOORl'l1lM

INPUT PUNCI10N PltOCBSS OENDATOI MODEL

slMULAnON MONlTOa

PIt oœss U'I'PU1' 0

~--------------------------------------------------------.------

Figure 3.2 The structure of the simulation program

controller. In the design of the program, various general purpose numerical simulation

methods were adopted and developed.

Tite structure of the simulation program is shown in Figure 3 2. The program

consists of four parts: the plant model, the input function generator, the simulation

monitor and the solution algorithm. The plant model consists of the physical process

models configuring the drum water level system. The function generator, supplied by the

45

...

• 3. Dynamie Analysis of the Process Model

user. is used to deliver plant input 50 that the transient response of the plant can be

generated correspondine to the input. The simulation monitor carries out the following

funetions:

a) Steady-state initialization (t = to): a steady-state solution of the plant process

models is determined based on the function inputs at t = tO'

b) Transient simulation (to < t < t,,): the plant is simulated over the period

tt, - to based on the function generated inputs.

c) 1/0 discretization: the step size for each finite time solution is determined by

usine the variable step-size multistep algorithm described in Section 3.2.1.

Then. bued on the step size and input functions. the solution algorithm exe

cutes each model once per iteration until a convergent solution is obtained.

The simulation program is only the simulation of the plant model and is used

to analyze the dynamic behavior of the plant. The simulation program should be combined

with the plant controller to become a drum water level simulator. In the simulator. the

plant inputs will come from the operator through the controller and steady-state will be

reached after a transient process.

3.3 Dynamic 8ehavior of the Process Model

Employing the simulation program described in the last section. the dynamic

behavior of the plant model will be presented both in the time-domain and the frequency

domain in this section. By time-domain. we mean obtaining the dependence of the system

46

1 3. Oynamic Analysis of the Process Model

variables on time by $Olvin, the dift'erential equations aescribinc the system. These dy

namic funetions tell us what is happenin, in the real world (here in simulation) as time

increases. By frequency-domain, we are permitted to look at the dynamic relationships be

tween input variables and output variables. Through these relationships, the controller for

the desired plant can be designed. A time-to-frequency domain transformation technique

was al50 developed.

3.3.1 Time-Domain Dynamies of the Pro cess Model

The purpose of the time-domain dynamic analysis of the pro cess model is

essentially to present the behavior of the plant 50 that a better understanding of the drum

water level system can be reached. Secondly, the transient response of the process model

can be used as a reference for the control system design. In the time-domaln analysls, the

types of systems and types of disturbances should be determined first ln this proJect, the

system is a set of diff'erential equations and the disturbances are step changes in feedwater

f10w rate, fuel flow rate, system pressure and steam f10w rate.

Starting from a set of steady-state values for the main dependent variables,

the simulation program is employed to determine the non-linear time behavior of the water

level and the steam dischar,e due to step chanles in fuel fJow rate, feedwater flow rate

and system pressure. The tabulated time data (plotted in Figures 3.3 to 38) are then

used to approximate the transfer funetions which describe the uncontrolled behavior of

the recirculation loop mode!.

Figures 3.3, 3.5 and 3.7 show the transient response of drum water level y

when there are s~ p changes in feedwater f10w rate, fuel flow rate, or system pressure

respectively. Figures 3.4, 3.6 and 3.8 shows the response of steam dlscharge WB for a

41

1 3. Oynamic Analysis o( the Process Model

1

0.9

O.,

c: 0.1

l 0.6

1 0.5

•• f G.4

0.3

J 1 1 • 1

0.2

0.1

00 5 10 15 3D

Time, NCIlIIdI

Filure 3.3 Chan,. in drum water level for 10 percent step incruse in f •• dwat., flow ,at.

0

·1

·2

·3

..

., -6

·1

"0 5 10 15 1) 2S

"., .... Filure 3.4 Chan,. in stum discharae (or 10 percent step increase

in (eedwater f10w rate

48

r 1

3 Oynamic Analysis o( the Process Model

1 001

0

-0.1

c -0.2

l -cu

1 -00" J

1 -00'

-006

-G07

-001

-0090 10 15 3D li)

n-.~

Filure 3.5 Chan,e in drum water level (or 10 percent step increase in fuel f10w rate

102

-J 001

1 006

1 • o. ..

1 0.2

00 , 10 15 3D li)

nme. MaIDIII

" Figure 3.6 Chan,e in steam discharge for 10 percent step increase in fuel f10w rate

49

1

c

l 1 JI

1

J 1 1 • 1

3. Oynamic Analysis o( the Process Model

0.9

O.,

0.7

06

0.5

0.4

0.3

0.2

0.1

0 0 S 10 IS 20

Tune. eecoadI

Filure l.7 Chanle in drum water level (or a 50-psi step decrease in system pressure

40

30

Il

10

°0 S 10 lS 20 2S

11me, leCOIIdI

Figure 3.8 Chan,e in stum dischar,e (or a 50-psi step decrease in system pressure

30

50

1

cf

r 1 .. J

3. Oynamic Analysis of the Process Model

0.5

0

.0-'

-1

-1.5

-2 • 0 5 10 15 20 ~ 30 35 40 ~5

TIme, leCœdI

Figure 3.9 Change in drum water leI/el for 10 percent Increase in steam flow rate

st

step-change in feedwater flow rate, fuel flow rate and system pressure respectlvely The

response curves indicate that the y/We, y/W" y/p, Ws/We, Ws/HI, and W.~h/ transfer

functions can each be approximated with reasonable accuracy by a single tlme constant

ln Figure 3.9, the response of drum water level wlth 10 percent step Increase ln steam

flow rate is presented. ft is interesting to note that far sudden ch<lnge in thE' steam flow

rate, the water level initially goes up. and then starts decreasing at a more or less u niform

rate. This is similar to the swell observed in bailers when there is a sudden Increase in

load. The swell observed here is the result of sudden evaporatlan in the rlser because

of the drum-pressure drop. Hence the set of equations developed will predlct swell and

shrink, at least qualitatively.

ln a similar manner, any of the boiler variables used ln the derivation can be

51

1

3 Oynamic Analysis of the Process Model

found as a function of time and afore-mentioned input variables. The effect of load or

fuel changes, for example, on the circulation rate, quality of mixture leaving riser, wall

temperatures, and 50 forth, can be studied and some qualitative understanding of the

system dynamics can be obtained.

3.3.2 Time-to-Frequency-Domain Tran.formation Method

Theoretical/y, the frequency-domain dynamics can be obtained by substituti"g

lW for s in the system transfer function. Practically, however, the system transfer function

is not easily available. In most engineering applications the system is too complicated to

al/ow the formulation of a realistic transfer function. In this case, the frequency-domain

dynamics have to be obtained from the time dependent experimental test data (from

simulation data in this project). In this section, two types of time-to-frequency-domain

transformation techniques will be discussed and a comparison of these two methods will

be presented.

3.3.2.1 Step Testina

A plant operator makes changes from time to time in various input variables

such as feed rate and steam rate from one operating level to a new level. These step

response data are often easily obtained by merely recording the variables of interest for a

few hours or days of plant operation. These data can also be converted into frequency

response curve (17), basical/y by difFerentiating both curves in the frequency domain.

Consider a process with an input Q(t) and an output y(t). By definition, the

transfer function of the process is:

52

r 1

3 Oynamic AnalySIS of the PrOCt5S Model

G( ) = }'(s)

s Q(s)

Employing Laplace tr.nsformation and substituting .Ii = 1""', it gives

Employing Euler identity, Equation (3 - 11) becomes:

where:

A - iB G{rw) = C _ iD

[Ty A = Jo y(t)cos(wt)dt

[TJI B = Jo y(t)sin(wt)dt

[TQ C = Jo Q(t)co.<,(wt)dt

fTQ D = Jo Q(t)sm(CN,t)dt

Finally, rationalization of Equation (3 - 12) gives:

R G(' ) _ AG + J3 D

e zw - C2 + D2

AD-BG ImG(rw) = C2 + D2

(3 - 10)

(3 - 11)

(3 - 12)

(3 - 13)

(3 - 14)

(3 - 15)

where ReG(zw) and ImG(iw) denote the real and Imaglnary parts of r"(lW),

respectively. The amplitude ratio and phase angle of G( l....J) may be obtalned from

• 3 Oynamic Analysis of the Process Model

AR = IG(iw)1 = J ReG2(iw) + ImG2(iw) (3 - 16)

,p = LG(,w) = tan- 1(ImG(iw}/ReG(iw)

Thus, the task of coalculating frequency respons! data from step test data

reduces to bein, able to evaluate the integrals A. B. C. and D. expressed in Equation

(3 - 13), for known funetions y(t) and Q(t). The integrations are with respect to lime

between the definite limits of zero and the end of the period of time of interest, TJI for

y(t) and TQ for Q(t).

ln this project, y(t) is drum water level or drum pressure obtained from the

simulation monitor (see Section 32.2) and Q(t) is the step change in feedwater flow rate,

fuel flow rate 01 steam flow rate.

3.3.2.2 Digital Evaluation

Equation (3-11) is the fundamental time-to-frequency domain transformation

technique. It is simple and easy to program. But the main disadvantage of this method

is the oscillatory behavior of the sire and cosine terms olt high values of frequency (For

details see Section 3.3.3). This problem Will cause an inaeeuracy of the frequeney response

of the process.

To improve the transformation technique. Fourier transformation WolS em

ployed to evaluate Equation (3 - ll) directly. The Fourier integral transform (FIT) is

defined as:

(3 - 17)

54

1 3 Oynamlc Analysis of the Process Model

We c,n break up the total interval (0 to TJI) into a number of sublOtervals of

length llti. Then the FIT can be written, with no loss of ngor, as a sum of IOtervals:

FIT = t (f~1 y(t)e-awtdt) i=1 j,.-1

(3 - 18)

After several mathematical steps, finally, the approximated Fourier transfor-

mation of y( t) becomes:

fo X) -iwt ~ -;wt [(e- iWl1t; - 1 e- a..;l1t a ) (f-,,,'A/ I - 1 1 )]

y(t)e dt ~ ~ e 1-1 YI 2 - - !Ia-l --2-- - -o ;=1 w Ilt; r.,.) ",,' Ill, 1 .... •

(3 - 19)

As mentioned before, the input function of the process is a step change of

height h and duration D, thus its Fourier transformation is given by

(3 - 20)

3.3.3 Frequency-Oomain Oynamics of the Process Model

There are two ways to obtain the frequency response of the process Mathe-

matical methods, based on the equatlons that describe the system, are used to obtétln the

frequency response directly from the system transfer functlon. Expeflmer ",1 methods,

discussed ln Section 3 3 2, are used when a mathemattcal model of the system IS not

avallable or the model is too complex to express as a transfer functlon ln thls proJect,

expenmental methods were used to obtaln the frequency response of the drum water level

1

:1


system from its simulating time domain response (shown in Figures 3.3 to 3 8). In order

to develop the transformation program, the following rules were established:

• The time-domain response values of water level and drum pressure must be

obtained first from the simulation monitor at each sample time step.

• In the step testing method. substitute the value into Equation (3 -12) as y( t);

ln the digital evaluation method. substitute the value into Equation (3 - 19)

as Yi.

• Pick up a specifie numerical value of frequency w Equations (3 - 12) and

(3-19) arethen Integrated, giving one point on the frequency-response curve.

Then the frequency is changed and the integrations repeated, using the same

experlmental time functions y(t) and Q(t). Repeating thls for frequencies

over the range of interest gives the complete G(rw) The sample selection of

frequency w is listed in Appendix A.

Based on these rules, a transformation program was developed to generate the

frequency response (Bode plots in this project), presented in Figures 3 10 to 3.15 The

transformation program reads input and output data, caleulates the integration of Equa·

tlon (3 -12) or the Fourier transformation of Equation (3 -19), gets the transfer function

by dividing the Input and output data, anrJ prints out log modulus and phase angle at

d,fTerent values of frequency. From the Bode plot, a closed·form transfer function is then

estimated. Using a digital optimization program, the coefficients of the estimated transfer

function are varied systematiully until the closest possible fit betwee'1 the tabulated fre·

quency data and the approximating function is obtained. To check the correctness of the

transfer function, an appropriate program is employed to perform the inverse transforma·

56

r

1 1

3 Dynamlc AnalySIS of the Procus Model

tion 50 that the original time response can be reproduced and the accuracy of the tr ansfer

function verified. The transfer functions for the drum water level system are presented as

Z transforms due to the digital simulation of the pro cess They .He descnbed as

1) Drum pressure transfer function caleulated from tlme and frequency responses

due to a la percent step incruse in feedwater mass flow rate (shawn ln

Figure 3.3 and 3.10),

G _ 1.1730 - 2.4791z-1 + 4.1805z-2 - 2.3440z- 3 + 0 5674:- 4

1 - 57.6376 _ 225.9200z-1 + 291.6848z-2 - 230.7271:- 3 + 130.8541:-4 - 23.5294:- ~ (3 - 21)

2) Drum pressure transfer function calculated from tlme and frequency responses

due to a la percent step increase ln fuel flow rate (shown en FIgure 34 and

311).

G _ -2.4596 - 2.9372z- 1 - 1.2671z-2 - 1.1361z-3

2 - 31.7017 - 71.8710z-1 + 61.3656:-2 - 24.1952:-3 + 4.2391z-4 - 0 2402:-5

(3 - 22)

3) Drum pressure transfer function calclliated from time and frequency responses

due to a 10 percent step increase in steam flow rate (shown ln Figure 3 5 and

3.12),

0.1701 - 0.3454z- 1 + 0.2430z- 2 - 0.07l3:- 3

Cl = 2.1314 _ 6.5700z-1 + 7.9134z-2 - 4.4748:- 3 + :-4 (3 - 23)

51

• 3 Oynamic Analysis of the Process Model

4) Drum witer level trinsfer function calculated from tlme and frequency re

sponses due to , 10 percent step increase in feedwater mass flow rate (shown

in Figure 3.6 ,nd 3.13).

54.28 0 4 = 2.59 - 1.59z- 1 (3 - 24)

5) Drum witer level transfer function calcufated {rom time and frequency re-

sponses due to a 10 percent step increase in fuel flow rate (shown in Figure 3.7

and 3.14).

G _ 0.5969 - 0.6610z-1 + O.0875z-2

5 - 1.9870 _ 4.2774:-1 + 3.3172:-2 _ z-3 (3 - 25)

6) Drum water level transfer function calculated from time and frequency re-

spons!s due to a 10 percent step increase in steam mass flow rate (shown in

Figure 3.8 and 3.15).

G _ -151.13 + 151.13z-1

6 - 2.59 _ 1.59z-1 (3 - 26)

These six transfer funetions were estimated based on the particular boiler

model discussed in this thesis. The physical dimensions and variabl'! values of the boiler

are listed in Table 3.1. The coefficients of the estimated transfer funetions may vary

for different boilers. But the techniques developed in this thesis can be applled on the

estimation of other boilers.

58

• 't

1

, J

1 j

.'

3 Dynamlc Analysis of the Procus Model

o.,

0

~.5

-1

-u

-2

-2.S

-)

-B

... 100

_....J.. ____ .l.. ___ ... ____ ~_.J.~ _______ .... ~ ___ .J. __ • ...l--.Jr. ..1_ &. ~

10' 10'

FreqUftlCY. radi.1nIIIecond

100

ID

60

«)

20

0

-20

.«)

.(rO

-10

-100 101 10' 102

",......,.~

Figure 3.10 Frequency response of drl.m water level for 10 percent step incruse in feedwater flow ,ate

59

1

J J

J l 1

J


100

10

flO

40

3)

0

.3)

.«)

~

..JO

·100 101 10· 102

Pr.-c7.,..... ........

Figure 3.11 Frequency response ofsteam discharge (or 10 percent step incruse in feedwater f10w rate

60

1

T

3 Oyn.mic An.lysls of the P,oc~ss Model

,...-------.................................................. -------------------------------05 9 ,

0

-05

1 -1

-1.5

J -2

-2.5

-3

-3.5 1()O

t ft f • ft ft

10'

100

10

CIO

~

J 20

i 0

1 -20

~

~

-10

·100 lOI

, 1 •• ft !

10'

Fiaure 3.12 Frequency response of drum water level for 10 percent step incruse ln fuel flow r.te

lOI

102

61

1

3 Oynamic Analysis o( the Process Model

1.'

J JO.,

o

~, if

·50

·SS

J .(j()

~

f ·70

1 ·75

...,

. ., .!JO

101 10' 10a

JIreqINDcy. l''d'_'Iecœd

Filure 3.13 Frequeney response of stum dise"ar,e (Ot 10 percent step inerease in fuel f10w rate

62

1

3 Dynamlc AnollySIS of the Process Model

o.,

0

~., ---

J -1

.1.5

J ·2

.2,j

.)

.)-, UJI 10' 101

PrequaM:y. ndianahecoDd

100

10

lIO

40

J 20

l 0

j ·20

~

..a)

·10

·100 IéJl 10' lOI

1'reqIMIacy.~

L-. __________________________________ ----

Figure 3.14 Frequency response of drum water level for a ~O- psi step decrease ln system pressure

63

~

1

1

1

1

•

1

1 J

1 " l J

l Dynam,c Analysis o( the Process Model

0, ~--..-

1 -10

-20

-lO

~

-~

.«J

-70

-10

-90 101

Figure 3.15 Frequency response o( steam discharge (or a 50-psi step decrease in system pressure

101

64

1

Chapter 4 Control System Structure

ln the two proceeding chapters we discussed the uncontrolled dynamlc behavlor

of the drum water level system, from the model development to Its dynamlc analysis

Based on the results achieved, we may now design a controller to make the plant run

more automatically, efficiently and safely

ln this Chapter, the 'hardware' part of the control system will be presented

It consists of the outline of the controlled plant and the structure of the controller.

4.1 The Outline of the Controlled Plant

Instrumentation hardware has been revolutionized in the last several decades

Mechanical and pneumatic components have been replaced by microprocessors that serve

several control loops simultaneously. Despite ail these changes ln hardware, the basic

concepts of the control system structure and control algorithms remaln essentlally the

same as they were thirty years ago [17]. With powerful computers, It IS now easler to

Impleme'1t "ontrol structures by just rewriting the program But the obJect of controller

design is the same. achieve a control system that will give good, stable, robust control

1 4 Control System Structure

As mentioned in Chapter 1, a boiler can be functionally divided into three

main loops comprising:

1) the combustion loop

2) the drum-feedwater loop

3) the stum-temperature loop

ln this project only the drum-feedwater loop is Involved and the other two

loops are assumed to operate satisfactorily. Thus in the control of the drum water system

only the following variables are of interest:

• Manipulated variable' The feedwater flow can be changed in order to control

the drum water level.

• Controlled variables: The drum water level and drum pressure are controlled

to remain as constant as possible.

• load disturbance' A change of steam fJow will cause the drum water level and

drum pressure to depart from their setpoint and the control system must be

able to keep the plant under control despite the efTects of the disturbance.

When a fet:dback controlstrategy is implemented digitally, the controller input

'nd output must be digital (sampled) signais rather than continuous-time signais. Thus,

the continuous-time signal from the transmitter is sampled and converted periodically to

a digital signal by an analog-to-digital converter (AOC). A digital control algorithm is

then used to caleulate the controller output, also a digital signal. Before the controller

output is sent to a f'nal control element (feedwater valve ln thls project), this digital

66

1 4 Control System ~truclure

CONl'lOL VA1.VI SBNSOI

----e.t{> Njo.-.----.4 PkOC'ESS

IIP

l'ŒlD

...... _AIR SUPPLY PLOW TRANSMJTll!lt

-----t------ ------------------------------------------ ----------CONTROL

ROOM

1 COt-rTROLl.J!R AND

MANUAlJAI!rOMATIC S~Q ~ __________ S~~

Figure 4.1 Feedback control loop for drum water level system

signal is converted to a corresponding continut:: .. s-time signal by a d'gital-to-analog con·

verter (DAC). Alternatively. the digital signal can be converted to a sequence of pulses

representing the change in controller output. The continuous-time signal or pulse train is

then sent directly to a final control element that utilizes one or the other form of input

to change its position.

Figure 4.1 shows the control loop ;or the drum water level system wh.ch

consists of a sensor to detect the process variable, a transm,tter to convert the sensor

signal into a digital signal which the controller can understand, a controller that compares

61

4 Control Syst~m Structur~

thls pro cess sign~1 with ~ desired setpoint value and produces an appropriate controller

output signil ind i control valve thit changes the manipulated variable (feedwater flow

rate)

Ali elements shown in Figure 4.1 were simulated by mathematlCal models and

the controller part will be discussed further in the following sections.

4.2 Orum Water Level Control System

1.. water tube boilers, the drum level control system must ensure that the water

levells always malnlalned above the top of the risers/downcomers to prevent overheating

of the tubes. The drum level also must ")ot rise such that water from the drum is carried

over into the steam system. During start*up or under abnormal conditions, the plant

operator may want to set the position of the control valve hlmself instead of having the

(ontroller position it. Thus a manual/automatic override switch must be provided in the

controller. Certain desirable controller readout features include:

1) Indication of the value of the controlled variable: the signal from the trans

mitter.

2) Indication of the value of the signal being sent to the feedwater valve: the

controller output.

3) Indication of the setpoint.

Drum level is difficult to control because of the inverse response of the level

to changes in steam demand.

68

~ 1

4 Control S~st~m Structurt

r-----------------------.-----------------..

WATER LSVBL MEASURBD SETPOINT WATBJt LEVEL

PlD CONTROlLER

+ +

SETPOINT

CONTROL

ACTUATOR

DRUM PRESSURE

S1"BAM PLOW

FEEDPORW ARC

CONTROLLER

L-_______________ . __________________________ _

Figure 4.2 General drum water level control system

The schematic representation of the general control system is shown in Fig-

ure 4.2. The system contains two control loops, a feedback loop using the deviation of

the measured drum water level from its set point as an input and a feedforward loop using

the stearn flow signal as the input. The feedback loop is an increlT ~ntal PID controller

with an adjustable proportional gain.

As mentioned before, due to the drum pressure change caused by the steam

69

1 4 Control System Structure

load change, 'swell' or 'shrinkage' will occur. To improve the control quallty, a feedforward

loop was designed to use steam flow and drum pressure signais directly to move the control

devlce before the 'swel/' and 'shrinkage' in the boiler water level occur. A predesigned

function can be defined based on the response of the process during simulation. In this

project immediatel)' following the drum pressure and the steam flow signais, a step sIgnai is

generated by the feedforward control/er for fast control action. Steam flow is summed with

the output of the PlO controller to establish the set point for the control actuator. This

scheme is effective because steam f10w changes ar/.! immediately fed forward to change

the final feedwater set point for the control actuator. In this way feedwater flow tracks

steam flow. The drum level to feedwater cascade will quickly arre5t any disturbances in

the feedwater system.

The controlled device evaluated in this project is the feedwater 41,,\VII valve.

This valve is mathematically simulated by a second-order transfer function (for detail see

Chapter 2). Through the control of the valve, the feed water flow rate 15 manipulated

and the drum water level is control/ed following the changes in several variables.

70

Chapter 5 Control Strategy

ln previous chapters the dynamic behavlor of the drum water level process was

considered and sorne of the mathematical tools required to analyze the process dynamics

were developed. Furthermore the drum water level control system elements were outlmcd

Now the 'core' of the control system, the control algorlthm, may be consldered

ln this chapter, the incrementai PlO combined with feedforward control algo-

rithm will be introduced first, then an improvement of the algonthm will be discussed

5.1 Control Aigorithm

Ouring the past two decades, there has been widespread application of digital

control systems due to their f1exibility, computational power, and cost effectiveness [291

ln this section, the digital drum water level control technique, considered to be a digital

version of PlO and f(~edforward control, will be introduced. The final combined digital

PIO-feedforward control algorithm will also be developed.

5.1.1 Digital PlO Control Technique

ln most process PID control applications, the derivatlve action can be applied

'( .

, S Control Stratfgy

to either the error signal or just the.process measurement (PM). If it is applied to the

errar signal. step changes in set point will produce I.arge bumps in the control element

Therefore in this projett, the derivative action is applied only to the process measuremen\

signal as il enters the controller. The proportion al and integral action is then a pplied to

the d.fTerence between the setpoint and the output signal from the derivative unit (see

Figure 5.1)

MANtPUl.ATBD VAAWLB

---4If

COm'ROL O\1t'P\11'

PaOCllSS

FllI!I>IACk COI'n'lOLU!ll

PlACT10N

CONTltou..eo VAJUABLB

SETPOINT ..... ---

Figure 5.1 PlO control with derivalive on protess measurement

The analog PlO controller equation can be expressed as:

72

1

l

5 Control Stratt&y

- (Ilot de) P(t) = P + Kc e(t) + - e(t)dt + TD-, TI 0 ( t

(5 - 1)

A striightforward way of deriving a digital version of the ideal PID control

law in Equation (5 - 1) is to replace the integral and derivative terms by thelr dlscrete

equivalents. Thus, approximating the integral by a summation and the derivatlve by a

first-order backwird difference gives:

(5 - 2)

Equation (5- 2) is referred to as the position (ofm of the PlO control algorlthrn

since the actual controller output IS calculated.

An alternative approach is to use the velocity (ofm of the algorithm ln whlch

the change in controller output is calculated. It can be described as

where:

[(; = I\c llt

TI

J' /\cTD \d= -

Ilt

(5 - 3)

73

1

f

tages:

5 Control Str~tegy

Comparing Equition (5 - .2) with (5 - 3), the velocity form has three advan-

1) It inherently contiins some provision for antireset windup since the summation

of errors is not explicitly calculated.

2) The output âPn is in i form directly usable by final control elements that

require in input specifying change in position.

3) Wh en putting the contraller in automatic mode, that is, sWltching It from

manual operation, it is not necessiry to initiallze the output (P ln Equation

(5 - 2». The valve has been placed in the appropriate position during the

shrt-up procedure.

After further anilysis, the velocity form PlO algorithm was adopted and com

bined with feedforward control to be the final control algorithm in this project.

5.1.2 Feedforward Control Aigorithm

PlO control is i type of feedback control. In feedback control, an error must

be detected in a controlled variable before the feedback controller can take action to

change the manipulated variable. Input disturbances must upset the system before the

feedback controller can do anything.

It seems very reasonable that if we could detect a disturbance entering a pro

cess, we might begin to correct for it before it upsets the process. This is the basic idea of

feedforward control. If we can measure the disturbance, we can send this signal through

74

5 (ontrol StrattSy

a feedforward control algorlthm that makes appropriate changes ln the manlpulated varI

able so as to keep the controlled variable near its desired value ln the drurn water level

system, the disturbances (feedwater flow rate, steam f10w rate and fuel flow rate) can be

easily monitored from the simulated dynamic response of the process 50 the feedforward

control is weil suited to drum water level control.

r-----------------------------------.--------.-------------

DRUM PRBSSUJtB

STBAMFLOW

TRANSMl'ITBR

FEEDR>RWARD CONTROU..I!R

...... LEAD-_"""I""'LA_O~'D~

..... _RA....,n.--o __ ' ~

FEEOBACK SIGNAL ACUATOR

----------4 .. ~ ~ FEPJ)WATER PLOW

Figure 5.2 The feedforward control algorithm

PROCBSS

Wh en designing parameter-optimized feedforward control, one assumes a fixed

75

1

5 Control Strategy

(realizable) structure, i.e. the structure ind order of the feedforward algorithm are given

and the free pu~meters ~re ~djusted by pirimeter optimization. Herein, feed{orward

control structures of the form

(5 - 4)

are assumed.

Now the response of P,( k) to a step change of the disturbance variable

c/(k) = l(k) 15 considered. In thls project, a first order lag is used in the feedfor-

ward controller 50 that the change 10 the manipulated variable is not instantaneous. Thus

{or / = l. Equation (5 _. 4) becomes

(5 - 5)

For e ,(k) = tek) we have:

P,(O) = hO

P,(l) = (1 - fdPj(O) + hl

Pj (2) = - hP/el) + (1 - h)p/(O) + hl + h2

(5 - 6)

76

5 Control Strat~gy

The initial manipulated variable P,(O) equals hO or hoc ,(0) Therefore "0 can

be fixed sim ply by a suitable choice of P,(O), 50 that a definite manlpulatlng range can

be easily considered. 8y means of the given P,(O) the number of optllnlzed parallleters

for 1 = 1 is reduced to one parameter. For 1 = 1 the equations, together wlth Equation

(5 - 6), become:

ho = P,(O)

-P,(I) - K, h=-~--.o.-

P,(O) - 1\, hl = P,{l) - P,(O)(1 - Id

l' ho + Il} \,= 1+11

(5 - 7)

(5 - 8)

(5 - 9)

(5 - 10)

Hence in this project (1 = 1), the deSign of the feedforward element wlth a

prescribed initial manipulated variable PICO) leads to the optimizatlon of a single parame

ter P,(l). The computational effort for parameter optlmizatlon in thls case IS partlcularly

small.

As shown in Figure 5.2, the steam flow IS measured and this flow signai 15

multiplied bya dynamic (first order) and a constant (desired ratio K,) element The

output of the multiplier is then combined with the output of the PlO controller to become

a control signal applied to the manipulated varia~'"

5.1.3 Combined PID-feedforward Control Aigorithm

ln most engineering applications, feedforward control systems are Installed as

part of combined feedforward-feedback systems. The feedforward controller takes care ot

77

1 5 Control Strategy

the large ird frequent measurible disturbances. The fet:oDack controller takes care of any

errors thit come through the process becausf! of inaccuracies in the feedforward ,ontroller

or other unmeasured disturb.1nces. As shawn in Figure 4.2 the manlpulated variable

IS changed by bath the feedforward controller and the PlO controller. The algorithm

equation is formed by'

(5 - 11)

The final output equation is:

Pn = Pn-l + âP~ (5 - 12)

The parameters in equations (5 - 3) ta (5 -12) will be calculated and adjusted

by certain parameter seUing methods based on the results of the simulation. Details will

be presented in Chapter 6.

5.2 Refinements

As indicated in Chipter 4. when a digital computer is used for control. con·

tinuous measurements are converted into digital form by an analog ta digital converter

(AOC). First the signal must be sampled at discrete points in time and then the samples

must be dlgitized. The time interval between successive samples is referred to as the

sampling period ât. In order ta get reasonably accu rate measurements. an appropriate

sampling rate should be selected and il filter may be installed if the measurements are

nOlsy. Process-induced noise can arise from variations due ta mixing. turbulence, and

78

5 Control Str ategy

nonuniform multiphue flows. The effect of both process noise and measurement noise

can be reduced by signal filteri",. In this section, the data sampling and flltering will be

discussed first. Then the improvement of the controller output Will be presented

5.2.1 Data Samplinl and Filte,inl

Sampling and filtering were used to improve the input signal character with

real data measurement or simulation generated noise. The sample period can be adjusted

based on the process. To eliminate or reduce uror due to nOise and converSion, the

variables are sampled several times dUflng one sample period, and the average value 15

used as sample data value. It is called average value flltering The average value i5

calculated by

(5 - 13)

Where:

Yi = the ith time sampling value

Yi = the average filtered output value

N = number of samples

To obtain a satisfactory sample data value, the number of sample5, IV, has

to be chosen carefully. If N is too large, it will take \.00 long to obtain an average input

signal value. If N is tao small, the effect of filtering will be reduced.

79

1 5 Control StratelY

5.2.2 Improvinl the Differentiai Character of Output Response

Due to the large time del~y in the controlled plant, it is nece!isary ta modify

the theoretic~1 PlO control a1lorithm before it c~n be used in the actual control system.

ln this cOl'trol system, a first vrder filter hu been added to improve the output due ta

the difTerential component. This filter has the same function as the one on the rnput

side of the controller. But this case the measured signal is the output signal from the

combined feedback-feedforward controller and the output signal is the final control signal

to the drum water level system. The finite difference equation of this filter 15 as follows

P~ = i1Pn + (1 - Ct)P~_l (5 -- 14)

where:

Equation (5 - 14) indicates that the filtered measurement is a weighted sum

of the current measurement Pn and the filtered value at the previous sampling instant

P~-l' limitinl eues for /3 are:

/3 = 1: No filtering (the filter output is the raw measurement Pn).

/3 ~ 0: The current measurement is ignored.

ln electrical engineering parlance, the term 'filter' is synonymous wlth 'transfer

function,' sinee a filter transforms input signais to yield output signais ln EquatIon (5-2).

80

5 Control Strategy

the filter tr.nsforms the output signal from the combined feedback-feedforward controller

(Pn) to the final control signal (P~) to manipulate the feed water valve. Through this

filter, the final control signal is improved so that the change in the manipulated variable

of drum water level Îs not instantaneous.

5.2.3 Antirelet Windup

An inherent disadvantage of integral control is a phenomenon known as reset

windup. Recall that the integral mode causes the controller output to change as long as

the error e( t) :f O. When a sustained error occurs, the integral term becomes quite large

and the controller output eventually saturates. Further buildup of the integral term while

the controller is saturated is referred to as reset windup.

Reset windup occurs, for example, during the start-up ,of a batch proeess or

after a large set-point change. It can also occur as a consequence of a large sustaioed load

disturbance that is beyond the range of the manipulated variable. 50 this reset windup

must be recognized and corrected.

This is accomplished in a number or different ways, depending on the con

troller hardware and software used. In computer control syst~m, the reset windup can be

reduced by temporarily halting the integral control action whenever the contreller output

saturates. The integral action resumes when the output is no longer saturated. In the

actual operation of PlO control, the integral " :tion may be turned off and on many times

based on the reset windup situation. Thus, the gain, Kef should h adjustùle sinee the

conirol charaeter is changed while the integral action is turned off. As shown in Figure 5.3,

I\c is increased when the integral action turned off to produce a faster control action and

reset to the original value wt.en the integral iction is resumed.

81

1 INPUT Yo.lII

SBTPD

PlDACf

N

y

y

SBTPID

PDAcr

y

N

RBSIn'Kc

CLl!AR.PID

Filure 5.3 The .djustment o( the Iain Kr

5.3 The Control Program Structure

5 Control Strategy

ADJUSTKc

a.EA.RPD

As mentioned in Chapter 3, one of the main purposes of the simulation pro-

gram is to provide a virtual control plant for the drum water level controller Further,

the simulation program must be combined with the controller to become a drum water

82

1 5 Contr ,1 Strategy

CONnOL ,.... MODBL saumON ALOOJt.I1HM

AJ..OOart1IM

1

1

1 PIt

fNPur PUNCI10N PROCESS OI!NElA TOIt NODBL

i

SIMlJI..AnON MONn'OI

Filure 5.4 The control prol,.m structure

level simulator We are now al the position to develop a control program (controller) to

control the entire plant (simulation program).

Figure 5.4 shows the structure of the control program. The program consÎ!;.ts

of four parts: the 1;0 devices, the manual/automatic override switch, the control monitor

and the control algorithm. The control monitor is used to indicate the controlled variable.

the controfler output signal and the setpoint value. The manualjautomatic override switch

83

...

j

5 Control Strategy

is provided for the plant operator to control the valve by himself instead of havlng the

controller position it. The 1/0 device consists of two filters, one is employed on the

input side of the controller and the other is u5ed to improve the output behavlor of the

controfler. The 1/0 device carries out the following functions'

a) Replace the input function generator in the simulation .. ;ogram (see Section

3.2.2) and generate the control signal for the plant.

b) Measure the output variables of the plant and transmit these variables to the

controller.

c) Read the operating commands supplied by the user and transmit the com

mand~ to the controller.

8ased on the input commands and the measured vartables, the control algo

rithm accesses and calculates these input variables and sends out the manipulated signai

to the plant. The control algorithm has an antireset windup function. Whenever the

controller output saturates, the integral action Will be turned off untll the output IS no

longer saturated .

84

f

Chapter 6 Selection of Design Parameters

An important consequence of feedback control is that it can cause oSCIllatory

response. If the oscillation has a sm ail amplitude and damps out quickly, then the control

system performance is generally considered to be satlsfactory. However, under certain

Clrcumstances the oscillations may be underdamped and the amplitude IOcreases with

tlme until a physical limit is reached ln thi~ case, the control system is said to be

unstable. The most important dynamic aspect of any control system is its stability.

Theoretically, the stability of a control system can be analyzed by the roots of

Its characteristic equation, transfer function or on the Z plane. Practically, as mentioned

several times before, it is hard or even impossible to derive the transfer function of a real

system. Thus, in this chapter, the stability analysis of the water level control system will

make use of the transient response of ils closed-Ioop.

6.1 Ziegler-Nichais Method

ln order to obtain approximately optimal settings of parameters for continuo:Js

lime controllers with PIO-behavio" tuning rules are often applied. These rules were mostly

evolved for slow processel, and are based on experiments with a P-controller at the stability

1 6 Selt"ctlon cf Design P .. ulmetm

limit, or on time constants of the process. A survey of these rulE's 15 given in e.g. Isermann

[12}. Well-known rule~ al~ those by Ziegler and Nichols.

The Ziegler-Nichols (ZN) method consists of first finding the ultimate gain

Ku, at which value the loop is at the limit of stability with a proportional-only feedback

controller. The period ofthe resulting oscillation iscalled the ultimate period. Pu (minutes

per cyde). The ZN setting are then calculated from Ku and Pli for a PID controller by

1.' _ Au l\e --1.7

Pu TI= -

2

Pu TD=-

8

(6 - 1)

The ZN controller 5etting5 are pseudostandards in the control field They are

easy to find and to use and give reasonable performance 01'1 sorne Joops. There are many

loops where the ZN settings are not very good. They tend to be too underdamped for

most process control applications. But the ZN settings are uSf:lul as a place to start

6.2 The Feedback Controller Parameters Setting

After further study of the available parameter tuning methods. Ziegler- Nichols

was adopted as the basic parameter setting method in this project. Based or. the ZN

method, the following on-line trial and error procedure was developed to obtain the final

controller parameters:

• Definitions:

86

1

J

o Selection of Des"n Parameters

Proportional Band (PB): This is an alternative term instead of controller gain.

It is defined u:

V'/here Ke is the control/er gain. The term proportional band refers to the

range over which the error must change t(' drive the controller output over its

full range .

• Procedure.

[1] Takin, ail the integral and derivative action out of the controller, i.e., set Tl

at maximum (minutb per repeat) and TD at minimum (minutes).

[2] Set the PB at a high value, 200 in this project.

[3] Make a smailload change (10 per cent steam flow rate change in this project)

and observe the response of the controlled variable. The gain is low so the

response will be slugish.

[4J Reduce the PB by a factor of 2 (double the gain) and make another small

change in load.

(5) Keep reducin, PB, by repeatin, step [4], until the loop becomes highly un-

derdamped and oscilla tory. The gain at which this occurs is the ultimate gain

[6) Calculate Ke, TI and TD by employing the ZN method.

87

t

J

6 Selection of Design Paramrtprs

(7) Now st,rt bringin, in integr~1 "tion by reducing Tl by factols of 2, maklng

sm,1I disturbinces it eich vilue of TI ta see the effect

(8) Find the value of TI thit makes the loop hlghly underdamped and set TI at

twice this value.

(9) load changes should be used ta disturb the system and the derlvatlve should

be ,cting on the process measurement sign .. !. Flnd the value of T D that glves

the tightest control without arnplifymg the nOise 10 the process measulement

signal.

[101 Then reduce the PB by steps of 10 p'2r cent, untt! the desired specifICation on

damping coeffiCient or overshoot is satisfied

There ire many other tun;ng methods. One of the most Simple user; the step

response cf the process ta determine steady-state gain, tlme constant, and deadtlme

Then controller tunlng constants can be calculated from these values The ultlmate

gain and ultimate frequency approach were adopted ln thls proJect because of the very

significant problem of nonhnearity that exists in thls proJect and most other engineering

thermai·f\uid process systems Step testing drives the process away from ItS initiai steady

state and is. therefore, much more sensitive ta nonhnearlty than IS the c1osed-loop ultimate

gain method in which the process is held in a region near the initiai steady-state

Based on the above procedure, an optimlzatlon program was developed to <.al

culate the coefficients of the controller. Usina this program, the controller gains Kr, 1\ J'

TI and rD were adjusted, in practice, to obtain the 'best' closed-Ioop tranSlent responses

The 'best' closed·loop responses were those Judged to provlde an acceptable tranSlent

88

1 6 Selection of Design Parameters

behavior of the process, due to the input disturbances, and that were not expected to

improve with continued tri~1 arld error.

The initial and final controller p~rilmeters ilre shown ln Table 6.1. The initiai

parameter villues were obtiined by using the ZN metnod. To arrive at the final parameter

values shown, twelve step responses were calculated. with readJustment of tne controller

parameters by applying the trial and error procedure after the evaluation of each response

The transient responses ulculilted from the initial and final controller parameters are

shown in Figure 6.1. A comparison of the values is indicative of the extent to which the

trial and error adjustments of the controller parameters may be consldered as 'informed'

Conlroller Plrlmeters

Kc K 1 TI TD

Initlll Values Final Values

10 25 05 200 225 100 020 025

Table 6.1 Controller parlmele' lettin,s by usina ZN combined tnal and error method

The addition of the feedforward controller has no effect on the closed·loop

stabllity of the system for il lineilrized process. Thus, in thls proJect. the feedforward

controller is ildded dter the feedback controller is tuned. Details of the feedforward

controller tun,"g will be discussed in Chapter 7.

6.3 Influence of the Sampling Time ~t

As is weil known. sampled data controllers have generally inferior performance

than continuous control systems. This is sometimes explained by the fact that sampled

89

6 Seltet/on of DtSlgn P,,'amtltr5

1 1 1 • J

1 l 1 • 1

Il 1

:[ (\1

2

o

·2

1 1

(~----_---f

~L ____ ~I __ ~I ____ ~' ____ ~I __ ~I ___ ~~-4-__ ~ __ -J

o 20 40 60 10 100 120 1.0 160 110 D)

n-.~

a) The c10ged-loop response based on ZN paJ'1lDeaer Benin,.

:~'--~~'--~'--~t--~'--~'--~'-~

3

o

.1~--~--~--~~--~--·~--~--~----~--~--~ o 210 40 el 10 100 120 140 160 110 .,

na.,1ealIIdI

b) The doeed.loop leIpODIe bMcd ouille 1riII-1Dd-ew panmelU teUÙIIJ

Figure 6.1 The closed-Joop respor.$es (rom the initial and final controller pa

rametefl

90

1 6 SelectIon of DesIgn Parameters

signais contain less information than continuous signais. However, not only the InformatIon

but also the use of thls information IS of interest. As the class and the frequency spectrulI1

of the disturbince signais also plays an important mie, general remarks on the control

performance of sampled data systems ire difficult to make. However, for parameter-

optimized controllers one can issume in general that the control perform~nce deteriorates

with increasing sample time. Therefore, the sample time dlould be as small as possible

considering only the control performance.

ln selecting a sampling period, two questions must be considered'

1) How many mealjurement points does the computer monitor?

2) What is the best sampling period from a process point of view?

Control loops in general have to be designed such that the medium frequency

range cornes wlthin that range of the disturbanc~ signal spectrum where the magnitude

of the spectrum is low. In addition, disturbances with high and medium frequency corn-

ponenls must be flltered in order to avoid unnecessary variations in the the manipulated

variable. If disturbances up to the frequency Wmaz = Wl have to be contro:led approx-

im~tely as in .a continuous loop, the sampl~ time has to be chosen in accordance with

Shannon's sampling theorem [12):

1r At<--

- Wmaz (6 - 3)

This sampling theorem can be applied to select sampling times for an entire

control process. If a digital control system is connected to a single measurement point,

then that measurement can be sampled as ohen as desired, or as rapidly as the computer

91

1

1

6 Selection of Design Parameters

can sample. However, rlpid sampling of 1 large number of measurement points may

unnecessarily load th~ computer Ind restnct Its ability to perform other tasks Sampllng

too slowly can also reduce the efTectlventss of the feedback control system. especla"y

its abllr:t to cope with disturbances. $0 It is dlfflcult to make any genel d Ilzatlons 011

the selection of sampling period. A number of gUldeline and rules for selectrng t',e sam·

pllng period have beoen reported (29). However. since the optlm um samplrng peflod IS

application-specifie, it is still believed that the best way to select the samplrng pcriod IS

to evaluate the entire process.

The efTect of the ~ampling penod on control system performance for the water

level protess has been evaluated Figure 6 2 to 6.5 show the dlscrete values of the control

and the manipulated variables for the drum water level process after a step change of the

steam load variable for th~ sample times L'lt=l. 2, 4, and 8 seconds For the relatlv.:>ly

small sample tlme ~t =1 second one obtalns a close approXimatIon to the cOlltrol behavlor

of a continuous PID-controller. For ~t=2 second .. the contlnuous signai of the control

variable can still be estlmated falrly weil for the process However, th,s IS no longer valrd

for L'lt=4 and 8 second. It can be seen from Figure 6 2 to 65 that a sample tlme L'lt = 2

sec. compared with l:!.t = 1 sec whlch is gaod approXimation of the '_ontlouous case, ledds

only to a small deterioration in control performance. If only the control performance /5 of

interest the sample time can usually be greater than that required to dosely approxlmate

the continuous control loop.

It should be noticed that the process condition is another factor that affects

the selection of the sampling period. If proc.ess conditions change significantly, then it may

be necessary to change the sample period. For example. In thls project, If the feedwater

flow rate is significantly increased, the residence time and hence the tlme constant for tl.e

92

6 Selection of Desi,n Parameters

drum water level system il reduced. Consequently, it may be necessuy to use a smaller

samplin, period in order to achieve satisfactory control. A simpler, more conservative

approach would be to select a samplin, period that corresponds to the worst possible

" condition, that is, the smallest samplin, period. But in this project, the controller design

is based on an identified process model, and parameter estimation methods are used

for the identification, 50 the sample time should not be too small in order to avoid the

numerical difficulties which result from the approximate linear dependence in the system

equations for small samp,le time.

This discussion shows that the sample time has to be chosen according to

many requirements which are partially contradictory. Therefore suitable compromises

must be found in each case

93

1

l'

6. Selection of Design Parameters

6

5 . .

J .. 3

1 1 2 . • 1

1

0

·1

·2 0 20 40 60 10 100 120 140 160 110 200

Tune. seconda

lA

1.2 . . ,

1

t G.I

j G.6

DA

G.l

0

-4.2 0 20 40 60 10 100 120 140 !fiO 110 200

Tune. leCOIIda

Filure 6.2 Transient response of the process for 10% incruse in steam flow with sample interval At=l second

94

1

1

6 Selection of Design Parameters

, r

~

1 ]

l 2

1 • 1 olJ \f-

·1 1 -- •

·2 0 10 20 30 40 50 60 70 10 90 100

nme, ......

1.2,---r----,--...,..----.----.---,-------.---.----..-----.

o .•

t J

0.6

o..

~ "1 o· 0 10 » JO 40 » 60 70 10 90 ICI)

11mI. .....

Fieure 6.3 Transient response o( the process (or 10% increase in steam flow with sample interval ~t=2 second

95

1 6 Selection of Design Parameters

6

5

J • 3

l 1 2

• 1

0

·1

·2 0 5 10 15 210 2.S lO 35 40 ., !O

nme. lec:oadI

0.9

1 O.,

1 G.1

0.6

o.s

G.4 1 0.3

0 , 10 15 JO 25 30 " 40 4S ~

nn.. ....

Figure 6.4 Transient response of the proceu for 10% incruse in steam flow with sample interval At=4 second

96

1 6 Selection of Design P3rameters

I~r-------~------~------~------~------'

1000

1 l ~ 1 .. 0

J

.10001.--___ ....... ____ ~ ___ __' _________ __J

OSlO 15

1.05.-------.-----....----....------T'"------,

o."

1 1 0.9

0.1,

o.. V

0.7', , 10 ., 210 2S

'1\me,'-'

Filur. 6.5 Trlnsient response of the proc:ess (or 10% inclease in steam flow with Simple intervil L'.t==8 second

97

1

Chapter 7 Presentation of the Results

ln this chapter the simulation results of the drum water level control system

will be evaluated. First, the closed loop response of the process wlth and wlthout the

feedforward controller will be presented. Then, the simulation results of feedback control

and combined feedback-feedforward control Will be compared Flnally, the simulation

results of the process closed loop response with the optimlzed controller par a meter settmgs

will be presented. Ali tests were performed on the Sun SPARC ™ workstatlon

7.1 Closed-Ioop Behavior of the Process

There are a number of criteria by which the desired performance of a closed

loop system can be specified in the time domain. For example, we could speclfy that the

closed-Ioop system be critically damped so that there is no overshoot or OSCillation We

must then select the type of controller and set its tuning constants so that Il will glve,

when coupled with the process. the desired closed-Ioop response Naturally the control

specification must be physically attainable. In the analysis of the closed·loop behavlor, not

only the stability of the control system is of concern but the quality of control performance

should also be considered. The analysis of the control quality is very much based upon

the specifications of the closed-Ioop response.

1 7 Presentation of the Results

7.1.1 Specification of Cloled-Loop Relponse

There .re • number of time-domain specifi('ations for closed-Ioop response.

But the specification to be selected must be physically attainable for the entire process.

ln this project, the dynamic specifications can be listed belt)w'

1) Closed-Ioop damping coefficient

2) Overshoot: the magnitude by which the controlled variable swings past the

setpoint

3) Rise t.me (speed of response): the time it takes the process to come up to

the set point

4) Decay ratio: the ratio of maximum amplitudes of successive oscillations

5) Settlin, time: the time it takes for the amplitude of the oscillations to decay

to some fraction of the change in setpoint

6) Integr.1 of the squared error:

Notice that the first five of these assume an underdamped c1osed-loop system,

i.e., one that has sorne oscillatory nature (the ,hum water level system is underdamped)

ln the design of the controller. what we want is a reasonable compromise

between performance (tight control; small closed-Ioop time constants) and robustness

99


(not too sensitive to ch~nges in process p~r~meters). This compromise IS ach,eved by

using ~ reason~ble clc~ed-Ioop d~mpinl coefficient to keep the real parts of the roots of

the closed-Ioop characteristic equ~tlon a reasonable distance from the IInaginary aXIS, the

point where the system becomes unstable.

The steady-st~te error is another specification. It 15 not a dynamic speCiflCa

-ion, but it is ~n import~nt performance criterion. In many loops ~ steady-state error of

zero is desired, i.e., the value of the controlled variable should eventually level out at the

setpoint.

7.1.2 Closed-Ioop 8ehavior Usina Feedback Control

The water level control system was evaluated by applying step changt's ln

the turbine governor valve area and observing the following tlme response water level,

steam pressure, steam mass flow rate and the feedwater flow rate The most Important

responses are the water level and feedwater flow rate The first one glves an indication

of the effectiveness of the control system ln performlOg Its main functlon The second

response shows the stability of the feedwater loop, wh,ch is the 'fastest'Ioop ln the system

and, as such, the most prone to exhibit unstable or underdamped behavlor

The effect of feedwater valve speed was first determlned Computer program

runs were conducted for different valve speeds, ranging from 2 to 40 second full stroke

time, without changing the controller parameter settings. Results of thls study Indicated

that the effect of the valve speed on controller performance was InslgniflCant A feedwater

valve with 20 second full stroke time was then selected since thls is an acceptable value

from the cost viewpoint.

100

l

-

7 Presentation of the Results

The effect of controller pu~meter seUings Kc, TI and TD' were then studied.

Computer progr~m runs, \Vith special ~ttention on system stability, were conducted. Re

sults of this study showed th~t the system performance is strongly affected by the settings

of A'c, TI and TD' By varyin, these parameters in a systematic way, a combination of

p.uameters was found for which the system response to a step change ln turbine gover

nor valve area was an optimum. The definition of 'optimal response' was based on the

inspection of the time response behavior (i.e., overshoot ar.d response time) rather than

a mathematical criterion.

Based on operating experience, the flow response of the fee·dwater loop (with

out water level and steam flow rate signais) was considered acceptable when the overshoot

was leu than 25 percent and the peak time not more than 2 second for a step change in

feedwater flow rate set point. In contrast, and in view of the lack of sufficient expenence

with large steam generators of the type studied here, it is more dif~cult to estabhsh a

performance criteria for the water level control system. However, it appears reasonable

to require that the water level return to the set point value within two minutes following

a step change in turbine governor valve area.

Studies on the controller parameter Kc indicate that the water level and feed

water flow response requirements impose lower and upper limits respectively, for this

parameter. However, there is a large range over which j(c can be varied without any

noticeable effect on system response. The upper and lower limits for the controller pa

rameter Kc were found to be equal to 0.5 and 3.0 respectively, which provides reasonable

freedom of final adjustment in the field.

Computer program runs on the controller parameter Tl show that, similar to

the case of j\c, the water-Ievel and feedwater response requirements respectively, impose

101

T

7 Presentltion of the Results

lower ind upper limits of this paumeter. Here, only i lower limlt of Tl = 0.5 sec

was established. The maximum possible value is best determlned under actual operatlng

conditions. However, an optimum response is achieved by choosing Tl = 10 sec Control

components for this optimum value are readlly avallable

The parlmeter TD' the differential time constant of the controller, also exerts

a large influence on system response. Computer program runs indicated that the optimal

value for TD is 0.25 sec, with upper li mit of 0 4 sec.

Typical water level responses for a vanety of controller parameter seUlngs are

shawn in Figures 7.2, 7 4, 7.6. These characteristics are determlned for a 10 percent

step increase in turbine governor valve area. In Figure 7.7, the water level behavlor is

shown for i step change in level set point

7.1.3 Feedbuk·Feedforward Control 8ehavior

The baSIC notion of feedforward control is to detect disturbances as they enter

the process and make adjustment in manipulated variables 50 that output variables are

held constant. We do not wait until the disturbance his worked .ts way through the

process and has disturbed everything to produce an error signal.

ln practice, many feedforward control systems are implemented by uSlng steady

state gain element (ratio control). In this project, in order to avoià any instantaneous

changes in the manipulated variables, a first-order lag is used in the feedforward controller.

Both dynamic element (first-order lag) and steady-state element feedforward control were

evaluated here.

102


Figure 7.8 ind 7.9 show the closed-Ioop response of drum water level change

to a 10 per cent step increase in lovernor valve irea for PlO and feedforward-feedback

control. A comparl50n of Figure 7.8 with 7.9 indlcates that feedforward controller design

using a dynamic element can result in sigllificantly improved load responses even though

the ideil feedforwud controller is approximited by a lead-Iag unit (see Figure 5 2 for lead

lag unit). In particular, the combined feedback-feedforwird controller is very effec.tive. A

compari50n of the controller output signils in the bottom portions of Figure 7.8 and 7.9

shows that the improved performance does not require excessive control action since the

required controller output responses in Figure 7.9 are comparable ln magnitude to those

10 Figure 7.8.

The parameter tuning for the feedforward controller was discussed in Chapter

5. Based on Equation (5 - 7) to (5 - 10), we can see the only independent variable in

parameter optimintion is P,(l) Using a trial-and-error procedure, it is very easy to fine

tune the parameter P,(l).

7.2 The Simulation Results

The time variation of the four most important steam generator variables is

shown in Figure 7.11 for a 10 percent step increase in turbine governor valvf area and

optimum controller seuings.

The control system wu tested for susceptibility to drift and noise. The results

have shown that the control system is not greatly effected by drift in feedwater valve

position or controller Input signais. The level variation approaches zero after a step change

in turbine governor valve area and remains at zero. The feeriwater f10w rate approaches

103

1 7 Present,tlon of the Results

a new steady-state value and then holds constant. Further runs of the digital program,

wlth noise injected lOto the system by a noise generator, have Indlcated that the control

system is not partlCularly affected by the noise ln feedwater valve position or lellel and

flow measuremtnt signaIs.

104


1 i .1

l

J l • 1

• 6

..

l

0

·2

... 0

Tune. leCOIlIb

K_cwl 0; ,_d-().23. U-5.0

3) 40 eo 10 100 13) 140 160 1. 200

......... IICXIIIIII

Figure 7.1 Step 'esponse of water level chan,e for a 10 percent step increase in turbine lovernor valve area for difTerent values of Kc

105

., " , f


) 1 1 i .. J

2

0

·1

·2 0

V 3) 40 CIO 80 100 120 140 160 110 200

nme. secmdI

---------

Figure 7.2 Step response of water level change for a 10 percent step Increase in turbine governor valve aru for different values of ne (Cont'd)

.-------------------------------------"--

j l a

k

) ,----,---r---.,.--"T---.....---....----,---,---"T---

2

o

·1

·2

·3~ __ ~ __ ~ __ ~ ____ ~ __ -L __ ~ ____ L-__ ~ __ _L ___ ~

o 3) 40 60 80 100 120 140 lM 180 200

Tune. seconds

Figure 7.3 Step response of water level change for a 10 percent step increase in turbine lovernor vllve area for different values of Tl

1

106


4 A

] U.S 0, K_cz2 0, ,_~.25

1 l

l a

1 0

V--1

-2 0 Il 40 60 10 100 120 140 160 110 lQO

TIme. leCOIIdI

J ] '_1=100: K_e-2.0,,_~.2J

l 2 1

1 0

·II....--~--~--~--~--~~--~--~--~--~---~ o Il 40 60 10 100 120 14C lC58 110 lQO

Filur. 7.4 Step response of water level chan,e (or a 10 percent step increue in turbine lovernor y.lve area for diff'erent values of TI (Cont'd)

107

1 7 Presenttltlon of the Results

j 1 o.

k

1 1 .1

!

3

2

1

o

-1

4

3

2

0

"

-2 0 :1)

60 10 100 120 140 160 110 200

Tune. seoonds

~---,--

t_cIaO 2.5, K_CZl2 O. U-=5

40 60 10 100 120 140 160 110 200

Tame. seconda

Figure 7.5 Step response o( water level change for a 10 percent step increase in lurbine lovernor valve area (or difTerent values of TD

108

•

f


4 -T

] l_d~.3'; K_os2 O. '_18 '

1 2

l • 1 0

-1

·2 0 20 40 !JO 10 100 120 l.a 160 110 200

11me.1eCODdI

Filur. 7.6 Step response o( water level chan,e (or a 10 percent step increase in turbine ,overnor valve arel (or difTerent values o( rD (Cont'd)

1 l •• f

4

3

2

10 20 3D 40 70 10 90 100

Figure 7.7 Response of water level (or a step change of 5 inches in set point

109

1 1

1 7 Presentation of the Rtsults

1 l 1 .. 1

" 3

2

o

·1

·2~--~--~--~----~--~---4--~----~--~---J o :m .eo fj() 10 100 120 140 l(il) 110 200

Figure 7.8 Closed-Ioop response of drum water level change to a 10 per cent step incruse in lovernor valve area (feedback control)

3

1 2

l J .. 1 0

V -1

-2 0 :m 40 60 10 100 120 140 III 110 2100

1'InII, lIiCIOIIdI

Filure 7.9 Closed-Ioop response of drum water level change to al 10 per cent step increase in governor valve area (feedforward-feedback control)

110

•

(


-------- -------_.-------------St

1 • 1

1 1

~f.1 ' , 1

j )

t ~ 2

• 1 .

0

·IL-__ ·~_~ __ ~ __ ~ ____ ~ __ ~ __ ~ __ ~ __ ~ __ ~ o ~ 4() 60 10 100 120 140 160 110 2100

4

2

1 f 0

J 1 -2

] J ~

1 -6 V

"0 20 ., CIO 10 100 UID 140 160 110 2100

TIme,"""

Filure 7.10 Step response of boile'. four most important variables for a 10 percent step increase in turbine lovernor valve aru for optimum controller set

tinls

111

1

l

L ..

1 PresentatIon o( the Reluits

4 ~ ].5 ~

1 ]

f 2.,

J 2

1 .. 1.'

1 O.,

0 0 ~) 40 60 10 100 120 140 160 110 200

nme, leCOIIdI

0 ~

-2

-4

1 ~

[ ...

J -10 .. -12

1 -14

-16

V -II

-20 0 20 40 60 10 100 120 140 160 110 200

11me, !eooadI

Filure 7.11 Slep response of boiler's four most important variables (or a 10 percent step increase in turbine governor valve area (or optimum controller settings

(Cont'd)

112

1

Chapter 8 Conclusions

The primary object of this thesis has been to develop a dynamic mathematical

model for the drum water level system and design a control system to apply on this model

as a controller. The model should be capable of simulating the transient responses in

both tlme and frequency domain. In the process , general simulation methods have been

developed. 8ased on the simulating transients of the process, an entire control algorithm

has been developed. The application of this model to the water level controller was tested

for stability and efficiency.

8.1 Drum Water level System Model

The model of the drum water level system has been derived based on the

conservati':m of mass, energy balance and the state equations of the system. Therefore,

the model is valid for liquid and low velocity steam f1ows, which ue the main variables

under study in this project.

The finite difFerence equation technique was chosen to develop the model for

two reasons. First by using this method, the complicated mass and energy equations can

be linearized so that the designed linear contro"er can be applied on this mode!. Second,

t 8 Conclusions

because the method is bued on relatively simple difTerence equations. a large system

simulator can be easily assembled from individual process models and therefore the method

is flexible. The linearized-model design method .1150 provides an analytlcal technique for

intergrating the controls of a strongly interacting process. The methods may .1150 be

particularly desirable under conditions of rapid load changes. and will have application for

improving the dynamic performance and traii;ïient stability of steam generating systems

using on li ne digital control.

It is irnperative to recognize that the water level swell is Inltiated from bOlier

pressure drop which causes rapid expansion of bubble volume in the water phase of both the

steam drum and the downcomer-riser loop. On the other hand. retardation of circulation

velocity reduces the bubble velocity in the water phase and therefore tends to increase the

water level swell. The simulated transient response of the model has proved that the model

can predict swell and shrink of the water level. The results .1150 support the feaslbllity of

using simplified linearized models for the online digital control of this nonlinear process.

8.2 Simulation Methods

The most important part of any process simulator is the solution algorithm. In

this thesis, the iteration method, a simple and fast optimum load allocation algorithm is

introduced. It is specifically adapted to the boiler drum water level system. The Iteration

m~thod is computationally compact. The great majority of instructions are nothing more

than elementary arithmeti..: or simple logical instructions. It can be practically and easlly

implemented as a computer program. The Ruga-KuUa method has been uscd as a

stad :'lg point to solve the linearized equations. The iteration method has in(orporated

a fine-tuning procedure which will maintain, but more usually improve upon, the cost

114

1

-

B Conclusions

correspondin, to this startin, point.

A larce portion of this work involved the development of variable step-size

multistep ilgorithms to optimize the speed and accuracy of the simulation by varying the

solution time step. In the development of the simulation algorithm. the four-step Adams

Bashforth method wu employed as predictor and the three-step Adams-Moulton method

as corrector in the error control procedure. These methods are multistep methods which

use approximation at more thin one previous step to determine the approximation at the

nex! step. Because of the 'multistep', these methods will generate a more accurate result

thin the 'one-step' method.

Employing the simulation method and time-to-frequency domain transforma

tion technique developed in this thesis, the dynamic behavior of the plant model was

evaluated both in the time-domain and the frequency-domain. In the time-domain, the

dependence of the system variables on time was obtained by solving the differential equa

tions describins the system. These dynamic functions tell us what is happening in the

real world (here in simulation) as time increases. In the frequency-domain, the dynamic

rel.ltionships between ih.,&ll variables and output variables were evaluated. From the time

and frequency domain response of the process, a set of closed-form transfer function was

estimated to describe the drum system.

8.3 Cor~t,ol Aigorithm

This thesis presented the development of a methodology for the design and

.n.llysis of drum water level system control and its application to the control of con ven

lional, drum-type. single reheat boilers. The design methodology is based on conventional

115

1 8 ConclusIons

control theory, incorpo"tes feedforw.rd, provides , method of state reconstruction, re-

t.ins the steady state accuracy adv'ntage of classical PlO controllers and is not dependent

upon unreason,ble model precision.

The application to the design .nd .nalysis of digital combined feedback-

feedforwifd control has been successful and the question as to whether or not the appli-

cation of modern digital control by simulation can improve the control of the conventional

boiler has been ,nswered. The improvement in dynamic response which can be obtdined

is shown to be quite significant. The simulation results were obtained using the hnearized

model from the nonlinear equations and the control system performed weil

The digital feedback·feedforward control scheme offers the posslbllity of achlev-

ing a closed·loop system performance which is comparable with the analogue scheme when

the sampling period is sufficiently short. In common with conventlonal analogue scheme

of control, digit,1 control systems may not require the development of the detalled process

dynamic model which 15 mandatory for convention al control schemes. The digital control

system was found to be more sensitive to the choice of sampling period than conventional

control schemes.

ln the study of digital feedback-feedforward control scheme, the selectIon and

adjustment of the control system parameters, to obtain acceptable transient responses,

presented very liule difficulty. Ali the systems were found to provide rapid seUling, with

zero steady·state offset in the controlled process variables, after input disturbances.

The study has iIIustrated the feasibility of applying optImal digital control to

a boiler model, based on minimization of a performance index related to state variables

and system inputs. A realistic stable system has been produced using the concepts of

116

, 8. Conclusions

dynJmic prl..orammIOI. Stability can be ensured by usinl the Ziegler-Nichols method.

The ZN me,"od has incorporated a controller parameter tuning procedure to improve the

system's s/,:~bility. Bued on the tuninl procedure, plus consldering the specifications of

the syste",'·, closed-Ioop behJvior, an optimal control performance has been obtained.

8.4 Future Work

The scope of development of mathematical model and control systems for

engineering thermal-fluid processes is virtually endless. Just for the boiler simulator alone,

many models and control s,'stems ha~e yet to be developed. From a modeling point of

view, any of the following could be possible subjects of future research:

• primary superheater

• superheater spray

• secondary superheater

• turbine

• reheater spray

• reheater

• mills

• combustion

• superheater furnace

117

1

t

8 Conclusions

• reheiter furnice

• fan ind pump

ln th~ modeling and simulation of any of the above elements, the methodology

introduced in this thesis could be applied. Idealy, for instance, in modelmg and simulatlng

the combustion loop of the boiler. the variable step-size multistep algorithm could be used

with the boiler efficiency curve to maintain the boiler operating at maximum efficiency.

From i control point of view, the following two loops could be subJects of

future study in the development of a boiler simulator.

• the combustion loop

• the steam-temperature loop.

The concept of two level control could be adapted ln a future development of

the whole boiler control simulator. The control of each individual process (e g combustion

loop) cou!d be considered as the low level controls. The control methods developed in

this thesis could be used in the control for each indlvldual loop at the lower level The

system level control would supervise the low level controls, calculate and process the input

variables. and transfer variables between the two levels and the low level controls. In the

development of the two level control for boiler simulation, parallel-processing could be

adopted since the two level concept would be well-sulted to parallelization. The system

level solution could be put on one processor to monitor solution convergence, calculate

time steps and trinsfer ~tream variables. The individual process models. distrlbuted in

space over the remaining parallel processors, would compute the single Iteration of the

solution without any externat requirements other than their input/output stream variables.

118

1 8 Conclusions

Further investigation mly reveal the true optimal system concerned with bal-

ancing boiler efficiency a,ainst loss of steam generation, and with steam-fJow-control at

the turbine governor valves under sliding pressure and temperature conditions The same

type of analysis may alsa be extended to the optimiution of the overall steam-generation

process, usine an inte,rated control system including effects of turbines and generators,

with energy input controlled from steam demand, and with the turbine valve regulated

for constant steam pressure.

119

1

,-..

References

References

(1] Amir, N. N., Abram, B., "Steam Generator Water-Level Control". rrans ASME, Journal of Basic Engineering. vol 88. 1966. pp 343-353.

(2] Anderson, J. H., "Dynamic Control of a Power Boiler". PROC. IEE. vol 116.

No. 7,1969.

(3] Auslander, D. M., Takihashi. Y., Tomizuka, M., "The Next Generation of Single loop Controllers: Hardware and Aigorithm for the Discrete/Decimal Process Controller", Trans ASM E, Journal of Oynamic Systems. Measurement, and Control, vol. 97, 1975, pp. 280.

[4] Chien, K. l., Ergin, E. J , Ling. C , Lee, A , "Dynamic Analysis of a BOlier".

T,ans ASME, vol. 80, 1958, pp. 1809-1819

[5] Chien, K. l.. Ergin. E. 1.. ling. c., "The Non-Interactmg Controller for a Steam Generating System", Control Engineering, vol 5. 1958, pp 95-101

[6] Connor, S., "Boiler Controls: Where They've Been, Where They're GOlng" ,

InTech Industry, April, 1989, pp. 36-38.

(7] Daniels, J. H., Enns, M., l-!ottenstine. RD., "Dynamic Representation of a Large Boiler-Turbine Unit", ASM E, Paper 61-5A-69, June. 1961.

[8] Ergin, E. 1., Ling. C, "Development of a Non-Interacting Controller for BOliers", Proe. lst InternationallFAC Conference. Moscow, vol. 4, 1960. pp 347

[9] Goldstein, P., uA Research Study on Internai Corrosion of Hign-Presure BOli

ers", Trans ASME, Journal of Engineering for Power, vol 90. 1968. pp. 21-37.

(10] Hougen, J. O., Hagber,. C. G., FrICke. l. H., Martin, O. R., "Process Identi

fication and Design", Chemical Engineering Progress. vol. 60, no 8, 1964.

[11] Hughes, F. M., Mallouppa, A., "Frequency Response Methods for Nuclear Station Boiler Control", Automatica, vol. 12. pp. 201-210, 1976

[12] Isermann, R., "Digital Control System" , Springer-Verlag. 1981.

(13] James, M. l.. Smith, G M., Wolford, J. C, "Applied Numerieal Methods

for Digital Computation", Harper & Row, Publishers, 2ed edltlon, New York.

1977.

[141 Jury, E. 1., "Sampled-Data Control Systems", John Wlley &. Sons. Ine .. New

York,1958.

120

1 References

(15) Kwan, J. P., Anderson, H. G., liA Mathematical Model of a 200MW Boiler", International Journal of Control, vol. 12, No. 6, 1970, op. 977-998.

(16) Lansin" E. G., 'Variable Pressure Peakin, BoHer, Operation, Testing. and Control". Trans ASME. Journal of Engineerint, for Power, vol. 97, 1975. pr 435-440.

(17J Luyben, W. L., "Process Modelin" Simulation. and Control for Chemical Engineers", McGraw-Hi". Inc., New York. 1990.

(18) MacDonald. J. P., Kwatny, K. G., Spare, J. H., "Non-linear Madel for Reheat Boiler-Turbine-Generator Systems Part 1 - General Description and Evaluation". Proc. 12th Joint Automatic Control Conference. Washington University. St. Louis, Missouri. August 11-13. 1971, pp. 219-226.

119) MacDonald, J. P., Kwatny, K. G .• Spare, J. H .• "Non-linear Madel for Reheat Boiler-Turbine-Generator Systems Part U - Development", Proc. 12th Joint Automatic Control Conference. Washington University, St. Louis, Missouri, August ll-13, 1971, pp. 227-236.

(20) MacDonald, J. P .• Kwatny, H. G., "Design and Analysis of Boiler-TurbineGenerator Con trois Using Optimallinear Regulator Theory". Proe. 12th Joint Automatic Contrel Conference, Washington University, St. Louis. Missouri, Au,ust ll-13, 1971.

(21) Morse, R. H., Brey, R. N., "An Electronic Feedwater Control System for the Experimental Boiling Water Reador", Nuclear Engineeril"î ~nd Science Conference, Session XVII, March 17-21, 1958.

(22) Nahavandi, A. N., yon Ho"en, R. F., "A Space-Dependent Cynalllic Analysis of Boilin, Water Reutor Systems", Journal of the American NucJear Society, Nuclear Science and Engineerin" vol. 20, 1964, pp. 392-413.

(23) Nicholson, H., "Integrated Control of a Nonlinear Boiler Madel", PROC. IEE, vol. ll4, no. 10, 1967, pp. 1569-1576.

(24) Nicholson, H., "Dynamic Optimization of a Boiler" PROC. IEE. vol. Ill, No. 8, 1964. pp. 1479-1500,.

(25J Poon, K. L., "EfTect of Rapid Steam Take-OfT on Natural Circulation and Water Level in Boilers", Trans ASME, Journal of Engineering for Power, vol. 97, 1975, pp. 645-654.

(26) Poon, K. L.. Chiu, P. c., "Changes in Water Level due ta Swell in a PoolBoilin, Plant", Journal of Mechanical Engineering Science, vol. 15, 1973, pp. 329-338.

121

1 1 L

1 References

(27) Robinson. R. W., H~nson, R. A., "Obtaining Baseline Data for Boiler Optimization", ISA, InTech, pp. 61-64, 1984.

(28) Roffel, B., Rijnsdorp, J. E., "Process Dynamics, Control and Protection", Ann Arbor Science Publishers, Michigan, 1982.

(29) Seborg, D. E., Ed,u, T. F., Mellichamp, D. A., "Process Dynamics and Control", John Wihey Il Sons, Inc., New York, 1989.

(30) Takahashi, V., Tomizuka, M., Auslander, D. M., "Simple Discrete Control of Industrial Processes (Finite Time Setting Control Aigorithm for Single-Loop Digital Controller)", Trans ASME, Journal of Dynamic Systems, Measurement, and Control, vol. 97, 1975, pp. 354-361.

(31) Thompson, F. T., "A dynamic Model of a Drum-Type Boiler System", IEEE Transactions on Power Apparatus and Systems, vol. PAS-86, No. 5, 1967,

pp. 625-635.

[32] Unbehauen, H., Schmid, c., Bouiger, F., "Comparison and Application of DOC Aigorithms for a Heat Exchanger", Automatica, vol. 12. pp 393-402.

1976.

(33) Vaitekunas, D. A., "A Generic Dynamic Model for Crossflow Heat Exchangers With One Fluid Mixed" Master Th es;s , McGili University, 1990.

(34) Wu, S. Z., Wormley, D. N., Rowell, O., Griffith, P., "Boiler Implosion Control in Fuel Power Plants" Trans ASME, Journal of Oynamic Systems. Measurement. and Control, vol. 107, 1985, pp. 267-269.

[35] Zhao, J., Vroomen, L. J., Zsombor-Murray, P. J., "Design of Boile. Drum Level Control by Simulation", Proe. Computer Applications in Design, Simulation and Analysis, ISMM, New Orleans, March 5-7, 1990, pp. 253-256.

122

Appendix A Sample Values of Frequency w

Appendix A. Sample Values of Frequency w

""1 = 0.010 ""18 = 0.501 ""35 = 5.012

""2 = 0.013 W19 = 0.631 ""36 = 5.623

""3 = 0.016 W20 = 0.794 ""31 = 6.310

W4 = 0.020 W21 = 1.000 ""38 = 7.079

Ws = 0.025 W22 = 1.112 ""39 = 7.943

W6 = 0.032 W23 = 1.259 W40 = 8.913

W7 = 0.040 W24 = 1.413 W41 = 10.00

W8 = 0.050 W2S = 1.585 W42 = 12.59

""9 = 0.063 W26 = 1.778 W43 = 15.85

""10 = 0.079 W21 = 1.995 "'-'44 = 19.95

Wu = 0.100 W28 = 2.239 W45 = 25.12

W12 = 0.126 W29 = 2.512 W46 = 39.81

""13 = 0.158 WlO = 2.818 W41 = 50.12

""14 = 0.200 Wl1 = 3.162 W48 = 63.10

""15 = 0.251 Wl2 = 3.548 W49 = 79.43

W16 = 0.316 Wl3 = 3.981 W50 = 100.0

Wl7 = 0.398 W34 = 4.467

123

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