Design and implementation of embedded adaptive controller using ARM processor

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Masters Theses Masters Theses and Graduate Research

Fall 2009

Design and implementation of embedded adaptivecontroller using ARM processorHoan The NguyenSan Jose State University

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DESIGN AND IMPLEMENTATION OF EMBEDDED ADAPTIVE CONTROLLER

USING ARM PROCESSOR

A Thesis

Presented to

The Faculty of the Department of Computer Engineering

San Jose State University

In Partial Fulfillment

of the Requirements for the Degree

Master of Science

Hoan The Nguyen

December 2009

UMI Number 1484326

INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted

In the unlikely event that the author did not send a complete manuscript and there are missing pages these will be noted Also if material had to be removed

a note will indicate the deletion

UMT Dissertation Publishing

ProQuest LLC 789 East Eisenhower Parkway

PO Box 1346 Ann Arbor Ml 48106-1346

copy2009

Hoan The Nguyen

SAN JOSE STATE UNIVERSITY

The Undersigned Thesis Committee Approves the Thesis Titled

DESIGN AND IMPLEMENTATION OF EMBEDDED ADAPTIVE CONTROLLER USING ARM PROCESSOR

by Hoan The Nguyen

APPROVED FOR THE DEPARTMENT OF COMPUTER ENGINEERING

mdashr ~ mdash^ yy

Dr Donald Hungry Department of Computer Engineering Date

Dr Lee Chang Department of Computer Engineering Date

Dr Xiao Su Department of Computer Engineering Date

APPROVED FOR THE UNIVERSITY C

Associate Dean Office of Graduate Studies and Research Date

ABSTRACT

by Hoan The Nguyen

This thesis is concerned with development of embedded adaptive controllers for

industrial applications Many industrial processes present challenging control problems

such as high nonlinearity time-varying dynamic behaviors and unpredictable external

disturbances Conventional controllers are too limited to successfully resolve these

problems Therefore the adaptive control strategy an advanced control theory is applied

to overcome deficiencies of the conventional controllers

Through the thesis an embedded adaptive controller is designed and implemented

for the specific case study a gasoline-refining plant The adaptive controller design is

initially achieved in continuous-time space and then converted to discrete-time space by

using z- transform It is finally implemented on an advanced reduced instruction set

computer machine (ARM) processor A plant simulator written in C++ executes

functions of the gasoline-refining plant Therefore an integrated testing environment is

developed in order that the embedded adaptive controller can interact in real-time fashion

with the plant simulator located in a remote computer In all system tests the embedded

adaptive controller successfully controlled the remote plant simulator and fully satisfied

all control objectives

ACKNOWLEDGMENTS

I wish to express my gratitude to my advisor Dr Donald Hung I am most

grateful for his invaluable advice and for the freedom he allowed me in conducting my

research I admire the illuminating inspiration of his ideas and his ability to motivate

people

I would like to thank Dr Lee Chang and Dr Xiao Su for serving as the members

of my thesis committee

TABLE OF CONTENTS

List of Tables xiv

List of Figures xvi

List of Abbreviations xxi

List of Symbols xxii

Chapter 1 Introduction 1

11 Background 1

12 Statement of the Problem 2

13 Objectives of the Study 3

14 Scope of the Study 4

15 Methodology 5

Chapter 2 Literature Review 7

21 Gasoline Refinery 7

22 Distillation Equipment 7

23 Distillation Operation Principles 9

24 Methods of Distillation Column Control 10

25 Principles of Adaptive Control 11

26 Adaptive Schemes 13

261 Gain Scheduling 13

262 Model Reference Adaptive Control Systems 14

27 Lyapunov Stability Theory 14

271 Definition of Lyapunov Stability 15

272 Lyapunov Stability Theorem 16

273 Lyapunov Function 16

28 ARM Processor 16

281 System Architecture of ARM Development Board 17

282 Memory Organization 19

Chapter 3 Plant Modeling and Simulation 20

31 Introduction 20

32 Process Description 20

33 Process Calculation 21

34 Process Description and Control Scheme 22

35 Plant Modeling 22

36 Plant Simulation 24

Chapter 4 Analog Controller Design 26

41 Introduction 26

42 System Architecture 26

43 Construction of the Reference Model 27

431 Stability Test 30

432 Controllability and Observability Test 30

44 Analog Controller Synthesis 31

441 Plant 31

442 Reference Model 32

443 Feedback Control Loop 32

444 Compatibility Condition 33

445 Error Equation 35

446 Adaptation Law 36

447 Stability of the Analog Controller 37

45 Analog Controller Simulation 38

451 Simulation Program 38

452 Simulation Result 39

453 Error Reduction 42

Chapter 5 Digital Controller Design 43

51 Introduction 43

52 Digital Controller Synthesis 44

521 Plant Model 44

523 Linear Feedback Controller 45

525 Adaptive Mechanism 47

Chapter 6 Simulation of the Adaptive Digital Controller 50

61 Introduction 50

62 Dynamic Simulation Using MATLAB 50

622 Error Calculation 51

623 MATLAB Simulation Result 52

63 C++ Simulation Project 55

631 Plant Model Class 55

632 Reference Model Class 57

633 Linear Control Class 58

634 Comparator Class 59

635 Adaptive Mechanism Class 60

636 Create Makefile and Build Project 62

637 C++ Simulation Result 62

Chapter 7 Implementation of the Embedded Adaptive Controller 66

71 Introduction 66

711 Embedded Adaptive Controller Using ARM Processor 66

712 In-Hardware Validation Scheme 67

713 System Architecture and Operations 68

714 Kernel Image of the ARM Board 72

72 Common Database 73

73 Plant Simulator 74

74 Development of the Main Testing Form in HTML 75

75 Adaptive Mechanism Program 77

751 CGI Program 78

752 NFS Server Setup 82

76 Building the Kernel Image 84

761 NFS Client Setup 84

762 Enabling the CGI Protocol 87

763 Enabling the Boa Web Server 89

77 Testing 93

771 Test Procedure 93

772 Test Results 98

Chapter 8 Conclusion and Future Work 104

81 Conclusion 104

82 Future Work 105

Appendix A Distillation Control Techniques 109

Al Column Pressure Control 109

All Coolant Manipulation 109

A12 Vent-bleed 110

A2 Column Level Control 111

A3 Methods of Distillation Column Control 113

A31 Degrees of Freedom of Distillation Process 113

A32 Control Structures 114

A33 Energy Balance Structure 116

A34 Material Balance Structure 117

Appendix B Process Calculation 119

Bl Basic Engineering Data 119

B2 Distillation Process Calculation 122

B21 Equilibrium Flash Vaporization Curves 122

B22 Yield of Fractions 123

B23 Operating Pressure 124

B3 Calculation for the Feed Section 124

B31 Description 124

B32 Calculation 125

B4 Calculation for the Stripping Section 126

B41 Description 126

B42 Calculation 127

B5 Calculation for the Rectifying Section 128

B51 Description 128

B52 Calculation 129

B6 Calculation Results 131

B61 Raw Gasoline Property 131

B62 Main Stream Property 131

B7 Process Description 132

B71 Simplified Process Flow Diagram 132

B72 Distillation Column 133

B73 Blending System and Product Distribution 134

B74 Feed Control 135

B75 Top Column Section 136

B76 Bottom Section 136

Appendix C Mathematical Model 137

Cl Introduction 137

C2 Dynamic Study of Distillation Process 138

C21 Generic Trays 138

C22 Feed Tray 140

C23 Top Section 141

C24 Bottom Section 143

C3 Mathematical Model of Distillation Process 145

C4 Simplified Model 145

C5 Mathematical Model of the Gasoline Refinery 147

C51 Relative Volatility 147

C52 Latent Heat and Boilup 147

C53 Liquid Holdups on Tray and Column Base 148

C54 Liquid Holdup in Reflux Drum 150

C6 Basic Mathematical Model of the Plant 150

Appendix D Dynamic Simulation 154

Dl Modular Decomposition of the Column 154

D2 Simulation with MATLAB Simulink 155

Appendix E Construction of Reference Model 161

El Model Construction 161

E2 Stability Test 167

Appendix F Source Code 169

Fl Adaptive Mechanism 169

F2 Plant Model 170

F3 Reference Model 171

F4 Linear Controller 172

F5 Comparator 173

F6 Controlled Output 174

F7 Reference Outputs 175

F8 CGI Program 175

Appendix G MATLABC++ Simulation Output Files 198

Gl State Variables Files 198

G2 Reference and Controlled Outputs 202

G3 Plant Error 206

G4 Adaptive Gains 210

Appendix H Hardware Validation Output Files 214

Hl Validation Output Files of State Variables 214

H2 Reference and Controlled Outputs 218

H3 Plant Error 222

H4 Adaptive Gains 225

References 230

LIST OF TABLES

Table 21 Main parameters of a distillation column 9

Table 22 Main features of the ARM-7 development board 18

Table 31 Main streams of the plant 21

Table 32 Steady-state compositions of the plant 25

Table 41 Plant output errors for different adaptation rates 42

Table 71 Structured data files 73

Table 72 Some key features of an HTML form 76

Table 73 Structured output data files 98

Table 74 Output data of state variables 99

Table 75 Comparison result between the embedded and software models 102

Table A 1 Manipulated variables and controlled variables of a distillation column 114

Table A2 Typical column control structures 115

Table Bl Condensate composition analyzed by gas chromatography 119

Table B2 Distillation data 120

Table B3 Gasoline quality requirement 121

Table B4 Relationship between ASTM TBP and EFV 122

Table B5 Material balances for the feed section 126

Table B6 Material and energy balances of the stripping section 128

Table B7 Material and energy balances around the boundary (A) 130

Table B8 ASTM distillation curve of the raw gasoline 131

Table B9 Main streams of the plant 132

Table Cl Parameters of a generic tray 138

Table Gl Simulation result of state variables 198

Table G2 Simulation result of reference and controlled outputs 202

Table G3 Simulation result of plant errors 206

Table G4 Simulation result of adaptive gains 210

Table Hl Validation result of state variables 214

Table H2 Simulation result of reference and controlled outputs 218

Table H3 Simulation result of plant errors 222

Table H4 Simulation result of adaptive gains 226

LIST OF FIGURES

Figure 21 Distillation column 8

Figure 22 Contacting between vapor and liquid phases at a tray 9

Figure 23 Energy balance control structure 10

Figure 24 Block diagram of an adaptive system 12

Figure 25 Procedure for selection of an appropriate adaptive scheme 12

Figure 26 Block diagram of a system with gain scheduling 13

Figure 27 Block diagram of a model reference adaptive control scheme 14

Figure 28 Illustration of Lyapunov stability 15

Figure 29 System block diagram of the ARM development board 17

Figure 210 Memory map 19

Figure 31 Simplified diagram of the condensate distillation 20

Figure 32 Process flow diagram of the gasoline refinery 22

Figure 33 Vapor liquid equilibrium relationship 24

Figure 34 Simulation result of the concentration on each stage 25

Figure 41 System architecture of the adaptive control system 26

Figure 42 Two-input two-output representation for the plant 28

Figure 43 Bode responses of two models 29

Figure 44 Simulation program for the analog adaptive controller 38

Figure 45 External disturbances 40

Figure 46 Reference states and plant states 40

Figure 47 Controlled outputs and reference outputs 41

Figure 48 Plot of plant output errors during simulation 41

Figure 51 Input and output signals of ZOH 43

Figure 52 Block diagram of a sampled-data system 43

Figure 53 Logic diagram of the adaptation law 48

Figure 61 Simulation program for the digital adaptive system 51

Figure 65 Error plots 54

Figure 66 Plant classs header file 56

Figure 67 Reference model classs header file 57

Figure 68 Linear control classs header file 59

Figure 69 Comparator classs header file 60

Figure 610 Adaptive mechanism classs header file 61

Figure 611 Running the adaptivecontrol executive file 63

Figure 612 State variables 63

Figure 614 Plant output errors 64

Figure 71 Elementary block diagram of the system 66

Figure 72 In-hardware validation scheme 67

Figure 73 Integrated testing environment 68

Figure 74 NFS clientserver interaction for mounting a network file system 69

Figure 75 Sequence diagram 71

Figure 76 Compile and build the plant simulator in a console terminal 75

Figure 77 Main testing form in HTML 76

Figure 78 Pseudo code of the adaptive mechanism program 78

Figure 79 Flow chart of the CGI program 80

Figure 710 Pseudo code of the CGI program 82

Figure 711 Enable NFS server for Ubuntu machine 83

Figure 712 Check rpc daemon status 83

Figure 713 Select network file systems 84

Figure 714 Select NFS supports 85

Figure 715 Select the mount option 85

Figure 716 Select the umount option 86

Figure 717 Modifications for Busybox Makefile 87

Figure 718 Start xinetd for Linux Ubuntu 91

Figure 719 Manually load the kernel image to the ARM board 92

Figure 720 Manually run the kernel image 92

Figure 721 Process status 93

Figure 722 Mount network files for the NFS client 94

Figure 723 Ping ARM board from the Linux machine 95

Figure 724 Ping the Linux machine from the ARM board 95

Figure 725 Open the main page of Boa web server 96

Figure 726 Start the plant simulator in a Linux machine 97

Figure 727 Testing result displayed on the web browser 97

Figure 728 Testing result displayed on the plant simulators monitor 98

Figure 729 Variable states during simulation of the embedded adaptive controller 101

Figure 91 Block diagram of the experimental pilot plant 106

Figure 92 Adaptive mechanism programmed in a PLC 107

Figure 93 Integrated testing environment for SoCs and other digital systems 108

Figure Al Column pressure control using coolant manipulation 110

Figure A2 Column pressure control using vent bleed I l l

Figure A3 Some typical types of reboiler 112

Figure A4 Energy balance structure 116

Figure A5 D-V control structure 117

Figure A6 L-B control structure 118

Figure Bl Yield curve 124

Figure B2 Equilibrium phase flows at the feed section 125

Figure B3 Equilibrium phase flows at the stripping section 127

Figure B4 Equilibrium phase flows at the rectifying section 129

Figure B5 Simplified process flow diagram of the gasoline plant 133

Figure B6 A local control devices for feed pumps 136

Figure Cl A generic tray 138

Figure C2 Variation of liquid depth across a generic tray 139

Figure C3 Feed section 140

Figure C4 Top section 141

Figure C5 Bottom section 143

Figure Dl Modular decomposition scheme for the distillation column 154

Figure D2 Hierarchical structure of the simulation program 155

Figure D3 Main program in MATLAB Simulink 155

Figure D4 Module of the rectifying section 156

Figure D5 Module of the stripping section 157

Figure D6 Module of the column base and reboiler 158

Figure D7 Module of a generic tray 158

Figure D8 Module of the feed tray 159

Figure D9 Module of the eighth tray 159

Figure D10 Module of the condenser and reflux drum 160

Figure El Model of a generic tray 161

LIST OF ABBREVIATIONS

American Petroleum Institute

Advanced RISC machine

American Society for Testing and Materials

Common gateway interface

Distributed control system

Equilibrium flash vaporization

Liquefied petroleum gas

Multi-input multi-output

Motor octane number

Model-reference adaptive control

Methyl tert-butyl ether

Network file system

Personal computer

Proportional integral differential

Programmable logic controller

Reduced instruction set computer

Research octane number

Reid vapor pressure

Single-input single-output

True boiling point

Zero-order hold

LIST OF SYMBOLS

A State matrix

B Input matrix

C Output matrix

e State error

L Feedback matrix

M Feedforward matrix

u Control signal

x State variable

y Controlled output

Greek Symbols

a Relative volatility

y Adaptation rate

0 Adaptive gain

Subscript

B Bottom product

D Distillate or overhead product

F Feed

m Reference model

r Reduced-order model

CHAPTER 1

INTRODUCTION

11 Background

We have seen that the price of microprocessors has dropped significantly since

their creation in the early 1970s As a consequence microprocessors have increasingly

become the main part of many control systems In the 1980s microcontrollers were

developed due to the integration of microprocessors and other peripheral devices in the

same chip Microcontrollers have widely increased applications of embedded systems

due to their low cost and high performance Therefore embedded controllers using

microprocessors such as ARM processors are aspired to develop for robotics and

industrial applications

ARM processor has a 32-bit RISC architecture invented by ARM Company

There are various ARM processors however they are based on a common architecture

and provide high performance low power consumption and reduced cost They are

licensed by most of leading semiconductor manufacturers who have shipped more than

ten billion ARM processors since the company was established in 1990 [1]

In this study an embedded adaptive controller is designed and implemented for a

gasoline refinery In the petroleum refining industry distillation is the most popular and

important process Crude oil a mixture of thousands of organic substances is refined by

the distillation process to produce a host of liquid fuels pure chemical substances and

petrochemicals [2] The size of the refining industry is truly immense with the total

processing capacity of approximately 4 billion tons per year [3] In addition the

percentage of energy consumption by distillation is very high about 40 for a typical

chemical plant [4] Humphrey [5] estimates that with advanced control strategy there is

potential for an average 15 reduction in the energy consumption by distillation in the

United States refining industry Therefore enhancement of distillation control would

result in major economic improvement for petroleum refineries

12 Statement of the Problem

Distillation processes are highly multivariable and nonlinear The dynamic

analysis and simulation of a distillation process are thus very complicated Its theoretical

model can contain several hundreds of state variables however in practice the amount

of information on the process is usually insufficient Therefore reduced state space

models should be employed [6]

Distillation processes are multiple-input multiple-output (MIMO) systems

Conventional PID controllers normally employ a single-input single-output (SISO)

approach with appropriate pairings For distillation processes a controlled variable is

affected by many manipulated variables so that conventional controllers will have

multiple control loops Consequently there exists coupling which causes serious

problems particularly in the cases of high-purity distillation systems De-couplers are

usually deployed to reduce the interaction between the control loops However the SISO

approach with pairing and de-coupling is only partially successful Shen and Lee [7]

believe that the use of multivariable controllers such as adaptive controllers can greatly

improve the situation since they treat the MIMO process as a single system instead of

many individual subsystems

Time-varying dynamic behaviors of distillation processes and the existence of

unpredictable external disturbances also present challenging control problems If

conventional controllers such as PID controllers are used they must be re-tuned for

different operating conditions This task is costly time-consuming and even unfeasible

Unlike conventional controllers adaptive control systems use special adaptation

mechanisms that can self-adjust their control settings to compensate unanticipated

changes in the process or in the environment [8] Therefore adaptive control strategy has

been progressively applied for solving the difficult control problems [9]

There has been some research on applying adaptive control strategy to distillation

processes For example Nguyen and Afzulpurkar [10] propose an adaptive control

system for a natural gasoline plant and Narenda and Annaswamy [11] suggest an

adaptive scheme for distillation column However most of these works focus on

continuous-time space To implement adaptive algorithms on digital computers they

must be discretized using z-transform

After the embedded adaptive controller is successfully implemented it must

interact with either a real pilot plant or a software-based plant simulator running on a

remote computer to close the control loop and allow real-time data transfer between the

plant and the controller Therefore an integrated testing environment must be developed

to be able to verify the controller performances

13 Objectives of the Study

The structure of distillation as well as other chemical processes has become

increasingly complex due to better management of energy and raw materials Hence the

design of the control system for a complete plant has become intimately related to the

design of the process itself [12]

In this study we design and implement the embedded adaptive controller and

plant simulator through various phases 1) development of mathematical model 2)

process calculation and modeling 3) controller design in both continuous-time and

discrete spaces and 4) hardware implementation and testing The objectives of the study

are described as follows

bull Create adaptive algorithms for the plant using Lyapunov stability theory

bull Design adaptive controllers for the plant in both continuous-time and discrete-

time spaces

bull Create a software-based plant simulator which executes functions of the

gasoline plant and its local auxiliaries

bull Implement the embedded adaptive controller using an ARM processor which

fully satisfies all control objectives under different operating conditions of the

bull Develop an integrated testing environment for verification of the embedded

adaptive controller

14 Scope of the Study

Building a pilot plant is not feasible for this study since it is very expensive

Hence identification method which requires operational data of the plant is not

applicable Instead the reference model of the gasoline refinery will be developed using

mathematical method

The embedded adaptive controller will be implemented on an ARM-7

development board It will interact with the plant simulator written in C++ language on a

remote computer through an Ethernet network

15 Methodology

The plant simulator a software simulator is created to play the roles of the

distillation column and other local auxiliaries The embedded adaptive controller is an

adaptive mechanism that governed by an adaptation law and programmed in the ARM

kernel image The embedded adaptive controller is thus physically an ARM processor

residing on an ARM development board An integrated environment is developed via an

Ethernet for testing the adaptive system The major steps in this study are as follows

bull Study the plant dynamics and adaptive control strategy

bull Develop the mathematical model of the plant

bull Perform the plant simulation using MATLAB a numerical computing

environment and fourth generation programming language developed by

Math works [13] to obtain the steady-state data

bull Construct the reference model of the plant using mathematical approach to

prepare for the next phase of adaptive controller design

bull Design the analog adaptive controller for the plant in continuous-time space

based on Lyapunov stability theory

bull Discretize the adaptive system using z-transform and design the digital

adaptive controller in discrete-time space

bull Simulate both analog and digital designs using either MATLAB or C++ and

verify their control performances

bull Implement the embedded adaptive controller on an ARM development board

bull Connect the embedded adaptive controller and the plant simulator via a local

network so that they form closed loop

bull Use network file system (NFS) technology to allow the embedded adaptive

controller and the plant simulator to have read or write access to the common

database in an NFS server

CHAPTER 2

LITERATURE REVIEW

21 Gasoline Refinery

Petroleum refining emphasizes distillation of crude oil into various fractions The

crude oil is heated to 370 degrees to 470 degrees Celsius and pumped into a distillation

column The crude oil is then separated into the following major fractions 1) naphtha 2)

light naphtha and 3) heavy naphtha The naphtha or light naphtha fraction can be used

as a component of finished gasoline The heavy naphtha needs further processing such as

catalytically reforming to become high-octane blending stock

In this thesis we study a gasoline refinery whose feed stream is condensate

produced from associated gas or natural gas fields It contains fewer high-boiling

components than crude oil does Moreover its antiknock quality is quite low since its

composition has a large amount of straight paraffinic hydrocarbons [2] In the gasoline

refinery the distillation process is responsible for cutting off light components as propane

and butane to ensure the saturated vapor pressure and volatility of the gasoline product

It will be finally blended with high octane number boosters and additives to ensure the

octane number and other quality criteria such as anti-oxidization

22 Distillation Equipment

Distillation process is done in a special chemical apparatus called distillation

column It is made up of several parts each of which is used to transfer heat energy or

enhance mass transfer A typical distillation column consists of the following

components 1) a vertical shell 2) column internals such as trays 3) a reboiler 4) a

condenser and 5) a reflux drum

The reboiler provides heat for vaporizing the feed stream The condenser is to

chill and condense overhead vapor The reflux drum stores the condensed vapor and

recycles liquid reflux back to the column The vertical shell covers the column internals

A schematic of a typical distillation column with a single feed and two product streams is

shown in Figure 21 Main parameters of a distillation column are shown in Table 21

RECTIFYING SECTION

F (feed flow rate)

FEED-cf (feed concentration)

(T) STRIPPING SECTION

Q n I (3) CONDENSER

rg fc mdash coolant flaw ^ j s J ^

reflux flow Li ^ bull bull bull

amp i v-v (4)REELUX DRUM stage N+l (Q) j hA (top toy) j DISTILLATE (OVERHEAD PRODUCT)

1 8 - D

stage f (feed tny)

stage rc

Q r2 heol flow stage 2 (Jgt ottam tray)

boil up roteV (pound($$

copy R E B O I L E R

BOTTOMS r BOTTOM PRODUCT)

Figure 21 Distillation column

Table-21 Main parameters of a distillation column

Material stream

Feed stream

Reflux stream Overhead

Distillate stream

Return stream Bottoms

Bottoms stream

Position

Stage f

Stage N

Reflux drum

Stage 1

Reboiler

Flow rate

Concentration

23 Distillation Operation Principles

The liquid mixture is fed onto the feed tray In normal operation there is a certain

amount of liquid on each plate The reboiler is used to supply energy for generating

vapor which moves upward and passes through the liquid on each tray The intimate

contact between liquid and vapor is usually accomplished by using bubble caps as shown

in Figure 22

Liquid phase

Stage it

(Trav gti-l)

bull bullbullbull

m^u - Bubble cap

Continuous contact between ascending vapor and descending liquid

Figure 22 Contacting between vapor and liquid phases at a tray

The overhead vapor upon leaving the top plate enters the condenser where it is

condensed The liquid is then collected in the reflux drum from which the reflux stream

and the top product stream are withdrawn The top product is also called distillate

The liquid that leaves the bottom tray of the column enters the reboiler where it is

vaporized The produced vapor is forced to flow back up through the column and the

liquid withdrawn from the reboiler is called bottoms or bottom product

24 Methods of Distillation Column Control

Distillation process has two degrees of freedom therefore there are various

control structures One of the most common control structures is energy balance

structure as shown in Figure 23 Refer to Appendix A for more details on control

structures

I |mdash0mdashI I

Figure 23 Energy balance control structure

The energy balance structure or LmdashV structure can be considered the standard

control structure for dual composition control In Figure 23 the reflux flow rate L and

the boilup manipulator V are used to control the primary outputs associated with the

product specifications The secondary outputs which are the liquid holdups in the reflux

drum and in the column base are usually controlled by distillate flow rate D and the

bottoms flow rate B

25 Principles of Adaptive Control

An adaptive control system can synthesize adaptive gains in such a way as to

compensate for variations in the characteristics of the process it controls There are many

types of adaptive control systems which differ only in the way the controller parameters

are adjusted [12]

Adaptive controllers are needed for chemical and petroleum processes since most

of them are nonlinear and nonstationary The linearized models that are used to design

linear controllers depend on particular steady states When their desired steady-state

operation has variation the best values of the controller parameters will change In

addition their time-varying dynamic characteristics usually cause deterioration in the

performance of the linear controller Therefore adaptation of the controller parameters is

required

Stephanopoulos [12] defines the objective of an adaptation law It must guide the

adaptive mechanism to the best adjustment of the controller parameters rather than keep

the controlled variables at the specified set points which can be accomplished by

conventional control loops

An adaptive control system can be considered as consisting of two loops as shown

in Figure 24 One loop is a conventional feedback loop The other loop is the parameter

adjustment loop [14]

Command_ signal

Adaptive mechanism

laquosj

Controller parameters

Control signal

Plant 1 Output

Figure 24 Block diagram of an adaptive system

There are two different methods for adjustment of the controller parameters 1)

direct method and 2) indirect method In the direct method the adaptation law directs

the controller parameters adjustment such as gain scheduling and model-reference

adaptive systems In the indirect method at any adjustment step new controller

parameters are obtained by solving the design problem such as self-tuning regulators

Process dynamics )

Siv-CSnftlteF----

unpredictable variations

Parametei-fixed Controller ^

Predictable variations

gtAdaptlraquolaquotraquoritfofMt SS9irgtsctftltluing

Figure 25 Procedure for selection of an appropriate adaptive scheme

Adaptive controllers being inherently nonlinear are more sophisticated than

conventional feedback controllers The decision whether to use adaptive control is based

on the dynamic behaviors of the process as depicted in Figure 25

26 Adaptive Schemes

261 Gain Scheduling

In many control systems it is possible to determine measurable variables that

have well-defined connections with changes in process dynamics These variables can be

used to adjust the controller parameters This approach is called gain scheduling because

the scheme was originally used to measure the gain and then change the controller

parameters as shown in Figure 26

Gain schedule trade~ I

i Controller parameters |

Command signal

Figure 26 Block diagram of a system with gain scheduling

The system can be viewed as consisting of two loops 1) an inner loop composed

of the plant and the controller and 2) an outer loop that adjusts the controller parameters

on the basis of operating conditions Gain scheduling can be considered as a mapping

Output

from plant parameters to controller parameters [14] hence it can be implemented as a

function or a lookup table

262 Model Reference Adaptive Control Systems

The model reference adaptive control (MRAC) scheme was originally proposed to

solve the problem in which the performance specifications are given in terms of a

reference model This model generates the desired output corresponding to the command

signal

Command signal CoHtrollet

MoctSI

Control signal

Controller parameters Adaptive

mechanism

Plant -bull Output

Figure 27 Block diagram of the model reference adaptive control scheme

The controller consists of two loops as shown in Figure 27 The inner loop is an

ordinary feedback loop composed of the plant and the controller The outer loop adjusts

the controller parameters in such a way that the error the difference between the plant

output and the model output is small The key problem is to design the adaptive

mechanism so that the adaptive control system is stable and the error goes zero [14]

27 Lyapunov Stability Theory

Lyapunov stability theory primarily addresses the stability problem of any system

regardless of being linear or nonlinear It is very significant for nonlinear control system

design since it is the only tool available when other methods are failed [15]

Lyapunov considers the nonlinear differential equation with zero initial condition

= ( ) bull (21)

Lyapunov investigates whether the solution of (21) is stable with respect to

disturbances or not

271 Definition of Lyapunov Stability

The solution x(f) = 0 is stable if for a given s gt 0 there exists a number Se) gt 0

such that all solutions with initial conditions ||x(0)|| lt Shave the following property

||x(OIIltpound for 0lttltoo

- mdash

yfdx dt

x = 0 i

-gt() =

Figure 28 Illustration of Lyapunov stability

The solution is asymptotically stable if a positive number Scan be found such that

all solutions with ||x(0)|| lt Shave the following property

||x(OII -gt 0 as t -gtQO

272 Lyapunov Stability Theorem

The solution x(t) = 0 is stable if there exists a function V R -gt R that is positive

definite such that its derivative along the solution of (21) is negative definite as

dV dVT dx dVT rr bdquobdquo

= = ( ) = -W(x) (22) dt dx dt dx

If dVldt is negative semi-definite the solution is asymptotically stable The

function Vs called a Lyapunov function for the system in (21)

273 Lyapunov Function

Assume that the following linear system is asymptotically stable

dx mdash = Ax (23)

For each symmetric positive definite matrix Q there exists a unique symmetric

positive definite matrix P such that

ATP + PA=-Q (24)

Equation (24) has always a unique solution with P positive definite and the

following function

V(x) = xTPx (25)

is a Lyapunov function [14]

28 ARM Processor

We use an ARM-7 development board manufactured by Samsung to implement

the embedded adaptive controller for the gasoline refinery The following sections

describe its architecture and key specifications

281 System Architecture of ARM Development Board

The S3C44B0X ARM-7 development board has various features including 8KB

cache internal SRAM LCD controller 2-channel UART with handshake 4-channel

DMA system manager with chip select logic and FPEDOSDRAM controller 5-channel

timers IO ports RTC 8-channel 10-bit ADC IIC-BUS interface and IIS-BUS interface

DB-9 DB-9

RS-232

Figure 29 System block diagram of the ARM development board

The S3C44B0X is developed using an ARM7TDMI core and new bus

architecture SAMBA II or Samsung ARM CPU embedded microcontroller bus

architecture [16] The main features are shown in Table 22

Table 22 Main features of the ARM-7 development board

Features

Memory

subsystem

GPIO ports

Ethernet

Descriptions

ARM7TDMI CPU core for 1632 bit operations

Cache 8KB for memory management

On-chip ICE breaker debug support with JTAG based debugging

solution

32x8 bit hardware multiplier

SAMBA II bus architecture up to 66MHz

Littlebig endian support

Address space total 256 MB

8 memory banks

Supports programmable 81632-bit data bus width for each bank

Fixed bank start address and programmable bank size for 7 banks

Programmable bank start address and bank size for one bank

Fully programmable access cycles for all memory banks

Supports self-refresh mode in DRAMSDRAM for power-down

Supports asymmetricsymmetric address of DRAM

8 external interrupt ports

71 multiplexed inputoutput ports

2-channel UART with DMA-based or interrupt based operation

Supports 5-bit 6-bit 7-bit or 8-bit serial data

Supports hardware handshaking during transmissionreceiving

Programmable baud rate

Supports IrDA 10 (1152kbps)

Loop back mode for testing

Each channel have two internal 32-byte FIFO for Rx and Tx

1 port 10 Base T (10100Mbps)

282 Memory Organization

The memory space is 256MB in total There are 8 memory banks 1) the first 6

memory banks are used only for ROM and 2) the last 2 memory banks can be realized

by RAM

The 8-MB SDRAM is in Bank 6 The beginning address of Bank 6 is

OxOcOOOOOO Therefore the kernel image will be load to the ARM board at address

0x0c008000 The memory map is shown in Figure 210

Figure 210 Memory map

CHAPTER 3

PLANT MODELING AND SIMULATION

31 Introduction

Process modeling is the first phase in the whole system design procedure This

phase is significant since it provides steady-state data of the plant We will base on these

data to design the adaptive control system In this section we study the distillation

process of the gasoline refinery and perform the process modeling and simulation

32 Process Description

Condensate which is condensed from associated gas or natural gas in gas

processing plants will be stabilized by cutting off light components such as propane and

butane in a distillation column

TOCASOLME MKR 4mdash

RffLlrtERLMl

Figure 31 Simplified diagram of the condensate distillation

The distillation column has 24 actual trays which is equivalent to 14 theoretical

trays Condensate is fed to the seventh tray The top product is Liquefied Petroleum Gas

(LPG) The bottom product is naphtha which will be blended with high octane number

boosters and additives to produce the finished gasoline

The control objective is to keep the product qualities within the following limits

under different operating conditions

xD gt 98

xB lt 20

where xo and x are the product compositions or the product qualities

33 Process Calculation

Based on the design basis we calculate steady-state values of the gasoline-

refining plant The process calculation is given in Appendix B The key values of the

plant design are listed in Table 31

Table 31

Temperature C

Pressure atm

Density kgm3

Volume flow rate m h

Mass flow rate kgh

Mass flow rate tonyear

Main streams oft

Condensate

130000

he plant

Raw gasoline

34 Process Description and Control Scheme

The process flow diagram of the plant is shown in Figure 32 Refer to Appendix

B for more details on process description

The control structure is selected as L-V structure that directly controls separation

quality Based on this structure we construct the control scheme for the distillation

system

Figure 32 Process flow diagram of the gasoline refinery

35 Plant Modeling

For the distillation column with 14 trays and 20 components the number of

differential and algebraic equations is equal to 14(220+3) = 602 equations [17] The

plant order should be reduced We can lump a group of components together to make

pseudo-component and the column dynamics are modeled on pseudo-component only

[18] The feed can be approximated by a pseudo binary mixture of LPG (iso-butane n-

butane and propane) and naphtha (iso-pentane n-pentane and heavier components)

As a result the mathematical model of the gasoline refinery is represented by a

set of 31 nonlinear differential and algebraic equations

1403 x16 =1646291^15 -756380x16 -927597xI6

58x15 =1646291(gtl4 -^1 5) + 756380(x16 -x15)

58x14 =164629103 -gtgt14) + 756380(x15-x4)

58x13 =1646291012 -_y]3) + 756380(x14 -x13)

58x12 =1646291(^n -y1 2) + 756380(x13 -x ] 2)

58xH =164629IO10 ~ ^ i ) + 756380(x12-x)

58x10 =164629109 -^1 0) + 756380(xn -x10)

58x9 = 661139gtgt8 -15638^9 + 756380(x10 -x9) + 5995

58x8 = 66113907 ~yamp) + 756380 x9 -18859x8 + 3399

58x7 = 661 39(y6-y7) + 798871 (x8 -x 7 )

58x6 =66113905-gt 6) + 1798871(x7-x6)

58x5 =66113904^) +179887 l (x 6 -x 5 )

58x4=66113903-^4) + 1798871(x5-x4)

58x3 =66113902-73) +1798871 (x 4 -x 3 )

58x2 =661139(^-gt2) +179887l(x3-x2)

2488x = 1798871x2-1109235x1 -661139^

Vapor liquid equilibrium (VLE) relationship on each tray

568x y = l + 468x

l + 468x

^ 1 5 =

568x 15

l + 468xbdquo (34)

CHART OF VAPOR

01 02 03 0 4 05 06 07 08 09

Figure 33 Vapor liquid equilibrium relationship

Refer to Appendix C for more detailed on establishment of mathematical model

36 Plant Simulation

We perform simulation of the plant using MATLAB Simulink In the simulation

program each stage of the plant is represented by a specific subsystem Refer to

Appendix D for more detailed on the simulation program The steady-state solution is

summarized in Table 32

Table 32

Steady-state compositions of the plant

CONCENTRATION OF LIGHT COMPONENT (LIGAS) ON EACH TRAY x D

bull L _ I i 1 l

6 8 10 12 14 16 18 20 Time (h)

Figure 34 Simulation result of the concentration on each stage

In summary the plan can obtain the operational objectives in which the purity of

the bottom product is greater than 98 and the impurity of the overhead product is less

than 2

CHAPTER 4

ANALOG CONTROLLER DESIGN

41 Introduction

We apply adaptive control strategy to design the control system for the gasoline

plant The adaptive system is more complicated than other conventional controller since

it was synthesized with adaptation law that enables it to operate properly for wide range

of operation as demonstrated in [19]mdash[21] In the following sections we will study

generic architecture of an analog adaptive controller We then establish the adaptation

law and design the adaptive controller for the plant in continuous-time space

42 System Architecture

As mentioned earlier in [14] Astrom and Wittenmark define adaptive control

strategy in which the system can self-adjust its settings to compensate for unpredictable

changes in the process or the environment The system architecture of the adaptive

controller is shown in Figure 41

Figure 41 System architecture of the adaptive control system

The adaptive control system will consist of two loops The inner loop is an

ordinary feedback loop composed of the plant and the conventional controller The outer

loop is an adaptive loop that adjusts the conventional controller parameters in such a way

that the plant error is small The adaptive loop will be synthesized based on the

Lyapunov stability theory introduced in Sec 27

There are two kinds of gains including adaptive gain and feedback gain The

purpose of the adaptive mechanism is to enable synthesis of the adaptive gains which

finally change the feedback gains as soon as state errors are detected The adaptive

mechanism is thus the most important component of the adaptive system

43 Construction of the Reference Model

Basically there are two different methods of reference model construction [22]

They include 1) mathematical approach and 2) experimental approach The

mathematical approach is based on physical laws and prior knowledge about the process

The advantages of this approach are 1) insightful understanding of the process and 2)

physical interpretations of process parameters and variables However it is quite difficult

and time-consuming to build the model from fundamental knowledge On the contrary

the experimental approach is based on experimentation It is also known as system

identification This approach includes the following tasks 1) experimental planning 2)

selection of model structure 3) parameter estimation and 4) validation For distillation

control system identification is sometimes impractical since the experimentation needs to

build a real distillation column or a pilot plant which is very expensive Therefore we

select the mathematical approach to construct the reference model

We observe that the plant has many internal variables however its input-output

relationship is quite simple as shown in Figure 5 We adjust the reflux flow rate L and

the vapor rate V so that the product quality is met the control objectives defined in (31)

and (32)

Disturbances

- External reflux flow(L) ~ lt~ LPG purity (xDi

Ditiilitirn Gy-tem

Internal vapor rate (V) bdquo ^ Raw Gasoline impurity (xB)

Figure 42 Two-input two-output representation for the plant

We can make linearization at the nominal operating point as follows

x(t) = A(xt) + Beu(t) (41)

y(t) = Cex(t) (42)

where Ae is a 16x16 matrix Be is a 16x2 matrix and Ce is a 2x16 matrix

The values of Ae Be and Ce matrices are calculated with an algebraic method

described in Appendix E

Many researchers state that the dynamic response of most distillation column is

dominated by one large time constant which is nearly the same regardless of where an

input or disturbance is introduced or where composition is measured This is well known

both from plant measurements [23] and from theoretical studies [24]-[25] This means

that most distillation columns can approximate by first order systems

We can use Gramian-based inputoutput balancing of state-space realizations as

[sysbg] = b a l r e a l ( s y s )

The last 14 elements of the balanced Gramian matrix are small or zero so we can

eliminate the last 14 states with the MATLAB command of model order reduction

sysmred = m o d r e d ( s y s b 3 1 6 d e l )

As the result the reduced-order model of the plant is a second-order two-input

two-output system

xm(t) = Amxm(t) + Bmuc(t) (43)

ym(t) = cmxm(t) (44)

where Abdquo = -67941

-09095

-02497 Bbdquo

-01461 02073

-00021 -00281 and C

-00624 -00281

02458 00009

Bode Diagram

~ ^ ~ ~ mdash ~ trade ~ trade r f trade ^ J

Original model Reduced order model

bull Original model bull Reduced order model

Frequency (radsec)

Figure 43 Bode responses of two models

In Figure 43 Bode diagram of the reduced-order model is nearly in agreement

with the one of the original model The reduced-order model will be checked with

stability and other tests before deciding whether it is a reference model or not

431 Stability Test

The system is stable because all eigenvalues of the state matrix -65832 -

04606 are in left-hand side of the complex plane

432 Controllability and Observability Test

A system is said to be controllable if and only if it is possible by means of the

input to transfer the system from any initial state x(t) = xto any other state xj = x(T) in a

finite time T-tgt0

For any system described in the following forms

x = Ax(t) + Bu(t) (45)

y(t) = Cx(t) + Duy) (46)

where A BC and D are matrices

The matrix M = [B AB AlB] where is the rank of B and n is the system

dimension is called controllability matrix The system is completely controllable if Mis

full rank of n

A system is said to be observable if and only if it is possible to determine any

arbitrary initial state x(t) = xt by using only a finite record y( r) for t lt r lt T of the

output

For the system in (45) and (46) the observability matrix S is defined as

S=[CCACA2CA]]T

where is the rank of C and n is the system dimension

The system is completely observable if S is full rank (n)

We can use the following MATLAB commands to test controllability and

observability of the reduced-order model

M = c t r b ( A r B r ) c o n t r o l l a b i l i t y mat r ix

S = obsv(Ar Cr) o b s e r v a b i l i t y mat r ix

As the result the M and S matrices have full rank therefore the model is

completely controllable and observable

In conclusion the reduced-order linear model fully satisfies the steady-state

property Therefore it is selected as the reference model for the MRAC system design in

the next section

44 Analog Controller Synthesis

441 Plant

The model of the plant can be expressed in the state space as

x(t) = Ax(t) + Bu(t)

yt) = Cx(t)

where A = au

an_ B =

bn_ and C =

-00624 -00281

02458 00009

The plant parameters including a an aj aji b bn bj and 622 are unknown

and dependent on the plant dynamics The plant model has the following vectors of

variables

1) A vector of state variables x = [x X2]

2) A vector of control signals u = [u u-$

3) A vector of controlled outputs y=ygt y-$

442 Reference Model

The reference model for the plant is a linear time-invariant system as developed in

Sec 43

xmlaquo) = Amxm(t) + Bmuc(t)

where Abdquo

ybdquo(t) = cmxm(t)

-67941 -09095

14686 -02497

5 = -01461 02073

-00021 -00281 and Cbdquo

-00624 -00281

02458 00009

443 Feedback Control Loop

A general linear control law is given by

ut) = Muct)-Lx(t)

The matrices L and Mmay be chosen as follows

The closed-loop system is obtained by substituting (411) into (49)

x = (A- BL)x + BMuc

The closed-loop system depends on a parameter 0 = [0 0i 0$ 04 0= 0$ 0j 0

hence we define

Ac(0) = (A-BL)

Bc6) = BM

As a result the closed-loop system can be expressed as

x(t) = Ac(0)x(t)+ Bc0)uct)

Ac(0) = A-BL au ~b ~^OT av-bu02-bn0

i2 ~b2

y22L3 ci~ mdash b-0 mdash b--0- ci-- mdash b--0- mdash b--0

l 2 11^2 ^12^4

22 _ ^ 2 1 ^ 2 ~ ^ 2 2 ^ 4

Bc(0) = BM = bu95+bnd7 bu66+b]2es

b2]65+b2281 b2Xdb+b22d (412)

444 Compatibility Condition

It is necessary to find at least one value of 0 such that the closed-loop equation is

equivalent to the reference equation (49) A sufficient condition is existence of at least

one special value 0deg such that

This condition ensures a perfect model-following x mdashraquo xm when t increases

Substitute 0deg = [lt9deg 02 0deg 0deg4 0deg 0deg 0deg 0] into the compatibility

condition we get

au-bu6-bnel =-67941

an -bu6a2 -bn6deg4= -09095

a2]-b2]6deg-b220deg =14686

a22-b2]e2-b229deg= -02497

6Adeg + M7deg =-01461

606deg + 6 X =02073

b2l6deg5+b229deg =-00021

b2]edeg6+b226degs =-00281 (413)

Clearly there always exists a parameter value 0deg satisfying the compatibility

condition

0 _ b22(au +67941)-bu(a2] -14686) 0 =

regp22 ^12^21

a o _ b22(an + 09095)-bn(a22 +02497)

^11^22 _ ^12^21

bdquobdquo -621(a + 6794l) + bu(a2] -14686) o3 mdash

buo22 mdashbnb2]

0 _ -b2](a]2 + 09095)+ bu(a22 +02497) 6gt =

bP 22 b]2b2]

n0 0002lfe2 -01461amp22 6gt5 mdash

-b2]bn+bub22

n0 002816I2+02073Zgt22

(J6 = -b2]bu+bub22

_0 - 000216+ 0146 b2x Uf =

-b2]bu+bub22

0 = 002816 +020736

-b2Xbu+bxxb (414)

Error Equation

The model following error is defined as

e(0= x(0-m(0

e() = ^ ( 0 + 5 i ( 0 - ^ I B ( 0 - 5 m laquo c ( 0 - (4-15)

Substitute the term of u(t) into (415) and rearrange the equation as follows

e(t) = Ame(t) + (A-Am- BL)x(t) + BM - Bm )uc ()

et) = Ame(t) + (Ac(eL) - Am )() + (BC(6U ) - Bm )uc (t)

e(t) = Ame(t) + (Ac (0L ) - Ac (0degL))x(t) + Bc (0M) - BC (0degM ))tc ()bull (416)

Finally the equation above is equivalent to the following

e(t) = Ame(t) + V(t)(0-O0) (417)

yen bullbxxxx -bux2 -bX2xx -bnx2 bxxucX buuc2 bnucX bnuc2

-b2xxx mdashb22x2 mdash b22xx mdashb22x2 b2xucX o2xuc2 b22ucX tgt22uc2

0-6deg =^-0 62-0 6i ~ 7deg 0laquo -01 bull

446 Adaptation Law

To derive a parameter adjustment law we introduce a Lyapunov candidate

function

V(e 0) = [yePe + (0 - 0deg f (0 - 0deg)) (418)

where e = [e e^ is a vector of state errors i s an adaptation rate and P = [1 0 0 1] is

chosen as a positive matrix

The function V is positive definite To find out whether it is a Lyapunov function

we calculate its total time derivative

f-sectlaquoolaquo+laquo-laquovr+claquo-of (419)

L =_LerQe + e_ey(dl + ryrpe J dt v

(420) dt 2

where Q is positive definite and such that

ltP + PAm = -a (4-21)

The matrix Q = [135882 -05591 -05591 04994] is a positive-definite matrix

Based on Lyapunov stability theory as introduced in (25) the function V(e 0) above is a

Lyapunov function In another way Nguyen and Afzulpurkar [26] proved the Lyapunov

function candidate in (418) as a Lyapunov function by using another approach

MATLAB Symbolic Algebra

As the result the adaptation law is chosen as

^ = -W(t)Pe(t) at

V bnxi bnx2 b2x bnx2 bUc bX]uc2 bnucX buuc2

mdash b2Xxx mdashb22x2 mdash b22xx mdashb22x2 b2ucX b2xuc2 b22ucX b22uc2

Therefore the adaptation law can be expanded as follows

y(buex+b2Xe2)xx

y(buex+b2]e2)x2

y(bnex+b22e2)xx

y(bx2ex+b22e2)x2

-y(bxxex+b2xe2)ucX

-y(bxxex+b2Xe2)uc2

-y(bX2ex+b22e2)ucX

-y(buex+b22e2)uc2

6 = (423)

447 Stability of the Analog Controller

We compute differentiation of the Lyapunov function in (418) Substitution of

the dOldt term determined in (422) we get

mdash = -05591lt -07066e2)2 +132756e2] dt 1

The system is stable because the time derivative of the Lyapunov function is

negative definite As the result the error goes to zero according to Lyapunov stability

theory which will be demonstrated with dynamic simulation in the next section

45 Analog Controller Simulation

451 Simulation Program

As shown in Figure 44 the program consists of all components of the adaptive

controller as follows

1) Reference signals uc(t)

2) Disturbances^)

3) Linear controller governed by the general linear control law

4) Reference model

5) Plant representing for the gasoline refinery with time-varying parameters

6) Adaptive mechanism governed by the adaptation law in (423)

a n n f l

SIMULATION OF ANALOG ADAPTIVE CONTROLLER

REFERENCE MODEL

bull y^n tollA ^ pound

dull In I

0ut2 In2

ADAPTIVE MECHANISM

Figure 44 Simulation program for the analog adaptive controller

To evaluate the controller performance we compute mean error of the plant

output As earlier mentioned the state error is defined as

= X Xm

_X2 Xm2 _

We now define mean error e based on root-mean-square of the vector e as

follows

e = RMS(e) = -^A for = 1 or 2

where nt is the dimension of the vector ec and |e| is the norm of the vector et

The norm of the vector et can be found by using the following MATLAB

commands

norm_el = norm(el)

norm_e2 = norm(e2)

When the simulation is finished all element values of the vector e and ej are sent

to MATLAB workspace so that we can easily calculate the mean errors

452 Simulation Result

Adaptation rate is set at value 10 The plant parameters are simulated by random

function The reference inputs are step functions External disturbances are simulated

with random noise as shown in Figure 45 The reference state and plant states are

shown in Figure 46

Figure - disturbance

(File Edit View Insert Tools Debug Desktop Window Help

m B s in

Figure 45 External disturbances

Figures - x vc xm

Debug Desktop Window File Edit View Insert Tools Desktop Window Help

Q a yi k tmm laquo d bull If cf |1 I i a

m B ampm

bull4s

Figure 46 Reference states and plant states

Figures - y vs ym File Edit View Insert Tools Debug Desktop Window Help

bullraquo i x

i m B raquo bull

Figure 47 Controlled outputs and reference outputs

The controlled outputs rapidly approach the desired values as shown in Figure

47 This is a clear illustration for the stability of the MRAC system as theoretically

proved in Sec 447 The state errors reduce when time increases as shown in Figure 48

I B Ufcajuy ue^Kiup winuuw m e CUIL

im B ffin

State error e1(t)

State error e2(t)

Figure 48 Plot of plant output errors during simulation

The mean errors in the simulation duration can be determined as follows

e = 00017

laquo VTobT = 5428410

n2 VTooT = 7106210

Error reduction will be introduced in the next section

453 Error Reduction

Adaptation rate has a strong effect on plant errors In general increasing

adaptation rate will weaken plant output errors In Table 41 the plant errors rapidly

reduce to zero when the adaptation rate increases

Table 41 Plant output errors for different adaptation rates

Plant errors

laquoi

Adaptation rate y

54304 105

71399105

5428410

7106210

54076 105

7100310-5

CHAPTER 5

DIGITAL CONTROLLER DESIGN

51 Introduction

In the previous chapter the control system is designed and analyzed in

continuous-time space However the plant will be controlled by a digital computer So

we will discretize the plant Zero-order hold (ZOH) is a mathematical model of the

practical signal reconstruction accomplished by a conventional digital-to-analog

converter (DAC) It describes the effect of converting a continuous-time signal into

discrete-time signal by holding each sample value for one sample interval The input and

output signals of a zero-order hold is shown in Figure 51

Figure 51 Input and output signals of ZOH

G(s) y ( t

Figure 52 Block diagram of a sampled-data system

In Figure 52 the zero-order-hold equivalent to G(s) is given by

where is the z-transform of the bracketed term in time continuous space

52 Digital Controller Synthesis

521 Plant Model

The plant in continuous-time space is given by

x(t) = Axt) + But)

y(t) = Cx(t)

where A = [au an a2 a22] B = [bu bn b2 b22] and C = [-00624 -00281 02458

00009] The elements of the matrices A and B above are unknown and dependent on the

dynamics of the system

The plant has the Laplace transform as

x(s) - ~[AX(S) + Bu(s) s

We assume that x(i) and u(t) are constant during the sampling interval T hence

the ZOH equivalence of the plant is given by

T x(z) = [AX(Z) + Bu(z)]

Now we can easily convert it to the new form of difference equations which is

conveniently implemented in a digital computer x(kT + T) = (In+TA)x(kT) + TBu(kT) (51)

The controlled output y(t) has ZOH equivalence as follow

y(kT) = CxkT) (52)

522 Reference Model

The reference model for the plant is a linear time-invariant system as developed

in Chapter 6

bdquo() = Amxmt) + Bmuc(t)

ybdquo(t) = cmxm(t)

where Am = [-67941 -09095 14686 -02497] Bm = [-01461 02073 -00021 -00281]

and Cm = [-00624 -00281 02458 00009]

Similarly to previous section the reference model has the ZOH equivalence as

follows

xm (kT + T) = (bdquo + TAm K (kT) + TBuc (kT) (53)

The reference output yjf) has ZOH equivalence as follow

ybdquo(kT) = Cxm(kT) (54)

523 Linear Feedback Controller

ut) = Muc(t)-Lx(t)

The ZOH equivalence is determined as

u(kT) = Muc(kT)-Lx(kT) (55)

All elements of the matrices L and Mare adjusted by the adaptive mechanism

L = 0kT) 62(kT)

0(kT) 0AkT

M 05(kT) 06(kT)

87(kT) 0s(kT)^ (56)

Similarly to the design in continuous-time space we need to determine

compatibility value 0deg = [lt 02 0 0deg 0deg 0deg 0deg 0deg] as follows

o _ ft2deg2(adeg +67941)-ft02(a20 -14686)

~ hdeghdeg -hdeghdeg 0]]Lgt22 T2

o _ 62deg2(adeg2 +09095)-b2a2 +02497) ~~ Adeg -Adeg

degdeg27 deg12deg21

8 0 _ -amp2 K + 67941) + ft (a2] -14686)

t O O _ r 0 r 0 deg11deg22 deg12deg2I

o _ - f t ^ + 09095) + ft0 (adeg2 +02497) ~~ Adeg mdash Adeg

deg11deg22 deg12deg2I

ftdeg =

00021ft0-01461ft0 22

-ft21 f t02+ft0 f t22

0028 lftbdquo+ 02073ft 22

-b2]b]2+bub22

q 0 - 0002 lftdeg+ 0146 lftdeg

-b2bn+bub22

n0 00281ft+02073ftdeg

201 deg]]deg22

525 Adaptive Mechanism

The adaptive law obtained in continuous-time space is given by

6(t) = -y^(t)Pe(t)

where y = - 0 | ] X ] O n X 2 0 | 2 X | bullbux2 buucl bnuc2 bl2uc] b]2uc2

t-)]Xi Ly-fJiy UyyJi-i UJJJL) l)- 1W i ~gt cl 77 c 77 c 7

The Laplace transform is as follows

= yy (s)Pe(s)

Then we determine the ZOH equivalence in z-space

0(z) = -^-y^(z)Pe(z) z mdash

The discrete-time adaptation law is therefore obtained as

0(kT) = 0(kT -T) + T[-yy r (kT - T)Pe(kT - T)] (5

The general adaptation law in (58) can be expanded as follows

0 (kT) = 6gt (kT -T) + Ty[b e (kT -T) + b2]e2 (kT - T)]x (kT - T)

02(kT) = O2(kT -T) + Ty[bue](kT-T) + b2]e2(kT-T)]x2(kT-T)

03(kT) = 03(kT-T) + Ty[bue(kT-T) + b22e2(kT-T)]X](kT-T)

04(kT) = 04(kT-T) + Ty[bne(kT-T) + b22e2(kT-T)]x2(kT-T)

05(kT) = 05(kT -T)- Ty[bue (kT -T) + b2]e2(kT - T)]uc] (kT - T)

06 (kT) = 06 (kT -T)- Ty[bne (kT -T) + b22e2 (kT - T)]uc2 (kT - T)

07 (kT) = 07 (kT -T)- Tybnex (kT -T) + b22e2 (kT - T)]uc] (kT - T)

0 (kT) = 6gt8 (kT -T)- Ty[bne (kT -T) + b22e2 (kT - T)]uc2 (kT - T) (5

Figure 53 Logic diagram of the adaptation law

The logic diagram of the adaptation law is shown in Figure 53 Base on the

adaptation law we are able to implement the embedded adaptive controller in hardware

using ARM processor FPGA or whatever type of digital computer For the one using

ARM development board the adaption law will be translated into C language and the

adaptive mechanism will be an executable running in Linux environment

CHAPTER 6

SIMULATION OF THE ADAPTIVE DIGITAL CONTROLLER

61 Introduction

The adaptive controller for the gasoline refinery is designed in Chapter 5 We

now perform simulation of the adaptive system to verify its control performance In the

realm of control system design MATLAB is normally used to perform simulation of

control systems hence we also follow this approach Moreover we develop an

alternative effective method for simulation of digital systems using C++ in which each

subsystem of the system will be represented by a C++ class

The simulation program written in C++ has many advantages First it is an

executable so it can directly run in popular operating systems such as DOSWindows or

Linux Second its IO file handling and data exchange with other software systems are

quite simple since C++ has plentiful IO library Third we can re-use the code to

develop the plant simulator in the next chapter which will interact with the embedded

adaptive controller via an Ethernet

62 Dynamic Simulation Using MATLAB

The simulation program consists of major components of the adaptive system in

discrete-time space as shown in Figure 61

1) Reference signals uckT)

2) Disturbances^^

3) Subsystem of Linear Controller governed by the general linear control law as

u(kT) = Muc(kT)-Lx(kT)

4) Subsystem of Reference Model representing the desired responses to

reference signals

xm(kT) = Amxm(kT) +Bmuc(kT)

5) Subsystem of Plant representing the unknown process model as

jc(Jfcr) = Ax(kT) + Bu(kT)

6) Subsystem of Adaptive Mechanism governed by the adaptive law as

6(kT) = 6(kT -T) + T[-yy (kT - T)Pe(kT - T)]

1 tnl uc(k)

In2 uc(k-1)

xmljc) uc(k) xm(k+1)Jgt

xm(k-1)

laquogt

REFERENCE MODEL

H Disturbances

bulleurogt

[B^_]M

0ut1 In)

0ut2 In2

i f MJi-1)

0 u ulaquoK-l)

ADAPTIVE MECHANISM

m lt raquo

Ot-1) Mux bull

Figure 61 Simulation program for the digital adaptive system

622 Error Calculation

As earlier mentioned the plant output errors is defined as

e(kT) = exkT)

e2(kT)

h(kT)-xnnkT)

x2(kT)-xm2(kT)_

Ax^kT)

Ax2(kT)

follows

e = RMSe) = ^L for = 1 or 2 (61)

where n is the dimension of vector e and ||e-|| is the norm of vector eh

623 MATLAB Simulation Result

The plant parameters are simulated by random functions The reference inputs

uc(kT) are step functions External disturbances are simulated with random noise as

shown in Figure 62

Disturbance f(t)

As a result the reference states (xm xm 2) are well tracked by plant states (xi X2)

as depicted in Figure 63

m gt P i laquo ^ e

The controlled outputs rapidly reach the desired values as shown in Figure 64

This is a clear illustration for the stability of the digital adaptive controller

B m 113 bullgt amplt S

The plant output errors approach zero and the system has good control

performance as depicted in Figure 65

a)e(7)

ns gt P l

a) eiikT)

Figure 65 Error plots

The mean errors over the simulation duration are calculated by using the error

equation (61) as follows

I U I 94543e-004 _ bdquo ^ - s

101 = 9407410-

M = 9 6557e -Q04 = 9 6 0 7 8 t l 0 5

4n2 vioi

63 C++ Simulation Project

The functional verification project written in C++ is to simulate all subsystems

including plant reference model linear controller comparator and adaptive mechanism

The algorithms and data structures of each C++ class are summarized in the following

sections

631 Plant Model Class

Plant model class is to simulate the plant It receives signals from the linear

controller and then generates plant state x(kT) The header file of the plant class is shown

in Figure 66

1 ifndef PLANT_MODEL_H

2 define PLANT_MODEL_H

3 include ltstdlibhgt

4 include tbdefsh

5 class Plant

6 private

7 Pkt u_k control signal

8 Pkt x_k plant state

9 double all al2 a21 a22

10 double bll bl2 b21 b22

11 double ell cl2 c21 c22

12 public

13 Plant()

14 -Plant()

15 void getPlantPkt(int k Pkt u_k Pkt x_k)

16 void genPlantPkt(int k Pkt ampx_kpl)

18 endif

Figure 66 Plant classs header file

The plant class has several important member functions

P l a n t ( )

void g e t P l a n t P k t ( i n t k Pkt u_k Pkt x_k)

void g e n P l a n t P k t ( i n t k Pkt ampx_kpl)

The algorithms of these functions are described below

1) The class constructor P l a n t () is to create a new object of plant whose

parameters are randomized due to invariant dynamics of the plant

a l l = - 6 7 9 4 1 + 0 6 7 ( r a n d ( ) 2 - 0 5 )

a l 2 = - 0 9 0 9 5 + 0 0 9 ( r a n d ( ) 2 - 0 5 )

a21 = 14686 + 015(rand()2-05)

a22 = -02497 + 002(rand()2-05)

bll = -01461 + 0014(rand()2-05)

bl2 = 02073 + 002 (rand()2-05)

b21 = -00021 + 00002(rand()2-05)

b22 = -00281 + 0003 (rand()2-05)

ell = -00624 + 0006(rand()2-05)

cl2 = -00281 + 0003(rand()2-05)

c21 = 02458 + 0025(rand()2-05)

c22 = 00009 + 000009(rand()2-05)

2) The member function ge tP l an tPk t is to receive input signals of the plant

such as control signals from the linear controller

3) The member function genPlantPkt is to generate plant states which will be

stored in the common database

632 Reference Model Class

Reference model class is to simulate the reference model It receives signals from

the reference signal generator and then produces reference state xm(kT) The header file

of the reference model class is shown in Figure 67

1 ifndef REFERENCE_MODEL_H

2 define REFERENCE_MODEL_H

4 include tbdefsh

5 class Refmdl

6 private

7 Pkt uc_k

8 Pkt xm_k

9 public

10 Refmdl()

11 -RefmdlO

12 void refmdlGetPkt(int k Pkt uc_k Pkt xm_k)

13 void genRefPkt(int k Pkt ampxm_kpl)

15 endif

Figure 67 Reference model classs header file

The plant class has two important member functions

void refmdlGetPkt ( in t k Pkt uc_k Pkt xm_k)

void genRefPkt( in t k Pkt ampxm_kpl)

The algorithms of these functions are quite simple

1) The function refmdlGetPkt is to receive reference signals from the

reference signal generator

2) The function genRef Pkt is to generate reference states which will be stored

in the common database

633 Linear Control Class

Linear control class is to simulate the linear controller It receives signals from

the reference signal generator and adaptive mechanism It then produces control signals

u(kT) to manipulate the plant The header file of the linear control class is shown in

Figure 68

1 ttifndef LINEAR_CONTROL_H

2 define LINEAR_CONTROL_H

4 include tbdefsh

5 class Linctrl

6 private

7 thetaPkt th_k

8 Pkt x_k

9 Pkt uc_k

10 public

11 LinctrlO

12 -LinctrlO

13 void getLinctrlPkt(int k thetaPkt th_k Pkt uc_k Pkt x_k)

14 void genLinctrlPkt(int k Pkt ampu_k)

16 endif

Figure 68 Linear control classs header file

The linear control class has two important member functions

void g e t L i n c t r l P k t ( i n t k t he t aPk t th_k Pkt uc_k Pkt

void g e n L i n c t r l P k t ( i n t k Pkt ampu_k)

1) The function g e t L i n c t r l P k t is to receive signals from the adaptive

mechanism the reference signal generator and the plant

2) The function genLinc t r lPk t is to generate control signals which directly

manipulate the plant The control signals are also stored in the common

database

634 Comparator Class

Comparator class is to simulate the comparator It receives signals from the

reference model and the plant It then compares them and computes the error e(kT)

which is an important element to synthesize adaptive gains The header file of the

comparator class is shown in Figure 69

1 ifndef COMPARATOR_H

2 Idefine COMPARATOR_H

4 include tbdefsh

5 class Comparator

6 private

7 Pkt x_k

8 Pkt xm_k

9 Pkt e_k

10 public

11 Comparator()

12 -Comparator()

13 void getCmprPkt(int k Pkt x_k Pkt xm_k)

14 void genCmprPkt(int k Pkt ampe_k)

16 endif

Figure 69 Comparator classs header file

void getCmprPkt( int k Pkt x_k Pkt xm_k)

void genCmprPkt(int k Pkt ampe_k)

1) The function getCmprPkt is to get state variables of the reference model

and the plant

2) The function genCmprPkt is to compare the state variables above and

generate error signals

635 Adaptive Mechanism Class

Adaptive mechanism class is to simulate the adaptive mechanism It receives

signals from the signal generator plant and comparator It then generates adaptive gains

6(kT) The header file of the adaptive mechanism is shown in Figure 610

1 ifndef ADAPTIVE_MECH_H

2 ttdefine ADAPTIVE JMECH_H

4 include tbdefsh

5 class AdaptiveMech

6 private

7 thetaPkt th_kml

8 Pkt x_kml

9 Pkt e_kml

10 Pkt uc_kml

11 public

12 AdaptiveMechO

13 -AdaptiveMechO

14 void getAdapMechPkt(int k Pkt x_kml Pkt e_kml Pkt

uc_kml thetaPkt th_kml)

15 void genAdapMechPkt(int k thetaPkt ampth_k)

17 endif

Figure 610 Adaptive mechanism classs header file

The adaptive mechanism class has two important member functions

void getAdapMechPkt(int k Pkt x_kml Pkt e_kml Pkt

uc_kml t he t aPk t th_kml)

void genAdapMechPkt(int k t he t aPk t ampth_k)

1) The function getAdapMechPkt is to get state variables of the reference

model and the plant

2) The function genAdapMechPkt is to compute all adaptive gains and store

them into the common database

636 Create Makefile and Build Project

We create the Makefile of the project with the following content

CC = g++

$(CC) -g -c -o AdaptiveMecho AdaptiveMechcpp

$(CC) -g -c -o Comparatoro Comparatorcpp

$(CC) -g -c -o LinearControlo LinearControlcpp

$(CC) -g -c -o PlantModelo PlantModelcpp

$(CC) -g -c -o ReferenceModelo ReferenceModelcpp

$(CC) -g -o adaptive_control AdaptiveMecho

Comparatoro LinearControlo PlantModelo

ReferenceModelo

In a console we run the Makefile to compile and build the adaptivecontrol

executive file

637 C++ Simulation Result

We run the executable to perform simulation of the adaptive system We find that

it gives the same results as MATLAB simulation in Sec 62 Thus we can deploy either

the simulation program written in C++ or the simulation written in MATLAB for testing

the embedded adaptive controller in the next chapter

The most significant results are shown in the following figures Refer to

Appendix G for more simulation data

j haut$ttum

Pile Edit view Terminal Tabs Help

th2[9] = -0519735 th3[9] =bull 8289982 thltt[9] = 0399865 th5[9] = 1028989 th6[9] = -6845742 th7[9] = 6017589 th8[9] - 1018935 Plant srodel has- been created wi th randans parameters A =[-6459199 -9864506 1543686 -623970G] B = [-8139199 6217366 -8662266 -8929666] C = [-B865468 -8029608 8233308 6883855] Adapmech receives s i g n a l s Adapmech generates adaptive gains t h i l l copy ] = 8371379 thZ l i e ] = -e510663 t r i3 [ ie ] = 8280843 th4[18] - -0309971 thSl lB] = 1632299 t he [ l e i = -0945S88 th7[18] = 08127X8 thSJiej = 1999059 Simulation is done

hoanfShoan-thesisadapcon$ |

ltOIgt gtiJ^Alt

plusmn1 f bull-lt

i gt bulli

lt euro f bull2

[ bull

Figure 611 Running the adaptive_control executive file

The reference state xm and plant states x are shown in Figure 612

Reference slates and plant states

mdash lt ^ mdash ^ y

- H J bullbull -

~ttttfc

bull=fmdashF^--

^ t ^ i i i = ^ ^

1 r T ~ ~ bullbull bull i - r - ci

Figure 612 State variables

This is a definite illustration for the stability of the digital control system

_ - 1 1 = - mdash J

^ J - - - ^ ^

p ^ _ _ r _ mdash bull

Reference outputs and controlled outputs

1 1 1 I

U ^ ^ bullbullbullbull

^S_^j ^PH^mdashrmdash tp U^

^ ^ r r r ^ - bull mdash

bull bullbull bull y 2

5 time

The plant output errors rapidly approach zero as shown in Figure 614

Figure 614 Plant output errors

The mean errors e in the simulation duration can be determined as follows

e = |N| s94543c-004 ^

96557e-004

VToi = 96078 105

The mean errors determined by the C++ simulation program is the same as the

ones calculated by the MATLAB Simulink program in Sec 62

CHAPTER 7

IMPLEMENTATION OF THE EMBEDDED ADAPTIVE CONTROLLER

71 Introduction

711 Embedded Adaptive Controller Using ARM Processor

In previous chapters we successfully design and simulate the adaptive controller

for the gasoline refinery We now implement it using the ARM-7 processor We firstly

develop a plant simulator which runs on a Linux machine to simulate the plant and other

local instruments such as the conventional feedback control loop The embedded

adaptive controller will be implemented in an ARM-7 development board which governs

the adaptation law and remotely controls the plant via an Ethernet network The

elementary block diagram of the plant simulator and embedded adaptive controller is

shown in Figure 71

Figure 71 Elementary block diagram of the system

712 In-Hardware Validation Scheme

In Chapter 6 we carried out simulation of the adaptive system in both MATLAB

and C++ in which the adaptive mechanism was represented by either a MATLAB

Simulink module or a C++ class The simulation results showed that the design fully

obtained the control objectives under variant environment such as time-varying process

dynamics of the plant and unpredictable disturbances Therefore we can consider these

software models as golden models which execute the functions of the adaptive

mechanism and generate accurate output data to compare against the actual results from

the hardware implementation [28]

MATLAB SIMULINK PROGRAM

Signal Generator Signal

_ Data J

Adaptive Mechanism mum MCHICI Output

5gt I Error

yV H Report

EmimdrtMi Adaptive Controller

Plant Slmsliitsr

lt = J Output

Linux yacnine

C++ SIMULATION PROGRAM

Adaptive Mechanism jPantMotfe Output

Figure 72 In-hardware validation scheme

In Figure 72 we use the same data of reference signal to feed the MATLAB

Simulink program C++ simulation program and the validation blocks Their output data

are collected and sent to the result comparator to prepare error reports

713 System Architecture and Operations

The integrated testing environment consists of the plant simulator the embedded

adaptive controller a Boa web server with a built-in CGI program an NFS server client

web clients and engineering stations These machines are connected by a LAN network

as shown in Figure 73

Figure 73 Integrated testing environment

The ARM board is an NFS client and a Linux machine plays the role of the NFS

server The ARM board will mount and open the shared database on the NFS server

The embedded adaptive controller resides on the ARM board whereas the plant simulator

runs on another Linux machine Moreover there is a type of computer called web client

engineering station which is either a personal computer (PC) or Linux computer A user

sitting on this station can use a web browser to open the main graphical user interface

(GUI) page of the Boa web server to begin testing the adaptive system He or she can

also access the shared database on the NFS server

By default the ARM board has an IP address 1921680128 and subnet mask

2552552550 We set the plant simulator machine an IP address 192168010

2552552550 and the NFS server an IP address 19216808

After the kernel image is loaded into the ARM board we perform the command

of NFS mount from the HyperTerminal In Figure 74 the interaction between the NFS

client and the NFS server for mounting a network file system is described as follows

bull The NFS client initiates mounting the network file system

bull The NFS client makes RPC get_port request

bull The NFS server performs RPC get_port reply

bull The NFS client requests the server to mount the file system

bull The NFS server performs local mount for the requested files [29]

|NFS Client| [NFS Seiver|

P I mount -t nfs 192168 0Bopttes1 vartmp I

RPC get_port request ^

RPC get_port reply

RPC mount request

RPC mount reply

Authenticate client

Perform local mount for the requested files

Figure 74 NFS clientserver interaction for mounting a network file system

After the network file system is successful mounted the ARM board (ie the

NFS client) can acces the shared database on the remote NFS server

The interactions among the web browser the Boa web server the CGI program

the embedded adaptive controller and the plant simulator are described as follows

1) A user opens the web browser to request the form by entering the URL

lthttpl 921680128embedded_adaptive_controllerhtmlgt

2) The browser makes a connection to the Boa server by the following steps

bull Break the URL into 3 parts including the protocol (http) the IP address

(1921680128) and the file name (embedded_adaptive_controllerhtml)

bull Form a connection to the IP address on the port 80

bull Send a get request to the Boa server

3) The web server responds the request by sending HTML text for the web page

to the browser

4) The browser reads HTML tags and displays the input form onto the screen

5) The user enters testing parameters and submits them by clicking on Run

button

6) The browser allows the user to enter testing parameters and submits

information to the Boa web server

7) The Boa web server forwards the information and activates the CGI program

8) The CGI program makes a function call for the adaptive mechanism

9) The plant simulator running on a Linux machine interacts with the embedded

adaptive controller and forms the closed control loop

10) At every step the CGI program sends the status to the Boa server

11) The Boa server then sends the status in HTML text to the browser

12) The browser reads HTML tags and formats the page onto the screen

As shown in Figure 75 the sequence diagram describes interactions among the

web browser the Boa web server the CGI program the embedded adaptive controller

and the plant simulator

User requests the mantes

lUser sufrmis fwm

r Output to wefc ltAti

arv-affe ie Camp

bull bullraquo ot^pistoeoA

j ftqjampiljyaampgcfiabullsgft | [ a i s r f r d j ^ t f a b ^ l Lffi i f fff lpound

jSyrSNssampe asfeifY9 gams

vas tor PlssrtSwi

Send adaptYS epoundipound2

Sens ( to i l sA i

Send gtsapiive sfct bullbullbullbullbullJ Feeiv slaquotsptive pwi

a stent ms 7 j Ntrade^

(J 0 0

SefieJ acispfcw BM2

~^ rtecasve sdapitre raquo

Oylpaito wefccfer

Figure 75 Sequence diagram

714 Kernel Image of the ARM Board

The uClinux kernel is developed for the ARM board using Cygwin and Armtools

software [30] The distribution CD provides installation files for Cygwin and Armtools

as well as various helpful documents such as datasheet and reference manual [31] We

write a C program that plays the role of the adaptive mechanism and combine this

program with other predefined source files to build the uClinux kernel image The kernel

image will consist of the following elements 1) the adaptive mechanism program 2) the

CGI program 3) the Boa web server and 4) the NFS client

The CGI protocol includes a standard for interfacing applications with

information servers such as web servers The executable in a CGI can be any type of

executable that handles standard input and output [32] CGI programs are the most

common server-side method for performing an executable that go beyond HTML In this

implementation the adaptive mechanism and the CGI program are written in C language

The Boa web servers is enabled from uClinux distribution through 3 steps 1)

customize kernel settings customize vendoruser settings and update default vendor

settings 2) select networking options and select network device support and 3) establish

Ethernet connection between the ARM board and other computers such as the plant

simulator and engineering stations throughout a LAN network

The Boa web server is enabled for the ARM board to allow a user to use a web

browser in a client machine or an engineering station to point to the Boa web server and

start the adaptive controller testing form The user then set testing mode to send the

information in the form to the CGI program It will make a function call for the adaptive

mechanism At every simulation step execution status is posted back to the Boa server

and finally received by the users browser

72 Common Database

The shared database is located in the NFS server The database can be accessed

by any computer in the LAN The database consists of a number of structured text files

as listed in Table 71

Table 71 Structured data files

File name

kucdat

ucldat

uc2dat

kthdat

thldat

th2dat

th3dat

th4dat

th5dat

th6dat

th7dat

Data description

Time stamp of plant state

Plant state xi

Plant state X2

Time stamp of error variables

Error variable ei

Error variable e2

Time stamp of reference signal

Reference signal uci

Reference signal uC2

Time stamp of adaptive gains

Adaptive gain Gi

Adaptive gain 02

Adaptive gain 63

Adaptive gain 64

Adaptive gain 85

Adaptive gain 96

Adaptive gain 67

th8dat

adapoutdat

kmaxdat

Adaptive gain 0g

Output data of embedded adaptive controller

Maximal step size

73 Plant Simulator

We build a C++ project so called plant simulator to simulate the plant and

other auxiliaries including feedback control loop reference model and comparator Each

subsystem is represented by a C++ class which has been well developed in Chapter 6

Hence we just create the Makefile of the new project as follows

CC = g++

$(CC) -g -o PlantSim AdaptiveMecho Comparatoro

LinearControlo PlantModelo ReferenceModelo

In a console terminal we run the Makefile to compile and build the PlantSim

executive file as shown in Figure 76

$ make

$ I s - 1 P l a n t S i m

1 iij-ji--^- - M - - I - - bull

File Edit yiew Jsrmtnal Tabs Hop hnafl8ntiar]~thsltipiant^iiraquo$ make g+ -g -c -o Comparatoro Comparatorepp g-w- -3 -c -o LinearControto LinearControlcpp 9-w- -3 -c -o Plan-Modelo PtsrtHcdelcpp g++ -bull -L -o Refereiicelludsty RefeioiteMoJeltpp A++ -g -c -o ReferenceOutputc RefereaceOutputcpp J H g c o ControllcdOutputo ControllcdOutputcpp

lt(++ -w -g -o Pan-siit t es t cpp tcmparatoro Llnearcontrolo planuwdelo Referen ceModela ReferenceOutputo CcntroledOutputa hoanrioai-thesisPlantSii$ s -I PlantSim -rwxr-xr- 1 hoan hoan 295822 29G9-10-19 2237 Pl^Viw hoanhoan--IthlaquosisPlantSin$ I

Figure 76 Compile and build the plant simulator in a console terminal

74 Development of the Main Testing Form in HTML

We write the testing form in HTML to allow user to enter testing parameters The

input form is quite simple and described as follows

1 lthtmlgt

2 ltheadgt

3 lttitlegt UDP streaming lttitlegt

4 ltheacigt

5 ltbodygt

6 ltdiv a l ign=cen te r gt

7 ltimg s r c= logo g i f gtltbrgt

8 ltiirig s rc= image jpg gtltbrgt

9 ltdivgt

10 lthlgtEmbedded Adaptive Controllerlthlgt

11 ltform action=cgi-binmycgi method=get target=destgt

12 lth3gtPlease enter simulation parameterslth3gt

13 ltpgtSampling time (T) ltinput type=text

name=sptime value= size=4 0gt

14 ltpgtAdaptation rate (gamma) ltinput type=text name=gamma

value= size=40gt

15 ltpgtltinput type=submit value = Runxinput type=resetgt

16 ltinput type=hidden name=cmd value=rungt

17 ltformgt

18 ltbodygt

19 lthtmlgt

Figure 77 Main testing form in HTML

The beginning section is normal HTML similarly to the start of any HTML web

page The next section starting with the line ltform a c t i o n = c g i - b i n m y c g i

method=get t a r g e t = d e s t gt is the actual form [30] Some key features of

HTML form needed for CGI interface are listed in Table 72

Table 72 Some key features of an HTML form

Feature

action=

method=

target=

Code example

ltform action=7cgi-binmycgi

method-get target=destgt

ltform action=7cgi-binrnycgi

method=get target=destgt

ltform action=cgi-binmycgi

ltinput type=text name=sptimegt

ltinput type = submit value =

Run gt

Description

Define the URL of the CGI

program

Define how the information is

passed to the server

Define the target frame to load

the destination page

Input tag to enter sampling

time and text type

Collect and post data

75 Adaptive Mechanism Program

The adaptive mechanism program the core of the embedded adaptive controller

will be run in the ARJVI-7 development board Similarly to the C++ simulation project in

Chapter 6 the adaptive mechanism program written in C has two basic functions as

follows

static void getAdapMechPkt (int k struct Pkt xk_i struct

Pkt ek_i struct Pkt uck_i struct thetaPkt thk_i)

void genAdapMechPkt (int k struct Pkt xk_ struct Pkt ek_1

struct Pkt uck_i struct thetaPkt thk_i struct thetaPkt

The first function getAdapMechPkt is to receive signals from the common

database and save them to local variables The second one genAdapMechPkt is to

synthesize adaptive gains and sent them to the plant simulator via the common database

The pseudo code of the adaptive mechanism program is shown in Figure 78

1 static void getAdapMechPkt(int k struct Pkt x[k-l]

struct Pkt e[k-l] struct Pkt uc[k-l] struct thetaPkt

th[k-l])

2 Receive signals from database

3 getsig(vartmpfkxdat ampkx)

4 getsig(vartmpfxldat ampxl)

5 getsig(vartmpfx2dat ampx2)

6 getsig(vartmpfkedat ampke)

7 getsig(vartmpfeldat ampel)

8 getsig(vartmpfe2dat ampe2)

10 g e t s i g ( v a r t m p f t h 8 d a t ampth8)

11 return

13 void genAdapMechPkt(int k struct Pkt x[k-l] struct Pkt

e[k-l] struct Pkt uc[k-l] struct thetaPkt th[k-l]

struct thetaPkt th[k])

14 compute adaptive gains

15 th-gtk = k

16 thl[k]=thl[k-l]+Tgamma(bllel[k-1]+b21e2[k-1])xl[k-

1]10000000

17 th2[k]=th2[k-l]+Tgamma(bllel[k-l]+b21e2[k-1])x2[k-

1] 10000000

19 th8[k]=th8[k-1]-Tgamma(bl2el[k-1]+b22e2[k-1] ) uc2[k-

1]10000000

2 0 write to database

21 fwritethpkt(vartmpadapoutdat th_k)

22 settime(vartmpfkadat k)

23 return

Figure 78 Pseudo code of the adaptive mechanism program

751 CGI Program

As described in the introduction section CGI programs are the most common

server-side method for interfacing applications with web servers Parameter passing will

be done in both ways of communication 1) from client (browser) to CGI and 2) from

CGI to the browser [30] There are three steps of parameter passing as described below

First the CGI program communicates with the browser via web server

printf(Content-type texthtmlnn)

p r in t f (lthtmlgt ltheadgt lt t i t l e gt Embedded Adaptive Mech

lt t i t l e gt lt headgtn )

Second the CGI program captures the value of the command from the browser

unsigned char strlstr2 cmd

cmd = getval((unsigned char )cmd)

We note that the HTML file on the web server uses hidden attribute to pass

variables

ltinput type=hidden name=cmd value=rungt

The CGI program captures parameters passed by HTML page through

getenv() as follows

vstr = (unsigned char) getenv(REQUEST_METHOD)

if(vstr==NULL) return 0

if(strcmp((const char)vstrPOST) == 0)

Third the CGI program captures parameters It finds the length of the

parameters

vstr = (unsigned char) getenv(CONTENT_LENGTH)

if (vstr==NULL || strlen((const char)vstr)==0)return 0

It then captures the parameters from the browser using fgets() function in the C

stdio library as shown below

i f (vstr==NULL)return 0

fgets((char)vstrcl+1stdin)

The flow chart of CGI program is shown in Figure 79

C End ) Figure 79 Flow chart of the CGI program

The C pseudo code of the CGI program is shown in Figure 710

1 main ()

3 i n t v a l i d

4 unsigned char usernamepassword cmd

5 Al Communicate with the browser

6 printf (Content-type texthtmlnn)

7 printf(lthtmlgt ltheadgt lttitlegt Embedded Adaptive Mech

lttitlegt ltheadgtn)

8 A2 Capture the value of cmd from browser

9 cmd = getval((unsigned char )cmd)

10 if(strcmp((const char )cmdrun)==0)

12 A3 Capture value of sampling time

13 sptime=getval((unsigned char)sptiine)60

14 A4 Capture value of gamma

15 gamma=getval((unsigned char)gamma)

16 A5 Run adaptive mech

17 while(klt kmax)

18 A6 Waiting for Linux machine sending input signals

19 while(Igetkt)

20 getkt = getcsig(vartmpfktdat ampkT)

21 wait(5000)

2 3 Check time stamp

24 while(k=kT)

25 getsig(vartmpfktdat ampkT)

26 wait(10000)

28 Al Receive signals

29 getAdapMechPkt(k ampx_kml ampe_kml ampuc_kml ampth_kml)

30 A8 Generate adaptive gains

31 genAdapMechPkt(k ampx_kml ampe_kml ampuc_kml ampth_kml

ampth_k)

32 A9 Step increment

33 k++

36 else

37 AID Error message

38 printf (ltpgtSorry the request is invalid n)

39 All Close body and html tags

40 printf (ltbodygtlthtmlgtn)

41 exit (0)

Figure 710 Pseudo code of the CGI program

752 NFS Server Setup

The NFS server resides in a Linux machine There are three utilities needed to

run an NFS server 1) portmap daemon 2) mount daemon and 3) NFS daemon The

following procedure describes the NFS server setup for Linux Ubuntu machine

1) Install the package

bull sudo apt-get install nfs-kernel-server nfs-common

2) Modify etcexports to make the file system

o p t t e s t 192 168 0 128( rw f s id=0 no_root_squash)

bull opttest is the directory to be exported

bull 1921680128 is the IP address of ARM board (NFS client)

bull rw is to allow client machine to read and write access to the directory

bull norootsquash is to allow root on the client machine to have the same level

of access to the files on the system as root on the server

3) Enable the NFS server which will start multiple services and export the file

system as shown in Figure 711

sudo etcinit dnfs-kernel-server s tar t

Fii Edt ^jraquoraquo Terminal Tabs Help

iootghosRnome^Odn sudo e U i n t f i i f s k e r n e l servet s t a r t Expor t ing d i r e c t o r i e s f o r NFS ke rne l daemon

e x p o r t f s e t c e x p o r t s [ 1 ] N e i t h e r s u b t r e e check o r sno subt ree check s p p c i f led for export 1921586^opt test

Assuming d e f a u l t behaviour no s u b t r e e ^ c h e c k ) NOTE t h i s d e f a u l t has changed s ince n f s - u t i l s ve rs ion i e x

e x p o r t f s e t c e x p o r t s [ 2 1 N e i t h e r degsubtree check o ied f o r export 1 9 2 1 6 8 9 - o p t t e s t h o a n t x t K

Assuming d e f a u l t behaviour n o subt ree c h e c k 1 NOTE t h i s d e f a u l t has changed s ince n f s - u t i l s ve rs ion 10x

S t a r t i n g NFS ke m e l oothoanhomehoan

program 109880

looses 10S824 188824 100883 100883 100883 19S821

Yers 2 2 1 1 2 3 4 1

p r o t o U p udp udp t c p udp udp udp udp

daemon r p c i o f o

port 111 111

48909 55541

2849 2849 2649

partFapper po r t t appe r s t a tus s t a tus n fs n fs n fs n lock^r

subtree check specif

Figure 711 Enable NFS server for Ubuntu machine

Finally we can check status of RPC daemon using the following command

sudo rpcinfo -p

I I Bin Edit yamp

hoanaoan-$

gt Terminal

rpc program vers loeoea 168800 169824 100024 168883 186803 198803 18SB21 196821 180821 188983 16B983 1813883 168621 188B21 168821 188895 leeaos 188885 109805 186885 188005

hoan^hoan ~$

2 2 1 1 2 3 4 1 3 4 2 3 A 1 3 4 1 1 2 2 3 3

i n f o -j r o t o

t cp udp udp t c p udp udp udp udp udp udp t c p t cp t c o t cp tco t c p udp t c p udp t c p udp t c p

P po r t

111 n i

35368 35832

2649 2649 2S49

44664 44694 44994

2049 2849 2949

41394 41894 41894 33383 44819 33389 44819 33389 44819

M ^ s t i k ^ ^ lt

portssapper portraapper s ta tus s ta tus nfs n fs n fs filockrcgr nlockngr nlockffKjr nfs n fs nfs nlockragr nlockoigr nlockmgr isosintd sountd syjuotd sountd ^ountd ssountd

Figure 712 Check rpc daemon status

76 Building the Kernel Image

761 NFS Client Setup

Firstly we do make menuconfig for configuring the uClinux kernel Under

FileSystems configuration we choose Network File Systems

Figure 713 Select network file systems

Now under Network File Systems the following options should be chosen 1)

NFS File System Support and 2) Provide NFSv3 client support as shown in Figure

714 This completes the required configuration for the NFS client set up

l - pound ig

Arrotraquo keys navigate the menu ltEhtergt se lec t s subgenus gt 3 Highlighted l e t t ers are hutkeypound Pressing (Ygt includes ltHgt excludes 3 ltHgt Modularizes features Press (Escgt(poundscgt to e x i t ltgt for Help 3 legend Elaquo3 bui l t - in t 3 excluded ltHgt module lt gt module capable 3

UAAftAAA^AAftft^A^fiaAAAAAAAftAAAnAflAAAnAM 3 3 [ ] oda f i l e system support (aduanced network fsgt 3 1 J nterlfeszo f i l e system support (experimental replicating f s ) 3 tmdash1 N S f i l e system support 3 l gt ] ^ rg^deHrelaquo3 c l i en t support

3 I J N S seruer support 3 pound 3 HB f i l e system support (to mount Windows shares e t c ) 3 t 3 N P f i l e systef support (to mount NetWare volumesgt 3 3 3 A

Figure 714 Select NFS supports

Secondly we add user level utility for remote mounting of the server exported

directory Since the mount under uClinux-distuser does not work well with Linux 24

kernel we use the busybox utility The busybox user level utility needs to be configured

to include mount and unmount We choose BusyBox configuration under Vendor

Settings and select mount and umount under BusyBox configuration

Arrott keys navigate the Highlighted letters are hotkeys Pressing ltlfgt modularizes features Press (EscXEsegt to exit ltgt for Help

bdquo^S^n^-^^HiJ~ift-A1sslttded __ ltHgt nodule _lt Aj^sbdquoltapable UAAAApoundAAAAAAAAAAA

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 a 3 3 3 3 3 3 A

qir3Bm lt e gt lt u gt 3 AflAAAAAAAftAAAAAAAAAAAAAAftftAAAftflO^

AAAAAAftftA^AAAAAAAflAAAflAAAAAAftAAAAAfiAA [ 3 n ltNEWgt [ 1 ogger ltNEWgt [ 3 ogname (NEHgt [ 1 s ltNEWgt [ 3 smod (N6raquogt C 1 ro kedevs (NEUgt [ 3 m 5sum CNEWgt [ 3 m d i r (NEMgt [ ) gt f s j m i n i x (NEW) t 3 ro nod (NHO [ 3 m temp (NEMgt [ I n dprobe ltNBI) [ l i t r e (NEWgt [bull1 m unt (NEtO ( 3 m unt loop dev ice s ltNEtfgt [ 3 m unt support e t c mtab ltHBO

mmmsamsmBBEMsmamsm l 3 mltNEWgt [ 3 n ltNBraquo

3 n lookup ltNEtO 3 idof ltW6W1 3 ing (NEUgt

Figure 715 Select the mount option

Figure 716 Select the umount option

Lastly we modify Makefile under userbusybox directory We make some

modifications for ROMFS as follows

romfs install-romfssh busyboxlinks

syslog-install

c p $(PROG) $ (ROMFSDIR) b in $ (PROG)

$(ROMFSINST) b i n $ ( P R O G )

$(SHELL) $lt $ ( R O M F S D I R ) b i n

We fix for env xargs and rm 1) change env -i to binenv 2) change xarg to

binxargs and 3) change rm -f to binrm -f The modifications are shown in Figure

Ill i i^i^ bull -sectB

Figure 717 Modifications for Busybox Makefile

762 Enabling the CGI Protocol

The CGI protocol is built into the Boa web server by default for the uClinux

distribution We do the following two steps to enable the CGI protocol 1) modify

boaconf to make sure cgi-bin is mapped to Boa document root directory and 2)

customize Boa Makefile to make sure cgi program is properly compiled built and

placed at the proper directory of the kernel image

In the first step we modify the boaconf configuration file We note that the

configuration file for Boa is located in uClinux-distuserboasrc directory The first

thing is to map the virtual location ofcgi-bin to the actual location usrlibcgi-bin We

usually set etc as the document root of Boa server hence we can use it as the physical

location for the CGI program We edit boaconf by replacing the line of the Boa server

root location as

ScriptAlias cgi-bin etc

In the final step we modify Boa Makefile to build the CGI program to the

kernel image as follows

1) Add one line to define mycgi as the CGI executable to be built

TESTEXEC = m y c g i

2) Add one line to define mycgio as the temporary object file of mycgi

during compilation

TESTOBJS = mycgio

3) Add multiple lines to define the way to build mycgi including depending

object (mycgio) the compiler ($(CC)) and the referenced libraries as

$(TESTEXEC) $(TESTOBJS)

$(CC) $(LDFLAGS) - o $

$(TESTOBJS) $(SSL_LIBS) $(EXTRALIBS) $(LDLIBS)

4) Add multiple lines under romfs entry to define the built program and other

files to the file systems

$(ROMFSINST) bin$(EXEC)

$(ROMFSINST) etc$(CONFIG)

$(ROMFSINST) etc$(MIME)

$(ROMFSINST) etc$ (INDEX)

$(ROMFSINST) etc$(TESTEXEC)

$(ROMFSINST) etcembedded_adaptive_controllerhtml

$(ROMFSINST) etclogogif

$(ROMFSINST) etcimagejpg

$(ROMFSINST) e t c c l i p m p g

763 Enabling the Boa Web Server

Enabling the Boa web server from uClinux distribution takes 3 steps 1)

a LAN connection of the ARM board and a laptop through a router

In the first step when performing make manuconfig make sure to check the

following three boxes

1) Customize kernel settings

2) Customize vendoruser settings

3) Update default vendor settings

In the second step we select networking options and select network device

support

1) TCPIP networking

2) IP kernel level autoconfig

3) IP DHCP support

4) IPBOOTP

5) IPRARP

Then exit from the networking options we enter network device support and

1) Ethernet (10 or 100 Mbit)

2) RTL8019AS

At the application settings customization we go to Network applications screen

and check

1) Boa

2) dhcpcd-new

3) dhclient

4) ifconfig

5) inetd

6) ping

7) portmap (to be used for NFS port mapping)

8) route

9) routed

10)telnetd

ll)tftpd

Finally we build the kernel image using the command make from the console

terminal

Once the kernel image is ready it can be loaded into the ARM board by using use

Trivial File Transfer Protocol (TFPT) from either Windows or Linux computer If a

Windows machine is used we run the TFTP utility tftp32exe under the

Cygwintftpboot directory Otherwise the following command is to enable TFTP server

for Linux machines

root etcinitdxinetd start

Figure 718 Start xinetd for Linux Ubuntu

We then copy the kernel image to the tftpboot directory When power up the

ARM board it automatically loads and run the kernel image

Alternately we can manually load and run the kernel image using the following

commands in the console terminal (Linux machine) or the hyperterminal (Windows

machine)

tftp 0x0c008000 linux_bootrambin

go 0x0c008000

RRMboot 182 (Aug 12 2084 - 104321)

RRMboot code 0c700000 -gt 0c719860 CFG_ENV_SIZE=00001000CFG_ENVJDDR=00040000 DRAM Configuration Bank tt0 0C0O0000 8 MB Flash Configuration Flash 2 MB raquo- Using default environment Hit any key to stop autoboot 0 S3C44B0 H tftp 0X0C008000 linux_bootrambin RTL8019HS ethernet driver vl0 20030918 ARP broadcast 1 eth addr 0015c57b8086 TFTP from server 19216807 our IP address is 1921680128 Filename linux_bootrambin Load address 0xc008000 Loading

done Bytes transferred = 1431920 (15d970 hex) S3C44B0 laquo go 0x0c008000_

Figure 719 Manually load the kernel image to the ARM board

i--l lly|if-i K irnir^i

File Edit View Call Transfer Help

a amp bullbullbull- s 0 a i f

Command mkdir varrun Command mkdir varlock Command ifconfig lo 127001 Command route add -net 127000 netmask 2552552550 Command dhcpcd -p -a eth0 amp [111 Command ifconfig eth0 1921680128 Command binboa -c etc amp [13] Command ps PID PORT STAT SIZE SHARED XCPU COMMAND 1 S 37K 0K 485 init 2 S 0K 0K 0 3 S 0K 0K 0 4 S 0K 0K 0 5 S 0K 0K 0 6 S 0K 0K 0 7 R 72K 0K 99 11 Z 0K 0K 0 13 S 136K 0K 0

0 keventd 0 ksoftirqd CPU0 0 kswapd 0 bdflush 0 kupdated 9 binsh etcrc 0 dhcpcd 0 binboa -c etc

Execution Finished Exiting

Sash command shell (version 111) gt _

Figure 720 Manually run the kernel image

We are now able to ping ARM board from the host and to ping the host from

ARM board With ping working we can now start the Boa server as follows

gt b in boa -c e t c amp

where etc is the internet document root directory of the Boa web server and amp makes

the Boa process run in the background

We can use ps to check out its status as shown in Figure 721

lcr H y p o lermiridl

p cs S O B f - - mdash bdquo mdash bdquo

Command mkdir uarlog Command mkdir varrun Command mkdir varlock Command ifconfig lo 12706 Command route add -net 127 Command dhcpcd -p -a eth0 i til]

bulltrade u u mdash

1 000 netmask 2552552550 lo

Command ifconfig eth0 1921680128 Execution Finished Exiting

Sash command shell (version gt binboa -c etc amp [141 gt ps PID PORT STAT SIZE SHARED 1 S 37K 0K 2 S 0K 0K 3 S 0K 0K 4 S 0K 0K 5 S 0K 0K 6 S 0K 0K 13 S0 R 71K 0K 14 S0 S 136K 0K

|Connected 01022 Auto detect 1152008-N-l

KCPU COMMAND 02 init 0 0 0 0 0 0 7

0 keventd 0 ksoftirqd_CPU0 0 kswapd 0 bdflush 0 kupdated 2 binsh 0 binboa -c etc

Figure 721 Process status

77 Testing

771 Test Procedure

The test procedure for the whole system is as follows

1) Establish the serial communication between a computer and the ARM board

using serial communication port 0

2) On the PC side run hyper terminal software by start gt all program gt

accessories gt communications gt hyper terminal

3) Set up a LAN network consisting of the ARM board the NFS server (Linux

machine) the plant simulator (PC Linux machine) and engineering stations

(PC Linux machine)

4) Power up the ARM board the hyper terminal console will display the

following information

bull TFTP service loading the kernel image

bull Uncompressing Linux and booting the kernel

bull Shell invoked to run the boot script file etcrc

5) Enable Boa and run commands for portmap and NFS mount as depicted in

Figure 722

bull test - HyperTermin File Edit View Call Tran

D Graquo S S if

5fw help

[11] Command ifconfig ethO 1921680128 Command boa -c etc 8 [13] Command portmap amp [14] Command ps PID PORT STAT SIZE SHARED CPU COMMAND 1 S 37K 0K 333 init 2 S OK OK 0 3 S OK OK 0 4 S OK OK 0 5 S 0K OK 0 6 S 0K OK 0 7 R 72K OK 78 11 Z OK OK 45 13 S 136K OK 0 14 S 91K OK 0

0 keventd 0 ksoftirqd_CPU0 0 kswapd 0 bdflush 0 kupdated 5 binsh etcrc 0 dhcpcd 0 boa -c etc 0 portmap

Command busybox mount -t nfs -o rsize=1024wsize=1024 192168020opttest v artmp Execution Finished Exiting

Connected 00238 Auto detect i 115200 8-N-l NUM

Figure 722 Mount network files for the NFS client

Mount the network file system for NFS client (ie ARM board) using the

following command

busybox mount - t n f s - o r s i z e = 1 0 2 4 w s i z e = 1 0 2 4

1 9 2 1 6 8 0 8 o p t t e s t v a r t m p

where 19216808 is the IP address of NFS server opttest is the exported

directory and vartmp is the local directory on NFS client

Ping the ARM board from the Linux machine and vice versa

| g haanhoan ~

file Edit ifiew Terminal Tabs Jdelp hoantlaquooan~$ ping mimvm PING 1921686128 (192168 64 bytes from 1921688128 64 bytes from 1921688128 54 byles Hum 1921689128 64 bytes from 1921686128

8128) 56(8-1) bytes of data lcmp_seq=l ttl=255 tisse=l47 ms icmp_seq=2 t t 1=255 twe=136 ms leap seq=3 LLl=255 Uine=141 mi icmp seq=4 tt1=255 time=14B ms

--bull 1971686178 ping statist ics ---4 packets transmitted 4 received reg packet loss time 3 rtt minavgiBaxrsdev = 1368141714798948 as hoanhoan--$ |

Figure 723 Ping ARM board from the Linux machine

I Oil hiypL i Icirmiidl

File Edit View CaB Transfer Help

D G aa f bingt ping 19216808 PING 19216808 (192168 64 bytes from 192168 64 bytes from 192168 64 bytes from 192168 64 bytes from 192168 64 bytes from 192168 64 bytes from 192168 64 bytes from 192168 64 bytes from 192168 64 bytes from 192168 64 bytes from 192 mdash 19216808 ping s 59 packets transmitted round-trip minaugmax bingt

08) icmp icmp icmp icmp icmp icmp icmp icmp icmp

56 dat _seq=0 _seq=l _seq=2 _seq=3 _seq=4 _seq=5 _seq=6 _seq=7 _seq=8

a bytes ttl=64 t ttl=64 t ttl=64 t ttl=64 t ttl=64 t ttl=64 t ttl=64 t ttl=64 t ttl=64 t

ime=20 ime=10 ime=10 ime=10 ime=10 ime=10 ime=10 ime=10 ime=10

tatistics 59 packets received 100101200 ms

0JS packet loss

Figure 724 Ping the Linux machine from the ARM board

8) A user using a web browser to open the main GUI page of the Boa web

server at the URL location lthttpl 921680128embedded_adaptive_

controllerhtmlgt

Main GUI of Embedded Adaptive Controller - Mozilla Firefox File Edit View History Bookmarks lools (Help

$01 C s- J http1921680^

J Main GUI of Embedded

SAN iOSfe STA OHIVERSiTY

Embedded Adaptive Controller

Please enter adaptive mechanism parameters

Sampling time (T msec) 110

Adaptive factor (gamma) 11000

Run Reset

Figure 725 Open the main page of Boa web server

9) Set sampling time and adaptation rate y and click Run to submit

information to the CGI program

10) At the same time run the plant simulator on a Windows Linux computer

and start testing the embedded adaptive system as shown in Figure 726

t ie edit View Terminal TaJ3s

hcangftoaa - t hes i s^P lan ts i i raquo i Time = 6T Plant parameters A = -7129180 -6954586 B - 3130388 6197300 B - -3959188 -6825686 u l [ 8 ] = 0517838 IIJ [HI = (JiHHHhH xi[8] = BEeeese x2[ei = scsesas M l [8] - 6666960 atr ia l = eeeeooo TisiC = IT Plant parameters A = -7129199 -6954566 B = -3139189 8197396 K = -tfBMOBB -KH74bB8

adap t i vecamro l

13S3603 6682830

6258383

1393689 -8pound62298 B JhK-iH-)

input pkt sent o Adaptive wechanlsu Meiil i i iy fui cstidiilive ydln pk l Press any hey to c c n t i n u e

-6239783 6626603

666G855

-9259783 -0629683 H HHI-li4s

Figure 726 Start the plant simulator in a Linux machine

11) The testing results can be observed at either the web browser (Figure 727)

or the plant simulators consol (Figure 728)

4 Bis Edit Yiaw History look

Gsxgte i

efk-Dpl =

e(k-l) p2 =

ucfk-ljk =

uc(k- l ) p l

uc(k-l) p2

thik-lj k =

th ik - l j th l

th ik- l ) th2

th(k- l ) th3

thk- l ] th4

thk- l ) th5

thfk- l j th

amp c l

= 50000

=10000

= 66000

= -309998

= 1 0 4 4 2 2 5 4

= -42712

= 4240

ITtdlk^ Turlb

o Htp iH9i

| IG^Search

16S0 1

raquo bull zfgt

b i r p

ycqr u

^Settings

Figure 727 Testing result displayed on the web browser

2SSpound2SSIiiSyi Ngjjpoundjlll file Edit iew Terminal tabs Help

Get t i i i ie Fress any key to con t inue 2 ltpgt Opening the input f i l e op t t es t f ka da t ltpgt Opening the input f i l e opt test adapout dat Adaptive gains synthesized th k |5 ] ~ 6881 t

t h l [ 5 ] = 9 371599 t i 2 [ 5 ) = -6 516686 I t h 3 [ 5 ] = fl286662 | t h 4 [ 5 ) = -8 389999 | t hS [5J = 1044283 I t h 6 [ S ] = -BB42788 | t h 7 [ 5 ] = 8 868449 t h 8 [ 5 ] = 1886624

u l [ 5 ] - 9 517732 u2[5J = 6 101256 x l [ 5 ] = -8 867699 JS x 2 [ 5 ] = -8 S85796 Jns l [5 ] s -8 887186 X B 2 [ S J = -8GS5626 J Titfve = 6T ^ Plant paraii^eters A = -7129188 -8954586 1543688 -8239788 B = -0153198 0217368 -8082696 -8829688 B - -8859488 -8829688 0233388 BOB8945 Input pkt sent to Adaptive Mechanise Waiting for adaptive gain pkt Press any key to cont inue

Figure 728 Testing result displayed on the plant simulators monitor

772 Test Results

As aforementioned all testing outputs are stored in the shared database which

can be accessed from any computer of the LAN network The output data files are listed

in Table 73

Table 73 Structured output data files

File name

t_xdat

t_xmdat

t_edat

t_ucdat

t_udat

t_thetadat

t_ydat

t_ymdat

Data description

Plant state x and X2

Reference state xm andxm2-

Error variables e and ej

Reference signals uc and uci-

Control signals u and U2

Adaptive gains 6 - 0

Controlled outputs y and_y2

Reference outputs ym and_yOT2-

The plant simulator has varying dynamics by randomized parameters and

interfered by unpredictable disturbances The embedded adaptive controller synthesizes

adaptive gains at every step time We find that the plant states always keep track of the

reference states all the testing time as shown in Table 74

Table 74 Output data of state variables

000000

-000521

-000667

-000817

-000764

-000770

-000815

-000738

-000650

-000665

-000641

-000623

-000645

-000594

-000587

-000551

-000514

-000587

-000641

000000

-000037

-000151

-000291

-000447

-000580

-000713

-000862

-000986

-001091

-001202

-001313

-001403

-001503

-001586

-001667

-001748

-001817

-001903

000000

-000523

-000687

-000730

-000731

-000719

-000702

-000685

-000669

-000652

-000637

-000622

-000608

-000595

-000582

-000569

-000558

-000546

-000536

000000

-000039

-000153

-000289

-000427

-000563

-000693

-000817

-000936

-001049

-001158

-001261

-001359

-001453

-001543

-001628

-001710

-001788

-001862

-000522

-000480

-000564

-000550

-000539

-000547

-000528

-000496

-000503

-000430

-000472

-000441

-000491

-000511

-000390

-000446

-000383

-000369

-000381

-000435

-000441

-000439

-000447

-000373

-000418

-000404

-000373

-000440

-001982

-002051

-002115

-002190

-002251

-002311

-002367

-002427

-002476

-002525

-002558

-002603

-002641

-002687

-002732

-002756

-002781

-002813

-002832

-002862

-002894

-002916

-002952

-002980

-002995

-003014

-003035

-003052

-000526

-000516

-000507

-000498

-000489

-000481

-000474

-000466

-000460

-000453

-000447

-000440

-000435

-000429

-000424

-000419

-000414

-000410

-000405

-000401

-000397

-000393

-000390

-000386

-000383

-000380

-000377

-000374

-001933

-002000

-002065

-002126

-002185

-002241

-002294

-002345

-002394

-002440

-002484

-002526

-002566

-002605

-002641

-002676

-002710

-002741

-002772

-002800

-002828

-002854

-002879

-002903

-002926

-002948

-002969

-002989

-000453

-000436

-000385

-000428

-003078

-003109

-003139

-003161

-000371

-000369

-000366

-000364

-003007

-003025

-003043

-003059

-0 025

Reference states and plant states

_ m _ _ ^ i = _ mdash p i r r F ^

~~-ti ===ii

-mdash^zr ~~ i

2(enfc) -

Figure 729 Variable states during simulation of the embedded adaptive controller

As introduced in Sec712 the output data of the embedded adaptive controller

will be compared with the result of software models the MATLAB Simulink program

and the C++ executable We note that MATLAB and C++-based simulation programs

have the same results The comparison result is shown in Table 75 We find that all data

are almost identical

Table 75 Comparison result between the embedded and software models

-00006

-00009

-00011

-00008

-00001

-00004

-00008

-00001

-00002

-00005

-00004

-00005

-00004

-00008

-00001

-00002

-00003

-00002

-00003

-00002

-00003

-00002

-00001

-00002

-00010

-00009

-00001

-00009

-00006

-00005

-00001

-00008

-00013

-00002

-00004

-00007

-00014

-00006

-00007

-00001

-00010

-00003

-00004

-00005

-00003

-00004

-00002

-00001

-00002

-00001

-00002

-00003

-00005

-00006

-00008

CHAPTER 8

CONCLUSION AND FUTURE WORK

81 Conclusion

Adaptive control is applied for solving the control problem of the gasoline

refinery with high nonlinearity and unpredictable disturbances For this class of control

problems conventional controllers are very limited and have a lot of deficiencies

The adaptive mechanism governed by an adaptation law is the heart of any

adaptive controller We establish the adaptation law for the plant control system using

Lyapunov stability theory This adaptation law is accurate for a generic second order

plant hence it is obviously applicable for adaptive control of other second order systems

in different realms such as chemical industry military industry and robotics

Adaptive control system design is much complicated than conventional controller

design due to the complexity of adaptive structure and the issue of unknown or time-

varying parameters We use an effective methodology for system modeling and design

using state space All computational works are based on matrix manipulation which is

fully supported by MATLAB We can apply this methodology to extend the result to

higher order systems

We have shown the design - verification flow with various phases 1)

mathematical model 2) process calculation and modeling 3) controller design in both

continuous-time and discrete spaces 4) controller simulation and 5) in-hardware

implementation and testing The mathematical model which is given in term of a set of

mathematical equations of energy and material balances provides insightful

understanding of the dynamic behaviors of the plant The process calculation is

necessary to obtain steady-state data for control system design in later phases The

reference model is constructed with mathematical approach and proven to be stable and

ensure the plants steady-state properties

We design the adaptive controller in continuous-time space and then convert it

into discrete-time space using z- transform The discrete-time version must be

accomplished prior to implementation of the adaptive design on digital computers We

successfully design and implement the embedded adaptive controller using ARM

processor We apply the state-of-the-art testing technique in which we employ NFS and

concept of distributed system over an Ethernet network We have overcome the new

challenges which require a reliable closed control loop and real-time data transfer

between the controller and the plant simulator As a result the embedded adaptive

controller remotely controls the plant simulator on a network node

82 Future Work

First we can design embedded adaptive controllers using combination of

Lyapunov theory and hyperstability concept which give better rejection of disturbances

and time-varying parameter problems [34] Many authors concern this perspective for

example Nguyen and Nitin [10] design an adaptive control system with hyperstability in

continuous-time space We can extend the existing works to discrete-time space and use

the same methodology proposed in the thesis to carry out in-hardware implementation

Second we can build a real pilot plant It is costly however we can carry out

experiments and measure actual control performance The experimental scheme is

proposed as displayed in Figure 91 Ideally the composition is continuously measured

by an online analyzer or gas chromatography However we can select tray temperatures

as secondary measurements which indicate product concentration in an indirect way

The reason is to reduce equipment cost Temperatures Ta and Tp are the most sensitive

temperatures which are best related to product concentrations x and xgt

xv2 r~

PILOT PLANT

Realtime (lata

D Xbdquo

B xbdquo

Online ineasui emait

Figure 91 Block diagram of the experimental pilot plant

The proposed scheme includes three main parts The first part is a distillation

column in laboratory The second part is an embedded adaptive controller implemented

in a PC or microcontroller The third part is a programmable logic controller (PLC)

system for handling control valves Vi and V2

Third adaptive mechanism can be programmed in a PLC By using this concept

we can upgrade existing conventional controllers using PLCs just by modification of their

programs This is important to save equipment and engineering cost

PE -W-V2

fc V -tvi

PILOT PLANT

PID Embedded

Adaptive Ccntroller

Online measurement

Figure 92 Adaptive mechanism programmed in a PLC

Fourth we can design adaptive controller as System on a Chip (SoC) which

contains the complete system SoCs are developed with Verilog or any HDL language

and can be implemented using a Field-Programmable Gate Array (FPGA) such as an

Ethernet-supported Xilinx FPGA board

Web client Engineering station

Hyperterminal

SoC Adaptive Controller

Figure 93 Integrated testing environment for SoCs and other digital systems

Finally we can extend testing environment introduced in Sec 713 by integrating

SoC adaptive controller and pilot plant as shown in Figure 93 The embedded adaptive

controller remotely controls the pilot plant over the LAN network Obviously we can

deploy this testing methodology for validation of SoCs and other digital systems

particularly distributed systems

APPENDIX A DISTILLATION CONTROL TECHNIQUES

Al Column Pressure Control

Most distillation control systems either conventional or advanced assume that

distillation columns operate at a constant pressure Maintaining constant operation gives

stable operation and increases overall plant profit

It is important to prevent pressure of a distillation column from changing rapidly

either up or down Sudden decreases in pressure can cause flashing of the liquid on the

trays and the excessive vapor rate can flood the column Sudden increase in pressure can

cause condensation of vapor and the low vapor rates can cause weeping and dumping of

We consider again the schematic of distillation column as shown in Figure 21

The overhead vapor after being heat removal in the condenser will consist of two phases

liquid and vapor The objective is to condense maximum quantity of distillate (ie

maximize the profit) at its true boiling point to minimize the energy cost for condenser

duty There is a pressure balance established between the column top and the reflux

drum for the purpose of stabilizing the column pressure Several common types of

column pressure control are described in the following sections

All Coolant Manipulation

As shown in Figure A 1 the condenser is normally a heat exchanger using coolant

(eg cooling water or refrigerant) The control valve adjusts the flow rate of coolant to

obtain the desired condenser duty

6gtpiKii(issUK flsiraquo CO -105-1 klai

reg Spf M -amp- 1

i KZ- ^ -n

(AV) t bull- Coolant CONDENSER T

REFLUX DRUM

Figure A 1 Column pressure control using coolant manipulation

Pressure signal from the pressure sensor installed in the overhead vapor flow is

transmitted to the pressure controller The control output which is a function of the error

signal based on the deviation of the measured pressure from the set point supplies

controlled pressurized air (207 - 1034 kPa) to the pneumatic valve actuator As the

result the coolant flow rate is adjusted to the desired value If the overhead flow rate

increases (or decreases) the coolant flow rate will increase (or decrease)

correspondingly This maintains the column pressure stable

A 12 Vent-bleed

As shown in Figure A2 inert gas is added or bled from the system using a dual

split-ranged valve system so that under normal conditions both control valves are closed

The reflux flow must be considerably sub-cooled in order to keep the product

concentration in the vent gas stream low The reflux temperature is directly affected by

the coolant temperature

CONDENSER^-

rlaquof|ugt flow i_i

mdash 4 6

i mdash amdashgtp j

Figure A2 Column pressure control using vent bleed

The cooling capacity of condenser is preset When the vapor rate increases

significantly it is not totally condensed As a consequence the pressure in the reflux

drum will increase To stabilize it the pressure controller will command the control

valve VI to vent the exceed vapor

In contrast the vapor rate is condensed too much which causes a pressure drop at

the top column section Consequently the control valve VI is gradually closed and the

control valve V2 is slightly open

A2 Column Level Control

The two liquid levels that must be controlled are in the reflux drum and column

base The levels are controlled in different ways depending on a number of factors [35]

If the column is part of a series of units in a plant it is usually important from a

plant-wide control viewpoint to use the liquid levels as surge capacities to reduce effect

of disturbances In such an environment it is usually preferable to control the base level

with the bottoms flow and the reflux drum level with the distillate flow

Inert gas O

mdash m ltV3

i te i iaal

J5) Input ho-ot IS)

r fgtrtge n-=j (stage n-0

B - t-t

a) Kettle type

o h m m I K I

i t t_e i i - 1 1

-amp Q

_ U ftau irav

P| vopor flow

V U heat -

- i _i r-f umdash r laquo

b) Vertical thermo-siphon type

r oiiiim lose f-1iifictl-f

c) Horizontal thermo-siphon type d) Forced-circulation type with heat

exchanger

bottom tray vopor flow

column bas i______mdash=

triage n=l) H = sect sect | i = 7

A WH-J

e) Forced-circulation type with heater

Figure A3 Some typical types of reboiler

In high reflux ratio columns (ie LID gt 5) using distillate stream to control level

would require large changes in D for fairy small changes in L or V Thus the

disturbances would be amplified in the distillate flow rate The reflux drum level should

be controlled by reflux in accordance with the Richardsons rule-we always control level

with the level with the largest stream [36]

In practice we should care of potential problems with inverse response that

may happen and cause the plant unstable An increase in reboiler heat input can quickly

increase the fraction of vapor In a thermo-siphon reboiler this can push liquid back into

the base of the column resulting in a momentary increase in the liquid level in the

column base In a kettle reboiler the increase in vapor fraction causes the material in the

reboiler to swell and more liquid flows over the outlet weir into the surge volume in the

end of the reboiler Therefore the liquid level in this section momentarily increases

Various reboiler types are shown in Figure A3

A3 Methods of Distillation Column Control

A31 Degrees of Freedom of Distillation Process

The degrees of freedom of a processing system are the independent variables that

must be specified in order to define the process completely Consequently the desired

control of a process will be achieved when and only when all the degrees of freedom

have been specified

The mathematical approach to finding the degrees of freedom of any process is to

total all the variables and subtract the number of independent equations [12] However

there is a simple approach developed by Luyben [35] In Figure 21 there are five

control valves one on each of the following streams distillate reflux coolant bottoms

and heating medium The feed stream is considered being set by the upstream process

So this column has five degrees of freedom But inventories in any process always must

be controlled Inventory loops involve liquid levels and pressures This means that the

liquid level in the reflux drum the liquid level in the column base and the column

pressure must be controlled

If we subtract the three variables that must be controlled from five we end up

with two degrees of freedom Thus there are two and only two additional variables that

can be controlled in the distillation column

Notice that we have made no assumptions about the number or type of chemical

components being distilled Therefore a simple ideal binary system has two degrees of

the freedom and a complex multi-component non-ideal distillation system also has two

degrees of freedom

A32 Control Structures

The manipulated variables and controlled variables of a distillation column are

displayed in Table A 1

Table A 1 Manipulated variables and controlled variables of a distillation column

Controlled variables

Concentration (temperature) of distillate

Concentration (temperature) of bottoms

Column pressure

Liquid level in the column base

Liquid level in the reflux drum

Manipulated

variables

Reflux flow rate

Reboiler duty

Condenser duty

Bottoms flow rate

Distillate flow rate

Control valve

location

Reflux flow (VI)

Heat flow (V4)

Coolant flow (V3)

Bottoms flow (V5)

Distillate flow (V2)

The column has 2 degrees of freedom hence a control structure is a selective

combination of two manipulated variables As shown in Table A2 there are many

common control structures are used in practical distillation [37]

Table A2 Typical column control structures

Control Structure

D-V(or D-QB)

L-V(or L-QB)

Role of valve

Manipulated variable

Inventory

Control (IC)

Separation

Control (SC)

For a binary distillation the most common structures are the energy balance

structure L-V and the material balance structure D-V and L-B Most industrial

distillation columns on two-point control are probably operated by one of these control

structures

Selecting a control structure is a complicated problem with many facets It

requires looking at the column control problem from several perspectives

1) A local perspective considering the steady state characteristics of the column

2) A local perspective considering the dynamic characteristics of the column

3) A global perspective considering the interaction of the column with other

units in the plant

A33 Energy Balance Structure

As shown in Figure A4 the energy balance structure which is usually called LmdashV

structure can be considered to be the standard control structure for dual composition

control of distillation In this control structure the reflux flow rate L and the boilup

manipulator V are used to control the primary outputs associated with the product

specifications The liquid holdups in the reflux drum and in the column base known as

the secondary outputs are usually controlled by distillate flow rate D and the bottoms

flow rate B

I raquo - sect I -

ATbdquo

Figure A4 Energy balance structure

A34 Material Balance Structure

Two other common control structures are the material balance structures D-V and

L-B As shown in Figure A5 the D-V structure seems very similar to the LmdashV structure

The only one difference between the L-Vand D-V structures is that the roles of L and D

are switched

Figure A5 D-V control structure

The L-B structure is depicted in Figure A6 There exists a possibility to occur an

inverse response between reboiler liquid level and boilup flow which causes difficulties

for inventory control in the bottom section This structure is very sensitive to

disturbances in feed

H amp J bull

Figure A6 L-B control structure

APPENDIX B PROCESS CALCULATION

Bl Basic Engineering Data

The plant feed stock is condensate whose actual composition always fluctuates

around the average composition as shown in Table Bl [44]

Table Bl Condensate composition analyzed by gas chromatography

Component

Propane

Normal Butane

Isobutane

Isopentane

Normal Pentane

Hexane

Heptane

Octane

Nonane

Normal Decane

n-CHH24

n-C12H26

Cyclopentane

Methylclopentane

Benzene

Toluen

O-Xylene

E-Benzene

Table B2 Distillation data

Cut point

(degC)

ASTM D86

(degC)

124024

Product specifications are given in Table B3 [44]

Table B3 Gasoline quality requirement

Properties

1 Octane Number

2 Lead Content (g1)

3 Distillation (deg C)

10 vol

50 vol

90 vol

Residue ( vol)

4 Corrosion 3h50degC

5 Existent Gum (mg100ml)

6 RVP 378 deg C (kPa)

7 Total sulfur content (wt)

8 Oxidation stability (min)

9 Density at 15 deg C (gcm3)

Testing method

ASTM D2699

ASTMD3341

ASTM D86

ASTM D130

ASTMD381

ASTM D323

ASTM D1266

ASTM D525

ASTMD1298

Requirements

min 87

max 015

max 70

max 120

max 190

max 210

max 20

maxN-1

max 40

min 43

max 80

max 015

min 240

070 - 074

The plants nominal capacity is 130000 tons of raw condensateyear based on 24

operating hours per day and 350 working days per year The plant capacity is quite low

due to depending on upstream processes The plant equipment is specified with a design

margin of 10 above the nominal capacity and turndown ratio is 50 of the nominal

capacity

82 Distillation Process Calculation

B21 Equilibrium Flash Vaporization Curves

According to W C Edmister method [45] the equilibrium flash vaporization

(EFV) curve is converted from the data of true boiling point (TBP) For example we

perform calculation for the 50-percent point as follows

tso (TBP) = 5842 C

t(30- io) (TBP) = 3599-2467=1132 degC

Look up TBP-EFV chart the temperature difference is determined as

t50 (EFV-TBP) = 1-5 C

Therefore

tso (EFV) = 5842+15=5962 degC

Repeat the procedure above for all TBP temperatures to determine EFV (1 atm)

temperatures Then convert the EFV (1 atm) data into the EFV (46 atm) data by using

the Cox chart [46] The results are shown in Table B4

Table B4 Relationship between ASTM TBP and EFV

EFV (1 atm)

EFV (46 atm)

B22 Yield of Fractions

Based on the TBP data the yield of fractions for the gasoline plant can be

determined as shown in Figure Bl

20 3840 60

Volume

80 100

Figure B 1 Yield curve

B23 Operating Pressure

The column is designed 14 trays and the pressure drop across each tray is

estimated approximately 80 kPa Therefore the pressures at the feed section and the top

section are 46 atm and 4 atm respectively

B3 Calculation for the Feed Section

B31 Description

The pre-heater rises the feed temperature towards the expected temperature at

which the required phase equilibrium is established As a result the feed split specified

by the yield curve is obtained

The key parameters will be determined as follows

1) Equilibrium phase flows into the feed section

2) Material balance at the feed section

3) The feed temperature

B32 Calculation

The feed has liquid-gas equilibrium with gas percentage of 38 volume

However it is usually to deeply cut more 4 (the unexpected heavy component will be

condensed and refluxed to the column) Thus there are two equilibrium phase flows 1)

vapor VF = 38+4 = 42() and 2) liquid LF =100 - 42 = 58()

The phase equilibrium is depicted in Figure B2

fegtegtd f l ow

tray f

Figure B2 Equilibrium phase flows at the feed section

The heavy fraction flow LF dissolved a small amount of light components is

descending to the column bottom These undesirable light components shall be caught by

the vapor flow Vf arising to the top column The vapor flow Vf can be assigned as 28

The bottom product is determined by the yield curve as 62vol hence the

internal reflux across the feed section can be calculated

Rf= B-LF+ Vf= 62 - 58 + 28 = 32 vol

Look up the EFV curve (46 atm) of the feed section the required feed

temperature is 118degC corresponding to the point of 42 vol

Table B5 Material balances for the feed section

Stream

Total light

fractions E S D

Bottoms B

Volume fraction

Liquid flow rate

-73916

133973

-64677

143213

Liquid density

Mass flow rate

-45458

-38677

104046

B4 Calculation for the Stripping Section

B41 Description

In the stripping section liquid flows which are descending from the feed section

include the equilibrium phase flow LF and the internal reflux flow RE They are

contacting with the arising vapor flow Vffox heat transfer and mass transfer The result is

that all undesirable light components should be completely removal from the bottoms

This process is accomplished with the aid of heat flow supplied by the reboiler

The main parameters should be determined as follows

1) The bottoms temperature

2) The reboiler duty QB

B42 Calculation

The column base pressure is approximately the pressure at the feed section (46

bars) because the pressure drop across this section can be neglected

The phase equilibrium is shown in Figure B3

stripping section

Figure B3 Equilibrium phase flows at the stripping section

Look up the EFV curve (1 atm) of the stripping section and the Cox chart the

equilibrium temperature at this section (46 atm) is 144 degC

The reboiler duty is equal to the heat input which generates boilup and increases

the temperature of the stripping section by an increment of 144-118=26degC

Table B6 Material and energy balances of the stripping section

kcalkg

kcalhlOJ

kJhl0 j

276860

131300

408161

kcalhlOJ

149134

kJhl0J

267136

357141

624280

As a result the reboiler duty is QB = (62428 - 408161) 103 = 2161190 kJh

B5 Calculation for the Rectifying Section

B51 Description

The overhead vapor flow which includes Frfrom the feed section and Vfrom the

stripping section passes through the condenser (to remove heat) and then enter into the

reflux drum There exist two equilibrium phases 1) liquid (butane) and 2) vapor

(propane vapor and dry gas) The liquid from the reflux drum is partly pumped back into

the top tray as the reflux flow L and partly removed from the system as the distillate flow

The liquid is still dissolved a very small amount of light components Therefore

the reflux flow whilst entering into the top tray will receive heat to vaporize completely

all light component dissolved and the liquid remained will be collected as the internal

reflux flow

B52 Calculation

The top pressure is 4 atm due to pressure drop across the rectifying section

The dew point of distillate is correspondingly the point 100 of the EFV curve of

rectifying section Based on the Cox chart the top section temperature is determined as

46degC

The equilibrium phase flows at the stripping section are display in Figure B4

Stage 15 (tray 14)

raquo- Uncondensed Gas (small quantity)

D Distillate

Figure B4 Equilibrium phase flows at the rectifying section

Table B7 Material and energy balances around the boundary (A)

9611+Ro

kcalkg

ZSD+Ro

5065+Ro

9611+Ro

kcalkg

kcalhlOJ

11053+24 R0

kJhlOJ

1005 R0

46263+1005 R0

kcalh103

49131+97Ro

56405+ 97R0

kJhl0J

205665+406R0

236111+406R0

Based on the energy balance we find the solution of R0

46263+1005 Ro= 236111+406 Ro

Therefore

Ro= 7415 (tonh)

We now calculate the (external) reflux flow L Enthalpy data of the reflux flow L

looked up the experimental chart for petroleums enthalpy are corresponding to the

liquid state of 40degC (liquid inlet at the top tray) and the vapor state of 46degC (vapor outlet

at the column top)

L inlet at 42degC Hiiqujd (inlet) = 22 kcalkg

L outlet at 46degC Hvapor (ouiet) = 106 kcalkg

We find the solution of the energy balance equation

AHRoR0= AHLL

(115-24) (742) = (106-22) I

Therefore

L = 804 (tonh)

B6 Calculation Results

B61 Raw Gasoline Property

The bottom product named raw gasoline is the major blend for manufacturing

the finished gasoline The distillation data of the raw gasoline is shown in Table B8

Table B8 ASTM distillation curve of the raw gasoline

Boiling point (degC)

B62 Main Stream Property

The specification of the finished gasoline product is presented in Table B9

Table B9 Main streams of the plant

Stream

Temperature (C)

Pressure (atm)

Density (kgm )

Volume flow rate (m h)

Mass flow rate (kgh)

Mass flow rate (tonyear)

Stream

Temperature (C)

RVP (kPa)

Density (kgm )

Condensate

130000

Reformate

105000

Raw gasoline

Gasoline

250000

B7 Process Description

B71 Simplified Process Flow Diagram

The simplified process flow diagram is shown in Figure B5 The gasoline plant

consists of many apparatuses and facilities for instance the distillation column the

mixer and storage tanks

a FEEDi BOTTOMS HEAT EXCHANGER

Condensate bull

bullff

RAW GASOLIHE CO ipound9 f l u IOLEP L J C

MTBE _ Reform ate mdash bull -

Raw Gasoline

amp V - 0 1

PEF l l OPUH

OampTILLATfcN COLUMN

-Gasoline

GSSOLINE MIXER

Figure B5 Simplified process flow diagram of the gasoline plant

B72 Distillation Column

Condensate is fed using feed pumps (P-01 AB) through the feedbottoms heat

exchanger (E-01) to the distillation column (C-01) The column (C-01) plays a very

important role in the plant Here condensate after processing in the column (called

naphtha or raw gasoline) is cut off the light fraction having a boiling point of less than

40degC The raw gasoline then mixes with Reformate or MTBE to produce the finished

gasoline

The column has 24 actual trays (equivalent to 14 theoretical trays) Condensate is

fed to the seventh tray and the raw gasoline is withdrawn off from the column base The

operating pressure is 46 atm The top temperature is 46degC and the bottom temperature

is 128degC

The raw gasoline (naphtha) is sent to the raw gasoline tanks (TK-11 AB) Its

heat has been removed by the feedbottoms heat exchanger and cooled by the raw

gasoline cooler (E-04) A part of the bottom stream is heated up in the reboiler furnace

(H-01) and returned to the distillation column to supply required heat for distillation

The distillation column overhead vapor is cooled at the column overhead

condenser (E-03) to produce the uncondensed gas so called off-gas and the reflux

liquid The former is mainly burnt off at the reboiler furnace and the remaining amount

for controlling the reflux drum pressure is burnt at flare The latter accumulated at the

reflux drum (V-01) is returned to the column at the top tray under controlled flow rate

for maintaining stable operations and maximizing the recovery of naphtha

B73 Blending System and Product Distribution

The blending system consists of an in-line static mixer an on-line multi-property

analyzer ratio control with DCS and an off-line blend simulator

The blending system will perform the following functions

1) Continuous ratio control of blend header qualities to meet specification with

minimum deviation from optimal recipe

2) Continuous monitoring of blends using infra-red analyzers and tracking

integrated blend quality

3) Offline optimization of header quality control and recipe targets based on

reconciled blend models and integrated blend results to optimally meet

scheduler-specified blend order quality recipe and inventory targets

Based on the quality requirements of gasoline as specified standard the off-line

simulator calculates precisely the necessary flow rate of octane booster to blend the

whole volume of raw gasoline

The other additives (detergent color anti-oxidation and metal deactivator) are

injected in a pre-determined amount directly into the raw gasoline stream just before the

Gasoline product blended at the gasoline mixer is analyzed with a multi-property

analyzer and sent to the gasoline storage tanks (TK-13 AB) In case of low quality the

gasoline will be pumped to off-spec storage tank and then returned to the mixer The off-

spec product tank is designed for 12 production hours

From the gasoline storage tanks gasoline after being checked the quality is

pumped out the plant through the tank truck filling station or through the jetty to load in

tankers

B74 Feed Control

The feed section has several components

1) A local flow controller (FC-11) to control the feed flow rate

2) A local controller for feed pumps

3) A local pressure controller (PIC-13) to keep the pressure of the feed flow at

46 atm

i T C - 1 r

mdashImdash I

--copy

l-MmdashJ

To Column

Figure B6 A local control devices for feed pumps

B75 Top Column Section

Column pressure control includes 1) vapor bypass line and 2) vent line to flare

If there is a pressure drop in reflux drum (V-01) the local pressure controller commands

to slightly open the control valve upstream (E-03) and gradually close the control valve in

the vent line If column pressure increases the local pressure controller commands to

gradually close the vapor bypass flow and open more flow to flare

B76 Bottom Section

The reboiler is a forced-circulation typed reboiler including pumps (P-0809) and

a heater (H-01) The discharge of the pump is split as two streams 1) a part is withdrawn

as raw gasoline and 2) a part is heated up in the heater to generate vapor back to the

column base When the temperature in the bottom section is changed the local

temperature controller TIC-34 will adjust the rate of fuel gas into the heater

APPENDIX C MATHEMATICAL MODEL

Cl Introduction

Distillation process is very complicated So we develop its mathematical model

to study its dynamics and then select appropriate control strategy The mathematical

model of distillation process is established on dynamic continuity equations of mass and

energy for trays condenser reflux drum and reboiler

In general the dynamic continuity equations state that the rate of accumulation of

mass or energy in a system is equal to the mass or energy flows entered and generated

less the amount leaving and consumed within the system The accumulation term is a

first order time derivatives of the total mass or energy The flow terms are algebraic

Therefore the results are first order ordinary differential equations that are usually nonshy

linear

The liquid rates throughout the column will not be the same dynamically They

will depend on the fluid mechanics of the tray Often a simple Francis weir formula

relationship is used to relate the liquid holdup on a tray to the liquid flow rate Lbdquo over the

outlet weir

Mbdquo = f(LJ (Cl)

We now develop the state equations that will describe the dynamic behavior of a

distillation column The fundamental quantities are total mass and mass of the light

component which is the more volatile component

C2 Dynamic Study of Distillation Process

C21 Generic Trays

A general tray is an nth stage such that n = 1 2 Nand n f

The total mole holdup in the nth tray Mbdquo is considered constant but the imbalance

in the input and output flows is accounted for in the component and heat balance

equations

d(Mbdquo)

dt = Zbdquo+I - Lbdquo + VnA - Vbdquo =Zbdquo+ 1 -Lbdquo (C2)

Table C 1 Parameters of a generic tray

Liquid

Flow rate

vbdquo Vn

Concentration

staae n

Figure C 1 A generic tray

The rate of change of holdup in the laquoth tray results in the change of exit liquid

flow after a hydraulic lag [38] or hydraulic time constant [35]

dL 1 dMbdquo dt x dt

where r is hydraulic time constant

The hydraulic lag can be treated as a liquid level problem which is complicated

somewhat by the change in level across the plate At the center of a tray the average

depth of clear liquid is usually less than at the either end and may even be less than the

weir height as shown in Figure C2

Foam height h height abova weir

Depth of clear liquid

^ ^ 1-hj average depth of clear liquid

Figure C2 Variation of liquid depth across a generic tray

The hydraulic time constant can be calculated with the formula [38]

dh dMbdquo x = A-

dLbdquo dL (C4)

where r is hydraulic lag for 1 plate Mbdquo is holding of liquid per plate and Ln is liquid rate

Component balance is given by

d(Mbdquoxbdquo) dt

Lbdquo+iXn+] + VbdquoA ynA - Lnxn - Vbdquo yn (C5)

By differentiating and substituting for the term we obtain

dXn = 4+1 Xlaquo+ + Vn -1 ybdquo -1 - (4 + l + Vn-X K - K (ybdquo ~ Xn )

dt Mbdquo (C6)

Energy balance is given by

d(Mnhn) dt

= hn+]Ln+l+HH_lVH_i-hnLbdquo-HllVn (C7)

at dt n+ n+ laquo - l nmdash n n n n (C8)

Because the mdash - term is approximately zero substituting for the change of the dt

holdup term we obtain dt

V = H-h

C22 Feed Tray

The feed section includes the feed tray as shown in Figure C3

stage (feed tray

LfXrbdquo

I-v vgt LrXf

Figure C3 Feed section

Total mass balance is given by

dt = F + Lf+] +VfA -Lf-Vf=F + Lf+] -Lf

Component balance is given by the following equations

d(Mfxf)

dt Fcf +Lf+xxf+x+VfAyfA -Lfxf-Vfyf

dxbdquo _ 4+1xbdquo+ + Vbdquo yn - (Ln+l + Vbdquo_x )xbdquo - Vn yn - xn)

dt Mbdquo

= KF +hn+]Ln+] +Hn_xVn_x -hnLn -HnVn

d(Mfhf)

V = hF +zbdquo+4+ +HnAVn_ -L^+V^K

C23 Top Section

The top section consists of the top tray and the reflux drum as shown in Figure

Vlaquobdquo

11 V M1

vbdquo

Stage N+1 (Nth Tray) Mo

Figure C4 Top section

Total mass balance of the top tray is determined as

d(MN+l) _ (C 13) dt

Component balance of the top tray is characterized as

d(M XN+])=Lx^ + y L _ y ( C 1 4 )

Energy balance for the top tray is given by the following equations

d M ^ ) = hDL + HNVN -hN+lLN+i -HN+]VN+I (C15) at

y =hDL + HNVN-(L + VN)hN+l (Q 6 ) N+] H -h

11 N+ nN+

Total mass balance for the reflux drum and condenser is given by

= VN+ -L -D CM) dMn) _

Component balance for the reflux drum and condenser is determined as

^MDXD) = VN+xyN+x -L + D)xD (C18)

We now define energy balance around condenser The condenser duty Qc is

equal to the latent heat required to condense the overhead vapor to its bubble point Qc = HmVw -houlLoul = VN(HN -hN) (C 19)

C24 Bottom Section

l I l I

-t4----K--I 1 st tray flaquo = 2)

ltHXr-B x F

Figure C5 Bottom section

Total mass balance for the bottom tray is given by

d(M2) dt

L3-L2+ VB -V2

Component balance for the bottom tray is given by

= L3x3+VByB-L2x2 - V2y2 dM2x2)

Energy balance for the bottom tray is as follows

dMRhB) dt

= 23Z3 +HBVB- h2L2 - H2V2

Therefore

V2 = h3L+HBVB-(L3+VB)h2

H2 -h2

The base of the column has some particular characteristics as follows

1) There is a reboiler heat flux QB to produce the boilup vapor flow VB

2) The holdup is a sensitive variable hence changes in sensible heat cannot

be neglected

3) The outflow of liquid from the bottoms B is determined externally

Total mass balance for the column base is given by the following equation

dMB) = L 2 _ V B B ( C 2 3 )

Component balance for the column base is determined as

J ( M g X i ) = L2x2-VByB-B xB (C24) dt

Energy balance for the column base is as follows

d(MBhB)

dt = h2L2+QB-hBB-HBVB (C25)

IT ^ i rgt dhbdquo dMR

h2L2+QH-hBB-MB-^--hBmdashf-VB = amp 2L- (c26)

All the equations above are state equations and describe the dynamic behavior of

the distillation column The state variables of the model are

1) Liquid hold ups M M2 Mf MN+2

2) Liquid concentrations xx2 x xN+

When all the equations above are resolved we find how the flow rate and

concentrations of the two product streams (distillate product bottoms product) change

with time in the presence of changes in the various input variables

3 Mathematical Model of Distillation Process

4 Simplified Model

To simplify the model we make the following assumptions [35]

1) The relative volatility a is constant throughout the column

2) The vapor - liquid equilibrium relationship can be expressed by

yn = r (C27)

+ (a-l)xbdquo

where xbdquo is the liquid composition on rath stage ybdquo is the vapor composition on

nth stage and a is the relative volatility

3) The overhead vapor is totally condensed in the condenser

4) The liquid holdups on each tray condenser and the reboiler are constant and

perfectly mixed (ie the same immediate liquid response dLi = dL = =

aZyv+2 = dL)

5) The holdup of vapor is negligible throughout the system (ie the same

immediate vapor response dV = dVj = = dV^+i = dV)

6) The molar flow rates of the vapor and liquid through the stripping and

rectifying sections are constant Vi = V2== VN+i

L2= LT~ = LN+2-

7) The column is numbered from bottom eg n mdash 1 for reboiler n = 2 for first

tray n =for feed tray n = N+ for top tray and n = N+2 for condenser

Under these assumptions the dynamic model can be expressed by the following

equations [12]

1) Condenser (n = N+2)

MDxn =(V + Vbdquo)y^ - Lxn - Dxn (C28)

2) Tray n(n=f+2 N+1)

M xn = (V + VF)(yn_ - yj + L(xn+] - xj (C29)

3) Above feed location (n=f+l)

Mxn=(V + V)(yn^ - yj + L(xn+ - xj + VFyF (C30)

4) Below feed location (n=f)

M Xn=(V + Vf)(y^ -yJ + L(xbdquo+l -xbdquo) + LFxF (C31)

5) Tray n(n = 2 - l)

M xn = F6v - yj + (L + LF)(xn+x - xj (C32)

6) Reboiler (laquo=1)

MBX] =(L + LF)X2 - Vy - fix (C33)

Flow rate are assumed as constant molar flows

1) LF=qFF

2) VF = F-LF

3) D=VN-L=V+VF-L (assuming condenser holdup constant)

4) B = L2-V] = L + LF-V(assuming boiler holdup constant)

Composition xF and yF in the liquid and vapor phase of the feed are obtained by

solving the flash equations

FcF = LFxF + VFyF (C34)

y = r bull (C35)

1 + a - )Xj

Although the model order is reduced the representation of the distillation system

is still nonlinear due to the vapor liquid equilibrium relationship between ybdquo and xbdquo in

C5 Mathematical Model of the Gasoline Refinery

In this section we use some data obtained by process calculation described in

Appendix B to plug in generic equations above As the result the mathematical model of

the plant is completely defined

C51 Relative Volatility

Using the formula ajJ = KjKj and looking up data in the handbook [39] for the

operating range of temperature and pressure the relative volatility is estimated as a- 568

C52 Latent Heat and Boilup

The heat input of QB (reboiler duty) to the reboiler is to increase the temperature

of stripping section and generate boilup Vo [40]

v^=QH-BcH(tH-tF) ( C 3 6 )

where A is the latent heat or heat of vaporization B is the flow rate of bottom product

(kg) CB is the specific heat capacity (kJkgdegC) tF is the inlet temperature (degC) and ts is

the outlet temperature (bottoms temperature degC)

The latent heat at any temperature is described in terms of the latent heat at the

normal boiling point [40]

X = yXB^- (C37) -laquo

where L is the latent heat at absolute temperature T (degR) LB is the latent heat at absolute

normal boiling point TB (degR) and y is the correction factor obtained from the empirical

The calculation results are summarized as follows

A = 730 (kJkg)

V0= 39098 (kgh) or 668871 (kmoleh)

The average vapor flow rate arising in the stripping section is calculated as

V = 0+ = 663407 (kmoleh)

C53 Liquid Holdups on Tray and Column Base

Liquid holdups are calculated with the methods proposed by McCabe [42] and

Joshi [43]

Velocity of vapor phase arising in the column

ffl^^M (C38)

where pi is the density of liquid phase pv is the density of vapor phase and C is a

correction factor depending flow rates

The actual velocity co is normally selected that co = (080^085)con for paraffinic

The diameter of the column is calculated with the following formula

4V Dk = J mdash (C39)

where Vm is the mean flow of vapor in the column

The height of the column is calculated on distance of trays The tray distance is

selected on basis of the column diameter

The holdup in the column base is given by

M ^ laquo A ^ (C40) B 4 WB

where HNB is normal liquid level in the column base (m) Wg is molar weight of the

bottom product (kgkmole) and de is density of the bottom product (kgm )

As a result the holdup in the column base is calculated as

314(175X1-4) Z ^ = 2488 (kmole) B 4 786

The holdup on each tray is given by

t 0957chD2k dr

M = mdash-mdash-4 Wr

where hr is average depth of clear liquid on a tray Wj is molar weight of the liquid

holdup on a tray and dr is the mean density of the liquid holdup on a tray

Therefore the holdup on each tray is calculated as

095(314)(028)(175)2 680 M = = 580 (kmole)

C54 Liquid Holdup in Reflux Drum

The retention time of distillate in the reflux drum is selected as 5 minutes

Liquid holdup MD is equal to the quantity of distillate contained in the reflux

MD = 5iL + D) (C41)

where MD is holdup in the reflux drum L is the reflux flow rate and D is the distillate

flow rate

As the result the liquid holdup in reflux drum is calculated as 5(7530 + 8215) 1 i m Mn= mdash = 1403 (kmole)

C6 Basic Mathematical Model of the Plant

Material balances for change in holdup of light component on each tray are as

follows

Condenser (n = 16) MDx]6 =(V + VF)y]5 - Zx16 - Dxl6

Tray 14 (laquo= 15) Mx]5=(V+ VF)(yH-y]5) + L(x]6-x]5)

Tray 13 (n = 14) Mx]4 = (V + V)(yu -yH) + L(xs -x1 4)

Tray 12 (n = 13) Mxu=(V+ VF)(yu -yu) + L(xu -x]3)

Tray 11 (w= 12) Mxn=(V+ VFyu-yn) + Lxn-xu)

TraylO(raquo=ll) Mxu = (V + Vbdquo )yw -yu) + L(xu -xu)

Tray 9(n= 10) Mxw=(V + VF)(y9 -y]0) + L(xu -xl0)

Tray 8 (n = 9) Mx9 = VFyF +Vys-(V + VF )y9 + L(x]0 - x9)

Tray 7 (n = 8) Mxg = V(y7 - y) + Lxg + LFxF - (Z + LF )x8

Tray 6 (n = 7) M7 = F(gt6 - j7) + (Z + LF )(x8 - x7)

Tray 5 (n = 6) M6 = F(^5 - y6) + (Z + LF )(x7 - x6)

Tray 4 (w = 5) Mx5 = V(y4 -y5) + (L +LF)(x6 - xs)

Tray 3 (n = 4) M4 = F(^3 - gt4) + (Z + ZF )(x5 - x4)

Tray 2 (laquo = 3) Mc3 = F(^2 - y3) + (Z + LF )(x4 - x3)

Tray 1 (laquo = 2) Mc2 = F(jgt - ^2) + (Z + Zr )(x3 - x2)

Reboiler (n = 1) MBi = (Z + Zf )x2 -Vyx- Bxl

Process data are summarized as follows

bull The liquid holdups MD = 1403 (kmole) M = 580 (kmole) and MB =

2488 (kmole)

bull Feed flow rates LF= 1042491 (kmoleh) and VF = 985152 (kmoleh)

bull Flow rates above the feed location Z9 = = Z)5 = Z = 756380 (kmoleh)

and V9 = = Fi5= V+ VF= 661139+ 985152 = 1646291 (kmoleh)

bull Flow rates below the feed location L = = Zg = Z + LF = 756380 +

1042491= 1798871 (kmoleh) and V = = V= V= 661139 (kmoleh)

bull Distillate flow rate D = 927597 (kmoleh)

bull Bottoms flow rate B = 1109235 (kmoleh)

bull Solving flash equations xF = 02609 and yF = 06672

In summary the dynamic model is represented by a set of 31 nonlinear

differential and algebraic equations

1403 x16 =1646291 y]5 - 756380x6 -927597x6

58x15 = 1646291(y14 -y ] 5) + 756380(x6 -x l 5)

58x4 = 1646291(73-gtgt4) + 756380(x5-x4)

58x13 = 1646291(712 - yn) + 756380(xl4 - x13)

58x12 =1646291(j |l-j12) + 756380(x13-x12)

58 = 1646291(710 -yu) + 756380(x2 -x )

58x0 = 1646291(79-^0) + 756380(x-x0)

58x9 = 661 39ys -15638gt-9 + 756380(xl0 -x 9 ) + 5995

58x8 = 661139(y7 -ya) + 756380 x9 - 18859x8 + 3399

58x7 = 661139(y6-y7) +179887 l (x 8-x 7)

58x6 = 661 39(y5-y6) + 179887 l (x 7 -x 6 )

58x5 = 661139(j4 - y5) +1798871 (x6 - x5)

58x4 =661139(^3 -yA) + 79887 l (x 5-x 4)

58x3 = 661 139(^2 - y 3 ) + l798871 (x4 - x3)

58x2 =661139(j -y2) +1798871 (x 3 -x 2 )

2488x = 1798871 x2 -1109235x -661139^ (C42)

Vapor liquid equilibrium (VLE) relationship on each tray is given as

568x y ~ l + 468x

y2 = 568x2

1 + 468x

^ 1 5 =

l + 468x (C43)

APPENDIX D DYNAMIC SIMULATION

Dl Modular Decomposition of the Column

Modular decomposition of the column is depicted in Figure Dl The column is

divided into two groups 1) rectifying section and 2) stripping section

bullCO

REfCBSER amp JSCFiLtf Ettlft

WJ6RfSEii [ bull ^ bull ^ t ^ ^ K j a

laquo r M |

3raquo lt pound A V 13 |

raquo ^ SA 11 j

Sgt lt^gt s e c BflV I f 1 -reg-

w r n i |

^ ltgt fM f 3 1

ET mAr pound |

~^ IT JWi a mdash i

Cgt $ IZ

sltw i f e f j f f tw-

1 ma r ii |

P $ mar t |

r TT s m raquo laquo laquo 1 SECi

ET r Jfifl V 3 1

b $ TWVlP 2 1

J ^ m d If f |

4gt gt _ bull bull JffBimil

A MSpound titisttiLu

WFYMtG

fiterttxm

Figure D 1 Modular decomposition scheme for the distillation column

D2 Simulation with MATLAB Simulink

For convenience the simulation program is organized as a hierarchical structure

with three levels as depicted in Figure D2 The lowest-level modules actually represent

1 COLUMN BASE R REBOILER

STRIPPING SECTION

GENERAL TRAY

COLUMN

1 TRAY 7

1 TRAYS

RECTI FYINO SECTION

GENERAL TRAY 1

CONDENSER amp REFLUX DRUM

Figure D2 Hierarchical structure of the simulation program

The highest level of the simulation program in MATLAB Simulink is shown in

Figure D3

GASOLINE REFINING PLANT Distillation Column Dynamic Simulation

Operational Objectives Purity of LPG xD gt 98 Impurity in Raw Gasoline xB lt 2

- w i 13411

~W 46804

RECTIFYING SECTION

bull bull l n 1 Out1

mdash bull In2 Out2

STRIPPING SECTION

bull XD

To Workspacel

-4L Scope 1

Raw Gasoline

bull | xB

To Workspace

H Scope

Figure D3 Main program in MATLAB Simulink

The second-level modules include the rectifying section as shown in Figure D4

and the stripping section as shown in Figure D5

In20ut2

Condenser amp Reflux Drum

Inl O u l l M

In 2 Ou2t

Tray 14

bull i n l Out1 |

- W i n 2 Oul2|

Tray 13

In 10ut 1

In20ut2

Tray 12

bull In lOu t l

In20ut2

Tray 11

InlOutl

In20ul2

Tray 10

bullbullbullbullbulljlnlOutl

bullNln20Ut2

Tray 9

l j mdash

~2~gt -In2

bull in 2

Tray 8

x 1 bull Outl

bull - K 2 Out2

Figure D4 Module of the rectifying section

_2 mdash

f bull

n 1 n n H I Wgt A

In 2 Ol l t l

Tray 7

mdash bull

In 10ut1

In20ut2

Tray 6

mdash bull i n l O u t l j-

- gt In20ut2

Tray 5

In lOut l -

bull ln20ut2

Tray 4

bull in lOut l

1 bull

In20ut2

Tray 3

In lOut l

In20ut2 [

Tray 2

[ bull

In lOut l H

In20ul2 |

1 Tray 1

__ Out1

bull In1

Out2 -gt lt_2_gt

Column base and Reboiler

Figure D5 Module of the stripping section

The third-level modules include some special components and generic trays as

depicted in the following figures

O bull72302

COLUMN BASE laquo REBOILER (Stage n1)

471 r Integrator 2

bull XI

To Workspace2

Scope 2

K 2 Olit2

2T899 ^ Function

VLE equation

Figure D6 Module of the column base and reboiler

GENERIC TRAY n

GL(n+1) iquid flow arrives

V bull L(n+1)Mn

GV(n-1) Vapoi flow arrives

2 ) bull bull bull V(n-1)Mn

In2 _ - -

Out 1 vapor flow leaves out the tray 1 -4

A i bull

-bull VnMn

bull 1 integrator 2

y lt bull

n MATLAB | ^ Function

V IE equa Son

bull xn

To Workspace2

bullbull bull -

Scope xn

Liquid flow leaves out the t oy

Figure D7 Module of a generic tray

TRAY 7 (Stage n -8)

bull 3 gtbull

bull 1

( 2 in2

IH130410 ~gt-

bull 119679

bullbullyenbullbull

y- Integrator 2

1 1 9 6 7 9 lt - - I trade trade Function

VLE equation

Figure D8 Module of the feed tray

To Workspaces

Scope 2

gt bull

1 lHn0410

bullbullbull xS

To Workspace

2 bull 119879 In2

Outl bull bull I

289533 N

li integrator 2

130410

Function

MATLAB Fen 2

bull gt bull bull

Scope2

Figure D9 Module of the eighth tray

( 1 In2

119666 1 I s J

Integrator 2

120027 K

Scope 2

Figure D 10 Module of the condenser and reflux drum

APPENDIX E CONSTRUCTION OF REFERENCE MODEL

El Model Construction

This section describes construction of full order model The outputs of interest

are the purity of overhead and bottom products These quantities are desired to be kept

within prescribed limits (XD ^ 98 and XB lt 2) under disturbances of the feed streams

or environment The selected control structure is L-V structure in which the reflux flow

L at the column top and the boilup rate in the column bottom V are the manipulated

inputs

Consider the nonlinear equations represented for a generic tray

Figure E 1 Model of a generic tray

Material balance is determined as follows

ACCUMULATION = INLET - OUTLET

MnXn = (Fbdquo_Fbdquo_1+4+Xn+1) (VnYn+LnXn)

V X=^^Y Mbdquo n- mdash Y + ^plusmnLX

M M n+ Mbdquo

-X (El)

where I i = = L = L + LF = L+ 1042491 L9= = Ll5 = L V = = V8= Fand V9

= = V15= F+ VF = V+ 985152

Vapor liquid equilibrium relationship at each tray is given by

aXbdquo 568X K = l + ( a - l ) x bdquo 1 + 468Xbdquo

Vw = l 15 (E2)

Therefore the concentrations of liquid on each tray are a vector functionof state

vector x and manipulated input vector u

X = f(Xut)

where X = (XX2X6)T and u = (L V)r

The above nonlinear system can be linearized around the steady state value at the

nominal operating point (X u) We define the perturbed states and control inputs as

dX = X-X

du = u - u

The linearized equations are given by

dX df] _lt3x_

dX + 8f] _du_ du

where df IdX stands for the Jacobian of the vector function with respect to the state

vector x and df I du stands for the Jacobian of the vector functionwith respect to the

manipulated input vector u

Make differentiation of (El) as follows

dXn = =LdYn_x +^dVn n-dYn ~-Z^dVn

Mn Mn Mn Mn

T X T X + -plusmndXn+ + plusmndLn+] --^dXn

Mn +1 Mn +1 Mn Mn

Substituting for terms of dYmd regrouping the equation give the following result

T T -t- V V K V

dXn=^dXbdquo+] -Lraquo+Kraquoyraquo dXn+^^tplusmndXn Y mdash Y V mdash V + A- A-]dL- ~]dV

where dLbdquo = dL for all n= 15 dVn = dV for all n = 1 15 Kbdquo is the linearized

VLE constant and ybdquo xbdquo Lbdquo and Vbdquo are the steady-state values at the nominal operating

In addition we make linearization for some special stages as follows

1) Reboiler(laquo = 1)

dX = -^dX2 + dL-^dY -^-dV-mdashdXv

2) Condenser (n = 16)

dXl6 =^dYi5 +-^dV--^dXl6 -^dL-mdashdX]6 Mi6 Ml6 M 1 6 M 1 6 M]6

As a result the model is represented in state space in terms of deviation variables

i ( 0 = Ax(t) + Bu(t) (E4)

y(t) = Cx(t) (E5)

where x - [dx dx2 dxe]r is the vector of composition deviations and u = [dx dxj

dxlt$ is the vector of manipulated inputs and y = [CIXB dXo]J = dX dX^ is the vector

of controlled outputs

The algorithm for calculating state matrix elements A (16x16) is described as

follows

1) Collect flow rates data

L ==LS = 1798871 (kmoleh)

L9 = = Z15= 756380 (kmoleh)

V = = V = 661139 (kmoleh)

V9 = = V]5 = 1646291 (kmoleh)

2) Collect liquid holdups data

MX=MB = 2488 (kmole)

M2 = M3 = = Mi5 = 580 (kmole)

M16 = MB = 2488 (kmole)

3) Calculate K K2 K6

4) Calculate the state matrix elements

i - l f l - mdash a]2- mdash M M

_KK _ (L]+K2V) _ L 21 M2

22 M2 23 M 2

-C bdquo (K+KX) bdquo _ ^ y bull 7 mdash f ~ - | y mdash f l ft mdash ff + bull laquo n - l unn ~ +1 j t Mbdquo Mbdquo Mbdquo

w = 1 6 a 6 1 5 = mdash mdash ^ a ] 6 1 6 = mdash ^ 6 A16

As a result the state matrix 4 (16x16) is tri-diagonal

The algorithm for calculating input matrix elements B (16x2) is as follows

1) Collect data

LPG product purity XD = X]6 =09851=9851

Raw Gasoline product purity -XB = 1 - X = 0989 = 989

w = 1 ^ 1 = 7 Z 6 i 2=TT

w =2 h _xlZx2) _-fe-i) 2 J ~ M2 2lt2~ M2

raquo bdquo 2 = -te-^)

laquo - 1 6 66gti = 6 ft162 ^ 1 6

The input matrix B (16x2) is

_ K M16

[00012 00063 00091 00098 00076 00044 00022 00021 00048

00111 00216 00306 00285 00178 00086 -00702

-00024 -00157 -00237 -00254 -00196 -00116 -00058 -00027 -00024

-00050 -00097 -00138 -00128 -00080 -00039 00704]r

The output matrix C (2x16) is

C = 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

E2 Stability Test

The stability of the system can be determined by using the Lyapunov direct

method Let us assume that the quadratic Lyapunov function is

V(x)=xTPx (E6)

where P is a symmetric positive definite matrix

The time derivative of V is

V(x) = xT Px + xTP x (E 7)

Since the system homogeneous differential equation x=Ax and (Ax)T = xTAT we

V(x) = (AxfPx + xrP x

V(x) = xTATPx + xTPAx = xT(ATP + PA)x (E8)

If A P + PA = -Q for some positive definite matrix Q then the system is

asymptotically stable

We choose Q = I where i s the identity (16x16) matrix The symmetric matrix P

is determined by solving the following equation

ATP + PA = -I (E9)

where A is the state matrix The system is asymptotically stable when matrix P is

positive definite

The system stability test can be done with the following MATLAB program

The condition V(0t) = 0 is obviously satisfied

P = lyap(AI)

Determinants of the principal minors

for i=l16

Pi = P (1 i 1 i)

det(Pi)

detPi=[det(P int2str(i) ) = num2str(det(Pi))]

d i s p ( d e t P i )

The results show that all principal minors are positive

d e t ( P l ) = 0 0 3 2 8 3 1

d e t ( P 2 ) = 0 0 0 0 9 0 8 4 9

d e t ( P 3 ) = 2 4 4 4 3 e - 0 0 5

d e t ( P 4 ) = 5 5 4 7 6 e - 0 0 7

d e t ( P 5 ) = 1 0 1 5 2 e - 0 0 8

d e t ( P 6 ) = 1 6 2 0 8 e - 0 1 0

d e t ( P 7 ) = 2 3 0 2 5 e - 0 1 2

d e t ( P 8 ) = 2 6 1 8 3 e - 0 1 4

d e t ( P 9 ) = 4 1 9 5 9 e - 0 1 6

d e t ( P l O ) = 1 2 8 8 6 e - 0 1 7

d e t ( P l l ) = 6 7 8 4 7 e - 0 1 9

d e t ( P 1 2 ) = 3 9 1 6 e - 0 2 0

d e t ( P 1 3 ) = 1 8 3 0 8 e - 0 2 1

d e t ( P 1 4 ) = 7 0 8 9 e - 0 2 3

d e t (P15) = 2 4 8 7 6 e - 0 2 4

d e t ( P 1 6 ) = 8 4 6 1 2 e - 0 2 6

The symmetric matrix P is positive definite hence the system is asymptotically

stable

APPENDIX F SOURCE CODE

Fl Adaptive Mechanism

include ltiostreamgt

include ltstdlibhgt

include AdaptiveMechh

using namespace std

AdaptiveMechAdaptiveMech()

AdaptiveMech-AdaptiveMech()

void AdaptiveMechgetAdapMechPkt(int k Pkt x_kml Pkt e_kml

Pkt uc_kml thetaPkt th_kml)

if(k = x_kmlk+l)

printf(AdaptiveMechgetAdapMechPkt=gtWrong x(k-l) time

stampn)

if(k = e_kmlk+l)

printf(AdaptiveMechgetAdapMechPkt=gtWrong e(k-l) time

stampn)

if(k = uc_kmlk+l)

printf(AdaptiveMechgetAdapMechPkt=gtWrong uc(k-l) time

stampn)

this-gtx_kml = x_kml

this-gte_kml = e_kml

this-gtuc_kml = uc_kml

this-gtth_kml = th_kml

return

void AdaptiveMechgenAdapMechPkt(int k thetaPkt ampth_k)

generate adaptive gains

th kk = k

t h _ k t h l = t h_kml t h l + Tgamma(blle_kmlpi +

b21e_kmlp2)x_kmlplbull

t h_k t h2 = th_kml th2 + Tgamma(blle_kmlpi +

b21e_kmlp2)x_kmlp2

t h _ k t h 3 = th_kml th3 + Tgamma(bl2e_kmlpi +

b22e_kmlp2)x_kmlpl

t h_k th4 = th_kml th4 + Tgamma(bl2e_kmlpi +

b22e_kmlp2)x_kmlp2

t h _ k t h 5 = th_kml th5 - Tgamma(blle_kmlpi +

b21e_kmlp2)uc_kmlpl

b21e_kmlp2)uc_kmlp2

t h_k t h7 = th_kml th7 - Tgamma(bl2e_kmlpi +

b22e_kmlp2)uc_kmlpl

b22e_kmlp2)uc_kmlp2

r e t u r n

F2 Plant Model

include ltstdlibhgt

include PlantModelh

using namespace std

PlantPlant()

all = -67941 + 067(rand()2-05)

al2 = -09095 + 009(rand()2-05)

a21 = 14686 + 015(rand()2-05)

a22 = -02497 + 002(rand()2-05)

bll = -01461 + 0014(rand()12-05)

bl2 = 02073 + 002(rand()2-05)

b21 = -00021 + 00002(rand()12-05)

b22 = -00281 + 0003(rand()2-05)

ell = -00624 + 0006(rand()2-05)

cl2 = -00281 + 0003(rand()2-05)

c21 = 02458 + 0025(rand()2-05)

c22 = 00009 + 000009(rand()2-05)

printf(A = ft ft ft ftn all al2 a21 a22

printf(B = ft ft ft ftn bll bl2 b21 b22

printf(B = ft ft ft ftn ell cl2 c21 c22

Plant~Plant ()

void PlantgetPlantPkt(int k Pkt u_k Pkt x_k)

if(k = u_kk)

printf(PlantgetPlantPkt =gt Wrong u(k) time stampn)

this-gtu_k = u_k

this-gtx_k = x_k

return

void PlantgenPlantPkt(int k Pkt ampx_kpl)

compute plant states

x_kplpl = (l+allT)x_kpl + al2Tx_kp2 + bllTu_kpl +

bl2Tu_kp2

x_kplp2 = a21Tx_kpl + (l+a22T)x_kp2 + b21Tu_kpl +

b22Tu_kp2

x_kplk = k+1

r e t u r n

F3 Reference Model

include ltstdlibhgt

include ReferenceModelh

using namespace std

RefmdlRefmdl()

Refmdl~Refmdl()

void RefmdlrefmdlGetPkt(int k Pkt uc_k Pkt xm_k)

if(k = uc_kk)

printf(RefmdlrefmdlGetPkt =gt Wrong uc(k) time

stampn)

this-gtuc_k = uc_k

if(k = xm_kk)

printf(RefmdlrefmdlGetPkt =gt Wrong xm(k) time

stampn)

this-gtxm_k = xm_k

return

void RefmdlgenRefPkt(int k Pkt ampxm_kpl)

compute reference states

xm_kplk = k+1

xm_kplpl = (l+amllT)xm_kpl + aml2Txm_kp2 +

bmllTuc_kpl + bml2Tuc_kp2

xm_kplp2 = am21Txm_kpl + (l+am22T)xm_kp2 +

bm21Tuc_kpl + bm22Tuc_kp2

return

F4 Linear Controller

include ltstdlibhgt

include LinearControlh

using namespace std

Linctrl Linctrl()

Linctrl -Linctrl ()

void LinctrlgetLinctrlPkt(int k thetaPkt th_k Pkt uc_k Pkt

if(th_kk = k) printf(LinctrlgetLinctrlPkt =gt Wrong th(k)

time stampn)

this-gtth_k = th_k

if(k = uc_kk) printf(LinctrlgetLinctrlPkt =gt Wrong uc(k)

time stampn)

this-gtuc_k = uc_k

if(k = x_kk) printf(LinctrlgetLinctrlPkt =gt Wrong x(k)

time stampn)

this-gtx_k = x_k

return

void LinctrlgenLinctrlPkt(int k Pkt ampu_k)

produce control signals

u_kpl = th_kth5uc_kpl + th_kth6uc_kp2 - th_kthlx_kpl

- th_kth2x_kp2

u_kp2 = th_kth7uc_kpl + th_kth8uc_kp2 - th_kth3x_kpl

- th_kth4x_kp2

u_kk = k

return

F5 Comparator

include ltstdlibhgt

include Comparatorh

using namespace std

ComparatorComparator()

Comparator~Comparator()

void ComparatorgetCmprPkt(int k Pkt x_k Pkt xm_k)

if(k = x_kk) printf(ComparatorWrong x(k) time stampn)

this-gtx_k = x_k

this-gtxm_k = xm_k

return

void ComparatorgenCmprPkt(int k Pkt ampe_k)

compute errors

e_kpl = x_kpl - xm_kpl

e_kp2 = x_kp2 - xm_kp2

e_kk = k

r e t u r n

F6 Controlled Output

include ltstdlibhgt

include ControlledOutputh

using namespace std

ControlledOutputControlledOutput()

ControlledOutput-ControlledOutput()

void ControlledOutputgetRefOutPkt(int k Pkt x_k)

if(k = x_kk) printf(ControlledOutputWrong x(k) time

stampn)

this-gtx_k = x_k

return

void ControlledOutputgenRefOutPkt(int k Pkt ampy_k)

produce controlled outputs

y_kpl = cllx_kpl + cl2x_kp2

y_kp2 = c21x_kpl + c22x_kp2

y_kk = k

return

F7 Reference Outputs

include ltstdlibhgt

include ReferenceOutputh

using namespace std

RefOutputRefOutput()

RefOutput -RefOutput()

void RefOutputgetRefOutPkt(int k Pkt xm_k)

if(k = xm_kk) printf(RefOutputgetRefOutPkt =gt Wrong xm(k)

time stampn)

this-gtxm_k = xm k

return

void RefOutputgenRefOutPkt(int k Pkt ampym_k)

ym_kpl = cmllxm_kpl + cml2xm_kp2

ym_kp2 = cm21xm_kpl + cm22xm_kp2

ym_kk = k

ym_kpi = ym_kpi

ym_kp2 = ym_kp2

r e t u r n

F8 CGI Program

inc lude lts td io hgt

inc lude lt s t d l i b h gt

inc lude ltctypehgt

ttinclude lt a s s e r t h gt

include

lterrnohgt

ltstringhgt

ltstdiohgt

ltunistdhgt

ltfcntlhgt

ltstringhgt

ltsyssockethgt

ltsystypeshgt

ltnetinetinhgt

ltarpainethgt

define DATA_PORT 2534

define CLIENTIP19216808

define LINELEN 1024

struct valinfo

unsigned char name

unsigned char text

struct thetaPkt

struct Pkt

int pi

int p2

static const int MAXSIZE = 2000

static const int T = 01

static const int Tgamma = 1

static const int MAXPKT = 11

static const int ucl = 500

static const int uc2 = 100

static

amll =

ami 2 =

am21 =

am22 =

bmll =

bml2 =

bm21 =

bm22 =

cmll =

cml2 =

cm21 =

cm22 =

all = -

al2 = -

a22 = -

bll = -

-67 94

static

= -510

= -310

= 1044

= 1006

unsigned char getval(unsigned char )

static int gotvals=0

static int nvals=0

static struct valinfo vals

static int hextobin(unsigned char)

static unsigned char httpunescape(unsigned char )

static int getvals(void)

static void getAdapMechPkt(int k struct Pkt x_kml struct Pkt

e_kml struct Pkt uc_kml struct thetaPkt th_kml)

static void fwritethpkt(char fname struct thetaPkt th)

static void fwritepkt(char fname struct Pkt pkt)

void itoch(int xl unsigned char c int len unsigned char

unsigned char getval(unsigned char name)

if (gotvals)

nvals = getvals()

gotvals = 1

if (nvals == 0) return NULL

for (i=0iltnvalsi++)

if(strcmp((const char )name (const char

)vals[i]name)==0)

return vals[i]text

return NULL

=============== httpunescape ===========

static unsigned char httpunescape(unsigned char sis)

unsigned char siptr

unsigned char soptr

unsigned char sos

sos = (unsigned char ) calloc (strlen((char )sis)+1sizeof

(unsigned char) )

if(sos == NULL) return NULL

soptr = sos

siptr = sis

while (siptr)

if(siptr == )

int c = 0 i

for (i=0ilt2i++)

siptr++

if (siptr == 0) break

if ( (h=hextobin(siptr)) == -1) break

c = claquo4 + h

if (i = 2)

free(sos)

return NULL

soptr++ = (unsigned char) c

else if (siptr == +)

soptr++ =

soptr++ = siptr

siptr++

soptr = 0

strcpy ((char )sis (const char )sos)

free (sos)

return sis

=============== hextobin =================

static int hextobin(unsigned char c)

if(isdigit(c))

return c-0

else if (isxdigit(c))

return tolower(c) - a + 10

return -1

=============== getvals ===================

int vent = 0

unsigned char vstr

unsigned char vptr

unsigned char eptr

unsigned char aptr

vstr = (unsigned char ) getenv ( REQUEST_METHOD)

if(vstr == NULL) return 0

if(stremp((const char )vstrPOST) == 0)

int 1 cl

vstr = (unsigned char ) getenv(CONTENT_LENGTH]

if (vstr == NULL | | strlen( (const char )vstr) ==

return 0

if ((cl = atoi((const char )vstr)) == 0)

return 0

vstr = (unsigned char )malloc(cl+2)

if(vstr == NULL)

return 0

fgets( (char )vstrcl + 1stdin)

1 = strlen((const char )vstr)

if(vstr[l-l] == n)

vstr[l-l]=0

vstr = (unsigned char ) getenv(QUERY_STRING)

vptr = vstr

while (vptr)

if(vptr++ == amp) vcnt++

vcnt++

vals = (struct valinfo )calloc(ventsizeof (struct

valinfo))

if(vals == NULL) return 0

vptr = vstr

for (i=0iltvcnti++)

eptr = (unsigned char )strchr((const char )vptr=)

aptr = (unsigned char )strchr((const char )vptramp)

if (eptr == NULL)

return 0

eptr = 0

vals[i]name = httpunescape(vptr)

if (vals[i]name == NULL) return 0

if (aptr)

aptr = 0

vptr = aptr+1

vals[i]text = httpunescape(eptr+1)

if(vals [i] text == NULL) return 0

return vent

=============== write adaptive gains ===================

unsigned char c

unsigned char cs

int fd len

fd=open(fname0_WRONLY | 0_CREAT 0 666)

if((fd==-l))

printf(Cant write sn fname)

exit (1)

c = (unsigned char) malloc(20)

cs = (unsigned char) malloc(2)

itoch(th-gtk c amplen cs)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

cs = (unsigned char) malloc(l)

itoch(th-gtthl c amplen cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

c = (unsigned char) malloc (20)

itoch(th-gtth2 c amplen cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

cs = (unsigned char) malloc (1)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

itoch(th-gtth7 c Slen cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== write signals ===================

unsigned char c

unsigned char cs

int fd len

fd=open(fnameOJAJRONLY | 0_CREAT 0 666)

fd=open(adapout0_WRONLY 0666)

if((fd==-l))

exit(1)

itoch(pkt-gtk c amplen cs)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

itoch(pkt-gtpl c amplen cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

itoch(pkt-gtp2 c amplen cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== write a signal ===================

static void fwritesig(char fname int sig)

unsigned char c

unsigned char cs

int fd len

fd=open(fname0_WRONLY | 0_CREAT 0666)

if((fd==-l))

exit (1)

itoch(sig c amplen cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== getsignal ===================

static void getsig(char fname int signal)

int fn s i m sn 1

unsigned char buf

buf = (unsigned char) malloc(20)

printf(ltpgt Opening the input filen)

fn = open(fname 0_RDONLY)

make sure it was really opened

if(fn==-l)

printf (ltpgt Cannot open the fndat filen)

exit(1)

return

read(fn buf 20)

s = atoi((const char) buf)

signal = s

free((void) buf)

close(fn)

return s

=============== get ascii signal ===================

static int getcsig (char fname int signal)

int fn s i m sn 1

unsigned char buf

if(fn==-l)

printf (ltpgt Cannot open the input file sn fname)

exit (1)

return 0

read(fn buf 20)

signal = s

free((void) buf)

close(fn)

return 1

=============== settime ===================

static void settime(char fname int k)

int t=0

unsigned char c

unsigned char cs

int len

f=open(fname 0_WRONLY I 0_CREAT 0666)

if((f==-l))

exit(l)

while(f==-l ampamptlt10000)

printf(ltpgtt=d cannot open sn t++ fname)

if(tgt=10000) exit(l)

itoch(k c amplen cs)

write(f c len)

write(f t 1)

free((void) c)

free((void) cs)

close (f)

return

=============== Wait ===================

static void wait(int n)

int i=0

while(i++ltn)

=============== gettime ===================

static void gettime(int kT)

Use for testing CGI running on ARM

getsig(vartmpfktdat ampk)

clear signals

clearsig(vartmpfktdat)

kT = k

printf(ltpgt x(k-l)k = dn k)

Write to files

fwritesig(vartmpchk_kTdat k)

return

=============== clear signal ===================

static void clearsig(char fname)

int fn

printf (ltpgt Opening the input filen)

fn = open(fname 0_WRONLY 0 666)

if(fn==-l)

printf(ltpgt Cannot open the input file sn fname)

exit(1)

return

write(fn20)

close(fn)

return

=============== integer to character ===================

unsigned char ch

ch = (unsigned char) malloc(128)

if (xl==0)

ch[0] = 0

len = 1

if(xllt0)

xl = -xl

sign[0] = -

sign[0] = +

while(xlgt0)

ch[i] = 0 + xl10

xl=xl10

len=i+l

for(i=0 iltlen i++)

c[i] = (const char) ch [len-i-l]

free((void) ch)

return

=============== getAdapMechPkt ===================

static void getAdapMechPkt(int k struct Pkt x_kml struct P

int kx xl x2 ke el e2 kuc ucl uc2 kth thl th2

th4 th5 th6 th7 th8

int outfile

Receive signals

getsig(vartmpfkxdat ampkx)

getsig(vartmpfxldat ampxl)

getsig(vartmpfx2dat ampx2)

getsig(vartmpfkedat ampke)

getsig(vartmpfeldat ampel)

getsig(vartmpfe2dat ampe2)

getsig(vartmpfkucdat ampkuc)

getsig(vartmpfucldat ampucl)

getsig

vartmpfuc2

vartmpfkth

vartmpfthl

vartmpfth2

vartmpfth3

vartmpfth4

vartmpfth5

vartmpfth6

vartmpfth7

vartmpfth8

ampuc2)

ampkth)

ampthl)

ampth2)

ampth3)

ampth4)

ampth5)

ampth6)

ampth7)

ampth8)

Display on HTML page

printf(lth3gt Embedded Adaptive Controller input signals

receivedlth3gtn)

printf

lth3gt Time = dT lth3gtn k)

ltpgt x(d)k = dn k-1 kx)

ltpgt xl(d) = dn k-1 xl)

ltpgt x2(d) = dn k-1 x2)

ltpgt e(d)k = dn k-1 ke)

ltpgt el(d) = dn k-1 el)

ltpgt e2(d) = dn k-1 e2)

ltpgt uc(d)k = dn k-1 kuc)

ltpgt ucl

ltpgt uc2

ltpgt thl

ltpgt th2

ltpgt th3

ltpgt th4

ltpgt th5

ltpgt th6

ltpgt th7

ltpgt th8

d) = dn k-1 ucl)

d) = dn k-1 uc2)

d)k = dn k-1 kth)

d) = dn k-1 thl)

d) = dn k-1 th2)

d) = dn k-1 th3)

d) = dn k-1 th4)

d) = dn k-1 th5)

d) = dn k-1 th6)

d) = dn k-1 th7)

d) = dn k-1 th8)

x_kml-gtk = kx

x_kml-gtpl = xl

x_kml-gtp2 = x2

e_kml-gtk = ke

e_kml-gtpl = el

e_kml-gtp2 = e2

uc_kml-gtk = kuc

uc_kml-gtpl = ucl

uc_kml-gtp2 = uc2

th_kml-gtk = kth

th_kml-gtthl = thl

th_kml-gtth2 = th2

th_kml-gtth3 = th3

th_kml-gtth4 = th4

th_kml-gtth5 = th5

th_kml-gtth6 = th6

th_kml-gtth7 = th7

th kml-gtth8 = th8

Write to files

fwritepkt(vartmpchk_xdat x_kml)

fwritepkt(vartmpchk_edat e_kml)

fwritepkt(vartmpchk_ucdat uc_kml)

fwritethpkt(vartmpchk_thdat th_kml)

return

=============== genAdapMechPkt ===================

void genAdapMechPkt(int k struct Pkt x_kml struct Pkt e_kml

struct Pkt uc_kml struct thetaPkt th_kml struct thetaPkt

th k-gtk = k

th_k-gtthl = th_kml-gtthl + Tgamma(blle_kml-gtpl + b21e_kml-

gtp2)x_kml-gtpl10000000

th_k-gtth2 = th_kml-gtth2 + Tgamma(blle_kml-gtpl + b21e_kml-

gtp2)x_kml-gtp210000000

th_k-gtth3 = th_kml-gtth3 + Tgamma(bl2e_kml-gtpl + b22e_kml-

th_k-gtth5 = th_kml-gtth5 - Tgamma(blle_kml-gtpl + b21e_kml-

gtp2)uc_kml-gtpl10000000

gtp2)uc_kml-gtp210000000

th_k-gtth7 = th_kml-gtth7 - Tgamma(bl2e_kml-gtpl + b22e_kml-

Write to files

fwritethpkt(vartmpadapoutdat th_k)

settime(vartmpfkadat k)

return

=============== main ============

main ()

int valid

int stime gamm

int i=0

int k kT

int kmax=2

struct Pkt x_kml

struct Pkt e_kml

struct Pkt uc_kml

struct thetaPkt th_kml

struct thetaPkt th_k

int getkt=0

int getkmax=0

printf (Content-type texthtmlnn)

printf(lthtmlgt ltheadgt lttitlegt Web Server of Embedded Adaptive

Controller lttitlegt

ltheadgtn)

if(strcmp((const char )cmd run) == 0)

strl = getval((unsigned char)sptime)

str2 = getval((unsigned char)gamma)

printf(ltbodygtlthlgtEmbedded Adaptive Controllerlthlgtn)

while(getkmax)

getkmax=getcsig(vartmpfkmaxdat ampkmax)

wait(5000)

printf(ltpgt Maximal step size kmax = dn kmax)

while(klt kmax)

printf(lth2gt Time = dTlth2gtn k)

Waiting for Plant Simulator sending signals

printf(ltpgt Waiting for Plant Simulator sending

signalsn)

while(Igetkt)

getkt = getcsig(vartmpfktdat ampkT)

wait (5000)

printf(ltpgt kT = d k = dn kT k)

while(k=kT)

getsig(vartmpfktdat ampkT)

wait(10000)

printf(ltpgt Adaptive Mech receiving input

signalsn)

getAdapMechPkt(k ampx_kml ampe_kml ampuc_kml ampth_kml)

printf(ltpgt Adaptive Mech synthesizing adaptive

gainsn)

genAdapMechPkt(k ampx_kml ampe_kml ampuc_kml ampth_kml

ampth_k)

printf (ltpgtSorry the request is invalidn)

printf (ltbodygtlthtmlgtn)

exit (0)

APPENDIX G MATLABC++ SIMULATION OUTPUT FILES

The simulation programs written in MATLAB and C++ give the same results

which are stored in output files The results are shown in the following tables

Gl State Variables Files

The content of state variables data files is shown in Table G 1

Table G 1 Simulation result of state variables

0000000

0100000

0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

1100000

1200000

1300000

1400000

1500000

1600000

1700000

1800000

0000000

-0005938

-0007274

-0007525

-0006703

-0006552

-0007393

-0007877

-0006929

-0006522

-0006511

-0005794

-0005655

-0005802

-0005829

-0005804

-0005700

-0006102

-0006161

0000000

-0000402

-0001596

-0002967

-0004377

-0005628

-0006885

-0008274

-0009549

-0010673

-0011823

-0012844

-0013834

-0014738

-0015578

-0016366

-0017279

-0018029

-0018812

0000000

-0005232

-0006874

-0007297

-0007309

-0007186

-0007024

-0006854

-0006686

-0006524

-0006369

-0006221

-0006080

-0005945

-0005816

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G2 Reference and Controlled Outputs

The content of simulation data files for reference and controlled outputs is shown

in Table G2

Table G2 Simulation result of reference and controlled outputs

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9600000

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10000000

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0001178

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Plant Error

The content of simulation data file for plant error is shown in Table G3

Table G3 Simulation result of plant errors

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Adaptive Gains

The content of simulation data file for adaptive gains is shown in Table G4

Table G4 Simulation result of adaptive gains

APPENDIX H HARDWARE VALIDATION OUTPUT FILES

Hl Validation Output Files of State Variables

The content of state variable data files is shown in Table Hl

Table H 1 Validation result of state variables

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-0004010

-0003440

-0003184

-0003502

-0004142

-0004063

-0003750

-0003078

-0003062

-0003270

-0004051

-0003045

-0003074

-0003973

-0003841

-0033687

-0033717

-0033822

-0033808

-0033813

-0033915

-0034075

-0034090

-0034174

-0034355

-0034481

-0034367

-0034446

-0034452

-0034402

-0034367

-0034495

-0034588

-0034652

-0034570

-0034511

-0034490

-0034669

-0034609

-0034624

-0034750

-0003301

-0003294

-0003287

-0003281

-0003275

-0003269

-0003264

-0003259

-0003254

-0003249

-0003244

-0003240

-0003236

-0003232

-0003228

-0003225

-0003221

-0003218

-0003215

-0003212

-0003209

-0003207

-0003204

-0003202

-0003199

-0003197

-0032944

-0032992

-0033038

-0033082

-0033124

-0033164

-0033202

-0033238

-0033272

-0033306

-0033337

-0033367

-0033396

-0033423

-0033449

-0033474

-0033498

-0033520

-0033542

-0033563

-0033582

-0033601

-0033619

-0033636

-0033652

-0033668

H2 Reference and Controlled Outputs

in Table H2

Table H2 Simulation result of reference and controlled outputs

0000000

0100000

0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

1100000

1200000

1300000

1400000

1500000

1600000

1700000

1800000

1900000

2000000

2100000

-0000000

0000320

0000436

0000563

0000573

0000611

0000674

0000668

0000648

0000685

0000701

0000719

0000756

0000753

0000770

0000832

0000887

0000837

0000830

0000897

0000000

-0001217

-0001558

-0001908

-0001787

-0001802

-0001909

-0001731

-0001525

-0001561

-0001507

-0001466

-0001518

-0001401

-0001383

-0001300

-0001215

-0001386

-0001514

-0001235

-0001138

-0001335

-0000000

0000337

0000472

0000536

0000576

0000607

0000633

0000657

0000680

0000702

0000723

0000742

0000761

0000779

0000796

0000813

0000828

0000843

0000858

0000871

0000884

0000896

0000000

-0001286

-0001691

-0001796

-0001800

-0001771

-0001733

-0001692

-0001652

-0001613

-0001576

-0001540

-0001507

-0001474

-0001443

-0001414

-0001386

-0001359

-0001334

-0001309

-0001286

-0001264

2200000

2300000

2400000

2500000

2600000

2700000

2800000

2900000

3000000

3100000

3200000

3300000

3400000

3500000

3600000

3700000

3800000

3900000

4000000

4100000

4200000

4300000

4400000

4500000

4600000

4700000

4800000

0000909

0000919

0000940

0000943

0000940

0000958

0000927

0000961

0000954

0000994

0001018

0000958

0000998

0000968

0000967

0000980

0001020

0001031

0001036

0001051

0001014

0001045

0001042

0001029

0001073

0001088

0001086

-0001304

-0001279

-0001298

-0001254

-0001181

-0001198

-0001027

-0001125

-0001054

-0001171

-0001218

-0000935

-0001067

-0000921

-0000888

-0000916

-0001041

-0001055

-0001052

-0001071

-0000897

-0001002

-0000971

-0000900

-0001055

-0001086

-0001048

0000908

0000919

0000930

0000940

0000950

0000959

0000968

0000977

0000985

0000992

0001000

0001007

0001013

0001020

0001026

0001032

0001037

0001042

0001047

0001052

0001057

0001061

0001065

0001069

0001073

0001077

0001080

-0001243

-0001223

-0001203

-0001185

-0001168

-0001151

-0001135

-0001120

-0001105

-0001091

-0001078

-0001066

-0001054

-0001042

-0001031

-0001021

-0001011

-0001001

-0000992

-0000984

-0000976

-0000968

-0000960

-0000953

-0000946

-0000940

-0000934

4900000

5000000

5100000

5200000

5300000

5400000

5500000

5600000

5700000

5800000

5900000

6000000

6100000

6200000

6300000

6400000

6500000

6600000

6700000

6800000

6900000

7000000

7100000

7200000

7300000

7400000

0001064

0001095

0001055

0001096

0001057

0001029

0001060

0001030

0001033

0001032

0001085

0001113

0001096

0001088

0001102

0001139

0001102

0001086

0001050

0001100

0001109

0001075

0001089

0001079

0001118

0001109

-0000928

-0001027

-0000844

-0000993

-0000827

-0000709

-0000830

-0000708

-0000718

-0000721

-0000930

-0001030

-0000941

-0000898

-0000941

-0001066

-0000899

-0000820

-0000682

-0000876

-0000905

-0000763

-0000824

-0000777

-0000923

-0000870

0001084

0001087

0001090

0001093

0001095

0001098

0001100

0001103

0001105

0001107

0001109

0001111

0001113

0001115

0001116

0001118

0001120

0001121

0001123

0001124

0001125

0001126

0001128

0001129

0001130

0001131

-0000928

-0000922

-0000917

-0000911

-0000907

-0000902

-0000897

-0000893

-0000889

-0000885

-0000882

-0000878

-0000875

-0000871

-0000868

-0000865

-0000863

-0000860

-0000857

-0000855

-0000853

-0000851

-0000848

-0000846

-0000845

-0000843

7500000

7600000

7700000

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

0001119

0001152

0001096

0001113

0001118

0001144

0001114

0001144

0001151

0001173

0001104

0001152

0001121

0001106

0001123

0001160

0001159

0001143

0001105

0001101

0001112

0001158

0001103

0001157

0001153

-0000908

-0001034

-0000804

-0000872

-0000892

-0000983

-0000849

-0000963

-0000983

-0001051

-0000767

-0000968

-0000835

-0000775

-0000849

-0000999

-0000980

-0000908

-0000751

-0000747

-0000796

-0000978

-0000743

-0000750

-0000960

-0000929

0001132

0001133

0001134

0001135

0001136

0001137

0001138

0001139

0001140

0001141

0001142

0001143

0001144

0001145

0001146

-0000841

-0000839

-0000838

-0000836

-0000835

-0000833

-0000832

-0000831

-0000830

-0000829

-0000827

-0000826

-0000825

-0000824

-0000823

-0000822

-0000821

-0000820

-0000819

-0000818

-0000817

-0000816

H3 Plant Error

The content of simulation data file for plant error is shown in Table H3

Table H3 Simulation result of plant errors

0000000

0100000

0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

1100000

1200000

1300000

1400000

1500000

1600000

1700000

1800000

1900000

2000000

2100000

000000

000002

000020

-000087

-000033

-000051

-000113

-000053

000019

-000012

-000004

-000001

-000037

000000

-000005

000019

000044

-000040

-000106

000004

000036

-000057

000000

000001

000003

-000002

-000020

-000017

-000021

-000045

-000049

-000042

-000045

-000052

-000044

-000049

-000043

-000038

-000030

-000041

-000049

-000050

-000051

2200000

2300000

2400000

2500000

2600000

2700000

2800000

2900000

3000000

3100000

3200000

3300000

3400000

3500000

3600000

3700000

3800000

3900000

4000000

4100000

4200000

4300000

4400000

4500000

4600000

4700000

4800000

4900000

-000052

-000050

-000065

-000054

-000030

-000044

000023

-000025

-000001

-000057

-000082

000034

-000027

000031

000040

000024

-000034

-000043

-000046

-000058

000014

-000035

-000024

000004

-000066

-000082

-000068

-000019

-000064

-000066

-000071

-000073

-000082

-000085

-000074

-000076

-000075

-000083

-000090

-000080

-000072

-000071

-000061

-000062

-000065

-000061

-000073

-000076

-000068

-000066

-000064

-000071

-000083

-000097

5000000

5100000

5200000

5300000

5400000

5500000

5600000

5700000

5800000

5900000

6000000

6100000

6200000

6300000

6400000

6500000

6600000

6700000

6800000

6900000

7000000

7100000

7200000

7300000

7400000

7500000

7600000

7700000

-000064

000013

-000053

000016

000065

000011

000061

000056

000053

-000039

-000083

-000046

-000029

-000049

-000103

-000033

000000

000058

-000026

-000040

000021

-000007

000013

-000050

-000029

-000046

-000100

-000002

-000102

-000112

-000108

-000109

-000100

-000089

-000082

-000071

-000054

-000040

-000042

-000052

-000055

-000056

-000068

-000080

-000089

-000080

-000072

-000074

-000075

-000061

-000065

-000067

-000076

-000074

-000072

-000078

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

-000032

-000041

-000081

-000024

-000073

-000082

-000112

000010

-000077

-000020

000005

-000027

-000092

-000084

-000053

000014

000015

-000006

-000084

000016

000013

-000077

-000064

-000073

-000069

-000075

-000087

-000085

-000090

-000105

-000114

-000100

-000105

-000103

-000095

-000089

-000100

-000107

-000111

-000101

-000093

-000089

-000105

-000097

-000108

H4 Adaptive Gains

Table H4 Simulation result of adaptive gains

e 03716

-05106

-03100

-00427

-00428

-05106

-03100

-03099

-00428

-05106

-03099

-03098

-00428

-05106

-03098

-00428

-00429

-00428

-00429

-00428

-00429

REFERENCES

[1] ARM Ltd (2009 Oct 19) ARM processor instruction set architecture [Online]

Available httpwwwarmcomproductsCPUsarchitecturehtml

[2] R N Shreve and G T Austin Petroleum Processing in Shreves Chemical

Process Industries 5th ed New York McGraw-Hill 1984 pp 713-725

[3] R C Darton Distillation and absorption technology Current market and new

developments Trans IChemE vol 70 pp 435^137 Sep 1992

[4] T J McAvoy Interaction Analysis Principles and Applications Durham NC

Instrument Society of America 1983

[5] J L Humphrey A F Seibert and R R Koort Separation Technologies -

Advances and Priorities Washington DC US DOE Report 1991

[6] B Dahho H Youlal A Hmamed and A Majdoul Identification and control of

a distillation column in IF AC 9th Triennial World Congress Budapest

Hungary vol 3 pp 1719-1724 1984

[7] G C Shen and W K Lee Adaptive inferential control for chemical processes

with intermittent measurements Ind Eng Chem Res vol 28 no 5 pp 557-

563 May 1989

[8] D E Seborg T F Edgar and S L Shah Adaptive control strategies for process

control A Survey AIChEJ vol 32 no 6 pp 881-913 Jun 1986

[9] M Agarwal and D E Seborg A multivariable nonlinear self-tuning controller

AIChE J vol 33 no 8 pp 1379-1386 Aug 1987

[10] H T Nguyen and N Afzulpurkar Application of multivariable adaptive control

design to natural gasoline plant in Proc 3rd Asian Conf Industrial Automation

and Robotics Bangkok Thailand 2003 pp 90-95

[11] K S Narenda and A M Annaswamy Stable Adaptive Systems Englewood Cliff

NJ Prentice Hall 1989

[12] G Stephanopoulos Chemical Process Control Englewood Cliffs NJ Prentice-

Hall 1984

[13] Wikipedia (2009 Sep 12) MATLAB [Online] Available httpenwikipedia

orgwikiMATLAB

[14] K J Astrom and B Wittenmark Adaptive Control New York NY Addison-

Wesley Publishing Company 1995

[15] G O Mutambara Design and Analysis of Control Systems Boca Raton FL CRC

Press 1999

[16] S3C44B0X RISC Microprocessor Datasheet Samsung Corporation 1998

[17] C D Holland Fundamentals of Multicomponent Distillation New York

McGraw-Hill 1981

[18] H Kehlen and M T Ratzsch Complex multicomponent distillation calculations

by continuous thermodynamics Chem Eng Sci 42 pp 221-232 1987

[19] R J Fuentes and M J Balas Robust model reference adaptive control with

disturbance rejection in 2002 Proc American Control Conf Anchorage AK

2002 pp 4003-4008

[20] G Kreisselmeier and K Narendra Stable model reference adaptive control in

the presence of bounded disturbances IEEE Trans Autom Control vol 27 no

6 pp 1169-1175 Dec 1982

[21] B Peterson and K Narendra Bounded error adaptive control IEEE Trans

Autom Control vol 27 no 6 pp 1161-1168 Dec 1982

[22] K J Astrom and B Wittenmark Computer-Controlled Systems Theory and

Design Englewood Cliffs NJ Prentice-Hall International 1990

[23] G A McNeill and J D Sachs High Performance Column Control Chem Eng

Prog vol 65 no 3 pp 33-39 Mar 1969

[24] J S Moczek R E Otto and T J Williams Approximation Model for the

Dynamic Response of Large Distillation Units Amsterdam Elsevier 1965

[25] S Skogestad and M Morari Understanding the dynamic behavior of distillation

columns Ind Eng Chem Res vol 27 pp 1848-1862 Jun 1987

[26] H T Nguyen and N Afzulpurkar Symbolic Algebra Approach for Adaptive

Controller Design in Proc 4th Asian Conf Industrial Automation and Robotics

Bangkok Thailand 2005

[27] C L Phillips and H Troy Digital Control System Analysis and Design

Englewood Cliffs NJ Prentice-Hall 1984

[28] D Hung Lecture Notes and Handouts ofCMPE 264 San Jose CA Computer

Engineering Department San Jose State University 2008

[29] EventHelix Inc (2009 Oct 2) NFS Protocol Diagrams [Online] Available

httpwwweventhelixcomRealtimeMantraNetworkingNFS_Protocol_Sequenc

e_Diagrampdf

[30] H Li Lecture Notes and Handouts ofCMPE 244 San Jose CA Computer

[31 ] ARM Software Development Toolkit Version 250 User Guide ARM Ltd 1998

[32] M Felton CGI Internet Programming with C++ and C Upper Saddle River NJ

Prentice Hall 1997

control A survey AIChE J vol 32 no 6 pp 881-913 Jun 1986

[34] V M Popov Hyper stability of Automatic Control Systems New York Springer

[35] W L Luyben Process Modeling Simulation and Control for Chemical

Engineers 2nd ed Auckland McGraw-Hill 1990

[36] R Richardson Lehigh Distillation Control Short Course Lehigh PA Lehigh

University 1990

[37] W L Luyben Practical Distillation Control New York Van Nostrand Reinhold

[38] P Harriott Process Control New York McGraw-Hill 1964

[39] J H Perry Ed Chemical Engineers Handbook 6th ed New York McGraw-

Hill 1984

[40] R G E Franks Modeling and Simulation in Chemical Engineering New York

Wiley-Interscience 1972

[41] W L Nelson Petroleum Refinery Engineering Auckland McGraw-Hill

International Book Company 1982

[42] W L McCabe and J C Smith Unit Operations of Chemical Engineering New

York McGraw-Hill 1976

[43] M V Joshi Process Equipment Design New Delhi Macmillan Company of

India 1979

[44] Feasibility Study of Condensate Processing Plant Petrovietnam Corp 1998

[45] W C Edmister Hydrocarbon adsorption and fractionation process design

methods Petroleum Engineer vol 21 pp 45-50 1949

[46] B I Lee J H Erbar and W C Edmister Properties for low temperature

hydrocarbon process calculation AIChE J vol 19 pp 349-356 Mar 1973

SJSU ScholarWorks

Fall 2009

Design and implementation of embedded adaptive controller using ARM processor

Hoan The Nguyen

Recommended Citation

ProQuest Dissertations

DESIGN AND IMPLEMENTATION OF EMBEDDED ADAPTIVE CONTROLLER

USING ARM PROCESSOR

A Thesis

Presented to

The Faculty of the Department of Computer Engineering

In Partial Fulfillment

of the Requirements for the Degree

Master of Science

Hoan The Nguyen

December 2009

UMI Number 1484326

copy2009

Hoan The Nguyen

by Hoan The Nguyen

mdashr ~ mdash^ yy

ABSTRACT

by Hoan The Nguyen

ACKNOWLEDGMENTS

people

TABLE OF CONTENTS

List of Tables xiv

List of Figures xvi

11 Background 1

15 Methodology 5

28 ARM Processor 16

31 Introduction 20

41 Introduction 26

441 Plant 31

51 Introduction 43

521 Plant Model 44

61 Introduction 50

71 Introduction 66

751 CGI Program 78

77 Testing 93

772 Test Results 98

81 Conclusion 104

82 Future Work 105

A12 Vent-bleed 110

B31 Description 124

B32 Calculation 125

B41 Description 126

B42 Calculation 127

B51 Description 128

B52 Calculation 129

Cl Introduction 137

C22 Feed Tray 140

C23 Top Section 141

F2 Plant Model 170

F5 Comparator 173

F8 CGI Program 175

G3 Plant Error 206

H3 Plant Error 222

References 230

LIST OF TABLES

LIST OF FIGURES

Motor octane number

Network file system

Personal computer

Reid vapor pressure

True boiling point

Zero-order hold

LIST OF SYMBOLS

A State matrix

B Input matrix

C Output matrix

e State error

L Feedback matrix

u Control signal

x State variable

y Controlled output

Greek Symbols

y Adaptation rate

0 Adaptive gain

Subscript

B Bottom product

F Feed

m Reference model

CHAPTER 1

INTRODUCTION

11 Background

time spaces

adaptive controller

mathematical method

15 Methodology

CHAPTER 2

LITERATURE REVIEW

RECTIFYING SECTION

F (feed flow rate)

Q n I (3) CONDENSER

1 8 - D

stage f (feed tny)

stage rc

Material stream

Feed stream

Distillate stream

Bottoms stream

Position

Stage f

Stage N

Reflux drum

Stage 1

Reboiler

Flow rate

Concentration

in Figure 22

Liquid phase

Stage it

(Trav gti-l)

bull bullbullbull

m^u - Bubble cap

structures

I |mdash0mdashI I

bottoms flow rate B

are adjusted [12]

required

Command_ signal

Adaptive mechanism

laquosj

Control signal

Plant 1 Output

Process dynamics )

Siv-CSnftlteF----

26 Adaptive Schemes

261 Gain Scheduling

Command signal

Output

signal

MoctSI

Control signal

mechanism

Plant -bull Output

= ( ) bull (21)

disturbances or not

- mdash

yfdx dt

x = 0 i

-gt() =

= = ( ) = -W(x) (22) dt dx dt dx

dx mdash = Ax (23)

ATP + PA=-Q (24)

following function

V(x) = xTPx (25)

28 ARM Processor

DB-9 DB-9

RS-232

Features

Memory

subsystem

GPIO ports

Ethernet

Descriptions

solution

8 memory banks

by RAM

CHAPTER 3

31 Introduction

RffLlrtERLMl

xD gt 98

xB lt 20

Table 31

Temperature C

Pressure atm

Density kgm3

Mass flow rate kgh

Main streams oft

Condensate

130000

he plant

Raw gasoline

system

35 Plant Modeling

1403 x16 =1646291^15 -756380x16 -927597xI6

58x15 =1646291(gtl4 -^1 5) + 756380(x16 -x15)

58x14 =164629103 -gtgt14) + 756380(x15-x4)

58x13 =1646291012 -_y]3) + 756380(x14 -x13)

58x12 =1646291(^n -y1 2) + 756380(x13 -x ] 2)

58xH =164629IO10 ~ ^ i ) + 756380(x12-x)

58x10 =164629109 -^1 0) + 756380(xn -x10)

58x9 = 661139gtgt8 -15638^9 + 756380(x10 -x9) + 5995

58x8 = 66113907 ~yamp) + 756380 x9 -18859x8 + 3399

58x7 = 661 39(y6-y7) + 798871 (x8 -x 7 )

58x6 =66113905-gt 6) + 1798871(x7-x6)

58x5 =66113904^) +179887 l (x 6 -x 5 )

58x4=66113903-^4) + 1798871(x5-x4)

58x3 =66113902-73) +1798871 (x 4 -x 3 )

58x2 =661139(^-gt2) +179887l(x3-x2)

2488x = 1798871x2-1109235x1 -661139^

568x y = l + 468x

l + 468x

^ 1 5 =

568x 15

l + 468xbdquo (34)

CHART OF VAPOR

01 02 03 0 4 05 06 07 08 09

36 Plant Simulation

Table 32

bull L _ I i 1 l

6 8 10 12 14 16 18 20 Time (h)

than 2

CHAPTER 4

41 Introduction

and (32)

Disturbances

Ditiilitirn Gy-tem

x(t) = A(xt) + Beu(t) (41)

y(t) = Cex(t) (42)

two-output system

-09095

-02497 Bbdquo

-01461 02073

-00021 -00281 and C

-00624 -00281

02458 00009

Bode Diagram

Frequency (radsec)

431 Stability Test

finite time T-tgt0

x = Ax(t) + Bu(t) (45)

y(t) = Cx(t) + Duy) (46)

full rank of n

output

S=[CCACA2CA]]T

the next section

441 Plant

yt) = Cx(t)

where A = au

an_ B =

bn_ and C =

-00624 -00281

02458 00009

variables

442 Reference Model

Sec 43

where Abdquo

ybdquo(t) = cmxm(t)

-67941 -09095

14686 -02497

5 = -01461 02073

-00021 -00281 and Cbdquo

-00624 -00281

02458 00009

ut) = Muct)-Lx(t)

x = (A- BL)x + BMuc

hence we define

Ac(0) = (A-BL)

Bc6) = BM

i2 ~b2

l 2 11^2 ^12^4

22 _ ^ 2 1 ^ 2 ~ ^ 2 2 ^ 4

b2]65+b2281 b2Xdb+b22d (412)

condition we get

au-bu6-bnel =-67941

an -bu6a2 -bn6deg4= -09095

a2]-b2]6deg-b220deg =14686

a22-b2]e2-b229deg= -02497

6Adeg + M7deg =-01461

606deg + 6 X =02073

b2l6deg5+b229deg =-00021

b2]edeg6+b226degs =-00281 (413)

condition

0 _ b22(au +67941)-bu(a2] -14686) 0 =

regp22 ^12^21

a o _ b22(an + 09095)-bn(a22 +02497)

^11^22 _ ^12^21

buo22 mdashbnb2]

0 _ -b2](a]2 + 09095)+ bu(a22 +02497) 6gt =

bP 22 b]2b2]

-b2]bn+bub22

n0 002816I2+02073Zgt22

(J6 = -b2]bu+bub22

_0 - 000216+ 0146 b2x Uf =

-b2]bu+bub22

0 = 002816 +020736

-b2Xbu+bxxb (414)

Error Equation

e(0= x(0-m(0

e() = ^ ( 0 + 5 i ( 0 - ^ I B ( 0 - 5 m laquo c ( 0 - (4-15)

e(t) = Ame(t) + V(t)(0-O0) (417)

446 Adaptation Law

function

V(e 0) = [yePe + (0 - 0deg f (0 - 0deg)) (418)

(420) dt 2

ltP + PAm = -a (4-21)

^ = -W(t)Pe(t) at

y(buex+b2Xe2)xx

y(buex+b2]e2)x2

y(bnex+b22e2)xx

y(bx2ex+b22e2)x2

-y(bxxex+b2xe2)ucX

-y(bxxex+b2Xe2)uc2

-y(bX2ex+b22e2)ucX

-y(buex+b22e2)uc2

6 = (423)

mdash = -05591lt -07066e2)2 +132756e2] dt 1

2) Disturbances^)

4) Reference model

a n n f l

REFERENCE MODEL

dull In I

0ut2 In2

ADAPTIVE MECHANISM

= X Xm

_X2 Xm2 _

follows

e = RMS(e) = -^A for = 1 or 2

commands

norm_el = norm(el)

norm_e2 = norm(e2)

shown in Figure 46

m B s in

Figures - x vc xm

m B ampm

bull4s

bullraquo i x

i m B raquo bull

im B ffin

State error e1(t)

State error e2(t)

e = 00017

n2 VTooT = 7106210

453 Error Reduction

Plant errors

laquoi

Adaptation rate y

54304 105

71399105

5428410

7106210

54076 105

7100310-5

CHAPTER 5

51 Introduction

G(s) y ( t

521 Plant Model

x(t) = Axt) + But)

y(t) = Cx(t)

x(s) - ~[AX(S) + Bu(s) s

T x(z) = [AX(Z) + Bu(z)]

y(kT) = CxkT) (52)

522 Reference Model

in Chapter 6

ybdquo(t) = cmxm(t)

where Am = [-67941 -09095 14686 -02497] Bm = [-01461 02073 -00021 -00281]

and Cm = [-00624 -00281 02458 00009]

follows

ut) = Muc(t)-Lx(t)

L = 0kT) 62(kT)

0(kT) 0AkT

M 05(kT) 06(kT)

87(kT) 0s(kT)^ (56)

o _ ft2deg2(adeg +67941)-ft02(a20 -14686)

degdeg27 deg12deg21

8 0 _ -amp2 K + 67941) + ft (a2] -14686)

ftdeg =

00021ft0-01461ft0 22

-ft21 f t02+ft0 f t22

-b2]b]2+bub22

-b2bn+bub22

n0 00281ft+02073ftdeg

201 deg]]deg22

6(t) = -y^(t)Pe(t)

= yy (s)Pe(s)

CHAPTER 6

61 Introduction

2) Disturbances^^

reference signals

1 tnl uc(k)

In2 uc(k-1)

xm(k-1)

laquogt

REFERENCE MODEL

H Disturbances

bulleurogt

[B^_]M

0ut1 In)

0ut2 In2

i f MJi-1)

0 u ulaquoK-l)

ADAPTIVE MECHANISM

m lt raquo

Ot-1) Mux bull

e(kT) = exkT)

e2(kT)

h(kT)-xnnkT)

x2(kT)-xm2(kT)_

Ax^kT)

Ax2(kT)

follows

e = RMSe) = ^L for = 1 or 2 (61)

shown in Figure 62

Disturbance f(t)

m gt P i laquo ^ e

a)e(7)

ns gt P l

a) eiikT)

I U I 94543e-004 _ bdquo ^ - s

101 = 9407410-

M = 9 6557e -Q04 = 9 6 0 7 8 t l 0 5

4n2 vioi

sections

in Figure 66

4 include tbdefsh

5 class Plant

6 private

12 public

13 Plant()

14 -Plant()

18 endif

P l a n t ( )

a l l = - 6 7 9 4 1 + 0 6 7 ( r a n d ( ) 2 - 0 5 )

a l 2 = - 0 9 0 9 5 + 0 0 9 ( r a n d ( ) 2 - 0 5 )

a21 = 14686 + 015(rand()2-05)

a22 = -02497 + 002(rand()2-05)

bll = -01461 + 0014(rand()2-05)

bl2 = 02073 + 002 (rand()2-05)

b21 = -00021 + 00002(rand()2-05)

b22 = -00281 + 0003 (rand()2-05)

ell = -00624 + 0006(rand()2-05)

cl2 = -00281 + 0003(rand()2-05)

c21 = 02458 + 0025(rand()2-05)

c22 = 00009 + 000009(rand()2-05)

4 include tbdefsh

5 class Refmdl

6 private

7 Pkt uc_k

8 Pkt xm_k

9 public

10 Refmdl()

11 -RefmdlO

15 endif

Figure 68

4 include tbdefsh

5 class Linctrl

6 private

7 thetaPkt th_k

8 Pkt x_k

9 Pkt uc_k

10 public

11 LinctrlO

12 -LinctrlO

16 endif

database

4 include tbdefsh

5 class Comparator

6 private

7 Pkt x_k

8 Pkt xm_k

9 Pkt e_k

10 public

11 Comparator()

12 -Comparator()

16 endif

and the plant

4 include tbdefsh

6 private

7 thetaPkt th_kml

8 Pkt x_kml

9 Pkt e_kml

10 Pkt uc_kml

11 public

12 AdaptiveMechO

13 -AdaptiveMechO

17 endif

model and the plant

CC = g++

ReferenceModelo

executive file

j haut$ttum

ltOIgt gtiJ^Alt

plusmn1 f bull-lt

i gt bulli

lt euro f bull2

[ bull

- H J bullbull -

~ttttfc

bull=fmdashF^--

^ t ^ i i i = ^ ^

_ - 1 1 = - mdash J

^ J - - - ^ ^

1 1 1 I

5 time

e = |N| s94543c-004 ^

96557e-004

VToi = 96078 105

CHAPTER 7

71 Introduction

shown in Figure 71

_ Data J

5gt I Error

yV H Report

Plant Slmsliitsr

lt = J Output

Linux yacnine

RPC get_port reply

RPC mount request

RPC mount reply

Authenticate client

to the browser

button

lUser sufrmis fwm

arv-affe ie Camp

vas tor PlssrtSwi

Sens ( to i l sA i

(J 0 0

SefieJ acispfcw BM2

Oylpaito wefccfer

72 Common Database

File name

kucdat

ucldat

uc2dat

kthdat

thldat

th2dat

th3dat

th4dat

th5dat

th6dat

th7dat

Data description

Plant state xi

Plant state X2

Error variable ei

Error variable e2

Adaptive gain Gi

Adaptive gain 02

Adaptive gain 63

Adaptive gain 64

Adaptive gain 85

Adaptive gain 96

Adaptive gain 67

th8dat

adapoutdat

kmaxdat

Adaptive gain 0g

Maximal step size

73 Plant Simulator

CC = g++

$ make

1 iij-ji--^- - M - - I - - bull

1 lthtmlgt

2 ltheadgt

4 ltheacigt

5 ltbodygt

9 ltdivgt

value= size=40gt

17 ltformgt

18 ltbodygt

19 lthtmlgt

Feature

action=

method=

target=

Code example

Run gt

Description

program

time and text type

follows

th[k-l])

11 return

15 th-gtk = k

1]10000000

1] 10000000

1]10000000

23 return

751 CGI Program

variables

getenv() as follows

parameters

1 main ()

3 i n t v a l i d

17 while(klt kmax)

19 while(Igetkt)

21 wait(5000)

24 while(k=kT)

26 wait(10000)

ampth_k)

33 k++

36 else

41 exit (0)

program 109880

looses 10S824 188824 100883 100883 100883 19S821

Yers 2 2 1 1 2 3 4 1

port 111 111

48909 55541

2849 2849 2649

sudo rpcinfo -p

I I Bin Edit yamp

hoanaoan-$

gt Terminal

hoan^hoan ~$

2 2 1 1 2 3 4 1 3 4 2 3 A 1 3 4 1 1 2 2 3 3

i n f o -j r o t o

P po r t

111 n i

35368 35832

2649 2649 2S49

44664 44694 44994

2049 2849 2949

41394 41894 41894 33383 44819 33389 44819 33389 44819

M ^ s t i k ^ ^ lt

l - pound ig

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 a 3 3 3 3 3 3 A

syslog-install

root location as

during compilation

TESTOBJS = mycgio

support

1) TCPIP networking

3) IP DHCP support

4) IPBOOTP

5) IPRARP

2) RTL8019AS

and check

1) Boa

2) dhcpcd-new

3) dhclient

4) ifconfig

5) inetd

6) ping

8) route

9) routed

10)telnetd

ll)tftpd

terminal

for Linux machines

machine)

go 0x0c008000

RRMboot 182 (Aug 12 2084 - 104321)

bulltrade u u mdash

1 000 netmask 2552552550 lo

77 Testing

771 Test Procedure

(PC Linux machine)

Figure 722

D Graquo S S if

5fw help

following command

1 9 2 1 6 8 0 8 o p t t e s t v a r t m p

| g haanhoan ~

0JS packet loss

controllerhtmlgt

$01 C s- J http1921680^

Run Reset

adap t i vecamro l

13S3603 6682830

6258383

1393689 -8pound62298 B JhK-iH-)

-6239783 6626603

666G855

-9259783 -0629683 H HHI-li4s

Gsxgte i

efk-Dpl =

e(k-l) p2 =

ucfk-ljk =

uc(k- l ) p l

uc(k-l) p2

thik-lj k =

th ik - l j th l

th ik- l ) th2

th(k- l ) th3

thk- l ] th4

thk- l ) th5

thfk- l j th

amp c l

= 50000

=10000

= 66000

= -309998

= 1 0 4 4 2 2 5 4

= -42712

= 4240

ITtdlk^ Turlb

o Htp iH9i

| IG^Search

16S0 1

raquo bull zfgt

b i r p

ycqr u

^Settings

772 Test Results

in Table 73

File name

t_xdat

t_xmdat

t_edat

t_ucdat

t_udat

t_thetadat

t_ydat

t_ymdat

Data description

000000

-000521

-000667

-000817

-000764

-000770

-000815

-000738

-000650

-000665

-000641

-000623

-000645

-000594

-000587

-000551

-000514

-000587

-000641

000000

-000037

-000151

-000291

-000447

-000580

-000713

-000862

-000986

-001091

-001202

-001313

-001403

-001503

-001586

-001667

-001748

-001817

-001903

000000

-000523

-000687

-000730

-000731

-000719

-000702

-000685

-000669

-000652

-000637

-000622

-000608

-000595

-000582

-000569

-000558

-000546

-000536

000000

-000039

-000153

-000289

-000427

-000563

-000693

-000817

-000936

-001049

-001158

-001261

-001359

-001453

-001543

-001628

-001710

-001788

-001862

-000522

-000480

-000564

-000550

-000539

-000547

-000528

-000496

-000503

-000430

-000472

-000441

-000491

-000511

-000390

-000446

-000383

-000369

-000381

-000435

-000441

-000439

-000447

-000373

-000418

-000404

-000373

-000440

-001982

-002051

-002115

-002190

-002251

-002311

-002367

-002427

-002476

-002525

-002558

-002603

-002641

-002687

-002732

-002756

-002781

-002813

-002832

-002862

-002894

-002916

-002952

-002980

-002995

-003014

-003035

-003052

-000526

-000516

-000507

-000498

-000489

-000481

-000474

-000466

-000460

-000453

-000447

-000440

-000435

-000429

-000424

-000419

-000414

-000410

-000405

-000401

-000397

-000393

-000390

-000386

-000383

-000380

-000377

-000374

-001933

-002000

-002065

-002126

-002185

-002241

-002294

-002345

-002394

-002440

-002484

-002526

-002566

-002605

-002641

-002676

-002710

-002741

-002772

-002800

-002828

-002854

-002879

-002903

-002926

-002948

-002969

-002989

-000453

-000436

-000385

-000428

-003078

-003109

-003139

-003161

-000371

-000369

-000366

-000364

-003007

-003025

-003043

-003059

-0 025

_ m _ _ ^ i = _ mdash p i r r F ^

~~-ti ===ii

-mdash^zr ~~ i

2(enfc) -

-00006

-00009

-00011

-00008

-00001

-00004

-00008

-00001

-00002

-00005

-00004

-00005

-00004

-00008

-00001

-00002

-00003

-00002

-00003

-00002

-00003

-00002

-00001

-00002

-00010

-00009

-00001

-00009

-00006

-00005

-00001

-00008

-00013

-00002

-00004

-00007

-00014

-00006

-00007

-00001

-00010

-00003

-00004

-00005

-00003

-00004

-00002

-00001

-00002

-00001

-00002

-00003

-00005

-00006

-00008

CHAPTER 8

81 Conclusion

82 Future Work

xv2 r~

PILOT PLANT

Realtime (lata

D Xbdquo

B xbdquo

PE -W-V2

fc V -tvi

PILOT PLANT

PID Embedded

Adaptive Ccntroller

Online measurement

Hyperterminal

reg Spf M -amp- 1

i KZ- ^ -n

REFLUX DRUM

A 12 Vent-bleed

CONDENSER^-

mdash 4 6

i mdash amdashgtp j

Inert gas O

mdash m ltV3

i te i iaal

J5) Input ho-ot IS)

B - t-t

a) Kettle type

o h m m I K I

i t t_e i i - 1 1

-amp Q

_ U ftau irav

P| vopor flow

V U heat -

exchanger

A WH-J

have been specified

degrees of freedom

Column pressure

Manipulated

variables

Reflux flow rate

Reboiler duty

Condenser duty

Bottoms flow rate

Control valve

location

Reflux flow (VI)

Heat flow (V4)

Coolant flow (V3)

Bottoms flow (V5)

Control Structure

D-V(or D-QB)

L-V(or L-QB)

Role of valve

Inventory

Control (IC)

Separation

Control (SC)

structures

units in the plant

flow rate B

I raquo - sect I -

ATbdquo

are switched

H amp J bull

Component

Propane

Normal Butane

Isobutane

Isopentane

Normal Pentane

Hexane

Heptane

Octane

Nonane

Normal Decane

n-CHH24

n-C12H26

Cyclopentane

Methylclopentane

Benzene

Toluen

O-Xylene

E-Benzene

Cut point

(degC)

ASTM D86

(degC)

124024

Properties

1 Octane Number

2 Lead Content (g1)

10 vol

50 vol

90 vol

Residue ( vol)

Testing method

ASTM D2699

ASTMD3341

ASTM D86

ASTM D130

ASTMD381

ASTM D323

ASTM D1266

ASTM D525

ASTMD1298

Requirements

min 87

max 015

max 70

max 120

max 190

max 210

max 20

maxN-1

max 40

min 43

max 80

max 015

min 240

070 - 074

capacity

tso (TBP) = 5842 C

t(30- io) (TBP) = 3599-2467=1132 degC

t50 (EFV-TBP) = 1-5 C

Therefore

tso (EFV) = 5842+15=5962 degC

EFV (1 atm)

EFV (46 atm)

20 3840 60

Volume

80 100

B31 Description

B32 Calculation

fegtegtd f l ow

tray f

Rf= B-LF+ Vf= 62 - 58 + 28 = 32 vol

Stream

Total light

fractions E S D

Bottoms B

Volume fraction

Liquid flow rate

-73916

133973

-64677

143213

Liquid density

Mass flow rate

-45458

-38677

104046

B41 Description

B42 Calculation

stripping section

kcalkg

kcalhlOJ

kJhl0 j

276860

131300

408161

kcalhlOJ

149134

kJhl0J

267136

357141

624280

B51 Description

reflux flow

B52 Calculation

46degC

Stage 15 (tray 14)

D Distillate

9611+Ro

kcalkg

ZSD+Ro

5065+Ro

9611+Ro

kcalkg

kcalhlOJ

11053+24 R0

kJhlOJ

1005 R0

46263+1005 R0

kcalh103

49131+97Ro

56405+ 97R0

kJhl0J

205665+406R0

236111+406R0

46263+1005 Ro= 236111+406 Ro

Therefore

Ro= 7415 (tonh)

at the column top)

AHRoR0= AHLL

(115-24) (742) = (106-22) I

Therefore

L = 804 (tonh)

Stream

Temperature (C)

Pressure (atm)

Density (kgm )

Stream

Temperature (C)

RVP (kPa)

Density (kgm )

Condensate

130000

Reformate

105000

Raw gasoline

Gasoline

250000

Condensate bull

bullff

Raw Gasoline

amp V - 0 1

PEF l l OPUH

-Gasoline

GSSOLINE MIXER

gasoline

is 128degC

tankers

B74 Feed Control

46 atm

i T C - 1 r

mdashImdash I

--copy

l-MmdashJ

To Column

B76 Bottom Section

Cl Introduction

linear

outlet weir

Mbdquo = f(LJ (Cl)

C21 Generic Trays

equations

d(Mbdquo)

Liquid

Flow rate

vbdquo Vn

Concentration

staae n

dh dMbdquo x = A-

dLbdquo dL (C4)

d(Mbdquoxbdquo) dt

dt Mbdquo (C6)

d(Mnhn) dt

V = H-h

C22 Feed Tray

stage (feed tray

LfXrbdquo

I-v vgt LrXf

d(Mfxf)

dt Mbdquo

d(Mfhf)

C23 Top Section

Vlaquobdquo

11 V M1

vbdquo

d(MN+l) _ (C 13) dt

d(M XN+])=Lx^ + y L _ y ( C 1 4 )

11 N+ nN+

C24 Bottom Section

l I l I

ltHXr-B x F

d(M2) dt

L3-L2+ VB -V2

dMRhB) dt

= 23Z3 +HBVB- h2L2 - H2V2

Therefore

H2 -h2

be neglected

dMB) = L 2 _ V B B ( C 2 3 )

d(MBhB)

4 Simplified Model

yn = r (C27)

+ (a-l)xbdquo

aZyv+2 = dL)

L2= LT~ = LN+2-

equations [12]

5) Tray n(n = 2 - l)

MBX] =(L + LF)X2 - Vy - fix (C33)

1) LF=qFF

2) VF = F-LF

y = r bull (C35)

1 + a - )Xj

A = 730 (kJkg)

V0= 39098 (kgh) or 668871 (kmoleh)

V = 0+ = 663407 (kmoleh)

Joshi [43]

ffl^^M (C38)

314(175X1-4) Z ^ = 2488 (kmole) B 4 786

t 0957chD2k dr

095(314)(028)(175)2 680 M = = 580 (kmole)

MD = 5iL + D) (C41)

flow rate

follows

Tray 5 (n = 6) M6 = F(^5 - y6) + (Z + LF )(x7 - x6)

Tray 3 (n = 4) M4 = F(^3 - gt4) + (Z + ZF )(x5 - x4)

2488 (kmole)

1403 x16 =1646291 y]5 - 756380x6 -927597x6

58x15 = 1646291(y14 -y ] 5) + 756380(x6 -x l 5)

58x4 = 1646291(73-gtgt4) + 756380(x5-x4)

58x13 = 1646291(712 - yn) + 756380(xl4 - x13)

58x12 =1646291(j |l-j12) + 756380(x13-x12)

58 = 1646291(710 -yu) + 756380(x2 -x )

58x0 = 1646291(79-^0) + 756380(x-x0)

58x9 = 661 39ys -15638gt-9 + 756380(xl0 -x 9 ) + 5995

58x8 = 661139(y7 -ya) + 756380 x9 - 18859x8 + 3399

58x7 = 661139(y6-y7) +179887 l (x 8-x 7)

58x6 = 661 39(y5-y6) + 179887 l (x 7 -x 6 )

58x5 = 661139(j4 - y5) +1798871 (x6 - x5)

58x4 =661139(^3 -yA) + 79887 l (x 5-x 4)

58x3 = 661 139(^2 - y 3 ) + l798871 (x4 - x3)

58x2 =661139(j -y2) +1798871 (x 3 -x 2 )

2488x = 1798871 x2 -1109235x -661139^ (C42)

568x y ~ l + 468x

y2 = 568x2

1 + 468x

^ 1 5 =

l + 468x (C43)

bullCO

laquo r M |

raquo ^ SA 11 j

w r n i |

^ ltgt fM f 3 1

ET mAr pound |

~^ IT JWi a mdash i

Cgt $ IZ

1 ma r ii |

P $ mar t |

ET r Jfifl V 3 1

b $ TWVlP 2 1

J ^ m d If f |

WFYMtG

fiterttxm

STRIPPING SECTION

GENERAL TRAY

COLUMN

1 TRAY 7

1 TRAYS

RECTI FYINO SECTION

GENERAL TRAY 1

Figure D3

- w i 13411

~W 46804

RECTIFYING SECTION

mdash bull In2 Out2

STRIPPING SECTION

bull XD

To Workspacel

-4L Scope 1

Raw Gasoline

bull | xB

To Workspace

H Scope

In20ut2

Inl O u l l M

In 2 Ou2t

Tray 14

bull i n l Out1 |

- W i n 2 Oul2|

Tray 13

In 10ut 1

In20ut2

Tray 12

bull In lOu t l

In20ut2

Tray 11

InlOutl

In20ul2

Tray 10

bullNln20Ut2

Tray 9

l j mdash

~2~gt -In2

bull in 2

Tray 8

x 1 bull Outl

bull - K 2 Out2

_2 mdash

f bull

n 1 n n H I Wgt A

In 2 Ol l t l

Tray 7

mdash bull

In 10ut1

In20ut2

Tray 6

- gt In20ut2

Tray 5

In lOut l -

bull ln20ut2

Tray 4

bull in lOut l

1 bull

In20ut2

Tray 3

In lOut l

In20ut2 [

Tray 2

[ bull

In lOut l H

In20ul2 |

1 Tray 1

__ Out1

bull In1

Out2 -gt lt_2_gt

O bull72302

471 r Integrator 2

bull XI

To Workspace2

Scope 2

K 2 Olit2

2T899 ^ Function

VLE equation

GENERIC TRAY n

V bull L(n+1)Mn

In2 _ - -

A i bull

-bull VnMn

bull 1 integrator 2

y lt bull

V IE equa Son

bull xn

To Workspace2

bullbull bull -

Scope xn

TRAY 7 (Stage n -8)

bull 3 gtbull

bull 1

( 2 in2

IH130410 ~gt-

bull 119679

bullbullyenbullbull

y- Integrator 2

VLE equation

To Workspaces

Scope 2

gt bull

1 lHn0410

bullbullbull xS

To Workspace

2 bull 119879 In2

Outl bull bull I

289533 N

li integrator 2

130410

Function

MATLAB Fen 2

bull gt bull bull

Scope2

( 1 In2

119666 1 I s J

Integrator 2

120027 K

Scope 2

inputs

M M n+ Mbdquo

-X (El)

= = V15= F+ VF = V+ 985152

Vw = l 15 (E2)

X = f(Xut)

dX = X-X

du = u - u

dX df] _lt3x_

dX + 8f] _du_ du

Mn Mn Mn Mn

Mn +1 Mn +1 Mn Mn

T T -t- V V K V

i ( 0 = Ax(t) + Bu(t) (E4)

y(t) = Cx(t) (E5)

follows

L ==LS = 1798871 (kmoleh)

L9 = = Z15= 756380 (kmoleh)

V = = V = 661139 (kmoleh)

V9 = = V]5 = 1646291 (kmoleh)

M2 = M3 = = Mi5 = 580 (kmole)

M16 = MB = 2488 (kmole)

_KK _ (L]+K2V) _ L 21 M2

22 M2 23 M 2

1) Collect data

w = 1 ^ 1 = 7 Z 6 i 2=TT

w =2 h _xlZx2) _-fe-i) 2 J ~ M2 2lt2~ M2

laquo - 1 6 66gti = 6 ft162 ^ 1 6

_ K M16

[00012 00063 00091 00098 00076 00044 00022 00021 00048

00111 00216 00306 00285 00178 00086 -00702

-00024 -00157 -00237 -00254 -00196 -00116 -00058 -00027 -00024

-00050 -00097 -00138 -00128 -00080 -00039 00704]r

C = 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

E2 Stability Test

V(x)=xTPx (E6)

ATP + PA = -I (E9)

positive definite

P = lyap(AI)

for i=l16

Pi = P (1 i 1 i)

det(Pi)

d e t ( P l ) = 0 0 3 2 8 3 1

d e t ( P 2 ) = 0 0 0 0 9 0 8 4 9

d e t ( P 3 ) = 2 4 4 4 3 e - 0 0 5

d e t ( P 4 ) = 5 5 4 7 6 e - 0 0 7

d e t ( P 5 ) = 1 0 1 5 2 e - 0 0 8

d e t ( P 6 ) = 1 6 2 0 8 e - 0 1 0

d e t ( P 7 ) = 2 3 0 2 5 e - 0 1 2

d e t ( P 8 ) = 2 6 1 8 3 e - 0 1 4

d e t ( P 9 ) = 4 1 9 5 9 e - 0 1 6

d e t ( P l O ) = 1 2 8 8 6 e - 0 1 7

d e t ( P l l ) = 6 7 8 4 7 e - 0 1 9

d e t ( P 1 2 ) = 3 9 1 6 e - 0 2 0

d e t ( P 1 3 ) = 1 8 3 0 8 e - 0 2 1

d e t ( P 1 4 ) = 7 0 8 9 e - 0 2 3

d e t (P15) = 2 4 8 7 6 e - 0 2 4

d e t ( P 1 6 ) = 8 4 6 1 2 e - 0 2 6

stable

include ltstdlibhgt

using namespace std

if(k = x_kmlk+l)

stampn)

if(k = e_kmlk+l)

stampn)

if(k = uc_kmlk+l)

stampn)

return

th kk = k

b21e_kmlp2)x_kmlp2

b22e_kmlp2)x_kmlpl

b22e_kmlp2)x_kmlp2

b21e_kmlp2)uc_kmlpl

b21e_kmlp2)uc_kmlp2

b22e_kmlp2)uc_kmlpl

b22e_kmlp2)uc_kmlp2

r e t u r n

F2 Plant Model

include ltstdlibhgt

include PlantModelh

using namespace std

PlantPlant()

all = -67941 + 067(rand()2-05)

al2 = -09095 + 009(rand()2-05)

a21 = 14686 + 015(rand()2-05)

a22 = -02497 + 002(rand()2-05)

bll = -01461 + 0014(rand()12-05)

bl2 = 02073 + 002(rand()2-05)

b21 = -00021 + 00002(rand()12-05)

b22 = -00281 + 0003(rand()2-05)

ell = -00624 + 0006(rand()2-05)

cl2 = -00281 + 0003(rand()2-05)

c21 = 02458 + 0025(rand()2-05)

c22 = 00009 + 000009(rand()2-05)

Plant~Plant ()

if(k = u_kk)

this-gtu_k = u_k

this-gtx_k = x_k

return

bl2Tu_kp2

b22Tu_kp2

x_kplk = k+1

r e t u r n

F3 Reference Model

include ltstdlibhgt

using namespace std

RefmdlRefmdl()

Refmdl~Refmdl()

if(k = uc_kk)

stampn)

this-gtuc_k = uc_k

if(k = xm_kk)

stampn)

this-gtxm_k = xm_k

return

xm_kplk = k+1

return

include ltstdlibhgt

using namespace std

Linctrl Linctrl()

Linctrl -Linctrl ()

time stampn)

this-gtth_k = th_k

time stampn)

this-gtuc_k = uc_k

time stampn)

this-gtx_k = x_k

return

- th_kth2x_kp2

- th_kth4x_kp2

u_kk = k

return

F5 Comparator

include ltstdlibhgt

include Comparatorh

using namespace std

this-gtx_k = x_k

this-gtxm_k = xm_k

return

compute errors

e_kk = k

r e t u r n

include ltstdlibhgt

using namespace std

stampn)

this-gtx_k = x_k

return

y_kk = k

return

include ltstdlibhgt

using namespace std

time stampn)

this-gtxm_k = xm k

return

ym_kk = k

ym_kpi = ym_kpi

ym_kp2 = ym_kp2

r e t u r n

F8 CGI Program

inc lude ltctypehgt

include

lterrnohgt

ltstringhgt

ltstdiohgt

ltunistdhgt

ltfcntlhgt

ltstringhgt

ltsyssockethgt

ltsystypeshgt

ltnetinetinhgt

ltarpainethgt

define LINELEN 1024

struct valinfo

unsigned char name

unsigned char text

struct thetaPkt

struct Pkt

int pi

int p2

static

amll =

ami 2 =

am21 =

am22 =

bmll =

bml2 =

bm21 =

bm22 =

cmll =

cml2 =

cm21 =

cm22 =

all = -

al2 = -

a22 = -

bll = -

-67 94

static

= -510

= -310

= 1044

= 1006

static int nvals=0

if (gotvals)

nvals = getvals()

gotvals = 1

)vals[i]name)==0)

return vals[i]text

return NULL

=============== httpunescape ===========

unsigned char siptr

unsigned char soptr

unsigned char sos

(unsigned char) )

soptr = sos

siptr = sis

while (siptr)

if(siptr == )

int c = 0 i

for (i=0ilt2i++)

siptr++

c = claquo4 + h

if (i = 2)

free(sos)

return NULL

soptr++ =

soptr++ = siptr

siptr++

soptr = 0

free (sos)

return sis

=============== hextobin =================

if(isdigit(c))

return c-0

return -1

=============== getvals ===================

int vent = 0

unsigned char vstr

unsigned char vptr

unsigned char eptr

unsigned char aptr

int 1 cl

return 0

if(vstr == NULL)

return 0

if(vstr[l-l] == n)

vstr[l-l]=0

vptr = vstr

while (vptr)

vcnt++

valinfo))

vptr = vstr

for (i=0iltvcnti++)

if (eptr == NULL)

return 0

eptr = 0

if (aptr)

aptr = 0

vptr = aptr+1

return vent

unsigned char c

unsigned char cs

int fd len

if((fd==-l))

exit (1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== write signals ===================

unsigned char c

unsigned char cs

int fd len

if((fd==-l))

exit(1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== write a signal ===================

unsigned char c

unsigned char cs

int fd len

if((fd==-l))

exit (1)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== getsignal ===================

int fn s i m sn 1

unsigned char buf

if(fn==-l)

exit(1)

return

read(fn buf 20)

signal = s

free((void) buf)

close(fn)

return s

=============== get ascii signal ===================

int fn s i m sn 1

unsigned char buf

if(fn==-l)

exit (1)

return 0

read(fn buf 20)

signal = s

free((void) buf)

close(fn)

return 1

=============== settime ===================

int t=0

unsigned char c

unsigned char cs

int len

if((f==-l))

exit(l)

write(f c len)

write(f t 1)

free((void) c)

free((void) cs)

close (f)

return

=============== Wait ===================

int i=0

while(i++ltn)

=============== gettime ===================

clear signals

kT = k

Write to files

return

=============== clear signal ===================

int fn

if(fn==-l)

exit(1)

return

write(fn20)

close(fn)

return

unsigned char ch

if (xl==0)

ch[0] = 0

len = 1

if(xllt0)

xl = -xl

sign[0] = -

sign[0] = +

while(xlgt0)

ch[i] = 0 + xl10

xl=xl10

len=i+l

for(i=0 iltlen i++)

free((void) ch)

return

=============== getAdapMechPkt ===================

th4 th5 th6 th7 th8

int outfile

Receive signals

getsig

vartmpfuc2

vartmpfkth

vartmpfthl

vartmpfth2

vartmpfth3

vartmpfth4

vartmpfth5

vartmpfth6

vartmpfth7

vartmpfth8

ampuc2)

ampkth)

ampthl)

ampth2)

ampth3)

ampth4)

ampth5)

ampth6)

ampth7)

ampth8)

receivedlth3gtn)

printf

ltpgt ucl

ltpgt uc2

ltpgt thl

ltpgt th2

ltpgt th3

ltpgt th4

ltpgt th5

ltpgt th6

ltpgt th7

ltpgt th8

d) = dn k-1 ucl)

d) = dn k-1 uc2)

d)k = dn k-1 kth)

d) = dn k-1 thl)

d) = dn k-1 th2)

d) = dn k-1 th3)

d) = dn k-1 th4)

d) = dn k-1 th5)

d) = dn k-1 th6)

d) = dn k-1 th7)

d) = dn k-1 th8)

x_kml-gtk = kx

x_kml-gtpl = xl

x_kml-gtp2 = x2

e_kml-gtk = ke

e_kml-gtpl = el

e_kml-gtp2 = e2

uc_kml-gtk = kuc

uc_kml-gtpl = ucl

uc_kml-gtp2 = uc2

th_kml-gtk = kth

th_kml-gtthl = thl

th_kml-gtth2 = th2

th_kml-gtth3 = th3

th_kml-gtth4 = th4

th_kml-gtth5 = th5

th_kml-gtth6 = th6

th_kml-gtth7 = th7

th kml-gtth8 = th8

Write to files

return

=============== genAdapMechPkt ===================

th k-gtk = k

Write to files

return

=============== main ============

main ()

int valid

int stime gamm

int i=0

int k kT

int kmax=2

struct Pkt x_kml

struct Pkt e_kml

struct Pkt uc_kml

int getkt=0

int getkmax=0

ltheadgtn)

while(getkmax)

wait(5000)

while(klt kmax)

signalsn)

while(Igetkt)

wait (5000)

while(k=kT)

wait(10000)

signalsn)

gainsn)

ampth_k)

exit (0)

0000000

0100000

0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

1100000

1200000

1300000

1400000

1500000

1600000

1700000

1800000

0000000

-0005938

-0007274

-0007525

-0006703

-0006552

-0007393

-0007877

-0006929

-0006522

-0006511

-0005794

-0005655

-0005802

-0005829

-0005804

-0005700

-0006102

-0006161

0000000

-0000402

-0001596

-0002967

-0004377

-0005628

-0006885

-0008274

-0009549

-0010673

-0011823

-0012844

-0013834

-0014738

-0015578

-0016366

-0017279

-0018029

-0018812

0000000

-0005232

-0006874

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-0007309

-0007186

-0007024

-0006854

-0006686

-0006524

-0006369

-0006221

-0006080

-0005945

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-0005693

-0005576

-0005464

-0005358

0000000

-0000386

-0001531

-0002888

-0004274

-0005626

-0006927

-0008172

-0009360

-0010494

-0011576

-0012609

-0013594

-0014533

-0015429

-0016284

-0017099

-0017877

-0018620

1900000

2000000

2100000

2200000

2300000

2400000

2500000

2600000

2700000

2800000

2900000

3000000

3100000

3200000

3300000

3400000

3500000

3600000

3700000

3800000

3900000

4000000

4100000

4200000

4300000

4400000

4500000

4600000

-0005840

-0005030

-0005135

-0005074

-0004855

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-0004671

-0004958

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-0004544

-0004603

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-0004316

-0003581

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-0004056

-0004004

-0003677

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-0002967

-0019639

-0020340

-0020948

-0021660

-0022270

-0022872

-0023498

-0023983

-0024360

-0024769

-0025263

-0025755

-0026125

-0026483

-0026923

-0027330

-0027685

-0027977

-0028329

-0028643

-0028964

-0029283

-0029457

-0029607

-0029793

-0029938

-0030105

-0030178

-0005256

-0005159

-0005067

-0004979

-0004894

-0004814

-0004737

-0004664

-0004595

-0004528

-0004465

-0004404

-0004346

-0004291

-0004239

-0004189

-0004141

-0004095

-0004052

-0004010

-0003971

-0003933

-0003897

-0003863

-0003830

-0003798

-0003769

-0003740

-0019327

-0020003

-0020647

-0021262

-0021848

-0022407

-0022941

-0023449

-0023935

-0024398

-0024840

-0025261

-0025663

-0026047

-0026413

-0026762

-0027095

-0027412

-0027715

-0028004

-0028280

-0028543

-0028794

-0029033

-0029261

-0029479

-0029687

-0029885

4700000

4800000

4900000

5000000

5100000

5200000

5300000

5400000

5500000

5600000

5700000

5800000

5900000

6000000

6100000

6200000

6300000

6400000

6500000

6600000

6700000

6800000

6900000

7000000

7100000

7200000

7300000

7400000

-0003945

-0003632

-0003741

-0003254

-0004091

-0003652

-0004092

-0004512

-0003289

-0002858

-0002967

-0003991

-0003572

-0003271

-0003674

-0003566

-0003464

-0003407

-0002696

-0002674

-0003472

-0003254

-0003053

-0003501

-0003466

-0003658

-0002994

-0003796

-0030245

-0030477

-0030604

-0030814

-0030945

-0031179

-0031310

-0031532

-0031857

-0031948

-0031971

-0032005

-0032227

-0032303

-0032298

-0032383

-0032482

-0032554

-0032590

-0032534

-0032468

-0032440

-0032512

-0032535

-0032586

-0032618

-0032758

-0032787

-0003713

-0003687

-0003662

-0003639

-0003616

-0003595

-0003574

-0003555

-0003536

-0003519

-0003502

-0003485

-0003470

-0003455

-0003441

-0003428

-0003415

-0003403

-0003391

-0003380

-0003370

-0003360

-0003350

-0003341

-0003332

-0003324

-0003316

-0003308

-0030074

-0030254

-0030426

-0030590

-0030747

-0030896

-0031039

-0031175

-0031304

-0031428

-0031546

-0031659

-0031766

-0031868

-0031966

-0032059

-0032148

-0032233

-0032314

-0032391

-0032465

-0032535

-0032602

-0032666

-0032727

-0032785

-0032840

-0032893

7500000

7600000

7700000

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

-0004422

-0003688

-0002866

-0003432

-0003142

-0002693

-0003564

-0003913

-0004231

-0004049

-0003128

-0002355

-0002156

-0002358

-0002603

-0003386

-0004014

-0004132

-0003349

-0003703

-0003246

-0003219

-0002317

-0002500

-0003393

-0032935

-0033168

-0033314

-0033233

-0033228

-0033288

-0033206

-0033185

-0033216

-0033382

-0033535

-0033510

-0033344

-0033200

-0033080

-0032950

-0032966

-0033023

-0033146

-0033219

-0033293

-0033271

-0033284

-0033355

-0033271

-0033212

-0003301

-0003294

-0003287

-0003281

-0003275

-0003269

-0003264

-0003259

-0003254

-0003249

-0003244

-0003240

-0003236

-0003232

-0003228

-0003225

-0003221

-0003218

-0003215

-0003212

-0003209

-0003207

-0003204

-0003202

-0003199

-0003197

-0032944

-0032992

-0033038

-0033082

-0033124

-0033164

-0033202

-0033238

-0033272

-0033306

-0033337

-0033367

-0033396

-0033423

-0033449

-0033474

-0033498

-0033520

-0033542

-0033563

-0033582

-0033601

-0033619

-0033636

-0033652

-0033668

in Table G2

0000000

0100000

0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

1100000

1200000

1300000

1400000

1500000

1600000

1700000

1800000

1900000

2000000

-0000000

0000365

0000479

0000535

0000528

0000556

0000643

0000713

0000694

0000703

0000737

0000724

0000745

0000781

0000807

0000829

0000850

0000896

0000923

0000928

0000901

0000000

-0001534

-0001880

-0001946

-0001735

-0001697

-0001915

-0002042

-0001798

-0001694

-0001692

-0001508

-0001472

-0001511

-0001519

-0001513

-0001487

-0001592

-0001608

-0001525

-0001317

-0000000

0000337

0000472

0000536

0000576

0000607

0000633

0000657

0000680

0000702

0000723

0000742

0000761

0000779

0000796

0000813

0000828

0000843

0000858

0000871

0000884

0000000

-0001286

-0001691

-0001796

-0001800

-0001771

-0001733

-0001692

-0001652

-0001613

-0001576

-0001540

-0001507

-0001474

-0001443

-0001414

-0001386

-0001359

-0001334

-0001309

-0001286

2100000

2200000

2300000

2400000

2500000

2600000

2700000

2800000

2900000

3000000

3100000

3200000

3300000

3400000

3500000

3600000

3700000

3800000

3900000

4000000

4100000

4200000

4300000

4400000

4500000

4600000

4700000

0000925

0000943

0000948

0000976

0000964

0000948

0000967

0001011

0001042

0001019

0001010

0001054

0001067

0001082

0001075

0001092

0001098

0001078

0001114

0001080

0001062

0001117

0001120

0001105

0001073

0001070

0001130

-0001344

-0001329

-0001273

-0001319

-0001185

-0001056

-0001088

-0001228

-0001302

-0001139

-0001051

-0001197

-0001212

-0001134

-0001173

-0001153

-0001025

-0001139

-0000950

-0000851

-0001073

-0001060

-0000975

-0000816

-0000792

-0001045

0000896

0000908

0000919

0000930

0000940

0000950

0000959

0000968

0000977

0000985

0000992

0001000

0001007

0001013

0001020

0001026

0001032

0001037

0001042

0001047

0001052

0001057

0001061

0001065

0001069

0001073

0001077

-0001264

-0001243

-0001223

-0001203

-0001185

-0001168

-0001151

-0001135

-0001120

-0001105

-0001091

-0001078

-0001066

-0001054

-0001042

-0001031

-0001021

-0001011

-0001001

-0000992

-0000984

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4800000

4900000

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0001100

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7500000

7600000

7700000

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

0001238

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0001156

0001188

0001170

0001145

0001195

0001215

0001235

0001229

0001178

0001132

0001115

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0001134

0001176

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0001185

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0001132

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0001135

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0001142

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0001145

0001146

-0000841

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Plant Error

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0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

1100000

1200000

1300000

1400000

1500000

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2000000

2100000

0000000

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0000129

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0000000

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0000042

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2200000

2300000

2400000

2500000

2600000

2700000

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3000000

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3200000

3300000

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3500000

3600000

3700000

3800000

3900000

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4100000

4200000

4300000

4400000

4500000

4600000

4700000

4800000

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0000055

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4900000

5000000

5100000

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5300000

5400000

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5600000

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6000000

6100000

6200000

6300000

6400000

6500000

6600000

6700000

6800000

6900000

7000000

7100000

7200000

7300000

7400000

-0000078

0000385

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-0000334

0000322

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-0000271

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0000095

0000090

0000130

0000141

0000167

0000082

0000106

7500000

7600000

7700000

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

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0000576

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0000884

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0000008

-0000176

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0000053

0000056

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-0000143

0000052

0000223

0000369

0000524

0000532

0000498

0000396

0000343

0000289

0000330

0000335

0000281

0000381

0000456

Adaptive Gains

0000000

0100000

0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

1100000

1200000

1300000

1400000

1500000

1600000

1700000

1800000

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2000000

0000000

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-0006413

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0000000

-0000372

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-0004473

-0005796

-0007132

-0008622

-0009855

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-0012023

-0013130

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-0015028

-0015859

-0016666

-0017478

-0018174

-0019033

-0019821

-0020508

0000000

-0005232

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-0006080

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-0005816

-0005693

-0005576

-0005464

-0005358

-0005256

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0000000

-0000386

-0001531

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-0004274

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-0006927

-0008172

-0009360

-0010494

-0011576

-0012609

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-0019327

-0020003

2100000

2200000

2300000

2400000

2500000

2600000

2700000

2800000

2900000

3000000

3100000

3200000

3300000

3400000

3500000

3600000

3700000

3800000

3900000

4000000

4100000

4200000

4300000

4400000

4500000

4600000

4700000

-0005636

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-0021153

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-0022509

-0023112

-0023668

-0024270

-0024759

-0025247

-0025581

-0026025

-0026411

-0026873

-0027315

-0027557

-0027813

-0028126

-0028324

-0028620

-0028935

-0029157

-0029522

-0029797

-0029945

-0030135

-0030351

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-0030781

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-0004528

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-0004291

-0004239

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-0004141

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-0003863

-0003830

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-0003769

-0003740

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-0020647

-0021262

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-0022407

-0022941

-0023449

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-0024398

-0024840

-0025261

-0025663

-0026047

-0026413

-0026762

-0027095

-0027412

-0027715

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-0029261

-0029479

-0029687

-0029885

-0030074

4800000

4900000

5000000

5100000

5200000

5300000

5400000

5500000

5600000

5700000

5800000

5900000

6000000

6100000

6200000

6300000

6400000

6500000

6600000

6700000

6800000

6900000

7000000

7100000

7200000

7300000

7400000

-0004364

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-0004275

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-0004283

-0003904

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-0003136

-0003398

-0003197

-0003819

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-0031089

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-0031608

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-0031972

-0032127

-0032175

-0032197

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-0032162

-0032284

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-0032604

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-0033116

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-0033267

-0033253

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-0033512

-0033652

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-0031659

-0031766

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-0031966

-0032059

-0032148

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-0032666

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-0032893

7500000

7600000

7700000

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

-0003756

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-0033687

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-0034402

-0034367

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-0034609

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-0003254

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-0033474

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-0033520

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-0033563

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-0033619

-0033636

-0033652

-0033668

in Table H2

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0100000

0200000

0300000

0400000

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0600000

0700000

0800000

0900000

1000000

1100000

1200000

1300000

1400000

1500000

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1700000

1800000

1900000

2000000

2100000

-0000000

0000320

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0000611

0000674

0000668

0000648

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0000770

0000832

0000887

0000837

0000830

0000897

0000000

-0001217

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-0001731

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-0000000

0000337

0000472

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0000680

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0000723

0000742

0000761

0000779

0000796

0000813

0000828

0000843

0000858

0000871

0000884

0000896

0000000

-0001286

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-0001733

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-0001264

2200000

2300000

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3000000

3100000

3200000

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4000000

4100000

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4700000

4800000

0000909

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0001073

0001088

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-0001304

-0001279

-0001298

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-0001067

-0000921

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-0000897

-0001002

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-0000900

-0001055

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-0001048

0000908

0000919

0000930

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0000950

0000959

0000968

0000977

0000985

0000992

0001000

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0001020

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0001077

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-0001243

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4900000

5000000

5100000

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5600000

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5800000

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6000000

6100000

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6300000

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6600000

6700000

6800000

6900000

7000000

7100000

7200000

7300000

7400000

0001064

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0001118

0001109

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0001084

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0001128

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0001131

-0000928

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7500000

7600000

7700000

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

0001119

0001152

0001096

0001113

0001118

0001144

0001114

0001144

0001151

0001173

0001104

0001152

0001121

0001106

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0001160

0001159

0001143

0001105

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0001112

0001158

0001103

0001157

0001153

-0000908

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-0000835

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0001132

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-0000841

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-0000816

H3 Plant Error

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0100000

0200000

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1000000

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2000000

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000000

000002

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000000

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000004

000036

-000057

000000

000001

000003

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2200000

2300000

2400000

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2900000

3000000

3100000

3200000

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3500000

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3700000

3800000

3900000

4000000

4100000

4200000

4300000

4400000

4500000

4600000

4700000

4800000

4900000

-000052

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-000030

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000023

-000025

-000001

-000057

-000082

000034

-000027

000031

000040

000024

-000034

-000043

-000046

-000058

000014

-000035

-000024

000004

-000066

-000082

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-000019

-000064

-000066

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-000082

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-000074

-000076

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5000000

5100000

5200000

5300000

5400000

5500000

5600000

5700000

5800000

5900000

6000000

6100000

6200000

6300000

6400000

6500000

6600000

6700000

6800000

6900000

7000000

7100000

7200000

7300000

7400000

7500000

7600000

7700000

-000064

000013

-000053

000016

000065

000011

000061

000056

000053

-000039

-000083

-000046

-000029

-000049

-000103

-000033

000000

000058

-000026

-000040

000021

-000007

000013

-000050

-000029

-000046

-000100

-000002

-000102

-000112

-000108

-000109

-000100

-000089

-000082

-000071

-000054

-000040

-000042

-000052

-000055

-000056

-000068

-000080

-000089

-000080

-000072

-000074

-000075

-000061

-000065

-000067

-000076

-000074

-000072

-000078

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

-000032

-000041

-000081

-000024

-000073

-000082

-000112

000010

-000077

-000020

000005

-000027

-000092

-000084

-000053

000014

000015

-000006

-000084

000016

000013

-000077

-000064

-000073

-000069

-000075

-000087

-000085

-000090

-000105

-000114

-000100

-000105

-000103

-000095

-000089

-000100

-000107

-000111

-000101

-000093

-000089

-000105

-000097

-000108

H4 Adaptive Gains

e 03716

-05106

-03100

-00427

-00428

-05106

-03100

-03099

-00428

-05106

-03099

-03098

-00428

-05106

-03098

-00428

-00429

-00428

-00429

-00428

-00429

REFERENCES

Hungary vol 3 pp 1719-1724 1984

563 May 1989

Hall 1984

orgwikiMATLAB

Press 1999

McGraw-Hill 1981

2002 pp 4003-4008

6 pp 1169-1175 Dec 1982

e_Diagrampdf

Prentice Hall 1997

University 1990

Hill 1984

India 1979

SJSU ScholarWorks

Fall 2009


Hoan The Nguyen



UMI Number 1484326

copy2009

Hoan The Nguyen

by Hoan The Nguyen

mdashr ~ mdash^ yy

ABSTRACT

by Hoan The Nguyen

ACKNOWLEDGMENTS

people

TABLE OF CONTENTS

List of Tables xiv

List of Figures xvi

11 Background 1

15 Methodology 5

28 ARM Processor 16

31 Introduction 20

41 Introduction 26

441 Plant 31

51 Introduction 43

521 Plant Model 44

61 Introduction 50

71 Introduction 66

751 CGI Program 78

77 Testing 93

772 Test Results 98

81 Conclusion 104

82 Future Work 105

A12 Vent-bleed 110

B31 Description 124

B32 Calculation 125

B41 Description 126

B42 Calculation 127

B51 Description 128

B52 Calculation 129

Cl Introduction 137

C22 Feed Tray 140

C23 Top Section 141

F2 Plant Model 170

F5 Comparator 173

F8 CGI Program 175

G3 Plant Error 206

H3 Plant Error 222

References 230

LIST OF TABLES

LIST OF FIGURES

Motor octane number

Network file system

Personal computer

Reid vapor pressure

True boiling point

Zero-order hold

LIST OF SYMBOLS

A State matrix

B Input matrix

C Output matrix

e State error

L Feedback matrix

u Control signal

x State variable

y Controlled output

Greek Symbols

y Adaptation rate

0 Adaptive gain

Subscript

B Bottom product

F Feed

m Reference model

CHAPTER 1

INTRODUCTION

11 Background

time spaces

adaptive controller

mathematical method

15 Methodology

CHAPTER 2

LITERATURE REVIEW

RECTIFYING SECTION

F (feed flow rate)

Q n I (3) CONDENSER

1 8 - D

stage f (feed tny)

stage rc

Material stream

Feed stream

Distillate stream

Bottoms stream

Position

Stage f

Stage N

Reflux drum

Stage 1

Reboiler

Flow rate

Concentration

in Figure 22

Liquid phase

Stage it

(Trav gti-l)

bull bullbullbull

m^u - Bubble cap

structures

I |mdash0mdashI I

bottoms flow rate B

are adjusted [12]

required

Command_ signal

Adaptive mechanism

laquosj

Control signal

Plant 1 Output

Process dynamics )

Siv-CSnftlteF----

26 Adaptive Schemes

261 Gain Scheduling

Command signal

Output

signal

MoctSI

Control signal

mechanism

Plant -bull Output

= ( ) bull (21)

disturbances or not

- mdash

yfdx dt

x = 0 i

-gt() =

= = ( ) = -W(x) (22) dt dx dt dx

dx mdash = Ax (23)

ATP + PA=-Q (24)

following function

V(x) = xTPx (25)

28 ARM Processor

DB-9 DB-9

RS-232

Features

Memory

subsystem

GPIO ports

Ethernet

Descriptions

solution

8 memory banks

by RAM

CHAPTER 3

31 Introduction

RffLlrtERLMl

xD gt 98

xB lt 20

Table 31

Temperature C

Pressure atm

Density kgm3

Mass flow rate kgh

Main streams oft

Condensate

130000

he plant

Raw gasoline

system

35 Plant Modeling

1403 x16 =1646291^15 -756380x16 -927597xI6

58x15 =1646291(gtl4 -^1 5) + 756380(x16 -x15)

58x14 =164629103 -gtgt14) + 756380(x15-x4)

58x13 =1646291012 -_y]3) + 756380(x14 -x13)

58x12 =1646291(^n -y1 2) + 756380(x13 -x ] 2)

58xH =164629IO10 ~ ^ i ) + 756380(x12-x)

58x10 =164629109 -^1 0) + 756380(xn -x10)

58x9 = 661139gtgt8 -15638^9 + 756380(x10 -x9) + 5995

58x8 = 66113907 ~yamp) + 756380 x9 -18859x8 + 3399

58x7 = 661 39(y6-y7) + 798871 (x8 -x 7 )

58x6 =66113905-gt 6) + 1798871(x7-x6)

58x5 =66113904^) +179887 l (x 6 -x 5 )

58x4=66113903-^4) + 1798871(x5-x4)

58x3 =66113902-73) +1798871 (x 4 -x 3 )

58x2 =661139(^-gt2) +179887l(x3-x2)

2488x = 1798871x2-1109235x1 -661139^

568x y = l + 468x

l + 468x

^ 1 5 =

568x 15

l + 468xbdquo (34)

CHART OF VAPOR

01 02 03 0 4 05 06 07 08 09

36 Plant Simulation

Table 32

bull L _ I i 1 l

6 8 10 12 14 16 18 20 Time (h)

than 2

CHAPTER 4

41 Introduction

and (32)

Disturbances

Ditiilitirn Gy-tem

x(t) = A(xt) + Beu(t) (41)

y(t) = Cex(t) (42)

two-output system

-09095

-02497 Bbdquo

-01461 02073

-00021 -00281 and C

-00624 -00281

02458 00009

Bode Diagram

Frequency (radsec)

431 Stability Test

finite time T-tgt0

x = Ax(t) + Bu(t) (45)

y(t) = Cx(t) + Duy) (46)

full rank of n

output

S=[CCACA2CA]]T

the next section

441 Plant

yt) = Cx(t)

where A = au

an_ B =

bn_ and C =

-00624 -00281

02458 00009

variables

442 Reference Model

Sec 43

where Abdquo

ybdquo(t) = cmxm(t)

-67941 -09095

14686 -02497

5 = -01461 02073

-00021 -00281 and Cbdquo

-00624 -00281

02458 00009

ut) = Muct)-Lx(t)

x = (A- BL)x + BMuc

hence we define

Ac(0) = (A-BL)

Bc6) = BM

i2 ~b2

l 2 11^2 ^12^4

22 _ ^ 2 1 ^ 2 ~ ^ 2 2 ^ 4

b2]65+b2281 b2Xdb+b22d (412)

condition we get

au-bu6-bnel =-67941

an -bu6a2 -bn6deg4= -09095

a2]-b2]6deg-b220deg =14686

a22-b2]e2-b229deg= -02497

6Adeg + M7deg =-01461

606deg + 6 X =02073

b2l6deg5+b229deg =-00021

b2]edeg6+b226degs =-00281 (413)

condition

0 _ b22(au +67941)-bu(a2] -14686) 0 =

regp22 ^12^21

a o _ b22(an + 09095)-bn(a22 +02497)

^11^22 _ ^12^21

buo22 mdashbnb2]

0 _ -b2](a]2 + 09095)+ bu(a22 +02497) 6gt =

bP 22 b]2b2]

-b2]bn+bub22

n0 002816I2+02073Zgt22

(J6 = -b2]bu+bub22

_0 - 000216+ 0146 b2x Uf =

-b2]bu+bub22

0 = 002816 +020736

-b2Xbu+bxxb (414)

Error Equation

e(0= x(0-m(0

e() = ^ ( 0 + 5 i ( 0 - ^ I B ( 0 - 5 m laquo c ( 0 - (4-15)

e(t) = Ame(t) + V(t)(0-O0) (417)

446 Adaptation Law

function

V(e 0) = [yePe + (0 - 0deg f (0 - 0deg)) (418)

(420) dt 2

ltP + PAm = -a (4-21)

^ = -W(t)Pe(t) at

y(buex+b2Xe2)xx

y(buex+b2]e2)x2

y(bnex+b22e2)xx

y(bx2ex+b22e2)x2

-y(bxxex+b2xe2)ucX

-y(bxxex+b2Xe2)uc2

-y(bX2ex+b22e2)ucX

-y(buex+b22e2)uc2

6 = (423)

mdash = -05591lt -07066e2)2 +132756e2] dt 1

2) Disturbances^)

4) Reference model

a n n f l

REFERENCE MODEL

dull In I

0ut2 In2

ADAPTIVE MECHANISM

= X Xm

_X2 Xm2 _

follows

e = RMS(e) = -^A for = 1 or 2

commands

norm_el = norm(el)

norm_e2 = norm(e2)

shown in Figure 46

m B s in

Figures - x vc xm

m B ampm

bull4s

bullraquo i x

i m B raquo bull

im B ffin

State error e1(t)

State error e2(t)

e = 00017

n2 VTooT = 7106210

453 Error Reduction

Plant errors

laquoi

Adaptation rate y

54304 105

71399105

5428410

7106210

54076 105

7100310-5

CHAPTER 5

51 Introduction

G(s) y ( t

521 Plant Model

x(t) = Axt) + But)

y(t) = Cx(t)

x(s) - ~[AX(S) + Bu(s) s

T x(z) = [AX(Z) + Bu(z)]

y(kT) = CxkT) (52)

522 Reference Model

in Chapter 6

ybdquo(t) = cmxm(t)

where Am = [-67941 -09095 14686 -02497] Bm = [-01461 02073 -00021 -00281]

and Cm = [-00624 -00281 02458 00009]

follows

ut) = Muc(t)-Lx(t)

L = 0kT) 62(kT)

0(kT) 0AkT

M 05(kT) 06(kT)

87(kT) 0s(kT)^ (56)

o _ ft2deg2(adeg +67941)-ft02(a20 -14686)

degdeg27 deg12deg21

8 0 _ -amp2 K + 67941) + ft (a2] -14686)

ftdeg =

00021ft0-01461ft0 22

-ft21 f t02+ft0 f t22

-b2]b]2+bub22

-b2bn+bub22

n0 00281ft+02073ftdeg

201 deg]]deg22

6(t) = -y^(t)Pe(t)

= yy (s)Pe(s)

CHAPTER 6

61 Introduction

2) Disturbances^^

reference signals

1 tnl uc(k)

In2 uc(k-1)

xm(k-1)

laquogt

REFERENCE MODEL

H Disturbances

bulleurogt

[B^_]M

0ut1 In)

0ut2 In2

i f MJi-1)

0 u ulaquoK-l)

ADAPTIVE MECHANISM

m lt raquo

Ot-1) Mux bull

e(kT) = exkT)

e2(kT)

h(kT)-xnnkT)

x2(kT)-xm2(kT)_

Ax^kT)

Ax2(kT)

follows

e = RMSe) = ^L for = 1 or 2 (61)

shown in Figure 62

Disturbance f(t)

m gt P i laquo ^ e

a)e(7)

ns gt P l

a) eiikT)

I U I 94543e-004 _ bdquo ^ - s

101 = 9407410-

M = 9 6557e -Q04 = 9 6 0 7 8 t l 0 5

4n2 vioi

sections

in Figure 66

4 include tbdefsh

5 class Plant

6 private

12 public

13 Plant()

14 -Plant()

18 endif

P l a n t ( )

a l l = - 6 7 9 4 1 + 0 6 7 ( r a n d ( ) 2 - 0 5 )

a l 2 = - 0 9 0 9 5 + 0 0 9 ( r a n d ( ) 2 - 0 5 )

a21 = 14686 + 015(rand()2-05)

a22 = -02497 + 002(rand()2-05)

bll = -01461 + 0014(rand()2-05)

bl2 = 02073 + 002 (rand()2-05)

b21 = -00021 + 00002(rand()2-05)

b22 = -00281 + 0003 (rand()2-05)

ell = -00624 + 0006(rand()2-05)

cl2 = -00281 + 0003(rand()2-05)

c21 = 02458 + 0025(rand()2-05)

c22 = 00009 + 000009(rand()2-05)

4 include tbdefsh

5 class Refmdl

6 private

7 Pkt uc_k

8 Pkt xm_k

9 public

10 Refmdl()

11 -RefmdlO

15 endif

Figure 68

4 include tbdefsh

5 class Linctrl

6 private

7 thetaPkt th_k

8 Pkt x_k

9 Pkt uc_k

10 public

11 LinctrlO

12 -LinctrlO

16 endif

database

4 include tbdefsh

5 class Comparator

6 private

7 Pkt x_k

8 Pkt xm_k

9 Pkt e_k

10 public

11 Comparator()

12 -Comparator()

16 endif

and the plant

4 include tbdefsh

6 private

7 thetaPkt th_kml

8 Pkt x_kml

9 Pkt e_kml

10 Pkt uc_kml

11 public

12 AdaptiveMechO

13 -AdaptiveMechO

17 endif

model and the plant

CC = g++

ReferenceModelo

executive file

j haut$ttum

ltOIgt gtiJ^Alt

plusmn1 f bull-lt

i gt bulli

lt euro f bull2

[ bull

- H J bullbull -

~ttttfc

bull=fmdashF^--

^ t ^ i i i = ^ ^

_ - 1 1 = - mdash J

^ J - - - ^ ^

1 1 1 I

5 time

e = |N| s94543c-004 ^

96557e-004

VToi = 96078 105

CHAPTER 7

71 Introduction

shown in Figure 71

_ Data J

5gt I Error

yV H Report

Plant Slmsliitsr

lt = J Output

Linux yacnine

RPC get_port reply

RPC mount request

RPC mount reply

Authenticate client

to the browser

button

lUser sufrmis fwm

arv-affe ie Camp

vas tor PlssrtSwi

Sens ( to i l sA i

(J 0 0

SefieJ acispfcw BM2

Oylpaito wefccfer

72 Common Database

File name

kucdat

ucldat

uc2dat

kthdat

thldat

th2dat

th3dat

th4dat

th5dat

th6dat

th7dat

Data description

Plant state xi

Plant state X2

Error variable ei

Error variable e2

Adaptive gain Gi

Adaptive gain 02

Adaptive gain 63

Adaptive gain 64

Adaptive gain 85

Adaptive gain 96

Adaptive gain 67

th8dat

adapoutdat

kmaxdat

Adaptive gain 0g

Maximal step size

73 Plant Simulator

CC = g++

$ make

1 iij-ji--^- - M - - I - - bull

1 lthtmlgt

2 ltheadgt

4 ltheacigt

5 ltbodygt

9 ltdivgt

value= size=40gt

17 ltformgt

18 ltbodygt

19 lthtmlgt

Feature

action=

method=

target=

Code example

Run gt

Description

program

time and text type

follows

th[k-l])

11 return

15 th-gtk = k

1]10000000

1] 10000000

1]10000000

23 return

751 CGI Program

variables

getenv() as follows

parameters

1 main ()

3 i n t v a l i d

17 while(klt kmax)

19 while(Igetkt)

21 wait(5000)

24 while(k=kT)

26 wait(10000)

ampth_k)

33 k++

36 else

41 exit (0)

program 109880

looses 10S824 188824 100883 100883 100883 19S821

Yers 2 2 1 1 2 3 4 1

port 111 111

48909 55541

2849 2849 2649

sudo rpcinfo -p

I I Bin Edit yamp

hoanaoan-$

gt Terminal

hoan^hoan ~$

2 2 1 1 2 3 4 1 3 4 2 3 A 1 3 4 1 1 2 2 3 3

i n f o -j r o t o

P po r t

111 n i

35368 35832

2649 2649 2S49

44664 44694 44994

2049 2849 2949

41394 41894 41894 33383 44819 33389 44819 33389 44819

M ^ s t i k ^ ^ lt

l - pound ig

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 a 3 3 3 3 3 3 A

syslog-install

root location as

during compilation

TESTOBJS = mycgio

support

1) TCPIP networking

3) IP DHCP support

4) IPBOOTP

5) IPRARP

2) RTL8019AS

and check

1) Boa

2) dhcpcd-new

3) dhclient

4) ifconfig

5) inetd

6) ping

8) route

9) routed

10)telnetd

ll)tftpd

terminal

for Linux machines

machine)

go 0x0c008000

RRMboot 182 (Aug 12 2084 - 104321)

bulltrade u u mdash

1 000 netmask 2552552550 lo

77 Testing

771 Test Procedure

(PC Linux machine)

Figure 722

D Graquo S S if

5fw help

following command

1 9 2 1 6 8 0 8 o p t t e s t v a r t m p

| g haanhoan ~

0JS packet loss

controllerhtmlgt

$01 C s- J http1921680^

Run Reset

adap t i vecamro l

13S3603 6682830

6258383

1393689 -8pound62298 B JhK-iH-)

-6239783 6626603

666G855

-9259783 -0629683 H HHI-li4s

Gsxgte i

efk-Dpl =

e(k-l) p2 =

ucfk-ljk =

uc(k- l ) p l

uc(k-l) p2

thik-lj k =

th ik - l j th l

th ik- l ) th2

th(k- l ) th3

thk- l ] th4

thk- l ) th5

thfk- l j th

amp c l

= 50000

=10000

= 66000

= -309998

= 1 0 4 4 2 2 5 4

= -42712

= 4240

ITtdlk^ Turlb

o Htp iH9i

| IG^Search

16S0 1

raquo bull zfgt

b i r p

ycqr u

^Settings

772 Test Results

in Table 73

File name

t_xdat

t_xmdat

t_edat

t_ucdat

t_udat

t_thetadat

t_ydat

t_ymdat

Data description

000000

-000521

-000667

-000817

-000764

-000770

-000815

-000738

-000650

-000665

-000641

-000623

-000645

-000594

-000587

-000551

-000514

-000587

-000641

000000

-000037

-000151

-000291

-000447

-000580

-000713

-000862

-000986

-001091

-001202

-001313

-001403

-001503

-001586

-001667

-001748

-001817

-001903

000000

-000523

-000687

-000730

-000731

-000719

-000702

-000685

-000669

-000652

-000637

-000622

-000608

-000595

-000582

-000569

-000558

-000546

-000536

000000

-000039

-000153

-000289

-000427

-000563

-000693

-000817

-000936

-001049

-001158

-001261

-001359

-001453

-001543

-001628

-001710

-001788

-001862

-000522

-000480

-000564

-000550

-000539

-000547

-000528

-000496

-000503

-000430

-000472

-000441

-000491

-000511

-000390

-000446

-000383

-000369

-000381

-000435

-000441

-000439

-000447

-000373

-000418

-000404

-000373

-000440

-001982

-002051

-002115

-002190

-002251

-002311

-002367

-002427

-002476

-002525

-002558

-002603

-002641

-002687

-002732

-002756

-002781

-002813

-002832

-002862

-002894

-002916

-002952

-002980

-002995

-003014

-003035

-003052

-000526

-000516

-000507

-000498

-000489

-000481

-000474

-000466

-000460

-000453

-000447

-000440

-000435

-000429

-000424

-000419

-000414

-000410

-000405

-000401

-000397

-000393

-000390

-000386

-000383

-000380

-000377

-000374

-001933

-002000

-002065

-002126

-002185

-002241

-002294

-002345

-002394

-002440

-002484

-002526

-002566

-002605

-002641

-002676

-002710

-002741

-002772

-002800

-002828

-002854

-002879

-002903

-002926

-002948

-002969

-002989

-000453

-000436

-000385

-000428

-003078

-003109

-003139

-003161

-000371

-000369

-000366

-000364

-003007

-003025

-003043

-003059

-0 025

_ m _ _ ^ i = _ mdash p i r r F ^

~~-ti ===ii

-mdash^zr ~~ i

2(enfc) -

-00006

-00009

-00011

-00008

-00001

-00004

-00008

-00001

-00002

-00005

-00004

-00005

-00004

-00008

-00001

-00002

-00003

-00002

-00003

-00002

-00003

-00002

-00001

-00002

-00010

-00009

-00001

-00009

-00006

-00005

-00001

-00008

-00013

-00002

-00004

-00007

-00014

-00006

-00007

-00001

-00010

-00003

-00004

-00005

-00003

-00004

-00002

-00001

-00002

-00001

-00002

-00003

-00005

-00006

-00008

CHAPTER 8

81 Conclusion

82 Future Work

xv2 r~

PILOT PLANT

Realtime (lata

D Xbdquo

B xbdquo

PE -W-V2

fc V -tvi

PILOT PLANT

PID Embedded

Adaptive Ccntroller

Online measurement

Hyperterminal

reg Spf M -amp- 1

i KZ- ^ -n

REFLUX DRUM

A 12 Vent-bleed

CONDENSER^-

mdash 4 6

i mdash amdashgtp j

Inert gas O

mdash m ltV3

i te i iaal

J5) Input ho-ot IS)

B - t-t

a) Kettle type

o h m m I K I

i t t_e i i - 1 1

-amp Q

_ U ftau irav

P| vopor flow

V U heat -

exchanger

A WH-J

have been specified

degrees of freedom

Column pressure

Manipulated

variables

Reflux flow rate

Reboiler duty

Condenser duty

Bottoms flow rate

Control valve

location

Reflux flow (VI)

Heat flow (V4)

Coolant flow (V3)

Bottoms flow (V5)

Control Structure

D-V(or D-QB)

L-V(or L-QB)

Role of valve

Inventory

Control (IC)

Separation

Control (SC)

structures

units in the plant

flow rate B

I raquo - sect I -

ATbdquo

are switched

H amp J bull

Component

Propane

Normal Butane

Isobutane

Isopentane

Normal Pentane

Hexane

Heptane

Octane

Nonane

Normal Decane

n-CHH24

n-C12H26

Cyclopentane

Methylclopentane

Benzene

Toluen

O-Xylene

E-Benzene

Cut point

(degC)

ASTM D86

(degC)

124024

Properties

1 Octane Number

2 Lead Content (g1)

10 vol

50 vol

90 vol

Residue ( vol)

Testing method

ASTM D2699

ASTMD3341

ASTM D86

ASTM D130

ASTMD381

ASTM D323

ASTM D1266

ASTM D525

ASTMD1298

Requirements

min 87

max 015

max 70

max 120

max 190

max 210

max 20

maxN-1

max 40

min 43

max 80

max 015

min 240

070 - 074

capacity

tso (TBP) = 5842 C

t(30- io) (TBP) = 3599-2467=1132 degC

t50 (EFV-TBP) = 1-5 C

Therefore

tso (EFV) = 5842+15=5962 degC

EFV (1 atm)

EFV (46 atm)

20 3840 60

Volume

80 100

B31 Description

B32 Calculation

fegtegtd f l ow

tray f

Rf= B-LF+ Vf= 62 - 58 + 28 = 32 vol

Stream

Total light

fractions E S D

Bottoms B

Volume fraction

Liquid flow rate

-73916

133973

-64677

143213

Liquid density

Mass flow rate

-45458

-38677

104046

B41 Description

B42 Calculation

stripping section

kcalkg

kcalhlOJ

kJhl0 j

276860

131300

408161

kcalhlOJ

149134

kJhl0J

267136

357141

624280

B51 Description

reflux flow

B52 Calculation

46degC

Stage 15 (tray 14)

D Distillate

9611+Ro

kcalkg

ZSD+Ro

5065+Ro

9611+Ro

kcalkg

kcalhlOJ

11053+24 R0

kJhlOJ

1005 R0

46263+1005 R0

kcalh103

49131+97Ro

56405+ 97R0

kJhl0J

205665+406R0

236111+406R0

46263+1005 Ro= 236111+406 Ro

Therefore

Ro= 7415 (tonh)

at the column top)

AHRoR0= AHLL

(115-24) (742) = (106-22) I

Therefore

L = 804 (tonh)

Stream

Temperature (C)

Pressure (atm)

Density (kgm )

Stream

Temperature (C)

RVP (kPa)

Density (kgm )

Condensate

130000

Reformate

105000

Raw gasoline

Gasoline

250000

Condensate bull

bullff

Raw Gasoline

amp V - 0 1

PEF l l OPUH

-Gasoline

GSSOLINE MIXER

gasoline

is 128degC

tankers

B74 Feed Control

46 atm

i T C - 1 r

mdashImdash I

--copy

l-MmdashJ

To Column

B76 Bottom Section

Cl Introduction

linear

outlet weir

Mbdquo = f(LJ (Cl)

C21 Generic Trays

equations

d(Mbdquo)

Liquid

Flow rate

vbdquo Vn

Concentration

staae n

dh dMbdquo x = A-

dLbdquo dL (C4)

d(Mbdquoxbdquo) dt

dt Mbdquo (C6)

d(Mnhn) dt

V = H-h

C22 Feed Tray

stage (feed tray

LfXrbdquo

I-v vgt LrXf

d(Mfxf)

dt Mbdquo

d(Mfhf)

C23 Top Section

Vlaquobdquo

11 V M1

vbdquo

d(MN+l) _ (C 13) dt

d(M XN+])=Lx^ + y L _ y ( C 1 4 )

11 N+ nN+

C24 Bottom Section

l I l I

ltHXr-B x F

d(M2) dt

L3-L2+ VB -V2

dMRhB) dt

= 23Z3 +HBVB- h2L2 - H2V2

Therefore

H2 -h2

be neglected

dMB) = L 2 _ V B B ( C 2 3 )

d(MBhB)

4 Simplified Model

yn = r (C27)

+ (a-l)xbdquo

aZyv+2 = dL)

L2= LT~ = LN+2-

equations [12]

5) Tray n(n = 2 - l)

MBX] =(L + LF)X2 - Vy - fix (C33)

1) LF=qFF

2) VF = F-LF

y = r bull (C35)

1 + a - )Xj

A = 730 (kJkg)

V0= 39098 (kgh) or 668871 (kmoleh)

V = 0+ = 663407 (kmoleh)

Joshi [43]

ffl^^M (C38)

314(175X1-4) Z ^ = 2488 (kmole) B 4 786

t 0957chD2k dr

095(314)(028)(175)2 680 M = = 580 (kmole)

MD = 5iL + D) (C41)

flow rate

follows

Tray 5 (n = 6) M6 = F(^5 - y6) + (Z + LF )(x7 - x6)

Tray 3 (n = 4) M4 = F(^3 - gt4) + (Z + ZF )(x5 - x4)

2488 (kmole)

1403 x16 =1646291 y]5 - 756380x6 -927597x6

58x15 = 1646291(y14 -y ] 5) + 756380(x6 -x l 5)

58x4 = 1646291(73-gtgt4) + 756380(x5-x4)

58x13 = 1646291(712 - yn) + 756380(xl4 - x13)

58x12 =1646291(j |l-j12) + 756380(x13-x12)

58 = 1646291(710 -yu) + 756380(x2 -x )

58x0 = 1646291(79-^0) + 756380(x-x0)

58x9 = 661 39ys -15638gt-9 + 756380(xl0 -x 9 ) + 5995

58x8 = 661139(y7 -ya) + 756380 x9 - 18859x8 + 3399

58x7 = 661139(y6-y7) +179887 l (x 8-x 7)

58x6 = 661 39(y5-y6) + 179887 l (x 7 -x 6 )

58x5 = 661139(j4 - y5) +1798871 (x6 - x5)

58x4 =661139(^3 -yA) + 79887 l (x 5-x 4)

58x3 = 661 139(^2 - y 3 ) + l798871 (x4 - x3)

58x2 =661139(j -y2) +1798871 (x 3 -x 2 )

2488x = 1798871 x2 -1109235x -661139^ (C42)

568x y ~ l + 468x

y2 = 568x2

1 + 468x

^ 1 5 =

l + 468x (C43)

bullCO

laquo r M |

raquo ^ SA 11 j

w r n i |

^ ltgt fM f 3 1

ET mAr pound |

~^ IT JWi a mdash i

Cgt $ IZ

1 ma r ii |

P $ mar t |

ET r Jfifl V 3 1

b $ TWVlP 2 1

J ^ m d If f |

WFYMtG

fiterttxm

STRIPPING SECTION

GENERAL TRAY

COLUMN

1 TRAY 7

1 TRAYS

RECTI FYINO SECTION

GENERAL TRAY 1

Figure D3

- w i 13411

~W 46804

RECTIFYING SECTION

mdash bull In2 Out2

STRIPPING SECTION

bull XD

To Workspacel

-4L Scope 1

Raw Gasoline

bull | xB

To Workspace

H Scope

In20ut2

Inl O u l l M

In 2 Ou2t

Tray 14

bull i n l Out1 |

- W i n 2 Oul2|

Tray 13

In 10ut 1

In20ut2

Tray 12

bull In lOu t l

In20ut2

Tray 11

InlOutl

In20ul2

Tray 10

bullNln20Ut2

Tray 9

l j mdash

~2~gt -In2

bull in 2

Tray 8

x 1 bull Outl

bull - K 2 Out2

_2 mdash

f bull

n 1 n n H I Wgt A

In 2 Ol l t l

Tray 7

mdash bull

In 10ut1

In20ut2

Tray 6

- gt In20ut2

Tray 5

In lOut l -

bull ln20ut2

Tray 4

bull in lOut l

1 bull

In20ut2

Tray 3

In lOut l

In20ut2 [

Tray 2

[ bull

In lOut l H

In20ul2 |

1 Tray 1

__ Out1

bull In1

Out2 -gt lt_2_gt

O bull72302

471 r Integrator 2

bull XI

To Workspace2

Scope 2

K 2 Olit2

2T899 ^ Function

VLE equation

GENERIC TRAY n

V bull L(n+1)Mn

In2 _ - -

A i bull

-bull VnMn

bull 1 integrator 2

y lt bull

V IE equa Son

bull xn

To Workspace2

bullbull bull -

Scope xn

TRAY 7 (Stage n -8)

bull 3 gtbull

bull 1

( 2 in2

IH130410 ~gt-

bull 119679

bullbullyenbullbull

y- Integrator 2

VLE equation

To Workspaces

Scope 2

gt bull

1 lHn0410

bullbullbull xS

To Workspace

2 bull 119879 In2

Outl bull bull I

289533 N

li integrator 2

130410

Function

MATLAB Fen 2

bull gt bull bull

Scope2

( 1 In2

119666 1 I s J

Integrator 2

120027 K

Scope 2

inputs

M M n+ Mbdquo

-X (El)

= = V15= F+ VF = V+ 985152

Vw = l 15 (E2)

X = f(Xut)

dX = X-X

du = u - u

dX df] _lt3x_

dX + 8f] _du_ du

Mn Mn Mn Mn

Mn +1 Mn +1 Mn Mn

T T -t- V V K V

i ( 0 = Ax(t) + Bu(t) (E4)

y(t) = Cx(t) (E5)

follows

L ==LS = 1798871 (kmoleh)

L9 = = Z15= 756380 (kmoleh)

V = = V = 661139 (kmoleh)

V9 = = V]5 = 1646291 (kmoleh)

M2 = M3 = = Mi5 = 580 (kmole)

M16 = MB = 2488 (kmole)

_KK _ (L]+K2V) _ L 21 M2

22 M2 23 M 2

1) Collect data

w = 1 ^ 1 = 7 Z 6 i 2=TT

w =2 h _xlZx2) _-fe-i) 2 J ~ M2 2lt2~ M2

laquo - 1 6 66gti = 6 ft162 ^ 1 6

_ K M16

[00012 00063 00091 00098 00076 00044 00022 00021 00048

00111 00216 00306 00285 00178 00086 -00702

-00024 -00157 -00237 -00254 -00196 -00116 -00058 -00027 -00024

-00050 -00097 -00138 -00128 -00080 -00039 00704]r

C = 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

E2 Stability Test

V(x)=xTPx (E6)

ATP + PA = -I (E9)

positive definite

P = lyap(AI)

for i=l16

Pi = P (1 i 1 i)

det(Pi)

d e t ( P l ) = 0 0 3 2 8 3 1

d e t ( P 2 ) = 0 0 0 0 9 0 8 4 9

d e t ( P 3 ) = 2 4 4 4 3 e - 0 0 5

d e t ( P 4 ) = 5 5 4 7 6 e - 0 0 7

d e t ( P 5 ) = 1 0 1 5 2 e - 0 0 8

d e t ( P 6 ) = 1 6 2 0 8 e - 0 1 0

d e t ( P 7 ) = 2 3 0 2 5 e - 0 1 2

d e t ( P 8 ) = 2 6 1 8 3 e - 0 1 4

d e t ( P 9 ) = 4 1 9 5 9 e - 0 1 6

d e t ( P l O ) = 1 2 8 8 6 e - 0 1 7

d e t ( P l l ) = 6 7 8 4 7 e - 0 1 9

d e t ( P 1 2 ) = 3 9 1 6 e - 0 2 0

d e t ( P 1 3 ) = 1 8 3 0 8 e - 0 2 1

d e t ( P 1 4 ) = 7 0 8 9 e - 0 2 3

d e t (P15) = 2 4 8 7 6 e - 0 2 4

d e t ( P 1 6 ) = 8 4 6 1 2 e - 0 2 6

stable

include ltstdlibhgt

using namespace std

if(k = x_kmlk+l)

stampn)

if(k = e_kmlk+l)

stampn)

if(k = uc_kmlk+l)

stampn)

return

th kk = k

b21e_kmlp2)x_kmlp2

b22e_kmlp2)x_kmlpl

b22e_kmlp2)x_kmlp2

b21e_kmlp2)uc_kmlpl

b21e_kmlp2)uc_kmlp2

b22e_kmlp2)uc_kmlpl

b22e_kmlp2)uc_kmlp2

r e t u r n

F2 Plant Model

include ltstdlibhgt

include PlantModelh

using namespace std

PlantPlant()

all = -67941 + 067(rand()2-05)

al2 = -09095 + 009(rand()2-05)

a21 = 14686 + 015(rand()2-05)

a22 = -02497 + 002(rand()2-05)

bll = -01461 + 0014(rand()12-05)

bl2 = 02073 + 002(rand()2-05)

b21 = -00021 + 00002(rand()12-05)

b22 = -00281 + 0003(rand()2-05)

ell = -00624 + 0006(rand()2-05)

cl2 = -00281 + 0003(rand()2-05)

c21 = 02458 + 0025(rand()2-05)

c22 = 00009 + 000009(rand()2-05)

Plant~Plant ()

if(k = u_kk)

this-gtu_k = u_k

this-gtx_k = x_k

return

bl2Tu_kp2

b22Tu_kp2

x_kplk = k+1

r e t u r n

F3 Reference Model

include ltstdlibhgt

using namespace std

RefmdlRefmdl()

Refmdl~Refmdl()

if(k = uc_kk)

stampn)

this-gtuc_k = uc_k

if(k = xm_kk)

stampn)

this-gtxm_k = xm_k

return

xm_kplk = k+1

return

include ltstdlibhgt

using namespace std

Linctrl Linctrl()

Linctrl -Linctrl ()

time stampn)

this-gtth_k = th_k

time stampn)

this-gtuc_k = uc_k

time stampn)

this-gtx_k = x_k

return

- th_kth2x_kp2

- th_kth4x_kp2

u_kk = k

return

F5 Comparator

include ltstdlibhgt

include Comparatorh

using namespace std

this-gtx_k = x_k

this-gtxm_k = xm_k

return

compute errors

e_kk = k

r e t u r n

include ltstdlibhgt

using namespace std

stampn)

this-gtx_k = x_k

return

y_kk = k

return

include ltstdlibhgt

using namespace std

time stampn)

this-gtxm_k = xm k

return

ym_kk = k

ym_kpi = ym_kpi

ym_kp2 = ym_kp2

r e t u r n

F8 CGI Program

inc lude ltctypehgt

include

lterrnohgt

ltstringhgt

ltstdiohgt

ltunistdhgt

ltfcntlhgt

ltstringhgt

ltsyssockethgt

ltsystypeshgt

ltnetinetinhgt

ltarpainethgt

define LINELEN 1024

struct valinfo

unsigned char name

unsigned char text

struct thetaPkt

struct Pkt

int pi

int p2

static

amll =

ami 2 =

am21 =

am22 =

bmll =

bml2 =

bm21 =

bm22 =

cmll =

cml2 =

cm21 =

cm22 =

all = -

al2 = -

a22 = -

bll = -

-67 94

static

= -510

= -310

= 1044

= 1006

static int nvals=0

if (gotvals)

nvals = getvals()

gotvals = 1

)vals[i]name)==0)

return vals[i]text

return NULL

=============== httpunescape ===========

unsigned char siptr

unsigned char soptr

unsigned char sos

(unsigned char) )

soptr = sos

siptr = sis

while (siptr)

if(siptr == )

int c = 0 i

for (i=0ilt2i++)

siptr++

c = claquo4 + h

if (i = 2)

free(sos)

return NULL

soptr++ =

soptr++ = siptr

siptr++

soptr = 0

free (sos)

return sis

=============== hextobin =================

if(isdigit(c))

return c-0

return -1

=============== getvals ===================

int vent = 0

unsigned char vstr

unsigned char vptr

unsigned char eptr

unsigned char aptr

int 1 cl

return 0

if(vstr == NULL)

return 0

if(vstr[l-l] == n)

vstr[l-l]=0

vptr = vstr

while (vptr)

vcnt++

valinfo))

vptr = vstr

for (i=0iltvcnti++)

if (eptr == NULL)

return 0

eptr = 0

if (aptr)

aptr = 0

vptr = aptr+1

return vent

unsigned char c

unsigned char cs

int fd len

if((fd==-l))

exit (1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== write signals ===================

unsigned char c

unsigned char cs

int fd len

if((fd==-l))

exit(1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== write a signal ===================

unsigned char c

unsigned char cs

int fd len

if((fd==-l))

exit (1)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== getsignal ===================

int fn s i m sn 1

unsigned char buf

if(fn==-l)

exit(1)

return

read(fn buf 20)

signal = s

free((void) buf)

close(fn)

return s

=============== get ascii signal ===================

int fn s i m sn 1

unsigned char buf

if(fn==-l)

exit (1)

return 0

read(fn buf 20)

signal = s

free((void) buf)

close(fn)

return 1

=============== settime ===================

int t=0

unsigned char c

unsigned char cs

int len

if((f==-l))

exit(l)

write(f c len)

write(f t 1)

free((void) c)

free((void) cs)

close (f)

return

=============== Wait ===================

int i=0

while(i++ltn)

=============== gettime ===================

clear signals

kT = k

Write to files

return

=============== clear signal ===================

int fn

if(fn==-l)

exit(1)

return

write(fn20)

close(fn)

return

unsigned char ch

if (xl==0)

ch[0] = 0

len = 1

if(xllt0)

xl = -xl

sign[0] = -

sign[0] = +

while(xlgt0)

ch[i] = 0 + xl10

xl=xl10

len=i+l

for(i=0 iltlen i++)

free((void) ch)

return

=============== getAdapMechPkt ===================

th4 th5 th6 th7 th8

int outfile

Receive signals

getsig

vartmpfuc2

vartmpfkth

vartmpfthl

vartmpfth2

vartmpfth3

vartmpfth4

vartmpfth5

vartmpfth6

vartmpfth7

vartmpfth8

ampuc2)

ampkth)

ampthl)

ampth2)

ampth3)

ampth4)

ampth5)

ampth6)

ampth7)

ampth8)

receivedlth3gtn)

printf

ltpgt ucl

ltpgt uc2

ltpgt thl

ltpgt th2

ltpgt th3

ltpgt th4

ltpgt th5

ltpgt th6

ltpgt th7

ltpgt th8

d) = dn k-1 ucl)

d) = dn k-1 uc2)

d)k = dn k-1 kth)

d) = dn k-1 thl)

d) = dn k-1 th2)

d) = dn k-1 th3)

d) = dn k-1 th4)

d) = dn k-1 th5)

d) = dn k-1 th6)

d) = dn k-1 th7)

d) = dn k-1 th8)

x_kml-gtk = kx

x_kml-gtpl = xl

x_kml-gtp2 = x2

e_kml-gtk = ke

e_kml-gtpl = el

e_kml-gtp2 = e2

uc_kml-gtk = kuc

uc_kml-gtpl = ucl

uc_kml-gtp2 = uc2

th_kml-gtk = kth

th_kml-gtthl = thl

th_kml-gtth2 = th2

th_kml-gtth3 = th3

th_kml-gtth4 = th4

th_kml-gtth5 = th5

th_kml-gtth6 = th6

th_kml-gtth7 = th7

th kml-gtth8 = th8

Write to files

return

=============== genAdapMechPkt ===================

th k-gtk = k

Write to files

return

=============== main ============

main ()

int valid

int stime gamm

int i=0

int k kT

int kmax=2

struct Pkt x_kml

struct Pkt e_kml

struct Pkt uc_kml

int getkt=0

int getkmax=0

ltheadgtn)

while(getkmax)

wait(5000)

while(klt kmax)

signalsn)

while(Igetkt)

wait (5000)

while(k=kT)

wait(10000)

signalsn)

gainsn)

ampth_k)

exit (0)

0000000

0100000

0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

1100000

1200000

1300000

1400000

1500000

1600000

1700000

1800000

0000000

-0005938

-0007274

-0007525

-0006703

-0006552

-0007393

-0007877

-0006929

-0006522

-0006511

-0005794

-0005655

-0005802

-0005829

-0005804

-0005700

-0006102

-0006161

0000000

-0000402

-0001596

-0002967

-0004377

-0005628

-0006885

-0008274

-0009549

-0010673

-0011823

-0012844

-0013834

-0014738

-0015578

-0016366

-0017279

-0018029

-0018812

0000000

-0005232

-0006874

-0007297

-0007309

-0007186

-0007024

-0006854

-0006686

-0006524

-0006369

-0006221

-0006080

-0005945

-0005816

-0005693

-0005576

-0005464

-0005358

0000000

-0000386

-0001531

-0002888

-0004274

-0005626

-0006927

-0008172

-0009360

-0010494

-0011576

-0012609

-0013594

-0014533

-0015429

-0016284

-0017099

-0017877

-0018620

1900000

2000000

2100000

2200000

2300000

2400000

2500000

2600000

2700000

2800000

2900000

3000000

3100000

3200000

3300000

3400000

3500000

3600000

3700000

3800000

3900000

4000000

4100000

4200000

4300000

4400000

4500000

4600000

-0005840

-0005030

-0005135

-0005074

-0004855

-0005031

-0004512

-0004009

-0004133

-0004671

-0004958

-0004323

-0003983

-0004546

-0004544

-0004603

-0004297

-0004450

-0004369

-0003873

-0004316

-0003581

-0003195

-0004056

-0004004

-0003677

-0003060

-0002967

-0019639

-0020340

-0020948

-0021660

-0022270

-0022872

-0023498

-0023983

-0024360

-0024769

-0025263

-0025755

-0026125

-0026483

-0026923

-0027330

-0027685

-0027977

-0028329

-0028643

-0028964

-0029283

-0029457

-0029607

-0029793

-0029938

-0030105

-0030178

-0005256

-0005159

-0005067

-0004979

-0004894

-0004814

-0004737

-0004664

-0004595

-0004528

-0004465

-0004404

-0004346

-0004291

-0004239

-0004189

-0004141

-0004095

-0004052

-0004010

-0003971

-0003933

-0003897

-0003863

-0003830

-0003798

-0003769

-0003740

-0019327

-0020003

-0020647

-0021262

-0021848

-0022407

-0022941

-0023449

-0023935

-0024398

-0024840

-0025261

-0025663

-0026047

-0026413

-0026762

-0027095

-0027412

-0027715

-0028004

-0028280

-0028543

-0028794

-0029033

-0029261

-0029479

-0029687

-0029885

4700000

4800000

4900000

5000000

5100000

5200000

5300000

5400000

5500000

5600000

5700000

5800000

5900000

6000000

6100000

6200000

6300000

6400000

6500000

6600000

6700000

6800000

6900000

7000000

7100000

7200000

7300000

7400000

-0003945

-0003632

-0003741

-0003254

-0004091

-0003652

-0004092

-0004512

-0003289

-0002858

-0002967

-0003991

-0003572

-0003271

-0003674

-0003566

-0003464

-0003407

-0002696

-0002674

-0003472

-0003254

-0003053

-0003501

-0003466

-0003658

-0002994

-0003796

-0030245

-0030477

-0030604

-0030814

-0030945

-0031179

-0031310

-0031532

-0031857

-0031948

-0031971

-0032005

-0032227

-0032303

-0032298

-0032383

-0032482

-0032554

-0032590

-0032534

-0032468

-0032440

-0032512

-0032535

-0032586

-0032618

-0032758

-0032787

-0003713

-0003687

-0003662

-0003639

-0003616

-0003595

-0003574

-0003555

-0003536

-0003519

-0003502

-0003485

-0003470

-0003455

-0003441

-0003428

-0003415

-0003403

-0003391

-0003380

-0003370

-0003360

-0003350

-0003341

-0003332

-0003324

-0003316

-0003308

-0030074

-0030254

-0030426

-0030590

-0030747

-0030896

-0031039

-0031175

-0031304

-0031428

-0031546

-0031659

-0031766

-0031868

-0031966

-0032059

-0032148

-0032233

-0032314

-0032391

-0032465

-0032535

-0032602

-0032666

-0032727

-0032785

-0032840

-0032893

7500000

7600000

7700000

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

-0004422

-0003688

-0002866

-0003432

-0003142

-0002693

-0003564

-0003913

-0004231

-0004049

-0003128

-0002355

-0002156

-0002358

-0002603

-0003386

-0004014

-0004132

-0003349

-0003703

-0003246

-0003219

-0002317

-0002500

-0003393

-0032935

-0033168

-0033314

-0033233

-0033228

-0033288

-0033206

-0033185

-0033216

-0033382

-0033535

-0033510

-0033344

-0033200

-0033080

-0032950

-0032966

-0033023

-0033146

-0033219

-0033293

-0033271

-0033284

-0033355

-0033271

-0033212

-0003301

-0003294

-0003287

-0003281

-0003275

-0003269

-0003264

-0003259

-0003254

-0003249

-0003244

-0003240

-0003236

-0003232

-0003228

-0003225

-0003221

-0003218

-0003215

-0003212

-0003209

-0003207

-0003204

-0003202

-0003199

-0003197

-0032944

-0032992

-0033038

-0033082

-0033124

-0033164

-0033202

-0033238

-0033272

-0033306

-0033337

-0033367

-0033396

-0033423

-0033449

-0033474

-0033498

-0033520

-0033542

-0033563

-0033582

-0033601

-0033619

-0033636

-0033652

-0033668

in Table G2

0000000

0100000

0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

1100000

1200000

1300000

1400000

1500000

1600000

1700000

1800000

1900000

2000000

-0000000

0000365

0000479

0000535

0000528

0000556

0000643

0000713

0000694

0000703

0000737

0000724

0000745

0000781

0000807

0000829

0000850

0000896

0000923

0000928

0000901

0000000

-0001534

-0001880

-0001946

-0001735

-0001697

-0001915

-0002042

-0001798

-0001694

-0001692

-0001508

-0001472

-0001511

-0001519

-0001513

-0001487

-0001592

-0001608

-0001525

-0001317

-0000000

0000337

0000472

0000536

0000576

0000607

0000633

0000657

0000680

0000702

0000723

0000742

0000761

0000779

0000796

0000813

0000828

0000843

0000858

0000871

0000884

0000000

-0001286

-0001691

-0001796

-0001800

-0001771

-0001733

-0001692

-0001652

-0001613

-0001576

-0001540

-0001507

-0001474

-0001443

-0001414

-0001386

-0001359

-0001334

-0001309

-0001286

2100000

2200000

2300000

2400000

2500000

2600000

2700000

2800000

2900000

3000000

3100000

3200000

3300000

3400000

3500000

3600000

3700000

3800000

3900000

4000000

4100000

4200000

4300000

4400000

4500000

4600000

4700000

0000925

0000943

0000948

0000976

0000964

0000948

0000967

0001011

0001042

0001019

0001010

0001054

0001067

0001082

0001075

0001092

0001098

0001078

0001114

0001080

0001062

0001117

0001120

0001105

0001073

0001070

0001130

-0001344

-0001329

-0001273

-0001319

-0001185

-0001056

-0001088

-0001228

-0001302

-0001139

-0001051

-0001197

-0001212

-0001134

-0001173

-0001153

-0001025

-0001139

-0000950

-0000851

-0001073

-0001060

-0000975

-0000816

-0000792

-0001045

0000896

0000908

0000919

0000930

0000940

0000950

0000959

0000968

0000977

0000985

0000992

0001000

0001007

0001013

0001020

0001026

0001032

0001037

0001042

0001047

0001052

0001057

0001061

0001065

0001069

0001073

0001077

-0001264

-0001243

-0001223

-0001203

-0001185

-0001168

-0001151

-0001135

-0001120

-0001105

-0001091

-0001078

-0001066

-0001054

-0001042

-0001031

-0001021

-0001011

-0001001

-0000992

-0000984

-0000976

-0000968

-0000960

-0000953

-0000946

-0000940

4800000

4900000

5000000

5100000

5200000

5300000

5400000

5500000

5600000

5700000

5800000

5900000

6000000

6100000

6200000

6300000

6400000

6500000

6600000

6700000

6800000

6900000

7000000

7100000

7200000

7300000

7400000

0001118

0001128

0001105

0001159

0001140

0001170

0001201

0001138

0001115

0001123

0001184

0001166

0001150

0001174

0001170

0001167

0001166

0001125

0001122

0001167

0001153

0001144

0001171

0001170

0001183

0001147

0001196

-0000964

-0000992

-0000867

-0001083

-0000970

-0001084

-0001192

-0000877

-0000766

-0000794

-0001058

-0000950

-0000873

-0000977

-0000949

-0000922

-0000908

-0000724

-0000718

-0000925

-0000868

-0000816

-0000932

-0000923

-0000973

-0000801

-0001009

0001080

0001084

0001087

0001090

0001093

0001095

0001098

0001100

0001103

0001105

0001107

0001109

0001111

0001113

0001115

0001116

0001118

0001120

0001121

0001123

0001124

0001125

0001126

0001128

0001129

0001130

0001131

-0000934

-0000928

-0000922

-0000917

-0000911

-0000907

-0000902

-0000897

-0000893

-0000889

-0000885

-0000882

-0000878

-0000875

-0000871

-0000868

-0000865

-0000863

-0000860

-0000857

-0000855

-0000853

-0000851

-0000848

-0000846

-0000845

-0000843

7500000

7600000

7700000

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

0001238

0001201

0001156

0001188

0001170

0001145

0001195

0001215

0001235

0001229

0001178

0001132

0001115

0001123

0001134

0001176

0001214

0001223

0001180

0001203

0001178

0001176

0001125

0001133

0001185

-0001170

-0000981

-0000769

-0000915

-0000840

-0000724

-0000949

-0001039

-0001121

-0001074

-0000837

-0000637

-0000585

-0000637

-0000701

-0000903

-0001065

-0001095

-0000893

-0000985

-0000867

-0000860

-0000627

-0000674

-0000905

0001132

0001133

0001134

0001135

0001136

0001137

0001138

0001139

0001140

0001141

0001142

0001143

0001144

0001145

0001146

-0000841

-0000839

-0000838

-0000836

-0000835

-0000833

-0000832

-0000831

-0000830

-0000829

-0000827

-0000826

-0000825

-0000824

-0000823

-0000822

-0000821

-0000820

-0000819

-0000818

-0000817

-0000816

Plant Error

0000000

0100000

0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

1100000

1200000

1300000

1400000

1500000

1600000

1700000

1800000

1900000

2000000

2100000

0000000

-0000706

-0000400

-0000229

0000606

0000634

-0000368

-0001023

-0000243

0000002

-0000142

0000427

0000425

0000143

-0000013

-0000110

-0000124

-0000638

-0000803

-0000584

0000129

-0000068

0000000

-0000016

-0000065

-0000079

-0000103

-0000002

0000042

-0000102

-0000189

-0000179

-0000247

-0000236

-0000241

-0000205

-0000149

-0000082

-0000180

-0000152

-0000193

-0000312

-0000337

-0000301

2200000

2300000

2400000

2500000

2600000

2700000

2800000

2900000

3000000

3100000

3200000

3300000

3400000

3500000

3600000

3700000

3800000

3900000

4000000

4100000

4200000

4300000

4400000

4500000

4600000

4700000

4800000

-0000096

0000040

-0000217

0000226

0000656

0000462

-0000143

-0000493

0000081

0000364

-0000255

-0000305

-0000414

-0000157

-0000355

-0000318

0000137

-0000345

0000352

0000702

-0000194

-0000175

0000122

0000709

0000773

-0000232

0000055

-0000399

-0000422

-0000465

-0000557

-0000534

-0000425

-0000371

-0000423

-0000494

-0000462

-0000436

-0000510

-0000569

-0000590

-0000565

-0000614

-0000639

-0000684

-0000740

-0000663

-0000574

-0000531

-0000459

-0000418

-0000293

-0000171

-0000223

4900000

5000000

5100000

5200000

5300000

5400000

5500000

5600000

5700000

5800000

5900000

6000000

6100000

6200000

6300000

6400000

6500000

6600000

6700000

6800000

6900000

7000000

7100000

7200000

7300000

7400000

-0000078

0000385

-0000474

-0000057

-0000518

-0000957

0000247

0000660

0000534

-0000505

-0000102

0000184

-0000232

-0000138

-0000049

-0000004

0000696

0000707

-0000103

0000106

0000297

-0000160

-0000134

-0000334

0000322

-0000488

-0000177

-0000224

-0000198

-0000283

-0000271

-0000357

-0000553

-0000520

-0000425

-0000347

-0000461

-0000434

-0000332

-0000324

-0000333

-0000321

-0000276

-0000143

-0000003

0000095

0000090

0000130

0000141

0000167

0000082

0000106

7500000

7600000

7700000

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

-0001121

-0000394

0000422

-0000151

0000133

0000576

-0000300

-0000655

-0000977

-0000800

0000116

0000885

0001080

0000874

0000625

-0000161

-0000792

-0000914

-0000134

-0000491

-0000037

-0000012

-0000015

0000884

0000699

-0000196

0000008

-0000176

-0000276

-0000152

-0000104

-0000124

-0000005

0000053

0000056

-0000076

-0000198

-0000143

0000052

0000223

0000369

0000524

0000532

0000498

0000396

0000343

0000289

0000330

0000335

0000281

0000381

0000456

Adaptive Gains

0000000

0100000

0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

1100000

1200000

1300000

1400000

1500000

1600000

1700000

1800000

1900000

2000000

0000000

-0005213

-0006672

-0008169

-0007644

-0007699

-0008154

-0007384

-0006498

-0006647

-0006411

-0006230

-0006451

-0005944

-0005865

-0005507

-0005139

-0005865

-0006413

-0005215

-0004796

0000000

-0000372

-0001506

-0002906

-0004473

-0005796

-0007132

-0008622

-0009855

-0010913

-0012023

-0013130

-0014033

-0015028

-0015859

-0016666

-0017478

-0018174

-0019033

-0019821

-0020508

0000000

-0005232

-0006874

-0007297

-0007309

-0007186

-0007024

-0006854

-0006686

-0006524

-0006369

-0006221

-0006080

-0005945

-0005816

-0005693

-0005576

-0005464

-0005358

-0005256

-0005159

0000000

-0000386

-0001531

-0002888

-0004274

-0005626

-0006927

-0008172

-0009360

-0010494

-0011576

-0012609

-0013594

-0014533

-0015429

-0016284

-0017099

-0017877

-0018620

-0019327

-0020003

2100000

2200000

2300000

2400000

2500000

2600000

2700000

2800000

2900000

3000000

3100000

3200000

3300000

3400000

3500000

3600000

3700000

3800000

3900000

4000000

4100000

4200000

4300000

4400000

4500000

4600000

4700000

-0005636

-0005499

-0005389

-0005468

-0005280

-0004964

-0005034

-0004301

-0004719

-0004414

-0004911

-0005111

-0003898

-0004461

-0003833

-0003692

-0003811

-0004348

-0004405

-0004391

-0004473

-0003726

-0004176

-0004041

-0003734

-0004398

-0004528

-0021153

-0021902

-0022509

-0023112

-0023668

-0024270

-0024759

-0025247

-0025581

-0026025

-0026411

-0026873

-0027315

-0027557

-0027813

-0028126

-0028324

-0028620

-0028935

-0029157

-0029522

-0029797

-0029945

-0030135

-0030351

-0030524

-0030781

-0005067

-0004979

-0004894

-0004814

-0004737

-0004664

-0004595

-0004528

-0004465

-0004404

-0004346

-0004291

-0004239

-0004189

-0004141

-0004095

-0004052

-0004010

-0003971

-0003933

-0003897

-0003863

-0003830

-0003798

-0003769

-0003740

-0003713

-0020647

-0021262

-0021848

-0022407

-0022941

-0023449

-0023935

-0024398

-0024840

-0025261

-0025663

-0026047

-0026413

-0026762

-0027095

-0027412

-0027715

-0028004

-0028280

-0028543

-0028794

-0029033

-0029261

-0029479

-0029687

-0029885

-0030074

4800000

4900000

5000000

5100000

5200000

5300000

5400000

5500000

5600000

5700000

5800000

5900000

6000000

6100000

6200000

6300000

6400000

6500000

6600000

6700000

6800000

6900000

7000000

7100000

7200000

7300000

7400000

-0004364

-0003851

-0004275

-0003488

-0004129

-0003415

-0002908

-0003426

-0002905

-0002945

-0002959

-0003857

-0004283

-0003904

-0003717

-0003901

-0004434

-0003717

-0003381

-0002788

-0003621

-0003745

-0003136

-0003398

-0003197

-0003819

-0003593

-0031089

-0031392

-0031608

-0031867

-0031972

-0032127

-0032175

-0032197

-0032248

-0032252

-0032197

-0032162

-0032284

-0032490

-0032604

-0032713

-0032914

-0033116

-0033278

-0033267

-0033253

-0033342

-0033419

-0033342

-0033439

-0033512

-0033652

-0003687

-0003662

-0003639

-0003616

-0003595

-0003574

-0003555

-0003536

-0003519

-0003502

-0003485

-0003470

-0003455

-0003441

-0003428

-0003415

-0003403

-0003391

-0003380

-0003370

-0003360

-0003350

-0003341

-0003332

-0003324

-0003316

-0003308

-0030254

-0030426

-0030590

-0030747

-0030896

-0031039

-0031175

-0031304

-0031428

-0031546

-0031659

-0031766

-0031868

-0031966

-0032059

-0032148

-0032233

-0032314

-0032391

-0032465

-0032535

-0032602

-0032666

-0032727

-0032785

-0032840

-0032893

7500000

7600000

7700000

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

-0003756

-0004296

-0003310

-0003600

-0003684

-0004076

-0003503

-0003989

-0004075

-0004365

-0003148

-0004010

-0003440

-0003184

-0003502

-0004142

-0004063

-0003750

-0003078

-0003062

-0003270

-0004051

-0003045

-0003074

-0003973

-0003841

-0033687

-0033717

-0033822

-0033808

-0033813

-0033915

-0034075

-0034090

-0034174

-0034355

-0034481

-0034367

-0034446

-0034452

-0034402

-0034367

-0034495

-0034588

-0034652

-0034570

-0034511

-0034490

-0034669

-0034609

-0034624

-0034750

-0003301

-0003294

-0003287

-0003281

-0003275

-0003269

-0003264

-0003259

-0003254

-0003249

-0003244

-0003240

-0003236

-0003232

-0003228

-0003225

-0003221

-0003218

-0003215

-0003212

-0003209

-0003207

-0003204

-0003202

-0003199

-0003197

-0032944

-0032992

-0033038

-0033082

-0033124

-0033164

-0033202

-0033238

-0033272

-0033306

-0033337

-0033367

-0033396

-0033423

-0033449

-0033474

-0033498

-0033520

-0033542

-0033563

-0033582

-0033601

-0033619

-0033636

-0033652

-0033668

in Table H2

0000000

0100000

0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

1100000

1200000

1300000

1400000

1500000

1600000

1700000

1800000

1900000

2000000

2100000

-0000000

0000320

0000436

0000563

0000573

0000611

0000674

0000668

0000648

0000685

0000701

0000719

0000756

0000753

0000770

0000832

0000887

0000837

0000830

0000897

0000000

-0001217

-0001558

-0001908

-0001787

-0001802

-0001909

-0001731

-0001525

-0001561

-0001507

-0001466

-0001518

-0001401

-0001383

-0001300

-0001215

-0001386

-0001514

-0001235

-0001138

-0001335

-0000000

0000337

0000472

0000536

0000576

0000607

0000633

0000657

0000680

0000702

0000723

0000742

0000761

0000779

0000796

0000813

0000828

0000843

0000858

0000871

0000884

0000896

0000000

-0001286

-0001691

-0001796

-0001800

-0001771

-0001733

-0001692

-0001652

-0001613

-0001576

-0001540

-0001507

-0001474

-0001443

-0001414

-0001386

-0001359

-0001334

-0001309

-0001286

-0001264

2200000

2300000

2400000

2500000

2600000

2700000

2800000

2900000

3000000

3100000

3200000

3300000

3400000

3500000

3600000

3700000

3800000

3900000

4000000

4100000

4200000

4300000

4400000

4500000

4600000

4700000

4800000

0000909

0000919

0000940

0000943

0000940

0000958

0000927

0000961

0000954

0000994

0001018

0000958

0000998

0000968

0000967

0000980

0001020

0001031

0001036

0001051

0001014

0001045

0001042

0001029

0001073

0001088

0001086

-0001304

-0001279

-0001298

-0001254

-0001181

-0001198

-0001027

-0001125

-0001054

-0001171

-0001218

-0000935

-0001067

-0000921

-0000888

-0000916

-0001041

-0001055

-0001052

-0001071

-0000897

-0001002

-0000971

-0000900

-0001055

-0001086

-0001048

0000908

0000919

0000930

0000940

0000950

0000959

0000968

0000977

0000985

0000992

0001000

0001007

0001013

0001020

0001026

0001032

0001037

0001042

0001047

0001052

0001057

0001061

0001065

0001069

0001073

0001077

0001080

-0001243

-0001223

-0001203

-0001185

-0001168

-0001151

-0001135

-0001120

-0001105

-0001091

-0001078

-0001066

-0001054

-0001042

-0001031

-0001021

-0001011

-0001001

-0000992

-0000984

-0000976

-0000968

-0000960

-0000953

-0000946

-0000940

-0000934

4900000

5000000

5100000

5200000

5300000

5400000

5500000

5600000

5700000

5800000

5900000

6000000

6100000

6200000

6300000

6400000

6500000

6600000

6700000

6800000

6900000

7000000

7100000

7200000

7300000

7400000

0001064

0001095

0001055

0001096

0001057

0001029

0001060

0001030

0001033

0001032

0001085

0001113

0001096

0001088

0001102

0001139

0001102

0001086

0001050

0001100

0001109

0001075

0001089

0001079

0001118

0001109

-0000928

-0001027

-0000844

-0000993

-0000827

-0000709

-0000830

-0000708

-0000718

-0000721

-0000930

-0001030

-0000941

-0000898

-0000941

-0001066

-0000899

-0000820

-0000682

-0000876

-0000905

-0000763

-0000824

-0000777

-0000923

-0000870

0001084

0001087

0001090

0001093

0001095

0001098

0001100

0001103

0001105

0001107

0001109

0001111

0001113

0001115

0001116

0001118

0001120

0001121

0001123

0001124

0001125

0001126

0001128

0001129

0001130

0001131

-0000928

-0000922

-0000917

-0000911

-0000907

-0000902

-0000897

-0000893

-0000889

-0000885

-0000882

-0000878

-0000875

-0000871

-0000868

-0000865

-0000863

-0000860

-0000857

-0000855

-0000853

-0000851

-0000848

-0000846

-0000845

-0000843

7500000

7600000

7700000

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

0001119

0001152

0001096

0001113

0001118

0001144

0001114

0001144

0001151

0001173

0001104

0001152

0001121

0001106

0001123

0001160

0001159

0001143

0001105

0001101

0001112

0001158

0001103

0001157

0001153

-0000908

-0001034

-0000804

-0000872

-0000892

-0000983

-0000849

-0000963

-0000983

-0001051

-0000767

-0000968

-0000835

-0000775

-0000849

-0000999

-0000980

-0000908

-0000751

-0000747

-0000796

-0000978

-0000743

-0000750

-0000960

-0000929

0001132

0001133

0001134

0001135

0001136

0001137

0001138

0001139

0001140

0001141

0001142

0001143

0001144

0001145

0001146

-0000841

-0000839

-0000838

-0000836

-0000835

-0000833

-0000832

-0000831

-0000830

-0000829

-0000827

-0000826

-0000825

-0000824

-0000823

-0000822

-0000821

-0000820

-0000819

-0000818

-0000817

-0000816

H3 Plant Error

0000000

0100000

0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

1100000

1200000

1300000

1400000

1500000

1600000

1700000

1800000

1900000

2000000

2100000

000000

000002

000020

-000087

-000033

-000051

-000113

-000053

000019

-000012

-000004

-000001

-000037

000000

-000005

000019

000044

-000040

-000106

000004

000036

-000057

000000

000001

000003

-000002

-000020

-000017

-000021

-000045

-000049

-000042

-000045

-000052

-000044

-000049

-000043

-000038

-000030

-000041

-000049

-000050

-000051

2200000

2300000

2400000

2500000

2600000

2700000

2800000

2900000

3000000

3100000

3200000

3300000

3400000

3500000

3600000

3700000

3800000

3900000

4000000

4100000

4200000

4300000

4400000

4500000

4600000

4700000

4800000

4900000

-000052

-000050

-000065

-000054

-000030

-000044

000023

-000025

-000001

-000057

-000082

000034

-000027

000031

000040

000024

-000034

-000043

-000046

-000058

000014

-000035

-000024

000004

-000066

-000082

-000068

-000019

-000064

-000066

-000071

-000073

-000082

-000085

-000074

-000076

-000075

-000083

-000090

-000080

-000072

-000071

-000061

-000062

-000065

-000061

-000073

-000076

-000068

-000066

-000064

-000071

-000083

-000097

5000000

5100000

5200000

5300000

5400000

5500000

5600000

5700000

5800000

5900000

6000000

6100000

6200000

6300000

6400000

6500000

6600000

6700000

6800000

6900000

7000000

7100000

7200000

7300000

7400000

7500000

7600000

7700000

-000064

000013

-000053

000016

000065

000011

000061

000056

000053

-000039

-000083

-000046

-000029

-000049

-000103

-000033

000000

000058

-000026

-000040

000021

-000007

000013

-000050

-000029

-000046

-000100

-000002

-000102

-000112

-000108

-000109

-000100

-000089

-000082

-000071

-000054

-000040

-000042

-000052

-000055

-000056

-000068

-000080

-000089

-000080

-000072

-000074

-000075

-000061

-000065

-000067

-000076

-000074

-000072

-000078

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

-000032

-000041

-000081

-000024

-000073

-000082

-000112

000010

-000077

-000020

000005

-000027

-000092

-000084

-000053

000014

000015

-000006

-000084

000016

000013

-000077

-000064

-000073

-000069

-000075

-000087

-000085

-000090

-000105

-000114

-000100

-000105

-000103

-000095

-000089

-000100

-000107

-000111

-000101

-000093

-000089

-000105

-000097

-000108

H4 Adaptive Gains

e 03716

-05106

-03100

-00427

-00428

-05106

-03100

-03099

-00428

-05106

-03099

-03098

-00428

-05106

-03098

-00428

-00429

-00428

-00429

-00428

-00429

REFERENCES

Hungary vol 3 pp 1719-1724 1984

563 May 1989

Hall 1984

orgwikiMATLAB

Press 1999

McGraw-Hill 1981

2002 pp 4003-4008

6 pp 1169-1175 Dec 1982

e_Diagrampdf

Prentice Hall 1997

University 1990

Hill 1984

India 1979

SJSU ScholarWorks

Fall 2009


Hoan The Nguyen



copy2009

Hoan The Nguyen

by Hoan The Nguyen

mdashr ~ mdash^ yy

ABSTRACT

by Hoan The Nguyen

ACKNOWLEDGMENTS

people

TABLE OF CONTENTS

List of Tables xiv

List of Figures xvi

11 Background 1

15 Methodology 5

28 ARM Processor 16

31 Introduction 20

41 Introduction 26

441 Plant 31

51 Introduction 43

521 Plant Model 44

61 Introduction 50

71 Introduction 66

751 CGI Program 78

77 Testing 93

772 Test Results 98

81 Conclusion 104

82 Future Work 105

A12 Vent-bleed 110

B31 Description 124

B32 Calculation 125

B41 Description 126

B42 Calculation 127

B51 Description 128

B52 Calculation 129

Cl Introduction 137

C22 Feed Tray 140

C23 Top Section 141

F2 Plant Model 170

F5 Comparator 173

F8 CGI Program 175

G3 Plant Error 206

H3 Plant Error 222

References 230

LIST OF TABLES

LIST OF FIGURES

Motor octane number

Network file system

Personal computer

Reid vapor pressure

True boiling point

Zero-order hold

LIST OF SYMBOLS

A State matrix

B Input matrix

C Output matrix

e State error

L Feedback matrix

u Control signal

x State variable

y Controlled output

Greek Symbols

y Adaptation rate

0 Adaptive gain

Subscript

B Bottom product

F Feed

m Reference model

CHAPTER 1

INTRODUCTION

11 Background

time spaces

adaptive controller

mathematical method

15 Methodology

CHAPTER 2

LITERATURE REVIEW

RECTIFYING SECTION

F (feed flow rate)

Q n I (3) CONDENSER

1 8 - D

stage f (feed tny)

stage rc

Material stream

Feed stream

Distillate stream

Bottoms stream

Position

Stage f

Stage N

Reflux drum

Stage 1

Reboiler

Flow rate

Concentration

in Figure 22

Liquid phase

Stage it

(Trav gti-l)

bull bullbullbull

m^u - Bubble cap

structures

I |mdash0mdashI I

bottoms flow rate B

are adjusted [12]

required

Command_ signal

Adaptive mechanism

laquosj

Control signal

Plant 1 Output

Process dynamics )

Siv-CSnftlteF----

26 Adaptive Schemes

261 Gain Scheduling

Command signal

Output

signal

MoctSI

Control signal

mechanism

Plant -bull Output

= ( ) bull (21)

disturbances or not

- mdash

yfdx dt

x = 0 i

-gt() =

= = ( ) = -W(x) (22) dt dx dt dx

dx mdash = Ax (23)

ATP + PA=-Q (24)

following function

V(x) = xTPx (25)

28 ARM Processor

DB-9 DB-9

RS-232

Features

Memory

subsystem

GPIO ports

Ethernet

Descriptions

solution

8 memory banks

by RAM

CHAPTER 3

31 Introduction

RffLlrtERLMl

xD gt 98

xB lt 20

Table 31

Temperature C

Pressure atm

Density kgm3

Mass flow rate kgh

Main streams oft

Condensate

130000

he plant

Raw gasoline

system

35 Plant Modeling

1403 x16 =1646291^15 -756380x16 -927597xI6

58x15 =1646291(gtl4 -^1 5) + 756380(x16 -x15)

58x14 =164629103 -gtgt14) + 756380(x15-x4)

58x13 =1646291012 -_y]3) + 756380(x14 -x13)

58x12 =1646291(^n -y1 2) + 756380(x13 -x ] 2)

58xH =164629IO10 ~ ^ i ) + 756380(x12-x)

58x10 =164629109 -^1 0) + 756380(xn -x10)

58x9 = 661139gtgt8 -15638^9 + 756380(x10 -x9) + 5995

58x8 = 66113907 ~yamp) + 756380 x9 -18859x8 + 3399

58x7 = 661 39(y6-y7) + 798871 (x8 -x 7 )

58x6 =66113905-gt 6) + 1798871(x7-x6)

58x5 =66113904^) +179887 l (x 6 -x 5 )

58x4=66113903-^4) + 1798871(x5-x4)

58x3 =66113902-73) +1798871 (x 4 -x 3 )

58x2 =661139(^-gt2) +179887l(x3-x2)

2488x = 1798871x2-1109235x1 -661139^

568x y = l + 468x

l + 468x

^ 1 5 =

568x 15

l + 468xbdquo (34)

CHART OF VAPOR

01 02 03 0 4 05 06 07 08 09

36 Plant Simulation

Table 32

bull L _ I i 1 l

6 8 10 12 14 16 18 20 Time (h)

than 2

CHAPTER 4

41 Introduction

and (32)

Disturbances

Ditiilitirn Gy-tem

x(t) = A(xt) + Beu(t) (41)

y(t) = Cex(t) (42)

two-output system

-09095

-02497 Bbdquo

-01461 02073

-00021 -00281 and C

-00624 -00281

02458 00009

Bode Diagram

Frequency (radsec)

431 Stability Test

finite time T-tgt0

x = Ax(t) + Bu(t) (45)

y(t) = Cx(t) + Duy) (46)

full rank of n

output

S=[CCACA2CA]]T

the next section

441 Plant

yt) = Cx(t)

where A = au

an_ B =

bn_ and C =

-00624 -00281

02458 00009

variables

442 Reference Model

Sec 43

where Abdquo

ybdquo(t) = cmxm(t)

-67941 -09095

14686 -02497

5 = -01461 02073

-00021 -00281 and Cbdquo

-00624 -00281

02458 00009

ut) = Muct)-Lx(t)

x = (A- BL)x + BMuc

hence we define

Ac(0) = (A-BL)

Bc6) = BM

i2 ~b2

l 2 11^2 ^12^4

22 _ ^ 2 1 ^ 2 ~ ^ 2 2 ^ 4

b2]65+b2281 b2Xdb+b22d (412)

condition we get

au-bu6-bnel =-67941

an -bu6a2 -bn6deg4= -09095

a2]-b2]6deg-b220deg =14686

a22-b2]e2-b229deg= -02497

6Adeg + M7deg =-01461

606deg + 6 X =02073

b2l6deg5+b229deg =-00021

b2]edeg6+b226degs =-00281 (413)

condition

0 _ b22(au +67941)-bu(a2] -14686) 0 =

regp22 ^12^21

a o _ b22(an + 09095)-bn(a22 +02497)

^11^22 _ ^12^21

buo22 mdashbnb2]

0 _ -b2](a]2 + 09095)+ bu(a22 +02497) 6gt =

bP 22 b]2b2]

-b2]bn+bub22

n0 002816I2+02073Zgt22

(J6 = -b2]bu+bub22

_0 - 000216+ 0146 b2x Uf =

-b2]bu+bub22

0 = 002816 +020736

-b2Xbu+bxxb (414)

Error Equation

e(0= x(0-m(0

e() = ^ ( 0 + 5 i ( 0 - ^ I B ( 0 - 5 m laquo c ( 0 - (4-15)

e(t) = Ame(t) + V(t)(0-O0) (417)

446 Adaptation Law

function

V(e 0) = [yePe + (0 - 0deg f (0 - 0deg)) (418)

(420) dt 2

ltP + PAm = -a (4-21)

^ = -W(t)Pe(t) at

y(buex+b2Xe2)xx

y(buex+b2]e2)x2

y(bnex+b22e2)xx

y(bx2ex+b22e2)x2

-y(bxxex+b2xe2)ucX

-y(bxxex+b2Xe2)uc2

-y(bX2ex+b22e2)ucX

-y(buex+b22e2)uc2

6 = (423)

mdash = -05591lt -07066e2)2 +132756e2] dt 1

2) Disturbances^)

4) Reference model

a n n f l

REFERENCE MODEL

dull In I

0ut2 In2

ADAPTIVE MECHANISM

= X Xm

_X2 Xm2 _

follows

e = RMS(e) = -^A for = 1 or 2

commands

norm_el = norm(el)

norm_e2 = norm(e2)

shown in Figure 46

m B s in

Figures - x vc xm

m B ampm

bull4s

bullraquo i x

i m B raquo bull

im B ffin

State error e1(t)

State error e2(t)

e = 00017

n2 VTooT = 7106210

453 Error Reduction

Plant errors

laquoi

Adaptation rate y

54304 105

71399105

5428410

7106210

54076 105

7100310-5

CHAPTER 5

51 Introduction

G(s) y ( t

521 Plant Model

x(t) = Axt) + But)

y(t) = Cx(t)

x(s) - ~[AX(S) + Bu(s) s

T x(z) = [AX(Z) + Bu(z)]

y(kT) = CxkT) (52)

522 Reference Model

in Chapter 6

ybdquo(t) = cmxm(t)

where Am = [-67941 -09095 14686 -02497] Bm = [-01461 02073 -00021 -00281]

and Cm = [-00624 -00281 02458 00009]

follows

ut) = Muc(t)-Lx(t)

L = 0kT) 62(kT)

0(kT) 0AkT

M 05(kT) 06(kT)

87(kT) 0s(kT)^ (56)

o _ ft2deg2(adeg +67941)-ft02(a20 -14686)

degdeg27 deg12deg21

8 0 _ -amp2 K + 67941) + ft (a2] -14686)

ftdeg =

00021ft0-01461ft0 22

-ft21 f t02+ft0 f t22

-b2]b]2+bub22

-b2bn+bub22

n0 00281ft+02073ftdeg

201 deg]]deg22

6(t) = -y^(t)Pe(t)

= yy (s)Pe(s)

CHAPTER 6

61 Introduction

2) Disturbances^^

reference signals

1 tnl uc(k)

In2 uc(k-1)

xm(k-1)

laquogt

REFERENCE MODEL

H Disturbances

bulleurogt

[B^_]M

0ut1 In)

0ut2 In2

i f MJi-1)

0 u ulaquoK-l)

ADAPTIVE MECHANISM

m lt raquo

Ot-1) Mux bull

e(kT) = exkT)

e2(kT)

h(kT)-xnnkT)

x2(kT)-xm2(kT)_

Ax^kT)

Ax2(kT)

follows

e = RMSe) = ^L for = 1 or 2 (61)

shown in Figure 62

Disturbance f(t)

m gt P i laquo ^ e

a)e(7)

ns gt P l

a) eiikT)

I U I 94543e-004 _ bdquo ^ - s

101 = 9407410-

M = 9 6557e -Q04 = 9 6 0 7 8 t l 0 5

4n2 vioi

sections

in Figure 66

4 include tbdefsh

5 class Plant

6 private

12 public

13 Plant()

14 -Plant()

18 endif

P l a n t ( )

a l l = - 6 7 9 4 1 + 0 6 7 ( r a n d ( ) 2 - 0 5 )

a l 2 = - 0 9 0 9 5 + 0 0 9 ( r a n d ( ) 2 - 0 5 )

a21 = 14686 + 015(rand()2-05)

a22 = -02497 + 002(rand()2-05)

bll = -01461 + 0014(rand()2-05)

bl2 = 02073 + 002 (rand()2-05)

b21 = -00021 + 00002(rand()2-05)

b22 = -00281 + 0003 (rand()2-05)

ell = -00624 + 0006(rand()2-05)

cl2 = -00281 + 0003(rand()2-05)

c21 = 02458 + 0025(rand()2-05)

c22 = 00009 + 000009(rand()2-05)

4 include tbdefsh

5 class Refmdl

6 private

7 Pkt uc_k

8 Pkt xm_k

9 public

10 Refmdl()

11 -RefmdlO

15 endif

Figure 68

4 include tbdefsh

5 class Linctrl

6 private

7 thetaPkt th_k

8 Pkt x_k

9 Pkt uc_k

10 public

11 LinctrlO

12 -LinctrlO

16 endif

database

4 include tbdefsh

5 class Comparator

6 private

7 Pkt x_k

8 Pkt xm_k

9 Pkt e_k

10 public

11 Comparator()

12 -Comparator()

16 endif

and the plant

4 include tbdefsh

6 private

7 thetaPkt th_kml

8 Pkt x_kml

9 Pkt e_kml

10 Pkt uc_kml

11 public

12 AdaptiveMechO

13 -AdaptiveMechO

17 endif

model and the plant

CC = g++

ReferenceModelo

executive file

j haut$ttum

ltOIgt gtiJ^Alt

plusmn1 f bull-lt

i gt bulli

lt euro f bull2

[ bull

- H J bullbull -

~ttttfc

bull=fmdashF^--

^ t ^ i i i = ^ ^

_ - 1 1 = - mdash J

^ J - - - ^ ^

1 1 1 I

5 time

e = |N| s94543c-004 ^

96557e-004

VToi = 96078 105

CHAPTER 7

71 Introduction

shown in Figure 71

_ Data J

5gt I Error

yV H Report

Plant Slmsliitsr

lt = J Output

Linux yacnine

RPC get_port reply

RPC mount request

RPC mount reply

Authenticate client

to the browser

button

lUser sufrmis fwm

arv-affe ie Camp

vas tor PlssrtSwi

Sens ( to i l sA i

(J 0 0

SefieJ acispfcw BM2

Oylpaito wefccfer

72 Common Database

File name

kucdat

ucldat

uc2dat

kthdat

thldat

th2dat

th3dat

th4dat

th5dat

th6dat

th7dat

Data description

Plant state xi

Plant state X2

Error variable ei

Error variable e2

Adaptive gain Gi

Adaptive gain 02

Adaptive gain 63

Adaptive gain 64

Adaptive gain 85

Adaptive gain 96

Adaptive gain 67

th8dat

adapoutdat

kmaxdat

Adaptive gain 0g

Maximal step size

73 Plant Simulator

CC = g++

$ make

1 iij-ji--^- - M - - I - - bull

1 lthtmlgt

2 ltheadgt

4 ltheacigt

5 ltbodygt

9 ltdivgt

value= size=40gt

17 ltformgt

18 ltbodygt

19 lthtmlgt

Feature

action=

method=

target=

Code example

Run gt

Description

program

time and text type

follows

th[k-l])

11 return

15 th-gtk = k

1]10000000

1] 10000000

1]10000000

23 return

751 CGI Program

variables

getenv() as follows

parameters

1 main ()

3 i n t v a l i d

17 while(klt kmax)

19 while(Igetkt)

21 wait(5000)

24 while(k=kT)

26 wait(10000)

ampth_k)

33 k++

36 else

41 exit (0)

program 109880

looses 10S824 188824 100883 100883 100883 19S821

Yers 2 2 1 1 2 3 4 1

port 111 111

48909 55541

2849 2849 2649

sudo rpcinfo -p

I I Bin Edit yamp

hoanaoan-$

gt Terminal

hoan^hoan ~$

2 2 1 1 2 3 4 1 3 4 2 3 A 1 3 4 1 1 2 2 3 3

i n f o -j r o t o

P po r t

111 n i

35368 35832

2649 2649 2S49

44664 44694 44994

2049 2849 2949

41394 41894 41894 33383 44819 33389 44819 33389 44819

M ^ s t i k ^ ^ lt

l - pound ig

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 a 3 3 3 3 3 3 A

syslog-install

root location as

during compilation

TESTOBJS = mycgio

support

1) TCPIP networking

3) IP DHCP support

4) IPBOOTP

5) IPRARP

2) RTL8019AS

and check

1) Boa

2) dhcpcd-new

3) dhclient

4) ifconfig

5) inetd

6) ping

8) route

9) routed

10)telnetd

ll)tftpd

terminal

for Linux machines

machine)

go 0x0c008000

RRMboot 182 (Aug 12 2084 - 104321)

bulltrade u u mdash

1 000 netmask 2552552550 lo

77 Testing

771 Test Procedure

(PC Linux machine)

Figure 722

D Graquo S S if

5fw help

following command

1 9 2 1 6 8 0 8 o p t t e s t v a r t m p

| g haanhoan ~

0JS packet loss

controllerhtmlgt

$01 C s- J http1921680^

Run Reset

adap t i vecamro l

13S3603 6682830

6258383

1393689 -8pound62298 B JhK-iH-)

-6239783 6626603

666G855

-9259783 -0629683 H HHI-li4s

Gsxgte i

efk-Dpl =

e(k-l) p2 =

ucfk-ljk =

uc(k- l ) p l

uc(k-l) p2

thik-lj k =

th ik - l j th l

th ik- l ) th2

th(k- l ) th3

thk- l ] th4

thk- l ) th5

thfk- l j th

amp c l

= 50000

=10000

= 66000

= -309998

= 1 0 4 4 2 2 5 4

= -42712

= 4240

ITtdlk^ Turlb

o Htp iH9i

| IG^Search

16S0 1

raquo bull zfgt

b i r p

ycqr u

^Settings

772 Test Results

in Table 73

File name

t_xdat

t_xmdat

t_edat

t_ucdat

t_udat

t_thetadat

t_ydat

t_ymdat

Data description

000000

-000521

-000667

-000817

-000764

-000770

-000815

-000738

-000650

-000665

-000641

-000623

-000645

-000594

-000587

-000551

-000514

-000587

-000641

000000

-000037

-000151

-000291

-000447

-000580

-000713

-000862

-000986

-001091

-001202

-001313

-001403

-001503

-001586

-001667

-001748

-001817

-001903

000000

-000523

-000687

-000730

-000731

-000719

-000702

-000685

-000669

-000652

-000637

-000622

-000608

-000595

-000582

-000569

-000558

-000546

-000536

000000

-000039

-000153

-000289

-000427

-000563

-000693

-000817

-000936

-001049

-001158

-001261

-001359

-001453

-001543

-001628

-001710

-001788

-001862

-000522

-000480

-000564

-000550

-000539

-000547

-000528

-000496

-000503

-000430

-000472

-000441

-000491

-000511

-000390

-000446

-000383

-000369

-000381

-000435

-000441

-000439

-000447

-000373

-000418

-000404

-000373

-000440

-001982

-002051

-002115

-002190

-002251

-002311

-002367

-002427

-002476

-002525

-002558

-002603

-002641

-002687

-002732

-002756

-002781

-002813

-002832

-002862

-002894

-002916

-002952

-002980

-002995

-003014

-003035

-003052

-000526

-000516

-000507

-000498

-000489

-000481

-000474

-000466

-000460

-000453

-000447

-000440

-000435

-000429

-000424

-000419

-000414

-000410

-000405

-000401

-000397

-000393

-000390

-000386

-000383

-000380

-000377

-000374

-001933

-002000

-002065

-002126

-002185

-002241

-002294

-002345

-002394

-002440

-002484

-002526

-002566

-002605

-002641

-002676

-002710

-002741

-002772

-002800

-002828

-002854

-002879

-002903

-002926

-002948

-002969

-002989

-000453

-000436

-000385

-000428

-003078

-003109

-003139

-003161

-000371

-000369

-000366

-000364

-003007

-003025

-003043

-003059

-0 025

_ m _ _ ^ i = _ mdash p i r r F ^

~~-ti ===ii

-mdash^zr ~~ i

2(enfc) -

-00006

-00009

-00011

-00008

-00001

-00004

-00008

-00001

-00002

-00005

-00004

-00005

-00004

-00008

-00001

-00002

-00003

-00002

-00003

-00002

-00003

-00002

-00001

-00002

-00010

-00009

-00001

-00009

-00006

-00005

-00001

-00008

-00013

-00002

-00004

-00007

-00014

-00006

-00007

-00001

-00010

-00003

-00004

-00005

-00003

-00004

-00002

-00001

-00002

-00001

-00002

-00003

-00005

-00006

-00008

CHAPTER 8

81 Conclusion

82 Future Work

xv2 r~

PILOT PLANT

Realtime (lata

D Xbdquo

B xbdquo

PE -W-V2

fc V -tvi

PILOT PLANT

PID Embedded

Adaptive Ccntroller

Online measurement

Hyperterminal

reg Spf M -amp- 1

i KZ- ^ -n

REFLUX DRUM

A 12 Vent-bleed

CONDENSER^-

mdash 4 6

i mdash amdashgtp j

Inert gas O

mdash m ltV3

i te i iaal

J5) Input ho-ot IS)

B - t-t

a) Kettle type

o h m m I K I

i t t_e i i - 1 1

-amp Q

_ U ftau irav

P| vopor flow

V U heat -

exchanger

A WH-J

have been specified

degrees of freedom

Column pressure

Manipulated

variables

Reflux flow rate

Reboiler duty

Condenser duty

Bottoms flow rate

Control valve

location

Reflux flow (VI)

Heat flow (V4)

Coolant flow (V3)

Bottoms flow (V5)

Control Structure

D-V(or D-QB)

L-V(or L-QB)

Role of valve

Inventory

Control (IC)

Separation

Control (SC)

structures

units in the plant

flow rate B

I raquo - sect I -

ATbdquo

are switched

H amp J bull

Component

Propane

Normal Butane

Isobutane

Isopentane

Normal Pentane

Hexane

Heptane

Octane

Nonane

Normal Decane

n-CHH24

n-C12H26

Cyclopentane

Methylclopentane

Benzene

Toluen

O-Xylene

E-Benzene

Cut point

(degC)

ASTM D86

(degC)

124024

Properties

1 Octane Number

2 Lead Content (g1)

10 vol

50 vol

90 vol

Residue ( vol)

Testing method

ASTM D2699

ASTMD3341

ASTM D86

ASTM D130

ASTMD381

ASTM D323

ASTM D1266

ASTM D525

ASTMD1298

Requirements

min 87

max 015

max 70

max 120

max 190

max 210

max 20

maxN-1

max 40

min 43

max 80

max 015

min 240

070 - 074

capacity

tso (TBP) = 5842 C

t(30- io) (TBP) = 3599-2467=1132 degC

t50 (EFV-TBP) = 1-5 C

Therefore

tso (EFV) = 5842+15=5962 degC

EFV (1 atm)

EFV (46 atm)

20 3840 60

Volume

80 100

B31 Description

B32 Calculation

fegtegtd f l ow

tray f

Rf= B-LF+ Vf= 62 - 58 + 28 = 32 vol

Stream

Total light

fractions E S D

Bottoms B

Volume fraction

Liquid flow rate

-73916

133973

-64677

143213

Liquid density

Mass flow rate

-45458

-38677

104046

B41 Description

B42 Calculation

stripping section

kcalkg

kcalhlOJ

kJhl0 j

276860

131300

408161

kcalhlOJ

149134

kJhl0J

267136

357141

624280

B51 Description

reflux flow

B52 Calculation

46degC

Stage 15 (tray 14)

D Distillate

9611+Ro

kcalkg

ZSD+Ro

5065+Ro

9611+Ro

kcalkg

kcalhlOJ

11053+24 R0

kJhlOJ

1005 R0

46263+1005 R0

kcalh103

49131+97Ro

56405+ 97R0

kJhl0J

205665+406R0

236111+406R0

46263+1005 Ro= 236111+406 Ro

Therefore

Ro= 7415 (tonh)

at the column top)

AHRoR0= AHLL

(115-24) (742) = (106-22) I

Therefore

L = 804 (tonh)

Stream

Temperature (C)

Pressure (atm)

Density (kgm )

Stream

Temperature (C)

RVP (kPa)

Density (kgm )

Condensate

130000

Reformate

105000

Raw gasoline

Gasoline

250000

Condensate bull

bullff

Raw Gasoline

amp V - 0 1

PEF l l OPUH

-Gasoline

GSSOLINE MIXER

gasoline

is 128degC

tankers

B74 Feed Control

46 atm

i T C - 1 r

mdashImdash I

--copy

l-MmdashJ

To Column

B76 Bottom Section

Cl Introduction

linear

outlet weir

Mbdquo = f(LJ (Cl)

C21 Generic Trays

equations

d(Mbdquo)

Liquid

Flow rate

vbdquo Vn

Concentration

staae n

dh dMbdquo x = A-

dLbdquo dL (C4)

d(Mbdquoxbdquo) dt

dt Mbdquo (C6)

d(Mnhn) dt

V = H-h

C22 Feed Tray

stage (feed tray

LfXrbdquo

I-v vgt LrXf

d(Mfxf)

dt Mbdquo

d(Mfhf)

C23 Top Section

Vlaquobdquo

11 V M1

vbdquo

d(MN+l) _ (C 13) dt

d(M XN+])=Lx^ + y L _ y ( C 1 4 )

11 N+ nN+

C24 Bottom Section

l I l I

ltHXr-B x F

d(M2) dt

L3-L2+ VB -V2

dMRhB) dt

= 23Z3 +HBVB- h2L2 - H2V2

Therefore

H2 -h2

be neglected

dMB) = L 2 _ V B B ( C 2 3 )

d(MBhB)

4 Simplified Model

yn = r (C27)

+ (a-l)xbdquo

aZyv+2 = dL)

L2= LT~ = LN+2-

equations [12]

5) Tray n(n = 2 - l)

MBX] =(L + LF)X2 - Vy - fix (C33)

1) LF=qFF

2) VF = F-LF

y = r bull (C35)

1 + a - )Xj

A = 730 (kJkg)

V0= 39098 (kgh) or 668871 (kmoleh)

V = 0+ = 663407 (kmoleh)

Joshi [43]

ffl^^M (C38)

314(175X1-4) Z ^ = 2488 (kmole) B 4 786

t 0957chD2k dr

095(314)(028)(175)2 680 M = = 580 (kmole)

MD = 5iL + D) (C41)

flow rate

follows

Tray 5 (n = 6) M6 = F(^5 - y6) + (Z + LF )(x7 - x6)

Tray 3 (n = 4) M4 = F(^3 - gt4) + (Z + ZF )(x5 - x4)

2488 (kmole)

1403 x16 =1646291 y]5 - 756380x6 -927597x6

58x15 = 1646291(y14 -y ] 5) + 756380(x6 -x l 5)

58x4 = 1646291(73-gtgt4) + 756380(x5-x4)

58x13 = 1646291(712 - yn) + 756380(xl4 - x13)

58x12 =1646291(j |l-j12) + 756380(x13-x12)

58 = 1646291(710 -yu) + 756380(x2 -x )

58x0 = 1646291(79-^0) + 756380(x-x0)

58x9 = 661 39ys -15638gt-9 + 756380(xl0 -x 9 ) + 5995

58x8 = 661139(y7 -ya) + 756380 x9 - 18859x8 + 3399

58x7 = 661139(y6-y7) +179887 l (x 8-x 7)

58x6 = 661 39(y5-y6) + 179887 l (x 7 -x 6 )

58x5 = 661139(j4 - y5) +1798871 (x6 - x5)

58x4 =661139(^3 -yA) + 79887 l (x 5-x 4)

58x3 = 661 139(^2 - y 3 ) + l798871 (x4 - x3)

58x2 =661139(j -y2) +1798871 (x 3 -x 2 )

2488x = 1798871 x2 -1109235x -661139^ (C42)

568x y ~ l + 468x

y2 = 568x2

1 + 468x

^ 1 5 =

l + 468x (C43)

bullCO

laquo r M |

raquo ^ SA 11 j

w r n i |

^ ltgt fM f 3 1

ET mAr pound |

~^ IT JWi a mdash i

Cgt $ IZ

1 ma r ii |

P $ mar t |

ET r Jfifl V 3 1

b $ TWVlP 2 1

J ^ m d If f |

WFYMtG

fiterttxm

STRIPPING SECTION

GENERAL TRAY

COLUMN

1 TRAY 7

1 TRAYS

RECTI FYINO SECTION

GENERAL TRAY 1

Figure D3

- w i 13411

~W 46804

RECTIFYING SECTION

mdash bull In2 Out2

STRIPPING SECTION

bull XD

To Workspacel

-4L Scope 1

Raw Gasoline

bull | xB

To Workspace

H Scope

In20ut2

Inl O u l l M

In 2 Ou2t

Tray 14

bull i n l Out1 |

- W i n 2 Oul2|

Tray 13

In 10ut 1

In20ut2

Tray 12

bull In lOu t l

In20ut2

Tray 11

InlOutl

In20ul2

Tray 10

bullNln20Ut2

Tray 9

l j mdash

~2~gt -In2

bull in 2

Tray 8

x 1 bull Outl

bull - K 2 Out2

_2 mdash

f bull

n 1 n n H I Wgt A

In 2 Ol l t l

Tray 7

mdash bull

In 10ut1

In20ut2

Tray 6

- gt In20ut2

Tray 5

In lOut l -

bull ln20ut2

Tray 4

bull in lOut l

1 bull

In20ut2

Tray 3

In lOut l

In20ut2 [

Tray 2

[ bull

In lOut l H

In20ul2 |

1 Tray 1

__ Out1

bull In1

Out2 -gt lt_2_gt

O bull72302

471 r Integrator 2

bull XI

To Workspace2

Scope 2

K 2 Olit2

2T899 ^ Function

VLE equation

GENERIC TRAY n

V bull L(n+1)Mn

In2 _ - -

A i bull

-bull VnMn

bull 1 integrator 2

y lt bull

V IE equa Son

bull xn

To Workspace2

bullbull bull -

Scope xn

TRAY 7 (Stage n -8)

bull 3 gtbull

bull 1

( 2 in2

IH130410 ~gt-

bull 119679

bullbullyenbullbull

y- Integrator 2

VLE equation

To Workspaces

Scope 2

gt bull

1 lHn0410

bullbullbull xS

To Workspace

2 bull 119879 In2

Outl bull bull I

289533 N

li integrator 2

130410

Function

MATLAB Fen 2

bull gt bull bull

Scope2

( 1 In2

119666 1 I s J

Integrator 2

120027 K

Scope 2

inputs

M M n+ Mbdquo

-X (El)

= = V15= F+ VF = V+ 985152

Vw = l 15 (E2)

X = f(Xut)

dX = X-X

du = u - u

dX df] _lt3x_

dX + 8f] _du_ du

Mn Mn Mn Mn

Mn +1 Mn +1 Mn Mn

T T -t- V V K V

i ( 0 = Ax(t) + Bu(t) (E4)

y(t) = Cx(t) (E5)

follows

L ==LS = 1798871 (kmoleh)

L9 = = Z15= 756380 (kmoleh)

V = = V = 661139 (kmoleh)

V9 = = V]5 = 1646291 (kmoleh)

M2 = M3 = = Mi5 = 580 (kmole)

M16 = MB = 2488 (kmole)

_KK _ (L]+K2V) _ L 21 M2

22 M2 23 M 2

1) Collect data

w = 1 ^ 1 = 7 Z 6 i 2=TT

w =2 h _xlZx2) _-fe-i) 2 J ~ M2 2lt2~ M2

laquo - 1 6 66gti = 6 ft162 ^ 1 6

_ K M16

[00012 00063 00091 00098 00076 00044 00022 00021 00048

00111 00216 00306 00285 00178 00086 -00702

-00024 -00157 -00237 -00254 -00196 -00116 -00058 -00027 -00024

-00050 -00097 -00138 -00128 -00080 -00039 00704]r

C = 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

E2 Stability Test

V(x)=xTPx (E6)

ATP + PA = -I (E9)

positive definite

P = lyap(AI)

for i=l16

Pi = P (1 i 1 i)

det(Pi)

d e t ( P l ) = 0 0 3 2 8 3 1

d e t ( P 2 ) = 0 0 0 0 9 0 8 4 9

d e t ( P 3 ) = 2 4 4 4 3 e - 0 0 5

d e t ( P 4 ) = 5 5 4 7 6 e - 0 0 7

d e t ( P 5 ) = 1 0 1 5 2 e - 0 0 8

d e t ( P 6 ) = 1 6 2 0 8 e - 0 1 0

d e t ( P 7 ) = 2 3 0 2 5 e - 0 1 2

d e t ( P 8 ) = 2 6 1 8 3 e - 0 1 4

d e t ( P 9 ) = 4 1 9 5 9 e - 0 1 6

d e t ( P l O ) = 1 2 8 8 6 e - 0 1 7

d e t ( P l l ) = 6 7 8 4 7 e - 0 1 9

d e t ( P 1 2 ) = 3 9 1 6 e - 0 2 0

d e t ( P 1 3 ) = 1 8 3 0 8 e - 0 2 1

d e t ( P 1 4 ) = 7 0 8 9 e - 0 2 3

d e t (P15) = 2 4 8 7 6 e - 0 2 4

d e t ( P 1 6 ) = 8 4 6 1 2 e - 0 2 6

stable

include ltstdlibhgt

using namespace std

if(k = x_kmlk+l)

stampn)

if(k = e_kmlk+l)

stampn)

if(k = uc_kmlk+l)

stampn)

return

th kk = k

b21e_kmlp2)x_kmlp2

b22e_kmlp2)x_kmlpl

b22e_kmlp2)x_kmlp2

b21e_kmlp2)uc_kmlpl

b21e_kmlp2)uc_kmlp2

b22e_kmlp2)uc_kmlpl

b22e_kmlp2)uc_kmlp2

r e t u r n

F2 Plant Model

include ltstdlibhgt

include PlantModelh

using namespace std

PlantPlant()

all = -67941 + 067(rand()2-05)

al2 = -09095 + 009(rand()2-05)

a21 = 14686 + 015(rand()2-05)

a22 = -02497 + 002(rand()2-05)

bll = -01461 + 0014(rand()12-05)

bl2 = 02073 + 002(rand()2-05)

b21 = -00021 + 00002(rand()12-05)

b22 = -00281 + 0003(rand()2-05)

ell = -00624 + 0006(rand()2-05)

cl2 = -00281 + 0003(rand()2-05)

c21 = 02458 + 0025(rand()2-05)

c22 = 00009 + 000009(rand()2-05)

Plant~Plant ()

if(k = u_kk)

this-gtu_k = u_k

this-gtx_k = x_k

return

bl2Tu_kp2

b22Tu_kp2

x_kplk = k+1

r e t u r n

F3 Reference Model

include ltstdlibhgt

using namespace std

RefmdlRefmdl()

Refmdl~Refmdl()

if(k = uc_kk)

stampn)

this-gtuc_k = uc_k

if(k = xm_kk)

stampn)

this-gtxm_k = xm_k

return

xm_kplk = k+1

return

include ltstdlibhgt

using namespace std

Linctrl Linctrl()

Linctrl -Linctrl ()

time stampn)

this-gtth_k = th_k

time stampn)

this-gtuc_k = uc_k

time stampn)

this-gtx_k = x_k

return

- th_kth2x_kp2

- th_kth4x_kp2

u_kk = k

return

F5 Comparator

include ltstdlibhgt

include Comparatorh

using namespace std

this-gtx_k = x_k

this-gtxm_k = xm_k

return

compute errors

e_kk = k

r e t u r n

include ltstdlibhgt

using namespace std

stampn)

this-gtx_k = x_k

return

y_kk = k

return

include ltstdlibhgt

using namespace std

time stampn)

this-gtxm_k = xm k

return

ym_kk = k

ym_kpi = ym_kpi

ym_kp2 = ym_kp2

r e t u r n

F8 CGI Program

inc lude ltctypehgt

include

lterrnohgt

ltstringhgt

ltstdiohgt

ltunistdhgt

ltfcntlhgt

ltstringhgt

ltsyssockethgt

ltsystypeshgt

ltnetinetinhgt

ltarpainethgt

define LINELEN 1024

struct valinfo

unsigned char name

unsigned char text

struct thetaPkt

struct Pkt

int pi

int p2

static

amll =

ami 2 =

am21 =

am22 =

bmll =

bml2 =

bm21 =

bm22 =

cmll =

cml2 =

cm21 =

cm22 =

all = -

al2 = -

a22 = -

bll = -

-67 94

static

= -510

= -310

= 1044

= 1006

static int nvals=0

if (gotvals)

nvals = getvals()

gotvals = 1

)vals[i]name)==0)

return vals[i]text

return NULL

=============== httpunescape ===========

unsigned char siptr

unsigned char soptr

unsigned char sos

(unsigned char) )

soptr = sos

siptr = sis

while (siptr)

if(siptr == )

int c = 0 i

for (i=0ilt2i++)

siptr++

c = claquo4 + h

if (i = 2)

free(sos)

return NULL

soptr++ =

soptr++ = siptr

siptr++

soptr = 0

free (sos)

return sis

=============== hextobin =================

if(isdigit(c))

return c-0

return -1

=============== getvals ===================

int vent = 0

unsigned char vstr

unsigned char vptr

unsigned char eptr

unsigned char aptr

int 1 cl

return 0

if(vstr == NULL)

return 0

if(vstr[l-l] == n)

vstr[l-l]=0

vptr = vstr

while (vptr)

vcnt++

valinfo))

vptr = vstr

for (i=0iltvcnti++)

if (eptr == NULL)

return 0

eptr = 0

if (aptr)

aptr = 0

vptr = aptr+1

return vent

unsigned char c

unsigned char cs

int fd len

if((fd==-l))

exit (1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== write signals ===================

unsigned char c

unsigned char cs

int fd len

if((fd==-l))

exit(1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== write a signal ===================

unsigned char c

unsigned char cs

int fd len

if((fd==-l))

exit (1)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== getsignal ===================

int fn s i m sn 1

unsigned char buf

if(fn==-l)

exit(1)

return

read(fn buf 20)

signal = s

free((void) buf)

close(fn)

return s

=============== get ascii signal ===================

int fn s i m sn 1

unsigned char buf

if(fn==-l)

exit (1)

return 0

read(fn buf 20)

signal = s

free((void) buf)

close(fn)

return 1

=============== settime ===================

int t=0

unsigned char c

unsigned char cs

int len

if((f==-l))

exit(l)

write(f c len)

write(f t 1)

free((void) c)

free((void) cs)

close (f)

return

=============== Wait ===================

int i=0

while(i++ltn)

=============== gettime ===================

clear signals

kT = k

Write to files

return

=============== clear signal ===================

int fn

if(fn==-l)

exit(1)

return

write(fn20)

close(fn)

return

unsigned char ch

if (xl==0)

ch[0] = 0

len = 1

if(xllt0)

xl = -xl

sign[0] = -

sign[0] = +

while(xlgt0)

ch[i] = 0 + xl10

xl=xl10

len=i+l

for(i=0 iltlen i++)

free((void) ch)

return

=============== getAdapMechPkt ===================

th4 th5 th6 th7 th8

int outfile

Receive signals

getsig

vartmpfuc2

vartmpfkth

vartmpfthl

vartmpfth2

vartmpfth3

vartmpfth4

vartmpfth5

vartmpfth6

vartmpfth7

vartmpfth8

ampuc2)

ampkth)

ampthl)

ampth2)

ampth3)

ampth4)

ampth5)

ampth6)

ampth7)

ampth8)

receivedlth3gtn)

printf

ltpgt ucl

ltpgt uc2

ltpgt thl

ltpgt th2

ltpgt th3

ltpgt th4

ltpgt th5

ltpgt th6

ltpgt th7

ltpgt th8

d) = dn k-1 ucl)

d) = dn k-1 uc2)

d)k = dn k-1 kth)

d) = dn k-1 thl)

d) = dn k-1 th2)

d) = dn k-1 th3)

d) = dn k-1 th4)

d) = dn k-1 th5)

d) = dn k-1 th6)

d) = dn k-1 th7)

d) = dn k-1 th8)

x_kml-gtk = kx

x_kml-gtpl = xl

x_kml-gtp2 = x2

e_kml-gtk = ke

e_kml-gtpl = el

e_kml-gtp2 = e2

uc_kml-gtk = kuc

uc_kml-gtpl = ucl

uc_kml-gtp2 = uc2

th_kml-gtk = kth

th_kml-gtthl = thl

th_kml-gtth2 = th2

th_kml-gtth3 = th3

th_kml-gtth4 = th4

th_kml-gtth5 = th5

th_kml-gtth6 = th6

th_kml-gtth7 = th7

th kml-gtth8 = th8

Write to files

return

=============== genAdapMechPkt ===================

th k-gtk = k

Write to files

return

=============== main ============

main ()

int valid

int stime gamm

int i=0

int k kT

int kmax=2

struct Pkt x_kml

struct Pkt e_kml

struct Pkt uc_kml

int getkt=0

int getkmax=0

ltheadgtn)

while(getkmax)

wait(5000)

while(klt kmax)

signalsn)

while(Igetkt)

wait (5000)

while(k=kT)

wait(10000)

signalsn)

gainsn)

ampth_k)

exit (0)

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in Table G2

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7500000

7600000

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7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

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9800000

9900000

10000000

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0000223

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0000396

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0000289

0000330

0000335

0000281

0000381

0000456

Adaptive Gains

0000000

0100000

0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

1100000

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1400000

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2000000

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0000000

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0000000

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0000000

-0000386

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2100000

2200000

2300000

2400000

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3000000

3100000

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4800000

4900000

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5100000

5200000

5300000

5400000

5500000

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5800000

5900000

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6200000

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6500000

6600000

6700000

6800000

6900000

7000000

7100000

7200000

7300000

7400000

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7500000

7600000

7700000

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

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-0033668

in Table H2

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1200000

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2100000

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4900000

5000000

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7000000

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10000000

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H3 Plant Error

0000000

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7800000

7900000

8000000

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9000000

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9900000

10000000

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-000100

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-000101

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-000089

-000105

-000097

-000108

H4 Adaptive Gains

e 03716

-05106

-03100

-00427

-00428

-05106

-03100

-03099

-00428

-05106

-03099

-03098

-00428

-05106

-03098

-00428

-00429

-00428

-00429

-00428

-00429

REFERENCES

Hungary vol 3 pp 1719-1724 1984

563 May 1989

Hall 1984

orgwikiMATLAB

Press 1999

McGraw-Hill 1981

2002 pp 4003-4008

6 pp 1169-1175 Dec 1982

e_Diagrampdf

Prentice Hall 1997

University 1990

Hill 1984

India 1979

SJSU ScholarWorks

Fall 2009


Hoan The Nguyen



by Hoan The Nguyen

mdashr ~ mdash^ yy

ABSTRACT

by Hoan The Nguyen

ACKNOWLEDGMENTS

people

TABLE OF CONTENTS

List of Tables xiv

List of Figures xvi

11 Background 1

15 Methodology 5

28 ARM Processor 16

31 Introduction 20

41 Introduction 26

441 Plant 31

51 Introduction 43

521 Plant Model 44

61 Introduction 50

71 Introduction 66

751 CGI Program 78

77 Testing 93

772 Test Results 98

81 Conclusion 104

82 Future Work 105

A12 Vent-bleed 110

B31 Description 124

B32 Calculation 125

B41 Description 126

B42 Calculation 127

B51 Description 128

B52 Calculation 129

Cl Introduction 137

C22 Feed Tray 140

C23 Top Section 141

F2 Plant Model 170

F5 Comparator 173

F8 CGI Program 175

G3 Plant Error 206

H3 Plant Error 222

References 230

LIST OF TABLES

LIST OF FIGURES

Motor octane number

Network file system

Personal computer

Reid vapor pressure

True boiling point

Zero-order hold

LIST OF SYMBOLS

A State matrix

B Input matrix

C Output matrix

e State error

L Feedback matrix

u Control signal

x State variable

y Controlled output

Greek Symbols

y Adaptation rate

0 Adaptive gain

Subscript

B Bottom product

F Feed

m Reference model

CHAPTER 1

INTRODUCTION

11 Background

time spaces

adaptive controller

mathematical method

15 Methodology

CHAPTER 2

LITERATURE REVIEW

RECTIFYING SECTION

F (feed flow rate)

Q n I (3) CONDENSER

1 8 - D

stage f (feed tny)

stage rc

Material stream

Feed stream

Distillate stream

Bottoms stream

Position

Stage f

Stage N

Reflux drum

Stage 1

Reboiler

Flow rate

Concentration

in Figure 22

Liquid phase

Stage it

(Trav gti-l)

bull bullbullbull

m^u - Bubble cap

structures

I |mdash0mdashI I

bottoms flow rate B

are adjusted [12]

required

Command_ signal

Adaptive mechanism

laquosj

Control signal

Plant 1 Output

Process dynamics )

Siv-CSnftlteF----

26 Adaptive Schemes

261 Gain Scheduling

Command signal

Output

signal

MoctSI

Control signal

mechanism

Plant -bull Output

= ( ) bull (21)

disturbances or not

- mdash

yfdx dt

x = 0 i

-gt() =

= = ( ) = -W(x) (22) dt dx dt dx

dx mdash = Ax (23)

ATP + PA=-Q (24)

following function

V(x) = xTPx (25)

28 ARM Processor

DB-9 DB-9

RS-232

Features

Memory

subsystem

GPIO ports

Ethernet

Descriptions

solution

8 memory banks

by RAM

CHAPTER 3

31 Introduction

RffLlrtERLMl

xD gt 98

xB lt 20

Table 31

Temperature C

Pressure atm

Density kgm3

Mass flow rate kgh

Main streams oft

Condensate

130000

he plant

Raw gasoline

system

35 Plant Modeling

1403 x16 =1646291^15 -756380x16 -927597xI6

58x15 =1646291(gtl4 -^1 5) + 756380(x16 -x15)

58x14 =164629103 -gtgt14) + 756380(x15-x4)

58x13 =1646291012 -_y]3) + 756380(x14 -x13)

58x12 =1646291(^n -y1 2) + 756380(x13 -x ] 2)

58xH =164629IO10 ~ ^ i ) + 756380(x12-x)

58x10 =164629109 -^1 0) + 756380(xn -x10)

58x9 = 661139gtgt8 -15638^9 + 756380(x10 -x9) + 5995

58x8 = 66113907 ~yamp) + 756380 x9 -18859x8 + 3399

58x7 = 661 39(y6-y7) + 798871 (x8 -x 7 )

58x6 =66113905-gt 6) + 1798871(x7-x6)

58x5 =66113904^) +179887 l (x 6 -x 5 )

58x4=66113903-^4) + 1798871(x5-x4)

58x3 =66113902-73) +1798871 (x 4 -x 3 )

58x2 =661139(^-gt2) +179887l(x3-x2)

2488x = 1798871x2-1109235x1 -661139^

568x y = l + 468x

l + 468x

^ 1 5 =

568x 15

l + 468xbdquo (34)

CHART OF VAPOR

01 02 03 0 4 05 06 07 08 09

36 Plant Simulation

Table 32

bull L _ I i 1 l

6 8 10 12 14 16 18 20 Time (h)

than 2

CHAPTER 4

41 Introduction

and (32)

Disturbances

Ditiilitirn Gy-tem

x(t) = A(xt) + Beu(t) (41)

y(t) = Cex(t) (42)

two-output system

-09095

-02497 Bbdquo

-01461 02073

-00021 -00281 and C

-00624 -00281

02458 00009

Bode Diagram

Frequency (radsec)

431 Stability Test

finite time T-tgt0

x = Ax(t) + Bu(t) (45)

y(t) = Cx(t) + Duy) (46)

full rank of n

output

S=[CCACA2CA]]T

the next section

441 Plant

yt) = Cx(t)

where A = au

an_ B =

bn_ and C =

-00624 -00281

02458 00009

variables

442 Reference Model

Sec 43

where Abdquo

ybdquo(t) = cmxm(t)

-67941 -09095

14686 -02497

5 = -01461 02073

-00021 -00281 and Cbdquo

-00624 -00281

02458 00009

ut) = Muct)-Lx(t)

x = (A- BL)x + BMuc

hence we define

Ac(0) = (A-BL)

Bc6) = BM

i2 ~b2

l 2 11^2 ^12^4

22 _ ^ 2 1 ^ 2 ~ ^ 2 2 ^ 4

b2]65+b2281 b2Xdb+b22d (412)

condition we get

au-bu6-bnel =-67941

an -bu6a2 -bn6deg4= -09095

a2]-b2]6deg-b220deg =14686

a22-b2]e2-b229deg= -02497

6Adeg + M7deg =-01461

606deg + 6 X =02073

b2l6deg5+b229deg =-00021

b2]edeg6+b226degs =-00281 (413)

condition

0 _ b22(au +67941)-bu(a2] -14686) 0 =

regp22 ^12^21

a o _ b22(an + 09095)-bn(a22 +02497)

^11^22 _ ^12^21

buo22 mdashbnb2]

0 _ -b2](a]2 + 09095)+ bu(a22 +02497) 6gt =

bP 22 b]2b2]

-b2]bn+bub22

n0 002816I2+02073Zgt22

(J6 = -b2]bu+bub22

_0 - 000216+ 0146 b2x Uf =

-b2]bu+bub22

0 = 002816 +020736

-b2Xbu+bxxb (414)

Error Equation

e(0= x(0-m(0

e() = ^ ( 0 + 5 i ( 0 - ^ I B ( 0 - 5 m laquo c ( 0 - (4-15)

e(t) = Ame(t) + V(t)(0-O0) (417)

446 Adaptation Law

function

V(e 0) = [yePe + (0 - 0deg f (0 - 0deg)) (418)

(420) dt 2

ltP + PAm = -a (4-21)

^ = -W(t)Pe(t) at

y(buex+b2Xe2)xx

y(buex+b2]e2)x2

y(bnex+b22e2)xx

y(bx2ex+b22e2)x2

-y(bxxex+b2xe2)ucX

-y(bxxex+b2Xe2)uc2

-y(bX2ex+b22e2)ucX

-y(buex+b22e2)uc2

6 = (423)

mdash = -05591lt -07066e2)2 +132756e2] dt 1

2) Disturbances^)

4) Reference model

a n n f l

REFERENCE MODEL

dull In I

0ut2 In2

ADAPTIVE MECHANISM

= X Xm

_X2 Xm2 _

follows

e = RMS(e) = -^A for = 1 or 2

commands

norm_el = norm(el)

norm_e2 = norm(e2)

shown in Figure 46

m B s in

Figures - x vc xm

m B ampm

bull4s

bullraquo i x

i m B raquo bull

im B ffin

State error e1(t)

State error e2(t)

e = 00017

n2 VTooT = 7106210

453 Error Reduction

Plant errors

laquoi

Adaptation rate y

54304 105

71399105

5428410

7106210

54076 105

7100310-5

CHAPTER 5

51 Introduction

G(s) y ( t

521 Plant Model

x(t) = Axt) + But)

y(t) = Cx(t)

x(s) - ~[AX(S) + Bu(s) s

T x(z) = [AX(Z) + Bu(z)]

y(kT) = CxkT) (52)

522 Reference Model

in Chapter 6

ybdquo(t) = cmxm(t)

where Am = [-67941 -09095 14686 -02497] Bm = [-01461 02073 -00021 -00281]

and Cm = [-00624 -00281 02458 00009]

follows

ut) = Muc(t)-Lx(t)

L = 0kT) 62(kT)

0(kT) 0AkT

M 05(kT) 06(kT)

87(kT) 0s(kT)^ (56)

o _ ft2deg2(adeg +67941)-ft02(a20 -14686)

degdeg27 deg12deg21

8 0 _ -amp2 K + 67941) + ft (a2] -14686)

ftdeg =

00021ft0-01461ft0 22

-ft21 f t02+ft0 f t22

-b2]b]2+bub22

-b2bn+bub22

n0 00281ft+02073ftdeg

201 deg]]deg22

6(t) = -y^(t)Pe(t)

= yy (s)Pe(s)

CHAPTER 6

61 Introduction

2) Disturbances^^

reference signals

1 tnl uc(k)

In2 uc(k-1)

xm(k-1)

laquogt

REFERENCE MODEL

H Disturbances

bulleurogt

[B^_]M

0ut1 In)

0ut2 In2

i f MJi-1)

0 u ulaquoK-l)

ADAPTIVE MECHANISM

m lt raquo

Ot-1) Mux bull

e(kT) = exkT)

e2(kT)

h(kT)-xnnkT)

x2(kT)-xm2(kT)_

Ax^kT)

Ax2(kT)

follows

e = RMSe) = ^L for = 1 or 2 (61)

shown in Figure 62

Disturbance f(t)

m gt P i laquo ^ e

a)e(7)

ns gt P l

a) eiikT)

I U I 94543e-004 _ bdquo ^ - s

101 = 9407410-

M = 9 6557e -Q04 = 9 6 0 7 8 t l 0 5

4n2 vioi

sections

in Figure 66

4 include tbdefsh

5 class Plant

6 private

12 public

13 Plant()

14 -Plant()

18 endif

P l a n t ( )

a l l = - 6 7 9 4 1 + 0 6 7 ( r a n d ( ) 2 - 0 5 )

a l 2 = - 0 9 0 9 5 + 0 0 9 ( r a n d ( ) 2 - 0 5 )

a21 = 14686 + 015(rand()2-05)

a22 = -02497 + 002(rand()2-05)

bll = -01461 + 0014(rand()2-05)

bl2 = 02073 + 002 (rand()2-05)

b21 = -00021 + 00002(rand()2-05)

b22 = -00281 + 0003 (rand()2-05)

ell = -00624 + 0006(rand()2-05)

cl2 = -00281 + 0003(rand()2-05)

c21 = 02458 + 0025(rand()2-05)

c22 = 00009 + 000009(rand()2-05)

4 include tbdefsh

5 class Refmdl

6 private

7 Pkt uc_k

8 Pkt xm_k

9 public

10 Refmdl()

11 -RefmdlO

15 endif

Figure 68

4 include tbdefsh

5 class Linctrl

6 private

7 thetaPkt th_k

8 Pkt x_k

9 Pkt uc_k

10 public

11 LinctrlO

12 -LinctrlO

16 endif

database

4 include tbdefsh

5 class Comparator

6 private

7 Pkt x_k

8 Pkt xm_k

9 Pkt e_k

10 public

11 Comparator()

12 -Comparator()

16 endif

and the plant

4 include tbdefsh

6 private

7 thetaPkt th_kml

8 Pkt x_kml

9 Pkt e_kml

10 Pkt uc_kml

11 public

12 AdaptiveMechO

13 -AdaptiveMechO

17 endif

model and the plant

CC = g++

ReferenceModelo

executive file

j haut$ttum

ltOIgt gtiJ^Alt

plusmn1 f bull-lt

i gt bulli

lt euro f bull2

[ bull

- H J bullbull -

~ttttfc

bull=fmdashF^--

^ t ^ i i i = ^ ^

_ - 1 1 = - mdash J

^ J - - - ^ ^

1 1 1 I

5 time

e = |N| s94543c-004 ^

96557e-004

VToi = 96078 105

CHAPTER 7

71 Introduction

shown in Figure 71

_ Data J

5gt I Error

yV H Report

Plant Slmsliitsr

lt = J Output

Linux yacnine

RPC get_port reply

RPC mount request

RPC mount reply

Authenticate client

to the browser

button

lUser sufrmis fwm

arv-affe ie Camp

vas tor PlssrtSwi

Sens ( to i l sA i

(J 0 0

SefieJ acispfcw BM2

Oylpaito wefccfer

72 Common Database

File name

kucdat

ucldat

uc2dat

kthdat

thldat

th2dat

th3dat

th4dat

th5dat

th6dat

th7dat

Data description

Plant state xi

Plant state X2

Error variable ei

Error variable e2

Adaptive gain Gi

Adaptive gain 02

Adaptive gain 63

Adaptive gain 64

Adaptive gain 85

Adaptive gain 96

Adaptive gain 67

th8dat

adapoutdat

kmaxdat

Adaptive gain 0g

Maximal step size

73 Plant Simulator

CC = g++

$ make

1 iij-ji--^- - M - - I - - bull

1 lthtmlgt

2 ltheadgt

4 ltheacigt

5 ltbodygt

9 ltdivgt

value= size=40gt

17 ltformgt

18 ltbodygt

19 lthtmlgt

Feature

action=

method=

target=

Code example

Run gt

Description

program

time and text type

follows

th[k-l])

11 return

15 th-gtk = k

1]10000000

1] 10000000

1]10000000

23 return

751 CGI Program

variables

getenv() as follows

parameters

1 main ()

3 i n t v a l i d

17 while(klt kmax)

19 while(Igetkt)

21 wait(5000)

24 while(k=kT)

26 wait(10000)

ampth_k)

33 k++

36 else

41 exit (0)

program 109880

looses 10S824 188824 100883 100883 100883 19S821

Yers 2 2 1 1 2 3 4 1

port 111 111

48909 55541

2849 2849 2649

sudo rpcinfo -p

I I Bin Edit yamp

hoanaoan-$

gt Terminal

hoan^hoan ~$

2 2 1 1 2 3 4 1 3 4 2 3 A 1 3 4 1 1 2 2 3 3

i n f o -j r o t o

P po r t

111 n i

35368 35832

2649 2649 2S49

44664 44694 44994

2049 2849 2949

41394 41894 41894 33383 44819 33389 44819 33389 44819

M ^ s t i k ^ ^ lt

l - pound ig

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 a 3 3 3 3 3 3 A

syslog-install

root location as

during compilation

TESTOBJS = mycgio

support

1) TCPIP networking

3) IP DHCP support

4) IPBOOTP

5) IPRARP

2) RTL8019AS

and check

1) Boa

2) dhcpcd-new

3) dhclient

4) ifconfig

5) inetd

6) ping

8) route

9) routed

10)telnetd

ll)tftpd

terminal

for Linux machines

machine)

go 0x0c008000

RRMboot 182 (Aug 12 2084 - 104321)

bulltrade u u mdash

1 000 netmask 2552552550 lo

77 Testing

771 Test Procedure

(PC Linux machine)

Figure 722

D Graquo S S if

5fw help

following command

1 9 2 1 6 8 0 8 o p t t e s t v a r t m p

| g haanhoan ~

0JS packet loss

controllerhtmlgt

$01 C s- J http1921680^

Run Reset

adap t i vecamro l

13S3603 6682830

6258383

1393689 -8pound62298 B JhK-iH-)

-6239783 6626603

666G855

-9259783 -0629683 H HHI-li4s

Gsxgte i

efk-Dpl =

e(k-l) p2 =

ucfk-ljk =

uc(k- l ) p l

uc(k-l) p2

thik-lj k =

th ik - l j th l

th ik- l ) th2

th(k- l ) th3

thk- l ] th4

thk- l ) th5

thfk- l j th

amp c l

= 50000

=10000

= 66000

= -309998

= 1 0 4 4 2 2 5 4

= -42712

= 4240

ITtdlk^ Turlb

o Htp iH9i

| IG^Search

16S0 1

raquo bull zfgt

b i r p

ycqr u

^Settings

772 Test Results

in Table 73

File name

t_xdat

t_xmdat

t_edat

t_ucdat

t_udat

t_thetadat

t_ydat

t_ymdat

Data description

000000

-000521

-000667

-000817

-000764

-000770

-000815

-000738

-000650

-000665

-000641

-000623

-000645

-000594

-000587

-000551

-000514

-000587

-000641

000000

-000037

-000151

-000291

-000447

-000580

-000713

-000862

-000986

-001091

-001202

-001313

-001403

-001503

-001586

-001667

-001748

-001817

-001903

000000

-000523

-000687

-000730

-000731

-000719

-000702

-000685

-000669

-000652

-000637

-000622

-000608

-000595

-000582

-000569

-000558

-000546

-000536

000000

-000039

-000153

-000289

-000427

-000563

-000693

-000817

-000936

-001049

-001158

-001261

-001359

-001453

-001543

-001628

-001710

-001788

-001862

-000522

-000480

-000564

-000550

-000539

-000547

-000528

-000496

-000503

-000430

-000472

-000441

-000491

-000511

-000390

-000446

-000383

-000369

-000381

-000435

-000441

-000439

-000447

-000373

-000418

-000404

-000373

-000440

-001982

-002051

-002115

-002190

-002251

-002311

-002367

-002427

-002476

-002525

-002558

-002603

-002641

-002687

-002732

-002756

-002781

-002813

-002832

-002862

-002894

-002916

-002952

-002980

-002995

-003014

-003035

-003052

-000526

-000516

-000507

-000498

-000489

-000481

-000474

-000466

-000460

-000453

-000447

-000440

-000435

-000429

-000424

-000419

-000414

-000410

-000405

-000401

-000397

-000393

-000390

-000386

-000383

-000380

-000377

-000374

-001933

-002000

-002065

-002126

-002185

-002241

-002294

-002345

-002394

-002440

-002484

-002526

-002566

-002605

-002641

-002676

-002710

-002741

-002772

-002800

-002828

-002854

-002879

-002903

-002926

-002948

-002969

-002989

-000453

-000436

-000385

-000428

-003078

-003109

-003139

-003161

-000371

-000369

-000366

-000364

-003007

-003025

-003043

-003059

-0 025

_ m _ _ ^ i = _ mdash p i r r F ^

~~-ti ===ii

-mdash^zr ~~ i

2(enfc) -

-00006

-00009

-00011

-00008

-00001

-00004

-00008

-00001

-00002

-00005

-00004

-00005

-00004

-00008

-00001

-00002

-00003

-00002

-00003

-00002

-00003

-00002

-00001

-00002

-00010

-00009

-00001

-00009

-00006

-00005

-00001

-00008

-00013

-00002

-00004

-00007

-00014

-00006

-00007

-00001

-00010

-00003

-00004

-00005

-00003

-00004

-00002

-00001

-00002

-00001

-00002

-00003

-00005

-00006

-00008

CHAPTER 8

81 Conclusion

82 Future Work

xv2 r~

PILOT PLANT

Realtime (lata

D Xbdquo

B xbdquo

PE -W-V2

fc V -tvi

PILOT PLANT

PID Embedded

Adaptive Ccntroller

Online measurement

Hyperterminal

reg Spf M -amp- 1

i KZ- ^ -n

REFLUX DRUM

A 12 Vent-bleed

CONDENSER^-

mdash 4 6

i mdash amdashgtp j

Inert gas O

mdash m ltV3

i te i iaal

J5) Input ho-ot IS)

B - t-t

a) Kettle type

o h m m I K I

i t t_e i i - 1 1

-amp Q

_ U ftau irav

P| vopor flow

V U heat -

exchanger

A WH-J

have been specified

degrees of freedom

Column pressure

Manipulated

variables

Reflux flow rate

Reboiler duty

Condenser duty

Bottoms flow rate

Control valve

location

Reflux flow (VI)

Heat flow (V4)

Coolant flow (V3)

Bottoms flow (V5)

Control Structure

D-V(or D-QB)

L-V(or L-QB)

Role of valve

Inventory

Control (IC)

Separation

Control (SC)

structures

units in the plant

flow rate B

I raquo - sect I -

ATbdquo

are switched

H amp J bull

Component

Propane

Normal Butane

Isobutane

Isopentane

Normal Pentane

Hexane

Heptane

Octane

Nonane

Normal Decane

n-CHH24

n-C12H26

Cyclopentane

Methylclopentane

Benzene

Toluen

O-Xylene

E-Benzene

Cut point

(degC)

ASTM D86

(degC)

124024

Properties

1 Octane Number

2 Lead Content (g1)

10 vol

50 vol

90 vol

Residue ( vol)

Testing method

ASTM D2699

ASTMD3341

ASTM D86

ASTM D130

ASTMD381

ASTM D323

ASTM D1266

ASTM D525

ASTMD1298

Requirements

min 87

max 015

max 70

max 120

max 190

max 210

max 20

maxN-1

max 40

min 43

max 80

max 015

min 240

070 - 074

capacity

tso (TBP) = 5842 C

t(30- io) (TBP) = 3599-2467=1132 degC

t50 (EFV-TBP) = 1-5 C

Therefore

tso (EFV) = 5842+15=5962 degC

EFV (1 atm)

EFV (46 atm)

20 3840 60

Volume

80 100

B31 Description

B32 Calculation

fegtegtd f l ow

tray f

Rf= B-LF+ Vf= 62 - 58 + 28 = 32 vol

Stream

Total light

fractions E S D

Bottoms B

Volume fraction

Liquid flow rate

-73916

133973

-64677

143213

Liquid density

Mass flow rate

-45458

-38677

104046

B41 Description

B42 Calculation

stripping section

kcalkg

kcalhlOJ

kJhl0 j

276860

131300

408161

kcalhlOJ

149134

kJhl0J

267136

357141

624280

B51 Description

reflux flow

B52 Calculation

46degC

Stage 15 (tray 14)

D Distillate

9611+Ro

kcalkg

ZSD+Ro

5065+Ro

9611+Ro

kcalkg

kcalhlOJ

11053+24 R0

kJhlOJ

1005 R0

46263+1005 R0

kcalh103

49131+97Ro

56405+ 97R0

kJhl0J

205665+406R0

236111+406R0

46263+1005 Ro= 236111+406 Ro

Therefore

Ro= 7415 (tonh)

at the column top)

AHRoR0= AHLL

(115-24) (742) = (106-22) I

Therefore

L = 804 (tonh)

Stream

Temperature (C)

Pressure (atm)

Density (kgm )

Stream

Temperature (C)

RVP (kPa)

Density (kgm )

Condensate

130000

Reformate

105000

Raw gasoline

Gasoline

250000

Condensate bull

bullff

Raw Gasoline

amp V - 0 1

PEF l l OPUH

-Gasoline

GSSOLINE MIXER

gasoline

is 128degC

tankers

B74 Feed Control

46 atm

i T C - 1 r

mdashImdash I

--copy

l-MmdashJ

To Column

B76 Bottom Section

Cl Introduction

linear

outlet weir

Mbdquo = f(LJ (Cl)

C21 Generic Trays

equations

d(Mbdquo)

Liquid

Flow rate

vbdquo Vn

Concentration

staae n

dh dMbdquo x = A-

dLbdquo dL (C4)

d(Mbdquoxbdquo) dt

dt Mbdquo (C6)

d(Mnhn) dt

V = H-h

C22 Feed Tray

stage (feed tray

LfXrbdquo

I-v vgt LrXf

d(Mfxf)

dt Mbdquo

d(Mfhf)

C23 Top Section

Vlaquobdquo

11 V M1

vbdquo

d(MN+l) _ (C 13) dt

d(M XN+])=Lx^ + y L _ y ( C 1 4 )

11 N+ nN+

C24 Bottom Section

l I l I

ltHXr-B x F

d(M2) dt

L3-L2+ VB -V2

dMRhB) dt

= 23Z3 +HBVB- h2L2 - H2V2

Therefore

H2 -h2

be neglected

dMB) = L 2 _ V B B ( C 2 3 )

d(MBhB)

4 Simplified Model

yn = r (C27)

+ (a-l)xbdquo

aZyv+2 = dL)

L2= LT~ = LN+2-

equations [12]

5) Tray n(n = 2 - l)

MBX] =(L + LF)X2 - Vy - fix (C33)

1) LF=qFF

2) VF = F-LF

y = r bull (C35)

1 + a - )Xj

A = 730 (kJkg)

V0= 39098 (kgh) or 668871 (kmoleh)

V = 0+ = 663407 (kmoleh)

Joshi [43]

ffl^^M (C38)

314(175X1-4) Z ^ = 2488 (kmole) B 4 786

t 0957chD2k dr

095(314)(028)(175)2 680 M = = 580 (kmole)

MD = 5iL + D) (C41)

flow rate

follows

Tray 5 (n = 6) M6 = F(^5 - y6) + (Z + LF )(x7 - x6)

Tray 3 (n = 4) M4 = F(^3 - gt4) + (Z + ZF )(x5 - x4)

2488 (kmole)

1403 x16 =1646291 y]5 - 756380x6 -927597x6

58x15 = 1646291(y14 -y ] 5) + 756380(x6 -x l 5)

58x4 = 1646291(73-gtgt4) + 756380(x5-x4)

58x13 = 1646291(712 - yn) + 756380(xl4 - x13)

58x12 =1646291(j |l-j12) + 756380(x13-x12)

58 = 1646291(710 -yu) + 756380(x2 -x )

58x0 = 1646291(79-^0) + 756380(x-x0)

58x9 = 661 39ys -15638gt-9 + 756380(xl0 -x 9 ) + 5995

58x8 = 661139(y7 -ya) + 756380 x9 - 18859x8 + 3399

58x7 = 661139(y6-y7) +179887 l (x 8-x 7)

58x6 = 661 39(y5-y6) + 179887 l (x 7 -x 6 )

58x5 = 661139(j4 - y5) +1798871 (x6 - x5)

58x4 =661139(^3 -yA) + 79887 l (x 5-x 4)

58x3 = 661 139(^2 - y 3 ) + l798871 (x4 - x3)

58x2 =661139(j -y2) +1798871 (x 3 -x 2 )

2488x = 1798871 x2 -1109235x -661139^ (C42)

568x y ~ l + 468x

y2 = 568x2

1 + 468x

^ 1 5 =

l + 468x (C43)

bullCO

laquo r M |

raquo ^ SA 11 j

w r n i |

^ ltgt fM f 3 1

ET mAr pound |

~^ IT JWi a mdash i

Cgt $ IZ

1 ma r ii |

P $ mar t |

ET r Jfifl V 3 1

b $ TWVlP 2 1

J ^ m d If f |

WFYMtG

fiterttxm

STRIPPING SECTION

GENERAL TRAY

COLUMN

1 TRAY 7

1 TRAYS

RECTI FYINO SECTION

GENERAL TRAY 1

Figure D3

- w i 13411

~W 46804

RECTIFYING SECTION

mdash bull In2 Out2

STRIPPING SECTION

bull XD

To Workspacel

-4L Scope 1

Raw Gasoline

bull | xB

To Workspace

H Scope

In20ut2

Inl O u l l M

In 2 Ou2t

Tray 14

bull i n l Out1 |

- W i n 2 Oul2|

Tray 13

In 10ut 1

In20ut2

Tray 12

bull In lOu t l

In20ut2

Tray 11

InlOutl

In20ul2

Tray 10

bullNln20Ut2

Tray 9

l j mdash

~2~gt -In2

bull in 2

Tray 8

x 1 bull Outl

bull - K 2 Out2

_2 mdash

f bull

n 1 n n H I Wgt A

In 2 Ol l t l

Tray 7

mdash bull

In 10ut1

In20ut2

Tray 6

- gt In20ut2

Tray 5

In lOut l -

bull ln20ut2

Tray 4

bull in lOut l

1 bull

In20ut2

Tray 3

In lOut l

In20ut2 [

Tray 2

[ bull

In lOut l H

In20ul2 |

1 Tray 1

__ Out1

bull In1

Out2 -gt lt_2_gt

O bull72302

471 r Integrator 2

bull XI

To Workspace2

Scope 2

K 2 Olit2

2T899 ^ Function

VLE equation

GENERIC TRAY n

V bull L(n+1)Mn

In2 _ - -

A i bull

-bull VnMn

bull 1 integrator 2

y lt bull

V IE equa Son

bull xn

To Workspace2

bullbull bull -

Scope xn

TRAY 7 (Stage n -8)

bull 3 gtbull

bull 1

( 2 in2

IH130410 ~gt-

bull 119679

bullbullyenbullbull

y- Integrator 2

VLE equation

To Workspaces

Scope 2

gt bull

1 lHn0410

bullbullbull xS

To Workspace

2 bull 119879 In2

Outl bull bull I

289533 N

li integrator 2

130410

Function

MATLAB Fen 2

bull gt bull bull

Scope2

( 1 In2

119666 1 I s J

Integrator 2

120027 K

Scope 2

inputs

M M n+ Mbdquo

-X (El)

= = V15= F+ VF = V+ 985152

Vw = l 15 (E2)

X = f(Xut)

dX = X-X

du = u - u

dX df] _lt3x_

dX + 8f] _du_ du

Mn Mn Mn Mn

Mn +1 Mn +1 Mn Mn

T T -t- V V K V

i ( 0 = Ax(t) + Bu(t) (E4)

y(t) = Cx(t) (E5)

follows

L ==LS = 1798871 (kmoleh)

L9 = = Z15= 756380 (kmoleh)

V = = V = 661139 (kmoleh)

V9 = = V]5 = 1646291 (kmoleh)

M2 = M3 = = Mi5 = 580 (kmole)

M16 = MB = 2488 (kmole)

_KK _ (L]+K2V) _ L 21 M2

22 M2 23 M 2

1) Collect data

w = 1 ^ 1 = 7 Z 6 i 2=TT

w =2 h _xlZx2) _-fe-i) 2 J ~ M2 2lt2~ M2

laquo - 1 6 66gti = 6 ft162 ^ 1 6

_ K M16

[00012 00063 00091 00098 00076 00044 00022 00021 00048

00111 00216 00306 00285 00178 00086 -00702

-00024 -00157 -00237 -00254 -00196 -00116 -00058 -00027 -00024

-00050 -00097 -00138 -00128 -00080 -00039 00704]r

C = 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

E2 Stability Test

V(x)=xTPx (E6)

ATP + PA = -I (E9)

positive definite

P = lyap(AI)

for i=l16

Pi = P (1 i 1 i)

det(Pi)

d e t ( P l ) = 0 0 3 2 8 3 1

d e t ( P 2 ) = 0 0 0 0 9 0 8 4 9

d e t ( P 3 ) = 2 4 4 4 3 e - 0 0 5

d e t ( P 4 ) = 5 5 4 7 6 e - 0 0 7

d e t ( P 5 ) = 1 0 1 5 2 e - 0 0 8

d e t ( P 6 ) = 1 6 2 0 8 e - 0 1 0

d e t ( P 7 ) = 2 3 0 2 5 e - 0 1 2

d e t ( P 8 ) = 2 6 1 8 3 e - 0 1 4

d e t ( P 9 ) = 4 1 9 5 9 e - 0 1 6

d e t ( P l O ) = 1 2 8 8 6 e - 0 1 7

d e t ( P l l ) = 6 7 8 4 7 e - 0 1 9

d e t ( P 1 2 ) = 3 9 1 6 e - 0 2 0

d e t ( P 1 3 ) = 1 8 3 0 8 e - 0 2 1

d e t ( P 1 4 ) = 7 0 8 9 e - 0 2 3

d e t (P15) = 2 4 8 7 6 e - 0 2 4

d e t ( P 1 6 ) = 8 4 6 1 2 e - 0 2 6

stable

include ltstdlibhgt

using namespace std

if(k = x_kmlk+l)

stampn)

if(k = e_kmlk+l)

stampn)

if(k = uc_kmlk+l)

stampn)

return

th kk = k

b21e_kmlp2)x_kmlp2

b22e_kmlp2)x_kmlpl

b22e_kmlp2)x_kmlp2

b21e_kmlp2)uc_kmlpl

b21e_kmlp2)uc_kmlp2

b22e_kmlp2)uc_kmlpl

b22e_kmlp2)uc_kmlp2

r e t u r n

F2 Plant Model

include ltstdlibhgt

include PlantModelh

using namespace std

PlantPlant()

all = -67941 + 067(rand()2-05)

al2 = -09095 + 009(rand()2-05)

a21 = 14686 + 015(rand()2-05)

a22 = -02497 + 002(rand()2-05)

bll = -01461 + 0014(rand()12-05)

bl2 = 02073 + 002(rand()2-05)

b21 = -00021 + 00002(rand()12-05)

b22 = -00281 + 0003(rand()2-05)

ell = -00624 + 0006(rand()2-05)

cl2 = -00281 + 0003(rand()2-05)

c21 = 02458 + 0025(rand()2-05)

c22 = 00009 + 000009(rand()2-05)

Plant~Plant ()

if(k = u_kk)

this-gtu_k = u_k

this-gtx_k = x_k

return

bl2Tu_kp2

b22Tu_kp2

x_kplk = k+1

r e t u r n

F3 Reference Model

include ltstdlibhgt

using namespace std

RefmdlRefmdl()

Refmdl~Refmdl()

if(k = uc_kk)

stampn)

this-gtuc_k = uc_k

if(k = xm_kk)

stampn)

this-gtxm_k = xm_k

return

xm_kplk = k+1

return

include ltstdlibhgt

using namespace std

Linctrl Linctrl()

Linctrl -Linctrl ()

time stampn)

this-gtth_k = th_k

time stampn)

this-gtuc_k = uc_k

time stampn)

this-gtx_k = x_k

return

- th_kth2x_kp2

- th_kth4x_kp2

u_kk = k

return

F5 Comparator

include ltstdlibhgt

include Comparatorh

using namespace std

this-gtx_k = x_k

this-gtxm_k = xm_k

return

compute errors

e_kk = k

r e t u r n

include ltstdlibhgt

using namespace std

stampn)

this-gtx_k = x_k

return

y_kk = k

return

include ltstdlibhgt

using namespace std

time stampn)

this-gtxm_k = xm k

return

ym_kk = k

ym_kpi = ym_kpi

ym_kp2 = ym_kp2

r e t u r n

F8 CGI Program

inc lude ltctypehgt

include

lterrnohgt

ltstringhgt

ltstdiohgt

ltunistdhgt

ltfcntlhgt

ltstringhgt

ltsyssockethgt

ltsystypeshgt

ltnetinetinhgt

ltarpainethgt

define LINELEN 1024

struct valinfo

unsigned char name

unsigned char text

struct thetaPkt

struct Pkt

int pi

int p2

static

amll =

ami 2 =

am21 =

am22 =

bmll =

bml2 =

bm21 =

bm22 =

cmll =

cml2 =

cm21 =

cm22 =

all = -

al2 = -

a22 = -

bll = -

-67 94

static

= -510

= -310

= 1044

= 1006

static int nvals=0

if (gotvals)

nvals = getvals()

gotvals = 1

)vals[i]name)==0)

return vals[i]text

return NULL

=============== httpunescape ===========

unsigned char siptr

unsigned char soptr

unsigned char sos

(unsigned char) )

soptr = sos

siptr = sis

while (siptr)

if(siptr == )

int c = 0 i

for (i=0ilt2i++)

siptr++

c = claquo4 + h

if (i = 2)

free(sos)

return NULL

soptr++ =

soptr++ = siptr

siptr++

soptr = 0

free (sos)

return sis

=============== hextobin =================

if(isdigit(c))

return c-0

return -1

=============== getvals ===================

int vent = 0

unsigned char vstr

unsigned char vptr

unsigned char eptr

unsigned char aptr

int 1 cl

return 0

if(vstr == NULL)

return 0

if(vstr[l-l] == n)

vstr[l-l]=0

vptr = vstr

while (vptr)

vcnt++

valinfo))

vptr = vstr

for (i=0iltvcnti++)

if (eptr == NULL)

return 0

eptr = 0

if (aptr)

aptr = 0

vptr = aptr+1

return vent

unsigned char c

unsigned char cs

int fd len

if((fd==-l))

exit (1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== write signals ===================

unsigned char c

unsigned char cs

int fd len

if((fd==-l))

exit(1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== write a signal ===================

unsigned char c

unsigned char cs

int fd len

if((fd==-l))

exit (1)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== getsignal ===================

int fn s i m sn 1

unsigned char buf

if(fn==-l)

exit(1)

return

read(fn buf 20)

signal = s

free((void) buf)

close(fn)

return s

=============== get ascii signal ===================

int fn s i m sn 1

unsigned char buf

if(fn==-l)

exit (1)

return 0

read(fn buf 20)

signal = s

free((void) buf)

close(fn)

return 1

=============== settime ===================

int t=0

unsigned char c

unsigned char cs

int len

if((f==-l))

exit(l)

write(f c len)

write(f t 1)

free((void) c)

free((void) cs)

close (f)

return

=============== Wait ===================

int i=0

while(i++ltn)

=============== gettime ===================

clear signals

kT = k

Write to files

return

=============== clear signal ===================

int fn

if(fn==-l)

exit(1)

return

write(fn20)

close(fn)

return

unsigned char ch

if (xl==0)

ch[0] = 0

len = 1

if(xllt0)

xl = -xl

sign[0] = -

sign[0] = +

while(xlgt0)

ch[i] = 0 + xl10

xl=xl10

len=i+l

for(i=0 iltlen i++)

free((void) ch)

return

=============== getAdapMechPkt ===================

th4 th5 th6 th7 th8

int outfile

Receive signals

getsig

vartmpfuc2

vartmpfkth

vartmpfthl

vartmpfth2

vartmpfth3

vartmpfth4

vartmpfth5

vartmpfth6

vartmpfth7

vartmpfth8

ampuc2)

ampkth)

ampthl)

ampth2)

ampth3)

ampth4)

ampth5)

ampth6)

ampth7)

ampth8)

receivedlth3gtn)

printf

ltpgt ucl

ltpgt uc2

ltpgt thl

ltpgt th2

ltpgt th3

ltpgt th4

ltpgt th5

ltpgt th6

ltpgt th7

ltpgt th8

d) = dn k-1 ucl)

d) = dn k-1 uc2)

d)k = dn k-1 kth)

d) = dn k-1 thl)

d) = dn k-1 th2)

d) = dn k-1 th3)

d) = dn k-1 th4)

d) = dn k-1 th5)

d) = dn k-1 th6)

d) = dn k-1 th7)

d) = dn k-1 th8)

x_kml-gtk = kx

x_kml-gtpl = xl

x_kml-gtp2 = x2

e_kml-gtk = ke

e_kml-gtpl = el

e_kml-gtp2 = e2

uc_kml-gtk = kuc

uc_kml-gtpl = ucl

uc_kml-gtp2 = uc2

th_kml-gtk = kth

th_kml-gtthl = thl

th_kml-gtth2 = th2

th_kml-gtth3 = th3

th_kml-gtth4 = th4

th_kml-gtth5 = th5

th_kml-gtth6 = th6

th_kml-gtth7 = th7

th kml-gtth8 = th8

Write to files

return

=============== genAdapMechPkt ===================

th k-gtk = k

Write to files

return

=============== main ============

main ()

int valid

int stime gamm

int i=0

int k kT

int kmax=2

struct Pkt x_kml

struct Pkt e_kml

struct Pkt uc_kml

int getkt=0

int getkmax=0

ltheadgtn)

while(getkmax)

wait(5000)

while(klt kmax)

signalsn)

while(Igetkt)

wait (5000)

while(k=kT)

wait(10000)

signalsn)

gainsn)

ampth_k)

exit (0)

0000000

0100000

0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

1100000

1200000

1300000

1400000

1500000

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-0005840

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-0033652

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in Table G2

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0100000

0200000

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0000000

-0001534

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-0000000

0000337

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0000000

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2100000

2200000

2300000

2400000

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2600000

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2900000

3000000

3100000

3200000

3300000

3400000

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3700000

3800000

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4200000

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4600000

4700000

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7600000

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8600000

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9600000

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10000000

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Plant Error

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0000000

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0000000

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2200000

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3700000

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4100000

4200000

4300000

4400000

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4800000

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4900000

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10000000

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Adaptive Gains

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1000000

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0000000

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0000000

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-0020508

0000000

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0000000

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2100000

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3000000

3100000

3200000

3300000

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4000000

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4700000

-0005636

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4800000

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7000000

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10000000

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0000000

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0000000

-0001286

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7500000

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9000000

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10000000

0001119

0001152

0001096

0001113

0001118

0001144

0001114

0001144

0001151

0001173

0001104

0001152

0001121

0001106

0001123

0001160

0001159

0001143

0001105

0001101

0001112

0001158

0001103

0001157

0001153

-0000908

-0001034

-0000804

-0000872

-0000892

-0000983

-0000849

-0000963

-0000983

-0001051

-0000767

-0000968

-0000835

-0000775

-0000849

-0000999

-0000980

-0000908

-0000751

-0000747

-0000796

-0000978

-0000743

-0000750

-0000960

-0000929

0001132

0001133

0001134

0001135

0001136

0001137

0001138

0001139

0001140

0001141

0001142

0001143

0001144

0001145

0001146

-0000841

-0000839

-0000838

-0000836

-0000835

-0000833

-0000832

-0000831

-0000830

-0000829

-0000827

-0000826

-0000825

-0000824

-0000823

-0000822

-0000821

-0000820

-0000819

-0000818

-0000817

-0000816

H3 Plant Error

0000000

0100000

0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

1100000

1200000

1300000

1400000

1500000

1600000

1700000

1800000

1900000

2000000

2100000

000000

000002

000020

-000087

-000033

-000051

-000113

-000053

000019

-000012

-000004

-000001

-000037

000000

-000005

000019

000044

-000040

-000106

000004

000036

-000057

000000

000001

000003

-000002

-000020

-000017

-000021

-000045

-000049

-000042

-000045

-000052

-000044

-000049

-000043

-000038

-000030

-000041

-000049

-000050

-000051

2200000

2300000

2400000

2500000

2600000

2700000

2800000

2900000

3000000

3100000

3200000

3300000

3400000

3500000

3600000

3700000

3800000

3900000

4000000

4100000

4200000

4300000

4400000

4500000

4600000

4700000

4800000

4900000

-000052

-000050

-000065

-000054

-000030

-000044

000023

-000025

-000001

-000057

-000082

000034

-000027

000031

000040

000024

-000034

-000043

-000046

-000058

000014

-000035

-000024

000004

-000066

-000082

-000068

-000019

-000064

-000066

-000071

-000073

-000082

-000085

-000074

-000076

-000075

-000083

-000090

-000080

-000072

-000071

-000061

-000062

-000065

-000061

-000073

-000076

-000068

-000066

-000064

-000071

-000083

-000097

5000000

5100000

5200000

5300000

5400000

5500000

5600000

5700000

5800000

5900000

6000000

6100000

6200000

6300000

6400000

6500000

6600000

6700000

6800000

6900000

7000000

7100000

7200000

7300000

7400000

7500000

7600000

7700000

-000064

000013

-000053

000016

000065

000011

000061

000056

000053

-000039

-000083

-000046

-000029

-000049

-000103

-000033

000000

000058

-000026

-000040

000021

-000007

000013

-000050

-000029

-000046

-000100

-000002

-000102

-000112

-000108

-000109

-000100

-000089

-000082

-000071

-000054

-000040

-000042

-000052

-000055

-000056

-000068

-000080

-000089

-000080

-000072

-000074

-000075

-000061

-000065

-000067

-000076

-000074

-000072

-000078

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

-000032

-000041

-000081

-000024

-000073

-000082

-000112

000010

-000077

-000020

000005

-000027

-000092

-000084

-000053

000014

000015

-000006

-000084

000016

000013

-000077

-000064

-000073

-000069

-000075

-000087

-000085

-000090

-000105

-000114

-000100

-000105

-000103

-000095

-000089

-000100

-000107

-000111

-000101

-000093

-000089

-000105

-000097

-000108

H4 Adaptive Gains

e 03716

-05106

-03100

-00427

-00428

-05106

-03100

-03099

-00428

-05106

-03099

-03098

-00428

-05106

-03098

-00428

-00429

-00428

-00429

-00428

-00429

REFERENCES

Hungary vol 3 pp 1719-1724 1984

563 May 1989

Hall 1984

orgwikiMATLAB

Press 1999

McGraw-Hill 1981

2002 pp 4003-4008

6 pp 1169-1175 Dec 1982

e_Diagrampdf

Prentice Hall 1997

University 1990

Hill 1984

India 1979

SJSU ScholarWorks

Fall 2009


Hoan The Nguyen



ABSTRACT

by Hoan The Nguyen

ACKNOWLEDGMENTS

people

TABLE OF CONTENTS

List of Tables xiv

List of Figures xvi

11 Background 1

15 Methodology 5

28 ARM Processor 16

31 Introduction 20

41 Introduction 26

441 Plant 31

51 Introduction 43

521 Plant Model 44

61 Introduction 50

71 Introduction 66

751 CGI Program 78

77 Testing 93

772 Test Results 98

81 Conclusion 104

82 Future Work 105

A12 Vent-bleed 110

B31 Description 124

B32 Calculation 125

B41 Description 126

B42 Calculation 127

B51 Description 128

B52 Calculation 129

Cl Introduction 137

C22 Feed Tray 140

C23 Top Section 141

F2 Plant Model 170

F5 Comparator 173

F8 CGI Program 175

G3 Plant Error 206

H3 Plant Error 222

References 230

LIST OF TABLES

LIST OF FIGURES

Motor octane number

Network file system

Personal computer

Reid vapor pressure

True boiling point

Zero-order hold

LIST OF SYMBOLS

A State matrix

B Input matrix

C Output matrix

e State error

L Feedback matrix

u Control signal

x State variable

y Controlled output

Greek Symbols

y Adaptation rate

0 Adaptive gain

Subscript

B Bottom product

F Feed

m Reference model

CHAPTER 1

INTRODUCTION

11 Background

time spaces

adaptive controller

mathematical method

15 Methodology

CHAPTER 2

LITERATURE REVIEW

RECTIFYING SECTION

F (feed flow rate)

Q n I (3) CONDENSER

1 8 - D

stage f (feed tny)

stage rc

Material stream

Feed stream

Distillate stream

Bottoms stream

Position

Stage f

Stage N

Reflux drum

Stage 1

Reboiler

Flow rate

Concentration

in Figure 22

Liquid phase

Stage it

(Trav gti-l)

bull bullbullbull

m^u - Bubble cap

structures

I |mdash0mdashI I

bottoms flow rate B

are adjusted [12]

required

Command_ signal

Adaptive mechanism

laquosj

Control signal

Plant 1 Output

Process dynamics )

Siv-CSnftlteF----

26 Adaptive Schemes

261 Gain Scheduling

Command signal

Output

signal

MoctSI

Control signal

mechanism

Plant -bull Output

= ( ) bull (21)

disturbances or not

- mdash

yfdx dt

x = 0 i

-gt() =

= = ( ) = -W(x) (22) dt dx dt dx

dx mdash = Ax (23)

ATP + PA=-Q (24)

following function

V(x) = xTPx (25)

28 ARM Processor

DB-9 DB-9

RS-232

Features

Memory

subsystem

GPIO ports

Ethernet

Descriptions

solution

8 memory banks

by RAM

CHAPTER 3

31 Introduction

RffLlrtERLMl

xD gt 98

xB lt 20

Table 31

Temperature C

Pressure atm

Density kgm3

Mass flow rate kgh

Main streams oft

Condensate

130000

he plant

Raw gasoline

system

35 Plant Modeling

1403 x16 =1646291^15 -756380x16 -927597xI6

58x15 =1646291(gtl4 -^1 5) + 756380(x16 -x15)

58x14 =164629103 -gtgt14) + 756380(x15-x4)

58x13 =1646291012 -_y]3) + 756380(x14 -x13)

58x12 =1646291(^n -y1 2) + 756380(x13 -x ] 2)

58xH =164629IO10 ~ ^ i ) + 756380(x12-x)

58x10 =164629109 -^1 0) + 756380(xn -x10)

58x9 = 661139gtgt8 -15638^9 + 756380(x10 -x9) + 5995

58x8 = 66113907 ~yamp) + 756380 x9 -18859x8 + 3399

58x7 = 661 39(y6-y7) + 798871 (x8 -x 7 )

58x6 =66113905-gt 6) + 1798871(x7-x6)

58x5 =66113904^) +179887 l (x 6 -x 5 )

58x4=66113903-^4) + 1798871(x5-x4)

58x3 =66113902-73) +1798871 (x 4 -x 3 )

58x2 =661139(^-gt2) +179887l(x3-x2)

2488x = 1798871x2-1109235x1 -661139^

568x y = l + 468x

l + 468x

^ 1 5 =

568x 15

l + 468xbdquo (34)

CHART OF VAPOR

01 02 03 0 4 05 06 07 08 09

36 Plant Simulation

Table 32

bull L _ I i 1 l

6 8 10 12 14 16 18 20 Time (h)

than 2

CHAPTER 4

41 Introduction

and (32)

Disturbances

Ditiilitirn Gy-tem

x(t) = A(xt) + Beu(t) (41)

y(t) = Cex(t) (42)

two-output system

-09095

-02497 Bbdquo

-01461 02073

-00021 -00281 and C

-00624 -00281

02458 00009

Bode Diagram

Frequency (radsec)

431 Stability Test

finite time T-tgt0

x = Ax(t) + Bu(t) (45)

y(t) = Cx(t) + Duy) (46)

full rank of n

output

S=[CCACA2CA]]T

the next section

441 Plant

yt) = Cx(t)

where A = au

an_ B =

bn_ and C =

-00624 -00281

02458 00009

variables

442 Reference Model

Sec 43

where Abdquo

ybdquo(t) = cmxm(t)

-67941 -09095

14686 -02497

5 = -01461 02073

-00021 -00281 and Cbdquo

-00624 -00281

02458 00009

ut) = Muct)-Lx(t)

x = (A- BL)x + BMuc

hence we define

Ac(0) = (A-BL)

Bc6) = BM

i2 ~b2

l 2 11^2 ^12^4

22 _ ^ 2 1 ^ 2 ~ ^ 2 2 ^ 4

b2]65+b2281 b2Xdb+b22d (412)

condition we get

au-bu6-bnel =-67941

an -bu6a2 -bn6deg4= -09095

a2]-b2]6deg-b220deg =14686

a22-b2]e2-b229deg= -02497

6Adeg + M7deg =-01461

606deg + 6 X =02073

b2l6deg5+b229deg =-00021

b2]edeg6+b226degs =-00281 (413)

condition

0 _ b22(au +67941)-bu(a2] -14686) 0 =

regp22 ^12^21

a o _ b22(an + 09095)-bn(a22 +02497)

^11^22 _ ^12^21

buo22 mdashbnb2]

0 _ -b2](a]2 + 09095)+ bu(a22 +02497) 6gt =

bP 22 b]2b2]

-b2]bn+bub22

n0 002816I2+02073Zgt22

(J6 = -b2]bu+bub22

_0 - 000216+ 0146 b2x Uf =

-b2]bu+bub22

0 = 002816 +020736

-b2Xbu+bxxb (414)

Error Equation

e(0= x(0-m(0

e() = ^ ( 0 + 5 i ( 0 - ^ I B ( 0 - 5 m laquo c ( 0 - (4-15)

e(t) = Ame(t) + V(t)(0-O0) (417)

446 Adaptation Law

function

V(e 0) = [yePe + (0 - 0deg f (0 - 0deg)) (418)

(420) dt 2

ltP + PAm = -a (4-21)

^ = -W(t)Pe(t) at

y(buex+b2Xe2)xx

y(buex+b2]e2)x2

y(bnex+b22e2)xx

y(bx2ex+b22e2)x2

-y(bxxex+b2xe2)ucX

-y(bxxex+b2Xe2)uc2

-y(bX2ex+b22e2)ucX

-y(buex+b22e2)uc2

6 = (423)

mdash = -05591lt -07066e2)2 +132756e2] dt 1

2) Disturbances^)

4) Reference model

a n n f l

REFERENCE MODEL

dull In I

0ut2 In2

ADAPTIVE MECHANISM

= X Xm

_X2 Xm2 _

follows

e = RMS(e) = -^A for = 1 or 2

commands

norm_el = norm(el)

norm_e2 = norm(e2)

shown in Figure 46

m B s in

Figures - x vc xm

m B ampm

bull4s

bullraquo i x

i m B raquo bull

im B ffin

State error e1(t)

State error e2(t)

e = 00017

n2 VTooT = 7106210

453 Error Reduction

Plant errors

laquoi

Adaptation rate y

54304 105

71399105

5428410

7106210

54076 105

7100310-5

CHAPTER 5

51 Introduction

G(s) y ( t

521 Plant Model

x(t) = Axt) + But)

y(t) = Cx(t)

x(s) - ~[AX(S) + Bu(s) s

T x(z) = [AX(Z) + Bu(z)]

y(kT) = CxkT) (52)

522 Reference Model

in Chapter 6

ybdquo(t) = cmxm(t)

where Am = [-67941 -09095 14686 -02497] Bm = [-01461 02073 -00021 -00281]

and Cm = [-00624 -00281 02458 00009]

follows

ut) = Muc(t)-Lx(t)

L = 0kT) 62(kT)

0(kT) 0AkT

M 05(kT) 06(kT)

87(kT) 0s(kT)^ (56)

o _ ft2deg2(adeg +67941)-ft02(a20 -14686)

degdeg27 deg12deg21

8 0 _ -amp2 K + 67941) + ft (a2] -14686)

ftdeg =

00021ft0-01461ft0 22

-ft21 f t02+ft0 f t22

-b2]b]2+bub22

-b2bn+bub22

n0 00281ft+02073ftdeg

201 deg]]deg22

6(t) = -y^(t)Pe(t)

= yy (s)Pe(s)

CHAPTER 6

61 Introduction

2) Disturbances^^

reference signals

1 tnl uc(k)

In2 uc(k-1)

xm(k-1)

laquogt

REFERENCE MODEL

H Disturbances

bulleurogt

[B^_]M

0ut1 In)

0ut2 In2

i f MJi-1)

0 u ulaquoK-l)

ADAPTIVE MECHANISM

m lt raquo

Ot-1) Mux bull

e(kT) = exkT)

e2(kT)

h(kT)-xnnkT)

x2(kT)-xm2(kT)_

Ax^kT)

Ax2(kT)

follows

e = RMSe) = ^L for = 1 or 2 (61)

shown in Figure 62

Disturbance f(t)

m gt P i laquo ^ e

a)e(7)

ns gt P l

a) eiikT)

I U I 94543e-004 _ bdquo ^ - s

101 = 9407410-

M = 9 6557e -Q04 = 9 6 0 7 8 t l 0 5

4n2 vioi

sections

in Figure 66

4 include tbdefsh

5 class Plant

6 private

12 public

13 Plant()

14 -Plant()

18 endif

P l a n t ( )

a l l = - 6 7 9 4 1 + 0 6 7 ( r a n d ( ) 2 - 0 5 )

a l 2 = - 0 9 0 9 5 + 0 0 9 ( r a n d ( ) 2 - 0 5 )

a21 = 14686 + 015(rand()2-05)

a22 = -02497 + 002(rand()2-05)

bll = -01461 + 0014(rand()2-05)

bl2 = 02073 + 002 (rand()2-05)

b21 = -00021 + 00002(rand()2-05)

b22 = -00281 + 0003 (rand()2-05)

ell = -00624 + 0006(rand()2-05)

cl2 = -00281 + 0003(rand()2-05)

c21 = 02458 + 0025(rand()2-05)

c22 = 00009 + 000009(rand()2-05)

4 include tbdefsh

5 class Refmdl

6 private

7 Pkt uc_k

8 Pkt xm_k

9 public

10 Refmdl()

11 -RefmdlO

15 endif

Figure 68

4 include tbdefsh

5 class Linctrl

6 private

7 thetaPkt th_k

8 Pkt x_k

9 Pkt uc_k

10 public

11 LinctrlO

12 -LinctrlO

16 endif

database

4 include tbdefsh

5 class Comparator

6 private

7 Pkt x_k

8 Pkt xm_k

9 Pkt e_k

10 public

11 Comparator()

12 -Comparator()

16 endif

and the plant

4 include tbdefsh

6 private

7 thetaPkt th_kml

8 Pkt x_kml

9 Pkt e_kml

10 Pkt uc_kml

11 public

12 AdaptiveMechO

13 -AdaptiveMechO

17 endif

model and the plant

CC = g++

ReferenceModelo

executive file

j haut$ttum

ltOIgt gtiJ^Alt

plusmn1 f bull-lt

i gt bulli

lt euro f bull2

[ bull

- H J bullbull -

~ttttfc

bull=fmdashF^--

^ t ^ i i i = ^ ^

_ - 1 1 = - mdash J

^ J - - - ^ ^

1 1 1 I

5 time

e = |N| s94543c-004 ^

96557e-004

VToi = 96078 105

CHAPTER 7

71 Introduction

shown in Figure 71

_ Data J

5gt I Error

yV H Report

Plant Slmsliitsr

lt = J Output

Linux yacnine

RPC get_port reply

RPC mount request

RPC mount reply

Authenticate client

to the browser

button

lUser sufrmis fwm

arv-affe ie Camp

vas tor PlssrtSwi

Sens ( to i l sA i

(J 0 0

SefieJ acispfcw BM2

Oylpaito wefccfer

72 Common Database

File name

kucdat

ucldat

uc2dat

kthdat

thldat

th2dat

th3dat

th4dat

th5dat

th6dat

th7dat

Data description

Plant state xi

Plant state X2

Error variable ei

Error variable e2

Adaptive gain Gi

Adaptive gain 02

Adaptive gain 63

Adaptive gain 64

Adaptive gain 85

Adaptive gain 96

Adaptive gain 67

th8dat

adapoutdat

kmaxdat

Adaptive gain 0g

Maximal step size

73 Plant Simulator

CC = g++

$ make

1 iij-ji--^- - M - - I - - bull

1 lthtmlgt

2 ltheadgt

4 ltheacigt

5 ltbodygt

9 ltdivgt

value= size=40gt

17 ltformgt

18 ltbodygt

19 lthtmlgt

Feature

action=

method=

target=

Code example

Run gt

Description

program

time and text type

follows

th[k-l])

11 return

15 th-gtk = k

1]10000000

1] 10000000

1]10000000

23 return

751 CGI Program

variables

getenv() as follows

parameters

1 main ()

3 i n t v a l i d

17 while(klt kmax)

19 while(Igetkt)

21 wait(5000)

24 while(k=kT)

26 wait(10000)

ampth_k)

33 k++

36 else

41 exit (0)

program 109880

looses 10S824 188824 100883 100883 100883 19S821

Yers 2 2 1 1 2 3 4 1

port 111 111

48909 55541

2849 2849 2649

sudo rpcinfo -p

I I Bin Edit yamp

hoanaoan-$

gt Terminal

hoan^hoan ~$

2 2 1 1 2 3 4 1 3 4 2 3 A 1 3 4 1 1 2 2 3 3

i n f o -j r o t o

P po r t

111 n i

35368 35832

2649 2649 2S49

44664 44694 44994

2049 2849 2949

41394 41894 41894 33383 44819 33389 44819 33389 44819

M ^ s t i k ^ ^ lt

l - pound ig

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 a 3 3 3 3 3 3 A

syslog-install

root location as

during compilation

TESTOBJS = mycgio

support

1) TCPIP networking

3) IP DHCP support

4) IPBOOTP

5) IPRARP

2) RTL8019AS

and check

1) Boa

2) dhcpcd-new

3) dhclient

4) ifconfig

5) inetd

6) ping

8) route

9) routed

10)telnetd

ll)tftpd

terminal

for Linux machines

machine)

go 0x0c008000

RRMboot 182 (Aug 12 2084 - 104321)

bulltrade u u mdash

1 000 netmask 2552552550 lo

77 Testing

771 Test Procedure

(PC Linux machine)

Figure 722

D Graquo S S if

5fw help

following command

1 9 2 1 6 8 0 8 o p t t e s t v a r t m p

| g haanhoan ~

0JS packet loss

controllerhtmlgt

$01 C s- J http1921680^

Run Reset

adap t i vecamro l

13S3603 6682830

6258383

1393689 -8pound62298 B JhK-iH-)

-6239783 6626603

666G855

-9259783 -0629683 H HHI-li4s

Gsxgte i

efk-Dpl =

e(k-l) p2 =

ucfk-ljk =

uc(k- l ) p l

uc(k-l) p2

thik-lj k =

th ik - l j th l

th ik- l ) th2

th(k- l ) th3

thk- l ] th4

thk- l ) th5

thfk- l j th

amp c l

= 50000

=10000

= 66000

= -309998

= 1 0 4 4 2 2 5 4

= -42712

= 4240

ITtdlk^ Turlb

o Htp iH9i

| IG^Search

16S0 1

raquo bull zfgt

b i r p

ycqr u

^Settings

772 Test Results

in Table 73

File name

t_xdat

t_xmdat

t_edat

t_ucdat

t_udat

t_thetadat

t_ydat

t_ymdat

Data description

000000

-000521

-000667

-000817

-000764

-000770

-000815

-000738

-000650

-000665

-000641

-000623

-000645

-000594

-000587

-000551

-000514

-000587

-000641

000000

-000037

-000151

-000291

-000447

-000580

-000713

-000862

-000986

-001091

-001202

-001313

-001403

-001503

-001586

-001667

-001748

-001817

-001903

000000

-000523

-000687

-000730

-000731

-000719

-000702

-000685

-000669

-000652

-000637

-000622

-000608

-000595

-000582

-000569

-000558

-000546

-000536

000000

-000039

-000153

-000289

-000427

-000563

-000693

-000817

-000936

-001049

-001158

-001261

-001359

-001453

-001543

-001628

-001710

-001788

-001862

-000522

-000480

-000564

-000550

-000539

-000547

-000528

-000496

-000503

-000430

-000472

-000441

-000491

-000511

-000390

-000446

-000383

-000369

-000381

-000435

-000441

-000439

-000447

-000373

-000418

-000404

-000373

-000440

-001982

-002051

-002115

-002190

-002251

-002311

-002367

-002427

-002476

-002525

-002558

-002603

-002641

-002687

-002732

-002756

-002781

-002813

-002832

-002862

-002894

-002916

-002952

-002980

-002995

-003014

-003035

-003052

-000526

-000516

-000507

-000498

-000489

-000481

-000474

-000466

-000460

-000453

-000447

-000440

-000435

-000429

-000424

-000419

-000414

-000410

-000405

-000401

-000397

-000393

-000390

-000386

-000383

-000380

-000377

-000374

-001933

-002000

-002065

-002126

-002185

-002241

-002294

-002345

-002394

-002440

-002484

-002526

-002566

-002605

-002641

-002676

-002710

-002741

-002772

-002800

-002828

-002854

-002879

-002903

-002926

-002948

-002969

-002989

-000453

-000436

-000385

-000428

-003078

-003109

-003139

-003161

-000371

-000369

-000366

-000364

-003007

-003025

-003043

-003059

-0 025

_ m _ _ ^ i = _ mdash p i r r F ^

~~-ti ===ii

-mdash^zr ~~ i

2(enfc) -

-00006

-00009

-00011

-00008

-00001

-00004

-00008

-00001

-00002

-00005

-00004

-00005

-00004

-00008

-00001

-00002

-00003

-00002

-00003

-00002

-00003

-00002

-00001

-00002

-00010

-00009

-00001

-00009

-00006

-00005

-00001

-00008

-00013

-00002

-00004

-00007

-00014

-00006

-00007

-00001

-00010

-00003

-00004

-00005

-00003

-00004

-00002

-00001

-00002

-00001

-00002

-00003

-00005

-00006

-00008

CHAPTER 8

81 Conclusion

82 Future Work

xv2 r~

PILOT PLANT

Realtime (lata

D Xbdquo

B xbdquo

PE -W-V2

fc V -tvi

PILOT PLANT

PID Embedded

Adaptive Ccntroller

Online measurement

Hyperterminal

reg Spf M -amp- 1

i KZ- ^ -n

REFLUX DRUM

A 12 Vent-bleed

CONDENSER^-

mdash 4 6

i mdash amdashgtp j

Inert gas O

mdash m ltV3

i te i iaal

J5) Input ho-ot IS)

B - t-t

a) Kettle type

o h m m I K I

i t t_e i i - 1 1

-amp Q

_ U ftau irav

P| vopor flow

V U heat -

exchanger

A WH-J

have been specified

degrees of freedom

Column pressure

Manipulated

variables

Reflux flow rate

Reboiler duty

Condenser duty

Bottoms flow rate

Control valve

location

Reflux flow (VI)

Heat flow (V4)

Coolant flow (V3)

Bottoms flow (V5)

Control Structure

D-V(or D-QB)

L-V(or L-QB)

Role of valve

Inventory

Control (IC)

Separation

Control (SC)

structures

units in the plant

flow rate B

I raquo - sect I -

ATbdquo

are switched

H amp J bull

Component

Propane

Normal Butane

Isobutane

Isopentane

Normal Pentane

Hexane

Heptane

Octane

Nonane

Normal Decane

n-CHH24

n-C12H26

Cyclopentane

Methylclopentane

Benzene

Toluen

O-Xylene

E-Benzene

Cut point

(degC)

ASTM D86

(degC)

124024

Properties

1 Octane Number

2 Lead Content (g1)

10 vol

50 vol

90 vol

Residue ( vol)

Testing method

ASTM D2699

ASTMD3341

ASTM D86

ASTM D130

ASTMD381

ASTM D323

ASTM D1266

ASTM D525

ASTMD1298

Requirements

min 87

max 015

max 70

max 120

max 190

max 210

max 20

maxN-1

max 40

min 43

max 80

max 015

min 240

070 - 074

capacity

tso (TBP) = 5842 C

t(30- io) (TBP) = 3599-2467=1132 degC

t50 (EFV-TBP) = 1-5 C

Therefore

tso (EFV) = 5842+15=5962 degC

EFV (1 atm)

EFV (46 atm)

20 3840 60

Volume

80 100

B31 Description

B32 Calculation

fegtegtd f l ow

tray f

Rf= B-LF+ Vf= 62 - 58 + 28 = 32 vol

Stream

Total light

fractions E S D

Bottoms B

Volume fraction

Liquid flow rate

-73916

133973

-64677

143213

Liquid density

Mass flow rate

-45458

-38677

104046

B41 Description

B42 Calculation

stripping section

kcalkg

kcalhlOJ

kJhl0 j

276860

131300

408161

kcalhlOJ

149134

kJhl0J

267136

357141

624280

B51 Description

reflux flow

B52 Calculation

46degC

Stage 15 (tray 14)

D Distillate

9611+Ro

kcalkg

ZSD+Ro

5065+Ro

9611+Ro

kcalkg

kcalhlOJ

11053+24 R0

kJhlOJ

1005 R0

46263+1005 R0

kcalh103

49131+97Ro

56405+ 97R0

kJhl0J

205665+406R0

236111+406R0

46263+1005 Ro= 236111+406 Ro

Therefore

Ro= 7415 (tonh)

at the column top)

AHRoR0= AHLL

(115-24) (742) = (106-22) I

Therefore

L = 804 (tonh)

Stream

Temperature (C)

Pressure (atm)

Density (kgm )

Stream

Temperature (C)

RVP (kPa)

Density (kgm )

Condensate

130000

Reformate

105000

Raw gasoline

Gasoline

250000

Condensate bull

bullff

Raw Gasoline

amp V - 0 1

PEF l l OPUH

-Gasoline

GSSOLINE MIXER

gasoline

is 128degC

tankers

B74 Feed Control

46 atm

i T C - 1 r

mdashImdash I

--copy

l-MmdashJ

To Column

B76 Bottom Section

Cl Introduction

linear

outlet weir

Mbdquo = f(LJ (Cl)

C21 Generic Trays

equations

d(Mbdquo)

Liquid

Flow rate

vbdquo Vn

Concentration

staae n

dh dMbdquo x = A-

dLbdquo dL (C4)

d(Mbdquoxbdquo) dt

dt Mbdquo (C6)

d(Mnhn) dt

V = H-h

C22 Feed Tray

stage (feed tray

LfXrbdquo

I-v vgt LrXf

d(Mfxf)

dt Mbdquo

d(Mfhf)

C23 Top Section

Vlaquobdquo

11 V M1

vbdquo

d(MN+l) _ (C 13) dt

d(M XN+])=Lx^ + y L _ y ( C 1 4 )

11 N+ nN+

C24 Bottom Section

l I l I

ltHXr-B x F

d(M2) dt

L3-L2+ VB -V2

dMRhB) dt

= 23Z3 +HBVB- h2L2 - H2V2

Therefore

H2 -h2

be neglected

dMB) = L 2 _ V B B ( C 2 3 )

d(MBhB)

4 Simplified Model

yn = r (C27)

+ (a-l)xbdquo

aZyv+2 = dL)

L2= LT~ = LN+2-

equations [12]

5) Tray n(n = 2 - l)

MBX] =(L + LF)X2 - Vy - fix (C33)

1) LF=qFF

2) VF = F-LF

y = r bull (C35)

1 + a - )Xj

A = 730 (kJkg)

V0= 39098 (kgh) or 668871 (kmoleh)

V = 0+ = 663407 (kmoleh)

Joshi [43]

ffl^^M (C38)

314(175X1-4) Z ^ = 2488 (kmole) B 4 786

t 0957chD2k dr

095(314)(028)(175)2 680 M = = 580 (kmole)

MD = 5iL + D) (C41)

flow rate

follows

Tray 5 (n = 6) M6 = F(^5 - y6) + (Z + LF )(x7 - x6)

Tray 3 (n = 4) M4 = F(^3 - gt4) + (Z + ZF )(x5 - x4)

2488 (kmole)

1403 x16 =1646291 y]5 - 756380x6 -927597x6

58x15 = 1646291(y14 -y ] 5) + 756380(x6 -x l 5)

58x4 = 1646291(73-gtgt4) + 756380(x5-x4)

58x13 = 1646291(712 - yn) + 756380(xl4 - x13)

58x12 =1646291(j |l-j12) + 756380(x13-x12)

58 = 1646291(710 -yu) + 756380(x2 -x )

58x0 = 1646291(79-^0) + 756380(x-x0)

58x9 = 661 39ys -15638gt-9 + 756380(xl0 -x 9 ) + 5995

58x8 = 661139(y7 -ya) + 756380 x9 - 18859x8 + 3399

58x7 = 661139(y6-y7) +179887 l (x 8-x 7)

58x6 = 661 39(y5-y6) + 179887 l (x 7 -x 6 )

58x5 = 661139(j4 - y5) +1798871 (x6 - x5)

58x4 =661139(^3 -yA) + 79887 l (x 5-x 4)

58x3 = 661 139(^2 - y 3 ) + l798871 (x4 - x3)

58x2 =661139(j -y2) +1798871 (x 3 -x 2 )

2488x = 1798871 x2 -1109235x -661139^ (C42)

568x y ~ l + 468x

y2 = 568x2

1 + 468x

^ 1 5 =

l + 468x (C43)

bullCO

laquo r M |

raquo ^ SA 11 j

w r n i |

^ ltgt fM f 3 1

ET mAr pound |

~^ IT JWi a mdash i

Cgt $ IZ

1 ma r ii |

P $ mar t |

ET r Jfifl V 3 1

b $ TWVlP 2 1

J ^ m d If f |

WFYMtG

fiterttxm

STRIPPING SECTION

GENERAL TRAY

COLUMN

1 TRAY 7

1 TRAYS

RECTI FYINO SECTION

GENERAL TRAY 1

Figure D3

- w i 13411

~W 46804

RECTIFYING SECTION

mdash bull In2 Out2

STRIPPING SECTION

bull XD

To Workspacel

-4L Scope 1

Raw Gasoline

bull | xB

To Workspace

H Scope

In20ut2

Inl O u l l M

In 2 Ou2t

Tray 14

bull i n l Out1 |

- W i n 2 Oul2|

Tray 13

In 10ut 1

In20ut2

Tray 12

bull In lOu t l

In20ut2

Tray 11

InlOutl

In20ul2

Tray 10

bullNln20Ut2

Tray 9

l j mdash

~2~gt -In2

bull in 2

Tray 8

x 1 bull Outl

bull - K 2 Out2

_2 mdash

f bull

n 1 n n H I Wgt A

In 2 Ol l t l

Tray 7

mdash bull

In 10ut1

In20ut2

Tray 6

- gt In20ut2

Tray 5

In lOut l -

bull ln20ut2

Tray 4

bull in lOut l

1 bull

In20ut2

Tray 3

In lOut l

In20ut2 [

Tray 2

[ bull

In lOut l H

In20ul2 |

1 Tray 1

__ Out1

bull In1

Out2 -gt lt_2_gt

O bull72302

471 r Integrator 2

bull XI

To Workspace2

Scope 2

K 2 Olit2

2T899 ^ Function

VLE equation

GENERIC TRAY n

V bull L(n+1)Mn

In2 _ - -

A i bull

-bull VnMn

bull 1 integrator 2

y lt bull

V IE equa Son

bull xn

To Workspace2

bullbull bull -

Scope xn

TRAY 7 (Stage n -8)

bull 3 gtbull

bull 1

( 2 in2

IH130410 ~gt-

bull 119679

bullbullyenbullbull

y- Integrator 2

VLE equation

To Workspaces

Scope 2

gt bull

1 lHn0410

bullbullbull xS

To Workspace

2 bull 119879 In2

Outl bull bull I

289533 N

li integrator 2

130410

Function

MATLAB Fen 2

bull gt bull bull

Scope2

( 1 In2

119666 1 I s J

Integrator 2

120027 K

Scope 2

inputs

M M n+ Mbdquo

-X (El)

= = V15= F+ VF = V+ 985152

Vw = l 15 (E2)

X = f(Xut)

dX = X-X

du = u - u

dX df] _lt3x_

dX + 8f] _du_ du

Mn Mn Mn Mn

Mn +1 Mn +1 Mn Mn

T T -t- V V K V

i ( 0 = Ax(t) + Bu(t) (E4)

y(t) = Cx(t) (E5)

follows

L ==LS = 1798871 (kmoleh)

L9 = = Z15= 756380 (kmoleh)

V = = V = 661139 (kmoleh)

V9 = = V]5 = 1646291 (kmoleh)

M2 = M3 = = Mi5 = 580 (kmole)

M16 = MB = 2488 (kmole)

_KK _ (L]+K2V) _ L 21 M2

22 M2 23 M 2

1) Collect data

w = 1 ^ 1 = 7 Z 6 i 2=TT

w =2 h _xlZx2) _-fe-i) 2 J ~ M2 2lt2~ M2

laquo - 1 6 66gti = 6 ft162 ^ 1 6

_ K M16

[00012 00063 00091 00098 00076 00044 00022 00021 00048

00111 00216 00306 00285 00178 00086 -00702

-00024 -00157 -00237 -00254 -00196 -00116 -00058 -00027 -00024

-00050 -00097 -00138 -00128 -00080 -00039 00704]r

C = 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

E2 Stability Test

V(x)=xTPx (E6)

ATP + PA = -I (E9)

positive definite

P = lyap(AI)

for i=l16

Pi = P (1 i 1 i)

det(Pi)

d e t ( P l ) = 0 0 3 2 8 3 1

d e t ( P 2 ) = 0 0 0 0 9 0 8 4 9

d e t ( P 3 ) = 2 4 4 4 3 e - 0 0 5

d e t ( P 4 ) = 5 5 4 7 6 e - 0 0 7

d e t ( P 5 ) = 1 0 1 5 2 e - 0 0 8

d e t ( P 6 ) = 1 6 2 0 8 e - 0 1 0

d e t ( P 7 ) = 2 3 0 2 5 e - 0 1 2

d e t ( P 8 ) = 2 6 1 8 3 e - 0 1 4

d e t ( P 9 ) = 4 1 9 5 9 e - 0 1 6

d e t ( P l O ) = 1 2 8 8 6 e - 0 1 7

d e t ( P l l ) = 6 7 8 4 7 e - 0 1 9

d e t ( P 1 2 ) = 3 9 1 6 e - 0 2 0

d e t ( P 1 3 ) = 1 8 3 0 8 e - 0 2 1

d e t ( P 1 4 ) = 7 0 8 9 e - 0 2 3

d e t (P15) = 2 4 8 7 6 e - 0 2 4

d e t ( P 1 6 ) = 8 4 6 1 2 e - 0 2 6

stable

include ltstdlibhgt

using namespace std

if(k = x_kmlk+l)

stampn)

if(k = e_kmlk+l)

stampn)

if(k = uc_kmlk+l)

stampn)

return

th kk = k

b21e_kmlp2)x_kmlp2

b22e_kmlp2)x_kmlpl

b22e_kmlp2)x_kmlp2

b21e_kmlp2)uc_kmlpl

b21e_kmlp2)uc_kmlp2

b22e_kmlp2)uc_kmlpl

b22e_kmlp2)uc_kmlp2

r e t u r n

F2 Plant Model

include ltstdlibhgt

include PlantModelh

using namespace std

PlantPlant()

all = -67941 + 067(rand()2-05)

al2 = -09095 + 009(rand()2-05)

a21 = 14686 + 015(rand()2-05)

a22 = -02497 + 002(rand()2-05)

bll = -01461 + 0014(rand()12-05)

bl2 = 02073 + 002(rand()2-05)

b21 = -00021 + 00002(rand()12-05)

b22 = -00281 + 0003(rand()2-05)

ell = -00624 + 0006(rand()2-05)

cl2 = -00281 + 0003(rand()2-05)

c21 = 02458 + 0025(rand()2-05)

c22 = 00009 + 000009(rand()2-05)

Plant~Plant ()

if(k = u_kk)

this-gtu_k = u_k

this-gtx_k = x_k

return

bl2Tu_kp2

b22Tu_kp2

x_kplk = k+1

r e t u r n

F3 Reference Model

include ltstdlibhgt

using namespace std

RefmdlRefmdl()

Refmdl~Refmdl()

if(k = uc_kk)

stampn)

this-gtuc_k = uc_k

if(k = xm_kk)

stampn)

this-gtxm_k = xm_k

return

xm_kplk = k+1

return

include ltstdlibhgt

using namespace std

Linctrl Linctrl()

Linctrl -Linctrl ()

time stampn)

this-gtth_k = th_k

time stampn)

this-gtuc_k = uc_k

time stampn)

this-gtx_k = x_k

return

- th_kth2x_kp2

- th_kth4x_kp2

u_kk = k

return

F5 Comparator

include ltstdlibhgt

include Comparatorh

using namespace std

this-gtx_k = x_k

this-gtxm_k = xm_k

return

compute errors

e_kk = k

r e t u r n

include ltstdlibhgt

using namespace std

stampn)

this-gtx_k = x_k

return

y_kk = k

return

include ltstdlibhgt

using namespace std

time stampn)

this-gtxm_k = xm k

return

ym_kk = k

ym_kpi = ym_kpi

ym_kp2 = ym_kp2

r e t u r n

F8 CGI Program

inc lude ltctypehgt

include

lterrnohgt

ltstringhgt

ltstdiohgt

ltunistdhgt

ltfcntlhgt

ltstringhgt

ltsyssockethgt

ltsystypeshgt

ltnetinetinhgt

ltarpainethgt

define LINELEN 1024

struct valinfo

unsigned char name

unsigned char text

struct thetaPkt

struct Pkt

int pi

int p2

static

amll =

ami 2 =

am21 =

am22 =

bmll =

bml2 =

bm21 =

bm22 =

cmll =

cml2 =

cm21 =

cm22 =

all = -

al2 = -

a22 = -

bll = -

-67 94

static

= -510

= -310

= 1044

= 1006

static int nvals=0

if (gotvals)

nvals = getvals()

gotvals = 1

)vals[i]name)==0)

return vals[i]text

return NULL

=============== httpunescape ===========

unsigned char siptr

unsigned char soptr

unsigned char sos

(unsigned char) )

soptr = sos

siptr = sis

while (siptr)

if(siptr == )

int c = 0 i

for (i=0ilt2i++)

siptr++

c = claquo4 + h

if (i = 2)

free(sos)

return NULL

soptr++ =

soptr++ = siptr

siptr++

soptr = 0

free (sos)

return sis

=============== hextobin =================

if(isdigit(c))

return c-0

return -1

=============== getvals ===================

int vent = 0

unsigned char vstr

unsigned char vptr

unsigned char eptr

unsigned char aptr

int 1 cl

return 0

if(vstr == NULL)

return 0

if(vstr[l-l] == n)

vstr[l-l]=0

vptr = vstr

while (vptr)

vcnt++

valinfo))

vptr = vstr

for (i=0iltvcnti++)

if (eptr == NULL)

return 0

eptr = 0

if (aptr)

aptr = 0

vptr = aptr+1

return vent

unsigned char c

unsigned char cs

int fd len

if((fd==-l))

exit (1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== write signals ===================

unsigned char c

unsigned char cs

int fd len

if((fd==-l))

exit(1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== write a signal ===================

unsigned char c

unsigned char cs

int fd len

if((fd==-l))

exit (1)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== getsignal ===================

int fn s i m sn 1

unsigned char buf

if(fn==-l)

exit(1)

return

read(fn buf 20)

signal = s

free((void) buf)

close(fn)

return s

=============== get ascii signal ===================

int fn s i m sn 1

unsigned char buf

if(fn==-l)

exit (1)

return 0

read(fn buf 20)

signal = s

free((void) buf)

close(fn)

return 1

=============== settime ===================

int t=0

unsigned char c

unsigned char cs

int len

if((f==-l))

exit(l)

write(f c len)

write(f t 1)

free((void) c)

free((void) cs)

close (f)

return

=============== Wait ===================

int i=0

while(i++ltn)

=============== gettime ===================

clear signals

kT = k

Write to files

return

=============== clear signal ===================

int fn

if(fn==-l)

exit(1)

return

write(fn20)

close(fn)

return

unsigned char ch

if (xl==0)

ch[0] = 0

len = 1

if(xllt0)

xl = -xl

sign[0] = -

sign[0] = +

while(xlgt0)

ch[i] = 0 + xl10

xl=xl10

len=i+l

for(i=0 iltlen i++)

free((void) ch)

return

=============== getAdapMechPkt ===================

th4 th5 th6 th7 th8

int outfile

Receive signals

getsig

vartmpfuc2

vartmpfkth

vartmpfthl

vartmpfth2

vartmpfth3

vartmpfth4

vartmpfth5

vartmpfth6

vartmpfth7

vartmpfth8

ampuc2)

ampkth)

ampthl)

ampth2)

ampth3)

ampth4)

ampth5)

ampth6)

ampth7)

ampth8)

receivedlth3gtn)

printf

ltpgt ucl

ltpgt uc2

ltpgt thl

ltpgt th2

ltpgt th3

ltpgt th4

ltpgt th5

ltpgt th6

ltpgt th7

ltpgt th8

d) = dn k-1 ucl)

d) = dn k-1 uc2)

d)k = dn k-1 kth)

d) = dn k-1 thl)

d) = dn k-1 th2)

d) = dn k-1 th3)

d) = dn k-1 th4)

d) = dn k-1 th5)

d) = dn k-1 th6)

d) = dn k-1 th7)

d) = dn k-1 th8)

x_kml-gtk = kx

x_kml-gtpl = xl

x_kml-gtp2 = x2

e_kml-gtk = ke

e_kml-gtpl = el

e_kml-gtp2 = e2

uc_kml-gtk = kuc

uc_kml-gtpl = ucl

uc_kml-gtp2 = uc2

th_kml-gtk = kth

th_kml-gtthl = thl

th_kml-gtth2 = th2

th_kml-gtth3 = th3

th_kml-gtth4 = th4

th_kml-gtth5 = th5

th_kml-gtth6 = th6

th_kml-gtth7 = th7

th kml-gtth8 = th8

Write to files

return

=============== genAdapMechPkt ===================

th k-gtk = k

Write to files

return

=============== main ============

main ()

int valid

int stime gamm

int i=0

int k kT

int kmax=2

struct Pkt x_kml

struct Pkt e_kml

struct Pkt uc_kml

int getkt=0

int getkmax=0

ltheadgtn)

while(getkmax)

wait(5000)

while(klt kmax)

signalsn)

while(Igetkt)

wait (5000)

while(k=kT)

wait(10000)

signalsn)

gainsn)

ampth_k)

exit (0)

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in Table G2

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Plant Error

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Adaptive Gains

0000000

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0000000

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-0002945

-0002959

-0003857

-0004283

-0003904

-0003717

-0003901

-0004434

-0003717

-0003381

-0002788

-0003621

-0003745

-0003136

-0003398

-0003197

-0003819

-0003593

-0031089

-0031392

-0031608

-0031867

-0031972

-0032127

-0032175

-0032197

-0032248

-0032252

-0032197

-0032162

-0032284

-0032490

-0032604

-0032713

-0032914

-0033116

-0033278

-0033267

-0033253

-0033342

-0033419

-0033342

-0033439

-0033512

-0033652

-0003687

-0003662

-0003639

-0003616

-0003595

-0003574

-0003555

-0003536

-0003519

-0003502

-0003485

-0003470

-0003455

-0003441

-0003428

-0003415

-0003403

-0003391

-0003380

-0003370

-0003360

-0003350

-0003341

-0003332

-0003324

-0003316

-0003308

-0030254

-0030426

-0030590

-0030747

-0030896

-0031039

-0031175

-0031304

-0031428

-0031546

-0031659

-0031766

-0031868

-0031966

-0032059

-0032148

-0032233

-0032314

-0032391

-0032465

-0032535

-0032602

-0032666

-0032727

-0032785

-0032840

-0032893

7500000

7600000

7700000

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

-0003756

-0004296

-0003310

-0003600

-0003684

-0004076

-0003503

-0003989

-0004075

-0004365

-0003148

-0004010

-0003440

-0003184

-0003502

-0004142

-0004063

-0003750

-0003078

-0003062

-0003270

-0004051

-0003045

-0003074

-0003973

-0003841

-0033687

-0033717

-0033822

-0033808

-0033813

-0033915

-0034075

-0034090

-0034174

-0034355

-0034481

-0034367

-0034446

-0034452

-0034402

-0034367

-0034495

-0034588

-0034652

-0034570

-0034511

-0034490

-0034669

-0034609

-0034624

-0034750

-0003301

-0003294

-0003287

-0003281

-0003275

-0003269

-0003264

-0003259

-0003254

-0003249

-0003244

-0003240

-0003236

-0003232

-0003228

-0003225

-0003221

-0003218

-0003215

-0003212

-0003209

-0003207

-0003204

-0003202

-0003199

-0003197

-0032944

-0032992

-0033038

-0033082

-0033124

-0033164

-0033202

-0033238

-0033272

-0033306

-0033337

-0033367

-0033396

-0033423

-0033449

-0033474

-0033498

-0033520

-0033542

-0033563

-0033582

-0033601

-0033619

-0033636

-0033652

-0033668

in Table H2

0000000

0100000

0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

1100000

1200000

1300000

1400000

1500000

1600000

1700000

1800000

1900000

2000000

2100000

-0000000

0000320

0000436

0000563

0000573

0000611

0000674

0000668

0000648

0000685

0000701

0000719

0000756

0000753

0000770

0000832

0000887

0000837

0000830

0000897

0000000

-0001217

-0001558

-0001908

-0001787

-0001802

-0001909

-0001731

-0001525

-0001561

-0001507

-0001466

-0001518

-0001401

-0001383

-0001300

-0001215

-0001386

-0001514

-0001235

-0001138

-0001335

-0000000

0000337

0000472

0000536

0000576

0000607

0000633

0000657

0000680

0000702

0000723

0000742

0000761

0000779

0000796

0000813

0000828

0000843

0000858

0000871

0000884

0000896

0000000

-0001286

-0001691

-0001796

-0001800

-0001771

-0001733

-0001692

-0001652

-0001613

-0001576

-0001540

-0001507

-0001474

-0001443

-0001414

-0001386

-0001359

-0001334

-0001309

-0001286

-0001264

2200000

2300000

2400000

2500000

2600000

2700000

2800000

2900000

3000000

3100000

3200000

3300000

3400000

3500000

3600000

3700000

3800000

3900000

4000000

4100000

4200000

4300000

4400000

4500000

4600000

4700000

4800000

0000909

0000919

0000940

0000943

0000940

0000958

0000927

0000961

0000954

0000994

0001018

0000958

0000998

0000968

0000967

0000980

0001020

0001031

0001036

0001051

0001014

0001045

0001042

0001029

0001073

0001088

0001086

-0001304

-0001279

-0001298

-0001254

-0001181

-0001198

-0001027

-0001125

-0001054

-0001171

-0001218

-0000935

-0001067

-0000921

-0000888

-0000916

-0001041

-0001055

-0001052

-0001071

-0000897

-0001002

-0000971

-0000900

-0001055

-0001086

-0001048

0000908

0000919

0000930

0000940

0000950

0000959

0000968

0000977

0000985

0000992

0001000

0001007

0001013

0001020

0001026

0001032

0001037

0001042

0001047

0001052

0001057

0001061

0001065

0001069

0001073

0001077

0001080

-0001243

-0001223

-0001203

-0001185

-0001168

-0001151

-0001135

-0001120

-0001105

-0001091

-0001078

-0001066

-0001054

-0001042

-0001031

-0001021

-0001011

-0001001

-0000992

-0000984

-0000976

-0000968

-0000960

-0000953

-0000946

-0000940

-0000934

4900000

5000000

5100000

5200000

5300000

5400000

5500000

5600000

5700000

5800000

5900000

6000000

6100000

6200000

6300000

6400000

6500000

6600000

6700000

6800000

6900000

7000000

7100000

7200000

7300000

7400000

0001064

0001095

0001055

0001096

0001057

0001029

0001060

0001030

0001033

0001032

0001085

0001113

0001096

0001088

0001102

0001139

0001102

0001086

0001050

0001100

0001109

0001075

0001089

0001079

0001118

0001109

-0000928

-0001027

-0000844

-0000993

-0000827

-0000709

-0000830

-0000708

-0000718

-0000721

-0000930

-0001030

-0000941

-0000898

-0000941

-0001066

-0000899

-0000820

-0000682

-0000876

-0000905

-0000763

-0000824

-0000777

-0000923

-0000870

0001084

0001087

0001090

0001093

0001095

0001098

0001100

0001103

0001105

0001107

0001109

0001111

0001113

0001115

0001116

0001118

0001120

0001121

0001123

0001124

0001125

0001126

0001128

0001129

0001130

0001131

-0000928

-0000922

-0000917

-0000911

-0000907

-0000902

-0000897

-0000893

-0000889

-0000885

-0000882

-0000878

-0000875

-0000871

-0000868

-0000865

-0000863

-0000860

-0000857

-0000855

-0000853

-0000851

-0000848

-0000846

-0000845

-0000843

7500000

7600000

7700000

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

0001119

0001152

0001096

0001113

0001118

0001144

0001114

0001144

0001151

0001173

0001104

0001152

0001121

0001106

0001123

0001160

0001159

0001143

0001105

0001101

0001112

0001158

0001103

0001157

0001153

-0000908

-0001034

-0000804

-0000872

-0000892

-0000983

-0000849

-0000963

-0000983

-0001051

-0000767

-0000968

-0000835

-0000775

-0000849

-0000999

-0000980

-0000908

-0000751

-0000747

-0000796

-0000978

-0000743

-0000750

-0000960

-0000929

0001132

0001133

0001134

0001135

0001136

0001137

0001138

0001139

0001140

0001141

0001142

0001143

0001144

0001145

0001146

-0000841

-0000839

-0000838

-0000836

-0000835

-0000833

-0000832

-0000831

-0000830

-0000829

-0000827

-0000826

-0000825

-0000824

-0000823

-0000822

-0000821

-0000820

-0000819

-0000818

-0000817

-0000816

H3 Plant Error

0000000

0100000

0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

1100000

1200000

1300000

1400000

1500000

1600000

1700000

1800000

1900000

2000000

2100000

000000

000002

000020

-000087

-000033

-000051

-000113

-000053

000019

-000012

-000004

-000001

-000037

000000

-000005

000019

000044

-000040

-000106

000004

000036

-000057

000000

000001

000003

-000002

-000020

-000017

-000021

-000045

-000049

-000042

-000045

-000052

-000044

-000049

-000043

-000038

-000030

-000041

-000049

-000050

-000051

2200000

2300000

2400000

2500000

2600000

2700000

2800000

2900000

3000000

3100000

3200000

3300000

3400000

3500000

3600000

3700000

3800000

3900000

4000000

4100000

4200000

4300000

4400000

4500000

4600000

4700000

4800000

4900000

-000052

-000050

-000065

-000054

-000030

-000044

000023

-000025

-000001

-000057

-000082

000034

-000027

000031

000040

000024

-000034

-000043

-000046

-000058

000014

-000035

-000024

000004

-000066

-000082

-000068

-000019

-000064

-000066

-000071

-000073

-000082

-000085

-000074

-000076

-000075

-000083

-000090

-000080

-000072

-000071

-000061

-000062

-000065

-000061

-000073

-000076

-000068

-000066

-000064

-000071

-000083

-000097

5000000

5100000

5200000

5300000

5400000

5500000

5600000

5700000

5800000

5900000

6000000

6100000

6200000

6300000

6400000

6500000

6600000

6700000

6800000

6900000

7000000

7100000

7200000

7300000

7400000

7500000

7600000

7700000

-000064

000013

-000053

000016

000065

000011

000061

000056

000053

-000039

-000083

-000046

-000029

-000049

-000103

-000033

000000

000058

-000026

-000040

000021

-000007

000013

-000050

-000029

-000046

-000100

-000002

-000102

-000112

-000108

-000109

-000100

-000089

-000082

-000071

-000054

-000040

-000042

-000052

-000055

-000056

-000068

-000080

-000089

-000080

-000072

-000074

-000075

-000061

-000065

-000067

-000076

-000074

-000072

-000078

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

-000032

-000041

-000081

-000024

-000073

-000082

-000112

000010

-000077

-000020

000005

-000027

-000092

-000084

-000053

000014

000015

-000006

-000084

000016

000013

-000077

-000064

-000073

-000069

-000075

-000087

-000085

-000090

-000105

-000114

-000100

-000105

-000103

-000095

-000089

-000100

-000107

-000111

-000101

-000093

-000089

-000105

-000097

-000108

H4 Adaptive Gains

e 03716

-05106

-03100

-00427

-00428

-05106

-03100

-03099

-00428

-05106

-03099

-03098

-00428

-05106

-03098

-00428

-00429

-00428

-00429

-00428

-00429

REFERENCES

Hungary vol 3 pp 1719-1724 1984

563 May 1989

Hall 1984

orgwikiMATLAB

Press 1999

McGraw-Hill 1981

2002 pp 4003-4008

6 pp 1169-1175 Dec 1982

e_Diagrampdf

Prentice Hall 1997

University 1990

Hill 1984

India 1979

SJSU ScholarWorks

Fall 2009


Hoan The Nguyen



ACKNOWLEDGMENTS

people

TABLE OF CONTENTS

List of Tables xiv

List of Figures xvi

11 Background 1

15 Methodology 5

28 ARM Processor 16

31 Introduction 20

41 Introduction 26

441 Plant 31

51 Introduction 43

521 Plant Model 44

61 Introduction 50

71 Introduction 66

751 CGI Program 78

77 Testing 93

772 Test Results 98

81 Conclusion 104

82 Future Work 105

A12 Vent-bleed 110

B31 Description 124

B32 Calculation 125

B41 Description 126

B42 Calculation 127

B51 Description 128

B52 Calculation 129

Cl Introduction 137

C22 Feed Tray 140

C23 Top Section 141

F2 Plant Model 170

F5 Comparator 173

F8 CGI Program 175

G3 Plant Error 206

H3 Plant Error 222

References 230

LIST OF TABLES

LIST OF FIGURES

Motor octane number

Network file system

Personal computer

Reid vapor pressure

True boiling point

Zero-order hold

LIST OF SYMBOLS

A State matrix

B Input matrix

C Output matrix

e State error

L Feedback matrix

u Control signal

x State variable

y Controlled output

Greek Symbols

y Adaptation rate

0 Adaptive gain

Subscript

B Bottom product

F Feed

m Reference model

CHAPTER 1

INTRODUCTION

11 Background

time spaces

adaptive controller

mathematical method

15 Methodology

CHAPTER 2

LITERATURE REVIEW

RECTIFYING SECTION

F (feed flow rate)

Q n I (3) CONDENSER

1 8 - D

stage f (feed tny)

stage rc

Material stream

Feed stream

Distillate stream

Bottoms stream

Position

Stage f

Stage N

Reflux drum

Stage 1

Reboiler

Flow rate

Concentration

in Figure 22

Liquid phase

Stage it

(Trav gti-l)

bull bullbullbull

m^u - Bubble cap

structures

I |mdash0mdashI I

bottoms flow rate B

are adjusted [12]

required

Command_ signal

Adaptive mechanism

laquosj

Control signal

Plant 1 Output

Process dynamics )

Siv-CSnftlteF----

26 Adaptive Schemes

261 Gain Scheduling

Command signal

Output

signal

MoctSI

Control signal

mechanism

Plant -bull Output

= ( ) bull (21)

disturbances or not

- mdash

yfdx dt

x = 0 i

-gt() =

= = ( ) = -W(x) (22) dt dx dt dx

dx mdash = Ax (23)

ATP + PA=-Q (24)

following function

V(x) = xTPx (25)

28 ARM Processor

DB-9 DB-9

RS-232

Features

Memory

subsystem

GPIO ports

Ethernet

Descriptions

solution

8 memory banks

by RAM

CHAPTER 3

31 Introduction

RffLlrtERLMl

xD gt 98

xB lt 20

Table 31

Temperature C

Pressure atm

Density kgm3

Mass flow rate kgh

Main streams oft

Condensate

130000

he plant

Raw gasoline

system

35 Plant Modeling

1403 x16 =1646291^15 -756380x16 -927597xI6

58x15 =1646291(gtl4 -^1 5) + 756380(x16 -x15)

58x14 =164629103 -gtgt14) + 756380(x15-x4)

58x13 =1646291012 -_y]3) + 756380(x14 -x13)

58x12 =1646291(^n -y1 2) + 756380(x13 -x ] 2)

58xH =164629IO10 ~ ^ i ) + 756380(x12-x)

58x10 =164629109 -^1 0) + 756380(xn -x10)

58x9 = 661139gtgt8 -15638^9 + 756380(x10 -x9) + 5995

58x8 = 66113907 ~yamp) + 756380 x9 -18859x8 + 3399

58x7 = 661 39(y6-y7) + 798871 (x8 -x 7 )

58x6 =66113905-gt 6) + 1798871(x7-x6)

58x5 =66113904^) +179887 l (x 6 -x 5 )

58x4=66113903-^4) + 1798871(x5-x4)

58x3 =66113902-73) +1798871 (x 4 -x 3 )

58x2 =661139(^-gt2) +179887l(x3-x2)

2488x = 1798871x2-1109235x1 -661139^

568x y = l + 468x

l + 468x

^ 1 5 =

568x 15

l + 468xbdquo (34)

CHART OF VAPOR

01 02 03 0 4 05 06 07 08 09

36 Plant Simulation

Table 32

bull L _ I i 1 l

6 8 10 12 14 16 18 20 Time (h)

than 2

CHAPTER 4

41 Introduction

and (32)

Disturbances

Ditiilitirn Gy-tem

x(t) = A(xt) + Beu(t) (41)

y(t) = Cex(t) (42)

two-output system

-09095

-02497 Bbdquo

-01461 02073

-00021 -00281 and C

-00624 -00281

02458 00009

Bode Diagram

Frequency (radsec)

431 Stability Test

finite time T-tgt0

x = Ax(t) + Bu(t) (45)

y(t) = Cx(t) + Duy) (46)

full rank of n

output

S=[CCACA2CA]]T

the next section

441 Plant

yt) = Cx(t)

where A = au

an_ B =

bn_ and C =

-00624 -00281

02458 00009

variables

442 Reference Model

Sec 43

where Abdquo

ybdquo(t) = cmxm(t)

-67941 -09095

14686 -02497

5 = -01461 02073

-00021 -00281 and Cbdquo

-00624 -00281

02458 00009

ut) = Muct)-Lx(t)

x = (A- BL)x + BMuc

hence we define

Ac(0) = (A-BL)

Bc6) = BM

i2 ~b2

l 2 11^2 ^12^4

22 _ ^ 2 1 ^ 2 ~ ^ 2 2 ^ 4

b2]65+b2281 b2Xdb+b22d (412)

condition we get

au-bu6-bnel =-67941

an -bu6a2 -bn6deg4= -09095

a2]-b2]6deg-b220deg =14686

a22-b2]e2-b229deg= -02497

6Adeg + M7deg =-01461

606deg + 6 X =02073

b2l6deg5+b229deg =-00021

b2]edeg6+b226degs =-00281 (413)

condition

0 _ b22(au +67941)-bu(a2] -14686) 0 =

regp22 ^12^21

a o _ b22(an + 09095)-bn(a22 +02497)

^11^22 _ ^12^21

buo22 mdashbnb2]

0 _ -b2](a]2 + 09095)+ bu(a22 +02497) 6gt =

bP 22 b]2b2]

-b2]bn+bub22

n0 002816I2+02073Zgt22

(J6 = -b2]bu+bub22

_0 - 000216+ 0146 b2x Uf =

-b2]bu+bub22

0 = 002816 +020736

-b2Xbu+bxxb (414)

Error Equation

e(0= x(0-m(0

e() = ^ ( 0 + 5 i ( 0 - ^ I B ( 0 - 5 m laquo c ( 0 - (4-15)

e(t) = Ame(t) + V(t)(0-O0) (417)

446 Adaptation Law

function

V(e 0) = [yePe + (0 - 0deg f (0 - 0deg)) (418)

(420) dt 2

ltP + PAm = -a (4-21)

^ = -W(t)Pe(t) at

y(buex+b2Xe2)xx

y(buex+b2]e2)x2

y(bnex+b22e2)xx

y(bx2ex+b22e2)x2

-y(bxxex+b2xe2)ucX

-y(bxxex+b2Xe2)uc2

-y(bX2ex+b22e2)ucX

-y(buex+b22e2)uc2

6 = (423)

mdash = -05591lt -07066e2)2 +132756e2] dt 1

2) Disturbances^)

4) Reference model

a n n f l

REFERENCE MODEL

dull In I

0ut2 In2

ADAPTIVE MECHANISM

= X Xm

_X2 Xm2 _

follows

e = RMS(e) = -^A for = 1 or 2

commands

norm_el = norm(el)

norm_e2 = norm(e2)

shown in Figure 46

m B s in

Figures - x vc xm

m B ampm

bull4s

bullraquo i x

i m B raquo bull

im B ffin

State error e1(t)

State error e2(t)

e = 00017

n2 VTooT = 7106210

453 Error Reduction

Plant errors

laquoi

Adaptation rate y

54304 105

71399105

5428410

7106210

54076 105

7100310-5

CHAPTER 5

51 Introduction

G(s) y ( t

521 Plant Model

x(t) = Axt) + But)

y(t) = Cx(t)

x(s) - ~[AX(S) + Bu(s) s

T x(z) = [AX(Z) + Bu(z)]

y(kT) = CxkT) (52)

522 Reference Model

in Chapter 6

ybdquo(t) = cmxm(t)

where Am = [-67941 -09095 14686 -02497] Bm = [-01461 02073 -00021 -00281]

and Cm = [-00624 -00281 02458 00009]

follows

ut) = Muc(t)-Lx(t)

L = 0kT) 62(kT)

0(kT) 0AkT

M 05(kT) 06(kT)

87(kT) 0s(kT)^ (56)

o _ ft2deg2(adeg +67941)-ft02(a20 -14686)

degdeg27 deg12deg21

8 0 _ -amp2 K + 67941) + ft (a2] -14686)

ftdeg =

00021ft0-01461ft0 22

-ft21 f t02+ft0 f t22

-b2]b]2+bub22

-b2bn+bub22

n0 00281ft+02073ftdeg

201 deg]]deg22

6(t) = -y^(t)Pe(t)

= yy (s)Pe(s)

CHAPTER 6

61 Introduction

2) Disturbances^^

reference signals

1 tnl uc(k)

In2 uc(k-1)

xm(k-1)

laquogt

REFERENCE MODEL

H Disturbances

bulleurogt

[B^_]M

0ut1 In)

0ut2 In2

i f MJi-1)

0 u ulaquoK-l)

ADAPTIVE MECHANISM

m lt raquo

Ot-1) Mux bull

e(kT) = exkT)

e2(kT)

h(kT)-xnnkT)

x2(kT)-xm2(kT)_

Ax^kT)

Ax2(kT)

follows

e = RMSe) = ^L for = 1 or 2 (61)

shown in Figure 62

Disturbance f(t)

m gt P i laquo ^ e

a)e(7)

ns gt P l

a) eiikT)

I U I 94543e-004 _ bdquo ^ - s

101 = 9407410-

M = 9 6557e -Q04 = 9 6 0 7 8 t l 0 5

4n2 vioi

sections

in Figure 66

4 include tbdefsh

5 class Plant

6 private

12 public

13 Plant()

14 -Plant()

18 endif

P l a n t ( )

a l l = - 6 7 9 4 1 + 0 6 7 ( r a n d ( ) 2 - 0 5 )

a l 2 = - 0 9 0 9 5 + 0 0 9 ( r a n d ( ) 2 - 0 5 )

a21 = 14686 + 015(rand()2-05)

a22 = -02497 + 002(rand()2-05)

bll = -01461 + 0014(rand()2-05)

bl2 = 02073 + 002 (rand()2-05)

b21 = -00021 + 00002(rand()2-05)

b22 = -00281 + 0003 (rand()2-05)

ell = -00624 + 0006(rand()2-05)

cl2 = -00281 + 0003(rand()2-05)

c21 = 02458 + 0025(rand()2-05)

c22 = 00009 + 000009(rand()2-05)

4 include tbdefsh

5 class Refmdl

6 private

7 Pkt uc_k

8 Pkt xm_k

9 public

10 Refmdl()

11 -RefmdlO

15 endif

Figure 68

4 include tbdefsh

5 class Linctrl

6 private

7 thetaPkt th_k

8 Pkt x_k

9 Pkt uc_k

10 public

11 LinctrlO

12 -LinctrlO

16 endif

database

4 include tbdefsh

5 class Comparator

6 private

7 Pkt x_k

8 Pkt xm_k

9 Pkt e_k

10 public

11 Comparator()

12 -Comparator()

16 endif

and the plant

4 include tbdefsh

6 private

7 thetaPkt th_kml

8 Pkt x_kml

9 Pkt e_kml

10 Pkt uc_kml

11 public

12 AdaptiveMechO

13 -AdaptiveMechO

17 endif

model and the plant

CC = g++

ReferenceModelo

executive file

j haut$ttum

ltOIgt gtiJ^Alt

plusmn1 f bull-lt

i gt bulli

lt euro f bull2

[ bull

- H J bullbull -

~ttttfc

bull=fmdashF^--

^ t ^ i i i = ^ ^

_ - 1 1 = - mdash J

^ J - - - ^ ^

1 1 1 I

5 time

e = |N| s94543c-004 ^

96557e-004

VToi = 96078 105

CHAPTER 7

71 Introduction

shown in Figure 71

_ Data J

5gt I Error

yV H Report

Plant Slmsliitsr

lt = J Output

Linux yacnine

RPC get_port reply

RPC mount request

RPC mount reply

Authenticate client

to the browser

button

lUser sufrmis fwm

arv-affe ie Camp

vas tor PlssrtSwi

Sens ( to i l sA i

(J 0 0

SefieJ acispfcw BM2

Oylpaito wefccfer

72 Common Database

File name

kucdat

ucldat

uc2dat

kthdat

thldat

th2dat

th3dat

th4dat

th5dat

th6dat

th7dat

Data description

Plant state xi

Plant state X2

Error variable ei

Error variable e2

Adaptive gain Gi

Adaptive gain 02

Adaptive gain 63

Adaptive gain 64

Adaptive gain 85

Adaptive gain 96

Adaptive gain 67

th8dat

adapoutdat

kmaxdat

Adaptive gain 0g

Maximal step size

73 Plant Simulator

CC = g++

$ make

1 iij-ji--^- - M - - I - - bull

1 lthtmlgt

2 ltheadgt

4 ltheacigt

5 ltbodygt

9 ltdivgt

value= size=40gt

17 ltformgt

18 ltbodygt

19 lthtmlgt

Feature

action=

method=

target=

Code example

Run gt

Description

program

time and text type

follows

th[k-l])

11 return

15 th-gtk = k

1]10000000

1] 10000000

1]10000000

23 return

751 CGI Program

variables

getenv() as follows

parameters

1 main ()

3 i n t v a l i d

17 while(klt kmax)

19 while(Igetkt)

21 wait(5000)

24 while(k=kT)

26 wait(10000)

ampth_k)

33 k++

36 else

41 exit (0)

program 109880

looses 10S824 188824 100883 100883 100883 19S821

Yers 2 2 1 1 2 3 4 1

port 111 111

48909 55541

2849 2849 2649

sudo rpcinfo -p

I I Bin Edit yamp

hoanaoan-$

gt Terminal

hoan^hoan ~$

2 2 1 1 2 3 4 1 3 4 2 3 A 1 3 4 1 1 2 2 3 3

i n f o -j r o t o

P po r t

111 n i

35368 35832

2649 2649 2S49

44664 44694 44994

2049 2849 2949

41394 41894 41894 33383 44819 33389 44819 33389 44819

M ^ s t i k ^ ^ lt

l - pound ig

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 a 3 3 3 3 3 3 A

syslog-install

root location as

during compilation

TESTOBJS = mycgio

support

1) TCPIP networking

3) IP DHCP support

4) IPBOOTP

5) IPRARP

2) RTL8019AS

and check

1) Boa

2) dhcpcd-new

3) dhclient

4) ifconfig

5) inetd

6) ping

8) route

9) routed

10)telnetd

ll)tftpd

terminal

for Linux machines

machine)

go 0x0c008000

RRMboot 182 (Aug 12 2084 - 104321)

bulltrade u u mdash

1 000 netmask 2552552550 lo

77 Testing

771 Test Procedure

(PC Linux machine)

Figure 722

D Graquo S S if

5fw help

following command

1 9 2 1 6 8 0 8 o p t t e s t v a r t m p

| g haanhoan ~

0JS packet loss

controllerhtmlgt

$01 C s- J http1921680^

Run Reset

adap t i vecamro l

13S3603 6682830

6258383

1393689 -8pound62298 B JhK-iH-)

-6239783 6626603

666G855

-9259783 -0629683 H HHI-li4s

Gsxgte i

efk-Dpl =

e(k-l) p2 =

ucfk-ljk =

uc(k- l ) p l

uc(k-l) p2

thik-lj k =

th ik - l j th l

th ik- l ) th2

th(k- l ) th3

thk- l ] th4

thk- l ) th5

thfk- l j th

amp c l

= 50000

=10000

= 66000

= -309998

= 1 0 4 4 2 2 5 4

= -42712

= 4240

ITtdlk^ Turlb

o Htp iH9i

| IG^Search

16S0 1

raquo bull zfgt

b i r p

ycqr u

^Settings

772 Test Results

in Table 73

File name

t_xdat

t_xmdat

t_edat

t_ucdat

t_udat

t_thetadat

t_ydat

t_ymdat

Data description

000000

-000521

-000667

-000817

-000764

-000770

-000815

-000738

-000650

-000665

-000641

-000623

-000645

-000594

-000587

-000551

-000514

-000587

-000641

000000

-000037

-000151

-000291

-000447

-000580

-000713

-000862

-000986

-001091

-001202

-001313

-001403

-001503

-001586

-001667

-001748

-001817

-001903

000000

-000523

-000687

-000730

-000731

-000719

-000702

-000685

-000669

-000652

-000637

-000622

-000608

-000595

-000582

-000569

-000558

-000546

-000536

000000

-000039

-000153

-000289

-000427

-000563

-000693

-000817

-000936

-001049

-001158

-001261

-001359

-001453

-001543

-001628

-001710

-001788

-001862

-000522

-000480

-000564

-000550

-000539

-000547

-000528

-000496

-000503

-000430

-000472

-000441

-000491

-000511

-000390

-000446

-000383

-000369

-000381

-000435

-000441

-000439

-000447

-000373

-000418

-000404

-000373

-000440

-001982

-002051

-002115

-002190

-002251

-002311

-002367

-002427

-002476

-002525

-002558

-002603

-002641

-002687

-002732

-002756

-002781

-002813

-002832

-002862

-002894

-002916

-002952

-002980

-002995

-003014

-003035

-003052

-000526

-000516

-000507

-000498

-000489

-000481

-000474

-000466

-000460

-000453

-000447

-000440

-000435

-000429

-000424

-000419

-000414

-000410

-000405

-000401

-000397

-000393

-000390

-000386

-000383

-000380

-000377

-000374

-001933

-002000

-002065

-002126

-002185

-002241

-002294

-002345

-002394

-002440

-002484

-002526

-002566

-002605

-002641

-002676

-002710

-002741

-002772

-002800

-002828

-002854

-002879

-002903

-002926

-002948

-002969

-002989

-000453

-000436

-000385

-000428

-003078

-003109

-003139

-003161

-000371

-000369

-000366

-000364

-003007

-003025

-003043

-003059

-0 025

_ m _ _ ^ i = _ mdash p i r r F ^

~~-ti ===ii

-mdash^zr ~~ i

2(enfc) -

-00006

-00009

-00011

-00008

-00001

-00004

-00008

-00001

-00002

-00005

-00004

-00005

-00004

-00008

-00001

-00002

-00003

-00002

-00003

-00002

-00003

-00002

-00001

-00002

-00010

-00009

-00001

-00009

-00006

-00005

-00001

-00008

-00013

-00002

-00004

-00007

-00014

-00006

-00007

-00001

-00010

-00003

-00004

-00005

-00003

-00004

-00002

-00001

-00002

-00001

-00002

-00003

-00005

-00006

-00008

CHAPTER 8

81 Conclusion

82 Future Work

xv2 r~

PILOT PLANT

Realtime (lata

D Xbdquo

B xbdquo

PE -W-V2

fc V -tvi

PILOT PLANT

PID Embedded

Adaptive Ccntroller

Online measurement

Hyperterminal

reg Spf M -amp- 1

i KZ- ^ -n

REFLUX DRUM

A 12 Vent-bleed

CONDENSER^-

mdash 4 6

i mdash amdashgtp j

Inert gas O

mdash m ltV3

i te i iaal

J5) Input ho-ot IS)

B - t-t

a) Kettle type

o h m m I K I

i t t_e i i - 1 1

-amp Q

_ U ftau irav

P| vopor flow

V U heat -

exchanger

A WH-J

have been specified

degrees of freedom

Column pressure

Manipulated

variables

Reflux flow rate

Reboiler duty

Condenser duty

Bottoms flow rate

Control valve

location

Reflux flow (VI)

Heat flow (V4)

Coolant flow (V3)

Bottoms flow (V5)

Control Structure

D-V(or D-QB)

L-V(or L-QB)

Role of valve

Inventory

Control (IC)

Separation

Control (SC)

structures

units in the plant

flow rate B

I raquo - sect I -

ATbdquo

are switched

H amp J bull

Component

Propane

Normal Butane

Isobutane

Isopentane

Normal Pentane

Hexane

Heptane

Octane

Nonane

Normal Decane

n-CHH24

n-C12H26

Cyclopentane

Methylclopentane

Benzene

Toluen

O-Xylene

E-Benzene

Cut point

(degC)

ASTM D86

(degC)

124024

Properties

1 Octane Number

2 Lead Content (g1)

10 vol

50 vol

90 vol

Residue ( vol)

Testing method

ASTM D2699

ASTMD3341

ASTM D86

ASTM D130

ASTMD381

ASTM D323

ASTM D1266

ASTM D525

ASTMD1298

Requirements

min 87

max 015

max 70

max 120

max 190

max 210

max 20

maxN-1

max 40

min 43

max 80

max 015

min 240

070 - 074

capacity

tso (TBP) = 5842 C

t(30- io) (TBP) = 3599-2467=1132 degC

t50 (EFV-TBP) = 1-5 C

Therefore

tso (EFV) = 5842+15=5962 degC

EFV (1 atm)

EFV (46 atm)

20 3840 60

Volume

80 100

B31 Description

B32 Calculation

fegtegtd f l ow

tray f

Rf= B-LF+ Vf= 62 - 58 + 28 = 32 vol

Stream

Total light

fractions E S D

Bottoms B

Volume fraction

Liquid flow rate

-73916

133973

-64677

143213

Liquid density

Mass flow rate

-45458

-38677

104046

B41 Description

B42 Calculation

stripping section

kcalkg

kcalhlOJ

kJhl0 j

276860

131300

408161

kcalhlOJ

149134

kJhl0J

267136

357141

624280

B51 Description

reflux flow

B52 Calculation

46degC

Stage 15 (tray 14)

D Distillate

9611+Ro

kcalkg

ZSD+Ro

5065+Ro

9611+Ro

kcalkg

kcalhlOJ

11053+24 R0

kJhlOJ

1005 R0

46263+1005 R0

kcalh103

49131+97Ro

56405+ 97R0

kJhl0J

205665+406R0

236111+406R0

46263+1005 Ro= 236111+406 Ro

Therefore

Ro= 7415 (tonh)

at the column top)

AHRoR0= AHLL

(115-24) (742) = (106-22) I

Therefore

L = 804 (tonh)

Stream

Temperature (C)

Pressure (atm)

Density (kgm )

Stream

Temperature (C)

RVP (kPa)

Density (kgm )

Condensate

130000

Reformate

105000

Raw gasoline

Gasoline

250000

Condensate bull

bullff

Raw Gasoline

amp V - 0 1

PEF l l OPUH

-Gasoline

GSSOLINE MIXER

gasoline

is 128degC

tankers

B74 Feed Control

46 atm

i T C - 1 r

mdashImdash I

--copy

l-MmdashJ

To Column

B76 Bottom Section

Cl Introduction

linear

outlet weir

Mbdquo = f(LJ (Cl)

C21 Generic Trays

equations

d(Mbdquo)

Liquid

Flow rate

vbdquo Vn

Concentration

staae n

dh dMbdquo x = A-

dLbdquo dL (C4)

d(Mbdquoxbdquo) dt

dt Mbdquo (C6)

d(Mnhn) dt

V = H-h

C22 Feed Tray

stage (feed tray

LfXrbdquo

I-v vgt LrXf

d(Mfxf)

dt Mbdquo

d(Mfhf)

C23 Top Section

Vlaquobdquo

11 V M1

vbdquo

d(MN+l) _ (C 13) dt

d(M XN+])=Lx^ + y L _ y ( C 1 4 )

11 N+ nN+

C24 Bottom Section

l I l I

ltHXr-B x F

d(M2) dt

L3-L2+ VB -V2

dMRhB) dt

= 23Z3 +HBVB- h2L2 - H2V2

Therefore

H2 -h2

be neglected

dMB) = L 2 _ V B B ( C 2 3 )

d(MBhB)

4 Simplified Model

yn = r (C27)

+ (a-l)xbdquo

aZyv+2 = dL)

L2= LT~ = LN+2-

equations [12]

5) Tray n(n = 2 - l)

MBX] =(L + LF)X2 - Vy - fix (C33)

1) LF=qFF

2) VF = F-LF

y = r bull (C35)

1 + a - )Xj

A = 730 (kJkg)

V0= 39098 (kgh) or 668871 (kmoleh)

V = 0+ = 663407 (kmoleh)

Joshi [43]

ffl^^M (C38)

314(175X1-4) Z ^ = 2488 (kmole) B 4 786

t 0957chD2k dr

095(314)(028)(175)2 680 M = = 580 (kmole)

MD = 5iL + D) (C41)

flow rate

follows

Tray 5 (n = 6) M6 = F(^5 - y6) + (Z + LF )(x7 - x6)

Tray 3 (n = 4) M4 = F(^3 - gt4) + (Z + ZF )(x5 - x4)

2488 (kmole)

1403 x16 =1646291 y]5 - 756380x6 -927597x6

58x15 = 1646291(y14 -y ] 5) + 756380(x6 -x l 5)

58x4 = 1646291(73-gtgt4) + 756380(x5-x4)

58x13 = 1646291(712 - yn) + 756380(xl4 - x13)

58x12 =1646291(j |l-j12) + 756380(x13-x12)

58 = 1646291(710 -yu) + 756380(x2 -x )

58x0 = 1646291(79-^0) + 756380(x-x0)

58x9 = 661 39ys -15638gt-9 + 756380(xl0 -x 9 ) + 5995

58x8 = 661139(y7 -ya) + 756380 x9 - 18859x8 + 3399

58x7 = 661139(y6-y7) +179887 l (x 8-x 7)

58x6 = 661 39(y5-y6) + 179887 l (x 7 -x 6 )

58x5 = 661139(j4 - y5) +1798871 (x6 - x5)

58x4 =661139(^3 -yA) + 79887 l (x 5-x 4)

58x3 = 661 139(^2 - y 3 ) + l798871 (x4 - x3)

58x2 =661139(j -y2) +1798871 (x 3 -x 2 )

2488x = 1798871 x2 -1109235x -661139^ (C42)

568x y ~ l + 468x

y2 = 568x2

1 + 468x

^ 1 5 =

l + 468x (C43)

bullCO

laquo r M |

raquo ^ SA 11 j

w r n i |

^ ltgt fM f 3 1

ET mAr pound |

~^ IT JWi a mdash i

Cgt $ IZ

1 ma r ii |

P $ mar t |

ET r Jfifl V 3 1

b $ TWVlP 2 1

J ^ m d If f |

WFYMtG

fiterttxm

STRIPPING SECTION

GENERAL TRAY

COLUMN

1 TRAY 7

1 TRAYS

RECTI FYINO SECTION

GENERAL TRAY 1

Figure D3

- w i 13411

~W 46804

RECTIFYING SECTION

mdash bull In2 Out2

STRIPPING SECTION

bull XD

To Workspacel

-4L Scope 1

Raw Gasoline

bull | xB

To Workspace

H Scope

In20ut2

Inl O u l l M

In 2 Ou2t

Tray 14

bull i n l Out1 |

- W i n 2 Oul2|

Tray 13

In 10ut 1

In20ut2

Tray 12

bull In lOu t l

In20ut2

Tray 11

InlOutl

In20ul2

Tray 10

bullNln20Ut2

Tray 9

l j mdash

~2~gt -In2

bull in 2

Tray 8

x 1 bull Outl

bull - K 2 Out2

_2 mdash

f bull

n 1 n n H I Wgt A

In 2 Ol l t l

Tray 7

mdash bull

In 10ut1

In20ut2

Tray 6

- gt In20ut2

Tray 5

In lOut l -

bull ln20ut2

Tray 4

bull in lOut l

1 bull

In20ut2

Tray 3

In lOut l

In20ut2 [

Tray 2

[ bull

In lOut l H

In20ul2 |

1 Tray 1

__ Out1

bull In1

Out2 -gt lt_2_gt

O bull72302

471 r Integrator 2

bull XI

To Workspace2

Scope 2

K 2 Olit2

2T899 ^ Function

VLE equation

GENERIC TRAY n

V bull L(n+1)Mn

In2 _ - -

A i bull

-bull VnMn

bull 1 integrator 2

y lt bull

V IE equa Son

bull xn

To Workspace2

bullbull bull -

Scope xn

TRAY 7 (Stage n -8)

bull 3 gtbull

bull 1

( 2 in2

IH130410 ~gt-

bull 119679

bullbullyenbullbull

y- Integrator 2

VLE equation

To Workspaces

Scope 2

gt bull

1 lHn0410

bullbullbull xS

To Workspace

2 bull 119879 In2

Outl bull bull I

289533 N

li integrator 2

130410

Function

MATLAB Fen 2

bull gt bull bull

Scope2

( 1 In2

119666 1 I s J

Integrator 2

120027 K

Scope 2

inputs

M M n+ Mbdquo

-X (El)

= = V15= F+ VF = V+ 985152

Vw = l 15 (E2)

X = f(Xut)

dX = X-X

du = u - u

dX df] _lt3x_

dX + 8f] _du_ du

Mn Mn Mn Mn

Mn +1 Mn +1 Mn Mn

T T -t- V V K V

i ( 0 = Ax(t) + Bu(t) (E4)

y(t) = Cx(t) (E5)

follows

L ==LS = 1798871 (kmoleh)

L9 = = Z15= 756380 (kmoleh)

V = = V = 661139 (kmoleh)

V9 = = V]5 = 1646291 (kmoleh)

M2 = M3 = = Mi5 = 580 (kmole)

M16 = MB = 2488 (kmole)

_KK _ (L]+K2V) _ L 21 M2

22 M2 23 M 2

1) Collect data

w = 1 ^ 1 = 7 Z 6 i 2=TT

w =2 h _xlZx2) _-fe-i) 2 J ~ M2 2lt2~ M2

laquo - 1 6 66gti = 6 ft162 ^ 1 6

_ K M16

[00012 00063 00091 00098 00076 00044 00022 00021 00048

00111 00216 00306 00285 00178 00086 -00702

-00024 -00157 -00237 -00254 -00196 -00116 -00058 -00027 -00024

-00050 -00097 -00138 -00128 -00080 -00039 00704]r

C = 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

E2 Stability Test

V(x)=xTPx (E6)

ATP + PA = -I (E9)

positive definite

P = lyap(AI)

for i=l16

Pi = P (1 i 1 i)

det(Pi)

d e t ( P l ) = 0 0 3 2 8 3 1

d e t ( P 2 ) = 0 0 0 0 9 0 8 4 9

d e t ( P 3 ) = 2 4 4 4 3 e - 0 0 5

d e t ( P 4 ) = 5 5 4 7 6 e - 0 0 7

d e t ( P 5 ) = 1 0 1 5 2 e - 0 0 8

d e t ( P 6 ) = 1 6 2 0 8 e - 0 1 0

d e t ( P 7 ) = 2 3 0 2 5 e - 0 1 2

d e t ( P 8 ) = 2 6 1 8 3 e - 0 1 4

d e t ( P 9 ) = 4 1 9 5 9 e - 0 1 6

d e t ( P l O ) = 1 2 8 8 6 e - 0 1 7

d e t ( P l l ) = 6 7 8 4 7 e - 0 1 9

d e t ( P 1 2 ) = 3 9 1 6 e - 0 2 0

d e t ( P 1 3 ) = 1 8 3 0 8 e - 0 2 1

d e t ( P 1 4 ) = 7 0 8 9 e - 0 2 3

d e t (P15) = 2 4 8 7 6 e - 0 2 4

d e t ( P 1 6 ) = 8 4 6 1 2 e - 0 2 6

stable

include ltstdlibhgt

using namespace std

if(k = x_kmlk+l)

stampn)

if(k = e_kmlk+l)

stampn)

if(k = uc_kmlk+l)

stampn)

return

th kk = k

b21e_kmlp2)x_kmlp2

b22e_kmlp2)x_kmlpl

b22e_kmlp2)x_kmlp2

b21e_kmlp2)uc_kmlpl

b21e_kmlp2)uc_kmlp2

b22e_kmlp2)uc_kmlpl

b22e_kmlp2)uc_kmlp2

r e t u r n

F2 Plant Model

include ltstdlibhgt

include PlantModelh

using namespace std

PlantPlant()

all = -67941 + 067(rand()2-05)

al2 = -09095 + 009(rand()2-05)

a21 = 14686 + 015(rand()2-05)

a22 = -02497 + 002(rand()2-05)

bll = -01461 + 0014(rand()12-05)

bl2 = 02073 + 002(rand()2-05)

b21 = -00021 + 00002(rand()12-05)

b22 = -00281 + 0003(rand()2-05)

ell = -00624 + 0006(rand()2-05)

cl2 = -00281 + 0003(rand()2-05)

c21 = 02458 + 0025(rand()2-05)

c22 = 00009 + 000009(rand()2-05)

Plant~Plant ()

if(k = u_kk)

this-gtu_k = u_k

this-gtx_k = x_k

return

bl2Tu_kp2

b22Tu_kp2

x_kplk = k+1

r e t u r n

F3 Reference Model

include ltstdlibhgt

using namespace std

RefmdlRefmdl()

Refmdl~Refmdl()

if(k = uc_kk)

stampn)

this-gtuc_k = uc_k

if(k = xm_kk)

stampn)

this-gtxm_k = xm_k

return

xm_kplk = k+1

return

include ltstdlibhgt

using namespace std

Linctrl Linctrl()

Linctrl -Linctrl ()

time stampn)

this-gtth_k = th_k

time stampn)

this-gtuc_k = uc_k

time stampn)

this-gtx_k = x_k

return

- th_kth2x_kp2

- th_kth4x_kp2

u_kk = k

return

F5 Comparator

include ltstdlibhgt

include Comparatorh

using namespace std

this-gtx_k = x_k

this-gtxm_k = xm_k

return

compute errors

e_kk = k

r e t u r n

include ltstdlibhgt

using namespace std

stampn)

this-gtx_k = x_k

return

y_kk = k

return

include ltstdlibhgt

using namespace std

time stampn)

this-gtxm_k = xm k

return

ym_kk = k

ym_kpi = ym_kpi

ym_kp2 = ym_kp2

r e t u r n

F8 CGI Program

inc lude ltctypehgt

include

lterrnohgt

ltstringhgt

ltstdiohgt

ltunistdhgt

ltfcntlhgt

ltstringhgt

ltsyssockethgt

ltsystypeshgt

ltnetinetinhgt

ltarpainethgt

define LINELEN 1024

struct valinfo

unsigned char name

unsigned char text

struct thetaPkt

struct Pkt

int pi

int p2

static

amll =

ami 2 =

am21 =

am22 =

bmll =

bml2 =

bm21 =

bm22 =

cmll =

cml2 =

cm21 =

cm22 =

all = -

al2 = -

a22 = -

bll = -

-67 94

static

= -510

= -310

= 1044

= 1006

static int nvals=0

if (gotvals)

nvals = getvals()

gotvals = 1

)vals[i]name)==0)

return vals[i]text

return NULL

=============== httpunescape ===========

unsigned char siptr

unsigned char soptr

unsigned char sos

(unsigned char) )

soptr = sos

siptr = sis

while (siptr)

if(siptr == )

int c = 0 i

for (i=0ilt2i++)

siptr++

c = claquo4 + h

if (i = 2)

free(sos)

return NULL

soptr++ =

soptr++ = siptr

siptr++

soptr = 0

free (sos)

return sis

=============== hextobin =================

if(isdigit(c))

return c-0

return -1

=============== getvals ===================

int vent = 0

unsigned char vstr

unsigned char vptr

unsigned char eptr

unsigned char aptr

int 1 cl

return 0

if(vstr == NULL)

return 0

if(vstr[l-l] == n)

vstr[l-l]=0

vptr = vstr

while (vptr)

vcnt++

valinfo))

vptr = vstr

for (i=0iltvcnti++)

if (eptr == NULL)

return 0

eptr = 0

if (aptr)

aptr = 0

vptr = aptr+1

return vent

unsigned char c

unsigned char cs

int fd len

if((fd==-l))

exit (1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== write signals ===================

unsigned char c

unsigned char cs

int fd len

if((fd==-l))

exit(1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== write a signal ===================

unsigned char c

unsigned char cs

int fd len

if((fd==-l))

exit (1)

write(fd cs 1)

write(fd c len)

write(fd t 1)

free((void) c)

free((void) cs)

close(fd)

return

=============== getsignal ===================

int fn s i m sn 1

unsigned char buf

if(fn==-l)

exit(1)

return

read(fn buf 20)

signal = s

free((void) buf)

close(fn)

return s

=============== get ascii signal ===================

int fn s i m sn 1

unsigned char buf

if(fn==-l)

exit (1)

return 0

read(fn buf 20)

signal = s

free((void) buf)

close(fn)

return 1

=============== settime ===================

int t=0

unsigned char c

unsigned char cs

int len

if((f==-l))

exit(l)

write(f c len)

write(f t 1)

free((void) c)

free((void) cs)

close (f)

return

=============== Wait ===================

int i=0

while(i++ltn)

=============== gettime ===================

clear signals

kT = k

Write to files

return

=============== clear signal ===================

int fn

if(fn==-l)

exit(1)

return

write(fn20)

close(fn)

return

unsigned char ch

if (xl==0)

ch[0] = 0

len = 1

if(xllt0)

xl = -xl

sign[0] = -

sign[0] = +

while(xlgt0)

ch[i] = 0 + xl10

xl=xl10

len=i+l

for(i=0 iltlen i++)

free((void) ch)

return

=============== getAdapMechPkt ===================

th4 th5 th6 th7 th8

int outfile

Receive signals

getsig

vartmpfuc2

vartmpfkth

vartmpfthl

vartmpfth2

vartmpfth3

vartmpfth4

vartmpfth5

vartmpfth6

vartmpfth7

vartmpfth8

ampuc2)

ampkth)

ampthl)

ampth2)

ampth3)

ampth4)

ampth5)

ampth6)

ampth7)

ampth8)

receivedlth3gtn)

printf

ltpgt ucl

ltpgt uc2

ltpgt thl

ltpgt th2

ltpgt th3

ltpgt th4

ltpgt th5

ltpgt th6

ltpgt th7

ltpgt th8

d) = dn k-1 ucl)

d) = dn k-1 uc2)

d)k = dn k-1 kth)

d) = dn k-1 thl)

d) = dn k-1 th2)

d) = dn k-1 th3)

d) = dn k-1 th4)

d) = dn k-1 th5)

d) = dn k-1 th6)

d) = dn k-1 th7)

d) = dn k-1 th8)

x_kml-gtk = kx

x_kml-gtpl = xl

x_kml-gtp2 = x2

e_kml-gtk = ke

e_kml-gtpl = el

e_kml-gtp2 = e2

uc_kml-gtk = kuc

uc_kml-gtpl = ucl

uc_kml-gtp2 = uc2

th_kml-gtk = kth

th_kml-gtthl = thl

th_kml-gtth2 = th2

th_kml-gtth3 = th3

th_kml-gtth4 = th4

th_kml-gtth5 = th5

th_kml-gtth6 = th6

th_kml-gtth7 = th7

th kml-gtth8 = th8

Write to files

return

=============== genAdapMechPkt ===================

th k-gtk = k

Write to files

return

=============== main ============

main ()

int valid

int stime gamm

int i=0

int k kT

int kmax=2

struct Pkt x_kml

struct Pkt e_kml

struct Pkt uc_kml

int getkt=0

int getkmax=0

ltheadgtn)

while(getkmax)

wait(5000)

while(klt kmax)

signalsn)

while(Igetkt)

wait (5000)

while(k=kT)

wait(10000)

signalsn)

gainsn)

ampth_k)

exit (0)

0000000

0100000

0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

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1300000

1400000

1500000

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4700000

4800000

4900000

5000000

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5200000

5300000

5400000

5500000

5600000

5700000

5800000

5900000

6000000

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6200000

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6800000

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7000000

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7300000

7400000

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7500000

7600000

7700000

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

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-0003432

-0003142

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-0033542

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-0033582

-0033601

-0033619

-0033636

-0033652

-0033668

in Table G2

0000000

0100000

0200000

0300000

0400000

0500000

0600000

0700000

0800000

0900000

1000000

1100000

1200000

1300000

1400000

1500000

1600000

1700000

1800000

1900000

2000000

-0000000

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0000829

0000850

0000896

0000923

0000928

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0000000

-0001534

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-0001735

-0001697

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-0001798

-0001694

-0001692

-0001508

-0001472

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-0001525

-0001317

-0000000

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0000633

0000657

0000680

0000702

0000723

0000742

0000761

0000779

0000796

0000813

0000828

0000843

0000858

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0000884

0000000

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-0001733

-0001692

-0001652

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2100000

2200000

2300000

2400000

2500000

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2700000

2800000

2900000

3000000

3100000

3200000

3300000

3400000

3500000

3600000

3700000

3800000

3900000

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4100000

4200000

4300000

4400000

4500000

4600000

4700000

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4800000

4900000

5000000

5100000

5200000

5300000

5400000

5500000

5600000

5700000

5800000

5900000

6000000

6100000

6200000

6300000

6400000

6500000

6600000

6700000

6800000

6900000

7000000

7100000

7200000

7300000

7400000

0001118

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0001100

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0001113

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0001118

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0001121

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0001124

0001125

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0001128

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0001130

0001131

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7500000

7600000

7700000

7800000

7900000

8000000

8100000

8200000

8300000

8400000

8500000

8600000

8700000

8800000

8900000

9000000

9100000

9200000

9300000

9400000

9500000

9600000

9700000

9800000

9900000

10000000

0001238

0001201

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0001214

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0001178

0001176

0001125

0001133

0001185

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Plant Error

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Adaptive Gains

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0000000

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0000000

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0000000

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7500000

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10000000

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-0033652

-0033668

in Table H2

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0000000

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0000000

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7500000

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10000000

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H3 Plant Error

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4000000

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5000000

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7800000

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9000000

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10000000

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H4 Adaptive Gains

e 03716

-05106

-03100

-00427

-00428

-05106

-03100

-03099

-00428

-05106

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-03098

-00428

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-03098

-00428

-00429

-00428

-00429

-00428

-00429

REFERENCES

Hungary vol 3 pp 1719-1724 1984

563 May 1989

Hall 1984

orgwikiMATLAB

Press 1999

McGraw-Hill 1981

2002 pp 4003-4008

6 pp 1169-1175 Dec 1982

e_Diagrampdf

Prentice Hall 1997

University 1990

Hill 1984

India 1979

SJSU ScholarWorks

Fall 2009


Hoan The Nguyen



Documents

Design and implementation of embedded adaptive controller using ARM processor