Formal Specification and Synthesis of Procedural Controllers for Process Systems

238 Pages·1996·6.873 MB·English

by  Arturo Sanchez Dr (auth.)

Lecture Notes
in Control and Information Sciences
212
Editor: M. Thoma
Arturo Sanchez
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and Synthesis of
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for ssecorP smetsyS
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Series Advisory Board
A. Bensoussan M.J. • Grimble • P. Kokotovic • H. Kwakernaak
J.L. Massey Y.Z. • Tsypkin
Author
Arturo Sanchez, Dr
Centre for Systems Process Engineering, Imperial College, London SW7 2BY, UK
ISBH 3-540-76021-0 Springer-Verlag Berlin Heidelberg New York
British Library Cataloguing in Publication Data
Sanchez, Arturo
Formal specification and synthesis of procedural
controllers for process systems. - (Lecture notes in
control and information science)
1.Process control
I. Title
629.8
ISBN 3540760210
Library of Congress Cataloging-in-Publication Data
A catalog record for this book is available from the Library of Congress
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as
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© Springer-Verlag London Limited 1996
Printed in Great Britain
The publisher makes no representation, express or implied, with regard to the accuracy of the
information contained in this book and cannot accept any legal responsibility or liability for any errors
or omissions that may be made.
Typesetting: Camera ready by author
Printed and bound at the Athengeum Press Ltd, Gateshead
69/3830-543210 Printed on acid-free paper
To Andres and Paulina
Contents
The Role of Procedural Control 1
1.1 Introduction
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Procedural Control in Process Systems .............. 2
1.3 DESs in Chemical Process Control ................ 3
1.3.1 Modelling aad Analysis ................... 3
1.3.2 Synthesis .......................... 6
1,4 Control of Discrete Event Systems ................ 7
1.4.1 Logic-based Frameworks .................. 8
1.4.2 Supervisory Control Theory ................ 01
1.4,2,1 Controllability and Supervision ......... 11
1.4.2.1.1 Basic Definitions and Modelling Issues. 11
1.4.2.1.2 Controllability and Existence of Super-
visors ................... 13
1.4.2.1.3 Calculations of Controllable Behaviour, 13
1.4.2.1.4 State and Event Approaches ...... 14
1.4.2.1.5 Modular Synthesis of Supervisors... 14
1.4.2.2 Supervision under Partial Observations .... 14
1.4,2.3 Decentralised and tlierarchical Supervision . . 14
1.4,2,4 Limited Lookahead Supervisor ......... 51
1.4.3 DuM-language Frameworks ................ 15
1.5 Behaviour Specification and Temporal Logic ........... 61
1.6 Summary and Conclusions ..................... 81
2 Modelling Framework 21
2.1 Introduction ............................. 12
2.2 Model Definition .......................... 22
2.3 Structural Properties ........................ 25
2.4 Lattices and a-machines ...................... 26
VUl
2.5 Languages and a-machines .................... 29
2.6 Operations with a-machines .................... 31
2.6.1 Asynchronous Product of a-machines .......... 13
2.6.2 Synchronous Product of a-machines ........... 32
2.7 Examples .............................. 33
2.7.1 Burner Systern ....................... 34
2.7.1.1 Elementary Models ............... 34
2.7.1.2 Process Model .................. 37
2.7,2 Buffer System ........................ 38
2.7.2.1 Elementary Models ............... 40
2.7.2,2 Process Model .................. 40
2.8 Summary .............................. 45
Specification Modelling 47
3.1 Introduction ............................. 47
3.2 Forbidden States Modelling .................... 48
3.3 Dynamic Specifications Modelling ................. 50
3.3.1 Structure (syntax) of TL ................. 51
3.3.I.1 Symbols and Operators ............. 51
3.3.1.2 Terms ....................... 15
3.3.1.3 Formulas ..................... 52
3.3.1.4 Frames arid Models ............... 53
3,3,2 Translation of TL Formulas into a-machines ...... 53
3.3.2.1 Generation of Initial State in the a-machine
Domain ...................... 55
3.3.2,2 Translation of Schemes involving TL Operator )~( 56
3.3.2.3 Translation of Schemes involving TL Operator ~ 58
3.3.2.4 Translation of Schemes involving TL Operator 5< 59
3.4 Modelling of Specifications for the Burner System ........ 61
3.4.1 Static Specifications .................... 62
3.4.2 Dynamic Specifications .................. 64
3.5 Summary .............................. 68
4 Supervisory Control Theory 71
4.1 Introduction ............................. 71
4.2 The Feedback Supervisory Model of Supervisory Control Theory 72
4.3 Controllability and Supervisors in Supervisory Control Theory 75
4.3.1 Controllability and Existence of Supervisors ....... 76
4.3.2 Computation of Controllable Languages ......... 77
Contents ix
4.4 Conditional Controllability and Supervisor Synthesis ...... 78
4.5 Modular Synthesis of Supervisors ................. 81
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5 Synthesis of Procedural Controllers 85
5.1 Introduction ............................. 85
5.2 Control Arrangement ........................ 86
5.2.1 Controller Definitions ................... 87
5.3 Synthesis Procedure ........................ 89
5.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9t
5.4.1 Burner System ....................... 91
5.4.1.1 Step 1.- Process Modelling ........... 92
5,4.1.2 Step 2: Specification Modelling ........ 93
5.4.i.3 Step 3: Supervisory Structure Synthesis . , . 93
5,4,1,4 Step 4.- Controller Synthesis .......... 94
5,4.I,4,1 Specification D1 ............. 94
5,4.1.4,2 Specification D2 ............. 96
5.4,t.4,3 Specification D3 ............. 96
5.4.1.4.4 Global Controller Synthesis ...... 100
5,4,1,5 Step 2,- Specification Modelling ........ 102
5,4.1.6 Step 4,- Controller Synthesis .......... 102
5.4.2 Augmented Burner System ................ 104
5.4.2.1 Step t.- Process Modelling ........... 107
5,4,2,2 Step 2.- Specification Modelling ........ 108
5.4,2.2.1 Static Specifications ........... 108
5.4.2.2.2 Dynamic Specifications ......... 109
5.4,2.3 Step 3.- Supervisory Structure Synthesis . . . 117
5.4.2,4 Step 4.- Controller Synthesis .......... 117
5,5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1t8
Implementation Issues 123
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.2 Buffer System ............................ 124
6.2.1 Step 1.- Process Modelling ................ t25
6.2.2 Step 2.- Specification Modelling .............. 126
6.2.2.1 Dynamic Specifications ............. 127
6.2.3 Step 4.- Controller Synthesis ............... 130
6.2.4 Controller Implementation and Simulation Results . . . 135
6.2.4.1 Controller Implementation ........... t35
×
6.2.4.2 SMORPg Model for the Buffer System ..... 138
6.3 Metering Tank System ....................... 140
6.3.1 Process Description .................... 142
6,3.2 Step 1,- Process Modelling ................ 146
6.3.3 Step 2.- Specification Modelling .............. 153
6.3.3,1 Static Specifications ............... 153
6.3,3,2 Dynamic Specifications ............. 154
6.3,4 Step 3,- Supervisory Structure Synthesis ......... i56
6,3.5 Step 4,- Controller Synthesis ............... 161
6,3.6 Controller Implementation and Simulation Results . . . 166
7 Epilogue 175
7.1 The Modelling Framework ..................... 175
7.1.1 Process Modelling ..................... 175
7.1.2 Specification Modelling .................. 177
7,2 Supervision and Control Aspects ................. 178
7,3 The Controller Synthesis Method ................. 180
A a-machines of Augmented Burner 183
A,1 Process Model ........................... 185
A,2 Dynamic Specifications ....................... 186
A.3 Supervisory Structure ....................... 198
A.4 Local Controllers .......................... 199
References 207
Glossary 217
Index 219
List of Figures
2.1 A case in which the synchronous product of two trim sl~k~F can
generate a non trim FSM ...................... 34
2.2 The burner system .......................... 35
2.3 a-machine Mi corresponding to air and fuel valves, i = t, 2... 35
2.4 a-machine aM corresponding to igniter .............. 37
2.5 a-machine 4M corresponding to flame detector .......... 37
2.6 Model of the burner system, a = initial/final state; b = normal
operation state ............................ 38
2.7 The buffer system .......................... 39
2.8 a-machine 4M corresponding to the level indicator model .... 40
2.9 Global model of the buffer system ........ ......... 41
2.10 a-machine prescribing functional behaviour of the buffer system
when both valves are closed ..................... 43
2.11 a-machine prescribing functional behaviour when FV is open
ancl DV is closed ........................... 44
2.12 a-machine prescribing functional behaviour when DV is open
and FV is closed ........................... 44
2.13 Model for the buffer system ..................... 45
1.3 a-machine corresponding to the asynchronous product of the a--
machine models of the air and fuel valves ............. 54
3.2 a-machine corresponding to specification D1 ........... 66
a.3 a-machine corresponding to specification D2 ........... 67
3.4 a-machine corresponding to specification Da ........... 68
4.1 Feedback control mode arrangement in Supervisory Control The-
ory ................................... 74
5.1 Feedback control mode arrangement ................ 87
5.2 Faulty logic proposed for the operation of burner system .... 93
xn
5.3 a-machine model after eliminating forbidden states ....... 95
5.4 Local controller corresponding to specification 1 ......... 97
5.5 LocaI controller corresponding to specification 2, satisfying the
standard controllability definition ................. 98
5.6 Local controller corresponding to specification 2 ......... 99
5.7 Local controller corresponding to specification 3 ......... 101
5.8 a-machine corresponding to the global controller for specifica-
tions D1, D2 and D3 ......................... 103
5.9 a-machine corresponding to specification D4 ........... 104
5.10 a-machine corresponding to the local controller Ibr specification
D4 ................................... 105
5.11 a-machine corresponding to the global controller for specifica-
tions D1, D2, D3 and D4 ...................... 106
5.12 a-machine corresponding to the finM logic/sequential controller
tbr the angmented burner system .................. 119
1.6 a-machine corresponding to dynamic specification D1 ...... 128
6.2 a-machine corresponding to dynamic specification D2 ...... 129
6.3 a-machine corresponding to dynamic specification D3 ...... 129
6.4 a-machine corresponding to dynamic specification D4a ..... 131
6.5 a-machine corresponding to dynamic specification D4b ..... 131
6.6 a-machine corresponding to the local controller for specification
132
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7 a-machine corresponding to the local controller for specification
132
2 . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . .
6.8 a-machine corresponding to the local controller for specification
133
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.6 a-machine corresponding to the IocM controller for specification
t33
a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.10 a-machine corresponding to the local controller for specification
D4b .................................. 134
6.11 a-machine corresponding to the controller composition of local
controllers ,1 2 and 3 ........................ 135
6.12 a-machine corresponding to the global controller for the buffer
system ................................ 136
6.13 gPROMS generic model of an on/off valve ............ 139
6.14 gPROMS teusks to open and close an on/off valve ........ 140
6.15 gPROMS model of an atmospheric tank ............. 141
6.16 gPROMS model of the metering system ............. 142