Architectural Analysis for Supervisory Control of Discrete-Event Systems by Ang Li A thesis ...

116 Pages·2017·4.46 MB·English

Architectural Analysis for Supervisory Control of
Discrete-Event Systems
by
Ang Li
A thesis submitted in conformity with the requirements
for the degree of Master of Applied Science
Graduate Department of Electrical and Computer Engineering
University of Toronto
c Copyright 2017 by Ang Li
�
Abstract
Architectural Analysis for Supervisory Control of Discrete-Event Systems
Ang Li
Master of Applied Science
Graduate Department of Electrical and Computer Engineering
University of Toronto
2017
Using probabilistic automata (PA) within the Ramadge and Wonham (RW) framework,
the model of discrete-event systems (DES) is extended to include probabilistic informa-
tion. The extended model can provide useful numerical results for performance analysis
of DES by exploiting Markov Chain properties, as well as allowing the use of logical
synthesis techniques. Using the extended model, performance evaluation and pros and
cons analysis of centralized and decentralized architectures are provided for two typical
DES, Small Factory and Transfer Line. Given estimated cost and profit data, the cen-
tralized and decentralized architectures are evaluated in these two examples, and various
summary rules as to which architecture to implement are obtained. For the Transfer
Line example, ‘material feedback’ in the loop and only partial knowledge of the global
system state in the decentralized architecture can result in blocking. Blocking removal
strategies are introduced and compared.
ii
Acknowledgements
The author is grateful for the help from Professor R.H. Kwong and Professor W.M.
Wonham. Their great patience and guidance encourages the author to delve further into
theunderstandingofstochasticaspectofdiscrete-eventsystemsandintothearchitectural
analysis of discrete-event systems.
The author would also like to thank Liyong Lin, Deguang Wang and other fellow stu-
dents for their assistance. Financial support, in the form of U of T Fellowship, Teaching
Assistantship, and Research Assistantship from Professor Kwong and Professor Wonham
during the course of this work is greatly appreciated.
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Contents
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
1 Introduction 1
1.1 Discrete-Event System (DES) Modeling . . . . . . . . . . . . . . . . . . 1
1.1.1 Stochastic Petri Net (SPN) Models . . . . . . . . . . . . . . . . . 1
1.1.2 Generalized Semi-Markov Process (GSMP) Models . . . . . . . . 2
1.1.3 Automaton Models . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Comparison of Modelling Methods with Earlier Work . . . . . . . . . . . 4
1.2.1 Small Factory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 Modelling Approaches and Assumptions in Earlier Work . . . . . 5
1.2.3 Modelling Approach and Assumptions in this Thesis . . . . . . . 6
1.3 Centralized and Decentralized Control Architectures for DES . . . . . . 6
1.4 Contribution of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Probabilistic Automaton Model 13
2.1 Probabilistic Automata (PA) . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
iv
3 Preliminary Performance Measurement and Analysis of Small Factory 17
3.1 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Production Rate vs. Speed of Machines . . . . . . . . . . . . . . . . . . . 18
3.3 Smoothing E↵ect of the Storage Bu↵er . . . . . . . . . . . . . . . . . . . 27
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4 Architectural Analysis of Small Factory 31
4.1 Centralized and Decentralized Control . . . . . . . . . . . . . . . . . . . 33
4.1.1 Centralized Supervisory Control . . . . . . . . . . . . . . . . . . . 33
4.1.2 Decentralized Supervisory Control . . . . . . . . . . . . . . . . . . 34
4.2 Cost Comparison of Centralized and
Decentralized Architectures . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3 A Possible Way to Improve Productivity . . . . . . . . . . . . . . . . . . 42
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5 Architectural Analysis of Transfer Line 47
5.1 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.2 Analysis of Machine Speed Concerning Production Rate . . . . . . . . . 50
5.3 An Example of Finding Optimal Sizes
of the Bu↵ers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.4 Centralized and Decentralized Control . . . . . . . . . . . . . . . . . . . 58
5.4.1 Centralized Supervisory Control . . . . . . . . . . . . . . . . . . . 58
5.4.2 Smart Decentralized Supervisory Control . . . . . . . . . . . . . . 59
5.4.3 Naive Decentralized Supervisory Control with Blocking Removal
Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.4.4 Pros and Cons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.5 Cost Comparison of Centralized and Decentralized Architectures . . . . . 64
5.6 A Possible Way to Improve Productivity . . . . . . . . . . . . . . . . . . 74
v
5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6 Conclusions and Future Work Directions 77
A Finite State Markov Chains 81
A.1 Specifying a Finite State Markov Chain . . . . . . . . . . . . . . . . . . . 81
A.2 Higher Order Transition Probabilities . . . . . . . . . . . . . . . . . . . . 82
A.3 Classification of States . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
A.3.1 Accessibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
A.3.2 Recurrence and Transience . . . . . . . . . . . . . . . . . . . . . . 84
A.3.3 Periodicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
(n)
A.4 Computation of f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
ij
B Mathematical Computation of the Expected Production Time 89
B.1 Small Factory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
C Random Walk 99
Bibliography 103
vi
List of Tables
3.1 Values of Probabilities in Case 1 . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 Values of Probabilities in Case 2 . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 Values of Probabilities in Case 3 and Case 4 . . . . . . . . . . . . . . . . 22
3.4 Values of Probabilities in Case 5 and Case 6 . . . . . . . . . . . . . . . . 24
4.1 Number of States and Transitions in CSIM with Respect to Di↵erent
Bu↵er Capacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 NumberofStatesandTransitionsinBUFSIMandBRSIMwithRespect
to Di↵erent Bu↵er Capacities . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3 Size of Controllers in Centralized and Decentralized Structures . . . . . . 37
4.4 Ranges of Coe�cients in Small Factory . . . . . . . . . . . . . . . . . . . 38
5.1 Events in M1, M2 and TU . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.2 Coe�cients of Validation for Situation I . . . . . . . . . . . . . . . . . . 51
5.3 Coe�cients of Validation for Situation II . . . . . . . . . . . . . . . . . 52
5.4 Coe�cients of Validation for Situation III . . . . . . . . . . . . . . . . 54
5.5 Number of States and Transitions in CSUP with Respect to Di↵erent
Bu↵er Capacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.6 NumberofStatesandTransitionsinBUF1SUP,BUF2SUPandLOOP-
SUP with Respect to Di↵erent Bu↵er Capacities . . . . . . . . . . . . . 62
5.7 Sizes of Controllers in Centralized and Decentralized Structures . . . . . 65
5.8 Ranges of Coe�cients in Transfer Line . . . . . . . . . . . . . . . . . . . 66
vii
List of Figures
1.1 Block Diagram of Small Factory . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 An Example of Probabilistic Automaton . . . . . . . . . . . . . . . . . . 16
3.1 Model of Machine 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Model of Machine 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3 Underflow/Overflow Specification: BUF . . . . . . . . . . . . . . . . . . 19
3.4 Production Time per Item in Case 1 . . . . . . . . . . . . . . . . . . . . 20
3.5 Production Time per Item in Case 2 . . . . . . . . . . . . . . . . . . . . 22
3.6 Bu↵er Occupancy History in Case 1 when Bu↵er Size is One . . . . . . . 23
3.7 Improvement in Production Rate in Case 3 and Case 4 . . . . . . . . . . 23
3.8 Bu↵er Occupancy History in Case 3 when Bu↵er Size is One . . . . . . . 24
3.9 Improvement in Production Rate in Cases 1, 5, 6 . . . . . . . . . . . . . 25
3.10 Productivity and Improvement in Production Rate . . . . . . . . . . . . 26
3.11 Bu↵er Occupancy History . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.1 Breakdown/Repair Specification: BR . . . . . . . . . . . . . . . . . . . . 32
4.2 Optimal Global Supervisor CSIM . . . . . . . . . . . . . . . . . . . . . . 34
4.3 Optimal Supervision of Underflow/Overflow BUFSIM . . . . . . . . . . 35
4.4 Optimal Supervision of Breakdown/Repair BRSIM . . . . . . . . . . . . 35
4.5 Costs of The Centralized and Decentralized Structures in First 20 Years . 41
4.6 New Bu↵er Specification NBUF . . . . . . . . . . . . . . . . . . . . . . 43
4.7 Optimal Global Supervisor NSIM . . . . . . . . . . . . . . . . . . . . . 44
viii
4.8 Production in Case 1, Case 5 and Case 6 . . . . . . . . . . . . . . . . . . 44
4.9 Profit Made in 20 Years in Case 1 . . . . . . . . . . . . . . . . . . . . . . 45
5.1 Block Diagram of Transfer Line . . . . . . . . . . . . . . . . . . . . . . . 47
5.2 Model of M1, M2 and TU . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.3 Bu↵er Specification BUF1 . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.4 Bu↵er Specification BUF2 . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.5 Validation Results for Situation I . . . . . . . . . . . . . . . . . . . . . 51
5.6 Validation Results for Situation II . . . . . . . . . . . . . . . . . . . . . 53
5.7 Validation Results for Situation III . . . . . . . . . . . . . . . . . . . . 54
5.8 Productivity Curve when p = p = p +p = 0.5 . . . . . . . . . . . . . 55
1 2 3 4
5.9 Gradient in Percentage of Productivity when p = p = p +p = 0.5 . . 56
1 2 3 4
5.10 Productivity Surface with p = p = p +p = 0.5 and Reject Ratio 5% . 57
1 2 3 4
5.11 Optimal Global Supervisor CSUP with Capacity of BUF1 and BUF2
both one . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.12 Supervision by Naive Decentralized Control NDCSUP . . . . . . . . . . 60
5.13 Loop Specification LOOP . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.14 Modified NDCSUP: Strategy I . . . . . . . . . . . . . . . . . . . . . . 63
5.15 Modified NDCSUP: Strategy II . . . . . . . . . . . . . . . . . . . . . 63
5.16 Average Cost of the Centralized Structure and the Smart Decentralized
Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.17 Comparison of Average Costs of the Centralized and Smart Decentralized
Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.18 Average Profits of Two Naive Decentralized Structures in First 20 Years 71
5.19 Average Profits of Three Structures in First 20 Years . . . . . . . . . . . 73
5.20 New Bu↵er Specification NBUF1 . . . . . . . . . . . . . . . . . . . . . . 74
5.21 Production of SUP and NSUP when Reject Ratio is 5% . . . . . . . . . 75
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A.1 Example of A Periodic Markov Chain . . . . . . . . . . . . . . . . . . . . 85
B.1 Model of Machine 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
B.2 Model of Machine 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
B.3 Global Supervisory Control of Small Factory with Bu↵er Size One . . . . 90
B.4 New Graphical Representation of the Global Supervisory Control of Small
Factory with Bu↵er Size One . . . . . . . . . . . . . . . . . . . . . . . . 92
B.5 New Graphical Representation with Probabilities of the Global Supervi-
sory Control of Small Factory . . . . . . . . . . . . . . . . . . . . . . . . 93
B.6 Simplified Transition Graph . . . . . . . . . . . . . . . . . . . . . . . . . 96
x