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A Petri net Approach for Dynamic Control Reconfiguration of Manufacturing Systems with Consideration of Resource Changes. Student: Tai-Lin Huang Advisor: Ming-Shan Lu, Ph.D. Outline. Introduction. Research motive and purpose. - PowerPoint PPT Presentation
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National Yunlin University of Science & TechnologyGraduate School of Industrial Engineering & Management
A Petri net Approach for Dynamic Control Reconfiguration of
Manufacturing Systems with Consideration of Resource Changes
Student: Tai-Lin HuangAdvisor: Ming-Shan Lu, Ph.D.
National Yunlin University of Science & Technology 2
Introduction
Literature Review
Research Methods
Expected Results
Outline
National Yunlin University of Science & Technology 3
Introduction
National Yunlin University of Science & Technology 4
Research motive and purpose• In the manufacturing process, the manufacturing system may
occur unexpected events, that will result changes of the available resource’s amount.
• After resources changes, according to the original control
rules will cause a lack of system resources.
• The purpose of this research is the manufacturing system return to normal in the situation of resource changes.
• Both of adjusting control rules and assigning the other department’s resources are the ways of troubleshooting.
Introduction Literature Review Research Methods Expected Results
National Yunlin University of Science & Technology 5
Research processIntroduction Literature Review Research Methods Expected Results
Research background and
motive
Research literature review
Use a petri net approach to model the manufacturing
systems
Adjust the control rules when resource
changes
Reachability analysis
Avoid deadlock
Conclusion and discussion
National Yunlin University of Science & Technology 6
Literature review
National Yunlin University of Science & Technology 7
Introduction Literature Review Research Methods Expected Results
Petri Net Reconfig-uration
RMS Deadlock
National Yunlin University of Science & Technology 8
RMS• A kinds of manufacturing Systems, that can revise and adjust
its structure. It can promise customized flexibility in a short time. (Mehrabi, et al. [2000])
• Reconfiguration can mainly divide into two classes:1. Reconfiguration in plan stage2. Reconfiguration in control stage
• Reconfiguration can be classified in terms of two levels:1. Hardware: Reconfiguration of resources2. Software: Reconfiguration of control rules(Bi, et al. [2008]、 Koren, et al. [1999]、Malhotra, et al. [2009])
Introduction Literature Review Research Methods Expected Results
Enterprises
Factories
Shop floors
Cells
Machines
Enterprise allies
Reconfigurable hardware
Reconfigurable control
System levels
National Yunlin University of Science & Technology 9
Petri Net(1/5)• Petri net are useful graphical tool for modeling the
manufacturing systems.
• Petri net are an appropriate tool for the study of discrete-event dynamical systems because of their modeling power and flexibility.(Yamalidou, et al. [1996]) (Reddy, et al. [1993])
Introduction Literature Review Research Methods Expected Results
National Yunlin University of Science & Technology 10
Petri Net(2/5)• Petri net includes four basic elements:
Token、 Place、 Transition、 Arc
Introduction Literature Review Research Methods Expected Results
Component GraphToken
Place
Transition
Arc
• Petri net is a five tuple:1. 2. 3. 4. 5.
1 2{ , , , } 0nP p p p n 1 2{ , , , } 0sT t t t s
: , {0,1,2, }I P T N N : , {0,1,2 }O T P N N
1 2: , [ ( ), ( ), , ( )]nm P N m m p m p m p
National Yunlin University of Science & Technology 11
Petri Net(3/5)• The analysis method of Petri net.
▫Reachability analysis method Reachability tree Reachability graph
▫ Invariant analysis method P-invariant T-invariant
Introduction Literature Review Research Methods Expected Results
National Yunlin University of Science & Technology 12
Petri Net(4/5)▫P-invariant
─ one can find subsets of place over which the sum of the tokens remains unchanged
▫T-invariant─ one can find that a transition firing sequence bring s the marking
back to the same one.
Introduction Literature Review Research Methods Expected Results
1k k km m Cu
1T T T
k k kx m x m x Cu
1T T
k kx m x m
→Define the posive integer solution x of CTx=0→Multiplying XT to both sides
→Since CTx=0, thus xTC=0
→ then x is a P-invariant
0 0m m Cu →Cu=0 , then u is a T-invariant
National Yunlin University of Science & Technology 13
Petri Net(5/5)• Literature Review about using Petri net on RMS
Introduction Literature Review Research Methods Expected Results
Author Year Method Application
Meng 2010 Object-oriented methods. Colored Petri nets. Modeling approach of RMSs.
Li, et al. 2009Activity diagram of
UML.Petri net.
Rapidly building Petri net models of RMS.
National Yunlin University of Science & Technology 14
Reconfiguration(1/2)• Reconfiguration
─ Control rules of the manufacturing system are used to handle the systems.
─ Reconfiguration have to reach two points:1. To safety the resources constraints2. To avoid the systems deadlocks
Introduction Literature Review Research Methods Expected Results
National Yunlin University of Science & Technology 15
Reconfiguration(2/2)• Literature review about reconfiguration:
Introduction Literature Review Research Methods Expected Results
Author Year Method ApplicationYamalidou, et
al. 1996 P-invariant
Feedback controller of petri net .
Sampath, et al. 2008 P-invariantController of the plant
reconfiguration procedure.
Kezic, et al 2009 P-invariantDesign maximally permissive controller which stops vessels
Baudouel and Oliver. 1998 Reconfigurable net.
The reconfigurable flow net dynamically modify their own
structure
Darabi, et al. 2003 Control switching model
The controller reconfigures the control system.
National Yunlin University of Science & Technology 16
Deadlock(1/2)• The deadlock situation lead to the manufacturing system can
not operate.
• Deadlock situations are as a result of inappropriate resource allocation policies or exhaustive use of some or all resources.
• These researches about solving deadlock can be divided into three groups:1. Schedule2. Circuit & Cycle3. Controller
Introduction Literature Review Research Methods Expected Results
National Yunlin University of Science & Technology 17
Deadlock(2/2)• Literature review about deadlock of manufacturing
system.
Introduction Literature Review Research Methods Expected Results
Author Year Method Application
Dohi, et al. 1996High speed Petri Net sequence controller
Petri net controller with hardware to avoid deadlocks
Mohan, et al. 2004Colored Petri net model.
The neighborhood deadlock avoidance policy.
Deadlock avoidance in automated flexible manufacturing cells
Xing, et al. 2005 Petri net controller.Deadlock avoidance for
manufacturing systems with multiple resource service
Aybar and Iftar 2008
Timed Petri nets.Stretching method.Stretched Petri net.Timed Petri nets.
Supervisory controller design approach to
avoid deadlock in TPNs
National Yunlin University of Science & Technology 18
SummaryIntroduction Literature Review Research Methods Expected Results
Model Reconfigure
level
Reconfigure
class
Reconfiguration Deadlock
Other
research
•Activity diagram.•Object-oriented.•Petri net.
•Plan stage •Reconfigure resource
•Static reconfiguration.
•Schedule•Circuit & cycle•Controller
This
research
•Flow of parts.•Petri net.•Resource controllers.•P-invariant method.
•Control stage
•Reconfigure control rules
•Dynamic reconfiguration.
•Controller
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Research methods
National Yunlin University of Science & Technology 20
Example• This research proposed a example about Reconfigurable
manufacturing system(RMS).
Machine1: 3Machine2: 2Machine3: 3Machine4: 2AGV: 4
▫ Part A: CI→AGV→mc1→AGV→mc3→AGV→mc4→CO.▫ Part B: CI→AGV→mc3→AGV→mc2→AGV→mc1→CO.
Starting workparts
W3 W4
Completed parts
M1W2
AGV
M3
M2
M4
W1
Introduction Literature Review Research Methods Expected Results
Machine1: 3 →1Machine2: 2 →1Machine3: 3 →2Machine4: 2 →2AGV: 4 →3
Operating
Resource changes
Starting workparts
W3 W4
Completed parts
M1W2
AGV
M3
M2
M4
W1
National Yunlin University of Science & Technology 21
Research methods• Because the lack of system resources, it have to reconfigure the
system.
• This research considers the reconfigure methods, including adjust control rules and assign the other department’s resources. Petri net P-invariant T-invariant & Reachability analysis
• This research totally using five petri net model:1. Flow Petri Net(FPN)2. Resource Petri Net Controller(RPNC)3. Original Petri Net(OPN)4. Deadlock free Petri Net Controller(DPNC)5. Deadlock free Petri Net(DPN)
Introduction Literature Review Research Methods Expected Results
National Yunlin University of Science & Technology 22
Methods processIntroduction Literature Review Research Methods Expected Results
Establish Deadlock-free
Petri net
Resourcechanges
Test and verify the
deadlock of system
YES
YES
NO
NO
Adjust the control rules
Establish the well-behavior
Original Petri net
Give a Well-behavior
manufacturing system
National Yunlin University of Science & Technology 23
Modeling(1/8)• Establish the Original Petri net.
Introduction Literature Review Research Methods Expected Results
List the resource constraints
Establish Petri net resources
controller based on P-invariant
Test and verify the deadlock of
the Original Petri net
Establish Original Petri net
by combining with FPN and
RPNC
Establish the Flow Petri net
National Yunlin University of Science & Technology 24
Modeling(2/8)• Step1 : Establish the Flow Petri Net(FPN)
1. 2. 3. 4. 5. 6.
Introduction Literature Review Research Methods Expected Results
{ , , , , }FPN FP FT FI FO fm
1 2 3 n{ , , , }n 0FP p p p p
1 2 3{ , , , }s 0sFT t t t t FI FP FT N :
FO FT FP N :fm FP N:
FD FO FI
AGVloading parts
AGVtransfer
AGVunloading parts/mc1
available
mc1working
t2 t3p2 p3 t4 p4
mc1work finish/AGV
loading parts
AGVtransfer
National Yunlin University of Science & Technology 25
Modeling(3/8)• Step2:List the resource constraints.
▫Resource constraints:
Introduction Literature Review Research Methods Expected Results
1 1 2 2( ) ( ) .......... ( )n nl m p l m p l m p b
1 1 2 2( ) ( ) .......... ( )n nl m p l m p l m p b
1 1 2 2( ) ( ) .......... ( )n nl m p l m p l m p b
1 1 2 2( ) ( ) .......... ( )n nl m p l m p l m p b
1 1 2 2( ) ( ) .......... ( ) 1q q qn n ql m p l m p l m p b q g
1 1 2 2( ) ( ) .......... ( ) 1q q qn n ql m p l m p l m p b g q k
1 1L m B
2 2L m B
Parameter of limit resources
Petri net places ‘s tokens
Numbers of limit resources
National Yunlin University of Science & Technology 26
Modeling(4/8)• Step3:Establish Resources Petri net Controller based on the P-
invariant.
1. 2. 3. 4. 5. 6.
Introduction Literature Review Research Methods Expected Results
{ , , , , }RPNC RP RT RI RO rm
1 2 3{ , , , } 0kRP rp rp rp rp k RT FT
RI RP RT N :
RO RT RP N :rm RP N:RD RO RI
mc1
National Yunlin University of Science & Technology 27
Modeling(5/8)• The places of RPNC.
─ P-invariant:
Introduction Literature Review Research Methods Expected Results
0L fm L fm B
1 1 00
2 0 2
B L fmrm
L fm B
1 0 0 1L fm rm B 2 0 0 2L fm rm B
Place of Petri net Controller
1 0 1L fm B
2 0 2L fm B
Satisfy
Resource constraints
National Yunlin University of Science & Technology 28
Modeling(6/8)• The arc of RPNC
─ P-invariant:
Introduction Literature Review Research Methods Expected Results
1
2
[ ] 0L I FDL I RD
1
2
00
L FD I RDL FD I RD
1
2
LI RD FD
L
1
2
L FDRD
L FD
National Yunlin University of Science & Technology 29
Modeling(7/8)• Step4: Establish Original Petri net(OPN).
─ OPN is consisted of FPN and RPNC.
1. 2. 3. 4. 5. 6.
Introduction Literature Review Research Methods Expected Results
{ , , , , }OPN OP OT OI OO om
OP FP RP
OP FP RP OT FT RT
OI OP OT N :
OO OT OP N :om OP N:OD OO OI
AGVloading parts
AGVtransfer
AGVunloading parts/mc1
available
mc1working
t2 t3p2 p3 t4 p4
mc1work finish/AGV
loading parts
AGVtransfer
00
National Yunlin University of Science & Technology 30
Modeling(8/8)• Step5:Test and verify the deadlock of OPN
─ Matlab Petri Net toolbox.
• Reduction of OPN
Introduction Literature Review Research Methods Expected Results
OP FP RP
(1) (2)
(3) (4)
(5) (6)
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Reconfiguration(1/5)• The procedure of reconfiguring system:
▫Step1: Decide the dynamic state of the resource changes.
▫Step2: According number of resources to update the resource constraints.(B →B*).
▫Step3: According B* to reconfigure the resource controller’s token.
▫Step4:Reconfigure the firing sequence.
Introduction Literature Review Research Methods Expected Results
National Yunlin University of Science & Technology 32
Reconfiguration(2/5)• The procedure of Step3 & Step4.
▫ Ⅰ : Reconfigure the resources controller’s token▫ Ⅱ : Determine the value of the om(Rpi)▫ Ⅲ : If the om(Rpi) 0≦ , to solve the reconfigure firing vector f .▫ Ⅳ : Determine whether the solution is feasible.▫ Ⅴ : If the solution is unfeasible, to revise the lb.▫ Ⅵ : Execute f , to adjust manufacturing systems.▫ Ⅶ : Reconfigure finish.
Introduction Literature Review Research Methods Expected Results
om(Rpi)≧0
Solve the reconfigure firing
vector f
Feasible
Execute f to adjust
manufacturing systems
NO
YES
Change lbNOYES
Reconfigurefinish
Reconfigure the resources
controller’ s token
Ⅰ
Ⅱ
Ⅲ
ⅣⅤ
Ⅵ
Ⅶ
National Yunlin University of Science & Technology 33
Reconfiguration(3/5)• The reconfiguration of firing sequence .
1. The transition of adjusting control rules.
2. The transition of assigning the other department’s resources.
Toff
af
Introduction Literature Review Research Methods Expected Results
TOTT
AT
National Yunlin University of Science & Technology 34
Reconfiguration(4/5)• The costs of the firing transition, this research list three
scenarios, we try to find the lowest cost of these scenarios:▫Scenario 1:
The costs of assign resources is very expensive.▫Scenario 2:
The costs of adjust control rules is slightly cheaper than assign the other department’s resources.
▫Scenario3:The costs of adjust the control rules is equal to assign the other
department’s resources.
Introduction Literature Review Research Methods Expected Results
National Yunlin University of Science & Technology 35
Objective function
Reconfiguration(5/5)• Mathematical models of solving the objective marking
omobj and transition firing vector f
Introduction Literature Review Research Methods Expected Results
1
Minimizes k
j jj
c f
0
0. . objFD
s t f om omRD AD
1
s k
j jj
c f lb
1
obj
iom N i n k
1jf N j s k
Correlation matrix of OPN Correlation matrix of assign resource Firing rule of Petri net:
0D f m m
Integer and non-negative constraints
Cost low bound
CostFiring vector
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Deadlock(1/3)• If deadlock occur, it must add Deadlock free Petri net
controller(DPNC) to establish Deadlock free petri net(DPN).
• Deadlock free Petri Net Controller(DPNC)
1. 2. 3. 4. 5. 6.
Introduction Literature Review Research Methods Expected Results
DPNC={CP,CT,CI,CO,cm}1 2 3{ , , , }vCP Cp Cp Cp Cp
CT OT
CI CP CT N :CO CT CP N :cm CP N:CD CO CI
National Yunlin University of Science & Technology 37
Deadlock(2/3)• Mathematical models of solving the Deadlock free Petri
Net Controller:
Introduction Literature Review Research Methods Expected Results
01 1 1 1
( ) ( )n n m n
NCP i CD ij cm ii i j i
Minimize K NCP Cp K CD K cm Cp
0. . 0 1ss t cm CD uf s y
0 0 1dcm CD ur d h
0 1eCD ul e p
Nonreachability restrictions
Circulation restrictions
Reachability restrictions
National Yunlin University of Science & Technology 38
Deadlock(3/3)• The procedure of Minimum controller search method
(Yun-Yi Wang [2011])
Introduction Literature Review Research Methods Expected Results
Add a controller.
Add a controller one more times.
Whether all the nonreachibilty restrictions is
satisfied.YES
NO
Finish
Solve value of satisfying all the restrictions.
Set the value to the nonreachability
restrictions.
Recode the value of controller place about it can satisfying nonreachibility and all of the
restrictions.
National Yunlin University of Science & Technology 39
Expected results
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Expected results• The expected results of this research hope that it can
resolve the problems about system’s resource changes by reconfiguring the manufacturing system and avoiding deadlock.
Introduction Literature Review Research Methods Expected Results
National Yunlin University of Science & Technology 41
Thanks for your listening