National Yunlin University of Science & Technology Graduate School of Industrial Engineering & Management 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.
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
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Introduction
Literature Review
Research Methods
Expected Results
Outline
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Introduction
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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
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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
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Literature review
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Introduction Literature Review Research Methods Expected Results
Petri Net Reconfig-uration
RMS Deadlock
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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
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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
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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
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Petri Net(3/5)• The analysis method of Petri net.
▫Reachability analysis method Reachability tree Reachability graph
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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