Student: Tai-Lin Huang Advisor: Ming-Shan Lu, Ph.D.

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


Introduction


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


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


Literature review



Petri Net Reconfig-uration

RMS Deadlock


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])


Enterprises

Factories

Shop floors

Cells

Machines

Enterprise allies

Reconfigurable hardware

Reconfigurable control

System levels


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])



Petri Net(2/5)• Petri net includes four basic elements:

Token、 Place、 Transition、 Arc


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


Petri Net(3/5)• The analysis method of Petri net.

▫Reachability analysis method Reachability tree Reachability graph

▫ Invariant analysis method P-invariant T-invariant



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.


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


Petri Net(5/5)• Literature Review about using Petri net on RMS


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.


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



Reconfiguration(2/2)• Literature review about reconfiguration：


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.


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



Deadlock(2/2)• Literature review about deadlock of manufacturing

system.


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


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


Research methods


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


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


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)



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


Modeling(1/8)• Establish the Original Petri net.


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


Modeling(2/8)• Step1 : Establish the Flow Petri Net(FPN)

1. 2. 3. 4. 5. 6.


{ , , , , }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


Modeling(3/8)• Step2:List the resource constraints.

▫Resource constraints:


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


Modeling(4/8)• Step3:Establish Resources Petri net Controller based on the P-

invariant.

1. 2. 3. 4. 5. 6.


{ , , , , }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


Modeling(5/8)• The places of RPNC.

─ P-invariant:


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


Modeling(6/8)• The arc of RPNC

─ P-invariant:


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


Modeling(7/8)• Step4: Establish Original Petri net(OPN).

─ OPN is consisted of FPN and RPNC.

1. 2. 3. 4. 5. 6.


{ , , , , }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


Modeling(8/8)• Step5:Test and verify the deadlock of OPN

─ Matlab Petri Net toolbox.

• Reduction of OPN


OP FP RP

(1) (2)

(3) (4)

(5) (6)


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.



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.


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


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


TOTT

AT


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.



Objective function

Reconfiguration(5/5)• Mathematical models of solving the objective marking

omobj and transition firing vector f


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


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.


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


Deadlock(2/3)• Mathematical models of solving the Deadlock free Petri

Net Controller:


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


Deadlock(3/3)• The procedure of Minimum controller search method

(Yun-Yi Wang [2011])


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.


Expected results


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.



Thanks for your listening

Student: Tai-Lin Huang Advisor: Ming-Shan Lu, Ph.D.

Documents

Transcript of Student: Tai-Lin Huang Advisor: Ming-Shan Lu, Ph.D.