Aticulo 2 Timed CPNversion Final

7/29/2019 Aticulo 2 Timed CPNversion Final

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Modeling, analysis and simulation of an automated

plates manufacturing system using

Timed Coloured Petri Nets

Angel Alberto Castro † , Jose Fernando Jimenez ‡.Department of Electrical and Electronics Enginnering,

Universidad de los Andes, Bogota. Colombia.

Abstract—This paper presents the modeling, simulation andanalysis of a three types of plates manufacturing system withtimed coloured Petri nets (CPNs). The main goal is to copethe problem of achieving the three processes in a concurrentmanner without conflict in the use of shared resources, that is,to achive a compact model for a flexible manufacturing system.At first we obtain an ordinary model by means of the union of the subnets, each of them representing an operation of the systemand then is shown the completed Petri net model simulated inWoPeD [1]. That model is folded in a coloured Petri net in orderto simplify the model to make the decision making easier. Inthe coloured Petri net we add the failure states and determinecertains parameters of the system and thus avoid conflicts, verifythe liveness and limitation of the system and obtain a model forcontrol all the process and improve the behavior of the plant.Finally we assign possibles transition times to the model to findthe time accumulated vector for the processes in the model, usingthis vector it is possible locate the best system sequence. Thetimed CPN has been simulated in CPN tools [2].

Index Terms—synchronized Petri net, Autonomous and Nonautonomous Petri nets, flexible manufacturing system, task con-currency, timed coloured Petri net, performance evaluation.

I. INTRODUCTION

NOWADAYS the production system is focused on ob-

taining the largest number of products in the shortest

time. So, it is normal the rise of flexible manufacturing

systems FMS that allow to connect several work stations to

complete a specific job. This structure allows manufacture

multiples products concurrently given to the system flexibility

and adaptability.

The discrete mode of operation of an automated manufac-

turing system makes that usual control theory do not apply

because there are not a continuos system that can be modeled

by a differential equation. Discrete event systems encompassa wide variety of physical systems that arise in technology .

These include manufacturing systems, traffic systems, logistic

systems, database management systems, communication pro-

tocol, and data communication networks [3].

As mentioned by Cassandras [4] the two main modeling for-

malisms of discrete event systems DES to represent languages

are automata and Petri nets PN. Like an automaton, a Petri net

† Angel Castro is with the Department of Electrical Enginnering, Univer-sidad de los Andes, Bogota, Colombia, e-mail: [email protected].

‡ Fernando Jimenez is with the Department of Electrical Enginnering, Uni-versidad de los Andes, Bogota, Colombia e-mail: [email protected].

is a device that manipulates events according to certain rules

allowing modelling systems as a parallel evolution with several

processes in cooperation, with a common goal.

In a PN, the places represent resources such as machines,

mobil robots, buffers, etc. A transition firing represents an

activity, beginning and ending with two consecutive events.

The transition is fired when there are enought resources in theplaces.

PN models fall into one of two classes: timed PN models

and untimed PN models [5]. A timed PN of an FMS captures

the actual physical behavior of the FMS by assuming specific

durations for various activities in the FMS. An untimed PN

model of the FMS does not associate any times with the ac-

tivities. Coloured PN is a graphical language for constructing

models of concurrent systems and analysing their properties

[8], [13]. CPN models are formal, in the sense that the CPN

modelling language has a mathematical definition of both its

syntax and its semantics. Such models can be manipulated by

a computer tool and can be used to verify system properties,

i.e., prove that certain desired properties are fullfilled or thatcertain undesired properties are guaranteed to be avoided [13],

[8].

To obtain high quality and low operating costs of the system,

we must ensure simple and flexible configuration of the system

and short time periods to solve the problem of planning and

control [10], for this reason the simulation of timed CPNs

is an excellent tool when we are designing, controlling and

analysing some system.

I I . GENERAL DESCRIPTION

A. Manufacturing System

The manufacturing system is an extension of the presented

in the paper by Jimenez and Castro [6], and it contains threeconcurrent flows of job processes that make three different

types of plates at the same time and exploits the use of shared

resources. Process one produces the first type of plate, process

two produces the second type of plate and the process three

produces the third type of plate. The first type is a blank plate,

the second is a painted plate, and the third one is a plate

engraved. To realize the operations of painting and engraving

were added two aditional machines or resources to system, i.e.

a robot spray painting and a press machine. The

table I shown the system’s resources, its respective labels

and the resources used by each process.

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Table ISYSTEM’S RESOURCES

LABEL RESOURCEPROCESS TYPE

I II III

M1 Conveyor Belt • • •

M2 Robot Arm 1 • • •

M3 Robot Arm 2 • • •

M4 Quarter Turn Table • • •

M5 Robot Spray Painting •

M6 Press Machine •

M7 Buffer 1 •

M8 Buffer 2 •

The conveyor belt brings the plates from an infinite source

to a location where the plate is caught either by the first robot

arm or by the robot painter. If the robot arm 1 catch the plate,

it convey the plate to the robot arm 2 by means of a rotative

and traslational movements. If the plate is caught by the robot

spray painting, there will be a wait time after to the painting

process for drying operation and then this machine returns the

plate to the buffer 1 to be take by robot arm 1 and follow the

same process that the blank plates. The robot arm 2 transport

the plates to a carousel by means of only traslational motion

and drop the plate in a specific location of the carousel to later

come back for other plate. If the plate needs a grab the robot

arm 1 must be give the plate to the press machine instead of

give it to the robot arm 2. Once the engraving process has

finished the plate is dropped in the buffer 2 where is taken

by robot arm 2 to be conveyed toward carousel. The carousel

have four position and makes a quarter turns when the task of

each position is finished.

Let assume that the conveyor belt is not a conveyor loop

that never stop but a conveyor belt that stops when a plate

arrive to the grap position and begins its conveyor again when

the plate has been caught. Obviusly the control system must

ensure that this timeout shall be minimal.

The four operations performed in the carousel are: drop

the plate, remove burr from the plate, clean the dish and to

evacuate the plate. The layout of the system parts is shown in

Figure 1.

B. Sensors and Actuators

All sensors are listed in table II and the commands are listed

in the Table III .

III . PROCESS MODELLING

To construct a PN model for the given FMS we use an usual

method that can be studied in more detail in Narahari, et. al.

[5] or in [9] . We first represent each machine operation by

a sub PN. Each operation is shown in the table IV with its

description.

Then we obtain the PN model for each specific process

as the union of the PNs corresponding to the operation that

composed the process. Next we obtain the PN model for the

a)

b)

Figure 1. a) Overall system layout. b) Top view. Left: lower level, Right:upper level.

Table IISYSTEM’S SENSORS. UNCONTROLLABLE EVENTS

SUB SYSTEM LABEL SIGNIFICANCE

CONVEYOR BELT SOP Optical pl ate Sensor

ROBOT ARM 1

FC1 Limit Switch 1

FC2 Limit Switch 2

SCU Sensor cylinder Up

SC D S en sor cyl ind er D own

SPB1 Sensor plate Arm 1

ROBOT ARM 2

SB2L Sensor Arm 2 Left

SB2R Sensor Arm 2 ri ght

SPB2 sensor plate Arm 2

CAROUSEL

CQTR Carousel Quarter Turn Rotated

DRDF Drop Plate Fi nished

ED F Eva cua te P lat e F ini sh

RBF Remove Burr Finish

CDF Clean Plate Finish

ROBOT ARM 3 SPB3 Sensor plate Arm 3 E NG PF E ng rav ed p la te F in is h

ROBOT ARM 4

SPB4 Sensor Plate Arm 4

DRYF Dry Finished

PP F Pai nted Pl ate Fi ni sh ed

whole system as the union of the PN models of the processes

that the system has. If the FMS is complex, the PN model will

be huge and its analysis will not be easy. One way to overcome

this problem is to use coloured PN instead of ordinary PN.

Coloured PNs lead to compact models for even complex FMS

[5]. Thus, after obtaining the PN models for each of the three



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Table IIISYSTEM’S COMMANDS. CONTROLLABLE EVENTS

SUB SYSTEM LABEL SIGNIFICANCE

CONVEYOR BELTCBAC Conveyor bel t advance command

C BS C C onv eyo r b el t s to p c om ma nd

ROBOT ARM 1

DCC Down Cylinder Command

UCC Up cylinder Command

DAC Down Arm command

UAC Up Arm Command

GD CA 1 Gr ip p lat e co mm an d A rm 1

GDCA1FB1 Grip plate command Arm 1 from Buffer 1

ROBOT ARM 2

A2LC Arm 2 left command

A2RC Arm 2 right command

GD CA 2 Gr ip p lat e co mm an d A rm 2

GDCA2FB2 Grip plate command Arm 2 from Buffer 2

CAROUSEL

CQTC Carousel Quart er Turn Command

RBC Remove Burr Command

CDC Clean plate Command

EDC Evacuate pl ate Command

DRDC Drop plate Command

ROBOT ARM 3

GD CA 3 Gr ip P lat e C omm an d A rm 3

EN GP C E ng rav ing Pl ate Com mand

DWPB 2 Dow nl oad Pl ate Buf fer 2

ROBOT ARM 4GD CA 4 Gr ip P lat e C omm an d A rm 4

DWPB 1 Dow nl oad Pl ate Buf fer 1

Table IVSYSTEM’S OPERATIONS

OPERATION DESCRIPTION

O1 transport plate by the conveyor belt

O2 Take the plate by the robot arm 1 and upload it

O3 Take the plate by the spray robot painting, paint it and return it

O4 Take the plate by robot arm 2 and deposit on the carousel

O5 Get down the arm robot 1

O6 move the robot arm 2 to the right

O7 Take the plate by the press machine, engraved it and return it to the robot arm 2

O8 Carry out the process involved in the carousel

processes we can folded that PNs in a coloured petri net with

tokens of three colours.

Like there are three processes running in the same system,

with the same resources we must stablish for each process its

respective operation sequence, Table V.

Table VSEQUENCE OF OPERATIONS

PROCESS SEQUENCE OF OPERATIONS

I O1-O2-O4-(O5||O6||O8)

II O1-O3-O2-O4-(O5||O6||O8)

III O1-O2-O7-O4-(O5||O6||O8)

A. Operations Sub-Petri nets

From Table IV we have eight basic operations. Below are

explained these operations and now are shown the respectives

sub PNs which have been modeled following the structure of

the figure 2 [9]

1) O1: Transport the plate by the conveyor belt: For this

operation we have the places and transitions listed in table

VI. Place 1 stablish the condition of a plate is ready to enter

Figure 2. Generic Model of an Operation

the operation. P2 corresponds to move the conveyor belt. P3

indicates that the belt is stopped and the plate is in position

to be caught. P4 can be seen as the execution of the operation

“up Arm 1” and P40 as “painting and drying the plate” . P5

indicates that the plate has finished the operation “Up Arm”,

i.e., the plate has been caught by the robot arm1 and is ready

for the next operation. P41 indicates that the plate is painted

and dry. P6 indicates that the resource M1 is available. P0

ensure that come one plate at a time. The sub petri net is

shown in figure 3.

Table VIPLACES AND TRANSITIONS FOR THE OPERATION 1

PLACE DESCRIPTION

P1 plate ready and waits

P2 moving conveyor belt

P3 conveyor belt stopped

P4 taking and uploading the plate

P5 End of operation P4

P6 Resource M1 available

P40 taking and painting the plate

P41 End of operation P40

P0 condition plate feeder

TRANSITION DESCRIPTION

T1 CBAC

T2 SOP

T3 GDCA1

T4 SPB1

T40 GDCA4

T41 SPB4

Figure 3. Transport operation by conveyor belt

2) O2: Take the plate by the robot arm 1 and upload it:

For this operation we have the places and transitions listed

in table VII. This petri net uses the resource M2 (robot arm



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1) to carry out the operation 2 (O2). The resource is released

when the plate is taken either by robot arm 2 or by press

machine. P3 and P19 or P44 and P19 must be marked to start

the operation. P4 to P11 can be seen as the execution of carry

up the plate that has been taking from the conveyor. P44 to

P11 can be seen as the execution of carry up the plate that has

been taking from the Buffer 1.. P19 indicates that the resource

M2 is free. The sub petri net is shown in figure 4.

Table VIIPLACES AND TRANSITIONS FOR THE OPERATION 2

PLACE DESCRIPTION


P4 taking the plate by arm 1 from the conveyor

P44 plate ready in Buffer 1

P45 taking the plate by arm 1 from the Buffer 1

P5 plate gripped by the arm 1 ready for operation 2

P7 moving up arm 1

P8 moving up cylinder 1

P9 moving up cylinder 1

P10 moving up arm 1

P11 plate ready for to be taken

P12 Taking plate by robot arm 2

P13 plate took by arm 2

P14 Taking plate by press machine

P15 plate took by press machine

P19 resource M2 available


T3 GDCA1

T4 SPB1

T443 GDCA1FB1

T444 SPB1

T5 UAC

T6 SBU

T7 SCU

T8 UCC

T9 SCU

T10 SBU

T11 GDCA2

T12 SPB2

T13 GDCA3

T14 SPB3

Figure 4. Taking plate operation by the robot arm 1 and upload it

3) O4: Grip the plate by the robot arm 2 and deposit it on

carousel: For this operation we have the places and transitions

listed in table VIII. This petri net uses the resource M3 (robot

arm 2) to carry the plate from the robot arm 1 or from the

Buffer 2 to carousel. The resource is released when the plate

is dropped on the table. The sub petri net is shown in figure

5.

Table VIIIPLACES AND TRANSITIONS FOR THE OPERATION 4

PLACE DESCRIPTION

P11 plate in conveyor ready for be take by the robot arm 2

P12 Taking plate by robot arm 2

P63 plate ready in Buffer 2

P64 taking plate by arm 2 from the Buffer 2


P21 moving arm 2 to the left

P22 arm 2 in the left

P23 arm 2 is depositing the plate

P24 plate on the carousel



T11 GDCA2

T12 SPB2

T631 GDCA2FB2

T632 SPB2

T20 A2LC

T21 SB2L

T22 DRDC

T23 DRDF

Figure 5. Grip plate operation by the robot arm 2 and deposit it on carousel

4) O5: Get down the arm robot 1: For this operation we

have the places and transitions listed in table IX. This petri

net uses the resource M2 (robot arm 1) to down the robot arm

1. The resource is released when the arm 1 is positioned in

the down position. The sub petri net is shown in figure 6.a.

(P56.P18) collects P56 to P18 its simplified net is shown in

figure 6.b.

5) O3: Take the plate by the spray robot painting, paint it and return the painted plate : For this operation we have the

places and transitions listed in table X. This petri net uses the

resource M5 (robot spray painting) to carry the plate from the

conveyor belt to a location to paint it and then returns it. The

resource is released when the plate is dropped on the Buffer

1. The sub petri net is shown in figure 7.6) O6: move the robot arm 2 to the right: For this operation

we have the places and transitions listed in table XI. This petri

net uses the resource M3 (robot arm 2) and its work is to put

this resource to the right. The resource is released when the

arm is in the right. The sub petri net is shown in figure 8.



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Table IXPLACES AND TRANSITIONS FOR THE OPERATION 5

PLACE DESCRIPTION




P14 moving down arm 1

P15 moving down cylinder 1

P16 moving down cylinder 1

P17 moving down arm 1

P18 arm 1 and cylinder 1 get down


T15 SPB3

T16 SPB2

T17 DCC

T18 SCD

T19 SBD

T20 DAC

T21 SBD

T22 SCD

T111 ’1’

Figure 6. Get down arm robot 1 operation

7) O7: Take the plate by the press machine, engraved it

and return it to the robot arm 2: For this operation we have

the places and transitions listed in table XII. This petri net

uses the resource M3 (robot arm 2) and its work is to put this

resource to the right. The resource is released when the arm

is in the right. The sub petri net is shown in figure 9.

8) O8: Carry out the process involved in the carousel: For

this operation we have the places and transitions listed in table

Table XPLACES AND TRANSITIONS FOR THE OPERATION 3

PLACE DESCRIPTION


P40 take plate by painting arm

P41 painting plate

P42 drying plate

P43 dowloading plate in buffer 1

P44 plate in Buffer 1



T2 SOP

T40 GDCA4

T41 SPB4

T42 PPF

T43 DRYF

T44 DWPB1

Figure 7. Operation: Take the plate by the spray robot painting, paint it andreturn the painted plate

Table XIPLACES AND TRANSITIONS FOR THE OPERATION 6

PLACE DESCRIPTION



P26 moving robot arm 2 to the right

P27 robot arm 2 in right position


T23 DRDC

T24 A2RC

T25 SB2R

XIII. This petri net uses the resource M4 (quarter turn table).

The sub petri net is shown in figure 10.

IV. ANALYSIS

To achieve an analysis of the Petri net we make the union of

the operations and we carry out a simulation over the ordinary

PN having in mind what token type can hold in a place. The

simulation was made in the software woPed [1]. The model

thus obtained have 37 places and 31 transitions and are found

3 estructural conflicts. The ordinary PN is shown in Figure

11.

Figure 8. Operation: move the robot arm 2 to the right



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Table XIIPLACES AND TRANSITIONS FOR THE OPERATION 7

PLACE DESCRIPTION

P11 plate ready for be take by the press machine

P14 taking plate by press machine


P61 engraving plate

P62 dowloading plate in buffer 2

P63 plate in Buffer 2



T13 GDCA3

T14 SPB3

T61 ENGPC

T62 ENGPF

T63 DWPB2

Figure 9. Operation: Take the plate by the press machine, engraved it andreturn it to the robot arm 2

A. Estructural conflicts and blocking

The first conflict arises in the place P13, this place indicates

the state in which the arm robot 2 has taken the plate. That

place is an input of the transitions T20 and T16. T20 leads

to the operation of carrying the plate to the carousel and T16

leads to the operation of lowering the arm 1. The conflict is

that it is no possible to execute concurrently the two operations

because the enabling of one transition involves deactivate the

Table XIIIPLACES AND TRANSITIONS FOR THE OPERATION 8

PLACE DESCRIPTION



P29 turning the quarter turn table

P30 removing burr

P31 burr removed

P32 cleaning the plate

P33 plate cleaned

P34 evacuating plate

P35 plate evacuated

P36 READY PLATES


T23 DRDF

T26 CQTC

T27 CQTR

T28 RBF

T29 CDF

T30 EDF

Figure 10. Operation: Carry out the process involved in the carousel

other transition.

The second structural conflict ocurrs in the place P24 which

indicates that the plate has been dropped on the carousel. P24

is an input place to transitions T24 and T26. T24 leads to the

operation of returning the robot arm 2 to the right position

and T26 leads to turn the quarter turn table. In this case, the

conflict makes that if the carousel is turned, it is disable the

process of return the robot arm 2 to the right, generating a

block when other plate should be collected by robot arm 2.

On the other hand, if the arm robot is returned, the carousel

can not be turned producing a block when the next plate should

be dropped on the carousel because that position is occupied.

The third estructural conflict is produced in the place P15

which indicates that the plate has been caught by the pressmachine. That place is an input place of T61 and T15. T61

leads to the engraving the plate and T15 to get down the robot

arm 1. The conflict makes that, if is performed the operation of

engraving, will not lower the robot arm 1 causing a block when

the next plate in the conveyor belt or in the buffer 1 should

be caught by the arm 1. If instead the robot arm is lowered,

a plate will be stuck in the press machine and therefore could

not reuse that resource.

1) Solution of conflicts: Because the structural conflicts

enabling one transition while disabling the other, the solution

proposed in this paper is to merge the two transitions. Thus,

when a token reaches the place and the transition will be fired,

the two operation will be performed concurrently.That solution implies restrictions over the system because

the respective transitions not only have as an input place the

common place but also others places that are not commons.

In this system, the restrictions are the following:

For the first conflict, merging T16 and T20 arise a transition

that leads to get down the robot arm 1 and to carry the plate

to the carousel. That transition have as an input place also P19

(represent resource robot arm 1 is free), then

• to carry the plate to the carousel is necessary that the

robot arm 1 is available

In the second structural conflict merging T24 and T26 results



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a transition that is enable not only by the place P24 but also

by P28 (resource: carousel) and P25 (resource: robot arm 2)

whence the restrictions are

• To move the robot arm 2 to the right position is necessary

that the carousel is free

• to turn the carousel is necessary that the robot arm 2 is

available.

In the third conflict, merging T61 and T15 arise a transi-tion that will be enable not only by P15 but also by P19

(resource:robot arm 1), thus the restriction is

• To engraving the plate is neccesary that robot arm 1 is

available.

Figure 11. Ordinary PN

V. DESCRIPTION OF THE COLOURED PN

Folding the PN obtained previously we obtain a reduction

in the number of places and the transitions. This is possible

because the three processes are similars and its use the same

resources.

When there are a set of objects allowed in several places

and a set of firing for the transitions, we need specify such

objects in order to construct the description matriz.

Let us define, the sets:

π := types of objects allowed in theplaces

τ := types of firingsallowed in thetransitions

We can describe all places and all transitions with an

aplication C P () that relates each place with the objects that

it can hold, and another aplicacion that relates each transition

with the firings that it can have.

C p : P −→ ρ(π)

C T : P −→ ρ(τ )

In this system, the objects that can occupy the places are

divided in the plates itself q j and the resources M i.

A = plate type1 B = plate type2 C = plate type3

M 1 = conveyorbelt M 2 = Robot Arm1

M 3 = Robot Arm2 M 4 = Carousel

M 5 = Robotspray painting M 6 = P ressmachine

Thus, we have:

π = {A , B , C , M 1, M 2, M 3, M 4, M 5, M 6}

To produce a plate type I, the firing type is the (a). To a

plate type II the firing is (b), and to a plate type III the firing

is (c). Thus,

τ = {a ,b ,c}

The coloured PN has 26 places and 19 transitions, the CPN

is shown in Figure 13. There are 9 objects and 3 processes.To

describe that PN by means of a description matrix will benecessary 22 × 9 = 198 rows and 21 × 3 = 6 3 columns,

because of that the matrix is omited.

VI . SIMULATION OF THE TIMED CP N

To simulate the timed CPN we have used the software CPN

tools [13], [2] because it allows specify colors marks and the

time stamps. Time stamp tell us the time at wich the token

is ready to be removed by an ocurring transition. First of all,

we must declare the set of colors that have the CPN. With the

model proposed are necessary 3 sets of token colors. These

sets are the following and its declaration is shown in Figure

12.

Colores = {A , B , C}

A : plateof type I (blank)

B : plateof typeI I (painted)

C : plateof typeII I (engraved)

Machines = {M 1, M 2, M 3, M 4, M 5, M 6}

M 1 : Machine 1 (Conveyor Belt)

M 2 : Machine 2 (RobotArm 1)

M 3 : Machine 3 (RobotArm 2)

M 4 : Machine 4 (Carousel)

M 5 : Machine 5 (RobotSpray Painting)

M 6 : Machine 6 (Press Machine)

Machines Carousel = {Burr, evac, Clean}

Burr : RemoveBurr

evac : evacuateplate

Clean : Clean theplate



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Figure 12. Color set Declarations

Each of the places in the CPN must be associated with a

set of colors that are hold there, and the transitions must be

associated to a variables of a set or subset of colors.

The next step is to assign unit times to the transitions as

follows:

unittimes =

1 toup the robotArm 1

6 topaintthe plate

7 todry theplate

5 toengraving theplate

3 tobring tothe carousel

2 toturn thecarousel

5 toremovethe burr

3 tocleanthe plate

1 toevacuate theplate

To simulate the model of the system we start with 5

tokens of each color, so that the CPN can choose in a non

deterministic way the token color that enters to the system.

The CPN is shown in Figure 13 and the description of its

Places are in the Table XIV.

Figure 13. Timed Coloured Petri Net model

The time vector is an array that specify the time needed by

each of the concurrent procceses,

Transitionsdelays :

T i(+unittimei )

Process 1 : T 9 (1) + T 15 (3) + T 17(2) + T 18 (5) + T 19 (3) + T 20(1)

P rocess 2 : T 5 (6) + T 6 (7) + T 7 (1) + T 15(3) + T 17 (2) + T 18 (5) + T 19(3) + T 20 (1)

Table XIVPLACE DESCRIPTION COLOURED PETRI NET

PLACE DESCRIPTION COLOR SET

P1 Plate entering to the system A,B,C

P2 trasporting plate by conveyor belt A,B,C

P3 taking plate by M5 or by M2 A,B,C

P4 plate took by M5 or by M2 A,B,C

P5 painting plate B

P6 drying plate B

P7 up the painted plate with M2 B

P8 up the blank plate with M2 A,C

P9 Plate ready in top position A,B,C

P10 plate took by arm 2 or by arm 3 A,B,C

P11 bringing the plate to the carousel A,B

P12 engraving plate C

P13 bringing the plate to the carousel C

P14 plate ready to be download on the carousel A,B,C

P15 Rotating carousel A,B,C

P16 removing burr A,B,C

P17 burr removed A,B,C

P18 cleaning plate A,B,C

P19 plate cleaned A,B,C

P20 evacuating plate A,B,C

P21 plate evacuated A,B,C

P22 plate ready A,B,C

Process 3 : T 9 (1) + T 12(5) + T 13 (3) + T 17 (2) + T 18(5) + T 19(3) + T 20 (1)

Adding the times we have,

Transitionsdelays =

Procc 1 = [ 15 ]

Procc 2 = [ 28 ]

Procc 3 = [ 20 ]

and the time vector is:Time vector :

TimeP rocess1, T i meProcess2, T i meProcess3

Time vector = [15, 28, 20]

That time is an indication of the time required by produce a

type of plate, but the real process is non deterministic because

the plates arrive randomly and the system does not know what

color is the next to arrive. We can simulate a lot of times the

system in order to stablish an average of the number of plates

of each type produces in an interval of time.

A. Optimal Sequence

The Table XV, shown some times required to get a product

when the sequence of arrivals are the follows:

Performing several simulations it was found that the best

sequence is ACBA which uses 31 unit times. That sequence

can be extended as ACBACBACBA... to optimized the

production time.

VII. MACHINE FAILURES

Let us assume that a failure can occurs only when the

machine (resource) is working or processing something, i.e.

in the places that represent an operation. That is, an event



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Table XVSOM E SEQUENCES IN THE ARRIVALS

A B C SEQUENCE TIMES

1 1 1 CAB

C @12A @19B @29

1 1 1 ABC

A @7B @21C @29

1 1 1 BCA

B @20C @28

A @35

1 1 1 CBA

C @12B @21A @28

1 1 1 ACB

A @7C @15B @24

1 1 1 BAC

B @20A @27C @35

2 1 1 BACA

B @20A @27C @35A @42

2 1 1 ACBA

A @7C @15B @24A @31

Figure 14. Model to failure Machine

fail causes that the processing state changes to a failure state

[9].That is shown is figure 14.

When occurs a fail in any machine the process will be block when the next plate arrive to the location to be caught by this

machine. For example if there is a failure in the press machine,

the next plate with color (C) that needs that resource can not

use it and it remains in a wait state generating that plates of

others colors can not pass to its respective resources and the

complete system will be blocked.

To solve this situation we need a supervisor or control

coordinator that when receives a signal indicating a failure

of certain machine prevents the arrival of the plates that are

processed by that machine, i.e, select a subset of tokens colors

that do not need that resource.

For example, if there is a failure in the painting machine,

the supervisor must choose the appropiate subset of colorsthat can arrive to the first place, in this case the subset is

{A, C } because the color B correspond to a plate that needs

be painted. Thus, the supervisor is just a filter of colors that

arrive at the first place.

VIII. CONCLUSIONS

The modeling of a FMS using Petri nets can be divided

in a low level design using the aproach ordinary and a high

level design using coloured Petri nets. This high level approach

is best suited for concurrent and similar processes with the

advantage that it have less number of places and transitions

allowing an analysis more clear without lost any state of the

system. We get the two models, but the second by its own

definition reduces the estructural conflicts because each arc

have assigned a subset of colors that can go through it. The

resources were modeled with its own colors, so these can

shared by all the processes and we can analyse the behaviour

of the model using just one of each resource. The machine

failures can be solved using a supervisor or control coordinator

that avoids the arrival of the tokens colors corresponding to

the plates that use the damage resource. The supervisor is

just a filter of colors that arrive at the first place. In order

to optimizing the production time, the sequence in the arrivals

must be ACBACBACBA..., so, the supervisor could do that.

REFERENCES

[1] WoPeD (Workflow Petri Net Designer) is an open-source soft-ware developed at the Cooperative State University Karlsruhe underthe GNU Lesser General Public License (LGPL).http://woped.dhbw-karlsruhe.de/woped.

[2] CPNtools, version 3.4.0. developed by the CPN Group at AarhusUniversity from 2000 to 2010. The main architects behind the toolare Kurt Jensen, Søren Christensen, Lars M. Kristensen, and MichaelWestergaard. From the autumn of 2010, CPN Tools is transferred tothe AIS group, Eindhoven University of Technology, The Netherlands.http://cpntools.org.

[3] Notes on Control of Discrete - Events Systems. W.M. Wonham.[4] Introduction to Discrete Event Systems. Christos G. Cassandras,

Stéphane Lafortune. Springer Science. 2008.[5] A Petri Net Approach to the modeling and analysis of flexible manufac-

turing systems. Y.Narahari, N. Viswanadham. Indian Institute of Science.[6] Modular Supervisory Control for an automated plates manufacturing

system with DES. Jimenez. Jose Fernando, Castro. Angel Alberto.Universidad de los Andes, Colombia. 2013

[7] Discrete, Continuous, and Hybrid Petri Nets. René David, Hassane Alla.Second edition, Springer. 2010.

[8] Coloured Petri Nets, Modeling and validation of concurrent system.Jensen Kurt, Kristensen Lars. Springer. 2009.

[9] Modeling of a manufacturing system using Petri Nets. Lefranc, Gaston.Universidad Catolica de Valparaiso, Chile.

[10] Modeling of manufacturing systems and robot motions. Kost. Gabriel,Zdanowics. Ryszard. Elsevier.

[11] Modeling, Analysis, Simulation, Scheduling, and Control of Semicon-ductor Manufacturing Systems: A Petri Net Approach. MengChu Zhou,Mu Der Jeng. IEEE transaction on semiconductor manufacturing, Vol11, No 3. 1998.

[12] Lectures on concurrency and Petri Nets. Jorg Desel, Wolfgang Reisig,Grzegorz Rozenberg. Springer. 2004.

[13] Coloured Petri Nets and CPN tools for modelling and validation of concurrent systems. Jensen Kurt, Kristensen Lars, Lisa Well. Springer.2007.

[14] Petri Nets. James L. Peterson. Department of computer sciences, Theuniversity of Texas.

[15] A timed Colored Petri Nets Approach to process scheduling. A. Camurri,P. Franchi and F. Gandolfo. University of Genoa, Italy.

[16] Automated Control Synthesis for an Assembly Line Using DiscreteEvent System Control Theory Vigyan Chandra, Zhongdong Huang, and

Ratnesh Kumar.[17] Control of Discrete event systems with modular or distributed structure

Jan Komenda, Jan H. van Schuppen. Science Direct.[18] Modular supervisory control of an experimental automated manufactur-

ing system M. Nourelfatha,*, E. Niel. Science Direct.[19] The simulation design and analysis of a flexible manufacturing system

with Automated Guided Vehicle AGV System. Insup Um, HyeonjaeCheon, Hongchul Lee.

http://woped.dhbw-karlsruhe.de/woped


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