MODELLING AND SIMULATION OF METHATRONICS SYSTEMS · Modelling and simulation of mechatronic...

Copyright: 2012 by Florin Sandu BLAGA

MODELLING AND SIMULATION OF METHATRONICS SYSTEMS

First Edition

Laboratory handbook of Series of

Advanced Mechatronics Systems

edited by Florin Sandu BLAGA

Debrecen (HU)

2012.


First edition: MODELLING AND SIMULATION OF METHATRONICS SYSTEMS- LABORATORY HANDBOOK, Florin Sandu BLAGA, 2012.

Although great care has been taken to provide accurate and current information, neither the author(s) nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage, or liability directly or indirectly caused or alleged to be caused by this book. The material contained herein is not intended to provide specific advice or recommendations for any specific situation.

Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identification and explanation without intent to infringe.

HU ISSN 2063-2657

HU ISBN 978-963-473-517-5

Copyright© 2012, Florin Sandu BLAGA

Reviewers:

Technical-scientific: Zsolt Tiba Ph.D, Géza HUSI Ph.D, University of

Debrecen Language: www.etraduceri.com Publisher: Dr. habil Edit Szűcs PhD, dean of Faculty of Engineering, University of Debrecen, Debrecen, Hungary

Publisher’s Note

The publisher has gone to great lengths to ensure the quality of this reprint but points out that some imperfections in the original may be apparent.


www.hungary-romania-cbc.eu www.huro-cbc.eu

The content of this book does not necessarily represent the official position of the European Union.


Advanced Mechatronics Systems

A Series of course book and laboratory handbook Debrecen (HU)

Editors

GÉZA HUSI, Ph.D.

Associate Professor

Head of Electrical Engineering and Mechatronics Department

University of Debrecen, Faculty of Engineering

Debrecen, Hungary

RADU-CATALIN TARCA Ph.D.,

Professor Head of Mechatronics Department

University of Oradea, Managerial and Technological Faculty Oradea, Romania


Series Introduction

Worldwide interest in Mechatronics and its associated activities continue to grow day by day. The multidisciplinary field of mechatronics brings together mechanical engineering, electrical and electronic engineering, control engineering, and computer science in a synergistic manner. In the latest period, major developments were noticed in this field showing that the mechatronics has advanced rapidly and gained maturity, through the development of an increasing number of degree programs, extensive research activities, product and system developments, and an increasingly broad range of industrial applications. Many textbooks have been developed in the field of Mechatronics and this series of books also lines up with the current trends. The appearance of this series of books was made possible as a result of HURO MECHA 0901/179/2.3.1 project implementation, funded by European Regional Development Fund. These books fully address both the theoretical and practical aspects of the multidisciplinary field of mechatronics and fit the needs in knowledge for students enrolled to MSc program in the field of mechatronics, implemented at both Oradea and Debrecen Universities. The purpose of these courses in mechatronics is to provide a focused interdisciplinary experience for graduate students in the field of mechanics, electrical and computer sciences. Knowledge will be provided in the fields of Advanced Mechatronics, Materials and Machine Parts for Mechatronics, Electrical Actuators, CAD for Mechatronics, Modeling and Simulation of Mechatronics Systems, PLC Programming, Mechatronics Control Systems, Robot and CNC Programming, Mechanical Design of a Mechatronic System, Management of Complex Production Systems, Software Reliability Engineering, Product Lifecycle Management, Finite Element Analysis, Diagnosis and Maintenance of Mechatronics Systems. This series presents books that draw on expertise from both the academic world and the application domains, and will be useful not only as academically recommended course texts but also as handbooks for practitioners in many application domains.

GÉZA HUSI, RADU-CĂTĂLIN ŢARCĂ, editors


Advanced Mechatronics Systems A Series of course book and laboratory handbook

Debrecen (HU)

Editors: GÉZA HUSI, RADU-CATALIN TARCA,

1. Radu Cătălin ȚARCĂ: ADVANCED MECHATRONICS - course book 2. Radu Cătălin ȚARCĂ: ADVANCED MECHATRONICS - laboratory handbook 3. Ioan Constantin ȚARCĂ: MATERIALS AND MACHINE PARTS FOR MECHATRONICS -

course book 4. Ioan Constantin ȚARCĂ: MATERIALS AND MACHINE PARTS FOR MECHATRONICS -

laboratory handbook

5. János TÓTH: ELECTRICAL ACTUATORS - course book 6. János TÓTH: ELECTRICAL ACTUATORS - laboratory handbook 7. Mircea Teodor POP: CAD FOR MECHATRONICS - course book

8. Mircea Teodor POP: CAD FOR MECHATRONICS - laboratory handbook 9. Florin Sandu BLAGA - MODELING AND SIMULATION OF MECHATRONICS SYSTEMS -

course book

10. Florin Sandu BLAGA - MODELING AND SIMULATION OF MECHATRONICS SYSTEMS - laboratory handbook

11. Géza HUSI, Péter SZEMES, István BARTHA: PLC PROGRAMMING - course book 12. Géza HUSI, Péter SZEMES, István BARTHA: PLC PROGRAMMING - laboratory

handbook

13. Géza HUSI: MECHATRONICS CONTROL SYSTEMS – course book 14. Géza HUSI: MECHATRONICS CONTROL SYSTEMS – laboratory handbook 15. Tiberiu VESSELENYI: ROBOT AND CNC PROGRAMMING– course book

16. Tiberiu VESSELENYI: ROBOT AND CNC PROGRAMMING– laboratory handbook 17. Edit SZÛCS: MANAGEMENT OF COMPLEX PRODUCTION SYSTEMS - course book 18. Zsolt TIBA: MECHANICAL DESIGN OF A MECHATRONICS SYSTEM – laboratory

handbook 19. Florin VLĂDICESCU POPENȚIU: SOFTWARE RELIABILITY ENGINEERING- course

book

20. Alexandru Viorel PELE: PRODUCT LIFECYCLE MANAGEMENT- course book 21. Alexandru Viorel PELE: PRODUCT LIFECYCLE MANAGEMENT– laboratory handbook 22. Flavius ARDELEAN: FINITE ELEMENT ANALYSIS – course book

23. Flavius ARDELEAN: FINITE ELEMENT ANALYSIS - laboratory handbook 24. Sorin Marcel PATER: DIAGNOSIS AND MAINTENANCE OF MECHATRONICS SYSTEMS

– course book

25. Sorin Marcel PATER: DIAGNOSIS AND MAINTENANCE OF MECHATRONICS SYSTEMS- laboratory handbook

Additional Volumes under Preparation


MODELLING AND SIMULATION OF METHATRONICS

SYSTEMS

LABORATORY HANDBOOK

First Edition

Florin Sandu BLAGA

Industrial Engineering Department

University of Oradea, Managerial and Technological Faculty

Oradea, Romania.

Debrecen 2012.

Modelling and simulation of mechatronic systems. Laboratory handbook

9

CONTENTS

1. MODELLING SYSTEMS WITH

PLACE-TRANSITION PETRI NETS ..................................................... 11

2 and 3. MODELLING SYSTEMS

WITH TIMED PETRI NETS ................................................................... 19

4. MODELLING COLORED PETRI NETS USING CPN TOOLS ........... 35

5. THE EVALUATION OF THE MANUFACTURING

SYSTEM PERFORMANCE USING

THE TAYLOR ED 2000® PROGRAM .................................................. 45

6. THE MOVEMENT SIMULATION

OF THE VIRTUAL PROTOTYPE ......................................................... 57

7. FUZZY CONTROL SYSTEMS - THE WASHING MACHINE ............ 67

BIBLIOGRAPHY ...................................................................................... 75


11

APPLICATION 1

1. MODELING SYSTEMS WITH PLACE-TRANSITION PETRI

NETS

1.1. The purpose The application has the purpose of presenting the fundamental

notions related to the construction of models with Petri nets of Place-

Transition (PT) type.

1.2. Theoretical background

Definition

A Petri Net (PN) is a graphic model belonging the oriented graphs

type [8, 9], which uses two categories of pivotal points:

• Places – which model the conditions which are imposed for the

performance of a certain event (represented by circles);

• Transitions – which model the events which develop if certain

conditions are fulfilled (represented by horizontal lines or by

rectangles).

The places and transitions are connected through arcs. The arcs

are oriented, connecting a place to a transition or a transition to a place.

In figure 1.1. a PN is presented which consists of 7 places, 6


12

transitions and 15 oriented arcs.

Notations:

• places are noted with Pi , i= 1, I;

• transitions are noted with Tj , j= 1, J;

• the aggregate of places of a PN is noted with P;

• the aggregate of transitions of a PN is noted with T;

For the example from figure 1.1 the aggregate of places is P = {

P1, P2, P3, P4, P5, P6, P7 } and the aggregate of transitions is T= { T1, T2, T3,

T4, T5, T6 }.

T1

P1

P3 P2

T3 T2

P5 P4

T4

P6

T5

P7

T6

T1

P1

P3 P2

T3 T2

P5 P4

T4

P6

T5

P7

T6

(a) (b)

Fig. 1.1. Petri Net: a) unmarked; b) marked


13

Regarding figure 1.1, it is stated that place P3 is an upstream or an

input place for transition T3 (the arc is oriented from P3 to T3). Place P5

is a downstream or an output place for transition T3. A transition

without input place is a source transition (generator). A transition

without an output place is a closed transition.

The marking

Another category used in the study of PN is the marking. Each

place contains a whole number (positive or null) of symbols (points)

which are called markings or tokens [9]. In figure 2.1.a is represented a

marked PN, and in figure 2.1.b an unmarked PN.

To each place, function of existence / inexistence of the point (of

the symbol in general), can be associated a marking. The marking of a

place Pi is noted with M(Pi) or mi. The proper markings for the places of

the net from figure 2.1.b. are: m2 = m4 = m5 = m7 = 0, m1 = m3 = 1, m6 =

2.The marking of the net is noted with M. For a PN with n places, this is

defined through vector M = (m1, m2, ..., mi, ..., mI). The marking of the net

from figure 2.1.b. is M = (1, 0, 1, 0, 0, 2, 0).

Note:

If n,1i},1,0{mi =∈ , PN is part of the binary Petri nets category [8].

The marking defines, at a certain point, the state of the system

modeled with the help of the PN.

The firing of a transition


14

Regarding transitions, a transition is executable only when each

place from upstream contains at least a marking. In this case it can be

stated that the transition is executable or validated.

A source transition is always validated.

3. The development of the paper

Application 1

The Petri net from figure 1.2. is taken in consideration, the

sequences of transitions {T1, T3} and {T2, T4} are found in the situation

of mutual exclusion, meaning that at a certain point one of the

sequences or the other will be executed.

The net must be modified so as sequence {T1, T3} should be

executed three times before sequence {T2, T4} is to be fired.

The net must be designed in the Visula Object Net++ environment.

P1

P3

P5

P4P2

P4

P6

T1

T3

T2

T4

T5

T6

Fig. 1.2. Petri net with sequences of transitions with

mutual exclusion [12]


15

Application 2

(a) The Petri nets from figure 1.3 are taken in consideration.

Which are the executable transitions as well as the markings

which result after their execution?

The nets must be designed in the Visula Object Net++

environment.

P1 P2

P3 P4

P5P6 P7 P8

P9

T1 T2 T3

Fig.1.3. Examples of Petri nets

(b) The net from figure 1.4 is taken in consideration. Arc P2T4 is an

inhibitor arc.

Which is the available markings graph ?

P1

P3

P2

T1

T4

T2

T3

Fig.1.4. Petri net with inhibitor arc


16

Application 3

In the manufacturing system from figure 1.5 two types of pieces

are processed: p1 and p2.

Fig. 1.5. Manufacturing system

The pieces arrive in stock 1, are processed onto machine 1, enter

stock 2 and are then processed onto machine M2. After finishing the

processing onto machine 2, the pieces leave the system. Each machine

processes, at a certain moment, one piece. The entry order of the pieces

in the system is random, but the processing onto the two machines is

done respecting the alternation: p1, p2, p1, p2, p1,….

The model of the manufacturing system, designed with Petri nets,

is presented in figure 1.6. The meanings of the places and transitions

are given on the figure. Two types of components of the model can be

identified: the component which models the processing of the type p1

pieces and the component which models the processing of the type p2

pieces. The entry of the pieces in the system is modeled through the

source transitions T1 (type p1 pieces) and T6 (type p2 pieces).

The alternative processing of the two types of pieces onto

machine 2 is modeled with the help of places P5 and P6. Therefore, the

presence of a marking in place P5 and in place P1 validates transition T2

(the loading of machine 1 with a type p1 piece). In the same way the

presence of a marking in place P9 and in place P6 models the fulfillment

Input pieces Machine 1 Machine 2 Exit

pieces

Stock 1 Stock 2


17

of the loading conditions of machine 1 with a type p2 piece.

In the machine 2 case, places P7 and P8 allow the modeling of the

alternative processing of two types of pieces.

The marking from figure 1.6: M(P5)=M(P7)=1, models the

processing conditions of the first piece of type p1 onto machine 1 as

well as onto machine 2.The model described will be implemented on

the Visual Object Net++ program.

P1

T1

P2

T2

Intrare p1

P3

T4

P4

T5

P9

T7

P10

T8

P11

T9

P12

T10

p1 instocul 1

p1 pemasina 1

T3

p1 instocul 2

p1 pemasina 2

Evacuare p1

P5 P6

Intrare p2

p2 instocul 1

p2 pemasina 1

p2 instocul 2

p2 pemasina 2

Evacuare p2

T6

P8P7

Prelucrarea pieselor de tip p1

Incarcare p1

pe masina 1

Descarcare p1

de pe masina 1

Incarcare p1

pe masina 2

Incarcare p2

pe masina 1

Descarcare p2

de pe masina 1

Incarcare p2

pe masina 2

Prelucrarea pieselor de tip p2

Fig. 1.6. Model with PN of the manufacturing system from figure 1.5

Entry p1

p1 in stock 1

Loading p1

onto

machine 1

p1 on

machine 1

Unloading p1

off machine 1

p1 in stock 1

Loading p1

onto

machine 2

p1 on

machine 1

Evacuation

p1

Entry p2

p2 in stock 1

Loading p2

onto

machine 1

p2 on

machine 1

Unloading

p2 off

machine 1

p2 in stock 1

Loading p2

onto

machine 2

p2 on

machine 2

Evacuation

p2

Processing type p1pieces

Processing type p2 pieces


18

The following things will be observed:

• Determining the correlations between the model components and

the elements and from the real system which they model;

• Determining the initial conditions modeled through the initial

marking, which is to respect the processing order of the two types of

pieces;

• Respecting the alternation of the two types of pieces during the

processing of a stock of 10 pieces of type 1, respectively 10 pieces of

type 2.


19

APPLICATIONS 2 AND 3

2. MODELING SYSTEMS WITH TIMED PETRI NETS

2.1. The purpose

The paper aims to highlight the modeling possibilities of the

systems (manufacturing systems) with timed Petri nets. Moreover, the

performance of the modeled systems through simulation will be

evaluated.

2. 2. Theoretical background

A timed Petri net allows the description of a system whose

performance depends on time. This Petri net category is used for

evaluating the performance of a system.

There are two possibilities to model a temporization:

• temporizations associated with places –P-timed PN;

• temporizations associated with transitions –T-timed PN.

P- timed Petri nets

A P-timed Petri net is a doublet of type <R, Tempo>, [9], where:

• R is a marked PN;

• Tempo is an application on the aggregate P of places in the

aggregate of positive rational or null numbers, so as:


20

Tempo (Pi) = di (2.1)

where di is the temporization associated with place Pi.

The performance principle

If a marking is deposited in a Pi place, this marking will remain in

the Pi place during di, the marking being unavailable at this time. After

di has elapsed, the marking becomes available.

During t, the M marking is the sum of two types of markings:

• Ma – the available marking;

• Mu - the unavailable marking.

Therefore:

M= Ma + Mu (2.2)

A transition is validated for the M marking, if it is validated for the

Ma marking.

If a marking is deposited in a Pi place, following a transition

executed during t, then this marking is unavailable during (t, t+ di).

T-timed Petri nets

A T-timed Petri net is a doublet of type <R, Tempo> [9], where:

• R is a marked Petri net;

• Tempo is an application of the aggregate of T transitions in the

aggregate of rational or null numbers, defined by the relation:

Tempo (Tj) = dj (2.3)

where dj is the temporization associated with transition Tj.


21

In case of T-timed PN, a marking may be in one of the following

stages:

reserved for the execution of transition Tj;

non-reserved.

In a random moment t, where marking M of the net is:

M= Mr + Mnr

where Mr is the reserved marking and Mnr is the non-reserved marking.

A transition is validated for marking M, if it is validated for

marking Mnr.

If t is the moment in which the firing of transition Tj şi t + dj is

decided, the moment in which the transition has been actually

performed is considered to be:

t- the beginning of the transition;

t+ dj – the end of the transition.

For T-timed PN, two ways of performance can be defined:

1. Performance at high speed – once a transition is validated; the

necessary markings for its execution are reserved.

2. Performance at its own speed – a marking deposited in a place

becomes reserved for the execution of a transition in downstream, after

a period of time which is different from zero.


22

3. The development of the application

Two manufacturing systems will be taken in consideration

which will be modeled with T-timed Petri nets and whose performance

parameters will be analyzed through simulation.

Application 1

A manufacturing system is taken in consideration consisting of the

working machines M1 and M2. The machines are served onto two

blades, each of them carrying a piece. The pieces gradually pass to

machines M1 and M2 (Fig. 2.1).

Machine M1 can process, at a certain moment, one piece and the

working period is TP1 = 20 [time units]. Machine M2 can process

simultaneously two pieces and the working period for a piece is TP2 =

30 [time units]. The loading, unloading on/off the blades of the semi-

products/ processed pieces is done in a loading/unloading point L/UP.

The modeling of the system with the help of a T-timed PN will

have to take in consideration the following aspects:

The processing of the pieces on each of the two machines will be

modeled with the help of transitions to which temporizations will

be associated matching the respective processing time units.

Stoc 1 Stoc 2M1 M2

TP 2 = 30 unit. timpTP 1 = 20 unit. timp

PI / D

Fig.2.1. Manufacturing system

Stock 1 M1 Stock 2 M2

TP1=20 time units TP2=30 time units

L/UP


23

• The relative condition to machine 1 – processing one piece at a

given moment – will be modeled with the help of “counter”

places, P4.

• Machine M2 processing two pieces simultaneously, it results the

fact that in Stock 2 there will never be pieces, therefore it isn’t

necessary to associate a place with it.

• The transport, loading, etc. time units are set aside.

The model of the system with the T-timed Petri nets is presented

in figure 2.2.

P1 (STOC 1)

P2

P3

P5

P6

P4

T1 ( Incarcare M1)

T2 (Prelucrare pe M1)

T3 (Descarcare M1; incarcare M2)

T4 ( Prelucrare pe M2)

T5 ( Descarcare M2; evacuare; introducere)

(Piesa neprelucratape M2)

d2 = 20

(Piesa neprelucrata pe M1)

(Piesa prelucrata pe M1)

(Limitarea incarcarii M1)

d3 = 30

(Piesa prelucrata pe M2)

Fig. 2.2. T-timed Petri net

(STOCK 1)

T1 (Loading M1) (Unprocessed piece on M1) T2 (Processing on M1) (Processed piece on M1) T3 (Unloading M1; loading M2)

Limiting the M1 loading)

(Unprocessed piece on M2) T4 (Processing on M2) (Processed piece on M2) T5 (Unloading M2; evacuation, introduction)


24

In the case of this application the following things will be

observed:

1. The implementation of the model in the Visual Object Net++®

environment;

2. The evolution diagrams of the number of markings from the

input places in the timed transitions will be highlighted.

Application 2- Modeling with T-time Petri nets of the flexible

manufacturing cell CFF-2R-2002

The flexible manufacturing cell CFF-2R-2002 has been designed

within the Faculty of Electronics hand in hand with the Faculty of

Management and Technological Engineering from the University of

Oradea.

Taking in consideration the cell as a complex system, the

subsystems which comprise it can be identified. These are:

1. Instruction subsystem;

2. L manipulation subsystem;

3. Processing subsystem;

4. Transfer subsystem;

5. Manipulation system II;

6. Storage subsystem.

In figure 2.3 is presented the layout of the flexible manufacturing

cell, the main components of each subsystem being highlighted.


25

SUBSISTEM DECOMANDA

(CONTROLERCELULA)

SUBSISTEMDE

PRELUCRARE

SUBSISTEM DEMANIPULARE I

SUBSISTEM DEMANIPULARE II

SUBSISTEMDE

DEPOZITARE

13

CP-20-UO(3.1)

PC(3.4 )

2

CP(2.3 )

RV-M1(2.1)

46

5

PC(4.3 )

AID-V5-EN(5.1)

PC(4.3 )

2

4

1

7

65

3

8

DTR(4.1)

SUBSISTEMDE

TRANSFER

EC(4.2 )

EC(2.2 )

CNC600(3.2)

CNC(4.2 )

DL(3.1)

Fig.2.3. The layout of the CFF-2R-2002 flexible manufacturing cell.

• The instruction subsystem (1) is materialized by a PC computer

called Cell Controller (CC). This indirectly accesses, through the

interface computers, the instruction equipment of the

manufacturing cell components (robot RV-M1, processing center,

transfer device, robot AID-V5-EN) [7].

• The manipulation subsystem I (2) has as component the industrial

robot RV-M1 (MITSUBISHI) (ii.1) with five mobility degrees, of RRRRR

structure. The role of this robot within the CFF-2R-2002 is to ensure the

processing of a semi-product off the transfer device (TRD) and its

placing in the working device of the processing center CP-20-UO.

Moreover, after finishing the processing, robot RV-M1 unloads the piece

from the working device of the processing center and it deposits it in

PROCESSING SUBSYSTEM

INSTRUCTION SUBSYSTEM (CONTROLLER CELL)

MANIPULATION SUBSYSTEM I

TRANSFER SUBSYSTEM

MANIPULATION SUBSYSTEM II

STORAGE SUBSYSTEM


26

the proper location from the transfer device TRD. The connection of the

robot’s controller (2.2) to the LAN net is performed through the PC

computer (2.3).

• The processing subsystem consists of the processing center CP-20-

UO (3.1), served by a type CNC600 equipment (3.2) which is connected

to the cell controller with the help of a (PC) computer (3.4). The

processing center carries a tool shop whose capacity is of 20 pieces. On

the table of the machine the working device WD (3.3) is situated, on

which the semi-product is oriented and fixed during the processing.

• The transfer subsystem (4) has as component a rotary table

(Transfer device TRD-4.4) on which there are eight positions in which

the semi-products, respectively the processed pieces are placed. The

transfer device has an indexed rotary flow (right-handed) with the

possibility of placing a certain position to robot RV-M1 for the

loading/unloading of a semi-product/piece in/from the working device

of the processing center. As well as in the case of the other components,

the connection of the instruction equipment of the transfer device to

the cell controller is done through a personal computer (4.3) connected

to the instruction equipment (4.2) of the rotary table.

• The manipulation subsystem II (v) has the following functions: the

withdrawal of the semi-products from the shelf type of stock in

Cartesian coordinates, the reversing of the semi-products situated on

the transfer device for the processing of the second face, the deposition

of the processed pieces in the stock.

As component of this subsystem is the type AID-V5-EN robot in 6 axes

(5.1), the instruction equipment of type CNC (Computer Numerical


27

Control) robot (5.2) and the PC computer (5.3) which ensures the

interface with the cell controller.

• The deposition subsystem (6) consists of a “high shelf” type of

stock, in Cartesian coordinates, structured on four lines and eight

columns. This structure determines the existence of 32 cells in which

the semi-products and processed pieces can be deposited.

Modeling with Petri nets of the flexible manufacturing cell

The model with Petri nets of the flexible manufacturing cell

highlights the performance means of its components having in mind the

interactions which appear in the dynamics of the sequence course,

during the manufacturing process.

In figure 2.4 are present the pieces that will be manufacturing in cell.

Fig. 2.4. The pieces that will be manufacturing

A

Piece 1

Piece 2

Piece 3

Piece 4

Piece 5

Piece 6

Piece 7

Piece 8

B

B A

A B

A B

A B

A B

A B

A B


28

In the performance of the cell five groups of sequences can be

identified (Fig.2.5).

• Processing of face A of each i piece, 8,1i = ;

• Reversing piece i;

• Processing face B of each i piece;

• Evacuation of piece i;

• Selecting a piece for processing.

Fig. 2.5. Model with Petri net of the CFF-2R-2002 flexible manufacturing

cell

Each place of the net models a condition which can be fulfilled or

not at a given moment. The transitions which model “actions”, “events”,


29

can be executed when the conditions, modeled through places, are

fulfilled. The meanings of places, respectively of transitions are

presented in table 2.1.

The model allows the describing of the performance of the flexible

manufacturing cell on the condition of processing a number of eight

pieces, this being the capacity of the transfer device TRD.

Table 21. The meanings of the pivotal points of the Petri net which

models CFF-2R-2002

SERIAL

NO. SYMBOL TYPE MEANING FEATURS

1 P1 Place RV-M1 is free m0(P1)=1

2 P2 Place Piece POZ(i)/A is placed to

robot RV-M1 for loading on

CP-20-UO

m0(P2)=0

3 T1 Transition RV-M1 apprehends piece

POZ(i)/A d2=5 sec

4 P3 Place Piece POZ(i)/A is found in

the prehensile device of the

RV-M1 robot

m0(P3)=0

5 P4 Place Location POZ(i) in front of

robot RV-M1 is free m0(P4)=0

6 P5 Place The WD of CP-20-UO is free m0(P5)=1

7 T2 Transition Piece POZ(i)/A is loaded on

the WD of CP-20-UO d2=10 sec

8 P6 Place Piece POZ(i)/A is fixed on

the WD of CP-20-UO m0(P6)=0

9 P7 Place The DP of the RV-M1 robot

is free m0(P7)=0

10 T3 Transition CP-20-UO processes piece

POZ(i)/A

d3=TT1(P

OZ(i))*60

[sec]


30

SERIAL


8,1i =

11 P8 Place The processed piece is in

the WD of CP-20-UO m0(P8)=0

12 T4 Transition RV-M1 unloads piece

POZ(i)/A from the WD of

CP-20-UO

d4=5 sec

13 P9 Place Piece i/A is found on the DP

of RV-M1 m0(P9)=0

14 T5 Transition RV-M1 deposits piece

POZ(i)/A in the location I of

the TRD

d5=11 sec


location I of the TRD m0(P10)=0

16 T6 Transition The TRD places piece

POZ(i)/A to robot AID-V5-

EN

d6=6 sec

17 P11 Place Piece POZ(i)/A is placed to

robot AID-V5-EN m0(P11)=0

18 P12 Place Robot AID-V5-EN is free m0(P12)=1

20 T7 Transition Robot AID-V5-EN

apprehends piece POZ(i)/A d7=5 sec


DP of robot AID-V5-EN m0(P13)=0

22 P14 Place Location POZ(i) from the

TRD is free m0(P14)=0

23 T8 Transition

Robot AID-V5-EN reverses

piece POZ(i) ( piece

POZ(i)/A → piece

POZ(i)/B)

d8=13 sec

24 P15 Place Piece POZ(i)/B is found in

the DP of robot AID-V5-EN m0(P15)=0

25 T9 Transition Piece POZ(i)/B is deposited

in location i of the TRD d9=5 sec

26 P16 Place Piece POZ(i)/B is in location

i of the TRD m0(P16)=0

27 T10 Transition TRD places piece POZ(i)/B

on RV-M1 d10=18 sec


31

SERIAL


28 P17 Place RV-M1 is free m0(P17)=0

29 P18 Place Piece POZ(i)/B is placed to

robot RV-M1 for loading on

CP-20-UO

m0(P18)=0

30 T11 Transition RV-M1 apprehends piece

POZ(i)/B d11=5 sec

31 P19 Place The WD of CP-20-UO is free m0(P19)=0


the prehensile device of

robot RV-M1

m0(P20)=0

32 P21 Place Location POZ(i) in front of

the robot RV-M1 is free

m0(P21)=0

33 T12 Transition Piece i/B is loaded in the

WD of the CP-20-UO d12=10 sec

34 P22 Place Piece POZ(i)/A is fixed in

the WD of al CP-20-UO m0(P19)=0

35 P23 Place The DP of robot RV-M1 is

free m0(P20)=0

36 T13 Transition CP-20-UO processes piece

POZ(i)/B

d13=TT2(P

OZ(i)) *60

[sec]

8,1i =

37 P24 Place Piece POZ(i)/B, processed,

is in the WD of the CP-20-

UO

m0(P24)=0

38 T14 Transition RV-M1 unloads piece

POZ(i)/A from the WD of

the CP-20-UO

d14=5 sec

39 P25 Place Piece i/B is found in the DP

of the RV-M1 m0(P25)=0

40 T15 Transition RV-M1 deposits piece

POZ(i)/B in location POZ(i)

of the TRD

d15=11 sec


32

SERIAL


41 P26 Place

Piece POZ(i)/B is found in

the POZ(i) location of the

TD

m0(P26)=0

42 T16 Transition The TRD places piece

POZ(i)/B to robot AID-V5-

EN

d16=6 sec

43 P27 Place Piece POZ(i)/B is placed to

robot AID-V5-EN m0(P27)=0

44 P28 Place Robot AID-V5-EN is free m0(P28)=1

45 T17 Place Robot AID-V5-EN

apprehends piece POZ(i)/B d17=5 sec


the DP of robot AID-V5-EN m0(P29)=0

47 T18 Transition Robot AID-V5-EN deposits

piece POZ(i) d18=13 sec

48 P30 Place Finished pieces stock m0(P30)=0

49 P31 Place Piece POZ(i) has been

processed and stored. m0(P31)=0

50 P32 Place The locations in which the

un-processed pieces are

found.

m0(P32)=0

51 T19 Transition

The selection of the

following piece which will

be processed according to

the temporization

associated with the

transition

d19 [sec]

(according

to the rates

resulted

from the

Gannt

graphic

theorizing

program)

52 T20 Transition Reinitializing the net d20


33

In the case of this application the following things will be

observed:

1. The implementation of the model in the Visual Object Net++®

environment;

2. The cell performance will be simulated for a manufacturing

instruction of eight pieces for which the rates of the transition

temporizations T3, T13 and T19 are the ones from table 2.2.

Table 2.2. Temporizations [sec] associated with transitions from the

model of Petri nets of the CFF-2R-2002 cell

Piece

Transition 1 2 3 4 5 6 7 8

T3 252 150 90 420 270 180 462 90

T13 174 114 150 90 180 120 90 402

T19 15 15 15 3 21 21 21 21


35

APPLICATION 4

4. MODELING COLORED PETRI NETS USING CPN TOOLS

4. 1. The purpose

The application presents modeling possibilities of the flexible

manufacturing systems using colored Petri nets. The evaluation of the

performance of flexible manufacturing systems is made using the CPN

Tools modeling and simulation program with colored Petri nets.

4. 2. Theoretical background

Colored Petri nets are used for modeling systems in which

interfere issues related to: parallelism, resources allocation,

synchronization. These issues explicitly define the flexible

manufacturing systems.

In general, in a Petri net, the information is „carried” by the places.

The presence of a marking (token) in a place can model, for example, a

free, available machine tool. The absence of the marking means the fact

that the machine tool is engaged.

More markings in a place can represent a stock of identical pieces. If the

diversity, the richness of the information associated with a place from a

PN is expected, a method must be adopted with the help of which


36

markings found in the same place can be distinguished. This kind of

method is conferred by Colored Petri Nets (CPN).

Model with colored Petri nets

A flexible manufacturing system is taken in consideration, with

two working machines, machine 1 and machine 2. The pieces are

carried through blades: n1 for p1 and n2 for p2. The blades are

reintroduced in the system at the end of the processing of a piece.

Stoc ST2Stoc ST1 ML1 ML2

PI/ Dp1,p2,p1,p2,....

Fig.4.1. Flexible manufacturing system

The ordering within the system consists of the alternative

processing of the two types of pieces in the sequence: p1,p2,p1,p2,p1. It is

implied that the loading/unloading of the blades is made immediately

(it has an insignificant period of time).The colored Petri net which

models the system is presented in figure 4.2.

Colors C1 and C2 are associated with the blades on which the

pieces are found. That is, C1 for the type 1 blade – corresponds to piece

p1 - and C2 for the type 2 pallets, which corresponds to piece p2. The

aggregate of colors C1, C2 is associated with all places and transitions.

Notations used:

• STi, places which model the stock in front of machine i;

• MFi, places which model the fact that machine i is free;

Stock ST1 WM1 Stock ST2 WM2

L/UP


37

• MEi, places which model the fact that machine i is engaged;

• Ti, transitions which model the loading of machine i;

• Ti`, transitions which model the unloading of machine i;

In all cases i={1,2}.

Fig. 4.2. Model with colored Petri net

Places ST1, ME1, ST2 and ME2 model the physical states of the

system.


38

Places ME1 and ME2 describe the fact that machine 1 and machine

2 are unique resources, each of them, in terms of piece 1, respectively

piece 2, these being split in more pieces.

In the model presented the succession function is also

encountered, defined like this:

Succ (C1) = C2 (4.1)

Succ (C2) = C1 (4.2)

This determining the ordering of the two types of pieces in the

system in the succession: p1, p2, p1, p2,p1.

The initial marking has two components:

Mo (ST1) = n1C1 + n2C2 (4.3)

meaning that in the input stock of machine ME1 there are no n1 pieces

and n2 pieces p2. As well as:

Mo (ME1) = Mo (ME2)=C1 (4.4)

the meaning of the relation is the one that each of the two machines are

waiting for a type p1 piece.

4.3. The development of the application

This application presented at point 2, is implemented using the

CPN Tools soft


39

Modeling using simple Colored Petri Nets.

Initially, two colors are declared:

colset color=with C1|C2 (4.5)

-colset is the key word from Modeling Language with the help of

which the colors are declared. In the previous line a set of colors is

declared formed of two elements C1 and C2.

The arcs are the elements which connect a transition to a place.

The rate of arcs is defined as being the type of color which is carried:

No. i:color; (4.6)

In the design of the model 6 places (A…F) and 4 transitions

(T1…T4) have been used. Initially, place A will consist of two colors:

1’C1++1`C2 (4.7)

-operator “++” is also used as a concatenation operator between the

two colors and operator “`” is used for stating the number of markings

from the respective color.

Places E,F is initiated with C1 (1’C1) color.

Places E,F will be alternately loaded by colors C1,C2 due to the

specified conditions on the arcs which enter them.

if i=C1 then 1`C2 else 1`C1 (4.8)

The meaning of this condition is the following: If number “i” of the

arc is C1 then the place in which the arc enters is loaded with marking

C2, otherwise C1 is the rate with which the place is loaded.


40

In the first step of the simulation moment transition T1 is

executed, this being validated because places A and E are loaded with

markings C1. At the execution of transition T1 the C1 color markings

are withdrawn from places A and E and marking C1 is deposited in

place B (Fig. 4.3).

Fig. 4.3 FMS model designed in CPN Tools – Initialization stage

At the execution of transition T2, marking C1 is withdrawn from

place B and deposited in place C and at the same time in place E

marking C2 will be deposited, due to the conditions specified on the arc

(Fig. 4.4).


41

Fig. 4.4.FMS model designed in CPN Tools– T2 transition execution

The resulted marking is presented in figure 4.5.

Fig. 4.5. FMS model designed in CPN Tools –T3 transition execution


42

Modeling a manufacturing system with Complex Colored Petri nets.

The manufacturing system presented above is taken in

consideration. The model of system with Colored Petri nets using

complex colors is the one presented below in figure 4.6. In this model

the notations have the following meaning:

• place A models the stock in front of each machine;

• place B models an engaged machine;

• place C models a free machine;

• transition T1 models the loading of a machine;

• transition T2 models the unloading of a machine.

Fig. 4.6. FMS model designed with complex colored Petri nets

In the design of the model the basic color (P1, M1) is used, which

defines piece p i (i={1,2}) is processed onto machine m j (j={1,2}). A


43

marking of color (Pi,Mj) in place A signifies the existence of a type P1

piece in the input stock of machine j. A marking of the same color in

place C signifies the fact that machine j is available and is to process a

type Pi piece.

The initial marking of place A is:

3`(P1,M1)++3`(P2,M1) (4.9)

-the meaning of this marking is that in the input stock in front of

machine 1, 3 pieces P1 and 3 pieces P2 are waiting.

The initial marking of place B is:

1`(P1,M1)++1`(P1,M2) (4.10)

- machines 1 and 2 are available and are to process a P1 piece.

Conclusions

Colored Petri nets offer remarkable facilities for the evaluation of

the performance of flexible manufacturing systems. This thing is

possible through the introduction of color type markings and of

functions (conditions) as loadings of net arcs. The models designed this

way describe more accurately the real systems and the different stages

in which they can be found. Using complex colors significantly reduces

the design of the model.

The modeling and simulation programs with Petri nets become a

useful tool for the improvement of management activities through the

information that they offer to decisive agents.

Among these programs, CPN Tools is distinguished due to the

diversity of facilities which it offers and to the friendly features,

approachable to the user.


45

APLICATION 5

5. THE EVALUATION OF THE MANUFACTURING SYSTEM

PERFORMANCE USING THE TAYLOR ED 2000® PROGRAM

5.1. The purpose

The paper has as the purpose of modeling and simulation of the

performance of manufacturing systems with different structures, using

the Taylor ED 2000 program.

5.2. Theoretical background

The real performance of a Flexible Manufacturing System (FMS)

implies random entries in the system; the entries generate random

fluctuations in the filling of the processing stations and the appearance

of stay series.

A queueing networks series requires the set-up of an area and/or

the layout of equipments in which the components which are to be

processed are going to be stored. This thing implies a FMS design which

needs to have in mind the set-up of storage area.

In figure 5.1 the processing means within the FMS is presented

which is assimilated with a queue system.

The significant elements are:


46

• The input flow in the system represents the way or the entry rule

of the components in the system. This rule can be expressed through

the fluctuation of the period of time between the two consecutive

entries or through the fluctuation of the entry rate in the time unit

(for example in an hour).

It will be taken in consideration the fact that the queue systems

are with random entries, meaning that the period of time between the

two consecutive entries or the entry rate on the time unit are random

variables. To a random variable is associated a probability density

(probability function).

Fig. 5.1. FMS assimilated with a queueing system

The entry flow is, in most cases, of Poisson type:

x

f ( x ) e ; x 0 ,1,2 ,...x !

λλ −= = (5.1)

where:

x – the entry rate in the time unit (random variable);


47

λ - the average rate of entries in the time unit.

• Queue

The components which enter the system and find the processing

station engaged sit in “line” – the proper queue – then as the station

becomes free they can enter for processing.

Another basic feature of the series is its length, which can be

considered infinite or limited to a predetermined size (N).

The discipline of the queue, another of its features. This can be

determined by the priority rule which has been preset in order to

establish the processing sequence of the components in series.

• Working stations (servers)

These are the ones which satisfy the service required by the

customer (the processing piece). In the FMS case, the working stations

are the machine tools, and the service they perform is the processing of

the working objects.

When the processing period is a random variable, to it is

associated a probability density (probability function). In many cases,

the probability density of the service period (processing) is a negative

exponential function of type:

tf ( t ) e µµ −= (5.2)

where:

t – service period (random variable);

µ - average rate of processed pieces in a time unit (for example in

an hour).

Another feature is the intensity of traffic in the system: ρ λ µ= .


48

• The output flow within the system is important in the case of

FMS, because, in most cases, it is itself, an entry flow for other

stay systems.

Starting from this data, the following performance parameters are

generally evaluated:

• The average rate of customers from the system – noted with N;

• The average remaining time of a customer in the system – noted

with T.

In this purpose the formula of Little is used [2]:

N T λ= (5.3)

or

NT

λ= (5.4)

5.3. The development of the application

Application 1

The manufacturing system from figure 5.2 is taken in

consideration. This consists of:

• Supply installation SA;

• Transfer system of conveyor Cv1 type, for the transport of semi-

products;

• Industrial robot IR;

• Working machine WM;

• Transfer system of conveyor Cv2 type, for the transport of

processed pieces;


49

• Evacuation installation EI.

• The main functional features of the system are the following:

• The period of time between two consecutive entries is 25 seconds;

ML

RI

OL

IA Cv1 Cv2 IE

Fig. 5.2. Manufacturing system with a working machine and an industrial

robot

• The capacity of the conveyors is of 10 semi-products (pieces);

• The rotation speed of the robot is of 30 degrees/ second;

• The loading/unloading time units proper to the industrial robot,

each are of 5 seconds;

• The processing period on the working machine is of 10 seconds;

• Issues to be resolved:

• The model of the system described will be designed using the

Taylor ED 2000 program;

• The performance of the system will be simulated for a period of 8

hours. In this period of time, 1152 semi-products will arrive in the

system due to the entry flow rate.

• The change regarding the state of the working object will be also

modeled, its passing from the semi-product state, before processing,

to the processed piece state, after processing.

WM

SA IR EI


50

• The performance parameters of the system components resulted

following the simulation will be highlighted.

Fig. 5.3. 2D model of the system from figure 5.2

The 2D model of the manufacturing system taken in

consideration is the one from figure 5.3. The channels connecting the

system components have also been highlighted. In figure 5.4 the 3D

model of the same system is presented.


In order to model the change regarding the state of the working

object following the processing onto the working machine in the


51

window which describes the specific parameters of the machine

(server) the following will be selected:

Trigger on exit: set(color(i),coloryellow)

The general results of the simulation are found in the following

report:

summary report

content throughput stay time

name current average input output average

Source1 1 0.397 695 694 16.439

Accumulating Co 9 8.888 694 685 368.858

Robot3 1 0.670 1370 1369 14.089

Server4 0 0.238 685 685 10.000

Accumulating Co 0 0.166 684 684 7.000

Sink6 0 0.000 684 684 0.000

Product 0 0.000 0 0 0.000

Model start time Wednesday, 17:28:35

Model end time Thursday, 01:28:35

Runlength (seconds) 28800.00

End of report.

It is determined that the system could not undertake all 1152

semi-products. Only 685 semi-products have been processed in the

system. 684 finished pieces have been carried off.


52

In figures 5.5, 5.6, 5.7 and 5.8, are presented graphs representing

information regarding the performance of the system elements,

performance highlighted through simulation.

Therefore, the working machine has had a loading degree of 24%

(Fig. 5.5).

From figure 5.6, regarding the industrial robot, the following data

results:

• The industrial robot has moved loaded 19% of the respective

time;

• The industrial robot has moved without a working object 9% of

the respective time;

• The industrial robot has apprehended (has loaded) 24% of the

time;

• The industrial robot has unloaded 24% of the time;

• The industrial robot was free 24% of the time.

Due to the fact that the entry flow could not be undertaken by the

other system components, conveyor 1 has been blocked (loaded at

maximum capacity) 95% of the time (Fig. 5.7). Regarding the length of

the semi-product series from conveyor 1, this is 90% of the time of 9

pieces (Fig. 5.8).

Fig. 5.5. Loading degree of the machine

Performance parameters of the machine


53

Fig. 5.6. Industrial robot

Fig. 5.7. Loading of Conveyor 1

Fig. 5.8. Stay queueing - Conveyor 1

Performance parameters of the robot

Conveyor 1

The length of the series – conveyor 1

The length of the queueing


54

In order to process the entire flow of semi-products which enters

the system a supply of the system modules is submitted.

Application 2.

In the configuration resulted the system consists of two industrial

robots (IR1 and IR2) and two working machines (WM1 and WM2). The

layout of the system is presented in figure 5.9.

ML1

OL

IA Cv1 Cv2 IE

ML2

RI1

RI2

OL

Fig. 5.9. Manufacturing system with two working machines and two

industrial robots

The solving of the following issues is aimed:

• Modeling the system using the Taylor ED 2000 program;

• The change regarding the state of the working object will be

modeled: its passing from the semi-product state, before

processing, to the processed piece state, after processing.

WM1

SA EI IR1

IR2

WM2


55



• The evaluation of the system performance through the simulation

of its performance in the following periods of time: 8 hours, 16

hours, 72 hours; 1 week.

• Taking in consideration the possibility of failure of the working

machines and of the industrial robots;

The 2D model of the manufacturing system is presented in figure

5.10, the channels connecting the system components being also

highlighted. The 3D model is presented in figure 5.11.

Modelling and simulation of mechatronic systems- laboratory handbook

57

APPLICATION 6

6. THE MOVEMENT SIMULATION OF THE VIRTUAL

PROTOTYPE

6.1. The purpose

In this work will ma made the analysis of an assembly’s

movement in the application Motion Simulation.

6.2. Theoretical notions

The virtual prototype simulation movement is a design tool used in

animation and motion analysis kinematic and dynamic models, to

determine the critical positions, forces, velocities and accelerations.

The virtual prototype simulation of motion is an application

software CAE (Computer Aided Engineering) used to model and analyze

the performance of moving parts in a mechanism located in the virtual

environment. Simulation of the movement is directed towards solving

problems from the rigid body mechanics (eg statics and dynamics).

Motion simulation reproduces a master set (original) previously

modeled and sets it in motion by means of simulations, without altering

the whole master (original). Once the optimal motion simulation,

assembly master can be updated to reflect the new optimal design.


58

The simulation of the movement of a virtual prototype behavior

may provide a mechanism before its actual implementation. These

predictions are based on advanced math and physics and engineering

principles. Although these mathematical principles, physical and

engineering are currently applied in the software, results should always

be assessed to the puncture of engineering: if the result is expected and

if it is feasible.

The motion simulation can analyze the mechanism by examining

interference, distances traveled, speeds, accelerations, movement and

reactive forces, torsion moments, etc.. Motion simulation analysis results

generally indicate the need for design changes in track geometry

(elongation / shortening elements levers, cams shape modification,

adjustment multiplier reports, etc.), Or material piece (easier, harder,

etc.). Design modifications can then be applied given set of simulation

duplicate and reanalyzed. Once the optimal motion simulation is

determined, design changes can be incorporated into all master.

A mechanism is considered as a collection of kinematic elements

related by kinematic joints and other constraints to make a move.

Simulation of motion can be created by following steps:

- Step 1: Create kinematic elements

Kinematic elements are solid bodies or assemblies of rigid bodies

without relative movement between them. Are defined to represent the

moving parts in the mechanism.

- Step 2: Creating joints and kinematic constraints. Kinematic

couplings constrain movement of kinematic elements. In some cases,

you can create other elements of coercion, such as springs, dampers,

bearings (bushings) or contacts.


59

- Step 3: Defining actuators (motion driver).

3. The development of the application

1. Open the file named Ansamblu3.prt from the gripping device

link directory. In the Assembly Navigator can be seen all constraints

applied under Constraints node (Fig. 6.1).

Fig. 6.1 Assembly3.prt file

2. It is started the motion simulation application using Start →

Motion Simulation (Fig. 6.2)


60

Fig. 6.2. Motion simulation application

3. Creating a new simulation

In the Motion Navigator areas right clicks on the node

represented by a whole and choose New Simulation (only by the way).

In the Environment window select the type of analysis by option

Dynamics.

Fig. 6.3. Creating a new simulation Fig. 6.4. Choosing the type of analysis


61

4. Defining a kinematic element

Creating kinematic elements can be done with the command link

which can be accessed as follows:

- The button on the toolbar at Motion, right click on the node

running the simulation of Motion Navigator, then choose

option New Link (Fig. 6.5.a);

- From the developing menu: Insert - Link (Fig. 6.5. b);

- From the menu bar by enabling the Link button (Fig. 6.5.c).

(a) (b) (c)

Fig. 6.5. Creating a kinematic element

After the command is activated, the window Select Object we

already have an active region (highlighted in red). Select the

component to be defined as a kinematic element. The gripping device,

it is the rod (Fig. 6.6).


62

Fig. 6.6. Defining the kinematic element The Rod

5. Creating kinematic joints

Creating kinematic joints is achieved by activating joint command.

This can be done as follows:

- The button on the toolbar at Motion, right click on the node

running the simulation of Motion Navigator, then choosing New Joint

(Fig. 6.7.a);

- Developong menu: Insert - Joint (Fig. 6.7. b);

- From the menu button by activating joint (Fig. 6.7.c).


63

(a) (b) (c)

Fig. 6.7. Creating a kinematic joint

For the case study, the park's clothing following steps define the

joint rod is slider of cylinder (Fig. 6.8):

1. In the Joint window the kinematic coupling type is selected: Slider

(translational joint)

2. Select the kinematic element rod, activating option Select Link,

Joint window.

3. To specify the orientation and origin, with the active region

Specify Orientation.

4. Select an item based kinematic (Base Link). In this case study, the

kinematic element is Corp_cilindru.

If the kinematic elements are not in proper position

(disassembled), we can assemble the Snap Links ticking box, then

selecting active regions as in the first link.


64

Fig. 6.8. Defining the kinematic joint

6. Creating a solution:

The Solution button is activated (or run right click and choose

New Solution motion_1 node )


65

Fig. 6.9. Creating solutions

In the Solution window we have to choose Run Normal type

solution and the type of analysis Kinematics / Dynamics.

In the Time field is introduced value 1, and in Steps, 50 (we

consider mechanisms for one second during the 50 intermediate

steps).

Select the box Solve with OK and then activates the OK button to

confirm and to calculate the solution.

The above steps are repeated for all the kinematic and for all

couplings in the Appliance shaped grip.


66

6. Animation of the mechanism

The Animation button is activated. Press the Play button in the

Animation window, order to the trigger mechanism. If you want going

through step by step, click Step Forward and Step Backward buttons.

Fig. 6.10. Animation

For a continuous advance motion - Retrace back button is

pressed. Confirm with OK the Animation window.

The file is closed. (File → Close → All Parts).


67

APPLICATION 7

7. FUZZY CONTROL SYSTEMS - THE WASHING MACHINE

7.1. Introduction

One of the important practical applications of fuzzy logic systems is

their use as process control systems. Using fuzzy logic systems as

controllers enjoy a solid theoretical basis, there are currently many

commercial applications incorporating a fuzzy control system.

When using a washing machine, the user typically selects the time of

washing the clothes depending on the amount and the type and degree

of their dirt. To automate the process of washing, the detection sensors

can be used for the volume of clothes, and the type and degree of dirt.

Based on these data, it will be chosen a washing time.

Unfortunately, we cannot define a precise mathematical relationship

between input quantities (the volume of clothing, type and degree of

dirt) and output size (washing time). Thus, the washing time is set

manually by the user, based on their experience and repeated attempts.

Making a washing machine with a self-determined washing time

involves the construction of two subsystems (Fig. 7.1):

- Sensor system - provides input signals of the washing machine, taken

from the outside (clothes from the machine)

- Control unit - based on information programming from the sensor


68

system, will decide on the time of washing, as a control output. Because

you cannot formulate a precise mathematical relationship between

input and output control unit will use a fuzzy logic control system.

Fig. 7.1. The fuzzy washing machine

7.2. Implementing the fuzzy control system

The implementation of control system based on fuzzy sets of the

type of cleaning involves the following steps:

A. Definition of input size into the automatic controller. The input

values are:

1. The Degree of Dirt of clothes: DD

2. Type of Dirt: TD


69

B. Definition of linguistic terms associated with each input quantity

The linguistic terms associated to the linguistic input variable

Degree of Dirt are:

{ }DDDD : LT s ,Md ,L= (7.1)

where: s-small: Md- Medium; L- Large.

The linguistic terms associated to the linguistic variable Type of

Dirt are:

{ }TDTD : LT NG ,Md ,G= (7.2)

where: NG-Not Greasy, M- Medium, G- Greasy.

C. The determination of membership functions associated with each

linguistic term corresponding to the input quantities

In the case of variable input quantities associated to Degree of

dirt and Type of dirt, to all linguistic terms are corresponding

membership functions of triangular type. (Fig. 7.2.)

Fig. 7.2. The inputs


70

D. Defining the output size of the decisional process. The output size is

the washing time. The linguistic variable is associated with the output

quantity of washing time.

The linguistic terms associated to the output size are:

{ }WTWT : LT Vs ,s ,Md ,L,VL= (7.3)

where: Tsf-Very Short, TS- Short, TMd- Medium, TL- Long, TFL-

Very Long.

E. Determination of membership functions associated with each

linguistic term corresponding to the output size

In the case of output variable size associated to Washing time, to

the linguistic terms are corresponding triangular type membership

functions (Fig.7.3).

Fig.7.3. The Output

F. Setting the method for connecting the various values of membership

functions

The multitude of linguistic variables and linguistic terms, which

were associated membership functions, characterize "vaguely" the


71

strong values the input sizes, and output sizes respectively. The

connection is made by the MIN-MAX method, resulting 9 inference rules

of the form:

1. If (DD is s) and (TD is NG) then (WT is Vs)

2. If (DD is s) and (TD is Md) then (WT is s)

3. If (DD is s) and (TD is L) then (WT is Md)

4. If (DD is Md) and (TD is NG) then (WT is s)

5. If (DD is Md) and (TD is Md) then (WT is Md)

6. If (DD is Md) and (TD is L) then (WT is L)

7. If (DD is L) and (TD is NG) then (WT is Md)

8. If (DD is L) and (TD is Md) then (WT is L)

9. If (DD is L) and (TD is L) then (WT is VL)

The decisional system implemented in Matlab ® Fuzzy Logic Toolbox is

presented in figure 7.4.

Fig. 7.4 The Fuzzy system

The dependence of the variable output of the input variables can

be highlighted also by the means of surface representation of variation

(Fig. 5).


72

Fig. 7.5. Surface of variation of the Washing time variation in relation to

the degree of soiling and type of soiling

Fig. 8.6. Inference Rules


73

An example of the fuzzy system's functioning for two strong

values of the inputs is shown in Figure 6, in which the rules are put in

evidence the inference rules. Thus, for the degree of soiling = 75 and for

the type of dirt = 90, type of washing = 170 minutes.

3. Carrying out the work

It will be implemented the fuzzy system described in the Fuzzy

Toolbox of Matlab.

It will be determined the type of wash for different values of the

type of dirt and soil.


75

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