GRAFCET and Petri Nets Outline Introduction GRAFCET
Contents
1. b si e et a si poussoirs avec les s curit s b si e et Al si z mise PO dans de marche tat d termin marches de v rification dans l ordre mise hors pr paration pour remise en route Oy NAA demand nude lt production normale gt apr s d faillance gt en fin de Nc remise en pression PO et d clenchement Dp d e ALLA mise hors lt pr paration pour agar nergie d d remise en route demand emand nande ED lt production normale gt apr s d faillance gt en fin de dans tat remise en pression cycle gt d termin gt PO et d clenchement d e de IA nergie de PC cycle de contr le de de PC l tanch it des soupapes cycle de contr le de l tanch it des soupapes diagnostic trai production tout Eo lt marches nergie tement d faillance de m me gt de test gt bee G2 dianosticrai D3 Ge lt marches de test gt nergie talo he Par d de Fe de PC cycle de test e arr t d urgence q de l tanch it mise hors et d nergie coupure de l alimentation de la partie b arret d urgence partie op rative PO D tection nergie coupure de l alimentation2. Liz stage 1 situation 1 2 UEM ii ma stage 5 1 2 et 3 enabled 7 HG 3Hp T cannot be cleared on e T 2 Ore i a stage 6 stable situation 1 2 SLT 6 1 A Ai HD 5 H6 6 Hp 7 c 8 d stage 4 no pulse shaped action stage 5 T2 6 stage 3 clearing 6 stage 2 m 1 on e T 3 stage 3 clearing 3 stage 4 no pulse shaped action stage 5 T stage 6 Agz O A stage 2 on Ta Ti 2 stage 3 clearing 2 stage 4 no pulse shaped action stage 5 T stage 6 Ao H D A D DUD 0 D DO D D D D D O D Real Time Programming GRAFCET and Petri nets 38 J D Decotignie 2007 stable cycle GRAFCET and Petri nets 39 Real Time Programming J D Decotignie 2007 cise Dav90 Let H1 and H2 be two wagons carrying goods from loading points C1 and C2 respectively to an unloaded point D Variables cl c2 and d correspond to end of track sensors They turn to when a wagon is present at the given point Variable al turns to 1 when the front wheels of wagon H1 are on the tracks between A1 and D same for a2 if wagon H2 is between A2 and D If wagon Hl is in C1 and if button ml is pressed a cycle Cl D CI starts with a possible wait in Al until the track common to both wagons is free then a wait in D during 100s Wagon H2 performs the same on C2 D C2 The path C1 D
3. tural properties a State graph tural properties 2 a State graph the involved transitions t2 oe Pi 3 Event graph iif each transition has exactly one input ti a Without conflict E and one output place p a Free choice a Extended free choice a Event graph 4 simple iif each place t has exactly one input a 2 pure S poe Pk and one output a Without loop transition Real Time Programming GRAFCET and Petri nets 97 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 98 J D Decotignie 2007 tural properties 3 ctural properties 4 Q Without conflit ps E Or d Free choice P3 Each place has at most t In case of conflict K U ml one output transition lt pj ti t2 gt none of the transitions 3 simple has another input place NP than p Each transition is one conflict DC S In case of conflict all 1 a 3 t L D Real Time Programming GRAFCET and Petri nets 99 J D Decotignie 2007 have the same input places Real Time Programming GRAFCET and Petri nets 100 OUS ty J D Decotignie 2007 tural properties 5 a Pure PN p3 There is no transition that has an input place that 1s also an output place 7 ea 3 4 Po t cise properties For each PN below respond to the following questions 1 Is it a state graph 2 Is it an event graph
4. 3 Execute actions d oto 1 Real Time Programming GRAFCET and Petri nets 34 Q J D Decotignie 2007 ted Clearing Stable GRAFCET and Petri nets 35 Real Time Programming J D Decotignie 2007 rpretation Algorithm with ility search 1 initialization activation initial step s execution of associated pulse shaped actions go to 5 2 If an external event Ei occurs determine the set T of transitions that can be cleared on Ei if T1z 2 goto 3 else modify conditional actions and goto 2 3 Clear transitions that can be If after clearing the state is unchanged goto 6 4 Execute the pulse shaped actions that are associated to the step that were activated at step 3 incl timers 5 Determine the set T2 of transitions that can be cleared on occurrence of e If T4 goto 3 Real Time Programming GRAFCET and Petri nets 36 J D Decotignie 2007 rpretation Algorithm with ility search 2 6 A stable situation has been reached l Determine the set Ap of continuous actions that must be deactivated incl conditional actions 2 Determine the set A of continuous actions that must be activated incl conditional actions 3 Set to O all the actions that belong to Ao and not to A1 Set to 1 all the actions that belong to A 4 goto 2 Real Time Programming GRAFCET and Petri nets 37 J D Decotignie 2007 rpretation Algorithm with ility search 3
5. 3 Is it without conflict 4 It is simple 5 s it pure 6 Is it without loop a Without loop Pi t If there exists t and p that is at the same time input p P3 ti e t and output place for t 7 3 then t has at least another input place p O Real Time Programming GRAFCET and Petri nets 101 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 102 J D Decotignie 2007 vioral properties hability a Reachability a Can the system reach a given state or exhibit a given 3 Boundedness behavior correct or not a Conservativeness To answer this question one has to find a sequence of firing that brings from M to Mj 2 Liveness A marking Mi is said reachable from Mo if there exists a a Reversibility home state sequence of firings that transforms Mo in M a Coverability Mi is said immediately reachable from Mo if there is a unique Persist firing that transforms Mo en M zd Lis S R Mo set of all reachable markings from Mo S a Synchronic distance a Fairness Real Time Programming GRAFCET and Petri nets 103 J D Decotignie 2007 L Mo set of all firing sequences from Mo Real Time Programming GRAFCET and Petri nets 104 Q J D Decotignie 2007 ded and safe a Places are often used to represent Information storage in communication systems and computers Products and tools in production systems a The boundedness property is useful to detec
6. GRAFCET and Petri Nets Prof J D Decotignie CSEM Centre Suisse d Electronique et de Microtechnique SA Jaquet Droz 1 2007 Neuch tel jean dominique decotignie epfl ch ine a introduction a GRAFCET a GEMMA a Petri nets Real Time Programming GRAFCET and Petri nets 2 J D Decotignie 2007 duction a Description of process evolution a Description of process interaction amp Petri nets a Functional specifications a Requirements for automata GRAFCET Real Time Programming GRAFCET and Petri nets 3 J D Decotignie 2007 FCET a Graphe de Commande Etape Transition Step Transition Control Graph a 2 levels Functional specification Operational specification Q Described in the international standard IEC 848 under the name of function charts a Dav90 R David A Alla Petri nets and Grafcet Prentice Hall 1992 a R David Grafcet a powerful tool for specification of logic controllers IEEE Trans on Control Systems Technology vol 3 Issue 3 Sept 1995 pp 253 268 Real Time Programming GRAFCET and Petri nets 4 J D Decotignie 2007 FCET a Definition a Evolution rules a Defining actions a Taking time into account a Defining transition conditions a Execution algorithm a Macrostep and macroactions Real Time Programming GRAFCET and Petri nets 5 J D Decotignie 2007 FCET definition a Directed graph derived from PN Quadru
7. tat initial demand emand en fin de dans tat cycle d termin production tout de m me demande gg de marche D tection d faillances nergie PROCEDURES EN DEFAILLANCE DE LA PARTIE OPERATIVE GUIDE DES MODES DE MARCHE ET D ARRET GEMMA E PROCEDURES DE FONCTIONNEMENT paration gt ED lt production normale gt lt marches de v rification en d sordre gt lt marches de v rification dans l ordre gt lt marches de test gt cycle de test du dispositif de contr le d tanch it P PROCEDURES DE FONCTIONNEMENT Syst me de test d tanch it de soupapes boucle de test Real Time Programming GRAFCET and Petri nets 59 J D Decotignie 2007 p mise hors nergie de PC mise en nergie de PC mise hors nergie partie comman de PC de hors nergie lt mise PO dans tat initial gt par boutons poussoirs avec les s curit s lt mise PO dans tat d termin gt lt pr paration pour remise en route apr s d faillance gt diagnostic trai tement d faillance lt arr t d urgence gt PROCEDURES EN DEFAILLANCE DE LA PARTIE OPERATIVE Syst me de test d tanch it de soupapes marche manuelle Real
8. CISE readers writers Siftton invariant READERS WRITERS Do p Q Look for a non trivial solution to Task Task O I T xT 0 avec x Xj Xj XMl 1 waiting waiting a M is the number of transitions ti t2 a Gives an indication of liveness Pi Sequence of transitions that can be fired repeatedly reading s pL writing tz S t4 q Real Time Programming GRAFCET and Petri nets 143 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 144 J D Decotignie 2007 esting information a http www informatik uni hamburg de TGI PetriNets a http home arcor de henryk a petrinet e hpsim e htm Real Time Programming GRAFCET and Petri nets 145 J D Decotignie 2007
9. and Petri nets 55 J D Decotignie 2007 OA ap io L487 T man M auto Real Time Programming GRAFCET and Petri nets 56 J D Decotignie 2007 UE partie comman mise en de hors nergie nergie de PC mise hors nergie de PC mise en nergie de PC mise hors nergie partie comman de PC de hors nergie Ca PROCEDURES D ARRET DE LA PARTIE OPERATIVE PO M A6 lt mise PO dans tat initial gt all setpoints to 0 lt mise PO dans tat d termin gt power on OP clear default acquilitement pr paration pour remise en route apr s d faillance clear setpoints stop lt diagnostic trai tement d faillance t arr t d urgence power off OP brake D PROCEDURES EN DEFAILLANCE DE LA PARTIE OPERATIVE Real Time Programming isplay time amp reason q Al lt arr t dans tat initial gt loader ready A4 lt arr t obtenu check ST propeller OP A2 lt arr t aspe demand demand en fin de dans tat cycle d termin i stop production tout de m me gt setpoint in any case display default and time PRODUCTIONI manual deman de marche auto PRODUCTION se ande d arr t top auto ind of tests or d for chec 2V V or 2C C or 2B B gt 10 Em Sto tec
10. de la partie comman de PC d faillances partie k op rative PO D tection de hors ip l energie PROCEDURES EN DEFAILLANCE DE LA PARTIE OPERATIVE E PROCEDURES DE FONCTIONNEMENT chon de PC d faillances x TW a 1 D PROCEDURES EN D FAILLANCE DE LA PARTIE OPERATIVE P PROCEDURES DE FONCTIONNEMENT Syst me de test d tanch it de soupapes arr t d urgence E Syst me de test d tqrnch t de soupapes GEMMA complet S Real Time Programming GRAFCET and Petri nets 61 J D Decotignie 2007 Real Time Programming y A ele Ge SOLR P J D Decotignie 2007 e test GRAFCET MA analysis ml y z a Advantages door closed part in position stop out check proofness concise and synthetic graphic bai Non ambiguous vocabulary Clearly shows manual parts t 4 t1 n Helps defining securities and operator commands May be used as user manual traer bad valve free amp repeat 6 z a Drawbacks E ed valve free amp no repeat e Difficult to use of complex cases Some of the limitations of GRAFCET stop in Real Time Programming GRAFCET and Petri nets 63 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 64 J D Decotignie 2007 Real Time Programming to manage an automation Ject a Phases according to GEMMA tenants Define requirements Use GEMMA for start stop operations Create GRAFCET Select control technology Tec
11. is set when V equals 1 otherwise path C2 D is set ml Gl DI Cid D Real Time Programming GRAFCET and Petri nets 40 J D Decotignie 2007 Real Time Programmin GRAFCET and Petri nets 41 J D Decotignie 2007 g g do macro step a Represents a set of steps a All arcs do not necessarily go to the same step no need for a unique entry step a All arcs do not necessarily go to the same step no need for a unique exit step a All arcs entering or leaving the pseudo macro step need be represented Real Time Programming GRAFCET and Petri nets 42 J D Decotignie 2007 do macro step Stop request Stop units end Real Time Programming GRAFCET and Petri nets 43 Q J D Decotignie 2007 ro actions a Globaly act on a GRAFCET a Do not increase the expression power a But ease specification a Exhibit same properties as actions Continuous For age forcing figeage freezing masquage masking Pulse shaped Forcer force masquer mask d masquer unmask figer freeze lib rer release Real Time Programming GRAFCET and Petri nets 44 J D Decotignie 2007 roaction Forcing Forcage d forcage E G2 12 d Real Time Programming GRAFCET and Petri nets 45 Q J D Decotignie 2007 roaction Freezing Figeage d 0 Real Time Programming GRAFCET and Petri nets 46 Q J D Decotignie 2007 roaction
12. said home state if for any marking M of R Mo M can be reached from M Model this behavior z Is the result conservative Show that the resulting PN is live Real Time Programming GRAFCET and Petri nets 113 Q J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 114 Q J D Decotignie 2007 ersibility and home state cise properties mple Pi a reversible i a Home state For each PN below please indicate if it is ti 1 bounded 2 live 3 Without blocking 4 conservative p2 P3 o Pole p 2 ZI LN E b t pi Pi n Pi a Not gt Pi pi reversible t ts A B C t2 E t M ee condemn S p2 D ps Real Time Programming GRAFCET and Petri nets 115 Q J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 116 J D Decotignie 2007 roperties a Reachable marking A marking that can reached from Mo a K bounded if K 1 safe Maximum number of tokens Vplace K a reversible Mo may be reached from any marking a live roperties 2 All transitions are live a Well shaped live bounded reversible J D Decotignie 2007 a conservative same weights strictly conservative Z a q q Weighted sum of tokens in places Constant Real Time Programming GRAFCET and Petri nets 117 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 118 J D Decotigni
13. C 1 Hill each tank until above h close valve V and open W until E level below b Procees cannot be repeated before both tanks are empty Real Time Programming GRAFCET and Petri nets 19 Q J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 20 J D Decotignie 2007 ng time into account 10s t 6 10s Vi V i i t 6 20s MEL h h i tank 1 tank 2 EEEE Ss b b Wi W Real Time Programming GRAFCET and Petri nets 21 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 22 J D Decotignie 2007 e e N e r behavior inuous actions niveau ar ot p bu OTa at em X21 Action A action A 4 7 b acionA l L p I oo ER bli 5 x i T a xi i voi 04 8 HT A PEE UBL bal 6 action A E xi 8 b action A Li Real Time Programming GRAFCET and Petri nets 23 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 24 J D Decotignie 2007 tion of a continuous action e shaped actions di a Continuous actions are only defined for stable situations QU i 7 i c3 EUM c4 E ur wl a D Dog 0 X3 EN b i a ax XA 1 X5 np Li l i Xs X6 por Tj EN action A m ii m E a open P d TE close P P open 0 Fl LLL Real Time Progra
14. Decotignie 2007 Real Time Programming GRAFCET and Petri nets 74 J D Decotignie 2007 cise syntax 2 Gr For each of the graphs below answer the following questions 1 Is it a PN 2 What are the validated transitions go Generalized PNs 3 What will be the marking after firing 4 What are the validated transitions There a weight on each arc Can be transformed into ordinary PN a PNS with predicates Cannot be transformed into ordinary PN M X b e e lt Y father of t ti lt Y Y Real Time Programming GRAFCET and Petri nets 75 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 76 J D Decotignie 2007 pes Z a PNS with capacity Po E B t fired Y DD s pes 3 a Colored PNs Tokens have colors Any colored PN with a finite number of colors may be transformed into an ordinary PN a PNS with priorities T fi Can be Que e uu Cannot be transformed into ordinary PN transformed ti t t a Continuous PNs into ordinary PN l S p2 p p2 p2 The number of tokens can be a real number b b b Cannot be transformed into ordinary PN Real Time Programming GRAFCET and Petri nets 77 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 78 J D Decotignie 2007 pes 4 cise 2 PNs with inhibiting arcs Transform this PN into an ordinary PN Cannot be transformed into ordinary PNs a No autono
15. Masking Masquage d Masquage G2 A d Real Time Programming GRAFCET and Petri nets 47 J D Decotignie 2007 rocaction Force Forcer Real Time Programming GRAFCET and Petri nets 48 Q J D Decotignie 2007 ine a introduction a GRAFCET a GEMMA a Petri nets Real Time Programming GRAFCET and Petri nets 49 Q J D Decotignie 2007 MA a Guide d Etude des Modes de Marche et d Arr t a Problems with GRAFCET a Objectives a Concepts a How to use GEMMA a Advantages a Drawbacks Real Time Programming GRAFCET and Petri nets 50 J D Decotignie 2007 lems with GRAFCET a GRAFCET is good to describe normal operation but Not well suited to describe Emergency cases Manual modes Degraded modes Does not favor a good separation of operating modes Does not give a clear vocabulary concerning modes Does not include any security aspect Real Time Programming GRAFCET and Petri nets 51 J D Decotignie 2007 ctives of GEMMA inventors a Create a graphical tool that can deal with Emergency cases Manual modes Degraded modes a Estblish a precise vocabulary a Tool show present itself as a guide checklist Real Time Programming GRAFCET and Petri nets 52 J D Decotignie 2007 MA concepts a Assumes that controlling part 1s operational a Separate production states from other states a Distinguishes 3 catego
16. Ps 1 1 2 O0 O t I 0 0 0 0 1 It pi po ps P4 ps 0 0 0 2 lt Tp It weight of arc p gt tj Oz 0 0 1 0 0 lr pi O t weight of arc tj pi Real Time Programming GRAFCET and Petri nets 70 J D Decotignie 2007 i nets marking a marking M m pi M pj M PN with m p number of tokens in place pi Initial marking Mo P4 example Mo 2 1 3 0 1 a Evolution by firing transitions a Can then represent behavior dynamic Real Time Programming GRAFCET and Petri nets 71 J D Decotignie 2007 evolution rules a a transition t may be fired uf for all 1 m pi 2 pi I tj a Only one transition may fired at a time a A transition is fired instantaneously by Removing in each place that immediately preceeds the transi tion a number of tokens equal the weight of arc that links them Adding in each place that immediately follows the transition a number of tokens equal the weight of arc that links them mp m pi pi ICt pi O t EVOLUTION I5 NOT DETERMINISTIC Real Time Programming GRAFCET and Petri nets 72 J D Decotignie 2007 ution rules cise syntax each of the graphs below answer the following questions 1 Is ita PN 2 What are the validated transitions 3 What will be the marking after firing LII LLLI LLLI F Real Time Programming GRAFCET and Petri nets 73 J D
17. Real Time Programming J D Decotignie 2007 cise a Reduce the following PN Real Time Programming GRAFCET and Petri nets 134 Q J D Decotignie 2007 cise a Reduce the PN below and find its place invariants Real Time Programming GRAFCET and Petri nets 135 Q J D Decotignie 2007 ormal analysis a Systematic evolution from the initial marking Gives the set of reachable markings From which the properties are derived a 3 techniques Reachability graph Reachability tree Matrix analysis Place invariant Transition invariant Real Time Programming GRAFCET and Petri nets 136 Q J D Decotignie 2007 hability graph a We create a graph of Pi reachable markings t t a Exhaustive search S ti Risk of combinatorial p2 p3 explosion t ts ty t 2 0 0 1 0 1 0 1 1 1 0 0 Real Time Programming GRAFCET and Petri nets 137 J D Decotignie 2007 hability tree Q If we want to show that the PN is not bounded it might be useless to continue QO This is the case 1f M that has been reached from M M 2M Vi m pi Zm pi a if MjzM we are back to the same marking a if Mj M it is possible to repeat the same firing sequence and increment again the number of tokens 1 0 1 1 1 0 Real Time Programming GRAFCET and Petri nets 138 J D Decotignie 2007 yis by reachability tree a The tree is always finite a The tree permits to ch
18. Time Programming aga GUIDE DES MODES DE MARCHE ET D ARRET GEMMA PROCEDURES DARRET DE LA PARTIE OPERATIVE PO arr t dans tat marches de initial v rification en d sordre par boutons poussoirs avec les s curit s b si e et a si y z demande ay de marche marches de v rification dans l ordre demand emand ED lt production normale gt en fin de dans tat cycle gt d termin gt lt production tout lt marches de m me gt de test gt D tection d faillances E PROCEDURES DE FONCTIONNEMENT GRAFCET and Petri nets 60 J D Decotignie 2007 GUIDE DES MODES DE MARCHE ET D ARRET GEMMA GUIDE DES MODES DE MARCHE ET D ARRET GEMMA E PROCEDURES DE FONCTIONNEMENT partie comman de hors lt mise PO dans tat lt arr t dans tat F4 lt marches de nergie initial gt initial v rification par boutons poussoirs avec les s curit s 9 lt mise PO dans tat lt arr t dans tat F4 lt marches de initial gt initial gt v rification par boutons poussoirs en d sordre gt en d sordre gt par boutons
19. e 2007 gn by refinement gn by refinement 2 Pi s ti a First step e P2 Simple net b Complex tasks associated to transitions i validation ts a Second step np Transitions are replace by a block a PN that begins with an initial transition and ends with a final transition t P13 P15 validation S Ist STEP S e q q a Following steps Pia P16 Repeat step 2 tia BLOCK Real Time Programming GRAFCET and Petri nets 119 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 120 ture approach a We only use blocks that have good properties E gt D ysis by reduction a Sequence simplification Eliminate sequences of places a Concatenate parallel paths a Suppress identity transitions ORIGINAL PROPERTIES MUST BE SEQUENCE WHILE DO PRESERVED s IF THEN ELSE Real Time Programming GRAFCET and Petri nets 121 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 122 J D Decotignie 2007 ysis by reduction 2 ction techniques pi a Preserving boundedness and liveness properties Pi N RI place substitution Pi R2 implicit place D R3 neutral transition R4 identical transitions d a Preserving invariants pi Ra non pure transition for ordinary PN EO Il Real Time Programming GRAFCET and Petri nets 123 J D Decotignie 2007 Rb pure transition for ordinary PN Real Time Programming GRAFCET and Petri n
20. eck the following properties Not bounded if there exsists MI2M Conservative if the number of tokens is constant LI Live is each transitions appears at least once in the tree Reversibility and home state a Complex to use Real Time Programming GRAFCET and Petri nets 139 Q J D Decotignie 2007 ix analysis a Uses I and O matrices a Look for a non trivial solution to O I xT 0 avec x xi Xj s XN 1 a Let M et M be two successive markings M M O tj I t5 after firing t 2 a Let pzlpi pi DN be a solution of 1 a Let multiply each term of 2 by p and sum up on i N N N 2m pi lo gt pin pi gt Pi lot i Pi l 1 D l l l Real Time Programming GRAFCET and Petri nets 140 J D Decotignie 2007 e invariant e invariant example PRODUCTEURS CONSOMMATEURS 01010 0 a result E 100010 N N 001000 mp X pimpi 000001 mag i i 101000 010001 O 10 001 0 0 a If all p have the same sign and are non zero 500 oe 38 The PN is conservative strictly is p are all equal 1 1 1 1 0 The PN is bounded O I x L 1 j a If all p have the same sign and some are zero s TUUS s ie A cuca ihe PN ie coneen eae a Possible solution x 1 invariant s 2 bounded strictly conservative Real Time Programming GRAFCET and Petri nets 141 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 142 J D Decotignie 2007
21. ets 124 J D Decotignie 2007 ction RI place substitution a Place Pi can be removed if it complies with the 3 following conditions Pi output transitions have no other input place than Pi There is no transition Tj that is at the same time input and output transition of Pi At least one output transition of Pi is not a sink transition Real Time Programming GRAFCET and Petri nets 125 Q J D Decotignie 2007 ction RI example Keeps bounded safe live without blocking home state conservative However bound and home state are not always known Q J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 126 ction R2 implicit place a Place Pi is implicit if it fulfils the following 2 conditions Marking of this place may never block the firing of its output transitions Its marking may be deducted from the marking of other places according to M B 7 Yia M P B kzi Real Time Programming GRAFCET and Petri nets 127 J D Decotignie 2007 ction R2 example 9 3 Ti to P C ps Keeps bound live without blocking home state conservative May be safe after reduction even if original is not It is not always possible to know the home state and the bound Real Time Programming GRAFCET and Petri nets 128 Q J D Decotignie 2007 ction R3 neutral transition a Transition T is neutral if the set of all its input places is identica
22. hnological realization Trial and commissioning GRAFCET and Petri nets 65 J D Decotignie 2007 ine a introduction a GRAFCET a GEMMA a Petri nets Real Time Programming GRAFCET and Petri nets 66 J D Decotignie 2007 Real Time Programming L nets a Invented by C Petri in 1962 in his PhD thesis Kommunikation mit Automaten a J Peterson Petri Net Theory and the Modelling of Systems Prentice Hall 1981 a R David A Alla Du Grafcet aux r seaux de Petri Hermes 1990 a T Murata Petri nets Properties analysis and applications Proc of the IEEE Vol 77 4 April 1989 pp 541 580 a 2 view points Theoretical Definitions and evolution rules Properties Application to functional specifications GRAFCET and Petri nets 67 Q J D Decotignie 2007 1 Nets a Definition a Marking a PN types a Modelling with Petri nets a Modelling synchronization and cooperation between tasks a Design a Analysis and validation Real Time Programming GRAFCET and Petri nets 68 J D Decotignie 2007 i nets definition a Directed graph tuple C P T I O N places p e P L transitions t e T Input matrix I LxN places transitions Output matrix O LxN transitions places Real Time Programming GRAFCET and Petri nets 69 J D Decotignie 2007 i net example a P pi Po ps pa Ps a T ti to Pi po ps Pa
23. ie 2007 ers writers problem ucers consumers READERS WRITERS PRODUCERS CONSUMERS p3 ps messa b ges production P 4 Pi p use GRAFCET and Petri nets 91 Real Time Programming J D Decotignie 2007 positions Real Time Programming GRAFCET and Petri nets 92 J D Decotignie 2007 ng Philosophers cise a A consulate let its clients enter then the entrance door is closed and the client may be served After being served each client leaves the consulate through another door The entrance door cannot be opened again before all the clients have left Design a PN with inhibitor arcs that represents this specification Modify the first solution so that only one client may enter at a time Describe the same case using an ordinary PN A maximum of 4 clients may enter before the door is closed Model this a case using an ordinary PN a Real Time Programming GRAFCET and Petri nets 93 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 94 J D Decotignie 2007 en and validation i nets properties a Petri nets properties a Structural properties 4 Design by successive refinements Are only dependent on the topology a Analysis by reduction a Behavioral properties Depend on the initial marking 1 1 Real Time Programming GRAFCET and Petri nets 95 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 96 J D Decotignie 2007
24. l to the set of all its output places Ti T Ti Ts P 2 P 2 Ta LT T Keeps bounded safe live without blocking home state conservative It is not always possible to know the home state and the bound Real Time Programming GRAFCET and Petri nets 129 Q J D Decotignie 2007 ction R4 identical transitions a 2 transtions are identical if they have the same set of input places and the same set of output places pa p4 p3 p4 ti t2 ti p3 p3 C Keeps bounded safe live without blocking home state conservative It is not always possible to find the home state and the bound Real Time Programming GRAFCET and Petri nets 130 Q J D Decotignie 2007 ction Ka non pure transition a Transition Tj with place Pi and arcs Tj gt Pi and Pi gt Tj a Reduction Suppress arcs Tj gt Pi and Pi gt Tj de Pi Suppress transition Tj if it is isolated Ti Cp Ti C P T P T4 2 T 2 p GRAFCET and Petri nets 131 Real Time Programming J D Decotignie 2007 ction Rb pure transition a The transition must possess at least one input and one output place a Reduction Pi Suppress transition Each couple of places Pi Pk such that Pi p is an input place and Pk is an output place is replaced by a place Pi Pk union of places y Real Time Programming GRAFCET and Petri nets 132 ction Rb example T5 GRAFCET and Petri nets 133
25. mming GRAFCET and Petri nets 25 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 26 J D Decotignie 2007 ditional Pulse Shaped Actions ns types PEE m al H L 5 a Continuous actions niveau 3 Ta MEE unconditional A if b 1 when 15 oe a A i A when X3 1 as soon as b L H conditiona Hc Condition is a boolean variable A when f X5 b Il I Condition is based on a timer pl a A if bis ambiguous Unsufficient notation 2 Pulse shaped actions a We shall not keep this capability z Always unconditional q Real Time Programming GRAFCET and Petri nets 27 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 28 J D Decotignie 2007 Qs drilling machine h upper position t High speed High speed up bl end of approach e Working speed i h upper position b3 end of drilling t High speed T ns and outputs Controlling part Operative part of the controlling part inputs a b m calculations timers actions A B D C outputs A B D E Control part of the controlling part described by the graph bl end of net d LORE S Operator or a otkin L TNR U a U Key K Vp supervising system ome pus drilling e processus to control Real Time Programming GRAFCET and Petri nets 29 Q J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 30 Q J D Decotignie 2007 Sition co
26. nditions LS a variables a Va e 0 1 si a t 1 when t e t1 t2 ett e t3 t4 External boolean variables definition 1 Ta occurs in t1 and in t3 Coming f th f th t ld Kad OMM AM c M C LM definition 2 La occurs in t2 and in t4 relative to time t 1 A mM oo ble definition 3 a b occurs at the same instant as a each time Relative to the state of a step Xi b at this instant State of the operative part of the controlling part definition 4 Ta Tb occurs when Ta and Tb occur at the same a receptivity R C E instant condition C boolean combination of variables F a Show that i event E rising falling edge of an external variable e always e a da Taa ta Taa U Va a 0 occurring event Tala Ta Ta Ta 0 Tae Ta Real Time Programming GRAFCET and Petri nets 31 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 32 J D Decotignie 2007 h interpretation a 2 persons in front of the same graph and assuming the same sequence of inputs should deduce the same sequence of outputs a Asumptions 2 uncorelated events may not occur at the same time The graph has enough time to reach a stable state before the occurrence of the next event Real Time Programming GRAFCET and Petri nets 33 J D Decotignie 2007 rpretation Algorithm without ility search i Read the state of the inputs evolve one or more simultaneous clearings
27. nous PNs Several types Synchronized PNs Time PNs Stochastic PNs 5 m Stochastic Time PNs F i Cannot be transformed into ordinary PNs Real Time Programming GRAFCET and Petri nets 79 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 80 J D Decotignie 2007 elling with PNs ditions and amp or a actions associated to places a type AND a type OR Activated by token presence nn Hoc waiting free B actions associated to Sanot transitions short duration Xi x x Activated by transition executing E firing End of execution 5 Tasked p4 lt ended Real Time Programming GRAFCET and Petri nets 81 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 82 J D Decotignie 2007 oduction of external conditions duction of external conditions a When synchronisation is required pi p Task Pine Task Processor f controlled system waiting free wale ds controlling system anes begin exec a Label on the transition o if condition action executing i ne a Transition may be fired 11T ended end exec external condition satisfied S Task a Timers extern or terminated mne minimal sejourn duration in a place Real Time Programming GRAFCET and Petri nets 83 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 84 Q J D Decotignie 2007 Pi oduction
28. of all immediately preceding steps a step that is activated and deactivated remains active 34 Lb Real Time Programming GRAFCET and Petri nets 11 J D Decotignie 2007 GRAFCET and Petri nets 12 Real Time Programming J D Decotignie 2007 cise transitions A enabled transitions B firable transitions if a 1 and b 0 C state after clearing the transitions when possible Lee ee Real Time Programming GRAFCET and Petri nets 13 J D Decotignie 2007 cise transitions 2 A enabled transitions B firable transitions if a 1 and b 0 C state after transition when possible Real Time Programming GRAFCET and Petri nets 14 J D Decotignie 2007 GRAFCET and Petri nets 15 Real Time Programming J D Decotignie 2007 Qs is there a conflict Real Time Programming GRAFCET and Petri nets 16 Q J D Decotignie 2007 ples of logical graphs Controlling system Real Time Programming GRAFCET and Petri nets 17 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 18 J D Decotignie 2007 o ement a counter reservoir ging o Initial conditions Tanks empty valves closed Q Sensors and actuators a 31 l fF V W 1 if open Stable he hi hy tation 2 IPH 2 3 h b 1 if level above sensor tank 1 tank 2 situation bi by C 0 i Q Oper ations Wi W CH
29. of external conditions chanisms a Mutual synchronisation rendez vous elling task synchronisation a seine p t start timer A Y B Bi B2 p3 i umei OR Ai Ag bo end timer y A i A y al B Bi B p4 o ae Real Time Programming GRAFCET and Petri nets 85 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 86 J D Decotignie 2007 elling task synchronisation elling task synchronisation chanisms 2 chanisms 3 a mailbox a Interrupt driven task As an external e condition P4 A on a transition e E e Interrupt handler t t2 interrupt t3 intekrupt modeled using A C ps B C B Pi B Biy B 2 places ts t4 te Real Time Programming GRAFCET and Petri nets 87 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 88 J D Decotignie 2007 elling task synchronisation chanisms 4 a Mutual exclusion Modeled by a single S B9 Cy p token ti P S AND condition on a transition V S OR condition on V S a transition al exclusion through semaphore Po p2 Task Task waiting waiting ti Critical Critical section section DAE e tii S t3 3 Critical section synchronized by an auxiliary Cp i s y place Po Real Time Programming GRAFCET and Petri nets 89 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 90 J D Decotign
30. ple C S TR A Mo N steps s S each step s may be active X true or not X false M denotes the set of steps active at startup L transitions tr TR to each transition is associated a boolean condition receptivity Steps and transitions are linked by arcs a A a EVOLUTION CONDITIONS Real Time Programming GRAFCET and Petri nets 6 J D Decotignie 2007 cise syntax Real Time Programming GRAFCET and Petri nets 7 J D Decotignie 2007 cise syntax 2 Real Time Programming GRAFCET and Petri nets 8 J D Decotignie 2007 cise syntax 3 FCET an example pr request O F P O E N R C A T T 2 I I N O a A N L A Operative part L Arrived at left wagon door Real Time Programming GRAFCET and Petri nets 9 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 10 J D Decotignie 2007 a Evolution is performed from the initial state defined as M by clearing transitions according to 5 rules all steps immediately preceding the transition must be active the a 2 transition is then enabled then if receptivity is true the transition may be cleared all transitions that may be cleared are cleared simultaneously a l veh kat LL E clearing clearing clearing a transition leads to the activation of all immediately following steps and deactivation
31. ries of operating modes Working procedures Stopping procedures Failure procedures CA OPERATIVE PART OP STOP PROCEDURES D lt prepare for p stop start after request in given state request 1 i diagnostic lt degraded Rm Qs lt deeraded a ailure production gt treatment I i T F T T ra 6 put OP in initial state gt ipl stop L D DL gt T t Y L cu RN e L 1 1 G 1 Gr put OPisa i A4 stop _ request start stop given state reached proce proce i 1 i 8m dures dures F PROCEDURES DE FONCTIONNEMENT lt random test procedures gt D lt emergency stop gt y D failure D OPERATIVE PART FAIL PROCEDURES detect F WORKING PROCEDURES Real Time Programming GRAFCET and Petri nets 53 J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 54 J D Decotignie 2007 to use GEMMA ple joint test bed a Selection of modes a 3 tested values V C p Showing relationships a Long tests on a typical run 7 d Periodic request for withdraw a Search for evolution conditions d and check Frein couple C en ans THIS vitesse V e e AU Verrin pour r glage a 1 angle B Real Time Programming GRAFCET
32. t overflows in resource usage a A PN is said k bounded if the number of tokens whichever the place does not exceed k for all markings in RM a A PN is said safe if k 1 1 bounded Real Time Programming GRAFCET and Petri nets 105 Q J D Decotignie 2007 ded and safe 2 Real Time Programming GRAFCET and Petri nets 106 Q J D Decotignie 2007 cise a 2 tasks T1 and T2 execute on the same processeur in time sharing part of T1 is executed then part of T2 is then part of T1 a Model the same behavior with 4 tasks a Is the resulting PN bounded Real Time Programming GRAFCET and Petri nets 107 Q J D Decotignie 2007 ervativeness a In areal system the number of resources is limited If tokens represent resources it may be a desired properties that the number of tokens remains constant whichever the marking in R Mo A BN is said strictly conservative if the number of tokens is constant A BN is said conservative if there exists a weighting vector W Wi Wi WN such that for each marking in R Mo gt wi m p remains constant Real Time Programming GRAFCET and Petri nets 108 J D Decotignie 2007 ervativeness example 3 PRODUCERS CONSUMERS ps ps messages Ness a The idea of liveness is closely related to blocking and interblocking cases a Necessary conditions all 4 together Limited access Resources can only be shared by a fini
33. te number of tasks No preemption Once allocated a resource cannot be withdrawn from the task i Multiple requests 3 Tasks already own resources when they additional resource requests positions The request graph has circular paths ness 2 ness example a A transition t of a PN is said a live d 3 LO0 live dead if t does not belong to any sequence of L Mo LI live potentialy firable if t may fired at least once in a p2 P3 sequence of L Mo ty L2 live if t may be fired k times k integer gt 1 in a sequence of L Mo a ty t are L1 L2 et L3 L3 live if t may be fired an infinite number of times in a live ts sequence of L Mo s 4 t is LI live D L4 live live if t is L1 live for any marking in R Mo ty ps Real Time Programming GRAFCET and Petri nets 111 Q J D Decotignie 2007 Real Time Programming GRAFCET and Petri nets 112 J D Decotignie 2007 cise a 2 computers share a common memory It is assumed that each computer may be in one of the following states Does not need the shared memory Needs the shared memory but it has not yet been assigned Uses the shared memory a Your assignment rsibility and home state a For a real time system it 1s of prime importance to recover in case of error and then return to a correct state A BN is said reversible if the initial marking Mo may be reached from any marking in R Mo A given state M of a PN is
34. tion d faillances GRAFCET and Petri nets 57 F PROCEDURES DE FONCTIONNEMENT 2 lt marches de pr paration gt time setup auto marche ED lt production normale gt TEST according to program marches de cl ture l l t 1 i i I i i i i T i l l e D D PRODUCTION or Vmax or Cmax exceeded 4 lt marches de v rification check d sordre feedback loops for V C and f by displaying min and max performances Tests with display of setpoints V C and f duration test marches de test B PROCEDURES DE FONCTIONNEMENT J D Decotignie 2007 Before feeding Real Time Programming ple valve test After feeding GRAFCET and Petri nets 58 Q J D Decotignie 2007 mise hors nergie lt lt de PC mise en nergie de PC mise hors nergie partie comman de PC de hors RES DARRET DE LA PARTIE OPERATIVE PO mise PO dans tat initial par boutons poussoirs mise PO dans tat d termin pr paration pour remise en route apr s d faillance diagnostic trai 4 7 tement get jllance talonnage du dis lt arr t d urgence gt agar aene d arr t dans
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