GRAFCET and Petri Nets Outline Introduction GRAFCET - EPFL

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Place invariant result: If all ρ i have the same sign and are non zero The PN is conservative (strictly is ρ i are all equal) The PN is bounded N ∑m = N i i i i= 1 1 ρ i= 1 ( p ) ρ ∑ m( p ) If all ρ i have the same sign and some are zero A subset of the PN is conservative i Place invariant - example I= O= ⏐O-I⏐.x T = 0 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 -1 1 -1 0 0 -1 1 0 0 -1 1 0 0 -1 1 0 0 0 0 0 0 1 -1 PRODUCTEURS p 3 messages Possible solution x i =1 , invariant = s+2; bounded, strictly conservative t 3 production . x T =0 p 4 p 1 t 1 s p 2 positions CONSOMMATEURS p 5 t 2 t 4 p 6 utilisation Real-Time Programming GRAFCET and Petri nets 141 © J.-D. Decotignie, 2007 Real-Time Programming GRAFCET and Petri nets 142 © J.-D. Decotignie, 2007 Exercise – readers-writers Transition invariant Task waiting READERS t 1 p 0 reading p 3 S p 1 s s WRITERS p 2 Task waiting t 2 p 4 writing Look for a non trivial solution to | O-I | T .x T =0 avec x= | x 1 , ...., x i , ...., x M | (1) M is the number of transitions Gives an indication of liveness Sequence of transitions that can be fired repeatedly t 3 s t 4 Real-Time Programming GRAFCET and Petri nets 143 © J.-D. Decotignie, 2007 Real-Time Programming GRAFCET and Petri nets 144 © J.-D. Decotignie, 2007
Interesting information http://www.informatik.uni-hamburg.de/TGI/PetriNets/ http://home.arcor.de/henryk.a/petrinet/e/hpsim_e.htm Real-Time Programming GRAFCET and Petri nets 145 © J.-D. Decotignie, 2007
Page 1 and 2: Outline GRAFCET and Petri Nets Prof
Page 3 and 4: Exercise - syntax (3) GRAFCET - an
Page 5 and 6: Divider by 2 Examples of logical gr
Page 7 and 8: Duration of a continuous action Co
Page 9 and 10: Graph interpretation 2 persons in
Page 11 and 12: (4) (5) 4 5 M30 6 Macro-step A a.d'
Page 13 and 14: Outline GEMMA introduction GRAFCE
Page 15 and 16: partie commande hors énergie parti
Page 17 and 18: How to manage an automation project
Page 19 and 20: Evolution rules p 1 p 2 p 3 2 Exerc
Page 21 and 22: Modelling with PNs Conditions « an
Page 23 and 24: Modelling task synchronisation mech
Page 25 and 26: Structural properties Structural pr
Page 27 and 28: Bounded and safe Bounded and safe (
Page 29 and 30: Exercise Reversibility and home sta
Page 31 and 32: Structure approach Analysis by redu
Page 33 and 34: Reduction R3: neutral transition Re
Page 35: Reachability graph Reachability tre

GRAFCET and Petri Nets Outline Introduction GRAFCET - EPFL

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