GRAFCET and Petri Nets Outline Introduction GRAFCET - EPFL
GRAFCET and Petri Nets Outline Introduction GRAFCET - EPFL
GRAFCET and Petri Nets Outline Introduction GRAFCET - EPFL
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Reduction R3: neutral transition<br />
Reduction R4 – identical transitions<br />
Transition T is neutral iif the set of all its input places is<br />
identical to the set of all its output places<br />
2 transtions are identical if they have the same set of<br />
input places <strong>and</strong> the same set of output places<br />
T 1<br />
T 3<br />
T 1<br />
T 3<br />
p 3<br />
p 4<br />
p 3<br />
p 4<br />
P 1<br />
T 5<br />
P 2<br />
P 1<br />
P 2<br />
t 1<br />
T 2<br />
T 4<br />
Keeps: bounded, safe, live, without blocking, home state,<br />
conservative. It is not always possible to know the home<br />
state <strong>and</strong> the bound.<br />
T 2<br />
T 4<br />
<strong>GRAFCET</strong> <strong>and</strong> <strong>Petri</strong> nets 130<br />
t 2<br />
t 1<br />
p 3<br />
Keeps: bounded, safe, live, without blocking, home state,<br />
conservative. It is not always possible to find the home<br />
state <strong>and</strong> the bound.<br />
p 3<br />
Real-Time Programming <strong>GRAFCET</strong> <strong>and</strong> <strong>Petri</strong> nets 129<br />
© J.-D. Decotignie, 2007<br />
Real-Time Programming © J.-D. Decotignie, 2007<br />
Reduction Ra – non pure transition<br />
Reduction Rb – pure transition<br />
T 1<br />
P 1<br />
Transition Tj with place Pi <strong>and</strong> arcs Tj->Pi <strong>and</strong> Pi->Tj<br />
Reduction<br />
Suppress arcs Tj->Pi <strong>and</strong> Pi->Tj<br />
Suppress transition Tj if it is isolated<br />
P 2 T 1<br />
P 2<br />
T 3 P 1<br />
T 3<br />
p 1<br />
The transition must possess at least one input <strong>and</strong> one<br />
output place<br />
Reduction<br />
p 1<br />
Suppress transition<br />
Each couple of places Pi,Pk such that Pi<br />
p 2<br />
is an input place <strong>and</strong> Pk is an output place,<br />
is replaced by a place Pi+Pk (union of places)<br />
T 2 P 2<br />
T 2<br />
P 2<br />
p 1<br />
p 1<br />
Real-Time Programming <strong>GRAFCET</strong> <strong>and</strong> <strong>Petri</strong> nets 131<br />
© J.-D. Decotignie, 2007<br />
Real-Time Programming <strong>GRAFCET</strong> <strong>and</strong> <strong>Petri</strong> nets 132<br />
© J.-D. Decotignie, 2007
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