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 R1: place substitution<br />
Reduction R1- example<br />
Place Pi can be removed if it complies with the 3<br />
following conditions<br />
Pi output transitions have no other input place than Pi<br />
There is no transition Tj that is at the same time input <strong>and</strong><br />
output transition of Pi<br />
At least one output transition of Pi is not a sink transition<br />
P 1<br />
P 2<br />
T 1 T 2<br />
P 3<br />
T 3 T 4<br />
P 4 P 5<br />
P 1<br />
P 2<br />
T 23<br />
T 13 T 24<br />
P 4 P 5<br />
T 14<br />
Keeps: bounded, safe, live, without blocking, home state,<br />
conservative. However, bound <strong>and</strong> home state are not<br />
always known<br />
Real-Time Programming <strong>GRAFCET</strong> <strong>and</strong> <strong>Petri</strong> nets 125<br />
© J.-D. Decotignie, 2007<br />
Real-Time Programming <strong>GRAFCET</strong> <strong>and</strong> <strong>Petri</strong> nets 126<br />
© J.-D. Decotignie, 2007<br />
Reduction R2: implicit place<br />
Reduction R2- example<br />
Place Pi is implicit if it fulfils the following 2 conditions<br />
Marking of this place may never block the firing of its output<br />
transitions<br />
Its marking may be deducted from the marking of other places<br />
according to<br />
M<br />
( P ) = ∑α M ( P ) + β<br />
i<br />
k≠i<br />
k<br />
k<br />
P 1<br />
P 1<br />
T 1 P 3 T 1<br />
P 2<br />
p 2<br />
p 3<br />
Keeps: bound, live, without blocking, home state,<br />
conservative. May be safe after reduction even if original<br />
is not. It is not always possible to know the home state<br />
<strong>and</strong> the bound.<br />
t 1<br />
t 2<br />
t 3<br />
p 1<br />
p 2<br />
p 3<br />
t 1<br />
t 2<br />
t 3<br />
Real-Time Programming <strong>GRAFCET</strong> <strong>and</strong> <strong>Petri</strong> nets 127<br />
© J.-D. Decotignie, 2007<br />
Real-Time Programming <strong>GRAFCET</strong> <strong>and</strong> <strong>Petri</strong> nets 128<br />
© J.-D. Decotignie, 2007
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