Indonesian
Journal
of
Electrical
Engineer
ing
and
Computer
Science
V
o
l. 10
, No
. 3, Jun
e
20
18
, pp
. 90
5
~
91
6
ISSN: 2502-4752,
DOI: 10.
11591/ij
eecs.v10
.i3.pp905-916
9
05
Jo
urn
a
l
h
o
me
pa
ge
: http://iaescore.c
om/jo
urnals/index.php/ijeecs
Algorith
m
to
Convert
Signal
In
terpreted
Petri
Net
models
to
Program
mable
L
ogi
c
Con
troller
Ladder
Logic
Diagram
Models
Z
.
Aspa
r
,
Nasir
Sha
i
kh-Husin,
M.
Kha
lil-Ha
ni
Facult
y
of
Ele
c
tr
ica
l
Eng
i
ne
ering
,
Universi
ti
Tekn
ologi Ma
la
ysia
,
Mala
y
s
ia
Article
Info
A
BSTRAC
T
Article histo
r
y:
Received
Ja
n 20, 2018
Rev
ised
Mar
17
, 20
18
Accepted
Mar 31, 2018
Signal Interpr
e
ted Petri Nets (SIPN)
modeling has been proposed as an
alt
e
rnat
ive to
L
a
dder Log
i
c Di
agra
m (LLD)
modeling for programming
complex programmable logic controllers
(PLCs) due to its high level o
f
abstraction
and
function
a
lities
.
This
pap
e
r p
roposes an alg
orithm to
efficiently
convert existing SIPN models
to their LLD models equivalences.
In order
to au
to
mate and
speed
up the
conversio
n process, matrix calculation
approach is used. A complex SIPN
m
odel was used to show t
hat existing
conversion tech
nique must be expanded in
order to cater for a more complex
SIPN mode
ls.
K
eyw
ords
:
Co
nv
ersion
Ladder Logic Diagram
Petri Net
Pro
g
r
am
m
a
bl
e Lo
gi
c C
o
nt
r
o
l
l
e
r
Copyright ©
201
8 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
ing
Autho
r
:
Z. Aspa
r,
Facu
lty of Electri
cal Engineering,
Un
i
v
ersiti Tekn
o
l
o
g
i
Malaysia,
8
131
0 Joho
r B
a
h
r
u
,
Joho
r, M
a
laysia.
1.
INTRODUCTION
Process c
ont
rol and aut
o
m
a
tion are
bec
o
m
i
ng inc
r
easing
ly co
m
p
lex
due to
th
e in
creases in
t
h
e
com
p
l
e
xi
t
y
of
pr
o
duct
s
p
eci
fi
cat
i
on,
sh
o
r
t
e
r
desi
g
n
cy
cles,
and s
h
orter
product
life cycles. T
o
s
p
ee
d
up
LL
D
pr
ocessi
ng
, a new a
r
chi
t
ect
u
r
e was p
r
op
os
ed i
n
[
2
]
. Thes
e
m
o
re dem
a
ndi
n
g
sy
st
em
s requi
rem
e
nt
s resul
t
i
n
t
h
e need
fo
r t
h
e con
v
ersi
on
o
f
LLD m
odel
s
t
o
hi
gh l
e
vel
of a
b
st
ract
i
o
n m
odel
s
. A hi
g
h
l
e
vel
of a
b
st
ract
i
o
n
m
odel
i
ng pa
ra
di
gm
such as
Pet
ri
Net
(P
N)
[6]
o
r Si
g
n
al
Int
e
r
p
ret
e
d Pet
ri
Net
(S
IP
N)
[1
6]
w
oul
d al
l
o
w t
h
e
desi
g
n
speci
fi
c
a
t
i
on t
o
be de
f
i
ned cl
ose
r
t
o
t
h
e pr
od
uct
or
sy
st
em
requi
re
m
e
nt
whi
l
e
reduci
ng t
h
e d
e
t
a
i
l
s
of
th
e lower lev
e
l
i
m
p
le
m
en
tatio
n
.
At th
is ab
st
ractio
n
lev
e
l, a
co
-d
esign
m
e
th
odo
log
y
[4
] an
d [7
] can b
e
ap
p
lied
fo
r P
L
C
i
m
pl
em
ent
a
t
i
on -
ei
t
h
er
i
n
s
o
ft
war
e
, ha
r
d
wa
re,
o
r a m
i
xt
ure
of
bot
h.
The
desi
gn
t
ra
d
e-
of
fs c
a
n
b
e
easily calcu
late
d
,
op
ti
m
i
zed, a
n
d im
ple
m
ente
d.
The rest
of t
h
e
paper i
s
or
ga
ni
zed as fol
l
o
w
s:
Sect
i
on 2
revi
e
w
s fu
n
d
a
m
ent
a
l
s
of LLD an
d SIP
N
.
Related
w
o
r
k
s o
n
PN
, LLD
and
PN-
to-LLD
conv
er
si
o
n
s
ar
e do
ne in
Sectio
n
3. Sev
e
r
a
l co
nv
er
si
on
alg
o
r
ith
m
s
h
a
v
e
b
e
en
pr
oposed
in
[1
], [
3
]
,
[
1
0
]
, [1
1
]
, [1
4
]-[1
6
]
to
con
v
e
r
t PN
to
LLD
.
Th
e an
al
ysis o
f
streng
th
s and
limita
tio
n
s
are
presen
ted
in
Sectio
n
3
.
2
.
Section
4 pr
opo
ses a
n
o
v
e
l algo
r
ithm
f
o
r
SI
PN-
to
-
LLD
con
v
e
r
si
o
n
. C
a
se st
udi
es
an
d
resul
t
s
fo
r t
h
e
pr
o
pose
d
c
o
nv
ersi
o
n
s a
r
e di
s
c
usse
d a
nd a
n
al
y
zed i
n
Sect
i
on
5
.
C
oncl
u
si
o
n
i
s
i
n
Sect
i
o
n
6.
2.
LADDER
LOGIC
AND
PE
TRI
NET:
A
REVIEW
B
o
t
h
PN
an
d LLD we
re bo
r
n
i
n
19
6
0
’s
b
u
t
fo
r di
f
f
ere
n
t
reaso
n
s
.
P
N
w
a
s
i
n
vent
e
d
by
C
a
rl
Adam
Petri to
stud
y asyn
chrono
us
n
a
ture in
co
mm
u
n
i
catio
n
.
Mean
wh
ile, LLD was i
n
v
e
n
t
ed
du
e to
t
h
e need
s t
o
m
i
nim
i
ze ret
r
ai
ni
ng t
i
m
e by
m
i
m
i
cki
ng the
existing electrom
echanical re
lays wh
en
PLC was in
troduced
. As
PN gro
w
s
with
m
o
re fun
c
tion
a
lity in
clu
d
i
ng
as an
an
al
ysis to
o
l
as p
r
opo
sed
in
[1
8
]
, [2
0
]
, an
d
[20
]
,
LLDs
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
502
-47
52
I
ndo
n
e
sian
J Elec Eng
& Com
p
Sci, V
o
l. 10
,
No
.
3
,
Jun
e
2
018
:
90
5 – 91
6
90
6
Figu
re
1.
LL
D
fo
r a
sim
p
le safety
circuit
evol
ves i
nt
o a
very
i
m
port
a
nt
t
ool
i
n PLC
i
m
pl
em
ent
a
t
i
on,
researc
h
on both areas st
arted
to
m
erg
e to
geth
er at
th
e
end
of
1
990
’
s
.
2.
1.
L
a
dder L
ogi
c
Di
a
g
r
a
m
An LLD m
o
d
e
ls th
e actu
a
l com
b
in
atio
n
of relay co
n
t
act
s.
A relay co
n
t
act o
r
a step
i
n
LLD is eith
er
norm
ally closed (NC) s
u
c
h
as
alarm
,
or n
or
m
al
ly
ope
n (
N
O) s
uc
h as m
a
in i
n Fi
gu
re
1.
They
are c
o
nt
r
ol
l
e
d by
l
ogi
cal
i
n
put
s
and
st
at
e vari
abl
e
s w
h
ich
are rep
r
esen
ted b
y
lab
e
ls.
Wh
en
an
i
n
pu
t trigg
e
rs t
h
e step
, the
co
rresp
ond
ing
relay state ch
an
g
e
s to
th
e
o
p
p
o
s
ite state, i.e., th
e NC step
is tu
rn
ed
ON
wh
ile th
e
NO
step
is
tu
rn
ed OFF. Th
e co
m
b
in
atio
n
o
f
NC and
NO
will affect
t
h
e Ou
tpu
t
Co
il
wh
ich
co
rresp
o
n
d
s
to a relay state.
I
n an
y LLD su
ch as i
n
Fi
gu
r
e
1, th
e rung
s ar
e c
o
nnect
ing t
h
e
powe
r source
re
pres
ented
by t
h
e
vert
i
cal
ba
r
on
t
h
e l
e
ft
, a
n
d
t
h
e gr
o
u
n
d
re
pre
s
ent
e
d
by
t
h
e
v
e
rt
i
cal
bar
o
n
t
h
e ri
ght
.
Eac
h
ru
n
g
can
be
di
vi
de
d
in
to
two
p
a
rts: at th
e en
d
o
f
t
h
e run
g
s on
th
e
righ
t are th
e
o
u
tp
u
t
s,
wh
ile the rest on
the left are the step i
n
puts
.
Th
e co
m
b
in
atio
n of
th
e step in
pu
ts i
n
a
r
ung is also
kn
own
as th
e
n
e
two
r
k
in
pu
t. Th
e co
mb
in
ation
o
f
all r
ung
out
puts in a L
L
D re
prese
n
ts
a state. The state can change
i
f
any
of t
h
e
ou
t
put
cha
nge
s d
u
e t
o
cha
nge
s i
n
any
of the step i
n
put. Thus, the
LLD state vari
es depe
nd
ing on the ste
p
s com
b
ination. T
h
e step inputs
change
ei
t
h
er c
h
an
ges
di
rect
l
y
fr
om
ext
e
r
n
al
o
r
phy
s
i
cal
i
nput
s
o
r
d
u
e t
o
t
h
e
fee
d
b
ack
fr
om
t
h
e ot
her
r
u
n
g
s
o
u
t
p
ut
s.
Thi
s
LL
D i
m
pl
em
ent
s
t
h
e sy
n
c
hr
o
n
o
u
s a
ssi
g
n
m
e
nt
s of t
h
e
B
ool
ea
n e
quat
i
ons
as:
start = m
ain • safe • alarm
st
op
= em
gcy
+ p
o
we
r +
pa
u
s
e
ru
n =
(start +
r
u
n
)
•
st
op
Furt
her
, t
h
ese
out
put
c
h
a
nges
can
be cl
assi
fi
ed ei
t
h
er
as sy
nch
r
on
o
u
s p
r
o
cess, se
que
nt
i
a
l
pr
ocess,
o
r
co
m
b
in
atio
n
o
f
bo
th
. So
m
e
t
i
m
es, th
e d
i
fference is h
a
rd to
notice with
ou
t any syste
m
at
ic an
alysis.
2.
1.
Si
g
n
al
In
terprete
d
Pe
tr
i
Net
Sig
n
a
l In
terpreted
Petri Nets (SIPN) is an
exten
s
ion
of Cond
itio
n
/Ev
en
t Petri Nets wh
ich
allo
ws t
h
e
han
d
l
i
n
g
of
bi
nary
I/
O-si
gn
a
l
s i
n
a wel
l
-
de
fi
ne
d way
.
Th
ey
are wel
l
sui
t
ed t
o
desi
g
n
c
ont
rol
al
g
o
r
i
t
h
m
s
for
d
i
screte ev
en
t
syste
m
s resu
ltin
g in
lan
g
u
a
g
e
s stand
a
rd
ized
in
IEC
61
131
-3
.
SIPN are
d
e
fin
e
d
as a
10
-t
u
p
e
l
SIP
N
= {P, T,
F, m
0
, I, O,
φ
,
ω
,
Ω
, v}
w
h
ere {P
, T, F,
m
0
} i
s
ordi
n
a
ry Petri Net. To
b
e
co
m
e
SIPN, th
e
extensi
ons
are
as:
I
–
inpu
t sign
als, |I
| >
0
,
φ
– B
ool
ea
n
fu
nct
i
o
n
i
n
I at
T
,
Ω
–
o
u
t
p
ut
f
u
n
c
t
i
on c
o
m
b
i
n
es t
h
e
out
put
ω
of all m
a
rked
pl
aces
O
–
out
put
si
g
n
al
s, |
O|
>
0
a
n
d
I
∩
O =
Ø
ω
– a m
a
pping
associating e
v
e
r
t Place
with a
n
out
put
v
–
v
a
riab
le d
e
fin
itio
n assign
s a nu
m
e
rical d
a
ta typ
e
main safe
alarm
start
start
run
run
stop
Cyclic
scan
emgcy
pow
er
paus
e
stop
1
2
3
Evaluation Warning : The document was created with Spire.PDF for Python.
In
d
onesi
a
n
J
E
l
ec En
g &
C
o
m
p
Sci
ISS
N
:
2
5
0
2
-
47
52
Al
gori
t
h
m t
o
C
onve
r
t
Si
gn
al
I
n
t
e
rpret
e
d Pet
r
i
N
e
t
mo
del
s
t
o
Pro
gr
am
m
abl
e
…
(
Z.
As
par)
90
7
For
a m
o
re fo
r
m
al
defi
ni
t
i
on
of S
I
P
N
, se
e [
1
]
, [
5
]
an
d [
1
8
]
. The dy
nam
i
c B
e
havi
or
of
an S
I
PN
i
s
gi
ve
n by
t
h
e fi
r
i
ng p
roces
s def
i
ned by
fo
ur
r
u
l
e
s:
1.
A tra
n
sition is
enable
d, if all
its pre
-
places a
r
e m
arked
and firi
ng ensures binary m
arking
of all its post-
places.
2.
A tran
sitio
n fires immed
i
atel
y
,
if it is en
ab
led
an
d its firi
n
g
co
nd
itio
n is fu
l
f
illed
.
3.
All tran
sition
s
th
at can
fire and
are
n
o
t
i
n
co
n
f
lict with o
t
h
e
r tran
sitio
n
s
fire sim
u
ltan
eo
u
s
ly.
The firi
ng process is iterate
d until a stabl
e
m
a
rk
ing is reached
(i.e. until no transition ca
n fire
an
ym
o
r
e).
Since firi
n
g
of a tran
sition
is supp
o
s
ed
to tak
e
no
time, iterativ
e
firin
g
is in
terpreted
as
sim
u
l
t
a
neous
, t
o
o
. Fo
r t
h
at
reaso
n
, n
o
cha
n
g
e
s of i
n
put
si
g
n
al
s
m
a
y
occur du
ri
n
g
t
h
e fi
r
i
ng p
r
oc
ess. A
f
t
e
r
a
new sta
b
le m
a
rki
ng is reac
hed, the
output signals
are c
o
m
puted according to the m
a
rki
ng a
n
d the
signal
algebra.
Fi
gu
re
2.
A
n
S
I
PN
m
odel
f
o
r
a r
o
b
o
t
arm
3.
RELATED
WORK
Al
t
h
o
u
gh
PN
h
a
s m
a
ny
advan
t
ages o
v
er
LL
D, P
L
C
w
ith
LLD as th
e d
e
si
g
n
en
try is th
e
m
o
st wid
e
ly
available in the world.
In
order to
m
ake PN bei
ng acce
pted by existing
LLD users
,
it is im
portant existing
PLC too
ls an
d
co
mm
o
n
d
e
sign
techn
iqu
es can
still b
e
reu
s
ed
.
3.
1.
P
N
t
o
L
L
D
Th
er
e ar
e
m
a
n
y
w
o
r
k
s r
e
lated
to
PN
to
LLD
conv
er
sio
n
e.g
.
[1
],
[3],
[
8
]-
[1
6
]
.
Wo
rk
[9
] is an
im
port
a
nt
s
u
r
v
ey
on al
l
rel
a
t
e
d w
o
r
k
s
on
LL
D.
Aft
e
r s
o
m
e
com
p
ari
s
on
o
n
vari
o
u
s t
e
c
hni
que
s i
n
[
1
]
,
[
3
]
,
[1
0]
,
[1
1]
, [1
4]
-
[
1
6
]
, t
h
e wo
rk
do
n
e
i
n
[1]
i
s
t
h
e
best
fo
r t
h
e j
o
b. Thei
r m
e
t
h
o
d
pr
o
v
i
d
es sy
s
t
em
at
i
c
conve
r
s
i
o
n
,
i
s
ol
at
i
on
fr
om
i
n
p
u
t
an
d
out
p
u
t
net
w
o
rks
, a
nd m
a
ke t
h
e L
L
D
pr
og
ram
m
o
re reada
b
l
e
i
n
o
rde
r t
o
l
o
c
a
t
e
t
h
e
fau
lt in
LLDs wh
ich
is a vital
issu
e. Th
ese co
n
s
i
d
erati
o
n
is i
m
p
o
r
tan
t
to
redu
ce
d
e
sign
ti
m
e
a
n
d
also
deb
u
ggi
ng
an
d
m
a
i
n
t
e
nance
t
i
m
e. Thei
r m
e
t
hod
can
be
ext
e
nde
d
f
o
r
SI
PN,
Ti
m
e
d and C
o
l
o
u
r
ed
P
N
.
The c
o
nve
rsi
o
n
pr
ocess i
s
i
m
port
a
nt
d
u
e
t
o
t
w
o i
m
port
a
nt
fact
ors:
m
a
i
n
t
a
i
n
i
n
g LL
D m
odel
i
n
g
para
di
gm
so t
h
at
use
r
s can
veri
fy
t
h
ei
r
w
o
r
k
usi
ng
k
n
o
w
n c
onc
ept
, a
nd
val
i
d
at
e t
h
e PN m
odel
that
i
t
i
s
con
s
t
ruct
e
d as
i
t
was i
n
t
e
nde
d
t
o
be.
An
ot
h
e
r
im
port
a
nt
t
h
i
n
g ab
o
u
t
t
h
ei
r
m
e
t
hod i
s
t
h
e
LLD
out
c
o
m
e
i
s
very
neat and
systematic.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
502
-47
52
I
ndo
n
e
sian
J Elec Eng
& Com
p
Sci, V
o
l. 10
,
No
.
3
,
Jun
e
2
018
:
90
5 – 91
6
90
8
3.
2.
Pre
v
i
o
us
PN
to
L
L
D
C
o
n
v
ersi
o
n
The m
e
t
hod
pr
op
ose
d
i
n
[1]
was t
o
i
d
e
n
t
i
f
y
PN s
u
b
n
et
s f
o
r f
o
u
r
di
ffe
rent
pat
t
e
rns a
s
su
m
m
a
ri
zed i
n
Fi
gu
re 3
. The
pat
t
e
rns ca
n b
e
di
vi
de
d i
n
t
o
f
o
u
r
t
y
pes i
n
t
w
o
pai
r
s
of set
and
reset
a ru
ng
. The set
r
u
l
e
i
s
t
h
e
condition to ac
tivate a r
ung while the reset
rule is
the c
o
ndition to
deactivate a rung. The
set rules c
o
nsist of
t
w
o
gene
ral
st
ruct
ures
k
n
o
w
n as Ty
pe
I a
nd
Ty
pe I
I
.
M
eanw
h
i
l
e
t
h
e reset
r
u
l
e
s c
onsi
s
t
of t
w
o
gene
ral
str
u
ctur
es kn
ow
n
as
Ty
p
e
I
I
I
an
d
Typ
e
IV
. Th
e d
e
ta
il exp
l
an
atio
n of t
h
e
ru
les can
b
e
referred
in [1
].
Fi
gu
re
3.
Ty
pe
s o
f
SE
T a
n
d
R
E
SET
4.
PROP
OSE
D
PN
TO
LLD
CO
NVE
RSI
O
N
In
or
der t
o
aut
o
m
a
t
e
and spe
e
d u
p
t
h
e c
o
n
v
e
rsi
o
n p
r
oce
ss,
bot
h PN a
nd
LLD s
u
b
n
et
s
were a
n
al
y
zed
i
n
t
h
ei
r eq
ui
va
l
e
nt
sub
-
I
n
ci
de
nce M
a
t
r
i
ces (
s
ub
-IM
) an
d s
u
b
-
B
o
ol
ean e
q
uat
i
o
n
s
(s
ub
-B
E) as sh
o
w
n i
n
t
h
e
sub
-
sect
i
o
ns 4.
1.
4.
1.
I
nciden
t
Ma
trices
Met
hod
The
out
put
c
o
i
l
i
n
a P
L
C
i
s
de
not
e
d
by
a pl
ac
e, P i
s
renam
e
d as P
j
, t
h
e
k-t
h
feedbac
k
input step is P
k
,
th
e n
-
t
h
step
inp
u
t
s t as T
1
, T
2
, to
tn
as T
n
, t
h
e anal
y
s
i
s
on t
h
e su
b-
IM
an
d
sub
-
B
E
were
do
ne o
n
al
l
t
y
pes of
p
a
ttern as illu
strated
in Figu
re 3
.
By referri
n
g
to
p
r
ev
iou
s
research
er [1
]
,
b
a
sically th
ere are
fou
r
types of
p
a
ttern
s to b
e
id
en
tified
in th
e PN. Th
ese in
cu
d
e
s Typ
e
I,
Typ
e
II
, Typ
e
III
an
d Typ
e
IV
. Th
e ru
le is th
e v
a
lue
‘1’ is th
e
ou
tpu
t
of th
e tran
sitio
n
,
(P
j
), wh
i
le th
e v
a
lu
e ‘-1
’ is t
h
e inp
u
t
o
f
t
h
e tran
sitio
n, (P
k
). The sub
-
incidenc
e m
a
tr
ix and
sub-B
oolean eq
uation
for each Type is
disc
usse
d:
i.
The s
u
b-i
n
cide
nce m
a
trix for
Type I:
ii.
The s
u
b-i
n
cide
nce m
a
trix for
Type II:
iii.
The s
u
b-i
n
cide
nce m
a
trix for
Type III:
P
j
P
1
P
2
P
3
.
..
P
k
T
1
1
-1
-1
-
1
...
-
1
Th
e sub
-
B
o
o
lean
eq
u
a
tion
fo
r Typ
e
I can
b
e
written
as:
P
j
= (P
1
.P
2
.P
3
. .
..
.
P
k
).
T
1
The B
ool
ea
n e
quat
i
o
n i
s
ge
ne
ral
i
zed as :
i
k
j
T
P
P
.
(1
)
P
0
P
1
P
2
P
3
...
P
n
T
1
1
-
1
0
0
..
.
0
T
2
1
0
-
1
0
..
.
0
...
T
n
1
0
0
0
..
.
-1
Th
e su
b-Boo
l
ean
equ
a
tion
for Typ
e
II can
b
e
written
as:
P
0
= (P
1
.T
1
) +
(P
2
.T
2
) +
(
P
3
.T
3
) +
...
(P
n
.T
n
)
The B
ool
ea
n e
quat
i
o
n i
s
ge
ne
ral
i
zed as :
i
k
j
T
P
P
.
(
2
)
P
0
P
1
P
2
P
3
.
..
P
n
T
1
-
1
1
1
1
..
.
1
Th
e sub
-
B
o
o
l
ean
equ
atio
n
for Typ
e III can b
e written
as:
P
0
= ..
. +
P
0
.(
P
k
+ T
1
)
The B
ool
ea
n e
quat
i
o
n i
s
ge
ne
ral
i
zed as :
)
.(
i
k
j
j
T
P
P
P
(3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
d
onesi
a
n
J
E
l
ec En
g &
C
o
m
p
Sci
ISS
N
:
2
5
0
2
-
47
52
Al
gori
t
h
m t
o
C
onve
r
t
Si
gn
al
I
n
t
e
rpret
e
d Pet
r
i
N
e
t
mo
del
s
t
o
Pro
gr
am
m
abl
e
…
(
Z.
As
par)
90
9
iv
.
th
e su
b-in
cidence m
a
trix
fo
r Typ
e
IV:
Whe
r
e,
,
The e
q
uations
are
analyzed
colum
n
by c
o
l
u
m
n
(k
) and
ro
w b
y
ro
w (i
) starting
with
th
e top
ro
w
(i
=0)
. T
h
ese
ge
neral
fo
rm
s equat
i
o
n
s
are
i
m
po
rt
ant
i
n
t
h
e
s
ubs
eq
ue
nt
anal
y
s
i
s
.
4.
2.
Cus
t
om T
r
ansi
ti
on
f
o
r
L
L
D
Fo
r PLC im
p
l
e
m
en
tatio
n
u
s
i
n
g
LLD m
o
d
e
l
,
it is a co
mmo
n
practice to
h
a
v
e
a sing
le step
in
pu
t to
activate or
dea
c
tivate a rung.
In a
PN
m
odel, the equivale
nt ele
m
ent to activ
ate or
deacti
v
ate an
output coil is
done by source
and sinks tra
n
sitions
respectively. By using
them
,
there
is no
need to i
n
itialize any place with
a to
k
e
n
.
Bu
t t
h
is will resu
lt
in
th
e PN
sub
-
n
e
t in
co
m
p
arab
le wit
h
an
y
o
f
p
a
ttern
ty
p
e
s pro
p
o
s
ed
in
[1
].
Pre
v
ious a
n
alysis shows
that
the Boolean
equation ca
n
be a
u
tom
a
ted only if t
h
ere
are val
u
e
‘1’
as the
o
u
t
p
u
t/inp
u
t
and
v
a
l
u
e ‘-1’ as
in
pu
t/o
u
t
p
u
t
resp
ectiv
ely in
a
row. Th
e algorith
m
d
o
e
s
n
o
t
h
a
v
e
a so
l
u
tio
n if in
th
e row th
ere i
s
o
n
l
y po
sitiv
e
n
u
m
b
e
rs
o
r
n
e
g
a
tiv
e nu
m
b
ers as sho
w
n
in
ex
am
p
l
e LLD Typ
e
I in
Fi
g
u
re 4
and
LLD
Typ
e
II in
Fi
g
u
re
7
.
The p
attern
s
d
o
no
t ex
ist i
n
th
e
PN m
o
d
el to be con
v
e
rted due to
;
a)
All p
o
s
itiv
e
o
r
all n
e
g
a
tiv
e co
efficien
ts wh
i
c
h
ind
i
cate th
e so
urce tran
sitio
n
o
r
sink
tran
sitio
n
o
n
l
y
.
Howev
e
r, th
ese typ
e
s
o
f
i
n
com
p
le
te p
a
tte
rn
always ex
ist in PLC ap
p
licatio
n
s
.
b)
Mean
wh
ile, for Typ
e
I or Ty
p
e
III
d
o
e
s no
t
ex
ist co
m
p
lete p
a
ir
o
f
tran
sitio
n
c)
On th
e
o
t
h
e
r
han
d
, Ty
p
e
II
o
r
Typ
e
IV do
es
n
o
t
h
a
v
e
co
m
p
lete p
a
ir
o
f
inpu
t and
ou
tpu
t
tran
sitio
n.
In
ord
er to
ob
tain
th
e correct resu
lts, PN m
o
d
els sh
ou
ld
h
a
v
e th
e
co
m
p
lete p
air o
f
tran
sition
.
Meanwhile, to gene
rate a Boolean equa
t
i
on i
f
t
h
ere are
onl
y
val
u
e ‘1
’ an
d val
u
e
‘0
’,
or
val
u
e ‘
-
1
’
an
d
val
u
e
‘0’ is
by a
ddi
ng a tem
pora
r
y (te
m
p) Place in
Petri Nets
a
n
d
it will becom
e
wire i
n
the
La
dder Logic
Diagram
.
Ty
pe
I
Ty
pe I P
N
su
bnet
prese
n
t
e
d
i
n
[1]
co
nsi
s
t
s
of
one t
r
a
n
si
t
i
on,
one
pl
ace
and
one a
r
c a
s
sho
w
n i
n
Fi
gu
re
4
w
h
i
c
h
has
i
n
c
o
m
p
l
e
te pai
r
o
f
a
r
c.
In
ord
e
r to so
lv
e th
e prob
lem
,
th
e in
cid
e
nt
m
a
trices
i
s
u
s
ed t
o
p
r
ovi
de
com
p
l
e
t
e
pai
r
of
i
n
put
a
n
d
out
put arc
s
by
addi
ng a tem
pora
r
y (Tem
p) Place in Petri
Nets as illustra
ted in Figure
5. The tem
porary place
also acts as
the
curre
nt activat
ed
place denot
e
d
by a toke
n.
The e
qui
val
e
nt
LLD
ru
n
g
by
usi
n
g t
y
pe I i
s
sho
w
n i
n
Fi
gu
r
e
6 o
n
t
h
e l
e
ft
.
Si
nce st
ep Te
m
p
i
s
al
way
s
ON, th
e inp
u
t
is always connected
and
acts
as a wi
re as sho
w
n
i
n
Fi
g
u
re
6
o
n
th
e
righ
t.
Th
is
p
r
o
c
ed
ure will
P
0
P
1
P
2
P
3
...
P
n
T
1
-
1
1
0
0
..
.
0
T
2
-
1
0
1
0
..
.
0
...
T
n
-
1
0
0
0
..
.
1
Th
e sub-Boo
l
ean
equ
ation
for Typ
e IV can b
e written
as:
P
0
= + P
0
.(P
1
+ T
1
).
(P
2
+ T
2
).
(
P
3
+ T
3
)
.
...
.
(
P
n
+ T
n
)
The B
ool
ea
n e
quat
i
o
n i
s
ge
ne
ral
i
zed as :
i
k
j
j
T
P
P
P
.
(4
)
Fi
gu
re
4.
A
su
bnet
wi
t
h
o
n
l
y
one
o
u
t
p
ut
a
rc
Fi
gu
re
5.
A
su
bnet
wi
t
h
i
n
p
u
t
an
d
out
put
a
rc
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
502
-47
52
I
ndo
n
e
sian
J Elec Eng
& Com
p
Sci, V
o
l. 10
,
No
.
3
,
Jun
e
2
018
:
90
5 – 91
6
91
0
en
su
re techn
i
qu
e in
[1
] can
always b
e
u
s
ed
in
a so
urce tran
sitio
n. Th
e si
milar p
r
o
cedure is also
ap
p
lied
for
Type II
pattern where
the
temporary i
n
put st
ep will
be repl
aced with
a wire.
Fi
gu
re
6.
Fi
nal
LLD
r
u
ng
f
o
r
PN s
u
bnet
Ty
p
e
I
Ty
p
e
I
II
Typ
e
III PN su
bn
et presen
ted
in
[1
] con
s
ists o
f
one t
r
ans
ition, one
plac
e and
one arc
as shown i
n
Fi
gu
re
7
w
h
i
c
h
has
i
n
c
o
m
p
l
e
te pai
r
o
f
a
r
c.
Fig
u
re
7
.
A PN sub
n
et with a
sin
k
transitio
n
In
ord
e
r to so
l
v
e th
is
prob
lem
,
th
e in
cid
en
t
m
a
trices
is u
s
ed
to prov
id
e a co
m
p
l
e
t
e
pai
r
of t
h
e a
rcs
by
addi
ng tem
porary (Tem
p) Place in Petri Nets as depict
ed in Figure
8. T
h
e te
m
pora
r
y place also acts as the
to
k
e
n
d
e
stin
atio
n wh
en
th
e curren
t tok
e
n is re
m
o
v
e
d fro
m
th
e activ
e p
lace.
Fi
gu
re
8.
A
su
bnet
t
o
be
deac
t
i
v
at
ed by
T1
Sin
ce it is a reset activ
ity, th
e eq
u
i
v
a
len
t
LLD ru
ng
b
y
usi
n
g t
y
pe I
II i
s
s
h
ow
n i
n
Fi
g
u
re
9 o
n
t
h
e l
e
ft
.
Sin
ce step
Tem
p
will b
e
OFF wh
en
it is activ
ated
, t
h
e i
npu
t is always
open
e
d and
acts
as an op
en
co
nn
ection
as
shown
i
n
Fi
g
u
re 9
o
n
th
e rig
h
t
. Th
is p
r
o
c
ed
ure will
en
su
re techn
iqu
e i
n
[1
] can
always b
e
u
s
ed
in
a sink
tran
sitio
n. Th
e similar p
r
o
cedu
r
e is also applied
fo
r
Ty
p
e
IV
p
a
ttern wh
ere th
e tem
p
o
r
ary in
pu
t step wi
ll b
e
repl
ace
d wi
t
h
an o
p
en c
o
n
n
e
c
t
i
on. T
h
e t
ech
ni
q
u
e t
o
use t
e
m
porary
st
ep i
n
ge
nerat
i
n
g t
h
e eq
ui
val
e
nt
sub
n
et
LLD is im
p
o
r
tan
t
to
en
sure co
n
s
isten
c
y in
th
e orig
i
n
al
algo
rith
m
in
[1
].
On
ce it is consisten
t
, it is ea
sier to
devel
o
p
t
h
e
p
r
og
ram
i
n
a co
m
put
er.
Fi
gu
re
9.
Fi
nal
LLD
r
u
ng
f
o
r
PN s
u
bnet
Ty
p
e
II
I
4
.
3
.
Critica
lly
Una
v
a
ila
ble
Pa
ttern
In a c
o
m
p
licated PN m
odel s
u
ch as i
n
Fi
gure 2,
certai
n
places cannot be c
o
nve
r
ted since the
s
u
bnet
s
do
not
resem
b
l
e
any
exi
s
t
i
ng pat
t
e
rn t
y
pe
s i
n
[1]
. Pre
v
i
ous
pr
o
pose
d
t
echni
q
u
e i
n
S
ect
i
on 4.
2 can
not
be
appl
i
e
d
si
nce
t
h
e s
u
bnet
s
i
n
F
i
gu
re
2 are
co
m
p
l
e
t
e
sub
n
et
s
. T
hus
,
fu
rt
he
r
adj
u
st
m
e
nt
i
s
n
eeded
.
T
1
P
1
P
1
T
1
Tem
p
In
co
m
p
lete p
air
wi
t
h
onl
y
a
n i
n
put
arc
T1
P
1
T1
P1
-1
Complete
pai
r
with
i
npu
t
and
output
arcs
T1
P1
‐
1
T1
P1
Evaluation Warning : The document was created with Spire.PDF for Python.
In
d
onesi
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J
E
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ec En
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C
o
m
p
Sci
ISS
N
:
2
5
0
2
-
47
52
Alg
o
r
ithm t
o
C
o
n
v
ert S
i
g
n
a
l
In
terp
reted
Petri Net mod
e
ls to Prog
ra
mma
b
l
e
…
(
Z
.
As
par)
91
1
P
j
Ps
1
P
s
2
Ps
3
..
. Ps
k
T
i
1
-
1
-
1
-1
..
. -
1
An
d Pd
1
= Pd
2
= ...
P
d
n
= P
j
Th
e sub
-
BE can
b
e
written
as:
a)
P
j
= (Ps
1
.Ps
2
.Ps
3
. ..
. .P
s
k
).
T
i
b)
The
B
ool
ea
n equat
i
o
n can
be gene
ral
i
zed
by
follo
win
g
t
h
is
fo
rm
ula:
i
k
j
T
Ps
P
.
(5
)
i.
SET
Fig
ur
e
10
sh
ow
s a P
4
s
u
bnet
o
f
S
I
P
N
fr
om
Fi
gu
re
2.
Th
e s
u
b
n
et
i
s
g
o
i
n
g
t
o
be
act
i
v
at
ed
o
r
set
at
P
5
.
Th
is typ
e
of
stru
ct
u
r
e do
es no
t ex
ist in
typ
e
I, II, II
I and
IV.
If th
e pro
c
ess is au
to
m
a
te
d
,
t
h
e
p
a
ttern
can
be
wr
on
gly
inter
p
reted as
Ty
pe
I
II si
nce
b
o
th l
o
ok
sim
i
lar. But
Ty
pe
II
I is
fo
r
reset.
There
is m
o
re
than a
single place
connecte
d
to tra
n
sition
TP1. If the
tra
n
sition
is activated, all the
places c
o
nnect
ed t
o
the
tra
n
si
tion
will
be
activated. This al
so
m
eans P9 c
a
n
be i
g
nored
since the
place to
be
set
i
s
P5
. B
a
se
d
on
t
h
i
s
as
su
m
p
ti
on, t
h
e s
u
bnet
has
bec
o
m
e
a Ty
pe I
p
a
t
t
e
rn.
Fi
gu
re 1
0
. A P
N
s
u
b
n
et
fr
om
Fi
gu
re 2
t
o
set
Give
n one or
m
o
re source
pl
aces, Ps and a
set of de
stination
places, Pd a
single destination
place, Pj
can be c
o
nvert
e
d at a time by ignori
ng the
other desti
n
ation places s
o
tha
t
Type I subne
t
can be ge
neralized
as:
,
ii.
RESET
Fi
gu
re
1
1
s
h
o
w
s a
su
b
n
et
o
f
SIP
N
fr
om
Fi
gure
2
. T
h
e
pat
t
e
rn
can
be
w
r
o
ngl
y
i
n
t
e
rp
ret
e
d as
Ty
pe
I
sin
ce
b
o
t
h
look similar
.
Bu
t Typ
e
I is fo
r set
w
h
ile th
is is a
reset.
Figu
re 1
1
. A P
N
s
u
b
n
et fr
om
Figu
re 2 fo
r re
set
A transitio
n
at
T6
is sh
ared
with
P1
and
P7
. To
d
i
sa
ble
P1,
P7 m
u
st also active s
o
that T6 can
be
activ
ated
.
Using
tran
sform
a
t
i
o
n techn
i
qu
e,
o
n
e
of t
h
e p
l
ace can
b
e
co
m
b
in
ed with th
e t
r
an
sitio
n and
eli
m
in
ate
the com
b
ined place from
the
subnet as shown in Figure
11
on the
righ
t. After the trans
f
orm
a
tion proces
s, the
PN
can
b
e
cat
eg
or
ized as Ty
p
e
I
I
I
.
N
o
w
,
resu
lt fr
o
m
tr
ansf
or
m
a
tio
n
is n
o
lon
g
e
r
pu
r
e
PN, it is know
n as
sig
n
a
l i
n
terp
r
e
t
e
d
p
e
tr
i
n
e
t (SIPN
)
. Th
e subnet I
M
is as:
Th
e
sub
n
e
t IM is
as:
P
4
P
5
P
9
TP
1
-
1
1
1
The
s
u
bnet
IM
can be gene
ral
i
zed fu
rt
he
r
as:
Ps
1
P
s
2
...
Ps
k
P
d
1
P
d
2
..
. P
j
T
-
1
-
1
-1
1
1
.
..
1
P
5
P
9
P
4
TP
1
=
T
2
.*P
5
P
1
P
7
T
6
P
4
P
1
TP
2
=
T
6
.P
7
P
4
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
502
-47
52
I
ndo
n
e
sian
J Elec Eng
& Com
p
Sci, V
o
l. 10
,
No
.
3
,
Jun
e
2
018
:
90
5 – 91
6
91
2
Give
n one or
m
o
re source pl
aces, P
s
and a set of destination
places, P
d
a single destinat
ion place, P
j
can
be c
o
n
v
e
r
t
e
d at
a t
i
m
e by
t
r
ans
f
o
r
m
i
ng o
t
her s
o
urce
pl
a
ces so
t
h
at
Ty
p
e
II
I s
u
bnet
ca
n
be
gene
ral
i
zed as:
,
iii.
SET
Fi
gu
re 1
2
s
h
o
w
s a su
bnet
of
SIP
N
fr
om
Figu
re 2
. The s
u
bnet
i
s
g
o
i
n
g t
o
be act
i
v
at
ed
or set
at
P
4
.
This type
of st
ruct
ure
does no
t exist in type
I, II,
III a
nd
IV. T
o
sim
p
lify the subnet, pl
ace P
8
can
be i
g
nore
d
for the sam
e
reason as in Type I. P1 and P7 places ar
e combine
d
to tran
s
f
orm
into a new subnet as shown
i
n
Figu
re 1
2
o
n
t
h
e rig
h
t. T
h
e trans
f
orm
a
tion is like in
Ty
pe III
but the s
u
bnet is m
o
re com
p
licated than the
exam
ple in Type
III.
Figu
re 1
2
. PN
fo
r
Ty
pe
I
I
Aft
e
r t
h
e t
r
a
n
s
f
o
r
m
a
ti
on p
r
oc
ess, t
h
e P
N
ca
n be
cate
g
oriz
ed as Type
II.
W
ith
ou
t tran
sform
a
t
io
n
pr
ocess
, t
h
e
re
sul
t
bec
o
m
e
s wr
on
g.
N
o
w,
r
e
sul
t
f
rom
transform
a
tio
n
is n
o
lon
g
e
r
pu
re PN, it is
k
nown as
sig
n
a
l i
n
terp
ret
e
d
p
e
tri
n
e
t (SIPN). Th
e
orig
i
n
al su
bn
et IM
is as:
P
14
P
1
T
1
P
4
P
7
T
6
P
8
T
1
TP
3
= P
1
.P
7
T
6
P
4
P
14
P
1
P
4
P
7
T
6
-1
1
-1
After tran
sfo
r
matio
n
:
P
1
P
4
TP
2
-
1
1
The
s
u
bnet
IM
can be gene
ral
i
zed fu
rt
he
r
as bel
o
w:
Ps
1
P
s
2
...
P
j
P
d
1
Pd
2
...
P
d
k
T
i
-1
-
1
-
1
1
1
...
1
P
j
P
d
1
P
d
2
.
..
Pd
k
TP
i
-
1
1
1
...
1
Whe
r
e T
P
i
=
T
i
. Ps
1
. Ps
2
..
. P
sn
Th
e sub
-
BE can
b
e
written
as:
a)
P0 =
..
. +
P0.(P
k
+ T1)
b)
The
B
ool
ea
n equat
i
o
n can
be gene
ral
i
zed
by
follo
win
g
t
h
is
fo
rm
ula
i
k
j
j
T
Pd
P
P
.
(6
)
P
1
P
4
P
7
P
8
P
14
T
1
0
1
0
1
-1
T
6
-
1
1
-
1
0
0
After tran
sfo
r
matio
n
:
TP
3
P
4
P
14
T
1
0
1
-1
T
6
-
1
1
0
The
s
u
bnet
IM
can be gene
ral
i
zed fu
rt
he
r
as bel
o
w:
P
j
P
s
1
Ps
2
Ps
3
P
s
4
T
i
1
0
-
1
-
1
0
T
i + 1
1
-
1
0
0
0
T
i + 2
1
0
0
0
-1
Evaluation Warning : The document was created with Spire.PDF for Python.
In
d
onesi
a
n
J
E
l
ec En
g &
C
o
m
p
Sci
ISS
N
:
2
5
0
2
-
47
52
Alg
o
r
ithm t
o
C
o
n
v
ert S
i
g
n
a
l
In
terp
reted
Petri Net mod
e
ls to Prog
ra
mma
b
l
e
…
(
Z
.
As
par)
91
3
Give
n one
or
m
o
re source pl
aces, P
s
fo
r
one tran
sition
,
P
j
can be
convert
e
d at a tim
e
by trans
f
orm
i
ng
othe
r s
o
urce
pl
aces so that Ty
pe
II
subnet ca
n
be
gene
ralized as:
Whe
r
e:
,
Analyze c
o
lum
n
by col
u
m
n
(k) a
n
d row by
ro
w (
i
) star
ting w
ith
th
e top
row
(
i
=0
)
iv
.
RESET
Fig
u
r
e
13
sh
ow
s a subn
et of
SI
PN
fro
m
Fig
u
r
e
3. Th
e
su
bn
et in
Fi
g
u
r
e
13
is th
e mo
st co
m
p
lex
subnet due to
feedbac
k
places
and share
d
tra
n
sitions at T
7
.P
5
. Due to fee
dbac
k
places and sha
r
ed tra
n
sitions,
th
e PN
can
b
e seen
as Typ
e I
d
u
e to
two
inpu
t tran
s
itio
ns w
h
ich
in
d
i
cates th
e SET rung. H
o
w
e
v
e
r, Figu
re
1
3
(
m
id
d
le)
shows th
e RESET ru
ng
, and th
e
sim
p
l
i
fi
cat
i
on a
n
d
by
el
im
i
n
ati
ng
re
du
n
d
ant
of
P
5
,
the Figure 13
(ri
g
h
t
)
gi
ves t
h
e co
rrect
i
n
t
e
rp
ret
a
t
i
on
of
Ty
p
e
I
V
R
E
SE
T r
u
ng
Figu
re 1
3
. PN
fo
r
Ty
pe
I
V
Give
n one
or m
o
re
source pl
aces,
P
s
for one
transition
a
n
d one
or
m
o
re destination places,
P
d
fo
r
on
e
tran
sitio
n, P
j
c
a
n be c
o
nve
rte
d
at a tim
e
by
trans
f
orm
i
ng othe
r s
o
urce and desti
n
ation
places so that T
y
pe IV
sub
n
et
ca
n be gene
ral
i
zed
a
s
:
P
j
Ps
2
Ps
3
TP
4
P
d
3
Ti
-1
0
0
0
1
TT
4
-
1
0
0
0
0
Whe
r
e T
T4 =
Ti.Ps1.Ps
2
….
P
sn
Ti here
is the
transition with
m
o
re
than one source places
a
n
d Ps is the
source
places.
TP4 = Pd1 +
Pd2 + …. Pdn
whe
r
e Pd
he
re is
the destionation places of
one
tra
n
sition.
Th
e sub
-
BE can
b
e
written
as:
P
4
T
2
.P
5
P
5
T
7
.P
5
P
9
P
11
P
4
T
2
.P
5
P
5
T
7
.P
5
P
9
P
11
P
5
P
4
T
2
.P
5
TT
4
=T
7
.P
5
.P
5
TP
4
=P
9
+ P
5
P
11
P
j
Ps
1
T
P
2
Ps
4
T
i
1
0
-1
0
T
i + 1
1
-
1
0
0
T
i + 2
1
0
0
-1
Whe
r
e T
P
2
=
Ps
2
. Ps
3
...
P
s
n
Th
e sub
-
BE can
b
e
written
as:
a)
P
0
= (P
1
.T
1
) +
(P
2
.T
2
) +
(
P
3
.T
3
) +
...
(P
n
.T
n
)
b)
The
B
ool
ea
n equat
i
o
n can
be gene
ral
i
zed
by
follo
win
g
t
h
is
fo
rm
ula:
i
k
j
T
P
P
.
(7
)
Ori
g
in
al su
bn
et IM is as
b
e
low:
P
4
P
5
P
9
P
11
T
2
-1
1
1
0
T
7
-1
-
1
0
1
After tran
sfo
r
matio
n
:
P
4
T
P
4
P
11
T
2
-
1
1
0
TT
4
-
1
0
1
The
s
u
bnet
IM
can be gene
ral
i
zed fu
rt
he
r
as bel
o
w:
P
j
Ps
1
P
s
2
P
s
3
Pd
1
P
d
2
Pd
3
T
i
-1
0
0
0
1
1
0
T
i + 1
-1
-1
0
0
0
0
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
502
-47
52
I
ndo
n
e
sian
J Elec Eng
& Com
p
Sci, V
o
l. 10
,
No
.
3
,
Jun
e
2
018
:
90
5 – 91
6
91
4
a)
P
0
= + P
0
.(P
1
+ T
1
).
(P
2
+ T
2
).
(
P
3
+ T
3
)
.
...
.
(
P
n
+ T
n
)
By u
s
ing
m
atri
x
calcu
lation
,
th
e
resu
lts is
sho
w
n
:
i
k
j
j
T
P
P
P
.
(
8
)
Whe
r
e:
,
Fi
gu
re
1
4
. L
L
D
f
o
r r
o
bot
ar
m
sy
s
t
em
from
SIP
N
i
n
Fi
gure 2
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