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o
p
s
(
P
L
L
)
alg
o
r
it
h
m
s
as s
h
o
w
n
i
n
Fi
g
u
r
e
1
[
4
-
6
].
O
r
t
h
o
g
o
n
a
l
s
y
s
t
e
m
g
e
n
e
r
a
t
i
o
n
P
I
0
*
q
v
v
q
v
d
v
n
f
*
*
2
1
*
f
R
MS
V
2
2
2
1
qv
v
'
v
'
qv
dq
Fig
u
r
e
1
.
Gen
er
al
s
tr
u
ct
u
r
e
o
f
th
e
p
h
ase
-
lo
c
k
ed
lo
o
p
(
P
L
L
)
P
L
L
d
esi
g
n
s
h
o
u
ld
h
a
v
e
a
r
ap
id
r
elea
s
e
an
d
a
v
er
y
lo
w
i
n
ac
c
u
r
ac
y
b
et
w
ee
n
th
e
o
b
tain
ed
p
h
ase
a
n
g
le
an
d
th
e
r
ea
l
p
h
ase
a
n
g
le,
m
ai
n
l
y
at
a
m
p
lit
u
d
e
o
r
f
r
eq
u
en
c
y
v
ar
iatio
n
[
6
]
-
[
12
]
.
T
h
ese
t
w
o
o
b
j
ec
tiv
es
ca
n
n
o
t
b
e
ac
h
iev
ed
s
i
m
u
ltan
eo
u
s
l
y
.
E
it
h
er
th
e
y
g
et
a
f
a
s
t
r
esp
o
n
s
e
w
it
h
m
ed
i
u
m
p
r
ec
is
io
n
o
r
g
o
o
d
ac
cu
r
ac
y
w
it
h
a
lo
n
g
er
s
y
n
c
h
r
o
n
izatio
n
ti
m
e
.
Mo
s
t
P
L
L
s
y
s
te
m
s
ar
e
i
m
p
le
m
en
ted
w
it
h
a
P
I
co
n
tr
o
ller
t
h
at
is
v
er
y
s
en
s
iti
v
e
to
d
is
tu
r
b
an
ce
s
,
as
th
e
co
n
tr
o
ll
er
p
ar
am
eter
s
ar
e
s
y
n
t
h
esize
d
ar
o
u
n
d
a
s
p
ec
i
f
ic
o
p
er
atin
g
p
o
in
t.
T
h
e
k
e
y
d
r
a
w
b
ac
k
o
f
t
h
is
co
r
r
ec
to
r
(
PI)
is
its
in
ab
ilit
y
to
r
ea
ct
to
s
u
d
d
en
ch
a
n
g
e
s
o
f
t
h
e
g
r
id
v
o
ltag
e.
T
h
e
co
n
tr
o
l
d
ev
ice
s
h
all
b
e
o
p
ti
m
ized
i
n
o
r
d
er
to
ac
h
iev
e
r
ap
id
lo
ck
in
g
w
it
h
ac
ce
p
tab
le
ac
c
u
r
ac
y
f
o
r
d
if
f
er
en
t
o
p
er
atin
g
p
o
in
ts
.
Fo
r
ea
s
ier
im
p
le
m
e
n
tatio
n
r
esear
ch
er
s
u
til
ized
v
ar
io
u
s
t
y
p
e
s
o
f
p
r
o
p
o
r
tio
n
al
in
teg
r
al
(
P
I
)
c
o
n
tr
o
ller
s
to
co
n
tr
o
l
th
e
P
L
L
.
Ho
w
e
v
e
r
,
th
e
w
e
ll
-
k
n
o
w
n
d
is
ad
v
a
n
t
ag
es
o
f
t
h
e
co
n
v
e
n
tio
n
al
P
I
an
d
t
h
eir
ad
ap
ti
v
e
v
er
s
io
n
s
e
n
co
u
r
a
g
e
r
esear
c
h
er
s
to
ap
p
l
y
th
e
i
n
telli
g
e
n
t
co
n
tr
o
ller
s
s
u
c
h
f
u
zz
y
lo
g
i
c,
n
e
u
r
al
n
et
w
o
r
k
,
n
eu
r
o
f
u
zz
y
,
etc.
Am
o
n
g
th
e
m
a
in
ad
v
a
n
ta
g
es
o
f
i
n
tel
lig
e
n
t
co
n
tr
o
ll
er
s
f
o
r
g
r
id
co
n
n
ec
ted
in
v
er
ter
s
y
s
te
m
[6
-
1
1
]
ar
e:
th
eir
ab
ilit
y
to
d
ea
l
w
it
h
an
y
n
o
n
-
li
n
ea
r
it
y
o
f
ar
b
itra
r
y
co
m
p
lex
i
t
y
an
d
t
h
eir
d
esig
n
s
d
o
n
o
t
r
eq
u
ir
e
a
m
a
th
e
m
atica
l
m
o
d
el
o
f
th
e
s
y
s
te
m
a
n
d
th
eo
r
etic
all
y
.
T
h
u
s
,
t
h
e
in
telli
g
en
t
co
n
tr
o
ller
s
ar
e
id
ea
ll
y
s
u
ited
f
o
r
co
n
tr
o
llin
g
g
r
id
co
n
n
ec
ted
i
n
v
er
ter
s
y
s
te
m
.
Am
o
n
g
t
h
e
v
ar
io
u
s
in
telli
g
en
t
co
n
tr
o
ller
s
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
(
FLC)
is
t
h
e
s
i
m
p
le
s
t
co
n
tr
o
l
an
d
b
etter
th
a
n
t
h
e
co
n
v
e
n
tio
n
al
co
n
tr
o
ller
s
i
n
ter
m
s
o
f
in
s
e
n
s
iti
v
it
y
to
p
ar
am
eter
an
d
g
r
id
v
ar
iatio
n
s
,
r
e
s
p
o
n
s
e
t
i
m
e,
s
e
t
tli
n
g
t
i
m
e
an
d
r
o
b
u
s
tn
es
s
[
1
3
-
1
5
]
.
T
h
is
d
o
cu
m
e
n
t
p
r
ese
n
ts
a
n
e
w
P
L
L
m
eth
o
d
f
o
r
g
r
id
-
co
n
n
ec
ted
P
V
i
n
v
er
ter
.
T
h
e
n
e
w
m
et
h
o
d
co
n
s
is
ts
i
n
g
en
er
ati
n
g
an
o
r
t
h
o
g
o
n
al
a
x
is
i
n
a
r
o
tati
n
g
f
r
a
m
e,
u
s
i
n
g
a
s
tr
u
ctu
r
e
b
ased
o
n
t
h
e
i
n
teg
r
atio
n
o
f
t
h
e
g
en
er
alize
d
s
ec
o
n
d
o
r
d
er
(
SOGI
)
,
f
o
llo
w
ed
b
y
a
P
ar
k
tr
an
s
f
o
r
m
at
io
n
to
b
r
in
g
i
t
b
ac
k
to
a
f
i
x
ed
r
ef
er
en
ce
[
3
]
.
T
h
e
lo
ck
in
g
o
f
th
e
p
h
ase
a
n
g
le
i
s
tr
an
s
lated
b
y
th
e
ca
n
c
ellatio
n
o
f
t
h
e
q
u
ad
r
atic
co
m
p
o
n
en
t
o
f
th
e
P
ar
k
tr
an
s
f
o
r
m
,
u
s
in
g
f
u
zz
y
lo
g
ic.
T
o
v
alid
ate
th
e
p
er
f
o
r
m
a
n
ce
s
o
f
th
is
n
e
w
m
et
h
o
d
,
w
e
w
ill
p
r
o
ce
ed
in
itiall
y
b
y
a
s
i
m
u
lat
io
n
u
n
d
er
th
e
P
SIM
s
o
f
t
w
ar
e,
b
y
u
s
i
n
g
th
e
D
L
L
b
lo
ck
f
o
r
th
e
i
m
p
le
m
e
n
tati
o
n
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
,
a
n
d
s
ee
its
r
esp
o
n
s
e
ag
ai
n
s
t
g
r
id
d
i
s
t
u
r
b
an
ce
s
.
Af
ter
,
w
e
w
ill
e
x
p
er
i
m
e
n
t
th
e
a
lg
o
r
i
th
m
,
o
n
a
r
ea
l
co
n
d
itio
n
s
u
s
in
g
a
p
r
o
to
t
y
p
e
b
ased
o
n
a
m
icr
o
co
n
tr
o
ller
S
T
M3
2
F4
0
7
.
Fo
r
v
alid
atio
n
,
we
w
i
ll
v
is
u
alize
t
h
e
s
h
i
f
ted
g
r
id
v
o
lta
g
e
s
e
n
t
to
t
h
e
A
DC
b
lo
ck
w
i
th
t
h
e
v
o
ltag
e
g
e
n
er
ated
b
y
t
h
e
D
A
C
b
lo
ck
t
h
at
r
ep
r
ese
n
ts
a
s
in
u
s
o
id
o
f
t
h
e
esti
m
ated
p
h
a
s
e
an
g
le.
2.
P
L
L
B
AS
E
D
O
N
T
H
E
SE
C
O
ND
O
RDER
G
E
N
E
RA
L
I
Z
E
D
I
NT
E
G
RA
T
O
R
(
SO
G
I
-
P
L
L
)
T
h
e
s
tr
u
ctu
r
e
o
f
th
e
s
ec
o
n
d
o
r
d
er
g
en
er
alize
d
in
teg
r
ato
r
(
SO
GI
)
is
illu
s
tr
ated
in
Fi
g
u
r
e
2.
T
h
e
in
p
u
t
s
ig
n
al
v’
i
s
t
h
e
v
o
lta
g
e
s
i
g
n
al
m
ea
s
u
r
ed
at
t
h
e
P
C
C
.
As
o
u
t
p
u
t
s
i
g
n
als,
t
w
o
s
i
n
u
s
o
id
al
w
a
v
es
v’
an
d
q
v
’
w
it
h
a
p
h
ase
s
h
if
t
o
f
2
ar
e
g
en
er
ated
s
o
th
at
t
h
e
co
m
p
o
n
e
n
t
h
a
s
th
e
s
a
m
e
p
h
a
s
e
an
d
a
m
p
l
itu
d
e
as
th
e
f
u
n
d
a
m
e
n
ta
l
in
p
u
t
v
o
ltag
e
s
ig
n
al
(
v
)
[
16
-
18
].
T
h
e
F
ig
u
r
e
2
,
s
h
o
w
s
t
h
e
s
t
r
u
ctu
r
e
o
f
t
h
e
s
ec
o
n
d
o
r
d
e
r
g
en
er
alize
d
in
te
g
r
ato
r
(
SOG
I).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
4
,
A
u
g
u
s
t 2
0
1
9
:
2
2
6
4
-
2273
2266
v
s
1
'
v
s
1
'
qv
k
)
si
n
(
in
g
r
i
d
v
v
gri
d
v
M
e
a
s
u
r
e
E
s
t
i
m
a
t
e
d
q
u
a
d
r
a
t
u
r
e
g
r
i
d
v
o
l
t
a
g
e
E
s
t
i
m
a
t
e
d
g
r
i
d
v
o
l
t
a
g
e
P
D
Fig
u
r
e
2
.
Or
th
o
g
o
n
al
s
ig
n
al
g
e
n
er
ato
r
b
ased
o
n
SOGI
T
h
e
s
ec
o
n
d
-
o
r
d
er
g
en
er
alize
d
in
te
g
r
ato
r
(
SOGI
)
ac
ts
as
a
b
an
d
p
ass
f
ilter
w
it
h
in
f
i
n
ite
g
ain
w
h
o
s
e
tr
an
s
f
er
f
u
n
ctio
n
is
d
e
f
in
ed
i
n
(
1
)
.
T
h
e
clo
s
ed
lo
o
p
tr
an
s
f
er
f
u
n
ctio
n
s
a
n
d
o
f
t
h
e
s
tr
u
ct
u
r
e
s
h
o
w
n
i
n
Fi
g
u
r
e
2
ar
e
d
ef
in
ed
as [
19
-
22
]:
=
2
+
2
(
1
)
(
)
=
′
(
)
=
2
+
+
2
(
2
)
(
)
=
′
(
)
=
2
2
+
+
2
(
3
)
w
h
er
e
n
r
ep
r
esen
ts
th
e
u
n
a
m
o
r
ti
ze
d
n
atu
r
a
l
f
r
eq
u
e
n
c
y
o
f
t
h
e
S
OGI
th
at
i
s
eq
u
al
to
t
h
e
es
ti
m
ated
f
r
eq
u
en
c
y
n
an
d
k
is
th
e
g
ai
n
th
at
a
f
f
ec
ts
t
h
e
SOGI
b
an
d
w
id
t
h
.
T
h
e
g
r
id
f
r
eq
u
e
n
c
y
ca
n
c
h
an
g
e;
th
er
e
f
o
r
e,
th
is
o
r
t
h
o
g
o
n
a
l
s
ig
n
a
l
g
e
n
er
ato
r
m
u
s
t
b
e
ab
le
t
o
tu
n
e
it
s
co
ef
f
icie
n
t
s
in
ca
s
e
o
f
g
r
id
f
r
eq
u
en
c
y
c
h
a
n
g
e.
T
o
ac
h
iev
e
th
is
,
tr
ap
ez
o
id
al
ap
p
r
o
x
im
at
io
n
is
u
s
ed
to
g
et
th
e
d
is
cr
ete
tr
an
s
f
er
f
u
n
ctio
n
a
s
f
o
llo
w
s
:
(
)
=
2
−
1
+
1
(
2
−
1
+
1
)
2
+
2
−
1
+
1
+
2
=
(
2
)
(
2
−
1
)
4
(
−
1
)
2
+
(
2
)
(
2
−
1
)
+
(
)
2
(
2
−
1
)
2
(
4
)
No
w
,
u
s
i
n
g
s
n
T
k
x
2
an
d
2
s
n
T
y
)
5
(
1
4
4
4
)
4
(
2
4
2
4
)
(
2
2
1
1
2
2
0
2
1
2
z
a
z
a
z
b
b
z
y
x
y
x
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y
x
y
y
x
x
y
x
x
z
H
d
(
5
)
)
6
(
1
4
4
4
)
4
(
2
4
.
4
.
2
4
.
)
(
2
2
1
1
2
2
1
1
0
2
1
2
1
z
a
z
a
z
qb
z
qb
qb
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y
x
y
x
z
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x
y
z
y
x
y
k
z
y
x
y
k
y
x
y
k
z
H
q
(
6
)
On
ce
t
h
e
o
r
th
o
g
o
n
al
s
i
g
n
al
h
as
b
ee
n
g
e
n
er
ated
,
p
ar
k
tr
an
s
f
o
r
m
i
s
u
s
ed
to
d
etec
t
th
e
Q
an
d
D
co
m
p
o
n
e
n
t
s
o
n
th
e
r
o
tati
n
g
r
e
f
er
en
ce
f
r
a
m
e.
T
h
is
is
t
h
e
n
f
ed
to
th
e
P
I
lo
o
p
th
at
co
n
tr
o
ls
th
e
VC
O
o
f
t
h
e
P
L
L
.
T
h
e
co
ef
f
icien
t
s
o
f
th
e
o
r
th
o
g
o
n
al
s
i
g
n
al
g
e
n
er
ato
r
ca
n
b
e
tu
n
ed
f
o
r
v
ar
y
i
n
g
g
r
id
f
r
eq
u
en
c
y
a
n
d
s
a
m
p
li
n
g
ti
m
e
[
20
-
22
].
As
ca
n
b
e
s
ee
n
,
t
h
e
tr
a
n
s
f
er
f
u
n
ctio
n
f
o
r
H
d
r
ese
m
b
le
s
t
h
at
o
f
a
B
a
n
d
P
ass
F
ilter
,
t
h
at
f
ilt
er
s
o
u
t
h
ar
m
o
n
ic
an
d
r
an
d
o
m
n
o
is
e
a
n
d
w
h
o
s
e
o
u
tp
u
t
i
s
in
p
h
ase
w
it
h
t
h
at
o
f
th
e
i
n
p
u
t
s
i
g
n
al.
T
h
e
tr
an
s
f
er
f
u
n
ct
io
n
f
o
r
H
q
is
th
e
s
a
m
e
a
s
t
h
at
o
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a
s
e
co
n
d
o
r
d
er
L
o
w
P
ass
F
ilter
,
t
h
at
n
o
t
o
n
l
y
f
i
lter
s
o
u
t
h
ar
m
o
n
ics
an
d
r
a
n
d
o
m
n
o
is
e,
b
u
t
also
i
n
tr
o
d
u
ce
s
a
p
h
a
s
e
s
h
i
f
t
o
f
2
/
r
ad
ian
s
[
20
-
22
]
.
Fig
u
r
e
3
Sh
o
w
s
t
h
e
b
lo
ck
d
iag
r
a
m
o
f
th
e
o
v
er
all
SO
GI
-
P
L
L
s
tr
u
ct
u
r
e
[
21
-
23
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
n
ew S
OGI
-
P
LL
meth
o
d
b
a
s
ed
o
n
f
u
z
z
y
lo
g
ic
fo
r
g
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co
n
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ted
P
V
in
ve
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ter
(
A
b
d
elh
a
d
i
B
o
u
kn
a
d
el
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2267
S
O
G
I
P
I
0
*
q
v
v
q
v
d
v
n
f
*
*
2
1
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f
R
MS
V
2
2
2
1
qv
v
'
v
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dq
Fig
u
r
e
3
.
Stru
ct
u
r
e
o
f
SOGI
-
P
L
L
3.
SO
G
I
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P
L
L
P
RO
P
O
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ASE
D
O
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F
U
Z
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L
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C
T
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tio
n
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t
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a
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e
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p
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ase
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ed
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o
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co
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o
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(
PLL
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f
o
r
a
g
r
id
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
in
v
er
ter
s
.
T
h
e
o
r
ig
i
n
alit
y
i
n
t
h
is
w
o
r
k
i
s
to
g
e
n
er
ate
an
o
r
th
o
g
o
n
al
p
o
w
er
v
o
lta
g
e
s
y
s
te
m
b
ased
o
n
a
s
ec
o
n
d
o
r
d
er
g
en
er
alize
d
in
teg
r
atio
n
s
tr
u
ct
u
r
e
(
SOGI
)
d
r
iv
en
b
y
f
u
zz
y
lo
g
ic
to
o
b
tain
f
a
s
t
d
et
ec
tio
n
an
d
a
m
o
r
e
ac
cu
r
ate
i
m
ag
e
o
f
t
h
e
p
h
a
s
e
an
g
le
[
24
-
25
].
T
h
e
F
ig
u
r
e
4
s
h
o
w
s
th
e
p
r
o
p
o
s
ed
s
ec
o
n
d
o
r
d
er
g
en
er
alize
d
in
te
g
r
ato
r
(
SOGI
)
s
tr
u
ctu
r
e
b
a
s
ed
o
n
f
u
zz
y
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g
ic.
S
O
G
I
F
u
z
z
y
l
o
g
i
c
0
*
q
v
v
q
v
d
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n
f
*
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2
1
*
f
R
MS
V
2
2
2
1
qv
v
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v
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dq
-
Fig
u
r
e
4
.
P
r
o
p
o
s
ed
s
tr
u
ctu
r
e
o
f
SOGI
-
P
L
L
b
ased
o
n
f
u
zz
y
l
o
g
ic
T
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
is
b
ase
d
o
n
th
e
ap
p
licatio
n
o
f
t
h
e
f
u
zz
y
lo
g
ic
o
n
t
h
e
q
u
ad
r
atic
co
m
p
o
n
en
t
o
f
P
ar
k
an
d
its
er
r
o
r
co
m
p
ar
ed
to
a
r
ef
er
en
ce
v
a
lu
e,
to
h
a
v
e
a
p
r
ec
is
e
an
d
f
as
t c
o
r
r
ec
tio
n
o
f
th
e
f
r
eq
u
e
n
c
y
,
w
h
ic
h
w
il
l
b
e
in
teg
r
ated
to
o
b
tain
th
e
p
h
ase
an
g
le
o
f
t
h
e
g
r
id
.
Fo
r
th
e
v
alid
atio
n
o
f
th
is
m
e
th
o
d
,
w
e
w
i
ll
p
er
f
o
r
m
th
e
d
is
cr
etiza
tio
n
an
d
th
e
i
m
p
le
m
e
n
tatio
n
o
f
t
h
e
eq
u
atio
n
s
d
ev
elo
p
ed
in
th
e
p
r
ev
io
u
s
s
ec
tio
n
,
in
th
e
f
o
r
m
o
f
th
e
f
u
n
ctio
n
s
i
n
p
r
o
g
r
a
m
m
i
n
g
lan
g
u
ag
e
C
.
Firs
tl
y
,
t
h
e
y
w
il
l
b
e
u
s
ed
i
n
th
e
DL
L
b
l
o
ck
w
h
ic
h
e
x
ec
u
te
s
th
e
r
o
u
ti
n
es
at
ea
ch
s
tep
s
i
m
u
latio
n
o
f
t
h
e
P
SIM
s
o
f
t
w
ar
e.
Seco
n
d
l
y
,
t
h
e
y
w
il
l
b
e
u
s
ed
f
o
r
th
e
g
en
er
atio
n
o
f
th
e
p
r
o
g
r
a
m
t
h
at
w
ill b
e
e
m
b
e
d
d
ed
in
th
e
ST
M3
2
F4
0
7
m
icr
o
co
n
tr
o
ller
f
o
r
ex
p
er
i
m
en
tal
v
alid
atio
n
.
3
.
1
.
F
uzzy
lo
g
ic
co
ntr
o
l
ler
des
ig
n
Def
i
n
i
n
g
i
n
p
u
t
an
d
o
u
tp
u
t
v
ar
iab
les,
an
d
co
n
tr
o
ller
f
u
n
ctio
n
s
is
o
n
e
o
f
t
h
e
m
o
s
t
i
m
p
o
r
ta
n
t
s
tep
s
i
n
th
e
f
u
zz
y
lo
g
ic
d
esi
g
n
p
r
o
ce
s
s
.
I
n
th
i
s
s
t
u
d
y
,
th
e
s
e
lectio
n
o
f
m
e
m
b
er
s
a
n
d
th
e
n
u
m
b
er
o
f
r
u
les
h
ad
to
b
e
m
i
n
i
m
ized
.
B
lu
r
r
ed
af
f
iliat
io
n
s
an
d
r
u
l
es
m
u
s
t a
ct
q
u
ick
l
y
to
s
p
ee
d
u
p
o
r
m
o
v
e
b
ac
k
w
ar
d
s
th
e
d
-
q
a
x
i
s
u
n
t
il i
t
r
ea
ch
es
s
y
n
ch
r
o
n
izatio
n
s
p
ee
d
an
d
p
o
s
itio
n
,
th
e
n
lo
c
k
th
e
a
x
is
to
it
s
co
r
r
ec
t
s
y
n
ch
r
o
n
izatio
n
s
tate.
T
h
is
r
eq
u
ir
es
m
o
r
e
atten
t
io
n
t
o
th
e
d
esig
n
o
f
ex
it r
u
le
s
[1
-
2]
.
T
h
e
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
is
d
esig
n
ed
w
it
h
t
w
o
v
ar
iab
les
(
q
u
ad
r
atu
r
e
co
m
p
o
n
e
n
t
o
f
P
ar
k
an
d
its
er
r
o
r
t
o
a
r
ef
er
en
ce
v
alu
e)
d
ef
in
ed
as
in
p
u
t
v
ar
iab
les.
T
h
ese
t
w
o
in
p
u
t
v
ar
iab
les
h
av
e
f
iv
e
tr
ia
n
g
le
m
e
m
b
er
s
h
ip
f
u
n
ct
io
n
s
f
o
r
e
ac
h
o
f
th
e
m
.
T
h
e
li
n
g
u
i
s
tic
v
ar
iab
les
"
p
o
s
itiv
e
lar
g
e
(
P
L
)
"
,
"p
o
s
itiv
e
s
m
all
(
P
S)
"
,
"
ze
r
o
(
Z
)
"
,
"
n
eg
ativ
e
s
m
all
(
N
S)"
,
"
n
eg
ati
v
e
lar
g
e
(
NL
)
"
f
o
r
t
w
o
i
n
p
u
t
v
ar
iab
le
s
ar
e
u
s
ed
to
ex
p
r
es
s
th
e
f
u
zz
y
v
ar
iab
le
s
.
T
h
u
s
t
h
e
c
o
n
tr
o
l a
ctio
n
is
d
ef
u
zz
i
f
ied
i
n
a
u
n
it r
a
n
g
e
al
s
o
w
it
h
f
i
v
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
d
ef
in
ed
as
o
u
tp
u
t
v
ar
iab
le
o
f
f
u
zz
y
lo
g
ic
to
ex
p
r
ess
t
h
e
v
a
lu
e
s
o
f
f
r
eq
u
e
n
c
y
co
r
r
ec
tio
n
[
1
,
26
-
28
].
T
h
e
d
etailed
d
esig
n
o
f
t
h
e
f
u
z
z
y
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
i
s
i
l
lu
s
tr
ated
in
Fi
g
u
r
e
5
.
E
s
tab
li
s
h
ed
o
n
th
e
b
asi
s
o
f
in
f
o
r
m
atio
n
ab
o
u
t
t
h
e
s
y
s
te
m
an
d
h
o
w
it
w
o
r
k
s
,
d
ep
en
d
i
n
g
o
n
er
r
o
r
v
ar
iatio
n
s
f
o
r
a
r
ap
id
tr
an
s
ie
n
t
r
esp
o
n
s
e.
T
h
e
f
u
zz
y
lo
g
ic
r
u
le
b
ase
s
f
o
r
o
u
tp
u
t v
ar
iab
le
s
ar
e
s
h
o
w
n
in
T
ab
le
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
4
,
A
u
g
u
s
t 2
0
1
9
:
2
2
6
4
-
2273
2268
(
a)
(
b
)
(
c)
Fig
u
r
e
5
.
(
a)
Vq
m
e
m
b
er
s
h
ip
,
(
b
)
E
r
r
o
r
m
e
m
b
er
s
h
ip
,
(
c)
Ou
t
p
u
t
m
e
m
b
er
s
h
ip
T
ab
le
1
.
B
asic r
u
le
f
o
r
o
u
tp
u
t
v
ar
ia
b
le
Err
Vr
PL
PS
Z
NZ
NL
PL
L
L
M
S
S
PS
L
M
M
M
S
Z
M
M
M
M
M
NS
S
S
M
L
L
NL
S
M
M
L
L
3
.
2
.
Dis
cr
et
iza
t
io
n o
f
t
he
t
w
o
m
et
ho
ds
a.
Meth
o
d
S
OGI
w
ith
P
I
/*
E
s
tim
atio
n
o
f
u
v
alu
e with
th
e
SOG
I
*
/
s
o
g
i_
u
[
n
]
=
(
b
0
*
(
u
[
n
]
-
u
[
n
-
2
]
)
)
+
(
a1
*
s
o
g
i_
u
[
n
-
1
]
)
+
(
a2
*
s
o
g
i_
u
[
n
-
2]
);
/*
Up
d
ate o
f
u
*
/
s
o
g
i_
u
[
n
-
2
]
=
s
o
g
i_
u
[
n
-
1
]
;
s
o
g
i_
u
[
n
-
1
]
=
s
o
g
i_
u
[
n
]
;
/*
E
s
tim
atio
n
o
f
u
v
alu
e with
th
e
SOG
I
*/
s
o
g
i_
q
u
[
n
]
=
(
q
b
0
*
u
[
n
]
)
+
(
b
1
*
u
[
n
-
1
]
)
+
(
q
b
2
*
u
[
n
-
2
]
)
+
(
a1
*
s
o
g
i
_
q
u
[
n
-
1
]
)
+
(
a2
*
s
o
g
i_
q
u
[
n
-
2
]
)
/*
Up
d
ate o
f
q
u
*
/
s
o
g
i_
q
u
[
n
-
2
]
=
s
o
g
i_
q
u
[
n
-
1
]
;
s
o
g
i_
q
u
[
n
-
1
]
=
s
o
g
i_
q
u
[
n
]
;
/*
u
p
d
ate o
f
g
r
id
v
o
ltag
e*
/
u
[
n
-
2
]
=
u
[
n
-
1
]
;
u
[
n
-
1
]
=
u
[
n
]
;
/*
Par
k
T
r
an
s
f
o
r
m
f
r
o
m
alp
h
a b
e
ta t
o
d
-
q
ax
is
*
/
u
_
Q[
n
]
=
(
co
s
*
s
o
g
i_
u
[
n
]
)
+
(
s
in
*
s
o
g
i_
q
u
[
n
]
)
;
u
_
D[
n
]
=
(
co
s
*
s
o
g
i_
q
u
[
n
]
)
-
(
s
in
*
s
o
g
i_
u
[
n
]
)
;
/*
P
I
p
r
o
cess
*
/
/*
E
r
r
o
r
u
p
d
ate*
/
E
r
r
o
r
=
u
_
Q[
n
]
-
u
_
Qr
ef
;
/*
p
r
o
p
o
r
tio
n
al t
er
m
*
/
u
p
=
v
.
K
p
*
E
r
r
o
r
;
/*
in
teg
r
al t
er
m
*
/
u
i
=
(
v
.
K
i
*
u
p
)
+
i1
;
i1
=
u
i;
/*
s
u
m
o
f
i
n
teg
r
al an
d
p
r
o
p
o
r
tio
n
al t
er
m
*
/
PI
_
f
[
n
]
=
u
p
+
u
i;
/*
E
s
tim
atio
n
o
f
o
u
tp
u
t
f
r
eq
u
e
n
c
y
*
/
f
o
=
f
n
+
PI
_
f
[
n
]
;
/*
Up
d
ate o
f
Uq
v
alu
e o
f
Par
k
co
m
p
o
n
en
t
*
/
u
_
Q[
n
-
1
]
=
u
_
Q[
n
]
;
/*
F
r
eq
u
en
c
y
in
teg
r
atio
n
to
o
b
tai
n
th
e
p
h
ase
an
g
le*
/
th
eta[
n
]
=
t
h
eta[
n
-
1
]
+
(
2
.
0
*
π*
tim
estep
*
f
o
)
;
/*
R
e
-
in
itializatio
n
o
f
p
h
ase
a
n
g
le o
v
er
2
p
i*
/
if
(
th
eta[
n
]
>
(
2
π))
th
eta[
n
]
=
0
.
;
/*
Up
d
ate o
f
p
h
ase
an
g
le*
/
T
h
eta[
n
-
1
]
=
th
eta
[
n
]
;
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
n
ew S
OGI
-
P
LL
meth
o
d
b
a
s
ed
o
n
f
u
z
z
y
lo
g
ic
fo
r
g
r
id
co
n
n
ec
ted
P
V
in
ve
r
ter
(
A
b
d
elh
a
d
i
B
o
u
kn
a
d
el
)
2269
b.
Meth
o
d
S
OGI
w
ith
fu
z
z
y
lo
g
ic
// E
s
ti
m
atio
n
o
f
u
v
alu
e
w
i
th
t
h
e
SOGI
//
s
o
g
i_
u
[
n
]
=(
b
0
*
(
u
[
n
]
-
u
[
n
-
2
]
)
)
+
(
a1
*
s
o
g
i_
u
[
n
-
1
]
)
+
(
a2
*
s
o
g
i
_
u
[
n
-
2
]
)
;
// u
p
d
at
o
f
u
//
s
o
g
i_
u
[
n
-
2
]
=so
g
i_
u
[
n
-
1
]
;
s
o
g
i_
u
[
n
-
1
]
=so
g
i_
u
[
n
]
;
// E
s
ti
m
atio
n
o
f
u
v
alu
e
w
i
th
t
h
e
SOGI
//
s
o
g
i_
q
u
[
n
]
=(
q
b
0
*
u
[
n
]
)
+
(
b
1
*
u
[
n
-
1
]
)
+
(
q
b
2
*
u
[
n
-
2
]
)
+
(
a1
*
s
o
g
i_
q
u
[
n
-
1
]
)
+
(
a2
*
s
o
g
i_
q
u
[
n
-
2
]
)
//
u
p
d
ate
o
f
q
u
//
s
o
g
i_
q
u
[
n
-
2
]
=so
g
i_
q
u
[
n
-
1
]
;
s
o
g
i_
q
u
[
n
-
1
]
=so
g
i_
q
u
[
n
]
;
// u
p
d
ate
o
f
g
r
id
v
o
lta
g
e
//
u
[
n
-
2
]
=u
[
n
-
1
]
;
u
[
n
-
1
]
=u
[
n
]
;
// P
ar
k
T
r
an
s
f
o
r
m
f
r
o
m
alp
h
a
b
eta
to
d
-
q
ax
is
//
u
_
Q[
n
]
=(
co
s
*
s
o
g
i_
u
[
n
]
)
+
(
s
in
*
s
o
g
i_
q
u
[
n
]
)
;
u
_
D[
n
]
=(
co
s
*
s
o
g
i_
q
u
[
n
]
)
-
(
s
i
n
*
s
o
g
i_
u
[
n
]
)
;
// Fu
zz
y
p
r
o
ce
s
s
//
// E
r
r
o
r
u
p
d
ate
//
E
r
r
o
r
=u
_
Q[
n
]
-
u
_
Qr
ef
;
// Fu
zz
i
f
icatio
n
o
f
t
h
e
q
ax
is
i
n
p
u
t v
o
lta
g
e//
Fu
zz
i
f
icatio
n
(
u
_
Q[
0
]
,
X1
,
X1
_
ab
cs);
// Fu
zz
i
f
icatio
n
o
f
t
h
e
q
ax
is
er
r
o
r
//
Fu
zz
i
f
icatio
n
(
E
r
r
o
r
,
X2
,
X2
_
ab
cs);
// A
p
p
licatio
n
o
f
b
asic r
u
le
s
b
et
w
ee
n
u
q
a
n
d
E
r
r
o
r
to
h
av
e
f
u
zz
i
f
ied
th
e
co
r
r
ec
tio
n
f
r
eq
u
e
n
c
y
/
/
Fu
zz
y
I
n
f
er
en
ce
(
X1
,
X2
,
Y)
;
//Def
u
zz
i
f
icatio
n
o
f
th
e
f
r
eq
u
e
n
c
y
co
r
r
ec
tio
n
//
Fu
zz
y
_
f
[
n
]
=D
if
u
zz
i
f
icatio
n
(
Y
,
Ou
tp
u
t
Fu
n
c)
;
// A
p
p
licatio
n
o
f
t
h
e
f
r
eq
u
e
n
c
y
co
r
r
ec
tio
n
//
f
o
=f
n
o
m
+
Fu
zz
y
_
f
[
n
]
;
// Up
d
ate
o
f
U
q
v
alu
e
o
f
P
ar
k
co
m
p
o
n
e
n
t //
u
_
Q[
n
-
1
]
=u
_
Q[
n
]
;
// Fr
eq
u
en
c
y
i
n
teg
r
atio
n
to
o
b
tain
e
th
e
p
h
ase
a
n
g
le
//
th
eta[
n
]
=t
h
eta[
n
-
1
]
+
(
2
.
0
*
π
*
t
i
m
es
tep
*
f
o
)
;
// R
e
-
in
i
tializatio
n
o
f
p
h
a
s
e
an
g
le
o
v
er
2
p
i //
if
(
th
e
ta[
n
]
>(
2
π)
)
th
eta[
n
]
=0
.
;
// Up
d
ate
o
f
p
h
ase
an
g
le//
th
eta
[n
-
1
]
=th
eta[
n
]
;
3
.
3
.
Si
m
ula
t
io
n
re
s
ults
I
n
th
is
s
ec
tio
n
,
w
e
p
r
esen
t
th
e
s
i
m
u
la
tio
n
r
es
u
lt
s
u
n
d
er
t
h
e
P
SIM
s
o
f
t
w
ar
e,
th
e
F
i
g
u
r
e
6
,
r
ep
r
esen
ts
th
e
t
w
o
b
lo
ck
s
u
s
ed
i
n
t
h
e
s
i
m
u
latio
n
,
a
C
b
lo
ck
t
h
at
g
en
er
at
es a
s
i
n
u
s
o
id
al
s
i
g
n
al
co
n
tr
o
ll
ed
in
f
r
eq
u
e
n
c
y
an
d
a
m
p
lit
u
d
e
to
s
i
m
u
late
t
h
e
d
is
t
u
r
b
an
ce
s
o
f
t
h
e
g
r
id
,
an
d
a
D
L
L
b
lo
ck
th
at
co
n
tai
n
s
th
e
f
u
n
ctio
n
s
SO
GI
,
P
ar
k
,
f
u
zz
y
lo
g
ic
an
d
VC
O
f
o
r
th
e
e
s
ti
m
atio
n
o
f
t
h
e
p
h
a
s
e
an
g
le
o
f
th
e
g
r
id
.
T
h
e
F
ig
u
r
e
7
s
h
o
w
s
t
h
e
r
esu
lt
s
o
f
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
w
it
h
d
if
f
er
en
t
v
ar
iat
io
n
s
(
a
m
p
lit
u
d
e
v
ar
iatio
n
,
f
r
eq
u
e
n
c
y
a
n
d
p
h
a
s
e
s
h
if
t)
.
Fig
u
r
e
7
s
h
o
w
s
t
h
a
t
th
e
p
r
o
p
o
s
ed
g
en
er
alize
d
in
teg
r
atio
n
s
tr
u
ct
u
r
e
(
SOGI
)
o
f
s
ec
o
n
d
o
r
d
er
co
n
tr
o
lled
b
y
f
u
zz
y
lo
g
ic,
h
as
a
v
er
y
g
o
o
d
b
eh
av
io
r
ag
ai
n
s
t
t
h
i
s
v
ar
iatio
n
d
esp
it
e
tr
an
s
ie
n
t
o
s
cil
latio
n
s
(
Am
p
li
t
u
d
e
v
a
r
iatio
n
as
s
h
o
w
n
i
n
Fi
g
u
r
e
7
-
a,
Am
p
li
tu
d
e
a
n
d
f
r
eq
u
en
c
y
v
ar
iatio
n
a
s
s
h
o
w
n
in
Fi
g
u
r
e
7
-
b
,
Fre
q
u
en
c
y
v
ar
iat
io
n
a
n
d
p
h
ase
j
u
m
p
a
s
s
h
o
w
n
i
n
F
ig
u
r
e
7
-
c
.
T
h
er
ef
o
r
e,
th
e
r
esp
o
n
s
e
o
f
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
is
v
er
y
ef
f
icie
n
t
a
n
d
ac
cu
r
ate,
a
n
d
th
is
ca
n
b
e
s
ee
n
b
y
co
m
p
a
r
in
g
t
h
e
g
en
er
ate
d
s
in
u
s
o
id
al
s
i
g
n
al
w
it
h
t
h
e
e
s
ti
m
ated
p
h
a
s
e
a
n
g
le
an
d
th
e
s
i
g
n
al
t
h
at
s
i
m
u
late
s
t
h
e
g
r
id
,
t
h
e
lo
ck
in
g
t
i
m
e
o
f
th
e
P
h
ase
a
n
g
le
i
s
v
er
y
f
a
s
t (
le
s
s
t
h
an
o
n
e
p
er
io
d
o
f
th
e
g
r
id
s
ig
n
al)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
4
,
A
u
g
u
s
t 2
0
1
9
:
2
2
6
4
-
2273
2270
Fig
u
r
e
6
.
Si
m
u
latio
n
s
tr
u
c
tu
r
e
(
a
)
(
b
)
(c
)
Fig
u
r
e
7
.
R
esu
lts
o
f
t
h
e
s
i
m
u
la
tio
n
,
(
a)
Am
p
l
itu
d
e
v
ar
iatio
n
,
(
b
)
Am
p
lit
u
d
e
an
d
f
r
eq
u
e
n
c
y
v
ar
iatio
n
,
(
c)
Fre
q
u
en
c
y
v
ar
iatio
n
a
n
d
p
h
ase
j
u
m
p
3
.
4
.
E
x
peri
m
e
nta
l r
esu
lt
T
h
e
p
r
o
p
o
s
ed
n
e
w
lo
g
ic
(
SO
GI
-
F
u
zz
y
)
is
v
er
i
f
ied
an
d
e
v
alu
ated
b
y
a
n
e
x
p
er
i
m
e
n
tal
t
est,
u
s
i
n
g
a
d
if
f
er
en
tia
l
v
o
ltag
e
lev
e
l
s
h
i
f
t
cir
c
u
it
to
s
a
m
p
le
t
h
e
n
et
w
o
r
k
v
o
lta
g
e
w
i
th
t
h
e
C
A
N
o
f
t
h
e
ST
M3
2
F4
-
d
is
co
v
er
y
ev
a
lu
at
io
n
b
o
ar
d
,
to
ev
alu
ate
t
h
e
ac
c
u
r
ac
y
o
f
S
O
GI
-
f
u
zz
y
lo
g
ic,
w
e
v
is
u
alize
u
s
in
g
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lts
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h
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8708
I
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&
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2273
2272
4.
CO
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6
k
VA
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v
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ter
s
.
RE
F
E
R
E
NC
E
S
[1
]
Ik
k
e
n
N.,
Bo
u
k
n
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d
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l
A
.
,
Ha
d
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A
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,
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y
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im
p
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tatio
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p
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tec
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iq
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s f
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g
rid
-
c
o
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n
e
c
ted
in
v
e
rters
s
y
ste
m
s
,"
J
o
u
rn
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l
o
f
El
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c
tr
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S
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ste
ms
,
v
o
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1
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,
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o
4
,
2
0
1
8
.
[2
]
Ik
k
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n
N.,
Bo
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k
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A
.
,
El
O
m
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p
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f
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ic co
n
tro
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r
g
rid
c
o
n
n
e
c
ted
in
v
e
rters
,"
In
:
Re
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wa
b
le
a
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d
S
u
sta
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a
b
le
E
n
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rg
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Co
n
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c
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(
IRS
EC)
,
2
0
1
6
I
n
ter
n
a
ti
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a
l.
I
EE
E
,
p
p
.
1
1
1
1
-
1
1
1
7
,
2
0
1
6
.
[3
]
Ja
a
la
m
N
.
,
Ra
h
im
N.,
Ba
k
a
r
A
.
,
e
t
a
l.
,
"
A
c
o
m
p
re
h
e
n
siv
e
re
v
ie
w
o
f
s
y
n
c
h
ro
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m
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th
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s
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te
d
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o
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v
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r
ters
o
f
re
n
e
w
a
b
le en
e
rg
y
s
o
u
rc
e
,
"
Ren
e
w.
S
u
sta
in
.
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9
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1
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,
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T
h
e
sis
su
b
m
it
ted
f
o
r
e
x
a
m
in
a
ti
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n
f
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re
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ste
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o
f
S
c
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n
c
e
in
T
e
c
h
n
o
lo
g
y
,
A
a
lt
o
u
n
iv
e
rsity
,
2014.
Evaluation Warning : The document was created with Spire.PDF for Python.
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[2
3
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[2
4
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K
jae
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.
[2
5
]
B
h
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o
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x
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s In
stru
me
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.
[2
6
]
H
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ter
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7
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"
Dig
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x
a
s In
stru
me
n
ts
,
2
0
1
3
.
[2
8
]
C
io
b
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taru
M
i
h
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m
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n
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w
sin
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p
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LL
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fer
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p
p
.
1
-
6
,
2
0
0
6
.
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