I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
w
er
E
lect
ro
nics
a
nd
Driv
e
Sy
s
t
e
m
(
I
J
P
E
DS
)
Vo
l.
7
,
No
.
4
,
Dec
em
b
er
2
0
1
6
,
p
p
.
120
0
~
1
2
1
1
I
SS
N:
2
0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
p
ed
s
.
v7
i
4
.
pp
1
2
0
0
-
1211
1200
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
jo
u
r
n
a
l.c
o
m/o
n
lin
e/in
d
ex
.
p
h
p
/I
JP
E
DS
A Nov
el App
ro
a
ch t
o
G
SA,
GA
a
n
d Wav
elet
Tra
ns
f
o
r
m
to
De
sig
n F
u
zz
y
Lo
g
ic Contro
ller
f
o
r
1
ϕ
M
ultilevel Inv
erte
r
V
a
rsh
a
Sin
g
h,
S.
G
u
pta
,
S.
P
a
t
t
na
ik
,
Aa
rt
i G
o
y
a
l
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
,
Na
ti
o
n
a
l
In
stit
u
te
o
f
T
e
c
h
n
o
lo
g
y
,
G
.
E.
Ro
a
d
,
Ra
ip
u
r
,
I
n
d
ia
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
A
p
r
3
,
2
0
1
6
R
ev
i
s
ed
No
v
8
,
2
0
1
6
A
cc
ep
ted
No
v
20
,
2
0
1
6
T
h
is
p
a
p
e
r
p
r
o
p
o
se
s
a
n
o
v
e
l
a
p
p
ro
a
c
h
f
o
r
o
b
tai
n
in
g
a
c
lo
se
d
lo
o
p
c
o
n
tr
o
l
sc
h
e
m
e
b
a
se
d
o
n
F
u
z
z
y
L
o
g
ic
Co
n
tr
o
ll
e
r
to
re
g
u
late
th
e
o
u
t
p
u
t
v
o
lt
a
g
e
w
a
v
e
f
o
r
m
o
f
m
u
lt
il
e
v
e
l
in
v
e
rter.
F
u
z
z
y
L
o
g
ic
Co
n
tro
ll
e
r
is
u
se
d
t
o
g
u
id
e
a
n
d
c
o
n
tro
l
th
e
in
v
e
rter
to
sy
n
th
e
siz
e
a
ste
p
p
e
d
o
u
t
p
u
t
v
o
lt
a
g
e
w
a
v
e
f
o
r
m
w
it
h
re
d
u
c
e
d
h
a
rm
o
n
ics
.
In
t
h
is
p
a
p
e
r,
th
re
e
d
if
f
e
r
e
n
t
in
telli
g
e
n
t
so
f
t
-
c
o
m
p
u
ti
n
g
m
e
th
o
d
s are
u
se
d
to
d
e
sig
n
a
f
u
z
z
y
s
y
st
e
m
to
b
e
u
se
d
a
s a c
lo
se
d
lo
o
p
c
o
n
tro
l
s
y
ste
m
f
o
r
re
g
u
latin
g
th
e
i
n
v
e
rter
o
u
t
p
u
t
.
G
ra
v
it
a
ti
o
n
a
l
S
e
a
rc
h
A
l
g
o
rit
h
m
a
n
d
G
e
n
e
ti
c
A
l
g
o
rit
h
m
a
re
u
s
e
d
a
s
o
p
ti
m
iz
a
ti
o
n
m
e
th
o
d
s
to
e
v
a
lu
a
te
sw
it
c
h
in
g
a
n
g
les
f
o
r
d
iff
e
re
n
t
c
o
m
b
in
a
ti
o
n
o
f
in
p
u
t
v
o
lt
a
g
e
s
a
p
p
li
e
d
to
M
L
I.
W
a
v
e
let
T
ra
n
sf
o
r
m
is
u
se
d
a
s
s
y
n
th
e
siz
in
g
tec
h
n
i
q
u
e
t
o
sh
a
p
e
ste
p
p
e
d
o
u
tp
u
t
w
a
v
e
f
o
r
m
o
f
in
v
e
rter
u
si
n
g
o
rth
o
g
o
n
a
l
w
a
v
e
let
se
ts.
T
h
e
p
ro
p
o
se
d
F
L
C
c
o
n
tro
ll
e
d
m
e
th
o
d
is
c
a
rried
o
u
t
f
o
r
a
w
id
e
r
ra
n
g
e
o
f
in
p
u
t
d
c
v
o
lt
a
g
e
s
b
y
c
o
n
sid
e
ri
n
g
±1
0
%
v
a
riatio
n
s
i
n
n
o
m
in
a
l
v
o
lt
a
g
e
v
a
lu
e
.
A
7
-
lev
e
l
in
v
e
rter
is
u
se
d
to
v
a
li
d
a
te
th
e
re
su
lt
s
o
f
p
ro
p
o
se
d
c
o
n
tr
o
l
m
e
th
o
d
s.
T
h
e
th
re
e
p
ro
p
o
se
d
m
e
th
o
d
s
a
re
th
e
n
c
o
m
p
a
re
d
in
term
s
o
f
v
a
rio
u
s
p
a
ra
m
e
ters
li
k
e
c
o
m
p
u
tatio
n
a
l
t
im
e
,
s
w
it
c
h
in
g
a
n
g
les
a
n
d
T
HD
to
ju
stif
y
th
e
p
e
rf
o
r
m
a
n
c
e
a
n
d
sy
ste
m
f
lex
ib
il
it
y
.
F
in
a
ll
y
,
h
a
rd
w
a
re
b
a
se
d
re
su
lt
s
a
re
a
lso
o
b
tain
e
d
to
v
e
ri
fy
th
e
v
iab
il
it
y
o
f
th
e
p
ro
p
o
se
d
m
e
th
o
d
.
K
ey
w
o
r
d
:
Fu
zz
y
lo
g
ic
co
n
tr
o
ller
Gr
av
itatio
n
al
s
ea
r
ch
al
g
o
r
ith
m
g
en
et
ic
a
g
o
r
it
h
m
Mu
ltil
e
v
el
i
n
v
er
ter
Selectiv
e
h
ar
m
o
n
ics
el
i
m
in
at
i
o
n
W
av
elet
tr
an
s
f
o
r
m
Co
p
y
rig
h
t
©
201
6
In
s
t
it
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts
re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Var
s
h
a
Si
n
g
h
Dep
ar
t
m
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
,
Natio
n
al
I
n
s
tit
u
te
o
f
T
ec
h
n
o
lo
g
y
,
R
aip
u
r
,
G.
E
.
R
o
ad
,
P
in
4
9
2
0
1
0
,
I
n
d
ia.
E
m
ail:
v
s
i
n
g
h
.
ele
@
n
itrr
.
ac
.
in
,
v
ar
s
h
a_
x
_
s
i
n
g
h
@
y
ah
o
o
.
co
m
1.
I
NT
RO
D
UCT
I
O
N
I
n
r
ec
en
t
y
ea
r
s
,
i
n
ter
est
i
n
p
o
w
er
elec
tr
o
n
ic
h
a
s
s
u
r
g
ed
d
u
e
to
in
cr
ea
s
e
i
n
d
ep
lo
y
m
en
t
o
f
elec
tr
ical
an
d
elec
tr
o
n
ic
eq
u
ip
m
en
t
i
n
i
n
d
u
s
tr
ial,
co
m
m
er
cial
as
w
ell
as
r
es
id
en
tial
ap
p
licatio
n
s
.
T
h
e
g
r
o
w
in
g
d
e
m
an
d
h
as
ac
ce
ler
ated
th
e
p
ac
e
o
f
d
ev
elo
p
m
e
n
t
i
n
m
o
d
u
latio
n
tech
n
iq
u
e
s
a
n
d
p
o
w
er
co
n
v
er
s
io
n
to
p
o
lo
g
ies
(
esp
ec
iall
y
i
n
m
u
lt
ilev
e
l
in
v
e
r
ter
s
)
.
I
n
a
tr
ad
itio
n
al
m
u
ltil
e
v
el
i
n
v
er
ter
‗
n
‘
s
ep
ar
ate
d
c
s
o
u
r
ce
s
ar
e
u
s
ed
to
p
r
o
d
u
ce
(
2
n
-
1
)
lev
els
at
t
h
e
o
u
tp
u
t
w
a
v
e
f
o
r
m
,
b
y
e
m
p
lo
y
i
n
g
p
o
w
er
s
w
i
tch
e
s
an
d
s
w
i
tch
i
n
g
t
h
e
m
s
u
c
h
th
at
th
e
s
tep
o
r
s
tair
ca
s
e
o
u
tp
u
t
is
as
cl
o
s
e
to
a
s
in
e
w
a
v
e
as
p
o
s
s
ib
le
[
1
]
-
[
2
]
.
T
h
e
d
c
s
o
u
r
ce
ca
n
b
e
a
b
atter
y
,
f
u
el
ce
lls
,
p
h
o
to
v
o
ltaic
ce
lls
o
r
a
r
ec
tif
ied
o
u
tp
u
t
o
f
a
w
i
n
d
t
u
r
b
in
e
[
3
]
.
ML
I
i
s
g
r
ad
u
all
y
g
a
in
i
n
g
w
id
e
ac
ce
p
tan
c
e
in
h
i
g
h
p
o
w
er
ap
p
licatio
n
s
,
es
p
ec
iall
y
i
n
in
d
u
s
tr
ia
l
u
s
e
lik
e
AC
m
o
to
r
d
r
iv
es,
elec
tr
ic
v
e
h
i
cle
d
r
iv
e
a
n
d
s
tatic
VAR
co
m
p
en
s
ato
r
s
o
w
in
g
to
its
ad
v
an
ta
g
es
o
f
o
f
f
er
i
n
g
l
o
w
er
s
w
itc
h
i
n
g
lo
s
s
es,
h
ig
h
e
r
ef
f
icie
n
c
y
,
b
etter
elec
tr
o
m
ag
n
etic
co
m
p
atib
il
it
y
,
s
m
aller
co
m
m
o
n
m
o
d
e
v
o
lt
ag
e
an
d
L
ess
T
o
tal
Har
m
o
n
i
c
Dis
to
r
ti
o
n
(
T
HD
)
o
v
er
th
e
u
s
u
al
t
w
o
lev
el
i
n
v
er
ter
[
4
]
-
[
6
]
.
W
h
ile
d
esig
n
i
n
g
an
in
v
er
ter
,
s
tr
ess
i
s
g
i
v
e
n
o
n
eli
m
i
n
atio
n
o
f
h
ar
m
o
n
ics
f
r
o
m
o
u
tp
u
t
v
o
lta
g
e
o
f
M
L
I
in
v
er
ter
s
o
th
a
t
T
HD
ca
n
b
e
r
ed
u
ce
d
as
s
p
ec
i
f
ied
b
y
Du
f
f
e
y
et
al
[
7
]
.
I
n
d
esig
n
i
n
g
M
L
I
i
m
p
o
r
ta
n
ce
is
g
i
v
en
to
r
estrict
t
h
e
n
o
o
f
s
w
itc
h
es
an
d
d
c
s
o
u
r
ce
s
to
m
i
n
i
m
u
m
t
h
is
ca
n
b
e
ac
h
iev
ed
b
y
t
h
e
u
s
e
o
f
h
y
b
r
id
to
p
o
lo
g
y
a
n
d
ad
v
an
ce
d
h
ar
d
war
e
im
p
le
m
e
n
tatio
n
tech
n
iq
u
e
s
lik
e,
d
ig
ita
l
s
i
g
n
al
co
n
tr
o
ller
,
FP
GA
[
8
]
-
[
9
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
7
,
No
.
4
,
Dec
em
b
er
2
0
1
6
:
120
0
–
1
2
1
1
1201
Mo
d
u
latio
n
tec
h
n
iq
u
es
p
la
y
a
n
i
m
p
o
r
ta
n
t
r
o
le
in
th
e
o
p
er
ati
o
n
o
f
M
L
I
,
th
e
p
r
i
m
e
ai
m
o
f
m
o
d
u
latio
n
tech
n
iq
u
es
is
m
in
i
m
izat
io
n
o
f
T
HD,
d
if
f
er
en
t
to
p
o
lo
g
ies
m
ig
h
t
u
s
e
o
n
e
o
f
th
e
m
o
d
u
lati
o
n
tech
n
iq
u
es
t
h
at
s
u
it
s
b
est.
Fro
m
a
g
a
m
u
t
o
f
av
ailab
le
m
o
d
u
latio
n
tec
h
n
iq
u
es
,
Selectiv
e
Har
m
o
n
ic
E
li
m
i
n
at
io
n
(
SHE
)
m
et
h
o
d
is
co
m
m
o
n
l
y
u
s
ed
to
m
i
n
i
m
iz
e
T
HD
b
y
eli
m
i
n
atin
g
s
o
m
e
p
er
-
s
elec
ted
h
ar
m
o
n
ics
i
n
o
u
t
p
u
t
w
a
v
ef
o
r
m
[
1
0
]
.
T
h
e
m
ain
ch
a
llen
g
e
w
it
h
S
HE
tech
n
iq
u
e
is
to
s
o
l
v
e
n
o
n
-
lin
ea
r
tr
an
s
ce
n
d
en
tal
eq
u
at
io
n
s
r
es
u
lt
in
g
f
r
o
m
Fo
u
r
ier
s
er
ies
ex
p
an
s
io
n
o
f
o
u
tp
u
t
h
alf
w
a
v
e
s
y
m
m
etr
ical
w
av
e
f
o
r
m
.
P
r
io
r
to
th
e
ad
v
e
n
t
o
f
o
p
ti
m
izatio
n
m
et
h
o
d
s
,
R
es
u
lta
n
t
t
h
eo
r
y
an
d
w
als
h
f
u
n
ctio
n
s
w
er
e
w
id
el
y
ac
ce
p
ted
m
et
h
o
d
s
f
o
r
s
o
lv
i
n
g
t
h
e
s
e
eq
u
atio
n
s
,
esp
ec
iall
y
w
al
s
h
f
u
n
ctio
n
w
a
s
u
s
ed
to
s
o
lv
e
lin
ea
r
eq
u
at
io
n
s
[
1
1
]
-
[
1
2
]
.
T
h
e
s
tr
ateg
y
to
r
ed
u
ce
p
r
eselecte
d
h
ar
m
o
n
ic
co
n
te
n
t
u
s
in
g
S
HE
tech
n
iq
u
e
i
n
v
o
lv
e
s
o
p
ti
m
iza
tio
n
m
eth
o
d
to
ca
lc
u
late
t
h
e
ac
cu
r
ate
s
w
i
tch
i
n
g
an
g
le
s
i
n
co
m
p
lex
to
p
o
lo
g
y
,
t
h
is
i
s
d
o
n
e
b
y
u
s
in
g
Fo
u
r
ier
s
e
r
ies f
o
r
a
s
tep
p
ed
in
v
er
ter
w
av
e
f
o
r
m
.
C
o
m
m
o
n
l
y
u
s
ed
o
p
ti
m
izati
o
n
tech
n
iq
u
es
ar
e
g
e
n
etic
alg
o
r
ith
m
(
G
A
)
a
n
d
P
ar
t
icl
e
s
w
ar
m
o
p
tim
izatio
n
(
P
SO)
[
1
3
]
-
[
1
4
]
.
GA
is
b
ased
o
n
t
h
e
co
n
ce
p
t
o
f
n
at
u
r
al
s
elec
tio
n
a
n
d
u
s
es
g
e
n
etic
o
p
er
ato
r
s
li
k
e
r
ep
r
o
d
u
ctio
n
,
cr
o
s
s
o
v
er
an
d
m
u
tatio
n
an
d
P
SO
i
s
[
R
u
s
s
ell
E
b
er
h
ar
t
et.
al
(
1
9
9
5
)
]
in
s
p
ir
ed
b
y
s
o
cial
b
eh
a
v
io
r
o
f
b
ir
d
s
f
lo
ck
i
n
g
o
r
f
is
h
s
ch
o
o
lin
g
h
a
s
p
r
o
v
e
n
to
b
e
v
er
y
f
ast
a
n
d
ef
f
ec
ti
v
e
w
h
e
n
ap
p
lie
d
to
a
d
iv
er
s
e
s
et
o
f
o
p
tim
izatio
n
p
r
o
b
le
m
.
R
ese
ar
ch
es
ar
e
also
w
o
r
k
i
n
g
o
n
s
o
m
e
n
e
w
o
p
ti
m
izatio
n
tech
n
iq
u
es
s
u
c
h
as
ev
o
lu
tio
n
ar
y
al
g
o
r
ith
m
,
Di
f
f
er
en
tial
E
v
o
lu
tio
n
A
l
g
o
r
ith
m
(
DE
)
an
d
an
all
n
e
w
o
p
ti
m
izat
io
n
th
eo
r
y
b
ased
o
n
Min
o
r
it
y
C
h
ar
g
e
C
ar
r
ier
(
M
C
I
)
to
g
en
er
ate
o
p
tim
al
s
w
i
tch
i
n
g
a
n
g
le
s
in
M
L
I
[
1
5
]
-
[
1
7
]
.
T
h
ese
all
ar
e
o
p
tim
izatio
n
tech
n
iq
u
e
s
ar
e
p
r
o
d
u
cin
g
e
n
co
u
r
a
g
in
g
r
e
s
u
l
t
s
w
h
en
ap
p
lied
to
t
h
e
p
r
o
b
lem
s
at
h
an
d
.
I
n
t
h
is
p
ap
er
an
in
n
o
v
at
iv
e
ap
p
r
o
ac
h
in
o
p
ti
m
izatio
n
m
eth
o
d
,
Gr
a
v
i
tatio
n
al
s
ea
r
ch
alg
o
r
it
h
m
(
GS
A
)
h
as
b
ee
n
u
s
ed
to
m
i
n
i
m
ize
th
e
h
ar
m
o
n
ic
s
at
th
e
o
u
tp
u
t
v
o
lta
g
e
o
f
m
u
lt
il
ev
el
in
v
er
ter
.
GS
A
is
a
h
eu
r
is
tic
o
p
ti
m
izatio
n
tech
n
iq
u
e
i
n
s
p
ir
ed
b
y
Ne
w
to
n
‘
s
la
w
o
f
g
r
av
it
y
a
n
d
m
o
tio
n
;
it
h
as
f
o
u
r
s
p
ec
i
f
icatio
n
s
f
o
r
ea
ch
o
f
its
ag
e
n
t
s
v
iz.
A
cti
v
e
Gr
a
v
itatio
n
al
Ma
s
s
,
P
ass
i
v
e
Gr
av
itatio
n
a
l
Ma
s
s
,
I
n
er
tial
Ma
s
s
a
n
d
P
o
s
itio
n
.
Ov
er
a
p
er
io
d
o
f
ti
m
e,
GS
A
h
a
s
u
n
d
er
g
o
n
e
m
aj
o
r
ch
an
g
e
s
i
n
th
e
b
as
ic
alg
o
r
ith
m
a
n
d
h
as
b
ee
n
a
d
ap
ted
f
o
r
s
p
ec
if
ic
ap
p
licatio
n
s
i
n
v
ar
ied
f
ield
s
o
f
s
cien
ce
[
1
8
]
-
[
19
]
.
An
o
th
er
ap
p
r
o
ac
h
u
s
ed
i
n
t
h
is
p
ap
er
f
o
r
h
ar
m
o
n
ic
r
ed
u
ct
io
n
is
W
av
ef
o
r
m
s
y
n
t
h
es
is
,
w
h
ich
is
b
ased
o
n
w
a
v
elets
tr
a
n
s
f
o
r
m
,
it
is
a
u
s
e
f
u
l
m
at
h
e
m
atica
l
to
o
l
f
o
r
d
esig
n
i
n
g
m
u
ltil
e
v
el
in
v
er
ter
s
tr
u
ct
u
r
es
an
d
co
n
tr
o
l
s
tr
ateg
ies,
f
ea
t
u
r
es
o
f
w
a
v
elets
s
u
c
h
as
d
ilatio
n
an
d
tr
an
s
latio
n
allo
w
t
h
e
m
to
b
e
u
s
ed
n
o
t
o
n
l
y
f
o
r
an
al
y
s
i
s
o
f
p
r
o
ce
s
s
e
s
co
n
s
i
s
ti
n
g
in
d
ec
o
m
p
o
s
itio
n
b
u
t
also
in
co
m
p
o
s
itio
n
o
f
s
i
g
n
al
s
an
d
s
tr
u
c
t
u
r
es in
p
o
w
er
elec
tr
o
n
ic
s
[
2
0
]
-
[
21
]
.
To
d
ay
m
o
r
e
an
d
m
o
r
e
r
es
ea
r
c
h
er
s
a
r
e
,
w
o
r
k
in
g
w
ith
F
u
zz
y
L
o
g
ic
s
y
s
te
m
alo
n
g
w
it
h
co
n
v
e
n
tio
n
al
co
n
tr
o
ller
s
(
a
h
y
b
r
id
s
y
s
te
m
)
to
ac
cu
r
atel
y
co
n
tr
o
l
t
h
e
o
p
er
atio
n
s
o
f
i
n
d
u
c
tio
n
m
o
to
r
d
r
iv
es,
d
c
m
o
to
r
s
a
n
d
m
an
y
o
th
er
ap
p
licatio
n
s
[
2
2
]
-
[
2
3
]
.
Fu
zz
y
co
n
tr
o
ller
w
h
en
u
s
ed
w
it
h
o
p
ti
m
izat
io
n
b
as
ed
s
o
f
t
co
m
p
u
ti
n
g
tech
n
iq
u
es
f
o
r
p
ar
am
eter
s
o
p
tim
izatio
n
h
a
v
e
g
i
v
en
b
etter
p
er
f
o
r
m
an
ce
t
h
an
co
n
v
e
n
tio
n
al
P
I
c
o
n
tr
o
ller
in
n
o
n
lin
ea
r
s
y
s
te
m
[
2
4
]
-
[
2
5
]
.
I
n
f
u
zz
y
s
y
s
te
m
,
t
h
e
n
u
m
b
er
o
f
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
a
n
d
s
y
s
t
e
m
ac
cu
r
ac
y
h
a
s
a
v
er
y
clo
s
e
r
elatio
n
,
th
e
m
o
r
e
th
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
t
h
e
g
r
ea
ter
is
th
e
s
y
s
te
m
co
m
p
le
x
it
y
a
n
d
th
e
les
s
th
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
,
le
s
s
er
t
h
e
s
y
s
te
m
ac
c
u
r
ac
y
,
h
e
n
ce
th
e
n
u
m
b
er
o
f
‗
m
f
s
‘
n
ee
d
s
to
b
e
ca
r
ef
u
ll
y
c
h
o
s
e
n
.
A
d
esi
r
ed
in
v
e
r
t
er
o
u
t
p
u
t
v
o
l
ta
g
e
ca
n
b
e
o
b
t
ain
e
d
b
y
r
eg
u
l
atin
g
v
ar
io
u
s
p
ar
am
eter
s
lik
e
m
o
d
u
latio
n
i
n
d
ex
,
s
w
itc
h
in
g
a
n
g
les,
i
n
p
u
t
v
o
lta
g
e
o
f
th
e
in
v
er
ter
.
I
n
t
h
e
p
r
es
en
ted
w
o
r
k
,
f
u
zz
y
lo
g
ic
h
as
b
ee
n
u
s
ed
as
clo
s
ed
lo
o
p
s
y
s
te
m
to
g
en
er
ate
i
n
v
er
t
er
o
u
tp
u
t
f
o
r
v
ar
iatio
n
i
n
s
w
i
tc
h
in
g
a
n
g
les (
G
A
an
d
G
S
A
b
as
ed
FLC co
n
tr
o
ller
)
an
d
m
o
d
u
latio
n
in
d
e
x
(
W
av
elet
b
ased
FL
C
co
n
tr
o
ller
)
.
Fo
r
ea
ch
v
alu
e
o
f
m
o
d
u
la
ti
o
n
in
d
ex
o
r
s
et
o
f
s
w
itc
h
in
g
an
g
le
s
,
f
u
zz
y
s
y
s
te
m
v
ar
ie
s
th
e
o
u
tp
u
t
v
o
lta
g
e
f
o
r
m
i
n
i
m
al
T
HD.
Hen
ce
,
f
u
zz
y
co
n
tr
o
ller
s
er
v
es
as
a
v
o
ltag
e
r
eg
u
lato
r
co
r
r
es
p
o
n
d
s
to
m
i
n
i
m
u
m
T
HD
in
an
i
n
v
e
r
ter
.
Fo
r
th
e
p
u
r
p
o
s
e
o
f
th
is
p
ap
er
,
it
i
s
a
s
s
u
m
ed
th
a
t
t
h
e
i
n
p
u
t
d
c
v
o
lta
g
es
to
t
h
e
m
u
ltil
e
v
el
in
v
er
ter
ar
e
f
ed
f
r
o
m
r
e
n
e
w
ab
le
en
er
g
y
s
o
u
r
ce
s
s
u
c
h
as
f
u
el
ce
ll
s
,
p
h
o
to
v
o
ltaic
ce
ll,
w
i
n
d
en
er
g
y
s
y
s
te
m
etc.
an
d
ac
co
r
d
in
g
l
y
a
v
ar
iatio
n
o
f
±
1
0
%
in
n
o
m
i
n
al
d
c
v
o
lta
g
e
s
o
u
r
ce
h
a
s
b
ee
n
tak
e
n
in
to
c
o
n
s
id
er
atio
n
f
o
r
all
ca
lcu
latio
n
p
u
r
p
o
s
es,
r
esu
lt
in
g
i
n
r
esp
ec
tiv
e
i
n
p
u
t
d
c
v
alu
es
V
1
=(
1
±
1
0
%)
p
.
u
.
,
V
2
=(
0
.
9
±
1
0
%)p
.
u
.
,
V
3
=(
0
.
8
±
1
0
%)p
.
u
.
b
y
co
n
s
id
e
r
in
g
all
p
o
s
s
ib
le
co
m
b
in
at
io
n
i.e
.
3
3
=2
7
d
if
f
er
en
t
in
p
u
t
s
et
s
[
2
5
]
.
GSA
an
d
G
A
ar
e
th
en
u
s
ed
to
ca
lc
u
late
s
w
it
ch
in
g
a
n
g
les
f
o
r
all
t
h
ese
2
7
i
n
p
u
t
s
ets.
Stu
d
y
s
h
o
w
s
t
h
at
p
e
r
f
o
r
m
an
ce
o
f
G
A
is
b
etter
th
an
P
SO
i
n
ter
m
s
o
f
T
HD
m
i
n
i
m
izat
io
n
a
n
d
co
m
p
u
tatio
n
a
l
ti
m
e
[
2
6
]
.
Hen
ce
,
t
h
e
p
ap
er
in
tr
o
d
u
ce
s
o
th
er
o
p
t
i
m
izatio
n
m
et
h
o
d
s
s
u
ch
a
s
G
A
a
n
d
GS
A
to
co
m
p
u
te
o
p
ti
m
al
s
w
itc
h
i
n
g
a
n
g
les.
W
av
elet
tr
an
s
f
o
r
m
h
as
b
ee
n
u
s
ed
to
s
y
n
t
h
esize
s
tep
p
ed
w
av
e
f
o
r
m
u
s
i
n
g
s
ets
o
f
o
r
th
o
g
o
n
al
w
a
v
elets
a
n
d
th
en
f
ed
to
d
esig
n
v
ar
iab
les an
d
r
u
le
-
b
ase
f
o
r
f
u
z
z
y
s
y
s
te
m
.
T
h
e
p
ap
e
r
is
ar
r
a
n
g
ed
as
f
o
llo
w
s
;
Sectio
n
2
p
r
esen
t
s
an
in
tr
o
d
u
ct
io
n
to
C
ascad
ed
H
-
b
r
id
g
e
m
u
ltil
e
v
el
i
n
v
er
ter
an
d
a
s
et
o
f
d
er
iv
ed
eq
u
a
tio
n
s
f
o
r
S
HE
m
et
h
o
d
.
Sectio
n
3
,
4
an
d
5
in
tr
o
d
u
ce
s
a
n
d
i
m
p
le
m
en
t
s
Ge
n
etic
al
g
o
r
ith
m
,
Gr
av
ita
tio
n
al
s
ea
r
ch
al
g
o
r
ith
m
a
n
d
W
av
elet
T
r
an
s
f
o
r
m
tec
h
n
iq
u
e
s
f
o
r
p
r
o
p
o
s
ed
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
to
co
n
tr
o
l
in
v
er
ter
o
u
tp
u
t.
Sectio
n
6
v
er
i
f
ies
th
e
p
er
f
o
r
m
an
ce
o
f
p
r
o
p
o
s
ed
co
n
tr
o
l
m
e
th
o
d
s
b
y
s
i
m
u
latio
n
o
f
7
-
lev
e
l
ML
I
s
.
P
er
f
o
r
m
a
n
ce
v
alid
atio
n
is
d
o
n
e
in
s
ec
tio
n
7
an
d
co
n
clu
s
io
n
s
ar
e
m
ad
e
i
n
8
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
A
N
o
ve
l A
p
p
r
o
a
ch
to
GS
A
,
G
A
a
n
d
W
a
ve
let
Tr
a
n
s
fo
r
m
to
Desig
n
F
u
z
z
y
Lo
g
ic
C
o
n
tr
o
ller
…
(
V
a
r
s
h
a
S
in
g
h
)
1202
2.
CASCAD
E
D
H
-
B
RID
G
E
M
UL
T
I
L
E
V
E
L
I
NV
E
RT
E
R
(
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N)
A
s
in
g
le
p
h
ase
7
-
le
v
el
ca
s
ca
d
ed
H
-
b
r
id
g
e
m
u
ltil
e
v
el
i
n
v
e
r
ter
co
n
s
is
t
s
o
f
t
h
r
ee
s
er
ies
co
n
n
ec
ted
H
–
b
r
id
g
e
in
v
er
ter
u
n
it
s
as
s
h
o
w
n
in
(
Fi
g
u
r
e
1)
.
Ou
tp
u
t
v
o
ltag
e
o
f
M
L
I
w
h
ic
h
is
i
n
t
h
e
f
o
r
m
o
f
p
er
io
d
ic
s
tair
ca
s
e
w
a
v
ef
o
r
m
ca
n
b
e
ex
p
r
ess
ed
b
y
Fo
u
r
ier
s
er
ies e
x
p
an
s
io
n
as:
V
out
(
w
t)
=
∑
s
in
(
n
w
t
)
(
1
)
Am
p
lit
u
d
e
o
f
f
u
n
d
a
m
e
n
tal
co
m
p
o
n
en
t
an
d
o
d
d
h
ar
m
o
n
ics
co
m
p
o
n
e
n
t
s
ar
e
g
iv
en
as
:
=
∑
co
s
(
n
)
a
n
d
=
∑
co
s
(
n
)
No
w
,
E
q
u
atio
n
(
1
)
is
r
e
w
r
itte
n
as:
V
out
(
w
t)
=
∑
∑
(
n
θ
k
)
]
s
i
n
(
n
w
t)
(
2
)
s
is
n
o
.
o
f
s
w
itc
h
in
g
a
n
g
le
s
to
b
e
ca
lcu
lated
an
d
let
‗
l
‘
b
e
th
e
n
o
.
o
f
in
v
er
ter
lev
els,
t
h
e
n
s
a
n
d
l a
r
e
r
elate
d
b
y
:
s
=
(
l
-
1
)
/2
(
3
)
Fin
all
y
,
b
ased
o
n
E
q
u
atio
n
(
3
)
,
th
r
ee
an
g
les
(
s
=3
)
ar
e
to
b
e
ca
lcu
lated
f
o
r
7
-
le
v
el
i
n
v
er
ter
s
u
c
h
t
h
at
t
h
ese
ar
e
li
m
ited
a
s
0
.
B
ased
o
n
SHE
m
et
h
o
d
,
m
i
n
i
m
izi
n
g
(
s
-
1
)
h
ar
m
o
n
ic
s
r
es
u
lt
s
5
th
an
d
7
t
h
h
ar
m
o
n
ics
to
b
e
m
in
i
m
ized
an
d
f
u
n
d
a
m
e
n
tal
co
m
p
o
n
en
t
is
m
ai
n
tai
n
ed
f
o
r
7
-
lev
e
l
ca
s
ca
d
ed
in
v
er
ter
as:
I
n
th
i
s
p
ap
er
,
m
o
d
u
lat
io
n
i
n
d
ex
M
is
g
iv
e
n
b
y
M
=
co
s
(
)+
co
s
(
)+
co
s
(
)
=
co
s
(
)+
co
s
(
3
)+
co
s
(
3
)
= 0
co
s
(
)+
co
s
(
5
)+
co
s
(
5
)
= 0
co
s
(
)+
co
s
(
7
)+
co
s
(
7
)
=
Min
i
m
izatio
n
o
f
h
ar
m
o
n
ics
r
ed
u
ce
d
to
tal
h
ar
m
o
n
ic
d
is
t
o
r
tio
n
(
T
HD)
o
f
in
v
er
ter
w
h
ich
is
g
iv
e
n
b
y
E
q
u
atio
n
(
4
)
.
2
2
2
23
2
1
.....
%
1
0
0
n
V
V
V
T
H
D
V
(
4
)
Fig
u
r
e
1
.
Sev
en
le
v
el
ca
s
ca
d
e
d
H
-
b
r
id
g
e
ML
I
3.
P
RO
P
O
SE
D
G
A
B
ASE
D
F
U
Z
Z
Y
L
O
G
I
C
CO
N
T
RO
L
L
E
R
I
n
th
is
ap
p
r
o
ac
h
th
e
ai
m
i
s
to
o
b
tain
d
ataset
f
o
r
in
p
u
t
-
o
u
tp
u
t
p
air
s
o
f
FLC
s
y
s
te
m
b
ased
o
n
ca
lcu
latio
n
o
f
o
p
ti
m
al
s
w
itc
h
i
n
g
an
g
les
(
f
o
r
7
-
le
v
el
in
v
er
t
er
.
I
n
liter
atu
r
e
r
e
v
ie
w
,
P
SO
alg
o
r
ith
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
7
,
No
.
4
,
Dec
em
b
er
2
0
1
6
:
120
0
–
1
2
1
1
1203
h
as
b
ee
n
e
m
p
lo
y
ed
to
c
alcu
late
s
w
itch
in
g
an
g
les
a
n
d
also
as
d
is
cu
s
s
ed
b
y
au
t
h
o
r
s
,
GA
p
er
f
o
r
m
an
ce
i
s
r
ated
b
etter
th
an
P
SO
i
n
ter
m
s
o
f
T
HD
m
i
n
i
m
izat
io
n
a
n
d
co
m
p
u
tat
io
n
a
l
ti
m
e
[
2
5
]
-
[
2
6
]
.
Hen
ce
i
n
t
h
is
p
ap
er
p
r
esen
ts
GA
h
as
b
ee
n
u
s
ed
to
ca
lcu
late
t
h
e
o
p
ti
m
al
v
al
u
es
o
f
s
w
itc
h
i
n
g
a
n
g
les,
t
h
e
ap
p
r
o
ac
h
r
eq
u
ir
es
co
n
s
id
er
in
g
in
p
u
t
v
o
lta
g
e
v
al
u
esat
V
1
=1
p
.
u
.
,
V
2
=0
.
9
p
.
u
.
an
d
V
3
=
0
.
8
p
.
u
.
,
an
d
ap
p
ly
i
n
g
1
0
%
v
ar
iatio
n
s
i
n
ea
ch
v
o
ltag
e
v
al
u
e
,
t
h
is
r
es
u
lts
i
n
a
s
et
o
f
to
tal
2
7
i
n
p
u
t
v
o
lta
g
e
v
a
lu
e
s
at
d
i
f
f
er
en
t
m
o
d
u
latio
n
i
n
d
ex
.
A
t
M=
0
.
7
9
1
,
GA
al
g
o
r
ith
m
g
iv
es
t
h
e
b
est
v
al
u
es
o
f
T
HD.
T
h
e
ap
p
r
o
ac
h
to
ca
lcu
late
s
w
i
tch
i
n
g
a
g
les
u
s
in
g
GA
i
s
s
h
o
w
n
i
n
th
e
f
o
r
m
o
f
a
f
lo
w
c
h
ar
t
i
n
Fig
u
r
e
2
.
T
h
e
r
esu
lt
o
f
G
A
al
g
o
r
ith
m
f
o
r
s
o
m
e
o
f
th
e
s
e
in
p
u
t
co
m
b
i
n
atio
n
s
is
tab
u
lated
in
T
ab
le
1
.
T
ab
le
1
.
R
esu
lt o
f
G
A
al
g
o
r
ith
m
f
o
r
S
w
i
tch
i
n
g
A
n
g
le
ca
lc
u
la
tio
n
V
1
(
v
o
l
t
)
V
2
(
v
o
l
t
)
V
3
(
v
o
l
t
)
θ
1
(
d
e
g
r
e
e
)
θ
2
(
d
e
g
r
e
e
)
θ
3
(
d
e
g
r
e
e
)
1
.
1
0
.
8
1
0
.
7
2
1
9
.
3
5
8
6
4
7
.
1
3
8
2
2
8
9
.
9
6
5
6
1
1
.
1
0
.
8
1
0
.
8
2
0
.
7
3
4
3
9
5
4
.
7
2
2
2
9
8
9
.
9
9
7
3
2
1
.
1
0
.
8
1
0
.
8
8
1
7
.
8
3
3
7
6
4
6
.
2
2
1
0
2
8
4
.
2
2
7
3
9
…….
.
……
…….
.
……
……
….
.
1
.
1
0
.
9
9
0
.
8
1
8
.
3
1
5
2
9
4
3
.
9
6
8
1
5
8
9
.
9
9
7
0
2
1
.
1
0
.
9
9
0
.
8
8
2
1
.
0
1
5
2
9
5
5
.
7
9
4
2
7
8
9
.
2
0
3
1
8
1
0
.
8
1
0
.
7
2
1
6
.
9
2
2
2
9
4
0
.
2
1
3
3
8
6
6
.
7
0
3
1
8
1
0
.
8
1
0
.
8
1
7
.
1
7
4
5
2
4
3
.
7
7
3
2
5
8
6
.
6
5
2
2
3
…….
…….
…….
…….
……
…….
1
0
.
9
9
0
.
8
1
7
.
2
6
6
2
4
4
2
.
5
8
0
8
9
8
9
.
7
1
3
3
8
1
0
.
9
9
0
.
8
8
1
7
.
5
7
0
0
6
4
6
.
4
6
1
7
8
8
4
.
0
8
9
8
1
0
.
9
0
.
8
1
0
.
7
2
1
9
.
1
2
9
3
4
6
.
0
4
9
0
4
6
4
.
6
0
5
1
0
.
9
0
.
8
1
0
.
8
1
5
.
4
5
4
7
8
4
2
.
1
8
5
3
5
8
3
.
7
2
2
9
3
…….
……
….
.
……
……
……
0
.
9
0
.
9
9
.
1
5
.
0
8
2
1
7
4
1
.
7
2
6
7
5
8
4
.
1
3
5
6
7
0
.
9
0
.
9
9
0
.
8
8
1
9
.
2
4
3
9
5
5
1
.
2
4
8
4
1
8
6
.
2
5
0
9
6
3
.
1
F
uzzy
L
o
g
ic
Co
ntr
o
ller
T
h
e
o
b
tain
ed
in
p
u
t
-
o
u
tp
u
t
d
atasets
o
f
G
A
(
T
ab
le
1
)
ar
e
i
m
p
le
m
e
n
ted
o
v
er
f
u
zz
y
s
y
s
te
m
u
s
i
n
g
d
if
f
er
e
n
t
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
a
n
d
R
u
le
-
B
ased
I
n
p
u
t
v
o
lt
ag
es
V
1
,
V
2
,
V
3
ar
e
r
ep
r
esen
ted
b
y
3
tr
ian
g
u
lar
MFs
(
L
o
w
,
No
m
,
Hi
g
h
)
co
v
er
in
g
t
h
e
e
n
tire
r
an
g
e
o
f
i
n
p
u
t
v
ar
iab
le
as
s
h
o
w
n
i
n
F
ig
u
r
e
3
(
a)
.
Fo
r
o
u
tp
u
t
s
w
itc
h
in
g
a
n
g
les
θ
1
,
θ
2
,
θ
3
,
in
s
tead
o
f
u
s
i
n
g
s
i
n
g
le
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
f
o
r
ea
ch
v
alu
e,
v
alu
es
t
h
at
ar
e
clo
s
e
to
ea
ch
o
t
h
er
a
r
e
m
er
g
ed
w
i
th
i
n
t
h
e
s
a
m
e
m
e
m
b
er
s
h
ip
f
u
n
ct
io
n
s
.
T
h
is
lead
s
to
7
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
f
o
r
θ
1
,
9
f
o
r
θ
2
an
d
9
f
o
r
θ
3
as
s
h
o
w
n
i
n
Fi
g
u
r
e
3
(
b
)
.
I
F
-
T
HE
N
r
u
le
is
u
s
ed
to
w
r
ite
2
7
r
u
les
f
o
r
d
esig
n
in
g
a
co
m
p
lete
r
u
le
-
b
ase
f
o
r
f
u
zz
y
s
y
s
te
m
w
h
ic
h
is
g
i
v
e
n
i
n
T
ab
le
2
.
A
n
ex
a
m
p
le
to
w
r
ite
i
f
-
t
h
e
n
r
u
le
is
as:
I
f
(
v
1
is
h
ig
h
)
an
d
(
v
2
i
s
n
o
m
)
an
d
)
(
v
3
is
n
o
m
)
t
h
e
n
(
θ
1
is
m
f
7
)
an
d
(
θ
2
is
m
f
9
)
an
d
(
θ
3
is
m
f
9
)
T
ab
le
2
.
R
u
le
B
ase
o
f
Fu
zz
y
Data
B
ase
I
N
P
U
T
M
F
s
O
U
T
P
U
T
M
F
s
V
1
V
2
V
3
θ
1
θ
2
θ
3
h
i
g
h
l
o
w
l
o
w
mf
5
mf
5
mf
8
h
i
g
h
l
o
w
n
o
m
mf
6
mf
8
mf
9
…
…
….
…
…
…
h
i
g
h
h
i
g
h
n
o
m
mf
5
mf
3
mf
9
h
i
g
h
h
i
g
h
h
i
g
h
mf
7
mf
9
mf
9
n
o
m
l
o
w
l
o
w
mf
3
mf
1
mf
3
n
o
m
l
o
w
n
o
m
mf
4
mf
3
mf
8
…
…
….
…
…
…
n
o
m
h
i
g
h
n
o
m
mf
4
mf
2
mf
9
n
o
m
h
i
g
h
h
i
g
h
mf
4
mf
5
mf
7
l
o
w
l
o
w
l
o
w
mf
5
mf
4
mf
2
l
o
w
l
o
w
n
o
m
mf
3
mf
3
mf
8
…
…
….
…
…
…
lo
w
hi
g
h
l
o
w
m
f
4
m
f
5
m
f
3
lo
w
hi
g
h
no
m
m
f
1
m
f
1
m
f
7
I
n
th
i
s
m
a
n
n
er
,
r
u
le
-
b
ase
d
d
atab
ase
is
o
b
tain
ed
f
o
r
f
u
z
z
y
lo
g
ic
co
n
tr
o
ller
to
p
r
o
v
id
e
co
n
tr
o
l
m
ec
h
a
n
i
s
m
f
o
r
7
-
lev
el
i
n
v
er
ter
to
g
en
er
ate
d
esire
d
o
u
tp
u
t
w
av
e
f
o
r
m
w
it
h
r
ed
u
ce
d
h
ar
m
o
n
ics.
A
ls
o
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
A
N
o
ve
l A
p
p
r
o
a
ch
to
GS
A
,
G
A
a
n
d
W
a
ve
let
Tr
a
n
s
fo
r
m
to
Desig
n
F
u
z
z
y
Lo
g
ic
C
o
n
tr
o
ller
…
(
V
a
r
s
h
a
S
in
g
h
)
1204
ev
alu
a
te
th
e
p
er
f
o
r
m
a
n
ce
o
f
p
r
o
p
o
s
ed
GA
o
p
ti
m
ized
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
,
s
i
m
u
latio
n
is
ca
r
r
ied
o
u
t
in
Sectio
n
6
an
d
th
e
r
es
u
lt
o
b
tain
ed
ar
e
co
m
p
ar
ed
w
it
h
o
th
er
te
ch
n
iq
u
es
f
o
r
v
alid
at
io
n
.
Fig
u
r
e
2
.
F
lo
w
c
h
ar
t f
o
r
G
A
al
g
o
r
ith
m
f
o
r
O
p
ti
m
al
S
w
itc
h
in
g
an
g
le
ca
lc
u
latio
n
Fig
u
r
e
3
.
(
a)
an
d
(
b
)
Me
m
b
er
s
h
ip
F
u
n
ctio
n
s
f
o
r
in
p
u
t
v
o
ltag
e
s
,
,
(
b
)
Me
m
b
er
s
h
ip
Fu
n
ct
io
n
s
f
o
r
O
u
tp
u
t a
n
g
les
,
,
4.
P
RO
P
O
SE
D
G
R
AVI
T
A
T
I
O
NAL
S
E
ARCH
A
L
G
O
RIT
H
M
B
ASE
D
F
U
Z
Z
Y
L
O
G
I
C
CO
NT
RO
L
L
E
R
I
n
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
o
f
th
e
s
ec
o
n
d
ap
p
r
o
ac
h
to
ca
lcu
late
o
p
ti
m
al
s
w
itc
h
i
n
g
a
n
g
les
G
S
A
alg
o
r
ith
m
h
a
s
b
ee
n
u
s
ed
f
o
r
an
g
le
o
p
ti
m
izatio
n
o
v
er
a
w
i
d
e
r
an
g
e
o
f
in
p
u
t
d
c
s
o
u
r
ce
s
.
T
h
e
tw
o
p
r
o
p
o
s
ed
m
et
h
o
d
s
,
i.e
.
GS
A
an
d
G
A
b
ased
FLC
co
n
tr
o
ller
h
a
v
e
t
h
e
s
a
m
e
ap
p
r
o
ac
h
to
d
esig
n
f
u
zz
y
lo
g
ic
s
y
s
te
m
an
d
th
i
s
i
s
d
o
n
e
i
n
o
r
d
er
to
co
m
p
ar
e
t
h
e
co
m
p
le
x
it
y
a
n
d
s
m
o
o
th
n
e
s
s
o
f
t
h
e
t
w
o
o
p
ti
m
izatio
n
tec
h
n
iq
u
es
.
Fo
r
7
-
lev
el
in
v
er
ter
,
GS
A
ca
lc
u
lates
3
o
p
ti
m
al
s
w
i
tch
i
n
g
an
g
les
(
θ
1
,
θ
2
,
θ
3
)
f
o
r
ea
ch
o
f
2
7
in
p
u
t
co
m
b
i
n
atio
n
s
an
d
h
en
ce
g
e
n
er
ates i
n
p
u
t
-
o
u
t
p
u
t p
air
d
ataset
s
f
o
r
F
L
C
s
y
s
te
m
.
4
.
1
G
ra
v
it
a
t
io
na
l Sea
rc
h Alg
o
rit
h
m
I
n
GS
A
,
an
ag
e
n
t
i
s
c
h
ar
ac
ter
ized
b
y
4
p
ar
a
m
eter
s
w
h
ich
a
r
e
to
b
e
ca
lcu
lated
a
n
d
u
p
d
ated
u
n
t
il
t
h
e
s
to
p
p
in
g
cr
iter
io
n
is
r
ea
c
h
e
d
.
T
h
ese
f
o
u
r
p
ar
a
m
eter
s
a
r
e
-
p
o
s
i
tio
n
(
)
,
I
n
er
tial
Ma
s
s
(
)
,
A
cti
v
e
Gr
av
itatio
n
al
Ma
s
s
(
)
an
d
Pas
s
i
v
e
Ma
s
s
(
)
.
GSA
al
g
o
r
ith
m
f
o
r
o
p
tim
izi
n
g
s
w
itc
h
i
n
g
an
g
les
i
s
f
o
r
m
u
lated
as
g
i
v
en
i
n
th
e
f
l
o
w
-
ch
ar
t,
Fi
g
u
r
e
4.
T
h
e
in
p
u
t
v
o
ltag
e
an
d
o
u
tp
u
t
s
w
i
tch
in
g
an
g
les
d
ataset
s
s
o
o
b
tain
ed
is
s
h
o
w
n
i
n
tab
le
3
,
f
u
r
t
h
er
f
r
o
m
t
h
e
d
ata
s
et
g
en
er
ated
,
F
L
C
s
y
s
te
m
i
s
d
esig
n
ed
u
s
i
n
g
t
h
e
8
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
f
o
r
θ
1
,
1
0
f
o
r
θ
2
an
d
8
f
o
r
θ
3
ar
e
g
en
er
ated
f
r
o
m
to
tal
2
7
f
u
zz
y
r
u
les
as
s
h
o
w
n
i
n
Fig
u
r
e
5
(
a)
an
d
5
(
b
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
7
,
No
.
4
,
Dec
em
b
er
2
0
1
6
:
120
0
–
1
2
1
1
1205
Fig
u
r
e
4
.
Flo
w
c
h
ar
t o
f
GS
A
al
g
o
r
ith
m
f
o
r
Op
ti
m
al
S
w
itc
h
in
g
An
g
le
C
alc
u
latio
n
Fig
u
r
e
5
.
(
a)
Me
m
b
er
s
h
ip
F
u
n
ctio
n
s
f
o
r
in
p
u
t
V
o
lta
g
es
,
,
(
b
)
Me
m
b
er
s
h
ip
F
u
n
ct
io
n
s
f
o
r
Ou
tp
u
t
A
n
g
le
s
,
,
T
ab
le
3
.
R
esu
lt o
f
G
S
A
alg
o
r
it
h
m
f
o
r
S
w
itc
h
i
n
g
An
g
le
C
alc
u
latio
n
V1
V2
V3
ϴ1
ϴ2
ϴ3
1
.
1
0
.
8
1
0
.
7
2
1
9
.
1
7
3
9
8
3
6
.
6
1
8
7
1
5
3
.
2
3
8
9
2
1
.
1
0
.
8
1
0
.
8
1
6
.
3
2
5
4
7
2
8
.
2
0
0
1
9
5
6
.
9
2
7
2
5
---
---
---
---
---
---
1
0
.
8
1
0
.
7
2
1
7
.
6
4
6
7
7
3
4
.
1
6
0
5
8
5
8
.
2
1
7
3
2
1
0
.
8
1
0
.
8
1
8
.
0
5
8
4
6
2
8
.
0
7
5
1
8
5
4
.
1
0
2
6
6
---
---
---
---
---
---
0
.
9
0
.
8
1
0
.
7
2
1
8
.
9
1
2
9
9
3
4
.
9
3
3
2
8
5
2
.
0
3
5
2
7
0
.
9
0
.
8
1
0
.
8
1
7
.
8
6
6
5
5
2
6
.
1
5
9
8
1
5
8
.
0
0
4
0
2
---
---
---
---
---
---
0
.
9
0
.
9
9
0
.
8
8
1
8
.
6
7
7
9
1
3
3
.
3
2
6
8
1
5
6
.
7
2
0
9
9
5.
WAVE
L
E
T
T
RANSF
O
RM
T
h
e
ter
m
w
av
ele
t
is
d
er
i
v
ed
f
r
o
m
Fre
n
c
h
ter
m
o
n
d
elette
s
,
w
h
ic
h
m
ea
n
s
li
ttle
w
a
v
es.
W
av
elet
T
r
an
s
f
o
r
m
is
b
ased
o
n
t
h
ese
s
m
al
l
w
a
v
elets
a
n
d
allo
w
s
to
an
al
y
ze
t
h
e
s
i
g
n
als
i
n
d
i
f
f
er
en
t
ti
m
e
s
ca
le,
w
it
h
d
if
f
er
e
n
t
r
eso
lu
tio
n
s
[
2
0
]
,
[
2
1
]
.
I
t
p
r
o
v
id
es
b
o
th
ti
m
e
an
d
f
r
eq
u
en
c
y
a
n
al
y
s
is
o
f
s
i
g
n
al
s
i
m
u
lta
n
eo
u
s
l
y
.
W
av
elet
is
d
ef
in
ed
as
a
m
at
h
e
m
a
tical
f
u
n
ctio
n
o
r
w
a
v
ef
o
r
m
th
at
h
as
f
i
n
ite
t
i
m
e
p
er
io
d
an
d
ze
r
o
av
er
ag
e
v
alu
e.
∫
(
5
)
W
h
er
e,
I
n
p
r
o
p
o
s
ed
w
o
r
k
,
Haa
r
f
u
n
d
a
m
en
tal
s
ca
li
n
g
f
u
n
ctio
n
a
n
d
w
av
elet
f
u
n
ct
io
n
ar
e
u
s
ed
f
o
r
wav
ef
o
r
m
s
y
n
t
h
e
s
is
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
A
N
o
ve
l A
p
p
r
o
a
ch
to
GS
A
,
G
A
a
n
d
W
a
ve
let
Tr
a
n
s
fo
r
m
to
Desig
n
F
u
z
z
y
Lo
g
ic
C
o
n
tr
o
ller
…
(
V
a
r
s
h
a
S
in
g
h
)
1206
Her
ein
p
u
t
f
u
n
ct
io
n
f
(
x
)
=si
n
(
x
)
is
s
e
lecte
d
in
t
h
e
i
n
ter
v
a
l
0
<x
<0
.
0
2
to
g
en
er
ate
ap
p
r
o
x
i
m
atio
n
f
u
n
ctio
n
f
ψ
(
x
)
w
h
ic
h
is
a
co
m
p
o
s
itio
n
o
f
s
u
cc
es
s
iv
e
w
a
v
elet
s
.
I
n
th
i
s
p
ap
er
,
w
a
v
elet
tr
an
s
f
o
r
m
is
a
p
p
lied
to
g
en
er
ate
ap
p
r
o
x
im
a
tio
n
f
u
n
ctio
n
f
ψ
(
x
)
f
o
r
7
-
lev
el
in
v
er
ter
o
u
tp
u
t.
W
av
ef
o
r
m
s
y
n
th
e
s
is
f
ψ
(
x
)
is
r
ep
r
esen
ted
as
a
co
m
p
o
s
i
tio
n
o
f
f
o
llo
w
i
n
g
w
a
v
elets
g
i
v
e
n
in
E
q
u
a
tio
n
(
6
)
an
d
E
q
u
atio
n
(
7
)
.
∑
∑
(
6
)
Fo
r
7
-
lev
el
w
a
v
ef
o
r
m
,
∑
∑
∑
∑
(
7
)
W
av
elet
f
a
m
ilies
ψ
0,
0
(
x
)
,
ψ
2,
s
(
x
)
an
d
ψ
3,
s
(
x
)
an
d
co
r
r
esp
o
n
d
in
g
ap
p
r
o
x
i
m
at
io
n
f
u
n
c
ti
o
n
s
f
ψ
00
(
x
)
,
f
ψ
2s
(
x
)
an
d
f
ψ
3s
(
x
)
ar
e
p
r
esen
ted
i
n
Fi
g
u
r
e
6
.
Valu
e
s
o
f
w
a
v
elet
co
ef
f
icie
n
ts
b
r,
s
ar
e
ca
lcu
lated
f
r
o
m
f
ψ
(
x
)
.
Fig
u
r
e
6
.
W
av
elet
ap
p
r
o
x
i
m
ati
o
n
f
u
n
ct
io
n
f
ψ
(
x
)
an
d
f
r
eq
u
en
c
y
s
p
ec
tr
u
m
o
f
ap
p
r
o
x
i
m
atio
n
f
u
n
ct
io
n
f
ψ
(
x
)
Fig
u
r
e
7
.
B
lo
ck
d
iag
r
a
m
r
ep
r
esen
tat
io
n
o
f
clo
s
ed
lo
o
p
FL
C
co
n
tr
o
ller
in
v
er
ter
5
.
1
F
uzzy
L
o
g
ic
Co
ntr
o
ller
I
m
p
le
m
e
nta
t
io
n
S
y
n
t
h
esized
f
ψ
(
x
)
i
n
Fi
g
u
r
e
6
h
as
p
r
o
v
ed
to
p
r
ese
n
t
a
b
etter
p
o
s
s
ib
ilit
y
to
co
n
tr
o
l
f
u
n
d
a
m
e
n
ta
l
v
o
ltag
e
an
d
f
r
eq
u
e
n
c
y
o
f
o
u
tp
u
t
w
a
v
e
f
o
r
m
a
n
d
h
en
ce
is
u
s
e
d
as r
ef
er
e
n
ce
w
a
v
e
f
o
r
m
i
n
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
.
Fig
u
r
e
6
(
a)
an
d
Fig
u
r
e
6
(
b
)
is
a
f
a
m
il
y
o
f
w
av
ele
ts
ψ
0
,
0
(
x
)
,
ψ
2
,
s
(
x
)
an
d
ψ
3
,
s
(
x
)
an
d
W
av
ele
t
ap
p
r
o
x
im
a
tio
n
f
u
n
ctio
n
s
f
ψ0
0
(
x
)
,
f
ψ2
s
(
x
)
an
d
f
ψ3
s
(
x
)
r
esp
ec
tiv
el
y
Fi
g
u
r
e
7
s
h
o
w
s
t
h
e
m
ec
h
a
n
i
s
m
o
f
F
L
C
e
m
b
ed
d
ed
to
in
v
er
ter
m
o
d
u
le
an
d
to
co
n
tr
o
l
t
h
e
i
n
v
er
ter
.
Ou
tp
u
t
v
o
lta
g
e
o
f
in
v
er
te
r
V
actual
is
co
m
p
ar
ed
to
r
ef
er
en
ce
v
o
lta
g
e
V
desired
to
o
b
tain
er
r
o
r
v
o
ltag
e
e.
T
w
o
in
p
u
ts
to
f
u
zz
y
s
y
s
te
m
ar
e
‗
e
‗
an
d
‗
d
e‘
w
h
ich
i
n
v
o
k
e
f
u
zz
y
r
u
le
-
b
ase
a
n
d
r
es
u
lts
i
n
o
u
tp
u
t
v
al
u
e
t
h
at
i
s
u
s
ed
as
a
co
n
tr
o
lled
p
ar
a
m
eter
f
o
r
s
w
itc
h
in
g
cir
c
u
it
o
f
in
v
er
ter
.
Fo
r
th
is
7
tr
ian
g
u
lar
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
ar
e
u
s
e
d
to
co
v
er
e
n
tire
r
an
g
e
o
f
in
p
u
t
-
o
u
tp
u
t
v
ar
iab
les
n
a
m
e
l
y
:
(
NH)
n
eg
a
tiv
e
h
ig
h
,
(
NN)
n
e
g
ati
v
e
n
o
r
m
al,
(
N
L
)
n
eg
at
iv
e
lo
w
,
(
Z
Z
)
ze
r
o
,
(
P
L
)
p
o
s
itiv
e
lo
w
,
(
P
N)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
7
,
No
.
4
,
Dec
em
b
er
2
0
1
6
:
120
0
–
1
2
1
1
1207
p
o
s
itiv
e
n
o
r
m
al,
(
P
H)
p
o
s
itiv
e
h
i
g
h
.
I
F
-
T
HE
N
r
u
le
i
s
u
s
ed
t
o
f
o
r
m
f
u
zz
y
r
u
le
b
ase
a
n
d
r
e
s
u
lt
s
i
n
4
9
r
u
les
ar
e
f
o
r
m
ed
.
A
n
e
x
a
m
p
le
o
f
if
-
t
h
e
n
r
u
le
is
:
i
f
(
e
is
NH)
an
d
(
d
e
is
NN)
th
en
(
V
i
s
NH)
.
Fo
r
d
e
-
f
u
zz
y
f
ica
tio
n
ce
n
tr
o
id
m
et
h
o
d
is
u
s
ed
.
Si
m
u
la
tio
n
is
ca
r
r
ied
o
u
t
f
o
r
7
-
lev
el
i
n
v
er
ter
i
n
(
Sectio
n
6
)
to
v
er
if
y
th
e
r
esu
l
t
s
o
f
p
r
o
p
o
s
ed
W
av
elet
T
r
an
s
f
o
r
m
b
ased
f
u
zz
y
lo
g
ic
co
n
tr
o
l
ler
.
B
u
t
th
is
m
o
d
el
ca
n
b
e
g
en
er
alize
d
to
co
n
tr
o
l o
u
tp
u
t
w
a
v
ef
o
r
m
o
f
an
y
le
v
el
in
v
er
ter
.
6.
RE
SU
L
T
S
AND
A
NA
L
YS
I
S
Fig
u
r
e
8
(
a)
.
s
ev
en
le
v
el
in
v
er
t
er
u
s
i
n
g
8
-
s
w
itc
h
es
Fig
u
r
e
8
(
b
)
.
C
lo
s
ed
lo
o
p
co
n
tr
o
l s
y
s
te
m
o
f
GS
A
/G
A
b
ased
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
6
.
1
Si
m
ula
t
io
n
Res
ults
f
o
r
G
A
a
nd
G
S
A
B
a
s
ed
F
uzzy
L
o
g
ic
Co
ntr
o
ller
Si
m
u
latio
n
i
s
p
er
f
o
r
m
ed
w
it
h
M
A
T
L
A
B
/SIM
U
L
I
NK
o
n
7
-
lev
el
in
v
er
ter
to
v
er
i
f
y
t
h
e
p
e
r
f
o
r
m
an
ce
o
f
p
r
o
p
o
s
ed
clo
s
ed
lo
o
p
c
o
n
tr
o
l
m
et
h
o
d
s
u
s
in
g
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
th
e
s
a
m
e
co
n
tr
o
l
m
eth
o
d
s
ca
n
b
e
ex
ten
d
ed
to
an
y
le
v
el
o
f
in
v
er
ter
an
d
f
o
r
an
y
d
e
f
in
ed
t
o
p
o
lo
g
y
.
T
o
v
alid
ate
th
e
r
es
u
lts
,
t
w
o
d
i
f
f
er
en
t
to
p
o
lo
g
ies
ar
e
d
esig
n
ed
o
n
e
u
s
in
g
F
L
C
f
o
r
a
7
-
lev
el
ca
s
ca
d
ed
H
-
b
r
id
g
e
in
v
er
t
er
an
d
th
e
o
th
er
7
-
lev
el
h
y
b
r
id
in
v
er
ter
to
p
o
lo
g
y
w
it
h
8
s
w
i
t
ch
es
a
s
s
h
o
w
n
in
Fi
g
u
r
e
8
(
a)
.
C
lo
s
ed
lo
o
p
FLC
co
n
tr
o
lled
m
o
d
el
u
s
in
g
(
G
A
an
d
GS
A
)
a
s
s
h
o
w
n
i
n
Fi
g
u
r
e
8
(
b
)
f
ee
d
s
t
h
e
o
u
tp
u
t
v
o
lta
g
e
o
f
i
n
v
er
ter
(
M
A
I
N
MO
D
E
L
)
to
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
w
h
ic
h
t
h
en
a
ctiv
a
t
es
f
u
zz
y
d
ec
is
io
n
r
u
le
a
n
d
s
u
itab
le
s
w
itc
h
i
n
g
a
n
g
les
ar
e
g
en
er
ated
to
co
n
tr
o
l
s
w
itc
h
in
g
cir
cu
it o
f
i
n
v
er
ter
.
Fig
u
r
e
9
(
a)
Fig
u
r
e
9
(
b
)
Fig
u
r
e
9
(
a)
&
9
(
b
)
.
Ou
tp
u
t v
o
ltag
e
w
av
e
f
o
r
m
a
n
d
FF
T
s
p
ec
tr
u
m
o
f
G
A
a
n
d
GS
A
b
ased
F
L
C
f
o
r
7
-
le
v
el
in
v
er
ter
w
it
h
8
s
w
itc
h
es
&
7
-
le
v
el
ca
s
ca
d
ed
H
b
r
id
g
e
in
v
er
ter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
A
N
o
ve
l A
p
p
r
o
a
ch
to
GS
A
,
G
A
a
n
d
W
a
ve
let
Tr
a
n
s
fo
r
m
to
Desig
n
F
u
z
z
y
Lo
g
ic
C
o
n
tr
o
ller
…
(
V
a
r
s
h
a
S
in
g
h
)
1208
T
h
is
clo
s
ed
lo
o
p
s
i
m
u
li
n
k
m
o
d
el
is
th
e
n
u
s
ed
to
co
n
tr
o
l
t
h
e
M
A
I
N
MO
DE
L
m
o
d
u
le
b
y
d
ef
i
n
ed
in
v
er
ter
m
o
d
u
le.
Fin
a
ll
y
,
F
L
C
co
n
tr
o
lled
m
o
d
el
is
u
s
ed
to
g
en
er
ate
d
esire
d
7
-
le
v
el
o
u
tp
u
t
v
o
ltag
e
w
av
e
f
o
r
m
f
o
r
all
d
ef
in
ed
2
7
co
m
b
i
n
atio
n
s
o
f
i
n
p
u
t
v
o
lta
g
e.
I
n
t
h
is
p
a
p
er
,
7
-
lev
el
i
n
v
er
ter
is
s
i
m
u
lat
ed
f
o
r
in
p
u
t
v
o
ltag
e
s
et
[
V
1
=1
p
u
,
V
2
=0
.
9
p
u
,
V
3
=0
.
8
p
u
]
an
d
co
r
r
esp
o
n
d
in
g
o
u
tp
u
t
v
o
ltag
e
w
a
v
ef
o
r
m
a
n
d
f
r
eq
u
en
c
y
s
p
ec
tr
u
m
f
o
r
b
o
th
7
-
lev
e
l
i
n
v
er
ter
to
p
o
lo
g
ie
s
ar
e
s
h
o
w
n
i
n
Fi
g
u
r
e
9
(
a)
an
d
Fig
u
r
e
9
(
b
)
.
Fro
m
t
h
e
F
ig
u
r
e
9
(
a)
it
ca
n
b
e
s
ee
n
th
at
t
h
e
f
r
eq
u
e
n
c
y
s
p
ec
tr
u
m
o
f
o
u
tp
u
t
w
av
e
f
o
r
m
s
o
b
tain
ed
b
y
G
A
b
ased
F
L
C
f
o
r
H
y
b
r
id
I
n
v
er
ter
h
as r
ed
u
ce
d
lo
w
er
o
r
d
er
h
ar
m
o
n
ic
a
s
co
m
p
ar
ed
to
ca
s
ca
d
e
H
-
b
r
id
g
e
b
y
1
.
3
2
%
an
d
Fig
u
r
e
9
(
b
)
g
iv
e
s
th
e
o
u
tp
u
t
v
o
lta
g
e
w
a
v
e
f
o
r
m
f
o
r
GS
A
b
ased
F
L
C
w
h
ic
h
s
h
o
w
s
th
a
t
th
e
T
HD
f
o
r
h
y
b
r
id
7
-
lev
e
l
in
v
er
t
er
is
r
ed
u
ce
d
o
v
e
r
ca
s
ca
d
ed
in
v
er
ter
b
y
1
.
9
5
%.
6
.
2
Sim
ula
t
io
n
Resul
t
s
f
o
r
Wa
v
elet
T
ra
ns
f
o
r
m
B
a
s
ed
F
uzzy
L
o
g
ic
Co
ntr
o
ller
Un
li
k
e
th
e
ap
p
r
o
ac
h
u
s
ed
to
d
esig
n
F
L
C
i
n
G
A
an
d
GS
A
a
d
if
f
er
e
n
t
ap
p
r
o
ac
h
is
ad
o
p
ted
to
d
esig
n
w
a
v
elet
T
r
an
s
f
o
r
m
b
ased
F
L
C
.
T
h
is
ca
n
b
e
s
ee
n
f
r
o
m
Fi
g
u
r
e
1
0
(
a)
th
at
th
e
f
ee
d
b
ac
k
o
f
7
-
l
ev
el
o
u
tp
u
t v
o
lta
g
e
is
co
m
p
ar
ed
w
it
h
g
e
n
er
ated
w
a
v
elet
ap
p
r
o
x
i
m
atio
n
f
u
n
c
ti
o
n
fψ
(
x
)
o
b
tain
ed
i
n
(
Sectio
n
5
)
to
p
r
o
d
u
ce
er
r
o
r
v
o
ltag
e.
Fig
u
r
e
10
(
a)
.
Sim
u
li
n
k
m
o
d
el
o
f
F
L
C
co
n
tr
o
lled
w
a
v
elet
m
o
d
u
latio
n
Fig
u
r
e
10
(
b
)
.
Ou
tp
u
t v
o
ltag
e
w
a
v
e
f
o
r
m
an
d
F
FT
s
p
ec
tr
u
m
o
f
W
T
b
ased
FL
C
7
-
lev
el
h
y
b
r
id
in
v
er
ter
an
d
7
-
lev
e
l c
ascad
ed
H
b
r
id
g
e
in
v
er
ter
T
h
e
tw
o
in
p
u
ts
to
FLC
co
n
tr
o
ller
ar
e
er
r
o
r
v
o
ltag
e
(
e)
an
d
d
er
iv
ativ
e
o
f
er
r
o
r
(
d
e/
d
t)
an
d
o
u
tp
u
t
o
b
tain
ed
is
ap
p
lied
to
s
w
itc
h
i
n
g
cir
c
u
it
o
f
i
n
v
er
ter
.
T
h
e
o
u
tp
u
t
o
f
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
i
s
th
e
n
f
ed
to
co
n
tr
o
l
P
W
M
s
w
itc
h
i
n
g
cir
c
u
it
o
f
i
n
v
er
ter
w
h
er
e
it
is
co
m
p
ar
ed
w
it
h
tr
ian
g
u
lar
w
a
v
e
f
o
r
m
to
g
en
er
ate
s
w
i
tch
i
n
g
p
u
ls
es.
Fi
g
u
r
e
1
0
(
b
)
s
h
o
w
s
f
r
eq
u
en
c
y
s
p
ec
tr
u
m
o
f
o
u
tp
u
t
v
o
lta
g
e
r
esu
lts
i
n
eli
m
in
a
tio
n
o
f
5
th
an
d
7
th
h
ar
m
o
n
ics.
T
HD
f
o
r
h
y
b
r
id
7
-
lev
el
i
n
v
er
ter
is
r
ed
u
ce
d
b
y
1
.
1
3
% o
v
er
ca
s
ca
d
ed
in
v
er
ter
.
6
.
3
E
x
peri
m
ent
Res
ults
A
p
r
o
to
ty
p
e
m
o
d
el
o
f
p
r
o
p
o
s
ed
to
p
o
lo
g
ies
h
a
s
b
ee
n
f
ab
r
icate
d
an
d
test
ed
i
n
A
r
d
u
in
o
Du
e
(
5
4
I
/0
,
1
4
PW
M
p
in
s
)
.
T
h
e
e
x
p
er
i
m
e
n
t
is
p
er
f
o
r
m
ed
f
o
r
1
0
V
in
p
u
t
d
c
v
al
u
es
f
o
r
h
y
b
r
id
7
lev
el
in
v
er
ter
an
d
th
e
o
u
tp
u
t
v
o
lta
g
e
w
av
e
f
o
r
m
an
d
f
r
eq
u
e
n
c
y
s
p
ec
tr
u
m
o
f
G
A
b
ased
F
L
C
s
y
s
te
m
a
n
d
GS
A
b
ased
F
L
C
s
y
s
te
m
ar
e
s
h
o
w
n
in
Fi
g
u
r
e
1
1
(
a)
an
d
Fig
u
r
e
1
1
(
b
)
r
esp
ec
tiv
el
y
.
F
FT
r
esu
lts
o
f
G
A
,
GS
A
an
d
W
av
elet
f
o
r
7
lev
e
l
h
y
b
r
id
in
v
er
t
er
ar
e
g
i
v
e
n
i
n
Fig
u
r
e
1
2
(
a,
b
,
c)
r
esp
ec
ti
v
el
y
.
T
h
e
r
es
u
lt
s
u
s
in
g
Har
d
w
ar
e
s
e
tu
p
ar
e
in
ag
r
ee
m
e
n
t
w
it
h
t
h
o
s
e
o
b
tain
ed
b
y
s
i
m
u
lat
io
n
.
Fig
u
r
e
1
1
(
a)
Fig
u
r
e
1
1
(
b
)
Fig
u
r
e
1
1
(
c)
Fig
u
r
e
1
1
.
(
a)
,
(
b
)
Ha
r
d
w
ar
e
r
esu
lt
s
o
f
7
lev
el
i
n
v
er
ter
(
GA
)
&
(
GS
A
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
7
,
No
.
4
,
Dec
em
b
er
2
0
1
6
:
120
0
–
1
2
1
1
1209
Fig
u
r
e
1
2
(
a)
Fig
u
r
e
1
2
(
b
)
Fig
u
r
e
1
2
(
c
)
Fig
u
r
e
1
2
(
a)
,
(
b
)
,
(
c)
.
FF
T
r
esu
lts
o
f
G
A
,
GS
A
an
d
w
a
v
elet
f
o
r
7
lev
el
in
v
er
ter
6
.
4
P
er
f
o
rm
a
nce
Co
m
pa
riso
n
O
f
P
r
o
po
s
ed
M
et
ho
ds
I
n
th
is
s
ec
tio
n
,
t
h
e
r
es
u
lt
s
o
b
tain
ed
b
y
o
p
ti
m
izat
io
n
tec
h
n
iq
u
es
as
d
is
c
u
s
s
ed
in
s
ec
tio
n
3
an
d
s
ec
tio
n
4
ar
e
co
m
p
ar
ed
f
o
r
p
ar
am
eter
s
s
u
c
h
as
T
HD,
S
w
itc
h
i
n
g
An
g
les
a
n
d
co
m
p
lex
it
y
.
Fi
g
u
r
e
13
(
a,
b,
c)
illu
s
tr
ates
d
if
f
er
e
n
t
p
ar
am
eter
co
m
p
ar
i
s
o
n
b
et
w
ee
n
GS
A
an
d
G
A
f
o
r
an
g
le
o
p
ti
m
iza
tio
n
at
m
o
d
u
latio
n
i
n
d
ex
M=
0
.
7
9
0
1
.
As
d
is
c
u
s
s
ed
ea
r
lier
G
S
A
h
a
s
m
o
r
e
co
m
p
u
tat
io
n
al
ti
m
e
t
h
a
n
G
A
d
u
e
to
s
lo
w
co
n
v
er
g
e
n
ce
i
n
last
iter
atio
n
s
w
h
ic
h
ca
n
al
s
o
b
e
s
ee
n
i
n
F
ig
u
r
e
1
3
(
a)
.
I
n
G
A
m
u
c
h
o
f
t
h
e
s
tep
p
ar
a
m
eter
s
m
u
s
t
b
e
f
in
e
t
u
n
ed
f
o
r
a
p
ar
ticu
lar
p
r
o
b
lem
,
m
a
k
in
g
m
u
ch
o
f
it
j
u
s
t
h
it
an
d
tr
ial.
T
h
es
e
d
r
a
w
b
ac
k
o
f
t
h
e
GA
ar
e
v
er
y
ea
s
il
y
o
v
er
co
m
e
b
y
t
h
e
GS
A
w
h
ich
i
s
a
d
eter
m
in
is
tic
tech
n
iq
u
e
as
o
p
p
o
s
ed
t
o
th
e
s
co
h
asti
c
G
A
,
h
en
ce
Fi
g
u
r
e
1
3
(
b
)
s
h
o
w
s
th
a
t
GS
A
h
as
b
etter
p
ar
a
m
e
ter
ap
p
r
o
ac
h
th
an
G
A
.
E
v
en
th
o
u
g
h
,
GS
A
h
as
i
n
h
er
en
t
co
m
p
u
tatio
n
al
d
ela
y
b
u
t
t
h
is
ca
n
b
e
co
n
tain
ed
b
y
u
s
e
o
f
f
aster
p
r
o
ce
s
s
o
r
s
w
id
el
y
a
v
ail
ab
le,
h
o
w
e
v
er
th
e
o
v
er
all
p
er
f
o
r
m
a
n
ce
o
f
G
S
A
i
s
b
etter
t
h
a
n
G
A
w
h
en
n
u
m
b
er
o
f
i
n
v
e
r
ter
le
v
el
i
n
cr
ea
s
e
s
w
h
ic
h
i
s
clea
r
f
r
o
m
th
e
s
i
m
u
latio
n
r
esu
l
ts
.
Fig
u
r
e
13.
C
o
m
p
ar
is
o
n
p
lo
ts
b
et
w
ee
n
G
A
a
n
d
GS
A
(
a)
Mo
d
u
latio
n
in
d
ex
v
er
s
u
s
C
o
m
p
u
tatio
n
al
ti
m
e
(
b
)
Mo
d
u
latio
n
i
n
d
ex
v
er
s
u
s
T
HD
(
c)
Mo
d
u
latio
n
in
d
ex
v
er
s
u
s
s
w
i
tch
in
g
an
g
le
s
Fig
u
r
e
1
4.
P
er
f
o
r
m
an
ce
co
m
p
ar
is
o
n
o
n
t
h
e
b
asis
o
f
T
HD
f
o
r
GA
,
GS
A
an
d
w
a
v
el
et
tr
an
s
f
o
r
m
Fin
all
y
,
t
h
e
r
es
u
lts
f
o
r
%
T
HD
v
al
u
es
o
b
tain
ed
b
y
ea
c
h
o
f
th
e
t
h
r
ee
tech
n
iq
u
e
s
-
G
A
,
GS
A
a
n
d
W
T
f
o
r
7
-
lev
el
i
n
v
er
ter
ar
e
co
m
p
ar
ed
b
y
m
ea
n
s
o
f
g
r
ap
h
ical
r
ep
r
esen
tatio
n
as
s
h
o
w
n
in
Fi
g
u
r
e
1
4
.
Fro
m
t
h
e
p
er
f
o
r
m
a
n
ce
co
m
p
ar
i
s
o
n
g
r
ap
h
it
ca
n
b
e
s
ee
n
th
at
f
o
r
7
le
v
el
in
v
er
ter
s
(
ca
s
ca
d
e
H
B
r
id
g
e
an
d
H
y
b
r
id
M
L
I
)
th
e
m
in
i
m
u
m
T
HD
o
cc
u
r
s
in
ex
p
er
i
m
en
t
r
e
s
u
lt
s
f
o
r
h
y
b
r
id
in
v
er
ter
w
h
er
ea
s
,
w
a
v
elet
b
ased
FL
C
g
i
v
e
s
ap
p
r
o
x
im
a
tel
y
1
1
%
les
s
T
HD
th
a
n
G
S
A
b
ased
F
L
C
a
n
d
3
1
%les
s
t
h
an
G
A
b
ased
F
L
C
.
Ho
w
e
v
er
,
I
t
is
s
ee
n
th
at
o
p
ti
m
iza
tio
n
tec
h
n
iq
u
es
-
GA
a
n
d
GS
A
ar
e
b
etter
th
an
W
av
elet
T
r
an
s
f
o
r
m
tec
h
n
iq
u
e
s
w
h
e
n
h
i
g
h
er
lev
el
o
f
in
v
er
ter
o
u
tp
u
t
i
s
co
n
s
id
er
ed
b
ec
au
s
e
in
w
av
e
let
tr
an
s
f
o
r
m
,
as
t
h
e
n
u
m
b
er
o
f
le
v
e
l
s
i
n
o
u
tp
u
t
w
a
v
ef
o
r
m
in
cr
ea
s
es,
m
o
r
e
ap
p
r
o
x
i
m
atio
n
f
u
n
ctio
n
s
b
r,
s
an
d
w
a
v
elet
f
a
m
il
y
ψ
r,
s
(
x
)
ar
e
n
ee
d
ed
to
b
e
g
en
er
ated
i
n
th
e
o
r
d
er
2
r
an
d
th
e
h
ar
m
o
n
ic
d
is
to
r
tio
n
in
GS
A
b
ased
FLC
is
less
th
a
n
G
A
b
ased
FLC
f
o
r
b
o
th
co
n
s
id
er
d
to
p
o
lo
g
ies.
Evaluation Warning : The document was created with Spire.PDF for Python.