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p
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ly
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DC
co
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ely
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[
1
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,
[
2
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T
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s
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ch
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r
g
in
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,
a
n
d
v
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latio
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[
3
]
.
Desig
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in
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an
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ec
tiv
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c
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tr
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l
s
tr
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ip
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in
p
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ts
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s
tate
v
ar
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an
d
o
u
tp
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ts
[
1
]
.
Ho
wev
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,
th
e
in
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t n
o
n
lin
ea
r
ity
o
f
DC
-
D
C
co
n
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ter
s
esp
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in
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tem
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s
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ch
allen
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s
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r
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W
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izatio
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tech
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a
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[
4
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,
n
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ated
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tab
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ar
ac
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is
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[
5
]
,
al
b
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at
th
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s
t
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cr
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s
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ch
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eg
r
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[
6
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,
[
7
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.
T
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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Dr
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2088
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8
6
9
4
Grey
w
o
lf o
p
timiz
a
tio
n
a
p
p
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ch
to
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l fo
r
b
u
ck
…
(
S
a
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a
Mo
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s
lim
)
641
tech
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iq
u
e,
o
r
ig
in
ally
i
n
tr
o
d
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ce
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b
y
Kr
s
tić
et
a
l.
[
8
]
in
1
9
9
1
,
t
o
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eg
u
late
th
e
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u
tp
u
t
v
o
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h
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[
8
]
,
[
9
]
.
I
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th
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ap
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g
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eh
a
v
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lv
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1
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]
is
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n
d
u
ctio
n
m
o
d
e
(
C
C
M)
,
tak
in
g
in
to
ac
co
u
n
t
f
lu
ctu
atio
n
s
in
b
o
th
in
p
u
t
v
o
ltag
e
an
d
lo
a
d
co
n
d
itio
n
s
.
T
h
e
co
n
v
er
ter
m
o
d
e
l
is
estab
lis
h
ed
u
s
in
g
th
e
s
tate
-
s
p
ac
e
av
er
ag
in
g
(
SS
A)
ap
p
r
o
ac
h
with
in
th
e
MA
T
L
AB
/S
im
u
lin
k
en
v
ir
o
n
m
en
t.
T
o
ac
h
iev
e
ac
c
u
r
ate
v
o
ltag
e
r
eg
u
latio
n
,
a
b
ac
k
s
tep
p
in
g
co
n
tr
o
l
law
is
i
m
p
lem
en
ted
,
an
d
its
p
ar
am
eter
s
ar
e
o
p
tim
ized
th
r
o
u
g
h
th
e
g
r
e
y
wo
lf
o
p
tim
izatio
n
(
GW
O)
alg
o
r
ith
m
.
R
ec
en
t
r
esear
ch
h
as
s
h
o
wn
th
at
GW
O
o
u
tp
er
f
o
r
m
s
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
an
d
g
en
etic
alg
o
r
ith
m
s
(
GA)
wh
en
tu
n
in
g
co
n
tr
o
ller
s
f
o
r
DC
-
DC
co
n
v
er
ter
s
in
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
s
,
d
u
e
to
its
ef
f
ec
tiv
e
ex
p
lo
r
atio
n
s
tr
ateg
y
an
d
f
aster
co
n
v
e
r
g
en
ce
.
Fo
r
e
x
am
p
le,
a
co
m
p
ar
ativ
e
s
tu
d
y
b
y
B
ar
ae
an
et
a
l
.
[
1
1
]
d
em
o
n
s
tr
a
ted
th
at
co
n
tr
o
ller
s
b
ased
o
n
GW
O
d
eliv
er
h
ig
h
er
ef
f
icien
cy
an
d
en
h
an
ce
d
s
tab
il
ity
in
PV
ap
p
licatio
n
s
co
m
p
ar
ed
to
PS
O
-
an
d
GA
-
b
ased
d
esig
n
s
.
Similar
ly
,
Kr
i
s
h
n
ar
am
et
a
l.
[
1
2
]
r
ep
o
r
te
d
th
at
GW
O
m
ain
tain
s
r
o
b
u
s
tn
ess
u
n
d
er
d
y
n
am
ic
en
v
ir
o
n
m
en
tal
ch
an
g
es,
im
p
r
o
v
in
g
v
o
ltag
e
r
eg
u
latio
n
in
PV
s
y
s
tem
s
.
T
h
ese
r
esu
lts
h
ig
h
li
g
h
t
th
e
p
o
te
n
tial
o
f
GW
O
to
en
h
an
ce
b
o
th
th
e
p
er
f
o
r
m
an
ce
an
d
r
eliab
ilit
y
o
f
DC
-
DC
co
n
v
er
ter
s
in
PV
ap
p
licati
o
n
s
.
Mo
r
eo
v
e
r
,
th
e
p
r
o
p
o
s
ed
co
n
v
er
ter
an
d
GW
O
-
b
ased
co
n
tr
o
ller
ar
e
v
alid
at
ed
ex
p
er
im
e
n
tally
.
T
h
e
s
tr
u
ct
u
r
e
o
f
t
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
ws:
Sectio
n
2
p
r
esen
ts
th
e
m
o
d
elin
g
an
d
p
ar
am
eter
s
izin
g
o
f
th
e
b
u
c
k
c
o
n
v
er
ter
;
Sectio
n
3
d
escr
ib
es
th
e
b
ac
k
s
tep
p
in
g
co
n
tr
o
ller
a
n
d
its
im
p
lem
e
n
tatio
n
;
Sectio
n
4
ex
p
lain
s
th
e
i
n
teg
r
atio
n
o
f
GW
O
f
o
r
p
ar
am
eter
o
p
tim
izatio
n
;
s
u
b
s
eq
u
en
t
s
ec
tio
n
s
d
etail
s
im
u
latio
n
an
d
ex
p
er
im
en
tal
r
e
s
u
lts
,
f
o
llo
wed
b
y
p
er
f
o
r
m
an
ce
ev
al
u
atio
n
a
n
d
c
o
n
clu
d
in
g
r
em
a
r
k
s
.
2.
M
O
DE
L
L
I
NG
AND
D
E
S
I
G
N
O
F
B
UCK
CO
NVER
T
E
R
R
e
n
o
w
n
e
d
f
o
r
i
ts
s
i
m
p
li
c
i
t
y
a
n
d
e
x
t
e
n
s
i
v
e
u
s
e
i
n
p
o
w
e
r
r
e
g
u
l
a
t
i
o
n
,
t
h
e
b
u
c
k
c
o
n
v
e
r
t
e
r
i
s
wi
d
e
l
y
e
m
p
l
o
y
e
d
i
n
p
o
w
e
r
el
e
c
t
r
o
n
i
cs
a
p
p
l
i
c
a
ti
o
n
s
.
I
t
s
p
r
i
m
a
r
y
f
u
n
c
ti
o
n
i
s
t
o
r
e
d
u
c
e
a
h
i
g
h
e
r
i
n
p
u
t
v
o
l
t
a
g
e
t
o
a
d
e
s
i
r
e
d
l
o
w
e
r
o
u
t
p
u
t
v
o
l
t
a
g
e
w
h
i
l
e
m
ain
t
a
i
n
i
n
g
e
f
f
i
c
i
e
n
t
e
n
e
r
g
y
c
o
n
v
e
r
s
i
o
n
.
T
h
e
b
a
s
i
c
s
c
h
e
m
a
t
i
c
o
f
a
b
u
c
k
c
o
n
v
e
r
t
e
r
w
i
t
h
a
r
e
s
is
t
i
v
e
l
o
a
d
i
s
p
r
es
e
n
t
e
d
i
n
F
i
g
u
r
e
1
[
1
4
]
,
i
l
l
u
s
t
r
a
t
i
n
g
it
s
f
u
n
d
a
m
e
n
t
a
l
c
o
m
p
o
n
e
n
t
s
a
n
d
o
p
e
r
a
t
i
n
g
s
t
r
u
ct
u
r
e
.
2
.
1
.
T
he
o
pera
t
ing
m
o
des
o
f
t
he
bu
ck
co
nv
er
t
er
T
h
e
b
u
ck
c
o
n
v
e
r
ter
ca
n
o
p
e
r
ate
in
two
d
is
tin
ct
m
o
d
es:
co
n
tin
u
o
u
s
c
o
n
d
u
ctio
n
m
o
d
e
(
C
C
M)
an
d
d
is
co
n
tin
u
o
u
s
co
n
d
u
ctio
n
m
o
d
e
(
DC
M)
.
I
n
th
is
wo
r
k
,
th
e
f
o
cu
s
is
o
n
m
o
d
elin
g
an
d
p
a
r
a
m
eter
s
izin
g
o
f
th
e
b
u
ck
c
o
n
v
e
r
ter
in
C
C
M.
I
n
th
is
m
o
d
e,
th
e
co
n
v
er
ter
alter
n
a
tes
b
etwe
en
o
n
ly
two
s
witch
i
n
g
s
tates:
“S
o
n
,
D
o
f
f
”
an
d
“S
o
f
f
,
D
o
n
.
”
Mo
r
e
o
v
er
,
th
e
in
d
u
cto
r
cu
r
r
en
t
n
ev
er
r
ea
ch
es
ze
r
o
[
1
5
]
.
C
o
n
s
eq
u
en
tly
,
th
e
an
aly
s
is
co
n
s
id
er
s
th
e
co
n
v
e
r
ter
in
th
e
s
e
two
s
witch
in
g
co
n
d
itio
n
s
.
Su
ch
cir
cu
its
ar
e
co
m
m
o
n
ly
r
ef
er
r
ed
to
as
s
er
ies
co
n
v
er
ter
s
,
as th
e
e
n
er
g
y
f
lo
w
s
d
ir
ec
tly
f
r
o
m
th
e
s
o
u
r
ce
to
t
h
e
lo
ad
.
F
i
g
u
r
e
2
s
h
o
w
s
t
h
e
o
p
e
r
at
i
o
n
o
f
s
wi
t
c
h
S
,
d
u
r
i
n
g
w
h
ic
h
t
h
e
s
o
u
r
c
e
e
n
e
r
g
y
i
s
d
e
l
i
v
e
r
e
d
t
o
t
h
e
l
o
a
d
w
h
i
l
e
a
l
s
o
b
e
i
n
g
s
t
o
r
e
d
i
n
t
h
e
i
n
d
u
c
t
o
r
[
1
6
]
.
W
h
e
n
t
h
e
s
w
i
t
c
h
i
s
t
u
r
n
e
d
o
f
f
,
t
h
e
d
i
o
d
e
a
l
l
o
w
s
t
h
e
i
n
d
u
c
t
o
r
t
o
r
e
l
e
a
s
e
i
t
s
s
t
o
r
e
d
e
n
e
r
g
y
.
F
i
g
u
r
e
3
i
ll
u
s
t
r
a
te
s
t
h
e
b
u
c
k
c
o
n
v
e
r
t
e
r
c
i
r
c
u
i
t
wh
e
n
s
w
i
tc
h
S
1
is
i
n
t
h
e
o
p
e
n
s
t
at
e
[
1
7
]
,
[
1
8
].
L
C
R
i
c
i
R
V
o
u
t
V
in
D
+
-
+
-
S
L
C
R
i
c
i
R
V
o
u
t
V
in
D
+
-
+
-
S
Fig
u
r
e
1
.
B
u
ck
c
o
n
v
e
r
ter
Fig
u
r
e
2
.
B
u
ck
c
o
n
v
e
r
ter
wh
e
n
S
1
is
clo
s
ed
L
C
R
i
c
i
R
V
o
u
t
V
in
D
ON
+
-
+
-
Fig
u
r
e
3
.
B
u
ck
c
o
n
v
e
r
ter
wh
e
n
S
1
is
o
p
en
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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Dr
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2
.
2
.
St
a
t
e
s
pa
ce
mo
dellin
g
o
f
DC
-
DC
bu
ck
co
nv
er
t
er
T
h
is
s
ec
tio
n
in
tr
o
d
u
c
es
th
e
s
tate
-
s
p
ac
e
av
er
ag
in
g
(
SS
A)
te
ch
n
iq
u
e
t
o
m
ath
em
atica
lly
r
e
p
r
esen
t
th
e
DC
-
DC
co
n
v
er
ter
u
n
d
er
v
ar
io
u
s
o
p
er
atin
g
co
n
d
itio
n
s
in
co
n
t
in
u
o
u
s
co
n
d
u
ctio
n
m
o
d
e.
B
y
ap
p
ly
in
g
Kir
ch
h
o
f
f
’
s
Vo
ltag
e
L
aw
(
KVL
)
an
d
Kir
c
h
h
o
f
f
’
s
C
u
r
r
en
t
L
aw
(
KC
L
)
,
t
h
e
d
if
f
er
en
tial
e
q
u
atio
n
s
d
escr
ib
in
g
th
e
co
n
v
er
ter
’
s
s
tate
v
ar
iab
les d
u
r
in
g
t
h
e
ON
s
tate
o
f
MO
SF
E
T
S1
ar
e
d
er
iv
ed
as
(
1
)
[1
9
]
.
{
=
−
=
−
(
1
)
Similar
ly
,
f
o
r
th
e
OFF s
tate
o
f
th
e
s
witch
,
th
e
r
ep
r
esen
tatio
n
in
s
tate
s
p
ac
e
is
tr
an
s
f
o
r
m
ed
i
n
to
(
2
)
[
20
]
.
{
=
−
=
−
(
2
)
I
n
m
atr
ix
f
o
r
m
,
in
(
1
)
an
d
(
2
)
ca
n
b
e
r
esp
ec
tiv
ely
s
h
o
wn
as
(
3
)
.
[
d
dt
d
v
dt
]
=
[
0
−
1
1
−
1
]
[
]
+
[
1
0
]
(
3
)
[
d
dt
d
v
dt
]
=
[
0
−
1
1
−
1
]
[
]
+
[
0
0
]
(
4
)
Fo
r
ea
ch
s
witch
in
g
p
o
s
itio
n
,
t
h
e
s
y
s
tem
is
lin
ea
r
;
th
er
ef
o
r
e
,
(
3
)
an
d
(
4
)
a
r
e
d
ef
in
e
d
b
y
s
tat
e
-
s
p
ac
e
eq
u
atio
n
s
in
th
e
s
tan
d
ar
d
f
o
r
m
as
(
5
)
an
d
(
6
)
[2
1
]
.
Ẋ
=
1
+
1
(
5
)
Ẋ
=
2
+
2
(
6
)
W
er
e
,
=
[
1
2
]
.
T
h
e
ter
m
x
is
t
h
e
b
u
ck
co
n
v
er
t
er
s
tate
v
ec
to
r
d
e
f
in
ed
as
in
d
u
cto
r
cu
r
r
en
t
i
L
an
d
ca
p
ac
ito
r
v
o
ltag
e
v
C
,
̇
it’s
d
er
iv
ativ
e
an
d
u
is
th
e
co
n
v
er
ter
DC
in
p
u
t
v
ec
to
r
.
A
1
,
B
1
r
ep
r
esen
t
th
e
s
tatu
s
o
f
in
p
u
t
m
atr
ices
f
o
r
th
e
s
witch
ON
s
tate
,
an
d
A
2
,
B
2
r
ep
r
esen
t
th
e
s
tatu
s
o
f
in
p
u
t m
atr
ices
f
o
r
th
e
s
witch
OFF
s
tate.
T
o
r
ep
r
esen
t
th
e
d
y
n
a
m
ic
o
f
th
e
s
y
s
tem
an
d
to
f
in
d
th
e
av
er
ag
e
d
b
e
h
av
io
r
o
f
t
h
e
b
u
ck
co
n
v
er
ter
o
v
er
o
n
e
s
witch
i
n
g
p
e
r
io
d
,
t
h
e
SS
A
m
eth
o
d
is
u
s
ed
.
B
y
d
ef
in
in
g
t
h
e
d
u
t
y
cy
cle
“d
”
as
a
weig
h
ti
n
g
f
ac
to
r
an
d
u
s
in
g
(
3
)
an
d
(
4
)
,
th
e
SS
A
eq
u
atio
n
in
C
C
M
is
o
b
tain
ed
:
Ẋ
=
+
(
7)
W
h
er
e
th
e
co
m
p
lete
s
tate
m
atr
ix
is
(
8
)
.
A=
A
1
d
+A
2
(1
-
d
)
(
8
)
B
=B
1
d
+
B
2
(1
-
d)
(
9
)
Hen
ce
,
th
e
d
y
n
am
ic
eq
u
atio
n
o
f
th
e
s
y
s
tem
ca
n
b
e
d
escr
ib
ed
b
y
[
1
]
.
[
d
dt
d
v
dt
]
=
[
0
1
−
1
1
−
1
]
[
]
+
[
0
]
d
(
1
0
)
2
.
3
.
Desig
nin
g
o
f
DC
-
DC
bu
ck
co
nv
er
t
er
pa
ra
met
er
s
Ass
u
m
in
g
th
e
d
u
ty
c
y
cle
o
f
th
e
b
u
ck
c
o
n
v
e
r
ter
o
p
er
atin
g
in
C
C
M
i
s
g
iv
en
b
y
(
1
1
)
[2
2
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Grey
w
o
lf o
p
timiz
a
tio
n
a
p
p
r
o
a
ch
to
o
p
tima
l b
a
ck
s
tep
p
i
n
g
c
o
n
tr
o
l fo
r
b
u
ck
…
(
S
a
n
a
Mo
u
s
lim
)
643
=
(
1
1
)
T
h
e
d
u
ty
cy
cle
v
a
r
ies d
ep
en
d
i
n
g
o
n
th
e
ap
p
lied
in
p
u
t v
o
ltag
e
in
o
r
d
e
r
to
h
av
e
a
c
o
n
s
tan
t o
u
tp
u
t v
o
ltag
e.
Fo
r
a
b
u
c
k
co
n
v
er
ter
,
t
h
e
r
ip
p
le
o
f
th
e
c
u
r
r
en
t i
n
th
e
in
d
u
ctan
ce
ca
n
b
e
d
em
o
n
s
tr
ated
b
y
(
1
2
)
[2
3
]
.
=
×
1
−
d
L
f
×
(
1
2
)
T
h
e
r
ip
p
le
o
f
th
e
cu
r
r
en
t
is
in
f
lu
en
ce
d
b
y
th
e
f
r
e
q
u
en
c
y
o
f
th
e
PW
M
s
ig
n
al,
th
e
d
u
ty
cy
cle
,
a
n
d
th
e
L
in
d
u
ctio
n
co
ef
f
icien
t.
So
,
t
h
e
in
d
u
ctan
ce
v
alu
e
is
ca
lcu
lated
b
y
(
1
3
)
[2
4
]
.
=
×
1
−
d
f
×
(
1
3
)
An
d
r
ip
p
le
i
n
th
e
o
u
tp
u
t c
a
p
ac
ito
r
is
co
n
s
id
er
ed
to
b
e
0
.
2
% o
f
th
e
o
u
t
p
u
t v
o
ltag
e.
=
×
(
1
−
d
)
8
×
×
²
×
(
1
4
)
E
m
p
lo
y
in
g
Sch
o
ttk
y
d
io
d
es
elim
in
ates
r
ev
er
s
e
r
ec
o
v
er
y
is
s
u
es,
wh
ich
in
tu
r
n
r
ed
u
ce
s
ex
tr
a
s
witch
in
g
lo
s
s
e
s
.
T
h
e
ef
f
ec
tiv
e
(
R
MS)
cu
r
r
en
t f
l
o
win
g
th
r
o
u
g
h
th
e
d
i
o
d
e
is
g
iv
en
b
y
(
1
5
)
.
(
)
=
√
(
1
−
)
√
(
1
−
)
(
1
5
)
3.
M
E
T
H
O
D
3
.
1
.
B
a
c
k
s
t
eppin
g
co
ntr
o
ller
C
o
n
tr
o
ller
s
b
ased
o
n
th
e
d
ir
ec
t
L
y
ap
u
n
o
v
m
eth
o
d
o
f
f
e
r
a
b
et
ter
alter
n
ativ
e.
T
h
e
ap
p
r
o
ac
h
c
o
n
s
is
ts
of
f
in
d
in
g
a
tr
ip
let
(
L
y
a
p
u
n
o
v
f
u
n
ctio
n
,
co
n
tr
o
l
law,
ad
ap
tatio
n
law)
th
at
m
ee
ts
th
e
s
p
ec
if
icat
io
n
s
an
d
tak
es
in
to
ac
co
u
n
t
th
e
d
y
n
am
ics
o
f
t
h
e
s
y
s
tem
[2
5
]
.
B
ac
k
s
tep
p
in
g
is
th
e
alg
o
r
ith
m
th
at
h
as
m
ad
e
th
is
ap
p
r
o
ac
h
ap
p
licab
le
to
a
lar
g
e
class
o
f
s
y
s
tem
s
,
in
d
ep
en
d
en
tly
o
f
th
ei
r
o
r
d
er
[2
6
]
.
Step
1
:
T
h
e
f
ir
s
t e
r
r
o
r
v
a
r
iab
le
is
d
ef
in
ed
b
y
(
1
6
)
.
1
=
1
−
(
1
6
)
W
ith
th
ese
v
ar
iab
les,
th
e
s
y
s
tem
(
1
6
)
is
wr
itten
(
1
7
)
.
̇
1
=
̇
1
−
̇
=
2
−
1
−
̇
(
1
7
)
Fo
r
s
u
ch
a
s
y
s
tem
,
th
e
q
u
ad
r
at
ic
f
u
n
ctio
n
1
is
a
g
o
o
d
ch
o
ice
o
f
th
e
L
y
ap
u
n
o
v
c
o
n
tr
o
l
f
u
n
ctio
n
.
I
ts
d
er
iv
ativ
e
is
g
iv
en
b
y
(
1
8
)
.
1
(
1
)
=
1
2
1
2
(
1
8
)
̇
1
=
1
̇
1
=
1
(
2
−
1
−
̇
)
(
1
9
)
A
ju
d
icio
u
s
ch
o
ice
o
f
2
wo
u
ld
m
ak
e
1
̇
n
e
g
ativ
e
an
d
e
n
s
u
r
e
th
e
s
tab
ilit
y
o
f
th
e
o
r
ig
i
n
o
f
th
e
s
u
b
s
y
s
tem
d
escr
ib
ed
b
y
(
1
9
)
.
T
a
k
e
as th
e
v
alu
e
o
f
2
th
e
f
u
n
ctio
n
1
s
u
ch
th
at
an
d
th
e
d
er
i
v
ativ
e
is
wr
itten
[2
7
]
:
̇
1
=
−
1
1
2
≤
0
(
2
0
)
Hen
ce
,
th
e
asy
m
p
to
tic
s
tab
ilit
y
o
f
th
e
o
r
ig
i
n
o
f
(
1
9
)
.
2
−
1
−
̇
=
−
1
1
(
2
1
)
W
h
er
e
1
>
0
is
a
d
esig
n
p
ar
a
m
eter
.
T
h
is
g
iv
es
in
(
2
2
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
640
-
6
52
644
2
=
(
−
1
1
+
̇
+
1
)
(
2
2
)
Step
2
: We c
o
n
s
id
er
th
e
s
u
b
s
y
s
tem
(
1
6
)
,
a
n
d
we
d
e
f
in
e
th
e
n
ew
er
r
o
r
v
ar
iab
le:
2
=
2
−
2
(
2
3
)
W
h
ich
r
ep
r
esen
ts
th
e
d
ev
iatio
n
b
etwe
en
th
e
s
tate
v
ar
iab
le
2
an
d
its
d
esire
d
v
alu
e
1
.
B
ec
au
s
e
2
ca
n
n
o
t
b
e
f
o
r
ce
d
to
in
s
tan
tan
e
o
u
s
ly
tak
e
o
n
a
d
esire
d
v
alu
e,
in
th
is
ca
s
e
,
th
e
er
r
o
r
2
is
n
o
t,
in
s
tan
tan
eo
u
s
ly
,
ze
r
o
.
T
h
e
d
esig
n
in
th
is
s
tep
co
n
s
is
ts
,
th
en
,
in
f
o
r
cin
g
it to
ca
n
ce
l its
elf
with
a
ce
r
tain
d
y
n
am
ic,
c
h
o
s
en
b
ef
o
r
eh
an
d
.
Fo
r
wh
ich
we
ch
o
o
s
e
as th
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
[
2
7
]
:
2
(
1
,
2
)
=
1
2
1
2
+
1
2
2
2
(
2
4
)
T
h
e
latter
h
as th
e
d
e
r
iv
ativ
e
(
2
5
)
.
̇
2
=
1
̇
1
+
2
̇
2
̇
2
=
1
[
(
(
2
+
2
)
1
−
1
1
−
̇
)
+
(
2
−
1
1
+
−
̇
2
)
]
=
−
1
1
2
+
2
(
1
1
−
1
1
+
−
̇
2
)
(
2
5
)
No
w
we
h
av
e
th
e
r
ea
l u
co
m
m
an
d
,
wh
ich
is
f
o
r
m
u
lated
as
(
2
6
)
an
d
(
2
7
)
.
1
1
−
1
1
+
−
̇
2
=
−
2
2
(
2
6
)
=
(
−
2
2
+
̇
2
+
1
1
−
1
1
)
(
2
7
)
W
h
er
e
2
>
0
is
a
s
ec
o
n
d
d
esig
n
p
ar
am
eter
.
W
ith
th
is
ch
o
ice,
we
h
av
e
in
(
2
8
)
.
̇
2
=
−
1
1
2
+
−
2
2
2
(
2
8
)
3
.
2
.
G
re
y
wo
lf
o
ptim
izer
Gr
ey
wo
lv
es
ar
e
class
if
ied
as
ap
ex
p
r
e
d
ato
r
s
,
o
cc
u
p
y
i
n
g
th
e
to
p
tier
o
f
th
e
f
o
o
d
c
h
ain
.
T
h
ey
u
s
u
ally
f
o
r
m
p
ac
k
s
,
with
an
av
er
a
g
e
s
ize
o
f
5
to
1
2
m
em
b
e
r
s
.
I
m
p
o
r
tan
tly
,
th
ese
p
ac
k
s
m
ain
tain
a
s
tr
ict
d
o
m
in
an
ce
-
b
ased
s
o
cial
h
ier
ar
ch
y
,
as
s
h
o
wn
in
Fig
u
r
e
4
[
2
9
].
Fro
m
a
m
ath
em
atica
l
p
er
s
p
ec
tiv
e,
th
e
th
r
ee
b
est
ca
n
d
id
at
e
s
o
lu
tio
n
s
in
th
e
GW
O
alg
o
r
ith
m
ar
e
d
en
o
ted
as a
lp
h
a
(
α
)
,
b
e
ta
(
β),
an
d
d
elta
(
δ)
.
All o
th
er
ca
n
d
id
ate
s
o
lu
tio
n
s
ar
e
class
if
ied
as o
m
eg
a
(
ω
)
.
T
h
e
s
ea
r
ch
an
d
h
u
n
tin
g
b
eh
av
io
r
in
GW
O
is
d
ir
ec
ted
b
y
t
h
e
al
p
h
a,
b
eta,
a
n
d
d
elta
wo
lv
es,
wh
er
ea
s
th
e
o
m
eg
a
wo
lv
es
ad
ju
s
t
th
eir
p
o
s
itio
n
s
b
y
f
o
llo
win
g
th
ese
lead
in
g
s
o
lu
tio
n
s
.
T
h
e
p
s
eu
d
o
co
d
e
o
f
th
e
GW
O
alg
o
r
ith
m
is
p
r
esen
ted
in
Alg
o
r
ith
m
1
[
30
]
.
Alg
o
r
ith
m
1
.
Gr
ey
wo
lf
o
p
tim
izatio
n
alg
o
r
ith
m
I
n
itialize
th
e
g
r
ey
w
o
lf
p
o
p
u
la
tio
n
Xi,
i=1
,
n
I
n
itialize
a,
A
an
d
C
C
alcu
late
th
e
f
itn
ess
o
f
ea
ch
s
ea
r
ch
ag
en
t
X
α
=
th
e
b
est s
ea
r
ch
ag
en
t
X
β
=
th
e
s
ec
o
n
d
b
est s
ea
r
ch
ag
en
t
X
δ
=
th
e
th
ir
d
b
est s
ea
r
ch
ag
e
n
t
wh
ile
t<m
ax
n
u
m
b
er
o
f
iter
ati
o
n
d
o
f
o
r
ea
ch
s
ea
r
ch
a
g
en
t d
o
R
an
d
o
m
ly
in
itialize
r
1
an
d
r
2
Up
d
ate
th
e
p
o
s
itio
n
o
f
th
e
cu
r
r
en
t sear
ch
ag
en
t
Up
d
ate
a,
A
an
d
C
C
alcu
late
th
e
f
itn
ess
o
f
al
l sear
ch
ag
en
ts
Up
d
ate
X
α
,X
β
an
d
X
δ
t
=
t
+
1
r
etu
r
n
X
α
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Grey
w
o
lf o
p
timiz
a
tio
n
a
p
p
r
o
a
ch
to
o
p
tima
l b
a
ck
s
tep
p
i
n
g
c
o
n
tr
o
l fo
r
b
u
ck
…
(
S
a
n
a
Mo
u
s
lim
)
645
Fig
u
r
e
4
.
Hier
ar
c
h
y
o
f
th
e
g
r
e
y
wo
lf
(
d
o
m
in
an
ce
d
ec
r
ea
s
es f
r
o
m
to
p
to
b
o
tto
m
)
T
h
e
p
ac
k
'
s
en
cir
clin
g
b
e
h
av
io
r
in
h
u
n
ti
n
g
p
r
ey
ca
n
b
e
ex
p
r
es
s
ed
as
(
29
)
.
(
+
1
)
=
(
)
−
∗
(
2
9
)
W
h
er
e
Xp
is
th
e
p
o
s
itio
n
o
f
th
e
p
r
ey
,
A
is
th
e
c
o
ef
f
icien
t
v
ec
to
r
,
an
d
D
is
d
ef
in
ed
as f
o
llo
w
s
:
=
|
∗
(
)
−
(
)
|
(
3
0
)
Her
e,
r
ep
r
esen
ts
th
e
co
ef
f
icie
n
t v
ec
to
r
,
d
en
o
tes th
e
p
o
s
itio
n
o
f
th
e
g
r
e
y
wo
lf
,
an
d
is
th
e
cu
r
r
en
t iter
atio
n
n
u
m
b
er
.
T
h
e
c
o
ef
f
icien
t
v
ec
to
r
s
an
d
ar
e
ca
lcu
lated
as f
o
llo
w
s
:
=
2
∗
1
−
,
(
3
1
)
=
2
2
(
3
2
)
I
n
th
is
co
n
tex
t,
1
an
d
2
ar
e
in
d
ep
e
n
d
en
t
r
an
d
o
m
n
u
m
b
e
r
s
u
n
if
o
r
m
ly
d
is
tr
ib
u
ted
b
etwe
en
0
a
n
d
1
,
an
d
d
en
o
tes
th
e
en
cir
clin
g
co
ef
f
icien
t.
W
ith
in
th
e
GW
O
alg
o
r
ith
m
,
th
e
co
ef
f
icien
t
d
ec
r
ea
s
es
lin
ea
r
ly
f
r
o
m
2
to
0
,
as
g
iv
en
in
(
33
)
.
=
2
−
2
(
)
(
3
3
)
Her
e,
t
r
ep
r
esen
ts
th
e
cu
r
r
en
t
iter
atio
n
in
d
ex
,
wh
ile
T
d
en
o
t
es
th
e
to
tal
n
u
m
b
er
o
f
iter
atio
n
s
allo
wed
.
W
ith
in
th
e
GW
O
f
r
am
ewo
r
k
,
th
e
alp
h
a
(
α
)
,
b
eta
(
β),
an
d
d
elta
(
δ)
wo
lv
es a
r
e
ass
u
m
ed
to
p
o
s
s
ess
s
u
p
er
io
r
k
n
o
wled
g
e
ab
o
u
t
th
e
p
r
o
b
ab
le
lo
ca
tio
n
o
f
th
e
p
r
ey
.
C
o
n
s
eq
u
e
n
tly
,
th
ese
lead
in
g
wo
lv
es
d
ir
ec
t
th
e
m
o
v
e
m
e
n
t
o
f
th
e
o
m
e
g
a
(
ω
)
wo
l
v
es
to
war
d
th
e
o
p
tim
al
s
o
lu
tio
n
.
T
h
e
p
o
s
itio
n
o
f
ea
c
h
wo
lf
is
m
ath
em
atica
lly
u
p
d
ated
ac
co
r
d
in
g
to
(
3
4
)
.
(
+
1
)
=
1
+
2
+
3
3
(
3
4
)
W
h
er
e
X
1
, X
2
et
X
3
ar
e
ca
lcu
lated
as
(
3
5
)
-
(
3
7
)
.
1
=
|
−
1
∗
|
(
3
5
)
2
=
|
−
2
∗
|
(
3
6
)
3
=
|
−
3
∗
|
(
3
7
)
W
h
er
e
X
α
, X
β
,
et
X
δ
ar
e
th
e
p
o
s
itio
n
s
o
f
alp
h
a,
b
eta
,
an
d
d
el
ta
at
iter
atio
n
t; a
n
d
D
α
,
D
β
,
an
d
D
δ
ar
e
d
ef
in
ed
as
in
(
3
8
)
-
(
4
0
)
.
=
|
1
∗
−
|
(
3
8
)
=
|
2
∗
−
|
(
3
9
)
=
|
3
∗
−
|
(
4
0
)
W
h
er
e
C
1
, C
2
,
et
C
3
ar
e
ca
lcu
l
ated
as in
(
32
)
.
As
s
h
o
wn
in
Fig
u
r
e
5
,
t
h
is
s
ec
tio
n
f
o
c
u
s
es
o
n
s
im
u
latin
g
t
h
e
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
B
u
ck
co
n
v
e
r
ter
u
s
in
g
a
b
ac
k
s
tep
p
in
g
c
o
n
tr
o
ll
er
en
h
a
n
ce
d
th
r
o
u
g
h
an
o
p
tim
izatio
n
s
tr
ateg
y
.
T
h
e
g
r
e
y
wo
l
f
o
p
tim
izer
(
GW
O)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8
6
9
4
I
n
t J Po
w
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lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
640
-
6
52
646
alg
o
r
ith
m
is
em
p
lo
y
e
d
to
id
en
tify
th
e
o
p
tim
al
co
n
tr
o
ller
p
ar
am
eter
s
.
T
h
e
o
p
tim
izatio
n
p
r
o
ce
s
s
in
v
o
lv
es
iter
ativ
ely
ev
alu
atin
g
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
co
n
tr
o
ller
o
v
er
a
p
r
ed
eter
m
in
e
d
n
u
m
b
er
o
f
s
te
p
s
to
d
eter
m
in
e
th
e
p
ar
am
eter
s
et
th
at
y
ield
s
th
e
b
est r
esu
lts
.
Fig
u
r
e
5
.
Ov
e
r
all
v
iew
o
f
t
h
e
clo
s
ed
-
lo
o
p
s
y
s
tem
with
th
e
B
ac
k
s
tep
p
in
g
co
n
tr
o
ller
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
4
.
1
.
H
a
rdwa
re
s
ec
t
io
n
I
n
th
is
s
ec
tio
n
,
we
p
r
esen
t
a
n
ex
p
er
im
e
n
tal
p
latf
o
r
m
,
as
i
llu
s
tr
ated
in
Fig
u
r
e
6
,
f
o
r
th
e
p
r
ac
tical
im
p
lem
en
tatio
n
o
f
a
DC
-
DC
co
n
v
er
ter
f
o
r
a
p
h
o
to
v
o
ltaic
ap
p
licatio
n
.
W
e
will
ap
p
ly
th
e
b
ac
k
s
tep
p
in
g
co
n
tr
o
l
tech
n
iq
u
e
to
r
e
g
u
late
th
e
co
n
v
er
ter
'
s
o
u
tp
u
t
v
o
ltag
e
in
o
r
d
er
to
p
o
wer
a
r
esis
tiv
e
lo
ad
.
B
ased
o
n
th
e
d
esig
n
o
f
th
e
b
u
ck
co
n
v
er
ter
d
ev
el
o
p
ed
in
th
e
s
ec
o
n
d
s
ec
tio
n
,
we
wer
e
ab
le
to
d
eter
m
in
e
th
e
n
o
r
m
a
lized
v
alu
es
o
f
th
e
co
n
v
er
ter
co
m
p
o
n
en
ts
f
o
r
th
e
i
n
d
u
cto
r
L
,
ca
p
ac
ito
r
C
,
an
d
s
witch
in
g
f
r
e
q
u
en
c
y
f
w
h
ile
o
p
tim
izin
g
th
em
th
r
o
u
g
h
p
r
ac
tical
test
s
af
ter
th
e
co
n
v
er
t
er
d
esig
n
,
as illu
s
tr
ate
d
in
T
a
b
le
1
.
Fig
u
r
e
6
.
Ov
e
r
v
iew
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
T
ab
le
1
.
C
o
m
p
o
n
en
t
v
alu
es o
f
th
e
b
u
c
k
co
n
v
er
ter
C
o
m
p
o
n
e
n
t
s
V
a
l
u
e
s
L
1
2
0
u
H
C
2
2
0
u
F
R
1
10Ω
V
re
f
12V
V
in
48V
f
s
4
0
K
h
z
M
o
sf
e
t
I
R
F
5
2
0
D
i
o
d
e
M
B
R
4
0
4
5
P
T
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Grey
w
o
lf o
p
timiz
a
tio
n
a
p
p
r
o
a
ch
to
o
p
tima
l b
a
ck
s
tep
p
i
n
g
c
o
n
tr
o
l fo
r
b
u
ck
…
(
S
a
n
a
Mo
u
s
lim
)
647
T
h
e
ex
p
er
im
en
tal
s
etu
p
,
d
ep
ict
ed
in
Fig
u
r
e
7
,
co
n
s
is
ts
o
f
a
b
u
ck
co
n
v
er
ter
co
n
s
tr
u
cted
with
an
I
R
F5
2
0
MO
SF
E
T
,
u
s
in
g
th
e
s
p
ec
if
ied
v
alu
es
f
o
r
L
an
d
C
.
T
h
e
o
u
tp
u
t
cu
r
r
en
t
o
f
th
e
co
n
v
er
ter
is
m
ea
s
u
r
ed
u
s
in
g
an
L
T
S
2
5
-
NP
Hall
ef
f
ec
t
s
en
s
o
r
,
wh
ile
th
e
o
u
tp
u
t
v
o
ltag
e
(
V
out
)
is
m
o
n
ito
r
ed
with
an
L
V2
5
-
P
s
en
s
o
r
.
T
h
e
in
p
u
t
v
o
ltag
e
(
V
in
)
ca
n
b
e
ad
ju
s
te
d
as
n
ee
d
e
d
.
T
h
e
s
en
s
ed
cu
r
r
en
t
an
d
v
o
ltag
e
s
ig
n
als
ar
e
s
en
t
to
th
e
s
ig
n
al
co
n
d
itio
n
in
g
b
o
a
r
d
an
d
th
en
t
o
th
e
DSP’s
an
alo
g
in
p
u
t
c
h
a
n
n
els.
T
h
ese
f
ee
d
b
ac
k
s
ig
n
als
ar
e
u
s
e
d
to
r
e
g
u
late
th
e
r
ef
er
en
ce
v
o
ltag
e.
T
h
e
PW
M
s
ig
n
als g
en
er
ated
b
y
th
e
D
SP
ar
e
r
o
u
ted
th
r
o
u
g
h
th
e
PW
M
o
u
tp
u
t,
a
m
p
lifie
d
v
ia
a
d
r
iv
e
r
cir
cu
it,
a
n
d
ap
p
lied
to
th
e
MO
SF
E
T
g
ate.
Fig
u
r
e
7
.
Ov
e
r
v
iew
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
4
.
2
.
Sim
ula
t
i
o
n r
esu
lt
s
In
th
is
s
ec
tio
n
,
we
aim
t
o
s
im
u
late
th
e
clo
s
ed
-
lo
o
p
s
y
s
tem
with
th
e
b
ac
k
s
tep
p
in
g
co
n
tr
o
ller
as
s
h
o
wn
in
Fig
u
r
e
8
,
b
u
t
with
o
u
t
o
p
t
im
izin
g
its
p
ar
am
eter
s
.
I
n
th
is
s
im
u
latio
n
,
th
e
co
n
tr
o
ller
p
ar
am
eter
s
will
b
e
r
an
d
o
m
l
y
ch
o
s
en
with
o
u
t a
n
y
p
r
io
r
o
p
tim
izatio
n
.
T
h
e
r
esu
lts
clea
r
ly
s
h
o
w
th
at
th
e
s
y
s
tem
f
ails
to
ac
cu
r
ately
tr
ac
k
th
e
d
esire
d
r
ef
er
e
n
ce
v
o
lta
g
e.
I
n
s
tead
,
s
ig
n
if
ican
t
o
v
er
s
h
o
o
ts
an
d
o
s
cillatio
n
s
ar
e
o
b
s
er
v
ed
in
th
e
s
y
s
tem
'
s
r
esp
o
n
s
e.
T
h
ese
r
esu
lts
h
ig
h
lig
h
t
th
e
im
p
o
r
tan
ce
o
f
o
p
tim
izin
g
t
h
e
p
ar
am
eter
s
o
f
th
e
b
ac
k
s
tep
p
in
g
c
o
n
tr
o
ller
.
B
y
ju
d
icio
u
s
ly
ad
ju
s
tin
g
th
ese
p
ar
am
eter
s
,
it
is
p
o
s
s
ib
le
to
s
ig
n
if
ican
tly
im
p
r
o
v
e
th
e
s
y
s
tem
's
p
er
f
o
r
m
an
ce
,
r
ed
u
cin
g
o
v
er
s
h
o
o
ts
an
d
en
s
u
r
in
g
a
m
o
r
e
s
tab
le
an
d
p
r
ec
is
e
r
esp
o
n
s
e
to
th
e
r
e
f
er
en
ce
v
o
ltag
e
,
as sh
o
wn
in
F
ig
u
r
e
9
.
Fig
u
r
e
9
d
ep
icts
th
e
ev
o
lu
tio
n
o
f
th
e
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
b
u
ck
co
n
v
er
ter
with
th
e
b
a
ck
s
tep
p
in
g
co
n
tr
o
ller
o
p
tim
ized
u
s
in
g
th
e
GW
O
alg
o
r
ith
m
.
T
h
e
r
esu
lts
d
em
o
n
s
tr
ate
a
s
ig
n
if
ican
t
im
p
r
o
v
em
en
t
c
o
m
p
ar
e
d
to
th
e
p
r
ev
io
u
s
s
im
u
latio
n
with
o
u
t
o
p
tim
izatio
n
o
f
th
e
co
n
tr
o
ller
p
ar
am
eter
s
.
Op
tim
izin
g
t
h
e
p
ar
am
eter
s
o
f
th
e
b
ac
k
s
tep
p
in
g
co
n
t
r
o
ller
u
s
in
g
th
e
GW
O
alg
o
r
ith
m
h
as
e
n
a
b
led
f
in
d
in
g
v
alu
es
th
at
en
s
u
r
e
a
p
r
ec
is
e
an
d
f
ast
s
y
s
tem
r
esp
o
n
s
e.
T
h
e
o
p
tim
a
l
co
n
tr
o
ller
p
ar
am
ete
r
s
h
av
e
b
ee
n
ad
j
u
s
ted
to
r
ed
u
ce
tr
ac
k
in
g
er
r
o
r
s
o
f
th
e
r
ef
er
en
ce
v
o
ltag
e,
r
esu
ltin
g
in
a
r
esp
o
n
s
e
p
r
ac
t
ically
f
r
ee
f
r
o
m
o
v
er
s
h
o
o
ts
,
as sh
o
wn
in
Fig
u
r
e
10
.
Fig
u
r
e
8
.
Ou
t
p
u
t
v
o
ltag
e
V
out
o
f
b
u
c
k
co
n
v
er
ter
with
b
ac
k
s
t
ep
p
in
g
c
o
n
tr
o
ller
with
o
u
t
o
p
tim
izatio
n
To
en
s
u
r
e
th
e
r
eliab
ilit
y
a
n
d
s
tab
ilit
y
o
f
th
e
co
n
tr
o
ller
u
s
ed
in
o
u
r
b
u
ck
co
n
v
er
ter
,
we
c
o
n
d
u
cte
d
a
s
tu
d
y
o
f
th
e
v
ar
i
o
u
s
d
is
tu
r
b
an
ce
s
th
at
ca
n
af
f
ec
t
its
o
p
er
atio
n
.
T
o
test
th
e
co
n
tr
o
ller
'
s
r
o
b
u
s
tn
ess
,
we
v
ar
ied
th
e
in
p
u
t
v
o
ltag
e
an
d
th
e
lo
ad
to
as
s
ess
it
s
ab
ilit
y
to
m
ain
tain
a
co
n
s
tan
t
o
u
tp
u
t
v
o
ltag
e
(
1
8
V)
d
e
s
p
ite
d
is
tu
r
b
an
ce
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
640
-
6
52
648
A
well
-
d
esig
n
ed
a
n
d
r
o
b
u
s
t
d
esig
n
will
en
s
u
r
e
c
o
n
s
is
ten
t
o
u
tp
u
t
v
o
ltag
e
d
esp
ite
f
lu
ctu
ati
o
n
s
to
e
n
s
u
r
e
s
tab
le
v
o
ltag
e
u
n
d
er
v
ar
iab
le
co
n
d
itio
n
s
,
we
co
n
d
u
cted
a
s
tu
d
y
o
f
v
ar
io
u
s
s
ce
n
ar
io
s
f
o
r
o
u
r
b
u
ck
c
o
n
v
er
ter
,
as
d
ep
icted
in
Fig
u
r
e
1
0
.
Fig
u
r
e
9
.
Ou
t
p
u
t v
o
ltag
e
V
out
o
f
b
u
c
k
co
n
v
er
ter
with
b
ac
k
s
t
ep
p
in
g
c
o
n
tr
o
ller
an
d
with
G
W
o
p
tim
izatio
n
Fig
u
r
e
1
0
.
Ou
tp
u
t
v
o
ltag
e
f
o
r
t
h
e
b
u
c
k
co
n
v
er
ter
with
v
ar
iab
l
e
in
p
u
t v
o
ltag
e
an
d
v
ar
iab
le
lo
ad
4
.
3
.
E
x
perim
ent
a
l r
esu
lt
s
T
h
e
r
esu
lts
o
f
o
u
r
s
tu
d
y
h
a
v
e
s
h
o
wn
a
s
ig
n
if
ican
t
im
p
r
o
v
em
en
t
in
r
eg
u
latio
n
p
er
f
o
r
m
a
n
ce
u
s
in
g
B
ac
k
s
tep
p
in
g
with
p
ar
am
eter
o
p
tim
izatio
n
b
y
t
h
e
g
r
e
y
wo
lf
alg
o
r
ith
m
(
Fig
u
r
e
1
2
)
.
T
h
e
r
eg
u
latio
n
er
r
o
r
h
as
b
ee
n
s
ig
n
if
ican
tly
r
e
d
u
ce
d
,
an
d
th
e
s
y
s
tem
h
as
d
em
o
n
s
tr
ated
a
b
etter
ab
ilit
y
to
m
ain
tain
a
s
tab
le
o
u
tp
u
t
v
o
ltag
e
d
esp
ite
d
is
tu
r
b
an
ce
s
.
Du
r
in
g
t
h
is
ex
p
er
im
en
tal
in
v
esti
g
atio
n
,
we
im
p
lem
en
ted
th
e
PID
co
n
tr
o
l
an
d
ev
al
u
ated
its
p
er
f
o
r
m
an
ce
in
ter
m
s
o
f
r
eg
u
latin
g
th
e
o
u
tp
u
t
v
o
ltag
e
o
f
t
h
e
B
u
ck
co
n
v
er
ter
i
n
th
e
p
r
ese
n
ce
o
f
d
is
tu
r
b
an
ce
s
.
T
h
en
,
we
in
tr
o
d
u
ce
d
th
e
SMC
co
n
tr
o
l,
n
o
tin
g
a
s
ig
n
if
ican
t
i
m
p
r
o
v
e
m
en
t
in
r
eg
u
latio
n
p
er
f
o
r
m
an
ce
c
o
m
p
ar
e
d
to
PID
co
n
tr
o
l
as
s
h
o
wn
i
n
T
a
b
le
2
.
Ho
we
v
er
,
we
also
n
o
tic
ed
th
at
tu
n
in
g
t
h
e
p
ar
a
m
eter
s
o
f
th
e
SMC
co
n
tr
o
l
was d
elica
te
an
d
r
eq
u
ir
e
d
d
ee
p
ex
p
er
tis
e.
Fig
u
r
e
1
1
.
E
x
p
e
r
im
en
tal
r
esu
lt
s
o
f
th
e
b
u
c
k
co
n
v
er
ter
o
u
tp
u
t
v
o
ltag
e
with
th
e
b
ac
k
s
tep
p
in
g
co
n
tr
o
ller
with
o
u
t
o
p
tim
izatio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Grey
w
o
lf o
p
timiz
a
tio
n
a
p
p
r
o
a
ch
to
o
p
tima
l b
a
ck
s
tep
p
i
n
g
c
o
n
tr
o
l fo
r
b
u
ck
…
(
S
a
n
a
Mo
u
s
lim
)
649
T
h
e
co
m
p
ar
ativ
e
r
esu
lts
p
r
e
s
en
ted
in
T
ab
le
2
clea
r
ly
s
h
o
w
th
at
b
o
th
SMC
an
d
B
a
ck
s
tep
p
in
g
co
n
tr
o
ller
s
o
u
tp
er
f
o
r
m
th
e
c
o
n
v
en
tio
n
al
PID
r
eg
u
lato
r
i
n
t
er
m
s
o
f
d
y
n
a
m
ic
r
esp
o
n
s
e
an
d
v
o
ltag
e
s
tab
ilit
y
.
W
h
ile
SMC
s
ig
n
if
ican
tly
en
h
an
ce
s
p
er
f
o
r
m
a
n
ce
b
y
r
e
d
u
cin
g
th
e
s
ettlin
g
tim
e
an
d
alm
o
s
t
elim
in
atin
g
o
v
er
s
h
o
o
t,
th
e
b
ac
k
s
tep
p
in
g
c
o
n
tr
o
ller
d
em
o
n
s
tr
ates
th
e
b
est
o
v
er
all
b
eh
a
v
io
r
.
I
t
ac
h
iev
es
th
e
f
astes
t
s
ettlin
g
tim
e
(
1
.
9
7
s
)
a
n
d
en
s
u
r
es
th
e
m
o
s
t
s
tab
le
v
o
ltag
e
r
eg
u
latio
n
with
v
er
y
n
a
r
r
o
w
s
ettlin
g
lim
its
,
co
n
f
ir
m
in
g
its
s
u
p
er
io
r
a
b
ilit
y
to
h
an
d
le
s
y
s
tem
n
o
n
lin
ea
r
ities
.
Desp
ite
a
s
l
ig
h
tly
h
i
g
h
er
o
v
er
s
h
o
o
t
t
h
an
S
MC,
B
ac
k
s
tep
p
in
g
m
ain
tain
s
ex
ce
llen
t d
am
p
in
g
c
h
ar
ac
ter
is
tics
an
d
d
eliv
er
s
a
m
o
r
e
p
r
ec
is
e
an
d
co
n
s
is
ten
t c
o
n
tr
o
l a
ctio
n
,
m
ak
in
g
it th
e
m
o
s
t e
f
f
ec
tiv
e
s
tr
ateg
y
a
m
o
n
g
t
h
e
th
r
ee
tech
n
iq
u
es.
Fig
u
r
e
1
2
.
E
x
p
e
r
im
en
tal
r
esu
lt
s
o
f
th
e
b
u
c
k
co
n
v
er
ter
o
u
tp
u
t
v
o
ltag
e
with
th
e
b
ac
k
s
tep
p
in
g
co
n
tr
o
ller
with
o
p
tim
izatio
n
T
ab
le
2
.
C
o
m
p
a
r
ativ
e
an
aly
s
is
o
f
th
e
3
co
n
t
r
o
l te
ch
n
i
q
u
es
C
o
n
t
r
o
l
l
e
r
P
I
D
S
M
C
B
a
c
k
s
t
e
p
p
i
n
g
S
e
t
t
l
i
n
g
-
t
i
m
e
(
s)
4
.
8
5
2
.
9
6
1
.
9
7
S
e
t
t
l
i
n
g
-
m
i
n
(
V
)
1
1
.
6
7
1
1
.
9
2
1
2
.
0
3
S
e
t
t
l
i
n
g
-
m
a
x
(
V
)
1
4
.
4
4
1
2
.
1
4
1
2
.
1
9
O
v
e
r
sh
o
o
t
(
%)
2
0
.
3
2
1
.
2
1
1
.
6
5
P
e
a
k
(
V
)
1
4
.
4
4
1
2
.
1
4
1
2
.
1
9
5.
CO
NCLU
SI
O
N
T
h
e
r
esear
ch
p
r
esen
ted
in
th
is
ar
ticle
h
as
f
o
cu
s
ed
o
n
t
h
e
m
o
d
elin
g
an
d
o
p
tim
izatio
n
o
f
B
ac
k
s
tep
p
in
g
co
n
tr
o
l
f
o
r
r
eg
u
latin
g
a
s
tatic
b
u
ck
c
o
n
v
e
r
ter
in
r
en
ewa
b
le
e
n
er
g
y
s
y
s
tem
s
,
p
ar
ticu
lar
ly
th
e
p
h
o
to
v
o
ltaic
(
PV
)
s
o
lar
en
er
g
y
c
o
n
v
e
r
s
io
n
ch
ain
.
I
t
in
v
o
lv
es
m
o
d
elin
g
n
o
n
-
is
o
l
ated
b
u
ck
c
o
n
v
e
r
ter
s
an
d
d
esi
g
n
in
g
B
ac
k
s
tep
p
in
g
co
n
tr
o
l
t
o
m
ee
t
p
r
e
d
ef
in
ed
co
n
v
er
s
io
n
o
b
jectiv
es.
Ad
d
itio
n
ally
,
it
ex
p
lo
r
es
th
e
u
s
e
o
f
o
p
tim
izatio
n
to
o
ls
f
o
r
o
p
tim
al
co
n
tr
o
l o
f
r
en
ewa
b
le
e
n
er
g
y
c
o
n
v
e
r
s
io
n
s
y
s
tem
s
.
Ou
r
m
o
s
t
n
o
tab
le
co
n
tr
ib
u
tio
n
lies
in
th
e
o
p
tim
izatio
n
o
f
th
e
b
ac
k
s
tep
p
in
g
co
n
tr
o
l
p
ar
am
et
er
s
u
s
in
g
th
e
GW
O
alg
o
r
ith
m
to
r
eg
u
late
th
e
b
u
ck
co
n
v
er
ter
.
T
h
is
ap
p
r
o
ac
h
s
tab
ilized
th
e
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
co
n
v
er
te
r
ag
ain
s
t
d
is
tu
r
b
an
ce
s
in
in
p
u
t
v
o
ltag
e
an
d
lo
ad
,
th
er
e
b
y
i
m
p
r
o
v
i
n
g
th
e
r
o
b
u
s
tn
ess
an
d
p
er
f
o
r
m
a
n
ce
o
f
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
.
Fu
r
th
er
m
o
r
e,
we
v
alid
ated
o
u
r
o
p
t
im
ized
co
n
tr
o
l
ap
p
r
o
ac
h
b
y
im
p
lem
en
tin
g
an
ex
p
er
im
en
tal
p
latf
o
r
m
co
n
s
is
tin
g
o
f
a
b
u
ck
co
n
v
er
ter
,
a
d
ata
ac
q
u
is
itio
n
ca
r
d
,
an
d
co
n
tr
o
l
b
ased
o
n
th
e
T
ex
as
I
n
s
tr
u
m
en
ts
T
SM3
2
0
F2
8
3
3
5
DSP.
T
h
e
r
esu
lts
o
f
th
e
ex
p
e
r
im
en
tal
test
s
co
n
f
ir
m
ed
t
h
e
ef
f
ec
tiv
en
ess
o
f
o
u
r
ap
p
r
o
ac
h
an
d
its
ab
ilit
y
to
o
p
er
ate
in
r
ea
l
-
wo
r
ld
c
o
n
d
itio
n
s
.
As
a
f
u
tu
r
e
p
er
s
p
ec
tiv
e,
th
e
GW
O
-
o
p
tim
ized
B
ac
k
s
tep
p
in
g
co
n
tr
o
l a
p
p
r
o
ac
h
co
u
ld
b
e
e
x
ten
d
e
d
to
m
o
r
e
c
o
m
p
lex
p
h
o
to
v
o
ltaic
s
y
s
tem
s
an
d
ev
alu
ate
d
u
n
d
e
r
v
ar
y
in
g
en
v
ir
o
n
m
e
n
tal
co
n
d
iti
o
n
s
to
b
etter
ass
ess
its
r
o
b
u
s
tn
ess
an
d
r
ea
l
-
tim
e
ef
f
ec
tiv
en
ess
.
ACK
NO
WL
E
DG
M
E
N
T
S
T
h
e
au
th
o
r
s
wo
u
ld
lik
e
to
th
an
k
all
in
d
iv
id
u
als
wh
o
p
r
o
v
id
e
d
tech
n
ical
s
u
p
p
o
r
t
an
d
v
alu
a
b
le
g
u
id
an
ce
d
u
r
in
g
th
is
wo
r
k
.
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