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p
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K
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:
DC
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DC
2
-
L
MB
C
Fra
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PID
Fu
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lo
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tr
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Neld
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M
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p
tim
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alg
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m
Stat sp
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av
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ag
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T
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p
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n
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c
c
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ss
a
rticle
u
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d
e
r th
e
CC B
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-
SA
li
c
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n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Gh
r
is
s
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ah
r
i
I
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s
titu
t
d
es Scien
ce
s
et
T
ec
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n
iq
u
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p
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s
(
I
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,
Un
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s
ité
Or
an
1
Ah
m
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B
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B
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Or
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,
Alg
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d
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g
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to
.
d
z
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
f
u
zz
y
lo
g
ic
c
o
n
tr
o
l
s
y
s
t
em
wh
ich
is
b
ased
o
n
h
u
m
a
n
ex
p
er
tis
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was
in
tr
o
d
u
ce
d
i
n
1
9
7
5
b
y
Ma
m
d
an
i
an
d
Ass
ilian
.
I
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wa
s
im
p
lem
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ted
as
an
ex
p
er
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t
o
n
lin
g
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tr
o
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s
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f
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a
s
team
en
g
in
e
-
b
ased
m
o
d
el
i
n
d
u
s
tr
ial
p
lan
t
[
1
]
.
Mo
r
e
o
v
er
,
s
in
ce
1
9
8
9
,
f
u
zz
y
l
o
g
ic
co
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tr
o
l
h
as
b
ee
n
u
s
ed
in
m
an
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d
o
m
esti
c
elec
tr
ic
ap
p
lian
ce
s
.
Fu
zz
y
lo
g
ic
allo
ws s
u
ch
ap
p
li
an
ce
s
to
b
e
ac
c
u
r
ate
a
n
d
s
tr
aig
h
tf
o
r
war
d
in
d
ea
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in
g
with
q
u
alitativ
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k
n
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wled
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e
o
f
o
p
er
atio
n
s
,
wh
ich
ar
e
d
escr
ib
ed
as
f
u
zz
y
if
-
th
e
n
r
u
les
[
2
]
.
F
r
ac
tio
n
al
ca
lcu
lu
s
,
as
a
f
ield
with
p
r
ac
tical
im
p
licatio
n
s
,
is
ap
p
lied
in
v
ar
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s
d
o
m
ain
s
s
u
ch
as
ec
o
n
o
m
ic
p
r
o
ce
s
s
es
[
3
]
,
s
ig
n
al
p
r
o
ce
s
s
in
g
[
4
]
,
ch
em
ical
p
r
o
c
ess
es
[
5
]
,
an
d
b
io
en
g
i
n
ee
r
in
g
[
6
]
.
I
n
th
e
last
d
ec
ad
e,
f
r
ac
ti
o
n
al
ca
lcu
lu
s
was
in
tr
o
d
u
ce
d
in
s
y
s
tem
th
e
o
r
y
an
d
a
u
to
m
ated
co
n
tr
o
l
[
7
]
.
T
h
er
ef
o
r
e
,
th
e
ap
p
licatio
n
o
f
f
r
ac
tio
n
al
d
if
f
er
en
tial
eq
u
atio
n
s
h
as
r
esu
lted
in
m
o
r
e
ac
cu
r
ate
d
y
n
am
ic
s
y
s
tem
m
o
d
els,
n
o
v
el
c
o
n
tr
o
l
s
tr
ateg
ies,
an
d
en
h
a
n
ce
d
co
n
tr
o
l
lo
o
p
ch
a
r
ac
ter
is
tics
,
d
em
o
n
s
tr
atin
g
f
r
ac
tio
n
al
ca
lc
u
lu
s
'
s
p
r
ac
tical
ad
v
an
tag
es a
n
d
b
en
ef
it
s
.
I
n
p
o
wer
elec
tr
o
n
ics,
co
n
v
er
ter
s
ar
e
h
ig
h
ly
n
o
n
lin
ea
r
an
d
th
eir
co
n
tr
o
l
is
cr
u
cial
f
o
r
in
d
u
s
tr
ial
ap
p
licatio
n
s
.
DC
-
DC
m
u
ltil
e
v
el
b
o
o
s
t
co
n
v
er
ter
s
as
h
ig
h
g
ain
DC
-
DC
s
o
u
r
ce
s
ar
e
a
k
ey
f
o
r
ad
v
an
ce
d
tech
n
o
lo
g
y
,
s
im
u
ltan
eo
u
s
ly
with
th
e
co
n
tin
u
o
u
s
ad
v
an
c
es
in
s
em
ico
n
d
u
cto
r
s
an
d
r
e
ac
tiv
e
co
m
p
o
n
en
ts
.
C
o
n
tr
astl
y
to
th
e
co
n
v
en
tio
n
al
DC
-
DC
b
o
o
s
t c
o
n
v
er
ter
,
th
e
DC
-
DC
m
u
ltil
ev
el
b
o
o
s
t c
o
n
v
er
ter
s
ca
n
o
p
er
ate
at
a
h
ig
h
-
d
u
ty
cy
cle
to
ac
h
iev
e
a
h
ig
h
o
u
tp
u
t
v
o
ltag
e,
th
u
s
r
ed
u
cin
g
s
witch
in
g
f
r
e
q
u
en
cy
an
d
d
ec
r
ea
s
in
g
elec
tr
o
m
a
g
n
etic
in
ter
f
e
r
en
ce
[
8
]
.
T
h
e
r
ef
o
r
e
,
DC
-
DC
m
u
lti
lev
el
co
n
v
er
ter
s
ca
n
b
e
u
s
ed
in
m
an
y
in
d
u
s
tr
ial
d
o
m
ain
s
,
lik
e
au
to
m
o
tiv
e
en
g
in
ee
r
in
g
,
p
h
o
to
v
o
ltaic
s
y
s
tem
s
,
an
d
f
u
el
ce
ll
a
p
p
licatio
n
s
[
9
]
.
Sev
er
al
DC
-
DC
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
5
,
No
.
4
,
Dec
em
b
er
20
2
4
:
2409
-
24
21
2410
m
u
ltil
ev
el
b
o
o
s
t
co
n
v
er
ter
(
M
B
C
)
to
p
o
lo
g
ies
wer
e
p
r
o
p
o
s
e
d
in
p
r
e
v
io
u
s
wo
r
k
s
[
10
]
.
T
h
e
y
ar
e
s
im
ilar
to
th
e
co
n
v
en
tio
n
al
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
b
y
a
d
d
in
g
m
o
r
e
ca
p
ac
i
to
r
s
an
d
d
io
d
es.
T
h
ese
to
p
o
lo
g
ies
ca
n
g
en
e
r
ate
a
h
ig
h
er
v
o
ltag
e
at
d
if
f
er
en
t
l
ev
els
b
y
u
s
in
g
o
n
ly
a
s
in
g
le
in
d
u
cto
r
an
d
s
witch
.
T
h
e
a
d
v
an
tag
es
o
f
th
ese
co
n
f
ig
u
r
atio
n
s
in
clu
d
e
th
e
p
o
s
s
ib
ilit
y
o
f
u
s
in
g
s
witch
ed
ca
p
ac
ito
r
co
n
v
e
r
ter
s
with
o
u
t
a
tr
a
n
s
f
o
r
m
er
o
r
a
lar
g
e
d
u
ty
cy
cle
to
ac
h
ie
v
e
h
ig
h
v
o
ltag
e
co
n
v
er
s
io
n
r
ati
o
s
[
11
]
.
I
t
i
s
th
e
b
est
in
s
tan
ce
o
f
t
h
e
s
witch
ed
ca
p
ac
ito
r
s
in
ce
th
e
in
p
u
t
cu
r
r
en
t
in
ten
s
ity
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co
n
s
tan
t.
T
h
e
d
i
o
d
es
h
av
e
r
ep
lace
d
all
co
n
tr
o
lle
d
s
witch
es
in
th
e
s
witch
ed
ca
p
ac
ito
r
m
ec
h
a
n
is
m
[
12
]
.
T
h
is
p
ap
er
aim
s
to
estab
lis
h
a
m
ath
em
atica
l
m
o
d
el
f
o
r
t
h
e
to
w
-
lev
el
b
o
o
s
t
co
n
v
er
ter
(
2
-
L
MBC
)
b
ased
o
n
th
e
s
tate
-
s
p
ac
e
av
er
ag
ed
(
S
SA
)
m
eth
o
d
f
o
r
d
e
v
elo
p
in
g
th
e
tr
an
s
f
er
f
u
n
ctio
n
s
o
f
t
h
e
in
p
u
t
cu
r
r
en
t
an
d
o
u
tp
u
t
v
o
ltag
e
r
elate
d
to
th
e
d
u
ty
cy
c
le.
T
wo
co
n
tr
o
l
tech
n
iq
u
es
ar
e
ap
p
lied
t
o
2
-
L
MBC
,
th
e
f
ir
s
t
is
th
e
f
u
zz
y
lo
g
i
c
co
n
tr
o
ller
(
FLC
)
an
d
th
e
s
ec
o
n
d
o
n
e
is
b
ased
o
n
a
f
r
ac
tio
n
a
l
-
o
r
d
er
p
r
o
p
o
r
tio
n
al
-
in
te
g
r
al
-
d
er
iv
ativ
e
(
FOPID
)
co
n
tr
o
ller
.
T
h
e
s
im
u
latio
n
r
es
u
lts
d
ev
elo
p
ed
u
n
d
e
r
MA
T
L
AB
/Si
m
u
lin
k
an
d
SimPo
wer
Sy
s
tem
s
to
o
lb
o
x
s
h
o
w
th
at
th
e
d
y
n
am
ic
r
esp
o
n
s
es
with
th
e
p
r
o
p
o
s
ed
FOPID
co
n
tr
o
ller
b
ased
o
n
th
e
Neld
er
-
Me
ad
o
p
tim
izatio
n
m
eth
o
d
ar
e
m
o
r
e
ac
cu
r
ate
a
n
d
f
aster
th
an
th
e
o
n
es o
b
tain
e
d
with
th
e
FLC co
n
tr
o
ller
.
2.
M
O
DE
L
L
I
NG
O
F
A
RE
DUCED
O
RDE
R
NO
NL
I
NE
AR
DYNA
M
I
C
SYS
T
E
M
O
F
A
2
-
L
M
B
C
WI
T
H
E
Q
UIVA
L
E
NT
C
AP
ACIT
Y
T
h
is
s
ec
tio
n
d
is
cu
s
s
es
th
e
d
if
f
er
en
t
s
tep
s
in
m
o
d
elin
g
th
e
2
L
-
MBC
b
ased
o
n
th
e
SS
A
m
eth
o
d
.
T
h
e
m
ath
em
atica
l m
o
d
el
o
f
th
e
2
L
-
MBC
i
s
n
o
n
-
lin
ea
r
.
Alth
o
u
g
h
th
is
s
y
s
tem
's n
o
n
lin
ea
r
ities
m
ask
,
o
n
av
er
ag
e,
all
th
e
in
f
o
r
m
atio
n
ass
o
ciate
d
wi
th
th
e
f
ast
d
y
n
am
ics
an
d
in
s
t
ab
ilit
y
o
f
s
u
b
h
ar
m
o
n
ic
o
s
cillatio
n
s
,
th
ey
a
r
e
n
o
t
ca
p
tu
r
ed
[
13
]
.
Du
e
to
th
e
m
u
ltip
licativ
e
co
m
p
o
n
en
ts
li
n
k
in
g
th
e
s
tate
v
ar
iab
les
to
th
e
d
u
ty
cy
cle,
t
h
e
d
ev
elo
p
m
e
n
t
o
f
th
e
m
ath
em
ati
ca
l
m
o
d
el
o
f
th
e
2
L
-
MBC
is
b
ased
o
n
th
e
SS
A
m
eth
o
d
in
co
n
tin
u
o
u
s
co
n
d
u
ctio
n
m
o
d
e
(
C
C
M)
[
14
]
,
[
15
]
.
T
h
e
in
p
u
t
cu
r
r
en
t
an
d
o
u
tp
u
t
v
o
l
tag
e
tr
an
s
f
er
f
u
n
ctio
n
s
ar
e
th
en
d
ev
elo
p
e
d
an
d
ca
lcu
lated
.
Fig
u
r
e
1
illu
s
tr
ates th
e
p
o
wer
ci
r
cu
it o
f
t
h
e
2
L
-
M
B
C
as
s
o
ciate
d
with
th
e
co
n
tr
o
l
ler
.
Stead
y
-
s
tate
an
d
s
m
all
s
ig
n
al
m
o
d
ellin
g
s
f
o
r
a
h
ig
h
e
r
-
o
r
d
er
s
y
s
tem
ar
e
v
er
y
co
m
p
lex
.
I
t is
s
u
itab
le
to
r
ed
u
ce
th
e
m
o
d
el
f
o
r
s
im
p
licity
.
Ho
wev
er
,
c
o
n
s
id
er
in
g
th
e
eq
u
iv
alen
t
ca
p
ac
ity
d
u
r
in
g
th
e
s
witch
-
o
n
an
d
s
witch
-
o
f
f
m
o
d
es,
a
p
p
ly
in
g
t
h
e
b
asic
p
r
in
cip
les
a
n
d
co
n
s
id
er
in
g
th
at
th
e
ca
p
ac
ito
r
s
ar
e
id
en
tical
:
C
1
=C
2
=C
3
=C.
I
n
ad
d
itio
n
,
th
e
v
o
ltag
e
ac
r
o
s
s
ea
ch
ca
p
ac
ito
r
is
eq
u
al
to
t
h
e
o
u
tp
u
t
v
o
ltag
e
g
en
er
ate
d
b
y
N
le
v
els
o
f
ca
p
ac
ito
r
s
.
W
h
er
e
th
e
s
tate
s
p
ac
e
v
ec
to
r
i
s
(
)
=
[
(
)
(
)
]
an
d
th
e
o
u
t
p
u
t
(
)
i
s
th
e
v
o
ltag
e
lo
ad
o
f
th
e
2
-
L
MBC
wh
ich
is
n
o
ted
b
y
.
T
h
er
e
a
r
e
two
b
asic
m
o
d
es
ac
co
r
d
in
g
to
th
e
s
tate
o
f
th
e
s
witch
.
T
h
e
2
-
L
MBC
ca
n
o
p
er
ate
in
d
if
f
er
e
n
t m
o
d
es.
Fig
u
r
e
1
.
T
h
e
p
o
we
r
cir
cu
it d
i
ag
r
am
o
f
th
e
2
L
-
MBC
co
n
tr
o
l
led
2
.
1
.
Switc
h
-
o
n m
o
de
re
du
ce
d o
rder
T
h
e
eq
u
iv
alen
t
r
ed
u
ce
d
o
r
d
er
cir
cu
it
in
s
witch
-
o
n
m
o
d
e
is
d
ep
icted
in
Fig
u
r
e
2
.
T
h
e
s
t
a
t
e
s
p
ac
e
r
e
p
r
e
s
e
n
t
a
ti
o
n
o
f
t
h
e
DC
-
DC
2
-
L
M
B
C
e
l
ec
t
r
i
c
al
m
o
d
e
l
i
n
s
wi
t
c
h
-
o
n
m
o
d
e
i
s
i
n
t
r
o
d
u
c
e
d
by
(
1
)
.
{
̇
(
)
=
1
(
)
+
1
(
)
=
1
(
)
(
1
)
T
h
e
m
atr
ix
1
A
an
d
th
e
v
ec
to
r
s
1
B
an
d
1
C
ar
e
p
r
esen
ted
b
y
(
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
F
r
a
ctio
n
a
l o
r
d
er P
I
D
co
n
tr
o
ller
d
esig
n
o
f a
DC
-
DC
mu
ltil
e
ve
l b
o
o
s
t c
o
n
ve
r
ter u
s
in
g
th
e
…
(
Gh
r
is
s
i Ta
h
r
i
)
2411
1
=
[
−
0
0
−
1
]
;
1
=
[
1
0
]
;
1
=
[
0
1
]
(
2
)
2
.
2
.
Switc
h
-
o
f
f
m
o
de
re
du
ce
d o
r
der
Fig
u
r
e
3
illu
s
tr
ates
th
e
eq
u
i
v
alen
t
r
ed
u
ce
d
o
r
d
er
cir
c
u
it
in
s
witch
-
o
f
f
m
o
d
e.
T
h
e
s
tate
s
p
ac
e
r
ep
r
esen
tatio
n
o
f
th
e
DC
-
DC
2
-
L
MBC
elec
tr
ical
m
o
d
el
in
s
witch
-
o
f
f
m
o
d
e
is
in
tr
o
d
u
ce
d
b
y
(
3
)
.
{
(
)
=
2
(
)
+
2
(
)
=
2
(
)
(
3
)
T
h
e
m
atr
ix
2
A
an
d
th
e
v
ec
to
r
s
2
B
an
d
2
C
ar
e
p
r
esen
ted
b
y
(
4
)
.
2
=
[
−
−
1
1
2
−
2
]
;
2
=
[
1
0
]
;
2
=
[
0
1
]
(
4
)
Fig
u
r
e
2
.
2
-
L
MBC
s
witch
-
o
n
m
o
d
e
r
e
d
u
ce
d
o
r
d
e
r
Fig
u
r
e
3
.
2
-
L
MBC
s
witch
-
o
f
f
m
o
d
e
r
e
d
u
ce
d
o
r
d
er
2
.
3
.
No
nli
nea
r
f
ull
-
o
rder
dy
na
m
ic
m
o
del
T
o
o
b
tain
th
e
f
u
ll
-
o
r
d
e
r
d
y
n
a
m
ic
m
o
d
el,
th
e
two
o
p
e
r
atin
g
m
ath
em
atica
l m
o
d
els ar
e
co
m
b
in
ed
in
to
a
s
in
g
le
m
o
d
el
b
y
th
e
m
ea
n
o
f
th
e
SAA
m
eth
o
d
p
r
esen
ted
b
y
(
5
)
.
{
=
1
+
2
(
1
−
)
=
1
+
2
(
1
−
)
;
{
=
1
+
2
(
1
−
)
=
1
+
2
(
1
−
)
(
5
)
A
1
,
B
1
,
C
1
,
an
d
D
1
ar
e
th
e
s
ta
te
m
atr
ices in
s
w
itch
-
o
n
m
o
d
e,
wh
er
ea
s
A
2
,
B
2
,
C
2
,
an
d
D
2
ar
e
th
e
o
n
es in
s
witch
-
o
f
f
m
o
d
e.
T
h
e
av
er
a
g
e
o
u
tp
u
t
v
o
ltag
e
an
d
cu
r
r
en
t a
r
e
e
x
p
r
es
s
ed
by
(
6
)
an
d
(
7
)
r
esp
ec
tiv
ely
:
=
(
1
−
)
(
6
)
=
(
1
−
)
(
7
)
W
h
er
e
N
is
th
e
DC
o
u
tp
u
t
lin
k
ca
p
ac
ito
r
n
u
m
b
er
;
d
:
is
th
e
d
u
ty
r
atio
;
V
in
:
is
th
e
in
p
u
t
v
o
l
tag
e
;
B
y
co
m
b
in
in
g
th
e
f
r
o
m
(
1
)
to
(
5
)
,
th
e
m
atr
ix
s
y
s
tem
o
b
tain
ed
b
y
(
8
)
an
d
(
9
)
r
e
p
r
esen
t
s
th
e
2
-
L
MBC
m
ath
em
atica
l
m
o
d
el
with
th
e
two
s
witch
m
o
d
es.
[
(
)
(
)
]
=
[
−
−
(
1
−
)
(
1
−
)
−
]
[
(
)
(
)
]
+
[
1
0
]
(
8
)
[
]
=
[
0
1
]
[
(
)
(
)
]
(
9
)
W
ith
th
e
eq
u
iv
alen
t c
ap
ac
ito
r
as g
iv
en
b
y
(
1
0
)
.
1
+
(
1
−
)
2
=
(
1
0
)
T
o
estab
lis
h
th
e
s
tate
s
p
ac
e
m
o
d
el,
wh
ich
is
a
co
m
b
in
atio
n
o
f
th
e
two
af
o
r
em
en
tio
n
ed
o
p
er
atio
n
m
o
d
els,
th
e
lin
ea
r
izatio
n
o
f
t
h
e
s
y
s
tem
is
d
o
n
e
b
y
(
1
1
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
5
,
No
.
4
,
Dec
em
b
er
20
2
4
:
2409
-
24
21
2412
=
[
1
+
2
(
1
−
)
]
+
[
1
+
2
(
1
−
)
]
(
1
1
)
2
.
4
.
Sta
t
e
s
pa
ce
a
v
er
a
g
ing
ma
t
he
m
a
t
ica
l
m
o
del o
f
t
he
2
-
L
M
B
C
T
h
e
SS
A
m
eth
o
d
co
n
s
is
ts
o
f
in
tr
o
d
u
cin
g
th
e
ter
m
r
ep
r
esen
ted
b
y
(
^)
as
a
s
m
all
p
er
tu
r
b
atio
n
.
Fo
r
in
s
tan
ce
,
th
e
v
ar
iab
le
(
)
is
wr
itten
b
y
(
1
2
)
:
(
)
=
+
̂
(
)
(
1
2
)
W
h
er
e
Y
is
th
e
DC
ter
m
an
d
ˆ
y
is
th
e
s
m
all
s
ig
n
al
ter
m
.
T
h
is
ap
p
r
o
ac
h
is
ap
p
lied
t
o
th
e
s
tate
s
p
ac
e
v
ec
to
r
(
)
,
th
e
in
p
u
t
v
o
ltag
e
(
)
an
d
d
u
ty
cy
cle
(
)
.
Ap
p
ly
in
g
th
e
s
m
all
p
er
tu
r
b
atio
n
ap
p
r
o
ac
h
to
(
1
1
)
wh
ic
h
g
iv
e
s
two
ex
p
r
ess
io
n
s
as g
iv
en
b
y
(
1
3
)
.
T
h
er
ef
o
r
e,
two
m
o
d
es
a
r
e
o
b
tain
ed
,
AC
an
d
DC
,
ex
p
r
ess
ed
b
y
(
1
4
)
an
d
(
1
5
)
r
esp
ec
tiv
ely
.
̂
0
+
̇
̂
(
)
=
[
1
(
+
̂
)
+
2
(
1
−
−
̂
)
]
(
0
+
̂
)
+
[
1
(
+
̂
)
+
2
(
1
−
−
̂
)
]
(
0
+
̂
)
(
1
3
)
-
I
n
DC
mode
All th
e
d
er
iv
ativ
e
ter
m
s
ar
e
e
q
u
al
to
ze
r
o
,
s
u
ch
as:
[
1
+
2
(
1
−
)
]
(
0
)
+
[
1
+
2
(
1
−
)
]
(
0
)
=
0
(
1
4
)
-
I
n
AC
m
o
d
e
Fu
r
th
er
m
o
r
e
,
in
th
e
AC
eq
u
ati
o
n
,
v
a
r
iab
les
h
av
in
g
p
r
o
d
u
cts
o
f
̂
,
̂
an
d
̂
ar
e
ig
n
o
r
e
d
(
s
m
all
v
ar
iatio
n
s
m
u
ltip
lied
b
y
t
h
e
s
am
e
o
n
es y
i
eld
s
an
ev
en
s
m
aller
r
esu
lt).
̇
̂
(
)
=
[
1
+
2
(
1
−
)
]
̂
(
)
+
[
1
+
2
(
1
−
)
]
̂
(
)
+
[
(
1
−
2
)
0
+
(
1
−
2
)
0
]
̂
(
)
(
1
5
)
W
h
er
e
th
e
ca
p
ac
ito
r
s
2
=
an
d
1
=
2
ar
e
r
ep
lace
d
in
(
3
)
an
d
(
4
)
,
an
d
tak
in
g
in
to
ac
co
u
n
t
th
at
th
e
DC
-
DC
co
n
v
er
ter
is
two
lev
els,
t
h
u
s
=
2
an
d
=
.
C
o
n
s
eq
u
en
tly
,
t
h
e
(
1
5
)
is
wr
itten
i
n
d
etailed
f
o
r
m
as
g
iv
en
b
y
(
1
6
)
.
[
̇
̂
1
(
)
̇
̂
2
(
)
]
=
[
−
−
(
1
−
)
2
(
1
−
)
−
2
]
[
̂
1
(
)
̂
2
(
)
]
+
[
1
0
]
̂
(
)
+
[
0
1
2
−
1
1
]
[
10
20
]
̂
(
)
(
1
6
)
2
.
5
.
Ste
a
dy
-
s
t
a
t
e
s
t
ud
y
In
o
r
d
er
to
d
ed
u
ce
th
e
s
o
lu
tio
n
s
o
f
x
10
an
d
x
20
in
a
s
tead
y
s
tate,
it
is
cr
u
cial
to
s
o
lv
e
t
h
e
s
y
s
tem
in
DC
co
n
tin
u
o
u
s
m
o
d
e.
T
h
e
s
tate
o
f
eq
u
ilib
r
iu
m
is
r
e
p
r
esen
ted
b
y
(
1
7
)
.
=
+
=
0
⇒
[
0
0
]
=
[
−
−
(
1
−
)
2
(
1
−
)
−
2
]
[
10
20
]
+
[
1
0
]
(
1
7
)
T
h
e
(
1
8
)
a
n
d
(
1
9
)
in
tr
o
d
u
ce
th
e
c
u
r
r
e
n
t
an
d
v
o
ltag
e
r
esp
ec
ti
v
ely
wh
ich
r
ep
r
esen
t
th
e
DC
v
alu
es
eq
u
iv
alen
t
to
x
10
an
d
x
20
q
u
a
n
titi
es,
wh
ich
ar
e
th
e
s
o
lu
tio
n
o
f
th
e
(
1
7
)
.
=
4
(
1
−
)
4
(
1
−
)
+
(
1
−
)
3
(
1
8
)
=
2
(
1
−
)
4
+
(
1
−
)
2
(
1
9
)
2
.
6
.
T
he
t
ra
ns
f
er
f
un
ct
io
n o
f
t
he
DC
-
DC
2
-
L
M
B
C
W
h
en
th
e
DC
m
o
d
e
ter
m
s
ar
e
o
m
itted
,
th
e
r
esu
ltin
g
m
atr
ix
s
y
s
tem
p
r
esen
ts
th
e
f
o
llo
win
g
s
m
all
-
s
ig
n
al
m
o
d
el
as g
iv
en
b
y
(
2
0
)
.
[
̂
(
)
̂
(
)
]
=
[
(
+
)
(
1
−
)
2
(
1
−
)
(
−
−
2
)
]
(
−
1
)
∗
[
[
]
̂
(
)
+
[
1
0
]
̂
(
)
]
(
2
0
)
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
F
r
a
ctio
n
a
l o
r
d
er P
I
D
co
n
tr
o
ller
d
esig
n
o
f a
DC
-
DC
mu
ltil
e
ve
l b
o
o
s
t c
o
n
ve
r
ter u
s
in
g
th
e
…
(
Gh
r
is
s
i Ta
h
r
i
)
2413
Fo
llo
win
g
th
at,
(
2
1
)
a
n
d
(
2
2
)
p
r
esen
t th
e
cu
r
r
en
t a
n
d
v
o
ltag
e
tr
an
s
f
er
f
u
n
ctio
n
s
,
r
esp
ec
tiv
e
ly
.
̂
(
)
̂
(
)
=
(
2
(
1
−
)
4
+
(
1
−
)
2
)
(
(
+
2
)
+
1
)
2
+
(
2
+
)
+
(
2
+
(
1
−
)
2
)
(
2
1
)
̂
(
)
̂
(
)
=
(
4
+
(
1
−
)
2
)
(
−
4
(
+
)
+
2
(
1
−
)
2
)
2
+
(
2
+
)
+
(
2
+
(
1
−
)
2
2
)
(
2
2
)
3.
CO
NT
RO
L
D
E
S
I
G
N
T
wo
co
n
tr
o
l m
eth
o
d
s
ar
e
ap
p
l
ied
to
th
e
DC
-
DC
2
-
L
M
B
C
:
t
h
e
FLC an
d
th
e
FOPID.
T
h
e
t
wo
co
n
tr
o
l
s
tr
ateg
ies ar
e
co
m
p
ar
ed
with
d
if
f
er
en
t te
s
ts
.
3
.
1
.
F
uzzy
lo
g
ic
co
ntr
o
ller
des
ig
n
T
h
e
f
u
zz
y
l
o
g
ic
co
n
tr
o
ller
'
s
in
p
u
ts
ar
e
er
r
o
r
a
n
d
its
d
er
iv
ativ
e,
an
d
th
e
o
u
tp
u
t c
o
r
r
esp
o
n
d
s
to
th
e
d
u
t
y
cy
cle
v
ar
iatio
n
,
wh
ich
a
r
e
th
e
m
o
s
t
r
elev
an
t
q
u
an
titi
es
o
f
th
e
co
n
tr
o
ller
an
d
ar
e
s
elec
ted
to
im
p
r
o
v
e
c
o
n
tr
o
l
clo
s
e
to
th
e
d
esire
d
o
p
e
r
atin
g
p
o
in
t.
C
o
n
s
eq
u
en
tly
,
it
r
eq
u
ir
es
a
s
et
o
f
r
u
les
p
r
im
a
r
ily
d
eter
m
in
e
d
b
y
t
h
e
o
p
er
ato
r
'
s
ex
p
er
tis
e
wh
en
m
an
ip
u
latin
g
th
e
s
y
s
tem
[
16
]
.
T
h
e
ch
ar
ac
ter
is
tic
p
ar
am
eter
s
o
f
th
e
in
p
u
ts
o
f
th
e
FLC
ar
e
d
en
o
te
d
b
y
(
)
an
d
(
)
an
d
o
u
t
p
u
t
(
)
.
Fig
u
r
e
4
d
ep
icts
th
e
f
u
zz
y
lo
g
ic
b
lo
ck
d
iag
r
a
m
,
wh
ich
is
co
m
p
o
s
ed
o
f
th
e
f
o
llo
win
g
f
o
u
r
ess
en
tial
b
lo
ck
s
.
T
h
e
n
o
r
m
aliza
tio
n
f
a
cto
r
s
in
clu
d
e
th
o
s
e
co
n
n
ec
ted
with
th
e
er
r
o
r
a
n
d
its
v
ar
iati
o
n
an
d
d
u
ty
c
y
cle
v
ar
iatio
n
.
T
h
e
f
u
zz
if
icatio
n
b
lo
ck
co
n
v
er
ts
in
p
u
t
v
alu
es
to
s
u
b
-
f
u
zz
y
s
ets.
T
h
e
f
u
zz
y
i
n
f
er
en
ce
m
ec
h
an
is
m
b
lo
ck
.
T
h
e
d
ef
u
zz
if
icatio
n
b
lo
ck
en
ab
les
u
s
to
id
en
tify
th
e
a
c
tu
al
o
u
tp
u
t
v
a
r
iab
le
v
alu
e
f
r
o
m
th
e
f
u
zz
y
in
f
er
en
ce
an
d
co
n
v
er
t it
in
to
a
n
u
m
e
r
ical
v
alu
e
f
o
r
ap
p
licatio
n
to
th
e
p
r
o
ce
s
s
.
a.
Fu
zz
if
icatio
n
Me
m
b
er
s
h
ip
f
u
n
ctio
n
s
(
MFs)
ar
e
u
s
ed
in
th
is
s
tep
to
co
n
v
e
r
t
ac
tu
al
q
u
a
n
titi
es
in
to
f
u
zz
y
v
ar
iab
les.
T
h
ese
MFs
co
m
e
in
v
ar
io
u
s
f
o
r
m
s
,
b
u
t
tr
ian
g
u
lar
an
d
tr
ap
e
zo
id
al
ar
e
th
e
m
o
s
t
co
m
m
o
n
.
Fig
u
r
e
5
d
ep
icts
th
e
MFs o
f
th
e
in
p
u
t a
n
d
o
u
tp
u
t
v
ar
iab
les.
b.
Fu
zz
y
in
f
er
e
n
ce
m
ec
h
a
n
is
m
T
h
e
co
n
tr
o
l
o
u
tp
u
t
is
g
en
e
r
ate
d
b
y
c
o
m
b
in
i
n
g
th
e
(
MFs)
an
d
co
n
tr
o
l
r
u
les.
T
h
e
f
u
zz
y
co
n
tr
o
l
r
u
les
ar
e
a
cr
u
cial
elem
en
t
o
f
th
is
s
tep
,
clo
s
ely
ass
o
ciate
d
with
h
u
m
an
ex
p
er
tis
e.
Dep
en
d
in
g
o
n
th
e
Ma
m
d
an
i
m
eth
o
d
[
1
]
,
[
17
]
,
4
9
f
u
zz
y
r
u
les o
f
e
r
r
o
r
an
d
th
eir
v
a
r
iatio
n
ar
e
s
elec
ted
in
T
ab
le
1
.
c.
Def
u
zz
if
icatio
n
T
h
e
d
ef
u
zz
if
icatio
n
s
tep
u
s
es
th
e
ce
n
tr
o
id
m
eth
o
d
,
wh
ich
p
er
m
its
d
eter
m
in
in
g
th
e
o
u
tp
u
t
v
ar
iab
le's
ac
tu
al
v
alu
e
f
r
o
m
th
e
f
u
zz
y
in
f
er
en
ce
m
ec
h
an
is
m
[
18
]
.
T
h
is
o
u
tp
u
t
v
al
u
e
is
th
en
co
n
v
er
ted
t
o
a
n
u
m
er
ical
v
alu
e
an
d
ap
p
lied
to
th
e
p
r
o
ce
s
s
[
19
]
.
T
ab
le
1
.
Fu
zz
y
r
u
le
b
ase
tab
le
f
o
r
a
d
u
ty
c
y
cle
Er
r
o
r
(
)
V
a
r
i
a
t
i
o
n
o
f
e
r
r
o
r
(
)
N
B
e
N
M
e
N
S
e
Ze
PSe
PMe
P
Be
NB∆e
P
B
∆d
P
B
∆d
P
B
∆d
N
B
∆d
N
M
∆d
Z∆d
Z∆d
NM∆
e
P
B
∆d
P
B
∆d
P
B
∆d
P
M
∆
d
P
S
∆d
Z∆d
Z∆d
NS∆
e
P
B
∆d
P
M
∆
d
P
S
∆d
P
S
∆d
P
S
∆d
Z∆d
Z∆d
Z∆e
P
B
∆d
P
M
∆
d
P
S
∆d
Z∆d
N
S
∆d
N
M
∆d
N
B
∆d
P
B∆e
Z∆d
Z∆d
N
M
∆d
N
S
∆d
N
S
∆d
N
M
∆d
N
B
∆d
NB∆e
Z∆d
Z∆d
N
S
∆d
N
M
∆d
N
B
∆d
N
B
∆d
N
B
∆d
NB∆e
Z∆d
Z∆d
N
M
∆d
N
B
∆d
N
B
∆d
N
B
∆d
N
B
∆d
Fig
u
r
e
4
.
B
lo
ck
d
esig
n
o
f
th
e
FLC f
o
r
DC
-
DC
2
-
L
MBC
o
u
tp
u
t v
o
ltag
e
c
o
n
tr
o
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
5
,
No
.
4
,
Dec
em
b
er
20
2
4
:
2409
-
24
21
2414
Fig
u
r
e
5
.
T
h
e
MFs o
f
th
e
er
r
o
r
(
)
,
its
v
ar
iatio
n
(
)
an
d
th
e
v
ar
iatio
n
o
f
th
e
co
n
tr
o
l
(
)
3
.
2
.
F
un
da
m
ent
a
l f
ra
ct
io
na
l c
a
lculu
s
pr
incip
les
T
h
e
ad
a
p
tatio
n
o
f
d
if
f
er
e
n
tiatio
n
a
n
d
i
n
teg
r
atio
n
to
n
o
n
-
in
te
g
er
o
r
d
er
o
p
e
r
ato
r
s
(
)
at
is
r
ef
er
r
e
d
to
as
f
r
ac
tio
n
al
ca
lcu
lu
s
s
o
th
at
t
h
e
o
p
er
atio
n
'
s
b
o
u
n
d
s
ar
e
(
)
an
d
(
)
,
an
d
a
r
ea
l
n
u
m
b
er
(
)
d
en
o
tes
f
r
ac
tio
n
al
o
r
d
er
[
20
]
.
T
h
e
f
r
ac
tio
n
al
o
p
er
ato
r
is
estab
lis
h
ed
in
s
ev
er
al
d
ef
in
itio
n
s
.
C
o
n
s
id
er
in
g
G
r
ü
n
wald
-
L
etn
i
k
co
v
d
ef
in
itio
n
[
21
]
,
[
22
]
.
T
h
is
is
o
n
e
o
f
th
e
m
o
s
t
u
s
ed
d
ef
in
itio
n
s
to
estab
lis
h
n
u
m
er
ical
s
o
lu
tio
n
s
o
f
th
e
d
if
f
er
en
tial
f
r
ac
tio
n
al
o
r
d
er
e
q
u
atio
n
s
,
an
d
d
eter
m
in
ed
b
y
(
2
3
)
.
(
)
(
)
(
)
(
)
0
0
1
l
i
m
1
N
k
at
at
h
k
d
f
t
f
t
f
t
k
h
k
d
t
h
→
=
=
=
−
−
(
2
3
)
T
h
e
L
ap
lace
tr
an
s
f
o
r
m
o
f
th
e
f
u
n
ctio
n
'
s
(
)
_
ℎ
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er
iv
ativ
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with
∈
ℝ
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d
s
u
p
p
o
s
in
g
t
h
e
in
itial
co
n
d
iti
o
n
is
ze
r
o
at
=
0
is
g
iv
en
b
y
(
2
4
)
.
ℓ
{
℘
(
)
}
=
(
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=
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1
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1
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1
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0
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−
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−
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1
1
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2
4
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3
.
2
.
1
.
F
ra
ct
i
o
na
l o
rder
2
L
-
M
B
C
m
o
del ident
if
ica
t
io
n
T
h
is
s
ec
tio
n
d
ef
in
es
th
e
i
d
en
t
if
icatio
n
o
f
t
h
e
f
r
ac
tio
n
al
o
r
d
er
m
o
d
el
f
o
r
th
e
DC
-
DC
2
L
-
MBC
.
T
h
e
Ou
s
talo
u
p
ap
p
r
o
x
im
atio
n
f
ilte
r
m
eth
o
d
is
u
s
ed
to
r
ep
r
esen
t
th
e
s
y
s
tem
d
y
n
am
ics
ef
f
icien
tly
an
d
g
iv
e
a
s
u
itab
le
f
r
ac
tio
n
al
o
p
er
ato
r
ap
p
r
o
x
i
m
atio
n
f
o
r
a
s
p
ec
if
ic
f
r
e
q
u
en
c
y
r
a
n
g
e
[
23
]
.
Ou
s
talo
u
p
f
ilter
s
ap
p
r
o
x
im
ate
f
r
ac
tio
n
a
l
o
p
er
ato
r
s
ef
f
icien
tly
d
escr
ib
ed
b
y
th
e
(
2
5
)
.
≈
∐
+
′
+
=
−
(
2
5
)
′
,
an
d
K
ar
e
ca
lcu
lated
u
s
in
g
f
o
r
m
u
las
g
iv
en
b
y
(
2
6
)
:
′
=
(
)
(
+
2
2
+
1
)
;
=
(
ℎ
)
(
−
2
2
+
1
)
;
=
ℎ
(
26
)
is
th
e
ap
p
r
o
x
im
atio
n
o
r
d
e
r
in
s
id
e
th
e
f
r
eq
u
en
cy
r
an
g
e
[
,
ℎ
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an
d
≥
1
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an
d
tak
i
n
g
in
to
co
n
s
id
er
atio
n
,
a
g
o
o
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a
p
p
r
o
x
i
m
atio
n
is
p
er
f
o
r
m
ed
u
s
in
g
th
e
eq
u
atio
n
(
2
6
)
with
=
10
an
d
=
9
[
20
]
.
T
h
e
tr
u
s
t
-
r
eg
io
n
-
r
ef
lectiv
e
an
d
L
e
v
en
b
er
g
-
Ma
r
q
u
ar
d
t
esti
m
atio
n
tech
n
iq
u
es
ar
e
u
s
ed
to
f
in
d
th
e
in
teg
er
o
r
d
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
6
9
4
F
r
a
ctio
n
a
l o
r
d
er P
I
D
co
n
tr
o
ller
d
esig
n
o
f a
DC
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mu
ltil
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l b
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ter u
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(
Gh
r
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i Ta
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i
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2415
s
y
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in
to
a
f
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tio
n
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tem
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Ass
u
m
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g
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les
y
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u
,
an
d
t
ar
e
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h
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id
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tify
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g
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ata
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u
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L
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u
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id
d
ata=
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id
ata
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y
r
ep
r
esen
t
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D
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ep
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e
tim
e
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to
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h
e
co
ef
f
i
cien
ts
ar
e
co
n
s
tr
ain
ed
in
th
e
in
ter
v
al
[
1
0
2
,
1
0
3
]
,
an
d
th
e
o
r
d
er
s
ar
e
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o
u
n
d
ed
i
n
th
e
in
te
r
v
al
o
f
[
1
0
−
9
,
5
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,
an
d
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p
r
o
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im
atio
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with
in
a
f
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e
q
u
en
c
y
r
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f
[
1
0
−
4
,
1
0
+
4
]
(
)
u
s
in
g
th
e
Ou
s
talo
u
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f
ilter
,
a
n
d
th
e
o
r
d
er
o
f
=
5
.
T
h
e
f
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ac
tio
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en
tific
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s
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er
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with
th
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ef
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e
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d
L
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e
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r
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o
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tim
izatio
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o
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ith
m
s
ar
e
d
e
f
in
ed
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elo
w,
r
esp
ec
tiv
ely
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y
(
2
7
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d
(
2
8
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(
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(
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(
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2
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2
8
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A
s
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r
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o
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s
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tili
ze
d
to
co
m
p
ar
e
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h
e
tem
p
o
r
al
d
o
m
ain
p
r
o
p
e
r
ties
o
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th
e
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er
iv
e
d
m
o
d
els
to
th
o
s
e
o
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th
e
o
r
ig
in
al
m
o
d
el
in
Fig
u
r
e
6
.
T
h
e
tr
u
s
t
-
r
eg
io
n
-
r
ef
lectiv
e
esti
m
ate
ap
p
r
o
ac
h
y
ield
s
a
m
o
r
e
p
r
ec
is
e
r
esu
lt
in
th
is
s
p
ec
if
ic
ca
s
e.
T
h
e
tim
e
d
o
m
a
in
f
it
is
ex
ce
llen
t
in
b
o
th
ca
s
es,
b
u
t
ex
a
m
in
in
g
th
e
tem
p
o
r
al
d
o
m
ain
r
esp
o
n
s
e
r
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ea
ls
th
e
d
is
tin
ct
d
if
f
er
e
n
ce
s
b
etwe
en
th
e
two
m
o
d
els.
3
.
2
.
2
.
F
ra
ct
i
o
na
l
o
rder
P
I
D
c
o
ntr
o
ller
(
F
O
P
I
D)
Po
d
lu
b
n
y
was th
e
f
ir
s
t to
in
tr
o
d
u
ce
th
e
n
o
tio
n
o
f
FOC
in
[
24
]
,
[
25
]
.
T
h
e
t
r
an
s
f
er
f
u
n
ctio
n
d
escr
ip
tio
n
o
f
th
e
FOPID
co
n
tr
o
ller
is
p
r
e
s
en
ted
b
y
ex
p
r
ess
io
n
(
2
9
)
:
_
(
)
=
+
−
+
(
2
9
)
I
t
is
ev
id
en
t
f
r
o
m
(
3
1
)
t
h
at
t
h
e
FOPID
co
n
tr
o
ller
h
as
f
iv
e
tu
n
in
g
p
ar
a
m
eter
s
:
a
p
r
o
p
o
r
t
io
n
al
g
ain
(
)
,
an
in
teg
r
ato
r
g
ain
(
)
with
an
o
r
d
er
(
)
a
n
d
a
d
if
f
er
e
n
tiato
r
g
ain
(
)
with
a
n
o
r
d
er
(
)
.
T
h
er
e
ar
e
s
ev
er
al
FOP
I
D
d
esig
n
m
eth
o
d
s
d
ep
en
d
en
t
o
n
th
e
co
n
tr
o
lled
s
y
s
tem
.
I
f
th
e
p
lan
t
is
r
ep
r
esen
ted
b
y
an
in
teg
er
-
o
r
d
er
m
o
d
el,
co
n
v
en
tio
n
al
tu
n
in
g
tech
n
iq
u
e
s
m
ay
b
e
u
s
ed
to
p
r
o
d
u
ce
in
t
eg
er
-
o
r
d
er
PID
p
ar
a
m
eter
s
.
T
h
en
,
FOPID
o
r
d
er
s
m
ay
b
e
ad
ju
s
ted
to
o
p
ti
m
al
p
er
f
o
r
m
an
ce
.
A
to
o
l
is
g
iv
en
th
at
id
en
tifie
s
th
e
p
r
o
ce
s
s
(
wh
ich
m
ay
also
b
e
f
r
ac
tio
n
al
-
o
r
d
er
)
b
y
u
s
in
g
k
n
o
wn
m
o
d
els,
wh
ich
wer
e
s
tu
d
ie
d
in
v
ar
i
o
u
s
p
r
e
v
io
u
s
s
cien
tific
wo
r
k
s
[
26
]
.
MA
T
L
AB
'
s
FO
MCO
N
to
o
lb
o
x
is
d
esig
n
ed
to
f
ac
ilit
ate
th
e
cr
ea
tio
n
o
f
f
r
ac
tio
n
al
-
o
r
d
er
m
o
d
els
an
d
co
n
tr
o
ller
s
an
d
ev
alu
ate
t
h
eir
p
er
f
o
r
m
an
ce
[
27
]
.
T
h
is
s
tu
d
y
u
s
es
th
e
FOPID
co
n
tr
o
ller
to
r
eg
u
late
th
e
DC
-
DC
2L
-
MBC
o
u
tp
u
t
v
o
ltag
e.
T
h
e
p
r
o
b
lem
o
f
o
p
tim
izin
g
p
ar
am
eter
s
is
r
eso
lv
ed
u
s
in
g
th
e
Neld
er
-
Me
a
d
o
p
tim
izatio
n
cr
iter
io
n
.
Ma
n
y
s
tu
d
ies d
is
cu
s
s
ed
th
e
co
n
v
er
g
e
n
ce
o
f
th
e
o
p
tim
izatio
n
with
a
f
am
ily
o
f
f
u
n
ctio
n
s
o
f
two
v
ar
iab
les.
T
h
ese
s
tu
d
ies
em
p
h
asize
o
n
th
e
n
ec
ess
i
ty
f
o
r
v
ar
ian
ts
o
f
th
e
o
r
ig
in
al
Neld
er
-
Me
ad
to
g
u
ar
an
tee
th
e
c
o
n
v
e
r
g
en
ce
p
r
o
b
lem
s
[
28
]
.
T
h
e
Neld
er
-
Me
a
d
alg
o
r
ith
m
was
im
p
r
o
v
ed
f
o
r
m
u
ltid
im
en
s
io
n
al,
u
n
co
n
s
tr
ain
e
d
o
p
tim
izatio
n
b
ased
o
n
th
e
s
elec
tiv
e
s
im
p
lex
th
at
allo
ws
th
e
alg
o
r
ith
m
to
ch
o
o
s
e
its
elem
en
ts
d
y
n
am
ically
in
co
n
tr
ast
t
o
th
e
co
n
v
en
tio
n
al
Neld
er
-
Me
a
d
al
g
o
r
ith
m
,
wh
ich
u
s
es
a
d
eter
m
in
an
t
s
im
p
lex
[
29
]
.
An
o
th
er
im
p
r
o
v
em
en
t
o
f
th
e
alg
o
r
ith
m
,
wh
ich
u
s
es
a
b
o
o
s
ted
in
cr
em
en
tal
Neld
er
-
Me
ad
s
im
p
lex
alg
o
r
ith
m
,
was
ap
p
lied
to
a
n
aly
ze
a
wir
eless
s
en
s
o
r
n
etwo
r
k
b
y
a
d
is
tr
ib
u
ted
r
e
g
r
ess
io
n
[
30
]
.
T
h
e
Ne
ld
er
-
Me
ad
s
im
p
lex
s
ea
r
ch
was
al
s
o
u
s
ed
with
th
e
m
etah
eu
r
is
tic
g
lo
b
al
o
p
tim
izatio
n
k
n
o
wn
as
th
e
s
tate
tr
an
s
itio
n
alg
o
r
ith
m
an
d
th
e
q
u
ad
r
atic
i
n
ter
p
o
latio
n
to
en
h
an
ce
a
lo
ca
l
s
ea
r
ch
[
31
]
.
T
h
e
Neld
er
-
Me
ad
o
p
tim
izatio
n
ca
n
also
b
e
ap
p
lie
d
t
o
th
e
au
to
m
atiza
tio
n
an
d
s
elec
tiv
e
p
r
o
tectio
n
with
th
e
l
o
west
tr
ip
p
in
g
tim
es
b
y
th
e
m
in
im
izatio
n
o
f
an
ap
p
r
o
p
r
iately
d
esig
n
ed
o
b
ject
f
u
n
ctio
n
[
32
]
.
Fo
r
h
ig
h
er
d
im
e
n
s
io
n
al
p
r
o
b
lem
s
,
a
m
u
ltil
ev
el
m
eth
o
d
o
lo
g
y
f
o
r
a
Neld
er
-
Me
ad
o
p
tim
izatio
n
was
d
ev
elo
p
ed
[
33
]
.
T
h
e
m
et
h
o
d
o
lo
g
y
ca
n
en
h
a
n
ce
th
e
o
p
tim
izer
'
s
s
p
ee
d
o
f
co
n
v
er
g
en
ce
as it g
ets clo
s
er
t
o
th
e
o
p
tim
al
s
o
lu
tio
n
.
T
h
e
p
r
o
b
lem
o
f
o
p
tim
izin
g
p
ar
am
eter
s
is
r
eso
lv
ed
u
s
in
g
th
e
Neld
er
-
Me
ad
o
p
tim
izatio
n
cr
it
er
io
n
[
34
]
.
T
h
is
is
p
r
esen
ted
b
y
Fig
u
r
e
7
.
C
o
n
s
id
er
th
e
tr
u
s
t
-
r
eg
io
n
-
r
ef
le
ctin
g
id
en
tific
atio
n
o
b
tain
ed
m
o
d
el
(
2
7
)
f
r
o
m
th
e
in
teg
er
m
o
d
el
o
f
th
e
2
L
-
MBC
.
T
h
e
FOMCON
to
o
lb
o
x
'
s
(
f
p
id
_
o
p
tim
ize)
f
u
n
ctio
n
g
iv
es
a
s
u
b
o
p
tim
al
FOPID
f
o
r
th
e
2
L
-
MBC
s
y
s
tem
u
n
d
er
th
ese
co
n
d
itio
n
s
:
=
=
=
1
,
=
0
.
9
an
d
=
0
.
7
.
T
h
e
p
r
o
p
o
r
tio
n
al
an
d
in
teg
r
al,
an
d
d
e
r
iv
ativ
e
g
ain
s
ar
e
d
ef
in
e
d
b
y
th
e
s
ea
r
ch
lim
its
:
[
,
,
]
∈
[
0
,
100
]
.
T
h
e
Ou
s
talo
u
p
f
ilter
ap
p
r
o
x
im
atio
n
is
u
s
ed
f
o
r
s
im
u
latio
n
with
d
ef
au
lt
s
ettin
g
s
th
at
∈
[
1
0
−
4
,
1
0
+
5
]
(
)
an
d
an
o
r
d
e
r
=
10
.
T
h
e
s
p
ec
if
icatio
n
s
ar
e
s
h
o
w
n
as
:
T
h
e
g
ain
m
ar
g
in
is
1
0
dB
,
an
d
th
e
p
h
ase
m
a
r
g
in
is
4
5
d
eg
r
ee
s
.
I
n
teg
r
al
ab
s
o
lu
te
er
r
o
r
(
I
AE
)
as
g
iv
en
b
y
(
3
0
)
,
is
u
s
ed
as
a
p
er
f
o
r
m
a
n
c
e
m
etr
ic
to
m
in
im
ize
th
e
o
v
e
r
s
h
o
o
t
an
d
th
e
s
ettlin
g
tim
e
in
th
e
clo
s
ed
-
lo
o
p
r
esp
o
n
s
e
o
f
th
e
s
y
s
tem
.
=
∫
|
(
)
|
0
(
3
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
5
,
No
.
4
,
Dec
em
b
er
20
2
4
:
2409
-
24
21
2416
T
h
en
,
t
h
e
n
ec
ess
ity
f
o
r
r
o
b
u
s
t
n
ess
to
g
ain
ch
an
g
es
is
im
p
o
s
ed
,
to
g
eth
er
with
th
e
r
ec
o
v
er
y
o
f
th
e
c
r
o
s
s
o
v
er
f
r
eq
u
e
n
cy
c
,
wh
ich
is
ca
lcu
lated
b
y
(
3
1
)
.
(
(
)
)
|
=
=
0
(
3
1
)
W
h
e
r
e
(
)
is
t
h
e
o
p
e
n
-
l
o
o
p
f
r
e
q
u
e
n
c
y
r
e
s
p
o
n
s
e
o
f
t
h
e
D
C
-
DC
2
L
-
MBC
s
y
s
te
m
a
n
d
F
O
P
I
D
c
o
n
t
r
o
l
l
e
r
.
M
o
r
e
o
v
e
r
,
t
o
a
v
o
i
d
g
a
i
n
f
l
u
ctu
a
t
i
o
n
,
t
h
e
p
h
as
e
r
es
p
o
n
s
e
at
c
r
i
t
i
c
al
f
r
e
q
u
e
n
c
y
m
u
s
t
b
e
f
l
at.
A
f
t
e
r
6
3
1
r
e
p
e
a
te
d
i
t
e
r
a
ti
o
n
s
o
f
t
h
e
N
e
l
d
e
r
-
M
ea
d
a
l
g
o
r
i
t
h
m
,
t
h
e
s
u
b
o
p
t
i
m
a
l
F
OP
I
D
c
o
n
t
r
o
l
l
e
r
s
et
t
i
n
g
s
a
r
e
c
o
m
p
u
t
e
d
a
s
g
i
v
e
n
b
y
(
3
2
)
.
{
=
0
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013775
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50021
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Fig
u
r
e
6
.
Step
r
esp
o
n
s
es o
f
id
en
tifie
d
an
d
o
r
ig
in
al
m
o
d
els
Fig
u
r
e
7
.
Neld
er
-
Me
ad
f
l
o
wch
ar
t to
tu
n
e
th
e
p
ar
am
ete
r
s
o
f
th
e
FOPID
co
n
tr
o
ller
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
F
r
a
ctio
n
a
l o
r
d
er P
I
D
co
n
tr
o
ller
d
esig
n
o
f a
DC
-
DC
mu
ltil
e
ve
l b
o
o
s
t c
o
n
ve
r
ter u
s
in
g
th
e
…
(
Gh
r
is
s
i Ta
h
r
i
)
2417
4.
SI
M
UL
A
T
I
O
N
A
ND
RE
SU
L
T
S
T
o
ev
alu
ate
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
FLC
an
d
FOPID
co
n
tr
o
ller
s
u
s
in
g
a
VM
C
co
n
tr
o
l
ap
p
r
o
ac
h
o
f
th
e
DC
-
DC
2
L
-
M
B
C
,
a
p
r
o
g
r
am
was
im
p
lem
en
ted
u
n
d
er
MA
T
L
AB
/Si
m
u
lin
k
to
ac
h
iev
e
a
s
e
t
o
f
s
im
u
latio
n
test
s
.
T
h
e
s
y
s
tem
'
s
s
im
u
latio
n
p
ar
am
eter
s
ar
e
g
iv
e
n
in
th
e
T
a
b
le
2
.
F
ig
u
r
es
8
a
n
d
9
s
h
o
w
th
e
d
u
ty
cy
cle,
in
p
u
t
cu
r
r
en
t
,
an
d
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
2
L
-
MBC
u
s
in
g
FLC
an
d
FOPID
co
n
tr
o
ller
s
.
R
ap
id
s
tep
c
h
an
g
e
s
ar
e
ap
p
lied
to
th
e
r
ef
er
en
ce
v
o
ltag
e
,
s
tar
tin
g
with
1
0
0
(
V)
f
r
o
m
0
to
0
.
0
7
s
,
8
0
(
V)
f
r
o
m
0
.
0
7
to
0
.
1
4
s
,
an
d
e
n
d
in
g
with
1
2
0
(
V)
f
r
o
m
0
.
1
4
t
o
0
.
2
s
.
Fig
u
r
es
1
0
a
n
d
1
1
d
ep
ict
in
p
u
t
cu
r
r
e
n
t
an
d
o
u
tp
u
t
v
o
ltag
e
u
s
in
g
FLC
an
d
FOPID
co
n
t
r
o
ller
s
to
ev
alu
ate
th
e
ef
f
icien
cy
o
f
th
e
p
r
o
p
o
s
ed
co
n
t
r
o
ller
s
.
First,
th
e
s
y
s
tem
is
in
itially
s
u
p
p
lied
with
an
in
p
u
t
v
o
ltag
e
o
f
5
0
v
o
lts
,
th
en
a
s
tep
ch
an
g
e
f
r
o
m
5
0
to
4
0
v
o
lts
is
ap
p
lied
at
t=0
.
0
7
s
,
s
u
cc
ee
d
ed
b
y
a
s
tep
ch
an
g
e
f
r
o
m
4
0
to
6
0
v
o
lts
at
t=
0
.
1
4
s
.
Fin
all
y
,
Fig
u
r
es
1
2
an
d
1
3
an
aly
ze
an
d
s
h
o
w
an
ess
en
tial
asp
ec
t
o
f
th
e
c
o
n
tr
o
ller
'
s
o
p
er
atio
n
:
th
e
s
y
s
tem
'
s
r
esp
o
n
s
e
to
lo
ad
ch
an
g
es.
At
t=0
.
0
7
s
,
th
e
lo
a
d
r
esis
to
r
is
d
r
o
p
p
e
d
f
r
o
m
its
n
o
m
in
al
v
alu
e
o
f
1
0
(
Ω
)
to
6
(
Ω
)
an
d
s
u
b
s
eq
u
en
tly
r
aised
f
r
o
m
6
(
Ω
)
to
1
6
(
Ω
)
at
t=
0
.
1
4
s
.
T
h
e
s
im
u
latio
n
r
esu
lts
d
em
o
n
s
tr
ate
th
at
t
h
e
v
o
ltag
e
d
r
o
p
is
r
ec
o
v
er
e
d
m
o
r
e
r
a
p
id
ly
b
y
th
e
FOPID
co
n
tr
o
ller
th
an
b
y
th
e
FLC
wh
en
a
s
u
d
d
en
ch
a
n
g
e
in
l
o
ad
o
cc
u
r
s
.
T
ab
le.
2
Simu
latio
n
p
ar
am
eter
s
Th
e
D
C
-
D
C
t
w
o
-
l
e
v
e
l
b
o
o
s
t
c
o
n
v
e
r
t
e
r
p
a
r
a
met
e
r
s
P
a
r
a
me
t
e
r
s
V
a
r
i
a
b
l
e
s
V
a
l
u
e
s
I
n
p
u
t
v
o
l
t
a
g
e
50
[
]
D
u
t
y
c
y
c
l
e
0
.
5
O
u
t
p
u
t
v
o
l
t
a
g
e
0
200
[
]
I
n
d
u
c
t
o
r
100
[
]
I
n
d
u
c
t
o
r
r
e
si
s
t
a
n
c
e
0
.
0516
[
]
C
a
p
a
c
i
t
o
r
200
[
]
Lo
a
d
r
e
si
s
t
o
r
10
[
]
S
w
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
25
[
ℎ
]
S
a
mp
l
i
n
g
t
i
me
1
[
]
Fig
u
r
e
8
.
Du
t
y
cy
cle
an
d
in
d
u
cto
r
cu
r
r
e
n
t o
f
th
e
DC
-
DC
2
-
L
MBC
with
ch
an
g
e
in
r
ef
er
e
n
c
e
v
o
ltag
e
(
1
0
0
,
8
0
,
an
d
1
2
0
v
o
lts
)
u
s
in
g
FLC an
d
FOPID
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
5
,
No
.
4
,
Dec
em
b
er
20
2
4
:
2409
-
24
21
2418
Fig
u
r
e
9
.
Du
t
y
cy
cle
an
d
o
u
tp
u
t v
o
ltag
e
o
f
th
e
DC
-
DC
2
-
L
MBC
wi
th
ch
an
g
e
in
r
ef
er
e
n
c
e
v
o
ltag
e
(
1
0
0
,
8
0
,
an
d
1
2
0
v
o
lts
)
u
s
in
g
FLC an
d
FOPID
Fig
u
r
e
1
0
.
I
n
d
u
cto
r
c
u
r
r
e
n
t o
f
th
e
DC
-
DC
2
-
L
MBC
wi
th
ch
an
g
e
in
th
e
in
p
u
t
v
o
ltag
e
u
s
in
g
FLC an
d
FOPID
Fig
u
r
e
1
1
.
Ou
tp
u
t
v
o
ltag
e
o
f
t
h
e
DC
-
DC
2
-
L
MBC
with
ch
a
n
g
e
in
th
e
in
p
u
t
v
o
ltag
e
u
s
in
g
FLC an
d
FOPID
Evaluation Warning : The document was created with Spire.PDF for Python.