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o
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rter
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p
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DC
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k
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c
it
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n
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d
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ra
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o
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e
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lo
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s
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ll
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e
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ra
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k
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g
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5
C
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tally
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K
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CC B
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Facu
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Un
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m
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DC
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k
v
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AC
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DC
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1
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–
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8
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.
I
n
th
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p
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s
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ec
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is
r
ar
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f
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I
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b
y
th
e
o
u
ter
v
o
ltag
e
co
n
tr
o
ller
,
with
th
e
in
n
er
lo
o
p
p
r
o
v
id
in
g
f
ast
cu
r
r
en
t
s
h
ap
i
n
g
an
d
d
am
p
in
g
.
T
h
e
tr
ad
iti
o
n
al
ch
o
ice
o
f
a
PI
co
n
tr
o
ller
in
th
e
o
u
ter
lo
o
p
i
s
attr
ac
tiv
e
f
o
r
its
ze
r
o
s
tead
y
-
s
tate
er
r
o
r
u
n
d
e
r
n
o
m
i
n
al
co
n
d
itio
n
s
,
b
u
t
its
b
an
d
wid
th
is
f
ix
ed
at
th
e
d
es
ig
n
o
p
e
r
atin
g
p
o
in
t,
t
h
er
ef
o
r
e
its
r
esp
o
n
s
e
d
eg
r
a
d
es
wh
en
th
e
o
p
er
atin
g
p
o
in
t
v
ar
ies s
ig
n
if
ican
tly
[
9
]
–
[
1
6
]
.
Sev
er
al
co
n
tr
o
l
s
tr
ateg
ies
h
av
e
b
ee
n
p
r
o
p
o
s
ed
in
t
h
e
liter
atu
r
e
to
co
m
p
en
s
ate
f
o
r
t
h
is
f
ix
ed
-
b
an
d
wid
th
lim
itatio
n
,
s
u
ch
as
in
teg
r
atin
g
f
u
zz
y
lo
g
ic
to
ad
ap
tiv
ely
ad
ju
s
t
PI
g
ain
s
u
n
d
er
v
ar
y
in
g
o
p
er
atin
g
co
n
d
itio
n
s
.
Fo
r
ex
am
p
le,
[
1
1
]
p
r
o
p
o
s
es
a
d
o
u
b
le
f
u
zz
y
PI
co
n
tr
o
ller
f
o
r
th
e
o
u
ter
v
o
lta
g
e
lo
o
p
o
f
a
n
AFE
r
ec
tifie
r
o
p
er
atin
g
ac
r
o
s
s
a
wid
e
r
an
g
e
o
f
AC
an
d
DC
v
o
lta
g
es.
T
h
e
co
n
tr
o
l
s
tr
u
ctu
r
e
c
o
m
b
in
es
a
m
ain
f
u
zz
y
b
lo
ck
th
at
a
d
ju
s
ts
PI
g
ain
s
b
a
s
ed
o
n
th
e
DC
-
lin
k
v
o
ltag
e
er
r
o
r
an
d
its
r
ate
o
f
ch
a
n
g
e
wit
h
a
s
u
b
f
u
zz
y
b
lo
ck
th
at
ap
p
lies
co
r
r
ec
tio
n
s
b
ased
o
n
th
e
AC
s
u
p
p
ly
an
d
D
C
r
ef
er
en
ce
v
o
ltag
es.
Alth
o
u
g
h
th
is
ap
p
r
o
ac
h
s
ig
n
if
ican
tly
im
p
r
o
v
es
b
o
th
d
y
n
am
ic
an
d
s
tead
y
-
s
tate
p
er
f
o
r
m
a
n
ce
,
co
n
s
tr
u
ctin
g
two
s
ep
ar
ate
s
ets
o
f
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
an
d
r
u
l
e
b
ases
ac
r
o
s
s
m
u
ltip
le
o
p
er
at
in
g
p
o
i
n
ts
d
em
an
d
s
e
x
ten
s
iv
e
o
f
f
lin
e
ca
lcu
latio
n
,
s
im
u
latio
n
,
an
d
e
x
p
er
im
e
n
tal
tu
n
in
g
,
lea
d
in
g
t
o
im
p
lem
en
tati
o
n
co
m
p
lex
ity
in
p
r
ac
tice
.
A
s
ec
o
n
d
d
ir
ec
tio
n
ap
p
lies
s
li
d
in
g
m
o
d
e
co
n
tr
o
l
(
SMC
)
,
v
a
lu
ed
f
o
r
its
f
ast
d
y
n
am
ic
r
esp
o
n
s
e
an
d
s
tr
o
n
g
r
o
b
u
s
tn
ess
ag
ain
s
t
p
ar
am
eter
u
n
ce
r
tain
ties
an
d
ex
t
er
n
al
d
is
tu
r
b
a
n
ce
s
[
1
7
]
.
Ho
w
ev
er
,
c
o
n
v
e
n
tio
n
al
SMC
s
u
f
f
er
s
f
r
o
m
ch
atter
in
g
-
h
ig
h
-
f
r
eq
u
en
cy
o
s
cillatio
n
s
in
th
e
co
n
tr
o
l
s
ig
n
al
t
h
at
d
eg
r
ad
e
p
er
f
o
r
m
a
n
ce
.
Stu
d
y
in
[
1
8
]
i
n
co
r
p
o
r
ates
a
f
r
ac
tio
n
al
d
o
u
b
le
p
o
wer
c
o
n
v
er
g
e
n
ce
r
ate
in
t
h
e
in
n
e
r
l
o
o
p
to
r
eso
lv
e
th
e
ch
atter
in
g
is
s
u
e
with
o
u
t
s
ac
r
if
icin
g
r
o
b
u
s
tn
ess
,
ac
h
iev
in
g
a
f
ast
d
y
n
am
ic
r
esp
o
n
s
e
an
d
lo
w
s
tead
y
-
s
tate
er
r
o
r
.
Desp
ite
th
ese
ad
v
an
ce
s
,
e
x
is
tin
g
ap
p
r
o
ac
h
es
th
at
s
im
u
ltan
e
o
u
s
ly
ad
d
r
ess
ch
atter
i
n
g
s
u
p
p
r
e
s
s
io
n
,
f
ast
d
y
n
a
m
ic
r
esp
o
n
s
e,
an
d
s
tead
y
-
s
tate
ac
cu
r
ac
y
s
till
r
ely
o
n
c
o
m
p
lex
alg
o
r
ith
m
s
,
a
d
d
itio
n
al
s
tate
v
ar
iab
les,
m
u
ltip
le
tu
n
in
g
p
ar
am
eter
s
,
an
d
in
cr
ea
s
ed
r
ea
l
-
tim
e
co
m
p
u
tatio
n
b
u
r
d
en
.
An
o
th
er
m
eth
o
d
th
at
r
ep
lace
s
th
e
PI
o
u
ter
lo
o
p
is
ac
tiv
e
d
is
tu
r
b
an
ce
r
ejec
tio
n
co
n
tr
o
l
(
ADR
C
)
,
wh
ich
lu
m
p
s
u
n
m
o
d
eled
d
y
n
am
ics,
p
ar
am
eter
v
ar
iatio
n
s
,
an
d
ex
te
r
n
al
d
is
tu
r
b
an
ce
s
as
a
s
in
g
le
d
is
tu
r
b
a
n
ce
ter
m
,
esti
m
ated
o
n
lin
e
b
y
an
ex
ten
d
ed
s
tate
o
b
s
er
v
er
(
E
SO)
an
d
ac
tiv
ely
co
m
p
en
s
ated
b
y
th
e
co
n
t
r
o
l
ac
tio
n
.
ADR
C
an
d
its
lin
ea
r
ized
v
er
s
io
n
,
lin
ea
r
ac
tiv
e
L
ADRC
,
im
p
r
o
v
e
t
h
e
DC
-
lin
k
v
o
l
tag
e
d
y
n
am
ics
an
d
d
is
tu
r
b
an
ce
r
ejec
tio
n
o
v
e
r
PI
co
n
tr
o
l
[
1
9
]
,
[
2
0
]
an
d
o
n
ly
r
e
q
u
ir
e
th
e
p
la
n
t’
s
r
elativ
e
o
r
d
er
an
d
h
ig
h
-
f
r
eq
u
e
n
cy
g
ain
,
m
ak
i
n
g
th
em
s
tr
u
ctu
r
ally
s
im
p
le
an
d
r
o
b
u
s
t to
m
o
d
el
u
n
ce
r
tain
ty
.
Ho
wev
er
,
ADRC
p
er
f
o
r
m
an
c
e
d
ep
e
n
d
s
o
n
ca
r
e
f
u
l
b
an
d
wid
th
an
d
g
ain
tu
n
i
n
g
,
an
d
o
n
th
e
ac
cu
r
ac
y
o
f
th
e
d
is
tu
r
b
a
n
ce
esti
m
atio
n
[
2
1
]
,
an
d
m
in
im
al
p
lan
t
in
f
o
r
m
atio
n
ca
n
b
e
in
s
u
f
f
icien
t
wh
en
th
e
s
y
s
tem
h
as
m
o
r
e
c
o
m
p
lex
d
y
n
am
ics
[
2
2
]
.
R
esear
ch
er
s
in
[
2
2
]
a
d
d
r
ess
th
is
b
y
s
h
o
win
g
th
at
L
ADRC
is
eq
u
iv
alen
t
to
a
two
-
d
eg
r
ee
-
of
-
f
r
ee
d
o
m
(
2
-
D
OF)
I
MC
s
tr
u
ctu
r
e,
in
wh
ich
th
e
L
ADRC
b
an
d
wid
th
tu
n
in
g
p
a
r
am
eter
s
co
r
r
esp
o
n
d
to
th
e
s
etp
o
i
n
t
an
d
d
is
tu
r
b
an
ce
-
r
ejec
tio
n
f
ilter
tim
e
co
n
s
tan
t
o
f
I
MC.
T
h
is
a
n
aly
s
is
p
r
o
v
id
es
a
th
eo
r
etica
l
b
asis
f
o
r
th
e
L
ADRC
co
n
tr
o
l
b
eh
av
io
r
an
d
s
u
g
g
ests
m
eth
o
d
s
f
o
r
in
co
r
p
o
r
ati
n
g
ad
d
itio
n
al
p
lan
t
d
y
n
am
ics to
f
u
r
th
er
en
h
a
n
ce
c
o
n
tr
o
l p
e
r
f
o
r
m
an
ce
.
B
u
i
l
d
i
n
g
o
n
t
h
is
I
M
C
-
L
A
DR
C
e
q
u
i
v
a
l
e
n
c
e
,
r
es
e
a
r
c
h
e
r
s
in
[
2
3
]
p
r
o
p
o
s
e
d
a
n
e
n
h
a
n
c
e
d
L
A
D
R
C
s
c
h
e
m
e
f
o
r
s
e
r
v
o
s
y
s
te
m
s
t
h
a
t
i
n
t
e
g
r
a
te
s
I
MC
p
r
i
n
ci
p
l
e
s
w
i
t
h
a
ct
i
v
e
d
a
m
p
i
n
g
a
n
d
S
MC
t
e
c
h
n
i
q
u
es
.
T
h
is
a
p
p
r
o
a
c
h
r
e
s
o
l
v
e
s
t
h
e
i
n
h
e
r
en
t
I
M
C
t
r
a
d
e
-
o
f
f
b
e
t
w
e
e
n
f
a
s
t
r
e
f
e
r
e
n
ce
t
r
a
c
k
i
n
g
p
e
r
f
o
r
m
a
n
c
e
a
n
d
s
t
r
o
n
g
d
i
s
t
u
r
b
a
n
c
e
r
e
je
c
t
i
o
n
.
B
y
a
d
d
i
n
g
a
c
t
i
v
e
d
a
m
p
i
n
g
,
d
is
t
u
r
b
a
n
c
e
r
e
j
e
c
t
i
o
n
i
s
i
m
p
r
o
v
e
d
w
i
t
h
o
u
t
i
n
c
r
e
a
s
i
n
g
c
o
n
t
r
o
ll
e
r
o
r
d
e
r
o
r
b
a
n
d
w
i
d
t
h
,
w
h
i
le
SM
C
i
m
p
r
o
v
e
s
r
o
b
u
s
t
n
ess
a
g
a
in
s
t
u
n
c
e
r
t
ai
n
t
i
es
.
T
h
e
I
MC
-
b
a
s
e
d
t
u
n
i
n
g
p
r
o
c
e
d
u
r
e
a
l
s
o
s
i
m
p
li
f
i
es
t
h
e
d
e
s
i
g
n
p
r
o
c
e
s
s
,
m
a
k
i
n
g
L
A
DR
C
e
as
i
er
t
o
i
m
p
l
e
m
e
n
t
i
n
p
r
a
c
t
ic
e
.
A
l
t
h
o
u
g
h
t
h
e
I
M
C
f
r
a
m
e
w
o
r
k
o
f
f
e
r
s
a
n
at
t
r
a
ct
i
v
e
a
l
t
e
r
n
a
ti
v
e
t
o
c
o
n
v
e
n
t
i
o
n
al
P
I
tu
n
i
n
g
b
y
t
a
k
i
n
g
a
d
v
a
n
t
a
g
e
o
f
th
e
e
s
t
a
b
l
is
h
e
d
I
MC
-
P
I
e
q
u
i
v
a
l
e
n
c
e
a
n
d
es
t
i
m
at
i
n
g
d
i
s
t
u
r
b
a
n
c
e
s
f
r
o
m
t
h
e
m
is
m
a
t
c
h
b
e
t
w
e
e
n
t
h
e
p
l
a
n
t
a
n
d
i
n
t
e
r
n
a
l
m
o
d
e
l
[
2
4
]
,
c
o
n
v
e
n
t
i
o
n
a
l
I
M
C
i
s
s
ti
l
l
d
es
i
g
n
e
d
a
r
o
u
n
d
a
s
p
e
c
i
f
i
c
o
p
e
r
a
t
i
n
g
p
o
i
n
t
,
in
t
h
e
s
a
m
e
way
as
P
I
co
n
t
r
o
l
.
T
h
e
in
ter
n
al
p
lan
t
m
o
d
el
an
d
th
e
f
ilter
ar
e
b
o
th
f
i
x
ed
at
t
h
e
d
esig
n
s
tag
e
;
f
o
r
ex
am
p
le
,
wh
en
th
e
ca
p
ac
itan
ce
d
e
g
r
ad
es o
r
AC
-
s
i
d
e
im
p
e
d
an
ce
d
r
if
ts
o
v
er
th
e
c
o
n
v
er
ter
life
tim
e,
th
e
em
b
ed
d
ed
m
o
d
el
n
o
l
o
n
g
e
r
m
atch
es
th
e
ac
tu
al
p
lan
t,
an
d
th
e
d
is
tu
r
b
an
ce
esti
m
ate
d
er
iv
ed
f
r
o
m
th
e
m
o
d
el
is
n
o
l
o
n
g
e
r
ac
cu
r
ate.
Sin
ce
λ
r
em
ain
s
f
ix
ed
,
th
is
tr
ad
eo
f
f
ca
n
n
o
t
b
e
ad
ju
s
ted
o
n
lin
e
wh
en
th
e
o
p
er
atin
g
co
n
d
itio
n
s
ch
a
n
g
e.
T
h
e
co
n
tr
o
ller
th
er
ef
o
r
e
m
u
s
t
b
e
tu
n
e
d
c
o
n
s
er
v
ativ
ely
,
wh
ich
ca
n
lim
it
eith
er
th
e
d
y
n
am
ic
r
esp
o
n
s
e
o
r
t
h
e
av
aila
b
le
r
o
b
u
s
tn
ess
m
ar
g
in
.
C
o
n
s
eq
u
en
tly
,
tr
ad
itio
n
al
I
MC
s
till
s
u
f
f
er
s
f
r
o
m
a
f
i
x
ed
-
b
an
d
wi
d
th
lim
itatio
n
an
d
th
er
ef
o
r
e
ca
n
n
o
t
co
n
s
is
ten
tly
m
ain
tain
th
e
d
esire
d
p
er
f
o
r
m
an
ce
ac
r
o
s
s
th
e
wid
e
an
d
tim
e
-
v
ar
y
in
g
o
p
e
r
atin
g
co
n
d
itio
n
s
with
o
u
t i
n
co
r
p
o
r
ati
n
g
an
o
n
lin
e
a
d
ap
tatio
n
m
ec
h
a
n
is
m
.
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
.
3
,
Sep
tem
b
er
20
2
6
:
1794
-
1
8
0
7
1796
T
o
a
d
d
r
ess
t
h
es
e
s
h
o
r
tc
o
m
in
g
s
o
f
f
i
x
e
d
-
p
a
r
a
m
et
er
PI
a
n
d
I
M
C
,
t
h
is
p
ap
er
p
r
o
p
o
s
es a
h
y
b
r
i
d
ca
s
c
a
d
e
d
co
n
t
r
o
l
a
r
c
h
i
tec
tu
r
e
f
o
r
A
FE
r
ec
ti
f
i
er
s
co
n
s
is
ti
n
g
o
f
a
n
a
d
a
p
tiv
e
i
n
te
r
n
al
m
o
d
el
c
o
n
t
r
o
l
–
PI
(
AI
MC
-
P
I
)
o
u
t
er
v
o
lta
g
e
lo
o
p
a
n
d
a
p
r
e
d
ic
ti
v
e
d
e
ad
b
ea
t
(
PDB
)
i
n
n
e
r
c
u
r
r
en
t
l
o
o
p
.
T
h
e
p
r
o
p
o
s
e
d
o
u
t
e
r
lo
o
p
d
if
f
e
r
s
f
r
o
m
co
n
v
e
n
ti
o
n
a
l
I
MC
i
n
f
o
u
r
w
ay
s
.
Fi
r
s
t
,
ac
t
iv
e
d
a
m
p
i
n
g
is
in
co
r
p
o
r
ate
d
in
to
t
h
e
I
MC
s
tr
u
ct
u
r
e
t
o
i
m
p
r
o
v
e
d
is
t
u
r
b
a
n
ce
r
eje
cti
o
n
w
it
h
o
u
t
i
n
c
r
e
asi
n
g
c
o
n
t
r
o
lle
r
o
r
d
er
o
r
b
an
d
wi
d
t
h
.
S
ec
o
n
d
,
a
n
in
te
r
n
al
f
e
ed
f
o
r
wa
r
d
g
ai
n
is
ad
d
e
d
to
e
n
h
an
ce
d
y
n
a
m
ic
t
r
a
ck
i
n
g
.
T
h
i
r
d
,
a
s
e
p
a
r
ate
r
e
f
er
e
n
c
e
f
ilt
er
is
i
n
c
o
r
p
o
r
a
te
d
,
m
a
k
in
g
t
h
e
s
tr
u
ct
u
r
e
a
two
-
d
e
g
r
ee
-
of
-
f
r
ee
d
o
m
(
2
-
D
OF)
I
MC
s
o
th
at
tr
ac
k
i
n
g
s
p
e
ed
a
n
d
d
is
t
u
r
b
an
ce
r
eje
c
tio
n
ca
n
b
e
t
u
n
e
d
in
d
e
p
e
n
d
e
n
t
ly
r
a
th
er
th
a
n
b
ei
n
g
c
o
u
p
le
d
t
h
r
o
u
g
h
a
s
i
n
g
le
λ
.
Fo
u
r
t
h
,
i
n
s
te
a
d
o
f
u
s
i
n
g
f
i
x
ed
f
ilt
e
r
p
ar
am
ete
r
s
,
a
L
y
ap
u
n
o
v
-
b
as
ed
a
d
ap
tat
io
n
la
w
is
e
m
p
lo
y
ed
t
o
u
p
d
at
e
b
o
t
h
t
h
e
e
m
b
e
d
d
e
d
p
l
an
t
m
o
d
el
a
n
d
p
a
r
a
m
e
te
r
λ
o
n
li
n
e
.
T
h
is
en
s
u
r
es
clo
s
ed
-
lo
o
p
s
tab
ilit
y
an
d
b
o
u
n
d
ed
tr
ac
k
in
g
er
r
o
r
wh
ile
en
ab
lin
g
th
e
co
n
tr
o
ller
to
ad
ju
s
t
to
r
ea
l
-
tim
e
o
p
er
atin
g
c
o
n
d
itio
n
s
,
wh
ich
ca
n
n
o
t
b
e
ac
h
iev
ed
with
f
ix
ed
-
λ
I
MC.
T
o
g
eth
er
,
t
h
ese
m
o
d
if
icatio
n
s
ad
d
r
ess
p
ar
am
eter
u
n
ce
r
tain
t
y
,
ex
ter
n
al
d
is
tu
r
b
an
ce
s
,
an
d
o
p
er
atin
g
p
o
in
t
v
ar
iatio
n
s
with
in
th
e
o
u
ter
lo
o
p
s
tr
u
ctu
r
e.
Sin
ce
th
is
p
ap
e
r
f
o
c
u
s
es
o
n
th
e
o
u
ter
v
o
ltag
e
lo
o
p
,
th
e
in
n
er
lo
o
p
c
u
r
r
en
t
is
k
e
p
t
id
en
tical
ac
r
o
s
s
all
co
m
p
ar
is
o
n
s
s
o
th
at
p
er
f
o
r
m
an
ce
d
if
f
er
e
n
ce
s
ar
e
attr
ib
u
te
d
to
th
e
o
u
te
r
v
o
ltag
e
lo
o
p
a
lo
n
e.
T
h
e
p
r
o
p
o
s
ed
AI
MC
-
PI/PD
B
s
ch
em
e
is
v
alid
ated
b
y
MA
T
L
AB
/Si
m
u
lin
k
s
im
u
latio
n
u
n
d
er
l
o
ad
ch
an
g
es,
r
ef
e
r
en
ce
v
ar
iatio
n
s
,
an
d
DC
-
lin
k
ca
p
ac
itan
ce
m
is
m
atch
.
T
h
e
r
em
ain
d
er
o
f
th
e
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
ws:
i)
Sect
io
n
2
p
r
esen
ts
th
e
AFE
r
ec
tifie
r
m
o
d
el;
ii)
Sectio
n
3
d
etails
th
e
AI
MC
-
PI
co
n
tr
o
ller
d
esig
n
;
iii)
Sectio
n
4
r
ep
o
r
ts
th
e
s
im
u
latio
n
an
d
e
x
p
er
im
e
n
t
al
r
esu
lts
an
d
d
is
cu
s
s
io
n
;
an
d
i
v
)
Sectio
n
5
p
r
esen
ts
th
e
co
n
clu
s
io
n
.
2.
M
O
DE
L
L
I
NG
O
F
ACT
I
VE
-
F
RO
NT
E
ND
R
E
C
T
I
F
I
E
R
A
co
n
v
en
tio
n
al
th
r
ee
-
p
h
ase
A
FE
r
ec
tifie
r
co
n
s
is
ts
o
f
in
p
u
t
l
in
e
in
d
u
cto
r
s
,
a
DC
-
lin
k
ca
p
a
cito
r
,
an
d
s
ix
b
id
ir
ec
tio
n
al
p
o
wer
s
witch
es,
as
illu
s
tr
ated
in
Fig
u
r
e
1
.
T
h
e
lin
e
in
d
u
cto
r
s
an
d
DC
-
lin
k
ca
p
ac
ito
r
p
r
o
v
id
e
in
p
u
t
cu
r
r
en
t
f
ilter
in
g
a
n
d
r
e
d
u
ce
th
e
DC
v
o
ltag
e
r
ip
p
le,
r
esp
ec
tiv
ely
.
Du
r
in
g
ea
ch
s
witch
in
g
cy
cle,
th
e
in
p
u
t
in
d
u
cto
r
s
an
d
DC
-
lin
k
ca
p
ac
ito
r
co
n
tin
u
o
u
s
ly
ex
ch
a
n
g
e
en
er
g
y
,
th
er
e
b
y
r
e
g
u
latin
g
th
e
s
o
u
r
ce
cu
r
r
en
t
an
d
m
ain
tain
in
g
th
e
DC
-
lin
k
v
o
lta
g
e.
Fig
u
r
e
1
.
T
h
r
ee
-
p
h
ase
AFE
r
e
ctif
ier
to
p
o
lo
g
y
I
n
th
is
d
esig
n
,
t
h
e
th
r
ee
-
lin
e
in
d
u
cto
r
s
a
r
e
ass
u
m
ed
id
en
tical,
in
clu
d
in
g
t
h
eir
eq
u
i
v
al
en
t
s
er
ies
r
esis
tan
ce
s
(
E
S
R
s
)
.
T
h
u
s
,
th
e
p
h
ase
-
a,
p
h
ase
-
b
,
an
d
p
h
ase
-
c
in
d
u
ctan
ce
s
ar
e
s
et
eq
u
al
L
sa
=
L
sb
=
L
sc
=
L
s
,
an
d
th
eir
co
r
r
esp
o
n
d
in
g
s
er
ies
r
esi
s
tan
ce
ar
e
also
s
et
eq
u
al,
R
sa
=
R
sb
=
R
sc
=
R
s
.
Fu
r
th
er
m
o
r
e
,
f
o
r
th
e
p
u
r
p
o
s
e
o
f
co
n
tr
o
l
d
esig
n
,
th
e
g
r
id
s
u
p
p
ly
is
m
o
d
elled
as
a
b
alan
ce
d
,
th
r
ee
-
p
h
ase
s
in
u
s
o
id
al
v
o
ltag
e
s
o
u
r
ce
with
o
u
t
h
ar
m
o
n
ic
d
is
to
r
tio
n
o
r
u
n
b
ala
n
ce
d
v
o
ltag
e.
T
h
is
ass
u
m
p
tio
n
is
a
s
tan
d
ar
d
p
r
ac
tice
in
AFE
r
ec
tifie
r
co
n
tr
o
l
d
esig
n
.
Ap
p
ly
i
n
g
Kir
ch
h
o
f
f
’
s
v
o
ltag
e
law
(
KVL
)
,
th
e
m
ath
e
m
atica
l
m
o
d
el
o
f
t
h
e
th
r
ee
-
p
h
ase
AFE
r
ec
tifie
r
in
th
e
a
b
c
-
f
r
am
e
c
o
u
ld
b
e
d
e
r
iv
ed
as
(
1
)
.
[
V
sa
(
t
)
V
sb
(
t
)
V
sc
(
t
)
]
=
R
s
[
I
sa
(
t
)
I
sb
(
t
)
I
sc
(
t
)
]
+
L
s
d
dt
[
I
sa
(
t
)
I
sb
(
t
)
I
sc
(
t
)
]
+
[
V
an
(
t
)
V
bn
(
t
)
V
cn
(
t
)
]
(
1
)
W
h
er
e
V
sa
,
V
sb
,
V
sc
ar
e
th
e
th
r
ee
-
p
h
ase
s
o
u
r
ce
v
o
ltag
es,
I
sa
,
I
sb
,
I
sc
ar
e
th
e
t
h
r
ee
-
p
h
ase
s
o
u
r
ce
cu
r
r
e
n
ts
,
an
d
V
an
,
V
bn
,
V
cn
ar
e
co
n
v
er
ter
p
h
ase
v
o
lt
ag
es.
B
y
Kir
ch
h
o
f
f
’
s
cu
r
r
en
t
law
(
KC
L
)
at
th
e
DC
-
lin
k
n
o
d
e,
th
e
co
n
v
er
ter
DC
-
s
id
e
cu
r
r
en
t c
an
b
e
ex
p
r
ess
ed
as
(
2
)
.
I
co
n
v
(
t
)
=
I
l
o
ad
(
t
)
+
C
dV
dc
(
t
)
dt
(
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
A
d
a
p
tive
in
tern
a
l m
o
d
el
co
n
tr
o
l
-
p
r
o
p
o
r
tio
n
a
l in
teg
r
a
l fo
r
r
o
b
u
s
t c
o
n
tr
o
l o
f
…
(
A
z
iz
a
h
A
b
d
u
l R
a
z
a
k
)
1797
W
h
er
e
I
co
n
v
is
th
e
co
n
v
er
ter
DC
-
s
id
e
cu
r
r
en
t,
I
l
o
ad
is
th
e
lo
ad
cu
r
r
en
t,
C
is
th
e
DC
-
lin
k
ca
p
ac
ita
n
ce
,
an
d
dV
dc
(
t
)
dt
is
th
e
r
ate
o
f
ch
a
n
g
e
o
f
th
e
D
C
-
lin
k
v
o
ltag
e.
3.
O
VE
RA
L
L
CO
N
T
RO
L
A
R
CH
I
T
E
CT
URE
T
h
e
o
v
er
all
b
l
o
ck
d
iag
r
am
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
m
eth
o
d
i
s
s
h
o
wn
in
Fig
u
r
e
2
.
T
h
e
o
u
t
er
v
o
ltag
e
lo
o
p
r
eg
u
lates
th
e
DC
-
lin
k
v
o
ltag
e
u
s
in
g
th
e
p
r
o
p
o
s
ed
L
y
ap
u
n
o
v
-
b
ased
AI
MC
-
PI,
i
n
wh
ich
an
in
n
er
f
ee
d
b
ac
k
g
ain
p
air
im
p
r
o
v
es
b
o
th
d
y
n
am
ic
r
esp
o
n
s
e
a
n
d
d
is
tu
r
b
a
n
ce
r
ejec
tio
n
,
a
n
d
an
a
d
ap
tiv
e
f
ilter
p
ar
am
eter
λ
p
r
o
v
i
d
es
r
o
b
u
s
tn
ess
to
p
lan
t
u
n
ce
r
tain
ties
.
I
n
ad
d
itio
n
,
a
s
ep
ar
ate
r
ef
er
e
n
ce
f
ilter
is
al
s
o
ad
d
ed
af
ter
th
e
r
ef
er
e
n
ce
in
p
u
t
,
allo
win
g
m
o
r
e
co
n
tr
o
l
o
n
r
ef
er
e
n
ce
tr
ac
k
in
g
p
er
f
o
r
m
a
n
ce
.
T
h
e
o
u
tp
u
t
o
f
th
e
o
u
ter
lo
o
p
s
er
v
es
as
th
e
d
-
ax
is
cu
r
r
en
t
r
ef
er
e
n
ce
f
o
r
th
e
i
n
n
er
cu
r
r
en
t
lo
o
p
,
w
h
ich
is
im
p
le
m
en
ted
u
s
in
g
PDB
co
n
tr
o
l.
T
h
e
d
esire
d
s
witch
in
g
s
ig
n
als
ar
e
g
en
e
r
ated
u
s
in
g
s
p
ac
e
-
v
ec
to
r
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
SVPW
M)
b
y
s
y
n
th
esizin
g
t
h
e
co
n
v
er
ter
o
u
tp
u
t
v
o
ltag
e,
⃗
.
Fig
u
r
e
2
.
Ov
e
r
all
b
lo
ck
d
iag
r
a
m
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
3
.
1
.
O
ute
r
v
o
lt
a
g
e
lo
o
p
T
h
is
s
ec
tio
n
p
r
esen
ts
th
e
d
etailed
d
esig
n
o
f
th
e
p
r
o
p
o
s
ed
L
y
ap
u
n
o
v
-
b
ased
AI
MC
-
PI
co
n
tr
o
ller
.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
in
teg
r
ates:
i)
A
n
I
MC
-
PI
s
tr
u
ctu
r
e
with
en
h
an
ce
d
d
is
tu
r
b
a
n
ce
r
eje
ctio
n
an
d
d
y
n
am
i
c
r
esp
o
n
s
e
v
ia
in
ter
n
al
f
ee
d
b
a
ck
an
d
f
ee
d
f
o
r
war
d
g
ain
s
;
ii
)
A
s
ep
ar
ate
r
ef
e
r
en
ce
f
ilter
is
in
co
r
p
o
r
ated
to
im
p
r
o
v
e
tr
ac
k
in
g
s
p
ee
d
p
er
f
o
r
m
an
ce
;
an
d
iii)
O
n
lin
e
p
lan
t
p
ar
am
eter
esti
m
atio
n
u
s
in
g
a
L
y
ap
u
n
o
v
-
s
tab
le
ad
ap
tatio
n
law
an
d
ad
ap
tiv
e
tu
n
in
g
o
f
th
e
I
MC f
ilter
p
a
r
am
et
er
λ
,
en
ab
lin
g
s
elf
-
tu
n
in
g
b
eh
a
v
io
r
.
3
.
1
.
1
.
IMC
-
PI
T
h
e
I
MC
-
PI
s
tr
u
ctu
r
e
o
f
f
er
s
th
e
ad
v
an
tag
e
o
f
ac
h
iev
in
g
ze
r
o
s
tead
y
-
s
tate
er
r
o
r
an
d
ef
f
ec
tiv
e
d
is
tu
r
b
an
ce
r
ejec
tio
n
with
a
s
im
p
le
im
p
lem
en
tatio
n
,
as
illu
s
tr
ated
in
th
e
I
MC
s
y
s
tem
b
lo
ck
d
iag
r
am
i
n
Fig
u
r
e
3
.
Fro
m
th
e
b
l
o
ck
d
ia
g
r
am
,
th
e
o
u
tp
u
t to
i
n
p
u
t r
elatio
n
s
h
ip
o
f
th
e
I
MC is
g
iv
en
b
y
(
3
)
.
Y
(
s
)
/
Y
∗
(
s
)
=
G
i
(
s
)
G
p
(
s
)
1
−
G
i
(
s
)
G
m
(
s
)
+
G
i
(
s
)
G
p
(
s
)
(
3
)
W
h
ile
o
u
tp
u
t to
d
is
tu
r
b
an
ce
r
e
latio
n
s
h
ip
o
f
th
e
I
MC is
g
iv
en
b
y
(
4
)
.
Y
(
s
)
/
V
(
s
)
=
1
−
G
i
(
s
)
G
m
(
s
)
1
−
G
i
(
s
)
G
m
(
s
)
+
G
i
(
s
)
G
p
(
s
)
(
4
)
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
.
3
,
Sep
tem
b
er
20
2
6
:
1794
-
1
8
0
7
1798
W
h
er
e
th
e
G
m
(
s
)
,
G
i
(
s
)
,
an
d
G
p
(
s
)
d
en
o
te
th
e
m
o
d
el,
in
v
e
r
s
e
m
o
d
el,
an
d
p
lan
t
tr
an
s
f
er
f
u
n
ctio
n
s
,
r
esp
ec
tiv
ely
.
T
o
m
ak
e
G
i
(
s
)
=1/
G
m
(s)
r
ea
lizab
le,
a
lo
w
-
p
ass
f
ilter
F
(
s
)
=1/
(λ
s
+1
)
1
is
in
tr
o
d
u
ce
d
.
B
ec
au
s
e
th
e
p
lan
t
h
as
a
p
o
le
at
th
e
o
r
ig
in
th
at
y
ield
s
a
s
lu
g
g
is
h
r
e
s
p
o
n
s
e,
an
in
n
er
f
ee
d
b
ac
k
g
a
in
k
f
an
d
an
i
n
n
er
f
ee
d
f
o
r
war
d
g
ain
k
g
ar
e
ad
d
e
d
,
wh
ich
p
r
o
v
id
e
ac
tiv
e
d
am
p
in
g
th
at
im
p
r
o
v
es
d
is
tu
r
b
an
ce
r
ejec
tio
n
a
n
d
im
p
r
o
v
es tr
an
s
ien
t r
esp
o
n
s
e
,
r
esp
ec
tiv
ely
.
Fig
u
r
e
1
.
I
MC b
lo
c
k
d
iag
r
am
T
h
e
m
o
d
el
o
f
th
e
p
lan
t
tr
a
n
s
f
er
f
u
n
ctio
n
is
g
iv
en
as
(
5
)
.
G
m
(
s
)
=
K
m
/
s
(
5
)
T
h
e
co
m
p
en
s
ated
p
la
n
t
m
o
d
el
,
G
co
m
p
(
s
)
tr
an
s
f
er
f
u
n
ctio
n
af
ter
in
tr
o
d
u
cin
g
an
in
n
e
r
f
ee
d
b
ac
k
g
ain
k
f
an
d
an
in
n
er
f
ee
d
f
o
r
war
d
g
ain
,
k
g
as sh
o
wn
in
Fig
u
r
e
4
,
is
g
iv
e
n
by
(
6
)
.
G
co
m
p
(
s
)
=
1
k
f
(
1
1
k
f
.
1
K
m
.
1
k
g
s
+
1
)
=
K
m2
(
1
T
m2
s
+
1
)
(
6
)
Usi
n
g
th
e
p
o
le
p
lace
m
en
t
m
et
h
o
d
,
t
h
e
v
alu
e
o
f
k
f
is
d
eter
m
in
ed
b
y
p
lacin
g
t
h
e
p
o
le
at
th
e
d
esire
d
o
u
ter
-
lo
o
p
b
an
d
wid
th
.
Me
an
wh
ile,
th
e
v
a
lu
e
o
f
k
g
is
s
elec
ted
to
b
e
1
.
2
5
ti
m
es
lo
wer
th
a
n
t
h
e
v
alu
e
o
f
th
e
in
n
er
f
ee
d
b
ac
k
g
ain
.
T
o
e
n
s
u
r
e
s
tab
ilit
y
a
n
d
p
r
o
p
er
o
u
ter
-
lo
o
p
b
a
n
d
wid
th
s
ep
ar
atio
n
,
th
e
v
alu
e
o
f
k
g
is
ch
o
s
en
s
u
ch
th
at
k
g
≤
α
v
k
m
.
k
f
,
wh
er
e
α
v
r
ep
r
esen
ts
th
e
d
esire
d
o
u
ter
lo
o
p
b
a
n
d
wid
th
.
Fig
u
r
e
4
.
C
lo
s
ed
-
lo
o
p
s
y
s
tem
with
co
m
p
en
s
ated
p
r
o
ce
s
s
an
d
s
etp
o
in
t f
ilter
(
)
T
h
e
eq
u
iv
ale
n
t c
o
n
tr
o
ller
tr
an
s
f
er
G
c
(
s
)
f
u
n
ctio
n
ca
n
b
e
o
b
tain
ed
as
(
7
)
.
G
c
(
s
)
=
G
i
(
s
)
1
−
G
i
(
s
)
.
G
c
o
m
p
(
s
)
(
7
)
W
ith
G
i
(
s
)
=
1
G
co
m
p
(
s
)
.F
(
s
)
,
th
u
s
,
th
e
p
r
o
p
o
r
tio
n
al
a
n
d
in
teg
r
al
g
ain
s
ca
n
b
e
ex
p
r
e
s
s
ed
as
(
8
)
.
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
A
d
a
p
tive
in
tern
a
l m
o
d
el
co
n
tr
o
l
-
p
r
o
p
o
r
tio
n
a
l in
teg
r
a
l fo
r
r
o
b
u
s
t c
o
n
tr
o
l o
f
…
(
A
z
iz
a
h
A
b
d
u
l R
a
z
a
k
)
1799
K
p
=
√
a
√
λ
.
K
m
an
d
K
i
=
1
K
m
.
λ
2
(
8
)
T
h
e
ad
ap
tiv
e
f
ilter
p
ar
am
ete
r
λ
ca
n
b
e
ex
p
r
ess
ed
as p
r
esen
ted
in
(
9
)
[
1
0
]
,
[
2
5
]
.
λ
=
λ
0
(
1
+
∫
|
e
|
ts
tr
|
e
m
|
⌈
y
m
⌉
dt
)
(
9
)
T
h
e
in
itial
v
alu
e
0
is
s
elec
ted
as
th
e
m
in
im
u
m
p
er
m
is
s
ib
le
v
alu
e
b
ased
o
n
ca
s
ca
d
e
d
co
n
tr
o
l
d
esig
n
g
u
id
elin
es
to
en
s
u
r
e
f
ast
tr
an
s
ien
t
r
esp
o
n
s
e
wh
ile
av
o
id
in
g
u
n
d
esira
b
le
d
y
n
am
ic
in
ter
ac
tio
n
b
etwe
en
th
e
in
n
e
r
an
d
o
u
te
r
lo
o
p
s
.
Fro
m
(
8
)
an
d
(
9
)
,
it
ca
n
b
e
o
b
s
er
v
ed
th
at
t
h
e
c
o
n
tr
o
ller
g
ain
s
K
p
an
d
K
i
,
ar
e
im
p
licitly
tu
n
ed
as
f
u
n
ctio
n
s
o
f
b
o
th
tr
ac
k
in
g
er
r
o
r
an
d
m
o
d
ellin
g
er
r
o
r
.
Her
e
,
th
e
tr
ac
k
in
g
er
r
o
r
is
d
ef
in
ed
as
e
=
y
−
r
,
wh
ile
th
e
m
o
d
ellin
g
e
r
r
o
r
is
d
e
f
in
e
d
as
e
m
=
y
−
y
m
,
wh
er
e
y
an
d
y
m
r
ep
r
esen
t
th
e
o
u
tp
u
ts
o
f
th
e
p
lan
t
a
n
d
t
h
e
p
lan
t
m
o
d
el,
r
esp
ec
tiv
ely
,
an
d
r
d
en
o
tes
th
e
r
ef
er
en
ce
s
ig
n
al.
Fu
r
th
er
m
o
r
e
tr
an
d
ts
d
en
o
te
th
e
in
s
tan
ts
at
wh
ich
th
e
ad
a
p
tatio
n
o
f
λ
s
tar
ts
an
d
s
to
p
s
.
W
h
en
eith
er
th
e
t
r
ac
k
in
g
e
r
r
o
r
o
r
m
o
d
ellin
g
er
r
o
r
b
ec
o
m
es
lar
g
e
,
th
e
λ
will
also
in
cr
ea
s
e,
wh
ich
in
tu
r
n
r
ed
u
ce
s
th
e
c
o
n
tr
o
ller
ag
g
r
ess
iv
en
ess
ag
ain
s
t
th
e
m
o
d
el
m
is
m
atch
an
d
u
n
m
o
d
eled
d
y
n
am
ics
b
y
r
ed
u
cin
g
th
e
I
MC
-
PI
g
ain
s
,
K
p
an
d
K
i
.
T
h
e
F
r
(
s
)
in
Fig
u
r
e
4
is
r
ea
lis
ed
a
s
a
f
ir
s
t
-
o
r
d
er
l
o
w
-
p
ass
f
ilter
,
F
r
(
s
)
=
1
λ
r
(
s
)
+
1
(
1
0
)
with
λ
r
=
β
R
λ
0
,
an
d
wh
e
r
e
β
r
≥
1
s
ets th
e
p
r
e
-
f
ilter
b
an
d
wid
th
r
elativ
e
to
λ
0
.
3
.
1
.
2
.
F
irst
-
o
rder
dis
cr
et
e
-
t
i
m
e
identif
ica
t
io
n mo
d
el
I
n
th
is
p
ap
er
,
th
e
p
lan
t
is
a
p
p
r
o
x
im
ated
b
y
a
f
ir
s
t
-
o
r
d
er
s
y
s
tem
to
r
e
d
u
ce
th
e
c
o
m
p
u
tatio
n
al
b
u
r
d
e
n
d
u
r
in
g
o
n
lin
e
p
ar
am
eter
i
d
en
ti
f
icatio
n
.
T
h
e
d
is
cr
ete
-
tim
e
tu
n
ab
le
p
lan
t m
o
d
el
is
ex
p
r
ess
ed
as
(
1
1
)
.
y
̂
(
k
)
=
−
a
1
y
̂
(
k
−
1
)
+
b
1
u
̂
(
k
−
1
)
=
θ
̂
T
∅
(
k
)
(
1
1
)
W
h
er
e
y
̂
is
th
e
p
r
ed
icted
m
o
d
el
o
u
tp
u
t,
u
̂
is
th
e
m
o
d
el
in
p
u
t,
θ
̂
is
th
e
esti
m
ated
p
ar
am
eter
v
ec
t
o
r
,
an
d
∅
(
k
)
is
th
e
r
eg
r
ess
o
r
.
T
h
e
in
d
ex
(
k
)
d
en
o
tes
th
e
cu
r
r
en
t
s
am
p
lin
g
in
s
tan
t,
wh
ile
(
k
−
1
)
d
en
o
tes
th
e
p
r
ev
io
u
s
s
am
p
lin
g
in
s
tan
t
.
T
h
e
p
ar
am
et
er
v
ec
to
r
a
n
d
r
e
g
r
ess
o
r
ar
e
d
ef
in
ed
as
(
1
2
)
.
θ
̂
T
=
[
a
1
,
b
1
]
an
d
∅
(
k
)
=
[
y
(
k
−
1
)
,
u
(
k
−
1
)
]
(
1
2
)
3
.
1
.
3
.
L
y
a
pu
no
v
-
ba
s
ed
a
da
pta
t
io
n la
w
I
n
th
is
s
ec
tio
n
,
th
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
is
d
er
iv
e
d
u
s
in
g
a
co
n
tin
u
o
u
s
-
tim
e
r
ep
r
esen
tatio
n
t
o
s
im
p
lify
th
e
an
aly
s
is
,
an
d
f
o
r
n
o
tatio
n
al
s
im
p
licity
,
tim
e
d
ep
en
d
en
ce
(
t
)
is
o
m
itted
.
C
o
n
s
id
er
th
e
f
ir
s
t
-
o
r
d
er
p
lan
t
d
y
n
am
ics
:
y
̇
=
−
ay
+
bu
(
1
3
)
T
h
e
co
r
r
esp
o
n
d
i
n
g
esti
m
ated
p
lan
t m
o
d
el
is
d
e
f
in
ed
as
(
1
4
)
.
y
̇
m
=
−
a
m
y
m
+
b
m
u
(
1
4
)
T
h
e
m
o
d
el
esti
m
atio
n
e
r
r
o
r
is
ex
p
r
ess
ed
as
(
1
5
)
.
e
̇
m
=
[
−
ay
+
bu
]
−
[
−
a
m
y
m
+
b
m
u
]
(
1
5
)
So
lv
in
g
(
1
5
)
,
th
e
m
o
d
el
esti
m
atio
n
er
r
o
r
is
s
im
p
lifie
d
:
e
̇
m
=
−
a
m
e
m
−
a
̃
y
+
b
̃
u
(
1
6
)
wh
er
e
(
a
m
−
a
)
=
a
̃
an
d
(
b
−
b
m
)
=
b
̃
d
en
o
te
th
e
p
ar
am
eter
esti
m
atio
n
er
r
o
r
s
.
T
o
d
er
i
v
e
th
e
ad
a
p
tatio
n
law
f
o
r
a
m
an
d
b
m
,
th
e
L
y
ap
u
n
o
v
ca
n
d
id
ate
is
d
ef
in
ed
as
(1
7
)
.
V
=
1
2
e
m
2
+
1
2
γ
a
a
̃
2
+
1
2
γ
b
b
̃
2
(
1
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
8
-
8
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4
I
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t J Po
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&
Dr
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s
t
,
Vo
l.
1
7
,
No
.
3
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Sep
tem
b
er
20
2
6
:
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1
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0
7
1800
with
γ
a
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γ
b
>
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.
T
o
ch
ec
k
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y
ap
u
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tab
ilit
y
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th
e
n
ex
t
s
tep
is
to
d
if
f
er
en
tiate
th
e
L
y
a
p
u
n
o
v
f
u
n
ctio
n
with
r
esp
ec
t to
tim
e
an
d
e
x
am
in
e
th
e
s
ig
n
o
f
its
d
er
iv
ativ
e
al
o
n
g
s
y
s
tem
tr
ajec
to
r
ies:
V
̇
=
e
m
e
m
̇
+
1
γ
a
a
̃
a
̃
̇
+
1
γ
b
b
̃
b
̃
̇
(
1
8
)
Su
b
s
titu
tin
g
(
1
6
)
in
to
(
1
8
)
y
ield
s
:
V
̇
=
−
a
m
e
m
2
−
a
̃
e
m
y
+
b
̃
e
m
u
+
1
γ
a
a
̃
a
̃
̇
+
1
γ
b
b
̃
b
̃
̇
(
1
9
)
T
o
ca
n
ce
l
th
e
en
er
g
y
in
jectio
n
ter
m
s
,
s
et
1
γ
a
a
̃
a
̃
̇
=
a
̃
e
m
y
an
d
1
γ
b
b
̃
b
̃
̇
=
−
b
̃
e
m
u
,
y
ield
in
g
th
e
co
n
tin
u
o
u
s
-
tim
e
ad
ap
tatio
n
laws:
a
̃
̇
=
γ
a
e
m
y
an
d
b
̃
̇
=
−
γ
b
e
m
u
(
2
0
)
Nex
t is to
s
u
b
s
titu
te
(
2
0
)
in
to
(
1
9
)
;
co
n
s
eq
u
en
tly
:
V
̇
=
−
a
m
e
m
2
≤
0
(
2
1
)
Sin
ce
V
̇
(
t
)
≤
0
is
n
eg
ativ
e
s
em
i
-
d
ef
in
ite
,
th
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
is
n
o
n
-
i
n
cr
ea
s
in
g
a
n
d
b
o
u
n
d
ed
b
elo
w
b
y
ze
r
o
.
T
h
e
r
ef
o
r
e
V
(
t
)
is
b
o
u
n
d
ed
f
o
r
all
t
≥
0
.
3
.
2
.
I
nn
er
curr
ent
lo
o
p:
predict
iv
e
dea
db
ea
t
co
ntr
o
ller
I
n
th
is
s
ec
tio
n
,
th
e
p
r
e
d
ictiv
e
d
ea
d
b
ea
t
cu
r
r
en
t
co
n
tr
o
ller
e
m
p
lo
y
ed
i
n
th
e
in
n
e
r
lo
o
p
is
d
escr
ib
ed
in
d
etail.
T
h
e
cu
r
r
e
n
t
r
e
f
er
en
ce
s
i
d
∗
an
d
i
q
∗
ar
e
p
r
o
v
i
d
ed
b
y
th
e
o
u
te
r
v
o
ltag
e
lo
o
p
is
ass
u
m
ed
to
b
e
i
d
∗
(
k
+
1
)
an
d
i
q
∗
(
k
+
1
)
r
esp
ec
tiv
ely
.
T
h
ese
r
ef
er
e
n
ce
s
in
dq
-
f
r
am
e
ar
e
th
en
tr
a
n
s
f
o
r
m
ed
to
th
e
α
-
f
r
am
e.
B
y
im
p
o
s
in
g
th
e
d
ea
d
b
ea
t
co
n
d
itio
n
I
s
α
(
k
+
1
)
=
I
s
α
∗
(
k
+
1
)
an
d
I
s
β
(
k
+
1
)
=
I
s
β
∗
(
k
+
1
)
u
s
in
g
th
e
f
o
r
wa
r
d
E
u
ler
ap
p
r
o
x
im
atio
n
,
th
e
d
esire
d
co
n
v
er
ter
o
u
tp
u
t
v
o
ltag
es c
an
b
e
d
er
iv
ed
as
(
2
2
)
an
d
(
2
3
)
.
V
co
n
v
α
∗
(
k
)
=
V
s
α
(
k
)
−
(
R
s
×
I
s
α
(
k
)
)
−
(
L
s
T
S
×
(
I
s
α
∗
(
k
+
1
)
−
I
s
α
(
k
)
)
an
d
V
co
n
v
β
∗
(
k
)
=
V
s
β
(
k
)
−
(
R
s
×
I
s
β
(
k
)
)
−
(
L
s
T
S
×
(
I
s
β
∗
(
k
+
1
)
−
I
s
β
(
k
)
)
(
2
2
)
V
⃗
⃗
r
ef
=
(
V
co
n
v
α
∗
+
jV
co
n
v
β
∗
)
,
a
n
d
θ
∗
=
ta
n
−
1
V
c
o
nv
β
∗
V
c
o
nv
α
∗
(
2
3
)
T
h
e
d
esire
d
co
n
v
er
ter
v
o
ltag
e
v
ec
to
r
is
s
y
n
th
esized
b
y
s
p
ac
e
-
v
ec
to
r
p
u
ls
e
-
wid
th
m
o
d
u
latio
n
(
SVPW
M)
at
a
co
n
s
tan
t switch
in
g
f
r
eq
u
en
cy
to
g
en
er
ate
s
witch
in
g
p
u
ls
es.
4.
RE
SU
L
T
AND
DI
SCUS
SI
O
N
T
h
is
s
ec
tio
n
p
r
esen
ts
s
im
u
lati
o
n
an
d
e
x
p
er
im
e
n
tal
r
esu
lts
t
o
v
alid
ate
th
e
p
r
o
p
o
s
ed
AI
M
C
co
n
tr
o
l
m
eth
o
d
u
n
d
e
r
v
ar
i
o
u
s
o
p
e
r
atin
g
co
n
d
itio
n
s
,
in
clu
d
in
g
ca
p
a
citan
ce
ch
an
g
es,
l
o
ad
d
is
tu
r
b
an
ce
s
,
an
d
DC
-
lin
k
v
o
ltag
e
r
ef
er
en
ce
ch
a
n
g
es.
T
h
e
s
im
u
latio
n
an
d
ex
p
er
im
en
tal
p
ar
am
eter
s
a
r
e
s
u
m
m
ar
ize
d
in
T
ab
le
1
.
T
h
e
p
r
o
p
o
s
ed
AI
MC
-
PI
o
u
ter
lo
o
p
co
n
tr
o
ller
is
b
e
n
ch
m
ar
k
ed
ag
ain
s
t
th
r
ee
b
aselin
e
co
n
tr
o
ller
s
th
at
s
h
ar
e
th
e
s
am
e
PDB
in
n
er
lo
o
p
cu
r
r
e
n
t
co
n
tr
o
l:
a
co
n
v
en
tio
n
al
PI
co
n
tr
o
ller
,
f
i
x
ed
-
λ
I
MC
-
PI,
an
d
L
ADR
C
.
C
o
n
tr
o
ller
p
er
f
o
r
m
an
ce
is
q
u
a
n
tifie
d
u
s
in
g
r
is
e
tim
e
an
d
s
ettlin
g
tim
e.
T
h
e
ev
alu
atio
n
p
r
o
ce
e
d
s
in
th
r
e
e
s
tag
es:
s
ec
tio
n
4
.
ex
am
in
es
th
e
d
y
n
am
ic
r
esp
o
n
s
e
u
n
d
er
n
o
m
in
al
co
n
d
itio
n
s
,
s
ec
tio
n
4
.
2
s
tr
ess
es
th
e
co
n
tr
o
ller
s
with
a
D
C
-
lin
k
ca
p
ac
itan
ce
m
is
m
atch
o
f
0
.
5
C
to
ass
e
s
s
r
o
b
u
s
tn
ess
to
c
ap
ac
ito
r
ag
ein
g
a
n
d
to
ler
a
n
c
e,
an
d
s
ec
tio
n
4
.
3
v
alid
ates
th
e
s
im
u
latio
n
f
in
d
i
n
g
s
o
n
a
h
ar
d
war
e
p
r
o
to
ty
p
e
o
f
a
th
r
ee
-
p
h
ase
AFE
r
ec
tifie
r
.
I
n
th
e
p
r
o
p
o
s
ed
m
eth
o
d
,
th
e
b
an
d
wid
th
o
f
th
e
o
u
ter
v
o
ltag
e
lo
o
p
is
s
elec
ted
at
5
0
Hz,
id
e
n
tical
to
th
o
s
e
o
f
th
e
b
en
c
h
m
ar
k
m
eth
o
d
s
,
en
s
u
r
in
g
a
f
air
co
m
p
ar
is
o
n
.
Fo
r
th
e
PI
m
eth
o
d
,
t
h
e
o
u
ter
v
o
ltag
e
lo
o
p
PI
co
n
tr
o
ller
is
d
esig
n
ed
b
y
tak
in
g
in
to
ac
c
o
u
n
t
t
h
e
d
y
n
a
m
ics
o
f
th
e
in
n
e
r
lo
o
p
s
;
th
er
e
f
o
r
e,
it
is
co
n
s
id
er
e
d
an
o
p
ti
m
al
d
esig
n
[
2
6
]
.
T
h
e
tu
n
in
g
p
ar
am
eter
s
f
o
r
all
co
n
tr
o
ller
s
ar
e
s
u
m
m
ar
ized
in
T
ab
l
e
2
.
4
.
1
.
Dy
na
m
ic
re
s
po
ns
e
un
de
r
no
m
ina
l c
o
nd
it
io
ns
T
h
e
d
y
n
am
ic
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
AI
MC
-
PI
c
o
n
tr
o
l
s
tr
ateg
y
is
f
ir
s
t
ev
alu
a
ted
u
n
d
er
n
o
m
in
al
s
y
s
tem
p
a
r
am
eter
s
a
n
d
co
m
p
ar
ed
with
th
e
b
en
ch
m
ar
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I
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ated
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u
r
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5
.
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lin
k
v
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s
e
at
n
o
m
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r
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4
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
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t J Po
w
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lec
&
Dr
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s
t
,
Vo
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1
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,
No
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3
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Sep
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u
r
e
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d
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o
1
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2
s
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lin
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b
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ab
le
5
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g
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n
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er
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itio
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C
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lin
k
at
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t
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e
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2
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2
.
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m
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al
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o
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F
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0
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.
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h
is
r
ep
r
e
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ts
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s
ig
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atch
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d
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t
d
y
n
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s
h
o
wn
in
Fig
u
r
e
7
,
th
e
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lin
k
v
o
ltag
e
r
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er
e
n
ce
is
in
cr
ea
s
ed
f
r
o
m
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2
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0
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at
t
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2
wh
ile
th
e
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esis
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ce
is
ch
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f
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o
m
5
0
Ω
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1
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at
t
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4
s
.
Un
d
er
th
ese
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n
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itio
n
s
,
AI
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PI,
I
MC
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an
d
L
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n
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r
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ased
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n
r
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e
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f
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,
1
6
m
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s
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r
esp
ec
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el
y
,
as su
m
m
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ized
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T
ab
le
6
.
Fig
u
r
e
7
.
DC
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lin
k
v
o
ltag
e
r
esp
o
n
s
e
u
n
d
e
r
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itan
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eg
r
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atio
n
0
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5
C
:
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ce
s
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f
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m
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at
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2
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d
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4
s
Alth
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th
e
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lin
k
v
o
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e
d
u
r
in
g
th
e
r
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e
n
ce
c
h
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g
e
at
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2
s
.
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n
c
o
m
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o
n
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th
e
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o
s
ed
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PI
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h
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h
tly
s
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r
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n
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e
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u
t
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s
m
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e
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T
h
e
I
MC
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PI
co
n
tr
o
ller
also
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r
o
v
id
es
a
co
m
p
a
r
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le
r
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e
tim
e
o
f
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6
m
s
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o
o
s
cillatio
n
s
,
in
d
icatin
g
th
at
th
e
I
MC
-
b
ased
co
n
tr
o
ller
s
ar
e
less
s
en
s
iti
v
e
to
th
e
ca
p
ac
itan
ce
v
ar
iati
o
n
.
I
n
co
n
tr
ast,
t
h
e
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
A
d
a
p
tive
in
tern
a
l m
o
d
el
co
n
tr
o
l
-
p
r
o
p
o
r
tio
n
a
l in
teg
r
a
l fo
r
r
o
b
u
s
t c
o
n
tr
o
l o
f
…
(
A
z
iz
a
h
A
b
d
u
l R
a
z
a
k
)
1803
co
n
v
en
tio
n
al
PI
s
h
o
ws
s
ig
n
if
i
ca
n
t
s
lo
wer
r
esp
o
n
s
e
i
n
th
is
c
ase
,
with
a
5
5
m
s
r
is
e
tim
e.
Du
r
in
g
d
is
tu
r
b
an
ce
r
ejec
tio
n
at
t
=
0
.
4
s
,
all
th
r
ee
AI
MC
-
PI,
I
MC
-
PI,
an
d
L
ADRC
s
h
o
w
co
m
p
ar
ab
le
p
e
r
f
o
r
m
an
ce
as
d
etailed
in
T
ab
le
7
,
with
L
ADRC
,
AI
MC
-
PI,
an
d
I
MC
-
PI
s
ettlin
g
tim
es
o
f
3
.
8
m
s
,
5
.
3
m
s
,
6
.
1
m
s
,
r
esp
ec
tiv
ely
.
T
h
e
co
n
v
en
tio
n
al
PI
r
eq
u
ir
es 7
0
.
7
m
s
to
s
ettle,
wh
ich
is
co
n
s
id
er
ab
ly
lo
n
g
er
th
an
th
e
o
th
e
r
co
n
tr
o
ller
s
.
Ta
b
le
6
.
R
is
e
tim
e
u
n
d
er
ca
p
a
citan
ce
m
is
m
atch
C
o
n
t
r
o
l
m
e
t
h
o
d
R
i
se
t
i
me
(
ms)
A
I
M
C
-
PI
15
I
M
C
-
PI
16
LA
D
R
C
14
PI
55
T
ab
le
7
.
S
ettlin
g
tim
e
u
n
d
er
c
ap
ac
itan
ce
m
is
m
atch
(
0
.
5
C
)
C
o
n
t
r
o
l
m
e
t
h
o
d
S
e
t
t
l
i
n
g
t
i
me
(
ms)
A
I
M
C
-
PI
5
.
3
I
M
C
-
PI
6
.
1
LA
D
R
C
3
.
8
PI
7
0
.
7
4
.
3
.
E
x
perim
ent
a
l
v
a
lid
a
t
io
n
T
o
f
u
r
th
er
ev
alu
ate
th
e
p
r
ac
ti
ca
l
im
p
lem
en
tatio
n
o
f
th
e
p
r
o
p
o
s
ed
c
o
n
tr
o
l,
an
ex
p
e
r
im
en
t
h
as
b
ee
n
im
p
lem
en
ted
.
T
h
e
h
ar
d
war
e
ex
p
er
im
en
tal
s
etu
p
is
s
h
o
wn
in
Fig
u
r
e
8
.
T
h
e
p
r
o
to
ty
p
e
th
r
ee
-
p
h
ase
AFE
r
ec
tifie
r
co
m
p
r
is
es
th
e
lin
e
in
d
u
cto
r
s
,
I
GB
T
,
g
ate
d
r
iv
e
r
,
D
C
-
lin
k
ca
p
ac
ito
r
,
l
o
ad
r
esis
to
r
,
v
o
ltag
e
a
n
d
c
u
r
r
en
t
s
en
s
in
g
with
th
eir
ass
o
ciate
d
an
alo
g
-
to
-
d
ig
ital
co
n
v
er
ter
(
A
DC
)
d
r
iv
er
cir
c
u
it
,
an
d
a
th
r
ee
-
p
h
ase
s
u
p
p
l
y
.
T
h
e
co
n
tr
o
ller
u
s
ed
in
th
is
ex
p
e
r
im
en
t is
a
m
icr
o
co
n
tr
o
ller
(
T
MS
3
2
0
F2
8
3
7
9
D)
to
p
er
f
o
r
m
th
e
c
o
n
tr
o
l a
lg
o
r
ith
m
.
Fig
u
r
e
8
.
E
x
p
er
im
e
n
tal
s
etu
p
o
f
th
e
s
y
s
tem
T
h
e
f
ir
s
t
ex
p
er
im
en
tal
co
n
d
itio
n
ev
alu
ates
th
e
p
e
r
f
o
r
m
a
n
ce
o
f
th
e
f
ix
ed
-
λ
I
MC
-
PI
co
n
tr
o
ller
.
T
h
e
co
n
tr
o
ller
g
ain
s
an
d
p
ar
am
eter
s
ar
e
s
elec
ted
co
n
s
is
te
n
tly
with
th
o
s
e
u
s
ed
in
s
im
u
latio
n
.
As
s
h
o
wn
i
n
Fig
u
r
e
9
,
th
e
f
ix
ed
-
λ
I
MC
-
PI
ex
h
ib
its
s
ig
n
if
ican
t
r
i
p
p
le
in
t
h
r
ee
-
p
h
ase
AC
s
u
p
p
ly
c
u
r
r
en
t
s
.
A
co
r
r
esp
o
n
d
in
g
r
ip
p
le
ca
n
also
b
e
o
b
s
er
v
ed
in
th
e
DC
-
lin
k
v
o
ltag
e.
T
h
is
b
eh
av
io
r
m
a
y
b
e
ca
u
s
ed
b
y
m
o
d
el
o
r
p
ar
am
ete
r
m
is
m
atch
b
etwe
en
th
e
ac
tu
al
h
ar
d
war
e
a
n
d
t
h
e
s
im
u
latio
n
m
o
d
el,
n
o
is
e
f
r
o
m
th
e
v
o
ltag
e
an
d
cu
r
r
e
n
t
s
en
s
o
r
s
,
an
d
th
e
f
in
ite
r
eso
lu
tio
n
an
d
u
p
d
ate
laten
cy
o
f
th
e
d
ig
ita
l
PW
M
,
wh
ich
in
tr
o
d
u
ce
a
p
er
s
is
ten
t
m
is
m
atch
b
etwe
en
th
e
ass
u
m
ed
an
d
ac
tu
al
p
lan
t
d
y
n
am
ics
th
at
a
f
ix
ed
-
λ
an
d
f
ix
ed
em
b
e
d
d
ed
m
o
d
el
ca
n
n
o
t
co
m
p
en
s
ate
f
o
r
.
T
h
e
s
am
e
t
u
n
in
g
p
ar
a
m
eter
s
ar
e
ap
p
lied
to
th
e
AI
MC
-
PI
co
n
tr
o
ller
to
p
r
o
v
id
e
a
co
n
s
is
ten
t
co
m
p
ar
is
o
n
with
th
e
f
ix
ed
-
λ
.
T
h
e
ex
p
e
r
i
m
en
tal
r
esu
lts
ar
e
s
h
o
wn
in
Fig
u
r
e
1
0
.
C
o
m
p
ar
ed
with
th
e
f
ix
ed
-
λ
I
MC
-
PI
r
esp
o
n
s
e
in
Fig
u
r
e
9
,
th
e
p
r
o
p
o
s
ed
AI
MC
-
PI
co
n
tr
o
ller
s
i
g
n
if
ican
tly
r
ed
u
ce
s
th
e
r
ip
p
le
in
th
e
th
r
ee
-
p
h
ase
s
u
p
p
ly
cu
r
r
en
ts
,
wh
ile
th
e
D
C
-
lin
k
v
o
ltag
e
ex
h
ib
its
a
m
o
r
e
s
tab
le
an
d
s
m
o
o
th
e
r
r
esp
o
n
s
e
in
s
tead
y
-
s
tate
co
n
d
itio
n
s
.
T
h
ese
r
esu
lts
d
em
o
n
s
tr
ate
th
e
ef
f
ec
tiv
en
ess
o
f
t
h
e
ad
ap
tiv
e
m
ec
h
an
is
m
in
im
p
r
o
v
in
g
th
e
p
r
ac
tical
v
o
ltag
e
r
eg
u
latio
n
p
e
r
f
o
r
m
an
c
e
in
r
ea
l
tim
e.
Nev
er
th
eless
,
a
m
in
o
r
d
is
cr
ep
a
n
cy
ex
is
ts
b
et
wee
n
ex
p
er
im
e
n
tal
an
d
s
im
u
latio
n
r
esu
lts
:
at
n
o
m
in
al
ca
p
ac
itan
ce
,
th
e
m
ea
s
u
r
ed
r
is
e
tim
e
is
1
.
4
x
lo
n
g
er
th
a
n
th
e
s
im
u
lated
v
alu
e
(
T
ab
le
3
)
.
I
n
th
e
n
ex
t
s
ce
n
ar
i
o
at
0
.
5
C
,
th
e
e
x
p
er
im
e
n
tal
r
e
s
u
lt
ca
n
b
e
o
b
s
er
v
ed
in
Fig
u
r
e
1
1
.
T
h
e
r
is
e
tim
e
v
alu
e
f
r
o
m
th
e
e
x
p
er
im
e
n
t
is
2
3
.
2
8
m
s
co
m
p
ar
ed
to
th
e
s
i
m
u
latio
n
v
alu
e
o
f
1
5
m
s
(
T
a
b
le
6
)
,
wh
ich
is
1
.
5
tim
es
lo
n
g
er
th
an
in
th
e
s
im
u
latio
n
.
T
h
ese
d
is
cr
ep
a
n
cies
ar
e
p
r
im
ar
ily
attr
ib
u
tab
le
to
m
o
d
el
m
is
m
atch
es
b
etwe
en
id
ea
l
s
im
u
latio
n
a
n
d
p
h
y
s
ical
co
n
v
er
te
r
s
etu
p
,
a
lo
n
g
s
id
e
d
ig
ital
c
o
n
tr
o
l
laten
cies
s
u
ch
as
ADC
s
am
p
lin
g
an
d
PW
M
u
p
d
ate
d
e
lay
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.