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ap
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s
[
1
]
,
[
2
]
.
I
n
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s
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a
v
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o
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e
t
h
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[
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[
5
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,
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[
8
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
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8
694
IJ
PEDS
Vo
l.
8
,
No
.
1
,
Ma
r
ch
2017
:
69
–
80
70
P
B
C
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[
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
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0
8
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IJ
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Vo
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8
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No
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1
,
Ma
r
ch
2017
:
69
–
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72
I
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o
s
ed
an
d
d
is
cu
s
s
ed
in
[
2
3
]
,
[
2
4
]
.
4.
T
H
E
P
RO
P
O
SE
D
CO
NT
R
O
L
L
E
R
T
h
r
o
u
g
h
th
e
av
er
a
g
i
n
g
tec
h
n
i
q
u
e,
th
e
co
n
tr
o
l
s
i
g
n
a
l
f
o
r
a
5
-
le
v
el
C
HM
I
i
s
e
x
te
n
d
ed
to
t
h
e
d
is
cr
ete
s
et
o
f
̅
*
+
.
T
h
is
av
er
ag
in
g
m
et
h
o
d
ca
n
also
b
e
ex
te
n
d
ed
to
a
h
i
g
h
er
o
u
tp
u
t
v
o
lta
g
e
lev
e
l
m
u
ltil
e
v
el
i
n
v
er
ter
;
g
iv
e
n
t
h
at
th
e
eq
u
atio
n
(
2
)
an
d
(
3
)
a
r
e
r
e
p
r
esen
ted
as:
̅
(
4
)
(
5
)
w
h
er
e
an
d
ar
e
th
e
av
er
ag
e
s
tates
co
r
r
esp
o
n
d
in
g
to
an
d
r
esp
ec
tiv
el
y
,
w
h
ile
̅
is
a
co
n
tin
u
o
u
s
s
ig
n
al
th
at
b
elo
n
g
s
to
t
h
e
co
n
ti
n
u
o
u
s
s
et
(
-
2
,
2
)
o
r
m
o
r
e.
Fo
r
t
h
e
m
u
ltil
e
v
el
i
n
v
er
ter
m
o
d
el,
eq
u
at
io
n
s
(
4
)
an
d
(
5
)
ar
e
co
n
s
tr
ain
ed
b
y
t
h
e
co
n
tr
o
l la
w
̅
̅
(
)
s
u
ch
t
h
at:
(
6)
f
o
r
cin
g
in
ter
n
al
s
tab
il
it
y
a
n
d
w
it
h
p
r
escr
ib
ed
b
eh
av
io
r
s
f
o
r
t
h
e
av
er
a
g
e
s
tate
o
f
t
h
e
s
y
s
te
m
[
2
5
]
.
4
.
1
.
P
o
rt
-
Co
ntr
o
lled H
a
m
ilto
nia
n (
P
CH
)
Sy
s
t
e
m
Det
a
ils
I
n
o
r
d
er
t
o
d
er
iv
e
th
e
I
DA
-
P
B
C
co
n
tr
o
l
alg
o
r
ith
m
,
th
e
P
o
r
t
C
o
n
tr
o
lled
Ham
ilto
n
ia
n
(
P
C
H)
d
escr
ip
tio
n
o
f
th
e
s
y
s
te
m
is
co
n
s
id
er
ed
[
2
5
]
:
{
̇
,
(
)
(
)
-
(
)
(
)
(
)
(
)
(
7
)
w
h
er
e
(
)
an
d
(
)
ar
e
th
e
in
ter
co
n
n
ec
tio
n
s
tr
u
ctu
r
e
a
n
d
d
a
m
p
in
g
ass
i
g
n
m
e
n
t
r
esp
ec
ti
v
el
y
;
is
th
e
s
tate
v
ar
iab
les
v
ec
to
r
;
is
th
e
in
p
u
t
v
ec
to
r
,
an
d
is
t
h
e
o
u
t
p
u
t
v
ec
to
r
.
an
d
ar
e
th
e
p
o
w
e
r
v
ar
iab
les,
w
h
ic
h
i
n
t
h
is
ca
s
e,
ar
e
th
e
i
n
d
u
c
to
r
cu
r
r
en
t
s
,
i
L
an
d
ca
p
ac
ito
r
v
o
lta
g
es,
v
C
.
(
)
is
th
e
en
er
g
y
(
Ha
m
ilto
n
ian
)
f
u
n
ct
io
n
.
T
h
e
(
)
(
)
r
ep
r
esen
ts
t
h
e
i
n
ter
co
n
n
ec
tio
n
s
tr
u
ct
u
r
e,
w
h
ile
(
)
(
)
is
th
e
d
is
s
ip
atio
n
m
atr
ix
d
u
e
t
o
r
esis
tan
ce
s
a
n
d
f
r
ictio
n
s
.
W
ith
th
e
a
i
m
to
r
ep
r
esen
t
t
h
e
tr
an
s
f
o
r
m
ed
m
o
d
el
i
n
P
C
H
f
o
r
m
,
an
d
ap
p
l
y
i
n
g
th
e
d
-
q
tr
an
s
f
o
r
m
atio
n
f
o
r
th
e
eq
u
i
v
alen
t
s
i
n
g
le
-
p
h
a
s
e
cir
cu
it,
th
e
s
tate
v
ar
iab
le
s
ca
n
b
e
tak
en
a
s
i
Ld
,
i
Lq
,
v
cd
an
d
v
cq
.
T
h
e
en
er
g
y
f
u
n
ctio
n
is
g
iv
e
n
as
:
(
)
(
8
)
T
h
e
d
-
q
m
o
d
el
is
d
ev
elo
p
ed
as
f
o
llo
w
s
:
[
̇
̇
̇
̇
]
[
]
[
]
[
]
[
̅
̅
]
(
9
)
I
n
o
r
d
er
to
d
esig
n
t
h
e
co
n
tr
o
ll
er
,
th
ese
t
w
o
i
m
p
o
r
tan
t
p
r
o
p
er
ties
w
er
e
tak
e
n
in
to
co
n
s
id
er
at
io
n
:
i)
P
r
o
p
er
ty
1
:
Fo
r
t
h
e
eq
u
ilib
r
ia
o
f
eq
u
atio
n
(
9
)
i
n
t
h
e
d
-
q
f
r
a
m
e,
th
e
d
e
s
ir
ed
ca
p
ac
ito
r
v
o
lta
g
e
s
i
g
n
al
(
a
p
u
r
e
h
ar
m
o
n
ic
f
r
ee
s
i
n
u
s
o
id
al
s
i
g
n
a
l
w
it
h
a
f
ix
ed
a
n
g
u
lar
f
r
eq
u
e
n
c
y
an
d
a
m
p
li
tu
d
e
)
is
co
n
s
id
er
ed
.
(
1
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
P
erfo
r
ma
n
ce
o
f I
n
terco
n
n
ec
ti
o
n
a
n
d
Da
mp
in
g
A
s
s
ig
n
men
t
P
a
s
s
ivity
B
a
s
ed
C
o
n
tr
o
ller
o
n
....
(
N
.
H.
R
a
mla
n
)
73
ii)
P
r
o
p
er
ty
2
:
I
t
is
p
o
s
s
ib
le
to
f
o
r
m
u
late
th
e
co
n
tr
o
l
p
r
o
b
lem
a
s
f
o
llo
w
s
,
s
in
ce
t
h
e
co
m
p
lete
s
y
s
te
m
is
m
ea
s
u
r
ab
le.
a.
A
co
n
tr
o
l
la
w
is
d
e
s
ig
n
ed
s
u
c
h
t
h
at
th
e
v
o
lta
g
e
r
e
g
u
la
tio
n
i
s
m
ai
n
tain
ed
u
n
d
er
d
if
f
er
en
t
lo
ad
co
n
d
itio
n
s
,
w
h
ile
m
ai
n
tai
n
in
g
a
lo
w
T
HD
v
alu
e.
T
h
e
en
er
g
y
eq
u
at
io
n
f
o
r
th
e
5
-
lev
el
C
HM
I
ca
n
b
e
d
ef
in
ed
as
[
1
2
]
:
(
)
(
)
(
)
(
)
(
11)
w
h
er
e
,
-
[
]
ar
e
th
e
eq
u
ilib
r
iu
m
p
o
in
ts
.
A
cc
o
r
d
in
g
to
[
2
5
]
,
it is
n
ec
ess
ar
y
to
as
s
i
g
n
t
h
e
i
n
ter
co
n
n
ec
ti
o
n
an
d
d
a
m
p
in
g
m
atr
ices i
n
o
r
d
er
to
tr
an
s
f
o
r
m
t
h
e
P
C
H
m
o
d
el
in
e
q
u
atio
n
(
9
)
to
th
e
f
o
r
m
,
̇
,
(
)
(
)
-
(
)
(
1
2
)
w
h
er
e
(
)
(
)
an
d
(
)
.
T
h
e
d
er
iv
ativ
e
o
f
(
)
ca
n
b
e
ex
p
r
ess
ed
as:
(
)
(
)
(
)
(
)
(
13)
B
y
co
n
s
i
d
er
in
g
t
h
e
f
o
llo
w
i
n
g
p
r
o
p
er
ties
,
i)
(
I
n
teg
r
ab
ilit
y
)
(
)
is
th
e
g
r
ad
ien
t
o
f
a
s
ca
lar
f
u
n
ct
io
n
:
(
)
[
(
)
]
ii)
(
E
q
u
ilib
r
iu
m
Ass
ig
n
m
en
t)
(
)
at
,
v
er
if
ie
s
:
(
)
(
)
iii)
(
L
y
ap
u
n
o
v
s
tab
ilit
y
)
T
h
e
J
ac
o
b
ian
o
f
(
)
,
at
,
s
atis
f
ies t
h
e
bound:
(
)
(
)
T
h
u
s
,
th
e
v
ec
to
r
f
u
n
ctio
n
(
)
s
atis
f
ie
s
th
e
f
o
llo
w
i
n
g
eq
u
a
tio
n
:
[
(
)
(
)
(
(
)
(
)
)
]
(
)
,
(
)
(
)
-
(
)
(
)
(
)
(
1
4
)
Un
d
er
th
ese
co
n
d
itio
n
s
,
t
h
e
cl
o
s
ed
-
lo
o
p
s
y
s
te
m
(
)
w
ill b
e
a
p
o
r
t
-
co
n
tr
o
lled
Ha
m
il
to
n
ia
n
s
y
s
t
e
m
as i
n
eq
u
atio
n
(
1
2
)
.
T
h
e
f
u
n
ctio
n
s
(
)
an
d
(
)
ar
e
g
iv
e
n
as:
(
)
(
)
[
]
(
1
5
)
T
h
e
co
n
tr
o
l
-
la
w
eq
u
atio
n
s
b
a
s
ed
o
n
th
e
P
C
H
I
D
A
-
P
B
co
n
tr
o
ller
is
o
b
tain
ed
in
ter
m
s
o
f
d
-
q
r
o
tatio
n
,
w
h
ic
h
is
[
1
2
]
:
̅
[
̃
]
(
1
6
)
̅
[
̃
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
1
,
Ma
r
ch
2017
:
69
–
80
74
w
h
er
e
̃
̃
an
d
̃
̃
.
Fin
all
y
,
t
h
e
co
n
tr
o
l si
g
n
al
i
s
g
i
v
en
b
y
̅
̅
̅
(
1
7
)
C
o
m
p
ar
in
g
th
e
co
n
tr
o
l
eq
u
ati
o
n
f
o
r
th
e
5
-
lev
el
C
HM
I
w
i
th
a
s
in
g
le
-
p
h
a
s
e
H
-
b
r
id
g
e
in
v
e
r
ter
as
in
[
1
2
]
,
th
e
f
i
n
al
co
n
tr
o
l
s
ig
n
al
i
s
r
ath
er
s
i
m
ilar
,
ex
ce
p
t
f
o
r
th
e
f
ac
t
th
at
th
r
o
u
g
h
av
er
ag
e
m
o
d
elin
g
o
f
th
e
C
HM
I
p
r
ev
io
u
s
l
y
ex
p
lai
n
ed
in
Sec
tio
n
2
,
th
e
co
n
tr
o
l si
g
n
al
f
o
r
th
e
5
-
lev
el
C
HM
I
is
r
ep
r
esen
ted
as,
̅
*
+
(
1
8
)
I
n
s
tead
o
f
th
e
t
h
r
ee
-
le
v
el
s
q
u
ar
e
w
a
v
e
v
o
ltag
e
i
n
a
s
in
g
le
H
-
b
r
id
g
e.
T
h
is
p
r
o
v
es
t
h
at
t
h
e
co
n
tr
o
l
eq
u
atio
n
i
n
[
1
2
]
,
ca
n
b
e
ea
s
ily
ex
ten
d
ed
to
ca
ter
f
o
r
C
HM
I
s
o
f
h
i
g
h
er
o
u
tp
u
t
v
o
lta
g
e
le
v
els
an
d
th
u
s
p
r
o
d
u
ce
s
h
ig
h
er
o
u
tp
u
t
v
o
ltag
e
w
i
th
r
ed
u
ce
d
T
HD.
T
h
e
f
o
llo
w
i
n
g
s
ec
t
io
n
s
p
r
esen
t th
e
i
m
p
le
m
e
n
tati
o
n
o
f
t
h
e
I
D
A
-
P
B
C
co
n
tr
o
l
s
ig
n
al
f
o
r
t
h
e
5
-
le
v
el
C
HM
I
t
h
r
o
u
g
h
s
i
m
u
latio
n
with
a
p
er
f
o
r
m
an
ce
co
m
p
ar
is
o
n
s
t
u
d
y
b
ased
o
n
a
s
in
g
le
-
p
h
a
s
e
H
-
b
r
id
g
e
i
n
v
er
ter
.
5.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
AND
DIS
CUSS
I
O
N
B
o
th
s
y
s
te
m
s
h
av
e
b
ee
n
s
i
m
u
lated
u
s
i
n
g
M
A
T
L
A
B
/Si
m
u
li
n
k
f
o
r
v
a
lid
atio
n
p
u
r
p
o
s
es.
T
h
e
p
ar
am
eter
s
u
s
ed
in
t
h
e
s
i
m
u
latio
n
ar
e
as
s
h
o
w
n
in
T
ab
le
1
.
T
h
e
s
w
itc
h
i
n
g
d
ev
ices
ar
e
I
GB
T
m
o
d
u
le
s
co
m
m
u
tated
at
a
f
r
eq
u
e
n
c
y
o
f
2
0
k
Hz
u
s
i
n
g
t
h
e
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I
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I
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PEDS
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