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r
o
p
o
s
ed
a
d
esig
n
m
eth
o
d
f
o
r
s
tate
-
f
ee
d
b
ac
k
co
n
tr
o
l
b
ased
o
n
L
MI
ap
p
r
o
ac
h
b
y
f
o
r
m
u
lat
in
g
a
n
L
MI
f
o
r
th
e
H∞
f
u
zz
y
[
1
7
]
,
L
QR
p
r
o
b
lem
[
1
8
]
,
an
d
d
er
iv
in
g
a
n
e
w
L
MI
al
g
o
r
ith
m
[
1
9
]
to
f
i
n
d
t
h
e
s
tate
-
f
ee
d
b
ac
k
g
ai
n
.
Ho
w
e
v
er
,
t
h
e
d
c
-
dc
-
c
o
n
v
er
ter
i
s
co
n
f
i
n
ed
to
a
b
o
o
s
t
co
n
v
er
ter
[
1
8
,1
9
]
o
r
a
b
u
ck
co
n
v
er
ter
[
1
7
,1
8
]
.
W
e
d
if
f
er
en
tiate
o
u
r
r
esear
ch
in
t
w
o
p
o
in
ts
o
f
v
ie
w
.
Firstl
y
,
a
b
o
o
s
t
co
n
v
er
ter
ca
n
o
n
l
y
s
tep
-
u
p
an
d
a
b
u
ck
co
n
v
er
ter
ca
n
o
n
l
y
s
tep
-
d
o
w
n
i
n
p
u
t
v
o
lta
g
e
w
h
er
ea
s
a
ze
ta
co
n
v
er
ter
ca
n
o
p
er
ate
in
b
o
th
w
a
y
s
.
T
h
u
s
,
t
h
e
co
n
tr
o
l
p
r
o
b
lem
f
o
r
a
ze
ta
co
n
v
er
ter
h
as
to
d
ea
l
w
ith
lar
g
e
u
n
ce
r
tai
n
t
y
ca
u
s
ed
b
y
t
h
e
t
wo
o
p
e
r
atio
n
s
(
s
tep
-
u
p
/s
tep
-
d
o
w
n
)
.
Ou
r
co
n
tr
ib
u
t
io
n
is
w
e
i
n
v
e
s
ti
g
ate
th
e
d
c
-
d
c
ze
ta
co
n
v
er
ter
r
esp
o
n
s
es
in
la
r
g
e
u
n
ce
r
tai
n
t
y
in
s
u
ch
a
w
a
y
th
at
th
er
e
i
s
tr
an
s
itio
n
o
f
o
p
er
atio
n
m
o
d
e
f
r
o
m
s
tep
-
d
o
w
n
to
s
tep
-
u
p
m
o
d
e
w
h
ic
h
h
as
n
e
v
er
b
ee
n
in
v
e
s
tig
ated
to
th
e
b
est
o
f
th
e
a
u
th
o
r
s
'
k
n
o
w
led
g
e.
Seco
n
d
l
y
,
w
e
i
n
v
e
s
ti
g
ate
t
h
e
r
ed
u
ctio
n
o
f
co
n
s
er
v
at
is
m
i
n
co
n
tr
o
l
p
er
f
o
r
m
a
n
ce
w
h
en
t
h
e
s
y
s
te
m
u
n
ce
r
tain
t
y
is
d
escr
ib
ed
b
y
a
s
m
aller
co
n
v
e
x
p
o
l
y
to
p
e.
B
y
th
i
s
w
a
y
,
w
e
ca
n
v
er
i
f
y
t
h
e
r
elatio
n
o
f
co
n
v
e
x
p
o
ly
to
p
e
r
ed
u
ctio
n
w
it
h
th
e
co
n
s
er
v
a
tiv
en
es
s
an
d
th
u
s
t
h
e
p
er
f
o
r
m
a
n
c
e
o
f
th
e
co
n
tr
o
ll
er
.
T
h
e
o
th
er
s
ec
tio
n
s
o
f
t
h
is
p
ap
er
ar
e
o
r
g
an
ized
as
f
o
llo
w
s
.
Firstl
y
,
i
n
Sectio
n
2
,
we
s
h
o
w
t
h
e
m
o
d
eli
n
g
o
f
t
h
e
d
c
-
d
c
ze
ta
c
o
n
v
er
ter
u
n
d
er
p
ar
a
m
eter
s
u
n
ce
r
tain
t
y
.
Nex
t,
i
n
Sect
io
n
3
,
w
e
g
i
v
e
L
MI
b
ased
f
ee
d
b
ac
k
co
n
tr
o
l
s
c
h
e
m
e
f
o
r
m
u
latio
n
.
Af
ter
t
h
at
i
n
Se
c
tio
n
4
,
w
e
p
r
ese
n
t
t
h
e
d
esi
g
n
e
x
a
m
p
les
to
ill
u
s
tr
ate
t
h
e
ad
v
an
ta
g
es
o
f
t
h
is
ap
p
r
o
ac
h
.
T
h
e
tr
an
s
ien
t
r
esp
o
n
s
e
s
h
a
v
e
b
ee
n
s
i
m
u
lated
w
it
h
P
SIM
®.
L
ast
l
y
i
n
Sectio
n
5
,
w
e
g
i
v
e
th
e
s
u
m
m
ar
y
.
2.
M
O
DE
L
I
N
G
O
F
T
H
E
DC
-
DC
Z
E
T
A
CO
NV
E
R
T
E
R
WI
T
H
P
ARAM
E
T
E
RS U
N
CE
R
T
AIN
T
Y
T
h
e
dc
-
d
c
ze
ta
co
n
v
er
ter
cir
c
u
it
is
s
h
o
w
n
in
Fi
g
u
r
e
1
.
T
h
e
cir
cu
it
co
n
s
i
s
ts
o
f
t
w
o
ca
p
ac
it
o
r
s
(
C
1
a
n
d
C
2
)
,
t
w
o
i
n
d
u
cto
r
s
(
L
1
a
n
d
L
2
)
,
an
id
ea
l
d
io
d
e,
a
d
c
v
o
ltag
e
s
o
u
r
ce
(
v
g
)
,
a
r
esis
to
r
(
R
)
,
an
d
an
id
ea
l
s
w
itc
h
(
S
)
.
T
h
e
in
ter
n
a
l
r
esi
s
ta
n
ce
s
ar
e
co
n
s
id
er
ed
s
m
a
ll
e
n
o
u
g
h
s
o
th
e
y
ca
n
b
e
n
eg
lecte
d
.
T
h
e
v
o
ltag
e
ac
r
o
s
s
th
e
ca
p
ac
ito
r
s
ar
e
d
en
o
ted
as
v
C1
an
d
v
C2
,
an
d
t
h
e
cu
r
r
e
n
t
t
h
r
o
u
g
h
th
e
i
n
d
u
c
to
r
s
ar
e
d
en
o
ted
as
i
L1
a
n
d
i
L2
.
T
h
e
p
u
r
p
o
s
e
o
f
th
e
cir
cu
it
is
to
d
r
a
w
p
o
w
er
f
r
o
m
t
h
e
d
c
v
o
ltag
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s
o
u
r
ce
,
an
d
s
u
p
p
l
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p
o
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to
th
e
lo
ad
at
a
lo
w
er
/
h
ig
h
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d
c
v
o
ltag
e
v
al
u
e.
Fo
r
o
u
r
w
o
r
k
,
it
is
as
s
u
m
ed
t
h
at
th
e
d
c
-
d
c
ze
ta
co
n
v
er
ter
o
p
er
ates
in
co
n
tin
u
o
u
s
co
n
d
u
ct
io
n
m
o
d
e
(
C
C
M)
all
t
h
e
ti
m
e.
Fig
u
r
e
1
.
A
d
c
-
d
c
ze
ta
co
n
v
er
t
er
cir
cu
it
W
ith
th
e
s
w
itc
h
b
ein
g
clo
s
ed
f
o
r
th
e
ti
m
e
d
T
an
d
o
p
en
f
o
r
(
1
-
d
)
T
,
th
e
w
eig
h
ted
av
er
a
g
e
o
f
th
e
eq
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,
1
1
g
o
f
f
on
o
f
f
on
v
d
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d
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d
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(
1
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w
h
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x
is
th
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s
tate
v
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w
h
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is
x
=
co
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(
i
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v
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v
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in
t
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p
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A
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ar
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s
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m
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itte
n
as
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v
~
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
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y
s
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I
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al
co
n
d
itio
n
,
w
h
en
th
er
e
i
s
n
o
p
er
tu
r
b
atio
n
,
th
e
y
h
av
e
n
o
m
i
n
al
v
o
=
9
V
a
n
d
i
o
=
6
A
.
A
t
t
=
0
.
5
m
s
,
t
h
e
r
esis
ti
v
e
lo
ad
R
i
s
s
w
itc
h
ed
to
3
Ω
w
h
ich
is
th
e
m
ax
i
m
u
m
lo
ad
allo
w
ed
in
th
e
d
esig
n
,
w
h
ile
at
t
=
3
m
s
,
r
esis
ti
v
e
lo
ad
R
is
s
w
itc
h
ed
b
ac
k
to
1
.
5
Ω
.
T
h
is
co
r
r
esp
o
n
d
to
lar
g
e
lo
ad
cu
r
r
en
t
i
o
d
e
v
iatio
n
o
f
±
3
A
o
r
eq
u
i
v
alen
t to
±
3
0
0
%.
A
lt
h
o
u
g
h
t
h
er
e
ex
is
t
s
lar
g
e
lo
ad
cu
r
r
en
t
p
er
tu
r
b
atio
n
i
o
,
all
t
h
e
co
n
tr
o
ller
s
ca
n
r
eg
u
late
th
e
o
u
tp
u
t
v
o
lta
g
e
v
o
.
Fro
m
th
e
o
u
t
p
u
t
v
o
lta
g
e
v
o
f
i
g
u
r
e,
ei
th
er
at
t
=
0
.
5
m
s
o
r
t
=
3
m
s
,
o
u
t
o
f
th
e
t
h
r
ee
co
n
tr
o
ller
s
,
th
e
K
LQR
p
r
o
d
u
ce
s
th
e
b
est
p
er
f
o
r
m
a
n
ce
in
ter
m
o
f
least
o
v
er
s
h
o
o
t
(
th
e
m
ag
n
it
u
d
e
is
al
m
o
s
t
th
e
s
a
m
e
w
it
h
K
LMI8
t
h
o
u
g
h
)
an
d
th
e
s
h
o
r
test
s
ettli
n
g
ti
m
e
(
ass
u
m
e
t
h
e
s
y
s
te
m
s
ta
y
s
at
±
5
%
o
f
th
e
o
p
er
atin
g
p
o
in
t
)
.
A
s
f
o
r
th
e
co
m
p
ar
is
o
n
b
e
t
w
ee
n
L
MI
b
ased
co
n
tr
o
ller
s
K
LMI16
a
n
d
K
LMI8
,
t
h
e
later
p
r
o
d
u
ce
s
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
f
o
r
b
o
th
o
v
er
s
h
o
o
t
an
d
s
ettli
n
g
t
i
m
e.
T
h
is
s
h
o
w
s
th
at
t
ig
h
te
n
i
n
g
t
h
e
co
n
v
e
x
p
o
l
y
to
p
e
h
as
r
ed
u
ce
d
th
e
co
n
s
er
v
ati
v
en
e
s
s
a
n
d
s
i
g
n
if
ica
n
tl
y
i
m
p
r
o
v
ed
th
e
r
esp
o
n
s
e
o
f
th
e
d
c
-
d
c
ze
ta
co
n
v
er
ter
.
On
th
e
o
th
er
h
a
n
d
,
th
e
n
o
n
-
n
o
m
in
al
co
n
d
it
io
n
o
cc
u
r
s
w
h
e
n
th
e
in
p
u
t
v
o
ltag
e
v
g
d
r
o
p
b
y
6
0
%
(
9
V)
to
s
ettle
at
6
V
as
s
h
o
w
n
i
n
Fi
g
u
r
e
5
.
B
y
s
o
l
v
i
n
g
f
o
r
D
i
n
(
1
5
)
,
th
is
i
m
p
l
y
t
h
at
d
u
r
in
g
n
o
n
-
n
o
m
i
n
al
co
n
d
it
io
n
,
th
e
d
u
t
y
-
r
atio
D
=
0
.
6
.
Fi
g
u
r
e
6
s
h
o
w
s
th
e
r
e
s
p
o
n
s
e
d
u
r
in
g
th
e
n
o
n
-
n
o
m
in
al
co
n
d
itio
n
.
A
s
s
h
o
w
n
i
n
t
h
e
f
i
g
u
r
e,
at
t
=
0
.
5
m
s
,
th
e
K
LQR
p
r
o
d
u
ce
s
th
e
lea
s
t
o
v
er
s
h
o
o
t
f
o
r
o
u
tp
u
t
v
o
lta
g
e
v
o
a
s
co
m
p
ar
ed
to
th
e
o
th
er
t
w
o
co
n
tr
o
ller
s
b
u
t
th
e
d
o
w
n
s
id
e
is
th
at
th
e
o
u
tp
u
t
v
o
lta
g
e
v
o
h
as
v
er
y
h
i
g
h
o
s
cillatio
n
.
F
u
r
th
er
m
o
r
e,
at
t
=
3
m
s
,
its
o
u
tp
u
t
v
o
lta
g
e
v
o
a
n
d
th
e
l
o
ad
cu
r
r
en
t
i
o
r
esp
o
n
s
e
s
d
eter
io
r
ate
in
s
u
ch
a
w
a
y
t
h
at
t
h
e
y
d
o
n
o
r
etu
r
n
to
th
e
ir
o
p
er
atin
g
p
o
in
t.
Ho
w
e
v
er
,
th
i
s
is
n
o
t
t
h
e
ca
s
e
f
o
r
th
e
L
MI
b
ased
co
n
tr
o
ller
s
.
B
o
th
th
e
co
n
tr
o
ller
s
ca
n
co
p
e
w
it
h
th
e
lar
g
e
lo
ad
cu
r
r
en
t
p
e
r
tu
r
b
atio
n
o
f
eit
h
er
-
3
0
0
%
o
r
+3
0
0
%
w
h
er
e
th
e
o
u
tp
u
t
v
o
lt
ag
e
v
o
a
n
d
t
h
e
lo
ad
cu
r
r
en
t
i
o
ar
e
s
u
cc
ess
f
u
ll
y
r
et
u
r
n
to
t
h
eir
o
p
er
atin
g
p
o
i
n
t
al
th
o
u
g
h
t
h
e
o
v
er
s
h
o
o
t
a
n
d
s
ett
lin
g
ti
m
e
ar
e
a
b
i
t
h
ig
h
er
co
m
p
ar
ed
to
t
h
o
s
e
d
u
r
i
n
g
n
o
m
i
n
al
co
n
d
itio
n
.
As
ex
p
ec
ted
also
,
th
e
r
ed
u
ctio
n
in
th
e
co
n
v
e
x
p
o
l
y
to
p
e
p
r
o
d
u
ce
s
b
etter
co
n
tr
o
ller
p
e
r
f
o
r
m
a
n
ce
.
W
e
h
av
e
s
h
o
w
n
t
h
e
r
esp
o
n
s
e
s
b
o
th
u
n
d
er
n
o
m
i
n
al
an
d
n
o
n
-
n
o
m
in
a
l
co
n
d
itio
n
w
h
en
s
u
b
j
ec
ted
to
lar
g
e
p
er
tu
r
b
atio
n
.
Ne
x
t,
w
e
w
il
l
s
h
o
w
t
h
e
co
n
tr
o
l
d
u
t
y
-
r
at
io
r
esp
o
n
s
e
w
h
ich
i
n
d
icate
s
th
e
co
n
tr
o
l
ef
f
o
r
t
th
a
t
n
ee
d
s
to
b
e
d
o
n
e
to
r
eg
u
late
th
e
o
u
tp
u
t
v
o
lta
g
e
o
f
th
e
d
c
-
d
c
ze
ta
co
n
v
er
ter
.
Un
d
er
th
e
n
o
m
i
n
a
l
co
n
d
itio
n
(
le
f
t
o
f
Fig
u
r
e
7
)
,
th
e
co
n
tr
o
l
ef
f
o
r
ts
ar
e
q
u
ite
m
i
n
i
m
u
m
at
b
o
th
in
s
ta
n
ce
s
(
t
=
0
.
5
m
s
an
d
t
=
3
m
s
)
f
o
r
all
th
r
ee
co
n
tr
o
ller
s
.
As
f
o
r
th
e
n
o
n
-
n
o
m
i
n
al
co
n
d
itio
n
(
r
i
g
h
t
o
f
Fi
g
u
r
e
7
)
,
lar
g
er
c
o
n
tr
o
l
ef
f
o
r
ts
n
e
ed
to
b
e
p
r
o
d
u
ce
d
at
t
=
0
.
5
m
s
f
o
r
th
e
s
a
m
e
a
m
o
u
n
t
o
f
lo
ad
cu
r
r
en
t
p
er
tu
r
b
ati
o
n
o
f
-
3
0
0
%
co
m
p
ar
ed
to
th
e
n
o
m
i
n
al
co
n
d
itio
n
.
T
h
e
co
n
tr
o
l
d
u
ty
-
r
atio
f
o
r
th
e
K
LQR
d
eter
io
r
ates
an
d
at
t
=
3
m
s
w
h
er
e
it
ev
en
tu
al
l
y
s
a
tu
r
at
ed
.
On
th
e
co
n
tr
ar
y
,
f
o
r
th
e
L
MI
b
ased
co
n
tr
o
ller
,
b
o
th
co
n
tr
o
l d
u
t
y
-
r
ati
o
ca
n
r
et
u
r
n
to
th
e
ir
o
p
er
atin
g
p
o
in
t.
Fig
u
r
e
4
.
Ou
tp
u
t
v
o
ltag
e
(
le
f
t)
an
d
lo
ad
cu
r
r
en
t (
r
ig
h
t)
r
esp
o
n
s
e
s
u
n
d
er
n
o
m
i
n
al
co
n
d
itio
n
f
o
r
K
LQR
(
d
ash
ed
li
n
e)
,
K
LMI16
(
d
o
tted
lin
e)
an
d
K
LMI8
(
s
o
lid
li
n
e)
.
T
im
e
(
s
)
T
im
e
(
s
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
1
8
:
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–
838
836
Fig
u
r
e
5
.
I
n
p
u
t v
o
lta
g
e
p
er
tu
r
b
atio
n
w
h
ic
h
p
r
o
d
u
ce
s
th
e
n
o
n
-
n
o
m
i
n
al
co
n
d
itio
n
.
Fig
u
r
e
6
.
Ou
tp
u
t
v
o
ltag
e
(
le
f
t)
an
d
lo
ad
cu
r
r
en
t (
r
ig
h
t)
r
esp
o
n
s
e
s
u
n
d
er
n
o
n
-
n
o
m
i
n
al
co
n
d
i
tio
n
f
o
r
K
LQR
(
d
ash
ed
li
n
e)
,
K
LMI16
(
d
o
tted
lin
e)
an
d
K
LMI8
(
s
o
lid
li
n
e)
.
Fig
u
r
e
7
.
C
o
n
tr
o
l d
u
t
y
-
r
atio
r
esp
o
n
s
e
u
n
d
er
n
o
m
in
al
(
le
f
t)
an
d
n
o
n
-
n
o
m
in
al
(
r
i
g
h
t)
co
n
d
itio
n
f
o
r
K
LQR
(
to
p
)
,
K
LMI16
(
m
id
d
le)
an
d
K
LMI8
(
b
o
tto
m
)
s
u
b
j
ec
t to
lo
ad
cu
r
r
en
t p
er
tu
r
b
atio
n
o
f
±
3
A
.
T
h
e
n
ex
t
i
m
p
o
r
ta
n
t
cr
iter
ia
t
h
at
w
e
w
a
n
t
i
n
v
est
ig
ate
is
th
e
a
m
o
u
n
t
o
f
r
ip
p
le
p
r
esen
t
i
n
t
h
e
co
n
tr
o
l
d
u
t
y
-
r
atio
s
ig
n
al
b
ec
au
s
e
ce
r
tain
li
m
it
(
<
2
0
%)
n
ee
d
to
b
e
i
m
p
o
s
ed
to
av
o
id
n
o
n
lin
ea
r
ef
f
ec
t
[
2
4
,
2
5
]
.
A
s
s
h
o
w
n
in
Fi
g
u
r
e
7
,
in
b
o
th
t
h
e
n
o
m
i
n
al
an
d
t
h
e
n
o
n
-
n
o
m
in
al
co
n
d
itio
n
s
,
K
LQR
p
r
o
p
ag
ates
th
e
lea
s
t
r
ip
p
le
(
9
.
6
%
an
d
4
.
8
%,
r
esp
ec
tiv
el
y
)
f
o
llo
w
ed
b
y
K
LMI8
(
1
9
%
an
d
1
0
%,
r
esp
ec
tiv
el
y
)
a
n
d
th
e
w
o
r
s
t
r
ip
p
le
i
s
b
y
K
LMI16
(
2
8
%
an
d
1
6
%,
r
esp
ec
t
iv
el
y
)
o
f
w
h
ic
h
th
e
f
o
r
m
er
co
u
ld
p
o
s
es
n
o
n
li
n
ea
r
b
eh
av
io
r
in
P
W
M
cir
cu
itry
i
f
i
m
p
le
m
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ted
e
x
p
er
i
m
en
ta
ll
y
b
ec
au
s
e
it
is
m
o
r
e
th
a
n
2
0
%.
Si
n
ce
o
u
r
f
o
c
u
s
is
to
p
r
o
v
e
t
h
at
t
h
e
L
MI
b
ased
T
im
e
(
s
)
T
im
e
(
s
)
T
im
e
(
s
)
4.
8%
9.
6%
16%
28%
10%
19%
T
im
e
(
s
)
T
im
e
(
s
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
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8
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694
Un
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r
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ter C
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p
r
o
a
ch
(
Ha
fez
S
a
r
ka
w
i)
837
co
n
tr
o
ller
is
b
etter
th
an
th
e
co
n
v
e
n
tio
n
al
L
QR
co
n
tr
o
ller
es
p
ec
iall
y
w
h
e
n
th
e
s
y
s
te
m
i
s
h
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g
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l
y
u
n
ce
r
tai
n
,
it
is
w
o
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th
to
m
en
t
io
n
t
h
at
b
y
r
ed
u
cin
g
t
h
e
n
u
m
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er
o
f
v
er
tices
f
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th
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co
n
v
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x
p
o
l
y
to
p
e,
it
’
s
p
er
f
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r
m
a
n
ce
s
n
o
t
o
n
l
y
i
m
p
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o
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es
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u
t
al
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o
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cr
ea
s
e
s
t
h
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tab
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ar
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ci
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o
f
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o
n
li
n
ea
r
b
eh
av
io
r
in
P
W
M
cir
cu
itr
y
.
5.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
h
as
p
r
o
p
o
s
ed
a
d
c
-
d
c
ze
ta
co
n
v
er
ter
co
n
tr
o
l
b
as
ed
o
n
L
MI
ap
p
r
o
ac
h
b
y
tak
in
g
ac
co
u
n
t
p
ar
am
eter
u
n
ce
r
tai
n
t
y
.
Si
m
u
la
tio
n
r
esu
lts
s
h
o
w
t
h
at
th
e
co
n
v
en
t
io
n
al
L
Q
R
co
n
tr
o
ller
o
n
l
y
p
r
o
d
u
ce
s
o
p
ti
m
al
r
esu
lt
d
u
r
in
g
t
h
e
n
o
m
i
n
al
c
o
n
d
itio
n
w
h
er
ea
s
t
h
e
p
r
o
p
o
s
ed
L
MI
b
ased
co
n
tr
o
ller
ca
n
co
p
e
w
i
th
h
i
g
h
l
y
u
n
ce
r
tai
n
d
c
-
d
c
ze
ta
co
n
v
er
te
r
.
Fu
r
th
er
m
o
r
e,
th
e
r
ed
u
ct
io
n
o
f
th
e
co
n
v
ex
p
o
l
y
to
p
e
n
o
t
o
n
l
y
i
m
p
r
o
v
es
t
h
e
o
u
tp
u
t
v
o
ltag
e
r
esp
o
n
s
e,
b
u
t
a
ls
o
an
d
m
o
r
e
cr
u
ciall
y
r
ed
u
ce
s
th
e
e
x
is
te
n
ce
o
f
t
h
e
r
ip
p
le
in
th
e
co
n
tr
o
l
d
u
t
y
-
r
atio
.
RE
F
E
R
E
NC
E
S
[1
]
D.
Ja
y
a
h
a
r,
R.
Ra
n
ih
e
m
a
m
a
li
n
i,
a
n
d
K.
Ra
t
h
n
a
k
a
n
n
a
n
,
“
De
sig
n
a
n
d
Im
p
lem
e
n
tatio
n
o
f
S
in
g
le
P
h
a
se
A
C
-
DC
Bu
c
k
-
Bo
o
st
Co
n
v
e
rter
f
o
r
P
o
w
e
r
F
a
c
to
r
Co
rre
c
ti
o
n
a
n
d
Ha
rm
o
n
ic
El
i
m
i
n
a
ti
o
n
”
,
In
t
.
J
o
u
rn
a
l
Po
w
.
El
e
c
.
Dr
ive
S
y
s.
,
V
o
l.
7
,
No
.
3
,
p
p
.
1
0
0
1
-
1
0
1
1
,
S
e
p
t
.
2
0
1
6
.
[2
]
S
.
S
.
Da
sh
a
n
d
B
.
Na
y
a
k
,
“
Bu
c
k
-
Bo
o
st
Co
n
tr
o
l
o
f
F
o
u
r
Q
u
a
d
ra
n
t
Ch
o
p
p
e
r
u
si
n
g
S
y
m
m
e
tri
c
a
l
I
m
p
e
d
a
n
c
e
Ne
t
w
o
rk
f
o
r
A
d
ju
sta
b
le S
p
e
e
d
Driv
e
”
,
In
t.
J
o
u
rn
a
l
P
o
w.
El
e
c
.
Dr
ive
S
y
s.
,
Vo
l.
5
,
No
.
3
,
p
p
.
4
2
4
-
4
3
2
,
F
e
b
.
2
0
1
5
.
[3
]
D.
S
a
ra
v
a
n
a
n
a
n
d
M
.
G
o
p
in
a
t
h
,
“
A
No
v
e
l
P
o
w
e
r
F
a
c
to
r
C
o
rre
c
ti
o
n
M
o
d
if
ied
Bri
d
g
e
L
e
ss
-
CUK
Co
n
v
e
rter
f
o
r
L
ED
L
a
m
p
A
p
p
li
c
a
ti
o
n
s”
,
I
n
t.
J
o
u
rn
a
l
Po
w.
El
e
c
.
Dr
ive
S
y
s.
,
Vo
l.
7
,
No
.
3
,
p
p
.
8
8
0
-
8
9
1
,
S
e
p
t.
2
0
1
6
.
[4
]
A
.
P
.
C.
Ra
o
,
Y.
P
.
Ob
u
les
h
,
a
n
d
C.
S
.
Ba
b
u
,
“
P
o
w
e
r
F
a
c
to
r
Co
rre
c
ti
o
n
i
n
T
w
o
L
e
g
In
v
e
rter
F
e
d
BLDC
Driv
e
Us
in
g
Cu
k
Dc
-
Dc
Co
n
v
e
rter”
,
In
t.
J
o
u
r
n
a
l
Po
w.
El
e
c
.
Dr
ive
S
y
s.
,
V
o
l.
6
,
No
.
2
,
p
p
.
1
9
6
-
2
0
4
,
Ju
n
e
2
0
1
5
.
[5
]
M
.
Ou
d
d
a
a
n
d
A
.
Ha
z
z
a
b
,
“
P
h
o
to
v
o
lt
a
ic
S
y
ste
m
w
it
h
S
EP
IC
Co
n
v
e
rter
Co
n
tro
l
led
b
y
th
e
F
u
z
z
y
L
o
g
ic
”
,
In
t.
J
o
u
rn
a
l
P
o
w.
El
e
c
.
Dr
ive
S
y
s.
,
Vo
l.
7
,
No
.
4
,
p
p
.
1
2
8
3
-
1
2
9
3
,
De
c
.
2
0
1
6
.
[6
]
E.
V
u
t
h
c
h
h
a
y
a
n
d
C.
Bu
n
lak
sa
n
a
n
u
so
r
n
,
“
M
o
d
e
li
n
g
a
n
d
Co
n
tr
o
l
o
f
a
Zeta
Co
n
v
e
rter”
,
in
Pr
o
c
.
IEE
E
In
t
.
P
o
w.
E
lec
.
Co
n
f
.
,
2
0
1
0
,
p
p
.
6
1
2
-
6
1
9
.
[7
]
E.
V
u
t
h
c
h
h
a
y
,
C.
Bu
n
lak
sa
n
a
n
u
s
o
rn
,
a
n
d
H.
Hira
ta,
“
Dy
n
a
m
i
c
M
o
d
e
li
n
g
a
n
d
C
o
n
tr
o
l
o
f
a
Zeta
Co
n
v
e
rter”
,
in
Pro
c
.
IEE
E
In
t.
S
y
m.
o
n
Co
mm
.
a
n
d
I
n
f
o
.
T
e
c
h
.
,
2
0
0
8
.
[8
]
M
.
M
.
G
a
r
g
,
Y.
V
.
Ho
te,
a
n
d
M
.
K.
P
a
th
a
k
,
“
P
I
Co
n
tr
o
ll
e
r
De
sig
n
o
f
a
d
c
-
d
c
Zeta
Co
n
v
e
rter
f
o
r
S
p
e
c
if
ic
P
h
a
s
e
M
a
rg
in
a
n
d
Cr
o
ss
-
o
v
e
r
F
re
q
u
e
n
c
y
”
,
in
Pro
c
.
I
EE
E
1
0
t
h
Asi
a
n
C
o
n
t.
Co
n
f.
,
2
0
1
5
,
p
p
.
1
-
6.
[9
]
B.
S
i
n
g
h
,
S
.
S
i
n
g
h
,
a
n
d
G
.
Bh
u
v
a
n
w
s
wa
ri,
“
A
n
a
l
y
sis
a
n
d
De
sig
n
o
f
a
Zeta
Co
n
v
e
rter
Ba
se
d
T
h
re
e
-
P
h
a
se
S
w
it
c
h
e
d
M
o
d
e
P
o
w
e
r
S
u
p
p
ly
”
,
in
Pro
c
.
IE
EE
4
th
I
n
t.
Co
n
f.
o
n
Co
mp
.
In
tel
.
a
n
d
Co
mm
.
Ne
tw
o
rk
s
,
2
0
1
2
,
p
p
.
5
7
1
-
5
7
5
.
[1
0
]
R.
C.
V
ier
o
,
F
.
B
.
D.
Re
is,
a
n
d
F
.
S
.
D
.
Re
is,
“
C
o
m
p
u
tatio
n
a
l
M
o
d
e
l
o
f
th
e
Dy
n
a
m
ic
Be
h
a
v
io
r
o
f
th
e
Zeta
Co
n
v
e
rter
in
Disc
o
n
ti
n
u
o
u
s Co
n
d
u
c
ti
o
n
M
o
d
e
”
,
in
Pro
c
.
IEE
E
3
8
th
A
n
n
u
a
l
C
o
n
f.
o
n
In
d
.
El
e
c
.
S
o
c
iety
,
2
0
1
2
,
p
p
.
2
9
9
-
3
0
3
.
[1
1
]
R.
C.
V
iero
a
n
d
F
.
S
.
D.
Re
is,
“
De
sig
n
in
g
Clo
se
d
-
L
o
o
p
Co
n
tr
o
ll
e
rs
Us
in
g
a
M
a
tl
a
b
®
D
y
n
a
m
i
c
M
o
d
e
l
o
f
th
e
Zeta
Co
n
v
e
rter i
n
DCM”,
in
Pro
c
.
IE
E
E
1
0
th
I
n
t.
Co
n
f.
o
n
I
n
d
.
A
p
p
s.
,
2
0
1
2
,
p
p
.
1
-
8.
[1
2
]
A
.
Iz
a
d
ian
a
n
d
P
.
Kh
a
y
y
e
r,
“
C
o
m
p
le
m
e
n
tar
y
a
d
a
p
ti
v
e
c
o
n
tr
o
l
o
f
Zeta
c
o
n
v
e
rters
”
,
in
Pro
c
.
IE
EE
In
t
.
El
e
c
tric
M
a
c
h
in
e
s
&
Dr
ive
s Co
n
f.
,
2
0
1
3
,
p
p
.
1
3
3
8
-
1
3
4
2
.
[1
3
]
B.
M
o
a
v
e
n
i,
H.
A
b
d
o
ll
a
h
z
a
d
e
h
,
a
n
d
M
.
M
a
z
o
o
c
h
i,
“
A
d
ju
sta
b
le
o
u
tp
u
t
v
o
lt
a
g
e
Zeta
c
o
n
v
e
rter
u
sin
g
n
e
u
ra
l
n
e
tw
o
rk
a
d
a
p
ti
v
e
m
o
d
e
l
re
fe
re
n
c
e
c
o
n
tro
l”
,
in
Pro
c
.
IEE
E
2
nd
In
t
.
Co
n
f.
o
n
Co
n
t.
,
In
str.
a
n
d
Au
t
o
.
,
2
0
1
1
,
p
p
.
5
5
2
-
5
5
7
.
[1
4
]
A
.
Iz
a
d
ian
,
P
.
Kh
a
y
y
e
r,
a
n
d
H.
Ya
n
g
,
“
A
d
a
p
ti
v
e
v
o
lt
a
g
e
trac
k
in
g
c
o
n
tro
l
o
f
z
e
ta
b
u
c
k
-
b
o
o
st
c
o
n
v
e
rters
”
,
in
Pro
c
.
IEE
E
E
n
e
rg
y
Co
n
v
.
Co
n
g
.
a
n
d
Exp
o
.
,
2
0
1
2
,
p
p
.
4
1
4
-
4
1
7
.
[1
5
]
H.
S
a
rk
a
w
i,
M
.
H.
Ja
li
,
T
.
A
.
Iz
z
u
d
d
i
n
,
a
n
d
M
.
Da
h
a
ri,
“
Dy
n
a
m
i
c
M
o
d
e
l
o
f
Zeta
Co
n
v
e
rter
w
it
h
F
u
l
l
-
sta
te
F
e
e
d
b
a
c
k
Co
n
tr
o
ll
e
r
Im
p
lem
e
n
tatio
n
”
,
I
n
t.
J
o
u
rn
a
l
o
f
Res
e
a
r
c
h
in
En
g
.
a
n
d
T
e
c
h
.
,
V
o
l
.
0
2
,
N
o
.
0
8
,
p
p
.
3
4
-
4
3
,
A
u
g
.
2
0
1
3
.
[1
6
]
H.
S
a
rk
a
w
i
a
n
d
Y.
O
h
ta,
“
Op
ti
m
a
l
sta
te
-
fe
e
d
b
a
c
k
a
n
d
P
ro
p
o
r
t
io
n
a
l
-
In
teg
ra
l
Co
n
tr
o
ll
e
r
P
e
rf
o
rm
a
n
c
e
Co
m
p
a
riso
n
f
o
r
Dc
-
d
c
Zeta
Co
n
v
e
rter Op
e
ra
ti
n
g
i
n
Co
n
ti
n
u
o
u
s C
o
n
d
u
c
ti
o
n
M
o
d
e
”
,
in
Pr
o
c
.
S
IC
E
An
n
u
a
l
C
o
n
f
.
,
2
0
1
6
,
p
p
.
4
4
8
-
4
5
1
.
[1
7
]
N.
Ka
e
w
p
ra
e
k
a
n
d
W
.
A
s
sa
w
in
c
h
a
ich
o
te,
“
H
∞
F
u
z
z
y
S
tate
-
f
e
e
d
b
a
c
k
Co
n
tro
l
P
lu
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tate
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ti
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tro
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th
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sis f
o
r
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to
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lt
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ic S
y
ste
m
s”
,
Asia
n
J
o
u
rn
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l
o
f
Co
n
tro
l
,
Vo
l.
1
8
,
No
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4
,
p
p
.
1
4
4
1
-
1
4
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0
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6
.
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8
]
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Ola
la,
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L
e
y
v
a
,
A
.
E.
A
ro
u
d
i,
I.
Qu
e
in
n
e
c
,
“
Ro
b
u
st
L
QR
Co
n
tro
l
f
o
r
P
W
M
Co
n
v
e
rt
e
rs:
A
n
L
M
I
A
p
p
ro
a
c
h
”
,
IEE
E
T
ra
n
s.
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n
d
.
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e
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tro
n
.
,
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l.
5
6
,
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o
.
7
,
p
p
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2
5
4
8
-
2
5
5
8
,
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u
ly
2
0
0
9
.
[1
9
]
C.
Ola
la,
I.
Qu
e
i
n
n
e
c
,
R.
L
e
y
v
a
,
A
.
E.
A
ro
u
d
i,
“
Op
ti
m
a
l
S
tate
-
f
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d
b
a
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k
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n
tr
o
l
o
f
Bil
in
e
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r
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-
d
c
Co
n
v
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rters
w
it
h
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u
a
ra
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tee
d
Re
g
io
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s o
f
S
tab
il
it
y
”
,
IEE
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T
r
a
n
s.
I
n
d
.
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e
c
tro
n
.
,
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l.
5
9
,
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o
.
1
0
,
p
p
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3
8
6
8
-
3
8
8
0
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No
v
.
2
0
1
2
.
[2
0
]
K.
Og
a
ta,
M
o
d
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Co
n
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En
g
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g
, 4
th
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it
io
n
,
P
re
n
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e
Ha
ll
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2
0
0
2
.
[2
1
]
B.
D.
O.
A
n
d
e
rso
n
a
n
d
J.
B.
M
o
o
re
,
Op
ti
ma
l
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n
tro
l:
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in
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r Qu
a
d
ra
ti
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M
e
th
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s
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re
n
ti
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e
Ha
ll
,
1
9
9
0
.
[2
2
]
E.
F
e
ro
n
,
V.
Ba
la
k
rish
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a
n
,
S
.
Bo
y
d
,
a
n
d
L
.
El
G
h
a
o
u
i,
“
Nu
m
e
rica
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m
e
th
o
d
s
f
o
r
H
2
re
late
d
p
ro
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lem
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in
Pr
o
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.
ACC
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9
2
,
p
p
.
2
9
2
1
–
2
9
2
2
.
[2
3
]
S
.
Bo
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d
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.
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G
h
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E.
F
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ro
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n
d
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.
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lak
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a
n
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n
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a
r
M
a
trix
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e
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ies
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n
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m
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lp
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A
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IA
M
,
1
9
9
4
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4
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A
.
El
A
ro
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d
i,
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A
larc
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d
rig
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z
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L
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y
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,
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.
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lar,
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.
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u
in
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n
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a
n
d
A
.
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o
v
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a
,
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se
d
in
d
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x
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re
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f
a
st
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sc
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le i
n
sta
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f
d
c
–
d
c
c
o
n
v
e
rters
in
CCM
a
n
d
DCM,
”
in
Pro
c
.
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E
In
d
.
T
e
c
h
n
o
.
Co
n
f.
,
2
0
0
6
,
p
p
.
1
9
4
9
–
1
9
5
3
.
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0
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p
p
.
2
4
2
3
–
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4
2
6
.
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6
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.
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a
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ro
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o
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tro
l.
Evaluation Warning : The document was created with Spire.PDF for Python.