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ee
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(
I
J
E
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Vo
l.
12
,
No
.
1
,
Feb
r
u
ar
y
20
22
,
p
p
.
1
~
11
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Gen
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m
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1.
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NT
RO
D
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p
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m
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ates t
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e
r
eq
u
ir
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d
f
lu
x
i
n
s
tead
o
f
th
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f
ield
w
i
n
d
in
g
s
[
1
]
,
[
2
]
.
T
h
e
p
o
w
er
o
f
t
h
ese
m
o
to
r
s
is
le
s
s
t
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m
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to
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s
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au
s
e
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f
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ated
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an
e
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t
m
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g
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et
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t
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an
th
e
f
lu
x
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ated
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h
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w
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d
in
g
s
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s
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t
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o
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s
m
all
DC
m
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to
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e
P
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m
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to
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h
ig
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s
p
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d
a
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d
lo
w
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r
q
u
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[
1
]
,
[
3
]
.
T
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e
m
an
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ap
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licatio
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s
f
o
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th
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P
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m
o
to
r
,
s
u
c
h
as
m
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v
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n
g
w
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n
d
o
w
s
in
ca
r
s
an
d
f
r
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t
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ea
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o
f
ca
r
s
.
I
t
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also
u
s
ed
in
c
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r
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's
to
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li
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f
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m
ix
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an
d
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er
s
[
4
]
,
[
5
]
an
d
its
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m
p
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tan
t
u
s
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i
n
co
m
p
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ter
n
u
m
er
ical
co
n
tr
o
l
(
C
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)
m
ac
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in
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s
as a
n
a
ctu
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r
,
elec
tr
ic
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icles
,
an
d
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o
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o
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[
6
]
,
[
7
]
.
T
h
e
m
ain
p
r
o
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lem
s
tate
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e
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t
in
th
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p
r
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p
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r
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r
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(
P
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ca
s
ca
d
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co
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tr
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to
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th
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m
o
s
t
ac
cu
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ate
r
es
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lts
f
o
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tr
ac
k
in
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tr
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to
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o
f
th
e
r
e
f
er
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ce
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it
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n
to
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ch
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s
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.
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o
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th
i
s
p
r
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lem
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co
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p
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i
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o
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t
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m
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clas
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o
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(
C
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g
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(
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,
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d
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ticle
s
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alg
o
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ith
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(
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ller
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s
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to
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t
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e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
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8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
12
,
No
.
1
,
Feb
r
u
ar
y
20
22
:
1
-
11
2
in
p
u
t
a
n
d
o
u
tp
u
t
o
f
th
i
s
s
y
s
te
m
.
T
h
e
ca
s
ca
d
e
P
-
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I
c
o
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tr
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ller
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s
ed
in
th
is
p
ap
er
co
n
s
is
t
s
o
f
th
r
ee
co
n
tr
o
ller
s
:
th
e
c
u
r
r
en
t
co
n
tr
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ller
as
a
n
i
n
n
er
lo
o
p
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p
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,
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h
e
p
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s
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co
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tr
o
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ter
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s
[
8
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.
P
,
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co
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tr
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tiv
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l
y
[
9
]
.
T
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p
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a
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s
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m
o
s
t
i
m
p
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tan
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f
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i
s
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tate
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s
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o
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[
1
0
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-
[
1
2
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.
T
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d
,
n
e
u
r
al
n
et
wo
r
k
,
an
d
f
u
zz
y
lo
g
ic
[
1
3
]
,
[
1
4
]
.
P
a
r
ticle
s
w
ar
m
o
p
tim
izatio
n
(
P
SO)
alg
o
r
it
h
m
[
1
5
]
,
[
1
6
]
a
n
d
g
en
etic
al
g
o
r
ith
m
[
1
7
]
.
T
o
co
m
p
ar
e
th
i
s
w
o
r
k
w
it
h
o
t
h
er
r
esear
ch
er
's
w
o
r
k
in
th
e
s
a
m
e
f
ield
,
t
h
e
f
o
llo
w
i
n
g
liter
at
u
r
e
r
ev
ie
w
w
a
s
m
ad
e:
I
n
2
0
1
4
,
Mu
s
taf
a
e
t
a
l
.
[1
8
]
p
r
esen
ted
a
b
r
u
s
h
les
s
DC
(
B
L
DC
)
m
o
to
r
s
p
ee
d
co
n
tr
o
l
s
y
s
te
m
u
s
i
n
g
GA
.
I
n
2
0
1
5
,
T
ah
a
et
a
l.
[
9
]
u
s
ed
th
r
ee
m
et
h
o
d
s
to
co
n
tr
o
l
t
h
e
ca
s
ca
d
e
co
n
tr
o
l
s
y
s
te
m
.
I
n
2
0
1
8
,
W
is
a
m
et
a
l
.
[
19
]
p
r
esen
ted
a
s
y
s
te
m
f
o
r
co
n
t
r
o
llin
g
P
MD
C
s
p
ee
d
u
s
i
n
g
GA
an
d
d
ir
ec
t
s
ea
r
ch
(
DS)
alg
o
r
ith
m
s
.
I
n
2
0
1
9
,
Fad
h
el
et
a
l.
[2
0
]
u
s
ed
a
f
r
ac
tio
n
al
P
I
D
c
o
n
tr
o
ller
to
c
o
n
tr
o
l
P
MD
C
s
p
ee
d
b
ased
o
n
P
SO.
I
n
2
0
2
1
,
A
h
m
ed
et
al
.
[2
1
]
p
r
esen
ted
a
s
y
s
te
m
to
co
n
tr
o
l th
e
p
o
s
itio
n
an
d
s
p
ee
d
o
f
a
s
er
v
o
m
o
to
r
.
T
h
is
p
ap
er
is
o
r
g
an
ized
as: T
h
e
s
ec
o
n
d
s
ec
tio
n
co
n
ta
in
s
th
e
m
ath
e
m
atica
l
m
o
d
el
o
f
t
h
e
P
MD
C
m
o
to
r
an
d
ex
p
lai
n
i
n
g
t
h
e
g
en
er
al
s
tr
u
ct
u
r
e
o
f
th
e
s
y
s
te
m
,
i
n
t
h
e
t
h
ir
d
s
ec
tio
n
,
t
h
e
t
h
r
ee
t
u
n
in
g
m
et
h
o
d
s
a
r
e
ex
p
lain
ed
w
it
h
t
h
e
o
b
j
ec
tiv
e
f
u
n
c
tio
n
(
I
T
A
E
)
.
T
h
e
f
o
u
r
th
s
ec
t
io
n
co
n
tai
n
s
th
e
r
esu
lts
a
n
d
co
m
p
ar
is
o
n
,
a
n
d
th
e
f
in
al
s
ec
tio
n
co
n
tain
s
th
e
c
o
n
clu
s
io
n
.
2.
M
AT
H
E
M
AT
I
CAL M
O
DE
L
AND
G
E
N
E
RA
L
S
T
RUC
T
UR
E
2
.
1
.
M
a
t
he
m
a
t
ica
l
m
o
del o
f
P
M
DC
m
o
t
o
r
Fig
u
r
e
1
s
h
o
w
s
t
h
e
eq
u
i
v
alen
t
cir
cu
it
o
f
a
P
MD
C
m
o
to
r
c
o
n
s
is
tin
g
o
f
a
n
ar
m
at
u
r
e
r
esi
s
tan
ce
(
R
a
)
an
d
in
d
u
cta
n
ce
(
L
a
)
co
n
n
ec
ted
in
s
er
ies.
T
h
e
b
ac
k
em
f
(
E
a
)
is
g
en
e
r
ated
w
h
e
n
th
e
f
l
u
x
li
n
es
g
e
n
e
r
ated
b
y
th
e
p
er
m
a
n
e
n
t
m
a
g
n
et
ar
e
c
u
tti
n
g
a
n
d
it
s
d
ir
ec
tio
n
o
p
p
o
s
ite
t
o
th
e
d
ir
ec
tio
n
o
f
t
h
e
ap
p
lied
v
o
lta
g
e.
W
h
ile
t
h
e
m
ec
h
a
n
ical
p
ar
t
c
o
n
s
i
s
ts
o
f
c
o
ef
f
icie
n
t
o
f
f
r
ictio
n
(
B
m
)
an
d
m
o
m
e
n
t
o
f
i
n
er
tia
(
J
m
)
.
I
n
ad
d
itio
n
to
o
th
er
p
ar
am
eter
s
ar
e
th
e
b
ac
k
e
m
f
co
n
s
ta
n
t
(
K
v
)
an
d
to
r
q
u
e
co
n
s
ta
n
t
(
K
t
)
.
A
ll
co
m
p
o
n
e
n
ts
o
r
p
ar
a
m
et
er
s
o
f
t
h
i
s
P
MD
C
m
o
to
r
an
d
th
eir
v
a
lu
e
s
ar
e
s
h
o
w
n
i
n
T
ab
le
1
dn
a
Fig
u
r
e
2
s
h
o
w
s
t
h
e
b
lo
ck
d
iag
r
a
m
o
f
P
MD
C
m
o
to
r
.
Fig
u
r
e
1
.
E
q
u
iv
ale
n
t c
ir
cu
it o
f
P
MD
C
m
o
to
r
[
2
2
]
T
ab
le
1
.
P
MD
C
p
ar
am
eter
s
[
9
]
M
o
t
o
r
p
a
r
a
me
t
e
r
s
V
a
l
u
e
T
o
r
q
u
e
c
o
n
st
a
n
t
K
t
=
2
.
3
5
Nm
/A
A
r
mat
u
r
e
i
n
d
u
c
t
a
n
c
e
L
a
=
2
.
6
1
*
1
0
-
10
H
A
r
mat
u
r
e
r
e
si
st
a
n
c
e
R
a
=
2
.
6
1
Ω
I
n
e
r
t
i
a
o
f
t
h
e
mo
t
o
r
Jm
=
0
.
0
6
8
k
g
.
m
2
F
r
i
c
t
i
o
n
c
o
n
st
a
n
t
Bm
=
0
.
0
0
8
N
m
s
/
ra
d
B
a
c
k
e
mf
c
o
n
st
a
n
t
Kv
=
2
.
3
5
Vs
/
r
a
d
N
o
mi
n
a
l
l
o
a
d
T
1
=
1
7
.
6
N
m
N
o
mi
n
a
l
v
o
l
t
a
g
e
V
a
=
2
3
0
v
Fig
u
r
e
2.
T
h
e
b
lo
ck
d
iag
r
am
o
f
P
MD
C
m
o
to
r
[
2
2
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
C
o
mp
a
r
is
o
n
o
f c
a
s
ca
d
e
P
-
P
I
c
o
n
tr
o
ller
tu
n
in
g
meth
o
d
s
fo
r
…
(
K
a
r
ee
m
Gh
a
z
i A
b
d
u
lh
u
s
s
ein
)
3
T
h
e
elec
tr
ical
an
d
th
e
m
ec
h
a
n
i
ca
l e
q
u
atio
n
s
co
r
r
esp
o
n
d
in
g
to
b
lo
ck
d
iag
r
a
m
f
r
o
m
Fi
g
u
r
e
2
ar
e
[
2
2
]
.
(
)
=
(
)
+
(
t
)
+
(
)
(
1
)
(
)
=
(
)
(
2
)
(
)
−
=
(
)
+
(
)
(
3
)
(
)
=
(
t
)
(
4
)
B
y
u
s
i
n
g
L
ap
lace
tr
a
n
s
f
o
r
m
ati
o
n
f
o
r
th
e
(
1
)
-
(
4
)
w
e
o
b
tain
;
(
)
=
(
)
+
(
)
+
(
)
(
5
)
(
)
=
(
)
(
6
)
(
)
−
=
(
)
+
(
)
(
7
)
(
)
=
(
s
)
(
8
)
T
h
e
o
v
er
all
tr
an
s
f
er
f
u
n
ctio
n
s
ar
e
d
ef
in
ed
f
o
r
s
p
ee
d
an
d
p
o
s
itio
n
co
n
tr
o
l o
f
P
MD
C
m
o
to
r
,
r
esp
ec
tiv
el
y
.
(
)
(
)
=
2
+
(
+
)
+
+
2
(
9
)
(
)
(
)
=
3
+
(
+
)
2
+
(
+
2
)
(
1
0
)
W
h
er
e
is
eq
u
al
to
[
2
3
]
an
d
R
a
=
ar
m
a
tu
r
e
r
esi
s
tan
ce
(
Ω
)
La
=
ar
m
a
y
u
r
e
i
n
d
u
c
tan
ce
(
H)
E
a
=
elec
tr
o
m
o
ti
v
e
f
o
r
ce
o
r
b
ac
k
e
m
f
(
v
)
θ(
s
)
=
ac
tu
al
p
o
s
itio
n
(
r
ad
)
Va
=
n
o
m
i
n
al
v
o
lta
g
e
(
v
)
J
m
=
m
o
m
e
n
t i
n
er
tia
(
k
g
.
m
2
)
T
L
=
n
o
m
i
n
al
lo
ad
to
r
q
u
e
(
N
m
)
K
t
=
to
r
q
u
e
co
n
s
tan
t (
N
m
/
A
)
K
v
=
b
ac
k
e
m
f
co
n
s
ta
n
t (
v
.
s
ec
/r
ad
)
B
m
=
f
r
ictio
n
co
ef
f
icie
n
t (
N
m
.
s
/r
a
d
)
ω
m
=
m
o
to
r
v
elo
cit
y
(
r
ad
/s
ec
)
2
.
2
.
G
ener
a
l st
ruct
ure
o
f
t
h
e
s
y
s
t
e
m
T
h
e
g
en
er
al
s
tr
u
ct
u
r
e
o
f
th
e
s
y
s
te
m
co
n
s
i
s
ts
o
f
a
ca
s
ca
d
e
P
-
P
I
co
n
tr
o
ller
as
s
h
o
w
n
i
n
Fi
g
u
r
e
3
.
T
h
i
s
co
n
tr
o
ller
co
n
s
is
t
s
o
f
th
r
ee
(
P
,
PI)
co
n
tr
o
ller
s
f
o
r
cu
r
r
en
t,
s
p
ee
d
,
an
d
p
o
s
itio
n
.
T
h
e
o
u
tp
u
t
o
f
t
h
e
p
o
s
itio
n
co
n
tr
o
ller
r
ep
r
esen
ts
th
e
r
ef
er
en
ce
s
p
ee
d
,
th
e
o
u
tp
u
t
o
f
th
e
s
p
ee
d
co
n
tr
o
ller
r
e
p
r
esen
ts
th
e
r
ef
er
en
ce
cu
r
r
en
t,
an
d
th
e
o
u
tp
u
t o
f
t
h
e
cu
r
r
en
t c
o
n
tr
o
ller
r
ep
r
esen
ts
th
e
co
n
tr
o
l v
o
ltag
e
(
V
C
)
.
Fig
u
r
e
3
.
Gen
er
al
s
tr
u
ct
u
r
e
o
f
ca
s
ca
d
e
P
I
D
co
n
tr
o
l sy
s
te
m
f
o
r
P
MD
C
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
12
,
No
.
1
,
Feb
r
u
ar
y
20
22
:
1
-
11
4
An
ad
v
an
ta
g
e
o
f
t
h
e
ca
s
ca
d
e
co
n
tr
o
l
s
y
s
te
m
,
i
n
ad
d
itio
n
to
th
e
o
t
h
er
ad
v
a
n
ta
g
es,
i
s
t
h
e
ab
ilit
y
to
s
et
li
m
it
s
i
n
o
r
d
er
to
p
r
o
tect
th
e
P
MD
C
m
o
to
r
an
d
t
h
e
p
o
w
er
el
ec
tr
o
n
ic
co
n
v
er
ter
.
I
n
t
h
is
p
ap
er
,
li
m
it
s
ar
e
p
lace
d
o
n
th
e
s
p
ee
d
r
ef
er
en
ce
b
y
a
n
a
m
o
u
n
t
n
o
t
e
x
ce
ed
in
g
th
e
m
o
to
r
'
s
r
ated
s
p
ee
d
.
A
s
w
ell
a
s
t
h
e
li
m
it,
p
lace
d
o
n
th
e
r
ef
er
e
n
ce
v
o
lta
g
e
ex
it
in
g
t
h
e
P
I
cu
r
r
en
t n
o
t e
x
ce
ed
i
n
g
t
h
e
m
o
to
r
'
s
ap
p
lied
v
o
lta
g
e
[
2
3
]
.
3.
T
UNI
NG
M
E
T
H
O
DS
3
.
1
.
Cla
s
s
ica
l
m
et
ho
d
(
CM
)
F
ig
u
r
e
4
r
ep
r
esen
ts
th
e
f
ir
s
t
c
o
n
tr
o
l
lo
o
p
o
r
th
e
in
n
er
co
n
tr
o
l
lo
o
p
.
Sin
ce
th
is
m
et
h
o
d
a
s
s
u
m
e
s
s
o
m
e
ass
u
m
p
tio
n
s
to
s
i
m
p
li
f
y
th
e
c
i
r
cu
it,
th
e
e
f
f
ec
t
o
f
t
h
e
to
r
q
u
e
l
o
ad
is
n
eg
lecte
d
,
a
n
d
th
e
e
f
f
ec
t
o
f
E
a
is
n
eg
lec
ted
b
ec
au
s
e
th
e
v
al
u
e
o
f
J
m
is
h
i
g
h
[
9
]
,
[
2
3
]
.
A
s
a
r
esu
lt,
t
h
e
s
i
m
p
li
f
ied
cu
r
r
en
t c
o
n
tr
o
l lo
o
p
as sh
o
w
n
in
F
ig
u
r
e
5
.
Fig
u
r
e
4
.
I
n
n
er
cu
r
r
en
t c
o
n
tr
o
l lo
o
p
Fig
u
r
e
5
.
Si
m
p
li
f
ied
in
n
er
cu
r
r
en
t c
o
n
tr
o
l lo
o
p
Fro
m
Fi
g
u
r
e
5
th
e
tr
an
s
f
er
f
u
n
ctio
n
o
f
t
h
e
c
u
r
r
en
t
co
n
tr
o
l
l
o
o
p
,
(s
)
,
an
d
it
ca
n
b
e
w
r
it
ten
lik
e
i
n
(
1
1
)
w
h
er
e,
is
t
h
e
in
te
g
r
al
g
ain
,
is
t
h
e
p
r
o
p
o
r
tio
n
al
g
ain
o
f
th
e
co
n
tr
o
ller
,
an
d
th
e
el
ec
tr
ical
ti
m
e
co
n
s
ta
n
t
,
is
ca
lcu
lated
u
s
in
g
(
1
2
)
.
(
s
)
=
(
1
+
⁄
)
∗
(
1
⁄
1
+
)
(
1
1
)
=
(
1
2
)
T
h
e
(
1
3
)
is
u
s
ed
to
ca
n
ce
l th
e
m
o
to
r
p
o
le,
w
h
ic
h
is
f
o
r
m
u
lat
ed
in
(
11
)
.
=
1
(
1
3
)
T
h
e
ca
n
ce
llatio
n
o
f
t
h
e
p
o
le
in
th
e
m
o
to
r
tr
an
s
f
er
f
u
n
ctio
n
ca
n
b
e
illu
s
tr
ated
as:
=
(
1
⁄
)
∗
(
1
⁄
1
+
)
=
(
1
+
)
∗
(
1
⁄
1
+
)
Fin
all
y
,
in
t
h
e
o
p
en
-
lo
o
p
tr
an
s
f
er
f
u
n
ctio
n
,
t
h
e
b
an
d
w
id
th
(
cr
o
s
s
o
v
er
)
f
r
eq
u
en
c
y
(
)
I
t
is
r
e
p
r
es
en
ted
b
y
(
1
4
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
C
o
mp
a
r
is
o
n
o
f c
a
s
ca
d
e
P
-
P
I
c
o
n
tr
o
ller
tu
n
in
g
meth
o
d
s
fo
r
…
(
K
a
r
ee
m
Gh
a
z
i A
b
d
u
lh
u
s
s
ein
)
5
ω
ci
=
(
1
4
)
A
l
s
o
,
th
e
cr
o
s
s
o
v
er
f
r
eq
u
en
c
y
o
f
th
e
c
u
r
r
en
t
o
p
en
-
lo
o
p
ca
n
b
e
ca
lcu
lated
f
r
o
m
t
h
e
f
o
llo
w
in
g
r
elatio
n
s
h
ip
=
2
an
d
its
v
al
u
e
ab
o
u
t
ten
ti
m
es
s
m
al
ler
th
an
t
h
e
s
w
i
tch
i
n
g
f
r
eq
u
e
n
c
y
f
o
r
DC
-
D
C
co
n
v
er
ter
[
9
]
.
So
,
th
e
p
ar
am
et
er
v
alu
es
o
f
t
h
e
P
I
cu
r
r
en
t
co
n
tr
o
ller
ca
n
b
e
f
o
u
n
d
f
r
o
m
(
1
3
)
,
(
1
4
).
T
o
f
in
d
th
e
s
p
ee
d
lo
o
p
p
ar
am
eter
s
it
is
ass
u
m
ed
th
a
t
th
e
clo
s
ed
cu
r
r
en
t
lo
o
p
is
id
ea
l
f
o
r
d
esig
n
p
u
r
p
o
s
es
an
d
is
r
ep
r
esen
ted
b
y
t
h
e
u
n
it
y
[
2
3
]
as sh
o
w
n
i
n
Fi
g
u
r
e
6
.
Fig
u
r
e
6
.
Ou
ter
s
p
ee
d
lo
o
p
Fro
m
Fi
g
u
r
e
6
,
th
e
tr
an
s
f
er
f
u
n
ctio
n
o
f
th
i
s
lo
o
p
(
s
)
,
ca
n
b
e
r
ep
r
esen
ted
in
(
1
5
)
.
(
s
)
=
(
1
+
⁄
)
∗
(
1
⁄
1
+
)
(
1
5
)
W
h
er
e
=
m
ec
h
a
n
ical
ti
m
e
co
n
s
ta
n
t =
(
1
6
)
J
u
s
t
li
k
e
th
e
i
n
n
er
cu
r
r
en
t
co
n
tr
o
l
lo
o
p
th
e
p
o
le
in
th
e
m
ec
h
an
ical
p
ar
t
o
f
th
e
m
o
to
r
w
ill
b
e
ca
n
ce
led
as
s
h
o
w
in
(
1
7
)
.
Her
e
,
is
th
e
i
n
teg
r
al
g
a
in
an
d
,
is
th
e
p
r
o
p
o
r
tio
n
al
g
ain
o
f
th
e
co
n
tr
o
ller
.
=
1
(
1
7
)
T
h
e
b
an
d
w
id
t
h
(
cr
o
s
s
o
v
er
)
f
r
e
q
u
en
c
y
o
f
th
e
s
p
ee
d
co
n
tr
o
l lo
o
p
,
ca
n
b
e
ch
o
s
e
n
to
b
e
te
n
t
i
m
es
lo
w
er
th
a
n
ω
ci
an
d
it c
an
b
e
r
ep
r
esen
ted
b
y
(
1
8
)
.
ω
cs =
.
(
1
8
)
T
h
u
s
,
an
d
ca
n
b
e
ca
lcu
lated
u
s
i
n
g
(
1
6
)
an
d
(
1
8
)
.
Fin
all
y
,
t
h
e
la
s
t
o
u
ter
lo
o
p
is
th
e
p
o
s
itio
n
co
n
tr
o
l
lo
o
p
it
ca
n
b
e
ill
u
s
tr
ated
i
n
Fi
g
u
r
e
7
.
T
o
f
in
d
t
h
e
k
_
p
P
p
ar
am
eter
o
f
t
h
e
p
o
s
itio
n
lo
o
p
it
is
as
s
u
m
ed
t
h
at
t
h
e
s
p
ee
d
lo
o
p
is
p
er
f
ec
t
an
d
is
r
ep
r
esen
ted
b
y
u
n
it
y
[
2
3
]
as
s
h
o
w
n
i
n
Fi
g
u
r
e
7
th
e
o
p
en
-
lo
o
p
tr
an
s
f
er
f
u
n
ctio
n
f
o
r
p
o
s
itio
n
co
n
tr
o
l
i
s
g
i
v
en
in
t
h
e
(
1
9
)
.
T
h
e
v
alu
e
o
f
th
e
p
o
s
itio
n
p
ar
am
e
ter
k
_
p
P
ca
n
b
e
ca
lcu
lated
f
r
o
m
(
2
0
)
w
h
er
e
th
e
b
an
d
w
id
t
h
f
r
eq
u
en
c
y
(
)
is
ch
o
s
e
n
to
b
e
ten
ti
m
es
s
m
a
ller
th
a
n
(
ω
cs).
Fig
u
r
e
7
.
Ou
ter
p
o
s
itio
n
lo
o
p
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
12
,
No
.
1
,
Feb
r
u
ar
y
20
22
:
1
-
11
6
(
s
)
=
(
1
9
)
ω
p
s
=
(
2
0
)
3
.
2
.
P
a
rt
icle
s
wa
r
m
o
pti
m
iz
a
t
io
n (
P
SO
)
P
ar
ticle
s
w
ar
m
al
g
o
r
ith
m
(
P
S
O
)
is
p
r
o
p
o
s
ed
b
y
Ke
n
n
ed
y
a
n
d
E
b
er
h
ar
t
an
d
it
w
as
m
o
d
if
i
ed
to
i
m
p
r
o
v
e
its
p
er
f
o
r
m
a
n
ce
b
y
ad
d
in
g
a
n
e
w
p
ar
a
m
e
ter
ca
lled
i
n
er
tia
w
e
ig
h
t
[
2
4
]
.
T
h
e
P
SO
alg
o
r
ith
m
b
ase
s
o
n
s
w
ar
m
in
telli
g
e
n
ce
tec
h
n
iq
u
e
s
f
o
r
th
e
o
b
s
er
v
atio
n
o
f
s
o
cial
b
e
h
av
io
r
o
f
m
o
v
i
n
g
o
r
g
a
n
i
s
m
s
s
u
c
h
a
s
a
g
at
h
er
in
g
o
f
f
i
s
h
o
r
b
ir
d
s
.
T
h
is
alg
o
r
it
h
m
is
r
elate
d
to
th
e
co
m
p
u
tatio
n
al
m
et
h
o
d
to
s
o
lv
e
th
e
p
r
o
b
lem
,
f
o
r
ex
a
m
p
le,
b
ir
d
f
lo
ck
s
ai
m
to
f
in
d
ea
tin
g
b
eh
a
v
io
r
s
an
d
u
s
e
r
ep
ea
ted
s
tep
s
to
r
ea
ch
th
e
b
est
s
o
lu
tio
n
s
.
T
h
is
m
e
an
s
t
h
at
th
e
ca
n
d
id
ate
s
o
lu
tio
n
s
ar
e
p
ar
ticles th
a
t
m
o
v
e
in
t
h
e
s
ea
r
c
h
s
p
ac
e
b
a
s
ed
o
n
a
s
p
ec
if
ic
f
o
r
m
u
la
ab
o
v
e
t
h
e
p
ar
ticle
p
o
s
itio
n
.
E
ac
h
p
ar
ticle'
s
m
o
v
e
m
en
t
i
s
a
f
f
ec
te
d
b
y
it
s
lo
ca
l
v
al
u
e,
a
n
d
it
s
o
b
j
ec
tiv
e
is
to
r
ea
ch
th
e
b
est
-
k
n
o
w
n
p
o
s
itio
n
s
i
n
th
e
s
ea
r
ch
s
p
ac
e
b
y
u
p
d
ati
n
g
b
ette
r
p
o
s
itio
n
s
f
o
u
n
d
b
y
o
th
er
p
ar
t
icles.
T
h
e
alg
o
r
ith
m
is
b
e
g
u
n
b
y
e
s
tab
lis
h
i
n
g
t
h
e
s
tar
ti
n
g
p
o
s
itio
n
a
n
d
s
p
ee
d
v
ec
to
r
s
.
A
t
ea
ch
iter
atio
n
,
th
e
b
est
v
al
u
e
i
s
d
eter
m
i
n
ed
b
y
e
v
alu
a
tin
g
p
o
s
itio
n
a
n
d
s
p
ee
d
v
ec
to
r
s
.
E
v
er
y
p
ar
ticle
h
a
s
v
a
r
iab
les
an
d
d
i
m
e
n
s
io
n
s
,
an
d
th
ese
v
ar
iab
les
ar
e
p
r
o
b
lem
s
t
h
at
n
ee
d
to
b
e
s
o
lv
ed
.
I
f
th
e
p
r
o
b
lem
co
n
s
is
t
s
o
f
f
i
v
e
d
if
f
er
en
t
v
ar
iab
les,
th
e
p
ar
ticles’
d
i
m
en
s
io
n
s
h
o
u
ld
b
e
ch
o
s
en
a
s
f
i
v
e.
E
ac
h
p
ar
ticle
’
s
b
est
v
al
u
e
is
ca
lled
a
lo
ca
l
b
est
v
al
u
e
an
d
r
ec
o
r
d
ed
in
to
th
e
P
b
est
m
atr
i
x
.
Af
ter
ea
ch
iter
atio
n
,
th
e
b
est
v
al
u
e
f
o
r
ea
ch
p
ar
ticle
is
u
p
d
ated
if
th
e
b
est
n
e
w
v
al
u
e
is
f
o
u
n
d
to
co
n
tr
o
l
ea
ch
cu
r
r
en
t
p
ar
ticle
an
d
th
e
p
r
ev
io
u
s
p
o
s
i
tio
n
s
.
B
esid
es,
th
e
p
o
s
itio
n
is
af
f
ir
m
ed
as
t
h
e
g
lo
b
al
b
est
af
ter
co
n
tr
o
lli
n
g
f
o
r
t
h
e
b
est
m
atr
i
x
v
a
lu
e
s
at
ea
c
h
ite
r
atio
n
w
h
ic
h
co
n
tin
u
es
u
n
til
i
t
r
ea
ch
es
t
h
e
s
p
ec
i
f
ied
n
u
m
b
er
,
as
th
e
la
s
t
u
p
d
ated
v
alu
e
f
o
r
th
e
b
est
p
o
s
itio
n
r
ep
r
esen
ts
t
h
e
o
p
ti
m
al
v
alu
e.
T
h
is
al
g
o
r
ith
m
d
ep
en
d
s
m
ai
n
l
y
o
n
f
i
n
d
i
n
g
t
h
e
p
o
s
itio
n
o
f
ea
ch
p
ar
ticle
w
i
th
t
h
e
b
est
lo
ca
l
v
al
u
e,
as
w
ell
a
s
f
i
n
d
in
g
t
h
e
b
est
g
e
n
er
al
s
w
ar
m
p
o
s
itio
n
i
n
ea
ch
iter
a
ti
o
n
.
T
h
e
p
o
s
itio
n
an
d
s
p
ee
d
a
r
e
u
p
d
ated
at
ea
ch
iter
atio
n
b
ased
o
n
(
2
1
)
an
d
(
2
2
)
[
2
0
]
,
[
2
5
]
.
,
(
+
1
)
=
.
,
(
)
+
1
1
[
,
(
)
−
,
(
)
]
+
2
2
[
,
(
)
−
,
(
)
]
(
2
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I
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2088
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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2
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8
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-
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I
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[
1
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.
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A
.
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[
9
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