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[
1
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th
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,
[
5
]
,
th
e
y
s
t
u
d
i
ed
a
tech
n
iq
u
e
to
ex
a
m
i
n
e
t
h
e
f
ea
t
u
r
es
o
f
t
h
e
elec
tr
o
m
a
g
n
et
ic
f
o
r
th
e
Ma
g
L
ev
w
h
ic
h
co
m
p
r
is
es
p
er
m
an
e
n
t
m
a
g
n
e
ts
(
P
Ms
)
an
d
h
i
g
h
te
m
p
er
at
u
r
e
s
u
p
e
r
co
n
d
u
cto
r
(
HT
S).
T
h
e
m
e
th
o
d
is
co
n
s
tr
u
cted
o
f
f
i
n
ite
ele
m
e
n
t
i
n
co
r
p
o
r
atin
g
w
it
h
H
in
f
i
n
it
y
f
o
r
m
u
latio
n
,
t
h
at
is
u
s
ef
u
l
f
o
r
ax
i
s
in
2
-
D
s
y
m
m
etr
ic
i
s
s
u
es
w
h
ic
h
co
m
p
r
i
s
e
t
h
e
m
ater
ial
o
f
h
i
g
h
te
m
p
er
atu
r
e
s
u
p
er
co
n
d
u
cto
r
.
T
h
e
f
o
r
ce
o
f
ax
ia
l
lev
itatio
n
f
o
r
th
e
m
o
d
el
i
s
ca
lcu
lated
p
r
o
p
er
ties
o
f
n
o
n
li
n
e
ar
f
o
r
HT
S
b
u
l
k
.
T
h
e
r
esu
lt
s
o
f
ex
p
er
i
m
en
t
o
f
th
e
s
y
s
te
m
ar
e
ac
q
u
ir
ed
an
d
co
n
tr
asted
w
it
h
r
esu
l
ts
o
f
s
i
m
u
lat
io
n
w
it
h
t
h
e
r
esu
lts
t
h
at
s
h
o
w
b
et
w
ee
n
s
i
m
u
lat
io
n
an
d
e
x
p
er
i
m
e
n
tal
a
r
e
m
a
tch
ed
w
ell.
Xu
,
et
al.
,
[
6
]
,
th
e
y
s
u
g
g
e
s
te
d
a
r
ea
l
-
ti
m
e
w
r
e
n
c
h
m
o
d
el
(
R
R
W
M)
w
it
h
FP
G
A
;
f
o
r
t
h
e
m
o
m
e
n
t
an
M
L
A
ab
le
o
f
r
o
tatio
n
a
n
d
t
r
an
s
latio
n
i
n
t
h
e
h
o
r
izo
n
tal
p
lan
e.
I
n
o
r
d
er
to
g
et
t
h
e
h
i
g
h
p
r
ec
is
io
n
w
it
h
p
er
f
ec
t
m
o
s
tl
y
;
t
h
e
d
is
tr
ib
u
tio
n
o
f
to
r
q
u
e
an
d
f
o
r
ce
is
w
o
r
k
ed
o
u
t
b
y
n
o
d
e
o
f
m
a
g
n
e
tic.
T
h
e
ca
lcu
latio
n
co
m
p
o
n
e
n
t
s
ar
e
ex
p
an
d
ed
o
n
(
FP
GA
)
b
y
u
tili
zin
g
t
h
e
p
ar
allel
ar
ch
itec
tu
r
e
p
r
o
ce
s
s
in
g
a
n
d
p
ip
elin
ed
ar
it
h
m
e
tic.
I
n
t
h
e
test
,
th
e
R
T
W
M
o
f
th
e
co
m
p
u
tati
o
n
al
ac
cu
r
ac
y
an
d
s
u
g
g
e
s
ted
ML
A
is
co
n
tr
asted
w
it
h
th
e
m
e
th
o
d
o
f
f
i
n
it
e
ele
m
e
n
t.
T
h
e
r
esu
l
ts
d
is
p
la
y
t
h
at
t
h
e
d
iv
er
g
en
ce
o
f
r
elati
v
e
is
n
o
t
m
o
r
e
th
a
n
2
%
s
elec
ti
n
g
th
e
r
es
u
lt
s
o
f
FEM
as a
p
o
in
t o
f
r
ef
er
en
ce
.
C
h
e
n
,
et
al.
,
[
7
]
,
th
e
y
s
u
g
g
e
s
ted
a
n
o
v
el
o
f
m
ag
n
etic
le
v
itatio
n
(
Ma
g
le
v
)
s
y
s
te
m
f
o
r
6
-
DOF
to
p
r
o
g
r
ess
t
h
e
d
esi
g
n
a
n
d
r
o
b
u
s
t.
T
h
e
co
n
ce
p
t
o
f
d
es
ig
n
e
n
d
ea
v
o
r
s
to
k
ee
p
ex
ce
l
len
t
p
er
f
o
r
m
a
n
ce
i
n
tr
ip
o
f
m
o
v
i
n
g
i
n
s
tead
th
a
n
p
o
s
it
io
n
to
p
o
s
itio
n
f
o
r
ac
cu
r
ac
y
.
T
h
e
y
atte
m
p
ted
to
e
x
p
an
d
th
e
s
y
s
te
m
w
it
h
r
a
n
g
e
o
f
lar
g
e
p
r
ed
icted
.
T
h
ey
s
tr
u
ct
u
r
ed
th
e
f
o
r
ce
m
o
d
el
in
r
elati
n
g
d
is
s
i
m
ilar
it
y
f
r
o
m
th
e
d
i
s
tan
ce
to
f
o
r
ce
s
o
f
m
ag
n
etic
le
v
itatio
n
an
d
o
b
v
iate
th
e
r
estrictio
n
o
f
m
a
g
le
v
to
b
e
r
e
p
u
ls
iv
e
le
v
itatio
n
.
T
h
ey
ad
o
p
te
d
an
d
b
u
ilt
th
e
s
y
s
te
m
a
n
d
m
atc
h
ed
th
e
e
x
p
er
im
e
n
tal
r
es
u
lt
s
.
Sp
ałek
[
8
]
,
h
e
p
r
o
p
o
s
ed
th
e
s
o
lu
tio
n
o
f
a
n
al
y
tical
m
e
th
o
d
f
o
r
m
ag
le
v
p
r
o
b
le
m
f
o
r
co
n
d
u
ctiv
e
b
all
s
an
d
m
a
g
n
et
icall
y
a
n
i
s
o
tr
o
p
ic.
T
h
e
m
a
g
n
e
tic
f
ie
ld
u
s
e
s
s
w
i
r
l
cu
r
r
en
ts
i
n
th
e
co
n
d
u
cti
v
e
b
alls
an
d
m
a
g
n
etic.
T
h
e
f
o
r
ce
o
f
m
ater
ial
b
y
in
h
o
m
o
g
e
n
eit
y
o
f
r
el
u
cti
v
it
y
a
n
d
t
h
e
f
o
r
ce
b
y
s
w
ir
l
cu
r
r
en
t
lead
in
to
le
v
itatio
n
b
all.
T
h
e
m
a
g
le
v
f
ie
ld
is
r
eg
u
late
d
b
y
m
a
n
n
er
s
o
f
m
et
h
o
d
o
f
v
ar
iab
le
s
ep
ar
atio
n
.
He
ca
lcu
la
ted
th
e
f
o
r
ce
s
o
f
m
ater
ial
ac
tin
g
o
n
t
h
e
b
all
a
n
d
L
o
r
en
tz
a
n
d
ca
lc
u
lated
t
h
e
p
o
w
er
lo
s
e
s
b
y
m
an
n
er
s
o
f
P
o
y
n
y
i
n
g
s
u
r
f
ac
e
in
te
g
r
al
an
d
J
o
u
le
v
o
lu
m
e
i
n
te
g
r
al
an
d
u
s
ed
Ma
x
w
ell
to
e
v
al
u
ate
th
e
to
tal
f
o
r
ce
.
Mo
r
an
d
i,
et
al.
,
[
9
]
,
th
ey
i
n
v
esti
g
a
ted
th
e
f
o
r
ce
o
f
lev
itati
o
n
is
b
et
w
ee
n
a
p
er
m
a
n
en
t
m
ag
n
et
an
d
y
ttri
u
m
b
ar
i
u
m
co
p
p
er
o
x
id
e
(
YB
C
O)
w
h
ic
h
it
is
s
i
n
g
le
-
g
r
in
.
T
h
e
f
o
r
ce
test
ed
in
co
n
d
iti
o
n
o
f
f
ield
co
o
lin
g
an
d
co
o
lin
g
w
i
th
ze
r
o
f
ie
ld
.
T
h
e
y
a
n
al
y
ze
d
th
e
p
o
w
er
d
i
s
s
ip
atio
n
an
d
p
ea
k
le
v
itati
o
n
f
o
r
ce
an
d
u
s
ed
a
n
u
m
er
ica
l
a
n
al
y
s
is
to
f
o
llo
w
u
p
t
h
e
elec
tr
o
d
y
n
a
m
ics
o
f
m
a
g
lev
s
y
s
te
m
.
T
h
e
y
o
b
tain
ed
a
p
er
tin
en
t
o
b
s
er
v
ed
f
o
r
cy
c
le
o
f
lev
itat
io
n
at
tem
p
er
at
u
r
e
w
it
h
h
i
g
h
d
eg
r
ee
an
d
a
g
o
o
d
p
r
o
d
u
ctio
n
f
o
r
t
h
e
m
ea
s
u
r
ed
d
ata.
T
h
ey
o
b
tain
ed
cr
itical
c
u
r
r
en
t
d
en
s
it
y
b
y
m
an
n
er
s
o
f
t
h
e
n
u
m
er
ical
m
o
d
el
to
f
ir
t
h
e
m
ea
s
u
r
ed
d
ata.
C
h
e
n
,
et
al.
,
[
1
0
]
,
th
e
y
s
t
u
d
ied
an
d
i
m
p
r
o
v
ed
t
h
e
s
ea
l
ca
p
a
cit
y
a
n
d
s
ea
l
in
g
l
if
e
f
o
r
m
a
g
l
ev
s
y
s
te
m
.
T
h
ey
u
s
ed
th
e
f
i
n
ite
ele
m
e
n
t
m
et
h
o
d
to
p
r
e
d
ict
th
e
m
ag
n
e
t
ic
f
ield
.
T
h
e
m
a
g
n
etic
f
lu
id
th
ick
n
es
s
o
n
th
e
r
ec
ip
r
o
ca
tin
g
f
ield
s
u
r
f
ac
e
an
d
th
e
m
ag
n
etic
f
l
u
id
f
lo
w
r
ate
ar
e
g
o
t
b
y
th
ea
tr
ical
m
et
h
o
d
;
th
e
ca
p
ac
it
y
o
f
s
tatic
s
ea
l
is
r
elate
d
to
th
e
v
o
lu
m
e
o
f
f
l
u
id
b
y
m
ea
s
u
r
e
m
en
ts
r
es
u
lt
s
.
T
h
e
ca
p
ac
ity
o
f
s
tatic
s
ea
l
g
o
t
b
y
ex
p
er
i
m
e
n
t
is
n
ea
r
l
y
eq
u
iv
a
le
n
t
to
th
e
s
i
m
u
lat
io
n
v
al
u
e
w
it
h
th
e
f
l
u
id
o
f
th
e
m
ag
n
etic.
T
h
e
y
g
o
t
a
g
o
o
d
r
esu
lt
b
et
w
ee
n
th
e
m
o
tio
n
o
f
s
h
a
f
t a
n
d
s
ea
li
n
g
li
f
e
a
n
d
it d
ec
r
ea
s
es
w
it
h
i
n
cr
ea
s
i
n
g
t
h
e
v
e
lo
cit
y
a
n
d
s
tr
o
k
e.
Qi
y
,
et
al.
,
[
1
1
]
,
th
e
y
p
r
o
p
o
s
ed
a
n
o
v
el
d
esi
g
n
f
o
r
co
n
tr
o
ller
t
ec
h
n
iq
u
e
w
h
ic
h
t
h
e
s
y
s
te
m
i
s
n
o
n
li
n
ea
r
.
T
h
ey
estab
li
s
h
ed
s
o
m
e
ad
eq
u
ate
co
n
d
itio
n
s
th
at
ar
e
ca
p
ab
le
f
o
r
s
tab
il
it
y
w
i
th
clo
s
ed
lo
o
p
b
y
m
eth
o
d
o
lo
g
y
o
f
class
ical
p
o
w
er
s
h
ap
i
n
g
.
B
y
L
y
ap
u
n
o
v
th
eo
r
y
,
t
h
e
y
d
id
th
e
co
n
tr
o
ller
w
it
h
n
o
n
li
n
e
ar
s
y
ate
m
a
n
d
th
e
as
y
m
p
to
te
o
f
r
eq
u
ir
ed
eq
u
i
li
b
r
ia
s
tab
ilit
y
.
T
h
e
y
d
e
s
ig
n
ed
a
p
er
f
o
r
m
a
n
ce
co
n
tr
o
ller
to
p
r
o
v
e
th
e
m
ag
le
v
s
y
s
te
m
m
et
h
o
d
o
lo
g
y
.
L
a
h
d
o
,
et
al.
,
[
1
2
]
,
th
e
y
p
r
o
p
o
s
ed
th
e
an
al
y
tical
ca
lc
u
latio
n
o
f
m
a
g
lev
s
y
s
te
m
is
alter
n
a
tiv
e
to
r
elate
d
to
ti
m
e
w
it
h
t
h
r
ee
d
i
m
e
n
s
io
n
s
b
y
f
i
n
ite
ele
m
e
n
t te
c
h
n
iq
u
e
d
u
e
to
lo
w
co
m
p
u
tatio
n
al
co
s
t a
n
d
h
ig
h
er
ac
cu
r
ac
y
.
T
h
ey
d
eter
m
i
n
ed
t
h
e
le
v
ita
tio
n
f
o
r
c
e
o
f
m
a
g
n
etic
g
u
id
an
ce
b
y
an
a
l
y
t
ical
m
et
h
o
d
th
a
t
h
as
a
s
i
g
n
if
ica
n
t
to
o
l
f
o
r
h
ig
h
p
r
ec
is
io
n
m
ag
lev
s
y
s
te
m
an
d
co
n
tr
o
lli
n
g
.
T
h
e
i
m
p
o
r
tan
t
r
esu
lt
is
th
e
p
o
s
it
io
n
d
ep
en
d
e
n
ce
o
f
th
e
f
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1
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1
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th
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1
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Si
m
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k
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p
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.
F
ir
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o
s
e
an
d
R
ao
[
2
1
]
,
th
e
y
i
n
tr
o
d
u
ce
d
a
p
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a
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iah
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R
ag
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a
v
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a
[
2
2
]
,
th
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,
[
2
3
]
,
th
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y
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n
v
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s
ti
g
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to
i
m
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C
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[
2
4
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th
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Hass
a
n
,
et
al.
,
[
2
5
]
,
th
e
y
d
esig
n
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a
co
n
tr
o
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w
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t
h
esti
m
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h
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R
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co
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A
l
k
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w
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n
d
Kh
a
m
as
[
2
6
]
,
th
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y
d
esi
g
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ed
a
m
d
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p
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A
l
k
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w
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[
2
7
]
,
h
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d
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n
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an
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d
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b
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Fi
g
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1
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w
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all
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tal
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all
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p
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T
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
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I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
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8
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2
-
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8
1
2
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4.
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F
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AG
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M
Mo
d
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d
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tr
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MP
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s
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n
u
s
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n
t
h
e
f
a
m
il
y
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co
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tr
o
l e
n
g
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n
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.
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h
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m
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ter
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o
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er
atio
n
o
f
p
r
o
ce
s
s
.
T
h
e
th
ir
d
s
tep
is
th
e
ca
p
ab
ilit
y
f
o
r
o
p
tim
izatio
n
to
ex
c
u
te
p
r
o
ce
s
s
o
n
-
li
n
e.
I
n
th
e
g
e
n
er
alit
y
o
f
ap
p
licatio
n
s
,
th
e
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
is
s
tr
u
ct
u
r
ed
to
f
o
llo
w
r
ej
ec
t
d
is
tu
r
b
an
ce
s
a
n
d
s
i
g
n
a
ls
o
f
co
n
s
ta
n
t
r
e
f
er
en
ce
t
h
at
h
a
v
e
m
o
s
t
l
y
lo
w
f
r
eq
u
en
c
y
co
n
t
en
ts
.
Nev
er
t
h
eles
s
,
th
ese
k
in
d
s
o
f
MP
C
ar
e
n
o
t
s
u
f
f
icie
n
t
to
s
u
p
p
l
y
t
h
e
p
er
f
o
r
m
a
n
ce
w
ith
clo
s
ed
-
l
o
o
p
r
eq
u
ir
ed
w
h
en
th
e
d
is
tu
r
b
a
n
ce
s
an
d
s
i
g
n
a
ls
o
f
s
et
-
p
o
i
n
t
h
a
v
e
p
er
io
d
ic
ele
m
en
ts
.
T
h
is
h
as
d
er
iv
ed
th
e
s
p
ea
k
er
s
to
estab
lis
h
a
n
e
w
cla
s
s
o
f
MP
C
th
at
u
s
e
t
h
e
d
esig
n
o
f
MP
C
f
r
a
m
e
w
o
r
k
w
h
ile
t
h
e
co
n
tr
o
llin
g
s
y
s
te
m
w
it
h
co
m
p
o
n
e
n
t
s
o
f
p
er
io
d
ic
f
o
r
ad
d
r
ess
in
g
,
t
h
at
n
a
m
ed
p
r
ed
ictiv
e
r
ep
etitiv
e
co
n
tr
o
ller
as sh
o
w
n
i
n
Fi
g
u
r
e
3
.
Fig
u
r
e
3
.
B
asic c
o
n
ce
p
t f
o
r
m
o
d
el
p
r
e
d
ictiv
e
co
n
tr
o
l
A
ll
t
h
e
al
g
o
r
ith
m
s
o
f
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
o
w
n
d
i
f
f
e
r
en
t
ch
o
ices
a
n
d
o
r
d
in
ar
y
p
ar
ts
ca
n
b
e
s
elec
ted
f
o
r
ea
ch
o
n
e
o
f
th
e
s
e
p
ar
ts
g
i
v
i
n
g
r
i
s
e
to
d
if
f
er
en
t
alg
o
r
ith
m
s
.
T
h
r
ee
ele
m
en
ts
f
o
r
MP
C
;
p
r
ed
ictio
n
m
o
d
el,
o
b
j
ec
tiv
e
f
u
n
ctio
n
a
n
d
co
n
tr
o
l
la
w
.
T
o
d
eter
m
in
e
th
e
p
r
ed
icted
o
u
tp
u
t
at
f
u
t
u
r
e
in
s
ta
n
t
s
b
y
u
s
i
n
g
th
e
p
r
o
ce
s
s
o
f
t
h
e
p
r
o
ce
s
s
th
at
is
ca
lcu
la
ted
b
y
t
h
e
n
ec
ess
i
t
y
ŷ
(
+
)
w
h
er
e
ŷ
is
a
p
-
d
i
m
en
s
io
n
al
v
ec
t
o
r
co
n
tain
in
g
t
h
e
s
y
s
te
m
p
r
ed
ictio
n
alo
n
g
th
e
h
o
r
izo
n
.
T
h
e
r
eq
u
ir
e
m
en
t
s
o
f
p
lan
t
o
p
er
atio
n
c
alcu
late
t
h
e
co
n
t
r
o
l
s
y
s
te
m
in
th
e
o
b
j
ec
tiv
e
f
u
n
ct
io
n
.
T
h
ese
cr
iter
ia
h
av
e
to
b
e
ca
lcu
lated
i
n
ter
m
s
o
f
m
at
h
e
m
a
tical
w
a
y
s
o
th
a
t
a
co
n
tr
o
l
l
a
w
ca
n
b
e
g
o
t
i
n
alg
o
r
ith
m
ic
p
atter
n
.
A
f
u
n
ctio
n
o
f
q
u
ad
r
atic
o
b
j
ec
tiv
e
is
:
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:
2
0
8
8
-
8708
Mo
d
el
p
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tr
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h
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in
f
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e
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ce
d
tr
an
s
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y
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cl
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h
e
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o
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lem
o
f
o
p
tim
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it
h
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in
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a
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q
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atic
o
b
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w
h
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Qu
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(
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−
(
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1
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(
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(
1
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5.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
Fo
r
test
i
n
g
th
e
r
esp
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n
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e
o
f
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ag
n
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ic
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itatio
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s
y
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te
m
in
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o
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ed
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p
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h
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an
d
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I
D
co
n
tr
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b
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g
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t
h
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d
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d
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ill
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m
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f
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d
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ettlin
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ti
m
e
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d
m
a
k
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t
h
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co
n
tr
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n
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m
f
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r
tab
le
f
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th
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te
m
as
s
h
o
w
n
i
n
F
ig
u
r
e
s
4
to
1
0
.
Fig
u
r
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4.
T
h
e
am
p
lit
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d
e
w
ith
Kp
=
1
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=
1
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Fig
u
r
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5.
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h
e
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p
lit
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d
e
w
ith
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,
Ki
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Fig
u
r
e
6.
T
h
e
am
p
lit
u
d
e
w
ith
Kp
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0
,
Ki
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1
Fig
u
r
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7.
T
h
e
am
p
lit
u
d
e
w
ith
Kp
=
1
,
Ki
=
1
0
,
=
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8708
I
n
t J
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&
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m
p
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n
g
,
Vo
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10
,
No
.
6
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Dec
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er
2
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2
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u
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u
r
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9.
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h
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am
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lit
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d
e
w
ith
Kp
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,
Ki
=
1
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,
=
0
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01
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u
r
e
10.
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h
e
a
m
p
litu
d
e
w
it
h
Kp
=
1
0
0
,
Ki
=
1
,
=
0
.
001
Fo
r
test
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n
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th
e
r
e
s
p
o
n
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e
t
h
e
m
ag
n
etic
lev
itatio
n
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y
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te
m
b
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el
p
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v
e
co
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tr
o
l
b
y
c
h
an
g
i
n
g
th
e
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al
u
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o
f
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g
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tin
g
m
atr
i
ce
s
an
d
an
d
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i
ll
s
ee
all
r
esp
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n
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es
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co
m
f
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r
tab
le
w
ith
th
is
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n
tr
o
ller
b
ec
au
s
e
t
h
e
p
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h
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d
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ap
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,
th
e
s
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te
e
r
r
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r
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r
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an
d
m
i
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i
m
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et
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g
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a
n
d
th
at
r
ef
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s
to
g
et
f
as
t
r
esp
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n
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e
.
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h
e
ch
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f
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e
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e
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t
i
m
e
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n
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tate
er
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r
.
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h
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b
est v
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f
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n
d
f
o
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th
e
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y
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te
m
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e
n
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h
a
v
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lar
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e
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e
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as s
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o
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n
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g
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s
11
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1
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.
Fig
u
r
e
1
1
.
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h
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a
m
p
litu
d
e
at
=
1
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=
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Fig
u
r
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1
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.
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h
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a
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S
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T
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e
(
s
e
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n
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A
m
p
l
i
t
u
d
e
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:
2
0
8
8
-
8708
Mo
d
el
p
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ictive
co
n
tr
o
l o
f
m
a
g
n
etic
levita
tio
n
s
ystem
(
La
ft
a
E
.
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ma
a
A
lku
r
a
w
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5811
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u
r
e
1
3
.
T
h
e
a
m
p
litu
d
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at
=
2
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=
10
6.
CO
NCLU
SI
O
N
T
h
e
w
o
r
k
ap
p
lied
i
n
t
h
is
p
ap
er
w
a
s
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g
n
ed
t
h
e
d
y
n
a
m
ic
m
ag
n
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itatio
n
o
f
n
o
n
l
in
ea
r
s
y
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te
m
th
at
w
a
s
in
v
es
tig
a
ted
in
ter
m
s
o
f
it
s
m
o
d
eli
n
g
,
s
i
m
u
la
tio
n
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d
lin
ea
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izatio
n
.
B
ec
au
s
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o
f
th
e
n
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n
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li
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ea
r
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d
u
n
s
tab
le
a
n
d
f
ea
t
u
r
o
f
m
a
g
n
etic
lev
i
tatio
n
s
y
s
te
m
s
,
i
n
t
h
is
p
ap
er
,
w
e
tr
ied
to
co
n
v
er
t
th
e
n
o
n
l
in
ea
r
to
th
e
li
n
ea
r
ize
m
o
d
el
b
y
a
n
al
y
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g
w
it
h
s
tate
-
s
p
ac
e
a
n
d
d
o
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g
a
s
i
m
u
latio
n
.
T
h
r
ee
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n
t
r
o
ller
s
ap
p
lied
to
th
e
s
y
s
te
m
to
ch
ec
k
w
h
a
t
it
is
th
e
b
est
co
n
tr
o
ller
.
T
h
e
f
ir
s
t
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d
s
ec
o
n
d
class
ic
co
n
tr
o
l
w
e
r
e
P
I
co
n
tr
o
ller
an
d
P
I
D
co
n
tr
o
ller
an
d
th
ese
co
n
tr
o
ller
s
w
er
e
n
o
t
s
at
is
f
ied
f
o
r
s
t
ab
ilit
y
an
d
s
tead
y
s
tate
er
r
o
r
.
T
h
e
th
ir
d
co
n
tr
o
ller
w
a
s
MP
C
to
p
r
ed
ict
th
e
f
u
t
u
r
e
r
esp
o
n
s
e
r
elate
d
to
r
ef
er
en
ce
i
n
p
u
t
a
n
d
th
is
co
n
tr
o
ller
w
as
s
ati
s
f
ied
f
o
r
s
tab
ilit
y
,
g
et
ze
r
o
s
tea
d
y
s
ta
te
er
r
o
r
an
d
f
ast
r
esp
o
n
s
e
w
it
h
m
i
n
i
m
u
m
s
e
ttli
n
g
ti
m
e.
F
u
r
t
h
er
,
a
n
e
w
r
esear
ch
u
s
e
s
lin
ea
r
q
u
ad
r
atic
f
o
r
m
to
co
n
tr
o
l
th
e
m
a
g
n
et
ic
lev
ita
ti
o
n
s
y
ate
m
to
en
s
u
r
e
t
h
e
s
tab
ilit
y
w
i
th
c
h
an
g
i
n
g
th
e
in
p
u
t.
RE
F
E
R
E
NC
E
S
[1
]
H
.
S
e
o
,
e
t
a
l.
,
“
A
lg
o
rit
h
m
o
f
L
in
e
a
r
In
d
u
c
ti
o
n
M
o
to
r
C
o
n
tro
l
f
o
r
L
o
w
No
r
m
a
l
F
o
rc
e
o
f
M
a
g
n
e
ti
c
L
e
v
it
a
ti
o
n
T
ra
in
P
r
o
p
u
lsio
n
S
y
ste
m
,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s o
n
M
a
g
n
e
ti
c
s
,
v
o
l.
5
4
,
n
o
.
1
1
,
p
p
.
1
-
4
,
2
0
1
8
.
[2
]
T
.
T
a
k
a
o
,
e
t
a
l.
,
“
I
m
p
ro
v
e
m
e
n
t
o
f
L
e
v
it
a
ti
o
n
P
ro
p
e
rti
e
s
o
w
in
g
t
o
Hig
h
M
a
g
n
e
ti
c
F
ield
in
a
M
a
g
n
e
ti
c
L
e
v
it
a
ti
o
n
S
y
st
e
m
w
it
h
M
a
g
n
e
ti
c
S
h
ield
i
n
g
Ef
fe
c
t
o
f
H
T
S
Bu
lk
,”
IEE
E
T
ra
n
sa
c
ti
o
n
o
n
Ap
p
li
e
d
S
u
p
e
rc
o
n
d
u
c
ti
v
it
y
,
v
o
l.
2
8
,
no.
4
,
p
p
.
1
-
5
,
2
0
1
8
.
[3
]
R
.
S
u
n
,
e
t
a
l.
,
“
Dy
n
a
m
i
c
Ch
a
ra
c
t
e
risti
c
s
o
f
th
e
M
a
n
n
e
d
Hy
b
rid
M
a
g
lev
V
e
h
icle
E
m
p
lo
y
in
g
P
e
rm
a
n
e
n
t
M
a
g
n
e
ti
c
L
e
v
it
a
ti
o
n
(
P
M
L
)
a
n
d
S
u
p
e
r
c
o
n
d
u
c
ti
n
g
M
a
g
n
e
ti
c
Lev
it
a
ti
o
n
(S
M
L
)
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
o
n
Ap
p
l
ied
S
u
p
e
rc
o
n
d
u
c
ti
v
it
y
,
v
o
l.
2
9
,
no.
3
,
p
p
.
1
-
5
,
2
0
1
9
.
[4
]
J
.
L
i
m
,
e
t
a
l.
,
“
A
S
tu
d
y
o
n
Op
ti
m
a
l
Op
e
ra
ti
n
g
P
o
i
n
t
o
f
L
in
e
a
r
I
n
d
u
c
t
io
n
M
o
t
o
r
Co
n
si
d
e
rin
g
No
r
m
a
l
F
o
rc
e
a
n
d
Eff
icie
n
c
y
in
M
AG
L
EV
V
e
h
icle
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
o
n
M
a
g
n
e
ti
c
s
,
v
o
l.
5
4
,
n
o
.
1
1
,
p
p
.
1
-
5
,
2
0
1
8
.
[5
]
W
.
Ch
e
n
,
e
t
a
l.
,
“
Lev
it
a
ti
o
n
F
o
rc
e
Co
m
p
u
tatio
n
o
f
H
T
S
/P
M
S
y
ste
m
Ba
s
e
d
o
n
H
-
F
o
rm
u
latio
n
,
”
IE
EE
T
ra
n
sa
c
ti
o
n
o
n
M
a
g
n
e
ti
c
s
,
v
o
l
.
5
4
,
n
o
.
1
1
,
p
p
.
1
-
5
,
2
0
1
8
.
[6
]
F
.
X
u
,
e
t
a
l.
,
“
F
P
GA
-
Ba
se
d
R
e
a
l
-
ti
m
e
W
r
e
n
c
h
M
o
d
e
l
o
f
Dire
c
t
Cu
rre
n
t
Driv
e
n
M
a
g
n
e
ti
c
L
e
v
it
a
t
io
n
A
c
tu
a
to
r
,”
IEE
E
T
ra
n
sa
c
ti
o
n
o
n
In
d
u
stri
a
l
E
lec
tro
n
ics
,
v
o
l.
6
5
,
n
o
.
1
2
,
p
p
.
9
6
3
5
-
9
6
4
5
,
2
0
1
8
.
[7
]
M
.
Y
.
Ch
e
n
,
e
t
a
l.
,
“
A
No
v
e
l
D
e
sig
n
a
n
d
Co
n
tr
o
l
t
o
Im
p
ro
v
e
P
o
siti
o
n
i
n
g
P
re
c
isi
o
n
a
n
d
Ro
b
u
st
n
e
ss
f
o
r
a
P
lan
a
r
M
a
g
lev
S
y
ste
m
,
”
IEE
E
T
ra
n
s
a
c
tı
o
n
s
o
n
I
n
d
u
stria
l
El
e
c
tro
n
ics
,
v
o
l
.
6
6
,
n
o
.
6
,
p
p
.
4
8
6
0
-
4
8
6
9
,
2
0
1
9
.
[8
]
D.
S
p
a
łek
,
“
L
e
v
it
a
ti
o
n
o
f
Co
n
d
u
c
ti
v
e
a
n
d
M
a
g
n
e
ti
c
a
ll
y
A
n
iso
tro
p
i
c
Ba
ll
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
o
n
M
a
g
n
e
ti
c
s
,
v
o
l.
5
5
,
no.
3
,
p
p
.
1
-
7
,
2
0
1
9
.
[9
]
A
.
M
o
ra
n
d
i,
e
t
a
l.
,
“
T
h
e
M
e
a
su
re
m
e
n
t
a
n
d
M
o
d
e
li
n
g
o
f
th
e
L
e
v
i
tatio
n
F
o
rc
e
b
e
tw
e
e
n
S
in
g
le
-
G
ra
i
n
YBCO
Bu
lk
S
u
p
e
rc
o
n
d
u
c
to
rs
a
n
d
P
e
rm
a
n
e
n
t
M
a
g
n
e
ts
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Ap
p
li
e
d
S
u
p
e
rc
o
n
d
u
c
ti
v
it
y
,
v
o
l
.
2
8
,
n
o
.
5
,
p
p
.
1
-
1
0
,
A
u
g
.
2
0
1
8
.
[1
0
]
Y
.
Ch
e
n
,
e
t
a
l.
,
“
Nu
m
e
ric
a
l
A
n
a
l
y
sis
a
n
d
Ex
p
e
ri
m
e
n
tal
S
tu
d
y
o
n
M
a
g
n
e
ti
c
F
lu
i
d
Re
c
ip
ro
c
a
ti
n
g
S
e
a
ls,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
M
a
g
n
e
ti
c
,
v
o
l.
5
5
,
n
o
.
1
,
p
p
.
1
-
6
,
Ja
n
.
2
0
1
9
.
[1
1
]
L
.
Qi
,
e
t
a
l.
,
“
A
n
o
v
e
l
n
o
n
li
n
e
a
r
c
o
n
tr
o
l
tec
h
n
iq
u
e
w
it
h
it
s
a
p
p
li
c
a
ti
o
n
t
o
m
a
g
n
e
ti
c
lev
it
a
ted
s
y
ste
m
s
,
”
IEE
E
Acc
e
ss
,
v
o
l.
6
,
p
p
.
7
8
6
5
9
-
7
8
6
6
5
,
2
0
1
8
.
[1
2
]
M
.
L
a
h
d
o
,
e
t
a
l.
,
“
Re
p
u
lsiv
e
M
a
g
n
e
ti
c
L
e
v
it
a
ti
o
n
F
o
rc
e
Ca
lcu
latio
n
f
o
r
a
Hig
h
P
re
c
isio
n
6
-
Do
F
M
a
g
n
e
ti
c
L
e
v
it
a
ti
o
n
P
o
siti
o
n
i
n
g
S
y
ste
m
,
”
I
EE
E
T
ra
n
sa
c
ti
o
n
s
o
n
M
a
g
n
e
ti
c
s
,
v
o
l.
5
3
,
no.
3,
p
p
.
1
-
6,
2
0
1
7
.
[1
3
]
L
.
E.
V
e
n
g
h
i
,
e
t
a
l.
,
“
I
m
p
le
m
e
n
tatio
n
a
n
d
Co
n
tro
l
o
f
a
M
a
g
n
e
ti
c
Lev
it
a
ti
o
n
S
y
ste
m
,
”
IEE
E
L
a
ti
n
Ame
ric
a
T
ra
n
sa
c
ti
o
n
s
,
v
o
l.
1
4
,
n
o
.
6
,
p
p
.
2
6
5
1
-
2
6
5
6
,
Ju
n
.
2
0
1
6
.
[1
4
]
S
.
S
iv
rio
g
lu
,
e
t
a
l.
,
“
M
u
l
ti
su
rf
a
c
e
H
T
S
-
P
M
lev
it
a
ti
o
n
f
o
r
a
f
l
y
w
h
e
e
l
s
y
ste
m
,
”
IEE
E
T
ra
n
sa
c
t
io
n
o
n
Ap
p
li
e
d
S
u
p
e
rc
o
n
d
u
c
ti
v
it
y
,
v
o
l.
2
6
,
n
o
.
8
,
p
p
.
1
-
6
,
2
0
1
6
.
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