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tio
n
a
l
co
n
tr
o
l
s
u
c
h
a
s
b
ac
k
s
tep
p
in
g
al
g
o
r
ith
m
co
m
b
i
n
ed
w
it
h
f
u
zz
y
al
g
o
r
ith
m
b
y
B
asri
et
al
[
5
]
f
o
r
r
o
ll,
p
itch
,
y
a
w
,
an
d
alti
tu
d
e
co
n
tr
o
l
o
f
q
u
ad
r
o
to
r
.
B
ac
k
s
teep
in
g
co
n
t
r
o
l
is
o
p
ti
m
ized
b
y
ch
an
g
i
n
g
t
h
e
p
ar
a
m
eter
v
al
u
e
s
i
n
t
h
e
al
g
o
r
ith
m
.
T
h
e
p
r
o
ce
s
s
o
f
c
h
an
g
i
n
g
th
e
p
ar
a
m
ete
r
s
o
f
b
ac
k
s
tep
p
in
g
tak
es
a
co
n
s
id
er
ab
le
ti
m
e,
s
o
t
h
at
to
ac
ce
ler
ate
t
h
e
p
r
o
ce
s
s
r
eq
u
ir
es
ad
ap
tiv
e
ar
ti
f
icial
in
te
llig
e
n
ce
al
g
o
r
ith
m
s
s
u
c
h
as
f
u
zz
y
lo
g
ic.
T
h
e
o
th
er
m
o
d
er
n
co
n
tr
o
l
alg
o
r
ith
m
s
s
u
c
h
as
s
lid
d
in
g
m
o
d
e
alg
o
r
ith
m
co
m
b
i
n
ed
w
i
t
h
f
u
zz
y
al
g
o
r
ith
m
b
y
B
ar
g
h
a
n
d
an
&
B
ad
a
m
ch
izad
e
h
[
6
]
to
co
n
tr
o
l
th
e
q
u
ad
r
o
to
r
attitu
d
e.
T
h
e
f
u
zz
y
al
g
o
r
ith
m
is
u
s
ed
to
ch
a
n
g
e
t
h
e
p
ar
a
m
eter
v
alu
e
s
co
n
tai
n
ed
in
s
lid
d
in
g
m
o
d
e
co
n
tr
o
l,
s
o
th
at
t
h
e
co
n
tr
o
l
is
m
o
r
e
op
tim
a
l.
Fu
r
t
h
er
m
o
r
e,
ad
ap
tiv
e
ar
ti
f
ici
al
in
tel
lig
e
n
ce
co
n
tr
o
l
h
a
s
b
e
en
ap
p
lied
to
q
u
ad
r
o
to
r
as
p
r
ac
ticed
b
y
Z
a
n
g
e
n
e
h
p
o
u
r
et
al
[
7
]
ap
p
l
y
in
g
f
u
zz
y
lo
g
ic
alg
o
r
it
h
m
f
o
r
co
n
tr
o
llin
g
t
h
e
s
p
ee
d
o
f
th
e
m
o
to
r
o
n
t
h
e
q
u
ad
r
o
to
r
.
Fu
zz
y
al
g
o
r
ith
m
h
a
s
b
ee
n
ap
p
lied
to
th
e
P
I
C
m
icr
o
co
n
tr
o
ller
w
it
h
in
p
u
ts
o
f
an
g
l
e
an
d
m
o
to
r
s
p
ee
d
an
d
o
u
tp
u
t
o
f
m
o
to
r
p
u
ls
e
w
it
h
t
h
e
b
asic
r
u
les
o
f
5
x
5
.
T
h
e
r
esu
lt
o
f
t
h
e
e
x
p
er
i
m
e
n
t
s
h
o
w
e
d
th
at
t
h
e
f
u
zz
y
ca
n
b
e
u
s
ed
to
co
n
tr
o
l
a
m
o
to
r
o
n
q
u
ad
r
o
to
r
.
T
h
e
o
th
er
r
esear
ch
er
s
n
a
m
ed
Sa
n
to
s
et
a
l
[
8
]
h
av
e
ap
p
lied
f
u
zz
y
lo
g
ic
co
n
tr
o
l
w
it
h
m
a
m
d
a
n
i
m
et
h
o
d
to
co
n
tr
o
l
t
h
e
x
,
y
,
a
n
d
z
p
o
s
itio
n
s
i
n
q
u
ad
r
o
to
r
.
T
h
is
al
g
o
r
ith
m
is
u
s
ed
an
d
m
o
d
i
f
ied
f
o
r
m
e
m
b
er
s
h
i
p
o
u
tp
u
t
m
e
m
b
er
s
w
it
h
5
m
e
m
b
er
s
to
co
n
tr
o
l
t
h
e
p
o
s
itio
n
s
o
f
x
,
y
,
an
d
z
in
q
u
ad
r
o
to
r
in
an
u
n
d
is
t
u
r
b
an
c
e
d
en
v
ir
o
n
m
e
n
t.
I
n
t
h
e
co
n
tr
o
l
s
y
s
te
m
ca
r
r
ied
o
u
t,
q
u
ad
r
o
to
r
m
o
d
ellin
g
i
n
d
y
n
a
m
ic
a
n
d
k
i
n
e
m
atic
h
as
n
o
t
b
ee
n
co
n
d
u
cted
.
T
h
e
q
u
ad
r
o
to
r
is
m
o
d
eled
b
y
u
s
in
g
a
g
g
r
e
g
atio
n
b
lo
ck
t
h
at
is
a
co
n
n
ec
ted
b
lo
ck
b
et
w
ee
n
t
h
e
co
n
tr
o
ller
an
d
th
e
d
y
n
a
m
ic
s
y
s
te
m
f
u
n
ctio
n
ed
to
i
m
p
le
m
en
t
th
e
co
n
n
ec
tio
n
o
f
th
e
co
n
tr
o
l a
ctio
n
o
f
t
h
e
f
o
u
r
c
o
n
tr
o
ller
s
.
I
n
ad
d
itio
n
,
Var
g
a
&
B
o
g
d
an
[
9
]
h
av
e
ap
p
lied
f
u
zz
y
-
L
y
ap
u
n
o
v
to
co
n
tr
o
l t
h
e
p
o
s
itio
n
s
o
f
x
,
y
,
a
n
d
z
in
q
u
ad
r
o
to
r
.
T
h
er
e
ar
e
s
ix
f
u
z
z
y
co
n
tr
o
ls
u
s
ed
to
co
n
tr
o
l
th
e
q
u
ad
r
o
to
r
n
am
e
l
y
x
-
a
x
i
s
,
y
-
a
x
is
,
z
-
ax
is
a
n
d
y
a
w
f
u
zz
y
co
n
tr
o
ls
.
T
h
e
t
w
o
i
n
p
u
t
s
n
a
m
el
y
a
ltit
u
d
e
er
r
o
r
an
d
al
titu
d
e
ch
a
n
g
e
r
ate
ar
e
u
s
ed
f
o
r
z
-
ax
i
s
co
n
tr
o
l.
A
n
o
n
li
n
ea
r
q
u
ad
r
o
to
r
m
o
d
eli
n
g
i
s
n
ee
d
ed
to
d
eter
m
i
n
e
t
h
e
s
tab
ilit
y
o
f
t
h
e
q
u
ad
r
o
to
r
b
y
u
s
i
n
g
L
y
ap
u
n
o
v
m
et
h
o
d
.
T
h
e
s
i
m
u
la
tio
n
r
es
u
lt
s
h
o
w
s
t
h
at
t
h
er
e
ar
e
s
t
ill
lo
n
g
o
v
er
s
h
o
o
t
an
d
r
i
s
e
ti
m
e.
T
h
e
o
th
er
r
esear
ch
er
s
s
u
c
h
as
Fa
k
u
r
ia
n
et
al.
[
1
0
]
h
av
e
m
o
d
i
f
ied
th
e
f
u
zz
y
in
p
u
t
s
et
s
w
it
h
tr
ia
n
g
u
lar
a
n
d
g
a
u
s
s
ia
n
t
y
p
e
’
s
f
u
zz
y
f
icatio
n
.
B
y
u
s
i
n
g
t
h
e
al
g
o
r
ith
m
,
q
u
ad
r
o
to
r
ca
n
h
o
v
er
at
a
p
re
-
d
eter
m
i
n
ed
h
e
ig
h
t
i
n
th
e
u
n
d
i
s
tu
r
b
an
ce
s
en
v
ir
o
n
m
e
n
t.
B
ased
o
n
th
e
p
r
ev
io
u
s
r
esear
ch
es,
o
n
th
e
altit
u
d
e
an
d
attit
u
d
e
u
s
in
g
ar
tif
ic
ial
in
tel
lig
e
n
ce
co
n
tr
o
l,
it
ca
n
b
e
s
ee
n
t
h
at
q
u
ad
r
o
to
r
ca
n
h
o
v
er
at
th
e
p
r
e
-
d
eter
m
i
n
ed
h
ei
g
h
t,
b
u
t
th
er
e
ar
e
s
till
o
v
er
s
h
o
o
t,
o
s
cillatio
n
an
d
a
lo
n
g
r
aise
t
i
m
e.
Qu
ad
r
o
to
r
ca
n
n
o
t
co
p
e
w
i
th
d
i
s
r
u
p
t
io
n
s
o
f
v
er
tical
w
i
n
d
b
ec
au
s
e
it
is
m
er
el
y
tes
ted
in
d
o
o
r
.
T
o
o
v
er
co
m
e
t
h
ese
p
r
o
b
lem
s
,
a
s
tr
ateg
y
o
r
m
et
h
o
d
o
f
in
telli
g
e
n
t
co
n
tr
o
l
alg
o
r
i
th
m
s
ar
e
n
ee
d
ed
to
o
b
tain
th
e
s
y
s
te
m
w
it
h
m
i
n
i
m
u
m
o
v
er
s
h
o
o
t
an
d
s
ett
lin
g
t
i
m
e
a
n
d
to
g
e
n
er
ate
o
u
tp
u
t
r
e
s
p
o
n
s
e
w
it
h
a
g
o
o
d
p
er
f
o
r
m
a
n
ce
a
n
d
s
tab
le
in
a
tr
an
s
ie
n
t sta
te.
2.
Q
UAD
RO
T
O
R
2
.
1
.
Q
ua
dro
t
o
r
M
o
delin
g
Qu
ad
r
o
to
r
h
as
6
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
,
n
a
m
el
y
t
h
r
ee
tr
a
n
s
latio
n
al
m
o
t
io
n
s
a
n
d
t
h
r
ee
r
o
tatio
n
al
m
o
tio
n
s
.
T
h
e
d
y
n
a
m
ic
m
o
tio
n
m
o
d
el
o
f
th
e
q
u
ad
r
o
to
r
is
r
ep
r
esen
ted
i
n
f
o
r
ce
an
d
to
r
q
u
e
g
en
er
ated
f
r
o
m
th
e
r
o
to
r
s
.
T
h
e
co
n
f
ig
u
r
atio
n
o
f
th
e
q
u
ad
r
o
to
r
b
ased
o
n
C
o
r
k
e’
s
m
o
d
el
s
[
11
]
is
s
h
o
w
n
i
n
Fi
g
u
r
e
1
w
ith
t
h
e
z
-
ax
i
s
d
ir
ec
tio
n
p
o
in
t
d
o
w
n
r
es
u
lts
i
n
a
n
eg
a
tiv
e
v
al
u
e.
T
h
e
p
o
s
itio
n
o
f
th
e
q
u
ad
r
o
to
r
f
o
r
|
|
ar
e
s
y
m
b
o
ls
a
s
x
-
a
x
i
s
,
y
-
ax
i
s
an
d
z
-
a
x
i
s
,
f
o
r
|
|
ar
e
s
y
m
b
o
ls
as
r
o
ll
an
g
le,
p
it
ch
,
y
a
w
,
f
o
r
|
|
ar
e
s
y
m
b
o
ls
a
s
s
p
ee
d
ca
u
s
ed
b
y
th
e
x
-
a
x
is
,
y
-
ax
is
,
z
-
a
x
is
,
a
n
d
f
o
r
|
|
ar
e
s
y
m
b
o
ls
as
a
n
g
u
lar
s
p
ee
d
ca
u
s
ed
b
y
th
e
x
-
ax
i
s
,
y
-
a
x
i
s
,
z
-
a
x
is
.
Fig
u
r
e
1
s
h
o
w
s
t
h
at
th
e
g
lo
b
al
f
r
a
m
e
w
o
r
k
f
g
w
it
h
co
o
r
d
in
ates
(
x
g
,
y
g
,
z
g
)
i
s
u
s
ed
a
s
a
q
u
ad
r
o
to
r
r
ef
er
en
ce
f
r
a
m
e
w
o
r
k
u
n
m
o
v
e
d
f
r
o
m
th
e
s
y
s
te
m
.
T
h
e
q
u
ad
r
o
to
r
f
r
a
m
e
w
o
r
k
f
q
w
it
h
co
o
r
d
i
n
ates
(
x
q
,
y
q
,
z
q
)
h
a
s
4
r
o
to
r
at
th
e
e
n
d
o
f
h
i
s
cr
o
s
s
-
ar
m
,
ea
c
h
r
o
to
r
co
n
s
i
s
ts
o
f
t
w
o
p
air
s
o
f
r
o
to
r
h
a
v
i
n
g
a
d
ir
ec
tio
n
al
r
o
tati
n
g
m
o
tio
n
.
R
o
to
r
s
1
an
d
3
r
o
tate
clo
ck
w
is
e,
w
h
er
ea
s
r
o
to
r
s
2
a
n
d
4
r
o
tate
co
u
n
ter
-
clo
c
k
w
is
e
r
esp
ec
tiv
el
y
.
E
ac
h
p
r
o
p
eller
p
r
o
d
u
ce
s
f
o
r
ce
;
all
h
av
e
th
e
s
a
m
e
d
ir
ec
tio
n
a
n
d
th
e
to
tal
f
o
r
ce
in
q
u
ad
r
o
to
r
(
ex
clu
d
i
n
g
g
r
av
i
t
y
)
as
f
o
llo
w
s
.
T
h
is
f
o
r
ce
p
r
o
d
u
ce
s
a
m
o
m
e
n
t
ar
o
u
n
d
t
h
e
ax
i
s
o
f
t
h
e
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I
SS
N
:
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0
8
8
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8
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IJ
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I
SS
N
:
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0
8
8
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8
694
IJ
PEDS
Vo
l.
8
,
No
.
1
,
Ma
r
ch
2
0
1
7
:
4
9
2
–
504
498
s
u
b
s
y
s
te
m
ar
e
r
o
ll,
p
itc
h
an
d
y
a
w
u
s
ed
f
o
r
s
u
b
s
y
s
te
m
tr
a
n
s
lat
io
n
al.
T
h
u
s
,
th
e
clo
s
ed
-
l
o
o
p
co
n
tr
o
l
ca
n
b
e
d
esig
n
ed
f
o
r
th
e
attit
u
d
e
an
d
a
ltit
u
d
e
.
Fig
u
r
e
3
.
B
lo
ck
Diag
r
a
m
o
f
(
A
)
altit
u
d
e
an
d
(
B
)
attitu
d
e
co
n
tr
o
l
2
.
3
.
Alt
it
ud
e
Co
ntr
o
l
A
lt
itu
d
e
co
n
tr
o
l
is
r
eq
u
ir
ed
to
en
s
u
r
e
t
h
at
t
h
e
q
u
ad
r
o
to
r
is
a
t
a
s
ec
u
r
e
a
ltit
u
d
e
[
1
5
]
-
[
1
8
]
.
S
o
th
at
it
i
s
also
r
esp
o
n
s
ib
le
f
o
r
r
esto
r
in
g
th
e
q
u
ad
r
o
to
r
to
a
s
ec
u
r
e
s
t
ate
at
a
ce
r
tain
altit
u
d
e
if
i
t
p
er
f
o
r
m
s
i
m
p
a
ir
ed
p
o
s
itio
n
d
u
e
to
air
t
u
r
b
u
len
ce
.
T
h
e
altitu
d
e
co
n
tr
o
l
in
p
u
t
o
f
t
h
e
q
u
ad
r
o
to
r
s
h
o
w
n
i
n
f
i
g
u
r
e
2
is
t
h
r
u
s
t
w
h
ic
h
is
th
e
m
u
lt
ip
licatio
n
o
f
r
elativ
e
t
h
r
u
s
t c
o
n
s
ta
n
t to
air
d
en
s
it
y
w
it
h
t
h
e
s
u
m
o
f
f
o
u
r
m
o
to
r
s
as
w
r
itte
n
in
eq
u
atio
n
6
.
Sev
er
al
al
g
o
r
it
h
m
s
h
a
v
e
b
ee
n
s
tu
d
ied
an
d
ap
p
l
ied
to
q
u
ad
r
o
to
r
altitu
d
e
b
y
p
r
ev
io
u
s
r
esear
ch
er
s
,
f
o
r
ex
a
m
p
le,
th
e
P
I
D
alg
o
r
ith
m
i
n
v
esti
g
ated
b
y
L
ee
et
al
.
[
19
]
,
th
e
s
lid
d
in
g
m
o
d
e
alg
o
r
ith
m
s
t
u
d
ied
b
y
Go
n
za
lez
et
a
l.
[
20
]
,
th
e
m
o
d
el
p
r
ed
ictin
g
co
n
tr
o
l
(
MP
C
)
a
lg
o
r
ith
m
in
v
est
ig
ated
b
y
Alex
is
et
a
l.
[
21
]
.
Fro
m
th
e
p
r
ev
io
u
s
s
t
u
d
ies,
th
e
r
esea
r
ch
er
s
h
av
e
u
s
ed
t
w
o
i
n
p
u
ts
to
d
esig
n
th
e
co
n
tr
o
l b
lo
ck
f
o
r
a
ltit
u
d
e
in
q
u
ad
r
o
to
r
as in
Fi
g
u
r
e
3
(
A
)
.
In
Fi
g
u
r
e
3
(
A
)
,
it
ap
p
ea
r
s
th
a
t
to
co
n
tr
o
l
th
e
alt
itu
d
e
t
w
o
i
n
p
u
ts
n
a
m
el
y
er
r
o
r
an
d
er
r
o
r
ch
an
g
e
r
ate
ar
e
r
eq
u
ir
ed
.
E
r
r
o
r
v
alu
e
of
(
)
o
b
tain
ed
f
r
o
m
th
e
d
i
f
f
er
en
ce
b
et
w
ee
n
th
e
s
et
p
o
in
t
w
it
h
t
h
e
ac
tu
al
h
e
ig
h
t
(
)
,
ca
n
b
e
ex
p
r
ess
ed
as
in
t
h
e
f
o
ll
o
w
i
n
g
eq
u
atio
n
:
(
31
)
W
h
er
e
is
th
e
h
ei
g
h
t
v
al
u
e
o
f
th
e
q
u
ad
r
o
to
r
.
T
h
e
h
eig
h
t
v
al
u
e
o
f
t
h
is
q
u
ad
r
o
to
r
is
n
eg
ati
v
e
b
ec
au
s
e
q
u
ad
r
o
to
r
is
ag
ain
s
t
t
h
e
ea
r
t
h
g
r
av
it
y
.
W
h
ile
is
th
e
v
al
u
e
to
th
e
d
esire
d
h
eig
h
t.
I
t
h
as
a
p
o
s
itiv
e
v
al
u
e
s
o
th
at
t
h
e
er
r
o
r
alg
o
r
ith
m
o
f
eq
u
atio
n
(
31
)
is
m
o
d
i
f
ied
in
to
t
h
e
f
o
llo
w
in
g
eq
u
at
io
n
:
(
3
2
)
2
.
4
.
At
t
it
ud
e
Co
ntr
o
l
A
tt
itu
d
e
co
n
tr
o
l
is
r
eq
u
ir
ed
to
s
tab
ilize
t
h
e
q
u
ad
r
o
to
r
w
h
ile
it
h
o
v
er
s
.
T
h
is
co
n
tr
o
l
is
r
esp
o
n
s
ib
le
f
o
r
en
s
u
r
in
g
t
h
at
th
e
a
n
g
les
o
f
r
o
ll,
p
itch
a
n
d
y
a
w
o
n
q
u
ad
r
o
to
r
h
av
e
a
m
in
i
m
u
m
v
alu
e
b
y
c
o
n
tr
o
llin
g
t
h
e
f
o
u
r
m
o
to
r
s
r
o
tates
at
th
e
s
a
m
e
s
p
e
ed
,
s
o
th
at
it
ca
n
h
o
v
er
s
tab
l
y
.
T
h
e
p
r
ev
io
u
s
r
esear
ch
er
s
h
av
e
u
s
ed
a
v
ar
iet
y
o
f
alg
o
r
ith
m
s
to
co
n
tr
o
l
attit
u
d
e
s
u
c
h
as
t
h
e
P
I
D
alg
o
r
ith
m
u
s
ed
b
y
L
ee
et
al.
[
1
9
]
,
th
e
Sli
d
in
g
Mo
d
e
C
o
n
tr
o
l
alg
o
r
ith
m
u
s
ed
b
y
B
o
u
ad
i
et
al.
[
2
2
]
,
an
d
th
e
b
ac
k
s
tep
p
in
g
alg
o
r
it
h
m
u
s
ed
b
y
C
o
lo
r
ad
o
et
al.
[
2
3
]
.
I
n
th
e
p
r
ev
io
u
s
s
tu
d
ie
s
,
th
e
r
esear
c
h
e
r
s
h
a
v
e
u
s
ed
a
s
ix
in
p
u
ts
a
n
d
t
h
r
ee
o
u
tp
u
t
s
to
d
esi
g
n
a
co
n
tr
o
l b
lo
ck
f
o
r
attitu
d
e
in
q
u
ad
r
o
to
r
as in
Fi
g
u
r
e
3
(
B
)
.
I
t
ca
n
b
e
s
ee
n
i
n
f
i
g
u
r
e
3
(
B
)
t
h
at
t
h
r
ee
co
n
tr
o
ller
s
ar
e
r
eq
u
ir
ed
f
o
r
attit
u
d
e
n
a
m
e
l
y
r
o
ll,
p
it
ch
co
n
tr
o
l
an
d
y
a
w
co
n
tr
o
ls
i
n
w
h
ic
h
ea
c
h
co
n
tr
o
l h
a
s
t
w
o
in
p
u
ts
an
d
a
n
o
u
tp
u
t.
R
o
ll
co
n
tr
o
l
h
a
s
a
t
h
r
u
s
t o
u
tp
u
t
a
n
d
t
w
o
in
p
u
t
s
o
f
r
o
ll
er
r
o
r
(
)
,
an
d
th
e
ch
an
g
e
r
ate
o
f
r
o
ll
(
̇
)
.
R
o
ll
e
r
r
o
r
v
alu
e
o
b
tain
ed
f
r
o
m
t
h
e
d
if
f
er
en
ce
b
et
w
ee
n
th
e
s
et
p
o
in
t
w
i
th
t
h
e
ac
t
u
al
r
o
ll a
n
g
le
(
)
,
ca
n
b
e
ex
p
r
ess
ed
as
in
th
e
f
o
llo
w
i
n
g
eq
u
a
tio
n
:
(3
3
)
is
th
e
v
al
u
e
o
f
t
h
e
r
o
ll
an
g
le
o
f
th
e
q
u
ad
r
o
to
r
,
an
d
is
th
e
d
esire
d
r
o
ll
an
g
le
v
al
u
e
in
w
h
ic
h
t
h
e
r
o
ll
an
g
le
i
s
0
f
o
r
th
e
q
u
ad
r
o
to
r
to
b
e
s
tab
le.
P
itch
co
n
tr
o
l
h
as
a
t
h
r
u
s
t
p
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h
o
u
tp
u
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a
n
d
t
w
o
in
p
u
t
s
n
a
m
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y
p
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r
o
r
(
)
an
d
ch
an
g
e
r
ate
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f
p
itch
(
̇
)
.
P
itch
er
r
o
r
v
alu
e
o
b
tain
ed
f
r
o
m
t
h
e
d
if
f
er
en
ce
b
et
w
ee
n
t
h
e
s
et
p
o
in
t
w
i
th
t
h
e
ac
t
u
al
p
itch
a
n
g
le
(
)
,
ca
n
b
e
ex
p
r
ess
ed
as
in
th
e
f
o
llo
w
in
g
eq
u
atio
n
:
(
34
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
Ho
ve
r
in
g
C
o
n
tr
o
l o
f Q
u
a
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r
o
t
o
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B
a
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o
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F
u
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z
y
Lo
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ic
(
N
ia
Ma
h
a
r
a
n
i R
a
h
a
r
ja
)
499
is
th
e
v
al
u
e
o
f
th
e
p
itch
an
g
le
o
f
th
e
q
u
ad
r
o
to
r
,
is
th
e
d
esire
d
p
icth
an
g
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v
al
u
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in
w
h
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h
t
h
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p
itch
an
g
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i
s
0
f
o
r
th
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q
u
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to
b
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tab
le.
Ya
w
co
n
tr
o
l
h
as
a
y
a
w
t
h
r
u
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t
o
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tp
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a
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d
t
w
o
i
n
p
u
t
s
n
a
m
el
y
y
a
w
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r
o
r
(
)
an
d
ch
an
g
e
r
ate
o
f
y
a
w
(
̇
)
.
Yaw
er
r
o
r
v
alu
e
o
b
tain
ed
f
r
o
m
th
e
d
if
f
er
en
ce
b
et
w
ee
n
th
e
s
e
t
p
o
in
t
w
i
th
t
h
e
ac
t
u
a
l r
o
ll a
n
g
le
(
)
,
ca
n
b
e
ex
p
r
ess
ed
as
in
th
e
f
o
llo
w
in
g
eq
u
at
io
n
:
,
(
3
5
)
w
h
er
e
is
t
h
e
v
alu
e
o
f
th
e
y
a
w
an
g
le
o
f
th
e
q
u
ad
r
o
to
r
,
is
t
h
e
d
esire
d
y
a
w
a
n
g
le
v
al
u
e
in
wh
ich
t
h
e
y
a
w
an
g
le
i
s
0
f
o
r
th
e
q
u
ad
r
o
to
r
to
b
e
s
tab
le
.
3.
CO
NT
RO
L
ST
R
AT
E
G
Y
T
h
is
s
tu
d
y
w
ill
d
i
s
cu
s
s
t
h
e
h
o
v
er
co
n
tr
o
l
s
y
s
te
m
f
o
r
q
u
ad
r
o
to
r
at
a
d
esire
d
altitu
d
e.
A
l
titu
d
e
an
d
attitu
d
e
co
n
tr
o
ls
ar
e
u
s
ed
to
m
ai
n
tai
n
th
e
s
tab
ilit
y
o
f
th
e
q
u
ad
r
o
to
r
.
Fu
zz
y
lo
g
ic
al
g
o
r
ith
m
i
s
o
n
e
o
f
th
e
ar
tif
icial
i
n
tell
ig
e
n
ce
alg
o
r
it
h
m
s
to
co
n
tr
o
l th
e
al
tit
u
d
e
an
d
attitu
d
e
b
y
u
s
i
n
g
Ma
m
d
a
n
i
m
e
th
o
d
s
[
2
4
]
–
[
2
6
]
.
3
.
1
.
Alt
it
ud
e
Sta
bil
it
y
Fig
u
r
e
3
(
A
)
s
h
o
w
s
t
h
at
th
e
al
titu
d
e
co
n
tr
o
l
h
a
s
t
w
o
i
n
p
u
ts
n
a
m
e
l
y
er
r
o
r
an
d
th
e
er
r
o
r
ch
an
g
e
r
ate.
T
h
is
co
n
tr
o
l
h
as
also
an
o
u
tp
u
t
th
at
is
u
s
ed
as
a
th
r
o
tel
th
r
u
s
t
in
p
u
t
to
co
n
tr
o
l
th
e
r
o
tatio
n
o
f
th
e
f
o
u
r
m
o
to
r
s
o
n
th
e
q
u
ad
r
o
to
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.
I
n
th
is
p
ap
er
,
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
is
f
u
zz
y
lo
g
ic
al
g
o
r
ith
m
w
h
ic
h
is
m
u
l
ti
in
p
u
t
s
i
n
g
l
e
o
u
tp
u
t
(
MI
SO)
co
n
s
i
s
ti
n
g
t
wo
in
p
u
t
s
a
n
d
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o
u
tp
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t.
F
u
r
t
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th
e
f
u
zz
y
co
n
tr
o
l
s
y
s
te
m
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lli
n
g
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e
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o
f
th
e
q
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ad
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n
th
e
b
lo
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d
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g
r
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m
in
Fi
g
u
r
e
4
i
s
d
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I
t
s
h
o
w
s
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at
t
h
i
s
co
n
tr
o
l
h
a
s
t
w
o
in
p
u
ts
an
d
a
n
o
u
tp
u
t.
T
h
e
in
p
u
t
s
a
n
d
o
u
tp
u
ts
ar
e
u
s
ed
to
d
esig
n
t
h
e
f
u
zz
y
lo
g
ic
co
n
tr
o
l
as
m
e
m
b
er
s
o
f
th
e
f
u
zz
y
s
et.
Fig
u
r
e
4
.
T
h
e
p
r
o
p
o
s
ed
a
l
titu
d
e
co
n
tr
o
l sy
s
te
m
T
h
e
altitu
d
e
co
n
tr
o
l
d
esig
n
u
s
in
g
f
u
zz
y
lo
g
ic
alg
o
r
it
h
m
p
r
o
p
o
s
ed
in
th
is
p
ap
er
.
T
h
is
al
g
o
r
ith
m
is
f
u
zz
y
MI
SO
w
h
ic
h
h
as
t
w
o
i
n
p
u
t
s
a
n
d
an
o
u
tp
u
t
u
s
i
n
g
m
a
m
d
a
n
i
m
eth
o
d
a
s
t
h
e
b
asic
r
u
les.
T
h
e
i
n
p
u
t
s
a
n
d
o
u
tp
u
t
ar
e
d
esi
g
n
ed
t
o
h
a
v
e
t
h
r
ee
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
c
o
n
tain
ed
i
n
t
h
e
u
n
iv
er
s
al
s
e
ts
.
T
h
e
u
n
i
v
er
s
al
s
et
s
h
av
e
d
if
f
er
en
t
r
an
g
e
v
alu
e
s
f
o
r
in
p
u
t
er
r
o
r
,
in
p
u
t
er
r
o
r
ch
an
g
e
r
ate
an
d
o
u
tp
u
t
.
T
h
er
e
ar
e
m
i
n
i
m
u
m
a
n
d
m
ax
i
m
u
m
v
al
u
es
f
o
r
th
e
u
n
i
v
er
s
al
s
et
s
r
an
g
e
o
f
th
e
in
p
u
t
e
r
r
o
r
w
h
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h
ca
n
b
e
d
eter
m
i
m
e
d
b
y
u
s
in
g
eq
u
a
tio
n
2
.
5
0
.
th
e
u
n
iv
er
s
a
l
s
ets
o
f
i
n
p
u
t
er
r
o
r
r
an
g
in
g
[
-
1
1
]
h
as
th
r
e
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
s
h
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w
n
in
F
ig
u
r
e
5
(
A
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.
I
n
th
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f
i
g
u
r
e,
it
ca
n
b
e
s
ee
n
t
h
at
m
e
m
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er
s
h
ip
f
u
n
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n
s
s
co
n
s
i
s
t
o
f
NS
(
n
e
g
ati
v
e
s
m
all)
,
Z
(
ze
r
o
)
,
an
d
P
S
(
p
o
s
itiv
e
s
m
all)
.
Fig
u
r
e
5
.
(
A
)
E
r
r
o
r
an
d
(
B
)
D
z
v
ar
iab
le
in
p
u
t d
esi
g
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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8
8
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8
694
IJ
PEDS
Vo
l.
8
,
No
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1
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Ma
r
ch
2
0
1
7
:
4
9
2
–
504
500
I
n
th
i
s
p
ap
er
,
th
e
m
i
n
i
m
u
m
a
n
d
m
a
x
i
m
u
m
v
al
u
es
f
o
r
th
e
u
n
i
v
er
s
al
s
et
s
o
f
in
p
u
t
er
r
o
r
ch
an
g
e
r
ate
h
as
th
e
s
a
m
e
v
a
lu
e
as
th
e
u
n
i
v
er
s
a
l set
s
o
f
i
n
p
u
t e
r
r
o
r
r
an
g
i
n
g
[
-
1
1
]
s
h
o
w
n
i
n
F
ig
u
r
e
5
(
B
)
.
I
n
th
is
f
ig
u
r
e
it
is
s
ee
n
th
at
t
h
e
m
e
m
b
er
s
h
ip
f
u
n
c
tio
n
s
in
t
h
e
u
n
iv
er
s
a
l
s
et
s
co
n
s
is
t
o
f
NS
(
n
e
g
ati
v
e
s
m
all)
,
Z
(
ze
r
o
)
,
an
d
P
S
(
p
o
s
itiv
e
s
m
al
l)
.
W
h
ile
t
h
e
m
i
n
i
m
u
m
an
d
m
a
x
i
m
u
m
v
a
lu
e
s
f
o
r
th
e
u
n
iv
er
s
al
s
et
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o
f
t
h
r
o
ttle
th
r
u
s
t
o
u
tp
u
t
ca
n
b
e
ca
lcu
lated
b
y
eq
u
atio
n
s
6
an
d
2
5
.
B
ec
au
s
e
o
f
th
e
co
n
s
id
er
ab
ly
s
m
a
ll
C
o
r
io
lis
E
f
f
ec
t,
th
e
e
f
f
ec
t
ca
n
b
e
ig
n
o
r
ed
s
o
th
at
t
h
e
eq
u
atio
n
2
5
is
s
u
b
s
t
itu
ted
in
to
eq
u
atio
n
6
to
b
e
as f
o
llo
w
s
:
̇
(3
6
)
T
h
e
m
i
n
i
m
u
m
v
al
u
e
o
f
t
h
r
u
s
t
ca
n
b
e
d
eter
m
in
ed
f
r
o
m
eq
u
ati
o
n
(
3
7
)
in
o
r
d
e
r
f
o
r
q
u
ad
r
o
to
r
to
b
e
ab
le
to
tak
e
o
f
f
.
T
h
e
o
b
tain
ed
eq
u
at
io
n
is
as t
h
e
f
o
llo
w
i
n
g
:
̇
(
37
)
h
en
ta
k
i
n
g
o
f
f
,
th
e
f
o
u
r
th
m
o
to
r
s
r
o
tate
at
th
e
s
a
m
e
s
p
ee
d
an
d
th
e
q
u
ad
r
o
to
r
h
as
n
o
s
tar
ti
n
g
ac
ce
ler
atio
n
,
z
=
0
th
u
s
t
h
e
ab
o
v
e
eq
u
atio
n
b
ec
o
m
e
s
:
√
w
h
er
e
m
=
th
e
q
u
ad
r
o
to
r
w
e
i
g
h
t
(
4
k
g
)
,
g
=
t
h
e
g
r
av
it
y
(
9
.
8
)
,
b
=
th
e
m
o
m
e
n
t
o
f
i
n
er
tia
f
o
r
ac
ce
ler
atio
n
o
f
z
(
1
.
3
2
3
4
e
-
0
0
5
)
.
Fro
m
th
e
ca
lc
u
latio
n
,
it
i
s
o
b
tain
ed
th
e
v
al
u
e
o
f
th
e
m
o
to
r
s
p
ee
d
o
f
8
6
0
s
o
th
at
th
e
m
i
n
i
m
u
m
an
d
m
a
x
i
m
u
m
r
a
n
g
e
v
al
u
e
s
o
f
u
n
i
v
er
s
al
s
ets
o
f
o
u
tp
u
t
s
p
ee
d
ca
n
b
e
s
et
e
x
ce
ed
in
g
t
h
e
v
alu
e
t
h
at
i
s
[
-
1
0
0
0
1
0
0
0
]
s
h
o
w
n
i
n
Fi
g
u
r
e
7
.
I
t
is
s
ee
n
in
th
e
f
ig
u
r
e
t
h
at
th
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
co
n
s
i
s
t
o
f
NS
(
n
e
g
ati
v
e
s
m
al
l)
,
Z
(
ze
r
o
)
,
an
d
P
S (
p
o
s
itiv
e
s
m
all)
.
Fig
u
r
e
7
.
Ou
tp
u
t
v
ar
iab
le
s
p
ee
d
d
esain
T
h
e
d
esig
n
o
f
t
h
e
f
u
zz
y
r
u
le
b
ase
u
s
es
lo
o
k
u
p
tab
le
co
n
s
i
s
t
in
g
o
f
9
r
u
les
to
d
eter
m
i
n
e
th
e
d
ec
is
io
n
.
A
ll r
u
les ar
e
s
h
o
w
n
i
n
Fi
g
u
r
e
8
co
n
n
ec
ted
w
i
th
t
h
e
A
ND
o
p
er
ato
r
.
Fig
u
r
e
8
.
R
u
le
b
ase
3
x
3
f
u
zz
y
m
a
m
d
a
n
i a
ltit
u
d
e
co
n
tr
o
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
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694
Ho
ve
r
in
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C
o
n
tr
o
l o
f Q
u
a
d
r
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t
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r
B
a
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ed
o
n
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u
z
z
y
Lo
g
ic
(
N
ia
Ma
h
a
r
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n
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a
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a
r
ja
)
501
Fig
u
r
e
1
0
s
h
o
w
s
t
h
e
d
e
s
ig
n
o
f
f
u
zz
y
lo
g
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co
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l s
y
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te
m
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es i
n
w
h
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h
t
h
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e
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t
h
r
ee
al
g
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ith
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s
to
s
tab
ilize
th
e
q
u
ad
r
o
to
r
w
h
e
n
h
o
v
er
in
g
n
a
m
el
y
:
1.
T
h
e
alg
o
r
ith
m
s
er
v
e
s
f
o
r
a
q
u
a
d
r
o
to
r
t
o
tak
e
o
f
f
.
2.
T
h
is
alg
o
r
ith
m
s
er
v
es to
d
a
m
p
en
o
v
er
s
h
o
o
t.
3.
T
h
is
alg
o
r
ith
m
s
er
v
es to
d
a
m
p
en
o
s
cillatio
n
s
a
n
d
h
ea
d
to
th
e
s
tead
y
s
tate.
3
.
2
.
At
t
it
ud
e
Co
ntr
o
l
Fig
u
r
e
3
(
B
)
s
h
o
w
s
t
h
at
t
h
e
at
titu
d
e
co
n
tr
o
l
h
as
s
ix
in
p
u
ts
t
h
at
is
er
r
o
r
s
o
f
r
o
ll,
p
itc
h
,
an
d
y
a
w
,
an
d
th
e
er
r
o
r
ch
a
n
g
e
r
ate
o
f
r
o
ll,
p
itch
,
a
n
d
y
a
w
.
A
d
d
itio
n
all
y
,
t
h
is
co
n
tr
o
l
h
as
th
r
ee
o
u
tp
u
t
s
n
a
m
el
y
t
h
r
u
s
t
o
f
r
o
ll,
p
itch
a
n
d
y
a
w
to
co
n
tr
o
l
t
h
e
r
o
tatio
n
o
f
t
h
e
f
o
u
r
m
o
to
r
s
o
n
th
e
q
u
ad
r
o
to
r
.
I
n
th
i
s
p
ap
er
,
t
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
is
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
(
F
L
C
)
,
m
ea
n
w
h
ile
th
e
al
g
o
r
ith
m
ca
n
n
o
t
co
n
tr
o
l
th
e
s
y
s
te
m
o
f
m
u
lti
i
n
p
u
t
m
u
lti
o
u
tp
u
t
(
MI
MO
)
,
th
er
e
f
o
r
e,
th
e
attit
u
d
e
co
n
tr
o
l
is
m
ad
e
in
to
t
h
r
ee
co
n
tr
o
ls
t
h
at
i
s
F
L
C
o
f
r
o
ll,
p
itch
,
a
n
d
y
a
w
as sh
o
w
n
i
n
F
i
g
u
r
e
9.
Fig
u
r
e
9
.
T
h
e
p
r
o
p
o
s
ed
attitu
d
e
co
n
tr
o
l sy
s
te
m
Fig
u
r
e
9
s
h
o
w
s
t
h
at
t
h
er
e
ar
e
th
r
ee
f
u
zz
y
co
n
tr
o
ls
,
n
a
m
el
y
f
u
zz
y
co
n
tr
o
ls
o
f
r
o
ll,
p
itch
an
d
y
a
w
.
Fu
zz
y
co
n
tr
o
l
o
f
r
o
ll
h
as
t
w
o
in
p
u
ts
t
h
at
is
r
o
ll
er
r
o
r
an
d
c
h
an
g
e
r
ate
o
f
r
o
ll
er
r
o
r
an
d
a
n
o
u
tp
u
t
t
h
r
u
s
t
r
o
ll.
Fu
zz
y
co
n
tr
o
l
o
f
p
itch
h
as
t
wo
in
p
u
ts
t
h
at
is
p
itc
h
er
r
o
r
an
d
ch
an
g
e
r
ate
o
f
p
itc
h
er
r
o
r
a
n
d
an
o
u
tp
u
t
th
r
u
s
t
p
itch
.
Fu
zz
y
co
n
tr
o
l h
a
s
t
w
o
i
n
p
u
t
s
n
a
m
el
y
y
a
w
er
r
o
r
an
d
ch
an
g
e
r
ate
o
f
y
a
w
e
r
r
o
r
an
d
an
o
u
tp
u
t
y
a
w
t
h
r
u
s
t.
Fig
u
r
e
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Fig
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r
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