I
nte
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l J
o
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f
Ro
bo
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Aut
o
m
a
t
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(
I
J
RA
)
Vo
l.
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,
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.
3
,
Sep
tem
b
er
2
0
1
5
,
p
p
.
2
1
9
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2
9
I
SS
N:
2089
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4856
219
J
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V
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in
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p
f
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w
in
g
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th
e
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ted
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p
tatio
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latio
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ica
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d
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tr
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ll
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li
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it
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st
to
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:
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d
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aw
Sli
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M
ode
S
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all
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ix
ed
W
in
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U
AV
Co
p
y
rig
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©
201
5
In
s
t
i
tu
te
o
f
A
d
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e
.
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rig
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ts
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rv
e
d
.
C
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s
p
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A
uth
o
r
:
Sa
m
a
n
eh
Am
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i
,
Dep
ar
t
m
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t o
f
Me
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E
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in
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Fer
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o
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co
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1.
I
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RO
D
UCT
I
O
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An
u
n
m
a
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ed
ae
r
ial
v
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h
icle
(
UAV)
is
a
p
o
w
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,
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ial
v
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at
d
o
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ar
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e
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tel
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,
a
n
d
ca
n
ca
r
r
y
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a
y
lo
ad
s
[
1
]
.
I
n
r
ec
en
t
y
ea
r
s
,
m
icr
o
an
d
s
m
a
ll U
A
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h
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attr
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w
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ld
s
i
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ce
th
e
y
h
a
v
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h
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p
o
ten
tial to
b
e
u
s
ed
i
n
m
i
litar
y
a
n
d
civ
ilia
n
ap
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licatio
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s
,
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g
.
tr
a
f
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u
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ap
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in
s
p
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io
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p
o
w
er
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e
s
,
o
il p
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es,
etc.
T
h
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attitu
d
e
co
n
t
r
o
l s
y
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te
m
d
e
s
ig
n
o
f
U
AVs is
a
c
h
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n
g
in
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task
d
u
e
to
v
ar
io
u
s
d
if
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ic
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lt
ie
s
f
ac
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w
h
e
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w
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r
k
in
g
w
it
h
t
h
e
m
.
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h
e
s
e
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te
m
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ar
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m
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lt
i
-
i
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p
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ti o
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tp
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t (
MI
MO
)
,
n
o
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l
in
ea
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,
co
u
p
led
b
et
w
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n
th
e
lo
n
g
it
u
d
in
al
a
n
d
later
al
d
y
n
a
m
ic,
an
d
v
er
y
s
en
s
ib
le
to
ex
ter
n
al
d
is
t
u
r
b
an
ce
s
.
Mo
r
eo
v
er
,
p
ar
am
etr
ic
u
n
ce
r
tai
n
tie
s
ch
ar
ac
ter
is
tics
m
a
y
also
ca
u
s
e
m
o
r
e
co
m
p
licati
o
n
s
d
u
r
i
n
g
t
h
e
d
esi
g
n
o
f
s
u
c
h
attitu
d
e
co
n
tr
o
l
s
y
s
te
m
s
.
A
n
u
m
b
er
o
f
co
n
tr
o
l
ap
p
r
o
ac
h
es
h
a
v
e
b
ee
n
p
r
esen
ted
in
t
h
e
liter
atu
r
es.
I
n
[
2
]
is
p
r
esen
ted
,
th
e
o
u
tp
u
t
f
ee
d
b
ac
k
co
n
tr
o
l
m
et
h
o
d
to
d
esig
n
th
e
attit
u
d
e
co
n
tr
o
l
s
y
s
t
e
m
f
o
r
UAV.
I
t
is
s
h
o
w
n
i
n
[
3
]
th
at
a
r
o
ll
-
ch
an
n
el
f
r
ac
tio
n
al
o
r
d
er
p
r
o
p
o
r
tio
n
al
in
te
g
r
al
f
li
g
h
t
co
n
tr
o
ller
f
o
r
a
s
m
all
f
i
x
ed
w
i
n
g
U
A
V
is
d
esig
n
ed
.
T
h
e
f
u
zz
y
s
lid
in
g
m
o
d
e
co
n
tr
o
l
b
ased
o
n
th
e
m
u
lti
o
b
j
e
ctiv
e
g
e
n
etic
al
g
o
r
ith
m
is
p
r
ese
n
ted
in
[
4
]
to
d
esig
n
th
e
alti
tu
d
e
au
to
p
ilo
t
o
f
U
A
V.
T
h
e
au
th
o
r
s
o
f
[
5
]
p
r
o
p
o
s
ed
an
L
1
ad
ap
tiv
e
co
n
tr
o
ller
as
au
to
p
ilo
t
in
n
er
lo
o
p
co
n
tr
o
ller
ca
n
d
id
ate,
d
esig
n
ed
an
d
te
s
te
d
its
co
n
tr
o
ller
b
ased
o
n
p
iec
e
w
i
s
e
co
n
s
ta
n
t
ad
ap
tiv
e
la
w
s
.
Nav
i
g
atio
n
o
u
ter
lo
o
p
p
ar
am
eter
s
ar
e
r
e
g
u
lated
v
ia
P
I
D
co
n
tr
o
l
m
et
h
o
d
.
I
n
[
6
]
,
th
e
attit
u
d
e
tr
ac
k
in
g
s
y
s
te
m
i
s
d
esi
g
n
ed
f
o
r
a
s
m
al
l
q
u
ad
r
o
to
r
UA
V
th
r
o
u
g
h
m
o
d
el
r
ef
er
en
ce
ad
ap
tiv
e
co
n
tr
o
l
m
et
h
o
d
.
T
h
e
m
ai
n
f
ea
t
u
r
e
o
f
[
7
]
is
th
at
th
e
ad
ap
tiv
e
co
n
tr
o
ll
er
is
d
esig
n
e
d
,
ass
u
m
in
g
t
h
at
all
o
f
t
h
e
n
o
n
li
n
ea
r
f
u
n
ct
io
n
s
o
f
th
e
s
y
s
te
m
h
a
v
e
u
n
ce
r
tai
n
tie
s
,
an
d
th
e
n
e
u
r
al
n
et
w
o
r
k
w
e
ig
h
ts
ar
e
ad
j
u
s
ted
ad
ap
tiv
el
y
v
ia
L
y
ap
u
n
o
v
t
h
eo
r
y
.
I
n
[
8
]
,
f
ee
d
b
ac
k
lin
ea
r
izatio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
4
,
No
.
3
,
Sep
tem
b
er
2
0
1
5
:
2
1
9
–
2
2
9
220
an
d
m
o
d
el
r
ef
er
en
ce
ad
ap
tiv
e
co
n
tr
o
l
(
MRAC
)
ar
e
in
teg
r
ate
d
to
d
esig
n
t
h
e
attit
u
d
e
co
n
tr
o
l
s
y
s
te
m
f
o
r
a
f
ix
ed
w
i
n
g
U
A
V.
Sli
d
in
g
m
o
d
e
co
n
tr
o
l (
SMC
)
h
as b
ee
n
s
u
g
g
ested
as a
p
o
w
er
f
u
l a
p
p
r
o
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h
f
o
r
co
n
tr
o
l s
y
s
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s
w
ith
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o
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li
n
ea
r
itie
s
,
u
n
ce
r
tain
d
y
n
a
m
ics a
n
d
b
o
u
n
d
ed
in
p
u
t d
is
tu
r
b
an
ce
s
.
T
h
e
m
o
s
t d
is
ti
n
g
u
i
s
h
e
d
f
ea
tu
r
e
o
f
SM
C
is
its
ab
ilit
y
to
p
r
o
v
id
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f
ast er
r
o
r
co
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v
er
g
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ce
a
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d
s
tr
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r
o
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tr
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s
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e
s
en
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t
h
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clo
s
ed
lo
o
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s
te
m
s
ar
e
co
m
p
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n
s
e
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s
it
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to
n
o
n
li
n
ea
r
it
ies an
d
u
n
ce
r
tai
n
d
y
n
a
m
ic
s
[
9
]
.
Ho
w
e
v
er
,
th
e
b
o
u
n
d
s
o
f
s
y
s
te
m
u
n
ce
r
tai
n
ti
es a
r
e
r
eq
u
ir
ed
f
o
r
s
lid
in
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m
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d
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co
n
tr
o
l a
n
d
th
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r
a
w
b
ac
k
atte
n
u
a
tes t
h
e
co
n
tr
o
l s
y
s
te
m
p
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f
o
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m
a
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.
I
n
t
h
is
p
ap
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,
d
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e
to
a
n
o
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d
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m
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p
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f
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tr
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l a
p
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ased
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ap
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li
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co
u
p
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U
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T
h
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ap
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t
y
an
d
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b
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t a
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n
g
alt
itu
d
e
tr
aj
ec
to
r
y
tr
ac
k
in
g
.
I
n
t
h
e
p
r
o
p
o
s
ed
s
ch
em
e,
th
e
u
n
k
n
o
w
n
s
lid
in
g
m
o
d
e
co
n
tr
o
l p
ar
am
eter
s
ar
e
ap
p
r
o
x
i
m
ated
v
ia
ad
ap
tatio
n
la
w
s
.
T
h
e
s
tab
ilit
y
o
f
th
e
co
n
tr
o
l s
y
s
te
m
i
s
d
e
m
o
n
s
tr
ated
b
ased
o
n
l
y
ap
u
n
o
v
th
eo
r
y
.
A
d
ap
tiv
e
s
lid
in
g
m
o
d
e
co
n
tr
o
l (
A
SM
C
)
,
th
e
co
m
b
in
a
tio
n
o
f
ad
ap
tiv
e
c
o
n
tr
o
l
m
et
h
o
d
an
d
SMC
ap
p
r
o
ac
h
,
is
m
o
r
e
f
le
x
ib
le
an
d
co
n
v
en
ie
n
t i
n
co
n
tr
o
ller
d
esig
n
t
h
an
SMC
.
I
n
co
m
p
ar
is
o
n
w
it
h
o
th
er
co
n
t
r
o
l a
p
p
r
o
ac
h
es,
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
b
en
ef
it
s
f
r
o
m
h
i
g
h
r
o
b
u
s
t
n
es
s
in
p
r
esen
ce
o
f
d
if
f
er
en
t p
ar
a
m
etr
ic
u
n
ce
r
tai
n
tie
s
,
i.e
.
ae
r
o
d
y
n
a
m
ic
co
ef
f
icie
n
t
s
,
in
er
tia
m
o
m
e
n
t a
n
d
co
n
f
i
g
u
r
atio
n
p
ar
a
m
eter
s
u
n
ce
r
tain
ties
a
n
d
d
is
t
u
r
b
an
ce
s
ca
u
s
ed
b
y
th
e
e
n
v
ir
o
n
m
en
t su
c
h
as
w
i
n
d
.
Fu
r
t
h
er
m
o
r
e,
th
e
c
h
atter
in
g
p
h
en
o
m
e
n
o
n
i
n
s
lid
i
n
g
m
o
d
e
co
n
tr
o
l is av
o
id
ed
b
y
u
s
in
g
s
at
u
r
atio
n
f
u
n
ctio
n
.
T
h
e
p
ap
er
is
o
r
g
an
ized
as
f
o
ll
o
w
s
:
I
n
s
ec
t
io
n
2
,
d
y
n
a
m
i
c
a
n
d
k
i
n
e
m
atic
eq
u
at
io
n
s
o
f
s
m
all
f
i
x
ed
w
i
n
g
UAV
f
o
r
d
y
n
a
m
ic
m
o
d
elin
g
ar
e
in
tr
o
d
u
ce
d
.
T
h
e
c
o
n
tr
o
l
s
tr
ateg
y
f
o
r
n
o
n
li
n
ea
r
d
y
n
a
m
ics
o
f
U
A
V
i
s
in
v
e
s
ti
g
ated
in
s
ec
tio
n
3
.
I
n
s
ec
tio
n
4
,
th
e
ad
ap
tiv
e
s
l
id
in
g
m
o
d
e
co
n
tr
o
ller
th
eo
r
y
is
p
r
e
s
en
ted
.
Si
m
u
latio
n
r
esu
l
t
s
ar
e
an
al
y
ze
d
i
n
s
ec
tio
n
5
.
Fin
all
y
,
co
n
c
lu
s
io
n
s
ar
e
p
r
e
s
en
ted
i
n
s
ec
tio
n
6
.
2.
DYNA
M
I
C
M
O
DE
L
I
N
G
I
t
is
ass
u
m
ed
in
m
o
d
eli
n
g
th
at
UA
V
is
a
r
ig
id
b
o
d
y
w
it
h
a
s
y
m
m
etr
ic
g
eo
m
etr
y
.
T
h
e
ce
n
ter
o
f
m
a
s
s
is
also
ass
u
m
ed
to
b
e
f
ix
ed
.
Attitu
d
e
o
f
a
r
ig
id
b
o
d
y
m
o
v
in
g
in
s
p
ac
e
is
ex
p
r
es
s
ed
in
E
u
ler
an
g
le
s
(
r
o
ll
-
p
itch
-
y
a
w
)
,
b
ased
o
n
a
b
o
d
y
f
r
a
m
e
as
s
h
o
w
n
in
Fig
.
1
.
T
h
e
co
n
tr
o
l
o
f
a
f
ix
ed
w
i
n
g
s
m
a
ll
U
AV
is
r
ep
r
esen
ted
b
y
th
r
ee
co
n
tr
o
l su
r
f
ac
es: ai
ler
o
n
,
elev
ato
r
an
d
r
u
d
d
er
s
,
an
d
th
e
th
r
u
s
t g
e
n
er
ated
b
y
an
e
n
g
in
e.
Fig
u
r
e
1
.
T
h
e
UA
V
o
n
b
o
d
y
f
r
a
m
e
T
h
e
UA
V
6
-
D
OF
f
li
g
h
t d
y
n
a
m
ic
eq
u
atio
n
s
o
f
m
o
tio
n
ar
e
d
er
iv
ed
f
r
o
m
t
h
e
Ne
w
to
n
-
E
u
ler
la
w
s
[
1
0
]
as f
o
llo
w
:
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
A
d
a
p
tive
s
lid
in
g
Mo
d
e
C
o
n
tr
o
ller
Desig
n
fo
r
A
ttit
u
d
e
S
ma
ll UA
V
(
S
.
A
min
i)
2
21
W
h
er
e
u
,
v,
w
,
ar
e
t
h
e
v
elo
ci
t
y
p
r
o
j
ec
tio
n
s
alo
n
g
th
e
b
o
d
y
f
r
a
m
e,
p
,
q
,
r
ar
e
t
h
e
p
r
o
j
ec
tio
n
s
o
f
th
e
U
A
V
an
g
u
lar
r
ate
→
alo
n
g
b
o
d
y
f
r
a
m
e
ax
es,
T
is
th
e
UA
V
t
h
r
u
s
t
f
o
r
ce
,
ɸ
,
θ
,
ψ
ar
e
th
e
attitu
d
e
a
n
g
le
s
(
r
o
ll,
p
itch
,
an
d
y
a
w
)
,
→
is
th
e
g
r
a
v
itatio
n
a
l
ac
ce
ler
atio
n
,
I
ij
r
ep
r
esen
t
s
t
h
e
in
er
tia
m
o
m
en
t
s
,
a
n
d
is
th
e
UAV
m
ass
.
T
h
e
ae
r
o
d
y
n
a
m
ic
f
o
r
ce
s
X
A
,
Y
A
,
Z
A,
an
d
m
o
m
en
ts
L
A
,
M
A
,
N
A
c
an
th
e
n
b
e
ca
lcu
lated
b
y
m
ea
n
s
o
f
ae
r
o
d
y
n
a
m
ic
co
ef
f
icie
n
t
s
as:
√
W
h
er
e
is
th
e
air
s
p
ee
d
an
d
w
in
g
s
u
r
f
ac
e
ar
ea
,
S,
th
e
w
i
n
g
s
p
an
,
b
,
t
h
e
m
ea
n
ae
r
o
d
y
n
a
m
ic
co
r
d
,
̅
an
d
th
e
air
d
en
s
it
y
,
ρ,
ar
e
co
n
s
id
er
ed
co
n
s
ta
n
t
p
ar
a
m
eter
s
.
T
h
e
d
i
m
en
s
io
n
le
s
s
co
ef
f
icie
n
t
s
in
th
e
f
o
r
ce
/
m
o
m
en
t
e
x
p
r
ess
io
n
s
ca
n
b
e
d
ec
o
m
p
o
s
ed
in
th
e
f
o
llo
w
i
n
g
s
et
o
f
eq
u
atio
n
s
[
1
1
]
:
W
h
er
e
th
e
li
f
t (
C
L
)
an
d
t
h
e
d
r
ag
(
C
D
)
co
ef
f
icie
n
ts
ar
e
ca
lcu
la
ted
u
s
i
n
g
t
h
e
f
o
llo
w
i
n
g
eq
u
ati
o
n
s
:
W
h
er
e
ar
e
α
,
β
th
e
attac
k
an
d
t
h
e
s
id
esli
p
a
n
g
le
s
.
δ
e,
δ
a
,
an
d
δ
r
r
ep
r
esen
t th
e
m
o
v
i
n
g
s
u
r
f
ac
es o
f
elev
ato
r
,
ailer
o
n
s
,
an
d
r
u
d
d
er
,
r
esp
ec
tiv
el
y
.
Mo
r
eo
v
er
,
e
is
th
e
Os
w
a
l
d
s
ef
f
icien
t n
u
m
b
er
,
an
d
AR
is
th
e
asp
ec
t r
atio
ca
lcu
lated
as
[
1
1
]
T
h
e
k
in
e
m
atics
o
f
t
h
e
air
cr
af
t
r
o
tatio
n
m
o
tio
n
r
elatin
g
b
o
d
y
a
n
g
u
lar
r
ates,
E
u
ler
an
g
le
s
an
d
ae
r
o
d
y
n
a
m
ic
an
g
le
s
ar
e
g
i
v
en
b
y
:
A
cc
o
r
d
in
g
to
f
o
llo
w
i
n
g
eq
u
a
tio
n
,
ac
tu
ato
r
d
y
n
a
m
ics
ar
e
s
ec
o
n
d
o
r
d
er
f
u
n
c
tio
n
s
an
d
t
h
e
co
n
tr
o
l
s
u
r
f
ac
e
b
o
u
n
d
s
ar
e
w
ith
in
-
2
0
an
d
+2
0
d
eg
r
ee
s
.
W
h
e
re
ω
a
(
th
e
n
at
u
r
al
f
r
eq
u
e
n
c
y
)
a
n
d
ξ
a
(
d
am
p
i
n
g
r
atio
)
,
ar
e
4
5
r
ad
/s
an
d
0
.
7
f
o
r
al
l
co
n
tr
o
l
s
u
r
f
ac
e
s
,
r
esp
ec
tiv
el
y
[
1
1
]
.
3.
CO
NT
RO
L
ST
R
AT
E
G
Y
As
ill
u
s
tr
ated
i
n
F
ig
.
2
,
t
h
e
m
u
lti
v
ar
iab
le
d
y
n
a
m
ic
co
n
tr
o
l
s
y
s
te
m
f
o
r
a
f
i
x
ed
w
i
n
g
U
A
V
is
d
iv
id
ed
in
to
lo
n
g
it
u
d
i
n
al
a
n
d
later
al
p
l
an
s
.
T
h
e
lo
n
g
i
tu
d
i
n
al
p
la
n
co
n
tr
o
ls
th
e
p
itch
an
g
le
(
θ
)
i
n
t
h
e
in
n
er
lo
o
p
an
d
t
h
e
altitu
d
e
(
h
)
in
th
e
o
u
ter
lo
o
p
b
y
ele
v
ato
r
co
n
tr
o
l
s
u
r
f
ac
e
(
δ
e
)
an
d
co
n
tr
o
ls
th
e
s
p
ee
d
b
y
th
r
o
ttle
(
δ
t
)
.
T
h
e
later
al
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
4
,
No
.
3
,
Sep
tem
b
er
2
0
1
5
:
2
1
9
–
2
2
9
222
p
lan
s
co
n
tr
o
ls
t
h
e
r
o
ll
an
g
le
(
ɸ)
in
th
e
i
n
n
er
lo
o
p
an
d
h
ea
d
in
g
a
n
g
le
(
ψ
)
in
th
e
o
u
ter
lo
o
p
b
y
ailer
o
n
co
n
tr
o
l
s
u
r
f
ac
e
(
δ
a
)
.
I
n
th
i
s
p
ap
er
,
th
e
ad
ap
tiv
e
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
is
ch
o
s
e
n
to
co
n
tr
o
l
th
e
i
n
n
er
n
av
i
g
atio
n
lo
o
p
s
(
θ,
ɸ)
th
o
s
e
n
ee
d
a
f
aster
r
esp
o
n
s
e
an
d
ar
e
m
o
r
e
p
r
o
n
e
to
b
e
af
f
ec
ted
b
y
p
ar
a
m
e
tr
ic
u
n
ce
r
tain
ties
.
Altit
u
d
e
h
an
d
h
ea
d
in
g
ψ
o
u
ter
n
av
i
g
atio
n
lo
o
p
s
ar
e
in
s
tead
co
n
tr
o
lled
b
y
s
i
m
p
le
P
I
Ds.
I
t
s
h
o
u
ld
b
e
n
o
ted
th
at
alth
o
u
g
h
n
o
r
u
d
d
er
is
u
s
ed
,
th
e
r
esp
o
n
s
e
o
n
th
e
h
ea
d
i
n
g
a
n
g
les i
s
s
til
l
s
atis
f
y
in
g
w
it
h
ailer
o
n
co
n
tr
o
l
.
Fig
u
r
e
2
.
T
h
e
co
n
tr
o
l sch
e
m
e
4.
A
DAP
T
I
VE
S
L
I
DIN
G
M
O
DE
C
O
NT
RO
L
OF
S
M
AL
L
UAV
T
h
is
s
ec
tio
n
co
n
s
is
t o
f
t
w
o
p
ar
ts
.
At
f
ir
s
t,
th
e
s
lid
in
g
m
o
d
e
c
o
n
tr
o
l la
w
i
s
d
esig
n
ed
f
o
r
th
e
t
w
o
lo
n
g
it
u
d
i
n
al
an
d
later
al
p
lan
s
.
Nex
t,
th
e
u
n
k
n
o
w
n
s
y
s
te
m
p
ar
a
m
eter
s
ar
e
ap
p
r
o
x
i
m
ated
v
ia
ad
ap
tatio
n
la
w
s
b
y
in
tr
o
d
u
ci
n
g
n
e
w
l
y
ap
u
n
o
v
f
u
n
ctio
n
s
.
4
.
1
.
Sli
di
ng
M
o
de
Co
ntr
o
l o
f
S
m
a
ll UA
V
I
n
o
r
d
er
to
a
p
p
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as:
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
A
d
a
p
tive
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lid
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ll UA
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S
.
A
min
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223
u
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m
ic
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s
m
al
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AV
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n
eq
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at
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s
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9
)
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d
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1
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1
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4
.
2
.
Ada
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Sli
din
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M
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Co
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s
m
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ll UA
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I
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s
lid
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l la
w
s
(
)
as:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
4
,
No
.
3
,
Sep
tem
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2
0
1
5
:
2
1
9
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2
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224
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1
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1
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1
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1
3
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(
2
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1
f
1
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1
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m
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s
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d
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s
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d
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3
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1
5
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b
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t
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t
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ap
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la
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s
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6
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y
ield
s
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
A
d
a
p
tive
s
lid
in
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Mo
d
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fo
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ttit
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S
ma
ll UA
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(
S
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A
min
i)
225
Re
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s
at
u
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i
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d
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5.
SI
M
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I
D
co
n
tr
o
ller
.
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o
u
p
lin
g
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f
ec
t o
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lo
n
g
it
u
d
in
a
l a
n
d
later
al
p
lan
s
r
es
u
lts
i
n
an
o
v
er
s
h
o
o
t in
th
e
P
I
D
co
n
tr
o
ller
,
w
h
i
le
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
in
th
is
ar
ticle
i
s
f
r
ee
o
f
t
h
es
e
d
r
aw
b
ac
k
s
.
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n
ad
d
itio
n
,
Fig
.
4
s
h
o
w
s
th
a
t e
lev
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r
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d
ailer
o
n
d
ef
lectio
n
s
b
o
th
alg
o
r
ith
m
s
r
e
m
ai
n
u
n
d
e
r
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e
i
m
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o
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ed
co
m
m
a
n
d
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at
u
r
atio
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li
m
it o
f
2
0
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eg
r
ee
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.
I
t is illu
s
tr
ated
clea
r
l
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Fig
s
.
5
an
d
6
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at
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es
ig
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ed
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s
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g
L
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o
v
m
eth
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ate
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k
n
o
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n
p
ar
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m
eter
s
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ac
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r
d
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t
o
in
itial v
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o
f
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ar
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eter
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g
ai
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o
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,
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e
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i
n
ed
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y
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e
o
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er
ato
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h
e
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m
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ar
is
o
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o
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h
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lt
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e
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n
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er
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o
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s
s
y
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te
m
w
it
h
th
e
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SM
C
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d
t
h
e
P
I
D
alg
o
r
ith
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s
i
n
th
e
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o
f
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0
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n
d
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ce
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ae
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ic
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icie
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e
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er
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m
o
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e
n
t,
r
esp
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y
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e
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s
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ated
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i
g
u
r
e
6
.
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itio
n
,
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e
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is
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r
b
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e
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ter
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r
r
e
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ts
in
x
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ir
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tio
n
s
w
it
h
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m
ag
n
i
tu
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e
o
f
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m
/s
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t =
8
s
.
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h
e
co
n
tr
o
l in
p
u
ts
ar
e
s
h
o
w
n
i
n
f
ig
u
r
e
8
.
I
t c
an
b
e
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n
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at
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h
e
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SM
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n
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o
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r
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m
o
r
e
r
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s
t c
lo
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ed
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s
y
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te
m
a
g
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n
s
t t
h
e
u
n
ce
r
tai
n
tie
s
an
d
d
is
tu
r
b
an
ce
s
.
Fig
u
r
e
1
3
illu
s
tr
ate
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th
e
f
u
ll n
o
n
lin
ea
r
d
y
n
a
m
ic
r
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n
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e
s
o
f
th
e
U
A
V
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o
r
th
e
ap
p
lied
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y
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r
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alg
o
r
ith
m
i
n
co
m
p
ar
is
o
n
w
i
th
th
e
P
I
D
co
n
tr
o
ller
.
A
cc
o
r
d
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g
to
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is
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ig
u
r
e,
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o
th
co
n
tr
o
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ar
e
ab
le
to
tr
ac
k
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e
d
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r
ies.
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s
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ar
as th
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il
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u
lar
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ates,
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ele
v
ato
r
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ailer
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n
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o
l su
r
f
ac
es
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o
r
b
o
th
co
n
tr
o
ller
s
in
f
ig
u
r
e
1
4
co
n
f
ir
m
th
is
f
ac
t.
Ho
w
e
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er
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th
e
P
I
D
co
n
tr
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h
o
w
s
a
p
o
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er
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o
r
m
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es d
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t
h
e
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u
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lan
s
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w
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ile
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h
e
A
S
MC h
y
b
r
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m
o
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ac
ts
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it
h
a
m
o
r
e
r
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u
s
t
in
n
er
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p
.
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o
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er
if
y
t
h
e
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r
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p
o
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et
h
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UAV
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t
h
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n
ce
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d
w
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is
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r
b
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ce
s
w
it
h
a
m
a
g
n
itu
d
e
o
f
5
m
/s
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s
i
n
x
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ir
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n
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s
i
t c
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n
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r
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Fig
u
r
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4
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s
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s
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d
A
SM
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n
f
r
o
n
tatio
n
Fig
u
r
e
5
.
P
ar
am
eter
s
est
i
m
a
tio
n
o
f
later
al
p
lan
e
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it
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Fig
u
r
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n
n
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ar
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n
d
er
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r
e
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n
n
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f
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e
s
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n
d
er
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n
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d
d
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r
b
an
ce
,
P
I
D
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d
A
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C
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o
r
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m
s
co
n
f
r
o
n
tat
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n
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o
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ar
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I
D
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A
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C
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o
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it
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m
s
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n
f
r
o
n
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Fig
u
r
e
10
.
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n
lin
ea
r
m
o
d
el
a
n
g
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ates,
P
I
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ith
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s
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n
f
r
o
n
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Fig
u
r
e
11
.
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r
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o
d
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o
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it
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s
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n
f
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o
n
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n
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