I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
p
ute
r
E
ng
in
ee
ring
(
I
J
E
CE
)
Vo
l.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
,
p
p
.
6
3
0
9
~
6
3
1
8
I
SS
N:
2
0
8
8
-
8708
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
ec
e
.
v
1
0
i
6
.
pp
6
3
0
9
-
6
3
1
8
6309
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ec
e.
ia
esco
r
e.
co
m/in
d
ex
.
p
h
p
/I
JE
C
E
PID vs
L
Q
R con
t
ro
ller f
o
r
tilt
ro
tor a
irpla
ne
Ao
ued H
o
ua
ri
1
,
I
m
ine B
a
chi
r
2
,
Della
K
ra
cha
i
M
o
ha
m
ed
3
,
M
o
ha
m
e
d K
a
ra
M
o
ha
m
e
d
4
1
De
p
a
rtme
n
t
o
f
El
e
c
tro
n
ics
,
Un
iv
e
rsit
y
o
f
S
c
ien
c
e
s a
n
d
T
e
c
h
n
o
lo
g
y
o
f
Ora
n
M
B,
A
lg
e
ria
2
De
p
a
rtme
n
t
o
f
M
e
c
a
n
ica
l
En
g
in
e
e
rin
g
,
Un
iv
e
rs
it
y
o
f
S
c
ien
c
e
s a
n
d
T
e
c
h
n
o
lo
g
y
o
f
Or
a
n
M
B,
A
lg
e
ria
3
De
p
a
rtme
n
t
o
f
A
u
to
m
a
ti
c
En
g
in
e
e
rin
g
,
Un
iv
e
rsity
o
f
S
c
ien
c
e
s a
n
d
T
e
c
h
n
o
lo
g
y
o
f
Or
a
n
M
B,
A
lg
e
ria
4
De
p
a
rtme
n
t
o
f
M
a
rit
im
e
a
n
d
M
e
c
h
a
n
ica
l
En
g
in
e
e
rin
g
,
L
iv
e
rp
o
o
l
J
o
h
n
M
o
o
re
’s Un
iv
e
rsity
,
Un
it
e
d
Kin
g
d
o
m
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
e
d
Dec
3
0
,
2
0
1
9
R
ev
i
s
ed
Ma
y
20
,
2020
A
cc
ep
ted
J
u
n
1
,
2
0
2
0
T
h
e
m
a
in
th
e
m
a
ti
c
o
f
th
is
p
a
p
e
r
is
c
o
n
tr
o
ll
i
n
g
th
e
m
a
in
m
a
n
o
e
u
v
e
rs
o
f
a
ti
lt
ro
to
r
UA
V
a
irp
lan
e
i
n
se
v
e
ra
l
m
o
d
e
s
su
c
h
a
s
v
e
rti
c
a
l
tak
e
o
ff
a
n
d
la
n
d
i
n
g
,
lo
n
g
it
u
d
i
n
a
l
tran
sla
ti
o
n
a
n
d
t
h
e
m
o
st
i
m
p
o
rtan
t
p
h
a
se
w
h
ich
d
e
a
l
w
it
h
th
e
tran
siti
o
n
f
ro
m
th
e
h
e
li
c
o
p
te
r
m
o
d
e
to
th
e
a
irp
lan
e
m
o
d
e
a
n
d
v
isv
e
rs
a
b
a
se
d
o
n
a
n
e
w
a
c
tu
a
to
rs co
m
b
in
a
ti
o
n
tec
h
n
iq
u
e
f
o
r
sp
e
c
ially
th
e
y
a
w
m
o
ti
o
n
w
it
h
n
o
t
re
fe
rrin
g
to
ro
to
r
sp
e
e
d
c
o
n
tro
l
stra
teg
y
w
h
ich
is
u
se
d
in
c
o
n
tro
ll
in
g
t
h
e
a
tt
it
u
d
e
o
f
a
h
u
g
e
n
u
m
b
e
r
o
f
v
e
h
icle
s
n
o
wa
d
a
y
s.
T
h
is
n
e
w
a
c
tu
a
to
r
c
o
m
b
in
a
ti
o
n
is
in
sp
ired
f
ro
m
th
a
t
th
e
tran
sie
n
t
re
sp
o
n
se
o
f
a
tri
ro
to
r
u
si
n
g
ti
lt
in
g
m
o
ti
o
n
d
y
n
a
m
ics
p
ro
v
id
e
s
a
fa
ste
r
re
sp
o
n
se
th
a
n
u
sin
g
r
o
to
r
sp
e
e
d
d
y
n
a
m
ics
.
In
th
e
li
tera
tu
re
,
a
lo
t
o
f
c
o
n
tro
l
tec
h
n
ics
a
re
u
se
d
f
o
r
sta
b
il
izin
g
a
n
d
g
u
a
ra
n
tee
th
e
n
e
c
e
ss
a
r
y
m
a
n
o
e
u
v
e
rs
f
o
r
e
x
e
c
u
ti
n
g
su
c
h
tas
k
,
a
m
u
lt
ip
le
A
tt
it
u
d
e
a
n
d
A
lt
it
u
d
e
P
ID
c
o
n
t
ro
ll
e
rs
w
e
re
c
h
o
se
n
f
o
r
a
si
m
p
le
li
n
e
a
r
m
o
d
e
l
o
f
o
u
r
ti
l
t
ro
t
o
r
a
irp
lan
e
in
o
rd
e
r
t
o
f
u
lf
il
l
th
e
d
e
sire
d
tr
a
jec
to
ry
,
f
o
r
re
a
so
n
s o
f
c
o
m
p
lex
it
y
o
f
o
u
r
m
o
d
e
l
th
e
m
u
lt
ip
le
P
ID
c
o
n
tr
o
ll
e
r
d
o
e
sn
t
tak
e
in
to
c
o
n
sid
e
ra
ti
o
n
a
ll
t
h
e
c
o
u
p
li
n
g
th
a
t
e
x
ists
b
e
t
w
e
e
n
th
e
d
e
g
re
e
s
o
f
f
re
e
d
o
m
in
o
u
r
m
o
d
e
l
,
s
o
a
n
L
QR
c
o
n
tro
l
ler
is
a
d
o
p
ted
f
o
r
m
o
re
fe
a
sib
le
so
lu
ti
o
n
o
f
c
o
m
p
lex
m
a
n
o
e
u
v
e
rin
g
,
th
e
b
o
t
h
c
o
n
tr
o
ll
e
rs
n
e
e
d
li
n
e
a
riza
ti
o
n
o
f
th
e
m
o
d
e
l
f
o
r
a
n
e
a
s
y
i
m
p
le
m
e
n
tatio
n
.
K
ey
w
o
r
d
s
:
A
ir
p
la
n
e
L
Q
R
co
n
tr
o
l
P
I
D
co
n
tr
o
l
T
ilt r
o
t
o
r
T
r
an
s
itio
n
UAV
VT
OL
Co
p
y
rig
h
t
©
2
0
2
0
In
stit
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
A
o
u
ed
Ho
u
ar
i,
A
er
o
n
a
u
tic
s
an
d
P
r
o
p
u
ls
iv
e
S
y
s
te
m
s
L
ab
o
r
ato
r
y
,
Un
i
v
er
s
it
y
o
f
Scie
n
ce
a
n
d
T
ec
h
n
o
lo
g
y
o
f
Or
a
n
-
MB
,
B
.
P 1
5
0
5
,
E
lMn
ao
u
er
,
Or
an
-
AL
g
er
ia.
E
m
ail
:
h
o
u
ar
i.a
o
u
ed
@
u
n
iv
-
u
s
to
.
d
z
1.
I
NT
RO
D
UCT
I
O
N
Sev
er
al
ap
p
licatio
n
s
ar
e
p
er
f
o
r
m
ed
n
o
w
ad
a
y
s
b
y
u
s
in
g
U
AVs
s
u
ch
a
s
r
escu
e
o
p
er
atio
n
s
,
d
etec
tio
n
an
d
s
u
r
v
eilla
n
ce
.
Ma
n
y
U
AVs
co
n
f
ig
u
r
atio
n
s
ar
e
estab
l
is
h
ed
i
n
o
r
d
er
to
en
s
u
r
e
s
o
m
e
o
b
j
ec
tiv
es
lik
e
tr
aj
ec
to
r
y
p
lan
i
f
icatio
n
d
is
c
u
s
s
ed
in
[
1
]
.
I
n
t
h
i
s
p
ap
er
is
s
t
u
d
ied
to
f
in
d
a
n
o
p
ti
m
a
l
tr
aj
ec
to
r
y
tr
ac
k
i
n
g
co
n
tr
o
l
o
f
a
tr
i
tilt
-
r
o
to
r
u
s
in
g
an
L
Q
R
co
n
tr
o
ller
.
A
n
e
w
m
o
d
el
o
r
m
at
h
e
m
atica
l
p
r
esen
ta
tio
n
f
o
r
co
n
tr
o
llin
g
a
tilt
r
o
to
r
is
th
e
aim
s
u
b
j
ec
t
in
[
2
]
.
A
r
ec
o
n
f
ig
u
r
ab
le
tr
i
tilt
r
o
to
r
UAV
is
d
esig
n
ed
in
[
3
]
f
o
r
au
to
n
o
m
o
u
s
tr
an
s
i
tio
n
b
et
w
ee
n
t
h
e
VT
OL
an
d
t
h
e
f
i
x
ed
w
i
n
g
f
li
g
h
t
m
o
d
es
b
y
e
m
p
lo
y
i
n
g
t
h
e
d
ir
ec
t
lo
n
g
it
u
d
in
al
ac
tu
a
tio
n
tech
n
iq
u
es.
I
n
[
4
]
a
d
ev
elo
p
m
en
t
o
f
a
q
u
ad
r
o
to
r
h
a
v
in
g
a
tilt
w
i
n
g
m
ec
h
an
i
s
m
u
s
i
n
g
an
L
Q
R
an
d
s
lid
i
n
g
m
o
d
e
co
n
tr
o
ller
f
o
r
s
ettli
n
g
t
h
e
attitu
d
e
an
d
th
e
altit
u
d
e
ar
e
p
r
esen
ted
v
ia
s
i
m
u
latio
n
s
.
A
p
r
o
p
o
s
ed
d
esig
n
s
in
[
5
]
in
co
r
p
o
r
ates
ad
v
an
ta
g
e
o
u
s
s
tr
u
ct
u
r
al
f
ea
tu
r
es
w
h
ic
h
en
h
a
n
ce
s
th
e
m
a
n
e
u
v
er
ab
ilit
y
o
f
t
h
e
r
o
to
r
cr
af
t,
s
o
m
e
n
e
w
tec
h
n
ics
ar
e
d
e
v
el
o
p
ed
s
p
ec
ially
f
o
r
h
o
v
er
in
g
c
o
n
tr
o
l
s
u
c
h
a
n
o
n
l
in
ea
r
s
tate
f
ee
d
b
ac
k
co
n
tr
o
ller
w
h
ic
h
i
s
p
r
o
v
ed
b
y
n
u
m
er
ic
al
s
i
m
u
latio
n
s
in
[
6
]
,
th
r
u
s
t
v
ec
to
r
i
n
g
tech
n
iq
u
e
w
i
th
t
h
e
h
i
g
h
est
lev
e
l
o
f
f
le
x
ib
ilit
y
,
m
a
n
e
u
v
er
ab
ili
t
y
a
n
d
m
i
n
i
m
u
m
r
eq
u
ir
e
m
en
t
o
f
p
o
w
er
is
d
is
c
u
s
s
ed
i
n
[
7
]
,
u
s
in
g
a
b
ac
k
s
tep
p
in
g
tech
n
iq
u
e
to
ac
h
iev
e
m
o
d
e
tr
an
s
it
io
n
co
n
tr
o
l
o
f
t
h
e
air
cr
af
t
w
a
s
th
e
s
u
b
j
ec
t
o
f
[
8
]
f
o
r
th
e
ab
ilit
y
o
f
h
i
g
h
s
p
ee
d
f
o
r
w
ar
d
f
li
g
h
t.
Oth
er
p
ap
er
r
e
s
ea
r
ch
es
ar
e
d
ea
led
w
ith
e
x
p
er
i
m
en
tal
i
m
p
le
m
e
n
tatio
n
o
f
c
o
n
tr
o
l
tech
n
ic
s
th
a
t
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.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
6
3
0
9
-
6
3
1
8
6310
w
h
at
w
e
s
ee
in
[
9
]
w
h
ic
h
p
r
esen
t
a
d
esi
g
n
an
d
v
er
i
f
icatio
n
o
f
a
h
y
b
r
id
v
er
tical
tak
eo
f
f
an
d
lan
d
in
g
U
A
V,
o
th
er
tech
n
ics
o
f
tr
aj
ec
to
r
y
p
l
an
i
f
icatio
n
a
n
d
p
ath
-
f
o
llo
w
in
g
g
u
id
a
n
ce
s
u
ch
th
e
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
i
s
d
is
cu
s
s
ed
in
[
1
0
]
ai
m
i
n
g
to
g
e
n
er
ate
r
ef
er
en
ce
s
f
o
r
a
lo
w
le
v
el
attit
u
d
e
co
n
tr
o
lle
r
f
o
r
tr
ac
k
in
g
a
p
r
ec
o
m
p
iled
tr
aj
ec
to
r
y
.
A
lo
n
g
er
f
li
g
h
t
t
i
m
e
i
s
o
n
e
o
f
th
e
m
o
s
t
co
n
s
tr
ain
t
s
th
a
t
h
as
t
o
b
ee
n
f
u
l
f
illed
b
y
a
n
U
A
V,
c
o
m
p
le
x
it
y
o
f
d
esig
n
an
d
m
ath
e
m
at
ical
m
o
d
el,
s
ize
an
d
co
s
t
m
u
s
t
b
e
r
esp
ec
ted
f
o
r
an
y
U
A
V
p
r
o
j
ec
t
[
1
1
]
,
f
o
r
th
at
th
e
tr
ir
o
to
r
is
th
e
id
ea
l
s
o
lu
tio
n
f
o
r
v
ar
io
u
s
p
r
o
j
ec
t a
n
d
m
is
s
i
o
n
s
[
1
2
]
.
Du
e
to
u
n
p
air
ed
r
o
to
r
a
y
a
w
in
g
m
o
m
e
n
t
is
g
e
n
er
ated
b
y
t
h
e
r
ea
ctio
n
t
o
r
q
u
e,
f
o
r
s
o
lv
i
n
g
th
is
p
r
o
b
lem
w
e
p
r
o
p
o
s
e
in
o
u
r
p
ap
er
to
u
s
e
t
h
e
ti
lti
n
g
a
n
g
les
o
f
th
e
t
w
o
f
r
o
n
t
m
o
to
r
s
d
if
f
e
r
en
tiall
y
.
I
n
[
1
3
]
a
n
e
w
m
e
th
o
d
f
o
r
co
n
tr
o
llin
g
tr
i
r
o
to
r
-
t
y
p
e
u
n
m
an
n
ed
ae
r
ial
v
eh
ic
les
(
U
A
V)
ad
ap
ted
f
r
o
m
th
e
SE
(
3
)
n
o
n
li
n
ea
r
g
eo
m
et
r
ic
m
eth
o
d
f
o
r
q
u
ad
r
o
to
r
-
t
y
p
e
UA
V.
I
n
o
r
d
er
to
en
s
u
r
e
a
g
o
o
d
f
le
x
ib
ilit
y
,
ad
ap
tab
ilit
y
a
n
d
b
etter
co
n
tr
o
l
ef
f
ec
t,t
h
e
a
u
th
o
r
s
o
f
[
1
4
]
h
ad
u
s
ed
a
g
e
n
etic
alg
o
r
ith
m
f
o
r
o
p
ti
m
izi
n
g
P
I
D
p
ar
am
e
ter
s
a
P
I
D
co
n
tr
o
ller
i
s
d
esi
g
n
ed
f
o
r
a
d
ec
o
u
p
led
MI
MO
s
y
s
te
m
u
s
i
n
g
Kh
ar
iti
n
o
v
’
s
t
h
eo
r
e
m
f
o
r
tu
n
i
n
g
P
I
D
p
ar
am
e
tr
s
in
[
1
5
]
.
A
h
m
ad
et
al
.,
[
1
6
]
tr
y
to
co
m
p
ar
e
th
e
p
er
f
o
r
m
an
ce
o
f
s
i
m
ilta
n
eo
u
s
p
er
tu
r
b
atio
n
s
s
t
o
ch
asti
c
ap
p
r
o
x
i
m
atio
n
(
SP
SA
)
b
ased
m
et
h
o
d
s
.
I
n
o
r
d
er
to
tu
n
e
th
e
P
I
D
co
n
tr
o
ller
a
m
e
th
o
d
i
s
d
ev
elo
p
ed
in
[
1
7
]
b
ased
o
n
ad
ap
tiv
e
s
af
e
e
x
p
er
i
m
en
ta
tio
n
d
y
n
a
m
ic
s
(
A
SED)
.
I
n
[
1
8
]
a
co
m
p
ac
t
tr
ico
p
ter
co
n
f
ig
u
r
a
tio
n
tilt
-
r
o
to
r
u
n
m
a
n
n
ed
ae
r
ial
v
eh
icle
w
it
h
f
u
ll
m
o
d
es
o
f
f
lig
h
t
f
r
o
m
t
h
e
r
o
to
r
m
o
d
e
to
t
h
e
f
ix
ed
w
i
n
g
m
o
d
e
an
d
v
ice
v
er
s
a.
Fo
r
en
ab
li
n
g
a
n
in
telli
g
en
t
s
elec
tio
n
o
f
co
n
tr
o
l
s
w
itch
,
a
F
u
zz
y
L
o
g
ic
Sl
id
in
g
Mo
d
e
C
o
n
tr
o
ll
er
is
ad
o
p
ted
f
o
r
a
T
iltro
to
r
air
cr
af
t;
a
n
e
x
p
er
i
m
e
n
tal
v
er
if
i
ca
tio
n
o
f
r
eliab
ilit
y
f
o
r
th
i
s
co
n
tr
o
ller
i
s
d
is
c
u
s
s
e
d
in
[
1
9
,
20
].
I
n
s
ec
tio
n
t
w
o
w
e
w
i
ll
g
i
v
e
an
o
v
er
v
ie
w
o
n
th
e
d
esi
g
n
o
f
o
u
r
tr
i
tilt
-
r
o
to
r
,
co
n
tr
o
l
s
tr
ateg
ie
s
w
i
ll
b
e
d
etailed
i
n
s
ec
t
io
n
f
o
u
r
t
o
co
n
tr
o
llin
g
att
itu
d
e
a
n
d
tr
a
n
s
latio
n
al
m
o
t
io
n
f
o
r
o
u
r
tilt
-
r
o
to
r
u
s
i
n
g
th
e
m
at
h
e
m
atica
l r
ep
r
esen
ta
tio
n
d
is
c
u
s
s
ed
in
s
ec
tio
n
t
h
r
ee
.
2.
T
RI
-
RO
T
O
R
AIRP
L
AN
E
D
E
SCR
I
P
T
I
O
N
T
h
e
tr
i
tilt
-
r
o
to
r
is
in
T
f
o
r
m
lik
e
d
ep
icted
in
Fig
u
r
e
1
is
co
m
p
o
s
ed
o
f
t
w
o
f
r
o
n
t
m
o
to
r
s
M
FR
,
M
FL
an
d
a
th
ir
d
m
o
to
r
in
th
e
r
ea
r
M
B
.
Ou
r
tr
ir
o
to
r
m
u
s
t
b
e
ab
le
to
t
ak
e
-
o
f
f
v
er
ticall
y
an
d
tr
an
s
it
t
o
co
n
v
en
tio
n
al
f
li
g
h
t
an
d
b
e
ab
le
to
r
etu
r
n
to
h
o
v
er
m
o
d
e
f
o
r
lan
d
in
g
.
T
h
e
VT
OL
m
o
tio
n
is
estab
lis
h
ed
b
y
v
er
ticall
y
ad
j
u
s
t
th
e
th
r
u
s
t o
f
th
e
t
h
r
ee
r
o
to
r
s
in
o
r
d
er
t
o
f
u
lf
ill t
h
e
d
esire
d
altitu
d
e
af
ter
co
m
p
e
n
s
ati
n
g
th
e
g
r
av
it
y
e
f
f
ect
.
T
h
e
lo
n
g
it
u
d
in
al
m
o
tio
n
is
g
en
er
ated
b
y
tilt
i
n
g
t
h
e
f
r
o
n
t
m
o
to
r
s
to
t
h
e
h
o
r
izo
n
tal
p
la
n
e
(
u
n
ti
l
t
h
e
m
o
to
r
s
v
er
tical
ax
i
s
r
ea
ch
th
e
lo
n
g
it
u
d
in
al
b
o
d
y
a
x
is
)
w
it
h
d
ec
r
ea
s
i
n
g
th
e
r
o
tatio
n
s
p
ee
d
o
f
th
e
r
ea
r
m
o
to
r
,
w
h
ile
r
ea
c
h
in
g
t
h
e
air
p
lan
e
m
o
d
e
t
h
e
r
ea
r
m
o
to
r
is
to
tall
y
s
to
p
p
ed
.
T
h
e
r
o
ll
m
o
ti
o
n
is
co
n
tr
o
lled
b
y
m
ak
in
g
a
th
r
u
s
t
d
i
f
f
er
en
ce
b
et
w
ee
n
t
h
e
t
w
o
f
r
o
n
t
m
o
to
r
s
;
o
th
er
w
is
e
t
h
e
r
ea
r
m
o
to
r
is
u
s
ed
to
s
tab
ilize
th
e
p
itch
m
o
tio
n
i
n
th
e
tr
a
n
s
it
io
n
p
h
ase
s
f
r
o
m
h
elico
p
t
er
m
o
d
e
to
air
cr
af
t
m
o
d
e
an
d
v
ice
v
er
s
a
b
y
co
m
p
e
n
s
at
in
g
t
h
e
f
o
r
ce
g
e
n
er
ated
b
y
th
e
f
r
o
n
t
m
o
to
r
s
,
t
h
e
y
a
w
m
o
tio
n
i
s
co
n
tr
o
lled
b
y
t
ilti
n
g
t
h
e
t
w
o
f
r
o
n
t
m
o
to
r
s
in
d
i
f
f
er
e
n
t d
ir
ec
tio
n
with
t
h
e
s
a
m
e
an
g
le
s
o
w
e
ca
n
g
en
er
ate
a
to
r
q
u
e
ab
o
u
t th
e
y
a
w
ax
is
.
Fig
u
r
e
1
.
T
r
i tilt
-
r
o
to
r
c
o
n
f
i
g
u
r
atio
n
3.
M
AT
H
E
M
AT
I
CA
L
M
O
DE
L
I
N
G
Gen
er
all
y
,
all
m
o
v
i
n
g
o
b
j
ec
ts
in
s
p
ac
e
ar
e
r
ef
er
r
ed
b
y
t
w
o
f
r
a
m
e
s
,
o
n
e
f
i
x
ed
o
n
t
h
e
b
o
d
y
o
f
th
e
o
b
j
ec
t
(
B
F)
an
d
th
e
s
ec
o
n
d
n
a
m
ed
ea
r
th
f
r
a
m
e
(
E
F)
l
ik
e
d
ep
icted
in
Fi
g
u
r
e
1
.
T
o
b
e
ab
le
to
d
esig
n
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
P
I
D
vs LQR
co
n
tr
o
ller
fo
r
tilt
r
o
to
r
a
ir
p
la
n
e
(
A
o
u
ed
Ho
u
a
r
i
)
6311
a
co
n
tr
o
l
s
tr
ateg
y
,
a
s
i
m
p
li
f
ie
d
m
at
h
e
m
atica
l
r
ep
r
esen
tatio
n
o
f
th
e
tr
i
-
r
o
to
r
is
n
ee
d
ed
.
Du
e
to
th
e
f
ac
t
t
h
at
s
o
m
e
s
tates
ar
e
m
ea
s
u
r
ed
in
(
B
F)
w
h
ile
s
o
m
e
o
th
er
s
ar
e
m
ea
s
u
r
ed
i
n
(
E
F)
a
f
r
a
m
e
tr
an
s
f
o
r
m
atio
n
m
atr
ix
T
w
il
l b
e
u
s
ed
to
en
s
u
r
e
tr
an
s
f
o
r
m
atio
n
b
et
w
ee
n
f
r
a
m
e
s
.
=
[
−
+
+
−
]
(
1
)
W
h
er
e
th
e
ab
b
r
ev
iatio
n
s
C
α
,
S
α
ar
e
u
s
ed
i
n
s
tead
o
f
C
os
α
,
Sin
α
.
T
o
d
ev
elo
p
th
e
d
y
n
a
m
ic
m
o
d
el
o
f
th
e
tr
i
tilt
-
r
o
to
r
w
e
co
n
s
id
er
th
at
th
e
s
tr
u
ct
u
r
e
o
f
o
u
r
UAV
is
r
ig
id
[
1
7
]
,
th
e
d
y
n
a
m
ic
o
f
th
e
ac
tu
ato
r
s
is
n
eg
lec
ted
ass
u
m
i
n
g
th
a
t
w
e
h
av
e
v
er
y
f
ast
ac
tu
ato
r
s
[
7
]
.
Du
e
to
lo
w
v
elo
cit
y
t
h
e
d
r
ag
ef
f
ec
t
i
s
as
s
u
m
ed
n
eg
l
ig
ib
le
f
o
r
b
o
th
la
ter
al
a
n
d
lo
n
g
it
u
d
in
al
m
o
tio
n
s
.
U
s
in
g
Ne
w
to
n
-
E
u
ler
f
o
r
m
ali
s
m
w
e
ca
n
r
ep
r
ese
n
t
th
e
eq
u
atio
n
s
o
f
m
o
tio
n
i
n
b
o
d
y
f
i
x
ed
f
r
a
m
e
(
BF
)
as f
o
llo
w
s
[
1
8
]
:
∑
=
̈
+
̇
×
(
̇
)
(
2
)
∑
=
Ω
̈
+
Ω
̇
×
(
Ω
̇
)
(
3
)
W
ith
:
th
e
E
u
ler
a
n
g
le
o
f
th
e
ti
lt
r
o
to
r
is
d
ef
in
ed
as
=
[
,
,
]
,
w
h
er
e
θ
th
e
p
itch
an
g
le
d
ef
i
n
ed
ar
o
u
n
d
t
h
e
y
b
ax
is
,
ϕ
th
e
r
o
ll
a
n
g
le
d
e
f
in
ed
a
r
o
u
n
d
t
h
e
x
b
ax
is
a
n
d
ψ
th
e
y
a
w
a
n
g
le
d
ef
in
ed
ar
o
u
n
d
t
h
e
z
b
ax
is
,
t
h
e
p
o
s
itio
n
o
f
th
e
tilt
r
o
t
o
r
ac
co
r
d
in
g
to
th
e
ea
r
t
h
f
r
a
m
e
is
d
ef
i
n
ed
as
P
e
=
[
x
,
y
,
z
]
,
=
[
]
th
e
ex
ter
n
al
f
o
r
ce
ac
ted
o
n
th
e
tilt
r
o
to
r
,
=
[
]
th
e
r
o
tatio
n
al
to
r
q
u
e
o
f
th
e
tilt
r
o
to
r
,
m
th
e
to
tal
m
a
s
s
o
f
t
h
e
b
o
d
y
an
d
=
[
]
is
th
e
m
o
m
e
n
t o
f
i
n
er
tia
o
f
t
h
e
b
o
d
y
.
T
h
e
ex
ter
n
al
f
o
r
ce
s
an
d
t
h
e
r
o
tatio
n
al
to
r
q
u
es
ac
ted
o
n
th
e
titl
r
o
to
r
ex
p
r
ess
ed
in
b
o
d
y
f
r
a
m
e
ar
e
d
ep
icted
in
th
e
eq
u
atio
n
ab
o
v
e
[
2
1
]
:
=
[
+
0
+
+
]
(
4
)
=
[
1
(
−
)
1
(
+
)
−
2
3
(
−
)
]
(
5
)
w
it
h
:
α
L
,
α
R
th
e
til
t
an
g
le
s
o
f
th
e
le
f
t
an
d
t
h
e
r
i
g
h
t
f
r
o
n
t
m
o
to
r
s
r
esp
ec
tiv
el
y
.
Si
n
ce
th
er
e
ar
e
n
o
f
o
r
ce
s
ac
ted
alo
n
g
t
h
e
y
b
ax
is
in
t
h
e
b
o
d
y
f
r
a
m
e,
th
e
m
o
tio
n
alo
n
g
t
h
i
s
ax
i
s
w
ill
n
o
t b
e
co
n
s
id
er
ed
.
T
h
e
f
in
al
eq
u
at
io
n
s
o
f
m
o
tio
n
ac
co
r
d
in
g
to
Ne
w
to
n
-
E
u
ler
f
o
r
m
alis
m
w
il
l b
e:
̈
=
(
+
)
(
6
)
̈
=
(
)
−
(
7
)
̈
=
(
−
)
̇
̇
+
(
8
)
̈
=
(
−
)
̇
̇
+
(
9
)
̈
=
(
−
)
̇
̇
+
(
1
0
)
W
ith:
[
]
=
[
1
+
+
+
(
+
)
−
2
2
(
−
)
3
(
−
)
]
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.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
6
3
0
9
-
6
3
1
8
6312
T
h
e
f
o
r
ce
g
en
er
ated
b
y
ea
ch
m
o
to
r
is
p
r
o
p
o
r
tio
n
al
w
it
h
its
s
u
p
p
l
y
v
o
ltag
e
F
=
k
t
∗
V
w
i
th
k
t
th
e
li
f
t c
o
ef
f
icie
n
t,
u
s
i
n
g
t
h
is
a
s
s
u
m
p
tio
n
w
e
ca
n
w
r
ite
t
h
e
n
e
w
v
ir
tu
a
l c
o
n
tr
o
l lik
e
i
n
eq
u
at
i
o
n
b
elo
w
:
[
]
=
[
1
cos
+
cos
s
in
+
s
in
+
(
cos
+
cos
)
−
2
2
(
cos
−
cos
)
3
(
s
in
−
s
in
)
]
(
1
1
)
4.
CO
NT
RO
L
ST
R
AT
E
G
I
E
S
I
n
liter
at
u
r
e
s
o
m
e
p
ar
a
m
eter
s
h
a
v
e
to
b
ee
n
v
er
if
i
ed
an
d
li
m
ited
i
n
ac
ce
p
tab
le
r
an
g
e
s
i
n
clu
d
i
n
g
o
v
er
s
h
o
o
t,
r
esp
o
n
s
e
ti
m
e
a
n
d
co
n
tr
o
l
p
r
ec
is
io
n
,
th
e
r
ec
o
m
m
en
d
ed
ac
ce
p
tab
le
r
an
g
e
f
o
r
th
e
o
v
er
s
h
o
o
t
is
s
et
to
n
o
t
ex
ce
ed
10%
an
d
th
e
co
n
tr
o
l
p
r
ec
is
io
n
to
n
o
t
ex
ce
ed
±
1%
[
1
9
]
,
th
e
r
esp
o
n
s
e
ti
m
e
i
s
d
ep
en
d
o
n
th
e
s
i
ze
o
f
th
e
U
A
V
an
d
th
e
q
u
alit
y
o
f
ac
tu
ato
r
s
u
s
ed
.
Du
e
to
its
s
i
m
p
li
cit
y
a
m
u
ltip
le
P
I
D’
s
w
er
e
ad
o
p
ted
f
o
r
s
tab
ilizin
g
th
e
U
AV
i
n
h
o
v
er
m
o
d
e
f
o
r
i
n
d
o
o
r
p
er
f
o
r
m
i
n
g
,
th
e
r
o
le
o
f
th
i
s
co
n
tr
o
ller
i
s
to
m
in
i
m
ize
a
co
s
t
f
u
n
ctio
n
b
y
ad
j
u
s
tin
g
th
e
i
n
p
u
t
v
al
u
e
in
o
r
d
er
to
r
e
d
u
ce
th
e
er
r
o
r
b
etw
ee
n
th
e
d
esire
d
an
d
t
h
e
m
ea
s
u
r
e
d
v
alu
es [
1
9
]
.
T
h
e
d
y
n
a
m
ic
m
o
d
el
p
r
ese
n
ted
in
p
r
ev
io
u
s
s
ec
tio
n
w
ill
b
e
tr
a
n
s
f
o
r
m
ed
i
n
to
a
li
n
ea
r
s
tate
s
p
ac
e
m
o
d
el
ass
u
m
in
g
th
at
f
o
r
a
s
m
all
tilt
in
g
a
n
g
le
c
os
(
α
)
=
1
an
d
s
in
(
α
)
=
α
an
d
ass
u
m
in
g
t
h
at
t
h
e
m
o
to
r
s
w
ill
b
e
r
u
n
n
i
n
g
at
a
v
o
ltag
e
n
ea
r
th
eir
h
o
v
er
v
o
lta
g
e
V
ho
v
[
1
8
]
,
w
i
th
a
c
h
o
s
en
s
tate
a
n
d
co
n
tr
o
l v
ec
to
r
:
=
[
̇
̇
̇
̇
̇
]
;
=
[
]
{
̇
=
+
=
+
(
1
2
)
w
it
h
:
=
[
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
]
;
=
[
0
0
0
0
0
3
−
3
0
0
0
0
0
0
0
0
1
1
−
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
ℎ
−
3
ℎ
0
0
0
0
0
0
0
0
ℎ
ℎ
]
=
[
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
]
;
=
0
.
A
ll t
h
e
p
ar
a
m
eter
s
u
s
ed
d
u
r
i
n
g
th
e
d
y
n
a
m
ic
m
o
d
el
i
n
g
ar
e
cited
in
th
e
T
ab
le
1
:
T
ab
le
1
.
P
ar
am
eter
s
o
f
T
ilt
r
o
to
r
P
a
r
a
me
t
e
r
s
V
a
l
u
e
s
3
0
.
05
m
2
1
.
2
m
1
0
.
5
m
0
.
7
0
.
5
0
.
1946
kg
.
2
0
.
1271
kg
.
2
0
.
2593
kg
.
2
2
.
5
kg
3
0
.
05
m
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
P
I
D
vs LQR
co
n
tr
o
ller
fo
r
tilt
r
o
to
r
a
ir
p
la
n
e
(
A
o
u
ed
Ho
u
a
r
i
)
6313
Usi
n
g
t
h
i
s
s
tate
s
p
ac
e
r
ep
r
esen
tatio
n
,
a
P
I
D
p
ar
allel
s
tr
u
ctu
r
e
f
o
r
m
u
lated
b
y
t
h
e
eq
u
atio
n
b
elo
w
i
s
u
s
ed
f
o
r
co
n
tr
o
lli
n
g
o
u
r
U
AV:
(
)
=
(
)
+
∫
(
)
0
+
̇
(
)
(
1
1
)
w
it
h
:
;
an
d
p
r
o
p
o
r
tio
n
al,
in
teg
r
al
a
n
d
d
er
iv
ati
v
e
g
ain
s
r
e
s
p
ec
tiv
el
y
a
n
d
(
)
is
t
h
e
er
r
o
r
b
et
w
ee
n
th
e
d
esire
d
an
d
th
e
m
ea
s
u
r
ed
v
alu
e
s
.
T
h
e
P
I
D
p
ar
am
eter
s
w
il
l
b
e
tu
n
ed
u
s
i
n
g
Z
ie
g
ler
Nich
o
ls
tec
h
n
iq
u
e
a
s
f
o
llo
w
s
[
2
2
,
2
3
]:
W
e
h
av
e
to
u
s
e
o
n
l
y
p
r
o
p
o
r
tio
n
al
f
ee
d
b
ac
k
co
n
tr
o
l.
R
ed
u
ce
t
h
e
in
te
g
r
ato
r
an
d
d
er
iv
ati
v
e
g
ai
n
s
to
ze
r
o
.
I
n
cr
ea
s
e
f
r
o
m
ze
r
o
to
s
o
m
e
cr
itical
v
al
u
e
=
at
w
h
ic
h
o
s
cilla
tio
n
s
o
cc
u
r
.
No
te
th
e
v
al
u
e
an
d
th
e
co
r
r
esp
o
n
d
in
g
p
er
io
d
o
f
s
u
s
tai
n
ed
o
s
cillatio
n
s
,
.
T
h
e
co
n
tr
o
ller
g
ai
n
s
ar
e
ca
lc
u
lated
lik
e
in
T
ab
le
2
.
B
y
ap
p
ly
in
g
th
e
Z
ieg
ler
Nich
o
l
s
tec
h
n
iq
u
e
c
ited
ab
o
v
e
an
d
ac
co
r
d
in
g
to
T
a
b
le
2
th
e
P
I
Ds
p
ar
am
eter
s
f
o
r
ea
ch
ch
a
n
n
e
l
a
r
e
ca
lcu
lated
an
d
m
e
n
tio
n
n
ed
in
T
ab
le
3
.
A
i
m
i
n
g
to
p
er
f
o
r
m
a
v
er
tical
tak
e
-
o
f
f
m
o
tio
n
at
(
Z
=
2
m
)
w
it
h
an
eq
u
ilib
r
i
u
m
p
o
in
t
(
ψ
=
ϕ
=
θ
=
0
r
a
d
;
X
=
0m
;
V
ho
v
=
10
)
,
th
e
s
i
m
u
lat
io
n
r
es
u
lt o
f
t
h
e
P
I
D
co
n
tr
o
ller
ar
e
d
ep
icted
in
Fig
u
r
e
2
.
T
ab
le
2
.
Z
ieg
ler
n
ic
h
o
ls
P
I
D
g
ain
s
ca
lc
u
lat
io
n
P
I
D
Ty
p
e
s
k
p
i
=
/
d
=
/
P
0
.
5
∞
0
PI
0
.
4
5
/
1
.
2
0
P
I
D
0
.
6
/
2
/
2
T
ab
le
3
.
P
I
D
p
a
r
am
eter
s
f
o
r
ea
ch
ch
a
n
n
e
l
P
I
D
Ty
p
e
s
k
p
R
o
l
l
0
.
0
3
6
0
.
0
0
1
0
.
1
8
9
P
i
t
c
h
0
.
0
3
6
0
.
0
0
1
7
0
.
1
9
2
Y
a
w
0
.
0
4
8
0
.
0
0
2
0
.
2
5
2
A
l
t
i
t
u
d
e
2
2
.
2
1
7
.
1
9
1
6
.
8
4
L
o
n
g
i
t
u
d
i
n
a
l
2
.
8
7
0
.
3
3
6
.
0
6
Fig
u
r
e
2
.
V
er
tical
tak
e
-
o
f
f
m
o
tio
n
P
I
D
o
u
tp
u
ts
(l
e
f
t)
,
V
er
tical
tak
e
-
o
f
f
m
o
tio
n
P
I
D
in
p
u
ts
(r
ig
h
t)
(
Z
=
2
m
;
ψ
=
ϕ
=
θ
=
0
r
a
d
;
X
=
0m
;
V
ho
v
=
10
)
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.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
6
3
0
9
-
6
3
1
8
6314
Fro
m
Fi
g
u
r
e
2
(
L
e
f
t)
,
w
e
ca
n
r
esu
m
e
t
h
at
o
u
r
P
I
D
is
p
er
f
o
r
m
i
n
g
g
o
o
d
ag
ai
n
s
t
th
e
altit
u
d
e
r
ef
er
en
ce
ch
an
g
es
tak
i
n
g
i
n
to
ac
co
u
n
t a
n
o
v
er
s
h
o
o
t o
f
17%
w
h
ic
h
d
o
n
’
t a
l
lo
w
o
u
r
U
AV
to
p
er
f
o
r
m
a
n
i
n
d
o
o
r
r
ef
er
en
ce
tr
ac
k
in
g
,
th
e
r
esp
o
n
s
e
ti
m
e
i
s
ab
o
u
t
8
.
5
s
e
c
.
T
h
e
tw
o
f
r
o
n
t
m
o
to
r
s
h
av
e
a
h
o
v
er
i
n
g
v
o
ltag
e
o
f
V
ho
v
=
10
vol
t
an
d
ca
n
atta
in
2
5
v
o
lt
s
m
ax
i
m
u
m
s
o
r
eg
ar
d
in
g
to
Fi
g
u
r
e
2
(
R
ig
h
t)
,
th
e
P
I
D
g
e
n
er
ate
t
h
e
n
e
ce
s
s
ar
y
v
o
lta
g
e
f
o
r
th
e
d
es
ir
ed
m
o
tio
n
r
esp
ec
ti
n
g
th
e
m
ax
i
m
u
m
v
al
u
e
a
n
d
r
et
u
r
n
to
h
o
v
er
in
g
v
o
lta
g
e
a
f
ter
th
e
s
tead
y
s
tate
i
s
ac
h
iev
ed
w
h
er
ea
s
th
e
r
ea
r
m
o
to
r
is
u
s
ed
j
u
s
t
f
o
r
s
tab
ilizi
n
g
th
e
p
itch
m
o
m
e
n
t
an
d
its
co
n
tr
ib
u
tio
n
i
n
VT
OL
m
o
tio
n
i
s
m
in
i
m
,
t
h
e
m
ax
i
m
u
m
s
u
p
p
lied
v
o
ltag
e
d
ep
en
d
o
n
th
e
lo
ca
tio
n
w
h
er
e
i
s
p
l
ac
ed
ac
co
r
d
in
g
to
th
e
ce
n
ter
o
f
g
r
a
v
it
y
o
f
t
h
e
T
iltr
o
to
r
(
th
e
r
ea
r
m
o
to
r
is
p
l
ac
ed
f
ar
f
r
o
m
t
h
e
ce
n
ter
o
f
g
r
av
it
y
,
in
t
h
e
f
ig
u
r
e
ab
o
v
e
th
e
r
ea
r
m
o
to
r
v
o
lta
g
e
attain
3
.
3
v
o
lts
f
o
r
s
tab
iliz
in
g
t
h
e
altit
u
d
e
w
h
ich
i
s
lo
w
er
th
a
n
th
e
t
w
o
f
r
o
n
t
m
o
to
r
s
b
ec
au
s
e
o
f
t
h
eir
lo
ca
ti
o
n
(
th
er
e
ar
e
n
ea
r
th
e
ce
n
ter
o
f
g
r
av
it
y
)
)
.
I
n
a
s
ec
o
n
d
te
s
t,
w
e
tr
y
to
p
er
f
o
r
m
a
lo
n
g
i
tu
d
i
n
al
m
o
tio
n
o
f
(
X
=
4m
)
at
an
eq
u
ilib
r
i
u
m
p
o
in
t
(
ψ
=
ϕ
=
θ
=
0
r
a
d
;
Z
=
2m
;
V
ho
v
=
10
)
lik
e
illu
s
tr
ate
in
Fi
g
u
r
e
3
.
Fro
m
Fi
g
u
r
e
3
,
o
u
r
UA
V
w
il
l
h
av
e
th
e
s
a
m
e
p
r
o
b
lem
f
o
r
i
n
d
o
o
r
r
ef
er
en
ce
tr
ac
k
i
n
g
f
o
r
lo
n
g
it
u
d
in
al
m
o
ti
o
n
b
ec
au
s
e
t
h
er
e
is
a
n
o
v
er
s
h
o
o
t
o
f
10%
;
w
e
n
o
tice
also
th
a
t
o
u
r
U
A
V
i
n
t
h
e
lo
n
g
it
u
d
in
al
m
o
tio
n
is
q
u
ick
co
m
p
ar
i
n
g
to
t
h
e
v
er
tical
ta
k
e
-
o
f
f
m
o
tio
n
w
it
h
a
r
esp
o
n
s
e
ti
m
e
ab
o
u
t
6
s
e
c
.
T
h
e
t
w
o
m
o
tio
n
p
er
f
o
r
m
ed
ab
o
v
e
in
d
icate
th
at
th
e
PID
co
n
tr
o
ller
s
ar
e
n
o
t
a
g
o
o
d
co
n
tr
o
ller
f
o
r
i
n
d
o
o
r
r
ef
er
en
ce
tr
ac
k
i
n
g
ac
c
o
r
d
in
g
to
t
h
e
s
i
m
u
lat
io
n
i
n
F
ig
u
r
es
2
an
d
3
b
ec
au
s
e
o
f
th
e
s
tr
o
n
g
co
u
p
lin
g
o
f
t
h
e
U
A
V
s
y
s
te
m
d
y
n
a
m
ics,
i
n
o
r
d
er
to
s
o
lv
e
th
i
s
p
r
o
b
le
m
,
w
e
h
a
v
e
to
c
h
o
o
s
e
an
o
th
er
co
n
tr
o
ller
th
a
t
tak
e
s
in
to
ac
co
u
n
t
all
t
h
e
c
o
u
p
li
n
g
e
f
f
ec
ts
o
f
t
h
e
U
A
V
d
y
n
a
m
ics,
t
h
e
m
o
s
t
w
ell
-
k
n
o
w
n
r
eg
u
lato
r
f
o
r
lin
ea
r
s
y
s
te
m
s
wh
ich
ca
n
p
er
f
o
r
m
w
ell
f
o
r
in
d
o
o
r
m
o
tio
n
,
m
i
n
i
m
izi
n
g
th
e
co
s
t
f
u
n
ct
io
n
an
d
g
i
v
e
u
s
m
o
r
e
f
ea
s
ib
le
s
o
lu
t
io
n
o
f
t
h
is
p
r
o
b
lem
is
a
t
h
e
L
QR
co
n
t
r
o
ller
.
Usi
n
g
a
s
i
n
g
le
L
QR
co
n
t
r
o
ller
w
ill
h
elp
u
s
to
f
ee
d
b
ac
k
all
th
e
s
tate
s
in
o
n
e
s
tep
(
b
ased
o
n
m
atr
i
x
ca
lcu
l
u
s
)
to
s
elec
t
th
e
d
esire
d
o
u
tp
u
t
h
o
w
e
v
er
in
P
I
D
co
n
tr
o
ller
w
e
h
av
e
u
s
ed
a
m
u
ltip
le
P
I
D’
s
b
ec
au
s
e
th
a
t
th
e
P
I
D
ca
n
co
v
er
j
u
s
t
o
n
e
ch
an
n
el
(
b
ased
o
n
s
ca
lar
ca
lcu
lu
s
)
s
o
f
iv
e
P
I
D’
s
ar
e
u
s
ed
f
o
r
co
m
p
ar
in
g
all
th
e
o
u
tp
u
ts
w
i
th
t
h
e
o
u
tp
u
ts
g
en
er
ated
f
r
o
m
L
Q
R
co
n
tr
o
ller
.
Fig
u
r
e
3
.
L
o
n
g
itu
d
i
n
al
m
o
tio
n
P
I
D
o
u
tp
u
ts
(l
e
f
t)
,
l
o
n
g
i
tu
d
i
n
al
m
o
tio
n
P
I
D
in
p
u
t
s
(r
ig
h
t)
(
Z
=
2
m
;
ψ
=
ϕ
=
θ
=
0
r
a
d
;
X
=
4m
;
V
ho
v
=
10
)
T
h
e
L
Q
R
co
n
tr
o
ller
is
u
s
ed
t
o
o
b
tain
t
h
e
b
est
co
n
tr
o
l
s
eq
u
en
ce
t
h
at
m
i
n
i
m
izes
t
h
e
co
s
t
f
u
n
ctio
n
d
etailed
in
th
e
eq
u
at
io
n
b
elo
w
[
1
4
,
2
4
,
an
d
2
5
]
,
u
s
in
g
t
h
e
s
ta
te
s
p
ac
e
r
ep
r
esen
tatio
n
i
n
(
1
2
)
:
=
∫
(
)
(
)
+
(
)
(
)
∞
0
(
1
2
)
w
h
er
e
R
is
a
p
o
s
itiv
e
d
ef
in
ite
w
eig
h
tin
g
m
a
tr
ix
an
d
Q
is
a
w
ei
g
h
tin
g
m
atr
i
x
th
at
ca
n
b
e
p
o
s
itiv
e
s
e
m
i
-
d
ef
i
n
ite,
U
(
t
)
r
ep
r
esen
ts
th
e
o
p
ti
m
al
co
n
tr
o
l
la
w
d
etailed
i
n
th
e
eq
u
a
tio
n
ab
o
v
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
P
I
D
vs LQR
co
n
tr
o
ller
fo
r
tilt
r
o
to
r
a
ir
p
la
n
e
(
A
o
u
ed
Ho
u
a
r
i
)
6315
(
)
=
−
(
)
=
−
−
1
(
)
(
1
3
)
is
th
e
li
n
ea
r
o
p
ti
m
al
f
ee
d
b
ac
k
g
ain
a
n
d
P
is
th
e
s
o
lu
t
io
n
o
f
R
icca
ti e
q
u
atio
n
r
ep
r
esen
ted
b
y
(
1
7
)
:
+
−
−
1
+
=
0
(
1
4
)
T
h
e
t
w
o
w
ei
g
h
ti
n
g
m
atr
ice
s
h
av
e
to
b
e
tu
n
ed
m
a
n
u
all
y
b
a
s
ed
o
n
t
h
e
p
r
io
r
it
y
o
r
w
eig
h
ti
n
g
o
f
ea
c
h
s
tate
(
Q
m
atr
ix
)
a
n
d
in
p
u
t(
R
m
atr
i
x
)
th
at
I
h
av
e
f
i
x
ed
i
n
o
r
d
er
to
f
in
d
a
co
m
p
r
o
m
i
s
e
b
etw
ee
n
t
h
e
s
tead
y
s
tat
e
p
er
f
o
r
m
a
n
ce
an
d
th
e
ac
tu
a
to
r
s
en
er
g
y
ap
p
lied
r
esp
ec
tin
g
th
e
p
ar
a
m
eter
s
li
m
it
r
an
g
es
d
is
cu
s
s
ed
ab
o
v
e
.
R
es
u
lts
o
f
t
h
e
L
Q
R
s
i
m
u
lat
io
n
f
o
r
a
v
er
tical
ta
k
e
-
o
f
f
(
Z
=
2
m
)
w
it
h
t
h
e
s
a
m
e
o
p
er
atin
g
p
o
in
t
u
s
ed
p
r
ev
io
u
s
l
y
f
o
r
t
h
e
P
I
D
co
n
tr
o
ller
ar
e
p
r
esen
ted
in
Fig
u
r
e
4
.
Fig
u
r
e
4
.
Ver
tical
T
ak
e
-
Of
f
m
o
tio
n
L
Q
R
o
u
tp
u
ts
(l
e
f
t)
, v
er
ti
ca
l T
ak
e
-
Of
f
m
o
t
io
n
L
QR
i
n
p
u
ts
(r
ig
h
t)
(
Z
=
2
m
;
ψ
=
ϕ
=
θ
=
0
r
a
d
;
X
=
0m
;
V
ho
v
=
10
)
I
t
ca
n
b
e
s
ee
n
in
Fig
u
r
e
4
th
at
th
e
o
v
er
s
h
o
o
t
is
r
ed
u
ce
d
to
0%
an
d
th
e
r
ep
o
n
s
e
ti
m
e
to
3
in
s
tead
o
f
17%
an
d
8
.
5
f
o
r
th
e
P
I
D
co
n
tr
o
ller
,
f
r
o
m
t
h
is
r
es
u
lt
w
e
ca
n
co
n
c
lu
d
e
th
at
t
h
e
L
Q
R
co
n
tr
o
ller
is
m
o
r
e
p
o
w
er
f
u
l
t
h
an
th
e
P
I
D
f
o
r
i
n
d
o
o
r
p
er
f
o
r
m
in
g
.
So
m
e
p
er
tu
r
b
atio
n
ill
u
s
tr
ate
s
i
n
Fi
g
u
r
e
4
f
o
r
th
e
r
est
o
f
o
u
tp
u
t
s
b
u
t
w
it
h
n
o
s
ig
n
i
f
ica
n
t
e
f
f
ec
t
o
n
th
e
d
esire
d
m
o
tio
n
,
t
h
ese
s
m
all
p
er
tu
r
b
atio
n
s
h
ig
h
li
g
h
t
t
h
e
s
tr
o
n
g
co
u
p
li
n
g
d
y
n
a
m
ics
o
f
th
e
U
A
V
a
n
d
p
r
o
v
e
th
e
ca
p
ab
ilit
y
o
f
th
e
L
QR
t
o
tak
e
in
to
ac
co
u
n
t
all
t
h
e
co
n
s
tr
ain
t
s
attac
h
ed
to
th
e
d
y
n
a
m
ics co
m
p
le
x
it
y
.
Fo
r
th
e
lo
n
g
itu
d
i
n
al
m
o
tio
n
w
it
h
a
d
esire
d
v
a
lu
e
o
f
(
X
=
4m
)
an
d
a
s
p
ec
i
f
ic
o
p
er
atin
g
p
o
i
n
t
(
ψ
=
ϕ
=
θ
=
0
r
a
d
;
Z
=
2m
)
,
th
e
L
Q
R
co
n
tr
o
ller
s
i
m
u
la
tio
n
r
esu
lts
ar
e
g
iv
e
n
i
n
Fi
g
u
r
e
5
.
C
o
m
p
ar
in
g
to
th
e
r
esp
o
n
s
e
c
h
ar
ac
ter
is
tic
s
o
b
tain
ed
i
n
P
I
D
co
n
tr
o
ller
f
o
r
lo
n
g
i
tu
d
i
n
al
m
o
tio
n
,
th
e
u
s
e
o
f
t
h
e
L
Q
R
co
n
tr
o
ller
is
m
o
r
e
f
ea
s
ib
le
s
u
c
h
th
e
p
er
f
o
r
m
a
n
ce
s
cr
iter
io
n
d
is
cu
s
s
ed
ab
o
v
e
ar
e
s
atis
f
ied
f
o
r
an
o
v
er
s
h
o
o
t
o
f
0%
an
d
a
ti
m
e
r
esp
o
n
s
e
o
f
3s
e
c
.
th
e
y
a
w
m
o
tio
n
is
a
f
f
ec
ted
b
y
th
e
lo
n
g
i
tu
d
i
n
al
m
o
tio
n
b
ec
au
s
e
th
er
e
is
a
s
tr
o
n
g
co
u
p
lin
g
b
et
w
ee
n
th
i
s
t
w
o
d
e
g
r
ee
s
o
f
f
r
ee
d
o
m
s
u
c
h
t
h
e
t
wo
m
o
tio
n
s
ar
e
p
er
f
o
r
m
ed
b
y
t
ilti
n
g
t
h
e
t
w
o
f
r
o
n
t
m
o
to
r
s
,
th
e
ac
t
u
ato
r
s
b
eh
av
io
r
f
o
r
th
e
L
Q
R
co
n
tr
o
ller
is
ill
u
s
tr
ated
in
Fig
u
r
e
5
an
d
w
e
ca
n
r
e
m
ar
k
clea
r
l
y
t
h
a
t
co
m
p
ar
i
n
g
to
th
e
P
I
D
ac
tu
ato
r
s
co
n
tr
o
l
s
ig
n
als
,
th
e
L
Q
R
ac
t
less
ag
g
r
ess
i
v
e
w
h
ich
g
iv
e
u
s
v
er
y
g
o
o
d
co
n
tr
o
l
m
ar
g
i
n
.
W
e
co
n
clu
d
e
th
is
p
ap
er
b
y
a
p
er
f
o
r
m
an
ce
i
n
d
ex
es
co
m
p
ar
is
o
n
f
o
r
b
o
th
co
n
tr
o
ller
s
w
h
ic
h
is
i
llu
s
tr
ated
in
T
ab
le
4
.
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.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
6
3
0
9
-
6
3
1
8
6316
Fig
u
r
e
5
.
L
o
n
g
it
u
d
in
al
m
o
tio
n
L
Q
R
o
u
tp
u
t
s
(f
e
f
t)
,
l
o
n
g
it
u
d
in
al
m
o
tio
n
L
QR
i
n
p
u
t
s
(r
ig
h
t)
(
Z
=
2
m
;
ψ
=
ϕ
=
θ
=
0
r
a
d
;
X
=
4m
;
V
ho
v
=
10
)
T
ab
le
4
.
P
I
D
an
d
L
QR
p
er
f
o
r
m
an
ce
i
n
d
ex
e
s
co
m
p
ar
is
o
n
P
I
D
Ty
p
e
s
P
I
D
V
T
O
L
L
Q
R
V
T
O
L
P
I
D
L
o
n
g
i
t
u
d
i
n
a
l
L
Q
R
L
o
n
g
i
t
u
d
i
n
a
l
O
v
e
r
sh
o
o
t
(
%)
17
0
10
0
R
e
sp
o
n
se
T
i
me
(
se
c
)
8
.
5
3
6
3
C
o
n
t
r
o
l
p
r
e
c
i
s
i
o
n
(
%)
0
.
016
0
.
001
0
.
012
0
.
001
5.
CO
NCL
U
SI
O
N
I
n
t
h
is
p
ap
er
w
e
h
av
e
d
ev
elo
p
ed
a
d
y
n
a
m
ic
m
a
th
e
m
atica
l
m
o
d
el
f
o
r
a
tilt
r
o
to
r
air
p
lan
e
,
ai
m
i
n
g
to
p
er
f
o
r
m
a
v
er
tical
ta
k
e
-
o
f
f
an
d
lo
n
g
it
u
d
i
n
al
m
o
tio
n
s
,
t
w
o
co
n
tr
o
l
tech
n
ics
ar
e
p
r
o
p
o
s
ed
an
d
ap
p
lied
o
n
a
lin
ea
r
d
y
n
a
m
ic
s
m
o
d
el.
T
h
e
s
i
m
u
latio
n
r
es
u
lt
s
o
f
b
o
th
o
f
th
e
co
n
tr
o
ller
s
w
er
e
co
m
p
ar
ed
u
s
i
n
g
s
o
m
e
p
er
f
o
r
m
a
n
ce
in
d
e
x
es
s
u
ch
as
th
e
o
v
er
s
h
o
o
t,
r
esp
o
n
s
e
ti
m
e
an
d
co
n
tr
o
l
p
r
ec
is
io
n
,
th
e
L
Q
R
co
n
tr
o
ller
w
as
m
o
r
e
p
o
w
er
f
u
l
co
m
p
ar
i
n
g
to
P
I
D
co
n
tr
o
ller
in
all
p
er
f
o
r
m
an
ce
in
d
e
x
es
f
o
r
b
o
th
v
e
r
tical
tak
e
-
o
f
f
an
d
lo
n
g
it
u
d
i
n
al
m
o
tio
n
s
.
RE
F
E
R
E
NC
E
S
[1
]
C.
P
a
p
a
c
h
risto
s
,
K.
A
lex
is,
A
.
Tze
s.,
“
L
in
e
a
r
Qu
a
d
ra
ti
c
Op
ti
m
a
l
T
ra
je
c
to
ry
-
T
ra
c
k
in
g
Co
n
tro
l
o
f
a
L
o
n
g
it
u
d
i
n
a
l
T
h
ru
st
V
e
c
to
ri
n
g
-
En
a
b
l
e
d
Un
m
a
n
n
e
d
T
ri
-
T
il
t
Ro
t
o
r,
”
T
h
irty
-
Nin
e
An
n
u
a
l
IEE
E
C
o
n
fer
e
n
c
e
In
d
u
st
ria
l
El
e
c
tro
n
ics
Soc
iety
,
p
p
.
4
1
7
4
-
4
1
7
9
,
2
0
1
3
.
[2
]
D.
A
n
h
T
a
,
I.
F
a
n
t
o
n
i,
R.
L
o
z
a
n
o
.
,
“
M
o
d
e
li
n
g
a
n
d
Co
n
tr
o
l
o
f
a
T
il
t
tri
-
ro
to
r
A
irp
lan
e
,
”
Ame
ric
a
n
Co
n
tro
l
Co
n
fer
e
n
c
e
,
p
p
.
1
3
1
-
1
3
6
,
2
0
1
2
.
[3
]
C.
P
a
p
a
c
h
risto
s,
K.
A
lex
is,
A
.
Tz
e
s.,
“
T
ra
j
e
c
to
r
y
Co
n
tro
l
o
f
a
n
Un
m
a
n
n
e
d
T
ri
-
T
il
t
Ro
to
r
in
Ho
v
e
r
F
li
g
h
t
v
ia
Dire
c
t
Lo
n
g
it
u
d
i
n
a
l
A
c
tu
a
ti
o
n
,
”
T
we
n
ty
-
Fi
rs
t
M
e
d
it
e
rr
a
n
e
a
n
Co
n
fer
e
n
c
e
in
Co
n
tro
l
a
n
d
Au
t
o
ma
ti
o
n
,
p
p
.
3
6
9
-
3
7
4
,
2
0
1
3
.
[4
]
K.T
.
On
e
r,
E.
Ce
ti
n
s
o
y
,
E.
S
iri
m
o
g
lu
,
C.
H
a
n
c
e
r,
T
.
Ay
k
e
n
,
a
n
d
M
.
Un
e
l.
,
“
L
QR
a
n
d
S
M
C
S
tab
il
iza
ti
o
n
o
f
a
Ne
w
Un
m
a
n
n
e
d
A
e
rial
V
e
h
icle
,
”
W
o
rld
Aca
d
e
my
o
f
S
c
ien
c
e
,
En
g
in
e
e
ri
n
g
a
n
d
T
e
c
h
n
o
l
o
g
y
,
p
p
.
5
5
4
-
5
5
9
,
2
0
0
9
.
[5
]
J.
Esc
a
re
f
io
,
A
.
S
a
n
c
h
e
z
,
O.
Ga
r
c
ia
a
n
d
R.
L
o
z
a
n
o
.
,
“
T
rip
le
T
il
ti
n
g
Ro
to
r
m
in
i
-
UA
V
:
M
o
d
e
li
n
g
a
n
d
Em
b
e
d
d
e
d
Co
n
tr
o
l
o
f
th
e
A
tt
it
u
d
e
,
”
Ame
ric
a
n
Co
n
tro
l
Co
n
fer
e
n
c
e
,
p
p
.
3
4
7
6
-
3
4
8
1
,
2
0
0
8
.
[6
]
L
.
F
e
n
g
,
Z.
W
il
li
a
m
,
D.B.
Ro
b
e
rt
.
,
“
Ro
b
u
st
Ho
v
e
rin
g
Co
n
tr
o
l
o
f
a
P
V
T
OL
A
ircra
f
t,
”
IEE
E
T
ra
n
sa
c
t
io
n
o
n
C
o
n
tr
o
l
S
y
ste
ms
T
e
c
h
n
o
l
o
g
y
,
v
o
l
.
7
,
n
o
.
3
,
pp.
3
4
3
-
3
5
1
,
1
9
9
9
.
[7
]
M
.
Ka
ra
,
A
.
L
a
n
z
o
n
.
,
“
De
sig
n
a
n
d
Co
n
tro
l
o
f
No
v
e
l
T
ri
-
ro
to
r
UA
V
,
”
Pro
c
e
e
d
i
n
g
s
o
f
2
0
1
2
UKACC
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Co
n
tro
l
,
p
p
.
3
0
4
-
3
0
9
,
2
0
1
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:
2
0
8
8
-
8708
P
I
D
vs LQR
co
n
tr
o
ller
fo
r
tilt
r
o
to
r
a
ir
p
la
n
e
(
A
o
u
ed
Ho
u
a
r
i
)
6317
[8
]
P
.
F
a
n
,
X.
W
a
n
g
,
K.Y.
Ka
i.
,
“
De
sig
n
a
n
d
C
o
n
tr
o
l
o
f
a
T
ri
-
ro
to
r
A
i
rc
ra
f
t,
”
In
ter
n
a
ti
o
n
a
l
c
o
n
fer
e
n
c
e
o
n
C
o
n
tr
o
l
a
n
d
Au
to
m
a
ti
o
n
,
p
p
.
1
9
7
2
-
1
9
7
9
,
2
0
1
0
.
[9
]
H.
G
u
,
X
.
L
y
u
,
Z.
L
i,
S
.
S
h
e
n
a
n
d
F
.
Zh
a
n
g
.
,
“
De
v
e
lo
p
m
e
n
t
a
n
d
Ex
p
e
rime
n
tal
V
e
rif
ica
ti
o
n
o
f
a
H
y
b
rid
v
e
rti
c
a
l
T
a
k
e
-
o
ff
a
n
d
L
a
n
d
in
g
(V
T
OL
)
U
n
m
a
n
n
e
d
Ae
rial
v
e
h
icle
(U
A
V
),
”
In
ter
n
a
t
io
n
a
l
Co
n
fer
e
n
c
e
o
n
Un
ma
n
n
e
d
Ai
rc
ra
ft
S
y
ste
ms
,
p
p
.
1
6
0
-
1
6
9
,
2
0
1
7
.
[1
0
]
G
.
F
ra
n
c
i
sc
o
,
V
.
Ra
f
a
e
l,
F
.
C.
Ed
u
a
rd
o
.
,
“
A
n
it
e
ra
ti
v
e
M
o
d
e
l
P
re
d
ictiv
e
c
o
n
tro
l
A
lg
o
rit
h
m
f
o
r
UA
V
G
u
id
a
n
c
e
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Aer
o
sp
a
c
e
a
n
d
El
e
c
tro
n
ic S
y
ste
ms
,
v
o
l.
5
1
,
n
o
.
3
,
p
p
.
2
4
0
6
-
2
4
1
9
,
2
0
1
5
.
[1
1
]
S
.
Yo
o
n
,
S
.
J.
L
e
e
,
B.
L
e
e
,
C
.
J.
Kim
,
Y.
J.
L
e
e
a
n
d
S
.
S
u
n
g
,
“
De
sig
n
a
n
d
F
li
g
h
t
T
e
st
o
f
a
S
m
a
ll
T
riRo
to
r
Un
m
a
n
n
e
d
V
e
h
icle
w
it
h
a
L
QR
Ba
se
d
On
b
o
a
rd
A
tt
it
u
d
e
Co
n
tr
o
l
S
y
ste
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
In
n
o
v
a
t
ive
Co
mp
u
t
in
g
,
I
n
fo
rm
a
ti
o
n
a
n
d
Co
n
tro
l,
p
p
.
2
3
4
7
-
2
3
6
0
,
2
0
1
3
.
[1
2
]
D.
W
.
Yo
o
,
H.
D.
Oh
,
D.
Y.
W
o
n
a
n
d
M
.
J.
T
a
h
k
,
“
D
y
n
a
m
ic
M
o
d
e
li
n
g
a
n
d
S
tab
il
iza
ti
o
n
T
e
c
h
n
iq
u
e
s
f
o
r
T
ri
-
Ro
t
o
r
U
n
m
a
n
n
e
d
A
e
r
i
a
l
V
e
h
i
c
l
e
s
,
”
I
n
t
e
r
n
a
t
i
o
n
a
l
J
o
u
r
n
a
l
o
f
A
e
r
o
n
a
u
t
i
c
a
l
a
n
d
S
p
a
c
e
S
c
i
e
n
c
e
,
v
o
l
.
1
1
,
n
o
.
3
,
p
p
.
1
6
7
-
1
7
4
,
2
0
1
0
.
[1
3
]
D.
T
.
Hu
a
n
g
,
T
.
H.
H.
L
e
a
n
d
N.
H.
Ng
u
y
e
n
,
“
A
d
a
p
ti
n
g
S
E
(3
)
N
o
n
li
n
e
a
r
G
e
o
m
e
tri
c
M
e
th
o
d
to
C
o
n
tro
l
S
in
g
le
-
T
ri
Ro
to
r
w
it
h
I
n
teg
ra
to
r,
”
A
me
ric
a
n
J
o
u
rn
a
l
o
f
Aer
o
sp
a
c
e
En
g
in
e
e
rin
g
,
p
p
.
9
6
-
1
0
5
,
2
0
1
8
.
[1
4
]
Y.
Q.
Zh
a
n
g
,
W
.
P
.
Zh
a
w
a
n
d
S
.
X
ian
g
,
“
Co
n
tro
l
L
a
w
a
n
d
S
im
u
latio
n
A
n
a
ly
sis
o
f
V
e
rti
c
a
l
T
a
k
e
-
O
ff
a
n
d
Lan
d
in
g
S
tag
e
o
f
T
il
t
-
Ro
to
r
A
ircra
f
t,
”
J
o
u
rn
a
l
o
f
A
d
v
a
n
c
e
d
M
a
ter
ia
ls R
e
se
a
rc
h
,
p
p
.
5
2
1
-
5
2
4
,
2
0
1
5
.
[1
5
]
S.
K.
P
a
n
d
e
y
,
J.
De
y
a
n
d
S
.
Ba
n
e
rjee
,
“
De
sig
n
o
f
Op
ti
m
a
l
P
ID Co
n
tro
ll
e
r
f
o
r
Co
n
tr
o
l
o
f
Tw
in
Ro
to
r
M
IM
O S
y
ste
m
(T
RM
S
)
,
”
Ad
v
a
n
c
e
s i
n
Po
we
r
a
n
d
Co
n
tro
l
En
g
in
e
e
rin
g
,
p
p
.
9
3
-
1
0
6
,
2
0
2
0
.
[1
6
]
M
.
A
.
A
h
m
a
d
,
S
.
I.
Az
u
m
a
a
n
d
T
.
S
u
g
ie,
“
P
e
rf
o
rm
a
n
c
e
a
n
a
l
y
sis
o
f
m
o
d
e
l
-
f
r
e
e
P
ID
tu
n
in
g
o
f
M
IM
O
s
y
ste
m
s
b
a
s
e
d
o
n
sim
u
lt
a
n
e
o
u
s p
e
rt
u
rb
a
ti
o
n
st
o
c
h
a
stic a
p
p
r
o
x
im
a
ti
o
n
,
”
Exp
e
rt S
y
ste
ms
wit
h
Ap
p
li
c
a
ti
o
n
s,
p
p
.
6
3
6
1
-
6
3
7
0
,
2
0
1
4
.
[1
7
]
M
.
R.
B.
G
h
a
z
a
l
i,
M
.
A
.
B.
A
h
m
a
d
a
n
d
R.
Ism
a
il
,
“
A
d
a
p
ti
v
e
s
a
f
e
e
x
p
e
rime
n
tatio
n
d
y
n
a
m
ics
fo
r
d
a
ta
-
d
riv
e
n
n
e
u
ro
e
n
d
o
c
ri
n
e
-
P
ID co
n
tro
l
o
f
M
IM
O sy
st
e
m
s
,
”
IET
E
J
o
u
rn
a
l
o
f
Res
e
a
rc
h
,
p
p
.
1
-
1
4
,
2
0
1
9
.
[1
8
]
C.
Ch
e
n
,
J
.
Zh
a
n
g
,
D.
Zh
a
n
g
a
n
d
L
.
S
h
e
n
,
“
Co
n
tr
o
l
a
n
d
F
li
g
h
t
T
e
st
o
f
a
T
il
tro
to
r
Un
m
a
n
n
e
d
Ae
rial
V
e
h
icle
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
A
d
v
a
n
c
e
d
Ro
b
o
ti
c
S
y
ste
ms
,
p
p
.
1
-
1
2
,
2
0
1
7
.
[1
9
]
C.
S
.
Yo
o
,
S
.
D.
Ry
u
,
B.
J
P
a
rk
,
Y.
S
Ka
n
g
,
C.
M
El
ias
a
n
d
S
.
B
J
u
n
g
,
“
A
c
tu
a
to
r
c
o
n
tro
l
ler
b
a
se
d
o
n
F
u
z
z
y
S
li
d
in
g
M
o
d
e
C
o
n
tr
o
l
o
f
T
il
t
Ro
to
r
U
n
m
a
n
n
e
d
A
e
rial
V
e
h
icle
s,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
C
o
n
tro
l,
Au
to
m
a
ti
o
n
a
n
d
sy
ste
ms
,
v
o
l.
1
2
,
n
o
.
6
,
p
p
.
1
2
5
7
-
1
2
6
5
,
2
0
1
4
.
[2
0
]
M.
Na
sr,
M
.
As
h
ra
f
,
M
.
S
Hu
ss
e
in
,
A
.
S
S
a
le
m
,
C.
M
El
ias
,
O.
M
S
h
e
h
a
ta
a
n
d
E.
I
M
o
ra
g
n
.
,
“
A
c
o
m
p
a
ra
ti
v
e
stu
d
y
o
n
t
h
e
c
o
n
tr
o
l
o
f
UA
V
s
f
o
r
T
r
a
jec
to
r
y
trac
k
in
g
b
y
M
P
C,
S
M
C,
Ba
c
k
ste
p
p
in
g
,
a
n
d
F
u
z
z
y
L
o
g
ic
c
o
n
tro
ll
e
rs,”
IEE
E
In
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
in
Veh
icu
l
a
r
El
e
c
tro
n
ics
a
n
d
S
a
fety
,
p
p
.
1
-
6
,
2
0
1
8
.
[2
1
]
Z.
P
rim
e
,
J.
S
h
e
r
w
o
o
d
,
M
.
S
m
it
h
,
a
n
d
A
S
tab
il
e
,
“
Re
m
o
te
Co
n
tro
l
V
e
rti
c
a
l
T
a
k
e
-
o
ff
a
n
d
L
a
n
d
in
g
M
o
d
e
l
A
ircra
f
t
,
”
L
e
v
e
l
4
Ho
n
o
rs
Pro
jec
t
F
in
a
l
Rep
o
rt,
2
0
0
5
.
[2
2
]
Ch
.
B.
P
ra
k
a
sh
,
R.
S
Na
ik
,
”
T
u
n
in
g
o
f
P
ID
Co
n
tro
ll
e
r
b
y
Zi
e
g
l
e
r
Nic
h
o
ls
A
lg
o
rit
h
m
f
o
r
P
o
siti
o
n
Co
n
tr
o
l
o
f
DC
M
o
to
r
,
”
In
ter
n
a
ti
o
n
a
l
j
o
u
r
n
a
l
o
f
I
n
n
o
v
a
ti
v
e
S
c
ien
c
e
,
E
n
g
i
n
e
e
rin
g
a
n
d
T
e
c
h
n
o
l
o
g
y
,
v
o
l
.
1
,
n
o
.
3
,
p
p
.
3
7
9
-
3
8
2
,
2
0
1
4
.
[2
3
]
T.
R.
Ku
rf
e
ss
,
"
Ge
tt
in
g
in
tu
n
e
w
it
h
Zi
e
g
ler
-
Nic
h
o
ls
,
"
Aca
d
e
mic
Vi
e
wp
o
in
t
c
o
lu
m
n
,
Co
n
tro
l
E
n
g
in
e
e
rin
g
ma
g
a
zi
n
e
,
2
0
0
7
.
[2
4
]
K.
K.
Yit,
P
.
Ra
je
n
d
ra
n
,
a
n
d
L
.
K
W
e
e
,
“
P
ro
p
o
rti
o
n
a
l
-
d
e
riv
a
ti
v
e
L
in
e
a
r
Qu
a
d
ra
ti
c
Re
g
u
lato
r
Co
n
tr
o
ll
e
r
De
sig
n
f
o
r
im
p
ro
v
e
d
L
o
n
g
it
u
d
i
n
a
l
M
o
ti
o
n
Co
n
t
ro
l
o
f
Un
m
a
n
n
e
d
A
e
rial
V
e
h
icle
s,”
In
ter
n
a
ti
o
n
a
l
jo
u
rn
a
l
o
f
M
icr
o
Ai
r
Veh
icle
s,
v
o
l.
8
,
n
o
.
1
,
p
p
.
4
1
-
5
0
,
2
0
1
6
.
[2
5
]
A
.
M
.
Ay
a
d
,
H.
W
a
h
id
,
”
Op
ti
m
a
l
T
u
n
in
g
o
f
L
in
e
a
r
Qu
a
d
ra
ti
c
Re
g
u
lato
r
c
o
n
tro
ll
e
r
Us
in
g
a
P
a
rti
c
le
S
w
a
r
m
Op
ti
m
iza
ti
o
n
f
o
r
Tw
o
-
Ro
to
r
A
e
r
o
d
y
n
a
m
ica
l
S
y
ste
m
,
”
In
tern
a
ti
o
n
a
l
jo
u
r
n
a
l
o
f
El
e
c
tro
n
ics
a
n
d
Co
m
m
u
n
ica
ti
o
n
En
g
in
e
e
rin
g
,
p
p
.
1
9
6
-
20
2
,
2
0
1
7
.
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
Ao
u
e
d
H
o
u
a
r
i
W
a
s
b
o
rn
o
n
1
9
8
5
in
Re
li
z
a
n
e
,
A
lg
e
ria.
He
re
c
e
iv
e
d
h
is
B.
S
(S
tate
e
n
g
in
e
e
r)
En
g
in
e
e
rin
g
d
e
g
re
e
in
a
u
to
m
a
ti
sm
f
ro
m
Un
iv
e
rsit
y
o
f
S
c
ien
c
e
s
a
n
d
T
e
c
h
n
o
l
o
g
y
o
f
Ora
n
(UST
O
-
M
B),
A
lg
e
ria,
in
2
0
0
8
.
He
re
c
e
iv
e
d
h
is
M
.
S
(M
a
g
ister)
d
e
g
re
e
in
El
e
c
tro
n
ics
,
A
u
to
m
a
ti
c
,
Ro
b
o
ti
c
a
n
d
p
ro
d
u
c
ti
c
o
p
ti
o
n
f
ro
m
UST
O
-
M
B
U
n
iv
e
rsit
y
in
2
0
1
2
.
He
is
c
u
rre
n
tl
y
a
n
a
ss
o
c
iat
e
p
ro
f
e
ss
o
r
a
t
UH
BC
u
n
iv
e
rsity
.
His
m
a
in
re
se
a
r
c
h
in
tere
st
is
w
it
h
i
n
th
e
c
o
n
tr
o
l
a
n
d
a
p
p
li
c
a
ti
o
n
s
o
f
a
d
v
a
n
c
e
d
c
o
n
tro
l
te
c
h
n
ics
,
d
e
si
g
n
a
n
d
c
o
n
tr
o
l
o
f
UA
V
.
I
m
in
e
B
a
c
h
ir
w
a
s
b
o
rn
o
n
1
9
6
2
i
n
Ora
n
,
A
lg
e
ria.
He
re
c
e
iv
e
d
h
is
B.
S
(S
tate
e
n
g
in
e
e
r)
En
g
in
e
e
rin
g
d
e
g
re
e
in
m
e
c
h
a
n
ica
l
e
n
g
in
e
e
rin
g
f
ro
m
Un
iv
e
rsit
y
o
f
S
c
ien
c
e
s
a
n
d
T
e
c
h
n
o
lo
g
y
o
f
Ora
n
(UST
OMB),
A
lg
e
ria,
in
1
9
8
6
.
He
re
c
e
iv
e
d
h
is
M
.
S
(
M
a
g
ister)
d
e
g
re
e
in
M
e
c
h
a
n
ica
l
e
n
g
in
e
e
rin
g
,
o
p
ti
o
n
:
E
n
e
rg
e
ti
c
a
l
f
ro
m
US
T
O
-
M
B
u
n
iv
e
rsit
y
in
1
9
9
3
.
He
re
c
e
i
v
e
d
h
is
P
Hd
i
n
M
e
c
h
a
n
ica
l
e
n
g
in
e
e
rin
g
,
o
p
ti
o
n
:
En
e
rg
e
ti
c
a
l
f
ro
m
UST
O
-
M
B
u
n
iv
e
rsit
y
in
2
0
0
4
.
He
is
c
u
rre
n
tl
y
a
n
a
ss
o
c
iate
p
ro
f
e
ss
o
r
in
US
TO
-
M
B
U
n
iv
e
rsit
y
sin
c
e
1
9
8
7
.
His
m
a
in
re
se
a
r
c
h
in
tere
st
is
U
A
V
a
e
ro
d
y
n
a
m
ic d
e
sig
n
.
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.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
6
3
0
9
-
6
3
1
8
6318
De
ll
a
K
r
a
c
h
a
i
M
o
h
a
m
e
d
wa
s
b
o
r
n
o
n
1
9
7
3
,
in
Ora
n
.
In
1
9
9
6
,
h
e
o
b
tai
n
e
d
h
is
e
lec
tro
n
ics
e
n
g
in
e
e
r
d
ip
l
o
m
a
f
ro
m
th
e
Un
iv
e
rsit
y
o
f
S
c
ien
c
e
a
n
d
T
e
c
h
n
o
lo
g
y
UST
O
-
M
B.
Af
t
e
r
th
a
t
h
e
o
b
tai
n
e
d
t
h
e
M
a
g
ister
d
e
g
re
e
in
2
0
0
1
,
th
e
n
th
e
D
o
c
to
ra
te
d
e
g
re
e
in
e
lec
tro
n
ics
in
2
0
0
9
.
He
is
c
u
rre
n
tl
y
a
re
se
a
rc
h
e
r/l
e
c
tu
re
r
a
t
th
e
De
p
a
rtm
e
n
t
o
f
A
u
to
m
a
ti
c
s
a
t
UST
O
-
M
B
U
n
iv
e
rsity
.
His res
e
a
rc
h
e
s
f
o
c
u
s o
n
r
o
b
o
ti
c
s,
c
o
n
tro
l
sy
ste
m
s,
a
n
d
re
n
e
w
a
b
le en
e
rg
ies
.
K
a
r
a
M
o
h
a
m
e
d
K
a
r
a
is
c
u
rre
n
tl
y
a
S
e
n
io
r
L
e
c
tu
re
r
in
Ro
b
o
ti
c
s.
Be
f
o
re
jo
in
in
g
L
iv
e
rp
o
o
l
Jo
h
n
M
o
o
re
s
U
n
iv
e
rsity
,
h
e
h
e
ld
se
v
e
ra
l
a
c
a
d
e
m
ic
a
n
d
re
se
a
rc
h
p
o
si
ti
o
n
s
w
it
h
Birm
in
g
h
a
m
Cit
y
Un
iv
e
rsit
y
,
T
h
e
Un
iv
e
rsit
y
o
f
M
a
n
c
h
e
ste
r
a
n
d
Co
v
e
n
tr
y
Un
iv
e
rsit
y
.
He
w
o
rk
e
d
a
lso
in
in
d
u
stry
a
s a
S
w
it
c
h
in
g
S
y
ste
m
s E
n
g
in
e
e
r
a
t
M
T
N
G
ro
u
p
b
e
f
o
re
m
o
v
in
g
to
a
c
a
d
e
m
ia.
Dr M
o
h
a
m
e
d
h
o
ld
s
a
P
h
D
d
e
g
re
e
in
Co
n
tro
l
En
g
i
n
e
e
rin
g
f
ro
m
T
h
e
Un
iv
e
r
sit
y
o
f
M
a
n
c
h
e
ste
r.
His
m
a
in
re
se
a
rc
h
in
tere
st
is
w
it
h
in
th
e
c
o
n
tro
l
a
n
d
a
p
p
li
c
a
ti
o
n
s
o
f
a
d
v
a
n
c
e
d
s
y
ste
m
s
in
c
lu
d
in
g
a
u
t
o
n
o
m
o
u
s
ro
b
o
ti
c
s
y
ste
m
s.
Evaluation Warning : The document was created with Spire.PDF for Python.