I
nte
rna
t
io
n
a
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.
9
,
No
.
6
,
Dec
em
b
er
201
9
,
p
p
.
4
7
2
8
~
4
7
3
7
I
SS
N:
2
0
8
8
-
8708
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
ec
e
.
v9
i
6
.
p
p
4
7
2
8
-
4737
4728
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
co
r
e
.
co
m/
jo
u
r
n
a
ls
/in
d
ex
.
p
h
p
/
I
JE
C
E
An i
m
ple
m
e
ntati
o
n of opti
m
a
l con
trol
m
ethods
(LQ
I,
LQ
G
,
LTR
)
for g
eo
sta
tiona
r
y
sa
tellit
e at
tit
ud
e
contro
l
F
a
rid D
j
a
ba
lla
h
1
,
M
.
A
.
Si
M
o
ha
mm
ed
2
,
Na
bil
B
o
ug
ha
n
m
i
3
1,
3
D
e
p
a
rt
m
e
n
t
d
’é
lec
tro
n
iq
u
e
,
Un
i
v
e
rsité d
e
s S
c
ien
c
e
s e
t
d
e
la T
e
c
h
n
o
l
o
g
ied
’Ora
n
M
o
h
a
m
e
d
Bo
u
d
iaf,
A
lg
e
rie
2
Ce
n
ter o
f
S
a
te
ll
it
e
De
v
e
lo
p
m
e
n
t,
A
lg
e
rie
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
J
u
n
27
,
2
0
1
8
R
ev
i
s
ed
Ma
y
4
,
2
0
1
9
A
cc
ep
ted
J
u
n
26
,
2
0
1
9
T
h
is
p
a
p
e
r
in
v
e
stig
a
tes
a
n
e
w
stra
teg
y
f
o
r
g
e
o
sta
ti
o
n
a
ry
sa
telli
te
a
tt
it
u
d
e
c
o
n
tro
l
u
sin
g
L
in
e
a
r
Qu
a
d
ra
ti
c
G
a
u
ss
ian
(
L
Q
G),
L
o
o
p
T
ra
n
sfe
r
Re
c
o
v
e
r
y
(LT
R),
a
n
d
L
in
e
a
r
Qu
a
d
ra
ti
c
In
teg
ra
l
(
L
QI)
c
o
n
tro
l
tec
h
n
iq
u
e
s.
T
h
e
su
b
-
s
y
ste
m
sa
telli
te
a
tt
it
u
d
e
d
e
term
in
a
ti
o
n
a
n
d
c
o
n
t
ro
l
o
f
a
g
e
o
sta
ti
o
n
a
ry
sa
telli
te
in
t
h
e
p
re
se
n
c
e
o
f
e
x
tern
a
l
d
istu
r
b
a
n
c
e
s,
t
h
e
d
y
n
a
m
ic
m
o
d
e
l
o
f
su
b
-
sa
telli
te
m
o
ti
o
n
is
f
irstl
y
e
sta
b
li
sh
e
d
b
y
Eu
ler
e
q
u
a
ti
o
n
s.
Du
ri
n
g
th
e
f
li
g
h
t
m
is
sio
n
a
t
3
5
0
0
0
Km
a
tt
it
u
d
e
,
th
e
sta
b
il
it
y
c
h
a
ra
c
teristic
s
o
f
a
tt
it
u
d
e
m
o
ti
o
n
a
re
a
n
a
l
y
z
e
d
w
it
h
a
larg
e
m
a
rg
in
e
rro
r
o
f
p
o
in
ti
n
g
,
th
e
n
a
h
e
ig
h
t
p
e
rf
o
r
m
a
n
c
e
-
o
rd
e
r
L
QI,
L
Q
G
a
n
d
L
T
R
a
tt
it
u
d
e
c
o
n
tro
l
ler
a
re
p
ro
p
o
se
d
to
a
c
h
iev
e
sta
b
le
c
o
n
tro
l
o
f
th
e
s
u
b
-
sa
telli
te
a
tt
it
u
d
e
,
w
h
ich
d
y
n
a
m
i
c
m
o
d
e
l
is
li
n
e
a
rize
d
b
y
u
sin
g
f
e
e
d
b
a
c
k
l
in
e
a
riza
ti
o
n
m
e
th
o
d
.
F
i
n
a
ll
y
,
v
a
li
d
it
y
o
f
th
e
L
T
R
o
rd
e
r
c
o
n
tro
ll
e
r
a
n
d
th
e
a
d
v
a
n
tag
e
s
o
v
e
r
a
n
in
teg
e
r
o
rd
e
r
c
o
n
tro
ll
e
r
a
re
e
x
a
m
in
e
d
b
y
n
u
m
e
ric
a
l
si
m
u
latio
n
.
C
o
m
p
a
rin
g
w
it
h
th
e
c
o
rre
sp
o
n
d
in
g
in
teg
e
r
o
rd
e
r
c
o
n
tr
o
ll
e
r
(L
QI,
LQG
),
n
u
m
e
rica
l
si
m
u
latio
n
re
su
lt
s
in
d
ica
te
th
a
t
th
e
p
ro
p
o
se
d
su
b
-
sa
telli
te
a
tt
i
tu
d
e
c
o
n
tr
o
ll
e
r
b
a
se
d
o
n
L
T
R
o
rd
e
r
c
a
n
n
o
t
o
n
ly
sta
b
il
ize
th
e
s
u
b
-
sa
telli
te
a
tt
it
u
d
e
,
b
u
t
a
lso
re
sp
o
n
d
f
a
ste
r
w
it
h
sm
a
ll
e
r
o
v
e
rsh
o
o
t.
K
ey
w
o
r
d
s
:
A
D
C
S
Geo
s
tatio
n
ar
y
s
atelli
te
KAL
M
AN
f
i
lter
L
QI
,
L
QG,
L
T
R
Sp
ac
ec
r
af
t a
ttit
u
d
e
d
y
n
a
m
ic
s
Co
p
y
rig
h
t
©
2
0
1
9
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
:
Far
id
Dj
ab
allah
,
Dep
ar
te
m
en
t d
’
élec
tr
o
n
iq
u
e
;
L
ab
o
r
ato
ir
e
d
e
R
ec
h
er
ch
e
en
S
y
s
tè
m
e
I
n
till
i
g
e
n
ts
(
L
AR
E
SI
)
,
Un
i
v
er
s
ité
d
es Scie
n
ce
s
et
d
e
l
a
T
ec
h
n
o
lo
g
ied
’
Or
an
Mo
h
a
m
ed
B
o
u
d
iaf
,
UST
O
-
Mb
.
B
P
1
5
0
5
,
E
l M
’
n
ao
u
er
,
3
1
0
0
0
Or
an
,
A
l
g
er
ie
.
E
m
ail:
f
ar
id
.
d
j
ab
allah
@
u
n
i
v
-
u
s
to
.
d
z
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
attitu
d
e
co
n
tr
o
l
o
f
g
eo
s
tatio
n
ar
y
s
p
ac
ec
r
af
ts
[1
-
4
]
,
h
as
im
p
o
r
tan
t
ap
p
licat
io
n
s
f
o
r
telec
o
m
m
u
n
icatio
n
s
p
ac
e
m
is
s
io
n
s
s
u
c
h
as
p
o
in
ti
n
g
a
n
d
f
o
r
m
o
tio
n
f
l
y
in
g
,
t
h
e
A
ttit
u
d
e
Dete
r
m
i
n
atio
n
an
d
C
o
n
tr
o
l
Su
b
s
y
s
te
m
(
ADCS
)
p
r
o
v
id
es
attitu
d
e
in
f
o
r
m
at
io
n
an
d
m
ain
tain
s
th
e
r
eq
u
ir
ed
s
p
ac
ec
r
af
t
attit
u
d
e
d
u
r
in
g
all
p
h
ase
s
o
f
t
h
e
m
i
s
s
i
o
n
,
s
tar
ti
n
g
at
s
p
ac
ec
r
af
t
s
ep
a
r
atio
n
f
r
o
m
t
h
e
la
u
n
ch
v
e
h
icle
an
d
t
h
r
o
u
g
h
o
u
t
it
s
o
p
er
atio
n
al
lif
et
i
m
e
[
5
-
8
]
.
T
h
e
s
elec
t
io
n
o
f
an
A
D
C
S
is
a
f
u
n
c
tio
n
o
f
m
a
n
y
f
ac
to
r
s
,
I
n
cl
u
d
in
g
m
i
s
s
io
n
o
b
j
ec
tiv
es,
s
ate
llit
e
d
esi
g
n
,
d
is
tr
ib
u
tio
n
s
to
r
q
u
es,
d
esi
g
n
co
n
s
tr
ain
ts
a
n
d
s
tab
il
izatio
n
r
eq
u
ir
ed
.
Sev
er
al
co
n
tr
o
l
m
et
h
o
d
s
h
a
v
e
b
ee
n
d
ev
elo
p
ed
o
v
er
th
e
p
ast
y
ea
r
s
s
i
n
ce
th
e
f
ir
s
t
s
atelli
te
w
a
s
la
u
n
c
h
ed
.
Mo
s
tl
y
r
esear
c
h
er
s
al
l
th
o
s
e
tec
h
n
iq
u
e
s
m
a
y
b
e
class
i
f
ied
a
s
ac
ti
v
e
o
r
p
as
s
iv
e,
th
er
e
ar
e
n
u
m
b
er
o
f
u
n
ce
r
tain
ties
th
a
t
th
e
co
n
v
en
tio
n
al
co
n
tr
o
l
d
o
es
n
o
t
ac
co
u
n
t
f
o
r
in
th
e
d
es
ig
n
o
f
s
atellite
co
n
tr
o
ller
.
T
h
e
m
ai
n
s
o
u
r
ce
is
th
e
li
n
ea
r
izatio
n
o
f
th
e
n
o
n
-
li
n
ea
r
s
y
s
te
m
.
T
h
ese
u
n
ce
r
tain
ti
es
ca
n
b
e
ad
ap
ted
to
a
lar
g
e
e
x
ten
t
b
y
u
s
i
n
g
L
T
R
(
L
in
ea
r
Q
u
ad
r
atic
Gau
s
s
ia
n
)
co
m
p
e
n
s
ato
r
.
T
h
e
d
esig
n
ap
p
r
o
ac
h
f
o
r
th
e
L
T
R
co
n
tr
o
ller
is
b
ased
o
n
th
e
p
r
in
cip
le
o
f
ce
r
tain
t
y
eq
u
iv
a
len
ce
in
w
h
ic
h
t
h
e
Kal
m
an
f
ilter
is
d
es
ig
n
ed
s
ep
ar
atel
y
f
r
o
m
t
h
e
L
QI
o
p
tim
a
l c
o
n
tr
o
ller
.
I
n
th
e
p
r
esen
t
w
o
r
k
,
w
e
co
n
s
id
er
th
e
p
r
o
b
lem
o
f
att
itu
d
e
co
n
tr
o
l
f
o
r
r
ig
id
s
atellite
s
b
ased
o
n
th
e
E
u
ler
r
ep
r
esen
tatio
n
,
t
h
e
p
er
f
o
r
m
a
n
ce
o
f
at
tit
u
d
e
m
o
d
el
in
s
tate
s
p
ac
e
f
o
r
m
w
i
th
L
QG
a
n
d
L
QI
ar
e
ex
a
m
in
ed
to
ac
h
iev
e
s
tab
ili
t
y
f
o
r
th
e
clo
s
ed
-
lo
o
p
s
y
s
te
m
in
s
ev
er
al
p
er
tu
r
b
atio
n
to
r
q
u
es
ac
tin
g
u
p
o
n
a
r
ig
id
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
A
n
imp
leme
n
ta
tio
n
o
f o
p
tima
l
co
n
tr
o
l m
eth
o
d
s
(
L
QI
,
LQG,
L
TR)
fo
r
g
eo
s
ta
tio
n
a
r
y…
(
F
a
r
i
d
Dja
b
a
lla
h
)
4729
s
atellite.
T
h
en
th
e
s
a
m
e
m
o
d
el
is
s
i
m
u
lated
w
it
h
L
T
R
co
m
p
e
n
s
ato
r
,
th
e
s
i
m
u
la
tio
n
w
i
th
L
QG
an
d
L
QI
r
esu
lt
s
,
in
d
icati
n
g
a
n
in
cr
ea
s
e
in
r
o
b
u
s
tn
e
s
s
at
h
ig
h
er
f
r
eq
u
en
c
y
m
ea
s
u
r
e
m
e
n
t
p
er
tu
r
b
atio
n
.
T
o
r
ec
o
v
er
th
e
r
o
b
u
s
t
n
es
s
o
f
th
e
L
QI
,
a
L
o
o
p
T
r
an
s
f
er
R
ec
o
v
er
y
(
L
T
R
)
in
v
o
lv
es
a
f
ictitio
u
s
n
o
is
e
s
o
u
r
ce
to
th
e
i
n
p
u
t
o
f
th
e
p
lan
t
i
n
Kal
m
a
n
f
il
ter
d
esig
n
.
A
s
t
h
e
a
m
p
li
tu
d
e
o
f
i
n
j
ec
ted
n
o
is
e
b
ec
o
m
e
s
lar
g
e
i
n
in
ten
s
it
y
,
th
e
L
QG
o
p
en
-
lo
o
p
tr
an
s
f
er
f
u
n
ctio
n
ap
p
r
o
ac
h
es th
at
o
f
t
h
e
L
QR
a
n
d
lo
o
p
r
ec
o
v
er
y
ta
k
e
s
p
lace
[
9
-
12]
T
h
e
o
r
g
an
izatio
n
o
f
th
e
p
ap
er
is
th
e
f
o
llo
w
in
g
:
m
ath
e
m
at
i
ca
l
p
r
elim
i
n
ar
ies
i
n
cl
u
d
in
g
m
o
d
elin
g
o
f
th
e
s
ate
llit
e
d
y
n
a
m
ics
a
n
d
k
in
e
m
atic
ar
e
p
r
esen
ted
i
n
t
h
e
n
ex
t
s
ec
tio
n
.
Sectio
n
3
p
r
esen
t
s
t
h
e
p
r
o
b
lem
f
o
r
m
u
latio
n
a
n
d
m
et
h
o
d
o
lo
g
y
in
clu
d
i
n
g
L
QI
,
L
QG
a
n
d
L
T
R
.
T
h
e
m
ai
n
co
n
tr
ib
u
tio
n
o
f
th
is
p
ap
er
w
ill
b
e
p
r
esen
ted
in
Sectio
n
4
.
Dis
cu
s
s
io
n
an
d
n
u
m
er
ical
s
i
m
u
latio
n
s
ar
e
also
p
r
esen
t
ed
in
Sectio
n
5
.
Sectio
n
6
p
r
o
v
id
es th
e
co
n
cl
u
d
in
g
r
e
m
ar
k
s
.
2.
P
RO
B
L
E
M
DE
F
I
NIT
I
O
N
AND
M
E
T
H
O
DO
L
O
G
Y
C
o
n
s
id
er
th
e
s
p
ac
ec
r
af
t
i
n
o
r
b
it
at
3
5
0
0
0
Km
,
w
h
er
e
is
e
x
p
o
s
ed
to
a
s
ev
er
al
E
x
ter
n
al
d
is
tu
r
b
an
ce
to
r
q
u
es,
in
cl
u
d
e
g
r
a
v
it
y
g
r
ad
i
en
t,
m
ag
n
etic
d
is
tu
r
b
an
ce
s
,
an
d
ae
r
o
d
y
n
a
m
ic
d
r
ag
.
T
o
en
s
u
r
e
th
e
m
is
s
io
n
w
i
t
h
h
eig
h
t
p
er
f
o
r
m
a
n
ce
,
it
’
s
n
ec
e
s
s
ar
y
to
d
esig
n
a
n
attit
u
d
e
co
n
tr
o
l
s
y
s
te
m
is
f
o
r
th
e
ca
s
e
o
f
co
n
s
ta
n
t
atti
tu
d
e
tr
ac
k
in
g
to
m
i
n
i
m
ize
a
p
o
in
tin
g
er
r
o
r
.
T
h
e
m
ai
n
o
b
j
ec
ti
v
e
an
d
m
et
h
o
d
o
lo
g
y
o
f
t
h
i
s
p
ap
er
is
to
f
in
d
th
e
o
p
ti
m
al
co
n
tr
o
ller
th
at
co
n
s
i
s
ts
o
f
t
h
e
r
ig
id
s
p
ac
ec
r
af
t
s
u
ch
t
h
at
as
y
m
p
to
tic
s
t
ab
ilit
y
is
ac
h
ie
v
ed
.
P
r
o
b
lem
d
e
f
in
itio
n
a
s
s
h
o
w
n
i
n
Fi
g
u
r
e
1
.
Fig
u
r
e
1
.
P
r
o
b
lem
d
ef
in
i
tio
n
T
h
e
v
ib
r
atio
n
s
g
e
n
er
ated
b
y
th
e
s
tatic
a
n
d
d
y
n
a
m
ic
f
o
r
ce
s
o
f
r
o
tatin
g
eq
u
ip
m
en
t,
w
h
ic
h
ar
e
g
en
er
all
y
t
h
e
r
ea
ctio
n
w
h
ee
ls
th
at
ar
e
u
s
ed
f
o
r
t
h
e
A
ttit
u
d
e
Dete
r
m
i
n
atio
n
a
n
d
C
o
n
tr
o
l
Su
b
s
y
s
te
m
(
A
D
C
S)
p
lace
d
in
th
e
n
eig
h
b
o
r
h
o
o
d
o
f
p
ay
lo
ad
,
ar
e
o
n
e
o
f
t
h
e
m
o
s
t
i
m
p
o
r
tan
t
f
ac
to
r
s
af
f
ec
ti
n
g
th
e
p
o
in
tin
g
p
a
y
lo
ad
s
an
d
p
r
ec
is
io
n
d
ev
ices
in
s
p
ac
e
p
latf
o
r
m
s
.
T
h
is
r
ea
ctio
n
w
h
ee
ls
h
as
a
co
m
p
lex
co
n
f
i
g
u
r
atio
n
w
i
th
g
ea
r
s
m
o
r
e
d
etail
in
F
ig
u
r
e
2
,
w
h
ich
m
ak
es
it
h
as
a
co
m
p
lex
v
ib
r
atio
n
m
ec
h
a
n
i
s
m
s
u
c
h
as
v
ib
r
atio
n
co
u
p
lin
g
s
tr
u
ct
u
r
e,
th
ese
v
ib
r
atio
n
s
ar
e
ca
u
s
ed
b
y
th
e
s
p
ee
d
co
n
tr
o
l
s
y
s
te
m
o
f
th
e
w
h
ee
l
s
,
an
d
m
a
in
l
y
d
u
e
to
th
e
p
ea
k
s
o
f
r
esp
o
n
s
e
in
tr
a
n
s
itio
n
al
r
eg
i
m
e
[
1
3
-
1
4
]
.
T
h
er
ef
o
r
e,
it
is
n
ec
es
s
ar
y
to
an
al
y
ze
an
d
m
i
n
i
m
ize
th
e
s
e
p
ea
k
s
.
On
t
h
e
b
asis
o
f
t
h
i
s
,
an
i
m
p
le
m
en
tatio
n
a
n
d
an
e
f
f
ec
t
iv
e
co
m
p
ar
i
s
o
n
s
o
f
t
h
r
ee
co
n
tr
o
l a
lg
o
r
ith
m
s
.
Fig
u
r
e
2
.
Mic
r
o
-
v
ib
r
atio
n
p
r
o
p
ag
atio
n
i
n
s
at
el
li
te
s
tr
u
c
tu
r
e
-
G
ra
vi
t
y
-
G
ra
di
e
nt
-
M
a
gne
t
i
c
-
S
ol
a
r
ra
di
a
t
i
on
-
A
e
rodyna
m
i
c
Exte
r
n
al
D
i
s
tu
r
b
an
c
e
tor
q
u
e
s
P
oi
n
ti
n
g
e
r
r
or
A
c
c
e
l
e
ra
t
i
on
Co
up
l
e
d
s
t
ru
c
t
ur
e
E
l
e
c
t
ri
c
M
ot
or
(v
i
br
a
t
i
on
s
ou
rc
e
)
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.
9
,
No
.
6
,
Dec
em
b
er
2
0
1
9
:
4
7
2
8
-
4
7
3
7
4730
T
h
e
n
atu
r
al
f
r
eq
u
e
n
cie
s
an
d
d
is
p
lace
m
e
n
t
co
n
f
ig
u
r
atio
n
s
f
o
llo
w
eq
u
atio
n
s
in
[
1
5
]
.
Fo
r
a
later
al
co
n
f
i
g
u
r
atio
n
,
th
e
n
at
u
r
al
f
r
eq
u
en
c
y
r
ea
d
s
:
=
0
.
560
√
.
3
(
1
)
T
h
e
later
al
d
is
p
lace
m
e
n
t
f
o
llo
w
s
:
=
0
.
125
(
3
.
)
.
(
2
)
E
:
Yo
u
n
g
m
o
d
u
le,
I
:
i
n
er
c
ie
o
f
s
atellite,
:
M
ass
o
f
s
atel
lit
e,
:
L
en
g
th
o
f
s
at
ell
i
te
an
d
:
T
h
e
ac
ce
l
er
ati
o
n
d
u
e
t
o
th
e
s
p
e
ed
m
o
to
r
c
o
n
tr
o
l
.
3.
DYNA
M
I
C
AND
K
I
NE
M
AT
I
C
S O
F
SPAC
E
C
RAF
T
I
n
th
i
s
s
ec
tio
n
,
a
r
ig
id
s
ate
lli
te
m
o
d
el
is
p
r
esen
ted
[
1
6
-
1
7
]
;
a
g
eo
s
t
atio
n
ar
y
s
atellite
i
s
s
h
o
w
n
i
n
F
ig
u
r
e
3
.
T
h
e
an
g
les
p
itch
,
y
a
w
an
d
r
o
ll
(
,
,
)
ar
e
d
ef
in
ed
r
esp
ec
tiv
el
y
a
s
a
r
o
tatio
n
ar
o
u
n
d
th
e
b
o
d
y
ax
es
an
d
(
,
,
)
a
r
e
th
e
an
g
u
lar
r
ate.
Fi
g
u
r
e
3
s
ho
w
s
al
l r
ef
er
en
ce
u
s
ed
.
Fig
u
r
e
3
.
Fra
m
e
s
y
s
te
m
s
(
b
o
d
y
an
d
r
ef
er
e
n
ce
f
r
a
m
e
an
d
i
n
er
tial f
r
a
m
e
s
y
s
te
m
an
d
i
n
m
o
tio
n
)
3
.
1
.
Dy
na
m
ic
m
ent
io
n
Fo
r
th
e
r
o
tatin
g
m
o
tio
n
o
f
th
e
s
atell
ite,
th
e
m
o
m
e
n
t
s
E
u
ler
eq
u
atio
n
ca
n
b
e
d
escr
ib
ed
as
th
e
f
o
llo
w
i
n
g
s
eq
u
at
io
n:
=
⌋
(
3
)
H
,
T
h
e
an
g
u
lar
m
o
m
e
n
t
u
m
o
f
th
e
s
atellite
ca
lc
u
lated
in
O
an
d
M
th
e
in
er
tial
r
es
u
lta
n
t
o
f
th
e
m
o
m
e
n
ts
ap
p
lied
to
th
e
s
atellite
a
s
s
h
o
w
n
i
n
F
ig
u
r
e
3
,
th
en
t
h
e
k
in
e
tic
m
o
m
e
n
t
o
f
th
e
s
atellite
is
ca
lcu
lated
b
y
s
u
m
m
atio
n
o
f
t
h
e
s
u
b
s
y
s
te
m
m
as
s
es o
f
t
h
e
s
at
ellite
.
=
∫
˄
1
=
∫
˄
+
∫
˄
(
⌋
˄
)
(
4
)
=
˄
∫
+
∫
˄
(
⌋
˄
)
Z
R
Y
R
X
R
Y
aw
Ψ
,r
P
i
tc
h
θ
,q
R
ol
l
Φ
,p
x
y
z
x
R
z
R
y
R
S
a
t
e
l
l
i
t
e
E
a
rt
h
k
j
i
o
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
A
n
imp
leme
n
ta
tio
n
o
f o
p
tima
l
co
n
tr
o
l m
eth
o
d
s
(
L
QI
,
LQG,
L
TR)
fo
r
g
eo
s
ta
tio
n
a
r
y…
(
F
a
r
i
d
Dja
b
a
lla
h
)
4731
Ass
u
m
in
g
t
h
at
O
is
t
h
e
ce
n
ter
o
f
m
a
s
s
o
f
t
h
e
s
atel
lite
∫
=
0
An
d
d
ev
elo
p
in
g
th
e
s
ec
o
n
d
ter
m
,
w
e
o
b
tain
in
t
h
e
b
ase
(
,
,
)
=
[
∫
(
2
+
2
)
−
∫
−
∫
−
∫
+
∫
(
2
+
2
)
−
∫
−
∫
−
∫
+
∫
(
2
+
2
)
]
(
5
)
Usi
n
g
t
h
e
d
ef
i
n
itio
n
o
f
th
e
i
n
er
tial
m
o
m
e
n
t
s
o
f
th
e
s
a
tellit
e
ar
o
u
n
d
its
o
r
th
o
g
o
n
al
a
x
es
as
w
e
ll
as
th
e
d
ef
i
n
itio
n
o
f
t
h
e
in
er
tial p
r
o
d
u
cts,
w
e
o
b
tai
n
th
e
f
o
llo
w
in
g
m
atr
i
x
f
o
r
m
u
latio
n
.
=
⌋
=
[
−
−
−
−
−
−
]
,
is
th
e
i
n
er
tial
m
a
tr
ix
o
f
t
h
e
s
a
tellite
P
r
o
j
ec
tin
g
th
i
s
eq
u
atio
n
o
n
th
e
ax
es o
f
t
h
e
r
ef
er
e
n
ce
B
(
o
r
ax
es
o
f
E
u
ler
)
,
w
e
o
b
tain
E
u
ler
'
s
eq
u
atio
n
s
:
=
̇
+
−
=
̇
+
−
=
̇
+
−
(
6
)
W
e
ass
u
m
i
n
g
t
h
at
t
h
e
ax
e
s
ar
e
th
e
m
ai
n
a
x
es o
f
i
n
er
tia
=
=
=
[
̇
̇
̇
]
=
[
(
−
)
+
+
(
−
)
+
+
(
−
)
+
+
]
(
7
)
(
,
,
)
:
T
h
e
co
m
p
o
n
e
n
ts
o
f
t
h
e
co
n
tr
o
l
m
o
m
e
n
t v
ec
to
r
(
,
,
)
: T
h
e
co
m
p
o
n
e
n
ts
o
f
t
h
e
m
o
m
en
t v
ec
to
r
o
f
t
h
e
ex
o
g
en
o
u
s
d
i
s
tu
r
b
an
ce
s
.
3
.
2
.
K
inet
ic
m
e
ntio
n
Fo
r
th
e
k
in
e
tic
m
e
n
ti
o
n
,
th
e
r
o
tatio
n
m
atr
ix
ca
n
th
e
n
b
e
g
en
er
ated
b
y
th
r
ee
ele
m
en
tar
y
r
o
tatio
n
s
d
ef
in
ed
b
y
t
h
e
m
a
tr
ices:
(
,
,
)
=
[
cos
−
s
in
0
s
in
cos
0
0
0
1
]
,
=
[
cos
0
s
in
0
1
0
−
s
in
0
cos
]
,
=
[
1
0
0
0
cos
−
s
in
0
s
in
cos
]
T
h
e
r
o
tatio
n
m
atr
i
x
is
th
e
n
=
[
cos
cos
cos
s
in
−
s
in
−
cos
s
in
+
s
in
s
in
cos
cos
cos
+
s
in
s
in
s
in
s
in
cos
s
in
s
in
+
cos
s
in
cos
−
s
in
cos
+
cos
s
in
s
in
cos
cos
]
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.
9
,
No
.
6
,
Dec
em
b
er
2
0
1
9
:
4
7
2
8
-
4
7
3
7
4732
T
h
e
co
o
r
d
in
ates
o
f
t
h
e
a
n
g
u
la
r
v
elo
cit
y
v
ec
to
r
o
f
t
h
e
r
ef
er
e
n
ce
p
o
in
t
li
n
k
ed
to
th
e
s
atelli
te
B
w
it
h
r
esp
ec
t to
th
e
r
ef
er
en
ce
R
ca
n
b
e
w
r
itte
n
as:
=
−
̇
s
in
+
̇
=
̇
c
os
s
in
+
̇
c
os
=
̇
c
os
s
in
+
̇
s
in
T
h
u
s
,
b
y
in
v
er
ti
n
g
t
h
e
p
r
ev
io
u
s
eq
u
atio
n
,
it
w
il
l
al
w
a
y
s
b
e
p
o
s
s
ib
le
to
ca
lcu
late
t
h
e
an
g
les
th
e
E
u
le
r
o
f
th
e
s
ate
llit
e
i
n
an
y
r
ef
er
e
n
c
e.
̇
=
+
[
s
in
+
c
os
]
ta
n
̇
=
c
os
−
s
in
̇
=
[
s
in
+
c
os
]
c
os
−
1
4.
L
Q
I
/
L
Q
R/L
T
R
O
P
T
I
M
AL
CO
NT
RO
L
S M
E
T
H
O
DS
A
m
ain
o
b
j
ec
tiv
e
o
f
f
ee
d
b
ac
k
s
y
s
te
m
d
esi
g
n
i
s
to
ac
h
iev
e
a
n
o
m
i
n
al
p
er
f
o
r
m
a
n
ce
s
p
ec
if
icatio
n
f
o
r
a
g
iv
e
n
d
esi
g
n
m
o
d
el
o
f
t
h
e
p
lan
t,
an
d
to
m
ai
n
tai
n
t
h
is
p
er
f
o
r
m
a
n
ce
o
v
er
a
r
an
g
e
o
f
ex
p
e
cted
er
r
o
r
s
b
etw
ee
n
th
e
d
esig
n
m
o
d
el
an
d
th
e
tr
u
e
p
lan
t
[
1
8
-
21
]
.
I
n
th
is
s
ec
tio
n
,
th
r
ee
co
n
tr
o
l
m
e
th
o
d
s
ar
e
p
r
o
p
o
s
ed
an
d
d
escr
ib
e
d
in
b
r
ief
:
L
QI
co
n
tr
o
ller
,
L
QG
an
d
L
T
R
b
ased
o
n
o
p
tim
al
co
n
tr
o
l
th
eo
r
y
,
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
in
th
i
s
p
ap
er
is
d
etai
led
in
t
h
e
s
ch
e
m
e
p
r
ese
n
ted
in
F
i
g
u
r
e
4
.
Fig
u
r
e
4
.
Op
ti
m
all
co
n
tr
o
ller
s
4
.
1
.
L
Q
I
:
L
i
nea
r
Q
ua
dra
t
ic
w
it
h
inte
g
ra
l
L
Q
I
(
lin
ea
r
q
u
ad
r
atic
w
i
th
i
n
teg
r
al)
co
n
tr
o
ller
s
ar
e
th
e
s
tati
c
f
ee
d
b
ac
k
co
n
t
r
o
ller
s
b
ased
u
p
o
n
p
lan
t
s
tate
an
d
in
te
g
r
al
(
f
o
r
co
n
tin
u
o
u
s
p
lan
t
s
)
o
r
s
u
m
(
f
o
r
d
is
cr
ete
p
lan
ts
)
o
f
tr
ac
k
i
n
g
er
r
o
r
.
T
h
ey
s
tab
ilize
th
e
o
u
ter
lo
o
p
s
an
d
m
i
n
i
m
ize
t
h
e
q
u
ad
r
atic
co
s
t
f
u
n
ctio
n
al
ass
o
ciat
ed
w
it
h
s
tep
ex
o
g
en
o
u
s
i
n
p
u
t
s
.
S
tep
r
ef
er
en
c
e
i
n
p
u
t a
n
d
s
tep
d
is
tu
r
b
an
ce
[
2
2
].
4
.
2
.
LQ
G
:
lin
ea
r
q
ua
dra
t
ic
g
a
us
s
ia
n
T
h
e
L
i
n
ea
r
-
Q
u
ad
r
atic
-
Gau
s
s
ia
n
(
L
QG)
co
n
tr
o
l
p
ar
ad
ig
m
i
s
g
en
er
all
y
w
e
ll
-
u
n
d
er
s
to
o
d
in
liter
atu
r
e.
T
h
er
e
ar
e
m
an
y
m
et
h
o
d
s
a
v
ail
ab
le
o
f
ca
lc
u
lati
n
g
a
n
d
m
in
i
m
izin
g
t
h
e
e
x
p
ec
ted
co
s
t
E
[
J
]
.
T
h
e
i
m
p
le
m
en
ta
ti
o
n
of
a
L
Q
G
co
n
tr
o
l
d
es
ig
n
m
eth
o
d
[
2
3
]
to
lin
ea
r
ized
p
o
r
t
Ha
m
ilto
n
ia
n
s
y
s
te
m
d
e
f
i
n
ed
b
y
(
6
)
to
d
er
iv
e
th
e
d
y
n
a
m
ic
o
b
s
er
v
er
b
ased
co
n
tr
o
ller
F
ig
u
r
e
5.
S
at
e
ll
it
e
m
at
h
e
m
at
ical
m
od
e
l
B
e
s
t
O
p
t
im
al
S
ol
u
t
io
n
s
e
t
poi
nt
s
Cons
t
ra
i
nt
s
LQ
I
S
ol
ut
i
on
E
rror
e
va
l
ua
t
i
on
s
e
t
poi
nt
s
Cons
t
ra
i
nt
s
LQ
G
S
o
l
u
t
i
o
n
E
rror
e
va
l
ua
t
i
on
s
e
t
poi
nt
s
Cons
t
ra
i
nt
s
L
TR
S
ol
ut
i
on
E
rror
e
va
l
ua
t
i
on
Eval
u
ate
ob
je
c
ti
ve
s
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
A
n
imp
leme
n
ta
tio
n
o
f o
p
tima
l
co
n
tr
o
l m
eth
o
d
s
(
L
QI
,
LQG,
L
TR)
fo
r
g
eo
s
ta
tio
n
a
r
y…
(
F
a
r
i
d
Dja
b
a
lla
h
)
4733
x
̂
=
[
(
J
−
R
)
Q
−
BK
−
FB
T
Q
]
x
̂
+
F
u
c
y
c
=
K
x
̂
(
8
)
W
h
er
e
th
e
s
tate
o
f
th
e
co
n
tr
o
ller
x
̂
r
ep
r
esen
ts
th
e
esti
m
a
ti
o
n
o
f
th
e
s
tate
x
o
f
th
e
s
y
s
te
m
,
th
e
f
ee
d
b
ac
k
g
ain
s
ar
e:
F
=
P
f
QB
R
ω
−
1
,
K
=
R
̃
−
1
B
T
P
c
(
9
)
W
h
er
e
P
f
=
P
f
T
>
0
ar
e
th
e
s
o
lu
tio
n
s
o
f
t
h
e
f
o
llo
w
in
g
R
icca
ti e
q
u
atio
n
s
:
(
J
−
R
)
Q
P
f
+
P
f
Q
(
J
−
R
)
T
−
P
f
QB
R
ω
−
1
B
T
Q
P
f
+
Q
v
=
0
(
1
0
)
Q
(
J
−
R
)
T
P
c
+
P
c
(
J
−
R
)
Q
−
P
c
B
R
̃
−
1
B
T
P
c
+
Q
̃
=
0
(
1
1
)
W
ith
Q
v
=
Q
v
T
>
0
,
R
ω
=
R
ω
T
≥
0
th
e
co
v
ar
ian
ce
m
atr
ic
es
an
d
Q
̃
=
Q
̃
T
>
0
an
d
R
̃
=
R
̃
T
≥
0
th
e
o
p
ti
m
al
co
n
tr
o
l
w
ei
g
h
ti
n
g
m
atr
ices.
T
h
e
co
s
t f
u
n
ctio
n
o
f
th
e
o
p
ti
m
al
co
n
tr
o
l is
J
c
=
∫
(
x
T
Q
̃
x
+
u
T
R
̃
u
)
dt
∞
0
(
1
2
)
Fig
u
r
e
5
.
C
lo
s
e
lo
o
p
w
it
h
k
al
m
an
f
il
ter
4
.
3
.
L
T
R:
lo
o
p t
ra
ns
f
er
t
re
co
v
e
ry
L
o
o
p
T
r
an
s
f
er
R
ec
o
v
er
y
i
s
a
t
o
o
l a
p
p
lied
in
r
o
b
u
s
t
m
u
l
ti
v
ar
iab
le
co
n
tr
o
l.
L
T
R
d
esi
g
n
is
th
e
last
s
tep
in
a
th
r
ee
s
tep
d
esi
g
n
p
r
o
ce
d
u
r
e
f
o
r
co
n
s
t
r
u
cti
n
g
d
y
n
a
m
ic
c
o
m
p
e
n
s
ato
r
s
[
2
4
].
Fo
r
a
×
d
im
e
n
s
io
n
al
(
)
h
as o
n
l
y
m
i
n
i
m
u
m
p
h
a
s
e
tr
an
s
m
is
s
io
n
ze
r
o
s
,
t
h
en
t
h
e
o
p
en
-
l
o
o
p
tr
an
s
f
er
f
u
n
ct
io
n
.
(
)
(
)
=
[
(
−
)
−
1
]
[
(
−
+
+
)
−
1
]
→
0
→
(
−
)
−
1
(
1
3
)
an
d
ar
e
f
r
o
m
[
(
,
)
,
(
,
)
]
=
∫
(
(
)
(
)
+
(
)
(
)
)
∞
0
(
1
4
)
=
(
)
+
(
)
(
1
5
)
5.
RE
SU
L
T
S
A
ND
D
I
SCU
SS
I
O
N
W
e
p
r
esen
t
in
th
is
s
ec
tio
n
th
e
d
if
f
er
en
t
r
es
u
lts
.
I
n
o
r
d
er
t
o
d
em
o
n
s
tr
ate
th
e
s
u
p
er
io
r
it
y
o
f
attitu
d
e
s
tab
ilizatio
n
co
n
tr
o
ller
p
r
esen
ted
in
th
i
s
p
ap
er
,
L
QI
,
L
QG
an
d
L
T
R
as
f
o
llo
w
s
is
co
m
p
ar
ed
.
T
h
e
r
esu
lt
s
p
r
esen
ted
in
t
h
is
s
u
b
-
s
ec
t
io
n
w
er
e
o
b
tain
ed
w
it
h
a
s
i
m
u
lat
o
r
th
at
i
m
p
le
m
en
ts
t
h
e
d
y
n
a
m
ics
o
f
th
e
s
atelli
te
u
s
i
n
g
M
A
T
L
A
B
a
n
d
SIM
U
L
I
NK.
T
h
e
s
p
ac
ec
r
af
t
s
i
m
u
l
atio
n
m
o
d
el
in
c
lu
d
es
t
h
e
atti
tu
d
e
d
y
n
a
m
ics
an
d
k
in
e
m
at
ics.
E
x
ter
n
al
d
is
t
u
r
b
an
ce
to
r
q
u
es,
in
c
lu
d
e
g
r
a
v
it
y
g
r
ad
ien
t,
m
a
g
n
et
ic
d
is
tu
r
b
a
n
ce
s
,
an
d
ae
r
o
d
y
n
a
m
ic
d
r
ag
ar
e
s
i
m
u
lated
.
T
h
e
F
ig
u
r
e
6
p
r
ese
n
t
t
h
e
SIM
U
L
I
N
K
b
lo
c
d
ev
elo
p
ed
in
t
h
is
s
t
u
d
y
w
it
h
I
x
x
=1
5
7
;
I
y
y
=1
5
3
; I
zz
=1
5
7
;
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.
9
,
No
.
6
,
Dec
em
b
er
2
0
1
9
:
4
7
2
8
-
4
7
3
7
4734
Fig
u
r
e
6
.
Si
m
u
li
n
k
b
lo
c
d
ev
o
ll
o
p
ed
T
h
e
A
,
B
,
C
,
D
m
atr
ix
ar
e
p
r
esen
ted
:
I
n
th
e
F
i
g
u
r
e
7
,
w
e
d
o
n
e
th
e
s
i
m
u
latio
n
r
e
s
u
l
ts
i
n
,
t
h
e
t
h
r
ee
a
n
g
le
s
P
itch
,
Ya
w
a
n
d
R
o
ll a
r
e
p
l
o
tted
in
s
p
in
m
o
d
e
i
n
t
h
e
p
r
esen
ce
o
f
d
is
tu
r
b
an
ce
to
r
q
u
es.
T
h
e
s
i
m
u
latio
n
r
e
s
u
l
ts
o
f
L
QI
/
L
Q
G
c
o
n
tr
o
ller
ar
e
g
iv
e
n
f
r
o
m
Fi
g
u
r
e
8
.
B
ased
o
n
Fig
u
r
e
ca
n
b
e
f
o
u
n
d
th
at
t
h
e
s
tab
ilizatio
n
ca
n
n
o
t
b
e
ac
h
ie
v
ed
,
co
u
ld
also
b
e
co
n
clu
d
ed
as t
w
o
asp
ec
ts
: lo
w
co
n
v
er
g
e
n
ce
r
ate
an
d
ex
ce
s
s
i
v
e
in
i
tial c
o
n
tr
o
l to
r
q
u
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
A
n
imp
leme
n
ta
tio
n
o
f o
p
tima
l
co
n
tr
o
l m
eth
o
d
s
(
L
QI
,
LQG,
L
TR)
fo
r
g
eo
s
ta
tio
n
a
r
y…
(
F
a
r
i
d
Dja
b
a
lla
h
)
4735
Fig
u
r
e
7
.
Sp
in
m
o
d
e
o
f
s
atel
lit
e
Fig
u
r
e
8
.
L
QI
/
L
QG
r
esp
o
n
s
e
T
h
e
s
i
m
u
latio
n
r
es
u
lt
s
o
f
L
T
R
co
n
tr
o
ller
ar
e
g
i
v
e
n
f
r
o
m
Fi
g
u
r
e
8
.
B
ased
o
n
Fig
u
r
e,
t
h
e
p
e
r
f
o
r
m
an
ce
an
d
r
o
b
u
s
tn
e
s
s
o
f
t
h
e
L
T
R
al
g
o
r
ith
m
co
n
t
r
o
l
f
o
r
g
eo
s
ta
tio
n
n
ar
y
s
ate
llit
e
i
s
ev
a
lu
ated
.
B
ased
o
n
Fi
g
u
r
e
9
it
ca
n
b
e
f
o
u
n
d
th
a
t
an
g
u
lar
v
el
o
cit
y
is
co
n
s
ta
n
t
d
u
r
i
n
g
t
h
e
s
i
m
u
latio
n
ti
m
e,
an
d
co
n
v
er
g
en
ce
r
ate
o
f
E
u
ler
s
is
m
ai
n
tai
n
ed
at
a
h
i
g
h
lev
el
d
u
r
in
g
th
i
s
s
tag
e.
T
h
i
s
r
ev
ea
l
s
t
h
at
t
h
e
L
T
R
co
n
tr
o
l
ler
h
as
a
b
etter
ef
f
icien
c
y
o
n
co
n
tr
o
l to
r
q
u
e
co
m
p
ar
in
g
w
it
h
L
QI
/
L
QG
co
n
tr
o
ller
.
A
co
m
p
ar
ativ
e
s
t
u
d
y
is
s
h
o
w
ed
i
n
F
ig
u
r
e
1
0
,
th
e
P
itch
an
d
R
o
ll
r
esp
o
n
s
e
s
a
x
es
ar
e
p
lo
tted
.
I
t
is
o
b
s
er
v
ed
th
at
th
e
a
n
g
le
s
co
n
v
er
g
e
w
it
h
i
n
r
ap
id
l
y
w
it
h
L
T
R
co
n
tr
o
ller
.
T
h
e
ap
p
lic
atio
n
o
f
R
e
s
p
o
n
s
e
Su
r
f
ac
e
Me
t
h
o
d
(
R
SM)
s
h
o
w
i
n
Fig
u
r
e
1
1
an
d
1
2
o
f
f
e
r
s
b
ased
o
n
p
ar
a
m
eter
est
i
m
ates,
an
e
m
p
ir
ica
l
r
elatio
n
s
h
ip
b
et
w
ee
n
t
h
e
r
esp
o
n
s
e
v
ar
iab
le
(
ex
tr
ac
tio
n
y
iel
d
o
f
L
T
R
)
an
d
th
e
te
s
t
v
ar
iab
l
es.
I
n
F
i
g
u
r
e
1
1
,
w
e
p
r
esen
t
th
e
v
ar
iatio
n
o
f
later
a
l
d
is
cp
lace
m
e
n
t
as
f
u
n
ct
io
n
o
f
g
eo
m
etr
y
o
f
s
ate
llit
e
e
n
d
ec
ce
ler
atio
n
d
u
e
to
o
f
r
ea
ctio
n
w
h
ee
ls
s
p
ee
d
co
n
tr
o
l.
W
e
n
o
te
th
at
th
e
d
is
cp
lace
m
e
n
t
in
cr
ea
s
e
as
ac
ce
ler
atio
n
i
n
c
r
ea
s
e.
I
n
F
ig
u
r
e
1
2
,
w
e
p
r
ese
n
t
t
h
e
v
ar
iatio
n
o
f
lat
er
al
f
r
eq
u
e
n
c
y
a
s
f
u
n
ctio
n
o
f
g
eo
m
etr
y
o
f
s
atelli
te
en
d
t
h
e
m
as
s
i
n
T
o
n
n
e.
W
e
n
o
te
th
at
t
h
e
f
r
eq
u
en
c
y
v
ar
ie
a
s
f
u
n
c
tio
n
o
f
t
h
e
g
eo
m
etr
y
a
n
d
th
e
m
a
s
s
.
F
ig
u
r
e
9
.
L
T
R
r
esp
o
n
s
e
Fig
u
r
e
10
.
A
n
g
le
s
r
ate
L
QI
/
L
QG/L
T
R
r
esp
o
n
s
e
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.
9
,
No
.
6
,
Dec
em
b
er
2
0
1
9
:
4
7
2
8
-
4
7
3
7
4736
Fig
u
r
e
11
.
R
esp
o
n
s
e
s
u
r
f
ac
e
p
lo
ts
s
h
o
w
i
n
g
th
e
e
f
f
ec
ts
o
f
v
ar
iab
les o
n
th
e
r
esp
o
n
s
e
(
L
ater
al
d
is
p
lace
m
e
n
t)
Fig
u
r
e
12
.
R
esp
o
n
s
e
s
u
r
f
ac
e
p
lo
ts
s
h
o
w
i
n
g
th
e
e
f
f
ec
ts
o
f
v
ar
iab
les o
n
th
e
r
esp
o
n
s
e
(
L
ater
al
f
r
eq
u
en
c
y
)
6.
CO
NCLU
SI
O
N
I
n
th
i
s
p
ap
er
,
w
e
an
a
l
y
ze
d
th
e
p
er
f
o
r
m
a
n
ce
o
f
a
g
eo
s
tat
io
n
ar
y
s
ate
llit
e
s
tab
i
lized
,
L
QI
,
L
QG
an
d
L
T
R
co
n
tr
o
ller
alg
o
r
it
h
m
s
w
a
s
in
tr
o
d
u
ce
d
a
n
d
s
i
m
u
la
ted
.
T
h
e
t
h
r
ee
co
n
tr
o
ller
s
w
as
e
v
al
u
ated
o
n
a
n
o
n
l
in
ea
r
s
y
s
te
m
o
f
a
g
eo
s
tatio
n
ar
y
s
atellite
w
i
th
h
e
ig
h
t
in
er
tia
c
o
m
p
ar
ed
w
i
th
m
icr
o
s
atellite,
p
r
o
p
o
s
ed
s
tab
ilit
y
an
al
y
s
is
f
o
r
th
e
co
n
tr
o
l
la
w
o
f
E
u
ler
’
s
-
b
ased
co
n
tr
o
l
s
y
s
te
m
th
at
e
m
p
lo
y
s
s
at
u
r
atio
n
f
u
n
ctio
n
h
as
b
ee
n
p
r
esen
ted
.
Fu
r
t
h
er
m
o
r
e,
th
e
E
u
ler
’
s
b
ased
E
x
te
n
d
ed
Kalm
an
Fil
ter
(
E
KF)
an
a
l
y
ze
d
in
t
h
is
p
ap
er
w
a
s
i
m
p
le
m
en
ted
.
T
h
e
s
i
m
u
latio
n
o
f
A
DC
S
s
u
b
-
s
y
s
te
m
w
a
s
p
er
f
o
r
m
ed
b
y
ap
p
l
y
in
g
d
if
f
e
r
en
t
p
er
tu
r
b
atio
n
.
T
h
e
r
esu
lts
s
h
o
w
ed
th
at
th
e
L
QI
an
d
L
QG
co
n
tr
o
ller
w
a
s
n
o
t
ab
le
to
ac
h
ie
v
e
s
tab
le
o
p
er
atio
n
i
n
t
h
e
p
r
esen
c
e
o
f
d
is
tu
r
b
an
ce
.
On
t
h
e
o
t
h
er
h
a
n
d
,
th
e
p
r
o
p
o
s
ed
m
eth
o
d
L
T
R
th
a
t
e
m
p
lo
y
s
E
KF
o
b
s
er
v
er
w
as
f
o
u
n
d
to
ef
f
ec
tiv
e
l
y
i
m
p
r
o
v
e
b
o
th
s
m
all
s
i
g
n
al
s
tab
ilit
y
a
n
d
tr
an
s
ie
n
t
s
ta
b
ilit
y
o
f
t
h
e
A
DC
S
s
u
b
-
s
y
s
te
m
s
u
b
j
ec
ted
to
s
ev
er
e
d
is
t
u
r
b
an
ce
s
.
RE
F
E
R
E
NC
E
S
[1
]
S.
Dh
i
n
g
ra
,
D.
Ku
m
a
r,
“
A
r
e
v
iew
o
f
re
m
o
tel
y
se
n
se
d
sa
tell
it
e
ima
g
e
c
las
si
f
ic
a
ti
o
n
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
9
,
n
o
.
3
,
p
p
.
1
7
2
0
-
1
7
3
1
,
J
u
n
2
0
1
9
.
[2
]
L
.
T
.
P
h
u
o
n
,
B.
J
o
u
r
n
e
t,
D.B.
G
ia,
“
A
m
icro
w
a
v
e
a
c
ti
v
e
f
il
ter
f
o
r
n
a
n
o
sa
telli
te’s
re
c
e
iv
e
r
f
ro
n
t
-
e
n
d
s
a
t
S
-
b
a
n
d
,
”
In
te
rn
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
9
,
n
o
.
2
,
p
p
.
9
7
3
-
9
8
1
,
A
p
r
2
0
1
9
.
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
A
n
imp
leme
n
ta
tio
n
o
f o
p
tima
l
co
n
tr
o
l m
eth
o
d
s
(
L
QI
,
LQG,
L
TR)
fo
r
g
eo
s
ta
tio
n
a
r
y…
(
F
a
r
i
d
Dja
b
a
lla
h
)
4737
[3
]
E.
H.
Ka
ra
m
,
N.
A
.
A
l
-
Aw
a
d
,
N.
S
.
A
b
d
u
l
-
Ja
lee
l
,
“
De
sig
n
n
o
n
li
n
e
a
r
m
o
d
e
l
re
f
e
re
n
c
e
w
it
h
f
u
z
z
y
c
o
n
tro
ll
e
r
f
o
r
n
o
n
li
n
e
a
r
S
IS
O
se
c
o
n
d
o
r
d
e
r
sy
ste
m
s,”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
m
p
u
ter
E
n
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
9
,
n
o
.
4
,
p
p
.
2
4
9
1
-
2
4
0
2
,
A
u
g
2
0
1
9
.
[4
]
T
.
S
o
m
e
s
w
a
ri,
A
.
K.
T
i
w
a
ri,
R.
N
a
g
a
ra
j
,
“
No
v
e
l
F
ra
m
e
w
o
rk
f
o
r
N
a
v
ig
a
ti
o
n
u
sin
g
En
h
a
n
c
e
d
F
u
z
z
y
A
p
p
ro
a
c
h
w
it
h
S
li
d
i
n
g
M
o
d
e
Co
n
tro
ll
e
r
,
”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
En
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
8
,
n
o
.
6
,
p
p
.
4
3
1
0
-
4
3
2
0
,
,
De
c
e
m
b
e
r
2
0
1
8
.
[5
]
A
.
Yu
.
A
lek
sa
n
d
ro
v,
E.
B.
A
lek
s
a
n
d
ro
v
a
,
A
.
A
.
T
ik
h
o
n
o
v
,
“
S
tab
il
iza
ti
o
n
o
f
a
p
ro
g
ra
m
m
e
d
ro
ta
ti
o
n
m
o
d
e
f
o
r
a
sa
telli
te
w
it
h
e
lec
tro
d
y
n
a
m
ic att
it
u
d
e
c
o
n
tr
o
l
sy
ste
m
,
”
Ad
v
a
n
c
e
s in
S
p
a
c
e
Res
e
a
rc
h
,
v
o
l
.
6
2
,
p
p
.
142
–
1
5
1
,
2
0
1
8
.
[6
]
P.
Z
h
a
n
g
,
A
.
M
il
ls,
J.
Zam
b
re
n
o
,
P
.
H.
Jo
n
e
s,
“
T
h
e
d
e
sig
n
a
n
d
in
teg
ra
ti
o
n
o
f
a
so
f
tw
a
re
c
o
n
f
ig
u
ra
b
le
a
n
d
p
a
ra
ll
e
li
z
e
d
c
o
p
ro
c
e
ss
o
r
a
rc
h
it
e
c
t
u
re
f
o
r
L
QR co
n
tro
l
,
”
J
.
P
a
ra
ll
e
l
Distrib
.
Co
m
p
u
t
.
,
v
o
l
.
1
0
6
,
p
p
.
1
2
1
–
1
3
1
,
2
0
1
7
.
[7
]
A.
F
a
d
a
v
i,
A
.
Be
h
e
sh
ti
2
,
P
.
Ke
rm
a
n
i,
“
Of
f
in
e
/On
li
n
e
Op
ti
m
u
m
Ro
u
ti
n
g
o
f
a
UA
V
u
sin
g
A
u
x
il
iar
y
P
o
in
ts
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
7
,
no
.
1
,
p
p
.
3
9
2
-
4
0
1
,
2
0
1
7
.
[8
]
Z.
P
e
n
g
,
L
.
Jik
a
i.
“
On
n
e
w
UA
V
f
li
g
h
t
c
o
n
tro
l
sy
ste
m
b
a
se
d
o
n
Ka
lm
a
n
&
P
ID
,
”
IEE
E
T
r
a
n
sa
c
t
io
n
,
In
ter
n
a
t
io
n
a
l
Co
n
fer
e
n
c
e
o
n
Ha
rb
in
,
2
0
1
1
,
v
o
l.
2
,
p
p
.
8
1
9
-
8
2
3
.
[9
]
M.R
.
Ra
h
im
i,
S
.
Ha
ji
g
h
a
se
m
i,
D.
S
a
n
a
e
i,
“
De
si
g
n
in
g
a
n
d
S
im
u
latio
n
f
o
r
V
e
rti
c
a
l
M
o
v
in
g
Co
n
tr
o
l
o
f
U
A
V
S
y
ste
m
u
sin
g
P
ID,
L
QR
a
n
d
F
u
z
z
y
l
o
g
ic
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
3
,
no
.
5
,
p
p
.
6
5
1
-
6
5
9
,
2
0
1
3
.
[1
0
]
F
.
S
h
a
b
a
n
in
ia,
K.Ja
f
a
ri,
“
Us
in
g
L
Q
G
/
L
T
R
Op
ti
m
a
l
Co
n
tro
lM
e
th
o
d
to
Im
p
ro
v
e
S
tab
il
it
y
a
n
d
P
e
rf
o
rm
a
n
c
e
o
f
In
d
u
strial
G
a
s
T
u
rb
in
e
S
y
ste
m
,
”
In
ter
n
a
ti
o
n
a
l
S
c
h
o
la
rly
Res
e
a
rc
h
Ne
two
rk
,
p
p
.
1
-
8
,
2
0
1
2
.
[1
1
]
H.
Bij
l,
J.W
.
W
in
g
e
rd
e
n
,
T
.
B.
S
c
h
ö
n
,
M.
V
e
rh
a
e
g
e
n
,
“
M
e
a
n
a
n
d
v
a
rian
c
e
o
f
th
e
L
Q
G
c
o
st
f
u
n
c
ti
o
n
,
”
Au
t
o
ma
ti
c
a
,
v
o
l.
67
,
p
p
.
2
1
6
–
2
2
3
,
2
0
1
6
.
[1
2
]
Y.
Eb
ih
a
ra
,
T
.
Ha
g
i
w
a
ra
,
M.
A
r
a
k
i.
,
“
S
e
q
u
e
n
ti
a
l
tu
n
in
g
m
e
th
o
d
s
o
f
L
Q/LQI
c
o
n
tro
ll
e
rs
f
o
r
m
u
lt
iv
a
riab
le
s
y
ste
m
s
a
n
d
t
h
e
ir
a
p
p
li
c
a
ti
o
n
to
h
o
t
stri
p
m
il
ls
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
C
o
n
tro
l
,
v
o
l
.
7
3
,
n
o
.
1
5
,
p
p
.
1
3
9
2
-
1
4
0
4
,
1
9
9
9
.
[1
3
]
A.
Isra
r,
“
V
ib
ra
ti
o
n
a
n
d
M
o
d
a
l
A
n
a
ly
sis o
f
L
o
w
Earth
Orb
it
S
a
tell
i
te
,
”
HIND
AW
I
,
v
o
l
.
2
0
1
4
,
2
0
1
4
.
[1
4
]
L.
L
i,
L.
T
a
n
,
L
.
Ko
n
g
3
,
H
.
Ya
n
g
,
D.
W
a
n
g
,
“
F
ly
w
h
e
e
l
m
i
c
ro
-
v
ib
ra
ti
o
n
c
h
a
ra
c
ters
o
f
a
h
ig
h
re
so
lu
ti
o
n
o
p
ti
c
a
l
sa
telli
te
,
”
J
VE
INT
ER
NAT
IONA
L
L
T
D.JO
URNAL
OF
VIB
ROENG
INEE
RING
,
v
o
l.
1
9
,
n
o
.
6
,
S
ep
2
0
1
7
.
[1
5
]
Zaf
ra
n
e
M
.
A
.
,
Bo
u
d
jem
a
i
A
.
a
n
d
Bo
u
g
h
a
n
m
i
N
.
,
“
In
tera
c
ti
v
e
d
e
sig
n
o
f
sp
a
c
e
m
a
n
u
fa
c
tu
rin
g
s
y
st
e
m
s,
o
p
ti
m
a
li
t
y
a
n
d
o
p
p
o
rt
u
n
it
y
,
”
In
t
J
I
n
ter
a
c
t
D
e
s M
a
n
u
f
,
2
0
1
8
.
[1
6
]
F.
P
ir
o
u
z
m
a
n
d
,
“
Ro
b
u
st
M
o
d
e
l
P
re
d
ictiv
e
Co
n
tro
l
Ba
se
d
o
n
M
RA
S
f
o
r
S
a
telli
te
A
tt
it
u
d
e
C
o
n
tr
o
l
S
y
ste
m
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
4
,
no
.
1
,
p
p
.
8
1
-
92
,
2
0
1
4
.
[1
7
]
S.
Re
z
a
n
e
z
h
a
d
,
“
De
sig
n
o
f
F
u
z
z
y
Op
ti
m
ize
d
Co
n
tro
ll
e
r
f
o
r
S
a
telli
te
A
tt
it
u
d
e
Co
n
tr
o
l
b
y
Tw
o
S
tate
a
c
tu
a
to
r
to
re
d
u
c
e
L
i
m
it
C
y
c
le
b
a
se
d
o
n
T
a
k
a
g
i
-
S
u
g
e
n
o
M
e
th
o
d
,
”
In
te
rn
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
4
,
no
.
2
,
p
p
.
3
0
3
-
3
1
3
,
2
0
1
4
.
[1
8
]
S.
S
a
lah
,
M
.
Ha
d
j
S
a
d
o
k
,
A
.
Gu
e
ss
o
u
,
“
A
No
v
e
l
Ne
u
ro
g
li
a
l
Arc
h
it
e
c
tu
re
f
o
r
M
o
d
e
ll
in
g
S
in
g
u
l
a
r
P
e
rtu
r
b
a
ti
o
n
S
y
st
e
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
8
,
n
o
.
6
,
p
p
.
4
8
1
0
-
4
8
2
2
,
2
0
1
8
.
[1
9
]
M
.
A
.
A
.
Al
-
M
e
k
h
laf
i,
H.
W
a
h
id
,
A
.
A
b
d
A
z
i,
“
A
d
a
p
ti
v
e
N
e
u
ro
-
F
u
z
z
y
Co
n
tro
l
A
p
p
ro
a
c
h
f
o
r
a
S
in
g
le
In
v
e
rted
P
e
n
d
u
lu
m
S
y
ste
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
.
v
o
l.
8
,
n
o
.
5
,
p
p
.
3
6
5
7
-
3
6
6
5
,
2
0
1
8
.
[2
0
]
S.
Ru
iz,
J.
P
a
t
i
n
o
a
n
d
J.
Es
p
in
o
sa
,
“
P
I
a
n
d
L
QR
c
o
n
tr
o
ll
e
rs
f
o
r
F
re
q
u
e
n
c
y
Re
g
u
latio
n
i
n
c
lu
d
in
g
W
in
d
G
e
n
e
ra
ti
o
n
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
8
,
n
o
.
5
,
p
p
.
3
7
1
1
–
3
7
2
1
,
2
0
1
8
.
[2
1
]
M.
Ya
ich
,
M
.
G
h
a
rian
i
,
“
A
No
v
e
l
T
e
c
h
n
iq
u
e
f
o
r
T
u
n
i
n
g
P
I
-
c
o
n
t
ro
ll
e
r
i
n
S
w
it
c
h
e
d
Re
l
u
c
tan
c
e
M
o
to
r
Driv
e
f
o
r
T
ra
n
sp
o
rtatio
n
S
y
ste
m
s
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
E
n
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
8
,
n
o
.
6
,
p
p
.
4
2
7
2
-
4
2
8
1
,
De
c
2
0
1
8
.
[2
2
]
F.
He
n
g
.
“
De
s
ig
n
o
f
Co
n
ti
n
u
o
u
s
a
n
d
D
isc
re
te
L
QI
Co
n
tr
o
l
S
y
s
tem
s
w
it
h
S
tab
le
I
n
n
e
r
L
o
o
p
s
,
”
Ch
in
a
a
c
a
d
e
mic
jo
u
rn
a
l
e
lec
tro
n
ic p
u
b
l
isc
h
in
g
h
o
u
se
,
1
0
0
7
2
1
1
7
2
0
6
2
0
7
8
7
2
0
6
,
2
0
0
7
.
[2
3
]
Y.
W
u
a
,
B.
Ha
m
ro
u
n
,
Y.
G
o
rre
c
,
B.
M
a
sc
h
k
e
,
“
Re
d
u
c
e
d
o
rd
e
r
L
Q
G
c
o
n
tro
l
d
e
sig
n
f
o
r
p
o
rt
Ha
m
il
to
n
ian
sy
ste
m
s
,
”
Au
to
m
a
ti
c
a
,
v
o
l.
9
5
,
p
p
.
86
–
92
,
2
0
1
8
.
[2
4
]
D.
Ho
rla,
A
.
Kro
li
k
o
w
s
k
i,
“
C
o
n
ti
n
u
o
u
s
-
T
im
e
A
d
a
p
ti
v
e
L
Q
G
/
LT
R
Co
n
tro
l,
”
Pro
c
e
e
d
in
g
s
o
f
th
e
7
th
IFA
C
S
y
mp
o
si
u
m
o
n
R
o
b
u
st
Co
n
tro
l
De
sig
n
T
h
e
In
ter
n
a
ti
o
n
a
l
Fed
e
r
a
ti
o
n
o
f
A
u
t
o
ma
ti
c
Co
n
tro
l
A
a
l
b
o
rg
,
De
n
m
a
r
k
,
Ju
n
2
0
1
2
,
p
p
.
20
-
22
.
Evaluation Warning : The document was created with Spire.PDF for Python.