Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol
.
4
,
No
. 2,
J
une
2
0
1
4
,
pp
. 30
3~
31
3
I
S
SN
: 208
8-8
7
0
8
3
03
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Design of Fuzzy Optimized Co
ntroller for Satellite Attitude
Control by Two State actuator
to reduce Limit Cycle based on
Takagi-
Sugeno Meth
od
Sob
u
tyeh Rez
a
nez
h
ad
Departem
ent
of
Control
Engine
e
r
ing, S
c
ien
ce
an
d Res
ear
ch Br
an
ch, Is
l
a
m
i
c A
zad
Univers
i
t
y
,
Bor
oujerd,
Iran
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Ja
n
4, 2014
Rev
i
sed
May
3, 201
4
Accepted
May 24, 2014
In this paper
,
an
algorithm
was presented
to con
t
rol the sa
te
lli
te
atti
tude i
n
orbit in order to reduce the fu
el c
onsumption and increase longevity
o
f
satellite. B
e
cause of prop
er operati
on
and simplicity
, fuzzy
con
t
roller was
us
ed to s
a
ve fu
e
l
and an
al
yz
e th
e uncer
ta
int
y
an
d nonline
a
rit
i
es
of s
a
tel
lit
e
c
ont
rol sy
ste
m
.
T
h
e
pre
s
e
n
te
d cont
rol
a
l
gorit
hm ha
s a
hi
gh le
vel
of re
li
a
b
ility
facing unwan
ted disturbances consid
ering th
e
satell
ite
lim
ita
tions. Th
e
controller was designed based o
n
Taka
gi-Sugen
o
satellite d
y
namic model, a
powerful tool fo
r modeling nonlinear s
y
stem
s. Inherent ch
atterin
g
related to
on-off contro
ller
produces limit
cy
cles
with low
frequen
c
y am
pl
itude
. Th
is
incre
a
s
e
s
the s
y
s
t
em
error and m
a
xim
i
zes
the s
a
tell
it
e fuel co
ns
um
ption.
Particl
e
Swarm
Optim
izat
ion (
PSO) algorithm
was used to
m
i
nim
i
ze the
s
y
stem
error. Th
e satel
lit
e sim
u
lati
on results show the high performance of
fuzz
y on-o
ff co
n
t
rolle
r with
th
e p
r
esented
a
l
gorith
m
Keyword:
Satellite att
itu
d
e
con
t
ro
l
Taka
gi
-S
uge
n
o
m
odel
f
u
zzy on
-o
ff
co
n
t
r
o
l
limit cycle
PSO
Copyright ©
201
4 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Departement
of Control Engineering
,
S
c
ienc
e
and Res
earch
B
r
a
n
c
h
,
I
s
l
a
m
i
c
A
z
a
d
University
,
Borou
j
erd
,
Iran
Em
ail: sobut.e
@gm
a
il.co
m
1.
INTRODUCTION
Th
e fu
el sav
i
n
g
is h
i
gh
ly d
e
sirab
l
e in
th
e satellite a
t
titu
d
e
co
n
t
ro
l
syste
m
. Two
-
lev
e
l on
-o
ff
co
n
t
ro
llers are
g
e
n
e
rally u
s
ed with
th
e th
rust reactio
n
actuato
r fo
r satellit
e atti
tu
d
e
con
t
ro
l. Th
ese co
n
t
ro
llers
act v
e
ry fast an
d
are tim
e
in
d
e
p
e
nd
en
t.
They co
n
t
ro
l th
e satellite a
tti
tu
d
e
with
o
r
with
ou
t thru
st
p
o
wer i
n
min
i
m
u
m
ti
me
.In
on
-o
ff con
t
ro
l system
s, th
e v
a
lv
es
o
p
e
rate reliab
l
y to
stay o
p
e
n
for a sh
ort ti
m
e
as
a few
mil
liseco
n
d
s.
Th
e fu
ll op
en
in
g
of v
a
l
v
es fo
r a
fin
ite
ti
me ch
ang
e
s t
h
e d
i
screte an
gular v
e
lo
city wi
th
th
e
actu
a
tio
n
s
.
As
a resu
lt, it’s imp
o
s
sib
l
e to ob
t
a
in
zero
residual an
gu
lar
qu
ick
n
e
ss. To
p
r
even
t th
e i
n
teract
io
n
o
f
t
h
r
u
st
ers,
a
de
ad
ba
nd
i
s
i
n
t
r
od
uce
d
bet
w
ee
n t
h
e
on
-
o
f
f
c
o
nt
r
o
l
,
a
n
d
t
h
e
cont
rol
l
e
r
i
s
s
h
ut
do
wn
i
n
t
h
i
s
dea
d
band re
gion.
Thus, the c
ont
rolled system
reaches t
h
e eq
uilibrium
point (ori
gin)
w
ith reduced
velocity or
i
n
crease
d
dam
pne
ss. T
h
i
s
ge
nerat
e
s l
o
w
f
r
e
que
ncy
(
a
n
d
am
pl
i
t
ude) l
i
m
i
t
-
cy
cl
es, and
di
ssi
pat
e
s t
h
e t
h
r
u
st
er
fo
rce.
Si
nce t
h
e sat
e
l
l
i
t
e
behavi
o
r
i
s
i
nhe
rent
l
y
no
nl
i
n
ear an
d u
n
ce
rt
ai
n, i
t
’
s reco
m
m
e
nded t
o
u
s
e no
nl
i
n
ear
cont
rol algorit
h
m
s
l
i
ke fuzzy
logic. This algorithm
is independe
n
t of the accurate m
odel of m
i
cro satellite
.
Stein
ap
p
lied
t
h
ree m
u
lti-in
pu
t sin
g
l
e-ou
tput (MISO) fu
zzy co
n
t
ro
llers to stab
ilize a s
m
all (
m
icro
) satellite
in
l
o
w eart
h
or
bi
t
.
He pr
ove
d t
h
at
fuzzy
co
nt
rol
l
e
rs ca
n era
s
e t
h
e cont
r
o
l
l
i
m
i
t
a
t
i
ons b
y
choosi
ng t
h
e best
mag
n
e
tic
m
o
men
t
, po
larity a
n
d
switch
i
ng
times [1
]. Satell
ite co
n
t
ro
l syste
m
can
sav
e
fu
el an
d
enh
a
nce th
e
satellite p
e
rforman
ce. on-off
attitu
d
e
co
n
t
rol b
y
on-off and
slid
i
n
g m
o
d
e
was inv
e
stigated
in
reference [2
].
One
o
f
t
h
e
pr
obl
em
s of
usi
n
g sl
i
d
i
n
g m
o
d
e
cont
rol
l
e
r i
s
t
h
at
i
t
gene
rat
e
s a gr
eat
co
nt
rol
si
g
n
al
due
t
o
t
h
e
syste
m
u
n
certain
ty. Fu
zzy con
t
ro
ller was u
s
ed
to
so
l
v
e th
i
s
problem
[3]. Fuzzy c
ont
rol
l
er is an a
p
propriate
choice t
o
control nonli
n
ear sy
ste
m
s.
Minim
i
zing t
h
e tim
e
requi
red
for the
sy
ste
m
to reach the stea
dy state is
an im
port
a
nt
poi
nt
i
n
fuzzy
cont
r
o
l
l
e
r de
si
gn
. Thi
s
i
s
achi
e
ve
d by
o
p
t
i
m
a
l
adjust
m
e
nt
of m
e
mbers
h
i
p
fun
c
tion
s
[4
].
Th
e con
t
ro
ller
in
v
e
stig
ated
in referen
ce
[5
]
n
eeds d
i
fferen
t
in
itial v
a
lu
es to
im
p
r
o
v
e
th
e
syste
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
4,
No
. 2,
Ju
ne
2
0
1
4
:
30
3 – 3
1
3
30
4
ope
ration and minimize the response tim
e.
But these appl
ications are not proper to
des
i
gn standard linear
cont
roller.
I
n
this case
,
on
-o
ff c
o
ntr
o
ller is
an
ap
pr
o
p
riat
e o
p
tio
n
[6
,7]
.
Refere
nce
[
8
]
com
p
ared
var
i
ou
s
cont
rol
l
e
rs a
n
d
concl
u
de
d t
h
at
t
h
e fuzzy
o
n
-
o
f
f
co
nt
r
o
ller is the best one base
d on the efficie
n
cy. Fuzz
y
co
n
t
ro
ller is a
m
u
l
ti-lev
e
l relay. It u
s
es av
erag
e least
sq
ua
r
e
s m
e
t
hod
f
o
r
def
u
zzi
fi
ca
tion. In the
present
pa
per,
a special hardware
was used to conve
r
t control signals
fr
om
defuzzi
fi
ca
t
o
r. T
h
e m
i
nim
u
m
cont
rol
t
i
m
e
of
fuzzy
o
n
-
o
ff c
ont
roller
usin
g
a relay
was prese
n
ted i
n
refere
nce [9]. Particle swarm optim
ization is an
o
p
tim
izat
io
n
tech
n
i
q
u
e
b
a
sed o
n
a po
pu
lation
o
f
in
itial
resp
on
ses. Th
is tech
n
i
q
u
e
was
desig
n
e
d
con
s
idering
t
h
e s
o
ci
al
be
h
a
vi
o
r
of
bi
rds
and
fi
s
h
es
i
n
b
unc
h
[
1
0
,
11].
It was widely
use
d
by
t
h
e researche
r
s
and
m
a
ny
eff
o
rt
s
were
pe
rf
orm
e
d t
o
im
pro
v
e i
t
s
effi
ci
e
n
cy
i
n
I
n
ert
i
a
f
o
rm
ul
a from
di
ffe
rent
p
o
i
n
t
s
of
vi
ew. C
a
l
c
u
l
at
i
ng
th
e v
e
lo
city o
f
th
ese ch
ang
e
s is a sta
tic ag
en
t [12
]
. Th
is
p
a
ram
e
ter
m
a
k
e
s eq
u
ilib
ri
u
m
b
e
tween
lo
cal
an
d
ove
rall searc
h
es in t
h
e
proble
m
space.
It
means that
highe
r
values
of this
param
e
te
r are
s
u
itable
for the
ove
rall search
and its lowe
r
values a
r
e appropriate for
the lo
cal search
. Grad
u
a
l redu
ctio
n
of th
is p
a
ra
m
e
ter
was als
o
inves
tigated in
[13]
. Its e
ffects
on the
pa
r
ticle o
p
tim
izat
io
n
param
e
ters were d
i
scu
ssed
in [14
]
.
Non
lin
ear
redu
ctio
n
o
f
th
is p
a
ram
e
ter d
u
e to
fu
zzificatio
n was
d
e
scrib
e
d in
[1
4
]
.
Th
is
v
a
lu
e was also
con
s
i
d
ere
d
i
n
[1
5]
exce
pt
re
set
t
i
ng t
i
m
e
s. Gra
d
ual
re
duct
i
on
of m
a
xi
m
u
m
vel
o
ci
t
y
was al
so i
n
t
r
o
d
u
ced i
n
[1
6]
. A
not
her
i
n
t
e
rest
i
ng
res
earch ar
ea i
s
m
a
ki
ng i
m
pro
v
em
ent
i
n
part
i
c
l
e
opt
im
i
zation t
h
r
o
u
g
h
de
si
gni
ng
d
i
fferen
t
v
i
cin
i
ty
m
o
d
e
ls. Thus, it wa
s assu
med
that non
lin
ear eq
u
a
tion
s
of satellite syste
m
are k
n
o
w
n
,
an
d its
actu
a
to
r is on-o
f
f th
ru
ster. The alg
o
r
ith
m
th
at tran
sfers
co
m
m
an
d
of ax
is co
n
t
ro
lling
m
o
men
t
s to
th
e th
ru
sters
is com
p
licated for two
reas
ons:
1.
Thrusters a
r
e
not
linear cont
rollers
beca
use
t
h
ei
r
o
u
t
p
ut
i
s
fi
x
e
d
.
T
h
ere
f
o
r
e t
h
e m
o
m
e
nt
gene
rat
e
d
by
t
h
r
u
st
ers de
pen
d
s on
i
t
s
st
art
i
n
g peri
od
.
2.
Thr
u
st
er
s can
onl
y
gene
rat
e
m
o
m
e
nt
i
n
one
di
rect
i
o
n.
Thus
, an
ot
he
r t
h
r
u
st
er i
s
n
eeded t
o
gene
rat
e
m
o
men
t
in
th
e
o
ppo
site d
i
rectio
n
.
In th
is
p
a
p
e
r, a th
ree-ax
is fu
zz
y on
-o
ff con
t
ro
ller
was
presen
ted fo
r satellit
e attitu
d
e
con
t
ro
l system
.
It
gene
rat
e
s t
w
o l
e
vel
s
of o
n
-
of
f swi
t
c
hi
n
g
on t
h
e
out
put
.
Sm
oot
h ope
rat
i
on o
f
t
h
e co
nt
rol
l
a
w was ac
hi
eve
d
b
y
fu
zzy laws
an
d
Mam
d
an
i
fu
zzy inferen
c
e. Th
ere is no
n
eed
t
o
h
a
rd
ware li
m
ita
to
r in th
e on
-o
ff contro
ller
due t
o
usi
n
g t
w
o s
w
i
t
c
hi
n
g
pl
at
es on t
h
e out
put
. T
w
o l
i
n
g
u
i
s
t
i
c
vari
a
b
l
e
s were use
d
i
n
t
h
e sy
st
em
. These
v
a
riab
les prov
i
d
e th
e t
h
ru
sters u
s
ed
to
o
r
ient th
e satellite.
In
o
r
d
e
r to
con
t
ro
l th
e attitu
d
e
,
o
n
e th
ru
ster was
u
s
ed
for clo
c
k
w
ise ro
tatio
n (p
ositiv
e an
gle) an
d
th
e o
t
h
e
r on
e was u
s
ed
for cou
n
terclo
ckwise ro
tation
(n
eg
ativ
e an
g
l
e).
Wh
en
thru
ster activ
ates, th
e fu
el is bu
rned
at h
i
gh
p
r
essu
re and
th
e
attitu
d
e
ch
an
ges.Th
i
s
pape
r incl
ude
s
7 sections.
Aft
e
r introd
uction, state space model
of satellite is prese
n
ted i
n
section 2. Ta
kagi
-
Sug
e
no m
o
d
e
l was d
e
scri
b
e
d in
sectio
n 3.
Sectio
n 4 is an in
tro
d
u
c
tion
t
o
fu
zzy
on
-off algo
rith
m
.
Sectio
n
5
descri
bes t
h
e
part
i
c
l
e
swa
r
m
al
go
r
ith
m
an
d u
s
ing
ab
so
lu
t
e
erro
r in
tegratio
n
to
red
u
c
e
li
mit cycle o
n
fu
zzy
sy
st
em
. The si
m
u
l
a
t
i
on re
sul
t
s are
gi
ve
n i
n
s
ect
i
on
6.
Fi
nal
l
y
,
t
h
e c
oncl
u
si
ons
are
d
o
w
n
i
n
sect
i
o
n
7
2.
THREE
DEGREE OF FRE
E
DOM SA
TE
LLITE STATE SPACE
MODEL
Th
e
rig
i
d satellite
m
o
d
e
l with
three
d
e
g
r
ees of free
d
o
m
is presen
ted
i
n
th
is section
.
Th
e satellite
m
odel
i
s
shown i
n
F
i
g
.
1
.
Axes
X
B
, Y
B
,
and
Z
B
define th
e satellite
b
o
d
y
ax
is frame
,
and
th
e orig
in
of
coordinates is
considere
d
at
th
e cen
t
r
e of grav
ity as sh
own in
th
is fig.. Th
e ro
ll (
), p
itch
(
), a
n
d y
a
w (
)
an
g
l
es are th
e
satellite ro
tatio
n
a
l sp
eed
s
ab
ou
t ax
es
X
B
, Y
B,
and
Z
B
i
n
t
h
e
bo
dy
fi
xed
fra
m
e
. The n
o
n
-l
i
n
ear
state
m
o
d
e
l o
f
th
e satellite
ca
n
b
e
d
e
riv
e
d
by p
a
rtial d
e
riv
a
tiv
es o
f
th
e m
o
d
e
l states
x
= [
p
b
, q
b
, r
b
,
I
,
I
,
I
]
T
.
Fig
u
re
1
.
Satellite referen
ce an
d bod
y coord
i
n
a
tes [17
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
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:
208
8-8
7
0
8
Design
o
f
Fu
zzy Op
timized Co
n
t
ro
ller fo
r Sa
tellite Attitu
d
e
Con
t
ro
l
b
y
Two
S
t
a
t
e
... (So
b
u
t
yeh Reza
nezha
d
)
30
5
)
cos(
)
cos(
.
r
)
sin(
.
q
)
sin(
.
r
)
cos(
.
q
)
cos(
)
sin(
))
cos(
.
r
)
sin(
.
q
(
p
I
p
.
I
.
q
r
.
I
.
p
M
I
r
.
I
.
p
p
.
I
.
r
M
I
q
.
I
.
r
r
.
I
.
q
M
)
u
,
x
(
f
r
q
p
zz
yy
xx
z
yy
yy
xx
y
xx
yy
xx
x
I
I
I
b
b
b
Tab
l
e
1
.
Satellite Param
e
ters [17
]
Value
Descr
i
ption
Para
m
e
ter
1.
928
2
kg
m
M
o
m
e
nt of iner
tia
along x-
axis
x
x
I
1.
928
2
kg
m
M
o
m
e
nt of iner
tia
along y
-
axis
yy
I
4.
953
2
kg
m
M
o
m
e
nt of iner
tia
along z-
axis
yy
I
1
2
kg
m
Satellite inlet
m
o
ments
(,
,
)
x
yZ
MM
M
Th
ru
ster
0.
362
rad
(
20 deg)
Initial value of roll Euler
angel
0
0.
524
rad
(
30 deg)
Initial value of pitch Euler angel
0
-
0
.
262
rad
(
-
15 deg)
Initial value of ya
w Euler angel
0
0
rad
s
Body
pitch r
o
ll r
a
te
p
0
rad
s
Body
y
a
w r
a
te
q
0
rad
s
Bo
d
y
ro
ll rat
e
r
0.
01 r
a
d (
0
.
58 deg)
Dead band
3.
T-S FUZ
Z
Y
MODEL IDENTIFICATION
F
R
O
M
NO
NLINE
A
R
M
O
DELS [
1
8
]
W
i
t
h
a k
n
o
w
n
no
nl
i
n
ea
r m
odel
,
i
t
s
appr
o
x
i
m
at
e T–S fuzz
y
m
odel
can b
e
obt
ai
ne
d
by
l
i
n
eari
zat
i
o
n
ab
ou
t an
in
terested
o
p
e
rating
p
o
i
n
t
. Thu
s
, the lo
cal lin
ear
m
odel
s
of T–S
fuzzy
sy
st
em
sho
u
l
d
be det
e
rm
i
n
ed.
In th
is case, t
h
e l
o
cal m
o
d
e
l o
f
T–
S
fu
zzy m
o
d
e
l
th
at approxim
a
tes the
nonlinea
r
syste
m
m
odel at
the
eq
u
ilibriu
m
can
b
e
ex
pressed
as:
(2)
(3)
The ne
xt
step is
to determ
ine
the fuzzy
m
e
m
b
ersh
ip
fun
c
t
i
o
n
s
fo
r fu
zzy
sets abou
t tho
s
e op
erating
poi
nts or
l
o
cal
re
gions. The
ideal
case
is t
o
select th
e me
m
b
ersh
i
p
functio
n
s
m
l
u
x
l
,.....
2
,
1
),
,
(
th
at
m
i
nim
i
ze t
h
e f
o
l
l
o
wi
ng
m
odel
i
ng e
r
r
o
r:
(
4
)
Th
is is a d
i
ffi
cu
lt n
o
n
lin
ear o
p
timizatio
n
p
r
ob
lem
.
Ho
wev
e
r, in
m
a
n
y
ap
p
licatio
n
s
, si
m
p
le an
d
typ
i
cal
m
e
m
b
e
r
sh
i
p
fun
c
tio
n
s
can
b
e
u
tilized
su
ch
as
t
r
iang
u
l
ar, trap
ezo
i
d
,
an
d
Gau
ssian
fun
c
tio
n
s
. On
e
of
th
e k
e
y
p
a
rameters
is
t
h
at
the
cen
ters o
f
these
m
e
m
b
ersh
ip
fun
c
tion
s
can
b
e
d
e
term
in
ed
b
y
th
e o
p
e
rating
poi
nt
s
m
l
u
x
,.....,
3
,
2
),
,
(
1
1
, and t
h
e
ot
her
param
e
ters suc
h
as t
h
e
wi
dt
h an
d de
c
a
y
rat
e
m
a
y
be sel
ect
ed by
the de
signer.
,
)
1
(
u
B
x
A
k
x
l
l
|
|
0
,
1
0
,
1
u
o
x
u
o
x
u
f
B
x
f
A
m
l
l
l
l
l
u
x
f
a
u
B
x
A
u
x
E
1
)
,
(
)
)(
,
(
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
4,
No
. 2,
Ju
ne
2
0
1
4
:
30
3 – 3
1
3
30
6
3.
1.
T
a
ka
gi
-S
ugen
o par
a
me
ters
, attitude
c
o
ntrol descrip
t
or
C
onsi
d
eri
ng
n
onl
i
n
ea
r ex
p
r
es
si
ons a
nd t
h
ei
r rel
a
t
i
ng m
e
m
b
ershi
p
f
unct
i
o
n
s
, t
h
ere are a l
a
rge
num
ber
of m
e
m
b
ershi
p
f
u
nct
i
o
n
s
,
fu
zzy
l
a
ws an
d
r
e
qui
red
su
bsy
s
t
e
m
s
t
o
sho
w
t
h
e sy
st
em
behavi
o
r
. T
h
ere
f
or
e, t
h
e
p
r
o
c
ed
ure is
as fo
llo
ws.
Satellite d
y
n
a
m
i
c p
a
ram
e
ters ar
e defin
e
d
acco
r
d
i
n
g
to th
e
sp
eci
fic ru
les
b
a
sed
o
n
th
e
selected
op
erat
in
g
p
o
i
n
t
s u
s
i
n
g
th
e state feed
b
a
ck
th
at stabilizes th
e respon
se to
i
n
itial c
o
nd
itio
ns.
Gaussian
-
typ
e
fu
n
c
tion
s
were selected
as:
(
5
)
Whe
r
e
4
3
2
1
,
,
,
are the widths of the corres
p
onding
fun
c
tion
s
, resp
ectiv
ely Then
, the
no
rm
al
i
zed m
e
m
b
ershi
p
fu
nct
i
ons
f
o
r local
m
odels are obt
a
ined a
s
:
(
6
)
In
satellite n
onlin
ear d
y
n
a
m
i
c
m
o
d
e
ling
,
th
e syste
m
m
a
trices are ex
tracted
con
s
i
d
eri
n
g
t
h
e satellite
dy
nam
i
c equat
i
ons
on m
a
i
n
coo
r
di
nat
e
s sy
st
em
and (
6
). T
h
ese m
a
t
r
i
ces
are p
r
esent
e
d i
n
Tabl
e
2. O
p
erat
i
n
g
p
o
i
n
t
(task
po
in
t) o
f
lo
cal
li
nearizatio
n
of dyn
amic
sa
tellit
e was selected
so
t
h
at th
e satellite o
p
e
rating
reg
i
o
n
w
a
s co
v
e
r
e
d.
Th
e ab
ov
e syste
m
w
a
s lin
ear
ized
b
a
sed
on Takg
i-
Su
g
e
no
m
o
d
e
l at f
our
po
in
ts ar
ound
th
e
equilibrium
point. F
o
ur linea
r s
ubsystem
s
were
de
rive
d
from
the satellite nonlinea
r
m
odel. It should
be
men
tio
n
e
d th
at
th
e system
B matrix
was t
h
e
sam
e
in
all fo
ur states.
Tabl
e
2.
Para
m
e
t
e
rs of
t
a
ka
gi
-s
uge
n
o
m
o
d
e
l
0
0
0
0
0
0
0
0
0
2018
.
0
0
0
0
5186
.
0
0
0
0
5186
.
0
1
B
Subsy
s
tem
1
T
x
]
0
,
0
,
0
,
0
,
0
,
0
[
)
1
(
Su
b
s
ys
te
m
2
T
x
]
2600
.
0
,
5240
.
0
,
3620
.
0
,
0
,
0
,
0
[
)
2
(
Su
b
s
ys
te
m
3
T
x
]
0388
.
0
,
0429
.
0
,
0220
.
0
,
1645
.
0
,
0908
.
0
,
0613
.
0
[
)
3
(
0
0051
.
0
0945
.
0
0007
.
1
0220
.
0
0
0
0
1625
.
0
0220
.
0
9998
.
0
0
0
1628
.
0
0910
.
0
0429
.
0
4420
.
0
1
0
0
0
0
0
0
0
0
0
0962
.
0
0
2581
.
0
0
0
0
1425
.
0
2581
.
0
0
3
A
222
222
12
3
4
5
6
2
1
1
22
222
2
12
3
4
5
6
2
2
2
22
222
2
12
3
4
5
6
2
3
3
22
222
2
12
3
4
5
6
2
4
4
ex
p
ex
p
ex
p
ex
p
x
xxx
xx
h
x
xx
xxx
h
x
x
xxx
x
h
x
xx
xxx
h
1
1
1
234
2
2
1
234
3
3
1
234
4
4
1
234
()
()
()
()
x
x
x
x
h
hh
h
h
h
hh
h
h
h
hh
h
h
h
hh
h
h
00
00
0
0
00
00
0
0
00
00
0
0
1
100
000
0
1
0
000
0
0
1000
A
0
0
0
0801
.
1
4090
.
0
0
0
0
0
3541
.
0
9352
.
0
0
0
0
0
5404
.
0
2047
.
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
A
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Design
o
f
Fu
zzy Op
timized Co
n
t
ro
ller fo
r Sa
tellite Attitu
d
e
Con
t
ro
l
b
y
Two
S
t
a
t
e
... (So
b
u
t
yeh Reza
nezha
d
)
30
7
0
4415
.
0
0063
.
0
0000
.
1
0
0
0
0
0075
.
0
0
1
0
0
0075
.
0
0063
.
0
0100
.
0
0
1
0
0
0
0
0
0
0
0
0
0138
.
0
0
0117
.
0
0
0
0
0099
.
0
0117
.
0
0
4
A
Su
b
s
ys
te
m
4
T
x
]
0084
.
0
,
0100
.
0
,
0
,
0075
.
0
,
0063
.
0
,
0088
.
0
[
)
4
(
4.
FUZZY ON-OFF CONTROL
L
E
R
The det
a
i
l
e
d
expl
a
n
at
i
on o
f
t
h
e
al
go
ri
t
h
m
can
be fo
u
nd i
n
refe
re
nce
[
17]
. A
b
r
i
e
f d
e
scri
pt
i
o
n
i
s
prese
n
ted he
re. The
differe
n
ce
is that
t
h
e ra
n
g
e
of m
e
m
b
ershi
p
fu
nct
i
o
n c
h
ange
s was
m
odi
fi
ed i
n
t
h
i
s
w
o
rk t
o
analyze the limit cycle. A fuzz
y on-off
co
nt
r
o
l
l
e
r was
de
vel
o
ped
i
n
t
h
i
s
sect
i
on.
The
co
nt
r
o
l
l
e
r was
de
vel
o
ped
for on
ly ro
ll-ax
is. It’s id
en
tical fo
r th
e o
t
h
e
r two
ax
es. Th
e co
n
t
ro
ller tak
e
s th
e ad
v
a
n
t
age o
f
Larg
est Max
i
m
a
Defuzzification (L
OM) technique to ob
tai
n
o
n
-
o
ff
out
pu
t directly
. The
follo
win
g
ra
n
g
es we
re selec
t
ed fo
r
sim
u
l
a
t
i
on p
u
r
pos
es:
Φ
(t)
= [-1
,
1]
ra
d,
)
t
(
=
[-
1,
1]
ra
d/
sec a
n
d c
ont
rol
si
gna
l
u
r
= [-
M
x
,
+
M
x
]
.
4
.
1
.
Ling
u
i
st
ic D
e
s
cript
io
n
The i
n
put
an
d
out
put
v
a
ri
abl
e
s of t
h
e f
u
zzy
cont
rol
l
e
rs
wer
e
expl
ai
ne
d i
n
t
h
i
s
sect
i
on. T
h
e i
n
p
u
t
s
x
i
є
i,
wh
er
e
i
, i
=1
, 2 is th
e
u
n
iv
erse of
d
i
scou
rse
o
f
th
e t
w
o inp
u
t
s.
For li
n
g
u
i
stic inp
u
t
v
a
riab
le,
1
x
~
= “e
rror
angle,”
the
universe
of
discourse
,
1
= [
-
1
,
1]
ra
d,
rep
r
ese
n
t
s
t
h
e
ra
nge
o
f
pe
rt
u
r
b
a
t
i
on
angl
e
fr
om
t
h
e ze
r
o
refe
rence
.
F
o
r
l
i
ngui
st
i
c
i
n
put
vari
a
b
l
e
2
x
~
= “error a
ngle
rate,” the un
i
v
e
r
se of di
sco
u
r
s
e
i
s
2
= [-
1,
1]
ra
d
/sec. Th
e
ou
tpu
t
un
iv
e
r
se of di
sco
u
r
s
e
=
[-M
z
, +M
z
] represents the
on-off
out
put
ỹ
є
. Th
e
set
j
i
A
~
defi
ne
s
th
e j
th
l
i
ngui
st
i
c
val
u
e of l
i
n
g
u
i
s
t
i
c
vari
abl
e
i
x
~
, defi
ne
d o
v
er t
h
e u
n
i
v
er
se of
di
sco
u
r
s
e
i
. Th
e con
t
ro
l lev
e
l o
f
th
e system
o
p
e
r
a
tio
n can b
e
def
i
n
e
d
for
input
1
x
~
b
y
t
h
e
fo
llowing
ling
u
i
stic v
a
lu
es:
LP
A
SP
A
Z
A
SN
A
LN
A
j
i
A
5
1
~
,
4
1
~
,
3
1
~
,
2
1
~
,
1
1
~
1
~
(7
)
Sim
i
l
a
r li
ngui
s
t
i
c
val
u
es are sel
ect
ed fo
r i
n
put
2
x
~
; i.e.,
j
2
A
~
j
1
A
~
. The set
j
1
B
~
d
e
no
tes the
l
i
ngui
st
i
c
val
u
e
s
f
o
r o
u
t
p
ut
l
i
n
gui
st
i
c
vari
a
b
l
e
ỹ
1
an
d i
s
de
fi
n
e
d as
]
1
2
1
~
,
2
1
1
~
[
~
J
B
J
B
j
i
B
(
8
)
whe
r
e
J1
and
J2
a
r
e
on/
of
f c
o
m
m
a
nds f
o
r
t
h
rust
e
r
s.
4.
2.
Fuz
z
y
Ru
l
e
s
The
rul
e
s
are
b
a
sed
o
n
t
w
o i
n
put
va
ri
abl
e
s.
These
va
ri
abl
e
s ha
ve
fi
ve l
i
ng
ui
st
i
c
val
u
e
s
. T
hus
, t
h
ere
are
2
5
po
ssi
b
l
e ru
les. Th
e
ru
les were
d
e
scri
bed
in m
a
trix
form
in
Tab
l
e
3
.
Th
e
ru
les p
a
rtitio
n
s
are
heu
r
i
s
t
i
cal
l
y
chose
n
t
o
reset
t
h
e an
gl
e sm
oot
h
l
y
ove
r t
h
e
u
n
i
v
erse
o
f
di
sco
u
r
se.
Tabl
e
3.
F
u
zz
y
R
u
l
e
s
.
LP
SP
Z
SN
LN
____
X
M
X
M
X
M
X
M
LN
X
M
____
X
M
X
M
X
M
SN
X
M
X
M
____
X
M
X
M
Z
X
M
X
M
X
M
____
X
M
SP
X
M
X
M
X
M
X
M
____
LP
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
4,
No
. 2,
Ju
ne
2
0
1
4
:
30
3 – 3
1
3
30
8
Fi
gu
re
2.M
e
m
b
ers
h
i
p
f
u
nct
i
o
ns
of
i
n
put
“e
rr
or
an
gl
e”
Fi
gu
re
3.M
e
m
b
ers
h
i
p
f
u
nct
i
o
ns
of
i
n
put
“er
ro
r a
ngl
e
rat
e
”
Fi
gu
re 4.
O
u
t
p
u
t
M
e
m
b
ershi
p
fu
nct
i
o
ns
5.
PARTICLE SWARM OPTIMIZ
A
TION (PSO) AL
GORITM
Particle swarm
o
p
t
i
m
iza
tio
n
m
e
th
o
d
in
cl
u
d
e
s a
d
e
fin
ite
nu
m
b
er o
f
p
a
rticles with
rando
m
in
itia
l
v
a
lu
es. Valu
es o
f
attitu
d
e
and
v
e
lo
city are d
e
fi
n
e
d
fo
r th
e p
a
rticles. Th
ese v
a
lu
es are
m
o
d
e
led
b
y
a
p
o
s
ition
vector and
velocity vector, re
spectiv
ely. These particles
move in n-dim
e
nsional space of th
e problem to find
new
options ba
sed
on t
h
e
opti
m
ality value as
the asse
ssm
ent criterion. T
h
e
problem
space dim
e
nsion is e
qual
to
th
e nu
m
b
er o
f
effectiv
e
p
a
ram
e
ters in
th
e o
p
tim
iza
ti
o
n
fu
n
c
tion
.
Th
e
best lo
catio
n
of
p
a
rticles in
th
e p
a
st
and t
h
e pa
rticle with the bes
t
conditions are saved
i
n
separate
m
e
m
o
ry spaces. Base
d
on t
h
ese m
e
mories
,
particles
decide how to m
ove
in
future
.
In the re
petiti
ons, a
ll particles m
ove i
n
n-dim
e
nsional
problem
space.
Fin
a
lly, th
e pub
lic o
p
tim
u
m
p
o
i
n
t
is fo
und
. Particles
m
o
d
i
fy th
eir v
e
l
o
city an
d
l
o
cation
b
a
sed
o
n
t
h
e lo
cal and
p
u
b
lic b
e
st so
l
u
tio
ns.
)
(
)
(
,
,
2
2
.
,
1
1
,
,
p
p
r
p
p
r
v
v
old
n
m
globa
l
b
est
n
m
ol
d
n
m
lo
c
a
lb
e
s
t
n
m
old
n
m
ne
w
n
m
v
p
p
ne
w
n
m
ol
d
n
m
new
n
m
,
,
,
(
9
)
whe
r
e
v
ne
w
n
m
,
is p
a
rticle v
e
lo
city,
p
n
m
,
is p
a
rticle v
a
riab
le,
r
r
2
1
,
are i
n
de
p
e
nde
nt
r
a
n
d
o
m
n
u
m
b
ers
with
un
ifo
r
m
d
i
strib
u
tion
,
2
1
,
are learning
fact
ors,
p
loc
a
lbe
s
t
n
m
,
i
s
t
h
e best
l
o
cal
resp
on
se, a
nd
p
globalbest
n
m
,
is th
e
best
abs
o
l
u
t
e
s
o
l
u
t
i
o
n. Pa
rt
i
c
l
e
swarm
opt
im
i
zat
i
on al
go
ri
t
h
m
updat
e
s t
h
e part
i
c
l
e
s vel
o
ci
t
y
vect
or an
d t
h
e
n
adds the new
velocity value to attitude or particle va
lue.
The velocity update is affect
ed by bot
h loc
a
l and
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Design
o
f
Fu
zzy Op
timized Co
n
t
ro
ller fo
r Sa
tellite Attitu
d
e
Con
t
ro
l
b
y
Two
S
t
a
t
e
... (So
b
u
t
yeh Reza
nezha
d
)
30
9
ab
so
lu
te b
e
st
so
lu
tion
s
. Th
e lo
cal an
d
ab
so
lu
te b
e
st
so
lu
tio
ns are th
e ev
er best so
l
u
tio
ns ob
tain
ed
b
y
a
p
a
rticle an
d
in th
e p
o
p
u
l
ation
,
resp
ectiv
ely. Co
n
s
tan
t
s
2
1
,
a
r
e co
gn
itiv
e (p
ercep
t
u
a
l
)
p
a
ram
e
ter an
d
soci
al
pa
ram
e
ter. T
h
e
m
a
i
n
adva
nt
age
s
of
part
i
c
l
e
swarm op
timizatio
n
are sim
p
licit
y an
d low
nu
m
b
er
o
f
effectiv
e
p
a
rameters. Also
, t
h
is alg
o
rith
m
c
a
n
op
ti
m
i
ze co
m
p
lex
co
st fu
nctio
n
s
with
a larg
e
n
u
m
b
e
r of lo
cal
m
i
n
i
mu
ms
.
Fi
gu
re 5.
Ge
ner
a
l
st
ruct
u
r
e of
part
i
c
l
e
swa
r
m
al
go
ri
t
h
m
5.
1.
A
ppl
yi
n
g
par
t
i
c
l
e
sw
ar
m al
gori
t
m i
n
fuz
z
y
on-
o
ff
s
y
ste
m
t
o
re
du
ce l
i
m
i
t
cycl
e
Particle swarm algo
rith
m
was u
s
ed
t
o
d
e
termin
e th
e m
e
mb
ersh
ip fun
c
tion
s
p
a
ram
e
ters o
f
th
e fu
zzy
sy
st
em
i
nput
s.
The i
n
t
e
rval
s
o
f
t
h
ese
param
e
t
e
rs sh
o
u
l
d
be
det
e
rm
i
n
ed fi
rs
t
.
Th
us, i
t
’
s
ne
cessary
t
o
obt
a
i
n t
h
e
in
terv
al ch
an
ges of t
h
e in
t
r
od
u
c
ed
ch
a
r
acters.
The
interva
l
cha
nge
is (-1
،
1
)
. Th
en, th
e
me
m
b
ersh
ip fun
c
tio
ns
param
e
t
e
rs of al
l
pri
n
ci
pl
es can be de
fi
ne
d by
anal
y
z
i
ng t
h
e i
n
t
e
r
v
al
s. T
h
e o
p
t
i
m
i
zat
i
o
n vari
a
b
l
e
s are
fuzz
y
param
e
ters selected according to t
h
e m
e
m
b
ershi
p
functions
. T
h
e num
b
er
of t
h
ese
varia
b
les is 30; t
h
ere
f
ore,
a
30-dim
ensional space was consi
d
ere
d
to find the optimum
s
t
ate. Then,
the factors
were s
u
pposed. The
m
i
nim
u
m
num
ber
o
f
fact
ors
i
s
t
w
i
ce t
h
e n
u
m
b
er o
f
va
ri
a
b
les.
90
factors were
consi
d
e
r
ed i
n
this
res
earch.
These factors sprea
d
i
n
the space. The
pa
rticles
m
ove
to the location
with lower val
u
e
of c
o
st function.
Fin
a
lly, after a few trials, th
e op
ti
m
u
m
p
o
i
nt was fou
n
d
with
th
e m
i
n
i
m
u
m
v
a
lu
e o
f
m
e
m
b
ersh
ip
fun
c
t
i
o
n
.
The
n
, t
h
e
out
p
u
t
wa
s c
o
m
put
ed
usi
n
g a
b
s
o
l
u
t
e
er
ro
r i
n
t
e
g
r
al
t
echni
que
f
o
r t
i
m
e range
o
f
1
0
0
0
t
o
2
5
0
0
t
h
at
i
s
eq
u
a
l t
o
1
0
to
2
5
seco
nd
s, i.e. th
e tim
e wh
en
state
v
a
ri
able
s reac
h the
ste
a
dy state;
in
fact, th
e tim
e wh
en
the
state o
s
cillates aroun
d
zero
an
d
reach
th
e
stead
y-state.
Th
e m
e
m
b
ersh
ip
fun
c
tio
n
shou
ld
b
e
in
teg
r
at
ed
to
red
u
ce t
h
e am
pl
i
t
ude. Fi
nal
l
y
,
t
h
e sy
st
em
out
put
s
,
E
u
l
e
r a
n
g
l
es, we
re c
o
m
put
ed.
6.
SIMULATION
In
th
is section th
e syste
m
re
sp
on
se to
i
n
itial co
nd
itio
n
s
(zero
inpu
t resp
on
se) was analyzed
.In
Fig
u
re 6, For fu
zzy on
-off co
n
t
ro
ller, the ro
ll an
g
l
e
o
s
cillates after 1
8
seco
nd
s
with
the a
m
p
litu
d
e
o
f
0
.
02
radi
a
n
s (
1
.
1
d
e
grees
) wi
t
h
fr
e
que
ncy
o
f
0
.
0
2
8
he
rt
z. Si
nce
rat
e
feed
bac
k
i
n
t
r
od
uces
dam
p
i
n
g t
o
t
h
e sy
s
t
em
,
the phase
pla
n
e traj
ect
ory sh
ows that t
h
e time response
decays towa
rd
the ori
g
in where
both
rate a
n
d position
are zero.
Fi
gu
re
6.
R
o
l
l
angl
e
o
p
erat
i
o
n
of
f
u
zzy
o
n
-
o
ff c
o
nt
r
o
l
l
e
r wi
t
h
dea
d
ba
nd
(
n
o
n
l
i
n
ea
r m
o
d
e
l
)
0
10
20
30
40
50
-1
0
0
10
20
30
r
o
ll a
ngle
(
deg
)
Ti
m
e
(
s
ec)
0
10
20
30
40
50
-1
5
-1
0
-5
0
5
r
o
ll r
a
t
e
angl
e (
d
p
s
)
Ti
m
e
(
s
ec)
0
10
20
30
40
50
-1
-0
.
5
0
0.
5
1
Mx
(
n
.
m
)
Ti
m
e
(
s
ec)
-10
0
10
20
30
-1
5
-1
0
-5
0
5
ang
l
e
(
d
e
g
)
angl
e r
a
t
e
(
dps
)
r
o
l
l
ph
as
e
pl
a
n
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
4,
No
. 2,
Ju
ne
2
0
1
4
:
30
3 – 3
1
3
31
0
Viewed
in
term
s
o
f
th
e ph
ase p
l
an
e traj
ecto
ry, a li
m
it
c
y
cle is a c
l
osed pat
h
which i
s
approache
d
from
a
startin
g
co
nd
itio
n
eith
er fro
m
in
sid
e
th
e closed
p
a
t
h
(u
su
ally with
th
e excep
tio
n
of
th
e
o
r
i
g
in
), or from th
e
out
si
de. i
n
t
h
e
fol
l
o
wi
n
g
,
we
use
d
a
dead
ba
n
d
f
o
r de
sign
ing con
t
r
o
ller,.
Wh
en
the a
n
gles
approach t
o
0.
01
radia
n
s (0.58
degrees
), the fuzzy c
o
n
t
ro
l leav
es th
e orb
it by a switch
an
d com
e
s
to zero. The control signal
rem
a
in
s zero
u
n
til th
e ang
l
e v
a
lue is i
n
t
h
is rang
e. Th
i
s
red
u
c
es th
e
o
s
cillatio
n
s
o
f
con
t
ro
l system
an
d
en
h
a
n
ces th
e
attitu
d
e
con
t
rol. Limit cycle p
e
rform
a
n
ce is d
e
term
in
ed
b
y
sim
u
latio
n
o
f
respo
n
s
e to sm
al
l
v
a
lu
es
o
f
i
n
itial co
nd
itio
n
s
for th
e con
t
ro
llers. Th
e sam
e
v
a
lu
e o
f
lim
it
cy
cle in
th
e sam
e
fu
zzy p
l
ate is
eq
u
a
l
to freque
ncy of the lim
it cycle
.
Fi
gu
re
7a sh
o
w
s t
h
e si
m
u
l
a
t
i
on
base
d o
n
Taka
gi
-S
uge
n
o
m
odel
.
A
s
sh
ow
n i
n
t
h
e si
m
u
l
a
t
i
on, t
h
e
rules re
pre
s
ent
the locus of the
m
ovi
ng line.
It
m
eans that the outputs
can m
ove
in
outpu
t space linearly. The
extent a
nd
displacem
ent values are
determ
ined
base
d on
the inputs.
Sim
u
la
tion results show t
h
at oscillation
am
pl
i
t
ude fo
r t
h
e r
o
l
l
i
ng a
ngl
e i
n
Fi
gu
re 7a
.
i
t
i
s
very
sm
all
aft
e
r 9 seco
n
d
s an
d t
h
e f
r
e
q
uency
i
s
0.
1
4
hert
z.
Th
en
we used p
a
rticle swarm
o
p
t
i
m
izatio
n
algo
rit
h
m
to
redu
ce t
h
e
o
s
cillatio
n
am
p
l
i
t
u
d
e
. Th
e id
ea was t
o
approxim
a
te
the integrals value by di
scre
te plurals on small
intervals. Because of using disc
rete tim
e
to
co
m
p
u
t
e th
e integ
r
al, its m
a
x
i
m
u
m
li
mit is u
s
u
a
lly co
nsid
ered
u
p
t
o
three
ti
m
e
s o
f
th
e summi
t ti
me. So
, an
acceptable res
u
lt is obtained
for the in
tegral. The cost func
ti
on shoul
d be
integrate
d
under the optim
um state
to
red
u
c
e th
e
oscillatio
n
am
p
l
itu
d
e
wh
ile th
e syste
m
state i
s
o
s
cillatin
g
aro
und
zero
.
Thu
s
, t
h
e ro
llin
g
an
g
l
e
was c
o
m
put
ed
fr
om
10 sec
o
n
d
s t
o
25
seco
n
d
s a
n
d t
h
e
o
p
t
i
m
u
m
st
at
e was sh
ow
n.
Fi
gu
re
7a.
R
o
l
l
an
gl
e o
p
e
r
at
i
o
n
of
f
u
zzy
o
n
-
o
ff c
o
nt
r
o
l
l
e
r (
T
-S m
odel
)
Fig
u
re
7b
. R
o
ll ang
l
e op
eration
o
f
op
timi
zed
fuzzy
o
n
-
o
f
f
c
ont
roller (T
-S m
odel)
As sho
w
n
i
n
Fig
u
re
7
b
, th
e
oscillatio
n
s
of co
n
t
ro
l
system
were red
u
ced.
Th
is
affects t
h
e ou
tpu
t
. Th
e
requ
ired
con
t
ro
l to
rq
u
e
s was redu
ced
an
d
t
h
e satellite p
o
w
er
d
ecreased
at th
e sa
m
e
t
i
m
e. It’s clear fro
m
th
e
si
m
u
latio
n
o
f
o
p
tim
ized
fu
zzy in
fig
7
b
th
at th
e o
s
cillatio
n
a
m
p
litu
d
e
is near 0
.
00
1
rad
i
an
s (0
.0
5
d
e
g
r
ees) fo
r
th
e ro
lling
angle after 2
5
seco
nd
s.
Desirab
l
e facto
r
s i
n
th
e fu
zzy p
l
ate are s
m
aller li
mi
t
cycle an
d
no
bias (i.e.
an
g
l
es cen
t
er sh
ou
ld
b
e
clo
s
e
to
zero). In
fu
zzy stru
ct
u
r
e, the syste
m
is o
b
s
erv
e
d
as nod
e o
r
o
s
cillatio
n
aroun
d
0
10
20
30
40
50
0
10
20
30
r
o
l
l
a
ngl
e
(
deg
)
Ti
m
e
(
s
ec)
0
10
20
30
40
50
-15
-10
-5
0
5
ro
l
l
ra
te
a
n
g
l
e
(d
p
s
)
Ti
m
e
(
s
ec)
0
10
20
30
40
50
-1
-0.
5
0
0.
5
1
Mx
(
n
.
m
)
Ti
m
e
(
s
ec)
0
10
20
30
-15
-10
-5
0
5
a
n
g
l
e
(
deg)
angl
e r
a
t
e
(
dps
)
r
o
l
l
p
h
a
s
e
pl
an
e
0
10
20
30
40
50
-1
0
0
10
20
30
r
o
l
l
a
ngl
e
(
deg
)
Ti
me(
s
e
c
)
0
10
20
30
40
50
-3
0
-2
0
-1
0
0
10
r
o
l
l
r
a
t
e
a
ngl
e (
d
p
s
)
Ti
me(
s
e
c
)
0
10
20
30
40
50
-1
-0
.
5
0
0.
5
1
Mx
(
n
.
m
)
Ti
me(
s
e
c
)
-1
0
0
10
20
30
-3
0
-2
0
-1
0
0
10
ang
l
e
(
d
e
g
)
angle r
a
t
e
(
dps
)
r
o
l
l
ph
as
e p
l
ane
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Design
o
f
Fu
zzy Op
timized Co
n
t
ro
ller fo
r Sa
tellite Attitu
d
e
Con
t
ro
l
b
y
Two
S
t
a
t
e
... (So
b
u
t
yeh Reza
nezha
d
)
31
1
zero. Accord
i
n
g
to
t
h
e fi
g
u
re o
f
fu
zzy p
l
ate, satellite
p
o
w
er red
u
ces and rem
a
in
s n
ear
zero
i
n
a limit
cycle.
The
diffe
re
nce
betwee
n the
optim
u
m
state a
nd t
h
e
pre
v
ious
one is that the circles
in the
optim
u
m
state
reach
to zero
faster.
In fact, the c
onverge
nce was
obtaine
d fa
st
er. Absol
u
te zero of error
va
lue
in the steady-st
ate is
anot
her
be
nefi
t
o
f
t
h
e
al
g
o
ri
t
h
m
.
Fig
u
re
8
co
m
p
ares th
e so
lu
tion
s
o
f
zero
i
n
put respon
se at
variou
s
ro
ll an
g
l
es. It is th
e
resu
lt of fu
zzy
on
-
o
f
f
wi
t
h
de
ad ban
d
(f
b
b
d
c
), fuzzy
o
n
-
o
f
f
Ta
kagi
-S
uge
no
m
odel
(t
s)
and
o
p
t
i
m
i
zed fuzzy
o
n
-
o
f
f
(t
s-ps
o
)
.
Resu
lts show th
at o
s
cillatio
n
a
m
p
litu
d
e
of
ro
llin
g
ang
l
e
was red
u
c
ed
from
. 1
.
1
d
e
grees to
0.05
d
e
g
r
ees u
s
i
ng
p
a
rticle swarm alg
o
rith
m
.
Stead
y-stat
e error
and system
dam
p
ing tim
e
we
re redu
ced using
th
is algo
rithm
.
Fi
gu
re
8
.
r
o
l
l
angl
e c
o
m
p
ari
s
on
o
f
c
o
nt
rol
l
e
rs
Tabl
e 4 sh
o
w
s
t
h
rust
er
po
we
r bef
o
re a
nd a
f
t
e
r ap
pl
y
i
ng t
h
e part
i
c
l
e
sw
arm
al
gori
t
h
m
.
The resul
t
s
den
o
t
e
t
h
at
t
h
e
po
wer wa
s re
duce
d
aft
e
r
usi
ng t
h
e al
g
o
r
i
t
h
m
and t
h
e gas
cons
um
pt
i
on was al
so re
d
u
c
e
d i
n
th
ru
sters. Th
is
is favorab
le.
Tabl
e
4.
P
o
w
e
r c
ons
um
pt
i
o
n
Yaw
angle(
NM
.
S
)
Pitch
angle(
NM
.
S
)
Roll
angle(
NM
.
S
)
contr
o
ller
4.
346
5.
222
4.
464
fuzzy
on-
off with
dead band
4.
441
5.
373
4.
442
fuzzy
on-
off based
on T
-
S
m
odel
4.
299
3.
17
2.
791
Opti
m
i
zed f
u
zzy on-of
f
6.1. The effects of
dis
t
urbance on the c
o
ntrollers perfor
mance
Attitu
d
e
co
n
t
ro
l syste
m
was ch
eck
e
d
un
d
e
r d
i
stur
b
a
n
ce an
d
con
t
ro
llers
resistan
ce
was ch
eck
e
d
by
st
ep di
st
u
r
banc
e ope
rat
i
o
n
)
20
(
5
.
0
)
(
k
u
k
dis
. Th
e ope
rat
i
o
n wa
s per
f
o
r
m
e
d by
st
ep i
n
p
u
t
o
f
1
0
de
gr
ees.
C
o
m
b
i
n
at
i
on
o
f
t
h
e
di
st
u
r
ban
ce an
d t
h
e
c
ont
rol
si
gnal
a
ffe
c
t
s t
h
e sy
st
em
stat
e.
Fi
gu
re
9.
R
o
l
l
angl
e
O
p
erat
i
o
n
of
f
u
zzy
o
n
-
o
ff c
o
nt
r
o
l
l
e
r wi
t
h
dea
d
ba
nd
u
nde
r
)
20
(
5
.
0
)
(
k
u
k
dis
(
non
lin
ear
m
odel
)
0
10
20
30
40
50
-5
0
5
10
15
20
25
(d
eg)
Ti
m
e
(
s
e
c
)
f
bbd
c
ts
ts
-
p
s
o
0
10
20
30
40
50
0
20
40
r
o
ll
angle (
d
e
g
)
Ti
m
e
(
s
ec
)
0
10
20
30
40
50
-2
0
0
20
r
o
l
l
r
a
t
e
a
ngl
e (
d
p
s
)
Ti
m
e
(
s
ec
)
0
10
20
30
40
50
-1
0
1
Mx
(
n
.
m
)
Ti
m
e
(
s
ec
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
4,
No
. 2,
Ju
ne
2
0
1
4
:
30
3 – 3
1
3
31
2
Figure
10a. R
o
ll angle
Ope
r
at
i
on o
f
f
u
zzy
on
-o
ff
co
nt
r
o
l
l
e
r
)
20
(
5
.
0
)
(
k
u
k
dis
(T-
S
m
odel)
Figu
re 1
0
b
.
R
o
ll
angle Ope
r
at
ion o
f
optim
ized fuzzy
o
n
-
o
f
f
cont
roller
)
20
(
5
.
0
)
(
k
u
k
dis
(T
-S
m
odel)
As shown, in
th
e pr
esen
ce of d
i
stur
ba
nce, the o
u
tp
uts rea
c
h to
the fi
nal value without the steady-
state error. Controller is als
o
capable t
o
rem
ove
dist
ur
banc
e.
7.
CO
NCL
USI
O
N
Fuzzy
o
n
-
o
ff
cont
roller al
go
rithm
was introduced and si
m
u
la
ted. This
cont
roller
was installed
on
no
nlinea
r sy
stem
of a satellite and taka
gi-s
ug
eno m
ode
l with three
degrees of freedom
. T
h
e sim
u
lat
i
on results
show t
h
at the
prese
n
t fuzzy
on
-
o
f
f
co
ntr
o
l
algo
rithm
has a g
o
o
d
resistan
ce against
dist
ur
ba
nce an
d m
a
kes the
syste
m
refractory, resista
n
t and stabilized. Particle
swarm
algorithm
obtained f
r
o
m
absol
u
te err
o
r i
n
teg
r
al
was used to opti
m
ize fuzzy syste
m
and reduce oscillation
a
m
plitude of limit
cycle.
This
results in increasing
fuel consum
pti
on
and decreasing
satellite
lo
ngevity. The algorithm
has a
hi
gh convergence rate and requi
res
lowe
r n
u
m
b
er
of
param
e
ters fo
r ad
justm
e
nt. B
a
sed
on t
h
e
results, t
h
e controller fini
s
h
e
d
the traci
ng without
steady-state error usi
ng t
h
e opti
m
i
zation algorithm
.
Outp
ut
oscillations am
pl
itude was
very sm
aller th
an the
othe
r controllers. T
h
e tim
e da
m
p
ing system
and thruster
s po
we
r
co
ns
um
ption we
re
als
o
re
d
u
ced usi
n
g
this
algorithm
.
REFERE
NC
ES
[1]
St
ey
n,
W.
H.
‘
’
F
uzzy control fo
r a non-linear MIMO pl
ant subject to con
t
rol
constraints’’
, IE
EE Tr
ansact
ions on
Man and C
y
b
e
rn
etics S
y
stem
s,24(Oct. 1994
)..
[2]
M
I
TOPENCOURSEW
ARE, M
a
ssachusetts
Ins
titute
of T
e
chnolog
y
,
ht
t
p
://ocw
.m
it
. ed
u/NR/
rdonly
r
es
/Aeronautics- and- Astronautics 1630Spri
ng2004 /AB473F2C- 8F92-4073- 8115 56A77A68116C /0/ch
3
_nnl_extr
a
.pdf
.
0
10
20
30
40
50
10
20
30
r
o
ll
angle (
d
e
g
)
Ti
m
e
(
s
ec
)
0
10
20
30
40
50
-2
0
0
0
0
20
00
r
o
l
l
r
a
t
e
ang
l
e
(
d
ps)
Ti
m
e
(
s
ec
)
0
10
20
30
40
50
-1
0
1
Mx
(
n
.
m
)
Ti
m
e
(
s
ec
)
0
10
20
30
40
50
0
20
40
r
o
ll
angle (
d
e
g
)
Ti
m
e
(
s
ec
)
0
10
20
30
40
50
-
2000
0
2000
r
o
l
l
r
a
t
e
ang
l
e
(
d
ps)
Ti
m
e
(
s
ec
)
0
10
20
30
40
50
-1
0
1
Mx
(
n
.
m
)
Ti
m
e
(
s
ec
)
Evaluation Warning : The document was created with Spire.PDF for Python.