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3
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[
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7
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Do
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[
1
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T
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1
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Oth
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2
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2
3
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Nev
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ted
p
en
d
u
l
u
m
t
h
eo
r
y
ap
p
lied
in
s
el
f
-
b
ala
n
cin
g
v
eh
ic
les
[
2
8
]
W
h
en
w
e
a
n
al
y
ze
d
t
h
e
d
y
n
a
m
ics
eq
u
atio
n
o
f
th
e
s
y
s
te
m
i
n
d
etail,
b
o
th
th
e
s
lid
in
g
f
r
icti
o
n
b
et
w
ee
n
th
e
ca
r
t
a
n
d
th
e
r
ai
l
an
d
t
h
e
r
o
t
atio
n
al
f
r
ictio
n
f
r
o
m
th
e
p
en
d
u
lu
m
it
s
elf
ar
e
co
n
s
id
er
ed
in
a
m
at
h
e
m
a
tical
m
o
d
el.
C
o
n
s
id
er
in
g
r
o
tatio
n
al
f
r
ictio
n
m
ak
e
s
t
h
e
s
y
s
te
m
m
o
r
e
c
o
m
p
le
x
a
n
d
d
if
f
ic
u
lt
to
b
alan
ce
.
I
n
ad
d
itio
n
to
s
tab
ilizi
n
g
t
h
e
in
v
er
ted
p
en
d
u
l
u
m
,
t
h
e
co
n
tr
o
ller
m
u
s
t
b
e
f
le
x
ib
le
an
d
ap
p
r
o
p
r
iate
f
o
r
s
o
lv
in
g
n
o
n
lin
ea
r
s
y
s
te
m
p
r
o
b
lem
s
.
F
u
zz
y
lo
g
ic
co
n
tr
o
l
is
s
u
itab
le
f
o
r
n
o
n
li
n
ea
r
s
y
s
te
m
s
li
k
e
t
h
e
in
v
er
ted
p
e
n
d
u
l
u
m
d
u
e
to
its
in
h
er
e
n
t
ca
p
ac
it
y
to
m
a
n
ag
e
th
e
s
y
s
te
m
w
ith
o
u
t
a
n
ee
d
f
o
r
an
ac
cu
r
ate
m
at
h
e
m
atica
l
s
y
s
te
m
m
o
d
el.
Fu
zz
y
lo
g
ic
co
n
tr
o
l
d
em
o
n
s
tr
ate
s
it
s
p
r
o
m
i
n
en
ce
w
h
e
n
co
m
p
ar
ed
to
p
o
p
u
lar
co
n
tr
o
ller
s
i
n
i
n
d
u
s
tr
ial
ap
p
licati
o
n
s
s
u
c
h
as
th
e
li
n
ea
r
q
u
ad
r
atic
r
eg
u
lato
r
(
L
Q
R
)
al
g
o
r
ith
m
.
F
u
zz
y
lo
g
ic
co
n
tr
o
l
r
eq
u
ir
es
th
e
d
es
ig
n
er
ex
p
er
ien
ce
in
th
e
s
y
s
te
m
[
2
9
]
,
[
3
0
]
.
T
h
e
r
u
le
b
ase
is
th
e
m
o
s
t
i
m
p
o
r
tan
t
co
n
d
itio
n
to
s
tab
ilize
th
e
s
y
s
te
m
.
Ot
h
er
p
ar
ts
,
s
u
ch
as
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
,
d
ef
u
zz
if
icatio
n
m
et
h
o
d
,
an
d
f
ee
d
b
a
ck
g
ain
i
m
p
r
o
v
e
th
e
p
er
f
o
r
m
a
n
ce
[
3
1
]
,
[
3
2
]
.
Hen
ce
,
d
esig
n
i
n
g
co
m
p
lica
ted
f
u
zz
y
i
s
d
elib
er
ated
.
T
h
e
s
tu
d
y
f
o
cu
s
o
n
i
m
p
r
o
v
in
g
f
u
zz
y
lo
g
ic
co
n
tr
o
l
f
o
r
s
tab
ili
zin
g
th
e
i
n
v
er
ted
p
en
d
u
l
u
m
s
y
s
te
m
w
i
t
h
in
tr
i
n
s
ic
r
es
is
ta
n
ce
.
Sp
ec
i
f
icall
y
,
th
e
s
t
u
d
y
ai
m
s
to
u
n
d
er
s
ta
n
d
h
o
w
th
e
f
u
zz
y
lo
g
ic
co
n
tr
o
l
m
et
h
o
d
p
er
f
o
r
m
s
i
n
co
m
p
ar
is
o
n
to
th
e
co
n
v
e
n
tio
n
al
L
QR
al
g
o
r
ith
m
w
h
e
n
ap
p
lied
to
an
in
v
er
ted
p
en
d
u
l
u
m
s
y
s
te
m
af
f
ec
ted
b
y
r
o
tatio
n
al
f
r
ictio
n
an
d
s
lid
in
g
f
r
ictio
n
,
w
h
ic
h
ar
e
co
n
s
id
er
ed
in
tr
i
n
s
ic
r
esis
ta
n
ce
.
T
h
e
f
o
cu
s
is
o
n
an
al
y
zi
n
g
th
e
s
y
s
te
m
’
s
s
tab
ilit
y
,
o
v
er
s
h
o
o
t,
an
d
p
er
f
o
r
m
a
n
ce
u
n
d
er
d
if
f
er
en
t
in
tr
in
s
ic
r
esis
tan
ce
v
alu
e
s
.
T
h
e
r
esu
lt
s
h
o
w
s
th
a
t
f
u
zz
y
lo
g
ic
co
n
tr
o
l
k
ee
p
s
th
e
s
tab
ilit
y
o
f
th
e
s
y
s
te
m
w
h
en
ap
p
ly
in
g
a
s
er
ies
o
f
d
if
f
er
en
t
in
tr
in
s
ic
r
esi
s
tan
ce
s
.
I
n
ad
d
itio
n
,
f
u
zz
y
lo
g
ic
co
n
tr
o
l
s
u
r
p
ass
es
t
h
e
L
Q
R
alg
o
r
ith
m
i
n
ter
m
s
o
f
o
v
er
s
h
o
o
t
p
er
ce
n
tag
e,
o
s
cillatio
n
,
an
d
s
tab
ilit
y
.
T
h
e
f
ea
s
ib
ili
t
y
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
ch
e
m
e
was
ass
e
s
s
ed
t
h
r
o
u
g
h
s
i
m
u
lat
io
n
r
es
u
lts
co
n
d
u
cted
u
s
i
n
g
M
A
T
L
A
B
Si
m
u
li
n
k
.
2.
I
NT
R
I
NS
I
C
R
E
SI
ST
A
NCE
ANALY
SI
S O
F
T
H
E
I
NV
E
RT
E
D
P
E
NDU
L
UM
M
O
DE
L
T
h
e
in
v
er
ted
p
en
d
u
l
u
m
co
n
s
i
s
ts
o
f
a
m
o
v
i
n
g
ca
r
t
an
d
a
r
o
tatin
g
p
en
d
u
l
u
m
.
T
h
e
r
esis
tan
ce
o
f
th
e
s
y
s
te
m
i
n
cl
u
d
es t
h
e
s
lid
i
n
g
f
r
i
ctio
n
f
o
r
ce
b
et
w
ee
n
t
h
e
ca
r
r
iag
e
an
d
th
e
s
lid
e
an
d
th
e
r
o
tatio
n
al
f
r
ict
io
n
f
o
r
ce
o
f
th
e
r
o
tatin
g
s
h
a
f
t.
T
h
e
o
th
er
r
esis
ta
n
ce
is
n
o
t
co
n
s
id
er
ed
.
T
h
e
m
o
d
el
o
f
t
h
e
i
n
v
er
ted
p
en
d
u
lu
m
is
s
h
o
w
n
i
n
Fig
u
r
e
2
.
I
n
Fi
g
u
r
e
2
,
is
t
h
e
m
as
s
o
f
t
h
e
ca
r
t,
is
t
h
e
m
as
s
o
f
t
h
e
p
en
d
u
lu
m
,
is
th
e
co
ef
f
i
cien
t
o
f
s
lid
in
g
f
r
ictio
n
,
β
i
s
th
e
co
e
f
f
ic
ien
t
o
f
r
o
tatio
n
al
f
r
ictio
n
,
is
th
e
ac
ce
ler
atio
n
o
f
g
r
a
v
it
y
.
is
th
e
f
o
r
ce
ac
tin
g
o
n
th
e
ca
r
t
.
T
h
e
ca
r
t
’
s
p
o
s
itio
n
i
s
.
T
h
e
ca
r
t v
elo
cit
y
is
̇
.
T
h
e
f
allin
g
an
g
le
i
s
an
d
th
e
an
g
u
lar
v
elo
c
it
y
is
̇
.
Fro
m
Fi
g
u
r
e
2
,
th
e
p
o
s
itio
n
o
f
th
e
p
en
d
u
l
u
m
is
d
er
iv
ed
:
=
+
=
(
1
)
Der
iv
ati
v
e
(
1
)
,
w
e
g
et
t
h
e
v
e
lo
cit
y
o
f
t
h
e
p
en
d
u
lu
m
as
(
2
)
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
Vo
l.
23
,
No
.
1
,
Feb
r
u
ar
y
20
25
:
2
3
4
-
2
4
5
236
̇
=
̇
+
̇
̇
=
−
̇
(
2
)
Fig
u
r
e
2
.
Mo
d
el
o
f
in
v
er
ted
p
en
d
u
l
u
m
Sin
ce
t
h
e
v
elo
cit
y
o
f
t
h
e
ca
r
t a
n
d
th
e
p
en
d
u
lu
m
,
t
h
e
k
i
n
etic
e
n
er
g
y
o
f
t
h
e
s
y
s
te
m
ca
n
b
e
ex
p
r
ess
ed
as
(
3
)
:
=
+
=
1
2
(
+
)
̇
+
1
2
2
̇
2
+
̇
̇
(
3
)
B
esid
es,
th
e
p
o
ten
tial e
n
er
g
y
o
f
th
e
s
y
s
te
m
i
s
ca
lcu
lated
as
(
4
)
:
=
+
=
(
4
)
C
o
m
b
i
n
in
g
b
o
th
k
in
e
tic
en
er
g
y
an
d
p
o
ten
tial e
n
er
g
y
,
w
e
g
et
th
e
L
a
g
r
an
g
ia
n
o
f
t
h
e
i
n
v
er
te
d
p
en
d
u
lu
m
:
=
−
=
1
2
(
+
)
̇
2
+
1
2
2
̇
2
+
̇
̇
−
(
5
)
T
h
e
ef
f
ec
t
o
f
t
h
e
s
lid
in
g
f
r
icti
o
n
f
o
r
ce
b
et
w
ee
n
th
e
ca
r
r
iag
e
an
d
th
e
s
lid
e
is
co
n
s
id
er
ed
to
g
eth
er
w
ith
th
e
e
f
f
ec
t
o
f
th
e
r
o
tatio
n
al
f
r
ic
tio
n
f
o
r
ce
o
f
t
h
e
r
o
tatin
g
s
h
a
f
t
.
Hen
ce
,
t
h
e
to
tal
r
es
is
ta
n
ce
e
n
er
g
y
ap
p
lied
to
t
h
e
in
v
er
ted
p
en
d
u
lu
m
i
s
d
er
iv
ed
as
(
6
)
:
=
1
+
2
=
1
2
̇
2
+
1
2
̇
2
(
6
)
T
h
e
E
u
ler
-
L
a
g
r
an
g
e
eq
u
atio
n
s
ar
e
u
s
ed
to
d
e
r
iv
e
th
e
eq
u
atio
n
s
o
f
m
o
tio
n
f
o
r
a
p
h
y
s
ica
l
s
y
s
te
m
,
an
d
th
ese
eq
u
a
tio
n
s
ar
e
g
iv
e
n
b
y
:
(
̇
)
−
+
̇
=
(
̇
)
−
+
̇
=
0
(
7
)
C
o
m
b
i
n
in
g
(
1
)
–
(
6
)
an
d
an
aly
z
in
g
(
7
)
,
w
e
g
et
t
h
e
d
if
f
er
en
t
ial
eq
u
atio
n
s
f
o
r
th
e
i
n
v
er
ted
p
en
d
u
lu
m
s
y
s
te
m
:
(
+
)
̈
+
̈
=
+
2
−
̇
2
̈
+
̈
=
−
̇
(
8
)
So
lv
i
n
g
(
8
)
,
w
e
g
et
t
h
e
d
y
n
a
m
ic
eq
u
atio
n
o
f
t
h
e
i
n
v
er
ted
p
en
d
u
lu
m
s
y
s
te
m
:
̈
=
(
+
̇
−
̇
)
−
(
−
̇
)
(
+
)
−
2
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
E
n
h
a
n
ce
d
fu
z
z
y
lo
g
ic
co
n
tr
o
l fo
r
o
ve
r
co
min
g
in
tr
in
s
ic
r
esis
t
a
n
ce
in
in
ve
r
ted
p
en
d
u
lu
m
…
(
Tin
Lu
Tr
u
n
g
)
237
̈
=
(
−
̇
)
(
+
)
−
(
+
̇
2
−
̇
)
(
+
)
2
−
2
2
2
(
10
)
Ass
u
m
in
g
t
h
e
s
tate
v
ar
iab
les
1
=
,
2
=
̇
,
3
=
,
3
=
̇
.
T
h
en
,
th
e
s
y
s
te
m
s
ta
te
-
s
p
ac
e
is
d
er
iv
ed
as
(
1
1
)
:
̇
1
=
2
̇
2
=
(
+
4
2
3
−
2
)
−
(
3
−
4
)
3
(
+
)
−
2
3
̇
3
=
4
̇
4
=
(
3
−
4
)
(
+
)
−
(
+
4
2
3
−
2
)
3
(
+
)
2
−
2
2
2
3
(
11
)
T
h
e
an
d
v
al
u
es
r
ep
r
esen
t
t
h
e
in
tr
i
n
s
ic
r
esi
s
ta
n
ce
s
o
f
t
h
e
in
v
er
ted
p
en
d
u
lu
m
s
y
s
te
m
,
co
n
tr
i
b
u
tin
g
to
in
cr
ea
s
ed
m
o
d
el
co
m
p
le
x
it
y
a
n
d
th
e
n
ec
es
s
it
y
f
o
r
ac
cu
r
at
e
p
ar
am
eter
s
i
n
co
n
v
en
t
io
n
al
c
o
n
tr
o
l
s
ch
e
m
es.
A
s
th
e
s
y
s
te
m
b
ec
o
m
e
s
h
i
g
h
l
y
n
o
n
li
n
ea
r
,
co
n
v
e
n
tio
n
al
li
n
ea
r
co
n
tr
o
l
th
eo
r
y
is
in
ap
p
licab
le.
T
h
er
ef
o
r
e,
th
e
ex
p
lo
r
atio
n
o
f
n
o
n
li
n
ea
r
co
n
tr
o
l
m
eth
o
d
s
,
tailo
r
ed
to
ad
d
r
ess
th
e
co
m
p
le
x
itie
s
in
h
er
en
t
in
t
h
i
s
n
o
n
l
in
ea
r
s
y
s
te
m
,
b
ec
o
m
e
s
i
m
p
er
ati
v
e.
3.
CO
NVEN
T
I
O
NA
L
AND
P
R
O
P
O
SE
D
F
U
Z
Z
Y
L
O
G
I
C
CO
NT
RO
L
M
E
T
H
O
DS
T
h
e
ad
o
p
tio
n
o
f
en
h
an
ce
d
f
u
z
z
y
lo
g
ic
co
n
tr
o
l
is
p
r
o
p
o
s
ed
f
o
r
co
n
tr
o
llin
g
t
h
e
in
v
er
ted
p
en
d
u
lu
m
w
it
h
in
tr
i
n
s
ic
r
e
s
is
ta
n
ce
s
.
On
e
n
o
ta
b
le
f
ea
t
u
r
e
o
f
f
u
zz
y
lo
g
ic
co
n
tr
o
l
is
t
h
at
it
is
a
m
o
d
el
-
f
r
ee
ap
p
r
o
ac
h
,
w
h
ich
is
esp
ec
iall
y
u
s
e
f
u
l
f
o
r
h
an
d
li
n
g
th
e
s
y
s
te
m
’
s
in
tr
i
n
s
ic
co
m
p
lex
it
y
a
n
d
n
o
n
l
in
ea
r
it
y
.
F
u
z
z
y
lo
g
ic
co
n
tr
o
l
,
in
co
n
tr
ast
to
co
n
v
en
tio
n
al
co
n
tr
o
l
tech
n
iq
u
es,
i
s
ex
ce
lle
n
t
at
c
ap
tu
r
in
g
an
d
m
an
a
g
i
n
g
u
n
ce
r
t
ain
tie
s
,
w
h
ic
h
m
ak
e
s
it
a
g
o
o
d
f
it
f
o
r
s
itu
atio
n
s
w
h
er
e
it
co
u
ld
b
e
d
if
f
icu
lt
to
b
u
ild
an
ac
cu
r
ate
m
at
h
e
m
at
ical
m
o
d
el.
E
f
f
ec
tiv
e
co
n
tr
o
l
tech
n
iq
u
es
f
o
r
th
e
in
v
er
ted
p
en
d
u
l
u
m
s
y
s
te
m
w
i
th
i
n
h
er
e
n
t
r
esis
ta
n
ce
s
ar
e
m
ad
e
p
o
s
s
ib
le
b
y
t
h
is
f
lex
ib
le
an
d
ad
ap
tab
le
f
u
zz
y
co
n
tr
o
l a
p
p
r
o
ac
h
,
p
o
ten
tia
ll
y
lead
in
g
to
in
cr
ea
s
ed
s
tab
ilit
y
a
n
d
p
er
f
o
r
m
a
n
c
e.
A
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
(
F
L
C
)
’
s
ar
ch
itect
u
r
e
an
d
d
esi
g
n
i
n
g
p
r
o
ce
s
s
i
n
g
ar
e
s
h
o
w
n
i
n
Fig
u
r
e
3
.
I
t
co
n
s
is
ts
o
f
es
s
en
t
ial
ele
m
e
n
t
s
:
a
co
n
tr
o
l
r
u
le
b
ase,
a
f
u
zz
if
ic
atio
n
p
r
o
ce
d
u
r
e
th
at
tr
an
s
f
o
r
m
s
s
y
s
te
m
f
ee
d
b
ac
k
s
ig
n
al
in
to
f
u
zz
y
v
al
u
e
s
to
s
u
p
p
o
r
t
r
u
le
-
b
ased
r
ea
s
o
n
i
n
g
,
an
d
a
d
ef
u
zz
i
f
icat
io
n
s
tep
t
h
at
c
o
n
v
er
ts
th
e
i
n
f
er
r
ed
f
u
zz
y
o
u
tp
u
t i
n
to
a
d
is
tin
ct
a
n
d
ac
cu
r
ate
co
n
tr
o
l sig
n
al
f
o
r
t
h
e
s
y
s
te
m
.
Fig
u
r
e
3
.
Fu
zz
y
lo
g
ic
co
n
tr
ol
’
s
ar
ch
itect
u
r
e
an
d
d
esig
n
i
n
g
p
r
o
ce
s
s
in
g
3
.
1
.
Co
nv
ent
i
o
na
l f
uzzy
lo
g
i
c
co
ntr
o
l
I
n
th
e
co
n
tr
o
ller
d
esig
n
i
n
g
p
r
o
ce
s
s
,
th
e
ch
o
ice
o
f
a
n
in
ter
f
e
r
en
ce
s
y
s
te
m
i
s
i
m
p
o
r
ta
n
t
b
ec
au
s
e
it
w
ill
af
f
ec
t
th
e
e
f
f
icien
c
y
a
n
d
co
m
p
u
tatio
n
a
l
co
m
p
lex
i
t
y
o
f
th
e
co
n
tr
o
ller
.
Ma
n
y
i
n
v
er
ted
p
en
d
u
l
u
m
s
t
u
d
ies
ar
e
u
s
i
n
g
Ma
m
d
an
i
-
t
y
p
e
in
ter
f
er
en
ce
s
y
s
te
m
s
to
d
esig
n
t
h
e
co
n
tr
o
ller
.
Fo
r
th
e
m
a
m
d
a
n
i
f
u
zz
y
i
n
ter
f
e
r
en
ce
s
y
s
te
m
(
FIS)
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
Vo
l.
23
,
No
.
1
,
Feb
r
u
ar
y
20
25
:
2
3
4
-
2
4
5
238
th
e
o
u
tp
u
t
o
f
ea
c
h
r
u
le
in
t
h
e
r
u
le
-
b
ase
i
s
t
h
e
f
u
zz
y
s
et
a
n
d
t
h
e
o
u
tp
u
t
o
f
t
h
e
m
o
d
el
is
ca
lc
u
lat
ed
as
a
co
m
b
i
n
atio
n
o
f
th
ese
f
u
zz
y
s
ets.
So
,
it
r
eq
u
ir
es
a
d
ef
u
zz
if
ica
tio
n
m
et
h
o
d
to
co
n
v
er
t
f
u
zz
y
s
et
v
al
u
es
in
t
o
n
u
m
er
ical
v
a
lu
e
s
f
o
r
co
n
tr
o
l
in
th
e
f
i
n
al
s
ta
g
es.
I
n
Ma
m
d
a
n
i
i
n
ter
f
er
en
ce
,
t
h
e
r
e
ar
e
t
w
o
p
o
p
u
lar
d
ef
u
zz
i
f
ic
atio
n
m
eth
o
d
s
:
th
e
m
ea
n
o
f
m
a
x
i
m
a
m
et
h
o
d
(
MO
M)
an
d
th
e
ce
n
tr
o
id
o
f
g
r
av
i
t
y
(
C
OG)
m
et
h
o
d
[
3
3
]
.
T
h
e
MO
M
m
et
h
o
d
ca
n
b
e
r
ep
r
esen
ted
th
r
o
u
g
h
m
at
h
e
m
a
t
ical
f
o
r
m
u
las a
s
(
1
2
)
:
∗
=
{
:
(
)
=
1
}
(
12
)
W
h
er
e
∗
is
th
e
cr
is
p
o
u
tp
u
t
v
a
lu
e,
(
)
is
th
e
m
e
m
b
er
s
h
ip
f
u
n
ct
io
n
o
f
o
u
tp
u
t.
T
h
e
MO
M
d
ef
u
zz
i
f
icatio
n
m
et
h
o
d
s
m
a
y
in
tr
o
d
u
ce
n
o
n
li
n
ea
r
b
eh
av
io
r
lead
in
g
to
s
y
s
te
m
in
s
tab
ilit
y
,
r
en
d
er
in
g
t
h
e
m
u
n
s
u
itab
le
f
o
r
co
n
tr
o
l
p
r
o
b
lem
s
[
3
4
]
.
I
n
t
h
e
C
O
G
d
ef
u
z
z
if
i
c
a
ti
o
n
m
et
h
o
d
,
th
e
o
u
t
p
u
t
o
f
t
h
e
c
en
t
r
o
i
d
-
b
a
s
e
d
m
e
th
o
d
is
c
o
m
p
u
t
e
d
b
y
(
1
3
)
:
∗
=
∫
(
)
∞
−
∞
∫
(
)
∞
−
∞
(
13
)
B
ec
au
s
e
th
e
co
m
p
u
ti
n
g
p
r
o
ce
s
s
h
as
a
n
in
teg
r
al
o
p
er
ato
r
,
th
e
C
OG
m
eth
o
d
s
r
eq
u
ir
e
a
h
i
g
h
c
o
m
p
u
tatio
n
in
d
is
cr
ete
ti
m
e.
C
o
n
s
eq
u
e
n
t
l
y
,
(
1
3
)
h
as
h
i
g
h
co
m
p
u
tatio
n
al
co
m
p
le
x
it
y
b
ec
a
u
s
e
it
i
n
v
o
lv
e
s
a
co
m
p
lete
f
r
ac
tio
n
al
ca
lc
u
latio
n
.
T
h
at
in
cr
ea
s
es
i
m
p
le
m
en
tatio
n
co
s
t
s
f
o
r
th
e
p
r
o
ce
s
s
i
n
g
u
n
it.
T
h
er
ef
o
r
e,
a
s
i
m
p
le
r
ca
lcu
latio
n
an
d
d
ef
u
zz
i
f
icatio
n
m
et
h
o
d
n
ee
d
s
to
b
e
f
o
u
n
d
to
s
av
e
co
s
ts
a
n
d
ca
lcu
la
tio
n
ti
m
e.
3
.
2
.
P
r
o
po
s
ed
f
uzzy
lo
g
ic
co
ntr
o
l w
it
h m
o
d
if
ied su
g
e
no
inte
rf
er
ence
s
T
o
o
p
tim
ize
th
e
ca
lcu
latio
n
p
r
o
ce
s
s
,
th
e
T
ak
ag
i
–
Su
g
e
n
o
–
Kan
g
(
T
SK)
in
ter
f
er
en
ce
s
ar
e
ad
o
p
ted
th
an
k
s
to
th
eir
s
i
m
p
licit
y
a
n
d
ef
f
icie
n
c
y
.
C
o
m
p
ar
ed
to
th
e
co
n
v
e
n
tio
n
al
Ma
m
d
a
n
i
FI
S,
th
e
Su
g
e
n
o
FIS
ca
lcu
latio
n
p
r
o
ce
s
s
r
elies
o
n
c
r
is
p
v
alu
e
s
f
o
r
t
h
e
co
n
tr
o
l,
all
o
w
i
n
g
u
s
to
b
y
p
as
s
d
ef
u
zz
i
f
ic
atio
n
s
tep
s
w
i
th
o
u
t
co
m
p
r
o
m
is
i
n
g
th
e
s
tab
ilit
y
a
n
d
ac
cu
r
ac
y
o
f
th
e
co
n
tr
o
l
s
y
s
te
m
.
I
n
t
h
e
p
r
o
p
o
s
ed
m
eth
o
d
,
t
h
e
co
n
s
eq
u
e
n
t
cla
u
s
e
o
f
′
ℎ
r
u
le
in
r
u
le
-
b
ase
s
y
s
te
m
is
a
m
ap
p
i
n
g
f
u
n
ct
io
n
b
elo
n
g
in
g
to
th
e
in
p
u
t
v
ar
iab
le:
=
(
1
,
2
,
3
,
4
)
(
14
)
I
n
g
en
er
al,
th
e
m
ap
p
in
g
f
u
n
cti
o
n
in
(
1
4
)
ca
n
b
e
a
n
o
n
lin
ea
r
,
lin
ea
r
f
u
n
ctio
n
,
o
r
o
n
ly
a
co
n
s
ta
n
t
v
al
u
e.
T
h
e
f
u
zz
y
o
u
tp
u
t
is
d
ev
id
ed
i
n
to
s
ev
e
n
lev
el
s
an
d
th
e
f
u
n
ct
io
n
is
d
ef
in
ed
as
a
co
n
s
tan
t
v
alu
e
f
o
r
ea
ch
lev
el
f
o
r
s
i
m
p
lic
it
y
i
n
t
h
is
s
tu
d
y
.
T
h
e
o
v
er
all
o
u
tp
u
t
v
alu
e
i
s
ca
lcu
l
ated
as
(
1
5
)
:
∗
=
∑
,
(
15
)
W
h
er
e
is
th
e
d
eg
r
ee
o
f
tr
u
th
f
o
r
th
e
i
th
r
u
le.
T
h
e
co
m
p
u
ti
n
g
p
r
o
ce
s
s
in
g
in
T
SK
(
1
5
)
is
m
o
r
e
s
i
m
p
le
th
a
n
m
a
m
d
a
n
i
FIS
o
u
tp
u
t
i
n
(
1
3
)
b
ec
au
s
e
t
h
er
e
i
s
n
o
i
n
te
g
r
al
f
u
n
ctio
n
in
(
1
5
)
.
C
o
n
s
eq
u
e
n
tl
y
,
th
e
ad
o
p
tio
n
o
f
th
e
T
SK
in
ter
f
er
en
ce
s
y
s
te
m
i
s
ad
v
o
ca
ted
f
o
r
its
ab
ilit
y
to
e
x
p
ed
ite
th
e
ca
lc
u
latio
n
p
r
o
ce
s
s
i
n
t
h
e
f
u
zz
y
co
n
tr
o
ller
d
esig
n
.
T
h
e
T
SK
FIS
h
as
m
i
n
i
m
ized
th
e
co
m
p
u
ta
tio
n
al
co
m
p
le
x
it
y
o
f
th
e
co
n
tr
o
ller
,
en
ab
lin
g
u
s
to
s
elec
t
ad
d
itio
n
al
in
p
u
ts
a
n
d
estab
li
s
h
m
o
r
e
co
n
tr
o
l
r
u
les.
T
o
co
n
d
u
ct
a
m
o
r
e
co
m
p
r
eh
e
n
s
i
v
e
s
y
s
te
m
e
v
al
u
atio
n
,
t
h
e
co
n
tr
o
ller
’
s
i
n
p
u
t
s
co
m
p
r
is
e
th
e
an
g
le,
p
o
s
itio
n
a
n
g
u
la
r
v
elo
cit
y
,
an
d
v
e
lo
cit
y
o
f
th
e
c
ar
t
(
1
=
;
2
=
̇
;
3
=
;
4
=
̇
)
.
Usi
n
g
t
h
ese
f
o
u
r
p
ar
a
m
eter
s
m
ak
e
s
t
h
e
co
n
tr
o
ller
m
o
r
e
e
f
f
e
ctiv
e
a
n
d
ac
cu
r
ate
b
ec
au
s
e
th
e
in
ter
f
er
en
ce
s
y
s
te
m
g
ets
m
o
r
e
ass
ess
m
en
t
s
ab
o
u
t
th
e
s
y
s
t
e
m
.
R
e
m
i
n
d
in
g
th
e
s
ta
te
-
s
p
ac
e
eq
u
atio
n
d
en
o
ted
as
(
1
1
)
,
th
e
s
tate
v
ar
iab
les
f
ea
t
u
r
ed
in
th
is
eq
u
atio
n
ar
e
also
t
h
e
f
u
zz
y
co
n
tr
o
ller
’
s
in
p
u
t
v
ar
i
ab
les.
T
h
e
o
b
j
ec
tiv
e
o
f
th
e
co
n
tr
o
ller
is
to
m
ain
tain
eq
u
ilib
r
iu
m
b
y
b
alan
ci
n
g
th
e
p
en
d
u
lu
m
at
a
d
ef
lectio
n
a
n
g
l
e
o
f
ze
r
o
(
=
0
).
I
n
itiati
n
g
th
e
d
esig
n
p
r
o
ce
s
s
,
w
e
e
m
b
ar
k
o
n
cr
af
tin
g
a
co
n
tr
o
l
r
u
le
b
ase
b
y
en
u
m
er
atin
g
c
o
n
ce
iv
ab
le
co
m
b
i
n
atio
n
s
o
f
s
ta
te
v
ar
iab
le
s
w
i
th
i
n
t
h
e
s
tate
s
p
ac
e
eq
u
ati
o
n
.
Fu
zz
y
v
al
u
es
s
u
c
h
as
n
e
g
at
iv
e
(
NE
)
,
ze
r
o
(
ZE
)
,
an
d
p
o
s
itiv
e
(
PO
)
ar
e
s
et
to
d
e
n
o
te
th
e
d
ir
ec
tio
n
o
f
th
e
s
tate
v
ar
iab
le
m
o
v
e
m
e
n
t.
Fo
r
th
e
o
u
tp
u
t
v
ar
i
ab
le
o
f
th
e
co
n
tr
o
ller
,
w
e
also
s
et
th
e
f
u
z
z
y
v
al
u
e
s
as
n
eg
ati
v
e
b
i
g
(
NB
),
n
eg
ativ
e
m
ed
i
u
m
(
NM
)
,
n
eg
ati
v
e
s
m
all
(
NS
)
,
ze
r
o
(
ZE
)
,
p
o
s
itiv
e
s
m
al
l
(
PS
)
,
p
o
s
itiv
e
m
ed
iu
m
(
PM
)
,
p
o
s
itiv
e
b
ig
(
PB
)
to
f
ea
tu
r
e
f
o
r
co
n
s
eq
u
en
t v
a
lu
e
s
in
(
1
3
)
.
Fig
u
r
es
4
(
a)
an
d
(
b
)
s
h
o
w
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
o
f
t
h
e
ca
r
t
’
s
p
o
s
it
io
n
(
)
an
d
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
o
f
t
h
e
ca
r
t
’
s
v
e
lo
cit
y
(
̇
)
.
Fi
g
u
r
es
4
(
c)
an
d
(
d
)
s
h
o
w
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
o
f
t
h
e
f
a
lli
n
g
a
n
g
le
(
)
an
d
m
e
m
b
er
s
h
i
p
f
u
n
ctio
n
o
f
th
e
a
n
g
u
lar
v
elo
cit
y
(
̇
)
.
Si
m
ilar
l
y
,
t
h
e
m
e
m
b
er
s
h
i
p
f
u
n
c
tio
n
o
u
tp
u
t
v
ar
iab
le
is
s
h
o
w
n
i
n
Fi
g
u
r
e
5
.
Fig
u
r
e
6
s
h
o
w
s
e
x
a
m
p
le
co
m
b
i
n
atio
n
s
o
f
co
n
tr
o
l
r
u
le
s
b
ased
o
n
s
tate
v
ar
iab
les
an
d
T
ab
le
1
s
h
o
w
s
t
h
e
co
m
p
o
s
ed
r
u
le
b
ase
f
o
r
th
e
i
n
v
er
ted
p
en
d
u
lu
m
s
y
s
te
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
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n
h
a
n
ce
d
fu
z
z
y
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g
ic
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n
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o
l fo
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o
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r
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min
g
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tr
in
s
ic
r
esis
t
a
n
ce
in
in
ve
r
ted
p
en
d
u
lu
m
…
(
Tin
Lu
Tr
u
n
g
)
239
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
4
.
P
r
o
p
o
s
ed
m
e
m
b
er
s
h
i
p
f
u
n
ctio
n
s
f
o
r
in
p
u
ts
o
f
f
u
zz
y
lo
g
ic
co
n
tr
o
l
;
(
a)
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
o
f
th
e
ca
r
t
’
s
p
o
s
itio
n
(
)
,
(
b
)
m
e
m
b
er
s
h
ip
f
u
n
c
tio
n
o
f
t
h
e
ca
r
t
’
s
v
e
lo
cit
y
(
̇
)
,
(
c
)
m
e
m
b
er
s
h
ip
f
u
n
ct
i
o
n
o
f
th
e
f
alli
n
g
an
g
le
(
)
,
an
d
(
d
)
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
o
f
t
h
e
a
n
g
u
lar
v
elo
cit
y
(
̇
)
Fig
u
r
e
5
.
Me
m
b
er
s
h
ip
f
u
n
ctio
n
o
f
t
h
e
f
o
r
ce
ac
tin
g
o
n
t
h
e
ca
r
t (
)
Fig
u
r
e
6
.
E
x
a
m
p
le
co
m
b
i
n
atio
n
s
o
f
co
n
tr
o
l r
u
le
b
ased
o
n
s
tat
e
v
ar
iab
les
T
o
o
p
tim
ize
co
n
tr
o
l
r
es
u
lts
,
b
esid
es
b
u
i
ld
in
g
m
e
m
b
er
s
h
ip
f
u
n
ct
io
n
s
an
d
o
u
tp
u
t
v
al
u
es
c
l
ea
r
l
y
,
th
e
in
p
u
t
g
ai
n
a
n
d
o
u
tp
u
t
g
ai
n
c
o
ef
f
icie
n
t
s
ca
n
a
ls
o
b
e
co
n
tr
o
lled
as
s
h
o
w
n
i
n
t
h
e
b
lo
ck
d
i
ag
r
a
m
i
n
F
ig
u
r
e
3
.
A
s
i
m
ilar
th
eo
r
y
o
f
tu
n
i
n
g
in
p
u
t
an
d
o
u
tp
u
t
g
ain
s
is
d
escr
ib
e
d
in
th
e
b
o
o
k
“
T
u
n
n
in
g
v
ia
Sc
alin
g
Un
iv
er
s
e
s
o
f
Dis
co
u
r
s
e”
p
r
esen
ted
b
y
P
ass
i
n
o
et
a
l.
in
[
3
4
]
.
B
ased
o
n
th
is
co
n
tr
o
l
th
eo
r
y
,
it
is
p
o
s
s
ib
le
to
tu
n
e
th
e
s
e
g
ai
n
s
to
i
m
p
r
o
v
e
th
e
co
n
tr
o
l
p
er
f
o
r
m
an
ce
o
f
th
e
i
n
v
er
ted
p
en
d
u
lu
m
.
T
h
e
p
r
o
p
o
s
ed
g
ain
s
co
n
s
is
t
o
f
th
e
o
u
tp
u
t
g
a
in
(
)
,
an
d
th
e
i
n
p
u
t
g
ain
f
o
r
ea
ch
s
y
s
te
m
v
ar
iab
le
(
,
̇
,
,
)
ar
e
s
h
o
w
n
in
T
ab
le
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
Vo
l.
23
,
No
.
1
,
Feb
r
u
ar
y
20
25
:
2
3
4
-
2
4
5
240
T
ab
le
1
.
R
u
le
b
ase
f
o
r
p
en
d
u
l
u
m
u
s
in
g
T
SK
t
y
p
e
f
u
zz
y
i
n
f
e
r
en
ce
s
y
s
te
m
:
̇
N
E:
NE
N
E:
ZE
N
E:
PO
Z
E:
NE
Z
E:
ZE
Z
E:
PO
P
O
:
NE
P
O
:
ZE
P
O
:
PO
:
̇
N
E:
NE
NB
NB
NM
NB
NM
NS
NM
NS
ZE
N
E:
ZE
NB
NM
NS
NM
NS
ZE
NS
ZE
PS
N
E:
PO
NM
NS
ZE
NS
ZE
PS
ZE
PS
PM
Z
E:
NE
NB
NM
NS
NM
NS
ZE
NS
ZE
PS
Z
E:
ZE
NM
NS
ZE
NS
ZE
PS
ZE
PS
PM
Z
E:
PO
NS
ZE
PS
ZE
PS
PM
PS
PM
PB
P
O
:
NE
NM
NS
ZE
NS
ZE
PS
ZE
PS
PM
P
O
:
ZE
NS
ZE
PS
ZE
PS
PM
PS
PM
PM
P
O
:
PO
ZE
PS
PM
PS
PM
PB
PM
PB
PB
T
ab
le
2
.
P
r
o
p
o
s
ed
in
p
u
t g
ai
n
an
d
o
u
tp
u
t
g
ain
s
G
a
i
n
s
V
a
l
u
e
s
100
2
.
5
̇
0
.
25
0
.
67
̇
0
.
25
4.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
AND
DIS
CUSS
I
O
N
4
.
1
.
I
nv
er
t
ed
pend
ulu
m
pa
ra
m
et
er
s
a
nd
s
i
m
u
la
t
io
n pla
t
f
o
r
m
I
n
th
i
s
s
ec
t
io
n
,
w
e
as
s
es
s
th
e
p
er
f
o
r
m
an
ce
o
f
t
h
e
p
r
o
p
o
s
ed
F
L
C
b
y
e
m
p
lo
y
i
n
g
M
A
T
L
A
B
Si
m
u
li
n
k
to
s
i
m
u
late
th
e
in
v
er
ted
p
en
d
u
l
u
m
s
y
s
te
m
.
T
h
e
s
i
m
u
lat
io
n
ai
m
s
to
ev
al
u
ate
t
h
e
e
f
f
ec
ti
v
en
e
s
s
o
f
o
u
r
co
n
tr
o
ller
i
n
m
ai
n
tai
n
in
g
t
h
e
s
tab
ilit
y
o
f
t
h
e
p
en
d
u
l
u
m
an
d
ac
h
iev
i
n
g
t
h
e
s
etp
o
in
t
p
o
s
itio
n
o
f
t
h
e
ca
r
t.
Fo
r
an
o
b
j
ec
tiv
e
co
m
p
ar
is
o
n
,
w
e
co
m
p
ar
ed
o
u
r
r
esu
lt
s
w
it
h
t
h
e
L
Q
R
co
n
tr
o
ll
er
d
is
cu
s
s
ed
in
[3
5]
b
ec
au
s
e
t
h
e
L
Q
R
co
n
tr
o
ller
i
s
th
e
p
o
p
u
lar
m
o
d
el
-
b
ased
co
n
tr
o
ller
f
o
r
n
o
n
li
n
ea
r
s
y
s
te
m
s
.
L
QR
i
s
a
m
o
d
el
-
b
ased
co
n
tr
o
l
s
ch
e
m
e
w
i
t
h
o
p
tim
ized
r
o
o
t
lo
cu
s
p
lace
m
e
n
t
an
d
m
i
n
i
m
ized
co
s
t
eq
u
ati
o
n
[
3
6
]
.
Fo
r
th
is
r
ea
s
o
n
,
th
e
L
Q
R
co
n
tr
o
l
s
c
h
e
m
e
o
b
tain
s
a
g
o
o
d
s
tead
y
s
ta
te
p
er
f
o
r
m
a
n
ce
.
T
h
e
s
i
m
u
latio
n
p
ar
am
eter
s
ar
e
p
r
esen
ted
i
n
T
ab
le
3
.
I
n
th
e
s
i
m
u
latio
n
s
ce
n
ar
io
,
th
e
v
al
u
e
o
f
is
co
n
s
tan
t,
w
h
i
le
d
if
f
er
en
t
v
alu
e
s
o
f
ar
e
tak
en
in
to
co
n
s
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T
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Fig
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r
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e.
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r
m
a
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ce
i
n
th
e
s
tead
y
-
s
tate.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
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6930
T
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m
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p
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,
Vo
l.
23
,
No
.
1
,
Feb
r
u
ar
y
20
25
:
2
3
4
-
2
4
5
242
(
a)
(
b
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(
c)
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u
r
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4
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Dis
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f
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a
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po
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l f
uture
re
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ith
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o
v
ed
p
er
f
o
r
m
an
ce
,
t
h
e
p
r
o
p
o
s
ed
f
u
zz
y
lo
g
ic
co
n
tr
o
l
h
as
ad
v
an
ta
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ter
m
s
o
f
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s
h
o
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t
p
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n
tag
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o
s
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tab
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alg
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m
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ter
m
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a
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ti
m
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th
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d
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lu
m
a
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is
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ea
r
l
y
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tical
f
o
r
b
o
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th
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p
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p
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s
ed
f
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zz
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ic
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o
l
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d
th
e
L
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co
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tr
o
l a
lg
o
r
it
h
m
.
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w
e
v
er
,
th
e
L
Q
R
co
n
t
r
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l
alg
o
r
ith
m
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x
h
ib
its
a
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ig
n
i
f
ica
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t
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h
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y
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t
its
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d
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ap
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5.
CO
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SI
O
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An
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p
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d
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m
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w
it
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tr
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tab
lis
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ed
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t
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F
L
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w
it
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d
etailed
m
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m
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f
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f
t
h
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p
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is
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to
th
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L
Q
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d
th
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FLC
s
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y
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0
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th
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v
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p
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d
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le
an
d
ca
r
t
p
o
s
itio
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.
T
h
is
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ta
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p
ar
ticu
lar
l
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p
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d
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d
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.
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s
h
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s
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f
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to
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s
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el
-
b
ased
co
s
t
f
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,
th
e
FLC
m
ai
n
tain
s
s
tab
ilit
y
w
it
h
r
ed
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ce
d
o
v
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s
h
o
o
t,
d
e
m
o
n
s
tr
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g
its
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f
f
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ti
v
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e
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s
in
n
a
v
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g
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g
t
h
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in
tr
i
n
s
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co
m
p
lex
i
t
y
a
n
d
n
o
n
li
n
ea
r
it
y
o
f
th
e
s
y
s
te
m
.
B
y
s
p
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if
ical
l
y
ad
d
r
ess
in
g
ch
alle
n
g
es
in
tr
o
d
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ce
d
b
y
s
lid
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n
g
a
n
d
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tatio
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al
f
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ic
tio
n
,
o
u
r
s
t
u
d
y
f
o
cu
s
es
o
n
e
n
h
a
n
ci
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g
s
tab
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y
a
n
d
p
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f
o
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m
a
n
ce
,
p
ar
ticu
lar
l
y
in
ap
p
licatio
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s
s
u
ch
as
s
el
f
-
b
alan
ci
n
g
v
eh
ic
les.
T
h
eo
r
etica
l
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al
y
s
is
a
n
d
s
i
m
u
latio
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es
u
lt
s
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av
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va
lid
ated
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e
f
f
icac
y
o
f
t
h
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p
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p
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s
ed
co
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tr
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l sch
e
m
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ACK
NO
WL
E
D
G
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M
E
NT
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k
n
o
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Ho
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Mi
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h
C
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Un
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it
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T
ec
h
n
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lo
g
y
(
H
C
MU
T
)
,
VNU
-
HC
M
f
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s
u
p
p
o
r
tin
g
th
is
s
t
u
d
y
.
RE
F
E
R
E
NC
E
S
[
1
]
I
.
C
h
a
w
l
a
a
n
d
A
.
S
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n
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l
a
,
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R
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t
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t
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si
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g
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l
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g
M
o
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C
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t
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”
Ara
b
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a
n
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o
u
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n
a
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f
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r
S
c
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n
c
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En
g
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v
o
l
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4
6
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o
.
3
,
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p
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2
5
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d
o
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:
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3
3
6
9
-
020
-
0
5
1
6
1
-
7.
[
2
]
D
.
H
.
V
u
,
S
.
H
u
a
n
g
,
a
n
d
T
.
D
.
T
r
a
n
,
“
H
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e
r
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r
c
h
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c
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l
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o
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u
st
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t
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mi
sm
a
t
c
h
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d
u
n
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e
r
t
a
i
n
t
i
e
s,”
T
EL
K
O
MN
I
K
A
(
T
e
l
e
c
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m
m
u
n
i
c
a
t
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o
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)
,
v
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.
1
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p
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7
–
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0
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9
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k
o
mn
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k
a
.
v
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7
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6
.
1
3
1
7
6
.
[
3
]
A
.
L
a
w
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l
,
K
.
A
b
e
d
-
M
e
r
a
i
m,
Q
.
M
a
y
y
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l
a
,
N
.
I
q
b
a
l
,
a
n
d
A
.
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e
r
g
u
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n
e
,
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l
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d
M
M
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E
q
u
a
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e
r
f
o
r
N
o
n
l
i
n
e
a
r
S
I
M
O
S
y
st
e
ms,”
2
0
2
1
1
8
t
h
I
n
t
e
rn
a
t
i
o
n
a
l
Mu
l
t
i
-
C
o
n
f
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r
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n
c
e
o
n
S
y
st
e
m
s,
S
i
g
n
a
l
s
&
D
e
v
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c
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s
(
S
S
D
)
,
2
0
2
1
,
M
o
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s
t
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r
,
T
u
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D
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5
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2
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.
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4
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9
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8
2
.
[
4
]
H
.
W
.
L
e
e
,
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P
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r
f
o
r
man
c
e
t
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b
a
l
a
n
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o
f
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d
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m
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g
L
Q
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c
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t
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o
l
l
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o
r
y
,
”
i
n
2
0
1
7
I
E
EE
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t
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rn
a
t
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o
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a
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C
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f
e
re
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s
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c
t
ro
n
i
c
s
-
T
a
i
w
a
n
(
I
C
C
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-
T
W)
,
T
a
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,
T
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w
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n
,
2
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7
,
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0
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1
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-
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n
a
.
2
0
1
7
.
7
9
9
1
1
7
2
.
[
5
]
B
.
A
.
S
h
a
r
i
f
a
n
d
A
.
U
c
a
r
,
“
S
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b
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