T
E
L
K
O
M
N
I
K
A
T
elec
o
m
m
un
ica
t
io
n,
Co
m
pu
t
ing
,
E
lect
ro
nics
a
nd
Co
ntr
o
l
Vo
l.
19
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
1
,
p
p
.
2
5
2
~
2
6
4
I
SS
N:
1
6
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,
ac
cr
ed
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First Gr
ad
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b
y
Kem
en
r
is
tek
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k
ti,
Dec
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ee
No
: 2
1
/E/KPT
/2
0
1
8
DOI
:
1
0
.
1
2
9
2
8
/TE
L
KOM
NI
K
A.
v
1
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i1
.
1
6
2
9
8
252
J
o
ur
na
l ho
m
ep
a
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:
h
ttp
:
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/TELK
OM
N
I
K
A
Applica
tion o
f
mo
del redu
ction
for
ro
bust contro
l o
f
self
-
ba
la
ncing
t
w
o
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wheeled
bicycle
Vu N
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c
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ien
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Ng
uy
en
H
o
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Q
ua
ng
,
Ng
o
K
ien Trun
g
T
h
ai
Ng
u
y
e
n
Un
iv
er
s
ity
o
f
T
e
ch
n
o
lo
g
y
,
T
h
ai
Ng
u
y
e
n
C
ity
,
Vietn
am
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
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Ap
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9
,
2
0
2
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R
ev
is
ed
J
u
l 1
6
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2
0
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0
Acc
ep
ted
Au
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2
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2
0
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In
re
c
e
n
t
y
e
a
rs,
b
a
lan
c
e
c
o
n
tro
l
o
f
tw
o
-
wh
e
e
led
b
icy
c
le
h
a
s
re
c
e
iv
e
d
m
o
re
a
tt
e
n
ti
o
n
o
f
sc
ien
ti
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On
e
d
iffi
c
u
lt
y
o
f
th
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p
ro
b
lem
is
th
e
c
o
n
tr
o
l
o
b
jec
t
is
u
n
sta
b
le an
d
c
o
n
sta
n
tl
y
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a
c
ted
b
y
n
o
ise
.
T
o
so
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e
t
h
is p
r
o
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lem
,
t
h
e
a
u
th
o
rs
o
ften
u
se
ro
b
u
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o
n
tr
o
l
a
lg
o
r
it
h
m
s.
Ho
we
v
e
r,
ro
b
u
st
c
o
n
tro
l
ler
o
f
se
lf
-
b
a
lan
c
in
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two
-
w
h
e
e
led
b
ic
y
c
le
a
re
o
ften
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m
p
lex
a
n
d
h
ig
h
e
r
o
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e
r
so
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ffe
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t
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q
u
a
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ri
n
g
re
a
l
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o
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g
.
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a
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tr
o
d
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ti
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a
l
g
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m
b
a
se
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S
c
h
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r
a
n
a
l
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d
a
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th
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e
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rd
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h
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ro
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c
o
n
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n
c
o
n
tr
o
l
b
a
lan
c
in
g
two
-
wh
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led
b
icy
c
le
p
ro
b
lem
.
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h
e
sim
u
latio
n
re
su
l
ts
sh
o
w
t
h
a
t
th
e
re
d
u
c
e
d
4
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a
n
d
5
th
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e
r
c
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tr
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ll
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rc
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rd
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g
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stic
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lan
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n
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ti
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m
b
a
se
d
o
n
S
c
h
u
r
a
n
a
ly
sis
c
a
n
c
o
n
tro
l
th
e
tw
o
-
wh
e
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led
b
ic
y
c
le
m
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d
e
l.
Th
e
re
d
u
c
e
d
3
rd
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rd
e
r
c
o
n
tr
o
ll
e
r
c
a
n
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o
t
c
o
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tr
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l
t
h
e
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lan
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e
o
f
th
e
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wo
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icy
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le
m
o
d
e
l.
T
h
e
re
d
u
c
e
d
4
th
a
n
d
5
th
o
rd
e
r
c
o
n
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ll
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a
n
re
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lac
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in
a
l
c
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y
ste
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Us
in
g
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d
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d
5
th
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4
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rd
e
r
c
o
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l
ler
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k
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ro
g
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m
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o
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p
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d
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lcu
latio
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ti
m
e
o
f
th
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lf
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b
a
lan
c
in
g
tw
o
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wh
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e
l
c
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n
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o
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sy
ste
m
.
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sim
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lt
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m
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d
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ti
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g
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a
n
d
th
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st
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l
a
lg
o
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f
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led
se
lf
-
b
a
lan
c
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g
t
wo
-
wh
e
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led
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icy
c
le.
K
ey
w
o
r
d
s
:
Mo
d
el
o
r
d
e
r
r
ed
u
ctio
n
R
o
b
u
s
t c
o
n
tr
o
l
Self
-
b
alan
cin
g
T
wo
-
wh
ee
led
b
ic
y
cle
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r
th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Ng
u
y
en
Ho
n
g
Qu
a
n
g
T
h
ai
Ng
u
y
e
n
Un
iv
er
s
ity
o
f
T
e
ch
n
o
lo
g
y
No
.
6
6
6
,
3
/2
Stre
et,
T
h
ai
Ng
u
y
en
C
ity
,
Vietn
am
E
m
ail:
q
u
an
g
.
n
g
u
y
en
h
o
n
g
@
tn
u
t.e
d
u
.
v
n
1.
I
NT
RO
D
UCT
I
O
N
I
n
r
ec
en
t
y
ea
r
s
,
r
esear
ch
o
n
s
elf
-
b
alan
cin
g
two
-
wh
ee
l
e
d
b
icy
cle
h
as
b
ee
n
in
ter
ested
b
y
m
an
y
s
cien
tis
t
s
.
I
n
p
ar
ticu
lar
,
a
d
if
f
icu
lt
p
r
o
b
lem
is
th
e
s
tu
d
y
o
f
s
elf
-
b
alan
cin
g
p
r
o
b
lem
o
f
th
e
r
o
b
o
t
.
T
o
s
o
lv
e
th
e
p
r
o
b
lem
o
f
b
ala
n
cin
g
two
-
wh
ee
l
ed
b
icy
cle
,
th
er
e
ar
e
th
r
ee
b
asic
m
eth
o
d
s
as
f
o
llo
ws
;
(
a)
c
o
n
tr
o
llin
g
b
alan
ce
by
th
e
f
l
y
wh
ee
l,
as
in
th
e
s
tu
d
ies
o
f
B
ez
n
o
s
[
1
]
,
Xu
[
2
]
,
an
d
Kim
[
3
]
.
L
ee
[
4
]
Gallasp
y
[
5
]
,
an
d
Su
p
r
ap
to
[
6
]
;
T
h
an
h
[
7
]
,
(
b
)
c
o
n
t
r
o
llin
g
b
al
an
ce
b
y
ce
n
tr
if
u
g
al
f
o
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ce
as
in
th
e
s
tu
d
y
o
f
T
a
n
ak
a
an
d
M
u
r
ak
am
i
[
8
]
,
an
d
(
c)
c
o
n
tr
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llin
g
b
alan
ce
b
y
c
h
an
g
in
g
th
e
ce
n
ter
o
f
g
r
av
ity
as
L
ee
an
d
Ham
'
s
r
esear
ch
[
9
]
.
Am
o
n
g
th
ese
th
r
ee
m
eth
o
d
s
,
c
o
n
tr
o
l
o
f
b
alan
c
e
u
s
in
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th
e
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ly
w
h
ee
l
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as
th
e
a
d
v
an
t
ag
e
o
f
b
ein
g
r
esp
o
n
s
iv
e
an
d
ca
n
b
e
b
alan
c
ed
e
v
e
n
wh
en
th
e
v
e
h
icle
is
n
o
t m
o
v
in
g
.
I
n
two
-
wh
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led
r
o
b
o
t
m
o
d
els
th
at
co
n
tr
o
l
t
h
e
b
alan
ce
b
y
u
s
in
g
th
e
f
ly
wh
ee
l,
two
-
wh
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led
b
i
cy
cle
u
s
es
th
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f
ly
wh
ee
l
ac
co
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d
in
g
to
th
e
p
r
in
cip
le
o
f
g
y
r
o
s
co
p
e
[
1
,
5
-
7
]
to
cr
ea
te
a
b
alan
ce
d
to
r
q
u
e
f
o
r
th
e
wh
ee
ls
.
T
h
e
m
o
m
en
tu
m
u
s
u
ally
r
ev
o
lv
es
at
h
ig
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s
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th
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ly
w
h
ee
l
d
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s
ip
ates
a
lar
g
e
am
o
u
n
t
o
f
en
er
g
y
.
T
h
is
p
r
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b
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lead
s
to
a
d
i
f
f
icu
lty
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n
th
e
o
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r
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th
e
r
o
b
o
t
as
th
e
r
o
b
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t
is
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n
l
y
p
o
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b
a
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with
a
lim
ited
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
A
p
p
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tio
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o
f m
o
d
el
r
ed
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fo
r
r
o
b
u
s
t c
o
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tr
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l o
f self
-
b
a
l
a
n
cin
g
tw
o
-
w
h
ee
led
b
icyc
le
(
V
u
N
g
o
c
K
ien
)
253
ca
p
ac
ity
.
I
n
c
o
n
tr
ast,
th
e
two
-
wh
ee
led
b
icy
cle
m
o
d
el
u
s
es
th
e
f
ly
wh
ee
l
ac
co
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d
in
g
to
th
e
p
r
in
cip
le
o
f
in
v
er
te
d
p
en
d
u
l
u
m
[
2
-
4
]
,
to
cr
ea
te
a
b
alan
ce
d
to
r
q
u
e
f
o
r
th
e
ca
r
,
th
e
f
ly
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ee
l
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o
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ly
at
v
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y
s
m
all
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,
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o
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g
y
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b
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e
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lo
w.
Du
e
to
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ea
s
o
n
,
th
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m
o
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is
s
u
itab
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in
ter
m
s
o
f
en
er
g
y
s
av
in
g
f
o
r
th
e
ca
r
.
T
h
er
ef
o
r
e,
th
e
au
th
o
r
s
p
r
o
p
o
s
ed
th
e
s
elf
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b
ala
n
cin
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two
-
wh
ee
led
r
o
b
o
t u
s
in
g
t
h
e
f
ly
wh
ee
l b
ased
o
n
th
e
p
r
in
cip
le
o
f
in
v
er
ted
p
en
d
u
lu
m
.
B
ec
au
s
e
two
-
wh
ee
led
b
icy
cle
s
o
f
ten
h
av
e
to
wo
r
k
in
d
if
f
er
e
n
t
co
n
d
itio
n
s
,
th
e
ca
r
r
y
in
g
ca
p
ac
ity
m
ay
v
ar
y
,
th
e
e
x
ter
n
al
f
o
r
ce
s
ac
tin
g
o
n
th
e
v
eh
icles
m
ay
ch
an
g
e.
I
t
is
d
if
f
icu
lt
to
f
in
d
th
e
m
o
d
el
o
f
s
elf
-
b
alan
cin
g
two
-
wh
ee
led
b
ic
y
cle,
an
d
T
w
o
-
wh
ee
l
b
ic
y
cle
c
an
b
e
c
o
n
s
id
er
ed
as
in
d
eter
m
in
ate
o
b
jects
[
5
]
.
Sev
e
r
al
co
n
tr
o
l
alg
o
r
ith
m
s
o
f
two
-
wh
ee
led
b
i
cy
cle
h
av
e
b
ee
n
p
r
o
p
o
s
ed
s
u
ch
as:
n
o
n
lin
ea
r
c
o
n
tr
o
l
b
y
B
ez
n
o
l
[
1
]
,
L
ee
v
à
Ham
[
9
]
,
th
e
co
m
p
en
s
ated
d
e
s
ig
n
u
s
in
g
th
e
o
r
b
ital
ap
p
r
o
ac
h
b
y
Gallasp
y
[
5
]
,
PD
co
n
t
r
o
l
ler
b
y
Su
r
p
ato
[
6
]
.
Du
e
to
th
e
u
n
ce
r
tain
ty
o
f
two
-
wh
ee
l m
o
d
el,
th
e
r
o
b
u
s
t c
o
n
tr
o
l m
eth
o
d
in
[
7
]
is
th
e
m
o
s
t su
itab
le.
Ho
wev
er
,
in
th
e
r
o
b
u
s
t
co
n
tr
o
l
d
esig
n
m
eth
o
d
R
H
∞
f
ir
s
t
in
tr
o
d
u
ce
d
b
y
Mc
Far
lan
e
an
d
Glo
v
e
r
in
1
9
9
2
[
1
0
]
,
th
e
co
n
tr
o
ller
s
u
s
u
ally
h
av
e
a
h
ig
h
o
r
d
er
(
co
n
tr
o
ller
lev
el
is
d
ef
in
ed
as
th
e
d
en
o
m
in
ato
r
)
.
T
h
e
h
ig
h
o
r
d
e
r
c
o
n
tr
o
ller
in
tr
o
d
u
ce
s
th
e
d
is
ad
v
an
tag
e
wh
en
we
u
s
e
it to
co
n
tr
o
l th
e
b
icy
cle.
T
h
e
p
r
o
g
r
a
m
is
co
m
p
lex
.
T
h
e
ca
lc
u
latio
n
tim
e
is
lo
n
g
,
s
o
th
e
r
esp
o
n
s
e
o
f
th
e
s
y
s
tem
i
s
s
lo
w.
T
h
er
ef
o
r
e,
r
ed
u
c
i
n
g
th
e
o
r
d
er
o
f
th
e
co
n
tr
o
ller
wh
ile
en
s
u
r
in
g
th
e
q
u
ality
o
f
th
e
co
n
tr
o
ller
h
as
a
s
ig
n
if
ican
t
m
ea
n
in
g
in
p
r
ac
tical
ap
p
licatio
n
s
.
I
n
o
r
d
er
to
r
e
d
u
ce
t
h
e
co
n
tr
o
ller
o
r
d
er
,
th
er
e
ar
e
2
m
eth
o
d
s
ca
n
b
e
f
o
l
lo
wed
:
T
h
e
f
ir
s
t
m
eth
o
d
:
th
is
m
eth
o
d
s
elec
ts
a
f
ix
ed
s
t
r
u
ctu
r
e
o
f
th
e
o
r
d
er
r
ed
u
ctio
n
co
n
t
r
o
lle
r
an
d
th
en
ap
p
lies
o
p
tim
al
alg
o
r
ith
m
s
to
f
in
d
th
e
p
ar
a
m
eter
s
o
f
th
e
o
r
d
er
r
ed
u
ctio
n
c
o
n
tr
o
ller
s
o
th
at
th
e
s
tan
d
ar
d
s
o
f
th
e
r
o
b
u
s
t
co
n
tr
o
l
ar
e
m
et.
T
h
e
s
ec
o
n
d
m
eth
o
d
:
d
esig
n
in
g
a
r
o
b
u
s
t
co
n
tr
o
ller
f
o
r
an
u
n
ce
r
tain
o
b
ject
will
o
b
tain
a
h
ig
h
-
o
r
d
er
c
o
n
tr
o
ller
,
t
h
en
p
er
f
o
r
m
a
h
ig
h
-
o
r
d
er
c
o
n
tr
o
ller
r
ed
u
ctio
n
ac
co
r
d
i
n
g
to
th
e
o
r
d
er
r
e
d
u
ctio
n
alg
o
r
ith
m
s
to
o
b
tain
a
r
e
d
u
ce
d
o
r
d
er
co
n
tr
o
ller
.
Acc
o
r
d
in
g
t
o
th
e
a
u
th
o
r
s
,
in
th
e
f
ir
s
t m
eth
o
d
,
th
e
co
n
tr
o
ller
c
an
b
e
a
lo
w
o
r
d
e
r
co
n
t
r
o
ller
[
7
]
,
b
u
t two
o
p
tim
izatio
n
p
r
o
b
lem
s
n
ee
d
t
o
b
e
s
o
v
le
s
im
u
ltan
eo
u
s
ly
(
p
r
o
b
lem
s
in
f
id
in
g
p
ar
a
m
eter
s
o
f
th
e
co
n
tr
o
ller
an
d
r
o
b
u
s
t
co
n
tr
o
l)
.
T
h
is
is
s
u
e
lead
s
to
d
if
f
icu
ty
o
f
th
is
m
eth
o
d
.
T
h
e
p
ar
am
eter
o
f
th
e
lo
w
o
r
d
e
r
co
n
tr
o
ller
m
a
y
n
o
t
b
e
f
o
u
n
d
if
th
e
ch
o
s
en
co
n
tr
o
ller
is
n
o
t
s
u
itab
le.
I
n
th
e
s
ec
o
n
d
m
eth
o
d
,
th
e
o
r
d
er
r
ed
u
c
tio
n
p
r
o
b
lem
is
an
in
d
ep
en
d
en
t
p
r
o
b
lem
,
s
o
it
al
way
s
g
iv
es
th
e
o
r
d
er
r
ed
u
ctio
n
r
esu
lt
as
in
[
1
1
]
.
D
u
e
to
th
a
t
r
ea
s
o
n
,
th
e
s
ec
o
n
d
m
eth
o
d
h
as th
e
ad
v
a
n
tag
e
o
v
e
r
th
e
f
ir
s
t m
eth
o
d
b
ec
a
u
s
e
th
e
lo
w
o
r
d
er
c
o
n
tr
o
ller
ca
n
b
e
f
o
u
n
d
in
an
y
s
en
ar
i
o
.
I
n
th
is
p
ap
er
,
th
e
au
t
h
o
r
s
p
r
o
p
o
s
ed
th
e
co
n
tr
o
l
m
eth
o
d
o
f
two
-
wh
ee
led
b
icy
cle
u
s
in
g
m
o
d
e
l
r
ed
u
ctio
n
alg
o
r
ith
m
in
two
s
tep
s
as
f
o
llo
w:
(
a
)
d
esig
n
th
e
R
H
co
n
tr
o
ller
to
co
n
tr
o
l th
e
b
alan
ce
o
f
two
-
wh
ee
led
b
icy
cle,
th
e
f
o
u
n
d
co
n
tr
o
ller
is
ca
lled
a
f
u
ll
-
lev
el
c
o
n
tr
o
ller
,
an
d
(
b
)
a
p
p
ly
in
g
o
r
d
er
r
ed
u
ctio
n
alg
o
r
ith
m
to
r
ed
u
ce
o
r
d
e
r
o
f
R
H
co
n
tr
o
ller
t
o
lo
wer
o
r
d
er
co
n
tr
o
ller
wh
ile
en
s
u
r
in
g
q
u
ality
.
T
h
is
s
tep
r
ed
u
ctio
n
is
m
ea
n
t
to
r
ed
u
ce
th
e
s
y
s
tem
r
esp
o
n
s
e
tim
e.
2.
DYNA
M
I
C
M
O
D
E
L
AND
M
AT
H
E
M
AT
I
CA
L
M
O
DE
L
O
F
T
H
E
SE
L
F
-
B
AL
A
N
CING
T
WO
-
WH
E
E
L
E
D
B
I
CYC
L
E
2
.
1
.
Dy
na
m
ic
m
o
del o
f
t
he
s
elf
-
ba
la
ncing
t
wo
-
wheele
d bi
cy
cle
T
h
e
two
-
wh
ee
l
ed
b
icy
cle
m
o
d
el
is
d
ev
elo
p
ed
b
ased
o
n
t
h
e
p
r
i
n
cip
le
o
f
b
ala
n
ce
u
s
in
g
f
ly
wh
ee
l
ac
co
r
d
in
g
to
th
e
p
r
i
n
cip
le
o
f
i
n
v
er
ted
p
en
d
u
lu
m
[
2
-
4
]
.
I
t
is
b
r
ief
ly
d
escr
ib
e
d
th
e
p
r
in
ci
p
le
o
f
b
alan
ci
n
g
o
f
th
e
v
eh
icle
as
f
o
llo
ws:
i
f
n
o
ex
ter
n
al
to
r
q
u
e
(
to
r
q
u
e)
is
ap
p
lied
t
o
an
o
b
ject
o
r
s
y
s
tem
(
o
r
th
e
t
o
tal
to
r
q
u
e
ap
p
lied
to
an
o
b
ject
is
ze
r
o
)
,
th
e
n
th
e
t
o
tal
to
r
q
u
e
o
f
th
e
o
b
ject
will b
e
p
r
eser
v
ed
.
T
h
e
v
e
h
icle
m
o
v
in
g
b
y
2
wh
ee
ls
,
wh
en
th
e
v
e
h
icle
d
ev
iates
f
r
o
m
th
e
b
ala
n
ce
p
o
s
itio
n
(
c
o
r
r
esp
o
n
d
in
g
to
a
q
an
g
le
ac
co
r
d
in
g
to
v
er
ti
ca
l
ax
is
)
.
T
h
e
g
r
av
ity
o
f
t
h
e
v
eh
icle
cr
ea
tes
a
to
r
q
u
e
th
at
m
ak
es
th
e
ca
r
ten
d
to
f
all
d
o
wn
.
T
o
m
ai
n
tain
a
s
tate
o
f
e
q
u
ilib
r
iu
m
,
we
p
u
t
o
n
th
e
v
eh
icle
a
f
ly
wh
ee
l
th
at
o
p
er
at
es
o
n
th
e
p
r
in
cip
le
o
f
"
th
e
in
v
er
te
d
p
en
d
u
lu
m
".
T
h
is
f
ly
wh
ee
l
will
r
o
tate
ar
o
u
n
d
th
e
ax
is
(
with
an
an
g
u
la
r
ac
c
eler
atio
n
o
f
)
an
d
cr
ea
te
a
to
r
q
u
e
to
co
m
p
e
n
s
ate
th
e
to
r
q
u
e
g
en
er
ated
b
y
th
e
v
e
h
icle'
s
g
r
av
ity
.
T
o
co
n
tr
o
l
th
e
ac
ce
ler
atio
n
o
f
th
e
f
ly
wh
ee
l,
we
u
s
es
a
DC
d
c
m
o
to
r
with
th
e
v
o
ltag
e
ap
p
lied
to
t
h
e
m
o
to
r
b
ein
g
U.
T
h
e
n
,
th
e
p
r
o
b
lem
o
f
b
alan
cin
g
co
n
tr
o
l b
ec
o
m
es
th
e
p
r
o
b
lem
o
f
co
n
tr
o
llin
g
th
e
an
g
le
(
o
u
tp
u
t)
b
y
co
n
tr
o
llin
g
th
e
v
o
ltag
e
U
(
in
p
u
t)
ap
p
ly
in
g
to
th
e
m
o
to
r
.
T
h
e
p
r
o
b
lem
r
eq
u
ir
es
th
at
th
e
an
g
le
(
o
u
tp
u
t)
al
way
s
g
o
to
ze
r
o
.
T
h
e
s
elf
-
b
ala
n
cin
g
two
-
wh
ee
led
b
icy
cle
th
at
th
e
au
t
h
o
r
s
b
u
ilt is
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
e
m
o
d
el
m
ac
h
a
n
ical
p
ar
am
eter
s
:
lo
n
g
:
1
.
1
9
m
;
h
eig
h
t:
0
.
5
m
;
wid
th
:
0
.
4
m
;
th
e
f
ly
wh
e
el
weig
h
t:
3
.
9
7
6
k
g
,
d
iam
eter
:
0
.
2
6
m
;
Dr
iv
in
g
th
e
f
ly
wh
ee
l
u
s
in
g
DC
m
o
to
r
:
1
0
0
W
-
15V
-
3
4
0
0
r
p
m
with
H
-
b
r
id
g
e
d
r
iv
er
;
Me
asu
r
in
g
th
e
f
l
y
wh
e
el
v
elo
city
b
y
E
n
co
d
er
Sh
ar
o
1
0
0
p
u
ls
e;
M
ea
s
u
r
in
g
th
e
q
am
g
le
b
y
s
en
s
o
r
GY
-
5
2
1
MPU
-
6
0
5
0
;
Fo
r
war
d
an
d
r
e
v
er
s
e
s
y
s
tem
co
n
s
is
ts
o
f
a
DC
m
o
to
r
,
H
-
b
r
id
g
e
d
r
iv
er
an
d
a
r
em
o
te
co
n
tr
o
ller
.
T
h
e
h
ar
d
war
e
s
y
s
tem
is
co
n
n
ec
ted
to
A
r
d
r
u
i
n
o
m
icr
o
p
r
o
ce
s
s
o
r
ac
co
r
d
in
g
to
t
h
e
f
o
llo
win
g
b
lo
ck
d
iag
r
am
as sh
o
wn
i
n
Fi
g
u
r
e
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
19
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
1
:
2
5
2
-
2
6
4
254
Fig
u
r
e
1
.
T
h
e
s
elf
-
b
alan
cin
g
t
wo
-
wh
ee
led
b
icy
cle
m
o
d
el
Fig
u
r
e
2
.
Sch
em
atic
s
tr
u
ctu
r
e
o
f
b
icy
cle
c
o
n
tr
o
ller
2
.
1
.
M
a
t
hema
t
ica
l
m
o
del o
f
t
he
s
elf
-
ba
la
ncing
t
wo
-
wheele
d bicy
cle
Dy
n
am
ic
m
o
d
el
o
f
th
e
s
elf
-
b
alan
cin
g
two
-
wh
ee
led
b
ic
y
cle
is
s
h
o
wn
in
Fig
u
r
e
3
.
W
h
er
e:
m
1
is
th
e
b
icy
cle
weig
h
t
(
in
clu
d
in
g
DC
m
o
to
r
)
,
m
2
is
th
e
f
ly
wh
ee
l
w
eig
h
t,
h
1
is
th
e
h
eig
h
t
o
f
th
e
c
en
ter
g
r
av
ity
o
f
th
e
b
icy
cle
(
ex
clu
d
in
g
th
e
f
ly
wh
e
el)
,
h
2
is
th
e
h
eig
h
t
o
f
th
e
ce
n
t
er
g
r
av
ity
o
f
th
e
f
ly
wh
ee
l,
I
1
is
th
e
in
er
tia
to
r
q
u
e
o
f
th
e
b
icy
cle,
I
2
is
th
e
in
er
tia
to
r
q
u
e
o
f
th
e
f
ly
wh
ee
l,
q
is
th
e
tilt
an
g
le
o
f
th
e
b
ic
y
cle
co
r
r
esp
o
n
d
in
g
to
th
e
v
er
tical
ax
is
,
j
is
th
e
r
o
tatio
n
an
g
le
o
f
th
e
f
ly
wh
ee
l.
W
e
h
av
e
:
th
e
ab
s
o
lu
te
v
elo
city
o
f
p
o
i
n
t
A
is
|
|
=
ℎ
1
̇
.
T
h
e
ab
s
o
lu
te
v
elo
city
o
f
p
o
in
t
B
is
|
|
=
ℎ
2
̇
.
I
n
[
5
]
,
th
e
au
th
o
r
u
s
ed
L
ag
r
an
g
e
eq
u
atio
n
to
d
e
v
elo
p
th
e
d
y
n
am
ic
m
o
d
el
o
f
th
e
v
e
h
icle.
{
̇
}
−
+
=
(
1
)
wh
er
e
:
T
is
th
e
to
tal
k
in
etic
en
er
g
y
o
f
th
e
s
y
s
tem
,
V
is
th
e
to
t
al
p
o
ten
tial
en
er
g
y
o
f
th
e
s
y
s
tem
,
Q
i
is
th
e
ex
ter
n
al
f
o
r
ce
,
q
i
is
th
e
g
en
er
alize
d
co
o
r
d
in
ate.
Fig
u
r
e
3
.
Self
-
b
alan
cin
g
two
-
wh
ee
l b
icy
cle
m
o
d
el
T
h
e
to
tal
k
in
etic
e
n
er
g
y
o
f
th
e
s
y
s
tem
d
ef
in
ed
b
y
:
=
1
+
2
.
T
1
,
wh
ic
h
is
th
e
k
in
etic
en
e
r
g
y
o
f
t
h
e
two
-
wh
ee
l
ed
v
eh
icles
,
is
d
eter
m
in
ed
b
y
th
e
f
o
llo
win
g
f
o
r
m
u
la:
1
=
1
2
2
|
|
2
+
1
2
1
̇
2
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
A
p
p
lica
tio
n
o
f m
o
d
el
r
ed
u
ctio
n
fo
r
r
o
b
u
s
t c
o
n
tr
o
l o
f self
-
b
a
l
a
n
cin
g
tw
o
-
w
h
ee
led
b
icyc
le
(
V
u
N
g
o
c
K
ien
)
255
T
2
,
wh
ich
is
th
e
f
ly
wh
ee
l
k
in
et
ic
en
er
g
y
,
is
d
eter
m
in
ed
b
y
th
e
f
o
llo
win
g
f
o
r
m
u
la:
2
=
1
2
2
|
|
2
+
1
2
2
(
̇
+
̇
)
W
e
h
av
e
:
=
1
2
1
|
|
2
+
1
2
2
|
|
2
+
1
2
1
̇
2
+
1
2
2
̇
2
+
1
2
2
̇
2
+
2
̇
̇
(
2
)
=
1
2
(
1
ℎ
1
2
+
2
ℎ
2
2
+
1
+
2
)
̇
2
+
1
2
2
̇
2
+
2
̇
̇
(
3
)
T
h
e
to
tal
p
o
ten
tial e
n
er
g
y
o
f
t
h
e
s
y
s
tem
:
=
.
.
(
1
ℎ
1
+
2
ℎ
2
)
(
4
)
W
ith
q
i
=
q
,
tak
in
g
(
1
-
4
)
,
we
g
et:
(
1
ℎ
1
2
+
2
ℎ
2
2
+
1
+
2
)
̈
+
2
̈
−
.
.
(
1
ℎ
1
+
2
ℎ
2
)
=
0
(
5
)
W
ith
q
i
=
j,
tak
in
g
(
1
–
4
)
,
we
g
et:
2
̈
+
2
̈
=
.
(
6
)
W
ith
T
m
is
th
e
m
o
to
r
s
h
af
t to
r
q
e
.
C
o
n
s
id
er
in
g
a
DC
d
c
m
o
to
r
with
a
g
ea
r
r
atio
o
f
a:1
,
th
e
to
r
q
u
e
o
f
th
e
DC
m
o
to
r
d
r
i
v
in
g
th
e
f
ly
wh
ee
l
is
as f
o
llo
ws:
=
=
[
−
̇
]
,
(
7
)
with
K
m
i
s
th
e
m
o
to
r
to
r
q
u
e
c
o
n
s
tan
t,
K
e
is
th
e
b
ac
k
-
em
f
co
n
s
tan
t
,
R
i
s
th
e
r
esi
s
tan
ce
o
f
th
e
m
o
to
r
.
Su
b
s
titu
te
(
7
)
in
to
(
6
)
,
we
g
et:
2
̈
+
2
̈
=
=
[
−
̇
]
.
(
8
)
I
n
(
5
)
an
d
(
8
)
ar
e
t
h
e
d
y
n
am
ic
s
y
s
tem
eq
u
atio
n
.
I
t
is
clea
r
th
at
th
e
s
y
s
tem
is
n
o
n
lin
ea
r
.
L
in
ea
r
iz
in
g
th
e
m
o
d
el
an
d
tu
r
n
it
in
to
a
s
tate
s
p
ac
e
m
o
d
el
.
Ass
u
m
e
th
at
wh
en
th
e
v
eh
icle
is
o
p
er
atin
g
,
t
h
e
v
eh
icle
'
s
in
clin
atio
n
an
g
le
is
v
er
y
s
m
all
(
<
1
0
0
)
.
L
in
ea
r
izin
g
i
n
(
5
)
ar
o
u
n
d
th
e
e
q
u
ilib
r
iu
m
p
o
in
t (
=
=
0
,
=
)
,
we
h
av
e:
(
1
ℎ
1
2
+
2
ℎ
2
2
+
1
+
2
)
̈
+
2
̈
−
.
.
(
1
ℎ
1
+
2
ℎ
2
)
=
0
(
9
)
2
̈
+
2
̈
=
=
[
−
̇
]
(
1
0
)
T
ak
in
g
1
=
(
1
ℎ
1
2
+
2
ℎ
2
2
+
1
+
2
)
;
1
=
(
1
ℎ
1
+
2
ℎ
2
)
T
ak
in
g
=
[
=
1
̇
=
2
̇
=
3
]
,
is
s
tate
v
ar
iab
le,
=
,
=
W
e
h
av
e
th
e
s
tate
s
p
ac
e
m
o
d
e
l
d
escr
ib
in
g
th
e
s
y
s
tem
as f
o
ll
o
w:
̇
=
+
(
1
1
)
=
+
with
:
=
[
0
1
0
1
(
1
−
2
)
0
(
1
−
2
)
−
1
(
1
−
2
)
0
−
1
2
(
1
−
2
)
]
;
=
[
0
−
(
1
−
2
)
1
2
(
1
−
2
)
]
=
[
1
0
0
]
;
=
[
0
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
19
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
1
:
2
5
2
-
2
6
4
256
T
h
e
n
o
m
i
n
al
p
ar
a
m
eter
s
o
f
th
e
two
-
wh
ee
l
ed
b
icy
cle
m
o
d
el
ar
e
s
h
o
wn
i
n
T
ab
le
1
a
s
f
o
llo
ws:
e
x
p
lain
in
g
r
esear
ch
ch
r
o
n
o
lo
g
ical,
in
clu
d
in
g
r
esear
ch
d
esig
n
,
r
esear
ch
p
r
o
ce
d
u
r
e
(
in
th
e
f
o
r
m
o
f
alg
o
r
ith
m
s
,
Ps
eu
d
o
co
d
e
o
r
o
th
er
)
,
h
o
w
to
test
an
d
d
ata
ac
q
u
is
itio
n
[1
-
3]
.
T
h
e
d
escr
ip
tio
n
o
f
th
e
co
u
r
s
e
o
f
r
esear
c
h
s
h
o
u
l
d
b
e
s
u
p
p
o
r
ted
r
ef
er
en
ce
s
,
s
o
th
e
ex
p
lan
atio
n
ca
n
b
e
ac
ce
p
t
ed
s
cien
tific
ally
[
2
,
4
]
.
T
ab
l
es
an
d
f
ig
u
r
es
ar
e
p
r
esen
ted
ce
n
ter
,
as
s
h
o
wn
b
elo
w
an
d
cited
in
th
e
m
an
u
s
cr
ip
t.
Su
b
s
titu
tin
g
f
o
r
th
e
s
y
s
te
m
o
f
(
1
1
)
,
we
o
b
tain
th
e
f
o
llo
win
g
p
ar
am
eter
s
:
=
[
0
1
0
47.2048
0
0.0100
-
47.2048
0
-
0.1248
]
;
=
[
0
-
0.2230
2
.
8541
]
;
=
[
1
0
0
]
.
C
o
n
v
er
t th
e
v
e
h
icle
m
o
d
el
i
n
to
tr
an
s
f
er
f
u
n
ctio
n
:
(
)
=
(
)
(
)
=
−
0.22
3
3
+
0
.
1284
2
−
47
.
2
−
5
.
589
(
1
2
)
T
ab
le
1
.
T
h
e
p
ar
am
ete
r
s
o
f
th
e
two
-
wh
ee
led
b
icy
cle
m
o
d
e
P
a
r
a
me
t
e
r
V
a
l
u
e
U
n
i
t
1
0
.
1
1
0
5
K
g
.
m
2
ℎ
1
0
.
1
0
5
m
2
0
.
0
3
2
8
9
K
g
.
m
2
ℎ
2
0
.
2
0
5
m
1
1
0
.
0
2
4
Kg
2
3
.
9
7
6
Kg
0
.
0
4
5
V
.
s/
R
a
d
0
.
0
4
5
N
m/
A
0
.
5
2
1
:
1
9
.
8
1
m/
s
2
R
em
ar
k
o
n
two
-
wh
ee
l
d
r
iv
e
m
o
d
els
.
T
h
e
s
elf
-
b
alan
cin
g
two
-
wh
ee
l
ed
b
icy
cle
m
o
d
el
s
h
o
ws
th
at
s
o
m
e
p
ar
am
eter
s
o
f
s
elf
-
b
alan
cin
g
t
wo
-
wh
ee
le
d
b
ic
y
cle
ar
e
u
n
ce
r
tain
s
u
ch
as
: th
e
ch
an
g
in
g
lo
ad
v
o
lu
m
e
(
lead
in
g
to
a
ch
an
g
e
in
th
e
ce
n
ter
o
f
g
r
av
i
ty
o
f
th
e
ca
r
)
,
t
h
e
in
er
tia
to
r
q
u
e
o
f
th
e
b
icy
cle
ch
a
n
g
ed
.
A
d
d
itio
n
ally
,
o
p
er
atin
g
two
-
wh
ee
led
b
ic
y
cle
m
a
y
b
e
i
n
f
lu
en
ce
d
b
y
e
x
ter
n
al
u
n
ce
r
tai
n
ties
s
u
ch
as:
th
e
ex
ter
n
al
f
o
r
c
e
an
d
u
n
ce
r
tain
n
o
is
e
d
u
e
to
th
e
ch
an
g
i
n
g
o
f
to
p
o
g
r
ap
h
y
.
T
h
e
r
ef
o
r
e
,
T
h
e
two
-
wh
e
eled
b
icy
cle
is
th
e
u
n
ce
r
tain
o
b
ject.
I
n
p
ar
ticu
lar
,
th
e
au
th
o
r
s
p
ay
th
e
m
o
s
t
atten
tio
n
to
th
e
u
n
ce
r
tain
ty
d
u
e
to
th
e
ch
an
g
e
o
f
lo
ad
weig
h
t.
Sp
ec
i
f
ically
,
th
e
au
th
o
r
s
co
n
s
id
er
4
ca
s
es o
f
two
-
wh
ee
l
ed
b
icy
cle
ca
r
r
y
in
g
d
if
f
er
en
t l
o
ad
s
as sh
o
wn
in
th
e
T
a
b
le
2.
Un
ce
r
tain
f
ac
to
r
s
m
a
y
r
e
d
u
c
e
t
h
e
ac
cu
r
ac
y
o
f
two
-
wh
ee
l
ed
m
ath
em
atica
l
m
o
d
els
.
T
h
e
r
ef
o
r
e,
th
e
co
n
tr
o
l
q
u
ality
is
r
ed
u
ce
d
an
d
t
h
e
s
y
s
tem
ca
n
ev
en
b
ec
o
m
e
u
n
s
tab
le
.
Du
e
to
th
e
u
n
ce
r
tain
p
r
o
p
er
ties
,
th
e
v
ar
io
u
s
co
n
tr
o
l
alg
o
r
ith
m
f
o
r
t
h
e
two
wh
ee
led
b
icy
cle
h
as
b
ee
n
p
r
o
p
o
s
ed
:
n
o
n
lin
ea
r
c
o
n
tr
o
l
b
y
B
ez
n
o
l
[
1
]
,
L
ee
v
à
Ham
[
4
]
,
th
e
co
m
p
e
n
s
ated
d
esig
n
u
s
in
g
th
e
o
r
b
ital
ap
p
r
o
ac
h
b
y
Gallasp
y
[
5
]
,
PD
co
n
tr
o
ller
b
y
Su
r
p
ato
[
8
]
.
T
h
e
m
o
s
t su
itab
le
alg
o
r
ith
m
to
co
n
tr
o
l th
e
u
n
ce
r
tain
o
b
ject
was th
e
alg
o
r
ith
m
in
[
1
0
]
.
T
ab
le
2
.
Par
am
eter
s
o
f
th
e
two
-
wh
ee
led
b
icy
cle
m
o
d
el
as th
e
lo
ad
is
d
if
f
er
e
n
t
C
a
se
Lo
a
d
v
o
l
u
me
(
k
g
)
H
e
i
g
h
t
o
f
t
h
e
c
e
n
t
e
r
o
f
g
r
a
v
i
t
y
ℎ
1
(
m)
M
o
me
n
t
o
f
i
n
e
r
t
i
a
1
(Kg
.m
2
)
1
5
0
.
2
0
5
0
.
6
3
1
4
2
5
0
.
1
5
5
0
.
3
6
0
9
3
7
0
.
0
5
5
0
.
0
5
1
5
4
7
0
.
1
5
5
0
.
4
0
9
3.
O
P
T
I
M
AL
D
E
S
I
G
N
RH
F
O
R
B
AL
A
NCE
WH
E
E
L
P
R
O
B
L
E
M
T
h
e
s
tr
u
ctu
r
e
o
f
th
e
b
alan
cin
g
co
n
tr
o
l
s
y
s
tem
f
o
r
s
elf
-
b
ala
n
cin
g
two
-
wh
ee
le
d
b
icy
cle
is
s
h
o
wn
in
Fig
u
r
e
4
.
T
h
e
b
alan
ci
n
g
c
o
n
tr
o
l
s
y
s
tem
co
n
s
is
ts
o
f
3
lo
o
p
c
o
n
tr
o
ls
,
n
am
ely
,
lo
o
p
c
o
n
tr
o
l
th
e
r
o
tatio
n
an
g
le
o
f
th
e
f
ly
wh
ee
l,
lo
o
p
co
n
tr
o
l
th
e
v
elo
city
tilt
an
g
le
o
f
b
icy
cle
a
n
d
lo
o
p
c
o
n
tr
o
l
th
e
tilt
an
g
le
o
f
b
icy
lce.
T
h
e
r
o
b
u
s
t
co
n
tr
o
ller
R
(
s
)
is
u
s
ed
in
lo
o
p
co
n
tr
o
l
th
e
tilt
an
g
le
o
f
b
icy
lce.
T
o
d
esig
n
a
r
o
b
u
s
t
co
n
tr
o
l
s
y
s
tem
f
o
r
s
elf
-
b
alan
cin
g
two
-
w
h
ee
led
b
i
cy
cle,
th
e
co
n
tr
o
l stru
ctu
r
e
d
ia
g
r
am
s
h
o
wn
i
n
Fig
u
r
e
4
is
u
s
ed
b
y
th
e
au
th
o
r
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
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n
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o
l
A
p
p
lica
tio
n
o
f m
o
d
el
r
ed
u
ctio
n
fo
r
r
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s
t c
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f self
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a
l
a
n
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tw
o
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w
h
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led
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icyc
le
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V
u
N
g
o
c
K
ien
)
257
Fig
u
r
e
4
.
T
h
e
r
o
b
u
s
t c
o
n
tr
o
l stru
ctu
r
e
f
o
r
s
elf
-
b
ala
n
cin
g
two
-
wh
ee
led
b
icy
cle
3
.
1
.
Dev
el
o
pin
g
t
he
s
elf
-
ba
la
ncing
t
wo
-
wheele
d bicy
cle
m
o
del
(
)
Ass
u
m
in
g
th
at
wh
en
th
e
v
eh
icle
is
in
o
p
er
atio
n
,
th
e
in
clin
atio
n
o
f
th
e
b
icy
cle
is
v
er
y
s
m
all,
we
lin
ea
r
ize
i
n
(
5
)
ar
o
u
n
d
t
h
e
eq
u
ilib
r
iu
m
p
o
in
t
(
=
=
0
,
=
)
.
W
e
h
av
e:
(
1
ℎ
1
2
+
2
ℎ
2
2
+
1
+
2
)
̈
+
2
̈
−
.
.
(
1
ℎ
1
+
2
ℎ
2
)
=
0
(
1
3
)
2
̈
+
2
̈
=
=
[
∗
−
(
+
1
)
̇
+
2
̇
]
(
1
4
)
T
ak
in
g
:
1
=
(
1
ℎ
1
2
+
2
ℎ
2
2
+
1
+
2
)
;
1
=
(
1
ℎ
1
+
2
ℎ
2
)
T
ak
in
g
=
[
=
1
̇
=
2
̇
=
3
]
,
is
s
tate
v
ar
iab
le,
=
,
=
∗
W
e
h
av
e
th
e
s
tate
s
p
ac
e
m
o
d
e
l d
escr
ib
in
g
th
e
s
y
s
tem
as f
o
ll
o
w:
̇
=
+
=
+
(
1
5
)
T
h
e
s
y
s
tem
p
ar
am
eter
s
:
=
[
0
1
0
1
(
1
−
2
)
2
(
1
−
2
)
(
+
1
)
(
1
−
2
)
−
1
(
1
−
2
)
−
2
1
2
(
1
−
2
)
−
(
+
1
)
1
2
(
1
−
2
)
]
;
=
[
0
−
(
1
−
2
)
1
2
(
1
−
2
)
]
;
=
[
1
0
0
]
;
=
[
0
]
.
C
h
o
s
in
g
1
=
2
,
2
=
5
.
Su
b
s
titu
tin
g
th
e
p
ar
am
eter
s
in
T
ab
le
1
in
to
(
1
5
)
,
th
e
m
o
d
el
is
co
n
v
e
r
ted
to
th
e
tr
a
n
s
f
er
f
u
n
ctio
n
f
o
r
m
:
(
)
=
(
)
(
)
=
−
0.22
3
3
+
4
.
722
2
−
47
.
2
−
254
(
1
6
)
T
o
d
esig
n
a
r
o
b
u
s
t
c
o
n
tr
o
lle
r
f
o
r
s
elf
-
b
alan
ci
n
g
two
-
wh
e
ele
d
b
icy
cle,
th
e
a
u
th
o
r
s
f
o
ll
o
w
ed
th
e
s
tep
s
o
f
d
esig
n
in
g
a
r
o
b
u
s
t
co
n
tr
o
ller
RH
∞
ac
co
r
d
in
g
t
o
[
1
0
,
1
2
]
.
W
e
g
et
th
e
r
o
b
u
s
t c
o
n
tr
o
ller
:
(
)
=
(
)
(
)
(
1
7
)
with
(
)
=
−
2
.
23
.
1
0
−
7
30
−
4
.
67
.
1
0
−
4
29
−
0
.
266
28
−
22
.
96
27
−
1006
26
−
2
.
853
.
1
0
4
25
−
5
.
837
.
1
0
5
24
−
4
.
199
.
1
0
11
18
−
9
.
144
.
1
0
6
23
−
1
.
139
.
1
0
8
22
−
1
.
158
.
1
0
9
21
−
9
.
776
.
1
0
9
20
−
6
.
949
.
1
0
10
19
−
2
.
172
.
1
0
12
17
−
9
.
663
.
1
0
12
16
−
3
.
71
.
1
0
13
15
−
1
.
231
.
1
0
14
14
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
.
Co
m
pa
re
t
he
r
o
bu
s
t
co
ntr
o
ller
wit
h a
no
t
her
co
ntr
o
ller
T
h
e
b
icy
cle
with
th
e
v
ar
y
i
n
g
p
ar
am
eter
is
co
n
tr
o
lled
b
y
PI
D
co
n
tr
o
l
m
eth
o
d
.
T
h
e
r
esu
lt
i
s
th
en
u
s
ed
to
co
m
p
ar
e
to
th
e
ca
s
e
wh
ich
th
e
r
o
b
u
s
t
co
n
tr
o
ller
is
ap
p
lied
.
Simu
latio
n
d
iag
r
am
o
f
s
elf
-
b
alan
cin
g
two
-
wh
ee
led
b
ic
y
cle
co
n
tr
o
l
s
y
s
tem
u
s
in
g
r
o
b
u
s
t
co
n
tr
o
l
ler
an
d
PID
co
n
tr
o
ller
a
r
e
s
h
o
wn
in
Fig
u
r
e
5
.
Simu
latio
n
r
esu
lts
o
f
s
elf
-
b
al
an
cin
g
two
-
wh
ee
led
b
icy
cle
c
o
n
tr
o
l
s
y
s
tem
wh
e
n
th
e
p
ar
a
m
eter
s
o
f
m
o
d
el
a
r
e
r
ated
an
d
w
h
en
th
e
m
o
d
el
p
ar
am
eter
s
ch
an
g
e
,
I
n
itially
,
th
e
b
icy
cle
d
e
v
iates
=
180
(
)
f
r
o
m
th
e
v
er
tical
ax
is
.
Par
am
eter
s
o
f
PID
co
n
tr
o
ller
:
K
p
=
-
4
5
0
,
K
I
=
-
3
0
,
K
D
=
-
1
5
.
T
h
e
r
esu
lts
s
h
o
wn
in
Fi
g
u
r
e
6
.
Fig
u
r
e
5
.
Simu
latio
n
d
iag
r
a
m
o
f
s
elf
-
b
alan
cin
g
two
-
wh
ee
led
b
icy
cle
co
n
tr
o
l sy
s
tem
u
s
in
g
r
o
b
u
s
t c
o
n
tr
o
ller
an
d
PID
co
n
tr
o
ller
R
em
ar
k
b
y
th
e
s
im
u
latio
n
r
es
u
lt
in
b
o
th
c
ases
th
e
n
o
m
in
al
p
ar
am
eter
s
o
f
th
e
b
icy
cle
a
n
d
t
h
e
v
ar
ia
b
le
p
ar
am
eter
s
o
f
th
e
b
icy
cle
d
u
e
to
th
e
lo
a
d
v
a
r
ied
.
PID
co
n
t
r
o
ller
ca
n
o
n
l
y
b
ala
n
ce
th
e
b
ic
y
cle
as
th
e
b
icy
cle
p
ar
am
eter
s
is
n
im
in
al
an
d
in
c
ase
3
.
PID
co
n
tr
o
ller
h
as
n
o
t
w
o
r
k
ed
in
th
e
ca
s
e
1
,
2
,
an
d
4
.
T
h
e
r
o
b
u
s
t
co
n
tr
o
ller
d
id
wo
r
k
in
all
4
ca
s
es.
I
t
ca
n
b
e
s
ee
n
th
at
th
e
r
o
b
u
s
t
co
n
tr
o
ller
was
ab
le
to
b
alan
ce
th
e
s
y
s
t
em
ev
en
t
h
e
s
y
s
tem
p
ar
am
eter
s
ar
e
v
ar
ie
d
(
l
o
ad
an
d
th
e
h
eig
h
t
o
f
th
e
ce
n
ter
o
f
g
r
av
ity
o
f
th
e
b
icy
cle)
.
T
h
e
r
o
b
u
s
t
co
n
tr
o
ller
h
as
th
e
ad
v
an
tag
e
o
v
er
t
h
e
PID
co
n
tr
o
ller
Ho
wer
v
er
,
th
e
3
0
th
o
r
d
e
r
c
o
n
tr
o
ller
co
u
ld
lea
d
to
th
e
d
if
f
ic
u
lty
o
f
o
p
er
atin
g
th
e
b
alan
ci
n
g
p
r
o
ce
s
s
.
Du
e
to
th
e
co
m
p
lex
p
r
o
g
r
am
,
th
e
lo
n
g
p
r
o
ce
s
s
in
g
tim
e,
th
e
lo
w
s
y
s
tem
r
esp
o
n
s
e,
th
e
s
y
s
tem
wil
l
n
o
t
b
e
ab
le
to
ad
ap
t
th
e
r
eq
u
ir
em
e
n
ts
o
f
r
ea
l
-
tim
e
ap
p
licatio
n
s
an
d
ca
n
b
ec
o
m
e
u
n
s
tab
le.
Fo
r
th
at
r
ea
s
o
n
,
r
ed
u
cin
g
th
e
o
r
d
er
o
f
th
e
co
n
tr
o
ller
is
n
ee
d
e
d
to
s
im
p
lif
y
th
e
p
r
o
g
r
am
.
T
h
e
s
y
s
tem
r
es
p
o
n
s
e
is
th
e
r
eb
y
in
cr
ea
s
ed
,
wh
ile
th
e
r
o
b
u
s
tn
ess
is
en
s
u
r
ed
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
A
p
p
lica
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n
o
f m
o
d
el
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n
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b
a
l
a
n
cin
g
tw
o
-
w
h
ee
led
b
icyc
le
(
V
u
N
g
o
c
K
ien
)
259
Fig
u
r
e
6
.
T
h
e
s
y
s
tem
o
u
tp
u
t r
e
s
p
o
n
s
e
o
f
s
elf
-
b
alan
ci
n
g
two
-
wh
ee
led
b
icy
cle
co
n
tr
o
l sy
s
tem
u
s
in
g
r
o
b
u
s
t
co
n
tr
o
ller
a
n
d
PID
co
n
tr
o
ller
4.
ST
O
CH
AS
T
I
C
B
A
L
ANC
E
T
RUNC
AT
I
O
N
AL
G
O
RI
T
H
M
B
AS
E
D
O
N
SCH
U
R
A
NALYS
I
S
4
.
1
.
M
o
del r
educt
io
n pro
blem
Giv
en
a
lin
ea
r
,
co
n
tin
u
o
u
s
,
tim
e
-
in
v
ar
ian
t
,
MI
MO
s
y
s
tem
d
escr
ib
ed
b
y
th
e
f
o
llo
win
g
s
tate
s
p
ac
e
m
o
d
el
:
̇
=
+
=
(
1
8
)
wh
er
e
,
∈
,
∈
,
∈
,
∈
,
∈
,
∈
.
T
h
e
g
o
al
o
f
th
e
o
r
d
er
r
ed
u
ctio
n
p
r
o
b
le
m
f
o
r
th
e
m
o
d
el
d
escr
ib
ed
b
y
s
tate
s
p
ac
e
m
o
d
el
g
iv
en
i
n
(
1
7
)
is
to
f
in
d
th
e
m
o
d
el
d
escr
ib
e
d
b
y
s
tate
s
p
ac
e
m
o
d
el
:
̇
=
+
=
(
1
9
)
wh
er
e
,
∈
,
∈
,
∈
,
∈
,
∈
,
∈
v
ớ
i
≪
.
So
th
at
th
e
m
o
d
el
d
escr
ib
ed
b
y
i
n
(
1
9
)
ca
n
r
ep
lace
th
e
m
o
d
el
d
escr
ib
ed
b
y
th
e
(
1
8
)
ap
p
licati
o
n
s
in
an
aly
s
is
,
d
esig
n
,
an
d
co
n
tr
o
l o
f
th
e
s
y
s
tem
.
0
0
.
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.
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4
4
.
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0
1
-
0
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0
0
5
0
0
.
0
0
5
0
.
0
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0
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0
1
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0
.
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2
T
i
m
e
(
s
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c
)
R
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A
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1
T
i
m
e
(
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c
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A
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p
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1
2
3
4
5
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7
8
9
10
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4
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6
T
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(
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(
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A
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P
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r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
19
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
1
:
2
5
2
-
2
6
4
260
4
.
2
.
St
o
cha
s
t
ic
ba
la
nced
t
runca
t
io
n a
lg
o
rit
hm
ba
s
ed
o
n Schur a
na
ly
s
is
Mo
s
t
o
f
th
e
m
o
d
el
r
ed
u
ctio
n
a
lg
o
r
ith
m
s
h
av
e
p
u
b
lis
h
ed
in
t
h
e
wo
r
ld
o
n
ly
a
p
p
ly
t
o
s
tab
le
h
ig
h
o
r
d
er
lin
ea
r
m
o
d
els
(
th
e
r
o
o
ts
o
f
t
h
e
ch
a
r
ater
is
tic
eq
u
atio
n
ar
e
n
eg
ativ
e
)
[
1
3
-
15]
.
Ho
wev
er
,
m
an
y
h
i
g
h
o
r
d
er
m
ath
em
atica
l
m
o
d
els
ar
e
u
n
s
tab
le
in
r
ea
lity
s
u
ch
as
th
e
m
o
d
el
in
s
ec
tio
n
3
.
T
h
er
e
f
o
r
e,
th
e
o
r
d
er
r
ed
u
ctio
n
alg
o
r
ith
m
s
h
o
u
ld
b
e
ap
p
licab
l
e
to
r
ed
u
ce
th
e
o
r
d
er
f
o
r
th
e
u
n
s
tab
le
lin
ea
r
s
y
s
tem
.
T
h
er
e
ar
e
two
b
asic
m
eth
o
d
s
f
o
r
m
o
d
el
r
e
d
u
ctio
n
o
f
u
n
s
t
ab
l
e
s
y
s
tem
.
T
h
e
f
ir
s
t
m
eth
o
d
(
in
d
ir
ec
t
o
r
d
er
r
e
d
u
ctio
n
alg
o
r
ith
m
)
.
T
h
is
alg
o
r
ith
m
d
iv
i
d
es
th
e
u
n
s
tab
le
o
r
i
g
in
al
s
y
s
tem
in
to
s
tab
le
an
d
u
n
s
tab
le
co
m
p
o
n
e
n
ts
,
th
en
ap
p
l
ies
th
e
o
r
d
e
r
r
ed
u
ctio
n
alg
o
r
ith
m
to
th
e
s
tab
le
c
o
m
p
o
n
en
ts
[
1
6
-
24]
.
A
t
th
e
en
d
,
to
g
et
th
e
o
r
d
er
o
f
r
e
d
u
ctio
n
o
f
th
e
r
o
o
t
s
y
s
tem
,
we
ad
d
th
e
r
ed
u
ce
d
s
tab
le
co
m
p
o
n
en
t
s
with
th
e
u
n
s
tab
le
co
m
p
o
n
en
t
s
.
T
h
e
s
ec
o
n
d
m
eth
o
d
(
d
ir
ec
t o
r
d
er
r
ed
u
ctio
n
alg
o
r
ith
m
)
.
Th
is
alg
o
r
ith
m
m
o
d
if
ies
an
d
ad
ju
s
t
s
th
e
o
r
d
er
r
ed
u
ctio
n
alg
o
r
ith
m
s
s
o
th
at
th
ese
alg
o
r
ith
m
s
ca
n
p
er
f
o
r
m
o
r
d
er
r
e
d
u
ctio
n
r
e
g
ar
d
less
o
f
wh
eth
er
th
e
o
r
ig
in
al
s
y
s
tem
is
s
tab
le
o
r
u
n
s
tab
le
[
2
5
-
29]
.
I
n
th
e
co
n
ten
t o
f
th
is
p
ap
er
,
th
e
au
th
o
r
in
tr
o
d
u
c
es
th
e
s
to
ch
asti
c
b
alan
c
ed
tr
u
n
ca
tio
n
alg
o
r
ith
m
b
ased
o
n
Sch
u
r
an
aly
s
is
[
2
3
,
24]
.
T
h
is
is
a
o
r
d
er
r
ed
u
ctio
n
alg
o
r
ith
m
ap
p
lied
to
th
e
u
n
s
tab
le
s
y
s
tem
b
y
in
d
i
r
ec
t o
r
d
er
r
ed
u
ctio
n
m
et
h
o
d
.
T
h
e
s
p
e
cif
ic
co
n
ten
ts
o
f
th
e
alg
o
r
ith
m
ar
e
as f
o
llo
ws:
I
n
p
u
t
:
T
h
e
s
y
s
tem
(
,
,
)
(
s
tab
le
o
r
u
n
s
tab
le)
d
escr
ib
ed
in
(
1
8
)
h
as
a
r
ep
r
esen
tatio
n
o
f
th
e
f
o
r
m
o
f
t
h
e
tr
an
s
f
er
f
u
n
ctio
n
:
(
)
:
=
(
−
)
−
1
.
Step
1
:
Fin
d
t
h
e
co
n
tr
o
llab
ilit
y
g
r
am
m
ia
n
an
d
o
b
s
er
v
ab
ilit
y
g
r
am
m
ian
b
y
s
o
lv
in
g
th
e
f
o
llo
win
g
L
y
ap
u
n
o
v
an
d
R
icca
ti e
q
u
atio
n
s
:
AP
+
+
=
0
;
=
+
;
+
+
(
−
)
(
−
)
(
−
)
=
0
Step
2
:
Fin
d
th
e
Sch
u
r
d
ec
o
m
p
o
s
itio
n
f
o
r
in
b
o
th
ascen
d
i
n
g
an
d
d
escen
d
in
g
o
r
d
er
,
r
esp
ec
t
iv
ely
,
=
[
1
.
.
.
.
.
.
0
.
.
.
.
.
.
0
0
]
;
=
[
.
.
.
.
.
.
0
.
.
.
.
.
.
0
0
1
]
Step
3
:
Fin
d
th
e
l
ef
t/rig
h
t
o
r
th
o
n
o
r
m
al
eig
en
-
b
ases
o
f
ass
o
ciate
d
with
th
e
k
th
b
ig
Han
k
el
s
in
g
u
lar
v
alu
es
o
f
th
e
all
-
p
ass
p
h
ase
m
atr
ix
(
∗
(
)
)
−
1
(
)
.
=
[
,
,
,
⏞
]
;
=
[
,
⏞
,
,
]
Step
4
: Fin
d
th
e
SVD
o
f
(
V
L
,
B
IG
T
V
R
,
B
IG
)
=
U
Σ
V
Step
5
:
Fo
r
m
th
e
lef
t/rig
h
t tr
an
s
f
o
r
m
atio
n
f
o
r
th
e
f
in
al
k
th
o
r
d
er
r
ed
u
ce
d
m
o
d
el.
,
=
,
(
1
:
,
1
:
)
−
1
/
2
;
,
=
,
(
1
:
,
1
:
)
−
1
/
2
Step
6
:
C
alcu
late
(
,
,
)
=
(
,
,
,
,
,
,
)
.
Ou
tp
u
t
:
T
h
e
r
e
d
u
ce
d
s
y
s
tem
(
,
,
)
.
5.
AP
P
L
I
E
D
L
Q
G
AL
G
O
R
I
T
H
M
F
O
R
RO
B
US
T
CO
NT
RO
L
P
RO
B
L
E
M
O
F
T
WO
-
WH
E
E
L
E
D
B
I
CY
CL
E
5
.
1
.
T
he
re
du
ce
d c
o
ntr
o
ller
o
f
s
ef
-
ba
la
ncing
t
wo
-
wheele
d bicy
cle
T
h
e
f
u
ll
o
r
d
er
RH
∞
co
n
tr
o
ller
is
d
esig
n
ed
as
(
1
7
)
,
wh
ich
is
a
3
0
th
o
r
d
er
co
n
tr
o
ller
.
T
o
o
b
tain
lo
w
co
n
tr
o
ller
,
we
p
er
f
o
r
m
o
r
d
er
r
ed
u
ctio
n
o
f
RH
∞
c
o
n
tr
o
ller
in
ac
co
r
d
an
ce
with
th
e
s
to
ch
asti
c
b
alan
ce
d
tr
u
n
ca
tio
n
alg
o
r
ith
m
b
ased
o
n
Sch
u
r
an
aly
s
is
in
s
ec
tio
n
4
.
T
h
e
r
esu
lt
s
o
f
th
e
o
r
d
er
r
ed
u
ctio
n
c
o
n
tr
o
ller
ar
e
s
h
o
w
n
in
T
ab
le
3
.
5
.
2
.
Co
ntr
o
llin
g
t
he
t
wo
-
wh
ee
led bicy
cle
us
i
ng
t
he
re
du
c
ed
4
t
h a
nd
5
t
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Evaluation Warning : The document was created with Spire.PDF for Python.