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[
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Kim
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1
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p
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6
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Mo
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7
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[
8
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Z
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p
ed
a
m
ath
em
atica
l m
o
d
el
o
f
a
p
en
d
u
lu
m
with
a
r
ea
ctio
n
w
h
ee
l
u
s
in
g
ca
s
ca
d
e
p
r
o
p
o
r
tio
n
al
–
in
teg
r
al
–
d
er
iv
a
tiv
e
(
PID
)
an
d
lin
ea
r
q
u
a
d
r
ati
c
Gau
s
s
ian
(
L
QG
)
co
n
tr
o
ller
s
f
o
r
s
tab
ilizatio
n
[
9
]
.
Yad
h
u
k
r
is
h
n
a
n
a
p
p
lied
t
h
e
g
y
r
o
s
co
p
e
ef
f
ec
t
t
o
s
tab
ilize
t
wo
-
wh
ee
led
v
eh
icles
in
d
ep
e
n
d
en
tly
[
1
0
]
.
Me
y
er
et
a
l.
p
r
o
p
o
s
ed
th
e
d
esig
n
,
m
o
d
elin
g
,
an
d
s
tab
il
izatio
n
o
f
a
m
o
m
en
t
ex
c
h
an
g
e
b
ased
in
v
er
ted
p
en
d
u
l
u
m
[
1
1
]
.
Go
g
o
i
et
a
l
.
co
n
d
u
cte
d
th
e
d
esig
n
an
d
f
a
b
r
icatio
n
o
f
a
s
elf
-
b
alan
cin
g
two
-
wh
ee
ler
v
eh
icle
u
s
in
g
a
g
y
r
o
s
co
p
e
[
1
2
]
.
Par
k
an
d
Yi
d
esig
n
ed
ac
tiv
e
b
alan
cin
g
co
n
tr
o
l
f
o
r
an
u
n
m
a
n
n
ed
b
icy
cle
u
s
in
g
a
s
ciss
o
r
ed
-
p
air
co
n
tr
o
l
m
o
m
en
t
g
y
r
o
s
co
p
e
[
1
3
]
.
C
h
ien
et
a
l.
d
esig
n
ed
a
two
-
w
h
ee
led
s
elf
-
b
alan
cin
g
v
eh
icle
b
ased
o
n
lo
ad
s
en
s
o
r
s
[
1
4
]
.
L
o
t
an
d
Flem
in
g
p
r
o
p
o
s
ed
g
y
r
o
s
co
p
ic
s
tab
ilizer
s
f
o
r
p
o
wer
ed
two
-
wh
ee
le
d
v
eh
icles
[
1
5
]
.
B
elascu
en
an
d
Ag
u
ilar
p
r
ese
n
ted
r
ea
ctio
n
wh
ee
l
in
v
er
ted
p
en
d
u
lu
m
s
y
s
tem
ca
n
b
e
o
p
tim
ized
to
m
ax
im
ize
r
ec
o
v
er
y
a
n
g
le
an
d
s
y
s
tem
p
er
f
o
r
m
a
n
ce
[
1
6
]
.
T
r
a
n
et
a
l
.
p
r
o
p
o
s
ed
PID
co
n
tr
o
l
f
o
r
a
b
ala
n
cin
g
b
ik
e
m
o
d
el
u
s
in
g
a
r
ea
ctio
n
wh
ee
l
with
o
u
t
r
ely
in
g
o
n
its
m
ath
em
atica
l
m
o
d
el
[
1
7
]
.
Patil
et
a
l
.
p
r
o
p
o
s
ed
m
o
d
elin
g
o
f
th
e
b
icy
cle
b
ased
o
n
th
e
i
n
v
er
ted
p
e
n
d
u
lu
m
m
o
d
el
an
d
u
s
ed
th
e
L
ag
r
an
g
ian
a
p
p
r
o
a
ch
o
f
d
y
n
am
ics
to
esti
m
ate
to
r
q
u
e
f
o
r
th
e
b
alan
c
in
g
o
f
th
e
b
ic
y
cle
[
1
8
]
.
C
h
en
et
a
l
.
d
e
v
elo
p
ed
a
two
-
wh
ee
l
ed
co
m
p
o
s
ite
s
elf
-
b
alan
cin
g
r
o
b
o
t
f
o
r
s
tatio
n
ar
y
o
p
er
atio
n
s
in
u
n
k
n
o
wn
ter
r
ai
n
b
y
u
s
in
g
a
r
ea
ctio
n
wh
ee
l
f
o
r
s
tab
ilizatio
n
[
1
9
]
.
Vu
an
d
Ng
u
y
en
p
r
o
p
o
s
ed
5
-
o
r
d
er
c
o
n
tr
o
ller
s
f
o
r
b
alan
ci
n
g
co
n
tr
o
l
o
f
two
-
wh
e
el
b
icy
cle
p
r
o
b
lem
s
[
2
0
]
.
Seek
h
ao
et
a
l.
co
n
tr
o
l
th
e
b
a
lan
ce
o
f
a
b
icy
cle
r
o
b
o
t
b
y
a
p
p
ly
in
g
a
p
e
n
d
u
lu
m
m
ass
m
o
v
in
g
to
g
eth
e
r
with
h
ea
d
in
g
s
teer
in
g
[
2
1
]
.
Z
h
a
n
g
an
d
No
r
c
o
n
d
u
cted
a
r
e
v
iew
o
f
th
e
co
n
tr
o
l
s
tr
ateg
ies
ap
p
lied
to
s
tab
ilize
a
two
-
wh
ee
led
r
o
b
o
t
[
2
2
]
.
Mo
n
to
y
a
an
d
Gil
-
Go
n
za
lez
test
ed
d
if
f
er
en
t
co
n
tr
o
ller
s
f
o
r
a
r
ea
ctio
n
wh
ee
l
p
en
d
u
lu
m
u
s
in
g
th
r
ee
s
im
u
latio
n
task
s
:
th
e
ty
p
ical
ca
s
e,
th
e
ca
s
e
with
u
n
ce
r
tain
ties
,
an
d
th
e
ca
s
e
with
ex
ter
n
al
d
is
tu
r
b
an
ce
s
[
2
3
]
.
T
h
e
m
ain
co
n
tr
ib
u
tio
n
s
o
f
th
is
r
esear
ch
to
th
e
d
ev
elo
p
m
en
t
o
f
two
-
wh
ee
ler
s
tab
ilizatio
n
s
y
s
tem
s
ar
e
as
f
o
llo
ws.
T
h
is
wo
r
k
is
u
n
i
q
u
e
c
o
m
p
ar
e
d
to
ex
is
tin
g
liter
atu
r
e
b
y
p
r
o
v
id
in
g
a
d
etailed
d
escr
ip
tio
n
o
f
its
co
m
p
o
n
en
ts
an
d
s
tep
-
by
-
s
tep
ex
p
lan
atio
n
o
f
h
ar
d
war
e
d
esig
n
an
d
co
n
tr
o
ller
d
esig
n
.
A
d
etailed
d
escr
ip
tio
n
o
f
th
e
co
m
p
o
n
en
ts
with
tech
n
ic
al
s
p
ec
if
icatio
n
s
h
as
b
ee
n
p
r
o
v
id
ed
,
wh
ich
h
elp
s
o
th
er
in
ter
ested
p
ar
ties
in
b
u
ild
in
g
th
is
s
tab
ilizatio
n
s
y
s
tem
.
T
h
is
p
a
p
er
is
o
r
g
an
ized
as
f
o
llo
ws.
Sectio
n
1
p
r
esen
ts
in
tr
o
d
u
ctio
n
,
s
ec
tio
n
2
d
is
cu
s
s
es
s
y
s
tem
m
o
d
elin
g
wh
ich
in
clu
d
es
m
ec
h
an
ical
co
m
p
o
n
en
ts
an
d
elec
tr
o
n
ic
cir
cu
its
an
d
d
is
cu
s
s
e
s
m
ath
em
atica
l
m
o
d
elin
g
o
f
t
h
e
s
y
s
tem
,
s
ec
tio
n
3
d
eliv
er
s
co
n
tr
o
l
d
esig
n
o
f
t
h
e
s
tab
ilizer
s
y
s
tem
,
s
ec
tio
n
4
s
h
o
ws
th
e
r
esu
lts
o
f
ex
p
er
im
en
ts
an
d
an
aly
s
is
o
f
th
e
b
alan
cin
g
s
y
s
tem
s
,
an
d
f
in
ally
s
ec
tio
n
5
p
r
esen
ts
th
e
co
n
clu
s
io
n
s
o
f
t
h
is
p
ap
er
.
2.
SYST
E
M
M
O
D
E
L
L
I
NG
2
.
1
.
H
a
rdwa
re
d
esig
n
T
h
e
two
wh
ee
le
d
v
e
h
icle
m
o
d
el
co
n
s
is
ts
o
f
two
m
ai
n
p
a
r
ts
:
m
ec
h
an
ical
p
ar
ts
with
a
DC
m
o
to
r
a
n
d
elec
tr
o
n
ic
p
ar
ts
f
o
r
co
n
tr
o
l.
T
h
e
two
-
wh
ee
led
v
eh
icle
m
o
d
e
l
is
s
h
o
wn
in
Fig
u
r
e
1
,
wh
ich
co
n
s
is
ts
o
f
a
v
eh
icle
f
r
am
e,
wh
ee
ls
,
a
r
ea
ctio
n
wh
e
el,
an
d
co
n
tr
o
ller
c
o
m
p
o
n
en
ts
.
T
h
e
f
r
a
m
e
is
m
ad
e
o
f
ac
r
y
lic
an
d
d
esig
n
e
d
u
s
in
g
C
AD
s
o
f
twar
e.
Fro
m
an
aly
s
is
u
s
in
g
C
AD
s
o
f
twar
e,
th
e
lo
c
atio
n
o
f
th
e
ce
n
ter
o
f
m
ass
o
f
ea
ch
co
m
p
o
n
en
t
o
f
th
e
two
-
wh
ee
led
v
eh
icle
m
o
d
el
was
o
b
tain
ed
.
T
h
e
o
n
ly
co
m
p
o
n
e
n
t
th
at
h
as
n
o
t
y
et
b
ee
n
d
esig
n
ed
is
th
e
r
ea
ctio
n
wh
ee
l,
f
o
r
wh
ich
th
e
m
ass
lim
it
h
as
b
ee
n
d
eter
m
in
ed
,
an
d
th
e
d
etailed
r
ea
ctio
n
w
h
ee
l
m
o
d
el
will
b
e
d
escr
ib
ed
later
.
Fro
m
an
aly
s
is
o
n
th
e
C
AD
m
o
d
el
an
d
DC
m
o
to
r
s
p
ec
if
icat
io
n
d
ata,
p
ar
a
m
eter
v
alu
es
o
f
m
ain
an
d
ad
d
itio
n
al
c
o
m
p
o
n
en
ts
wer
e
s
h
o
wn
in
T
ab
le
s
1
an
d
2
,
r
esp
ec
tiv
ely
.
T
h
e
elec
tr
o
n
ic
co
n
t
r
o
l
cir
cu
it
s
ch
em
atic
f
o
r
th
e
b
alan
cin
g
s
y
s
tem
is
s
h
o
wn
in
Fig
u
r
e
2
,
wh
ich
co
n
s
is
t
s
o
f
a
D
C
m
o
to
r
,
an
Ar
d
u
in
o
Nan
o
b
o
a
r
d
,
a
g
y
r
o
s
co
p
e
s
en
s
o
r
,
a
p
o
wer
s
u
p
p
ly
,
an
d
a
m
o
to
r
d
r
iv
er
.
T
h
e
DC
m
o
to
r
h
as
a
m
a
x
im
u
m
r
o
tatio
n
s
p
ee
d
o
f
1
3
6
0
R
PM,
a
m
ax
im
u
m
to
r
q
u
e
o
f
0
.
1
Nm
,
a
g
ea
r
r
ati
o
o
f
4
.
5
with
an
1
1
PP
R
en
co
d
er
m
o
u
n
ted
o
n
th
e
m
o
to
r
s
h
af
t.
Fro
m
th
e
id
e
n
tific
atio
n
o
f
th
e
DC
m
o
to
r
,
its
p
ar
am
eter
s
ar
e
o
b
tain
ed
as sh
o
wn
in
T
a
b
le
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
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&
C
o
m
p
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I
SS
N:
2088
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8
7
0
8
Desig
n
a
n
d
ma
n
u
fa
ctu
r
e
o
f a
s
elf
-
b
a
la
n
cin
g
s
ystem
fo
r
…
(
I
n
d
r
a
w
a
n
to
)
1855
Fig
u
r
e
1
.
C
AD
m
o
d
el
o
f
th
e
t
wo
-
wh
ee
led
v
e
h
icle
m
o
d
el
T
ab
le
1
.
Ma
in
c
o
m
p
o
n
en
t m
as
s
es
C
o
m
p
o
n
e
n
t
M
a
ss
(
k
g
)
C
e
n
t
e
r
o
f
mass
o
n
t
h
e
y
-
a
x
i
s (m
)
A
c
r
y
l
i
c
f
r
a
me
0
.
1
3
2
0
.
0
4
6
D
C
m
o
t
o
r
0
.
1
5
0
0
.
1
0
5
R
e
a
c
t
i
o
n
w
h
e
e
l
0
.
2
5
0
0
.
1
0
5
Eq
u
i
p
me
n
t
0
.
1
2
6
0
.
0
3
8
A
l
l
c
o
m
p
o
n
e
n
t
s
0
.
7
7
9
0
.
0
7
3
T
ab
le
2
.
Ad
d
itio
n
al
co
m
p
o
n
e
n
t m
ass
es
Eq
u
i
p
me
n
t
M
a
ss
(
k
g
)
C
e
n
t
e
r
o
f
mass
o
n
t
h
e
y
-
a
x
i
s (m
)
A
r
d
u
i
n
o
n
a
n
o
+
sh
i
e
l
d
0
.
0
4
0
.
0
2
2
M
i
c
r
o
S
D
0
.
0
0
5
0
.
0
5
5
M
o
t
o
r
d
r
i
v
e
r
0
.
0
3
2
0
.
0
5
4
M
P
U
6
0
5
0
0
.
0
0
2
0
.
0
0
7
B
e
a
r
i
n
g
+
s
h
a
f
t
0
.
0
1
7
0
.
0
2
0
Fig
u
r
e
2
.
Sch
em
atic
o
f
th
e
ele
ctr
o
n
ic
co
n
t
r
o
l c
ir
cu
it; 1
.
DC
m
o
to
r
with
en
c
o
d
er
,
2
.
Ar
d
u
in
o
Nan
o
b
o
ar
d
,
3
.
Gy
r
o
s
en
s
o
r
MPU6
0
5
0
,
4
.
Po
wer
s
u
p
p
ly
,
5
.
Mo
to
r
d
r
i
v
er
T
B
6
6
1
2
FNG,
6
.
Pu
s
h
-
b
u
tto
n
T
ab
le
3
.
T
h
e
DC
m
o
to
r
p
ar
am
eter
s
P
a
r
a
me
t
e
r
s
V
a
l
u
e
M
o
t
o
r
a
r
ma
t
u
r
e
r
e
s
i
st
a
n
c
e
1
0
.
6
8
Ω
M
o
t
o
r
a
r
ma
t
u
r
e
i
n
d
u
c
t
a
n
c
e
4
.
6
9
.
1
0
-
1
H
To
r
q
u
e
c
o
n
st
a
n
t
0
.
0
8
0
2
N
.
m
/
A
B
a
c
k
e
mf
c
o
n
st
a
n
t
0
.
0
8
0
4
V
/
r
a
d
.
s
-
1
M
o
t
o
r
a
r
ma
t
u
r
e
i
n
e
r
t
i
a
1
.
2
4
2
.
1
0
-
5
k
g
.
m
2
F
r
i
c
t
i
o
n
c
o
e
f
f
i
c
i
e
n
t
2
.
1
0
-
5
N
.
m
.
s/
r
a
d
2
.
2
.
M
a
t
hema
t
ica
l
m
o
dellin
g
T
h
e
s
tab
ilizatio
n
s
y
s
tem
d
ev
elo
p
ed
in
th
is
r
esear
ch
is
b
ased
o
n
a
lin
ea
r
s
y
s
tem
ap
p
r
o
ac
h
; t
h
er
ef
o
r
e
,
a
d
y
n
am
ic
m
o
d
el
o
f
th
e
s
y
s
tem
is
r
eq
u
ir
ed
.
T
h
e
v
eh
icle
m
o
d
el
in
th
is
s
tu
d
y
is
ap
p
r
o
x
im
ated
as
an
in
v
er
ted
p
en
d
u
l
u
m
with
a
r
ea
ctio
n
wh
e
el
to
s
tab
ilize
it.
T
h
e
m
o
d
elin
g
o
f
th
is
two
-
wh
ee
led
v
eh
icle
m
o
d
el
is
s
im
p
lifie
d
in
two
-
d
im
en
s
io
n
al
m
o
tio
n
.
As
an
ap
p
r
o
x
im
atio
n
,
th
e
in
v
er
ted
p
en
d
u
lu
m
co
n
s
is
ts
o
f
t
wo
p
ar
ts
:
th
e
r
ea
ctio
n
wh
ee
l
an
d
th
e
l
o
wer
p
ar
t
(
t
h
e
p
en
d
u
lu
m
,
wh
ich
r
ep
r
esen
ts
th
e
two
-
wh
ee
led
v
e
h
icle
m
o
d
el)
.
T
h
e
r
ea
ctio
n
wh
ee
l
co
n
s
is
ts
o
f
a
wh
ee
l
an
d
a
DC
m
o
to
r
,
wh
ile
th
e
lo
wer
p
ar
t
co
n
s
is
ts
o
f
a
m
o
d
el
f
r
am
e
an
d
elec
tr
o
n
ic
co
m
p
o
n
en
ts
.
T
o
s
im
p
lify
th
e
a
n
aly
s
is
,
th
e
f
r
ictio
n
o
f
th
e
w
h
e
els
ag
ain
s
t
th
e
f
lo
o
r
an
d
t
h
e
f
r
ictio
n
b
etwe
en
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
4
,
Au
g
u
s
t
20
2
6
:
1
8
5
3
-
1
866
1856
r
ea
ctio
n
wh
ee
l
a
n
d
t
h
e
air
a
r
e
ig
n
o
r
e
d
.
I
n
th
is
m
o
d
elin
g
,
t
h
e
g
r
a
v
itatio
n
al
f
o
r
ce
is
ass
u
m
ed
to
a
p
p
ly
at
th
e
ce
n
ter
o
f
m
ass
.
Fig
u
r
e
3
s
h
o
w
s
th
e
s
ch
em
atic
o
f
th
e
in
v
er
ted
p
en
d
u
l
u
m
with
a
r
ea
ctio
n
wh
ee
l:
Fig
u
r
e
3
.
An
in
v
er
ted
p
en
d
u
lu
m
with
a
r
ea
ctio
n
wh
ee
l
wh
er
e:
: g
r
av
itatio
n
ac
ce
ler
atio
n
(
m
/s
2
)
1
: p
en
d
u
l
u
m
m
ass
(
k
g
)
2
: r
ea
ctio
n
wh
ee
l m
ass
an
d
DC
m
o
to
r
(
k
g
)
1
:
an
g
le
o
f
p
en
d
u
lu
m
(
r
o
d
)
ab
o
u
t
z
-
ax
is
(
p
o
in
t
O
)
(
r
ad
)
̇
1
:
an
g
u
lar
v
elo
city
o
f
p
en
d
u
lu
m
ab
o
u
t
z
-
a
x
is
(
r
ad
/s
)
̈
1
:
an
g
u
lar
ac
ce
ler
atio
n
o
f
p
en
d
u
lu
m
ab
o
u
t
z
-
ax
is
(
r
ad
/s
2
)
21
:
an
g
le
o
f
r
ea
ctio
n
wh
ee
l
with
r
esp
ec
t to
p
en
d
u
lu
m
(
r
ad
)
̇
21
: a
n
g
u
lar
v
elo
city
o
f
r
ea
ctio
n
wh
ee
l
with
r
esp
ec
t to
p
en
d
u
lu
m
(
r
ad
/s
)
̈
21
: a
n
g
u
lar
ac
ce
ler
atio
n
o
f
r
ea
cti
o
n
wh
ee
l
with
r
esp
ec
t to
p
en
d
u
lu
m
(
r
ad
/s
2
)
1
:
in
er
tia
o
f
p
en
d
u
lu
m
a
b
o
u
t i
ts
ce
n
ter
m
ass
(
k
g
.
m
2
)
2
:
in
er
tia
o
f
r
ea
ctio
n
wh
ee
l
ab
o
u
t its
ce
n
ter
m
ass
(
k
g
.
m
2
)
1
:
in
er
tia
o
f
p
en
d
u
lu
m
ab
o
u
t
z
-
ax
is
(
p
o
in
t
O
)
(
k
g
.
m
2
)
2
:
in
er
tia
o
f
r
ea
cti
o
n
wh
ee
l a
b
o
u
t
z
-
ax
is
(
p
o
in
t
O
)
(
k
g
.
m
2
)
1
:
d
is
tan
ce
o
f
th
e
ce
n
ter
o
f
m
a
s
s
o
f
p
en
d
u
l
u
m
to
th
e
r
o
tatio
n
ax
is
O
(m)
2
:
d
is
tan
ce
o
f
th
e
ce
n
ter
o
f
m
a
s
s
o
f
th
e
r
ea
ctio
n
wh
ee
l
t
o
th
e
r
o
tatio
n
ax
is
O
(m)
T
h
e
d
y
n
am
ic
eq
u
atio
n
o
f
an
in
v
er
ted
p
en
d
u
lu
m
with
a
r
ea
ctio
n
wh
ee
l c
an
b
e
d
er
iv
e
d
f
r
o
m
th
e
f
o
r
ce
s
in
Fig
u
r
e
3,
a
s
g
iv
en
i
n
(
1
)
.
(
1
+
2
)
̈
1
=
(
1
1
+
2
2
)
s
in
1
−
(
1
)
wh
er
e
is
th
e
ef
f
ec
tiv
e
to
r
s
io
n
r
eq
u
ir
ed
to
b
alan
ce
th
e
s
y
s
tem
,
an
d
is
g
iv
e
n
in
(
2
)
:
=
2
̈
21
(
2
)
T
h
e
r
e
ac
t
io
n
wh
ee
l
wi
ll
ac
ce
l
e
r
at
e
i
n
p
r
o
p
o
r
ti
o
n
to
t
h
e
DC
m
o
t
o
r
t
o
r
q
u
e
(
)
.
T
h
e
ele
ct
r
o
m
e
c
h
a
n
i
ca
l
eq
u
a
ti
o
n
o
f
a
DC
m
o
t
o
r
is
g
i
v
e
n
in
(
3
)
a
n
d
(
4
)
:
=
=
−
̇
2
(
3
)
∙
+
=
−
̇
2
(
4
)
wh
er
e:
:
m
o
to
r
f
r
ictio
n
co
e
f
f
icien
t
(
Ns
/
m
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Desig
n
a
n
d
ma
n
u
fa
ctu
r
e
o
f a
s
elf
-
b
a
la
n
cin
g
s
ystem
fo
r
…
(
I
n
d
r
a
w
a
n
to
)
1857
: M
o
to
r
to
r
q
u
e
co
n
s
tan
t
(
Nm
/
A
)
: Back
E
MF
co
n
s
tan
t
(
V
/
(
r
a
d
.
s
−
1
)
: e
lectr
ic
cu
r
r
en
t
(
A
)
: m
o
to
r
ar
m
atu
r
e
r
esis
tan
ce
(
Ω
)
: m
o
to
r
ar
m
atu
r
e
in
d
u
ctan
ce
(
H
)
: v
o
ltag
e
in
p
u
t
(
V
)
̇
2
: a
n
g
u
lar
v
elo
city
o
f
DC
m
o
to
r
(
r
a
d
/
s
)
2
.
3
.
M
o
del
lin
ea
riza
t
io
n
T
h
e
s
y
s
tem
is
lin
ea
r
ized
ar
o
u
n
d
a
s
tead
y
s
tate
p
o
in
t.
I
n
(
1
)
,
f
o
r
s
m
all
,
s
in
ca
n
b
e
a
p
p
r
o
x
im
ated
as
s
o
th
at
(
1
)
ca
n
b
e
wr
itten
a
s
(
5
)
(
1
+
2
)
̈
1
=
(
1
1
+
2
2
)
1
−
(
5
)
−
State
s
p
ac
e
m
o
d
el
T
h
e
s
y
s
tem
s
tate
v
ar
iab
les ar
e
ch
o
s
en
as f
o
llo
ws:
1
=
1
2
=
̇
1
3
=
̇
2
Sin
ce
is
s
m
all
co
m
p
ar
ed
to
o
th
er
p
ar
a
m
eter
s
,
it
m
ay
b
e
ig
n
o
r
ed
.
B
y
co
m
b
in
in
g
(
3
)
an
d
(
4
)
,
an
d
s
u
b
s
titu
tin
g
̇
2
with
3
we
g
et
th
e
m
o
to
r
to
r
q
u
e
(
6
)
:
=
(
−
3
)
−
3
(
6
)
T
h
e
d
y
n
am
ic
eq
u
atio
n
f
o
r
th
e
s
ec
o
n
d
s
tate
v
ar
iab
le
is
o
b
tain
ed
b
y
s
u
b
s
titu
tin
g
(
6
)
i
n
to
(
5
)
,
we
g
et
̇
2
(
7
):
̇
2
=
(
1
1
)
(
1
+
2
)
1
+
(
(
1
+
2
)
+
(
1
+
20
)
)
3
−
(
1
+
2
)
(
7
)
T
h
e
d
y
n
am
ic
eq
u
atio
n
f
o
r
th
e
th
ir
d
s
tate
v
ar
iab
le
is
o
b
tain
e
d
b
y
s
u
b
s
titu
tin
g
(
6
)
in
t
o
(
2
)
as sh
o
wn
in
(
8
)
:
2
(
̇
3
+
̇
2
)
=
(
−
3
)
−
3
(
8
)
B
y
s
u
b
s
titu
tin
g
(
5
)
an
d
(
7
)
in
t
o
(
8
)
,
th
e
v
al
u
e
o
f
̇
3
is
o
b
tain
ed
as g
iv
en
in
(
9
)
:
̇
3
=
−
(
1
1
+
2
2
)
(
1
+
2
)
1
−
1
+
2
+
2
2
(
1
+
2
)
(
+
)
3
+
1
+
2
+
2
2
(
1
+
2
)
(
9
)
T
h
en
,
b
y
en
ter
in
g
t
h
e
v
alu
es
̇
1
,
̇
2
,
̇
3
an
d
as
an
in
p
u
t
in
to
th
e
s
tate
s
p
ac
e
m
atr
ix
eq
u
atio
n
,
we
g
et
(
1
0
)
an
d
(
1
1
)
:
̇
=
+
(
1
0
)
=
+
(
1
1
)
w
h
er
e
=
[
0
1
0
(
1
1
+
2
2
)
(
1
+
2
)
0
(
(
1
+
2
)
+
(
1
+
2
)
)
−
(
1
1
+
2
2
)
(
1
+
2
)
0
−
1
+
2
+
2
2
(
1
+
2
)
(
+
)
]
(
1
2
)
=
[
0
−
(
1
+
2
)
1
+
2
+
2
2
(
+
2
)
]
(
1
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
4
,
Au
g
u
s
t
20
2
6
:
1
8
5
3
-
1
866
1858
Sin
ce
a
ll st
ate
v
ar
iab
les will b
e
r
ec
o
r
d
e
d
,
th
e
o
u
tp
u
t
m
atr
ix
is
d
ef
in
ed
b
y
(
1
4
)
:
=
[
1
0
0
0
1
0
0
0
1
]
(
1
4
)
=
[
0
]
(
1
5
)
2
.
4
.
Rea
c
t
io
n
wheel
des
ig
n
T
h
e
r
ea
ctio
n
wh
ee
l
is
a
n
im
p
o
r
tan
t
p
ar
t
o
f
t
h
e
b
ala
n
cin
g
s
y
s
tem
wh
er
e
th
e
r
ea
ctio
n
wh
ee
l
will
p
r
o
d
u
ce
a
f
o
r
ce
to
b
alan
ce
th
e
m
o
d
el
s
o
th
at
it
r
em
ain
s
u
p
r
ig
h
t.
I
n
d
esig
n
in
g
th
e
r
ea
ctio
n
wh
ee
l,
th
e
d
esig
n
co
n
s
tr
ain
ts
ap
p
r
o
p
r
iate
to
th
e
t
wo
-
wh
ee
led
v
e
h
icle
m
o
d
el
a
r
e
tak
en
as f
o
llo
ws:
−
T
h
e
m
ax
im
u
m
d
iam
eter
is
1
0
0
m
m
,
wh
ich
is
ac
co
r
d
in
g
to
th
e
s
p
ac
e
av
ailab
le
in
th
e
m
o
d
el
f
r
am
e.
−
T
h
e
m
ax
im
u
m
m
ass
is
2
5
0
g
r
.
−
T
h
e
m
o
m
e
n
t o
f
i
n
er
tia
is
lim
ited
ac
co
r
d
i
n
g
to
t
h
e
to
r
q
u
e
o
f
t
h
e
DC
m
o
to
r
u
s
ed
i
n
th
is
b
ala
n
cin
g
s
y
s
tem
.
B
ased
o
n
th
e
C
AD
m
o
d
el
o
f
th
e
v
eh
icle
m
o
d
el,
t
h
e
ce
n
ter
o
f
m
ass
o
f
th
is
m
o
d
el
is
esti
m
a
ted
at
a
h
eig
h
t
o
f
7
9
mm
f
r
o
m
th
e
g
r
o
u
n
d
.
Usi
n
g
th
e
s
im
p
le
p
en
d
u
lu
m
o
s
cillatio
n
n
atu
r
al
f
r
eq
u
en
c
y
f
o
r
m
u
la,
=
1
2
√
,
th
e
n
atu
r
al
f
r
eq
u
e
n
cy
o
f
th
is
m
o
d
el
is
esti
m
ated
to
b
e
=
1
.
77
Hz.
T
h
er
ef
o
r
e,
t
h
e
m
ax
im
u
m
tim
e
co
n
s
tan
t
f
o
r
th
e
b
ala
n
c
in
g
s
y
s
tem
to
b
e
a
b
le
to
k
ee
p
th
is
two
-
wh
ee
led
v
e
h
icle
m
o
d
el
in
u
p
r
ig
h
t
co
n
d
itio
n
is
≤
4
=
0
.
141
s.
B
ased
o
n
(
3
)
an
d
(
4
)
a
n
d
ass
u
m
in
g
th
at
th
e
v
alu
e
o
f
is
s
m
all,
th
en
r
elatio
n
b
etwe
en
th
e
m
o
t
o
r
v
elo
cit
y
̇
2
an
d
in
p
u
t v
o
ltag
e
m
ay
b
e
g
iv
e
n
b
y
(
1
6
)
.
Θ
̇
(
)
(
)
=
+
+
+
1
(
1
6
)
Fro
m
(
1
6
)
,
th
e
tim
e
c
o
n
s
tan
t o
f
th
e
m
o
to
r
ca
n
b
e
d
e
f
in
ed
as
(
1
7
)
.
=
+
(
1
7
)
Fro
m
T
ab
le
3
an
d
th
e
m
ax
i
m
u
m
tim
e
co
n
s
tan
t
τ
to
s
tab
iliz
e
th
e
m
o
d
el
is
0
.
1
4
1
s
,
b
y
u
s
in
g
(
1
7
)
th
e
n
th
e
m
ax
im
u
m
i
n
er
tia
th
at
ca
n
b
e
b
o
r
n
e
b
y
th
e
m
o
t
o
r
to
r
q
u
e
i
s
=
8
.
8
3
1
.
1
0
-
5
k
g
.
m
2
.
Sin
ce
co
n
s
is
t
s
o
f
an
d
in
er
tia
o
f
th
e
r
ea
ctio
n
w
h
ee
l,
th
er
ef
o
r
e
=
−
=
7
.
5
8
8
.
1
0
-
5
k
g
.
m
2
.
T
h
e
d
esig
n
o
f
th
e
in
er
tia
an
d
m
ass
o
f
th
e
r
ea
ctio
n
wh
ee
l
is
ca
r
r
ied
o
u
t
b
y
s
im
p
lify
in
g
its
s
h
ap
e
,
wh
ic
h
co
n
s
is
ts
o
f
th
e
r
ea
ctio
n
wh
ee
l sp
o
k
es a
n
d
th
e
o
u
ter
r
in
g
o
f
th
e
r
ea
ctio
n
w
h
ee
l
,
as sh
o
wn
in
Fig
u
r
e
4
.
Fig
u
r
e
4
.
T
h
e
r
ea
ctio
n
wh
ee
l d
esig
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Desig
n
a
n
d
ma
n
u
fa
ctu
r
e
o
f a
s
elf
-
b
a
la
n
cin
g
s
ystem
fo
r
…
(
I
n
d
r
a
w
a
n
to
)
1859
W
h
er
e
: is
th
e
wid
th
o
f
th
e
s
p
o
k
es
.
: is th
e
th
ick
n
ess
o
f
th
e
r
ea
ctio
n
wh
ee
l
.
:
is
th
e
wid
th
o
f
th
e
r
ea
ctio
n
w
h
ee
l r
in
g
.
: is th
e
o
u
ter
d
iam
eter
o
f
th
e
r
ea
ctio
n
wh
ee
l.
T
o
d
eter
m
in
e
t
h
e
d
im
e
n
s
io
n
s
o
f
th
e
r
ea
ctio
n
wh
ee
l,
f
o
u
r
m
ain
v
ar
iab
les
ar
e
c
h
o
s
en
as
m
o
d
if
ier
s
,
n
am
ely
,
,
,
an
d
.
T
h
e
s
elec
tio
n
o
f
v
ar
ia
b
le
v
alu
es
is
ca
r
r
ied
o
u
t
b
y
co
m
p
ar
in
g
th
e
m
o
m
e
n
t
o
f
in
er
ti
a
with
th
e
m
ass
o
f
th
e
r
ea
ctio
n
wh
ee
l,
s
o
th
at
th
e
d
im
e
n
s
io
n
s
s
elec
ted
ar
e
th
e
m
o
s
t o
p
tim
al.
Fro
m
Fig
u
r
e
4
,
th
e
r
ea
ctio
n
w
h
ee
l
in
er
tia
ca
n
b
e
d
i
v
id
ed
in
t
o
two
p
ar
ts
,
n
am
ely
s
p
o
k
e
in
e
r
tia
2
an
d
r
in
g
in
er
tia
1
.
T
h
e
s
p
o
k
e
in
er
tia
2
,
an
d
t
h
e
r
in
g
in
er
tia
1
ar
e
d
escr
ib
ed
in
(
1
8
)
a
n
d
(
1
9
)
,
r
esp
ec
ti
v
ely
.
2
≅
3
(
1
12
2
(
2
+
(
−
)
2
)
+
1
2
2
(
−
)
2
)
(
1
8
)
2
≅
3
(
1
12
2
(
2
+
(
−
)
2
)
+
1
2
2
(
−
)
2
)
(
1
9
)
with
,
2
≅
3
(
1
12
2
(
2
+
(
−
)
2
)
+
1
2
2
(
−
)
2
)
(
2
0
)
2
≅
3
(
1
12
2
(
2
+
(
−
)
2
)
+
1
2
2
(
−
)
2
)
(
2
1
)
wh
er
e:
:
r
ea
ctio
n
wh
ee
l d
e
n
s
ity
1
:
m
o
m
en
t
o
f
in
er
tia
o
f
th
e
r
ea
ctio
n
wh
ee
l r
in
g
2
:
m
o
m
en
t
o
f
in
er
tia
o
f
th
e
r
ea
ctio
n
wh
ee
l sp
o
k
e.
1
:
r
ea
ctio
n
wh
ee
l r
in
g
m
ass
2
:
m
ass
o
f
th
e
r
ea
ctio
n
w
h
ee
l sp
o
k
e.
=
1
+
2
=
1
+
2
Fro
m
(
1
8
)
–
(
2
0
)
,
t
h
er
e
a
r
e
f
o
u
r
p
ar
a
m
eter
s
to
b
e
s
ea
r
ch
ed
.
H
o
wev
er
,
to
s
im
p
lify
th
e
d
esig
n
with
o
u
t
lo
s
in
g
its
g
en
er
ality
,
th
e
th
r
ee
p
ar
am
eter
s
,
,
an
d
ar
e
p
r
e
s
et
in
ac
co
r
d
an
ce
with
th
e
g
eo
m
et
r
ic
co
n
s
tr
ain
ts
o
f
th
e
m
o
d
el,
wh
ile
th
e
o
n
ly
p
ar
am
eter
to
b
e
o
p
tim
ized
is
.
T
h
e
v
alu
es o
f
,
,
an
d
ar
e
g
iv
en
in
T
ab
le
4
.
T
ab
le
4
.
Pre
s
et
r
ea
ctio
n
w
h
ee
l p
ar
am
eter
s
P
a
r
a
me
t
e
r
U
n
i
t
(
mm
)
8
2
50
Fro
m
th
e
s
im
u
latio
n
r
esu
lts
b
ased
o
n
(
1
8
)
–
(
2
1
)
,
it
is
o
b
tain
e
d
th
at
th
e
o
p
tim
al
v
alu
e
,
n
am
e
ly
th
e
h
ig
h
est
v
alu
e
o
f
/
an
d
f
u
lf
illi
n
g
th
e
tim
e
co
n
s
tan
t
=
0
.
1
4
1
s
,
is
= 6
mm
.
3.
CO
NT
RO
L
L
E
R
DE
SI
G
N
T
h
is
b
alan
cin
g
s
y
s
tem
c
o
n
tr
o
ller
is
d
esig
n
ed
u
s
in
g
th
e
L
Q
R
m
eth
o
d
with
g
ai
n
s
is
g
iv
e
n
in
(
2
2
)
an
d
R
icca
ti e
q
u
atio
n
to
s
o
lv
e
m
atr
ix
is
g
iv
en
in
(
2
3
)
[
2
4
]
:
=
−
1
(
2
2
)
+
−
−
1
+
=
0
(
2
3
)
wh
er
e
S
is
a
s
y
m
m
etr
ic
m
atr
i
x
an
d
an
d
ar
e
weig
h
in
g
m
atr
ic
es
.
T
o
d
eter
m
in
e
th
e
weig
h
tin
g
a
n
d
,
B
r
y
s
o
n
’
s
r
u
le
m
eth
o
d
is
u
s
ed
[
2
4
]
.
T
h
e
an
d
v
alu
es a
r
e
g
iv
en
b
y
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
4
,
Au
g
u
s
t
20
2
6
:
1
8
5
3
-
1
866
1860
11
=
1
1
2
(
2
4
)
22
=
1
2
2
(
2
5
)
33
=
1
3
2
(
2
6
)
11
=
1
1
2
(
2
7
)
T
h
e
n
ex
t
s
tep
is
to
m
u
ltip
ly
b
y
th
e
s
ca
lar
,
wh
ich
is
m
an
u
ally
tu
n
ed
u
n
til
it
m
ee
ts
th
e
m
a
x
im
u
m
allo
wab
le
in
p
u
t
v
o
ltag
e
to
th
e
m
o
to
r
.
T
h
e
an
d
ar
e
g
iv
e
n
in
(
2
8
)
an
d
(
2
9
)
,
r
esp
ec
tiv
ely
.
T
a
b
le
5
s
h
o
ws
th
e
p
ar
am
eter
s
f
o
r
an
d
th
at
we
u
s
ed
in
th
is
wo
r
k
.
=
[
11
0
0
0
22
0
0
0
33
]
(
2
8
)
=
11
(
2
9
)
T
ab
le
5
.
Par
am
eter
s
f
o
r
an
d
P
a
r
a
me
t
e
r
s
V
a
l
u
e
1
5°
2
55°
−
1
3
1
3
6
0
R
P
M
1
1
2
V
T
h
e
v
alu
e
o
f
in
(
28)
is
o
b
tai
n
ed
th
r
o
u
g
h
s
im
u
latio
n
s
with
th
e
f
o
llo
win
g
i
n
itial
co
n
d
iti
o
n
s
:
th
e
in
itial
an
g
le
th
e
m
o
d
el
is
5
º,
th
e
an
g
u
la
r
v
elo
city
o
f
th
e
m
o
d
el
is
0
/s
,
an
d
th
e
an
g
u
lar
s
p
ee
d
o
f
th
e
r
ea
ctio
n
wh
ee
l
is
0
º
/s
.
T
h
e
v
alu
e
o
f
th
at
is
s
o
u
g
h
t
is
th
e
o
n
e
th
at
p
r
o
v
id
es
a
m
a
x
im
u
m
i
n
p
u
t
v
o
lt
ag
e
o
f
1
2
V
to
th
e
m
o
to
r
.
T
a
b
le
6
s
h
o
ws th
e
s
im
u
latio
n
r
esu
lts
f
o
r
v
er
s
u
s
m
o
t
o
r
v
o
ltag
e
.
T
ab
le
6
.
Mo
t
o
r
v
o
ltag
e
f
o
r
d
if
f
er
en
t v
alu
es o
f
V
o
l
t
a
g
e
(
V
)
1
/
21
1
2
.
0
8
5
1
/
22
1
2
.
0
5
6
1
/
23
1
2
.
0
2
9
1
/
24
1
2
.
0
0
1
1
/
25
1
1
.
9
8
1
Fro
m
T
ab
le
6
,
th
e
o
b
tain
ed
v
a
lu
e
f
o
r
the
s
ta
b
il
iza
tion
s
ys
te
m
is
1
/2
5
wh
ich
g
iv
es a
m
ax
i
m
u
m
in
p
u
t v
o
ltag
e
o
f
1
1
.
9
8
V
with
a
v
alu
e
o
f
=
[
−
137
.
3
−
13
.
069
−
0
.
168
]
(
3
0
)
Su
b
s
titu
tin
g
th
e
K
v
alu
e
in
to
(
1
2
)
,
we
o
b
tain
a
clo
s
ed
lo
o
p
s
tate
s
p
ac
e
m
o
d
els g
iv
en
in
(
3
1
)
an
d
(
3
2
)
,
̇
=
(
−
)
+
(
)
(
3
1
)
=
+
(
)
(
3
2
)
wh
ich
y
ield
s
in
clo
s
ed
lo
o
p
s
y
s
tem
p
o
les at
−6
.
0
6
; −
1
1
; a
n
d
−1
4
.
1
.
T
o
m
ea
s
u
r
e
th
e
tilt
an
g
le
o
f
th
e
v
eh
icle
m
o
d
el
,
t
h
e
ac
c
eler
o
m
eter
an
d
g
y
r
o
s
co
p
e
s
ig
n
als
ar
e
p
r
o
ce
s
s
ed
u
s
in
g
a
c
o
m
p
lem
e
n
tar
y
f
ilter
,
(
3
3
)
[
2
5
]
,
=
(
1
−
)
(
+
̇
∙
)
+
∙
(
3
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Desig
n
a
n
d
ma
n
u
fa
ctu
r
e
o
f a
s
elf
-
b
a
la
n
cin
g
s
ystem
fo
r
…
(
I
n
d
r
a
w
a
n
to
)
1861
W
ith
=
+
(
3
4
)
wh
er
e:
:
tilt
an
g
le
: c
o
m
p
lem
en
tar
y
f
ilter
co
e
f
f
ici
en
t
̇
: g
y
r
o
s
co
p
e
s
en
s
o
r
o
u
tp
u
t
: a
cc
eler
o
m
eter
s
en
s
o
r
o
u
tp
u
t
: tim
e
co
n
s
tan
t
: tim
e
s
am
p
lin
g
4.
E
XP
E
R
I
M
E
N
T
R
E
SU
L
T
S AN
D
ANA
L
YS
I
S
T
h
e
ex
p
er
im
en
t
was
ca
r
r
ied
o
u
t
in
two
way
s
.
I
n
th
e
f
ir
s
t
ex
p
er
im
en
t,
th
e
m
o
d
el
was
tilt
ed
to
a
n
in
itial a
n
g
le
o
f
5
º
.
I
n
th
e
s
ec
o
n
d
ex
p
er
im
en
t,
th
e
m
o
d
el
was i
n
an
eq
u
ilib
r
iu
m
s
tate,
th
en
im
p
u
ls
e
d
is
tu
r
b
an
ce
s
wer
e
ap
p
lied
to
th
e
m
o
d
el.
D
ata
o
b
tain
ed
f
r
o
m
ex
p
e
r
im
en
t
s
in
clu
d
e
th
e
m
o
d
el’
s
an
g
les,
th
e
m
o
d
el’
s
an
g
u
lar
s
p
ee
d
,
th
e
r
ea
ctio
n
wh
ee
l
’
s
an
g
u
lar
s
p
ee
d
,
th
e
in
p
u
t
v
o
ltag
e,
an
d
th
e
elec
tr
ic
c
u
r
r
en
t
to
t
h
e
DC
m
o
to
r
.
T
h
e
two
-
wh
ee
led
v
eh
icle
m
o
d
el
is
s
h
o
wn
in
Fig
u
r
e
5
.
Fig
u
r
e
6
s
h
o
ws
a
s
k
etch
o
f
th
e
ex
p
er
im
en
t
with
an
i
n
itial
tilt
co
n
d
itio
n
.
T
h
e
ex
p
e
r
im
en
t
w
as
ca
r
r
ied
o
u
t
b
y
f
ir
s
t
p
o
s
itio
n
in
g
t
h
e
m
o
d
el
at
5
º
tilt
an
g
le
an
d
t
h
en
th
e
b
alan
cin
g
s
y
s
tem
was
ac
tiv
ated
.
T
h
e
ex
p
er
im
en
tal
r
esu
lts
with
an
i
n
itial a
n
g
le
ar
e
s
h
o
wn
in
Fig
u
r
es 7
-
10.
Fig
u
r
e
5
.
T
h
e
d
e
v
elo
p
ed
two
-
wh
ee
led
v
eh
icle
m
o
d
el
Fig
u
r
e
6
.
T
h
e
ex
p
er
im
en
t w
ith
an
in
itial a
n
g
le
o
n
th
e
m
o
d
el.
On
ce
th
e
co
n
tr
o
ller
is
ac
tiv
ated
,
im
m
ed
iately
its
s
u
p
p
o
r
t is r
em
o
v
ed
.
T
h
e
ex
p
er
im
en
t r
esu
lts
ar
e
s
h
o
wn
in
Fig
u
r
e
7
-
10
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
4
,
Au
g
u
s
t
20
2
6
:
1
8
5
3
-
1
866
1862
T
h
e
s
ec
o
n
d
ex
p
e
r
im
en
t
was
ca
r
r
ied
o
u
t
b
y
ap
p
ly
in
g
im
p
u
ls
e
f
o
r
ce
s
to
th
e
m
o
d
el,
wh
ic
h
was
in
a
b
alan
ce
d
co
n
d
itio
n
,
as
s
h
o
wn
in
Fig
u
r
e
1
1
.
W
h
en
ex
p
er
ien
cin
g
an
im
p
u
ls
e
d
is
tu
r
b
an
ce
,
th
e
m
o
d
el
d
ev
iates
f
r
o
m
th
e
b
alan
ce
s
tate;
h
o
w
ev
er
,
t
h
e
b
alan
cin
g
s
y
s
tem
im
m
ed
iately
r
esto
r
es
it.
Fig
u
r
e
1
2
s
h
o
ws
th
e
ex
p
er
im
en
tal
r
esu
lts
.
Fig
u
r
e
7
.
T
h
e
ex
p
er
im
en
t r
esu
lts
with
an
in
itial tilt an
g
le
o
n
th
e
m
o
d
el.
T
h
e
in
itial a
n
g
le
at
t
=
0
is
5
º.
T
h
e
ex
p
er
im
en
t
r
esu
lts
s
h
o
w
th
at
th
e
b
alan
cin
g
s
y
s
tem
ca
n
q
u
ick
ly
b
r
in
g
th
e
m
o
d
el
to
v
e
r
tical
co
n
d
itio
n
i
n
less
th
an
0
.
5
s
ec
o
n
d
s
Fig
u
r
e
8
.
T
h
e
an
g
u
lar
v
el
o
city
o
f
th
e
f
r
am
e
f
o
r
th
e
i
n
itial tilt an
g
le
ex
p
e
r
im
en
t.
W
h
en
s
u
p
p
o
r
t is tak
en
o
u
t,
th
e
f
r
am
e
m
o
v
es to
an
in
cr
ea
s
in
g
an
g
u
lar
d
e
v
iatio
n
at
a
s
p
ee
d
o
f
u
p
to
3
2
º
/s
.
H
o
wev
e
r
,
th
e
co
n
tr
o
l sy
s
tem
im
m
ed
iately
r
esto
r
es th
e
m
o
d
el's d
ir
ec
tio
n
o
f
m
o
tio
n
s
o
t
h
at
th
e
m
o
d
el'
s
an
g
u
lar
s
p
ee
d
d
ec
r
ea
s
es to
ar
o
u
n
d
5
º
/s
in
less
th
an
2
s
ec
o
n
d
s
Fig
u
r
e
9
.
An
g
u
lar
v
elo
city
o
f
t
h
e
DC
m
o
to
r
f
o
r
th
e
i
n
itial tilt
an
g
le
ex
p
er
im
en
t.
T
h
e
ex
p
er
i
m
en
t r
esu
lts
s
h
o
w
th
at
th
e
an
g
u
lar
v
elo
city
o
f
th
e
DC
m
o
to
r
is
with
in
th
e
m
o
to
r
r
o
tatio
n
s
p
ee
d
with
o
u
t e
x
p
er
i
en
cin
g
s
atu
r
atio
n
Evaluation Warning : The document was created with Spire.PDF for Python.