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I
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1
210
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ler
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e
m
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th
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.
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d
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CC B
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li
c
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n
se
.
C
o
r
r
e
s
p
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A
uth
o
r
:
Ng
u
y
en
Xu
a
n
C
h
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Dep
ar
tm
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to
m
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Han
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Vietn
am
E
m
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ch
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x
@
m
ta.
ed
u
.
v
n
1.
I
NT
RO
D
UCT
I
O
N
W
ith
th
e
r
ap
id
ad
v
an
ce
m
en
t
o
f
au
to
m
o
tiv
e
tech
n
o
lo
g
y
,
m
o
d
er
n
v
e
h
icle
s
u
s
p
en
s
io
n
s
y
s
tem
s
h
av
e
g
ain
ed
in
cr
ea
s
in
g
atten
tio
n
as
a
m
ea
n
s
to
en
h
an
ce
r
id
e
co
m
f
o
r
t
an
d
v
e
h
icle
h
a
n
d
lin
g
p
er
f
o
r
m
a
n
ce
.
Am
o
n
g
v
ar
io
u
s
s
u
b
s
y
s
tem
s
,
th
e
s
u
s
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s
io
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s
y
s
tem
p
lay
s
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cr
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cial
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o
le
in
en
s
u
r
in
g
s
m
o
o
th
r
id
e
q
u
ality
,
r
o
ad
-
h
o
ld
in
g
ca
p
ab
ilit
y
,
an
d
o
v
e
r
all
v
eh
icle
s
tab
ilit
y
.
T
h
is
s
y
s
tem
h
as
attr
ac
ted
s
ig
n
if
ican
t
r
esear
ch
in
ter
est,
as
p
r
esen
ted
in
s
tu
d
ies
[
1
]
–
[
2
7
]
,
d
u
e
to
its
ab
ilit
y
to
ad
ap
t
d
y
n
am
ic
ch
a
r
ac
t
er
is
tics
in
r
ea
l
tim
e
th
r
o
u
g
h
t
h
e
u
s
e
o
f
ad
v
an
ce
d
s
en
s
o
r
s
an
d
m
icr
o
p
r
o
ce
s
s
o
r
s
f
o
r
s
ig
n
al
ac
q
u
is
itio
n
an
d
p
r
o
ce
s
s
in
g
.
Su
ch
ca
p
ab
ilit
y
allo
ws
th
e
s
u
s
p
en
s
io
n
s
y
s
tem
to
ad
ju
s
t
its
b
eh
av
io
r
ac
co
r
d
in
g
to
d
if
f
er
en
t
r
o
ad
c
o
n
d
itio
n
s
,
th
er
eb
y
co
n
s
id
er
ab
ly
im
p
r
o
v
i
n
g
v
e
h
icle
p
er
f
o
r
m
an
ce
.
I
n
g
en
e
r
al,
th
e
p
er
f
o
r
m
a
n
ce
r
eq
u
ir
em
en
ts
f
o
r
a
ctiv
e
v
eh
icle
s
u
s
p
en
s
io
n
s
y
s
tem
s
,
as
d
is
cu
s
s
ed
in
s
tu
d
ies
[
1
]
–
[
4
]
,
in
clu
d
e:
i
)
R
id
e
co
m
f
o
r
t
–
is
o
latin
g
t
h
e
v
eh
icle
b
o
d
y
f
r
o
m
s
h
o
c
k
s
an
d
v
i
b
r
atio
n
s
in
d
u
ce
d
b
y
r
o
ad
ir
r
e
g
u
lar
ities
to
en
s
u
r
e
p
ass
en
g
er
co
m
f
o
r
t;
ii
)
R
o
a
d
h
o
ld
i
n
g
-
elim
in
atin
g
wh
ee
l
h
o
p
t
o
m
ain
tain
co
n
tin
u
o
u
s
tire
-
r
o
ad
co
n
tact;
an
d
iii
)
Su
s
p
en
s
io
n
tr
av
el
lim
itatio
n
co
n
s
tr
ain
ed
b
y
th
e
m
e
ch
an
ical
s
tr
u
ctu
r
e
.
Ho
wev
er
,
as
r
ep
o
r
ted
in
[
3
]
,
i
t
is
n
o
t
f
ea
s
ib
le
to
s
im
u
ltan
eo
u
s
ly
s
atis
f
y
all
th
r
ee
p
e
r
f
o
r
m
a
n
ce
cr
iter
ia
at
th
eir
o
p
tim
al
lev
els,
s
in
ce
th
ese
o
b
jectiv
es
ten
d
to
b
e
m
u
tu
all
y
co
n
f
lictin
g
.
T
o
m
ee
t
th
ese
r
eq
u
ir
em
e
n
ts
,
b
o
th
p
ass
iv
e
an
d
ac
tiv
e
s
u
s
p
en
s
io
n
s
y
s
tem
s
h
av
e
b
ee
n
d
ev
elo
p
ed
.
W
h
ile
p
ass
iv
e
s
u
s
p
en
s
io
n
s
y
s
tem
s
r
ely
s
o
lely
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s
p
r
in
g
s
an
d
d
a
m
p
er
s
with
f
i
x
ed
p
ar
am
eter
s
,
r
esu
ltin
g
in
lim
ited
v
ib
r
atio
n
is
o
latio
n
p
er
f
o
r
m
an
ce
,
ac
tiv
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
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J
R
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b
&
A
u
to
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I
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N:
2722
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2
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Mo
d
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s
imu
la
tio
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f a
n
a
ctive
q
u
a
r
ter
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ca
r
s
u
s
p
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s
io
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s
ystem
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s
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…
(
Da
o
Tr
o
n
g
Du
n
g
)
211
s
u
s
p
en
s
io
n
s
y
s
tem
s
ca
n
g
e
n
er
ate
co
n
t
r
o
llab
le
f
o
r
ce
s
t
h
at
allo
w
d
y
n
am
ic
ad
ju
s
tm
en
t
o
f
s
u
s
p
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n
ch
ar
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ter
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tics
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b
etter
ad
ap
t t
o
v
ar
y
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n
g
o
p
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atin
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n
d
itio
n
s
.
No
wad
ay
s
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au
to
n
o
m
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s
m
o
b
ile
r
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b
o
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ap
id
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ch
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ilit
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licatio
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Platfo
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r
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icles
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UGVs)
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y
,
ac
tu
ato
r
life
s
p
an
,
a
n
d
p
ay
lo
ad
s
af
ety
.
T
h
er
ef
o
r
e,
i
n
teg
r
atin
g
an
ac
tiv
e
s
u
s
p
en
s
io
n
s
y
s
tem
i
n
to
m
o
b
ile
r
o
b
o
tic
p
latf
o
r
m
s
h
as
b
ec
o
m
e
a
n
ess
en
tial
r
eq
u
ir
em
en
t
t
o
en
h
a
n
c
e
s
tr
u
ctu
r
al
d
u
r
a
b
ilit
y
,
en
v
ir
o
n
m
en
tal
p
er
ce
p
tio
n
ca
p
ab
ilit
y
,
an
d
o
v
er
all
s
y
s
tem
p
er
f
o
r
m
an
ce
[
5
]
,
[
6
]
.
Nu
m
er
o
u
s
s
tu
d
ies
h
av
e
p
r
o
p
o
s
ed
an
d
ap
p
lied
v
ar
io
u
s
co
n
tr
o
l
s
tr
ateg
ies
f
o
r
ac
tiv
e
s
u
s
p
en
s
io
n
s
y
s
tem
s
.
Fo
r
in
s
tan
ce
,
PID
co
n
tr
o
l,
as
p
r
esen
ted
b
y
R
am
et
a
l.
[
4
]
,
ac
h
ie
v
ed
s
atis
f
ac
to
r
y
p
er
f
o
r
m
a
n
ce
b
u
t
was
lim
ited
to
s
m
all
o
p
er
atin
g
r
an
g
es
an
d
was
s
ig
n
if
ican
tly
in
f
l
u
en
ce
d
b
y
n
o
n
lin
ea
r
c
o
m
p
o
n
e
n
ts
.
I
n
r
esear
ch
[
7
]
,
[
8
]
,
a
lin
ea
r
q
u
ad
r
atic
r
eg
u
lato
r
(
L
QR
)
-
b
ased
ad
ap
tiv
e
co
n
tr
o
l
was
d
ev
elo
p
ed
;
h
o
wev
e
r
,
its
p
er
f
o
r
m
an
ce
r
em
ain
ed
lim
ited
d
u
e
to
th
e
u
s
e
o
f
a
lin
ea
r
co
n
tr
o
ller
.
Neu
r
al
n
etwo
r
k
–
b
ased
c
o
n
tr
o
l
s
tr
at
eg
ies,
p
r
esen
ted
in
[
9
]
,
[
1
1
]
,
d
em
o
n
s
tr
ated
g
o
o
d
s
y
s
tem
p
er
f
o
r
m
an
ce
u
n
d
e
r
m
o
d
el
u
n
ce
r
tain
ties
,
b
u
t
t
h
ey
s
u
f
f
er
ed
f
r
o
m
lo
n
g
r
esp
o
n
s
e
tim
es
an
d
wer
e
d
if
f
icu
lt
to
im
p
lem
e
n
t
in
e
m
b
ed
d
e
d
s
y
s
tem
s
.
Ad
ap
tiv
e
co
n
tr
o
l
b
ased
o
n
b
ac
k
s
tep
p
in
g
,
as
p
r
o
p
o
s
ed
b
y
C
h
en
et
a
l.
[
1
2
]
,
y
ield
e
d
im
p
r
ess
iv
e
r
esu
lts
b
u
t
was
co
n
s
tr
ai
n
ed
b
y
th
e
p
h
y
s
ical
lim
its
o
f
th
e
s
y
s
tem
.
Var
io
u
s
s
lid
in
g
m
o
d
e
co
n
tr
o
l
(
SMC
)
s
ch
em
es
an
d
th
eir
m
o
d
if
icatio
n
s
h
av
e
b
ee
n
r
ep
o
r
ted
in
[
1
3
]
–
[
1
6
]
,
[
2
5
]
,
p
r
o
d
u
cin
g
f
av
o
r
ab
le
r
esu
lts
,
alth
o
u
g
h
th
e
s
y
s
tem
r
esp
o
n
s
es
at
eq
u
ilib
r
iu
m
s
till
ex
h
ib
ited
o
s
cillatio
n
s
.
R
o
b
u
s
t
co
n
tr
o
l
ap
p
r
o
ac
h
es
wer
e
d
ev
elo
p
ed
in
[
1
7
]
–
[
1
9
]
;
h
o
wev
er
,
im
p
r
o
v
em
e
n
ts
in
co
n
tr
o
l
q
u
ality
an
d
r
esp
o
n
s
e
ti
m
e
ar
e
s
till
r
eq
u
ir
ed
.
A
d
d
itio
n
ally
,
f
u
zz
y
l
o
g
ic
–
b
ased
c
o
n
tr
o
l
laws
h
av
e
s
h
o
wn
p
r
o
m
is
in
g
o
u
tco
m
es
i
n
[
2
0
]
,
[
2
1
]
,
y
et
th
e
s
y
s
tem
r
esp
o
n
s
e
tim
e
r
em
ain
s
r
elativ
ely
lo
n
g
.
Ad
ap
tiv
e
c
o
n
tr
o
l
co
m
b
in
ed
with
r
ein
f
o
r
ce
m
e
n
t
lear
n
in
g
,
p
r
o
p
o
s
ed
b
y
Kim
b
al
l
et
a
l.
[
2
2
]
,
d
e
m
o
n
s
tr
ated
g
o
o
d
p
er
f
o
r
m
an
ce
b
u
t
f
ac
ed
ch
allen
g
es
in
s
atis
f
y
in
g
th
e
p
h
y
s
ical
co
n
s
tr
ain
ts
o
f
th
e
s
y
s
tem
.
Ma
ch
in
e
lear
n
in
g
–
b
as
ed
ap
p
r
o
ac
h
es
ca
n
allev
iate
th
ese
lim
itat
io
n
s
b
y
ex
p
lo
itin
g
m
ea
s
u
r
e
d
f
ee
d
b
ac
k
s
ig
n
als
to
r
ef
in
e
eith
er
th
e
p
lan
t
m
o
d
el
o
r
th
e
co
n
tr
o
l
p
o
licy
its
elf
,
as
r
e
p
o
r
t
ed
in
[
2
2
]
.
I
n
p
ar
ticu
lar
,
s
tu
d
y
[
2
2
]
c
o
m
p
ar
e
d
s
ev
er
al
lear
n
in
g
-
d
r
iv
en
co
n
tr
o
l
s
tr
ateg
ies
f
o
r
th
is
s
y
s
tem
,
in
clu
d
in
g
ad
a
p
tiv
e
s
ch
em
es,
s
tab
ilit
y
-
o
r
ien
ted
o
n
lin
e
lear
n
in
g
,
an
d
r
ein
f
o
r
ce
m
e
n
t
lear
n
in
g
m
eth
o
d
s
th
at
s
ee
k
p
er
f
o
r
m
an
ce
im
p
r
o
v
em
en
t
th
r
o
u
g
h
r
e
p
ea
ted
in
te
r
ac
tio
n
with
th
e
s
y
s
tem
.
Fu
r
th
er
m
o
r
e
,
s
ev
er
al
wo
r
k
s
h
av
e
in
v
esti
g
ated
L
y
a
p
u
n
o
v
-
b
ased
co
n
tr
o
l
laws
th
at
ex
p
l
icitly
ac
co
u
n
t
f
o
r
p
h
y
s
ical
co
n
s
tr
ain
ts
[
2
3
]
,
[
2
5
]
.
Fro
m
a
n
o
n
lin
ea
r
co
n
tr
o
l
p
er
s
p
ec
tiv
e,
m
o
s
t
ex
is
tin
g
s
tu
d
ie
s
r
ely
o
n
d
esig
n
in
g
a
s
u
itab
le
L
y
ap
u
n
o
v
ca
n
d
id
a
te
f
u
n
ctio
n
to
en
s
u
r
e
clo
s
ed
-
lo
o
p
s
tab
ilit
y
.
T
r
ad
itio
n
al
co
n
tr
o
ller
s
b
ased
o
n
q
u
ad
r
atic
L
y
ap
u
n
o
v
f
u
n
ctio
n
s
h
av
e
p
r
o
v
e
n
ef
f
ec
tiv
e
i
n
m
a
n
y
s
ce
n
ar
io
s
;
h
o
wev
er
,
th
e
y
e
n
co
u
n
ter
lim
itatio
n
s
wh
en
ap
p
lied
to
s
y
s
tem
s
with
s
tr
ict
s
tate
co
n
s
tr
ain
ts
.
T
o
ad
d
r
ess
th
is
is
s
u
e,
a
b
a
r
r
ier
L
y
ap
u
n
o
v
f
u
n
cti
o
n
(
B
L
F)
-
b
ased
ap
p
r
o
ac
h
h
as
b
e
en
d
e
v
elo
p
ed
f
o
r
c
o
n
s
tr
ain
ed
n
o
n
lin
ea
r
co
n
tr
o
l
p
r
o
b
lem
s
,
a
s
p
r
esen
ted
i
n
[
2
4
]
.
T
h
e
k
e
y
f
ea
tu
r
e
o
f
th
is
m
eth
o
d
is
th
e
u
s
e
o
f
a
ca
n
d
id
ate
L
y
ap
u
n
o
v
f
u
n
ctio
n
th
at
ap
p
r
o
a
ch
es
in
f
in
ity
as
t
h
e
s
y
s
tem
s
tate
n
ea
r
s
th
e
co
n
s
tr
ai
n
t
b
o
u
n
d
ar
y
,
th
e
r
eb
y
en
s
u
r
in
g
th
at
th
e
c
o
n
s
tr
ain
ts
ar
e
n
e
v
er
v
io
lated
.
T
h
e
B
L
F
-
b
ased
ap
p
r
o
ac
h
en
a
b
les
th
e
d
e
s
ig
n
o
f
m
o
r
e
s
tab
le
an
d
r
o
b
u
s
t
co
n
tr
o
l
laws,
ev
en
wh
e
n
th
e
i
n
itial
s
y
s
tem
s
tate
s
ar
e
clo
s
e
to
th
e
co
n
s
tr
ain
t b
o
u
n
d
ar
ies.
Alth
o
u
g
h
th
e
af
o
r
em
e
n
tio
n
ed
s
tu
d
ies h
av
e
s
u
cc
ess
f
u
lly
r
ed
u
ce
d
s
y
s
tem
o
s
cillatio
n
s
,
m
o
s
t h
av
e
n
o
t e
x
p
licitly
in
co
r
p
o
r
ated
th
e
p
h
y
s
i
ca
l c
o
n
s
tr
ain
ts
am
o
n
g
t
h
e
s
y
s
tem
s
tate
v
ar
iab
les.
An
o
th
er
wid
el
y
ad
o
p
ted
ap
p
r
o
ac
h
f
o
r
c
o
n
tr
o
llin
g
co
m
p
lex
m
ec
h
atr
o
n
ic
s
y
s
tem
s
is
th
e
ap
p
l
icatio
n
o
f
s
y
n
er
g
etic
co
n
tr
o
l
th
e
o
r
y
,
as
p
r
esen
ted
in
th
e
liter
atu
r
e
[
2
8
]
–
[
3
0
]
.
T
h
e
co
r
e
co
n
ce
p
t
in
v
o
lv
es
d
esig
n
in
g
a
co
n
tr
o
l
f
r
a
m
ewo
r
k
ca
p
ab
le
o
f
“in
teg
r
atin
g
”
m
u
ltip
le
s
u
b
c
o
n
tr
o
ller
s
,
ea
ch
r
esp
o
n
s
ib
le
f
o
r
a
s
p
ec
if
ic
o
b
jectiv
e
with
in
th
e
clo
s
ed
-
lo
o
p
s
y
s
tem
,
b
ased
o
n
th
e
d
y
n
am
ics
o
f
in
d
iv
id
u
al
co
n
tr
o
l
lo
o
p
s
[
2
8
]
,
[
2
9
]
.
I
n
s
y
n
er
g
is
tic
co
n
tr
o
l
th
eo
r
y
,
d
esire
d
v
alu
es a
r
e
ex
p
r
ess
ed
as
in
v
ar
ian
ts
th
a
t
ca
n
b
e
co
n
s
tr
u
cte
d
b
ased
o
n
th
e
p
h
y
s
ical
n
atu
r
e
o
f
th
e
s
y
s
tem
,
n
o
t
ju
s
t
o
n
m
ath
em
atica
l
m
o
d
els;
th
is
is
a
n
ad
v
an
tag
e
o
v
er
o
t
h
er
co
n
tr
o
l
m
eth
o
d
s
.
Sev
er
a
l
s
tu
d
ies
h
av
e
p
r
o
p
o
s
ed
s
y
n
er
g
etic
co
n
tr
o
ller
s
f
o
r
ac
tiv
e
s
u
s
p
en
s
io
n
s
y
s
tem
s
an
d
r
ep
o
r
ted
p
r
o
m
is
in
g
r
esu
lts
.
Fo
r
in
s
tan
ce
,
in
s
tu
d
y
[
3
0
]
,
a
s
y
n
er
g
etic
co
n
tr
o
ller
was
d
ev
elo
p
ed
b
ased
o
n
a
p
ar
ticu
l
ar
m
an
if
o
ld
wh
ile
ac
co
u
n
tin
g
f
o
r
th
e
p
h
y
s
ical
c
o
n
s
tr
ain
ts
o
f
th
e
s
y
s
tem
.
Ho
wev
er
,
an
in
-
d
ep
th
a
n
aly
s
is
o
f
th
e
o
v
er
all
s
y
s
tem
s
tab
ilit
y
u
n
d
er
th
is
co
n
t
r
o
l la
w
h
as n
o
t y
et
b
ee
n
co
n
d
u
cte
d
.
T
h
is
p
ap
er
f
o
cu
s
es
o
n
th
e
m
o
d
elin
g
an
d
s
im
u
latio
n
o
f
an
ac
tiv
e
q
u
ar
ter
-
ca
r
s
u
s
p
en
s
io
n
s
y
s
tem
(
AQCS
S)
em
p
lo
y
in
g
a
s
y
n
e
r
g
etic
co
n
tr
o
l
s
tr
ateg
y
.
T
h
e
s
y
s
t
em
d
y
n
a
m
ics
ar
e
d
er
i
v
ed
v
ia
th
e
E
u
ler
–
L
ag
r
an
g
e
f
o
r
m
u
latio
n
,
wh
ich
ex
p
licitly
ac
co
u
n
ts
f
o
r
t
h
e
co
u
p
lin
g
a
m
o
n
g
th
e
m
ec
h
an
ical
elem
en
ts
as
well
as
r
o
ad
-
in
d
u
ce
d
d
is
tu
r
b
an
ce
s
.
T
h
e
s
y
n
er
g
etic
co
n
tr
o
ller
p
r
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ed
in
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y
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ed
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ased
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o
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p
ab
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atis
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y
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th
e
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y
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’
s
tech
n
ical
r
eq
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ir
em
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.
T
h
is
ap
p
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ac
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o
f
f
er
s
th
e
ad
v
an
tag
e
o
f
in
teg
r
atin
g
tech
n
ical
r
eq
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ir
em
en
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in
to
th
e
co
n
tr
o
l
law,
t
h
er
eb
y
s
ig
n
if
ica
n
tly
en
h
a
n
cin
g
th
e
s
tab
ilit
y
o
f
th
e
ac
tiv
e
s
u
s
p
en
s
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n
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y
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u
n
d
er
v
ar
io
u
s
o
p
er
atin
g
c
o
n
d
itio
n
s
.
T
h
e
s
y
s
tem
s
tab
ilit
y
u
n
d
er
t
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
law
is
r
ig
o
r
o
u
s
ly
p
r
o
v
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u
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in
g
L
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ap
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eth
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n
d
MA
T
L
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s
im
u
latio
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em
o
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ate
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p
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ed
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n
tr
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ller
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ig
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ica
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f
o
r
m
s
tr
ad
itio
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p
a
s
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iv
e
s
u
s
p
en
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io
n
s
y
s
tem
s
.
T
h
e
r
em
ain
d
er
o
f
th
e
p
ap
er
is
o
r
g
an
ize
d
as
f
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llo
w
s
:
Sectio
n
2
p
r
esen
ts
th
e
m
o
d
elin
g
m
eth
o
d
o
lo
g
y
f
o
r
th
e
co
n
s
tr
ain
ed
ac
tiv
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
1
5
,
No
.
1
,
Ma
r
ch
20
2
6
:
210
-
2
2
1
212
s
u
s
p
en
s
io
n
s
y
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tem
;
Sectio
n
3
d
etails
th
e
s
y
n
th
esis
o
f
t
h
e
co
n
s
tr
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ed
s
y
n
er
g
etic
co
n
tr
o
lle
r
,
s
tab
ilit
y
an
aly
s
is
u
n
d
er
ex
ter
n
al
d
is
tu
r
b
an
ce
s
,
an
d
th
e
d
esig
n
o
f
an
SMC
co
n
tr
o
ller
;
Sectio
n
4
p
r
o
v
id
es
s
im
u
latio
n
s
ce
n
ar
io
s
to
v
alid
ate
th
e
ef
f
ec
tiv
e
n
ess
o
f
th
e
p
r
o
p
o
s
ed
co
n
t
r
o
l la
w;
an
d
S
ec
tio
n
5
co
n
clu
d
es th
e
p
ap
er
.
2.
DYNA
M
I
C
M
O
DE
L
I
NG
I
n
th
is
s
tu
d
y
,
th
e
AQCS
S
is
il
lu
s
tr
ated
in
Fig
u
r
e
1
,
wh
ich
is
wid
ely
ad
o
p
ted
in
r
esear
ch
[
1
]
–
[
7
]
.
T
h
e
m
o
d
el
co
n
s
id
er
s
two
m
ass
es:
T
h
e
s
p
r
u
n
g
m
ass
=
+
,
r
ep
r
esen
tin
g
th
e
v
eh
icle
b
o
d
y
m
ass
(
m
)
to
g
eth
er
with
th
e
p
ass
en
g
er
s
an
d
p
ay
lo
a
d
(
)
an
d
th
e
u
n
s
p
r
u
n
g
m
ass
mᵤ
a
s
s
o
ciate
d
with
th
e
wh
ee
l
-
ax
le
ass
em
b
ly
.
T
h
e
s
u
s
p
en
s
io
n
s
y
s
tem
co
n
s
is
ts
o
f
a
s
p
r
in
g
–
d
am
p
er
u
n
it
d
e
f
in
ed
b
y
th
e
p
ar
am
et
er
s
k
1s
,
k
2s
,
c
1s
,
an
d
c
2s
.
Her
e,
k
1s
an
d
k
2s
d
en
o
te
th
e
lin
ea
r
an
d
cu
b
ic
s
tiff
n
ess
co
ef
f
icien
ts
,
wh
ile
c
1s
an
d
c
2s
d
e
n
o
te
th
e
lin
ea
r
an
d
cu
b
ic
d
am
p
i
n
g
co
e
f
f
icien
ts
,
r
esp
ec
tiv
ely
,
wh
ich
to
g
eth
e
r
d
escr
ib
e
th
e
n
o
n
lin
ea
r
c
h
ar
ac
ter
is
tics
o
f
th
e
s
u
s
p
en
s
io
n
s
y
s
tem
.
T
h
e
tire
i
s
m
o
d
eled
with
s
tiff
n
ess
k
t
an
d
d
am
p
in
g
c
t
;
n
e
v
er
th
eless
,
in
n
u
m
er
o
u
s
s
tu
d
ies
[
1
]
,
[
2
]
,
it
is
co
m
m
o
n
ly
s
im
p
lifie
d
as
a
p
u
r
ely
lin
ea
r
el
asti
c
elem
en
t
r
ep
r
esen
ted
o
n
ly
b
y
th
e
s
tiff
n
ess
p
ar
am
eter
k
t
.
T
h
e
co
n
tr
o
l
v
ar
i
ab
le
u
r
ep
r
esen
ts
th
e
f
o
r
ce
g
e
n
er
ated
b
y
t
h
e
ac
tiv
e
s
u
s
p
e
n
s
io
n
ac
tu
ato
r
,
ac
tin
g
o
n
th
e
s
p
r
u
n
g
m
ass
,
wh
ile
a
n
eq
u
al
a
n
d
o
p
p
o
s
ite
r
ea
ctio
n
f
o
r
ce
-
u
ac
ts
o
n
th
e
u
n
s
p
r
u
n
g
m
ass
.
T
h
e
s
y
s
tem
s
tates
ar
e
r
ep
r
esen
ted
b
y
t
h
e
v
er
tical
d
is
p
lace
m
en
ts
o
f
th
e
s
p
r
u
n
g
m
ass
z
s
,
th
e
u
n
s
p
r
u
n
g
m
a
s
s
z
u
,
an
d
th
e
r
o
a
d
ex
citatio
n
z
r
.
m
s
m
u
F
d
F
s
u
z
s
z
u
z
r
F
t
F
b
Fig
u
r
e
1
.
Mo
d
el
o
f
an
AQCS
S
I
n
p
r
ac
tical
s
y
s
tem
s
,
eith
er
el
ec
tr
ic
m
o
to
r
ac
tu
ato
r
s
o
r
h
y
d
r
au
lic
ac
tu
ato
r
s
ar
e
co
m
m
o
n
ly
em
p
lo
y
e
d
to
g
en
er
ate
t
h
e
co
n
tr
o
l
f
o
r
ce
,
wh
ich
ac
ts
s
im
u
ltan
eo
u
s
ly
o
n
b
o
th
th
e
s
p
r
u
n
g
m
ass
(
)
an
d
th
e
u
n
s
p
r
u
n
g
m
ass
(
)
[
3
1
]
,
[
3
2
]
.
T
h
e
d
is
p
lace
m
en
ts
o
f
t
h
e
s
p
r
u
n
g
a
n
d
u
n
s
p
r
u
n
g
m
ass
es
ar
e
ty
p
ically
m
ea
s
u
r
ed
u
s
in
g
co
m
m
er
cial
lin
ea
r
v
ar
iab
le
d
if
f
er
en
tial
tr
a
n
s
f
o
r
m
er
s
,
lin
ea
r
p
o
ten
tio
m
eter
s
,
o
p
tical
e
n
co
d
er
s
,
u
ltra
s
o
n
ic
s
en
s
o
r
s
,
o
r
laser
-
b
ased
s
en
s
o
r
s
in
lab
o
r
ato
r
y
-
s
ca
le
p
latf
o
r
m
s
.
T
h
e
v
el
o
cities
o
f
th
ese
m
ass
es
ar
e
o
b
tain
ed
eith
er
f
r
o
m
d
ir
ec
t
v
elo
city
s
en
s
o
r
s
,
ac
ce
ler
o
m
eter
s
,
o
r
in
d
i
r
ec
tly
esti
m
ated
f
r
o
m
t
h
e
m
ea
s
u
r
ed
d
is
p
lace
m
en
t
s
ig
n
als d
escr
ib
ed
ab
o
v
e
[
3
1
]
–
[
3
3
]
.
T
h
e
to
tal
k
in
etic
en
er
g
y
o
f
th
e
q
u
ar
ter
-
ca
r
m
o
d
el
is
o
b
tain
ed
b
y
s
u
m
m
in
g
th
e
co
n
tr
ib
u
tio
n
s
o
f
th
e
s
p
r
u
n
g
a
n
d
u
n
s
p
r
u
n
g
m
ass
es,
an
d
is
wr
itten
as
(
1
)
.
=
1
2
̇
2
+
1
2
̇
2
(
1
)
Fo
r
m
o
d
elin
g
c
o
n
v
e
n
ien
ce
,
th
e
tire
is
ass
u
m
ed
to
m
ain
tain
co
n
tin
u
o
u
s
co
n
tact
with
th
e
r
o
ad
.
C
o
n
s
eq
u
e
n
tly
,
th
e
p
o
ten
tial
e
n
er
g
y
f
o
r
m
u
lat
io
n
ac
co
u
n
ts
f
o
r
th
e
elastic
d
ef
o
r
m
atio
n
o
f
th
e
s
p
r
in
g
,
i
n
clu
d
in
g
th
e
c
u
b
ic
n
o
n
lin
ea
r
s
tiff
n
ess
ef
f
ec
t th
at
o
cc
u
r
s
d
u
r
in
g
c
o
m
p
r
ess
io
n
,
a
n
d
is
ex
p
r
ess
ed
as
(
2
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
Mo
d
elin
g
a
n
d
s
imu
la
tio
n
o
f a
n
a
ctive
q
u
a
r
ter
-
ca
r
s
u
s
p
en
s
io
n
s
ystem
u
s
in
g
…
(
Da
o
Tr
o
n
g
Du
n
g
)
213
=
1
2
1
(
−
)
2
+
1
4
2
(
−
)
4
+
1
2
(
−
)
2
(
2
)
T
h
e
s
y
s
tem
L
ag
r
an
g
ia
n
is
d
ef
in
ed
as
=
−
,
wh
er
e
an
d
r
ep
r
esen
t
th
e
k
in
etic
an
d
p
o
ten
tial
en
er
g
ies,
r
esp
ec
tiv
ely
.
T
h
e
d
a
m
p
in
g
-
r
elate
d
en
er
g
y
lo
s
s
is
m
o
d
eled
u
s
in
g
th
e
R
ay
leig
h
d
i
s
s
ip
atio
n
f
u
n
ctio
n
:
=
1
2
1
(
̇
−
̇
)
2
+
1
4
2
(
̇
−
̇
)
4
+
1
2
(
̇
−
̇
)
2
(
3
)
Fo
r
ea
ch
g
en
er
alize
d
co
o
r
d
in
ate
=
[
,
]
,
th
e
E
u
ler
–
L
ag
r
an
g
e
eq
u
atio
n
with
a
d
is
s
ip
atio
n
ter
m
an
d
ex
ter
n
al
f
o
r
ce
s
is
g
iv
en
b
y
(
4
)
:
(
̇
)
−
+
̇
=
(
4
)
Her
e,
Q
i
r
ep
r
esen
ts
th
e
g
e
n
er
a
lized
ex
ter
n
al
f
o
r
ce
s
,
in
clu
d
i
n
g
th
e
co
n
tr
o
l in
p
u
t
u
in
th
e
p
r
e
s
en
t f
o
r
m
u
latio
n
.
Af
t
er
s
u
b
s
tit
u
t
in
g
a
n
d
,
th
e
g
o
v
e
r
n
i
n
g
eq
u
ati
o
n
s
o
f
t
h
e
ac
t
iv
e
q
u
a
r
te
r
-
ca
r
s
u
s
p
e
n
s
i
o
n
ar
e
o
b
t
ain
e
d
in
t
h
e
f
o
r
m
o
f
t
h
e
d
i
f
f
er
en
tia
l
e
q
u
ati
o
n
s
o
f
(
5
)
,
{
̈
+
+
=
̈
−
−
+
(
−
)
+
(
̇
−
̇
)
=
−
(
5
)
w
h
er
e
=
1
(
−
)
+
2
(
−
)
3
;
=
1
(
̇
−
̇
)
+
2
(
̇
−
̇
)
2
;
(
6
)
I
n
th
e
AQCS
S,
th
e
v
er
tical
r
o
ad
p
r
o
f
ile
is
p
r
ac
tically
d
if
f
i
cu
lt to
m
ea
s
u
r
e,
an
d
d
esig
n
in
g
a
r
eliab
le
o
b
s
er
v
er
f
o
r
s
u
c
h
a
n
u
n
m
ea
s
u
r
a
b
le
d
is
tu
r
b
an
ce
is
in
h
e
r
en
tly
ch
allen
g
in
g
.
C
o
n
s
eq
u
en
tly
,
d
u
r
in
g
t
h
e
s
y
n
th
esis
o
f
th
e
co
n
tr
o
l
law,
th
e
ter
m
in
v
o
lv
in
g
th
is
v
ar
iab
le
is
r
eg
ar
d
ed
as
an
ex
ter
n
al
d
is
tu
r
b
a
n
ce
.
L
et
t
h
e
s
tate
v
ar
iab
les
b
e
d
ef
in
ed
as:
1
=
,
2
=
̇
,
3
=
,
4
=
̇
.
T
h
en
,
th
e
s
y
s
tem
(
5
)
ca
n
b
e
r
ep
r
esen
ted
i
n
s
tate
-
s
p
ac
e
f
o
r
m
as
(
7
)
,
{
̇
1
=
2
̇
2
=
(
+
)
−
1
(
−
−
+
)
̇
3
=
4
̇
4
=
−
1
(
+
−
3
−
4
−
+
(
)
)
(
7
)
w
h
er
e
(
)
=
+
̇
.
T
h
e
g
o
al
o
f
th
is
s
tu
d
y
is
to
s
y
n
th
esize
a
co
n
tr
o
l la
w
u
in
th
e
s
y
s
tem
(
7
)
b
ased
o
n
m
an
if
o
ld
co
m
p
o
s
ite
co
n
tr
o
l th
e
o
r
y
t
h
at
en
s
u
r
es th
e
AQCS
S m
ee
t
s
th
e
f
o
llo
win
g
r
eq
u
ir
em
en
ts
:
−
T
h
e
m
ain
c
o
n
tr
o
l
o
b
jectiv
e
is
th
at
th
e
co
n
tr
o
ller
m
u
s
t
s
tab
ilize
th
e
v
er
tical
m
o
ti
o
n
o
f
th
e
s
p
r
u
n
g
m
ass
with
in
th
e
m
ec
h
an
ical
lim
its
o
f
th
e
s
y
s
tem
wh
en
th
er
e
is
a
ch
an
g
e
in
th
e
s
y
s
tem
p
ar
am
eter
s
an
d
th
e
im
p
ac
t o
f
v
a
r
io
u
s
ty
p
es
o
f
r
o
a
d
s
u
r
f
ac
e
d
is
tu
r
b
an
ce
s
:
→
∞
(
(
)
)
→
0
(
8
)
−
Def
in
e
th
e
r
elativ
e
s
u
s
p
en
s
io
n
d
ev
iatio
n
(
R
SD)
as
t
h
e
s
u
s
p
e
n
s
io
n
d
e
f
lectio
n
n
o
r
m
alize
d
b
y
th
e
m
ax
im
u
m
v
ib
r
atio
n
-
s
p
ac
e
lim
it
z
m
ax
.
T
h
is
q
u
an
tity
m
u
s
t satis
f
y
<
1
,
wh
ich
ca
n
b
e
ex
p
r
ess
ed
as
(
9
)
:
=
−
<
1
(
9
)
−
C
o
n
tin
u
o
u
s
tire
–
r
o
a
d
co
n
tact
m
u
s
t
b
e
m
ain
tain
ed
wh
ile
av
o
id
in
g
ex
ce
s
s
iv
e
tire
lo
ad
s
.
A
cc
o
r
d
in
g
l
y
,
th
e
r
elativ
e
tire
f
o
r
ce
(
R
T
F),
d
ef
i
n
ed
as
th
e
tire
d
y
n
a
m
ic
lo
ad
n
o
r
m
alize
d
b
y
th
e
s
tatic
lo
ad
,
s
h
o
u
ld
s
atis
f
y
<
1
:
=
(
−
)
+
(
̇
−
̇
)
(
+
)
<
1
(
1
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
1
5
,
No
.
1
,
Ma
r
ch
20
2
6
:
210
-
2
2
1
214
3.
SYNT
H
E
S
I
S O
F
CO
NT
RO
L
L
A
WS F
O
R
AN
AC
T
I
V
E
Q
UARTE
R
-
CAR
SU
SPEN
SI
O
N
SYST
E
M
3
.
1
.
Sy
nerg
et
ic
co
ntr
o
l la
w
des
ig
n
I
n
s
y
n
er
g
etic
co
n
tr
o
l
th
e
o
r
y
,
t
h
e
s
et
o
f
co
n
tr
o
l
o
b
jectiv
es
o
r
p
er
f
o
r
m
a
n
ce
cr
iter
ia
is
d
ef
i
n
ed
in
th
e
f
o
r
m
o
f
a
s
y
s
tem
o
f
in
v
ar
ian
t
s
.
Fo
r
elec
tr
o
m
ec
h
an
ical
s
y
s
tem
s
,
s
tu
d
ies
[
2
8
]
,
[
2
9
]
d
is
tin
g
u
is
h
ed
th
r
ee
m
ai
n
ty
p
es o
f
in
v
a
r
ian
ts
: te
ch
n
o
lo
g
i
ca
l,
elec
tr
o
m
ag
n
etic,
a
n
d
en
e
r
g
y
in
v
ar
ia
n
ts
.
T
h
e
tech
n
o
lo
g
ic
al
in
v
ar
ian
t d
ef
i
n
es
th
e
tar
g
et
s
tatic
o
r
d
y
n
am
ic
c
o
n
d
itio
n
o
f
th
e
s
y
s
tem
ass
o
ciate
d
with
a
g
iv
en
tech
n
o
l
o
g
i
ca
l
task
to
ac
h
ie
v
e
m
ec
h
an
ical
m
o
tio
n
.
T
h
e
elec
t
r
o
m
ag
n
etic
in
v
a
r
ian
t
is
s
elec
ted
to
en
s
u
r
e
th
e
s
tab
le
o
p
er
ati
o
n
o
f
elec
tr
ical
an
d
m
ag
n
etic
v
ar
iab
les
with
in
th
e
ac
tu
ato
r
.
Fin
ally
,
th
e
en
er
g
y
in
v
ar
ian
t
ex
p
r
ess
es
th
e
r
elatio
n
s
h
ip
s
b
etwe
en
s
y
s
tem
v
ar
iab
les
th
at
r
ef
lect
o
p
tim
al
en
er
g
y
co
n
v
er
s
io
n
c
o
n
d
itio
n
s
,
p
a
r
ticu
lar
ly
th
o
s
e
m
in
im
izin
g
en
er
g
y
lo
s
s
es d
u
r
in
g
o
p
e
r
atio
n
.
T
h
e
ch
o
ice
o
f
in
v
ar
ia
n
ts
is
es
s
en
tial
f
o
r
co
n
tr
o
l
s
y
s
tem
s
y
n
th
esis
an
d
is
b
ased
o
n
th
e
tec
h
n
o
lo
g
ical
r
eq
u
ir
em
e
n
ts
an
d
th
e
n
u
m
b
er
o
f
p
h
y
s
ical
co
n
tr
o
l
in
p
u
ts
.
Fo
r
an
ac
tiv
e
q
u
ar
te
r
-
ca
r
s
u
s
p
e
n
s
io
n
s
y
s
tem
,
th
ese
co
n
tr
o
l
ch
an
n
els
co
r
r
esp
o
n
d
to
th
e
v
er
tical
d
is
p
lace
m
en
t
am
p
litu
d
es
o
f
th
e
two
m
ass
ce
n
ter
s
,
mₛ
an
d
mᵤ
.
Fo
r
th
is
s
y
s
tem
,
th
e
in
v
ar
ian
t
m
an
if
o
ld
m
u
s
t
ac
cu
r
ately
r
ef
lect
t
h
e
r
eq
u
ir
em
e
n
ts
im
p
o
s
ed
o
n
t
h
e
co
n
tr
o
l
law
an
d
m
u
s
t
ex
clu
d
e
a
n
y
s
tate
v
ar
iab
l
es
th
at
ar
e
n
o
t
d
ir
ec
tly
m
ea
s
u
r
ab
le.
B
ased
o
n
th
e
a
b
o
v
e
an
al
y
s
is
,
to
g
eth
er
with
th
e
co
n
tr
o
l
r
e
q
u
ir
em
e
n
ts
f
o
r
t
h
e
s
y
s
tem
p
r
esen
ted
in
s
ec
tio
n
2
,
an
d
r
ely
in
g
o
n
th
e
in
v
a
r
i
an
t
m
an
if
o
ld
–
b
ased
s
y
n
er
g
etic
co
n
tr
o
l th
eo
r
y
,
o
n
e
ca
n
s
elec
t th
e
f
o
r
m
f
o
r
s
y
s
tem
as in
(
7
)
.
=
2
+
1
(
1
+
2
2
(
+
1
−
3
−
(
1
−
3
)
)
)
(
1
1
)
wh
er
e
k
1
, k
2
> 0
a
r
e
p
o
s
itiv
e
c
o
n
s
tan
ts
.
W
h
en
th
e
s
y
s
tem
o
p
er
ates o
n
th
e
m
an
if
o
l
d
d
ef
i
n
ed
b
y
(
1
1
)
,
i.
e.
,
wh
en
ψ
=0
,
it f
o
llo
ws th
at:
2
+
1
(
1
+
2
2
(
+
1
−
3
−
(
1
−
3
)
)
)
=
0
⇒
1
2
(
+
1
−
3
−
(
1
−
3
)
=
−
2
−
1
1
1
2
)
Acc
o
r
d
in
g
ly
,
b
y
ap
p
ly
i
n
g
th
e
i
n
v
er
s
e
o
f
t
h
e
tan
h
f
u
n
ctio
n
,
we
o
b
tain
(
1
2
)
.
1
−
3
=
ℎ
(
2
+
1
1
1
2
)
(
1
2
)
Sin
ce
th
e
h
y
p
er
b
o
lic
tan
g
e
n
t
f
u
n
ctio
n
is
b
o
u
n
d
e
d
,
f
r
o
m
th
e
R
SD
r
eq
u
ir
em
en
t
(
9
)
it
ca
n
b
e
in
f
er
r
e
d
th
at
th
e
d
am
p
in
g
tr
a
v
el
is
lim
ited
b
y
t
h
e
m
ax
im
u
m
allo
wab
le
v
alu
e
.
Ass
u
m
in
g
2
is
a
s
m
all
p
o
s
iti
v
e
co
n
s
tan
t
an
d
as th
e
s
y
s
tem
ev
o
lv
es
o
n
m
an
if
o
ld
ψ=0
,
we
o
b
tain
(
1
3
)
.
2
≈
−
1
1
(
1
3
)
Fro
m
(
1
3
)
,
co
m
b
in
ed
with
th
e
f
ir
s
t
eq
u
atio
n
o
f
th
e
s
y
s
tem
(
7
)
,
we
g
et
a
f
ir
s
t
-
o
r
d
er
d
if
f
er
e
n
tial
eq
u
atio
n
in
1
.
I
t
is
ea
s
y
to
p
r
o
v
e
t
h
at
with
k
1
>0
,
1
→0
wh
en
t→∞
s
at
is
f
ies
co
n
d
itio
n
(
8
)
.
Sin
ce
th
is
eq
u
atio
n
is
au
to
n
o
m
o
u
s
,
ac
co
r
d
in
g
t
o
(
1
2
)
,
we
ca
n
co
n
clu
d
e
th
at
wh
e
n
co
n
d
itio
n
(
9
)
is
s
atis
f
ied
,
th
e
d
is
p
lace
m
en
t
o
f
th
e
s
u
s
p
en
d
ed
m
ass
m
s
b
ec
o
m
es n
eg
lig
ib
le
r
eg
ar
d
less
o
f
th
e
ch
a
n
g
e
in
th
e
r
o
ad
s
u
r
f
ac
e.
Fo
llo
win
g
th
e
an
aly
tical
d
esig
n
o
f
a
g
g
r
e
g
ated
r
eg
u
lato
r
s
m
eth
o
d
o
l
o
g
y
f
o
r
co
n
tr
o
ller
s
y
n
th
esis
,
th
e
in
v
ar
ian
t m
an
i
f
o
ld
(
9
)
s
atis
f
ies th
e
d
if
f
er
en
tial c
o
n
s
tr
ain
t:
1
0
T
+=
(
1
4
)
wh
er
e
T
1
>0
is
a
d
esig
n
tim
e
co
n
s
tan
t
th
at
g
o
v
er
n
s
th
e
c
o
n
v
er
g
en
ce
s
p
ee
d
o
f
th
e
s
y
s
tem
tr
ajec
to
r
ies
to
war
d
th
e
m
an
if
o
ld
ψ
=0
.
B
ased
o
n
th
e
s
o
lu
tio
n
o
f
(
1
2
)
an
d
tak
in
g
in
to
ac
co
u
n
t
th
e
p
lan
t
m
o
d
el
(
7
)
,
an
d
u
n
d
er
th
e
ass
u
m
p
tio
n
th
at
=
0
,
th
e
s
y
n
er
g
eti
c
co
n
tr
o
l la
w
ca
n
b
e
d
e
r
iv
ed
a
s
(
1
5
)
.
̇
2
+
1
(
̇
1
+
2
(
2
−
4
)
2
−
(
1
−
3
)
2
+
1
=
0
)
(
1
5
)
Su
b
s
titu
tin
g
in
to
th
e
s
ec
o
n
d
e
q
u
atio
n
o
f
s
y
s
tem
(
7
)
,
we
o
b
ta
in
(
1
6
)
.
−
1
(
−
−
+
)
+
1
(
̇
1
+
2
(
2
−
4
)
2
−
(
1
−
3
)
2
+
1
=
0
)
(
1
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
Mo
d
elin
g
a
n
d
s
imu
la
tio
n
o
f a
n
a
ctive
q
u
a
r
ter
-
ca
r
s
u
s
p
en
s
io
n
s
ystem
u
s
in
g
…
(
Da
o
Tr
o
n
g
Du
n
g
)
215
Hen
ce
,
=
+
−
1
(
2
+
2
(
2
−
4
)
2
−
(
1
−
3
)
2
−
1
)
(
1
7
)
+
W
e
b
eg
in
b
y
ass
ess
in
g
th
e
s
tab
ilit
y
o
f
th
e
s
p
r
u
n
g
m
ass
d
y
n
am
ics
m
s
g
o
v
e
r
n
ed
b
y
c
o
n
tr
o
l
law
(
1
7
)
an
d
th
e
f
ir
s
t
two
eq
u
atio
n
s
in
(
7
)
.
A
L
y
a
p
u
n
o
v
ca
n
d
id
ate
i
s
th
en
in
tr
o
d
u
ce
d
to
en
s
u
r
e
th
at
th
e
tr
ajec
to
r
ies
co
n
v
er
g
e
to
th
e
m
an
if
o
l
d
ψ=
0
.
=
0
.
5
2
(
1
8
)
T
ak
in
g
th
e
tim
e
d
er
iv
ativ
e,
th
ese
y
ield
s
(
1
9
)
.
̇
=
(
̇
2
+
1
(
2
+
2
(
2
−
4
)
2
−
(
1
−
3
)
2
)
)
(
1
9
)
Su
b
s
titu
tin
g
(
1
7
)
an
d
(
7
)
i
n
to
(
1
9
)
,
we
o
b
tain
(
2
0
)
.
̇
=
(
1
(
−
1
(
2
+
2
(
2
−
4
)
2
−
(
1
−
3
)
2
)
−
1
)
+
1
(
2
+
2
(
2
−
4
)
2
−
(
1
−
3
)
2
)
)
(
2
0
)
Hen
ce
,
̇
=
1
(
2
+
2
(
2
−
4
)
2
−
(
1
−
3
)
2
)
−
1
2
(
2
1
)
W
h
en
th
er
e
is
n
o
v
ar
iatio
n
in
th
e
m
ass
=
0
,
we
o
b
tain
̇
=
−
1
2
≤
0
,
an
d
t
h
u
s
th
e
s
y
s
tem
is
g
lo
b
ally
asy
m
p
to
tically
s
tab
le.
W
h
en
≠
0
,
ap
p
ly
in
g
th
e
Yo
u
n
g
’
s
in
eq
u
ali
ty
,
we
h
av
e
(
2
2
)
.
̇
≤
−
2
1
−
1
2
2
+
1
2
(
2
+
2
(
2
−
4
)
2
−
(
1
−
3
)
2
)
2
(
2
2
)
I
t is ea
s
y
to
o
b
s
er
v
e
th
at,
u
n
d
e
r
<
2
1
/
1
,
a
s
u
f
f
icien
t c
o
n
d
itio
n
to
en
s
u
r
e
̇
≤
is
g
iv
en
b
y
(
2
3
)
.
(
2
+
2
(
2
−
4
)
2
−
(
1
−
3
)
2
)
2
≤
2
1
(
2
3
)
T
h
is
i
m
p
lies
t
h
at
w
h
e
n
x
is
s
u
f
f
ic
ie
n
tl
y
f
a
r
f
r
o
m
th
e
o
r
ig
in
wi
th
a
p
o
s
iti
v
e
,
we
o
b
t
ai
n
̇
≤
0
.
C
o
n
s
eq
u
e
n
t
ly
,
th
e
s
p
r
u
n
g
-
m
ass
s
u
b
s
y
s
tem
m
s
is
s
tab
ilized
in
a
n
eig
h
b
o
r
h
o
o
d
o
f
t
h
e
eq
u
ilib
r
iu
m
p
o
in
t,
n
am
ely
with
in
a
b
all
o
f
r
ad
i
u
s
ce
n
ter
ed
at
t
h
e
o
r
ig
i
n
.
T
h
e
s
ec
o
n
d
s
tep
is
to
estab
li
s
h
th
e
s
tab
ilit
y
o
f
s
y
s
tem
(
7
)
.
T
o
en
s
u
r
e
all
th
e
n
ec
ess
ar
y
asy
m
p
to
tically
s
tab
le
s
tate
s
o
f
th
e
s
y
s
tem
,
th
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
is
co
n
s
tr
u
cted
b
ased
o
n
th
e
V
s
f
u
n
ctio
n
i
n
th
e
f
ir
s
t step
,
an
d
ad
d
s
th
e
p
o
s
itiv
e
d
e
f
in
ite
co
m
p
o
n
en
t
o
f
x
4
.
=
+
0
.
5
4
2
(
2
4
)
T
ak
in
g
th
e
tim
e
d
er
iv
ativ
e,
th
ese
y
ield
s
(
2
5
)
.
̇
=
(
̇
2
+
1
(
2
+
2
(
2
−
4
)
2
−
(
1
−
3
)
2
)
)
+
4
̇
4
(
2
5
)
Su
b
s
titu
tin
g
(
7
)
a
n
d
(
1
3
)
i
n
to
(
2
0
)
,
we
o
b
tain
(
2
6
)
.
̇
=
̇
+
1
4
(
−
3
−
4
+
1
(
2
+
2
(
2
−
4
)
2
−
(
1
−
3
)
2
)
+
1
+
(
)
)
(
2
6
)
B
y
s
im
p
lific
atio
n
,
we
o
b
tain
(
2
7
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
1
5
,
No
.
1
,
Ma
r
ch
20
2
6
:
210
-
2
2
1
216
̇
=
̇
−
(
+
1
2
2
−
(
1
−
3
)
2
)
4
2
+
−
3
+
1
(
2
+
2
2
2
−
(
1
−
3
)
2
)
+
(
)
4
(
2
7
)
B
ased
o
n
th
e
an
aly
s
is
in
th
e
f
ir
s
t
s
tep
,
th
e
s
u
s
p
en
d
ed
m
ass
s
y
s
tem
m
s
i
s
a
s
y
m
p
to
tically
s
tab
le,
i.e
.
,
x
1
→
0
an
d
x
2
→
0
.
As a
r
esu
lt,
e
q
u
atio
n
(
2
7
)
ca
n
b
e
r
ec
ast in
to
th
e
f
o
r
m
o
f
(
2
8
)
.
̇
=
̇
−
(
+
1
2
2
−
3
2
)
4
2
+
−
3
+
(
)
4
(
2
8
)
B
y
ap
p
ly
in
g
t
h
e
Yo
u
n
g
’
s
in
eq
u
ality
,
we
o
b
tain
(
2
9
)
.
̇
=
̇
−
(
+
1
2
2
−
3
2
−
1
)
4
2
+
1
(
−
3
+
(
)
)
2
(
2
9
)
Un
d
e
r
t
h
e
p
r
ac
tic
al
co
n
d
it
io
n
t
h
at
t
h
e
r
o
a
d
s
u
r
f
a
ce
ir
r
e
g
u
l
ar
i
ti
es
a
r
e
b
o
u
n
d
e
d
,
x
3
is
co
n
s
t
r
ai
n
ed
ac
c
o
r
d
i
n
g
t
o
(
9
)
wh
e
n
t
h
e
i
n
v
a
r
ia
n
t
m
a
n
i
f
o
ld
(
8
)
is
s
a
tis
f
ie
d
,
i.
e.
,
(
−
3
+
(
)
)
2
<
.
T
o
en
s
u
r
e
̇
≤
0
,
th
is
i
m
p
lies
t
h
a
t
(
−
3
+
(
)
)
2
≤
−
(
−
1
+
1
2
2
−
3
2
)
4
2
(
3
0
)
I
t
is
s
tr
aig
h
tf
o
r
war
d
to
o
b
s
er
v
e
th
at
wh
en
4
is
s
u
f
f
icien
tly
f
ar
f
r
o
m
t
h
e
o
r
i
g
in
,
co
n
d
itio
n
(
3
0
)
h
o
l
d
s
.
T
h
is
im
p
lies
th
at
s
y
s
tem
(
7
)
u
n
d
er
c
o
n
tr
o
l
law
(
1
7
)
will
m
o
v
e
to
war
d
a
n
eig
h
b
o
r
h
o
o
d
o
f
t
h
e
o
r
ig
i
n
wh
en
it
is
o
u
ts
id
e
th
e
r
eg
i
o
n
Δ
.
On
ce
th
e
tr
ajec
to
r
ies
en
te
r
Δ
,
t
h
e
s
y
s
tem
will
r
em
ain
with
in
th
is
r
eg
io
n
an
d
all
s
tate
v
ar
iab
les
will
co
n
v
er
g
e
to
ze
r
o
.
Mo
r
eo
v
e
r
,
with
a
s
u
f
f
icien
tly
s
m
all
Δ
,
th
e
s
tead
y
-
s
tate
t
r
ac
k
in
g
er
r
o
r
s
s
till
s
atis
f
y
th
e
r
eq
u
ir
ed
p
e
r
f
o
r
m
a
n
ce
s
p
ec
if
icatio
n
s
an
d
co
n
t
r
o
l
o
b
jectiv
es.
I
n
o
r
d
er
to
p
r
o
v
id
e
an
ad
d
itio
n
al
co
m
p
ar
is
o
n
a
n
d
ass
ess
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l la
w
(
1
7
)
,
we
d
es
ig
n
a
SMC
f
o
r
s
y
s
tem
(
7
)
.
3
.
2
.
Sli
di
ng
m
o
de
co
ntr
o
l la
w
des
ig
n
T
h
e
d
esig
n
o
f
th
e
SMC
co
n
tr
o
ller
f
o
r
s
u
s
p
en
s
io
n
s
y
s
tem
s
h
a
s
b
ee
n
p
r
esen
ted
i
n
v
ar
i
o
u
s
s
tu
d
ies
[
2
5
]
.
Sli
d
in
g
-
m
o
d
e
co
n
tr
o
l
is
a
r
o
b
u
s
t
n
o
n
lin
ea
r
co
n
tr
o
l
ap
p
r
o
ac
h
ca
p
a
b
le
o
f
m
ain
tain
in
g
s
tab
le
co
n
tr
o
l
p
er
f
o
r
m
an
ce
ev
en
in
th
e
p
r
es
en
ce
o
f
d
is
tu
r
b
an
ce
s
an
d
p
ar
a
m
eter
u
n
ce
r
tain
ties
.
T
h
e
m
ain
id
ea
o
f
SMC
is
to
co
n
s
tr
u
ct
a
s
lid
in
g
s
u
r
f
ac
e
s
u
ch
th
at,
o
n
ce
th
e
s
y
s
tem
tr
ajec
t
o
r
ies r
ea
ch
an
d
r
em
ain
o
n
th
is
s
u
r
f
ac
e,
th
e
s
y
s
tem
ex
h
ib
its
th
e
d
esire
d
d
y
n
am
ic
s
an
d
s
tab
ilit
y
i
s
g
u
ar
an
teed
.
T
h
e
SMC
d
esig
n
m
eth
o
d
u
s
ed
in
th
is
s
ec
tio
n
f
o
llo
ws
th
e
ap
p
r
o
ac
h
r
e
p
o
r
ted
in
[
2
5
]
.
T
h
e
co
n
tr
o
l
o
b
jectiv
e
o
f
t
h
e
ac
tiv
e
s
u
s
p
e
n
s
io
n
s
y
s
tem
is
to
en
s
u
r
e
th
a
t
th
e
ac
tu
al
s
u
s
p
en
s
io
n
d
ef
lecti
o
n
y=x
1
-
x
3
q
u
ick
ly
an
d
ac
cu
r
ately
tr
ac
k
s
its
d
esire
d
r
ef
er
e
n
ce
y
d
.
B
ased
o
n
th
e
s
y
s
tem
eq
u
atio
n
s
in
(
7
)
a
n
d
f
o
llo
win
g
th
e
ab
o
v
e
-
m
e
n
tio
n
e
d
s
tu
d
y
,
th
e
o
u
tp
u
t
t
r
ac
k
in
g
e
r
r
o
r
o
f
th
e
s
y
s
tem
is
d
ef
in
ed
as:
=
−
1
+
3
(
3
1
)
T
h
e
co
n
tr
o
ller
s
lid
in
g
s
u
r
f
ac
e
s
is
d
ef
in
ed
as:
=
̈
+
2
̇
+
1
(
3
2
)
wh
er
e
c
1
>
0
an
d
c
2
>
0
ar
e
p
o
s
itiv
e
co
n
s
tan
ts
en
s
u
r
in
g
asy
m
p
t
o
tic
s
tab
ilit
y
o
n
th
e
s
lid
in
g
s
u
r
f
ac
e.
T
h
e
s
lid
in
g
-
m
o
d
e
co
n
tr
o
l
in
p
u
t
is
co
m
p
o
s
ed
o
f
two
p
a
r
ts
:
th
e
eq
u
iv
alen
t
ter
m
an
d
th
e
s
witch
in
g
ter
m
.
T
h
e
eq
u
i
v
alen
t
co
n
tr
o
l
co
m
p
en
s
ates
th
e
n
o
m
in
al
d
y
n
am
ics
s
o
th
at
th
e
m
o
tio
n
r
em
ain
s
o
n
th
e
s
lid
in
g
m
an
if
o
ld
;
it
is
o
b
tain
e
d
b
y
en
f
o
r
cin
g
̇
=
0
.
I
n
co
n
tr
ast,
t
h
e
s
witch
in
g
c
o
n
tr
o
l
d
r
i
v
es
th
e
tr
ajec
to
r
ies
to
war
d
th
e
m
a
n
if
o
ld
,
en
s
u
r
in
g
th
e
r
ea
ch
in
g
co
n
d
itio
n
.
Acc
o
r
d
in
g
ly
,
t
h
e
SMC
law
is
g
iv
en
b
y
(
3
3
)
:
=
+
(
3
3
)
T
h
e
co
m
p
o
n
en
ts
o
f
th
e
co
n
tr
o
l
law
in
(
3
3
)
ar
e
g
i
v
en
b
y
(
3
4
)
:
=
−
1
(
⃛
+
2
̈
+
1
̇
+
1
1
+
2
2
+
3
3
+
4
4
+
5
5
)
=
−
1
(
)
(
3
4
)
I
n
th
is
f
o
r
m
u
latio
n
,
th
e
v
ar
ia
b
le
5
is
in
tr
o
d
u
ce
d
t
o
r
ep
r
esen
t
th
e
s
tate
o
f
th
e
ac
tu
ato
r
,
an
d
th
e
p
a
r
am
eter
s
(
=
1
…
5
)
ar
e
also
d
eter
m
in
e
d
ac
co
r
d
in
g
to
th
e
ex
p
r
ess
io
n
s
p
r
o
v
i
d
ed
in
th
e
s
am
e
s
tu
d
y
[
2
5
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
Mo
d
elin
g
a
n
d
s
imu
la
tio
n
o
f a
n
a
ctive
q
u
a
r
ter
-
ca
r
s
u
s
p
en
s
io
n
s
ystem
u
s
in
g
…
(
Da
o
Tr
o
n
g
Du
n
g
)
217
4.
NUM
E
RIC
AL
S
I
M
UL
A
T
I
O
N
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
o
v
alid
ate
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
tr
ateg
y
,
we
co
m
p
a
r
e
t
h
r
ee
ca
s
es
in
s
im
u
latio
n
:
t
h
e
p
ass
iv
e
s
u
s
p
en
s
io
n
s
y
s
tem
(
PS
S),
s
li
d
in
g
m
o
d
e
co
n
tr
o
l
(
SMC
)
,
a
n
d
s
y
n
er
g
etic
co
n
tr
o
l
(
.
)
.
T
h
e
q
u
ar
ter
-
ca
r
m
o
d
el
p
a
r
am
eter
s
u
s
ed
in
th
e
s
im
u
latio
n
s
ar
e
g
iv
en
in
T
ab
le
1
[
3
]
.
C
o
n
tr
o
ller
p
ar
am
ete
r
s
ar
e
tu
n
ed
f
o
llo
win
g
th
e
s
tab
ilit
y
co
n
d
itio
n
s
d
er
i
v
ed
ea
r
lier
.
All
p
r
o
p
o
s
ed
c
o
n
tr
o
ller
p
a
r
am
eter
s
T
1
,
k
1
,
an
d
k
2
ar
e
p
o
s
itiv
e
co
n
s
tan
ts
.
Acc
o
r
d
in
g
to
t
h
e
an
aly
s
is
o
f
(
1
1
)
an
d
(
1
4
)
,
k
2
is
a
s
m
all
p
o
s
itiv
e
co
n
s
tan
t a
n
d
is
th
er
ef
o
r
e
c
h
o
s
en
as
k
2
=
0
.
0
0
5
.
T
h
e
p
a
r
am
eter
k
1
=3
0
m
ain
ly
a
f
f
ec
ts
th
e
s
ettlin
g
tim
e
o
f
th
e
s
y
s
tem
,
an
d
it
is
s
elec
ted
to
en
s
u
r
e
f
ast
s
tab
ilit
y
in
ac
co
r
d
an
ce
with
(
1
1
)
.
Similar
ly
,
T
1
=
10
is
c
h
o
s
en
to
g
u
ar
an
tee
an
ap
p
r
o
p
r
iate
s
ettlin
g
tim
e
f
o
r
th
e
o
v
er
all
s
y
s
tem
,
t
h
er
eb
y
en
s
u
r
in
g
its
s
tab
ilit
y
.
Fo
r
th
e
SM
C
co
n
tr
o
ller
s
elec
ted
ac
co
r
d
in
g
to
th
e
r
ef
er
e
n
ce
d
s
tu
d
y
,
th
e
p
ar
a
m
eter
s
ar
e
ch
o
s
en
as
f
o
llo
ws:
K=
2
,
c
1
=
8
,
c
2
=
4
an
d
th
e
r
em
ain
in
g
p
a
r
am
e
ter
s
ar
e
co
m
p
u
ted
u
s
in
g
th
e
f
o
r
m
u
las
th
at
d
ep
e
n
d
o
n
t
h
e
s
y
s
tem
p
ar
am
eter
s
r
ep
o
r
ted
i
n
[
2
5
]
.
T
h
e
s
im
u
l
atio
n
p
r
o
g
r
am
was
im
p
lem
en
ted
in
MA
T
L
AB
u
s
in
g
th
e
f
o
r
war
d
E
u
ler
m
et
h
o
d
with
a
s
am
p
lin
g
tim
e
o
f
=
0
.
001
.
T
ab
le
1
.
AQCS
S m
o
d
el
p
ar
am
eter
s
P
a
r
a
me
t
e
r
V
a
l
u
e
U
n
i
t
s
6
0
0
kg
60
kg
1
1
8
0
0
0
N
/
m
2
1
0
0
0
N
/
m
3
1
2
5
0
0
N
s/
m
2
2
2
0
0
Ns
2
/m
2
1
0
0
0
N
s/
m
2
0
0
0
0
0
N
/
m
z
m
a
x
0
.
1
5
m
4
.
1
.
Scena
rio
1
–
Ro
a
d dis
t
urba
nce:
B
um
p inp
ut
Fo
r
th
e
f
ir
s
t
s
im
u
latio
n
s
ce
n
ar
io
,
a
b
u
m
p
-
ty
p
e
r
o
ad
p
r
o
f
ile
i
s
u
s
ed
as
th
e
ex
citatio
n
an
d
is
d
escr
ib
ed
by
(
3
5
)
:
(
)
=
{
(
)
;
−
(
−
3
.
5
)
3
+
(
−
3
.
5
)
2
+
(
)
;
3
.
5
≤
<
5
(
−
6
.
5
)
3
+
(
−
6
.
5
)
2
+
(
)
;
5
≤
<
6
.
5
(
−
8
.
5
)
3
−
(
−
8
.
5
)
2
+
(
)
;
8
.
5
≤
<
10
−
(
−
11
.
5
)
3
−
(
−
11
.
5
)
2
+
(
)
;
10
≤
<
11
.
5
(
3
5
)
wh
er
e
=
0
.
0592
,
=
0
.
1332
,
an
d
(
)
=
0
.
002
(
(
2
)
+
(
7
.
5
)
)
(
)
r
ep
r
esen
ts
a
s
in
u
s
o
id
al
d
is
tu
r
b
an
ce
.
T
h
e
s
im
u
latio
n
r
esu
lts
o
f
th
e
s
u
s
p
en
s
io
n
s
y
s
tem
'
s
r
esp
o
n
s
e
ar
e
illu
s
tr
ated
in
Fig
u
r
e
2
.
T
h
e
tim
e
-
d
o
m
ain
r
esp
o
n
s
e
o
f
t
h
e
s
u
s
p
en
s
io
n
m
ass
d
is
p
lace
m
e
n
t
is
co
m
p
ar
ed
in
Fig
u
r
e
2
(
a)
.
Acc
o
r
d
in
g
to
th
e
o
s
cillatio
n
r
esp
o
n
s
es
s
h
o
wn
in
th
e
f
ig
u
r
e,
t
h
e
PS
S
s
h
o
ws
th
e
lar
g
est
d
is
p
lace
m
en
t
am
p
litu
d
e
o
f
th
e
s
u
s
p
en
s
io
n
m
ass
,
r
ea
ch
in
g
ap
p
r
o
x
im
ately
±
0
.
12
.
I
n
co
n
t
r
ast,
th
e
s
y
s
tem
u
s
in
g
th
e
SMC
co
n
tr
o
ller
m
ain
tain
s
th
e
am
p
litu
d
e
with
in
±
0
.
02
,
wh
ile
th
e
s
y
s
tem
with
th
e
.
co
n
tr
o
ller
co
n
tin
u
es
to
r
ed
u
ce
th
e
am
p
litu
d
e
to
ap
p
r
o
x
im
ately
±
0
.
017
.
T
h
is
d
em
o
n
s
tr
ates
th
at
th
e
p
r
o
p
o
s
ed
ac
tiv
e
co
n
tr
o
l
s
ch
e
m
e
.
s
ig
n
if
ican
tly
r
ed
u
ce
s
th
e
v
ib
r
atio
n
am
p
litu
d
e
o
f
th
e
s
u
s
p
e
n
s
io
n
m
ass
.
R
eg
ar
d
in
g
th
e
w
o
r
k
in
g
s
p
ac
e
o
f
th
e
AQCS
S,
th
e
s
y
s
tem
m
u
s
t
m
ai
n
tain
its
d
ef
lectio
n
with
in
p
er
m
is
s
ib
le
lim
its
.
As
illu
s
tr
ated
in
Fig
u
r
e
2
(
b
)
,
th
e
R
SD
o
f
th
e
AQCS
S
with
th
e
.
co
n
tr
o
ller
is
with
in
±
0
.
6
,
wh
ile
th
e
R
SD
o
f
th
e
SMC
co
n
t
r
o
ller
is
alwa
y
s
with
in
±
0
.
7
.
T
h
is
r
esu
lt
s
h
o
ws
th
at
b
o
th
co
n
tr
o
ller
s
en
s
u
r
e
th
e
co
n
d
itio
n
(
9
)
.
T
h
is
m
ea
n
s
th
at
th
e
s
y
s
tem
en
s
u
r
es
s
af
e
o
p
er
atio
n
with
in
its
m
ec
h
an
ical
lim
its
.
Fig
u
r
e
2
(
c)
s
h
o
ws
th
at
th
e
R
T
F
o
f
PS
S,
SMC
,
an
d
.
ar
e
all
less
th
an
1
(
1
0
)
,
in
d
icatin
g
th
at
th
e
co
n
tact
b
etwe
en
th
e
tire
an
d
th
e
r
o
ad
s
u
r
f
ac
e
is
well
m
ain
tain
ed
,
th
u
s
im
p
r
o
v
in
g
s
tab
ilit
y
an
d
s
af
ety
d
u
r
in
g
c
o
n
t
r
o
l.
Ho
wev
er
,
t
h
e
R
T
F
o
f
th
e
.
co
n
tr
o
l
law
h
as
th
e
h
ig
h
est
v
alu
e
at
ce
r
tain
tim
es,
in
d
icatin
g
th
at
th
is
co
n
tr
o
l
law
ex
h
ib
its
a
s
tr
o
n
g
r
esp
o
n
s
e
to
d
is
tu
r
b
an
ce
s
,
en
a
b
lin
g
t
h
e
s
y
s
tem
to
q
u
ick
ly
r
etu
r
n
to
its
in
itial
p
o
s
itio
n
.
T
h
e
co
n
tr
o
l
s
ig
n
als
o
f
th
e
AQCS
S
ac
co
r
d
in
g
to
th
e
SMC
an
d
.
co
n
tr
o
l
laws
ar
e
p
r
esen
ted
in
Fi
g
u
r
e
2
(
d
)
.
B
o
th
c
o
n
tr
o
l
s
tr
ate
g
ies
g
en
er
ate
two
m
ain
co
n
tr
o
l
p
u
ls
es
with
an
am
p
litu
d
e
o
f
ap
p
r
o
x
im
ately
±
1900
wh
en
r
o
ad
d
is
tu
r
b
an
c
es
o
cc
u
r
.
Nev
er
th
eless
,
co
m
p
ar
e
d
with
SMC
,
th
e
.
s
ch
em
e
ac
h
iev
e
s
s
im
ilar
p
er
f
o
r
m
a
n
ce
with
a
m
ar
g
in
ally
r
ed
u
ce
d
c
o
n
tr
o
l a
m
p
litu
d
e,
s
u
p
p
o
r
tin
g
th
e
ef
f
ec
tiv
en
ess
o
f
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
1
5
,
No
.
1
,
Ma
r
ch
20
2
6
:
210
-
2
2
1
218
0
5
10
15
-0
.
5
0
0
.
5
T
i
m
e
(s
)
RSD
R
S
D
(
P
S
S
)
R
S
D
(
S
M
C
)
R
S
D
(
S
yn
.
C
)
(
a)
(
b
)
0
5
10
15
-0
.
1
0
0
.
1
0
.
2
T
i
m
e
(s
)
RT
F
R
T
F
(
P
S
S
)
R
T
F
(
S
M
C
)
R
T
F
(
S
yn
.
C
)
0
5
10
15
-2
0
0
0
-1
0
0
0
0
1000
2000
T
i
m
e
(s
)
u
(N
)
u(
P
S
S
)
u(
S
M
C
)
u(
S
yn
.
C
)
(
c)
(
d
)
Fig
u
r
e
2
.
Sy
s
tem
r
esp
o
n
s
e
in
t
h
e
s
ce
n
ar
io
1
:
(
a)
v
e
r
tical
m
o
ti
o
n
o
f
th
e
s
p
r
u
n
g
m
ass
m
s
,
(
b
)
t
h
e
r
elativ
e
s
u
s
p
en
s
io
n
d
ev
iatio
n
,
(
c)
th
e
r
elativ
e
tire
f
o
r
ce
,
a
n
d
(
d
)
c
o
n
tr
o
l
s
ig
n
al
in
th
e
ac
tiv
e
s
u
s
p
en
s
i
o
n
s
y
s
tem
4
.
2
.
Scena
rio
2
–
Ro
a
d ste
p e
x
cit
a
t
io
n
I
n
th
e
s
ec
o
n
d
s
ce
n
ar
io
,
th
e
b
u
m
p
-
in
d
u
ce
d
r
o
ad
e
x
citatio
n
is
d
escr
ib
ed
b
y
(
3
6
)
.
(
)
=
{
0
.
05
(
1
−
(
16
)
)
,
0
≤
≤
0
.
025
0
,
>
0
.
025
,
(
3
6
)
T
h
e
s
im
u
la
tio
n
o
u
tco
m
e
s
f
o
r
s
ce
n
ar
io
2
h
ig
h
l
ig
h
t
c
le
ar
d
if
f
er
e
n
ce
s
am
o
n
g
th
e
th
r
e
e
c
a
s
e
s
:
t
h
e
ac
tiv
e
s
u
s
p
en
s
io
n
wi
th
th
e
.
law
,
th
e
s
y
s
te
m
g
o
v
er
n
ed
b
y
t
h
e
S
M
C
l
aw
,
an
d
th
e
p
a
s
s
iv
e
s
u
s
p
en
s
io
n
,
a
s
s
u
m
m
ar
ized
in
T
ab
l
e
2
an
d
il
l
u
s
tr
a
ted
in
F
ig
u
r
e
3
.
A
s
s
h
o
w
n
in
F
ig
u
r
e
3
(
a)
,
th
e
v
er
ti
ca
l
d
is
p
la
ce
m
en
t
o
f
th
e
s
p
r
u
n
g
m
a
s
s
i
s
at
ten
u
at
ed
m
u
ch
m
o
r
e
r
ap
id
ly
u
n
d
er
.
th
an
i
n
th
e
p
a
s
s
iv
e
ca
s
e
,
lea
d
in
g
to
s
m
a
l
ler
p
ea
k
am
p
l
it
u
d
e
s
an
d
a
s
h
o
r
ter
s
e
tt
li
n
g
t
im
e
,
a
s
s
h
o
wn
in
T
ab
le
2
.
T
h
is
co
n
f
i
r
m
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ig
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Fig
u
r
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3
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s
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CO
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N
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ates
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ical
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eh
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e
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s
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h
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.
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o
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d
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ap
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tr
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m
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o
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u
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d
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th
e
p
h
y
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ical
co
n
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tr
ain
ts
o
f
th
e
s
y
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h
e
p
r
o
p
o
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ed
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f
ir
s
t
d
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es
t
h
e
s
tates
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m
a
n
if
o
ld
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d
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en
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u
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elf
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ce
o
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al
d
is
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r
b
an
ce
s
an
d
p
ar
a
m
e
ter
u
n
ce
r
tain
ties
is
estab
lis
h
ed
v
ia
L
y
ap
u
n
o
v
a
n
aly
s
is
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latio
n
o
u
tco
m
e
s
s
h
o
w
th
at
th
e
p
r
o
p
o
s
ed
s
y
n
er
g
etic
c
o
n
tr
o
ller
p
r
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v
id
es
n
o
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le
p
er
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ce
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er
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o
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th
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SMC
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ased
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s
u
s
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d
th
e
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ass
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n
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ig
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r
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n
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er
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t r
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n
tr
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s
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e
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et
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s
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ess
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er
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en
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e,
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ate
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h
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Evaluation Warning : The document was created with Spire.PDF for Python.