I
AE
S In
t
er
na
t
io
na
l J
o
urna
l o
f
Ro
bo
t
ics a
nd
Aut
o
m
a
t
io
n
(
I
J
RA)
Vo
l.
11
,
No
.
1
, M
a
r
ch
20
22
,
p
p
.
43
~
61
I
SS
N:
2722
-
2
5
8
6
,
DOI
:
1
0
.
1
1
5
9
1
/i
jr
a
.
v
11
i
1
.
pp
43
-
61
43
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
r
a
.
ia
esco
r
e.
co
m
An ef
fec
tive a
ppr
o
a
ch t
o
enhance
t
he bala
ncing
cont
ro
l in
by
cy
co
ro
bo
t
using
t
he so
ft
com
put
i
ng
t
echniq
ues
Aswa
nt
K
um
a
r
Sh
a
rm
a
,
Dh
a
nes
h K
um
a
r
Sa
m
ba
riy
a
D
e
p
a
r
t
me
n
t
o
f
El
e
c
t
r
i
c
a
l
En
g
i
n
e
e
r
i
n
g
,
R
a
j
a
s
t
h
a
n
Te
c
h
n
i
c
a
l
U
n
i
v
e
r
si
t
y
,
R
a
j
a
st
h
a
n
,
I
n
d
i
a
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
No
v
8
,
2
0
2
1
R
ev
is
ed
Dec
2
5
,
2
0
2
1
Acc
ep
ted
Dec
3
0
,
2
0
2
1
Th
e
b
a
lan
c
in
g
a
n
d
c
o
n
tro
l
o
f
b
y
c
y
c
o
ro
b
o
t
is
a
c
h
a
ll
e
n
g
i
n
g
tas
k
.
Th
e
p
re
-
sp
e
c
ifi
e
d
c
o
n
tro
ll
e
r
a
v
a
il
a
b
le
in
t
h
e
li
tera
tu
re
fo
r
b
a
lan
c
i
n
g
h
a
s
b
e
e
n
re
d
u
c
e
d
with
n
o
v
e
l
o
p
ti
m
iza
ti
o
n
to
i
m
p
ro
v
e
th
e
e
ffe
c
ti
v
e
n
e
ss
o
f
b
a
lan
c
in
g
,
u
n
c
e
rtain
t
y
,
a
n
d
th
e
c
o
m
p
lex
it
y
o
f
t
h
e
c
o
m
p
lete
sy
ste
m
.
Th
e
n
o
v
e
l
Ha
rris
h
a
wk
op
ti
m
iza
ti
o
n
(HH
O)
wh
ic
h
is
b
a
se
d
o
n
t
h
e
h
u
n
t
in
g
b
e
h
a
v
io
r
o
f
t
h
e
h
a
wk
h
a
s
b
e
e
n
u
ti
li
z
e
d
to
imp
r
o
v
e
th
e
b
a
lan
c
in
g
o
f
t
h
e
b
y
c
y
c
o
r
o
b
o
t.
Th
e
p
a
p
e
r
p
r
o
p
o
se
s
th
e
d
e
c
re
a
se
d
o
rd
e
r
c
o
n
tr
o
ll
e
r
o
f
a
p
re
-
sp
e
c
ifi
e
d
c
o
n
tro
ll
e
r
fo
r
a
b
y
c
y
c
o
ro
b
o
t
.
T
h
e
o
b
tai
n
e
d
c
o
n
tro
ll
e
r
re
sp
o
n
se
wit
h
b
y
c
y
c
o
r
o
b
o
t
i
n
t
h
e
c
o
m
p
lete
c
lo
se
d
l
o
o
p
is
a
n
a
ly
z
e
d
,
a
n
d
t
h
e
b
e
st
p
e
rfo
rm
a
n
c
e
is
c
o
m
p
a
re
d
with
t
h
e
re
d
u
c
e
d
o
rd
e
r
c
o
n
tr
o
ll
e
r
a
v
a
il
a
b
le
in
th
e
l
it
e
ra
tu
re
.
T
h
e
c
o
m
p
a
riso
n
is b
a
se
d
o
n
t
h
e
re
sp
o
n
se
in
d
ice
s a
n
d
re
sp
o
n
se
c
h
a
ra
c
teristics
.
K
ey
w
o
r
d
s
:
Ba
lan
cin
g
co
n
tr
o
l
B
y
cy
co
r
o
b
o
t
Har
r
is
h
awk
o
p
tim
izatio
n
R
ed
u
ce
d
co
n
tr
o
ller
R
ed
u
ce
d
-
o
r
d
er
m
o
d
ellin
g
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
:
Aswan
t K
u
m
ar
Sh
ar
m
a
Dep
ar
tm
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
,
R
ajasth
an
T
ec
h
n
ical
Un
iv
er
si
ty
Ak
elg
ar
h
,
Ko
ta,
R
ajasth
an
3
2
4
0
1
0
,
I
n
d
ia
E
m
ail:
aswan
tk
s
h
ar
m
a@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
As
th
e
f
ir
s
t
k
in
d
o
f
p
er
s
o
n
al
m
o
b
ilit
y
v
eh
icle
ev
e
r
in
v
en
te
d
,
b
icy
cles
p
lay
an
im
p
o
r
tan
t
r
o
le
in
th
e
h
is
to
r
y
o
f
tr
an
s
p
o
r
t.
B
icy
cles
ar
e
lig
h
tweig
h
t
an
d
ar
e
s
o
lely
p
r
o
p
elled
b
y
h
u
m
an
p
o
wer
.
T
h
ey
ca
n
co
n
tr
ib
u
te
to
th
e
r
ed
u
ctio
n
o
f
tr
af
f
ic
co
n
g
esti
o
n
an
d
air
p
o
llu
tio
n
in
u
r
b
an
ar
ea
s
.
B
icy
cles
ar
e
class
if
ied
as
s
in
g
le
-
tr
ac
k
v
eh
icles
an
d
d
is
p
lay
in
ter
esti
n
g
d
y
n
a
m
ic
b
eh
av
io
r
.
T
h
e
in
tr
ig
u
in
g
b
e
h
av
io
r
o
f
b
icy
cles
p
o
s
es
ch
allen
g
in
g
p
r
o
b
lem
s
in
m
o
d
elin
g
an
d
c
o
n
tr
o
l
,
wh
ich
h
a
v
e
attr
ac
ted
atten
tio
n
f
r
o
m
th
e
au
to
m
ati
c
co
n
tr
o
l
r
esear
ch
co
m
m
u
n
ity
[
1
]
.
T
h
e
b
alan
cin
g
co
n
t
r
o
l
p
r
o
b
lem
o
f
th
e
b
y
c
y
co
r
o
b
o
ts
is
n
o
t
n
ew
in
th
e
f
i
eld
o
f
r
o
b
o
tics
.
T
h
e
b
y
cy
co
r
o
b
o
t
is
in
g
r
ea
t
d
em
a
n
d
d
u
e
to
its
b
asic
co
n
s
tr
u
ctio
n
,
s
im
p
ler
d
y
n
am
ics,
an
d
a
p
p
licab
ilit
y
in
wid
e
s
ec
to
r
s
s
u
ch
as
tr
an
s
p
o
r
tatio
n
,
s
ec
u
r
ity
,
s
ea
r
c
h
an
d
r
escu
e
,
a
n
d
lab
o
r
r
ed
u
ctio
n
.
T
h
ese
r
o
b
o
ts
ar
e
i
n
h
er
en
tly
u
n
s
tab
le
an
d
s
u
s
ce
p
tib
le
to
e
x
t
er
n
al
d
is
tu
r
b
an
ce
s
.
R
o
b
u
s
t
co
n
tr
o
l
s
ap
p
r
o
ac
h
ed
a
r
e
r
e
q
u
i
r
ed
f
o
r
a
p
p
r
o
p
r
iate
an
d
s
m
o
o
th
b
alan
cin
g
co
n
tr
o
l
an
d
m
o
v
em
e
n
t
o
f
s
u
ch
r
o
b
o
ts
[
2
]
.
T
h
e
s
tab
ilit
y
o
f
b
icy
cles
is
an
is
s
u
e
th
at
h
as
s
ca
r
ce
ly
b
ee
n
u
n
d
e
r
s
to
o
d
in
d
y
n
am
ics
an
d
is
a
co
m
m
o
n
ly
ig
n
o
r
ed
p
r
o
b
lem
.
A
f
ter
two
ce
n
t
u
r
ies
o
f
d
eb
ate
a
n
d
u
n
f
in
is
h
ed
m
o
d
elin
g
,
n
ew
r
esear
ch
es
ar
e
p
a
v
in
g
t
h
e
g
r
o
u
n
d
wo
r
k
f
o
r
i
n
cr
ea
s
in
g
s
tu
d
ies
r
eg
ar
d
in
g
th
is
is
s
u
e
[
3
]
.
T
h
er
eb
y
,
s
o
m
e
r
esear
ch
e
r
s
h
av
e
ap
p
ea
r
e
d
th
an
k
s
to
n
e
w
d
y
n
am
ics
m
o
d
els
an
d
th
e
c
o
m
p
u
tatio
n
al
p
o
wer
av
ailab
le
n
o
wad
ay
s
.
T
h
ei
r
p
u
r
p
o
s
e
is
to
p
r
o
p
o
s
e
an
d
test
d
if
f
er
en
t
alter
n
ativ
es
to
s
tab
ilize
a
b
icy
cle.
Desp
ite
th
eir
co
m
m
o
n
g
o
al
o
f
m
ak
in
g
a
b
y
cy
c
r
o
b
o
t
s
tab
le,
th
e
y
p
r
o
p
o
s
e
a
wid
e
v
ar
iety
o
f
ap
p
licatio
n
s
f
o
r
th
ei
r
s
tab
ilized
b
y
cy
cr
o
b
o
t
[
4
]
.
T
h
e
b
icy
cle
ca
n
b
e
b
alan
ce
d
u
s
in
g
th
e
r
o
tatio
n
o
f
th
e
f
r
o
n
t
wh
ee
l
in
t
h
e
d
ir
ec
tio
n
o
f
l
e
an
,
wh
ich
ch
an
g
es
th
e
t
i
r
e
c
o
n
tact
p
o
i
n
t
with
t
h
e
g
r
o
u
n
d
in
th
e
s
am
e
d
ir
ec
tio
n
an
d
is
s
im
ilar
to
b
al
an
cin
g
an
in
v
er
te
d
p
en
d
u
l
u
m
.
I
n
ad
d
itio
n
,
th
e
ce
n
tr
if
u
g
a
l
f
o
r
ce
co
n
tr
ib
u
tes
to
b
alan
ce
b
ec
au
s
e
o
f
th
e
cir
cu
la
r
m
o
tio
n
.
Mo
r
e
o
v
er
,
u
n
co
n
tr
o
lled
b
icy
cles
ca
n
b
a
lan
ce
th
em
s
elv
es
with
in
ce
r
tain
v
elo
city
r
a
n
g
es
,
wh
ich
d
ep
en
d
o
n
d
if
f
er
en
t
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
.
11
,
No
.
1
,
M
a
r
ch
20
22
:
43
-
61
44
b
icy
cle
-
d
esig
n
p
ar
am
ete
r
s
[
5
]
.
Fo
r
ex
am
p
le,
g
y
r
o
s
co
p
e,
p
er
tu
r
b
atio
n
s
tatio
n
ar
y
b
y
c
y
cr
o
b
o
t
s
y
s
tem
,
in
v
er
ted
p
en
d
u
l
u
m
n
o
n
lin
ea
r
c
o
n
tr
o
lle
r
s
,
r
o
b
u
s
t
two
-
s
tag
e
ac
tiv
e
d
i
s
tu
r
b
an
ce
r
ejec
tio
n
co
n
tr
o
l,
f
u
zz
y
s
lid
in
g
-
m
o
d
e
u
n
d
er
ac
tu
ate
d
c
o
n
tr
o
l,
p
r
o
p
o
r
tio
n
al
d
er
i
v
ativ
e
(
PD
)
co
n
tr
o
ller
s
,
an
d
p
r
o
p
o
r
ti
o
n
al
i
n
teg
r
al
d
er
iv
ativ
e
(
PID
)
co
n
tr
o
ller
s
h
a
v
e
b
ee
n
p
r
esen
te
d
in
d
is
tin
ctiv
e
r
esear
c
h
es
[
6
]
–
[
1
1
]
.
T
h
e
PID
co
n
tr
o
ller
h
as
th
r
ee
p
ar
am
ete
r
s
to
b
e
tu
n
e
d
s
u
itab
le
f
o
r
b
y
c
y
cr
o
b
o
t
b
ec
a
u
s
e
o
f
th
eir
d
eg
r
ee
o
f
f
r
ee
d
o
m
-
o
n
e
f
o
r
tilt
,
o
th
er
f
o
r
s
p
ee
d
,
an
d
s
u
b
ject
u
p
o
n
t
h
e
ap
p
lica
b
ilit
y
o
f
th
e
y
aw.
N
u
m
er
o
u
s
tech
n
iq
u
es
ar
e
g
iv
en
in
th
e
liter
atu
r
e
f
o
r
b
alan
cin
g
co
n
tr
o
l
o
f
b
y
cy
co
r
o
b
o
t
lik
e
a
f
ly
wh
ee
l,
m
ass
,
an
d
s
teer
in
g
b
alan
cin
g
[
1
2
]
–
[
1
4
]
.
Alth
o
u
g
h
m
u
ch
ef
f
o
r
t
h
as
b
ee
n
d
o
n
e
t
o
u
n
d
er
s
tan
d
th
is
f
asci
n
atin
g
p
h
en
o
m
en
o
n
,
th
e
s
tu
d
ies
n
o
w
h
av
e
b
ee
n
r
estricte
d
to
a
s
in
g
le
s
itu
atio
n
in
wh
ich
th
e
b
icy
cle
r
id
es
o
n
a
h
o
r
iz
o
n
tal
s
u
r
f
ac
e
[
1
5
]
.
T
h
e
a
d
ap
tiv
e
in
teg
r
al
ter
m
in
al
s
lid
in
g
m
o
d
e
was
u
s
ed
to
p
r
o
v
id
e
r
o
b
u
s
t
co
n
t
r
o
l
o
f
th
e
r
ea
ctio
n
wh
ee
l
o
f
b
y
cy
c
o
r
o
b
o
t
[
1
6
]
.
T
h
e
p
r
o
p
o
s
ed
a
d
ap
tiv
e
in
teg
r
al
ter
m
i
n
al
s
lid
in
g
m
o
d
e
(
AI
T
SM
)
c
o
n
t
r
o
l
s
ch
em
e
ca
n
n
o
t
o
n
l
y
s
tab
ilize
th
e
b
icy
cle
r
o
b
o
t
an
d
r
ejec
t
ex
ter
n
al
d
is
tu
r
b
an
ce
s
g
en
er
ated
b
y
u
n
ce
r
tain
ties
an
d
u
n
-
m
o
d
elled
d
y
n
am
ics,
b
u
t
also
elim
in
ate
th
e
n
ee
d
o
f
th
e
r
eq
u
ir
ed
b
o
u
n
d
in
f
o
r
m
atio
n
in
th
e
c
o
n
tr
o
l
law
v
ia
t
h
e
d
esig
n
ed
ad
a
p
tiv
e
laws.
T
h
e
ex
p
er
im
en
tal
r
esu
lts
v
er
if
y
th
e
ex
ce
llen
t
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
c
o
n
tr
o
l
s
ch
e
m
e
in
ter
m
s
o
f
s
tr
o
n
g
r
o
b
u
s
tn
ess
,
f
ast
er
r
o
r
co
n
v
er
g
en
ce
in
c
o
m
p
a
r
is
o
n
with
o
th
er
co
n
tr
o
l
s
ch
em
es.
T
h
e
“scis
s
o
r
-
p
air
co
n
t
r
o
l
m
o
m
en
t
g
y
r
o
s
co
p
e
tech
n
iq
u
e
”
[
1
7
]
f
o
r
ac
tiv
e
b
alan
cin
g
o
f
th
e
u
n
m
an
n
e
d
b
i
cy
cle
s
y
s
tem
.
A
m
in
iatu
r
e
b
icy
cle
s
y
s
tem
wa
s
co
n
s
tr
u
cted
,
a
n
d
its
3
D
s
o
lid
m
o
d
el
was
u
s
ed
to
ac
q
u
ir
e
th
e
d
y
n
a
m
ics
m
o
d
el’
s
p
ar
am
ete
r
v
alu
es.
T
h
er
e
ar
e
two
ty
p
es
o
f
d
is
tu
r
b
a
n
ce
s
th
at
m
ig
h
t
ca
u
s
e
a
b
icy
cle
with
a
n
u
n
s
tab
le
e
q
u
ilib
r
iu
m
p
o
i
n
t
t
o
b
ec
o
m
e
u
n
s
tab
le
im
p
u
ls
iv
e
ex
ter
n
al
d
is
tu
r
b
an
ce
s
an
d
s
tatic
co
n
tin
u
es
d
is
tu
r
b
an
ce
s
.
T
h
e
ex
p
er
im
en
tal
r
esu
lt
d
ep
icts
th
e
p
er
f
o
r
m
an
ce
o
f
ac
tiv
e
b
alan
ci
n
g
f
o
r
a
b
icy
cle
eq
u
ip
p
ed
with
a
s
ciss
o
r
-
p
air
co
n
tr
o
l
m
o
m
e
n
t
g
y
r
o
s
co
p
e
(
C
MG
)
in
th
e
p
r
esen
ce
o
f
s
u
ch
d
is
tu
r
b
an
ce
s
.
A
b
icy
cle
r
o
b
o
t
b
alan
cin
g
wit
h
s
teer
in
g
an
d
a
n
o
n
-
in
v
er
ted
p
en
d
u
l
u
m
[
1
8
]
.
E
u
ler
-
L
a
g
r
an
g
e
eq
u
atio
n
o
f
m
o
tio
n
was
u
s
ed
to
cr
ea
te
a
n
o
n
lin
ea
r
m
ec
h
an
ical
m
o
d
el
o
f
th
e
b
y
cy
co
r
o
b
o
t
m
o
v
in
g
at
a
co
n
s
tan
t
f
o
r
war
d
s
p
ee
d
,
wh
ich
was
th
en
lin
ea
r
ized
ar
o
u
n
d
th
e
u
p
r
ig
h
t
p
o
s
itio
n
.
T
h
e
p
en
d
u
lu
m
an
d
s
teer
in
g
m
o
to
r
m
o
d
els
wer
e
also
in
clu
d
ed
in
th
e
lin
ea
r
ized
m
ec
h
an
ical
m
o
d
el
to
o
b
tain
t
h
e
co
m
p
licated
v
o
ltag
e
-
i
n
p
u
t
s
y
s
tem
r
ep
r
esen
ted
b
y
th
e
s
tate
-
s
p
ac
e
m
o
d
el.
T
h
e
elec
tr
o
-
m
ec
h
an
ical
p
a
r
ts
o
f
th
e
r
o
b
o
t
wer
e
d
esig
n
ed
co
n
s
id
er
in
g
th
e
c
o
n
tr
o
lle
r
f
o
r
s
tab
iliz
in
g
t
h
e
s
y
s
tem
.
T
h
e
s
im
u
latio
n
o
u
tp
u
t
r
ev
ea
led
th
at
th
e
s
y
s
tem
with
th
e
p
en
d
u
lu
m
-
em
p
h
asize
d
g
ain
m
atr
ix
o
u
tp
e
r
f
o
r
m
ed
th
e
s
y
s
tem
with
th
e
s
teer
in
g
-
em
p
h
asized
g
ain
m
atr
ix
in
ter
m
s
o
f
lear
n
in
g
an
d
p
at
h
-
tr
ac
k
in
g
r
an
g
es.
T
h
e
s
im
u
latio
n
r
esu
lts
wer
e
,
lik
ewise
,
i
n
li
n
e
with
t
h
e
r
ea
l
o
u
tc
o
m
e
o
n
t
h
e
s
tr
aig
h
t
r
o
ad
an
d
tu
r
n
in
g
p
o
in
ts
.
On
e
o
f
th
e
m
ajo
r
p
r
o
b
lem
s
in
th
e
d
ev
elo
p
m
en
t
o
f
b
y
c
y
c
o
r
o
b
o
t
is
b
alan
ci
n
g
at
m
o
d
e
s
t
f
o
r
war
d
s
p
ee
d
s
.
T
h
er
ef
o
r
e,
T
o
f
ig
h
et
a
l
.
[
1
9
]
d
e
m
o
n
s
tr
ated
a
n
o
v
e
l
g
y
r
o
s
tab
ili
z
er
with
a
d
u
al
-
f
ly
w
h
ee
l
co
n
f
ig
u
r
atio
n
th
at
ca
n
g
iv
e
an
y
r
eq
u
ir
e
d
g
y
r
o
s
co
p
ic
r
o
ll
m
o
m
e
n
t.
E
x
ten
s
i
v
e
s
im
u
latio
n
co
m
p
a
r
is
o
n
h
as
b
ee
n
b
ein
g
ca
r
r
ied
o
u
t
to
ass
ess
th
e
ap
p
r
o
ac
h
a
n
d
d
em
o
n
s
tr
ate
th
e
im
p
ac
t
o
f
in
co
r
p
o
r
atin
g
th
e
n
ew
ac
tu
ato
r
.
T
h
e
r
esu
lt
in
[
1
9
]
s
h
o
w
ed
th
at
th
e
p
r
o
p
o
s
al
p
r
o
v
id
es
h
ig
h
er
p
e
r
f
o
r
m
an
ce
wh
ile
k
ee
p
in
g
t
h
e
co
n
tr
o
l
ef
f
o
r
t
with
in
th
e
ca
p
a
b
i
liti
es
o
f
s
tan
d
ar
d
ac
tu
ato
r
s
.
A
s
tr
u
c
tu
r
e
-
s
p
ec
if
ied
m
i
x
ed
“
H
2
/H∞
”
co
n
tr
o
ller
was
d
esig
n
ed
u
s
i
n
g
p
a
r
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
f
o
r
c
o
n
t
r
o
l
b
ala
n
cin
g
o
f
b
y
cy
co
r
o
b
o
t.
T
h
e
u
n
s
tab
le
s
y
s
tem
with
m
an
y
s
o
u
r
ce
s
o
f
u
n
ce
r
tain
ty
d
u
e
to
u
n
-
m
o
d
el
d
y
n
am
ics,
p
ar
am
eter
v
ar
iati
o
n
s
,
an
d
ex
ter
n
al
d
is
tu
r
b
a
n
ce
s
[
2
0
]
.
T
h
e
d
esig
n
p
r
o
ce
s
s
,
o
n
th
e
o
th
er
h
a
n
d
,
f
r
eq
u
en
tly
g
en
er
ates
a
c
o
m
p
li
ca
ted
an
d
n
o
n
-
c
o
n
v
e
x
o
p
tim
izatio
n
is
s
u
e
th
at
is
d
if
f
icu
lt
to
a
d
d
r
ess
u
s
in
g
tr
a
d
i
tio
n
al
o
p
tim
izatio
n
a
p
p
r
o
ac
h
e
s
.
PS
O
was
a
r
ec
en
tly
u
s
ed
m
eta
-
h
eu
r
is
tic
s
ea
r
ch
ap
p
r
o
ac
h
f
o
r
s
o
l
v
in
g
n
o
n
-
c
o
n
v
ex
an
d
m
u
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
p
r
o
b
lem
s
.
PS
O
was
u
tili
ze
d
in
th
e
ap
p
r
o
ac
h
to
f
in
d
p
ar
am
ete
r
s
o
f
a
s
tr
u
ctu
r
e
-
s
p
ec
if
ied
co
n
tr
o
ll
er
th
at
s
atis
f
y
th
e
co
m
b
in
ed
H2
/H∞
p
er
f
o
r
m
an
ce
in
d
ex
.
T
h
e
s
im
u
latio
n
an
d
e
x
p
er
im
en
tal
f
in
d
in
g
s
d
em
o
n
s
tr
ate
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
’
s
r
esil
ien
ce
wh
en
co
m
p
ar
ed
to
t
h
e
tr
ad
itio
n
al
P
D
co
n
tr
o
ller
,
as
well
as
th
e
s
u
g
g
ested
alg
o
r
ith
m
s
’
ef
f
icien
cy
wh
en
c
o
m
p
ar
e
d
to
th
e
g
en
etic
alg
o
r
ith
m
(
GA
)
.
Sik
an
d
ar
an
d
Pra
s
ad
[
2
1
]
s
u
g
g
ested
co
m
b
in
in
g
r
e
d
u
ce
d
o
r
d
er
m
o
d
elin
g
a
n
d
a
cu
ck
o
o
s
ea
r
ch
alg
o
r
ith
m
to
d
e
v
elo
p
a
p
r
e
-
s
p
ec
if
ie
d
s
tr
u
ctu
r
a
l
co
n
tr
o
ller
f
o
r
b
alan
cin
g
co
n
t
r
o
l
o
f
two
-
wh
ee
led
m
o
b
ile
r
o
b
o
t.
A
lo
wer
o
r
d
e
r
p
r
e
-
s
p
ec
if
ied
s
tr
u
ctu
r
al
c
o
n
tr
o
ll
er
was
cr
ea
ted
in
th
is
s
tu
d
y
,
a
n
d
it
was
f
o
u
n
d
to
b
e
ef
f
icien
t
en
o
u
g
h
t
o
d
ea
l
with
u
n
k
n
o
wn
d
y
n
am
ics.
T
h
e
u
n
d
eter
m
in
ed
p
ar
am
eter
s
o
f
t
h
e
p
r
o
p
o
s
ed
r
ed
u
ce
d
o
r
d
er
co
n
tr
o
ller
s
ar
e
d
eter
m
in
ed
u
s
in
g
th
e
cu
ck
o
o
s
ea
r
ch
m
eth
o
d
.
T
h
e
s
u
g
g
ested
co
n
tr
o
ller
s
’
r
esu
lt
s
s
wa
s
co
m
p
ar
ed
to
th
o
s
e
o
f
GA,
P
SO
,
Sch
u
r
a
n
aly
s
is
,
b
alan
ce
tr
u
n
ca
tio
n
,
m
o
d
el
tr
u
n
ca
tio
n
an
d
tr
a
d
itio
n
al
PD
co
n
tr
o
ller
.
T
h
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
was
f
o
u
n
d
to
h
av
e
s
u
p
er
io
r
p
er
f
o
r
m
a
n
ce
wh
en
co
m
p
ar
ed
t
o
o
th
e
r
co
n
tr
o
ller
s
.
I
n
ter
m
s
o
f
tim
e
r
esp
o
n
s
e
r
e
q
u
ir
em
en
ts
an
d
p
er
f
o
r
m
an
ce
in
d
ices
s
u
ch
as
in
te
g
r
al
o
f
s
q
u
ar
e
er
r
o
r
(
I
SE
)
,
tim
e
-
weig
h
ted
in
te
g
r
al
o
f
ab
s
o
lu
te
er
r
o
r
(
I
T
AE
)
,
in
te
g
r
al
o
f
ab
s
o
lu
te
er
r
o
r
(
I
AE
)
,
t
h
e
p
er
f
o
r
m
an
ce
o
f
h
ig
h
er
a
n
d
lo
wer
co
n
tr
o
ller
s
was a
ls
o
in
v
esti
g
ated
u
s
in
g
a
p
e
r
tu
r
b
ed
two
-
wh
ee
le
d
m
o
b
ile
r
o
b
o
t.
C
o
n
tr
o
llin
g
th
e
eq
u
ilib
r
iu
m
o
f
a
b
y
cy
c
o
r
o
b
o
t
is
a
p
ar
ticu
l
ar
ly
to
u
g
h
task
.
Ma
n
y
b
alan
ce
co
n
tr
o
l
m
eth
o
d
s
f
o
r
two
-
wh
ee
l
ed
b
ic
y
cles
h
av
e
b
ee
n
s
u
g
g
ested
in
clu
d
in
g
n
o
n
-
lin
ea
r
co
n
t
r
o
l,
c
o
m
p
en
s
ato
r
d
esig
n
u
tili
zin
g
th
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o
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lo
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iq
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PD
c
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PID
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Ho
wev
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co
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o
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alg
o
r
ith
m
s
ar
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n
o
t
r
o
b
u
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t;
th
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two
-
wh
ee
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b
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m
o
d
el
ca
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n
o
t
b
ea
r
v
ar
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in
g
weig
h
t
lo
a
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ca
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o
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ea
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g
weig
h
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d
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p
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ate
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o
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itu
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As
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e
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lt,
a
r
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u
s
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co
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o
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m
eth
o
d
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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J
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&
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N:
2722
-
2
5
8
6
A
n
effec
tive
a
p
p
r
o
a
c
h
to
e
n
h
a
n
ce
th
e
b
a
la
n
cin
g
co
n
tr
o
l in
b
yc
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b
o
t u
s
in
g
… (
A
s
w
a
n
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K
u
ma
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a
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45
ap
p
r
o
p
r
iate
f
o
r
th
e
r
ea
l
-
wo
r
l
d
ap
p
licatio
n
s
o
f
th
e
two
-
w
h
ee
led
b
icy
cle
m
o
d
el
f
o
r
th
is
,
co
m
p
o
s
ite
m
eth
o
d
H2
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c
o
n
tr
o
l
is
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r
esen
ted
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wh
ich
is
a
s
o
p
h
is
ticated
a
p
p
r
o
ac
h
f
o
r
co
n
s
tr
u
ctin
g
d
u
r
ab
le
an
d
o
p
tim
u
m
co
n
tr
o
ller
s
f
o
r
s
y
s
tem
s
w
ith
u
n
k
n
o
wn
s
o
u
r
ce
s
.
Ho
wev
er
,
it
is
wid
ely
u
n
d
er
s
to
o
d
th
at
th
e
s
tr
u
ctu
r
e
-
s
p
ec
if
ied
m
ix
ed
H2
/H∞
c
o
n
tr
o
ller
d
esig
n
ty
p
ically
cr
ea
tes
a
co
m
p
li
ca
ted
an
d
n
o
n
-
co
n
v
ex
o
p
tim
iz
atio
n
is
s
u
e
th
at
is
d
if
f
icu
lt
to
ad
d
r
ess
u
s
in
g
tr
ad
itio
n
al
o
p
tim
iz
atio
n
m
eth
o
d
s
.
T
h
e
o
p
tim
izatio
n
ap
p
r
o
ac
h
es u
s
in
g
GA,
PS
O,
an
d
C
u
ck
o
o
s
ea
r
ch
h
a
v
e
b
ee
n
s
u
g
g
ested
to
tack
le
th
is
p
r
o
b
lem
.
T
h
ese
tech
n
iq
u
es
h
av
e
o
f
f
e
r
e
d
to
b
alan
ce
b
u
t
th
e
im
p
r
o
v
em
e
n
t
o
f
b
alan
cin
g
a
ls
o
h
as
th
e
p
o
s
s
ib
ilit
y
in
b
y
cy
co
r
o
b
o
t
ag
ain
s
t
u
n
ce
r
tain
t
y
an
d
ex
ter
n
al
d
is
r
u
p
tio
n
.
T
h
e
r
ea
s
o
n
o
f
u
n
m
o
ld
e
d
d
y
n
a
m
ics,
p
ar
am
eter
ch
an
g
es,
an
d
ex
ter
n
al
d
is
tu
r
b
an
ce
s
co
m
p
lic
ate
s
th
e
s
y
s
tem
an
d
n
ec
ess
itate
s
a
s
tr
o
n
g
co
n
tr
o
lle
r
.
As
a
r
esu
lt,
a
n
o
v
el
ap
p
r
o
a
ch
is
r
eq
u
ir
e
d
to
en
h
a
n
ce
th
e
b
alan
ce
co
n
tr
o
l
in
b
y
cy
co
r
o
b
o
t.
T
h
e
m
o
d
el
o
r
d
e
r
r
ed
u
ctio
n
m
eth
o
d
o
l
o
g
y
h
as
b
ee
n
a
p
p
li
ed
in
o
r
d
er
to
o
b
tain
t
h
e
r
e
d
u
ce
d
o
r
d
er
co
n
tr
o
ller
.
T
h
e
MM
tech
n
iq
u
es
[
2
2
]
,
c
o
n
tin
u
e
d
f
r
ac
tio
n
[
2
3
]
,
m
ix
ed
m
eth
o
d
s
[
2
4
]
–
[
2
8
]
ar
e
tr
ad
itio
n
al
m
eth
o
d
s
test
ed
an
d
f
ailed
.
T
h
e
m
ain
o
b
jectiv
e
o
f
th
is
m
an
u
s
cr
ip
t
is
to
o
b
tain
th
e
ef
f
ec
tiv
e
ly
r
ed
u
ce
d
o
r
d
e
r
co
n
tr
o
l
ler
with
b
y
cy
co
r
o
b
o
t
r
esp
o
n
s
e
an
d
en
h
a
n
ce
t
h
e
b
ala
n
ce
co
n
tr
o
l
o
f
it
u
n
d
er
u
n
ce
r
t
ain
ty
a
n
d
ex
ter
n
al
d
is
tu
r
b
an
ce
s
.
Fo
r
th
is
,
Har
r
is
h
awk
o
p
tim
iz
atio
n
(
HHO)
is
h
av
in
g
b
ee
n
s
elec
ted
d
u
e
to
ag
g
r
ess
iv
e
an
d
s
war
m
b
eh
av
io
r
to
d
esig
n
th
e
co
n
tr
o
ller
ef
f
icien
tly
.
T
h
e
ap
p
r
o
ac
h
r
ep
r
esen
ts
th
e
s
y
s
tem
s
’
m
o
d
el
u
n
ce
r
tain
ty
as
m
u
ltip
licativ
e
u
n
ce
r
tain
ty
,
a
n
d
th
e
s
y
s
tem
is
c
o
n
s
id
er
ed
to
b
e
in
f
lu
e
n
ce
d
b
y
ex
ter
n
al
d
is
tu
r
b
an
ce
s
.
HHO
h
as
b
ee
n
u
tili
ze
d
f
o
r
s
ea
r
ch
p
ar
a
m
eter
s
o
f
an
d
ad
m
is
s
ib
le
s
tr
u
ctu
r
e
-
s
p
ec
if
ied
co
n
tr
o
ller
th
at
m
in
im
izes
th
e
I
SE
wh
ile
b
ein
g
s
u
b
jecte
d
to
r
o
b
u
s
t
s
tab
ilit
y
co
n
s
tr
ain
ts
(
H∞
n
o
r
m
)
ag
ai
n
s
t
m
o
d
el
u
n
ce
r
t
ain
ty
an
d
ex
ter
n
al
d
is
tu
r
b
an
ce
s
.
T
h
e
s
u
g
g
ested
m
eth
o
d
is
u
s
ed
to
r
eg
u
late
th
e
b
alan
ce
o
f
a
b
icy
cle
r
o
b
o
t
eq
u
ip
p
e
d
with
a
g
y
r
o
s
co
p
ic
s
tab
ilizer
,
k
n
o
wn
as
b
y
cy
c
o
r
o
b
o
t.
Usi
n
g
th
e
L
a
g
r
an
g
e
tech
n
i
q
u
e,
a
s
im
p
lifie
d
d
y
n
am
ics
m
o
d
el
o
f
a
b
y
cy
co
r
o
b
o
t
is
co
n
s
tr
u
cted
b
y
d
is
r
eg
ar
d
in
g
f
o
r
ce
s
ca
u
s
ed
b
y
f
o
r
wa
r
d
in
g
m
o
v
em
e
n
t
an
d
s
teer
in
g
.
T
o
ev
alu
ate
th
e
p
er
f
o
r
m
a
n
c
e
p
r
o
p
o
s
ed
s
y
s
tem
,
it
was
co
m
p
ar
e
d
with
o
th
er
tech
n
iq
u
es
av
aila
b
le
in
th
e
liter
atu
r
e.
T
h
e
p
r
o
p
o
s
ed
s
y
s
tem
is
im
p
lem
en
ted
u
s
in
g
MA
T
L
AB
s
o
f
twar
e.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
-
b
ased
co
n
tr
o
ller
will
b
e
ef
f
ec
tiv
ely
en
h
an
ce
d
t
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
b
alan
c
in
g
co
n
tr
o
l
in
b
y
cy
c
o
r
o
b
o
t
w
h
ich
is
an
u
n
s
tab
le
s
y
s
tem
with
u
n
-
m
o
d
ele
d
d
y
n
a
m
ics,
p
ar
am
eter
ch
a
n
g
es,
an
d
ex
ter
n
al
d
is
tu
r
b
a
n
ce
s
as so
u
r
c
es o
f
u
n
ce
r
tain
t
y
.
2.
H
ARRIS
H
AWK
O
P
T
I
M
I
Z
AT
I
O
N
(HHO)
HHO
is
b
ased
o
n
th
e
s
tu
d
ies
o
f
h
awk
b
eh
av
i
o
r
u
s
u
ally
in
t
h
e
p
e
r
io
d
o
f
h
u
n
tin
g
.
T
h
e
s
tu
d
y
h
as
b
ee
n
ca
r
r
ied
o
u
t
b
y
L
o
u
is
L
ef
e
b
v
r
e.
T
h
e
m
ath
em
atica
l
im
p
lem
e
n
t
atio
n
in
th
e
en
g
in
ee
r
in
g
d
esig
n
in
g
f
ield
u
s
in
g
t
h
e
HHO
is
ca
r
r
ied
o
u
t
[
2
9
]
.
T
h
e
b
eh
av
io
r
o
f
h
u
n
tin
g
an
d
c
h
a
s
in
g
p
atter
n
s
f
o
r
th
e
ca
p
tu
r
e
o
f
p
r
ey
in
n
atu
r
e
is
k
n
o
wn
as
a
s
u
r
p
r
is
e
p
o
u
n
ce
.
T
h
e
s
ea
r
ch
in
g
o
f
p
r
ey
is
a
task
d
o
n
e
b
y
th
e
p
r
e
d
ato
r
u
s
in
g
th
e
h
ig
h
est
p
o
in
t
o
f
th
e
ar
ea
s
u
c
h
as
s
tan
d
in
g
o
n
to
p
o
f
tr
ee
s
o
r
f
l
y
in
g
in
th
e
s
k
y
.
T
h
e
attac
k
o
f
th
e
h
awk
o
n
p
r
e
y
is
ca
lled
a
p
o
u
n
ce
.
As
th
e
p
r
ey
is
s
p
o
tte
d
an
o
th
er
m
em
b
er
is
in
f
o
r
m
ed
b
y
v
is
u
al
d
is
p
lay
in
g
o
r
v
o
ca
li
za
tio
n
.
T
h
e
HHO
is
d
iv
id
ed
i
n
to
th
r
e
e
-
p
h
ase
n
a
m
in
g
ex
p
lo
r
atio
n
,
th
e
tr
an
s
itio
n
f
r
o
m
ex
p
lo
r
atio
n
to
e
x
p
lo
itatio
n
,
an
d
th
e
ex
p
lo
itatio
n
p
h
ase.
T
h
e
e
x
p
lo
i
tatio
n
s
tag
e
is
s
ep
ar
ated
in
to
f
o
u
r
s
tag
es
n
am
ely
s
o
f
t
b
esieg
e
,
h
ar
d
b
esieg
e,
s
o
f
t
b
esie
g
e
with
a
d
v
an
ce
d
q
u
ick
d
iv
es,
an
d
h
ar
d
b
esieg
e
with
p
r
o
g
r
ess
iv
e
s
p
ee
d
y
d
iv
es
.
Fig
u
r
e
1
is
s
h
o
win
g
th
e
f
lo
w
c
h
ar
t o
f
HHO
.
2
.
1
.
T
he
ex
plo
ra
t
io
n
ph
a
s
es
T
o
s
tar
t
th
is
p
h
ase,
th
e
Haw
k
r
ea
ch
es
th
e
p
ea
k
o
f
t
r
ee
/p
o
le/t
o
p
o
f
th
e
h
ill
to
tr
ac
e
th
e
p
r
e
y
an
d
also
co
n
s
id
er
th
e
o
t
h
er
o
f
Haw
k
s
p
o
s
itio
n
s
.
T
h
e
s
itu
atio
n
is
q
≥
0
.
5
o
f
b
r
an
ch
o
n
r
a
n
d
o
m
g
ian
t
tr
ee
s
f
o
r
th
e
s
itu
atio
n
o
f
q
≤
0
.
5
.
T
h
e
co
n
d
itio
n
id
s
ar
e
m
o
d
el
ed
as
(
1
)
.
(
+
1
)
=
{
(
)
−
1
|
(
)
−
2
2
(
)
|
≥
0
.
5
(
(
)
−
(
)
−
3
(
+
4
(
)
)
)
≤
0
.
5
(
1
)
W
h
er
e
(
+
1
)
is
th
e
p
o
s
it
io
n
v
ec
to
r
o
f
th
e
h
awk
in
th
e
s
u
cc
ee
d
in
g
iter
atio
n
t
.
(
)
is
th
e
p
r
esen
t
p
o
s
itio
n
v
e
cto
r
o
f
h
awk
s
1
,
2
,
3
,
4
an
d
ar
e
th
e
r
an
d
o
m
n
u
m
b
er
co
n
f
i
d
en
tial
(
0
,
1
)
u
p
g
r
a
d
ed
with
iter
atio
n
.
L
B
is
th
e
lo
wer
b
o
u
n
d
s
,
an
d
UB
is
th
e
u
p
p
er
b
o
u
n
d
s
o
f
n
u
m
b
er
s
(
)
r
ep
r
esen
ts
th
e
ar
b
itra
r
ily
h
awk
r
ep
r
esen
ts
th
e
ar
b
itra
r
y
h
awk
f
r
o
m
th
e
p
r
esen
t p
o
p
u
latio
n
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an
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s
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ag
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ca
tio
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is
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b
tain
ed
u
s
in
g
(
2
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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2
7
2
2
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2
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8
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11
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1
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20
22
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43
-
61
46
(
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2
.
4
.
B
esieg
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cc
urs
B
esieg
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th
e
p
r
o
ce
s
s
at
th
e
t
im
e
o
f
ca
p
tu
r
in
g
p
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t
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d
iv
id
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in
to
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f
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b
esieg
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d
h
a
r
d
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r
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esp
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tiv
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2
.
5
.
So
f
t
b
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T
h
e
p
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as
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g
y
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d
tr
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s
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u
s
in
g
r
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d
o
m
co
n
f
u
s
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ju
m
p
s
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h
e
v
al
u
e
f
o
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escap
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g
en
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u
s
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d
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f
t
h
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alu
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ar
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n
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m
p
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p
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ak
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iv
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eled
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les r
e
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4
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d
(
5
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(
+
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2
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6
.
H
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d
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ar
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th
e
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ten
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p
r
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n
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f
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ally
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ated
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6
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Div
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ep
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T
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last
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r
ap
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g
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e
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o
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t b
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a
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d
g
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n
in
(
9
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
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t
J
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b
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to
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I
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N:
2722
-
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8
6
A
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47
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I
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11
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20
22
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-
61
48
3.
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2
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h
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m
ain
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g
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o
f
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is
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er
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o
r
ith
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s
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e
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r
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t
d
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n
am
ics
i
s
d
er
iv
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u
s
in
g
t
h
e
L
an
g
r
ag
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(
1
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.
{
̇
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−
+
=
(
1
3
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W
h
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d
en
o
tes
th
e
to
tal
k
in
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ep
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e
t
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tal
p
o
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tial
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,
is
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ate,
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al
f
o
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h
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d
r
elatio
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ar
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(
1
4
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-
(
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B
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t d
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e
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g
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14)
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=
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+
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1
7
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h
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an
d
r
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weig
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t
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T
h
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ch
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t
r
an
s
m
is
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io
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a
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d
DC
Mo
to
r
d
y
n
am
ics
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ass
u
m
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to
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e
5
:
1
an
d
th
e
r
elatio
n
o
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tain
e
d
is
g
iv
en
i
n
(
1
9
)
an
d
(
2
0
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.
=
5
(
1
9
)
=
+
+
̇
(
2
0
)
W
h
er
e
in
(
1
9
)
,
r
ep
r
esen
ts
th
e
to
r
q
u
e
c
o
n
s
tan
t o
f
m
o
to
r
an
d
i
n
(
2
0
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is
b
ac
k
e
,
m
,
f.
co
n
s
tan
t,
an
d
ar
e
ar
m
atu
r
e
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esis
t
an
ce
an
d
in
d
u
ctan
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m
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T
h
e
eq
u
ati
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n
(
1
9
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is
s
u
b
s
titu
ted
in
(
1
8
)
a
n
d
lin
ea
r
izin
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1
7
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an
d
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ar
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iu
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h
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̈
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2
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0
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2
1
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̈
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̇
+
̇
−
5
=
0
(
2
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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41
T
h
e
s
tate
s
p
ac
e
in
to
tr
a
n
s
f
er
f
u
n
ctio
n
.
T
h
e
o
b
tain
e
d
tr
an
s
f
er
f
u
n
cti
o
n
o
f
th
e
two
wh
ee
l
ed
m
o
b
ile
r
o
b
o
t is g
iv
e
n
as
(
2
8
)
.
(
)
=
(
)
(
)
=
4887
4
+
683
.
3
3
+
1208
2
+
109700
−
6949
(
2
8
)
T
h
e
o
u
t
p
u
t
lean
an
g
le
an
d
th
e
in
p
u
t
v
o
ltag
e
t
o
th
e
DC
m
o
to
r
th
at
co
n
tr
o
ls
th
e
f
ly
wh
ee
l
c
o
n
tr
o
l
ax
is
.
Ass
u
m
in
g
th
e
f
o
llo
win
g
two
ca
s
es
:
i)
C
ase
-
1:
t
he
ad
d
itio
n
al
1
0
K
g
lo
a
d
a
n
d
d
ec
r
ea
s
e
th
e
s
p
ee
d
o
f
th
e
f
ly
wh
ee
l
u
p
-
to
1
4
7
r
a
d
/s
ec
.
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
f
r
o
m
th
is
co
n
d
itio
n
is
as
(
2
9
)
;
ii)
C
ase
-
2
:
i
n
th
is
ca
s
e
,
m
o
r
e
1
0
Kg
lo
a
d
is
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d
ed
s
p
ee
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o
f
f
ly
wh
ee
l is in
cr
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s
ed
to
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6
7
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a
d
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.
th
e
tr
an
s
f
er
f
u
n
ctio
n
is
as
(
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0
)
.
1
(
)
=
3784
4
+
683
.
3
3
+
1162
2
+
7
8
2
90
−
6857
(
2
9
)
2
(
)
=
4299
4
+
683
.
3
3
+
1197
2
+
102300
−
6857
(
3
0
)
B
y
cy
co
r
o
b
o
t
in
clu
d
in
g
b
o
th
th
e
s
p
ec
ial
ca
s
e
o
f
t
h
e
s
y
s
tem
r
ep
r
esen
ts
in
s
tab
ilit
y
in
Fig
u
r
e
3
.
T
h
e
b
alan
cin
g
c
o
n
tr
o
l
o
f
t
h
e
s
y
s
tem
is
g
iv
en
b
y
T
h
an
h
an
d
Par
n
ich
k
u
n
in
[
2
0
]
with
a
co
n
tr
o
ll
er
b
ased
o
n
p
a
r
ticle
s
war
m
o
p
tim
izatio
n
u
s
in
g
s
p
e
cif
ically
m
ix
ed
H2
/H∞
co
n
tr
o
ller
.
T
h
e
tr
a
n
s
f
er
f
u
n
ctio
n
o
f
t
h
e
co
n
tr
o
ller
is
as
(
3
1
)
.
(
∞
)
(
)
=
1275
5
+
8
.
695
×
1
0
5
4
+
5
.
151
×
1
0
5
3
+
1
.
359
×
1
0
8
2
+
2
.
435
×
1
0
7
+
1
.
091
×
1
0
6
6
+
715
.
7
5
+
2
.
355
×
1
0
4
4
+
2
.
789
×
1
0
5
3
+
3
.
802
×
1
0
6
2
+
6
.
519
×
1
0
5
+
2
.
872
×
1
0
4
(
3
1
)
4.
DE
S
I
G
N
O
F
F
I
RST
O
RD
E
R
CO
NT
RO
L
L
E
R
US
I
NG
HHO
T
E
CH
NIQU
E
T
h
e
s
tr
u
ctu
r
e
o
f
f
ir
s
t
o
r
d
er
co
n
tr
o
ller
is
o
b
tain
ed
u
s
in
g
th
e
HHO
b
y
m
in
im
izin
g
th
e
I
SE.
T
h
e
u
n
k
n
o
wn
r
e
d
u
ce
d
o
r
d
e
r
m
o
d
el
o
f
f
ir
s
t o
r
d
er
is
r
ep
r
esen
ted
as
(
3
2
)
.
−
(
)
=
1
1
+
1
(
3
2
)
T
h
e
u
n
k
n
o
wn
v
alu
e
o
f
th
e
p
r
o
p
o
s
ed
f
ir
s
t
o
r
d
er
co
n
tr
o
ll
er
is
o
p
tim
ized
u
s
in
g
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e
HHO.
Evaluation Warning : The document was created with Spire.PDF for Python.