I
AE
S In
t
er
na
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io
na
l J
o
urna
l o
f
Ro
bo
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ics a
nd
Aut
o
m
a
t
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n
(
I
J
RA)
Vo
l.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
,
p
p
.
5
9
7
~
6
0
6
I
SS
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2722
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1
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606
597
J
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r
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Perf
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rma
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a
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fraction
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PID
co
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for a
2
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fle
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Ali H
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r
2
0
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2
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ev
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J
u
l 2
9
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g
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lex
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in
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ro
b
o
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m
a
n
i
p
u
lat
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rs (F
JM)
e
x
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ig
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li
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a
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ts,
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a
k
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ir
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ro
p
o
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c
ti
o
n
a
l
o
r
d
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r
P
ID
(F
OPID)
c
a
sc
a
d
e
c
o
n
tro
l
stra
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e
g
y
fo
r
a
2
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F
F
JM.
Th
e
c
o
n
tr
o
ll
e
r
p
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rfo
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a
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c
e
is
c
o
m
p
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re
d
with
th
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t
o
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a
slid
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g
m
o
d
e
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o
n
tr
o
ll
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r
(
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M
C)
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n
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n
ti
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a
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ti
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g
c
o
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d
it
io
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s.
Bo
t
h
c
o
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rs’
p
a
ra
m
e
ters
a
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o
p
ti
m
a
ll
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e
d
u
sin
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th
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p
a
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o
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iza
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(
P
S
O)
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m
to
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re
a
fa
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e
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n
.
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e
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sists
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m
in
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3
5
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F
O
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1
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f
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1
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wh
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s
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a
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d
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ra
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a
ti
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n
.
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se
fin
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g
s
il
lu
stra
te
t
h
e
trad
e
-
o
ffs
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e
twe
e
n
e
n
e
rg
y
e
fficie
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c
y
a
n
d
r
o
b
u
st
p
re
c
isio
n
i
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F
JM
c
o
n
tro
l
.
K
ey
w
o
r
d
s
:
Fra
ctio
n
al
o
r
d
er
PID
Flex
ib
le
jo
in
t m
an
ip
u
lato
r
No
n
lin
ea
r
r
o
b
o
tic
s
y
s
tem
s
Par
ticle
s
war
m
o
p
tim
izatio
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Sli
d
in
g
m
o
d
e
c
o
n
tr
o
l
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
:
Ah
m
ed
Alk
am
ac
h
i
Me
ch
atr
o
n
ics E
n
g
i
n
ee
r
in
g
De
p
ar
tm
en
t,
Al
-
Kh
war
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o
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Un
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v
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Al
-
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iy
a,
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ag
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r
aq
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m
ed
7
8
@
k
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u
.
u
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g
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ad
.
ed
u
.
i
q
1.
I
NT
RO
D
UCT
I
O
N
Flex
ib
le
jo
in
t
m
an
ip
u
lato
r
s
(
FJ
Ms)
h
av
e
attr
ac
ted
co
n
s
id
er
ab
le
in
ter
est
d
u
e
to
th
eir
lig
h
t
weig
h
t
s
tr
u
ctu
r
e,
lo
w
en
er
g
y
c
o
n
s
u
m
p
tio
n
,
an
d
s
u
itab
ilit
y
f
o
r
h
ig
h
-
s
p
ee
d
au
to
m
ated
ap
p
licat
io
n
s
.
Ho
wev
er
,
th
e
p
r
esen
ce
o
f
f
lex
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le
jo
in
t
in
tr
o
d
u
ce
s
s
tr
o
n
g
n
o
n
lin
ea
r
ities
,
co
u
p
lin
g
ef
f
ec
ts
,
a
n
d
c
o
m
p
le
x
d
y
n
am
ics,
m
ak
i
n
g
co
n
tr
o
ller
d
esig
n
ch
alle
n
g
in
g
[
1
]
,
[
2
]
.
FJ
Ms
ar
e
g
r
o
win
g
ly
em
p
lo
y
ed
in
lig
h
t
weig
h
t
in
d
u
s
tr
ial
r
o
b
o
tic
a
r
m
s
,
p
ar
ticip
ated
r
o
b
o
ts
,
an
d
a
u
to
m
ated
m
an
u
f
ac
tu
r
in
g
an
d
ass
em
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ly
s
y
s
tem
s
th
at
r
eq
u
ir
e
l
o
w
weig
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t,
en
er
g
y
ef
f
icien
cy
,
an
d
s
af
e
in
ter
ac
tio
n
.
R
ec
en
t
s
tu
d
ies
h
av
e
p
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o
p
o
s
ed
ad
v
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ce
d
v
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s
u
p
p
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e
s
s
io
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d
tr
ajec
to
r
y
tr
ac
k
in
g
tech
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iq
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es
f
o
r
FJ
M
t
o
im
p
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v
e
th
ei
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s
tab
ilit
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an
d
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f
o
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m
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n
d
er
n
o
n
lin
ea
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d
y
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am
ics,
d
is
tu
r
b
an
ce
s
,
an
d
u
n
ce
r
tai
n
ties
[
3
]
,
[
4
]
.
C
lass
ical
PID
b
ased
co
n
tr
o
ller
s
ar
e
wid
ely
u
s
ed
d
u
e
to
th
eir
s
im
p
licity
an
d
ea
s
e
o
f
im
p
le
m
en
tatio
n
,
an
d
th
ey
h
a
v
e
b
e
en
ap
p
lied
to
d
if
f
er
en
t
r
o
b
o
tic
s
y
s
tem
s
[
5
]
,
[
6
]
.
Nev
er
th
eless
,
th
eir
p
er
f
o
r
m
an
ce
is
o
f
ten
d
eg
r
ad
ed
wh
en
d
e
alin
g
with
n
o
n
lin
ea
r
s
y
s
tem
s
s
u
ch
as
FJ
Ms.
T
o
o
v
er
co
m
e
t
h
ese
lim
itatio
n
s
,
r
esear
ch
er
s
d
ev
elo
p
e
d
ad
v
a
n
ce
d
co
n
tr
o
l
tec
h
n
iq
u
es.
Neu
r
al
n
etwo
r
k
b
ased
a
n
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
.
3
,
Sep
tem
b
er
20
2
6
:
5
9
7
-
6
0
6
598
ad
ap
tiv
e
co
n
tr
o
l
m
eth
o
d
s
h
a
v
e
b
ee
n
em
p
l
o
y
ed
to
esti
m
ate
s
y
s
tem
u
n
ce
r
tain
ties
an
d
im
p
r
o
v
e
tr
ac
k
in
g
p
er
f
o
r
m
an
ce
[
7
]
–
[
9
]
.
Ad
ap
tiv
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f
u
zz
y
an
d
lea
r
n
in
g
b
ased
co
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tr
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f
o
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m
o
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n
ce
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tain
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[
1
0
]
,
[
1
1
]
.
M
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ased
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L
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m
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s
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also
b
ee
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in
t
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d
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d
in
[
1
2
]
to
s
im
p
lif
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n
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n
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s
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d
y
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ics.
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ased
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id
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ed
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o
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p
o
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tan
t
d
ir
e
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n
,
wh
er
e
it
h
as
b
ee
n
u
s
ed
f
o
r
s
tate
f
ee
d
b
ac
k
co
n
tr
o
l
an
d
o
n
lin
e
tu
n
i
n
g
o
f
co
n
tr
o
ller
p
a
r
am
eter
s
[
1
3
]
,
[
1
4
]
.
I
n
ad
d
itio
n
,
s
lid
in
g
m
o
d
e
co
n
tr
o
l
(
SMC
)
h
as
b
ee
n
wid
ely
em
p
lo
y
ed
to
co
n
tr
o
l
FJ
Ms
s
y
s
tem
s
d
u
e
to
it
s
r
o
b
u
s
tn
ess
ag
ain
s
t
d
is
tu
r
b
an
ce
s
an
d
p
ar
am
ete
r
v
ar
iatio
n
s
.
T
o
ad
d
r
ess
s
o
m
e
o
f
th
e
p
r
o
b
lem
s
ass
o
ciate
d
with
class
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SM
C
an
d
f
u
r
th
er
im
p
r
o
v
e
its
p
er
f
o
r
m
an
ce
,
h
y
b
r
id
a
p
p
r
o
ac
h
es
co
m
b
in
in
g
SMC
with
f
u
zz
y
lo
g
ic
o
r
o
b
s
er
v
er
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
in
[
1
5
]
–
[
1
7
]
.
Dis
tu
r
b
a
n
ce
o
b
s
er
v
er
b
ased
an
d
o
b
s
er
v
e
r
ass
is
ted
s
lid
in
g
m
o
d
e
ap
p
r
o
ac
h
es
h
a
v
e
r
ec
en
tly
ap
p
lied
to
FJ
M
an
d
s
h
o
wn
an
i
m
p
r
o
v
e
d
r
o
b
u
s
tn
ess
an
d
r
ed
u
ce
d
s
en
s
itiv
ity
to
u
n
ce
r
tain
ties
[
1
8
]
,
[
1
9
]
.
Alo
n
g
s
id
e
co
n
tr
o
ller
d
esig
n
,
p
ar
am
eter
tu
n
in
g
r
em
ain
s
an
im
p
o
r
tan
t
p
ar
t
o
f
th
e
d
esig
n
ch
allen
g
e.
Op
tim
izatio
n
alg
o
r
ith
m
s
s
u
ch
as
p
ar
ticle
s
war
m
o
p
tim
izati
o
n
(
PS
O)
an
d
g
e
n
etic
alg
o
r
ith
m
s
(
GA)
h
av
e
b
ee
n
wid
ely
u
s
ed
to
d
eter
m
in
e
o
p
tim
al
co
n
tr
o
ller
p
ar
am
eter
s
in
co
m
p
lex
n
o
n
lin
ea
r
s
y
s
tem
s
[
2
0
]
,
[
2
1
]
.
R
ec
en
t
s
tu
d
ies
p
r
o
p
o
s
ed
a
co
n
tr
o
ller
th
at
co
m
b
in
es
PS
O
wi
th
ad
v
an
ce
d
n
o
n
lin
ea
r
co
n
tr
o
l
tech
n
iq
u
es
to
s
u
p
p
r
ess
v
ib
r
atio
n
a
n
d
en
h
an
ce
tr
ajec
to
r
y
tr
ac
k
in
g
ch
ar
ac
te
r
is
tics
[
3
]
,
[
2
2
]
.
Mo
s
t
ex
is
tin
g
s
tu
d
ies
f
o
c
u
s
o
n
s
in
g
le
co
n
tr
o
ller
,
with
o
u
t
p
r
o
v
id
in
g
f
air
co
m
p
ar
ativ
e
ev
alu
atio
n
s
u
n
d
er
id
e
n
tical
tu
n
in
g
,
o
p
er
ati
n
g
co
n
d
itio
n
s
,
an
d
test
s
ce
n
ar
io
s
.
I
n
co
n
tr
ast,
th
is
p
ap
er
p
r
e
s
en
ts
a
s
y
s
tem
atic
co
m
p
ar
ativ
e
s
tu
d
y
b
etwe
en
a
ca
s
ca
d
ed
FOPID
co
n
tr
o
ller
a
n
d
SMC
f
o
r
a
2
DOF
f
lex
ib
le
jo
in
t
m
an
ip
u
lato
r
.
B
o
th
co
n
tr
o
ller
s
ar
e
im
p
lem
e
n
ted
u
s
in
g
s
im
ilar
ca
s
ca
d
e
f
r
a
m
ewo
r
k
a
n
d
tu
n
ed
u
s
in
g
PS
O
with
s
am
e
s
ettin
g
s
an
d
co
n
d
itio
n
s
to
en
s
u
r
e
a
f
ai
r
co
m
p
ar
is
o
n
.
T
h
e
m
ain
co
n
tr
ib
u
tio
n
o
f
th
is
wo
r
k
is
to
ev
al
u
ate
th
e
tr
ad
e
-
o
f
f
s
b
etwe
en
tr
ac
k
in
g
p
er
f
o
r
m
an
ce
,
r
o
b
u
s
tn
ess
,
an
d
co
n
tr
o
l
co
n
s
u
m
ed
e
n
er
g
y
.
Simu
latio
n
r
esu
lts
co
llected
u
n
d
e
r
n
o
m
in
al
c
o
n
d
itio
n
s
,
ex
ter
n
al
d
is
tu
r
b
an
ce
s
,
an
d
v
ar
ia
b
le
p
ay
lo
ad
s
r
ev
ea
l
th
at
FOPID
p
r
o
v
id
es
s
u
p
er
i
o
r
tr
ac
k
in
g
ac
cu
r
ac
y
an
d
r
o
b
u
s
tn
ess
,
wh
er
ea
s
SMC
o
f
f
er
s
s
m
o
o
th
er
ac
tu
at
o
r
r
esp
o
n
s
es
with
lo
wer
co
n
tr
o
l
en
er
g
y
.
T
h
ese
r
esu
lts
p
r
o
v
id
e
p
r
ac
tical
g
u
id
e
to
s
elec
t
s
u
it
ab
le
co
n
tr
o
l
s
ch
em
e
an
d
d
ete
r
m
in
e
th
e
r
eq
u
ir
e
d
ac
tu
ato
r
s
en
er
g
y
r
atin
g
to
b
e
u
s
ed
in
f
lex
ib
le
r
o
b
o
tic
s
y
s
tem
s
.
2.
M
AT
H
E
M
AT
I
CA
L
M
O
D
E
L
I
NG
O
F
2
DO
F
F
J
M
T
h
e
d
y
n
am
ic
eq
u
atio
n
s
o
f
th
e
2
DOF
f
lex
ib
le
jo
in
t
m
an
ip
u
lato
r
,
as
s
h
o
wn
in
Fig
u
r
e
1
,
wer
e
o
b
tain
ed
b
ased
o
n
th
e
r
o
tatio
n
al
m
o
tio
n
f
o
r
ea
c
h
lin
k
.
Du
e
t
o
th
e
f
lex
ib
le
jo
i
n
t
s
tr
u
ctu
r
e,
th
er
e
ar
e
two
s
ep
a
r
ate
d
y
n
am
ic
e
q
u
atio
n
s
f
o
r
ea
ch
j
o
in
t:
o
n
e
f
o
r
th
e
lin
k
s
id
e
an
d
t
h
e
o
th
er
f
o
r
th
e
m
o
to
r
s
id
e.
T
h
e
v
ar
ia
b
les
u
s
ed
in
th
e
s
y
s
tem
ar
e:
1
,
2
:
lin
k
an
g
les,
1
,
2
:
m
o
to
r
an
g
les,
an
d
1
,
2
:
m
o
to
r
in
p
u
t
to
r
q
u
es.
T
h
e
o
th
er
s
y
s
tem
p
ar
am
eter
s
u
s
ed
in
t
h
e
s
tu
d
y
a
r
e
g
iv
en
i
n
T
ab
le
1
,
ass
u
m
in
g
th
at
b
o
th
lin
k
s
ar
e
id
en
tical.
I
n
r
ea
l
2
DOF
r
o
b
o
t
s
y
s
tem
s
,
th
e
m
o
v
em
e
n
t
o
f
o
n
e
jo
i
n
t
af
f
ec
ts
th
e
o
th
er
.
T
o
in
clu
d
e
th
i
s
ef
f
ec
t
in
th
e
m
o
d
el,
t
h
e
g
r
a
v
ity
ter
m
s
ar
e
ar
r
an
g
e
d
as
(
1
)
:
1
=
1
1
[
s
in
(
1
)
+
s
in
(
1
+
2
)
]
2
=
2
2
s
in
(
1
+
2
)
(
1
)
wh
er
e
r
ep
r
esen
ts
th
e
co
u
p
lin
g
co
ef
f
icien
t.
T
h
en
,
th
e
lin
k
s
id
e
d
y
n
am
ics ca
n
b
e
ex
p
r
ess
ed
a
s
(
2
)
.
̈
1
=
−
1
1
1
−
1
1
(
1
−
1
)
+
1
1
1
+
1
̇
2
̈
2
=
−
1
2
2
−
2
2
(
2
−
2
)
+
1
2
2
+
2
̇
1
(
2
)
On
th
e
o
th
er
s
id
e
is
th
e
m
o
to
r
s
id
e
d
y
n
am
ics wh
ich
ca
n
b
e
d
eter
m
in
ed
u
s
in
g
(
3
)
.
̈
1
=
1
1
(
1
−
1
)
+
1
1
1
̈
2
=
2
2
(
2
−
2
)
+
1
2
2
(
3
)
A
f
ee
d
f
o
r
wa
r
d
g
r
av
ity
b
ala
n
ce
r
is
d
esig
n
ed
in
t
h
e
s
y
s
tem
to
r
ed
u
ce
th
e
ef
f
ec
t
o
f
g
r
av
ity
an
d
im
p
r
o
v
e
co
n
tr
o
l
p
er
f
o
r
m
a
n
ce
.
T
h
an
k
s
to
th
is
s
tr
u
ctu
r
e,
th
e
co
n
tr
o
ller
is
en
ab
led
to
f
o
c
u
s
o
n
ly
o
n
th
e
tr
ac
k
in
g
er
r
o
r
.
Gr
a
v
ity
co
m
p
en
s
ato
r
c
o
n
tr
o
l in
p
u
ts
ar
e
d
ef
in
e
d
as
(
4
)
:
1
=
1
(
1
−
1
)
+
1
2
=
2
(
2
−
2
)
+
2
(
4
)
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
P
erfo
r
ma
n
ce
a
s
s
ess
men
t o
f fr
a
ctio
n
a
l o
r
d
er P
I
D
c
o
n
tr
o
l fo
r
a
2
DOF
flexib
le
jo
in
t
…
(
A
h
med
A
lka
ma
ch
i
)
599
I
n
th
is
ap
p
r
o
ac
h
,
th
e
f
i
r
s
t
ter
m
co
m
p
en
s
ates
f
o
r
th
e
f
lex
i
b
le
jo
in
t
ef
f
ec
t,
wh
ile
th
e
s
e
co
n
d
ter
m
co
m
p
en
s
ates
f
o
r
th
e
g
r
av
ity
ef
f
ec
t.
T
h
e
r
esu
ltin
g
m
o
d
el
t
ak
es
in
to
ac
co
u
n
t
f
lex
ib
le
jo
in
t
d
y
n
a
m
ics
an
d
co
u
p
lin
g
b
etwe
en
lin
k
s
.
I
n
th
is
way
,
it
o
f
f
er
s
a
m
o
r
e
r
ea
lis
tic
s
tr
u
ctu
r
e
in
ter
m
s
o
f
b
o
t
h
co
n
tr
o
l
d
esig
n
a
n
d
s
y
s
tem
an
aly
s
is
.
I
n
p
a
r
ticu
lar
,
th
e
in
clu
s
io
n
o
f
g
r
av
ity
co
u
p
li
n
g
in
th
e
m
o
d
el
p
r
o
v
id
es
a
s
ig
n
if
ican
t
ad
v
an
tag
e
in
ev
alu
atin
g
t
h
e
p
er
f
o
r
m
a
n
ce
o
f
m
u
ltiv
ar
iate
c
o
n
tr
o
l a
l
g
o
r
it
h
m
s
.
Fig
u
r
e
1
.
T
wo
lin
k
s
f
lex
ib
le
j
o
in
t m
an
ip
u
lato
r
[
2
3
]
T
ab
le
1
.
Flex
ib
le
jo
in
t
m
an
ip
u
lato
r
p
ar
am
eter
s
[
2
4
]
P
a
r
a
me
t
e
r
D
e
scri
p
t
i
o
n
V
a
l
u
e
1
,
2
Li
n
k
mass
0
.
2
5
K
g
1
,
2
Li
n
k
l
e
n
g
t
h
0
.
3
5
m
1
,
2
Jo
i
n
t
sp
r
i
n
g
c
o
n
s
t
a
n
t
2
0
N
·
m/
r
a
d
1
,
2
Li
n
k
mo
m
e
n
t
o
f
i
n
e
r
t
i
a
0
.
2
K
g
.
m
2
1
,
2
M
o
t
o
r
mo
me
n
t
o
f
i
n
e
r
t
i
a
1
K
g
.
m
2
G
r
a
v
i
t
a
t
i
o
n
a
l
a
c
c
e
l
e
r
a
t
i
o
n
9
.
8
m
/
s
2
G
r
a
v
i
t
a
t
i
o
n
a
l
c
o
e
f
f
i
c
i
e
n
t
0
.
3
N
·
m/
K
g
1
,
2
V
e
l
o
c
i
t
y
c
o
u
p
l
i
n
g
c
o
e
f
f
i
c
i
e
n
t
0
.
0
5
N
·
m·
s./
r
a
d
3.
CO
NT
RO
L
L
E
R
DE
SI
G
N
3
.
1
.
F
O
P
I
D
co
ntr
o
ller
des
ig
n
T
h
e
FOPID
co
n
tr
o
ller
s
h
av
e
m
o
r
e
ad
j
u
s
tab
le
p
ar
am
eter
s
co
m
p
ar
e
d
to
class
ical
PID
co
n
tr
o
ller
s
.
T
h
ey
o
f
f
e
r
a
m
o
r
e
f
lex
i
b
le
co
n
tr
o
l
p
er
f
o
r
m
a
n
ce
,
esp
ec
ially
in
n
o
n
lin
ea
r
a
n
d
co
u
p
led
s
y
s
tem
s
s
u
ch
as
F
J
M
s
y
s
tem
s
,
b
ec
au
s
e
th
e
o
p
er
at
o
r
s
(
,
)
p
r
o
v
id
e
a
d
d
itio
n
al
d
eg
r
e
es
o
f
f
r
ee
d
o
m
h
elp
in
g
in
ca
n
ce
l
o
u
t
f
lex
ib
le
jo
in
t
elasticiti
e
s
.
I
n
th
is
s
ec
tio
n
,
th
e
d
esig
n
d
etails
o
f
FOPID
ar
e
d
is
cu
s
s
ed
.
T
h
e
o
u
tp
u
t
o
f
co
n
tr
o
ller
b
ased
o
n
th
e
d
if
f
er
e
n
ce
b
etwe
en
th
e
d
es
ir
ed
o
u
tp
u
t a
n
d
ac
tu
al
o
u
t
p
u
t.
T
h
e
tim
e
d
o
m
ai
n
r
ep
r
esen
tatio
n
o
f
FOPID
is
(
5
)
,
=
(
)
+
−
(
)
−
+
(
)
(
5
)
wh
er
e
,
,
an
d
d
en
o
te
th
e
p
r
o
p
o
r
tio
n
al
g
ain
,
in
teg
r
al
g
ain
an
d
d
er
iv
ativ
e
g
ain
r
esp
ec
tiv
ely
.
r
ef
er
s
to
th
e
f
r
ac
tio
n
al
in
te
g
r
al
s
ca
lar
a
n
d
r
ef
er
s
to
th
e
f
r
ac
tio
n
al
d
e
r
iv
ativ
e
s
ca
lar
.
(
)
r
ep
r
esen
ts
th
e
er
r
o
r
s
ig
n
al.
T
h
e
p
r
o
p
o
s
ed
c
o
n
tr
o
l
a
r
ch
ite
ctu
r
e
co
n
s
is
ts
o
f
two
lay
er
s
:
I
n
n
er
lo
o
p
wh
ic
h
will
b
e
r
es
p
o
n
s
ib
le
o
f
co
n
tr
o
llin
g
m
o
to
r
an
g
les,
wh
i
le
th
e
o
u
ter
l
o
o
p
c
o
n
tr
o
ls
lin
k
an
g
les.
T
h
u
s
,
th
e
s
y
s
tem
in
clu
d
es
f
o
u
r
FOPID
co
n
tr
o
ller
s
in
to
tal.
T
h
e
p
u
r
p
o
s
e
o
f
th
e
in
n
er
lo
o
p
is
to
en
s
u
r
e
th
at
th
e
m
o
to
r
an
g
les
f
o
llo
w
th
e
r
ef
er
en
ce
v
alu
es
q
u
ick
ly
a
n
d
s
tead
ily
.
I
n
th
is
lo
o
p
,
t
h
e
er
r
o
r
s
ig
n
al
is
d
ef
in
ed
as
=
,
−
.
T
h
e
in
n
er
lo
o
p
i
s
cr
itical
to
s
u
p
p
r
ess
th
e
f
ast
d
y
n
am
ics
o
f
th
e
s
y
s
tem
an
d
r
ed
u
ce
o
s
cillatio
n
s
ca
u
s
ed
b
y
elasticity
.
T
h
e
p
u
r
p
o
s
e
o
f
th
e
o
u
ter
lo
o
p
is
to
b
r
i
n
g
th
e
lin
k
an
g
les to
th
e
d
esire
d
r
ef
er
en
ce
v
alu
es.
T
h
e
o
u
t
p
u
t p
r
o
d
u
ce
d
in
t
h
is
lo
o
p
is
th
e
r
ef
er
e
n
ce
m
o
to
r
a
n
g
les
f
o
r
th
e
in
n
er
lo
o
p
,
an
d
th
e
er
r
o
r
s
ig
n
al
in
t
h
is
lo
o
p
is
d
ef
in
ed
as
=
−
.
T
h
e
d
ec
en
tr
alize
d
ca
s
ca
d
e
c
o
n
tr
o
l
s
tr
u
ctu
r
e
ca
n
b
e
s
ca
led
ef
f
ec
tiv
ely
to
m
u
lti
DOF
in
d
u
s
tr
ial
r
o
b
o
ts
an
d
co
llab
o
r
ativ
e
s
y
s
tem
s
(
c
o
b
o
ts
)
.
Sp
litt
in
g
co
n
tr
o
l
ac
tio
n
s
in
t
o
an
in
n
er
lo
o
p
an
d
an
o
u
ter
lo
o
p
,
lead
s
to
th
e
p
o
s
s
ib
ilit
y
o
f
ap
p
ly
in
g
th
e
c
o
n
tr
o
ller
i
n
d
ep
e
n
d
en
tly
o
n
a
jo
in
t
-
by
-
j
o
in
t
b
asis
.
I
n
o
r
d
er
to
in
cr
ea
s
e
co
n
tr
o
l
p
er
f
o
r
m
an
ce
,
t
h
e
FOPID
co
n
t
r
o
ller
s
tr
u
ctu
r
e
is
u
s
ed
to
g
eth
e
r
with
th
e
g
r
av
ity
s
tab
ilizer
.
I
n
th
is
ca
s
e,
th
e
to
tal
co
n
tr
o
l in
p
u
t is ex
p
r
ess
ed
as
(
6
)
:
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
.
3
,
Sep
tem
b
er
20
2
6
:
5
9
7
-
6
0
6
600
=
,
+
,
,
=
1
,
2
(
6
)
wh
er
e
,
is
th
e
FOPID
co
n
tr
o
ller
o
u
tp
u
t,
a
n
d
,
is
th
e
g
r
av
ity
b
alan
cin
g
ter
m
.
Fo
llo
win
g
th
is
ap
p
r
o
ac
h
,
th
e
c
o
n
tr
o
ller
f
o
cu
s
es
o
n
ly
o
n
th
e
tr
ac
k
in
g
e
r
r
o
r
with
o
u
t
h
a
v
in
g
to
c
o
m
p
e
n
s
ate
f
o
r
th
e
e
f
f
ec
t
o
f
g
r
av
ity
.
T
h
is
p
r
o
v
id
es
a
s
ig
n
if
ican
t
p
er
f
o
r
m
an
ce
in
cr
ea
s
e,
esp
ec
ially
in
s
y
s
tem
s
wh
er
e
n
o
n
lin
ea
r
ef
f
ec
ts
d
o
m
in
ate,
wh
ile
e
n
s
u
r
in
g
s
m
o
o
th
co
n
tr
o
l sig
n
als th
at
p
r
e
v
en
t a
ctu
ato
r
th
er
m
al
s
tr
ess
.
3
.
2
.
L
y
a
pu
no
v
s
t
a
bil
it
y
a
na
ly
s
is
o
f
F
O
P
I
D
co
ntr
o
ller
I
n
th
is
s
ec
tio
n
,
th
e
s
tab
ilit
y
o
f
th
e
clo
s
ed
lo
o
p
s
y
s
tem
u
n
d
er
th
e
FOPID
co
n
t
r
o
ller
is
a
n
aly
ze
d
u
s
in
g
L
y
ap
u
n
o
v
a
p
p
r
o
ac
h
.
C
o
n
s
id
er
th
e
f
o
llo
win
g
p
o
s
itiv
e
d
ef
i
n
ite
L
y
ap
u
n
o
v
f
u
n
ctio
n
:
=
1
2
2
(
7
)
B
y
tak
in
g
th
e
f
ir
s
t d
e
r
iv
ativ
e
o
f
(
7
)
:
̇
=
̇
(
8
)
T
h
e
FOPID
co
n
tr
o
ller
g
e
n
er
at
es a
co
n
tr
o
l a
ctio
n
b
ased
o
n
p
r
o
p
o
r
tio
n
al,
in
teg
r
al,
an
d
d
er
iv
ativ
e
ter
m
s
:
=
,
+
,
−
+
,
(
9
)
T
h
is
co
n
tr
o
l
law
ac
ts
to
r
ed
u
c
e
b
o
th
t
h
e
er
r
o
r
an
d
its
r
ate
o
f
ch
an
g
e.
W
ith
p
r
o
p
er
ly
tu
n
ed
co
n
tr
o
lle
r
g
ain
s
,
th
e
p
r
o
p
o
r
tio
n
al
ter
m
r
ed
u
ce
s
th
e
in
s
tan
tan
eo
u
s
er
r
o
r
wh
ile
th
e
f
r
ac
tio
n
al
in
teg
r
al
an
d
th
e
f
r
ac
tio
n
al
d
er
iv
ativ
e
ter
m
elim
in
ates
s
tead
y
s
tate
er
r
o
r
an
d
p
r
o
v
id
es
d
am
p
in
g
r
esp
ec
tiv
el
y
.
I
n
th
is
co
n
tex
t,
th
e
c
o
n
tr
o
l
in
p
u
t
en
s
u
r
es
th
at
̇
<
0
,
wh
ich
im
p
lies
̇
<
0
.
T
h
er
e
f
o
r
e,
th
e
e
r
r
o
r
d
y
n
am
ics
ar
e
s
tab
le
in
th
e
s
en
s
e
o
f
L
y
ap
u
n
o
v
,
a
n
d
th
e
tr
ac
k
in
g
er
r
o
r
co
n
v
er
g
es to
war
d
ze
r
o
.
3
.
3
.
Sli
di
ng
m
o
de
co
ntr
o
ller
des
ig
n
Sli
d
in
g
m
o
d
e
co
n
tr
o
ller
(
SM
C
)
with
b
o
u
n
d
ar
y
lay
er
is
em
p
lo
y
ed
as
a
co
m
p
ar
is
o
n
b
e
n
ch
m
ar
k
f
o
r
m
o
r
e
co
m
p
r
eh
e
n
s
iv
e
ev
alu
ati
o
n
o
f
th
e
p
r
o
p
o
s
ed
ca
s
ca
d
ed
FOPID
co
n
tr
o
ller
.
Similar
to
t
h
e
FOPID
d
esig
n
,
a
ca
s
ca
d
e
co
n
tr
o
l
ar
c
h
itectu
r
e
is
em
p
lo
y
e
d
wh
e
r
e
th
e
o
u
ter
l
o
o
p
is
r
esp
o
n
s
ib
le
f
o
r
lin
k
p
o
s
itio
n
tr
ac
k
in
g
.
T
h
e
s
lid
in
g
s
u
r
f
ac
e
is
d
ef
in
e
d
as
(
1
0
)
:
1
=
2
+
1
(
1
0
)
wh
er
e
1
=
1
,
−
1
,
2
=
̇
1
,
−
̇
1
,
an
d
>
0
is
th
e
s
lid
in
g
s
u
r
f
ac
e
g
ain
.
A
v
ir
tu
al
ac
ce
l
er
atio
n
in
p
u
t
1
is
d
esig
n
ed
as
(
1
1
)
:
1
=
̈
1
,
−
2
−
1
,
s
at
(
1
1
,
)
(
1
1
)
Usi
n
g
th
e
lin
k
s
id
e
d
y
n
am
ics,
th
e
d
esire
d
m
o
t
o
r
an
g
le
1
,
is
o
b
tain
ed
as
(
1
2
)
:
1
,
=
1
+
1
1
+
1
1
s
i
n
(
1
)
1
(
1
2
)
T
h
e
in
n
er
lo
o
p
en
s
u
r
es
th
at
th
e
m
o
to
r
an
g
le
tr
ac
k
s
th
e
r
ef
er
en
ce
g
en
er
ate
d
b
y
th
e
o
u
te
r
lo
o
p
.
T
h
e
s
lid
in
g
s
u
r
f
ac
e
f
o
r
th
e
in
n
er
lo
o
p
is
d
ef
in
e
d
as
(
1
3
)
:
2
=
̇
3
+
3
(
1
3
)
wh
er
e
3
=
1
,
−
1
is
th
e
m
o
to
r
tr
ac
k
in
g
er
r
o
r
,
̇
3
=
̇
1
,
−
̇
1
,
an
d
>
0
.
T
h
en
th
e
co
n
tr
o
l
law
wh
ich
r
ep
r
esen
ts
th
e
m
o
to
r
to
r
q
u
e
in
p
u
t is d
esig
n
ed
as
(
1
4
)
:
1
=
−
,
3
−
,
̇
3
−
2
,
s
at
(
2
2
,
)
(
1
4
)
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
P
erfo
r
ma
n
ce
a
s
s
ess
men
t o
f fr
a
ctio
n
a
l o
r
d
er P
I
D
c
o
n
tr
o
l fo
r
a
2
DOF
flexib
le
jo
in
t
…
(
A
h
med
A
lka
ma
ch
i
)
601
wh
er
e
1
,
an
d
2
,
d
ef
in
e
th
e
b
o
u
n
d
ar
y
lay
e
r
th
ick
n
ess
es
f
o
r
t
h
e
o
u
ter
a
n
d
in
n
er
lo
o
p
s
,
r
esp
ec
t
iv
ely
.
Fo
r
th
e
p
u
r
p
o
s
e
o
f
f
air
co
m
p
a
r
is
o
n
,
th
e
p
r
o
p
o
s
ed
SMC
i
s
co
m
b
in
ed
with
g
r
av
ity
co
m
p
en
s
atio
n
s
im
ilar
to
th
e
FOPID
s
tr
u
ctu
r
e:
=
,
+
,
,
=
1
,
2
(
1
5
)
wh
er
e
,
is
s
lid
in
g
m
o
d
e
co
n
tr
o
l
in
p
u
t,
a
n
d
,
=
(
−
)
+
3
.
4
.
P
a
ra
m
e
t
er
t
un
ing
wit
h o
ptim
iza
t
io
n a
l
g
o
rit
hm
s
T
h
e
FOPID
ca
s
ca
d
e
c
o
n
tr
o
l
s
tr
u
ctu
r
e
p
r
o
p
o
s
ed
in
t
h
is
s
tu
d
y
i
n
clu
d
es
a
to
tal
o
f
2
0
ad
ju
s
tab
le
p
ar
am
eter
s
.
Dete
r
m
in
in
g
th
ese
p
ar
am
eter
s
with
class
ical
m
et
h
o
d
s
is
q
u
ite
d
if
f
icu
lt a
n
d
tim
e
co
n
s
u
m
in
g
d
u
e
to
th
e
n
o
n
lin
ea
r
an
d
co
u
p
led
s
t
r
u
ctu
r
e
o
f
th
e
s
y
s
tem
.
I
n
th
i
s
co
n
tex
t,
a
p
a
r
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
alg
o
r
ith
m
[
2
5
]
is
u
tili
ze
d
to
s
ea
r
ch
th
e
p
ar
a
m
eter
s
p
ac
e
e
f
f
icien
tly
an
d
clo
s
e
to
g
lo
b
al
o
p
tim
a.
I
n
teg
r
al
o
f
ab
s
o
lu
te
er
r
o
r
(
I
AE
)
f
o
r
t
h
e
t
wo
lin
k
s
’
an
g
les
wer
e
tak
e
n
i
n
to
co
n
s
id
er
atio
n
to
g
et
h
er
in
o
r
d
er
t
o
ev
alu
ate
th
e
co
n
tr
o
l p
e
r
f
o
r
m
an
ce
.
=
∫
∣
0
1
(
)
∣
+
∫
∣
0
2
(
)
∣
(
1
6
)
T
h
e
o
p
er
atio
n
al
PS
O
p
ar
am
et
er
s
u
s
ed
th
r
o
u
g
h
th
e
tu
n
i
n
g
p
r
o
ce
s
s
ar
e
s
war
m
s
ize
o
f
4
0
,
8
0
iter
atio
n
s
,
i
n
er
tia
weig
h
t
o
f
0
.
9
,
an
d
co
g
n
itiv
e
/s
o
cial
co
ef
f
icien
ts
o
f
2
.
B
ased
o
n
th
ese
co
n
f
i
g
u
r
atio
n
s
,
t
h
e
f
in
al
o
p
tim
ize
d
co
n
tr
o
ller
p
ar
am
eter
s
f
o
r
b
o
t
h
th
e
FOPID
an
d
SMC
f
r
am
ewo
r
k
s
ar
e
lis
ted
in
T
ab
le
2
.
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
T
o
illu
s
tr
ate
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
co
n
t
r
o
ller
,
d
if
f
er
en
t
s
ce
n
ar
io
s
h
a
v
e
b
ee
n
d
o
n
e
t
o
ch
ec
k
th
e
ab
ilit
y
o
f
co
n
tr
o
ller
in
tr
ajec
to
r
y
tr
ac
k
i
n
g
an
d
in
t
h
e
ex
is
ten
ce
o
f
ex
ter
n
al
d
is
tu
r
b
an
ce
an
d
p
ay
lo
a
d
v
ar
iatio
n
s
.
T
h
e
f
o
llo
win
g
p
er
f
o
r
m
an
ce
m
etr
ics
a
r
e
u
s
ed
to
ev
alu
ate
co
n
tr
o
ller
p
er
f
o
r
m
a
n
ce
:
in
teg
r
al
tim
e
ab
s
o
lu
te
er
r
o
r
(
I
T
AE
)
ev
alu
at
es
tr
an
s
ien
t
p
er
f
o
r
m
an
ce
q
u
ali
ty
,
Stead
y
s
tate
er
r
o
r
m
ea
s
u
r
e
s
tr
ac
k
in
g
ac
cu
r
ac
y
,
%
r
ep
r
esen
ts
p
er
ce
n
tag
e
m
ax
i
m
u
m
o
v
er
s
h
o
o
t,
d
en
o
tes
s
e
ttli
n
g
tim
e,
in
d
icate
s
r
i
s
e
ti
m
e,
an
d
in
teg
r
al
o
f
s
q
u
ar
ed
c
o
n
tr
o
l e
f
f
o
r
t
(
I
SC
E
)
g
iv
es a
n
i
n
d
icatio
n
o
n
th
e
e
n
er
g
y
co
n
s
u
m
e
d
b
y
th
e
ac
tu
ato
r
.
T
ab
le
2
.
FOPID
an
d
SMC
co
n
tr
o
ller
s
tu
n
ed
p
a
r
am
eter
s
F
O
P
I
D
S
M
C
P
a
r
a
me
t
e
r
s
F
O
P
I
D
(
1
)
F
O
P
I
D
(
2
)
P
a
r
a
me
t
e
r
s
S
M
C
(
1
)
S
M
C
(
2
)
O
u
t
e
r
I
n
n
e
r
O
u
t
e
r
I
n
n
e
r
5
6
.
9
3
9
9
2
.
6
9
8
4
9
.
2
8
1
8
6
.
1
6
3
6
.
3
0
7
2
9
.
2
2
8
5
1
1
.
8
5
4
1
.
3
0
8
1
5
.
9
0
3
4
1
.
5
7
5
8
1
,
1
7
.
7
4
9
1
2
.
7
0
1
1
7
.
8
2
2
2
.
3
2
0
4
2
.
9
0
8
0
1
2
.
8
5
0
1
,
0
.
5
0
0
0
0
.
4
6
7
9
0
.
9
9
0
9
1
.
5
6
6
2
1
.
3
8
7
1
1
.
1
3
5
9
,
6
1
.
1
1
6
4
3
.
5
4
3
0
.
3
4
8
7
1
.
6
5
8
0
0
.
5
3
6
1
1
.
2
6
9
5
,
2
.
4
6
5
1
2
6
.
7
9
5
2
,
5
.
3
8
4
7
5
.
6
4
5
5
6
.
9
0
7
1
8
.
2
3
9
2
2
,
0
.
0
1
4
4
0
.
0
2
8
4
4
.
1
.
Scena
rio
1
:
no
m
ina
l sy
s
t
em
(
no
dis
t
urba
nce,
no
pa
y
lo
a
d
)
I
n
th
e
f
ir
s
t te
s
t,
th
e
s
y
s
tem
wa
s
ev
alu
ated
u
n
d
er
id
ea
l n
o
m
in
al
co
n
d
itio
n
s
.
A
s
tep
r
ef
er
en
ce
o
f
0
.
5
r
ad
was
ap
p
lied
to
lin
k
1
at
=
0
s
,
an
d
a
0
.
2
r
ad
s
tep
was
ap
p
lied
to
lin
k
2
at
=
2
s
.
Per
f
o
r
m
an
ce
in
d
ices
f
o
r
b
o
th
co
n
tr
o
ller
s
ar
e
lis
ted
in
T
ab
le
3
.
T
h
e
lin
k
s
’
an
g
les
r
esp
o
n
s
es
an
d
th
e
ac
tu
ato
r
s
’
r
esp
o
n
s
es
ar
e
d
ep
icted
in
Fig
u
r
e
2
an
d
Fig
u
r
e
3
r
esp
ec
tiv
ely
.
T
h
e
r
esu
lts
r
ev
ea
l
a
clea
r
d
if
f
er
en
ce
in
th
e
tr
a
n
s
ien
t
b
eh
av
io
r
o
f
th
e
two
co
n
tr
o
ller
s
.
Fo
r
lin
k
1
,
th
e
S
MC
d
em
o
n
s
tr
ated
an
en
tire
ly
d
am
p
ed
r
esp
o
n
s
e
with
0
%
o
v
er
s
h
o
o
t,
wh
er
ea
s
th
e
FOPID
co
n
tr
o
ller
e
x
h
ib
ited
an
o
v
er
s
h
o
o
t
o
f
8
.
5
5
%.
Similar
b
eh
a
v
io
r
was
o
b
s
er
v
ed
in
lin
k
2
.
Ho
wev
e
r
,
FOPID
ac
h
iev
ed
s
u
p
er
io
r
o
v
e
r
all
tr
ac
k
in
g
ac
c
u
r
ac
y
,
m
in
im
i
zin
g
th
e
I
T
AE
er
r
o
r
co
m
p
ar
ed
to
SMC
'
s
.
FOPID
also
m
ai
n
ta
in
ed
a
t
ig
h
t
e
r
s
te
a
d
y
s
ta
te
er
r
o
r
(
0
.
0
0
1
9
)
t
h
an
SMC
(
0
.
0
0
3
7
)
.
M
o
s
t
n
o
ta
b
l
y
,
th
e
c
o
n
t
r
o
l
e
f
f
o
r
t
(
I
SC
E
)
w
h
e
r
e
SMC
e
x
p
e
n
d
e
d
s
ig
n
i
f
ic
a
n
tl
y
less
e
n
e
r
g
y
c
o
m
p
ar
ed
t
o
FOPI
D'
s
h
ig
h
l
y
a
g
g
r
es
s
iv
e
c
o
n
t
r
o
l
ac
ti
o
n
.
As
s
h
o
wn
in
Fig
u
r
e
s
3
(
a)
a
n
d
3
(
b
)
,
th
e
ac
t
u
ato
r
s
ig
n
als
ass
o
ciate
d
with
FOPID
ex
h
ib
it
m
o
r
e
f
lu
ctu
atio
n
s
,
ex
p
lain
i
n
g
th
e
h
ig
h
v
alu
e
o
f
I
SC
E
wh
en
co
m
p
ar
ed
with
th
o
s
e
o
f
SMC
.
I
n
p
r
ac
tical
r
o
b
o
tic
s
y
s
tem
s
,
h
ig
h
co
n
tr
o
l
ac
tiv
ity
lead
s
to
a
n
in
cr
ea
s
e
i
n
ac
tu
at
o
r
p
o
wer
co
n
s
u
m
p
tio
n
an
d
th
er
m
al
s
tr
ess
,
wh
ich
ca
n
r
ed
u
ce
ac
tu
ato
r
e
f
f
icien
cy
an
d
r
eq
u
ir
e
lar
g
e
r
m
o
t
o
r
r
atin
g
s
.
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
.
3
,
Sep
tem
b
er
20
2
6
:
5
9
7
-
6
0
6
602
T
ab
le
3
.
Per
f
o
r
m
an
ce
in
d
ices
f
o
r
n
o
m
in
al
s
y
s
tem
test
(
Scen
ar
io
1
)
P
e
r
f
o
r
ma
n
c
e
me
t
r
i
c
S
M
C
(
1
)
F
O
P
I
D
(
1
)
S
M
C
(
2
)
F
O
P
I
D
(
2
)
I
TA
E
e
r
r
o
r
0
.
2
4
2
3
0
.
1
1
6
5
0
.
5
7
4
9
0
.
1
9
6
2
S
t
e
a
d
y
st
a
t
e
e
r
r
o
r
0
.
0
0
3
7
0
.
0
0
1
9
0
.
0
0
7
7
0
.
0
0
1
5
M
P
%
0
8
.
5
5
2
9
0
9
.
2
3
7
9
8
Ts
1
.
1
9
7
3
0
.
9
7
8
7
1
.
1
2
5
1
.
0
0
3
6
9
Tr
0
.
5
5
2
4
0
.
2
2
9
1
0
.
5
6
5
2
0
.
2
2
9
3
6
I
S
C
E
2
3
.
3
5
1
5
4
.
7
8
8
.
8
6
4
5
.
2
9
Fig
u
r
e
2
.
L
i
n
k
an
g
le
tr
ac
k
in
g
r
esp
o
n
s
es o
f
th
e
n
o
m
in
al
s
y
s
tem
(
a)
(
b
)
Fig
u
r
e
3
.
C
o
n
tr
o
l sig
n
al
(
ac
tu
a
to
r
ef
f
o
r
t)
u
n
d
er
n
o
m
in
al
s
y
s
te
m
:
(a
)
f
ir
s
t lin
k
a
n
d
(
b
)
s
ec
o
n
d
lin
k
4
.
2
.
Scena
rio
2
:
dis
t
urba
nce
a
t
lin
k
1
T
o
test
d
is
tu
r
b
a
n
ce
r
ejec
tio
n
,
ex
ter
n
al
lo
a
d
p
er
tu
r
b
atio
n
s
w
er
e
ap
p
lied
to
th
e
s
y
s
tem
.
T
h
e
co
m
p
lete
lin
k
an
g
le
tr
ac
k
in
g
r
esp
o
n
s
e
s
an
d
th
eir
co
r
r
esp
o
n
d
in
g
co
n
tr
o
l
ef
f
o
r
t
s
ig
n
als
ar
e
s
h
o
wn
in
Fig
u
r
e
4
an
d
Fig
u
r
e
5
r
esp
ec
tiv
ely
,
wh
ile
th
e
p
er
f
o
r
m
a
n
ce
in
d
ices
v
alu
es
ar
e
lis
ted
in
T
ab
le
4
.
First,
a
0
.
5
N.
m
d
is
tu
r
b
an
ce
was
in
jecte
d
at
l
in
k
1
at
=
5
s
.
FOPID
s
u
cc
ess
f
u
lly
s
u
p
p
r
ess
ed
th
e
d
is
tu
r
b
an
ce
with
n
eg
l
ig
ib
le
im
p
ac
t
(
Fig
u
r
e
4
(
a)
)
,
m
ain
tain
in
g
a
n
I
T
AE
o
f
0
.
1
4
6
1
.
SMC
s
h
o
wed
a
s
lig
h
t
d
eg
r
ad
atio
n
in
p
er
f
o
r
m
an
ce
,
with
its
I
T
AE
in
cr
ea
s
in
g
to
0
.
3
7
9
3
a
n
d
s
tead
y
-
s
tate
er
r
o
r
r
is
in
g
t
o
0
.
0
0
7
5
o
n
lin
k
1
.
T
h
e
co
n
t
r
o
l
ef
f
o
r
t
f
o
r
SMC
s
lig
h
tly
in
cr
ea
s
ed
to
3
1
.
7
6
to
co
m
p
en
s
ate
f
o
r
t
h
e
d
is
tu
r
b
an
c
e,
ac
co
m
p
an
ie
d
b
y
s
ig
n
al
ch
at
ter
in
g
in
its
ac
tu
ato
r
s
ig
n
al
af
ter
=
5
s
wh
ile
FO
PID
's e
f
f
o
r
t r
e
m
ain
ed
h
ig
h
f
o
r
b
o
th
li
n
k
s
as illu
s
tr
ated
in
Fig
u
r
e
s
5
(
a)
an
d
5
(
b
)
.
W
h
en
th
e
d
is
tu
r
b
an
ce
o
n
lin
k
1
was
in
cr
ea
s
ed
to
1
.
0
N.
m
at
=
5
s
,
th
e
lim
itatio
n
s
o
f
th
e
S
MC
d
esig
n
b
ec
am
e
h
ig
h
l
y
ev
id
en
t.
As
s
h
o
wn
in
th
e
p
lo
tted
r
esp
o
n
s
es
in
Fig
u
r
e
4
(
b
)
an
d
th
e
co
r
r
esp
o
n
d
i
n
g
co
n
tr
o
l
s
ig
n
al
b
eh
a
v
io
r
s
in
Fig
u
r
e
s
5
(
c
)
an
d
5
(
d
)
,
th
e
SM
C
f
ailed
to
s
u
p
p
r
ess
th
e
d
is
t
u
r
b
an
ce
,
lead
in
g
to
s
ev
er
e
ch
atter
in
g
,
c
o
n
tin
u
o
u
s
s
atu
r
atio
n
in
th
e
ac
tu
at
o
r
s
ig
n
al
(
±
20
.
.
)
an
d
s
ev
er
e
in
s
tab
ilit
y
i
n
lin
k
1
.
T
h
e
n
u
m
er
ical
r
esu
lts
f
o
r
th
is
test
in
T
ab
le
4
clea
r
ly
in
d
icatin
g
th
e
lo
s
s
o
f
tr
ac
k
in
g
.
C
o
n
v
er
s
ely
,
th
e
FOPID
co
n
tr
o
ller
ex
h
ib
ited
r
em
a
r
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ab
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s
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Desp
ite
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e
r
e
1
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0
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is
tu
r
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a
n
ce
,
it
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ain
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s
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le
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ac
k
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d
in
th
e
s
am
e
tim
e
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ep
t th
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co
n
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o
l e
f
f
o
r
t sm
o
o
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ly
d
a
m
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with
in
s
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e
o
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e
r
atio
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lim
it
s
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T
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le
4
.
Per
f
o
r
m
an
ce
in
d
ices
f
o
r
d
is
tu
r
b
a
n
ce
test
s
(
Scen
ar
io
2
)
P
e
r
f
o
r
ma
n
c
e
me
t
r
i
c
0
.
5
N
.
m
d
i
st
u
r
b
a
n
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e
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0
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.
m
d
i
st
u
r
b
a
n
c
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S
M
C
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1
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F
O
P
I
D
(
1
)
S
M
C
(
2
)
F
O
P
I
D
(
2
)
S
M
C
(
1
)
F
O
P
I
D
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1
)
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M
C
(
2
)
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O
P
I
D
(
2
)
I
TA
E
0
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3
7
9
3
0
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1
4
6
1
0
.
5
8
0
4
0
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1
9
6
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3
9
.
4
4
0
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1
7
8
0
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8
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1
0
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6
2
S
t
e
a
d
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st
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r
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r
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0
0
7
5
0
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0
0
2
2
0
.
0
0
7
9
0
.
0
0
1
5
N
a
n
0
.
0
0
2
5
0
.
0
2
5
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1
5
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S
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3
1
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8
6
.
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4
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6
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3
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4
9
9
4
.
8
1
9
2
.
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.
4
4
6
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.
4
9
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
P
erfo
r
ma
n
ce
a
s
s
ess
men
t o
f fr
a
ctio
n
a
l o
r
d
er P
I
D
c
o
n
tr
o
l fo
r
a
2
DOF
flexib
le
jo
in
t
…
(
A
h
med
A
lka
ma
ch
i
)
603
(
a)
(
b
)
Fig
u
r
e
4
.
L
i
n
k
an
g
le
tr
ac
k
in
g
r
esp
o
n
s
es u
n
d
er
d
is
tu
r
b
an
ce
te
s
ts
: (
a)
0
.
5
N.
m
d
is
tu
r
b
a
n
ce
an
d
(
b
)
1
N.
m
d
is
tu
r
b
a
n
ce
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
5
.
C
o
n
tr
o
l sig
n
al
(
ac
tu
a
to
r
ef
f
o
r
t)
u
n
d
er
d
if
f
er
e
n
t e
x
te
r
n
al
lo
ad
d
is
tu
r
b
an
ce
s
(
a)
lin
k
1
with
0
.
5
N
.
m
,
(
b
)
lin
k
2
with
0
.
5
N
.
m
,
(
c)
lin
k
1
with
1
.
0
N·
m
,
an
d
(
d
)
lin
k
2
with
1
.
0
N
.
m
4
.
3
.
Scena
rio
3
:
v
a
ria
ble pa
y
lo
a
d
I
n
th
e
f
in
al
s
ce
n
ar
io
,
th
e
s
y
s
te
m
was
s
u
b
jecte
d
to
a
v
ar
iab
le
p
ay
lo
ad
,
s
tep
p
in
g
to
0
.
1
k
g
a
t
=
5
s
,
an
d
f
u
r
th
er
to
0
.
3
k
g
at
=
7
s
.
As
s
h
o
wn
in
Fig
u
r
e
6
,
b
o
th
c
o
n
tr
o
ller
s
s
u
cc
ess
f
u
lly
ad
ap
ted
to
th
e
p
ar
am
etr
i
c
v
ar
iatio
n
s
with
o
u
t
lo
s
in
g
s
tab
ilit
y
.
FOPID
o
n
ce
ag
ain
p
r
o
v
id
ed
s
u
p
er
io
r
tr
ac
k
in
g
,
k
ee
p
in
g
th
e
I
T
AE
o
n
lin
k
1
at
0
.
1
0
8
2
.
SMC
h
an
d
led
th
e
p
ay
lo
ad
c
h
an
g
es
ad
eq
u
ately
b
u
t
r
esu
lted
in
h
ig
h
er
tr
ac
k
in
g
d
ev
iatio
n
s
as
s
h
o
w
n
in
T
ab
le
5
.
C
o
n
tr
o
l
ef
f
o
r
t
s
h
o
wn
in
Fig
u
r
e
7
f
o
llo
wed
th
e
e
s
tab
lis
h
ed
tr
en
d
,
with
SMC
o
p
er
atin
g
ef
f
icien
tly
v
er
s
u
s
FOPID
'
s
h
ea
v
y
en
er
g
y
u
s
ag
e.
Fo
r
b
o
th
lin
k
s
,
SMC
i
n
tr
o
d
u
ce
s
h
ig
h
f
r
e
q
u
en
c
y
ch
a
tter
in
g
r
ea
ctio
n
s
at
th
e
p
ay
l
o
ad
tr
an
s
itio
n
p
o
in
ts
(
=
5
s
)
a
n
d
(
=
7
s
)
as
s
h
o
wn
in
Fig
u
r
e
s
7
(
a
)
an
d
7
(
b
)
.
Ov
e
r
all,
t
h
e
to
ta
l
en
er
g
y
m
etr
ics
in
T
ab
le
6
s
h
o
w
th
at
SMC
o
p
er
atin
g
with
lo
wer
cu
m
u
lativ
e
n
u
m
er
ical
in
d
i
ce
s
v
er
s
u
s
FOPID'
s
h
ig
h
er
en
er
g
y
u
s
ag
e.
T
o
illu
s
t
r
ate
th
e
ac
t
u
ato
r
en
er
g
y
r
eq
u
ir
em
en
ts
o
f
b
o
th
co
n
tr
o
ller
s
,
Fi
g
u
r
e
8
p
r
esen
ts
th
e
I
SC
E
v
alu
es o
b
tain
ed
u
n
d
er
al
l th
e
ab
o
v
e
s
ce
n
ar
io
s
.
I
t c
an
b
e
o
b
s
er
v
ed
th
at
th
e
SMC
g
en
er
ally
r
eq
u
ir
es lo
wer
co
n
tr
o
l e
n
e
r
g
y
co
m
p
a
r
ed
to
F
OPI
D
u
n
d
er
all
test
s
.
T
ab
le
5
.
Per
f
o
r
m
an
ce
in
d
ices
f
o
r
p
a
y
lo
ad
v
ar
iatio
n
test
(
Sce
n
ar
io
3
)
.
P
e
r
f
o
r
ma
n
c
e
me
t
r
i
c
Th
e
t
a
1
S
M
C
Th
e
t
a
1
F
O
P
I
D
Th
e
t
a
2
S
M
C
Th
e
t
a
2
F
O
P
I
D
I
TA
E
0
.
6
7
4
6
0
.
1
0
8
2
0
.
9
5
8
7
0
.
2
3
5
3
S
t
e
a
d
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st
a
t
e
e
r
r
o
r
0
.
0
1
9
0
.
0
0
1
4
0
.
0
2
0
.
0
0
2
1
I
S
C
E
3
5
.
9
5
1
9
2
.
7
6
2
5
.
8
8
5
4
.
7
1
c
on
t
i
n
u
o
u
s
r
ail
-
to
-
r
ail
ac
t
u
a
t
or
s
at
u
r
at
i
on
P
oin
t
of
ap
p
lyi
n
g
0.
5
N.
m
d
is
t
u
r
b
a
n
c
e
P
oin
t
of
ap
p
lyi
n
g
1.
0
N.
m
d
is
t
u
r
b
a
n
c
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
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t
J
R
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b
&
A
u
to
m
,
Vo
l
.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
5
9
7
-
6
0
6
604
Fig
u
r
e
6
.
L
i
n
k
an
g
le
tr
ac
k
in
g
r
esp
o
n
s
es u
n
d
er
p
ay
lo
ad
v
ar
iat
io
n
s
(
a)
(
b
)
Fig
u
r
e
7
.
C
o
n
tr
o
l sig
n
al
(
ac
tu
a
to
r
ef
f
o
r
t)
u
n
d
er
p
ay
lo
a
d
v
ar
ia
tio
n
(
a)
f
i
r
s
t
lin
k
,
(
b
)
s
ec
o
n
d
lin
k
Fig
u
r
e
8
.
C
o
m
p
a
r
is
o
n
o
f
ac
tu
a
to
r
ef
f
o
r
t (
I
SC
E
)
u
n
d
er
d
i
f
f
er
e
n
t o
p
er
atin
g
co
n
d
itio
n
s
5.
CO
NCLU
SI
O
N
T
h
e
m
ain
n
o
v
elty
o
f
th
is
wo
r
k
is
a
f
air
co
m
p
ar
ativ
e
e
v
alu
a
tio
n
b
etwe
en
ca
s
ca
d
ed
FOPID
an
d
SMC
co
n
tr
o
ller
s
ap
p
lied
t
o
f
lex
i
b
le
jo
in
t
m
a
n
ip
u
lato
r
.
B
o
th
co
n
t
r
o
ller
s
wer
e
p
r
o
v
i
d
ed
with
g
r
av
ity
co
m
p
en
s
ato
r
an
d
tu
n
ed
u
n
d
e
r
id
en
tical
co
n
d
itio
n
s
u
s
in
g
PS
O
an
d
ex
a
m
in
ed
u
n
d
er
id
en
tical
co
n
d
it
io
n
s
to
en
s
u
r
e
f
air
ass
es
s
m
en
t.
T
h
r
ee
d
i
f
f
er
en
t
s
im
u
latio
n
s
ce
n
ar
io
s
wer
e
co
n
d
u
cted
r
ev
ea
lin
g
a
p
r
ac
tically
s
ig
n
if
ican
t
tr
ad
e
-
o
f
f
.
Un
d
er
n
o
m
in
al
co
n
d
itio
n
s
,
S
MC
p
r
o
v
id
ed
s
m
o
o
th
,
ze
r
o
o
v
er
s
h
o
o
t
tr
a
n
s
ien
t
r
esp
o
n
s
es
with
lo
wer
co
n
tr
o
l
ef
f
o
r
t,
m
ak
in
g
it
s
u
itab
le
f
o
r
en
er
g
y
s
av
in
g
ap
p
licatio
n
s
in
co
n
t
r
o
lled
e
n
v
ir
o
n
m
en
ts
.
Ho
wev
er
,
wh
e
n
s
u
b
jecte
d
to
a
r
elativ
ely
h
ig
h
ex
ter
n
al
d
is
tu
r
b
an
ce
,
SMC
ex
h
ib
ited
s
ev
er
e
ch
atter
in
g
a
n
d
i
n
s
tab
ilit
y
,
wh
er
ea
s
FOPID
m
ain
tain
ed
s
tab
le
an
d
ac
cu
r
ate
tr
ac
k
in
g
,
d
em
o
n
s
tr
atin
g
h
ig
h
r
o
b
u
s
tn
ess
.
Similar
s
u
p
er
io
r
ity
was
o
b
s
er
v
ed
u
n
d
er
v
a
r
iab
le
p
ay
l
o
ad
co
n
d
itio
n
s
,
wh
er
e
FOPID
ac
h
iev
ed
lo
wer
I
T
AE
an
d
s
tead
y
s
tate
er
r
o
r
s
ac
r
o
s
s
b
o
th
lin
k
s
.
I
n
c
o
n
clu
s
io
n
,
SMC
is
th
e
p
r
ef
er
r
ed
c
h
o
ice
f
o
r
a
p
p
licatio
n
s
wh
er
e
e
n
er
g
y
ef
f
icien
cy
a
n
d
s
m
o
o
th
tr
an
s
ien
t
b
eh
av
io
r
ar
e
o
f
h
ig
h
p
r
io
r
ity
.
T
h
e
r
ed
u
ce
d
co
n
tr
o
l
e
f
f
o
r
t
o
f
SMC
d
ec
r
ea
s
es
ac
tu
ato
r
h
ea
tin
g
an
d
im
p
r
o
v
es
its
ef
f
icien
cy
in
p
r
ac
tical
im
p
lem
e
n
tatio
n
s
.
FOPID
is
th
e
s
u
p
er
io
r
ch
o
ic
e
f
o
r
e
n
v
ir
o
n
m
en
ts
s
u
b
ject
to
h
ea
v
y
,
u
n
p
r
ed
ictab
le
d
is
tu
r
b
an
ce
s
an
d
d
y
n
am
ic
p
ay
l
o
ad
v
ar
iatio
n
s
,
p
r
o
v
id
ed
th
e
ac
tu
ato
r
s
ca
n
s
af
ely
s
u
p
p
ly
its
h
ig
h
en
er
g
y
d
em
an
d
s
.
Sin
ce
f
lex
ib
le
jo
in
t
m
an
i
p
u
la
to
r
s
r
ely
h
ea
v
ily
o
n
s
en
s
o
r
f
ee
d
b
ac
k
,
s
en
s
o
r
ac
cu
r
ac
y
h
a
s
a
lar
g
e
im
p
ac
t
o
n
s
y
s
tem
p
e
r
f
o
r
m
an
c
e.
Me
asu
r
em
en
t
n
o
is
e
m
ain
ly
af
f
ec
ts
d
er
iv
ativ
e
a
n
d
s
witch
in
g
co
n
tr
o
l
ac
tio
n
s
an
d
,
in
t
h
is
co
n
tex
t,
SMC
is
g
en
er
ally
m
o
r
e
s
en
s
itiv
e
to
s
en
s
o
r
n
o
is
e
d
u
e
to
its
ass
o
ciate
d
s
witch
in
g
ac
tio
n
,
wh
er
ea
s
FOPID
p
r
o
v
id
es
s
m
o
o
th
er
c
o
n
tr
o
l
s
ig
n
als.
Sen
s
o
r
d
elay
m
ay
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