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io
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l J
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urna
l o
f
Ro
bo
t
ics a
nd
Aut
o
m
a
t
io
n
(
I
J
RA
)
Vo
l.
6
,
No
.
4
,
Dec
em
b
er
201
7
,
p
p
.
2
4
1
~
251
I
SS
N:
2089
-
4
8
5
6
,
DOI
: 1
0
.
1
1
5
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1
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j
r
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v
6
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.
p
p
2
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-
251
241
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ticle
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7
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6
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On
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e
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th
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rk
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re
y
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lf
Op
ti
m
ize
r
(
GWO)
tec
h
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m
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sig
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o
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UPF
C
b
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se
d
d
a
m
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g
c
o
n
tr
o
ll
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r
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:
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izer
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la
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tr
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ller
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n
tr
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ller
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w
er
s
y
s
te
m
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s
ci
llatio
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UP
FC
Co
p
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rig
h
t
©
2
0
1
7
In
stit
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
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g
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n
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Al
l
rig
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d
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C
o
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p
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A
uth
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r
:
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an
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ar
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llick
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ar
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lectr
ical
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d
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lectr
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g
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I
n
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ia
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E
m
ail: r
k
m
.
iter
@
g
m
a
il.c
o
m
1.
I
NT
RO
D
UCT
I
O
N
Mo
d
er
n
p
o
w
er
s
y
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m
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tr
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o
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an
d
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r
it
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e.
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tab
ilit
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f
p
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w
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s
y
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m
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as
b
e
en
a
c
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n
g
in
g
is
s
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f
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ch
.
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h
is
w
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k
f
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cu
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p
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w
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y
s
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d
y
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ic
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tab
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to
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p
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g
o
f
p
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w
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s
y
s
te
m
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s
cillatio
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s
.
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h
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in
ter
co
n
n
ec
tio
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o
f
d
if
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lo
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y
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c
h
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n
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m
[
1
]
.
P
o
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tab
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P
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)
h
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t,
t
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e
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ab
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ce
s
an
d
o
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lead
p
o
w
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f
ac
to
r
[
2
]
.
On
th
e
o
t
h
er
h
a
n
d
F
AC
T
S
b
ased
P
SS
ar
e
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m
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ea
s
o
n
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lik
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li
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t
u
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i
n
g
,
f
le
x
ib
ilit
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i
n
o
p
er
atio
n
[
3
,
4
]
.
T
h
e
FAC
T
S
b
ased
co
n
tr
o
ller
m
a
y
e
m
p
lo
y
UP
FC
,
T
C
S
C
,
S
SS
C
e
tc.
,
b
u
t
UP
F
C
is
m
o
r
e
v
er
s
ati
le
w
it
h
t
h
r
ee
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
an
d
ca
n
p
r
o
v
id
e
u
n
co
n
s
tr
ain
ed
s
er
ies
v
o
ltag
e
[
5
,
6
]
.
Stead
y
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tate
m
o
d
el
o
f
p
o
w
er
s
y
s
te
m
w
it
h
UP
FC
h
as a
lr
ea
d
y
b
ee
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r
ep
o
r
ted
ea
r
lier
[
7
]
.
T
h
e
s
m
all
s
i
g
n
al
Hef
f
r
o
n
P
h
illi
p
s
m
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el
p
r
esen
ted
in
[
8
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h
as
b
ee
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u
s
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f
o
r
d
y
n
a
m
ic
s
tab
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ass
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en
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s
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te
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n
t
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ller
h
as
n
o
t
b
ee
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r
ep
o
r
ted
h
er
e
[
9
]
.
Dif
f
er
en
t
r
o
b
u
s
t te
c
h
n
iq
u
es
h
a
v
e
b
ee
n
c
o
m
p
ar
ed
i
n
[
1
0
]
to
d
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n
th
e
d
am
p
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n
g
co
n
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o
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.
Fo
r
s
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p
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l
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en
tar
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n
tr
o
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ased
o
n
UP
FC
to
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a
m
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s
c
il
latio
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s
,
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t
m
a
y
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e
o
f
P
I
t
y
p
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o
r
lead
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lag
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e.
No
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t
h
e
m
att
er
o
f
s
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ti
o
n
o
f
P
I
o
r
lead
-
lag
co
n
tr
o
ller
i
s
a
d
ec
is
iv
e
ap
p
r
o
ac
h
.
I
n
t
h
i
s
w
o
r
k
a
b
r
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ad
co
m
p
ar
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o
n
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a
s
b
ee
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er
f
o
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m
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w
ee
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o
p
tim
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P
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d
lead
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g
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ctu
r
e
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o
r
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lectio
n
o
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d
a
m
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n
g
co
n
tr
o
ller
.
T
h
e
n
e
x
t
p
ar
t
o
f
t
h
is
w
o
r
k
is
o
n
li
n
e
tu
n
in
g
o
f
P
I
an
d
lead
-
lag
co
n
tr
o
ller
,
f
o
r
w
h
ic
h
a
s
u
i
tab
le
o
p
ti
m
izatio
n
tech
n
iq
u
e
is
to
b
e
ad
o
p
ted
.
P
SO
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
6
,
No
.
4
,
Dec
em
b
er
201
7
:
2
4
1
–
2
5
1
242
tech
n
iq
u
e
h
as
b
ee
n
v
er
y
p
o
p
u
lar
d
u
e
to
s
o
m
a
n
y
ad
v
a
n
ta
g
e
s
an
d
h
as
b
ee
n
u
s
ed
to
d
e
s
ig
n
d
a
m
p
in
g
co
n
tr
o
ller
[
1
1
,
1
2
]
.
P
SO
is
a
s
i
m
p
le
a
n
d
r
o
b
u
s
t
m
et
h
o
d
,
b
u
t
i
t
m
a
y
tr
ap
in
lo
ca
l
o
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ti
m
a
w
h
en
h
a
n
d
lin
g
a
co
m
p
lex
p
r
o
b
lem
.
Dif
f
er
en
t
ial
E
v
o
l
u
tio
n
(
DE
)
i
s
an
e
v
o
lu
t
io
n
ar
y
t
y
p
e
al
g
o
r
ith
m
b
ein
g
u
s
ed
to
d
esig
n
S
S
SC
b
ased
d
am
p
i
n
g
co
n
tr
o
ller
in
[
1
3
]
.
R
ec
en
tl
y
o
t
h
er
tech
n
iq
u
es
li
k
e
ad
ap
tiv
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P
SO,
GA
,
GS
A
etc.
h
av
e
b
ee
n
r
ep
o
r
ted
f
o
r
o
p
tim
a
l
co
n
tr
o
ller
d
e
s
ig
n
[
1
4
-
1
6
]
.
Fo
r
o
p
tim
al
co
n
tr
o
ller
d
esig
n
m
eta
h
eu
r
i
s
tic
tech
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e
s
ar
e
g
ain
i
n
g
m
o
r
e
p
o
p
u
lar
it
y
n
o
w
a
d
a
y
s
.
T
h
ese
tech
n
iq
u
es
ar
e
s
i
m
p
le,
ef
f
icien
t
an
d
ca
n
h
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n
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le
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y
c
o
m
p
le
x
o
p
ti
m
izatio
n
p
r
o
b
lem
[
1
7
]
.
GW
O
is
a
r
ec
en
tl
y
r
e
v
ea
led
o
p
ti
m
iza
tio
n
t
ec
h
n
iq
u
e
[
1
7
]
in
s
p
ir
ed
b
y
th
e
b
eh
av
io
r
o
f
Gr
e
y
W
o
lf
s
to
h
u
n
t
f
o
r
a
p
r
ey
.
GW
O
h
as
s
o
m
an
y
ad
v
a
n
tag
e
s
as
co
m
p
ar
ed
to
p
r
ev
ailin
g
o
p
tim
izatio
n
tech
n
iq
u
e
s
lik
e
i
ts
s
i
m
p
l
icit
y
,
r
o
b
u
s
t
n
es
s
,
s
tr
aig
h
t
f
o
r
w
ar
d
n
es
s
a
n
d
ca
n
ea
s
il
y
h
a
n
d
le
a
n
y
co
m
p
le
x
o
p
ti
m
izat
io
n
p
r
o
b
le
m
w
it
h
o
u
t
tr
ap
p
in
g
i
n
lo
ca
l
o
p
tim
a
[
1
8
]
.
Hen
ce
GW
O
h
as
b
e
en
u
s
ed
h
er
e
to
tu
n
e
UP
FC
b
ased
P
I
an
d
lead
-
lag
co
n
tr
o
ller
f
o
r
d
a
m
p
i
n
g
o
f
o
s
ci
llatio
n
s
i
n
p
o
w
er
s
y
s
te
m
,
a
n
d
it
h
a
s
b
ee
n
co
m
p
ar
ed
w
it
h
s
ta
n
d
ar
d
P
SO
an
d
DE
tech
n
iq
u
es to
j
u
s
ti
f
y
its
s
u
p
r
e
m
ac
y
.
T
h
e
m
ai
n
co
n
tr
ib
u
tio
n
o
f
t
h
is
w
o
r
k
i
n
clu
d
e
s
:
(
i)
t
h
e
s
u
p
p
lem
e
n
tar
y
UP
FC
b
ased
co
n
tr
o
ller
is
d
esig
n
ed
w
ith
P
I
an
d
lead
-
la
g
co
n
tr
o
ller
.
(
ii)
T
h
e
p
ar
am
ete
r
s
o
f
co
n
tr
o
ller
s
ar
e
o
p
ti
m
ize
d
b
y
P
SO,
DE
an
d
r
ec
en
tl
y
d
ev
elo
p
ed
GW
O
tech
n
iq
u
es.
(
iii)
A
b
r
o
ad
co
m
p
ar
is
o
n
h
as
b
ee
n
p
er
f
o
r
m
ed
b
etw
ee
n
o
p
ti
m
ized
P
I
an
d
lead
-
la
g
co
n
tr
o
ller
.
(
iv
)
T
h
is
w
o
r
k
h
a
s
b
ee
n
ex
ten
d
ed
t
o
m
u
lt
i
m
ac
h
i
n
e
s
y
s
te
m
w
i
th
a
d
if
f
er
e
n
t
k
in
d
o
f
n
eg
at
iv
e
r
ea
ctiv
e
p
o
w
er
lo
ad
in
g
f
o
r
co
m
p
lete
v
alid
atio
n
.
(
v
)
Deta
il
ei
g
e
n
v
alu
e
an
a
l
y
s
is
h
as
b
ee
n
p
er
f
o
r
m
ed
f
o
r
ea
ch
o
p
er
atin
g
co
n
d
it
io
n
t
o
j
u
s
tify
t
h
e
e
f
f
icac
y
o
f
m
o
s
t d
ee
m
ed
f
it
GW
O
o
p
ti
m
ized
lead
-
lag
co
n
tr
o
ller
2.
T
H
E
S
I
N
G
L
E
M
ACH
I
NE
P
O
WE
R
SY
ST
E
M
UNDER S
T
UDY
I
n
t
h
is
ca
s
e
a
s
i
n
g
le
m
ac
h
in
e
c
o
n
n
ec
ted
to
i
n
f
i
n
ite
b
u
s
is
co
n
s
id
er
ed
as s
h
o
w
n
in
Fi
g
u
r
e
.
1
.
T
h
e
in
itial
co
n
d
itio
n
o
f
t
h
e
s
y
s
te
m
is
g
iv
en
in
ap
p
en
d
ix
A
1
.
T
h
e
UP
FC
co
n
s
is
t
s
o
f
t
w
o
v
o
lta
g
e
s
o
u
r
c
e
co
n
v
er
ter
s
(
VSC
)
is
co
n
n
ec
ted
b
et
w
ee
n
g
en
er
at
o
r
an
d
in
f
i
n
ite
b
u
s
.
O
n
e
VSC
i
s
s
er
ie
s
co
n
n
ec
ted
a
n
d
an
o
t
h
e
r
is
s
h
u
n
t
co
n
n
ec
ted
w
it
h
t
h
e
l
in
e.
UP
F
C
h
a
s
f
o
u
r
co
n
tr
o
l
ac
tio
n
s
w
h
ic
h
ar
e
m
B
,
δB
,
m
E
an
d
δE.
O
u
t
o
f
w
h
i
ch
m
B
a
n
d
δB
ar
e
m
o
d
u
latio
n
in
d
e
x
an
d
p
h
ase
a
n
g
le
o
f
s
er
ies V
SC
r
esp
ec
ti
v
el
y
.
So
o
n
m
E
a
n
d
δE
ar
e
ar
e
m
o
d
u
latio
n
in
d
e
x
an
d
p
h
ase
an
g
le
o
f
s
h
u
n
t V
S
C
r
es
p
ec
tiv
el
y
.
Fig
u
r
e
1
.
T
h
e
SMI
B
s
y
s
te
m
u
n
d
er
s
tu
d
y
2
.
1
.
DYNA
M
I
C
M
O
DE
L
O
F
T
H
E
SYS
T
E
M
2
.
1
.
1
No
n
L
inea
r
M
o
del
B
y
ig
n
o
r
in
g
r
esi
s
ta
n
ce
o
f
th
e
lin
e,
n
o
n
lin
ea
r
m
o
d
el
o
f
s
in
g
le
m
ac
h
i
n
e
p
o
w
er
s
y
s
t
e
m
ca
n
b
e
r
ep
r
esen
ted
b
y
f
o
llo
w
in
g
eq
u
a
tio
n
s
[
8
]
)
(
.
M
D
P
P
e
i
(
1
)
)
1
ω
(
ω
δ
0
.
(
2
)
0
d
fd
q
.
q
T
/
)
E
E
(
E
(
3
)
a
t
r
e
f
a
fd
fd
T
V
V
K
E
E
/
)
(
.
(
4
)
E
Eq
E
Ed
dc
B
E
Eq
E
Ed
dc
E
dc
δ
c
o
s
I
δ
s
i
n
I
C
4
m
3
δ
c
o
s
I
δ
s
i
n
I
C
4
m
3
V
(
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
E
ffica
cy
o
f G
W
O
Op
tim
iz
ed
P
I
a
n
d
Lea
d
-
La
g
C
o
n
tr
o
ller
fo
r
Desig
n
o
f U
P
F
C
...
(
R
a
n
ja
n
K
u
ma
r
Ma
llick
)
243
T
h
e
r
ea
l p
o
w
er
b
alan
ce
b
et
w
e
en
s
h
u
n
t V
S
C
a
n
d
s
er
ies VS
C
ca
n
b
e
r
ep
r
esen
ted
b
y
eq
u
a
tio
n
-
(
6
)
as
0
)
I
V
I
V
R
e
(
*
E
E
*
B
B
(
6
)
2
.
1
.
2
.
L
inea
r
Dy
na
m
ic
M
o
del
T
h
e
lin
ea
r
m
o
d
el
o
f
p
o
w
er
s
y
s
te
m
ca
n
b
e
o
b
tai
n
ed
b
y
li
n
e
ar
izin
g
th
e
n
o
n
li
n
ea
r
m
o
d
el
ar
o
u
n
d
th
e
in
itial o
p
er
atin
g
co
n
d
itio
n
r
ep
r
esen
ted
b
y
f
o
llo
w
in
g
eq
u
atio
n
s
.
ω
Δ
ω
δ
Δ
0
.
(
7
)
M
ω
Δ
D
P
Δ
ω
Δ
e
.
(
7
)
0
d
fd
q
.
q
T
/
)
E
Δ
E
Δ
(
E
Δ
(
8
)
a
t
r
e
f
a
fd
.
fd
T
/
)
V
Δ
V
Δ
(
K
E
Δ
E
Δ
(
9
)
B
b
c
B
cb
E
e
c
E
cE
dc
q
dc
K
m
K
K
m
K
V
K
E
K
K
V
9
'
8
7
(
1
0
)
W
h
er
e
B
b
p
B
pi
E
E
p
E
pe
dc
pd
q
e
K
m
K
K
m
K
V
K
E
K
K
P
'
3
1
(
1
1
)
B
q
B
qb
E
q
E
qe
dc
qd
q
d
B
E
k
m
k
k
m
k
V
k
E
k
k
E
'
3
4
(
1
2
)
B
b
v
B
vb
E
E
v
E
v
dc
d
q
t
k
m
k
k
m
k
V
kV
E
k
k
V
'
6
5
(
1
3
)
3.
SM
AL
L
SI
G
NA
L
M
O
DE
L
O
F
SI
NG
L
E
M
ACH
I
NE
SY
ST
E
M
T
h
e
Hef
f
r
o
n
P
h
ilip
s
tr
an
s
f
er
f
u
n
ct
io
n
m
o
d
el
o
f
s
in
g
le
m
ac
h
in
e
p
o
w
er
s
y
s
te
m
i
s
s
h
o
w
n
in
Fig
u
r
e
2
.
T
h
e
‘
K’
co
n
s
ta
n
ts
o
f
t
h
is
m
o
d
el
ar
e
ca
lcu
lated
w
i
th
r
e
f
e
r
en
ce
to
in
it
ial
o
p
er
atin
g
co
n
d
itio
n
a
n
d
s
y
s
te
m
p
ar
am
eter
s
[
9
]
.
T
h
e
in
itial
o
p
er
atin
g
co
n
d
itio
n
is
g
i
v
e
n
in
ap
p
en
d
ix
A
1
.
T
h
is
m
o
d
el
h
as
b
ee
n
d
ev
elo
p
ed
b
y
u
s
i
n
g
E
q
u
atio
n
(7
-
1
1
)
an
d
m
o
d
if
icatio
n
o
f
b
asic
He
f
f
r
o
n
P
h
ilip
s
m
o
d
el
w
ith
UP
F
C
.
I
n
th
is
m
o
d
el
[
Δ
U]
is
th
e
co
n
tr
o
l
v
ec
to
r
in
co
l
u
m
n
f
o
r
m
a
n
d
[
K
pu
]
,
[
K
vu
]
,
[
K
qu
]
,
[
K
cu
]
v
ec
to
r
s
ar
e
i
n
r
o
w
f
o
r
m
g
iv
e
n
b
y
f
o
llo
w
i
n
g
ex
p
r
ess
io
n
s
.
[
Δ
U]
=[
Δ
m
E
Δδ
E
Δm
B
Δδ
B
]
T
,
[
K
pu
]
=[
,
[
K
vu
]
=[
]
,
[
K
qu
]
=[
,
[K
cu
]
=[
Fig
u
r
e
2
.
Mo
d
if
ied
Hef
f
r
o
n
-
P
h
illi
p
s
m
o
d
el
w
it
h
UP
FC
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
6
,
No
.
4
,
Dec
em
b
er
201
7
:
2
4
1
–
2
5
1
244
4.
DAM
P
I
N
G
CO
NT
RO
L
L
E
R
T
h
e
o
b
j
ec
tiv
e
o
f
d
a
m
p
i
n
g
co
n
tr
o
ller
is
to
p
r
o
v
id
e
s
u
p
p
le
m
en
tar
y
co
n
tr
o
l
ac
tio
n
to
th
e
g
en
er
ato
r
to
d
am
p
lo
w
f
r
eq
u
en
c
y
o
s
cilla
tio
n
s
an
d
t
h
is
ac
tio
n
is
b
ased
o
n
UP
FC
.
T
h
e
UP
F
C
h
as
f
o
u
r
co
n
tr
o
l a
ctio
n
s
m
B
,
δ
B,
m
E
an
d
δ
E.
Ou
t
o
f
t
h
ese
f
o
u
r
ac
tio
n
s
t
w
o
co
n
tr
o
l
ac
tio
n
s
ar
e
tak
en
h
er
e
to
p
r
o
v
id
e
d
am
p
in
g
to
r
q
u
e
b
ec
au
s
e
,
as p
er
r
esear
ch
es th
e
s
e
ar
e
b
est co
n
tr
o
l a
ctio
n
s
to
d
esig
n
d
a
m
p
in
g
co
n
tr
o
ller
[
6
]
4
.
1
P
ro
po
rt
io
na
l In
t
eg
ra
l (
P
I
)
s
t
ruct
ure
T
h
e
s
tr
u
ctu
r
e
o
f
a
p
o
p
u
lar
P
I
co
n
tr
o
ller
is
g
i
v
en
i
n
Fi
g
u
r
e
3
.
T
h
e
in
p
u
t
to
P
I
co
n
tr
o
ller
is
s
p
ee
d
d
ev
iatio
n
,
b
ei
n
g
th
e
er
r
o
r
s
i
g
n
al
a
n
d
o
u
tp
u
t
o
f
co
n
tr
o
ller
p
r
o
v
id
es
th
e
co
n
tr
o
l
ac
tio
n
to
b
e
ex
ec
u
ted
.
K1
a
n
d
K2
ar
e
th
e
g
ai
n
s
o
f
p
r
o
p
o
r
tio
n
al
an
d
i
n
te
g
r
al
c
o
n
tr
o
ller
s
r
esp
ec
tiv
el
y
,
w
h
ich
ar
e
to
b
e
o
p
ti
m
ized
b
y
t
h
e
o
p
tim
izatio
n
tec
h
n
iq
u
es.
Fig
u
r
e
3
.
P
I
c
o
n
tr
o
ller
s
tr
u
ctu
r
e
Fig
u
r
e
4
.
Stru
ct
u
r
e
o
f
lead
-
la
g
co
n
tr
o
ller
4
.
2
T
he
lea
d
-
la
g
s
t
ruct
ure
T
h
e
lead
-
lag
co
n
tr
o
ller
h
a
s
t
h
r
ee
b
lo
ck
s
,
g
ai
n
,
w
as
h
o
u
t
a
n
d
p
h
ase
co
m
p
e
n
s
atio
n
as
s
h
o
w
n
in
Fi
g
u
r
e
4
.
T
h
e
g
ain
r
eq
u
ir
ed
b
y
t
h
e
co
n
tr
o
ller
is
p
r
o
v
id
ed
b
y
th
e
g
ai
n
b
lo
ck
o
f
g
ai
n
Kp
.
T
h
e
w
as
h
o
u
t
b
lo
ck
ac
ts
lik
e
a
h
ig
h
p
as
s
f
ilter
w
it
h
ti
m
e
co
n
s
tan
t
(
T
w
)
1
-
2
0
s
ec
.
C
h
o
o
s
i
n
g
o
f
t
h
i
s
v
al
u
e
i
s
n
o
t
s
o
cr
u
ci
al
an
d
is
ta
k
e
n
as
1
0
s
ec
.
in
th
i
s
w
o
r
k
.
T
h
e
p
h
a
s
e
c
o
m
p
e
n
s
at
io
n
b
lo
ck
p
r
o
v
id
es
n
ec
ess
ar
y
p
h
ase
lead
t
h
er
e
b
y
c
o
m
p
e
n
s
at
in
g
f
o
r
th
e
r
eq
u
ir
ed
p
h
ase
lag
b
et
w
ee
n
i
n
p
u
t
an
d
o
u
tp
u
t
o
f
co
n
tr
o
ller
w
it
h
t
i
m
e
co
n
s
ta
n
t
s
T
1
an
d
T
2
.
No
w
Kp
,
T
1
an
d
T
2
ar
e
to
b
e
o
p
ti
m
ized
b
y
th
e
o
p
tim
izatio
n
tec
h
n
iq
u
es.
5.
O
B
J
E
CT
I
V
E
F
UNC
T
I
O
N
T
h
e
p
r
o
b
lem
o
f
d
a
m
p
i
n
g
o
f
o
s
cillatio
n
i
s
p
u
t
to
an
o
b
j
ec
tiv
e
f
u
n
ctio
n
,
w
h
ich
is
o
f
I
T
A
E
t
y
p
e.
Fo
r
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
,
th
e
d
is
tu
r
b
an
ce
co
n
s
id
er
ed
is
1
0
p
er
ce
n
t
r
is
e
in
m
ec
h
an
ica
l
in
p
u
t
p
o
w
e
r
to
g
en
er
ato
r
.
T
h
e
o
b
j
ec
tiv
e
f
u
n
c
tio
n
is
r
ep
r
ese
n
t
ed
b
y
E
q
-
2
9
,
w
h
ic
h
co
n
s
id
er
s
s
p
ee
d
,
lin
e
p
o
w
er
an
d
d
c
b
u
s
v
o
ltag
e
d
ev
iatio
n
.
dt
P
Δ
t
dt
V
Δ
t
dt
ω
Δ
t
J
t
s
i
m
0
e
t
s
i
m
0
dc
t
s
i
m
0
(
1
4
)
T
h
e
p
r
o
b
lem
n
o
w
i
s
m
in
i
m
iza
tio
n
o
f
‘
J
’
s
u
b
j
ec
t to
f
o
llo
w
in
g
co
n
s
tr
ain
t
s
K1
i
m
in
≤
K1
≤
K1
i
m
ax
K2
i
m
in
≤
K2
≤
K2
i
m
ax
K
pi
min
≤
K
pi
≤
Kpim
ax
(
1
5
)
T
1i
m
in
≤
T
1i
≤
T
1i
m
ax
T
2i
m
in
≤
T
2i
≤
T
2i
m
ax
W
h
er
e
t
sim
is
th
e
s
i
m
u
latio
n
ti
m
e,
th
e
s
u
p
er
s
cr
ip
ts
m
i
n
an
d
m
a
x
ar
e
th
e
lo
w
er
an
d
u
p
p
er
lim
iti
n
g
v
alu
e
s
o
f
r
esp
ec
tiv
e
p
ar
a
m
ete
r
s
.
K1
,
K2
ar
e
o
n
l
y
f
o
r
P
I
co
n
tr
o
ller
an
d
Kp
,
T
1
,
T
2
a
r
e
f
o
r
lead
-
lag
co
n
tr
o
ller
.
T
h
e
r
an
g
e
o
f
K1
a
n
d
Kp
h
a
s
b
ee
n
ta
k
en
f
r
o
m
1
to
1
0
0
.
T
h
e
r
an
g
e
o
f
K2
,
T
1
an
d
T
2
is
ta
k
e
n
f
r
o
m
0
to
1
.
No
w
th
e
p
r
o
b
lem
i
s
to
o
p
ti
m
ize
t
h
e
s
e
p
ar
am
e
ter
s
b
y
Gr
e
y
W
o
lf
O
p
ti
m
is
er
6.
P
SO
T
E
CH
N
I
Q
UE
P
SO
is
a
s
i
m
p
le
a
n
d
f
ast
p
o
p
u
latio
n
b
ased
m
eta
h
eu
r
i
s
tic
t
ec
h
n
iq
u
e
[
1
1
]
.
I
n
P
SO
th
e
p
ar
ticles
ar
e
allo
w
ed
to
m
o
v
e
ar
o
u
n
d
th
e
s
ea
r
ch
s
p
ac
e
in
m
u
lti
d
i
m
e
n
s
io
n
al
p
ath
.
T
h
e
p
o
s
itio
n
o
f
a
p
ar
ticle
is
u
p
d
ated
b
y
its
o
w
n
ex
p
er
ie
n
ce
an
d
n
ei
g
h
b
o
r
p
ar
ticle.
E
f
f
icac
y
o
f
P
SO
is
ev
en
c
h
alle
n
g
i
n
g
to
g
en
et
ic
alg
o
r
ith
m
.
T
h
e
v
elo
cit
y
o
f
s
w
ar
m
is
g
iv
e
n
b
y
E
q
u
atio
n
3
1
as g
i
v
en
b
elo
w
.
T
h
e
v
elo
cit
y
o
f
ea
c
h
s
w
ar
m
ca
n
b
e
g
iv
en
b
y
:
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
E
ffica
cy
o
f G
W
O
Op
tim
iz
ed
P
I
a
n
d
Lea
d
-
La
g
C
o
n
tr
o
ller
fo
r
Desig
n
o
f U
P
F
C
...
(
R
a
n
ja
n
K
u
ma
r
Ma
llick
)
245
)
(
)
(
,
2
2
,
1
1
1
k
i
k
g
b
e
st
i
k
i
k
p
b
e
st
i
k
i
k
i
x
P
r
a
n
c
x
P
r
a
n
c
wv
v
(
1
6
)
W
h
er
e,
c
1
an
d
c
2
ar
e
th
e
ac
ce
l
er
atio
n
co
ef
f
icie
n
ts
,
w
is
th
e
i
n
er
tial
w
ei
g
h
t
v
ar
y
i
n
g
b
et
w
ee
n
0
.
9
to
0
.
4
r
an
1
an
d
r
an
2
ar
e
th
e
t
w
o
r
an
d
o
m
v
ar
ia
b
les in
t
h
e
r
an
g
e
o
f
[
0
,
1
]
.
T
h
e
s
w
ar
m
p
o
s
itio
n
is
u
p
d
ated
b
y
i
i
n
e
w
i
v
x
x
(
1
7
)
T
h
e
b
est s
o
lu
tio
n
f
o
r
th
e
n
e
x
t i
ter
atio
n
s
is
g
i
v
en
b
y
o
th
e
r
w
i
s
e
i
x
)
i
x
(
f
)
n
e
w
,
i
x
(
i
f
f
n
e
w
,
i
x
1
k
i
x
(
1
8
)
7.
DE
T
E
CH
NI
Q
U
E
I
t
is
a
n
e
v
o
lu
t
io
n
ar
y
al
g
o
r
ith
m
t
y
p
e
tec
h
n
iq
u
e,
w
h
er
e
t
h
e
p
r
o
ce
s
s
o
f
s
ea
r
ch
i
n
g
i
s
g
u
id
ed
b
y
d
is
ta
n
ce
as
w
ell
as
d
ir
ec
tio
n
f
r
o
m
cu
r
r
e
n
t p
o
p
u
latio
n
[
1
3
]
.
T
h
e
m
o
s
t
i
m
p
o
r
ta
n
t
s
ea
r
ch
m
ec
h
a
n
is
m
in
DE
i
s
m
u
tatio
n
.
I
n
DE
,
a
tr
ail
v
ec
to
r
is
o
b
tain
ed
b
y
o
p
er
atin
g
th
e
tar
g
et
a
n
d
d
if
f
er
en
ce
v
ec
to
r
.
I
n
a
M
-
d
i
m
e
n
s
io
n
al
s
ea
r
ch
s
p
ac
e
m
u
tan
t
v
ec
to
r
ca
n
b
e
o
b
tain
ed
as
)
(
*
,
3
,
2
,
1
1
,
g
a
g
a
g
a
g
i
x
x
F
x
v
(
1
9
)
W
h
er
e
2
,
1
a
a
….
.
ar
e
r
an
d
o
m
i
n
te
g
er
s
.
T
o
ex
p
an
d
th
e
d
iv
er
s
it
y
o
f
t
h
e
p
ar
a
m
eter
s
cr
o
s
s
o
v
er
is
d
o
n
e
w
h
er
e
p
ar
en
t
v
ec
to
r
is
m
i
x
ed
w
it
h
m
u
tated
v
ec
to
r
to
p
r
o
d
u
ce
a
tr
ail
v
ec
to
r
v
ji,
g+
1
as g
i
v
en
b
y
v
ji
,
g
+1
if (r
a
n
d
mj
≤
CRO)
or
,
j
=
j
rand
m
x
ji,
g+
1
if (
r
a
n
d
mj> CRO
)
o
r
,
j ≠
j
randm
(
2
0
)
j
=1
,
2
,
3
……….
.
M,
C
R
O
is
t
h
e
cr
o
s
s
o
v
er
co
n
s
ta
n
t [
0
,
1
]
.
8.
G
R
E
Y
WO
L
F
O
P
T
I
M
I
Z
E
R
(
G
WO
)
T
E
CH
NI
Q
U
E
I
t
is
a
s
w
ar
m
in
telli
g
en
ce
t
y
p
e
m
etah
e
u
r
is
t
ic
alg
o
r
it
h
m
r
ec
en
tl
y
p
u
b
lis
h
ed
[
1
7
]
.
T
h
is
tech
n
iq
u
e
h
a
s
b
ee
n
i
m
i
tated
b
y
th
e
w
a
y
Gr
e
y
W
o
lf
s
h
u
n
t
f
o
r
th
eir
p
r
e
y
.
T
h
e
y
r
e
m
ai
n
w
it
h
i
n
a
p
ac
k
o
r
g
r
o
u
p
.
T
h
e
w
o
l
f
s
ar
e
r
an
k
ed
in
th
e
g
r
o
u
p
as
alp
h
a
(
α
)
,
b
eta
(
β),
d
elta
(
δ)
an
d
o
m
e
g
a
(
ω
)
.
T
h
e
m
o
s
t
d
ee
m
ed
f
it
s
o
lu
tio
n
is
p
r
o
v
id
ed
b
y
th
e
p
o
s
i
tio
n
o
f
α
f
o
llo
w
ed
b
y
β,
δ
a
n
d
r
est
s
o
lu
t
io
n
b
y
p
o
s
itio
n
o
f
ω
.
W
h
e
n
t
h
e
h
u
n
t
in
g
p
r
o
ce
s
s
b
eg
i
n
s
,
th
e
y
e
n
cir
cle
t
h
e
p
r
e
y
,
w
h
ic
h
i
s
m
at
h
e
m
atica
ll
y
f
o
r
m
u
lated
as:
)
(
)
(
.
t
X
t
X
C
D
P
(
2
1
)
D
A
t
X
t
X
P
.
)
(
)
1
(
(
2
2
)
W
h
er
e,
th
e
cu
r
r
en
t i
ter
atio
n
is
r
ep
r
esen
ted
b
y
‘
t
’
.
⃗
,
⃗
b
ein
g
co
e
f
f
icie
n
t v
ec
to
r
s
an
d
⃗
⃗
⃗
⃗
⃗
is
t
h
e
p
o
s
itio
n
v
ec
to
r
o
f
p
r
ey
.
T
h
e
g
r
e
y
w
o
l
f
p
o
s
itio
n
i
s
d
en
o
ted
b
y
⃗
.
A
a
n
d
C
v
ec
to
r
s
ar
e
g
i
v
e
n
b
y
a
r
a
A
1
.
.
2
(
2
3
)
2
.
2
r
C
(
2
4
)
W
h
er
e,
r
1
an
d
r
2
ar
e
r
an
d
o
m
v
ec
to
r
s
b
et
w
ee
n
[
0
1
]
.
I
n
th
e
co
u
r
s
e
o
f
i
ter
atio
n
s
,
th
e
co
m
p
o
n
en
t
‘
a
’
d
ec
r
ea
s
es
f
r
o
m
2
to
0
lin
ea
r
l
y
f
o
r
ea
ch
it
er
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
6
,
No
.
4
,
Dec
em
b
er
201
7
:
2
4
1
–
2
5
1
246
Fo
r
in
it
ializi
n
g
t
h
e
h
u
n
ti
n
g
p
r
o
ce
s
s
,
it
is
as
s
u
m
ed
t
h
at
α
,
β
an
d
δ
w
o
lv
e
s
k
n
o
w
t
h
e
e
x
ac
t
p
o
s
itio
n
o
f
p
r
e
y
an
d
th
e
cu
r
r
en
t p
o
s
itio
n
o
f
t
h
ese
wo
lv
es a
r
e
u
p
d
ated
b
y
t
h
e
f
o
llo
w
i
n
g
eq
u
atio
n
s
.
X
X
C
D
.
1
,
X
X
C
D
.
2
,
X
X
C
D
.
3
(
2
5
)
)
.(
),
.(
,
)
.(
3
3
2
2
1
1
D
A
X
X
D
A
X
X
D
A
X
X
(
2
6
)
T
o
f
in
d
th
e
b
est lo
ca
tio
n
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IJ
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I
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8
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11.
CO
NCLU
SI
O
N
I
n
t
h
is
w
o
r
k
UP
FC
b
ased
s
u
p
p
le
m
en
tar
y
co
n
tr
o
ller
is
e
m
p
l
o
y
ed
to
d
a
m
p
in
tr
a
p
lan
t
an
d
in
ter
ar
ea
o
s
cillatio
n
s
in
p
o
w
er
s
y
s
te
m
.
A
b
r
o
ad
co
m
p
ar
is
o
n
h
as
b
ee
n
p
er
f
o
r
m
ed
e
m
p
lo
y
in
g
UP
FC
b
ased
P
I
an
d
lead
-
lag
co
n
tr
o
ller
to
d
a
m
p
o
s
c
illa
tio
n
s
in
p
o
w
er
s
y
s
te
m
s
u
b
j
ec
t
to
w
id
e
r
a
n
g
e
o
f
lo
ad
in
g
co
n
d
itio
n
w
it
h
d
etail
eig
en
v
al
u
e
an
al
y
s
is
.
R
ec
e
n
tl
y
r
ev
ea
led
GW
O
tech
n
iq
u
e,
P
S
O
an
d
DE
tech
n
iq
u
es
ar
e
ex
p
l
icitl
y
u
s
ed
to
tu
n
e
th
e
p
ar
a
m
eter
s
o
f
P
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an
d
lead
-
la
g
co
n
tr
o
ller
s
.
I
t
h
a
s
b
ee
n
f
o
u
n
d
th
a
t
f
o
r
d
a
m
p
i
n
g
co
n
tr
o
ller
d
esig
n
lea
d
-
la
g
co
n
tr
o
ller
is
a
b
etter
ch
o
ice
th
an
P
I
co
n
tr
o
ller
an
d
also
GW
O
o
p
tim
izatio
n
tec
h
n
iq
u
e
is
m
u
ch
b
etter
t
h
an
P
SO
an
d
DE
tech
n
iq
u
e.
Hen
ce
G
W
O
o
p
tim
ized
s
u
p
p
le
m
en
tar
y
UP
FC
b
ased
lead
-
lag
co
n
tr
o
ller
is
m
u
c
h
s
u
p
er
io
r
to
d
am
p
p
o
w
er
s
y
s
te
m
o
s
cil
lat
io
n
s
.
RE
F
E
R
E
NC
E
S
[1
]
.
P
a
d
iy
a
r
K R,
F
A
C
T
S
c
o
n
tro
ll
e
rs i
n
p
o
w
e
r
tran
s
m
issio
n
a
n
d
d
istri
b
u
ti
o
n
.
Ne
w
a
g
e
In
ter
n
a
ti
o
n
a
l
(
P)
L
imit
e
d
2
0
0
7
.
[2
]
.
Ke
ri
A
JF,
L
o
m
b
a
rd
X
,
Ed
ris
AA
.
,
Un
if
ied
p
o
w
e
r
f
lo
w
c
o
n
tro
ll
e
r:
m
o
d
e
ll
in
g
a
n
d
a
n
a
ly
si
s.
IEE
E
T
ra
n
s
Po
we
rD
e
li
v
e
r
1
9
9
9
;
14
(
2
):6
4
8
–
5
4
.
[3
]
.
D.
Na
ra
si
m
h
a
R
a
o
,
V
.
S
a
rit
h
a
.
,
P
o
w
e
r
S
y
ste
m
O
sc
il
latio
n
Da
m
p
in
g
Us
in
g
N
e
w
F
a
c
ts
De
v
i
c
e
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
),
V
o
l
5
N
o
2
,
2
0
1
5
p
a
g
e
s 1
9
8
-
2
0
4
[4
]
.
No
ro
o
z
ian
M
,
A
n
d
e
rso
n
G
,
Da
m
p
in
g
o
f
p
o
w
e
r
s
y
ste
m
o
sc
il
latio
n
s
b
y
u
se
o
f
c
o
n
tro
ll
a
b
le
c
o
m
p
o
n
e
n
ts.
IEE
E
T
ra
n
s
PW
RD
1
9
9
4
;
9
:
2
0
4
6
–
5
4
.
[5
]
.
M
a
h
m
o
u
d
Zad
e
h
b
a
g
h
e
ri
,
Ra
h
im
Ild
a
ra
b
a
d
i
,
M
a
ji
d
Ba
g
h
a
e
iNe
jad
,
R
e
v
ie
w
o
f
th
e
UP
F
C
Dif
f
e
re
n
t
M
o
d
e
ls
in
Re
c
e
n
t
Ye
a
rs
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r E
lec
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
(
IJ
PE
DS
)
,
V
o
l
4
N
o
3
,
2
0
1
4
p
a
g
e
s 3
4
3
-
3
5
5
[6
]
.
R.
K.
P
a
n
d
e
y
,
N.K.
S
in
g
h
,
UPF
C
c
o
n
tro
l
p
a
ra
m
e
ter
id
e
n
ti
f
ica
ti
o
n
f
o
r
e
ff
e
c
ti
v
e
p
o
w
e
r
o
sc
il
l
a
ti
o
n
d
a
m
p
in
g
,
El
e
c
trica
l
Po
we
r a
n
d
En
e
rg
y
S
y
st
e
ms
3
1
(2
0
0
9
)
2
6
9
–
2
7
6
.
[7
]
.
Na
b
a
v
i
-
Nia
k
i
A
,
Ir
a
v
a
n
i
M
R
,
S
tea
d
y
-
st
a
te
a
n
d
d
y
n
a
m
i
c
m
o
d
e
ls
o
f
u
n
if
i
e
d
p
o
w
e
r
f
lo
w
c
o
n
tro
ll
e
r
(UPF
C)
f
o
r
p
o
w
e
r
s
y
ste
m
stu
d
ies
.
IEE
E
T
ra
n
s P
o
we
r S
y
st
,
1
9
9
6
;
1
1
(
4
):1
9
3
7
–
4
3
.
[8
]
.
W
a
n
g
HF,
S
w
if
t
F
J,
A
Un
if
ied
m
o
d
e
l
f
o
r
th
e
a
n
a
ly
sis
o
f
F
A
C
T
S
d
e
v
ice
s
in
d
a
m
p
in
g
p
o
w
e
r
sy
ste
m
o
sc
il
latio
n
s
p
a
r
t
I:
sin
g
le
-
m
a
c
h
in
e
in
f
in
it
e
-
b
u
s p
o
w
e
r
s
y
ste
m
s.
IEE
E
T
ra
n
s P
o
we
r
De
li
v
e
r
1997
;
1
2
:9
4
1
–
6
.
[9
]
.
T
a
m
b
e
y
N,
Ko
th
a
ri
M
L
,
D
a
m
p
in
g
o
f
p
o
w
e
r
s
y
ste
m
o
sc
il
latio
n
s
w
it
h
u
n
if
ied
p
o
w
e
r
f
lo
w
c
o
n
tro
ll
e
r
(UP
F
C).
IEE
Pro
c
Ge
n
e
r T
ra
n
s Distri
b
2
0
0
3
;
1
5
0
:
1
2
9
–
40.
[1
0
]
.
T
a
h
e
r
S
A
,
He
m
m
a
ti
R,
A
b
d
o
lalip
o
u
r
A
,
A
k
b
a
ri
S
,
Co
m
p
a
riso
n
o
f
d
if
fe
re
n
t
ro
b
u
st
c
o
n
tr
o
l
m
e
th
o
d
s
i
n
th
e
d
e
sig
n
o
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