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co
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(
L
FC
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[
1
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in
a
p
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s
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s
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is
to
m
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t
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s
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s
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[
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Go
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s
m
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Flu
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[
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f
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an
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147
f
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m
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[
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Sig
n
if
ican
t
f
r
eq
u
en
c
y
f
lu
ctu
atio
n
s
m
ay
h
av
e
a
d
et
r
im
en
tal
im
p
ac
t
o
n
elec
tr
ical
eq
u
ip
m
en
t
a
n
d
t
h
e
q
u
ality
o
f
elec
tr
icity
;
ii)
en
er
g
y
b
alan
ce
[
9
]
:
L
FC
h
elp
s
th
e
s
y
s
tem
m
ain
tain
an
eq
u
ilib
r
iu
m
b
etwe
en
p
o
wer
p
r
o
d
u
ctio
n
a
n
d
co
n
s
u
m
p
tio
n
;
an
d
iii)
em
e
r
g
en
c
y
p
r
ev
en
ti
o
n
:
m
ain
tain
in
g
th
e
f
r
eq
u
en
c
y
with
in
p
r
escr
ib
e
d
lim
its
m
itig
ates
th
e
lik
elih
o
o
d
o
f
ca
tast
r
o
p
h
ic
e
v
en
ts
[
1
0
]
,
s
u
ch
as
wid
esp
r
ea
d
p
o
wer
o
u
tag
es.
L
FC
is
a
v
ital
an
d
in
tr
icate
p
r
o
ce
d
u
r
e
th
at
e
n
s
u
r
es
th
e
s
tab
ilit
y
an
d
d
ep
e
n
d
ab
ilit
y
o
f
a
p
o
wer
s
y
s
tem
.
I
t
o
p
er
ates
in
tan
d
em
with
th
e
m
ain
co
n
tr
o
l
to
e
f
f
icien
tly
ad
ap
t
to
f
lu
ct
u
atio
n
s
in
p
o
wer
r
eq
u
ir
em
en
ts
,
g
u
a
r
an
te
ein
g
th
at
th
e
s
y
s
tem
f
r
eq
u
e
n
cy
s
tay
s
with
in
ac
ce
p
t
ab
le
p
ar
am
eter
s
.
I
n
d
u
s
tr
ial
c
o
n
tr
o
l
s
y
s
tem
s
u
s
e
a
p
r
o
p
o
r
tio
n
al
-
i
n
teg
r
al
-
d
er
iv
a
tiv
e
(
PID
)
[
1
1
]
c
o
n
tr
o
ller
as
a
f
ee
d
b
ac
k
m
ec
h
an
is
m
.
T
h
e
c
o
m
b
in
atio
n
o
f
its
s
im
p
licity
an
d
ef
f
icac
y
m
ak
es
it
a
wid
ely
f
av
o
r
ed
o
p
tio
n
f
o
r
o
v
er
s
ee
in
g
d
iv
er
s
e
o
p
e
r
atio
n
s
[
1
2
]
.
T
h
e
PID
co
n
tr
o
ller
co
m
p
u
tes
th
e
er
r
o
r
v
alu
e
b
y
s
u
b
tr
ac
tin
g
t
h
e
in
ten
d
ed
s
etp
o
in
t
f
r
o
m
th
e
o
b
s
er
v
ed
p
r
o
ce
s
s
v
ar
iab
le
[
1
3
]
an
d
th
en
ad
ju
s
ti
n
g
it
u
s
in
g
p
r
o
p
o
r
tio
n
al,
in
te
g
r
al,
a
n
d
d
er
iv
ativ
e
ter
m
s
.
A
two
-
d
eg
r
ee
-
of
-
f
r
ee
d
o
m
(
2
-
DOF)
PID
co
n
tr
o
ller
e
n
h
an
ce
s
th
e
ca
p
ab
ilit
ies
o
f
th
e
co
n
v
e
n
tio
n
al
PID
co
n
tr
o
ller
.
T
h
e
s
y
s
tem
h
as
tw
o
d
is
tin
ct
s
ets
o
f
PID
p
ar
am
e
ter
s
[
1
4
]
:
o
n
e
s
p
ec
if
ically
d
es
ig
n
ed
f
o
r
ac
cu
r
ate
m
o
n
ito
r
in
g
o
f
t
h
e
d
esire
d
s
et
p
o
in
t,
an
d
an
o
t
h
er
aim
ed
at
e
f
f
ec
tiv
ely
r
ejec
tin
g
d
is
tu
r
b
an
c
es.
T
h
is
in
n
o
v
ativ
e
s
etu
p
en
ab
les
en
h
a
n
ce
d
p
r
ec
is
io
n
an
d
ef
f
icien
cy
in
co
n
tr
o
l.
W
h
en
th
in
g
s
g
et
co
m
p
licated
in
th
e
wo
r
k
p
lace
,
a
2
-
DOF
PID
co
n
tr
o
ller
s
ca
n
m
ak
e
th
e
wh
o
le
s
y
s
tem
wo
r
k
m
u
ch
b
etter
b
y
f
in
d
in
g
th
e
b
est
way
to
r
esp
o
n
d
to
ch
an
g
es in
th
e
s
etp
o
in
t a
n
d
d
is
tu
r
b
an
ce
s
.
T
h
is
r
esu
lts
in
im
p
r
o
v
ed
s
tab
ilit
y
an
d
r
esp
o
n
s
iv
e
n
ess
.
T
h
e
ch
ess
alg
o
r
ith
m
[
1
5
]
i
s
a
b
io
-
in
s
p
ir
ed
o
p
tim
izatio
n
tech
n
iq
u
e
th
at
u
tili
ze
s
th
e
s
tr
ateg
ic
m
an
eu
v
er
s
an
d
p
o
s
itio
n
al
p
lay
s
ee
n
in
ch
ess
.
T
h
is
alg
o
r
ith
m
aim
s
to
d
eter
m
in
e
th
e
m
o
s
t
ad
v
an
tag
eo
u
s
s
o
lu
tio
n
s
b
y
m
eth
o
d
ically
in
v
esti
g
atin
g
an
d
ca
p
italizin
g
o
n
th
e
s
ea
r
ch
s
p
ac
e,
u
s
in
g
t
ec
h
n
iq
u
es
s
im
ilar
to
th
o
s
e
u
s
ed
in
ch
ess
.
T
h
e
ch
ess
alg
o
r
ith
m
m
im
ics
th
e
co
g
n
itiv
e
p
r
o
ce
s
s
th
at
ch
ess
p
lay
er
s
em
p
lo
y
to
m
ak
e
d
ec
is
io
n
s
.
Du
r
in
g
a
g
a
m
e
o
f
ch
ess
,
p
lay
er
s
co
n
tin
u
ally
e
v
alu
ate
th
eir
ci
r
cu
m
s
tan
ce
s
a
n
d
m
a
k
e
ca
lcu
lated
d
ec
is
io
n
s
to
o
u
ts
m
ar
t
th
eir
ad
v
er
s
ar
ies.
T
h
is
en
co
m
p
a
s
s
es
b
o
th
th
e
ac
t
o
f
e
x
am
i
n
in
g
n
ew
p
o
s
s
ib
le
p
o
s
s
ib
ilit
ies
(
ex
p
lo
r
ato
r
y
ac
tio
n
s
)
[
1
6
]
a
n
d
u
s
in
g
ex
is
tin
g
ad
v
an
tag
es
(
ex
p
lo
itativ
e
m
an
eu
v
er
s
)
.
u
s
in
g
th
ese
co
n
ce
p
ts
,
th
e
ch
ess
alg
o
r
ith
m
ef
f
icien
tly
ex
am
in
es
o
p
tim
al
s
o
lu
tio
n
s
.
T
h
e
alg
o
r
ith
m
m
ay
i
n
v
esti
g
ate
d
if
f
er
en
t
ar
ea
s
o
f
th
e
s
ea
r
ch
s
p
ac
e
b
y
p
er
f
o
r
m
in
g
ex
p
lo
r
ato
r
y
m
o
v
e
m
en
ts
,
p
o
ten
tially
u
n
co
v
er
in
g
n
o
v
el
an
d
f
ea
s
ib
le
s
o
lu
tio
n
s
.
C
o
n
v
er
s
ely
,
ex
p
lo
it
ativ
e
s
tr
ateg
ies al
lo
w
th
e
alg
o
r
ith
m
to
co
n
ce
n
tr
ate
o
n
en
h
an
c
in
g
an
d
f
in
e
-
tu
n
in
g
th
ese
s
o
lu
tio
n
s
af
ter
th
eir
d
i
s
co
v
er
y
.
t
h
e
c
h
ess
alg
o
r
ith
m
ef
f
ec
tiv
ely
lev
er
a
g
es
th
e
d
u
al
n
atu
r
e
o
f
c
h
ess
s
tr
ateg
y
,
wh
ich
en
tails
b
alan
cin
g
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
,
to
n
av
ig
ate
co
m
p
lex
o
p
tim
izatio
n
is
s
u
es
an
d
d
is
co
v
er
h
ig
h
-
q
u
ality
s
o
lu
tio
n
s
.
Usi
n
g
th
e
c
h
ess
alg
o
r
ith
m
to
i
m
p
r
o
v
e
2
-
DOF
PID
co
n
tr
o
ller
s
in
L
FC
s
y
s
tem
s
lead
s
to
a
b
ig
b
o
o
s
t
in
co
n
tr
o
l p
er
f
o
r
m
a
n
ce
.
A
ch
ess
alg
o
r
ith
m
'
s
ab
ilit
y
to
ef
f
ec
tiv
e
ly
o
p
tim
ize
co
m
p
licated
co
n
tr
o
l sy
s
tem
s
is
d
u
e
to
its
ca
p
ac
ity
to
b
alan
ce
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
.
Su
b
s
eq
u
en
t
s
tu
d
ies
m
ay
ex
p
an
d
u
p
o
n
th
is
m
eth
o
d
to
in
clu
d
e
p
o
wer
s
y
s
tem
s
s
p
an
n
in
g
m
a
n
y
r
eg
io
n
s
an
d
ex
p
l
o
r
e
t
h
e
d
if
f
ic
u
lties
ass
o
ciate
d
with
im
p
lem
en
tin
g
it
in
r
ea
l
-
tim
e.
T
h
e
s
u
g
g
ested
ap
p
r
o
ac
h
co
m
b
in
es
s
o
p
h
is
ticated
co
n
tr
o
l
m
eth
o
d
s
with
b
io
-
in
s
p
ir
ed
o
p
tim
izatio
n
tech
n
iq
u
es
to
im
p
r
o
v
e
th
e
r
esil
ien
ce
an
d
ef
f
ec
tiv
e
n
ess
o
f
f
r
e
q
u
en
cy
r
eg
u
latio
n
in
th
e
p
o
wer
s
y
s
tem
.
T
h
is
h
as
th
e
p
o
ten
tial to
e
n
h
an
ce
t
h
e
s
tab
ilit
y
an
d
d
e
p
en
d
a
b
ilit
y
o
f
c
u
r
r
en
t p
o
wer
g
r
id
s
.
2.
T
H
E
M
O
DE
L
O
F
T
H
E
S
T
UDIE
D
P
O
WE
R
S
YS
T
E
M
AND
CO
NT
RO
L
L
E
R
S
T
R
UCTUR
E
2
.
1
.
T
wo
-
a
re
a
inte
rc
o
nn
ec
t
ed
t
herm
a
l po
wer
s
y
s
t
em
s
T
h
is
s
tu
d
y
f
o
cu
s
es
o
n
a
p
o
we
r
s
y
s
tem
co
n
s
is
tin
g
o
f
two
lin
k
ed
ar
ea
s
[
1
7
]
,
ea
c
h
o
f
wh
ich
in
clu
d
es
a
th
er
m
al
u
n
it
with
a
n
o
n
-
r
eh
ea
t
tu
r
b
in
e.
An
ab
r
u
p
t
f
lu
ct
u
atio
n
in
th
e
lo
ad
in
an
y
in
ter
co
n
n
ec
ted
p
ar
t
o
f
th
is
s
y
s
tem
r
esu
lts
in
a
f
r
eq
u
en
cy
d
ev
iatio
n
ac
r
o
s
s
all
r
eg
io
n
s
an
d
a
f
lu
ctu
atio
n
in
th
e
p
o
wer
tr
an
s
m
itted
o
v
er
th
e
tie
-
lin
es.
C
o
m
p
ar
ed
to
th
e
lo
ad
f
r
eq
u
e
n
cy
co
n
t
r
o
l
s
y
s
tem
,
th
e
ex
citatio
n
co
n
tr
o
l
s
y
s
tem
h
as
a
s
h
o
r
ter
tim
e
co
n
s
tan
t
[
1
8
]
.
T
h
is
m
ea
n
s
th
a
t
th
e
tr
an
s
ien
ts
in
th
e
e
x
citatio
n
v
o
ltag
e
c
o
n
tr
o
l
f
ad
e
awa
y
m
o
r
e
q
u
ick
l
y
,
b
u
t
th
ey
d
o
n
o
t
c
h
an
g
e
h
o
w
th
e
l
o
ad
f
r
eq
u
e
n
cy
co
n
tr
o
l
wo
r
k
s
[
1
9
]
.
T
h
e
lack
o
f
in
ter
ac
tio
n
b
etwe
en
ex
citatio
n
co
n
tr
o
l
a
n
d
l
o
ad
f
r
eq
u
e
n
cy
c
o
n
tr
o
l
is
d
u
e
to
th
eir
i
n
ab
ilit
y
to
r
esp
o
n
d
t
o
m
in
o
r
lo
ad
f
l
u
ctu
atio
n
s
.
T
h
u
s
,
we
m
ay
co
n
s
tr
u
ct
a
r
ep
r
esen
tati
o
n
an
d
ass
ess
it
s
ep
ar
ately
.
T
h
is
v
ital
in
f
o
r
m
atio
n
s
im
p
lifie
s
th
e
p
r
o
ce
s
s
o
f
b
u
ild
in
g
th
e
m
o
d
el
f
o
r
lo
ad
f
r
eq
u
en
cy
c
o
n
tr
o
l
in
a
two
-
a
r
ea
p
o
wer
s
y
s
tem
[
2
0
]
.
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
m
o
d
el
f
o
r
a
n
o
n
-
r
eh
ea
t th
er
m
al
p
o
we
r
s
y
s
tem
co
n
s
is
ts
o
f
two
r
eg
io
n
s
,
as seen
in
Fig
u
r
e
1
.
T
wo
s
ep
ar
at
e
co
n
tr
o
l
ac
tio
n
s
im
p
lem
en
t
lo
ad
f
r
eq
u
en
cy
m
an
ag
em
en
t
in
two
-
ar
ea
p
o
w
er
s
y
s
t
em
s
.
T
h
e
p
r
i
m
ar
y
co
n
tr
o
ll
er
i
s
r
e
s
p
o
n
s
ib
l
e
f
o
r
th
e
f
ir
s
t
r
u
d
im
en
tar
y
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at
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im
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a
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t
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h
i
s
g
u
ar
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te
e
en
s
u
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es
th
e
s
y
s
tem
's
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
1
,
Feb
r
u
ar
y
20
25
:
1
46
-
1
55
148
f
r
eq
u
en
cy
an
d
p
o
we
r
f
lo
w
s
o
n
th
e
t
ie
l
in
e
r
e
m
ai
n
a
t
th
e
ir
d
es
ig
n
.
A
s
s
h
o
wn
in
th
e
f
o
llo
win
g
eq
u
at
io
n
,
th
e
ad
d
i
tio
n
al
co
n
tr
o
l
ler
f
o
r
th
e
ℎ
ar
ea
s
p
e
cif
ic
al
ly
r
e
s
p
o
n
d
s
to
t
h
e
a
r
ea
co
n
tr
o
l
er
r
o
r
(
)
,
wh
i
c
h
ac
t
s
a
s
an
in
p
u
t
to
th
e
co
n
tr
o
ll
er
:
=
∑
∆
,
+
∆
(
1
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w
h
er
e,
is
ar
ea
co
n
tr
o
l e
r
r
o
r
o
f
th
e
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th
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∆
,
is
tit
-
lin
e
p
o
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f
lo
w
er
r
o
r
b
etwe
en
i
th
an
d
j
th
ar
ea
s
,
is
f
r
eq
u
en
cy
b
ias co
ef
f
icien
t
o
f
i
th
ar
ea
,
∆
is
f
r
eq
u
en
cy
er
r
o
r
o
f
i
th
ar
ea
.
Fig
u
r
e
1
.
A
th
e
r
m
al
p
o
wer
s
y
s
tem
with
two
lin
k
ed
s
ec
tio
n
s
d
iag
r
am
I
t
is
p
r
esu
m
ab
le
th
at
th
e
lo
ad
in
co
n
tr
o
l
ar
ea
s
1
an
d
2
will
ab
r
u
p
tly
alter
d
u
r
in
g
th
e
s
im
u
latio
n
p
r
o
ce
s
s
.
B
ased
o
n
th
e
d
ata
p
r
esen
ted
in
Fig
u
r
e
1
,
it
is
clea
r
th
at
1
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d
2
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t
p
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tem
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en
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iatio
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P
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3
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1
7
2
2
.
2
.
Co
ntr
o
ller
s
t
ruct
ure
T
h
e
2
-
DOF
PID
co
n
tr
o
ller
[
2
1
]
en
h
an
ce
s
th
e
co
n
v
e
n
tio
n
al
PID
co
n
tr
o
l
tech
n
iq
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e
b
y
in
clu
d
in
g
d
is
tin
ct
f
u
n
ctio
n
alities
f
o
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etp
o
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ac
k
in
g
a
n
d
n
o
is
e
r
ejec
tio
n
.
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h
is
en
ab
les
en
h
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ce
d
c
u
s
to
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izatio
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,
h
en
ce
en
ab
lin
g
th
e
2
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DOF
PID
co
n
tr
o
ller
to
m
o
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e
ef
f
ec
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r
e
g
u
l
ate
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tr
icate
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d
d
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am
ic
s
y
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tem
s
.
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a
r
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it
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ed
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ig
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r
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2
d
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icts
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co
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ig
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th
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co
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tr
o
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[
2
2
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.
1
B
1
1
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r
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r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Op
tima
l tu
r
n
in
g
o
f a
2
-
DOF
p
r
o
p
o
r
tio
n
a
l
-
in
te
g
r
a
l
-
d
eriva
tive
co
n
tr
o
ller
…
(
Tech
a
ta
t B
u
r
a
n
a
a
u
d
s
a
w
a
ku
l
)
149
A
t
wo
-
d
eg
r
ee
-
of
-
f
r
ee
d
o
m
(
2
-
DOF)
PID
co
n
tr
o
ller
s
[
2
3
]
.
T
h
e
s
y
s
tem
h
as
th
r
ee
co
n
tr
o
l
lo
o
p
s
s
in
ce
it
h
as
th
r
ee
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
.
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h
e
AC
E
o
f
th
e
r
esp
ec
tiv
e
r
e
g
io
n
is
r
ep
r
esen
te
d
b
y
(
)
in
th
is
in
s
tan
ce
.
T
h
e
f
r
eq
u
e
n
cy
d
ev
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n
in
ea
ch
ar
ea
is
in
d
icate
d
b
y
(
)
,
an
d
th
e
co
n
tr
o
ller
'
s
o
u
tp
u
t,
(
)
,
s
er
v
es
as
th
e
g
en
er
atin
g
u
n
its
'
in
p
u
t.
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h
e
b
asic
d
if
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er
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ce
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etwe
en
a
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r
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of
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o
m
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DOF)
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co
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is
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e
d
is
tu
r
b
an
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Fig
u
r
e
2
.
B
lo
ck
d
iag
r
am
t
h
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2
DOF
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PID
co
n
tr
o
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3.
P
RO
B
L
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M
F
O
R
M
U
L
AT
I
O
N
AND
O
P
T
I
M
I
Z
AT
I
O
N
T
E
CH
N
I
Q
UE
3
.
1
.
P
ro
blem
f
o
r
m
ula
t
io
n
Sy
s
tem
co
n
tr
o
l
i
n
p
o
wer
s
y
s
t
em
s
[
2
4
]
aim
s
to
r
ed
u
ce
f
r
e
q
u
en
cy
d
is
cr
ep
an
cies
to
ze
r
o
wh
en
lo
ad
s
ch
an
g
e
is
th
e
g
o
al
is
to
r
ed
u
ce
th
e
i
n
teg
r
al
o
f
th
e
f
r
eq
u
en
cy
er
r
o
r
an
d
co
n
tr
o
l
s
y
s
tem
c
h
ar
ac
ter
is
tics
m
u
s
t
m
ain
tain
s
y
s
tem
s
tab
ili
ty
.
B
as
ed
o
n
th
e
in
f
o
r
m
atio
n
s
u
p
p
lie
d
,
co
n
tr
o
l o
b
jectiv
es m
ay
b
e
s
tated
as e
q
u
atio
n
s
in
th
e
f
o
llo
win
g
wa
y
:
−
I
n
teg
r
al
a
b
s
o
lu
te
er
r
o
r
(
I
AE
)
=
∫
[
|
(
)
|
]
∞
0
⋅
(
2
)
−
I
n
teg
r
al
s
q
u
a
r
ed
er
r
o
r
(
I
SE)
=
∫
[
2
(
)
]
∞
0
⋅
(
3
)
−
I
n
teg
r
al
o
f
tim
e
m
u
ltip
ly
ab
s
o
l
u
te
er
r
o
r
(
I
T
AE
)
=
∫
[
|
(
)
|
]
∞
0
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⋅
(
4
)
−
I
n
teg
r
al
tim
e
s
q
u
a
r
ed
er
r
o
r
(
I
T
SE)
=
∫
[
2
(
)
]
∞
0
∙
⋅
(
5
)
As
a
r
esu
lt,
th
e
o
b
jectiv
e
f
u
n
ctio
n
f
o
r
ad
ju
s
tin
g
2
-
DOF
PID
co
n
tr
o
ller
s
b
ased
o
n
th
e
ch
ess
alg
o
r
ith
m
will
b
e
th
e
p
er
f
o
r
m
an
ce
i
n
d
i
ce
s
r
ep
r
esen
ted
b
y
(
2
)
–
(
5
)
[
2
5
]
.
I
n
s
h
o
r
t,
th
e
g
o
al
o
f
ch
e
s
s
alg
o
r
ith
m
-
b
ased
o
p
tim
izatio
n
in
th
is
ca
s
e
is
to
f
in
d
an
ex
ac
t
co
m
b
in
atio
n
o
f
a
2
-
DOF
PID
p
ar
am
eter
s
th
at
wo
u
ld
r
esu
lt
in
th
e
f
ee
d
b
ac
k
co
n
tr
o
l
s
y
s
tem
h
av
i
n
g
th
e
l
o
west
p
er
f
o
r
m
an
ce
in
d
ex
.
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
m
u
s
t
b
e
ac
co
m
p
lis
h
ed
with
in
th
e
p
a
r
am
eter
s
'
u
p
p
er
an
d
lo
wer
b
o
u
n
d
s
[
2
6
]
.
T
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I
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2
0
8
8
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7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
1
,
Feb
r
u
ar
y
20
25
:
1
46
-
1
55
150
3
.
2
.
O
ptim
iza
t
io
n t
ec
hn
iqu
e
3
.
2
.
1
.
Chess
a
lg
o
rit
hm
o
ptimiza
t
io
n t
ec
hn
iqu
e
T
h
e
tech
n
iq
u
e
d
escr
ib
ed
in
t
h
is
wo
r
k
,
k
n
o
w
n
as
th
e
ch
ess
alg
o
r
ith
m
o
p
tim
izatio
n
tech
n
iq
u
e
[
2
7
]
,
[
2
8
]
,
u
s
es
th
e
id
ea
s
an
d
s
tr
ateg
ies
u
s
ed
in
th
e
g
am
e
o
f
in
ter
n
atio
n
al
ch
ess
to
id
en
tify
th
e
b
est
v
alu
e.
Fu
r
th
er
m
o
r
e
,
th
e
u
s
er
s
h
o
u
ld
ev
alu
ate
ea
ch
ch
ess
p
iece
'
s
p
ar
ticu
lar
ac
tio
n
s
as
well
as
th
e
g
am
e'
s
g
en
er
al
s
tr
ateg
ic
ap
p
r
o
ac
h
.
I
f
th
e
ab
o
v
e
-
m
en
tio
n
e
d
ap
p
r
o
ac
h
is
u
s
ed
to
d
eter
m
in
e
th
e
o
p
tim
al
v
a
lu
e,
th
e
p
lay
er
will
win
th
e
g
am
e
[
2
9
]
.
T
h
is
wil
l
r
esu
lt
in
an
alg
o
r
ith
m
with
v
ar
ied
p
r
o
p
er
ties
ac
r
o
s
s
s
ev
er
al
d
o
m
ain
s
.
T
h
is
ap
p
r
o
ac
h
lead
s
to
th
e
cr
ea
tio
n
o
f
an
alg
o
r
ith
m
b
ec
au
s
e,
d
ep
en
d
in
g
o
n
th
e
g
am
e'
s
s
ty
le,
ea
ch
ch
ess
p
iece
ca
n
m
o
v
e
in
ce
r
tain
way
s
b
ased
o
n
a
p
r
e
d
eter
m
in
ed
s
et
o
f
r
u
les
[
3
0
]
:
Step
1:
Div
id
e
th
e
eig
h
t
p
aw
n
s
(
n
p
)
t
o
r
an
d
o
m
ize
t
h
e
an
s
wer
.
R
ea
ctio
n
s
h
av
e
to
b
e
p
r
ac
tical
g
iv
en
t
h
e
lim
itatio
n
s
.
T
h
er
e
ca
n
b
e
ju
s
t o
n
e
iter
atio
n
b
ec
au
s
e
th
er
e
a
r
e
s
o
m
an
y
r
e
q
u
ir
e
d
r
eq
u
ir
em
en
t
s
.
Step
2:
Ass
es
s
th
e
ass
ig
n
m
en
ts
o
f
p
awn
s
at
r
an
d
o
m
.
T
h
r
o
u
g
h
ev
al
u
atin
g
t
h
e
s
y
s
tem
at
e
v
er
y
a
n
s
wer
.
At
th
e
f
u
n
ctio
n
'
s
wo
r
s
t v
alu
e,
th
e
r
es
p
o
n
s
e
is
r
ea
d
y
f
o
r
class
if
icatio
n
.
Step
3:
Sh
o
ws
th
e
r
esp
o
n
s
es
in
o
r
d
e
r
.
C
o
m
p
r
is
es
,
in
th
at
o
r
d
er
,
two
r
o
o
k
s
,
two
k
n
ig
h
ts
,
two
b
is
h
o
p
s
,
o
n
e
k
in
g
,
a
n
d
o
n
e
q
u
ee
n
.
Step
4:
Giv
e
ea
ch
o
b
ject
a
u
n
i
q
u
e
ass
ig
n
m
en
t
.
Dete
r
m
in
e
th
e
s
o
lu
tio
n
lo
ca
lly
b
ased
o
n
th
e
m
o
v
em
en
ts
o
f
t
h
e
co
m
p
o
n
en
ts
.
Step
5:
Ass
es
s
n
eig
h
b
o
r
in
g
an
s
wer
s
.
C
o
n
s
id
er
th
e
p
u
r
p
o
s
e
o
f
ev
e
r
y
an
s
wer
.
lo
ca
te
th
e
b
est
o
p
tio
n
s
in
y
o
u
r
ar
ea
ev
er
y
s
in
g
le
th
in
g
Step
6:
R
ea
r
r
an
g
e
th
e
p
ar
ts
.
D
eter
m
in
e
wh
ich
co
m
p
o
n
en
t
-
en
v
ir
o
n
m
e
n
t c
o
m
p
atib
ilit
y
s
o
lu
ti
o
n
is
o
p
tim
al.
Step
7:
E
v
alu
ate
all
ch
ess
p
ie
ce
s
ag
ain
s
t
s
ea
r
ch
r
esu
lts
.
W
h
ich
r
esp
o
n
s
e
h
as
th
e
m
ax
i
m
u
m
f
u
n
ctio
n
v
alu
e?
Nam
e
it th
e
o
p
tim
al
an
s
wer
f
o
r
th
at
p
ar
ticu
lar
s
ea
r
c
h
iter
atio
n
.
Step
8:
Ver
if
y
t
h
e
cir
c
u
m
s
tan
ce
s
an
d
i
n
clu
d
e
a
r
eg
io
n
al
an
s
wer
.
Pro
v
id
ed
th
at
th
e
co
n
d
itio
n
s
ar
e
s
atis
f
ied
.
L
et's b
r
ea
k
f
r
ee
f
r
o
m
co
n
s
tr
ai
n
ed
an
s
wer
s
.
Step
9:
E
x
am
in
e
th
e
g
r
o
u
n
d
s
f
o
r
ter
m
in
atio
n
.
Sear
ch
n
o
f
ar
t
h
er
if
th
e
r
e
q
u
ir
em
e
n
ts
ar
e
s
atis
f
ied
.
I
ter
ate
m
o
r
e
if
n
ec
ess
ar
y
if
th
e
p
r
er
eq
u
is
ites
ar
e
n
o
t satis
f
ied
.
T
o
o
b
tain
th
e
u
p
d
ated
v
alu
e,
tak
e
th
e
cu
r
r
en
t I
ter
atio
n
v
alu
e
an
d
ad
d
1
.
Step
1
0
: D
iv
id
e
th
e
ei
g
h
t p
iec
es e
q
u
ally
an
d
b
eg
in
o
v
er
.
Step
11:
C
o
m
b
in
e
t
h
e
in
itial
p
awn
co
n
f
ig
u
r
atio
n
(
8
p
iece
s
)
with
th
e
cu
r
r
en
t
o
p
tim
al
s
o
lu
tio
n
f
o
r
all
ch
ess
p
iece
s
(
1
k
in
g
,
1
q
u
ee
n
,
2
r
o
o
k
s
,
2
k
n
i
g
h
ts
,
an
d
2
b
is
h
o
p
s
)
,
in
ad
d
itio
n
to
f
ig
u
r
in
g
o
u
t
th
e
f
u
n
ctio
n
v
alu
e
o
f
t
h
e
r
an
d
o
m
p
awn
p
ic
k
o
u
tco
m
e.
T
h
e
1
6
r
esp
o
n
s
es we
r
e
ar
r
an
g
e
d
in
o
r
d
er
o
f
p
r
ef
er
en
ce
.
Step
12:
Un
til th
e
h
altin
g
co
n
d
itio
n
is
s
atis
f
ied
,
s
tep
3
is
r
ep
ea
ted
u
s
in
g
th
e
to
p
8
r
esp
o
n
s
e
s
.
T
ab
le
2
.
Min
im
u
m
an
d
m
ax
im
u
m
v
alu
e
o
f
co
n
tr
o
l
p
ar
am
eter
C
o
n
t
r
o
l
l
e
r
P
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r
a
me
t
e
r
M
i
n
i
m
u
m
M
a
x
i
m
u
m
0
1
0
1
0
1
N
10
3
0
0
PW
0
2
DW
0
5
4.
RE
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D
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r
ith
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ju
s
ts
th
e
p
a
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am
eter
s
o
f
a
2
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DOF
PID
co
n
tr
o
ller
s
,
it
co
n
tr
o
ls
th
e
p
o
wer
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etwo
r
k
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o
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tio
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b
etwe
en
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f
E
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test
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d
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ess
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th
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MA
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A
to
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p
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with
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u
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ta
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o
r
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y
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s
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a
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z
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ti
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F
i
g
u
r
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s
3
(
a
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t
o
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(
c
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i
ll
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s
t
r
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t
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m
i
c
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y
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a
ct
i
o
n
I
AE
a
n
d
I
S
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o
f
ea
c
h
l
o
c
a
t
i
o
n
:
a
r
e
a
1
,
a
r
e
a
2
a
n
d
T
i
e
l
i
n
e
.
T
h
e
s
e
r
e
s
p
o
n
s
es
a
r
e
d
e
p
ict
e
d
i
n
F
i
g
u
r
e
s
3
(
a
)
t
o
3
(
c
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Op
tima
l tu
r
n
in
g
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f a
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p
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n
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(
Tech
a
ta
t B
u
r
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a
a
u
d
s
a
w
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ku
l
)
151
T
ab
le
3
.
Op
tim
izatio
n
co
n
tr
o
ller
p
ar
am
eter
I
AE
an
d
I
SE
P
a
r
a
me
t
e
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1
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8
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2
2
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6
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4
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9
3
7
3
0
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1
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3
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3
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6
5
8
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.
0
8
6
9
0
T
ab
le
4
.
Op
tim
izatio
n
co
n
tr
o
ller
p
ar
am
eter
I
T
AE
an
d
I
T
SE
P
a
r
a
me
t
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r
I
TA
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TSE
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3
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0
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4
2
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5
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1
7
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1
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2
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1
5
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1
1
4
.
4
4
0
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4
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6
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1
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2
8
6
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4
.
1
2
2
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3
6
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2
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2
3
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5
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3
9
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2
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2
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3
9
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2
.
9
9
2
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(
a)
(
b
)
(
c)
Fig
u
r
e
3
.
Dy
n
am
ic
p
o
wer
s
y
s
tem
r
esp
o
n
s
e
I
AE
a
n
d
I
SE
(
a
)
ar
ea
1
,
(
b
)
ar
ea
2
,
a
n
d
(
c
)
tie
lin
e
T
ab
le
5
an
d
Fig
u
r
e
s
4
(
a)
to
4
(
c)
s
h
o
w
th
e
I
T
AE
an
d
I
T
SE
m
ea
s
u
r
es
an
d
illu
s
tr
ate
th
e
d
y
n
am
ic
p
o
wer
s
y
s
tem
r
ea
ctio
n
I
AE
an
d
I
SE
o
f
ea
ch
lo
ca
tio
n
:
ar
ea
1
,
ar
ea
2
a
n
d
T
ie
lin
e
.
T
h
ese
r
esp
o
n
s
es
ar
e
d
ep
icted
in
th
e
f
ig
u
r
e
,
wh
ich
ar
e
2
%
s
ettin
g
tim
e
an
d
p
ea
k
v
alu
es
f
o
r
th
e
ch
ess
an
d
p
ar
ticle
s
war
m
alg
o
r
ith
m
s
,
r
esp
ec
tiv
ely
.
W
e
d
is
p
lay
th
e
d
ata
f
o
r
two
d
is
tin
ct
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ea
s
,
a
r
ea
1
an
d
a
r
ea
2
,
alo
n
g
with
th
e
tie
lin
e
co
n
n
ec
tin
g
th
em
.
Def
in
itio
n
s
ar
e
n
ec
ess
ar
y
.
W
ith
th
e
ex
ce
p
tio
n
o
f
a
r
ea
1
,
th
e
p
ar
ticle
s
war
m
alg
o
r
ith
m
'
s
av
er
ag
e
co
n
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ig
u
r
atio
n
tim
e
is
2
%
f
aster
th
an
th
at
o
f
b
o
th
ch
ess
alg
o
r
ith
m
s
(
I
T
AE
an
d
I
T
SE)
.
I
n
a
r
ea
1
,
th
e
ch
ess
alg
o
r
ith
m
(
I
T
AE
)
ac
h
iev
es
th
e
lo
west
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ettlin
g
tim
e
o
f
2
%
(
0
.
0
1
1
9
s
ec
o
n
d
s
)
.
T
h
e
p
ar
ticle
s
war
m
m
eth
o
d
,
wh
ich
is
d
ef
in
ed
as
th
e
in
teg
r
al
o
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tim
e
m
u
ltip
lied
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y
th
e
ab
s
o
lu
te
er
r
o
r
(
I
T
AE
)
cr
iter
io
n
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o
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tain
s
th
e
lo
west
s
ettlin
g
tim
e
o
f
2
%
(
0
.
0
0
7
6
s
ec
o
n
d
s
in
a
r
ea
2
an
d
0
.
0
0
3
s
ec
o
n
d
s
in
th
e
tie
lin
e)
.
T
h
e
p
ar
ticle
s
war
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
1
,
Feb
r
u
ar
y
20
25
:
1
46
-
1
55
152
alg
o
r
ith
m
(
I
T
AE
)
is
th
e
s
ec
o
n
d
-
f
astes
t
alg
o
r
ith
m
in
a
r
ea
2
an
d
T
ie
L
in
e,
with
a
s
ettlin
g
tim
e
o
f
2
%.
T
h
e
tie
lin
e
an
d
a
r
ea
2
h
av
e
r
esp
ec
tiv
e
tim
in
g
s
o
f
0
.
0
0
3
1
s
ec
o
n
d
s
an
d
0
.
0
0
7
5
s
ec
o
n
d
s
,
r
esp
ec
tiv
ely
.
C
o
m
p
ar
ed
to
b
o
th
p
ar
ticle
s
war
m
alg
o
r
ith
m
s
(
I
T
AE
an
d
I
T
SE)
,
th
e
ch
ess
alg
o
r
ith
m
h
as
a
lo
wer
av
er
ag
e
p
ea
k
v
alu
e
o
n
th
e
p
ea
k
s
id
e,
with
th
e
ex
ce
p
tio
n
o
f
a
r
ea
1
(
I
T
AE
)
.
T
h
e
p
ar
ticle
s
war
m
(
I
T
AE
)
alg
o
r
ith
m
ac
h
iev
es
th
e
lo
west
p
ea
k
v
alu
e
(
0
.
0
0
9
8
)
in
a
r
ea
1
.
T
h
e
ch
ess
alg
o
r
ith
m
'
s
I
T
AE
cr
iter
io
n
ex
h
ib
its
th
e
lo
west p
ea
k
v
alu
es o
f
0
.
0
0
7
6
an
d
0
.
0
0
3
in
ar
ea
2
an
d
th
e
tie
lin
e,
r
esp
ec
tiv
ely
.
T
h
e
ch
ess
alg
o
r
ith
m
,
s
o
m
etim
es k
n
o
wn
as I
T
SE,
r
ec
o
r
d
s
th
e
s
ec
o
n
d
-
lo
west m
ax
im
al
v
alu
e
in
ar
ea
2
an
d
th
e
tie
lin
e,
m
ea
s
u
r
in
g
0
.
0
0
7
4
an
d
0
.
0
0
3
s
ec
o
n
d
s
,
r
esp
ec
tiv
ely
.
T
ab
le
5
.
Valu
es o
f
s
ettlin
g
tim
e
an
d
p
ea
k
(
I
AE
&
I
SE)
A
l
g
o
r
i
t
h
m
A
r
e
a
S
e
t
t
l
i
n
g
t
i
me
2
%
P
e
a
k
C
h
e
ss
a
l
g
o
r
i
t
h
m
(
I
A
E)
A
r
e
a
1
4
7
6
.
9
8
0
6
0
.
0
1
4
1
A
r
e
a
2
3
5
5
.
0
4
2
3
0
.
0
0
9
6
Ti
e
l
i
n
e
4
9
1
.
2
4
4
4
0
.
0
0
3
2
P
a
r
t
i
c
l
e
s
w
a
r
m
(
I
A
E)
A
r
e
a
1
4
0
4
.
4
1
4
9
0
.
0
1
4
6
A
r
e
a
2
3
4
4
.
0
6
5
7
0
.
0
1
0
2
Ti
e
l
i
n
e
4
4
4
.
4
3
7
2
0
.
0
0
3
4
C
h
e
ss
a
l
g
o
r
i
t
h
m
(
I
S
E)
A
r
e
a
1
4
9
3
.
3
5
9
9
0
.
0
0
9
9
A
r
e
a
2
4
3
7
.
3
8
8
1
0
.
0
0
7
1
Ti
e
l
i
n
e
5
2
5
.
7
4
1
3
0
.
0
0
3
P
a
r
t
i
c
l
e
sw
a
r
m
(
I
S
E)
A
r
e
a
1
5
5
9
.
5
3
9
1
0
.
0
0
9
8
A
r
e
a
2
4
8
0
.
6
7
2
9
0
.
0
0
7
Ti
e
l
i
n
e
5
6
7
.
2
3
2
3
0
.
0
0
3
(
a)
(
b
)
(
c)
Fig
u
r
e
4
.
Dy
n
am
ic
p
o
wer
s
y
s
tem
r
esp
o
n
s
e
I
T
AE
a
n
d
I
T
SE
(
a)
ar
ea
1
,
(
b
)
ar
ea
2
,
a
n
d
(
c)
T
i
e
lin
e
T
ab
le
6
d
is
p
lay
s
t
h
e
er
r
o
r
v
alu
es
f
o
r
th
e
f
o
u
r
c
h
ess
an
d
p
ar
ti
cle
s
war
m
alg
o
r
ith
m
s
,
n
am
ely
I
AE
,
I
SE,
I
T
AE
,
an
d
I
T
SE.
W
h
en
co
m
p
ar
in
g
th
e
I
AE
v
alu
es
o
f
th
e
ch
ess
an
d
p
ar
ticle
s
war
m
alg
o
r
ith
m
s
,
we
s
ee
th
at
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Op
tima
l tu
r
n
in
g
o
f a
2
-
DOF
p
r
o
p
o
r
tio
n
a
l
-
in
te
g
r
a
l
-
d
eriva
tive
co
n
tr
o
ller
…
(
Tech
a
ta
t B
u
r
a
n
a
a
u
d
s
a
w
a
ku
l
)
153
th
ey
ar
e
f
air
ly
clo
s
e,
with
v
al
u
es
o
f
0
.
0
3
3
6
4
an
d
0
.
0
3
3
6
3
,
r
esp
ec
tiv
ely
.
T
h
e
ch
ess
alg
o
r
i
th
m
h
as
a
s
lig
h
tly
lo
wer
I
SE
v
alu
e
co
m
p
ar
ed
to
th
e
p
ar
ticle
s
war
m
m
eth
o
d
,
w
ith
v
alu
es
o
f
0
.
0
0
0
3
5
a
n
d
0
.
0
0
0
3
6
,
r
esp
ec
tiv
ely
.
T
h
e
ch
ess
alg
o
r
ith
m
h
as so
m
ewh
at
r
ed
u
ce
d
I
T
AE
v
alu
es c
o
m
p
ar
ed
to
th
e
p
ar
ticle
s
war
m
m
eth
o
d
,
with
v
alu
es
o
f
0
.
0
7
6
4
7
an
d
0
.
0
7
9
2
9
,
r
esp
ec
tiv
ely
.
t
h
e
I
T
SE
v
alu
e
o
f
th
e
c
h
ess
alg
o
r
ith
m
is
s
o
m
ewh
a
t
lo
wer
t
h
an
th
at
o
f
th
e
p
ar
ticle
s
war
m
m
eth
o
d
,
with
v
alu
es
o
f
0
.
0
0
0
7
2
a
n
d
0
.
0
0
0
7
6
,
r
esp
ec
tiv
ely
.
I
n
c
o
n
clu
s
io
n
,
th
e
ch
ess
alg
o
r
ith
m
h
as
s
o
m
ewh
at
s
u
p
e
r
io
r
o
v
er
all
p
er
f
o
r
m
a
n
ce
co
m
p
ar
ed
to
th
e
p
ar
ticle
s
war
m
alg
o
r
ith
m
in
ter
m
s
o
f
m
is
tak
e
r
ates.
t
h
e
d
is
p
ar
ity
in
er
r
o
r
lev
els
b
etwe
en
th
e
two
t
ec
h
n
iq
u
es
is
m
in
im
al.
T
h
e
o
p
t
im
al
alg
o
r
ith
m
f
o
r
p
r
ac
tical
u
s
e
is
co
n
tin
g
en
t
u
p
o
n
th
e
s
p
ec
i
f
ic
r
eq
u
ir
em
en
ts
.
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h
e
ch
ess
alg
o
r
ith
m
is
lik
ely
to
b
e
a
m
o
r
e
s
u
itab
le
o
p
tio
n
if
a
h
ig
h
lev
el
o
f
ac
cu
r
ac
y
is
d
esire
d
.
T
h
e
p
ar
ticle
s
war
m
m
eth
o
d
is
lik
ely
a
s
u
p
er
io
r
o
p
tio
n
if
y
o
u
p
r
ef
er
a
m
o
r
e
s
tr
aig
h
tf
o
r
war
d
s
y
s
tem
,
T
h
e
v
alu
es
o
f
s
ettlin
g
tim
e
an
d
p
ea
k
(
I
T
AE
an
d
I
T
SE)
ar
e
s
h
o
wn
in
T
ab
le
7
,
as m
ay
b
e
s
ee
n
.
T
ab
le
6
.
Valu
es o
f
e
r
r
o
r
A
l
g
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r
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t
h
m
F
u
n
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Er
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5.
CO
NCLU
SI
O
N
T
h
is
ex
p
er
im
en
t
aim
s
to
ev
al
u
ate
an
d
co
m
p
ar
e
th
e
e
f
f
icac
y
o
f
ch
ess
an
d
p
a
r
ticle
s
war
m
alg
o
r
ith
m
s
in
s
y
s
tem
co
n
tr
o
l.
T
h
e
ev
alu
at
io
n
is
b
ased
o
n
two
p
r
im
ar
y
f
ac
to
r
s
:
th
e
s
ettin
g
tim
e
o
f
2
%
an
d
th
e
p
ea
k
o
f
th
e
h
ig
h
est
d
ev
iatio
n
,
as
well
as
th
e
er
r
o
r
v
alu
e
o
f
th
e
s
ettin
g
ti
m
e
o
f
2
%.
Ov
e
r
all,
th
e
p
a
r
ticle
s
war
m
m
eth
o
d
h
as
a
2
%
f
aster
s
ettin
g
tim
e,
e
x
c
ep
t
in
s
o
m
e
ca
s
es.
W
h
en
ap
p
ly
in
g
I
AE
to
a
r
ea
1
o
f
ten
r
es
u
lts
in
p
ea
k
ch
ess
m
eth
o
d
s
ex
h
ib
itin
g
lo
wer
p
ea
k
v
alu
es,
in
d
icatin
g
less
d
ev
iat
io
n
.
v
er
,
th
is
is
n
o
t th
e
ca
s
e
w
h
en
em
p
lo
y
i
n
g
I
A
E
in
ar
ea
1.
An
e
r
r
o
r
h
as
o
cc
u
r
r
ed
.
T
h
e
ch
ess
alg
o
r
ith
m
h
as
a
s
lig
h
tly
n
ar
r
o
wer
to
tal
m
a
r
g
in
o
f
er
r
o
r
.
Ho
wev
e
r
,
th
e
d
is
p
ar
ity
b
etwe
en
th
e
two
m
eth
o
d
s
is
n
o
t
v
er
y
s
u
b
s
tan
tial.
Simp
ly
p
u
t,
th
e
o
u
tco
m
e
d
ep
en
d
s
o
n
wh
o
s
e
r
eq
u
ir
em
e
n
ts
tak
e
p
r
ec
ed
en
ce
.
T
h
e
p
ar
ticle
s
war
m
alg
o
r
ith
m
is
lik
ely
to
b
e
a
s
u
p
e
r
io
r
o
p
tio
n
if
y
o
u
n
ee
d
a
s
y
s
tem
th
at
ex
h
ib
its
r
ap
id
r
esp
o
n
s
iv
en
ess
.
I
f
y
o
u
n
ee
d
a
s
y
s
tem
th
at
ex
h
ib
its
h
ig
h
p
r
ec
is
io
n
an
d
litt
le
v
ar
ian
ce
,
th
e
ch
ess
alg
o
r
ith
m
wo
u
ld
lik
el
y
b
e
a
s
u
p
er
i
o
r
o
p
tio
n
.
Var
iab
les
s
u
ch
as
th
e
m
an
ip
u
lated
s
y
s
tem
m
ay
in
f
lu
e
n
ce
th
e
ex
p
er
im
en
t'
s
o
u
tco
m
e.
Par
am
eter
s
an
d
n
o
is
e
in
alg
o
r
ith
m
s
.
RE
F
E
R
E
NC
E
S
[
1
]
M
.
M
.
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.
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)
st
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m
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4
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I
b
r
a
h
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m
,
N
i
z
a
m
u
d
d
i
n
,
a
n
d
T.
S
.
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h
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15
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Feb
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46
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154
[
5
]
Q
.
V
.
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g
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.
Y
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[
6
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A
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7
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m
th
e
Kh
o
n
k
a
e
n
Un
iv
e
rsity
(KK
U),
Th
a
il
a
n
d
a
n
d
th
e
P
h
.
D
.
d
e
g
re
e
in
e
n
g
i
n
e
e
rin
g
fro
m
S
ir
in
d
h
o
rn
In
tern
a
ti
o
n
a
l
In
stit
u
te
o
f
Tec
h
n
o
l
o
g
y
(S
IIT
),
Th
a
m
m
a
sa
t
Un
iv
e
rsit
y
,
Th
a
il
a
n
d
.
His
re
se
a
rc
h
in
tere
sts
in
c
lu
d
e
a
n
a
l
o
g
c
ircu
it
s
a
n
d
p
o
we
r
sy
ste
m
s.
S
in
c
e
2
0
0
7
,
h
e
h
a
s
b
e
e
n
with
F
a
c
u
lt
y
o
f
E
n
g
i
n
e
e
rin
g
,
M
a
h
a
sa
ra
k
h
a
m
Un
iv
e
rsity
(M
S
U),
Th
a
il
a
n
d
,
wh
e
re
h
e
is
c
u
rre
n
tl
y
a
P
r
o
fe
ss
o
r
o
f
El
e
c
tri
c
a
l
E
n
g
i
n
e
e
rin
g
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
wo
r.
n
u
i@g
m
a
il
.
c
o
m
.
Ra
tta
p
o
n
Dul
y
a
l
a
re
c
e
iv
e
d
h
is
B.
S
.
Tec
h
.
Ed
.
d
e
g
re
e
in
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
,
fro
m
th
e
P
a
th
u
m
wa
n
In
sti
tu
te
o
f
Tec
h
n
o
l
o
g
y
(P
IT)
a
n
d
t
h
e
M
.
S
.
T
e
c
h
.
Ed
.
d
e
g
re
e
in
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
,
fr
o
m
th
e
Kin
g
M
o
n
g
k
u
t'
s
Un
iv
e
rsity
o
f
Tec
h
n
o
l
o
g
y
T
h
o
n
b
u
ri
(KMUT
T)
,
Th
a
il
a
n
d
.
His
re
se
a
rc
h
in
tere
sts
in
c
lu
d
e
p
o
we
r
tec
h
n
o
l
o
g
y
a
n
d
p
o
we
r
sy
ste
m
s.
S
in
c
e
2
0
0
7
,
h
e
h
a
s
b
e
e
n
with
F
a
c
u
l
ty
o
f
In
d
u
strial
Tec
h
n
o
lo
g
y
,
Uttara
d
it
R
a
jab
h
a
t
Un
iv
e
rsit
y
(URU
),
Th
a
il
a
n
d
,
wh
e
re
h
e
is
c
u
rre
n
tl
y
a
lec
tu
re
r
o
f
e
lec
tri
c
a
l
e
n
g
i
n
e
e
rin
g
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
ra
tt
a
p
o
n
.
d
u
l@
li
v
e
.
u
ru
.
a
c
.
t
h
.
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