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13
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1345
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Kp
,
Ki,
Kd
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T
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a
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d
T
s res
p
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ti
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y
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K
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s
:
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PID
co
n
tr
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P
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ticle
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ar
m
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izatio
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T
h
is i
s
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o
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c
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n
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CC B
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SA
li
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C
o
r
r
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s
p
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A
uth
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Gh
as
s
an
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m
ed
Su
ltan
No
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th
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n
T
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h
n
ical
U
n
i
v
er
s
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h
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ical
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n
g
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C
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Dep
ar
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m
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Me
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n
s
tr
u
m
en
tatio
n
T
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h
n
ica
l E
n
g
i
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ee
r
in
g
Mo
s
u
l,
I
r
aq
E
m
ail:
g
h
a
s
s
a
n
k
ass
ab
@
n
tu
.
ed
u
.
iq
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
m
o
s
t
p
o
p
u
lar
an
d
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s
e
f
u
l
co
n
tr
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l
u
n
it
in
t
h
e
in
d
u
s
tr
ial
f
ield
s
is
t
h
e
p
r
o
p
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tio
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al
-
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n
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g
r
al
-
d
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ativ
e
(
P
I
D
)
co
n
tr
o
ller
d
u
e
to
its
u
n
iq
u
e
n
ess
i
n
its
s
i
m
p
le
s
tr
u
ctu
r
e
an
d
ea
s
y
i
m
p
le
m
e
n
tatio
n
i
n
m
o
d
er
n
ap
p
licatio
n
s
a
n
d
co
m
p
lex
in
d
u
s
tr
ie
s
.
Desp
ite
th
e
s
i
m
p
licit
y
an
d
ea
s
e
o
f
i
m
p
le
m
e
n
tatio
n
o
f
th
e
P
I
D
co
n
tr
o
ller
,
it
n
ee
d
s
co
n
ti
n
u
o
u
s
i
m
p
r
o
v
e
m
en
t
to
o
b
tain
th
e
b
est
p
er
f
o
r
m
an
ce
r
esu
l
ts
.
T
h
e
P
I
D
p
e
r
f
o
r
m
an
ce
ca
n
b
e
f
u
r
th
er
en
h
a
n
ce
d
th
r
o
u
g
h
t
h
e
p
r
o
ce
s
s
o
f
m
a
k
i
n
g
u
s
e
o
f
f
r
ac
tio
n
al
o
r
d
er
d
er
iv
ativ
e
an
d
in
t
eg
r
als.
T
h
er
ef
o
r
in
f
r
ac
tio
n
al
o
r
d
er
co
n
tr
o
ller
n
o
t
o
n
l
y
th
e
p
r
o
p
o
r
tio
n
al
(
Kp
)
i
s
tu
n
ed
,
h
o
w
e
v
er
th
e
ad
d
itio
n
al
t
w
o
p
ar
a
m
e
ter
s
(
d
er
iv
ativ
e
m
u
μ
an
d
lam
b
d
a
λ
)
ar
e
o
p
tim
ized
as
w
ell.
T
h
is
ac
tio
n
ad
d
s
f
lex
ib
ilit
y
a
n
d
m
o
r
e
r
o
b
u
s
tn
e
s
s
to
th
e
s
y
s
te
m
,
a
s
a
r
esu
lt
d
y
n
a
m
ic
s
y
s
te
m
p
er
f
o
r
m
an
ce
is
e
n
h
a
n
ce
d
in
co
m
p
ar
is
o
n
w
i
th
it
s
c
o
u
n
ter
p
ar
t
in
te
g
er
s
y
s
te
m
[
1
]
.
T
h
er
ef
o
r
e,
w
h
e
n
co
m
p
ar
i
n
g
t
h
e
cla
s
s
ic
th
r
ee
-
p
ar
a
m
eter
co
n
tr
o
l
u
n
it
a
n
d
t
h
e
f
r
ac
ti
o
n
al
o
r
d
er
p
r
o
p
o
r
tio
n
al
–
in
teg
r
al
–
d
er
iv
ati
v
e
(
FOP
I
D
)
co
n
tr
o
ller
,
th
e
f
r
a
ctio
n
al
o
r
d
er
co
n
tr
o
ller
h
as t
wo
ad
d
itio
n
al
co
n
tr
o
l
p
ar
am
eter
s
w
h
o
s
e
f
u
n
ctio
n
s
a
r
e
em
p
lo
y
ed
as
d
if
f
er
en
tiatio
n
an
d
in
teg
r
atio
n
co
m
m
an
d
s
to
g
iv
e
t
h
e
co
n
tr
o
ller
m
o
r
e
o
p
p
o
r
tu
n
ities
f
o
r
f
le
x
ib
i
lit
y
,
co
n
tr
o
l
an
d
s
tab
ilit
y
.
A
p
r
o
p
o
s
al
h
as
b
ee
n
g
i
v
e
n
b
y
r
es
ea
r
ch
er
s
f
o
r
s
tr
o
n
g
co
n
tr
o
l
b
y
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e
g
m
en
ti
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g
in
te
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e
r
o
r
d
er
in
teg
r
als
in
t
h
e
P
I
D
co
n
tr
o
l
s
y
s
te
m
,
also
b
y
u
s
in
g
th
e
n
ea
r
-
o
p
ti
m
a
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
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4752
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
22
,
No
.
3
,
J
u
n
e
2
0
2
1
:
1
3
4
5
-
1
3
5
3
1346
ap
p
r
o
x
im
a
tio
n
o
f
th
e
ar
r
an
g
e
m
en
t
tr
an
s
f
er
f
u
n
ctio
n
[
2
]
.
B
a
s
ed
o
n
w
h
at
w
as
m
en
tio
n
ed
p
r
ev
io
u
s
l
y
,
th
e
P
I
D
co
n
tr
o
ller
ca
n
b
e
b
etter
o
p
tim
ized
b
y
u
s
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n
g
t
h
e
s
o
-
ca
lled
p
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th
eo
r
y
o
f
s
o
-
ca
lled
p
r
o
p
o
r
tio
n
al
-
in
teg
r
ati
v
e
-
d
er
iv
ativ
e
p
ar
tial
ar
r
an
g
e
m
en
t
.
T
h
e
r
an
d
o
m
o
p
ti
m
izatio
n
s
tr
ateg
y
f
r
o
m
th
e
ev
o
l
u
tio
n
ar
y
co
m
p
u
tatio
n
g
r
o
u
p
i
s
th
e
p
r
in
cip
les
o
f
t
h
e
p
ar
ticle
s
w
ar
m
o
p
ti
m
izatio
n
(
P
SO
)
alg
o
r
ith
m
.
T
h
e
tech
n
o
lo
g
y
o
f
t
h
i
s
id
ea
is
in
s
p
ir
ed
b
y
a
b
io
lo
g
ical
tech
n
iq
u
e
[
3
]
.
I
t
h
as
b
ee
n
v
astl
y
co
n
s
id
er
ed
as
a
p
r
o
m
i
s
i
n
g
o
p
ti
m
izat
io
n
al
g
o
r
ith
m
b
ec
a
u
s
e
its
lo
w
co
m
p
u
tatio
n
co
s
t,
g
o
o
d
p
er
f
o
r
m
an
ce
,
a
n
d
s
i
m
p
licit
y
[
4
]
.
T
h
e
P
SO
alg
o
r
ith
m
s
r
elies
o
n
co
llecti
v
e
ac
tio
n
s
th
r
o
u
g
h
t
h
e
v
ar
io
u
s
li
n
es
o
f
r
esear
ch
t
h
at
h
a
v
e
w
o
r
k
e
d
ef
f
icie
n
tl
y
to
s
o
lv
e
m
o
s
t
o
f
th
e
in
te
g
r
ati
v
e
o
p
tim
izatio
n
tr
o
u
b
le
s
.
T
h
e
id
ea
o
f
P
SO
w
a
s
s
u
g
g
e
s
t
ed
an
d
b
ased
o
n
th
e
f
u
n
c
tio
n
s
o
f
b
ir
d
s
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h
o
w
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f
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m
atio
n
.
T
h
e
ai
m
o
f
t
h
is
p
ap
er
is
to
o
p
tim
ize
th
e
FO
P
I
D
co
n
tr
o
ller
p
ar
am
eter
s
b
ased
o
n
P
SO
alg
o
r
ith
m
.
T
h
is
alg
o
r
ith
m
is
u
ti
lize
d
to
o
p
tim
ize
th
e
co
n
tr
o
ller
p
ar
am
etr
s
a
n
d
it’s
a
p
p
lied
in
th
e
co
n
tr
o
llin
g
t
h
e
d
ir
ec
t c
u
r
r
en
t
(
DC
)
m
o
to
r
[
5
]
.
T
h
e
w
o
r
k
i
n
g
p
r
in
c
ip
le
o
f
th
e
DC
m
o
to
r
is
to
co
n
v
er
t
elec
tr
ical
en
er
g
y
i
n
to
k
i
n
etic
e
n
er
g
y
.
Du
e
to
th
eir
s
i
m
p
licit
y
a
n
d
co
n
s
ta
n
t
co
n
tr
o
l
p
r
o
p
er
ties
,
th
e
ap
p
licatio
n
s
o
f
D
C
m
o
to
r
s
h
a
v
e
b
ee
n
m
o
s
t
u
tili
ze
d
in
m
o
s
t
i
n
d
u
s
tr
ial
e
m
p
lo
y
m
en
t
l
ik
e
a
r
o
b
o
tic
m
a
n
eu
v
er
s
a
n
d
elec
tr
ic
lev
er
a
g
e.
DC
m
o
to
r
s
p
r
o
v
id
e
ad
eq
u
ate
co
n
tr
o
l
o
f
p
o
s
itio
n
an
d
id
le
o
r
ac
ce
ler
atio
n
s
p
ee
d
.
Fo
r
th
ese
r
ea
s
o
n
s
,
r
esear
ch
er
s
h
a
v
e
p
aid
g
r
ea
t
in
ter
esti
n
g
in
th
e
f
ield
o
f
co
n
tr
o
llin
g
th
e
p
o
s
itio
n
an
d
DC
m
o
to
r
s
p
ee
d
an
d
th
ey
d
ev
elo
p
ed
s
ev
er
al
m
et
h
o
d
s
f
o
r
co
n
tr
o
llin
g
its
p
o
s
itio
n
a
n
d
s
p
ee
d
.
On
e
s
u
ch
m
et
h
o
d
is
t
h
e
p
r
o
p
o
r
tio
n
al
-
d
er
iv
ati
v
e
-
i
n
teg
r
ated
co
n
tr
o
ller
(
P
I
D)
w
h
ich
is
co
m
m
o
n
l
y
u
s
ed
to
co
n
tr
o
l
v
elo
cit
y
a
n
d
p
o
s
itio
n
.
A
d
j
u
s
ti
n
g
th
e
p
ar
a
m
eter
s
o
f
t
h
e
P
I
D
co
n
tr
o
ller
is
v
er
y
i
m
p
o
r
tan
t
b
ec
au
s
e
it
h
as
a
g
r
ea
t
im
p
ac
t
o
n
th
e
p
er
f
o
r
m
a
n
ce
an
d
s
tab
ilit
y
o
f
th
e
co
n
tr
o
l
s
y
s
te
m
[
6
]
.
T
h
er
e
ar
e
m
an
y
w
a
y
s
t
h
at
ca
n
b
e
u
s
ed
t
o
co
n
tr
o
l
th
e
DC
m
o
to
r
s
p
ee
d
an
d
d
ir
ec
tio
n
.
On
e
o
f
t
h
ese
m
et
h
o
d
s
u
s
ed
is
t
h
e
co
n
v
e
n
tio
n
al
P
I
an
d
P
I
D
co
n
tr
o
ller
s
.
W
e
m
a
y
f
ac
e
m
an
y
d
il
e
m
m
as
to
g
ai
n
p
er
f
ec
t
co
n
tr
o
l
r
esu
lts
w
h
e
n
u
s
in
g
a
co
n
v
e
n
tio
n
al
P
I
D
co
n
tr
o
ller
,
esp
ec
iall
y
in
h
ig
h
-
o
r
d
er
s
y
s
t
e
m
s
w
h
e
re
th
e
co
n
v
en
t
io
n
al
P
I
D
co
n
tr
o
ller
d
o
es
n
o
t
w
o
r
k
w
ell
[
7
]
.
T
h
er
ef
o
r
e,
d
u
r
ab
ilit
y
o
f
t
h
e
d
ev
ice
w
it
h
g
o
o
d
s
y
s
te
m
p
er
f
o
r
m
an
ce
i
s
t
h
e
m
ai
n
r
eq
u
ir
e
m
e
n
t
w
h
e
n
d
esig
n
i
n
g
a
n
e
f
f
icien
t
co
n
tr
o
llin
g
s
y
s
te
m
.
A
s
a
r
es
u
lt
,
m
an
y
ad
v
a
n
ce
d
co
n
tr
o
l
u
n
it
s
y
s
te
m
s
h
a
v
e
b
ee
n
ap
p
lied
to
en
s
u
r
e
d
u
r
ab
ilit
y
a
n
d
n
o
n
-
r
ej
ec
tab
ilit
y
w
o
r
k
in
g
d
ev
ices [
8
]
.
2.
M
T
E
RIAL
S AN
D
M
E
T
H
O
DS
2
.
1
.
F
r
a
ct
io
na
l c
a
lculu
s
T
h
e
f
r
ac
tio
n
al
o
r
d
er
ca
lcu
lu
s
(F
OC
)
illu
s
tr
ates
t
h
e
id
ea
o
f
ex
ten
s
io
n
t
h
e
d
er
iv
ati
v
e
-
in
te
g
r
al
f
ac
to
r
th
at
is
d
er
iv
ed
f
r
o
m
an
in
te
g
er
“
k
”
to
an
ar
b
itra
r
y
o
r
d
er
o
r
to
n
o
n
-
i
n
teg
er
(
f
r
ac
tio
n
al)
o
r
d
e
r
[
9
]
.
Dif
f
er
-
in
te
g
r
al
o
p
er
ato
r
is
d
en
o
ted
b
y
,
it
is
a
m
i
x
t
u
r
e
o
f
d
if
f
er
en
tial
an
d
in
te
g
r
al
p
r
o
ce
s
s
es
t
h
a
t
ar
e
f
r
eq
u
en
tl
y
u
s
ed
in
f
r
ac
tio
n
al
ca
lc
u
l
u
s
.
So
,
th
e
f
r
ac
tio
n
al
ca
lc
u
l
u
s
ca
n
b
e
r
ep
r
esen
ted
b
y
(
d
k
y
/d
t
k
)
,
k
-
f
o
ld
in
teg
r
als
w
h
er
e
k
is
t
h
e
i
r
r
atio
n
al
,
f
r
ac
tio
n
al,
o
r
co
m
p
l
ex
[
1
0
]
.
FOC
i
s
b
ased
o
n
g
en
er
aliz
in
g
ca
lcu
lu
s
in
a
n
ar
b
itra
r
y
s
y
s
te
m
,
w
h
ic
h
ca
n
b
e
ir
r
atio
n
al
,
co
m
p
lex
,
o
r
ev
en
r
atio
n
al.
T
h
is
g
e
n
er
aliz
atio
n
led
to
th
e
in
tr
o
d
u
ctio
n
o
f
th
e
f
u
n
d
a
m
e
n
tal
co
n
t
in
u
o
u
s
d
if
f
er
in
te
g
r
al
o
p
er
ato
r
[
1
1
]
.
T
h
ese
m
at
h
e
m
atica
l
o
p
er
atio
n
s
ca
n
m
o
r
e
a
cc
u
r
atel
y
d
escr
ib
e
a
r
ea
l
o
b
ject
th
a
n
tr
ad
itio
n
a
l
in
te
g
er
o
r
d
er
in
g
m
et
h
o
d
s
[
1
2
]
.
T
h
e
o
p
e
r
ato
r
is
g
iv
e
n
b
y
(
1
)
:
a
D
t
α
=
{
1
for
α
=
0
d
α
d
t
α
for
α
>
0
∫
(
d
τ
)
−
α
for
α
<
0
t
a
}
(
1
)
w
h
er
e
a,
an
d
t a
r
e
th
e
s
y
s
te
m
l
i
m
it
co
n
d
it
io
n
s
,
a
n
d
(
∈
ℜ
)
is
th
e
o
p
er
atio
n
o
r
d
er
.
T
h
er
e
ar
e
th
r
ee
m
o
r
e
f
a
m
o
u
s
d
ef
in
itio
n
s
r
eg
ar
d
in
g
to
th
i
s
m
e
th
o
d
,
th
ese
ar
e
Gr
ü
n
w
ald
-
L
etn
ik
o
v
R
ie
m
an
n
-
L
io
u
v
ille,
a
n
d
C
ap
u
t
o
d
ef
in
it
io
n
s
[
1
3
]
.
T
h
e
th
r
ee
f
a
m
o
u
s
d
ef
i
n
itio
n
s
ar
e
r
eq
u
ir
ed
in
o
r
d
er
to
o
b
tain
th
e
co
n
tr
o
l a
lg
o
r
it
h
m
.
T
h
e
Gr
u
n
w
ald
–
L
et
n
i
k
o
v
eq
u
atio
n
is
:
a
D
t
a
f
(
t
)
=
l
im
h
→
0
1
h
a
∑
(
−
1
)
j
[
t
−
a
h
]
j
=
0
j
a
f
(
t
−
jh
)
(
2
)
w
h
er
e
th
e
R
ie
m
an
n
-
L
io
u
v
ille
d
ef
in
i
tio
n
is
:
a
D
t
a
f
(
t
)
=
1
Γ
(
1
−
a
)
d
k
d
t
k
∫
f
(
τ
)
(
t
−
τ
)
a
−
k
+
1
d
τ
t
a
(
3
)
w
h
e
n
th
e
eq
u
atio
n
in
i
tial
co
n
d
itio
n
a
is
b
o
u
n
d
ed
b
y
(
k
-
1
<
a
<k
)
,
th
e
i
n
te
g
r
als
f
o
ld
in
g
f
a
cto
r
an
d
th
e
g
a
m
m
a
f
u
n
ctio
n
Г
(
.
)
is
g
i
v
en
b
y
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4752
S
p
ee
d
c
o
n
tr
o
l o
f D
C
mo
to
r
u
s
in
g
fr
a
ctio
n
a
l
o
r
d
er P
I
D
co
n
tr
o
ller
b
a
s
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on
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(
Gh
a
s
s
a
n
A
.
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u
lta
n
)
1347
Г
(
y
)
=
∫
r
y
−
1
e
−
r
∞
0
dr
(
4
)
i
n
th
e
L
ap
lace
tr
an
s
f
o
r
m
n
u
tat
io
n
th
e
Di
f
f
er
-
i
n
te
g
r
al
o
p
er
ato
r
ca
n
b
e
w
r
itte
n
as:
ℒ
[
a
D
t
α
f
(
t
)
]
=
∫
e
−
st
∞
0
a
D
t
α
f
(
t
)
dt
(
5
)
ℒ
[
a
D
t
a
f
(
t
)
]
=
s
a
F
(
s
)
−
∑
s
(
−
1
)
j
k
−
1
m
=
0
0
D
t
a
−
m
−
1
f
(
t
)
(
6
)
t
h
e
s
y
m
b
o
l
α
is
b
et
w
ee
n
k
-
1
<α
≤
k
.
2.
2
.
F
r
a
ct
io
na
l
o
rder
P
I
D
c
o
ntr
o
ller
T
h
e
P
I
D
c
o
n
tr
o
ller
ar
e
alm
o
s
t
u
s
ed
in
t
h
e
i
n
d
u
s
tr
ial
p
r
o
ce
s
s
in
g
s
y
s
te
m
,
s
p
ec
ial
l
y
,
w
h
en
clo
s
e
lo
o
p
ch
ar
ac
ter
is
tic
s
ar
e
co
n
s
id
er
ed
.
Mo
s
tl
y
t
h
e
i
n
ter
est
lies
in
th
e
f
o
u
r
(
o
v
er
s
h
o
o
t,
r
is
e
t
i
m
e,
s
te
ad
y
-
s
tate
er
r
o
r
,
an
d
s
ettli
n
g
ti
m
e)
m
aj
o
r
clo
s
ed
-
lo
o
p
s
tep
r
esp
o
n
s
e
ch
ar
ac
ter
is
tic
s
[
1
4
]
,
[
1
5
]
.
Fo
r
th
e
an
al
y
s
e
s
an
d
d
esig
n
o
f
li
n
ea
r
d
y
n
a
m
ic
co
n
tr
o
l
s
y
s
te
m
,
th
e
i
n
itial
co
n
d
itio
n
s
o
f
F
O
d
if
f
er
e
n
tial
eq
u
a
tio
n
s
ar
e
ze
r
o
ass
u
m
ed
to
d
eter
m
i
n
e
t
h
e
tr
an
s
f
er
f
u
n
ctio
n
r
ea
ctio
n
s
o
f
th
e
s
y
s
te
m
.
T
h
e
f
r
eq
u
en
c
y
d
o
m
a
in
is
u
s
u
all
y
r
ep
r
esen
ted
in
ti
m
e
d
o
m
ai
n
o
p
er
ato
r
as
,
h
o
w
e
v
er
,
th
e
FO
P
I
D
o
r
P
I
λ
D
μ
co
n
tr
o
ller
ca
n
b
e
illu
s
tr
ated
as
w
ei
g
h
ted
s
u
m
o
f
s
u
c
h
o
p
er
ato
r
s
w
it
h
ad
d
itio
n
al
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
f
o
r
s
etti
n
g
t
h
e
w
ei
g
h
t
s
(
co
n
tr
o
ller
g
ain
s
)
alo
n
g
s
id
e
w
it
h
th
e
in
te
g
r
o
-
d
if
f
er
e
n
tial o
r
d
er
o
f
th
e
o
p
er
ato
r
s
[
1
6
]
.
Fig
u
r
e
1
s
h
o
w
s
th
e
b
l
o
ck
d
iag
r
a
m
f
o
r
f
r
ac
tio
n
al
o
r
d
er
P
I
D
c
o
n
tr
o
ller
.
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
a
m
o
f
t
h
e
f
r
ac
tio
n
al
o
r
d
er
P
I
D
c
o
n
tr
o
ller
T
h
e
co
n
tr
o
l
p
r
o
ce
d
u
r
e
f
o
r
th
e
f
r
ac
tio
n
al
o
r
d
er
P
I
D
co
n
tr
o
ller
,
ca
n
b
e
p
r
esen
ted
b
y
t
h
e
in
te
g
r
o
-
d
if
f
er
e
n
tial
m
at
h
e
m
a
tic
(
7
)
,
g
iv
en
,
a
n
d
th
e
tr
an
s
f
er
f
u
n
ct
io
n
o
f
th
e
s
u
c
h
co
n
tr
o
ller
is
ill
u
s
tr
ate
b
y
(
8
)
.
o
(
t
)
=
K
p
∈
(
t
)
+
K
i
D
−
λ
∈
(
t
)
+
K
d
D
−
μ
∈
(
t
)
(
7
)
G
F
O
PID
(
s
)
=
K
p
+
K
i
s
λ
+
K
d
s
μ
(
8
)
W
h
er
e
th
e
λ
an
d
μ
p
ar
a
m
e
ter
s
r
ep
r
esen
t
r
a
n
d
o
m
r
ea
l
n
u
m
b
er
s
.
W
h
en
μ
=
1
a
n
d
λ
=
1
,
w
e
ca
n
g
et
a
c
lass
ic
P
I
D
co
n
tr
o
ller
.
Fig
u
r
e
2
s
h
o
ws th
e
F
OP
I
D
(
μ
an
d
λ
)
p
ar
a
m
e
ter
s
w
h
ic
h
g
en
er
alize
th
e
c
lass
ical
P
I
D
co
n
tr
o
ller
,
an
d
ex
p
an
d
s
it
f
r
o
m
p
o
in
t
to
p
lan
e.
So
,
th
is
a
w
ar
d
s
u
s
m
o
r
e
to
ler
an
ce
f
o
r
d
esig
n
i
n
g
b
etter
P
I
D
co
n
tr
o
ller
,
an
d
it
a
w
ar
d
a
g
o
o
d
ch
an
ce
f
o
r
ex
ce
llen
t
s
ett
in
g
o
f
th
e
co
n
tr
o
l
s
y
s
te
m
d
y
n
a
m
ics
[
1
7
]
.
T
h
e
r
es
ea
r
ch
s
u
g
g
e
s
ted
th
e
m
et
h
o
d
o
f
p
ar
ticle
s
w
ar
m
o
p
ti
m
izatio
n
(
P
SO)
w
h
ich
ca
n
i
m
p
le
m
e
n
t
a
n
u
m
b
er
o
f
o
p
ti
m
i
za
tio
n
tech
n
iq
u
e
s
to
g
et
th
e
b
etter
p
ar
a
m
eter
s
v
al
u
e
s
o
f
th
e
co
n
tr
o
ller
[
1
8
]
,
[
1
9
]
.
(
a)
(
b
)
Fig
u
r
e
2
.
C
lass
ical
P
I
D
co
n
tr
o
ller
an
d
(
b
)
FOP
I
D
c
o
n
tr
o
ller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4752
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
22
,
No
.
3
,
J
u
n
e
2
0
2
1
:
1
3
4
5
-
1
3
5
3
1348
2
.
3
.
M
a
t
he
m
a
t
ica
l
m
o
del
T
h
e
b
lo
ck
d
iag
r
am
o
f
co
n
tr
o
llin
g
th
e
D
C
m
o
to
r
i
n
w
h
ic
h
th
e
ar
m
at
u
r
e
is
s
elec
ted
,
is
s
h
o
w
n
i
n
F
ig
u
r
e
3
.
I
n
(
9
)
g
iv
es
th
e
o
v
er
all
tr
an
s
f
er
f
u
n
ctio
n
o
f
t
h
is
DC
m
o
to
r
[
2
0
]
.
A
f
ter
ap
p
l
y
i
n
g
t
h
e
s
ta
n
d
ar
d
p
ar
am
eter
v
al
u
es
as
s
h
o
w
n
i
n
T
ab
le
1
,
to
th
e
DC
m
o
to
r
,
th
e
f
i
n
al
DC
m
o
to
r
tr
an
s
f
er
f
u
n
cti
o
n
ca
n
b
e
o
b
tain
ed
as
(
1
0
)
.
Fig
u
r
e
3
.
B
lo
ck
d
iag
r
a
m
s
y
s
te
m
DC
-
s
p
ee
d
m
o
to
r
z
(
s
)
e
a
(
s
)
=
k
t
[
(
r
+
Ls
)
(
js
+
b
)
+
k
t
k
p
]
(
9
)
z
(
s
)
e
a
(
s
)
=
0
.
023
0
.
005
s
2
+
0
.
01s
+
0
.
000559
(
1
0
)
T
ab
le
1
.
T
h
e
v
alu
es o
f
t
h
e
p
ar
a
m
eter
s
D
C
m
o
to
r
S
t
a
n
d
a
r
d
s
p
e
c
i
f
i
c
a
t
i
o
n
o
f
t
h
e
D
C
mo
t
o
r
D
a
mp
i
n
g
B
0
.
0
0
0
0
3
N
m*
s/
r
a
d
I
n
d
u
c
t
a
n
c
e
L
0
.
5
H
M
o
me
n
t
o
f
i
n
e
r
t
i
a
J
0
.
0
1
k
.
m2
G
a
i
n
K
0
.
0
2
3
R
e
si
st
a
n
c
e
R
1
Ω
3.
P
ARTI
C
L
E
SWA
RM
O
P
T
I
M
I
Z
AT
I
O
N
SY
ST
E
M
Du
r
in
g
p
r
ev
io
u
s
y
ea
r
s
,
t
h
e
d
ev
elo
p
m
e
n
t
o
f
th
e
p
ar
ticle
s
w
ar
m
o
p
ti
m
izatio
n
(
P
SO)
s
y
s
te
m
w
a
s
r
esear
ch
ed
an
d
d
ev
elo
p
ed
b
y
m
an
y
s
cie
n
ti
s
ts
i
n
cl
u
d
in
g
J
.
Ken
ed
y
an
d
R
.
E
b
er
h
ar
t
in
1
9
9
5
.
T
h
e
P
SO
th
eo
r
y
d
ep
en
d
s
o
n
t
h
e
i
n
tell
ig
e
n
t
m
o
v
e
m
e
n
t
p
r
in
cip
le
o
f
a
s
w
ar
m
t
h
at
m
o
v
e
s
i
n
t
h
e
s
ea
r
ch
ar
ea
,
l
o
o
k
in
g
f
o
r
th
e
b
e
s
t
s
o
lu
tio
n
f
o
r
it.
T
h
er
ef
o
r
e,
ea
ch
p
ar
ticle
i
n
t
h
e
v
ac
a
n
t
r
eg
i
o
n
is
tr
ea
ted
as
a
n
N
-
d
i
m
e
n
s
io
n
al
p
o
in
t
w
h
ic
h
atte
m
p
ts
to
o
p
ti
m
ize
its
p
o
s
iti
o
n
u
tili
z
in
g
t
h
e
ex
i
s
ti
n
g
lo
ca
ti
o
n
an
d
its
s
p
ee
d
.
T
h
e
p
r
ac
tical
d
i
m
en
s
io
n
b
et
w
ee
n
th
e
ex
i
s
ti
n
g
s
ite
an
d
th
e
b
est
s
ite
ca
lled
"
p
b
est
"
,
an
d
its
d
im
en
s
io
n
b
et
w
ee
n
ex
i
s
ti
n
g
lo
c
ati
o
n
an
d
a
g
lo
b
al
s
ite
ca
lled
"
g
b
est"
[
2
1
]
.
P
SO
th
eo
r
y
u
s
es
m
an
y
n
u
m
b
er
s
o
f
s
w
ar
m
co
n
s
ti
tu
e
n
t
p
ar
ti
cles
lo
o
k
in
g
f
o
r
th
e
b
est
s
o
l
u
t
io
n
in
t
h
e
s
ea
r
ch
s
p
ac
e,
s
o
it
is
co
n
s
id
er
e
d
o
n
e
o
f
th
e
alg
o
r
ith
m
s
t
h
at
d
o
es
n
o
t
i
m
p
le
m
en
t
s
u
r
v
i
v
al
o
f
th
e
f
i
ttes
t
[
2
2
]
.
Fo
r
m
u
lti
d
i
m
e
n
s
io
n
p
r
o
b
lem
as
i
n
P
SO
s
y
s
te
m
,
t
h
e
v
elo
cit
y
an
d
p
o
s
itio
n
o
f
th
e
p
ar
ticles
ca
n
b
e
d
eter
m
in
ed
an
d
u
p
d
ated
ac
co
r
d
in
g
to
th
e
f
o
llo
w
i
n
g
eq
u
atio
n
s
[
2
3
]
;
u
j
(
t
+
1
)
=
v
.
u
j
(
t
)
+
k
1
.
r
a
n
d
.
(
pb
e
s
t
(
t
)
−
d
j
(
t
)
)
+
k
2
.
r
a
n
d
.
(
gb
e
s
t
(
t
)
−
d
j
(
t
)
)
(
1
1
)
d
j
(
t
+
1
)
=
d
j
(
t
)
+
u
j
(
t
+
1
)
(
1
2
)
w
h
er
e
,
uj
(
t+1
)
is
th
e
s
p
ee
d
o
f
th
e
j
th
p
ar
ticle
at
(
t+1
)
r
e
p
etitio
n
.
d
j
(
t+
1
)
is
th
e
p
o
s
itio
n
o
f
t
h
e
j
th
p
ar
ticle
at
(
t+1
)
r
ep
etitio
n
.
v
is
t
h
e
in
er
tia
l
w
eig
h
t
f
ac
to
r
(
w
ei
g
h
ti
n
g
f
u
n
ct
io
n
)
.
k
1
an
d
k
2
ar
e
ac
ce
ler
atio
n
co
n
s
ta
n
t
s
an
d
ca
n
b
e
d
ef
in
ed
as
co
g
n
iti
v
e
lear
n
i
n
g
r
ate
an
d
g
r
eg
ar
io
u
s
lear
n
i
n
g
r
ate
r
esp
ec
tiv
el
y
.
r
an
d
is
in
d
is
cr
i
m
i
n
ate
n
u
m
b
er
b
et
w
ee
n
1
an
d
0
.
p
b
est is
th
e
p
er
s
o
n
all
y
b
est lo
c
atio
n
f
o
r
th
e
p
ar
ticle.
g
b
est is
t
h
e
g
lo
b
al
b
est lo
ca
tio
n
f
o
r
th
e
p
ar
ticles
s
w
ar
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4752
S
p
ee
d
c
o
n
tr
o
l o
f D
C
mo
to
r
u
s
in
g
fr
a
ctio
n
a
l
o
r
d
er P
I
D
co
n
tr
o
ller
b
a
s
ed
on
…
(
Gh
a
s
s
a
n
A
.
S
u
lta
n
)
1349
T
h
is
b
alan
ce
b
et
w
ee
n
lo
ca
l
an
d
g
lo
b
al
r
ese
ar
ch
,
w
h
ic
h
is
w
it
h
i
n
t
h
e
r
esp
o
n
s
ib
ilit
y
o
f
t
h
e
w
ei
g
h
tin
g
f
u
n
ctio
n
(
v
)
,
is
also
r
esp
o
n
s
ib
le
f
o
r
th
e
d
y
n
a
m
ic
ad
j
u
s
t
m
en
t
o
f
p
ar
ticle
v
elo
cities
,
th
e
w
ei
g
h
ti
n
g
f
u
n
ctio
n
v
is
ca
lcu
lated
as:
v
=
v
m
ax
−
(
v
m
ax
−
v
m
in
)
.
i
t
er
i
t
er
m
ax
(
1
3
)
w
h
er
e
;
v
m
a
x
an
d
v
m
i
n
ar
e
d
ef
i
n
ed
as p
r
e
m
ier
an
d
ev
e
n
t
u
al
w
ei
g
h
t
s
iter
is
k
n
o
w
n
as a
ti
m
e
o
f
t
h
e
r
ep
etitio
n
cu
r
r
en
t
iter
m
a
x
is
t
h
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
r
ep
etitio
n
s
.
T
h
e
d
ef
in
itio
n
i
s
a
s
u
g
g
es
ted
f
itn
es
s
f
u
n
ctio
n
to
o
p
ti
m
ize
P
I
D
co
n
tr
o
ller
p
ar
am
eter
s
:
F
=
v
m
ax
×
(
1
−
e
−
1
)
×
(
Mp
+
Ess
)
+
v
m
i
n
×
e
−
1
×
(
Ts
−
Tr
)
(
1
4
)
w
h
er
e
;
MP
: is th
e
Ma
x
i
m
u
m
Ov
er
s
h
o
o
t,
T
r
: is th
e
R
is
e
T
i
m
e,
T
s
: is th
e
Settli
n
g
ti
m
e
T
h
e
o
p
tim
iza
tio
n
s
tep
s
o
f
th
e
p
ar
am
e
ter
s
o
f
th
e
P
SO
-
P
I
D
co
n
tr
o
ller
f
o
r
co
n
tr
o
lli
n
g
th
e
DC
m
o
to
r
s
p
ee
d
ar
e
im
p
le
m
en
ted
ac
co
r
d
in
g
to
t
h
e
P
SO
alg
o
r
ith
m
.
T
h
ese
s
tep
s
ar
e
i
m
p
l
m
en
ted
i
n
MA
T
L
A
B
–
Si
m
u
in
k
p
r
o
g
r
am
.
T
h
e
m
a
in
s
tep
s
i
n
cl
u
d
e
a
m
o
d
el
f
o
r
DC
m
o
to
r
s
p
ee
d
s
o
th
at
th
e
Mp
,
T
p
&
T
s
p
ar
am
eter
s
o
f
t
h
e
m
o
to
r
m
o
d
el
s
tep
r
esp
o
n
s
e
ar
e
ca
lcu
lated
.
A
s
a
r
esu
lt,
th
e
f
it
n
es
s
f
u
n
ctio
n
ass
i
g
n
m
e
n
t
an
d
co
m
p
ar
is
o
n
b
et
w
ee
n
p
b
est
an
d
g
b
est
ca
n
also
b
e
ca
lcu
lated
.
Fi
n
all
y
,
t
h
e
p
ar
tical
s
p
ee
d
an
d
lo
ca
tio
n
ca
n
b
e
f
o
llo
w
ed
a
n
d
th
ese
s
tep
s
ar
e
illu
s
tr
ated
in
t
h
e
f
lo
w
c
h
ar
t a
s
s
h
o
w
n
in
Fig
u
r
e
4
.
Fig
u
r
e
4
.
T
h
e
b
asic P
SO a
lg
o
r
ith
m
ch
ar
t
4.
P
SO
-
F
O
P
I
D
CO
NT
RO
L
L
E
R
SYST
E
M
I
n
th
i
s
p
ap
er
,
th
e
P
SO
alg
o
r
ith
m
is
ap
p
lied
to
s
ea
r
ch
f
o
r
th
e
b
est
o
r
o
p
tim
ized
FOP
I
D
co
n
tr
o
ller
p
ar
am
eter
s
.
T
h
e
P
SO
is
a
r
esear
ch
i
n
g
s
y
s
te
m
b
ased
o
n
t
h
e
id
ea
o
f
t
h
e
s
o
cial
b
eh
a
v
i
o
r
o
f
f
is
h
an
d
b
ir
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
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2
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4752
I
n
d
o
n
esia
n
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E
lec
E
n
g
&
C
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m
p
Sci,
Vo
l.
22
,
No
.
3
,
J
u
n
e
2
0
2
1
:
1
3
4
5
-
1
3
5
3
1350
s
ch
o
o
lin
g
.
P
SO
e
x
p
lo
its
a
s
war
m
o
f
p
ar
ticles
t
h
at
e
x
p
lo
r
e
p
r
o
m
i
s
in
g
r
e
g
io
n
s
o
f
th
e
D
-
d
i
m
e
n
s
io
n
al
s
ea
r
c
h
s
p
ac
e
w
it
h
ad
ap
tiv
e
s
p
ee
d
.
I
t
w
o
r
k
s
u
n
til
th
e
s
to
p
co
n
d
itio
n
is
m
et.
B
etter
p
ar
ticle
p
lace
m
en
t
g
iv
e
s
o
p
ti
m
u
m
p
ar
am
eter
s
s
elec
tio
n
f
o
r
th
e
c
o
n
tr
o
ller
[
1
]
.
T
h
er
ef
o
r
e,
th
e
P
SO
s
y
s
te
m
,
w
h
ic
h
w
as
d
e
v
elo
p
ed
in
1
9
9
5
ca
n
b
e
d
ef
in
ed
as
an
i
m
p
r
o
v
e
m
en
t
m
eth
o
d
b
ased
o
n
ev
o
lu
tio
n
ar
y
ca
lcu
latio
n
,
an
d
th
e
in
er
ti
al
w
eig
h
t
w
a
s
ad
d
ed
in
1
9
9
8
[
2
4
]
,
[
2
5
]
.
I
n
th
e
n
o
r
m
a
l
co
n
tr
o
llin
g
s
y
s
t
e
m
h
a
s
th
r
ee
(
K
p
,
K
i
,
an
d
K
d
)
ess
e
n
tial
p
ar
a
m
eter
s
,
h
o
w
e
v
er
,
ac
co
r
d
in
g
to
th
e
p
r
o
p
o
s
ed
FOP
I
D
co
n
t
r
o
ller
an
o
th
er
p
ar
am
eter
s
λ
(
in
teg
er
o
r
d
er
)
an
d
μ
(
d
er
iv
ativ
e
o
r
d
er
)
ar
e
ad
d
e
d
,
th
ese
t
w
o
p
ar
a
m
eter
s
ar
e
d
eter
m
in
ed
t
h
r
o
u
g
h
t
h
e
ap
p
licatio
n
o
f
th
e
P
SO
alg
o
r
it
h
m
,
s
o
th
at
th
e
b
est
o
u
tp
u
t
r
esp
o
n
s
e
f
o
r
th
e
co
n
tr
o
l
s
y
s
t
e
m
is
o
b
tain
ed
.
T
h
e
“
p
er
s
o
n
a
lit
y
”
i
s
u
s
ed
to
s
u
b
s
tit
u
te
t
h
e
“
p
ar
ticle”
an
d
t
h
e
“
i
n
h
ab
ita
n
ce
”
is
u
s
ed
to
s
p
e
cif
y
t
h
e
“g
r
o
u
p
”.
Ass
u
m
e
th
at
th
e
s
e
p
ar
am
eter
s
(
K
p
,
K
i
an
d
,
K
d
)
an
d
th
e
p
ar
am
eter
s
λ
(
in
teg
er
o
r
d
er
)
an
d
μ
(
d
er
iv
ativ
e
o
r
d
er
)
ar
e
p
er
s
o
n
alit
y
,
s
o
th
e
p
er
s
o
n
alit
y
co
n
tain
s
th
e
f
i
v
e
m
e
m
b
er
s
,
a
n
d
as
s
ig
n
ed
as
r
ea
l
v
al
u
e.
No
w
ass
u
m
e
t
h
at
t
h
er
e
ar
e
n
p
er
s
o
n
alitie
s
i
n
t
h
e
in
h
a
b
itan
ce
,
s
o
t
h
e
n
x
5
is
th
e
in
h
ab
ita
n
ce
d
i
m
en
s
io
n
.
Usi
n
g
a
s
et
o
f
g
o
o
d
co
n
tr
o
l
p
ar
am
eter
s
K
p
,
K
i
,
K
d
,
λ
,
an
d
μ
ca
n
ac
h
iev
e
g
o
o
d
r
esu
lt
s
an
d
f
in
e
-
t
u
n
ed
v
al
u
es
to
ac
h
iev
e
a
g
o
o
d
s
y
s
te
m
o
u
t
p
u
t
r
esp
o
n
s
e,
as
a
r
es
u
lt
o
f
t
h
is
ac
tio
n
t
h
e
v
alu
e
p
er
f
o
r
m
a
n
ce
p
ar
a
m
eter
s
i
s
r
ed
u
ce
d
in
th
e
t
i
m
e
d
o
m
ai
n
,
t
h
es
e
p
ar
am
eter
s
i
n
cl
u
d
e
r
is
e
ti
m
e
(
T
r
)
,
s
ettlin
g
ti
m
e
(
T
s
)
,
s
tead
y
-
s
tate
er
r
o
r
(
ess
)
,
a
n
d
m
a
x
i
m
u
m
o
v
er
s
h
o
t
(
m
p
%)
.
Fig
u
r
e
5
ill
u
s
tr
ate
s
s
y
s
t
e
m
o
f
th
e
b
lo
ck
d
iag
r
a
m
th
e
P
SO
-
FOP
I
D
co
n
tr
o
ller
f
o
r
th
e
DC
m
o
to
r
[
2
6
]
.
Fig
u
r
e
5
.
B
lo
ck
d
iag
r
a
m
s
y
s
te
m
o
f
t
h
e
P
SO
-
FOP
I
D
co
n
tr
o
ller
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
I
n
t
h
is
s
t
u
d
y
t
h
e
p
ar
a
m
eter
v
al
u
es
tak
e
n
f
o
r
r
u
n
n
in
g
t
h
e
P
SO
alg
o
r
it
h
m
in
M
A
T
L
A
B
e
n
v
ir
o
n
m
e
n
t
i
s
g
iv
e
i
n
T
ab
le
2
.
T
h
e
u
n
it
s
t
ep
r
esp
o
n
s
e
o
f
s
p
ee
d
co
n
tr
o
l
o
f
DC
-
m
o
to
r
u
s
i
n
g
P
SO
-
FO
P
I
D
an
d
P
SO
-
P
I
D
co
n
tr
o
ller
ar
e
s
h
o
w
n
i
n
F
i
g
u
r
e
s
6
an
d
7
r
esp
ec
tiv
e
l
y
.
T
h
e
P
SO
-
FOP
I
D
co
n
tr
o
ller
p
ar
a
m
eter
s
ar
e
s
h
o
w
n
i
n
T
ab
le
3
.
T
h
e
o
b
tain
ed
r
esu
lts
ill
u
s
tr
ate
t
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
P
SO
a
lg
o
r
it
h
m
i
n
c
h
o
o
s
in
g
th
e
b
est
a
v
er
ag
e
p
ar
am
eter
s
v
al
u
es
f
o
r
th
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
p
r
o
p
o
s
ed
P
S
O
-
FOP
I
D
co
n
tr
o
ller
.
T
h
e
co
n
v
er
g
e
n
ce
cu
r
v
e
f
o
r
ea
ch
g
ai
n
is
ca
l
led
as
p
ar
ticle
f
o
r
Kp
,
Ki
,
Kd
,
λ
an
d
μ
ar
e
p
lo
tted
to
g
iv
e
an
i
d
ea
h
o
w
t
h
e
P
SO
Alg
o
r
it
h
m
co
n
v
er
g
ed
to
its
f
in
al
v
a
lu
e
h
a
s
b
ee
n
illu
s
tr
ated
in
Fig
u
r
es
8
an
d
9
is
th
e
o
u
tco
m
e
o
f
co
n
v
er
g
e
n
ce
cu
r
v
e
f
o
r
o
u
tp
u
t r
esp
o
n
s
e.
T
ab
le
2
.
T
h
e
v
alu
es o
f
t
h
e
p
ar
t
icle
s
w
ar
m
p
ar
a
m
e
ter
s
N
a
me
o
f
P
a
r
a
me
t
e
r
T
h
e
V
a
l
u
e
s
C
o
g
n
i
t
i
v
e
C
o
mp
o
n
e
n
t
k
1
2
M
i
n
i
m
u
m
I
n
e
r
t
i
a
W
e
i
g
h
t
0
.
4
M
a
x
i
m
u
m
S
p
e
e
d
10
M
a
x
i
m
u
m
N
o
.
o
f
I
t
e
r
a
t
i
o
n
s
1
0
0
N
u
mb
e
r
o
f
P
a
r
t
i
c
l
e
s
20
M
a
x
i
m
u
m
I
n
e
r
t
i
a
W
e
i
g
h
t
0
.
9
S
o
c
i
a
l
C
o
m
p
o
n
e
n
t
k
2
2
T
ab
le
3
.
C
o
m
p
ar
is
o
n
p
ar
a
m
e
t
er
v
alu
es
f
o
r
th
e
v
ar
io
u
s
co
m
p
o
n
en
t
s
o
f
μ
an
d
λ
C
o
n
t
r
o
l
l
e
r
P
a
r
a
me
t
e
r
Kp
K
i
K
d
mp
%
Tr
Ts
L
a
md
a
(
λ
)
M
u
(
μ)
PSO
-
F
O
P
I
D
v
a
l
u
e
s
1
0
.
4
7
9
5
1
.
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8
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8
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4
6
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3
5
0
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0
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3
8
3
0
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0
0
6
9
3
0
.
7
1
6
9
9
7
0
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0
1
2
2
5
5
4
PSO
-
P
I
D
v
a
l
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e
s
9
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1
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1
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2
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7
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5
.
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4
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2
6
0
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0
3
2
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0
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0
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7
0
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0
0
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7
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
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J
E
lec
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u
r
e
6
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h
e
DC
m
o
to
r
u
n
it
s
tep
r
esp
o
n
s
e
f
o
r
th
e
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SO
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I
D
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n
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o
l
ler
Fig
u
r
e
7
.
T
h
e
DC
m
o
to
r
u
n
it
s
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r
esp
o
n
s
e
f
o
r
th
e
P
SO
-
P
I
D
co
n
tr
o
ller
Fig
u
r
e
8
.
Gen
er
atin
g
t
h
e
v
al
u
e
s
o
f
th
e
Kp
,
Ki,
Kd
,
λ
an
d
μ
o
f
th
e
P
SO
-
FOP
I
D
co
n
tr
o
ller
Fig
u
r
e
9
.
Gen
er
atin
g
t
h
e
v
al
u
e
s
o
f
th
e
Kp
,
Ki,
Kd
o
f
th
e
P
SO
-
P
I
D
co
n
tr
o
ller
0
0
.
5
1
1
.
5
2
2
.
5
3
3
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5
4
4
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5
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[1
]
M
.
Zam
a
n
i,
M
.
K
.
G
h
a
rtem
a
n
i,
a
n
d
Na
se
e
r
S
a
d
a
ti
,
“
F
OP
ID
c
o
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sig
n
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u
st
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rm
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n
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e
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g
p
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le
sw
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rm
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p
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n
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Fra
c
ti
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Ca
lcu
lu
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Ap
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An
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lys
is
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v
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l.
1
0
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o
.
2
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0
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.
[2
]
J
.
Y
.
Ca
o
a
n
d
B
.
G
.
Ca
o
,
“
De
sig
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t.
J
.
Co
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to
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ms
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2
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.
[3
]
Dz
ielin
sk
i
a
n
d
D.
S
iero
c
iu
k
,
“
S
im
u
latio
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d
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x
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to
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[4
]
S
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M
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n
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R.
El
-
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h
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z
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li
,
a
n
d
I.
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.
Ba
ti
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a
,
“
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Pro
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,
[5
]
K.
M
ish
ra
,
a
n
d
A
.
Na
ra
in
,
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d
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M
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to
r
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ti
m
iza
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T
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c
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,
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In
ter
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Res
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8
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,
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l.
2
,
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o
.
6
,
Ju
n
e
,
2013.
[6
]
A
.
Ra
sto
g
i
a
n
d
P
.
T
iw
a
ri,
“
Op
ti
m
a
l
T
u
n
in
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o
f
F
ra
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ti
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Ord
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g
P
a
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S
w
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r
m
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m
iza
ti
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n
,
”
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ter
n
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l
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o
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g
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n
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g
in
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g
(
IJ
S
CE)
,
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S
N:
2
2
3
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7
,
v
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.
3
,
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o
.
2
,
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y
2
0
1
3
.
[7
]
A
.
Id
ir,
M
.
Ki
d
o
u
c
h
e
,
Y
.
Be
n
sa
f
ia,
K
.
K
h
e
tt
a
b
,
a
n
d
S
.
A
.
T
a
d
jer,
“
S
p
e
e
d
Co
n
tro
l
o
f
DC
M
o
t
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r
Us
in
g
P
ID
a
n
d
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ID
C
o
n
tr
o
ll
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rs
Ba
se
d
o
n
Di
ff
e
r
e
n
ti
a
l
Ev
o
lu
ti
o
n
a
n
d
P
S
O
,
”
I
n
ter
n
a
ti
o
n
a
l
j
o
u
rn
a
l
o
f
I
n
telli
g
e
n
t
En
g
in
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rin
g
&
S
y
ste
ms
,
M
a
rc
h
3
1
,
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0
1
8
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d
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i:
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0
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2
2
2
6
6
/
ij
ies
2
0
1
8
.
0
8
3
1
.
2
4
.
[8
]
A
.
A
h
u
ja
a
n
d
S
.
K
.
A
g
g
a
r
w
a
l,
“
De
sig
n
o
f
f
ra
c
ti
o
n
a
l
o
rd
e
r
P
I
D
c
o
n
tro
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r
f
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r
DC
m
o
to
r
u
sin
g
e
v
o
lu
ti
o
n
a
ry
o
p
ti
m
iza
ti
o
n
tec
h
n
iq
u
e
s
,
”
Arti
c
le
in
W
S
EA
S
T
r
a
n
sa
c
ti
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n
s
o
n
S
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ste
ms
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d
Co
n
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l
,
Ja
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u
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ry
2
0
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4
,
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ik
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.
v
1
2
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2
.
6
4
7
0
.
[9
]
O
.
S
.
P
e
ñ
a
a
n
d
H
.
Ca
sta
ñ
e
d
a
,
a
n
d
J
.
d
e
L
e
ó
n
-
M
o
ra
les
,
“
Ro
b
u
st
A
d
a
p
ti
v
e
Co
n
tr
o
l
f
o
r
a
DC
S
e
rv
o
m
o
to
r
w
it
h
w
id
e
Ba
c
k
las
h
No
n
li
n
e
a
rit
y
,
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On
li
n
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IS
S
N
1
8
4
8
-
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8
0
,
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ri
n
t
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S
N
0
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-
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4
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KAF
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,
v
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6
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o
.
4
,
pp
.
4
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6
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2
,
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5
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1
4
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2
0
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5
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1
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8
6
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.
[1
0
]
R
.
M
a
tu
su
,
“
A
p
p
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c
a
ti
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n
o
f
f
ra
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ti
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rd
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ry
,
”
In
ter
n
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ti
o
n
a
l
J
o
u
rn
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l
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f
M
a
th
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ma
ti
c
a
l
M
o
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e
ls a
n
d
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e
th
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s i
n
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p
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l
ied
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e
s
,
v
o
l
5
,
n
o
.
7
,
2
0
1
1
.
[1
1
]
R.
E.
G
u
ti
é
rre
z
,
J.
M
.
R
o
sá
rio
,
a
n
d
J.
T
.
M
a
c
h
a
d
o
,
“
F
ra
c
ti
o
n
a
l
O
rd
e
r
Ca
lcu
lu
s:
Ba
sic
Co
n
c
e
p
ts
a
n
d
E
n
g
in
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rin
g
A
p
p
li
c
a
ti
o
n
s
,
”
M
a
t
h
e
ma
ti
c
a
l
Pro
b
lem
s in
E
n
g
in
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rin
g
,
v
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l.
2
0
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1
9
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.
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2
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1
1
5
5
/2
0
1
0
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3
7
5
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5
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.
[1
2
]
A
.
Dz
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sk
i
a
n
d
D
.
S
iero
c
iu
k
,
“
S
im
u
latio
n
a
n
d
e
x
p
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rim
e
n
tal
to
o
ls
f
o
r
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ra
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ti
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l
o
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d
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r
c
o
n
tr
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l
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d
u
c
a
ti
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n
,
”
Pro
c
.
IFA
C
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,
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[1
3
]
R
.
M
a
tu
šů
,
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p
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,
In
ter
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d
s i
n
A
p
p
l
ied
S
c
ien
c
e
s
, v
ol
.
5
,
n
o
.
7
,
2
0
1
1
.
[1
4
]
S
.
G
h
o
sa
l,
R
.
K
.
Da
rb
a
r,
B
.
Ne
o
g
i,
A
.
Da
s,
a
n
d
D
.
N.
T
ib
a
re
wa
la,
“
A
p
p
li
c
a
ti
o
n
o
f
S
wa
r
m
In
telli
g
e
n
c
e
Co
m
p
u
tatio
n
T
e
c
h
n
iq
u
e
s
in
P
ID
C
o
n
tr
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ll
e
r
T
u
n
in
g
:
A
Re
v
ie
w
,
”
Pro
c
e
e
d
in
g
s o
f
th
e
In
Co
n
INDIA
2
0
1
2
,
A
IS
C
1
3
2
,
p
p
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1
9
5
-
2
0
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o
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0
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1
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7
8
-
3
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642
-
2
7
4
4
3
-
5
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2
3
.
[1
5
]
P
.
S
h
a
rm
a
a
n
d
V
.
K
u
m
a
r
,
“
De
sig
n
o
f
No
v
e
l
BEL
BIC
Co
n
tr
o
ll
e
d
S
e
m
i
-
A
c
ti
v
e
S
u
sp
e
n
sio
n
a
n
d
C
o
m
p
a
ra
ti
v
e
A
n
a
l
y
si
s w
it
h
P
a
ss
iv
e
a
n
d
P
ID C
o
n
tr
o
ll
e
d
S
u
s
p
e
n
sio
n
,
”
W
a
l
a
il
a
k
J
o
u
rn
a
l
o
f
S
c
ien
c
e
a
n
d
T
e
c
h
n
o
l
o
g
y
,
EIS
S
N:
2
2
2
8
-
8
3
5
X,
A
c
c
e
p
ted
:
2
6
M
a
rc
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2
0
2
0
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d
o
i:
1
0
.
4
8
0
4
8
/w
jst.
2
0
2
1
.
8
9
8
9
.
[1
6
]
Ch
a
tt
e
rjee
,
V
.
M
u
k
h
e
rjee
,
a
n
d
S
.
G
h
o
sh
a
l,
“
V
e
lo
c
it
y
re
lax
e
d
a
n
d
c
ra
z
in
e
ss
-
b
a
se
d
sw
a
rm
o
p
ti
m
ize
d
in
telli
g
e
n
t
P
ID
a
n
d
P
S
S
c
o
n
tro
ll
e
d
A
V
R
sy
ste
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
Po
we
r
&
En
e
rg
y
S
y
ste
ms
,
v
o
l.
3
1
,
n
o
.
7
-
8
,
p
p
.
3
2
3
-
3
3
3
,
2
0
0
9
,
d
o
i:
1
0
.
1
0
1
6
/j
.
ij
e
p
e
s.2
0
0
9
.
0
3
.
0
1
2
.
[1
7
]
Na
sri
M
.
I,
p
o
u
r
H.
N,
a
n
d
M
a
g
h
fo
o
ri
M
,
"
A P
S
O
-
Ba
se
d
Op
ti
m
u
m
De
sig
n
o
f
P
ID Co
n
tro
l
ler f
o
r
a
L
i
n
e
a
r
Bru
sh
les
s
DC M
o
t
o
r
,
"
Pro
c
e
e
d
in
g
s o
f
W
o
rl
d
Aca
d
e
my
o
f
S
c
ien
c
e
,
En
g
in
e
e
ri
n
g
a
n
d
T
e
c
h
n
o
l
o
g
y
,
v
o
l.
2
0
A
p
ril
,
2
0
0
7
.
[1
8
]
D.
M
a
it
i,
S
.
Bisw
a
s,
a
n
d
A
.
Ko
n
a
r,
“
De
sig
n
o
f
a
f
ra
c
ti
o
n
a
l
o
r
d
e
r
P
ID
c
o
n
tro
ll
e
r
u
si
n
g
p
a
rti
c
le
sw
a
rm
o
p
ti
m
iza
ti
o
n
tec
h
n
iq
u
e
,
”
S
e
c
o
n
d
N
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Rec
e
n
t
T
re
n
d
s i
n
In
f
o
r
ma
ti
o
n
S
y
ste
ms
, v
o
l.
3
0
,
2
0
0
8
.
[1
9
]
Z.
L
.
Ga
in
g
,
“
A
p
a
rti
c
le
s
wa
r
m
o
p
ti
m
iza
ti
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n
a
p
p
r
o
a
c
h
f
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o
p
t
i
m
u
m
d
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si
g
n
o
f
P
ID
c
o
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tr
o
ll
e
r
i
n
A
V
R
s
y
ste
m
,
”
En
e
rg
y
Co
n
v
e
rs
io
n
,
I
EE
E
T
r
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n
s
a
c
ti
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n
s
on
,
v
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l.
1
9
,
n
o
.
2
,
p
p
.
3
8
4
-
3
9
1
,
2
0
0
4
,
d
o
i:
1
0
.
1
1
0
9
/T
EC.
2
0
0
3
.
8
2
1
8
2
1
.
[2
0
]
R
.
S
in
g
h
a
l,
S
.
P
a
d
h
e
e
,
a
n
d
G
.
Ka
u
r,
“
De
sig
n
o
f
F
ra
c
ti
o
n
a
l
Ord
e
r
P
ID
Co
n
tro
l
ler
f
o
r
S
p
e
e
d
Co
n
tr
o
l
o
f
DC
M
o
to
r
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
S
c
ien
ti
fi
c
a
n
d
Res
e
a
rc
h
P
u
b
li
c
a
ti
o
n
s
, v
o
l
2
,
n
o
.
6
,
Ju
n
e
2
0
1
2
.
[2
1
]
D.
M
a
it
i,
S
.
Bisw
a
s
,
a
n
d
A
.
Ko
n
a
r,
“
De
sig
n
o
f
f
ra
c
ti
o
n
a
l
o
r
d
e
r
P
ID
c
o
n
tro
l
ler
u
sin
g
p
a
rti
c
le
sw
a
r
m
o
p
ti
m
iz
a
ti
o
n
tec
h
n
iq
u
e
,
”
2
nd
in
ter
n
a
ti
o
n
a
l
c
o
n
f
e
re
n
c
e
o
n
re
c
e
n
t
t
re
n
d
s i
n
i
n
fo
rm
a
ti
o
n
sy
ste
ms
(
ReTIS
-
08)
,
2
0
0
8
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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[2
2
]
H
.
R
.
S
.
Ba
lo
c
h
ian
a
n
d
A
.
Zar
e
,
“
De
sig
n
o
f
Op
ti
m
a
l
F
ra
c
ti
o
n
a
l
-
Ord
e
r
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ID
Co
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Us
in
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c
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w
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iza
ti
o
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m
f
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to
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c
V
o
lt
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g
e
Re
g
u
lato
r
(A
V
R)
S
y
ste
m
,
”
J
o
u
rn
a
l
o
f
C
o
n
tr
o
l,
Au
to
m
a
ti
o
n
a
n
d
El
e
c
trica
l
S
y
ste
ms
,
IS
S
N
2
1
9
5
-
3
8
8
0
,
2
9
M
a
y
2
0
1
3
,
d
o
i:
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0
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1
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0
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/s4
0
3
1
3
-
0
1
3
-
0
0
5
7
-
7
.
[2
3
]
M
.
R
.
Da
stra
n
j,
M
.
R
o
u
h
a
n
i,
a
n
d
A
.
Ha
ji
p
o
o
r,
“
De
sig
n
o
f
Op
ti
m
a
l
F
ra
c
ti
o
n
a
l
Ord
e
r
P
ID
C
o
n
tr
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ll
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r
Us
in
g
P
S
O
A
l
g
o
rit
h
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
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rn
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l
o
f
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o
mp
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ter
T
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En
g
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3
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0
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2
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o
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0
7
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0
3
1
3
-
0
1
3
-
0
0
5
7
-
7
.
[2
4
]
A
.
K.
Ha
m
o
u
d
i,
“
Op
ti
m
u
m
S
e
tt
in
g
o
f
P
ID
Co
n
tro
l
ler
u
sin
g
P
a
rti
c
le
S
wa
r
m
Op
ti
m
iza
ti
o
n
f
o
r
a
P
o
siti
o
n
Co
n
tro
l
S
y
st
e
m
,
”
Al
-
Na
h
ra
i
n
J
o
u
rn
a
l
fo
r
En
g
i
n
e
e
rin
g
S
c
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c
e
s (
NJ
ES
),
v
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l
.
2
0
,
n
o.
1
,
p
p
.
2
9
2
-
2
9
7
,
2
0
1
7
.
[2
5
]
M
.
G
.
Do
z
e
in
,
A
.
G
h
o
la
m
i,
a
n
d
M
.
Ka
lan
tar,
“
S
p
e
e
d
Co
n
tr
o
l
o
f
DC
M
o
to
r
Us
in
g
Dif
f
e
r
e
n
t
Op
ti
m
iza
ti
o
n
T
e
c
h
n
iq
u
e
s Ba
se
d
P
ID Co
n
tro
ll
e
r
,
”
J
.
Ba
sic
.
A
p
p
l
.
2
0
1
2
.
[2
6
]
T
.
Ki
m
,
I.
M
a
ru
ta
a
n
d
T
.
S
u
g
ie,
“
Ro
b
u
st
P
ID
c
o
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tro
ll
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g
b
a
se
d
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n
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o
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i
n
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p
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sw
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o
p
ti
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iza
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ti
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a
,
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4
4
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4
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0
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7
.
B
I
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G
RAP
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I
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S O
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AUTH
O
RS
G
h
a
sa
a
n
A.
S
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lta
n
.
He
w
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s
b
o
rn
in
M
o
su
l
in
Ira
q
in
1
9
6
2
.
He
h
a
s
g
o
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is
BBc
in
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tri
c
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l
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g
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Ra
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ia
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8
5
.
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h
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S
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El
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El
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En
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Be
lg
ra
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e
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1
9
8
7
.
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p
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sh
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rre
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tl
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tu
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in
th
e
d
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a
rtm
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m
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No
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h
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Un
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–
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q
.
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m
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S
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t
.
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wa
s
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o
rn
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o
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in
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4
.
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h
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s
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ia
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1
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8
6
.
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S
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El
e
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tro
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m
in
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h
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tri
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g
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in
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f
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lg
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1
9
8
8
.
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h
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s
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h
D
o
f
m
icro
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le
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tro
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c
o
m
m
u
n
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ti
o
n
.
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p
u
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sh
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ten
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p
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rre
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ly
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e
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tu
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N
o
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e
rn
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c
h
n
ica
l
Un
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e
rsit
y
–
Ira
q
.
Abd
u
ls
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tta
r
M
.
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.
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