In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
4, D
e
c
e
m
ber
201
9,
pp.
1724~
17
33
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
4.pp1724-1733
1724
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Fractional-order PID controll
er for perman
ent magnet DC
motor based
on PSO algorithm
Fad
h
i
l
A
.
Hasan
,
Lin
a
J. R
ash
a
d
D
e
part
men
t
o
f Electri
cal E
ngin
e
eri
n
g
,
U
n
i
v
e
rsity
of
T
echn
o
lo
gy
,
I
raq
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Dec
2
4
,
2
018
Re
vise
d Mar
1,
201
9
Ac
ce
p
t
ed
M
ar 1
0
,
2
019
Th
is
p
ap
er
p
ro
p
o
s
e
s
t
h
e
f
r
act
ion
a
l-ord
e
r
pro
portio
n
a
l
in
te
gra
l
de
riva
tive
(F
OP
ID) cont
ro
ller, as a s
p
eed
co
n
t
ro
ller fo
r
p
erman
e
nt
m
agn
e
t
direct current
(
P
M
D
C
)
m
o
t
or
,
in
s
t
e
a
d
o
f
th
e
t
r
a
d
it
io
na
l
i
n
te
g
e
r
-
o
r
d
e
r
P
I
D
c
o
n
t
rol
l
er.
The
F
O
P
I
D
co
n
t
ro
ller
i
s
th
e
g
e
nera
l
f
o
rm
o
f
t
h
e
integer-order
P
ID
c
on
trol
lers,
wh
ich
f
o
u
n
d
wi
d
e
a
ppl
icat
io
ns
i
n
al
l
en
gi
neerin
g
field
s
.
In
t
hi
s
work
a
h
ybrid
M-fi
l
e
a
nd
S
IMU
L
IN
K
program
is
d
evel
oped
t
o
s
im
ula
t
e
t
h
e
overa
l
l
sys
t
em,
th
e
F
O
P
I
D
c
o
nt
rol
l
er
h
as
f
iv
e
as
so
ciated
p
aram
eters.
T
he
opt
im
u
m
va
lu
e
s
o
f
th
os
e
p
a
ram
e
ters
a
re
f
ou
nd
o
u
t
b
y
u
sin
g
p
a
r
t
i
cl
e
s
w
arm
op
timiza
ti
on
tech
ni
que.
Sim
u
lati
on
r
esults
s
h
o
w
ex
cellen
t
c
om
m
a
nd
s
p
eeds
tra
ck
ing
and
su
peri
or
d
y
n
amic
r
es
po
nse
i
n
c
on
ju
ncti
on
w
it
h
that
o
f
th
e
i
n
t
e
g
er-order
P
ID
con
t
ro
ller.
T
h
e
p
r
op
osed
c
on
trol
ler
sh
o
w
s
a
high
a
bi
lit
y
t
o
ove
rcom
e
any
ext
e
rnal
d
istu
rb
ance
t
h
e
sy
st
em
m
ay
b
e
exp
o
sed
;
a
ls
o,
it
p
e
rf
o
r
m
s
a
h
i
g
h
deg
r
ee
of
r
ob
ust
n
es
s
to
c
on
trol
t
he
s
ystem
in
m
ot
orin
g
and
rege
ner
a
tive
op
erati
ng
m
odes.
K
eyw
ord
s
:
F
r
actio
nal-or
d
e
r c
ont
r
o
l
l
er
Pa
rti
c
le sw
a
rm opt
imiza
tio
n
Pe
rm
anent
ma
g
n
e
t
DC m
o
tor
PID
c
o
ntro
ller
Tun
i
ng
p
a
r
amet
e
r
s o
f
PID
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Fa
dhil
A. Hasan,
D
e
pa
rtme
nt
o
f
El
e
c
t
rica
l
Eng
i
ne
eri
ng,
Uni
v
ersi
ty o
f
Tech
no
l
o
g
y
,
Ba
gh
da
d,
I
ra
q.
Em
ail:
Fadhi
l.a
.
hassa
n@
g
m
a
il.c
o
m
1.
I
N
TR
OD
U
C
TI
O
N
F
r
ac
ti
o
n
a
l
O
rd
e
r
P
ropor
ti
o
n
al
I
n
t
e
g
ral D
e
riv
a
ti
ve c
o
n
tro
l
l
e
r (F
OP
ID)
is
a
m
ost
pow
er
ful ty
pe of
P
I
D
con
t
ro
l
l
er
i
n
w
h
ic
h
the
order
of
d
e
r
iva
t
i
v
e
a
nd
in
te
gra
l
a
re
f
r
acti
ona
l
(
PI
D
)
rather
t
ha
n
inte
g
e
r
num
ber.
I
t
offe
rs
a
n
effec
tive
t
o
ol
t
o
des
c
r
i
p
t
t
he
i
nh
e
r
i
t
i
n
g
m
e
m
o
ry
f
ea
t
ur
es
o
f
var
i
ous
a
rt
icle
s.
T
hi
s
is
a
g
re
at
p
ropert
y
of
t
h
i
s c
ontr
o
l
l
e
r
in con
ju
nc
ti
on w
i
th or
d
i
n
a
r
y P
I
D c
ont
r
o
ll
er
;
a
ct
u
a
l
l
y
,
t
h
i
s
e
f
f
e
c
t
i
s
not
c
o
n
s
id
e
r
ed
[
1
]
.
In
a
d
d
iti
o
n
,
the
fr
act
io
na
l
orde
r
c
o
ntr
o
lle
r
is
m
ore
c
o
n
v
en
ie
n
t
t
h
an
i
n
t
eg
er-o
rd
er
m
o
d
e
ls
i
n
the
con
t
ro
l
o
f
d
y
n
a
m
ica
l
s
y
s
t
e
ms.
A
not
her
a
dva
nt
a
g
e i
s
t
he
f
ac
t
t
h
a
t
frac
tio
na
l
order
c
ontro
l
l
ers
ar
e
i
n
sens
it
ive
t
o
para
me
ters variat
i
on o
f
t
he sy
s
tem
an
d
a
l
s
o
the
c
o
n
t
r
o
ller
p
a
r
a
m
e
ter
s
[2].
T
h
e
F
O
P
I
D
c
ont
r
o
l
s
y
ste
m
prese
n
t
s
a
hi
g
h
d
e
g
re
e
of
s
tiffness
t
o
o
ve
rcom
e
a
n
y
d
i
st
urba
nce
or
l
oa
d
varia
t
i
o
n,
a
l
s
o
i
t
s
t
i
me
a
nd
fre
q
u
e
nc
y
respo
n
ses
ca
n
be
a
d
j
uste
d
ef
fic
i
e
n
t
l
y
a
s
c
o
mpa
r
ed
w
ith
t
he
m
ode
l
pr
ed
ict
i
ve
c
o
n
t
roll
e
r
[
3].
The
frac
t
i
o
na
l
order
c
o
n
t
r
o
l
l
e
r
(F
O
C
)
has
a
l
rea
dy
c
o
m
e
i
n
be
ne
fic
i
a
l
i
n
m
a
ny
a
t
t
r
ac
t
i
ve
e
ngi
ne
e
r
in
g
a
r
ea
s
such
a
s
elec
tr
on
i
c
s,
r
o
b
o
tic
s,
b
i
o
e
n
g
i
nee
r
i
ng,
c
on
trol
t
he
or
y
a
n
d
si
gna
l
pr
oces
si
ng
[
4
].
C
onc
epci
o
n
A
.
M.
e
t
a
l
,
prese
n
t
e
d
a
sel
f
-
t
u
n
i
ng
a
n
d
aut
o
-t
u
n
in
g
to
e
st
i
m
ate
t
h
e
c
ontr
oller
parameters
o
f
the
F
O
PID
con
t
rol
l
er,
th
e
m
e
t
h
o
d
g
a
v
e
r
o
b
u
s
t
a
n
d
m
o
r
e
r
e
l
i
a
b
l
e
c
o
n
t
r
o
l
[
5
]
.
R
i
n
u
P
.
S
.
e
t
a
l
presen
t
e
d
t
h
e
N
e
l
d
er
-me
a
d
me
tho
d
a
nd
t
h
e
A
B
C
(a
rtif
icia
l
bee
c
o
lo
ny
a
l
gor
it
hm)
to
o
p
timiz
e
t
h
e
fi
ve
p
ara
meters
o
f
F
r
act
i
onal-or
d
er
P
ID
c
ontroller
[
6
]
.
H
a
ssan
N
.
A
e
t
a
l
prese
n
te
d
P
a
re
to
m
e
t
h
o
d
for
n
u
me
rical
o
pt
imiza
tio
n
o
f
t
he
f
rac
tio
na
l
or
d
e
r
P
I
D
to
g
ive
a
n
est
i
ma
t
i
o
n
o
f
the
co
n
t
ro
ller
p
a
ram
e
ter
to
m
e
e
t
t
h
e
e
n
g
i
ne
erin
g
spec
ifica
t
i
o
n
nee
d
s,
a
n
d
c
ompa
re
d
r
e
su
lt
s
b
y
trad
it
iona
l
PI
D c
o
n
t
r
o
l
l
er
[7]
.
F
r
om
t
h
e
l
i
t
e
r
a
t
ure
,
i
t
can
b
e
no
t
e
d
tha
t
t
he
r
e
a
re
no
pr
ev
i
ous
a
t
t
e
m
p
t
s
t
o
i
n
v
e
s
ti
ga
te
t
he
n
on-
line
a
r
beha
v
i
or
o
f
th
e
P
M
D
C
by
pa
ram
e
ter
s
v
a
r
iat
i
o
n
d
u
r
in
g
ope
rati
on.
The
r
e
sista
n
ce
of
t
he
a
rm
ature
w
i
nd
i
ngs
i
s
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Frac
tio
na
l-or
d
e
r P
I
D c
ont
r
o
l
l
er f
o
r pe
rm
an
e
n
t m
a
gne
t D
C
m
o
t
o
r
b
a
se
d o
n
PSO
… (Fad
hi
l A.
H
a
san)
1
725
one
o
f
t
h
e
m
a
i
n
p
ara
m
e
t
er
w
hos
e
has
n
on-
li
ne
ar
b
eha
v
ior
due
t
o
the
gen
e
rated
an
d
rise
d
hea
t
i
n
t
h
e
w
i
n
d
i
ng
s
by
re
pe
t
i
t
i
on
o
f
ope
ra
ti
o
n
,
whic
h
m
a
ke
s
the
syst
e
m
n
o
n
-
l
i
n
ea
r
i
n
na
t
u
re
.
This
p
ape
r
p
rop
o
ses
the
u
s
e
of
t
he
FO
P
I
D
c
o
nt
roll
e
r
a
s
a
n
onl
in
ear
c
o
n
t
r
oll
e
r
of
P
M
D
C
by
t
a
k
i
n
g
i
n
t
o
c
on
si
de
ra
t
i
on
t
he
n
o
n
line
a
rt
y
be
ha
vi
or
o
f
arm
a
ture
r
esista
nce,
w
hi
c
h
i
s
the
m
a
i
n
c
on
t
r
ibu
t
io
n
of th
i
s w
o
r
k.
T
his
pa
p
e
r
exp
l
o
its
t
he
a
dva
nce
d
f
e
a
t
u
r
es
o
f
the
F
O
c
ontr
o
ller
as
a
n
a
d
j
u
s
t
ab
le
s
pee
d
d
ri
ver
of
a
P
M
D
C.
T
he
do
m
i
nan
t
p
ar
am
eters,
o
f
t
h
e
p
r
op
osed
con
t
ro
l
l
er,
a
r
e
tu
ne
d
by
u
sin
g
t
h
e
Pa
rti
c
le
S
wa
rm
O
ptim
i
z
ati
o
n
(
P
S
O
)
t
e
chn
i
que.
T
h
e
r
e
su
lt
s
o
f
t
he
p
rop
o
se
d
con
t
ro
l
l
er
w
i
ll
be
c
ompa
red
w
i
t
h
t
ha
t
o
f
t
he
t
radi
ti
ona
l i
n
t
e
g
e
r-
order P
I
D
con
t
r
o
l
l
er
.
2.
T
H
E DIFFER
-
INTE
GRAL
AND FRA
C
TIONAL
O
R
D
E
R
S
Y
S
T
E
MS
The
fr
ac
ti
o
n
al
a
na
lys
i
s
is
t
he
s
ec
tor
t
h
a
t
d
ea
ls
w
ith
t
he
a
b
i
li
t
y
o
f
pow
eri
n
g
t
h
e
in
te
gr
al
a
nd
di
ffe
re
nt
ia
l
o
p
e
ra
t
o
r
s
b
y
fra
c
ti
o
n
n
umbe
r
in
st
e
a
d
o
f
a
n
i
n
t
eger
numbe
r.
M
a
t
he
ma
t
i
c
a
lly,
the
frac
t
i
o
n
a
l
or
der
in
t
e
gral
a
nd
d
e
r
i
v
a
t
i
v
e
ca
n
be
d
efi
n
ed
i
n
nu
me
rous
w
a
y
s.
The
g
e
n
era
l
p
rese
nt
a
tio
n
of
t
he
d
i
f
fer
-
in
t
e
g
r
ator
opera
to
r
is
:
(1)
Where
“
q
”
re
presents
t
he
r
ea
l
orde
r
of
t
he
d
iffer
-
i
n
t
e
gral,
“
t
”
i
s
var
i
a
t
i
o
n
d
o
ma
in
,
and
“
a”
i
s
t
he
low
e
r
lim
it
.
In
t
he
N
i
n
e
t
ee
n
S
i
xt
ies,
C
a
p
u
t
o
pr
esen
te
d
a
po
pu
la
r
form
t
o
calculate
t
he
d
iff
e
r-integral.
A
fra
c
ti
o
n
a
l
d
eri
v
a
t
i
v
e
of
o
rde
r
“
λ”
w
ith
v
aria
ti
o
n
i
n
“
t
”
do
m
a
in
a
n
d
w
it
h
i
n
iti
a
l
c
ond
it
io
n
t
=
0
i
s
b
e
c
o
m
e
a
s
[8]
-
[1
0]
:
(2)
,
∈
,
0
1
Where
Γ(z
)
i
s
Eu
l
e
r’s
G
amma
f
u
n
c
t
i
o
n.
W
hen
γ
<
0,
t
he
n
r
e
pre
s
en
t
a
fr
acti
ona
l
i
n
te
g
r
al
o
pe
rator
w
ith
−γ
o
r
d
e
r
:
,
(3)
O
n
e
w
o
nde
rfu
l
be
ne
fit
o
f
u
sing
thi
s
d
e
f
i
n
it
io
n
is
p
r
e
s
e
nt
ing
ea
sy
e
xp
la
na
ti
on
s
to
i
ni
tia
l
an
d
bo
u
ndar
y
c
o
n
d
i
t
i
on
s,
i
n
w
h
ic
h
t
h
e
der
i
va
tio
n
o
f
a
n
y
c
o
n
s
t
ant
va
lue
e
q
u
a
ls
t
o
ze
ro.
I
n
t
he
t
ime
doma
i
n,
a
n
n-
term
of fr
acti
o
nal or
de
r
d
i
f
f
ere
n
ti
al
e
qu
a
tio
ns
a
re
p
r
e
s
e
n
t
t
he
fr
actio
na
l or
de
r system
:
(4)
Where
D
D
is the
Ca
pu
to’
s
f
ra
cti
ona
l de
ri
v
a
tio
n
of orde
r
“
λ”
.
Ta
ck
in
g t
h
e
Laplac
e tra
n
sform
to
(4) the
f
ra
cti
ona
l or
de
r tra
n
s
fer
fu
nc
ti
o
n
ca
n be
obta
i
ne
d,
⋯
(5)
Where
;
B
k
0
,
1
,
….,n
is
a
r
ea
l
num
be
r,
β
β
⋯β
β
0
a
nd
a
k0
,
1
,
…
.
,
n
i
s
c
onstant.
The
fr
act
io
na
l de
ri
vat
i
v
e
in L
a
p
lace
for
m
i
s
:
∑
(6)
The
sum
m
a
t
i
o
n in
t
he
rig
h
t
-h
and
o
f
(
6) m
ust
be
canc
e
le
d
i
f
γ
<
0.
3.
FRACTIO
NA
L
O
RDER
C
O
N
T
ROL
The
P
I
D
c
ont
r
o
ller
is
a
u
n
i
ve
rsal
c
on
t
r
o
lle
r
base
d
o
n
a
c
lo
sed-
lo
op
m
e
c
h
an
ism
has
w
i
des
p
re
ad
app
l
ica
t
i
o
ns
i
n
i
n
d
u
s
t
r
i
a
l
s
c
o
ntr
o
l
lin
g
s
y
s
t
e
m
s.
T
he
P
ID
c
on
tro
l
l
e
r
a
t
t
e
m
p
t
s
t
o
c
o
r
r
e
c
t
t
h
e
e
r
r
o
r
b
e
t
w
e
e
n
a
n
ac
t
u
a
l
s
yste
m
fee
d
bac
k
a
n
d
a
r
e
f
er
ence
s
et
-po
i
n
t
b
y
e
v
al
uat
i
ng
a
n
d
the
n
o
u
t
p
u
t
t
i
ng
a
cor
r
ec
t
i
ve
a
c
t
i
on
t
h
at
cou
l
d a
d
jus
t
t
h
e
s
yste
m
acc
ordi
n
g
to t
h
a
t
.
The
t
r
ans
f
er
fun
c
t
i
o
n of a
n ord
i
nary
P
I
D
contr
o
l
l
er
i
s:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w El
ec &
D
ri S
y
s
t
Vo
l. 1
0
,
No
. 4
,
D
e
c
2
0
19
:
1
724
–
1
733
1
726
1
(7
)
The
a
l
gor
i
t
hm
o
f
t
h
e
P
I
D
con
t
r
o
ll
e
r
i
n
c
l
u
des
t
h
r
e
e
i
n
depe
nde
n
t
par
a
me
t
e
r
s
;
t
h
e
P
r
op
or
t
i
on
g
a
i
n
(
K
p)
a
nd
t
h
e
I
n
te
gr
a
l
a
n
d
D
e
r
iv
ati
v
e
t
i
me
c
o
n
s
ta
nts
(
T
i
&
T
d
)
r
e
s
pe
ct
i
v
e
l
y.
K
p
e
va
lua
t
e
s
t
he
r
e
s
p
o
n
s
e
to
t
he
in
sta
n
t
e
rror
,
w
hi
l
e
(
)
es
t
i
m
a
t
e
s
t
h
e
i
nt
e
g
r
a
l
re
ac
ti
on
a
c
c
o
r
d
i
n
g
to
t
he
s
u
m
mat
i
on
o
f
r
e
cen
t
er
rors
a
nd
(
K
T
)
dr
i
v
e
the
d
e
r
i
va
ti
ve
r
espo
n
s
e
a
ccor
d
i
n
g
to
t
he
r
a
t
e
of
c
ha
n
g
i
n
g
e
rror
s
.
The
alge
b
r
ai
c
sum
m
a
tion
o
f
the
s
e
ac
tio
ns
i
s
uti
l
i
z
e
d
t
o
ad
j
u
s
t
t
he
s
y
s
tem
by
an
a
p
p
r
o
pr
i
a
t
e
con
t
r
o
l
l
i
n
g
si
gna
l.
I
n
f
a
c
t
,
the
r
e
a
l
c
on
tr
o
l
l
e
d
s
y
stem
s
ha
ve
f
r
a
cti
o
nal
nat
u
r
e
i
n
ge
ner
a
l
.
N
ev
e
r
the
l
ess,
t
he
f
r
a
cti
o
na
l
i
t
y
c
o
u
l
d
be
s
ma
ll
.
Br
oa
dly,
t
he
a
ppr
ox
im
ate
i
n
teger
-
or
de
r
o
f
t
he
f
r
a
c
t
i
o
na
l
sys
t
em
l
e
a
ds
t
o
a
ser
i
ous
d
i
ffe
r
e
nc
e
be
t
w
ee
n
the
ac
tua
l
s
yste
m
an
d
th
e
m
a
the
m
a
t
ic
a
l
m
o
d
e
l
.
Be
ca
use
o
f
th
e
f
r
a
c
t
i
on
al
-o
rd
er
d
i
f
f
e
ren
t
i
a
l
e
q
u
a
ti
o
n
s
is
a
d
i
fficu
l
t
c
alcu
l
u
s
proc
ed
ure
t
h
e
n
t
h
e
i
n
t
e
g
er-
o
rder
m
o
d
e
l
s
a
r
e
u
se
d
w
i
de
ly.
T
h
e
ge
ner
a
l
i
zed
f
or
m
of
t
h
e
P
I
D
-
c
ontr
o
lle
r
,
w
hich
a
lso
k
n
o
w
n
a
s
PI
D
c
o
n
t
r
o
ll
e
r
s
,
i
s
a
s
f
o
l
l
o
w
:
Wher
e
,
λ
a
nd
γ
a
r
e
the
in
te
gr
a
t
or
a
n
d
d
i
ffe
r
e
nt
ia
tor
or
der
s
r
es
pec
tive
l
y.
The
n
,
G
s
K
1
T
s
,
λ,
γ
0
(8
)
Th
e ti
me d
o
m
a
i
n
out
put
i
s:
(9
)
Where,
an
d
.
I
n
o
t
h
e
r
w
or
ds,
t
he
f
r
a
ct
io
na
l
or
de
r
PI
D
c
ontr
o
ll
e
r
i
s
the
gl
oba
l
for
m
o
f
the
co
nve
n
t
i
o
nal
P
I
D
c
o
n
t
r
o
ller
,
w
hic
h
i
s
a
par
t
ic
ul
a
r
c
ase
contr
o
l
l
e
r
.
A
s
show
n
i
n
F
i
gur
e
1,
t
he
PI
D
c
ontr
o
l
l
e
r
e
xp
and
s
t
he
c
o
n
v
e
n
t
i
ona
l
P
I
D
con
t
r
o
l
l
er
a
nd
ex
te
nd
s
it
f
r
om
poi
nt
t
o
s
u
r
f
a
c
e.
This e
x
t
e
nsio
n
inc
r
ea
se
s the
fle
x
ib
ili
t
y
to
c
o
n
t
r
o
ller
adj
u
stme
n
t
,
a
nd per
f
orm
s
m
ore
accura
te r
espo
nse
of t
he
act
ua
l
sys
t
em
.
[8]
,
[
9]
.
F
i
gur
e
1
.
Ext
e
n
d
t
he
P
I
D
c
ontr
o
l
f
r
o
m
po
i
n
t
to
s
ur
fa
ce
4.
M
A
TH
E
M
A
T
IC
A
L
M
O
D
EL
O
F
P
M
D
C
M
O
TO
R
P
e
rm
anent
m
a
gne
t
m
o
t
o
r
s
a
r
e
u
sed
in
v
ar
ious
i
nd
us
t
r
i
a
l
app
l
i
c
a
t
ion
s
b
ec
a
u
se
o
f
th
eir
rel
i
abi
lit
y
,
c
o
n
t
r
o
llab
i
li
ty,
d
on’
t
nee
d
e
x
t
e
r
na
l
e
x
c
ita
ti
o
n
,
an
d
ine
x
pen
s
i
v
e
[
1
1]
,
[
1
2]
.
P
e
r
m
ane
n
t
m
a
gne
t
D
C
m
o
t
or
i
s
fou
n
d
i
n
sev
e
r
a
l
l
o
w
a
n
d
hi
gh
-po
w
er
i
ndu
stri
a
l
a
pp
l
i
cati
ons.
Th
e
e
q
ui
va
l
e
nt
c
ir
cui
t
o
f
t
h
e
P
M
D
C
m
o
t
or
i
s
show
n
i
n
F
i
gur
e
2,
f
rom whic
h
(10),
(
11) a
n
d
(12)
ca
n
be
writte
n.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Frac
tio
na
l-or
d
e
r P
I
D c
ont
r
o
l
l
er f
o
r pe
rm
an
e
n
t m
a
gne
t D
C
m
o
t
o
r
b
a
se
d o
n
PSO
… (Fad
hi
l A.
H
a
san)
1
727
F
i
gure
2.
T
he
e
qu
iva
l
e
n
t circ
u
i
t
o
f
a
pe
r
ma
nent m
agne
t
D
C
m
achi
ne
(10)
(11)
(12)
Where
:
V
in th
e
suppl
y vo
ltag
e
(V
)
, Ia cur
re
nt of the ar
ma
t
u
r
e
(
A)
,
i
s t
h
e
po
le ma
gne
tic flu
x (Wb)
,
(R
a
)
resistance
o
f
the
armature
(
Ω),
(L
a
)
i
n
duc
ta
nc
e
o
f
t
h
e
a
rm
ature
(H
),
K
m
a
c
hine
c
onsta
n
t
(
V
.
s/ra
d)
,
ω
m
rot
o
r
spe
e
d
(r
ad/
s
),
T
e
de
vel
ope
d
t
o
rq
ue(
N
m),
TL
Load
t
or
que
(
N
m),
Bm
d
am
ping
co
efficie
n
t
(N
.m
.s/rad)
,
and
J
i
ner
t
ia
c
ons
t
a
n
t
(
kg.m
2
).
C
lea
r
ly,
fr
o
m
(
1
0
)
,
t
he
a
rm
atu
re
r
esist
a
nce
an
d
i
n
duc
t
a
nce
are
the
d
o
mina
nt
para
me
ters w
hi
c
h
j
ud
ge
d the
tra
n
sie
n
t
a
nd st
e
a
dy sta
t
e re
sp
ons
e
.
The
va
r
i
ati
on o
f
arm
atu
r
e
re
si
stanc
e
i
s
tak
e
n
peri
od
ica
l
l
y
a
b
o
u
t
1
0% of i
t
s
col
d
va
l
ue
as
show
n in F
i
g
ur
e
3.
F
i
g
u
r
e
3
.
The
var
i
a
tio
n
of a
rm
ature
resista
n
ce
5.
PART
ICLE SW
A
RM OPTIMI
Z
ATIO
N
(
P
S
O
)
The
pa
rt
i
c
le
s
w
a
rm
opt
imiz
atio
n
is
f
irst
l
y
p
re
sente
d
b
y
Jam
e
s
a
nd
Ru
ssel
l
i
n
1
9
9
5
[1
3],
a
seekin
g
alg
o
ri
t
h
m
hav
i
ng
a
ra
n
dom
p
roba
bil
i
t
y
d
is
trib
u
t
i
o
n
or
p
a
t
t
e
rn
i
ns
p
i
r
i
ng
b
y
a
c
omm
u
n
i
t
y
h
ab
i
t
o
f
t
h
e
fl
ock
of
bir
d
s
[1
4],
it
is
one
o
f
t
h
e
p
o
w
erful
o
p
timiz
a
t
i
o
n
tec
h
n
i
q
u
e
s.
It
h
as
b
ee
n
obs
e
r
ved
to
b
e
stron
g
i
n
n
o
n
l
i
near
ly
op
tim
iza
t
i
o
n
is
sue
s
[
1
5
],
[
16]
.
A
n
i
m
p
rove
d
P
S
O
w
a
s
pr
esente
d
i
n
1
9
9
8
t
o
u
pgra
d
e
t
h
e
perfor
ma
nce
of
t
he
con
v
e
n
t
i
ona
l
P
S
O
.
A
n
a
dd
i
t
i
on
c
o
e
f
fic
i
e
n
t
kn
ow
n
a
s
i
nert
ia
w
e
i
g
ht
i
s
i
n
tr
o
d
uc
ed
[
14]
.
P
S
O
is
a
s
e
t
o
f
ru
le
s
assoc
i
ate
s
b
o
t
h
cogn
i
t
i
o
n a
n
d pu
b
l
i
c
c
o
lla
bor
atio
n
of b
irds.
I
n
t
h
i
s
m
e
th
o
d
,
ea
ch
b
ir
d
"partic
le"
sea
r
che
s
f
or
t
he
o
pt
i
m
u
m
p
osi
t
i
o
n
b
y
u
p
d
a
t
e
s
i
ts
l
oc
a
tio
n
w
i
t
h
i
n
the
sw
arm
,
a
ccord
ing
t
o
t
he
a
dva
n
t
a
g
e
of
i
t
s
m
em
ory
of
t
h
e
b
est
p
osi
t
i
o
n
a
nd
k
n
ow
i
n
g
abo
u
t
t
he
g
lob
a
l
be
st
loca
t
i
o
n
[15]
. The
o
pt
imiza
t
i
on
pr
oced
ur
e obta
i
ne
d
b
y
(13)
and
(14).
1
(13)
1
1
(14)
i
=1,2,
…
,
n
Where
:
vi
is the i
th p
a
r
ti
cl
e
ve
l
o
cit
y
,
xi
i
s t
h
e
i
t
h
p
a
rti
c
l
e
p
o
s
iti
on,
k i
ter
a
t
i
o
n
n
umbe
r, C1
,
C2 kn
o
w
n
a
s
t
h
e
c
o
g
n
i
t
i
v
e
a
n
d
s
o
c
i
a
l
c
o
e
f
f
i
c
i
e
n
t
s
,
w
i
n
e
r
t
i
a
w
e
i
g
h
t
f
a
c
t
or,
R1,
R2
r
andom
v
a
r
ia
ble
s
o
f
from
0
t
o
1,
p
,
i
n
d
i
v
i
d
ua
l
be
st
p
osi
tio
n
o
f
p
ar
t
i
c
l
e
i
,
g
b
e
s
t
gl
o
b
al
pos
iti
o
n
of
a
l
l
t
he
p
a
r
tic
les
i
n
t
he
s
w
a
rm,
and
n
numbe
r of b
ird
s
(
particles).
I
f
the
c
on
d
i
t
i
o
n
i
n
(1
5)
i
s
me
t
,
then
the p
o
s
i
tio
n
i
s
u
pda
te
d t
hro
u
g
h
(
16):
f
(
)
<
f
(
)
(15)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
7
2
4
– 1
733
1
728
=
(16)
Where
:
f perf
o
rm the min
imi
z
a
tio
n ob
j
e
c
t
i
v
e
fit
n
ess fu
nc
ti
on. T
he
f
low
c
h
a
rt o
f the
P
S
O
alg
o
ri
thm
i
s
ill
us
trate
d
i
n
F
i
gure
4.
U
s
ua
ll
y,
i
n
o
p
t
imiz
a
tio
n
tec
h
ni
q
u
es,
there
a
r
e
seve
ral
fi
tne
s
s
cr
i
t
er
ia
t
o
e
v
alua
te
s
ys
tem
pe
rform
a
nc
e
as
s
uch
as
I
ntegral
Abs
o
l
u
te
E
rro
rs
(IAE)
,
the
I
n
t
e
gral
o
f
Squa
r
e
E
rr
ors
(IS
E),
and
I
n
t
e
gral
o
f
T
i
m
e
S
quar
e
Error
s
(ITS
E
).
T
he
se
p
e
r
for
m
anc
e
c
riteria
are
inc
l
us
i
v
e
t
h
e
o
v
e
rsh
o
o
t,
r
isi
ng
t
i
m
e
,
settl
e
d
time
a
nd
st
e
a
dy-
st
a
t
e
e
r
ro
r.
I
n
ad
di
t
i
on
,
it
h
as
b
een
s
p
e
ci
fi
e
d
t
h
e
o
p
t
i
m
i
z
a
t
i
o
n
p
r
o
c
e
ss
a
nd
t
h
e
ti
ght
n
e
ss
o
f
t
h
e
d
ri
vi
ng
sy
st
e
m
[
1
7].
In
t
his
w
o
rk
t
he
I
TSE
fitn
e
ss
f
u
n
c
ti
on
,
il
lu
st
ra
t
e
d
in
(
1
7),
is
u
se
d
as
t
h
e
p
erf
o
r
m
a
n
ce
c
r
it
e
r
ia
o
f
the
ou
tpu
t
r
espo
ns
e of the
s
ystem
:
.
(17)
The
b
l
oc
k
d
i
a
g
ram
of
t
he
o
pt
i
m
iza
tio
n
pr
oce
s
s
f
o
r
F
O
P
I
D
-
PS
O
sys
tem
is
s
how
n
i
n
F
igure
5.
A
MA
TLA
B
pr
o
g
ram
is
d
e
v
el
o
p
ed
t
o
find
ou
t
the
o
p
t
i
m
a
l
va
lue
s
o
f
t
h
e
f
i
v
e
c
o
nt
roll
er
p
a
r
amet
e
r
s
λ,
γ
,
K
p
,
T
i
,
and
T
d
.
A
m
i
nim
i
za
tio
n
a
l
g
o
rit
h
m
i
s
a
p
p
l
i
e
d
i
n
t
h
e
se
arc
h
doma
i
n
of
t
h
e
p
ar
ticle
s
p
o
s
i
t
i
on
a
n
d
ve
l
o
c
i
t
y
,
th
e
op
tim
um
v
al
ue
s
o
f
the
F
O
P
ID
c
ontr
o
l
l
e
r
a
re
ob
t
a
i
ne
d i
n
1
0
0
i
t
e
r
a
t
i
o
ns as
show
n
in F
i
gur
e
6.
F
i
gure
4.
F
low
char
t
of
t
he
P
S
O
a
lgor
ithm
F
i
gure
5.
T
he
b
loc
k
dia
gra
m
of
the
o
p
t
i
m
i
ze
d
F
O
P
I
D
control
l
er
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Frac
tio
na
l-or
d
e
r P
I
D c
ont
r
o
l
l
er f
o
r pe
rm
an
e
n
t m
a
gne
t D
C
m
o
t
o
r
b
a
se
d o
n
PSO
… (Fad
hi
l A.
H
a
san)
1
729
F
i
gure
6.
The
c
on
tro
l
ler
para
me
t
e
rs dur
i
n
g
the
op
t
i
m
i
za
t
i
o
n
pr
o
cess
6.
SIMULATIO
N
R
E
S
ULT
S
The
ove
ral
l
s
ystem
si
m
u
la
t
i
o
n
i
s
sh
o
w
n
in
F
igure
7.
A
M
A
TLA
B-S
I
MU
LIN
K
m
odel
is
d
es
ig
ne
d;
a
bu
ilt-
in
M
-
f
ile
i
s
de
ve
l
o
pe
d
to
c
a
l
c
u
la
te
t
h
e
f
r
acti
o
nal
or
der
in
te
gra
l
a
n
d
d
er
iva
tive
i
n
a
s
pe
ci
fic
sa
m
p
lin
g
ti
m
e
.
The
spe
e
d
,
tor
que
,
a
n
d
arm
a
ture
c
ur
rent
r
e
s
p
onse
to
r
ated
s
pe
e
d
c
om
m
a
nd
o
f
t
he
P
MD
C
m
o
tor
un
d
e
r
the
fu
l
l
-
l
oa
d
c
o
n
d
i
t
i
on
a
r
e
d
e
pic
t
e
d
i
n
F
i
g
u
re
8
.
A
l
so,
th
e
re
s
ponse
of
t
he
s
ys
t
e
m
to
a
s
ta
i
r
s
te
ps
i
n
p
u
t
o
f
di
ffe
re
nt spee
d
c
o
m
m
a
nds un
d
e
r
full-l
o
a
d
c
on
d
iti
on
ca
n
b
e
show
n
i
n
F
i
gu
r
e
9
.
F
i
gure
7.
The
overa
l
l
s
y
s
tem
sim
u
l
a
t
i
on
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
7
2
4
– 1
733
1
730
F
i
gure
8.
Rate
d
spe
e
d
a
nd ful
l
-l
oad
resp
onse
o
f
the
F
O
P
ID con
tr
oll
e
r
F
i
gur
e 9.
S
t
a
ir r
espo
nse
of t
he
F
O
P
ID c
ont
r
o
l
l
e
r
In
o
rd
e
r
t
o
re
a
l
i
z
e
t
h
e
f
e
a
t
u
r
e
s
o
f
t
h
e
p
r
o
p
o
s
ed
c
ont
ro
ll
er,
a
c
o
mpa
r
is
on
pe
rform
a
nc
e
is
i
n
v
es
ti
ga
ted
in
c
on
junc
ti
on
w
ith
t
he
t
rad
i
tiona
l
i
n
teg
e
r
-
order
P
I
D
contro
lle
r
.
T
he
p
er
fo
rm
ance
f
or
b
o
t
h
ra
ted
of
s
pe
e
d
a
n
d
st
a
i
r
com
m
a
nd
s
are
show
n
i
n
F
igure
1
0
a
n
d
F
i
gure
1
1
.
M
o
re
o
v
er,
the
robus
t
n
ess
of
t
he
p
r
o
p
o
se
d
co
n
t
rol
l
e
r
ca
n
be
p
r
o
v
e
n
in
f
our-
q
uadr
ant
opera
tio
n
con
d
i
t
i
on
s
of
t
he
P
MD
C
m
ot
or.
P
o
sit
i
ve
a
nd
ne
ga
t
i
ve
s
p
e
e
d
com
m
a
nds
a
re
a
pp
lied
t
o
t
he
m
otor
u
n
d
er
v
ar
ious
pos
iti
ve
a
n
d
n
e
ga
tive
l
o
ad
t
orq
u
es.
T
h
e
spe
e
d,
t
orq
u
e
,
a
n
d
curr
ent pe
rform
anc
e
of the
s
y
stem
f
or this
ope
ra
ti
o
n
ar
e
show
n
i
n
F
ig
ure
12.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Frac
tio
na
l-or
d
e
r P
I
D c
ont
r
o
l
l
er f
o
r pe
rm
an
e
n
t m
a
gne
t D
C
m
o
t
o
r
b
a
se
d o
n
PSO
… (Fad
hi
l A.
H
a
san)
1
731
F
i
gure
1
0
. A
c
om
par
i
s
on
perfor
m
a
n
ce
of
r
ated
s
pee
d
c
om
ma
nd
F
i
gure
11.
A
c
om
pariso
n pe
rfo
r
m
a
nc
e of diffe
rent
s
pe
e
d
c
o
m
m
a
nd
F
i
gure
1
2
.
F
our
-quadra
n
t
o
p
e
r
a
t
i
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
7
2
4
– 1
733
1
732
7.
DISC
USSION
O
b
v
i
o
u
s
l
y,
t
he
p
e
r
form
anc
e
o
f
t
h
e
P
M
D
C
u
n
d
er
t
h
e
a
c
t
io
n
of
t
he
FOP
I
D
c
o
nt
rol
l
er
s
ho
ws
a
n
exc
e
l
l
e
n
t
re
sponse
,
f
or
b
o
t
h o
f
r
ate
d
s
te
p
an
d
sta
i
r
ste
p
s
i
n
pu
t
c
o
mm
ands,
alt
h
ou
g
h
t
he n
on-
line
a
r
be
ha
vi
or
o
f
the
ms
ys
tem
.
F
igure
8
a
n
d
F
i
gur
e
9
sh
ow
a
c
c
ura
t
e
s
p
ee
d
t
r
ac
king
f
or
a
t
no-
loa
d
a
nd
fu
ll-
loa
d
c
on
d
iti
ons,
th
e
perform
ance
s
how
s
a
s
u
perio
r
dyn
am
ic
r
esp
ons
e.
A
lso,
t
he
c
om
par
is
on
in
ve
sti
g
a
t
i
o
n,
b
et
w
e
e
n
t
he
f
r
act
i
ona
l-
order
a
n
d
t
h
e
i
n
t
e
ger-
order
P
I
D
c
o
n
t
ro
lle
rs,
show
s
em
in
en
t
fea
t
u
r
es
o
f
th
e
p
r
opo
se
d
co
ntro
l
l
e
r.
F
i
g
u
r
e
10
a
nd
F
i
gure
1
1
i
ll
u
s
trate
the
dy
na
mic
respo
n
se
(
ma
xi
m
u
m
oversh
o
o
t
,
r
i
s
e
t
i
me
,
se
t
t
l
i
n
g
ti
me,
an
d
s
t
eady
-
st
at
e
err
o
r)
to
t
he
r
ated
s
t
e
p
in
p
u
t
o
f
t
he
i
n
t
eg
er
-orde
r
P
ID
c
on
t
r
ol
ler
a
b
ou
t
26
%,
0
.
23s,
1s,
a
nd
1.3%
r
e
s
p
e
cti
v
e
l
y.
Whe
r
ea
s,
t
he
d
ynam
i
c
re
sp
onse
s
o
f
t
h
e
F
O
P
I
D
contr
o
l
l
e
r
a
re:
1.
7
%
,
0
.
2
3s,
0.37s,
an
d
0
.
2%
r
espec
t
ive
l
y.
I
n
add
i
tio
n,
t
he
s
tar
tin
g
curr
en
t
pe
rio
d
o
f
t
h
e
F
O
PI
D
is
a
bou
t
ha
l
f
of
t
ha
t
o
f
t
he
i
nte
g
e
r
-order
P
ID
,
t
h
i
s
w
ill
reduc
e
the
w
i
nd
i
ng
tem
p
era
t
ur
e
due
t
o
m
u
l
ti-
sta
r
t
i
ng
o
pe
rati
on.
M
o
r
eover
,
t
he
t
ra
n
s
ien
t
r
es
po
nse
o
f
t
h
e
trad
it
iona
l
PI
D
c
o
n
t
r
o
l
l
e
r
d
ue
t
o
f
u
ll-loa
d
d
istur
b
a
n
ce s
how
s:
m
a
ximum
o
v
e
r
sh
oo
t
=
2.7
%
a
n
d
se
t
t
lin
g t
i
m
e
=
0.5s.
Wh
ils
t
,
t
h
e
F
O
P
I
D
c
ont
r
o
ller
s
how
s
:
m
axim
um
o
v
e
rsho
o
t
=
0
.7%
a
n
d
se
ttl
in
g
t
i
m
e
=
0
.2
5s.
F
i
na
ll
y,
t
he
fo
ur-
qua
dran
t
opera
t
i
o
n
o
f
t
h
e
P
M
D
C
m
oto
r
i
n
F
i
gure
12
s
h
o
w
s
a
hi
gh
d
e
g
r
ee
o
f
robu
st
n
e
ss
fo
r
di
ff
ere
n
t
pos
it
ive
a
n
d
n
e
ga
t
i
ve
s
pe
ed
a
nd
l
o
ad
t
orq
u
e
.
A
supe
rior
s
pe
ed
t
ra
cki
n
g
is
p
e
r
fo
rmed
u
n
d
er
b
oth
of
d
el
i
v
ered
and
co
ns
ume
d
pow
er
m
odes.
8.
CONCL
U
S
ION
T
h
i
s
p
a
p
e
r
p
r
o
p
o
s
e
d
t
h
e
F
O
P
I
D
c
o
n
t
r
o
l
l
e
r
,
i
n
s
t
e
a
d
o
f
t
h
e
i
n
t
e
g
e
r-o
r
d
e
r
P
I
D
c
o
nt
roll
e
r
,
to
c
on
t
r
ol
t
h
e
sp
e
e
d
of
t
h
e
P
M
D
C
w
i
th
c
onsi
d
eri
n
g
th
e
non
-li
n
e
a
r
b
e
h
avio
r
o
f
a
rm
ature
resista
n
ce
.
B
o
th
o
f
t
h
e
fr
act
i
ona
l-
order
and
the
inte
ger-or
d
er
P
ID
c
ontro
ll
e
r
s
ar
e
sim
u
l
a
te
d,
a
nd
t
h
e
re
spons
es
o
f
th
em
a
re
i
nv
est
i
g
a
t
e
d
u
n
d
e
r
di
ffe
re
nt
ope
ra
ti
n
g
c
o
n
d
i
tio
n
s
.
S
i
m
u
la
tio
n
resul
t
s
sh
ow
e
xcel
le
n
t
c
omm
a
nd
spe
e
d
s
t
ra
cki
n
g
an
d
su
pe
rior
dy
nam
i
c
re
sp
o
n
se
a
l
t
ho
u
gh
t
h
e
va
ria
t
io
n
o
f
s
yst
e
m
para
me
t
e
r.
T
h
e
prop
ose
d
c
o
n
t
r
o
lle
r
show
s
a
h
i
g
h
a
bi
l
ity
to
ove
rc
om
e
any
in
terna
l
o
r
e
x
t
e
r
n
al
d
i
s
t
u
rba
n
ce
th
e
sys
t
e
m
m
ay
b
e
e
x
p
o
se
d;
a
l
s
o,
i
t
p
e
rforms
a
hig
h
degre
e
of
r
ob
ust
n
e
s
s
to
c
on
tro
l
t
he
s
y
s
tem
in
m
otor
in
g a
n
d re
gene
ra
tiv
e
oper
a
ti
ng
mode
s.
REFE
RENCES
[1]
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Z
h
ong
a
n
d
L
.
L
i
,
“
T
unin
g
F
ra
ct
io
nal
-
O
r
der
PI
λ
D
μ
C
o
n
t
r
o
l
l
e
r
s
f
o
r
a
S
o
l
i
d
-
C
o
r
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M
a
g
n
e
t
i
c
B
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p
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nta
t
io
n
o
f
d
ig
i
t
a
l
f
r
actio
na
l
ord
e
r
PID
con
t
ro
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u
s
i
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o
p
tim
a
l
p
o
l
e-zero
ap
pr
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i
mat
i
on
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eth
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d
fo
r
m
a
gnet
i
c
l
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tem
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in
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r
d
e
r
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t
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es
ign
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f
requ
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d
ev
iati
on
i
n
a
hy
bri
d
r
en
ewable
e
n
e
rg
y gen
e
r
a
t
i
o
n
a
n
d
s
to
rage sys
tem,
"
i
n
CIRED
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p
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n
u
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d
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a
m
e
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,
“
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s
i
g
n
a
n
d
A
n
a
l
y
s
i
s
o
f
O
p
t
i
m
a
l
F
r
acti
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-
Ord
e
r
P
I
D
Co
n
t
roller,”
International
J
o
urna
l o
f
App
l
i
e
d
En
gine
e
r
in
g
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se
arc
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, IS
S
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0
9
7
3
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45
62
vo
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,
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01
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.
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L
.
A
ngel
an
d
J
.
M
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Sebas
tian
,
"
Desi
g
n
a
nd
ro
bu
st
p
e
r
f
orm
a
nce
ev
alu
a
t
i
o
n
o
f
a
f
r
action
a
l
o
r
der
P
I
D
c
o
ntrol
l
e
r
a
pp
lie
d
t
o
a
DC
m
o
t
o
r
,"
i
n
I
EEE
/
C
A
A
Jo
ur
nal
of
A
u
to
ma
ti
ca S
i
ni
ca
,
v
o
l.
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,
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.
2,
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.
3
0
4
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Ap
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[6]
L.
L
u,
S
.
L
i
ang
,
D
.
Yuew
ei,
L.
C
hen
g
l
i
n
and
Q
.
Z
hi
don
g
,
"
Im
prov
ed
q
u
a
ntu
m
b
acterial
f
o
ra
g
i
ng
alg
o
rit
h
m
f
o
r
tun
i
n
g
pa
ra
m
e
te
rs
o
f
fra
c
t
io
na
l-
ord
e
r
PID
c
o
ntro
lle
r
,"
i
n
Jo
ur
nal of
Syst
ems
E
ngin
eerin
g a
nd
E
l
e
c
tr
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6
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u
i,
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avi
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r
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"
Con
i
cal
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an
k
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t
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t
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ractional
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Fracti
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n
a
l
o
r
der
fu
z
z
y
P
I
D
co
nt
rol
l
er
f
or
w
in
d
energy
-based
h
y
b
r
i
d
p
o
wer
s
y
stem
us
in
g
qu
asi
-
o
ppos
it
ion
a
l
h
a
rm
ony
s
earch
a
lg
orithm,
"
in
I
E
T G
e
n
e
ra
tion
,
T
r
an
sm
is
s
i
o
n
&
D
i
st
rib
u
t
io
n
,
v
o
l
.
1
1
,
no
.
1
3,
p
p.
3
2
99-330
9,
7
9
2
0
1
7
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[9]
P.
B
haskara
Prasad,
M.
P
adma
L
a
litha,
a
nd
B
.
Sarvesh,
"
Fra
c
t
i
on
al
O
rder
P
ID
C
o
n
t
r
oll
e
d
Cascaded
R
e-bo
os
t
S
e
ven
Level
Invert
er
F
ed
I
nd
uct
i
o
n
M
o
t
or
S
y
s
tem
w
i
t
h
E
n
h
an
ced
R
e
s
po
nse
,
"
I
n
te
r
n
at
io
na
l J
o
u
r
n
a
l
of
P
o
w
e
r
El
ectro
n
i
cs
a
n
d
Dr
ive S
y
s
t
em
(
I
JPEDS)
, V
o
l
. 9
,
No
. 4, pp. 1
78
4-17
91
, Decem
b
e
r 20
18
.
[10]
Deep
ti
Y
a
dav,
A
run
i
m
a
V
erm
a
,
"Com
perat
i
ve
P
erf
o
rm
an
ce
A
n
al
ysis
of
P
MSM
Dri
v
e
U
s
ing
MPSO
and
ACO
Tech
niq
u
es
,"
Int
e
rn
ation
a
l
Jo
ur
nal
of Powe
r
Elect
ron
i
cs
a
nd Dr
ive Syst
em
(
I
JPED
S
)
,
V
o
l
.
9
,
N
o
.
4
,
pp
. 1
510
-15
2
2
, Decem
b
e
r 20
18
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[11]
M
.
R
eza
ei
E
st
ak
h
r
ou
iyeh
,
M
.
V
a
l
i
and
A
.
G
h
a
ra
veis
i,
"
Ap
pl
icatio
n
of
f
ractio
nal
order
it
erati
v
e
le
arn
i
n
g
c
on
troller
f
o
r a typ
e
o
f
batc
h
b
i
oreact
or," in
IE
T Control Theor
y
&
Applicati
ons
,
vo
l. 10
, no
.
1
2,
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D
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K
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n
d
C
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I
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n
escu
,
"
T
heo
r
etical
A
nal
y
sis
and
Exp
e
rim
e
n
t
al
V
alid
ati
on
o
f
a
S
i
m
p
lifi
ed
F
ractio
nal
Ord
e
r
Con
t
ro
ll
e
r
f
or
a
M
agnet
i
c
Lev
i
ta
t
i
o
n
S
y
s
t
e
m
,
"
i
n
IEE
E
Tr
ansacti
ons o
n
Co
n
t
ro
l
Sys
t
ems
T
echn
o
log
y
,
v
o
l
.
24,
n
o
.
2
,
p
p.
756
-76
3
,
M
a
rch
20
16
.
[13]
James
K
.
a
nd
R
u
s
sel
l
E
., "Pa
r
ticle Swarm Op
t
i
m
iza
t
ion
"
,
IEEE In
t
e
r
n
a
t
i
o
n
a
l con
f
eren
ce
, 4, 1
99
5.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Frac
tio
na
l-or
d
e
r P
I
D c
ont
r
o
l
l
er f
o
r pe
rm
an
e
n
t m
a
gne
t D
C
m
o
t
o
r
b
a
se
d o
n
PSO
… (Fad
hi
l A.
H
a
san)
1
733
[14]
Y.
S
hi
a
nd
R.
E
b
e
rhart,
"
A
m
o
d
i
fi
ed
p
article
sw
arm
optimizer,"
19
98
IEE
E
In
tern
a
t
io
nal Confer
ence o
n
Evo
l
utio
nary Comp
ut
a
t
ion
Pro
ceedin
gs
.
IEEE
W
o
r
l
d
Co
n
g
res
s
on
Com
p
u
t
atio
nal In
t
e
lli
g
en
ce
(
C
at.
No.
9
8T
H
836
0
)
,
Anch
o
r
age, AK,
US
A
,
p
p
. 6
9-7
3
, 1
99
8.
[15]
Mah
m
u
d
I
.
S
.,
L
ee
F.
T
.
and
Mo
ey
L
.
K.
,
"Tun
i
n
g
of
P
ID
C
on
t
r
o
l
l
er
Using
P
artic
l
e
S
w
arm
O
p
t
i
mi
zatio
n
(PS
O
)",
Pr
oceedi
n
g
o
f
th
e Int
e
rn
ation
a
l Co
nf
erence
on
Ad
van
ced
Scie
n
ce, E
n
g
i
n
e
er
ing
an
d
In
fo
rm
a
t
io
n T
ech
no
log
y
,
Ma
la
ysia
, 2
01
1.
[16]
A.
S
o
und
arrajan
,
S
.
S
u
m
a
thi,
a
nd
C
.
S
u
nd
ar,
"
P
art
i
cle
S
w
arm
O
p
t
imizati
o
n
Bas
e
d
LF
C
and
AVR
o
f
A
u
t
onom
ou
s
P
o
w
e
r
Generat
i
ng
S
y
st
em,
"
IA
E
N
G In
te
rna
tio
na
l J
o
urna
l o
f
Co
mp
ute
r
S
c
ie
nc
e
, Vo
l
. 3
7,
No
.
1,
20
10
.
[17]
Ah
m
e
d
S
.
A
l
-
A
r
aj
i
a
n
dA
hm
ed
I
.
Abd
u
l
k
areem
,
“
A
N
onlin
ear
N
eural
Con
t
roller
D
esi
g
n
f
o
r
th
e
S
i
ng
le
A
x
i
s
Magnetic
B
all
L
e
vitati
on
S
ys
tem
Ba
se
d
on
S
l
i
c
e
Ge
ne
tic
Alg
o
r
i
th
m,”
Eng.
An
d T
e
ch
.
Jour
na
l
,
vo
l.
34,
part
(
A),
201
2.
B
I
OGRAPHIES
O
F AUTHO
RS
F
a
d
h
il A
. Has
an was
born
i
n
Bag
hdad
,
Iraq
in
F
ebru
ary 1
7
,
197
0.
He recei
ved
th
e B.S
c
.
f
r
om
t
he
un
iv
e
r
sity
o
f A
l
-
m
us
ta
n
s
iry
a
h,
B
a
g
hd
a
d
,
Ira
q,
i
n
19
9
1
,
in
e
le
c
t
ri
ca
l
en
gin
eerin
g. And
h
e
received
t
h
e
M
.
S
c
.
and
Ph.D
.
degrees
from
Uni
v
ersit
y
o
f
T
e
ch
no
lo
gy
,
in
2
00
8
and
201
7
r
e
sp
ecti
v
el
y,
i
n
el
ectrical
m
achine
and
con
t
rol
en
gin
eerin
g.
I
n
2
0
0
8
,
he
j
oi
ned
t
h
e
d
e
partm
e
n
t
o
f
el
ectrical
en
gin
eerin
g
at
u
ni
vers
ity
of
t
echn
o
lo
gy
,
Bag
h
d
a
d,
i
n
Iraq,
a
s
a
n
As
s
t
.
L
ecturer.
Curren
t
l
y
h
e
is
a
l
ecturer
i
n
th
e
d
e
partm
e
n
t
o
f
el
ectrical
e
n
g
in
eerin
g
at
u
ni
vers
ity
o
f
technology,
Bag
h
dad,
i
n
Iraq.
H
e
h
as
p
u
b
li
shed
o
ver
1
6
r
ef
ereed
j
ou
rnal
a
nd
c
on
f
e
ren
ce
pa
p
e
rs
i
n
t
h
e
areas
o
f
i
n
d
u
cti
o
n
h
eatin
g,
control s
y
st
e
m
s,
p
o
w
er elect
ron
i
cs
a
nd
e
l
ectri
cal m
ach
ine.
L
i
na
J
.
Ras
h
ad
w
as
born
in
B
agh
d
ad
,
Iraq
i
n
M
ay
7
,
1
9
8
3
.
She
re
ceiv
e
d
t
h
e
B.S
c
.,
M
.S
c.
a
nd
P
h
.
D
.
deg
r
ees
from
U
n
i
v
ersity
o
f
T
echno
lo
g
y
,
Bag
hdad
,
Ira
q
,
i
n
20
06
,
200
8
and
2
016
res
p
ecti
v
el
y.
I
n
2
0
0
8
,
sh
e
joi
n
ed
t
he
d
ep
artmen
t
of
e
lect
rical
en
gi
neerin
g
at
u
ni
versity
o
f
t
echno
lo
gy
,
Baghd
ad,
in
I
raq
,
a
s
an
A
s
s
t.
L
ectu
r
er.
Cu
rrent
ly
s
he
i
s
a
lect
urer
i
n
the
dep
a
rtm
e
nt
o
f
elect
rical engineer
i
n
g
at u
ni
vers
ity
of
tech
nol
ogy,
B
aghd
ad,
i
n
Iraq.
S
h
e
h
as p
ub
lis
hed
ov
er 15
ref
e
reed
j
o
u
rnal
a
n
d
c
o
n
f
e
ren
c
e
pap
e
rs
i
n
th
e
a
r
eas
o
f
co
nt
rol
sy
st
em
s
,
pow
er
e
l
e
ct
ron
i
cs
a
nd
el
ectrical
m
achine.
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