Int
ern
at
i
onal
Journ
al of
P
ower E
le
ctr
on
i
cs a
n
d
Drive
S
ystem
(I
J
PE
D
S
)
Vo
l.
11
,
No.
1
,
M
a
r
ch
20
20
, p
p.
24
~
33
IS
S
N:
20
88
-
8694
,
DOI: 10
.11
591/
ij
peds
.
v11.i
1
.
pp
24
-
33
24
Journ
al h
om
e
page
:
http:
//
ij
pe
ds
.i
aescore.c
om
Des
i
gn o
f H
∞
f
or
induction m
otor
Amm
ar
Iss
a
i
smael
1
,
L
afta
E.
Juma
a
2
,
N
i
sreen K
ha
m
as
3
1,3
Depa
rteme
nt
of
Elec
tr
ical
po
wer
and
Mac
hin
e
Eng
ine
e
ring,
C
oll
eg
e
of
Engi
n
e
eri
ng
,
Univer
si
ty
of
D
i
ya
la,
Ir
aq
2
Depa
rteme
nt
of
Elec
tron
ic
s
Eng
ine
er
ing,
Coll
eg
e
of Engin
ee
ring
,
Univer
si
ty
of
D
iya
l
a, I
raq
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
A
pr
28
,
2019
Re
vised
Ju
l
8
,
2019
Accepte
d
Aug
17
,
2019
F
or
Induc
ti
on
m
otor
is
a
sys
te
m
tha
t
works
a
t
their
spe
ed,
nev
ert
h
el
ess
th
ere
are
app
lications
at
which
the
s
pee
d
oper
ations
are
n
ee
ded
.
Th
e
cont
ro
l
o
f
ran
ge
of
spe
ed
o
f
induc
t
ion
mot
o
r
te
chn
ique
s
is
a
vai
l
abl
e
.
Th
e
ro
bust
cont
rol
is
used
with
in
duct
ion
mot
or
a
nd
the
p
erf
orm
a
nce
of
the
sys
tem
with
the
cont
roller
wil
l
b
e
im
prov
ed.
Th
e
ma
th
em
a
ti
c
al
m
odel
to
th
e
con
tr
oll
er
,
which
were
cod
ed
in
MA
TL
AB.
The
mode
li
ng
and
co
ntrol
ler
will
b
e
s
hown
by
the
condi
ti
ons
of
ro
bustness of
∞
be
l
ess t
han
on
e.
Ke
yw
or
d
s
:
Con
tr
ol
Ind
uction M
ot
or
Robust C
on
tr
ol
The
T
ra
ns
fe
r
F
un
ct
io
n
This
is an
open
acc
ess arti
cl
e
un
der
the
CC BY
-
SA
li
ce
nse
.
Corres
pond
in
g
Aut
h
or
:
Amm
a
r Issa
is
mael
,
Dep
a
rteme
nt of Elect
rical
po
wer an
d Mac
hin
e E
ngineeri
ng
,
Diyala
Un
i
ver
s
it
y,
Quds sqa
ure,
ba
quba, di
yala,
Ir
a
q.
Emai
l:
ammaris
sa1
978@gmail
.co
m
1.
INTROD
U
CTION
The
small
sig
nal
besid
es
ste
ady
sta
te
pa
ra
mete
rs
of
cag
e
inducti
on
m
otor
are
est
im
at
ed
in
a
bi
g
range
op
e
rati
on
by
us
in
g
fi
nite
-
el
ement
(
FE
)
meth
od.
A
m
achine
desig
ne
d
f
or
a
fr
e
quen
cy
co
nverter
s
upply
[1].
On
the
othe
r
ha
nd,
t
he
pa
rameters
of
th
r
ee
-
phase
f
or
in
du
ct
io
n
mo
t
or
s
can
determi
ne
by
impleme
nt
at
ion
of
a
ra
pid
on
li
ne
met
hod,
t
his
proce
dure
is
bu
il
t
data
sam
pling
t
hro
ugh
making
t
he
spe
ed
a
normal
r
un
u
p
exam.
And
al
s
o
t
he
l
ock
e
d
-
r
ot
or
besi
des
t
he
sy
nc
hro
nous
s
peed
data
hav
e
bee
n
te
ste
d
du
rin
g
t
he
run
up
exa
m
[2].
On
e
of
a
dvance
meth
od
for
co
mputes
the
re
qu
i
red
s
yst
em
sign
al
s
a
re
(
M
PC)
mea
ns
m
od
el
pr
e
di
ct
ive
con
t
ro
l,
t
his
method
is
c
on
sider
direct
a
nd
eas
y
al
gorit
hm
a
nd
f
or
nonlinea
riti
es
in
the
te
c
hniq
ue
[3].
A
sli
din
g
m
od
e
(M
R
AS)
bene
fits
to
kee
p
t
he
sta
bili
ty
in
case
lo
w
s
pee
d
a
rea.
H∞
m
et
hod
im
plem
ents
to
cal
culat
e
the
sl
iding
m
ode
gai
n,
that
pro
gres
s
the
r
obust
nes
s
of
the
ob
se
r
ve
r
s
ys
te
m
c
ompare
with
t
he
s
peed
of
in
duct
ion
m
achine
that
in
de
pende
nt
of
volt
age
m
od
e
.
This
proce
dure
mini
mize
s
th
e
impa
ct
of
the
er
ror
durin
g
the
pre
dicti
on
a
nd
ob
serv
e
r
m
odel
[
4].
A
nother
m
et
hod
use
d
Self
Tu
ning
(S
T
)
te
chn
iq
ue
de
pe
nd
on
Taka
gi
-
S
ug
e
no
(
TS
) fu
zz
y r
ules [5]
.
The
H
-
in
finity
con
tr
oller
c
onsider
the
s
olu
ti
on
t
o
a
maxim
um
a
nd
t
he
mi
nimum
di
ff
e
re
ntial
game,
the
co
n
tr
oller
can
re
duce
a
qu
a
drat
ic
cost
functi
on
relat
ed
to
the
e
rro
r
of
sta
te
vect
or
fro
m
the
ma
chine,
wh
e
reas t
he de
sign
i
ng er
rors a
nd ex
te
rn
al
di
sturbance
att
empt to
r
e
duce i
t [6
-
10
].
Ther
e
a
re
tw
o
sta
ges
meth
od
to
c
ontrol
the
i
nductio
n
m
otor,
the
fi
rst
is
by
by
us
i
ng
t
he
first
orde
r
o
f
Taylo
r
series
e
xtensi
on
to
li
ne
arize
of
the
dyna
mic
m
odel
mo
to
r
so
ca
n
use
Jac
ob
ia
n
m
at
rices
to
co
m
pu
te
it
.
The
n
the
sec
ond
sta
ge
us
e
d
li
near
iz
e
d
mode
l
for
t
he
i
nduct
ion
m
oto
r
by
s
olv
in
g
an
al
ge
br
ai
c
Ri
ccat
i
e
qu
at
io
n
to
desi
g
n
a
n
H
-
infi
nity
fee
db
ack
co
ntr
ol
r
ule
by
cal
c
ulati
ng
in
eac
h
re
pet
it
ion
of
the
c
ontr
ol
al
gorithm
[11].
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Desig
n of
H∞
f
or
i
nductio
n m
oto
r
(
A
mmar
Iass
Is
ma
el
)
25
Sti
ll
the
de
riva
ti
ve
of
t
he
t
ransfer
f
unct
ion
of
the
m
otor
by
man
ual
met
hod
is
us
e
f
ul
a
nd
has
a
n
imp
ort
ant
r
ol
e
to
simpli
f
y
as
su
m
ptio
n
of
t
he
dev
ia
ti
on
[
12].
Re
ce
ntly
com
pu
te
t
he
pole
s
of
tra
nsfe
r
f
unct
ion
has
more
at
tract
ive
for
t
he
re
searc
her
s
,
wh
ic
h
ca
n
c
omp
ute
the
pole
s
by
the
ei
ge
nval
ues
of
the
s
tructu
ral
sta
te
matri
x
[13].
I
n
t
his
pa
per
pro
pose
d
a
meth
od
to
de
sign
r
obus
t
w
it
h
I
-
P
c
on
t
ro
ll
er
f
or
an
in
duct
ion
m
otor,
a
nd
the
dynamic
be
ha
vior
of
i
nduction
m
otor
is
s
how
n
with
t
he
t
ran
s
fer
f
unct
io
n
m
otor.
The
inducti
on
m
otor
ha
s
pro
blems
in
th
e
co
ntr
ol
if
we
us
e
ma
ny
va
ri
ables
in
desi
gn
ing
of
the
syst
em
bec
ause
in
the
co
ntr
ol
s
uc
h
as
P,
PI
,
P
ID,
or
MPC
con
t
ro
ll
er
,
it
need
s
one
va
riable
as
in
put
and
one
ou
t
put
but
it
do
es
n’t
wor
k
with
man
y
var
ia
bles.
In
t
his
pa
per
w
e
fou
nd
a
s
olu
t
ion
s
t
o
the
pro
blem
of
c
on
tr
ol
li
ng
with
t
he
var
ia
bles
of
th
e
sy
ste
m
by
mixin
g
I
-
P
c
ontrolle
r
with
r
obus
t
co
ntr
ol
(
∞
)
to
get
the
r
obus
t
ness
a
nd
sta
bili
ty
with
w
hole
of
the
va
riable
s
and
this
c
ontr
ol
le
r
is
ve
ry
good
for
desig
ning
[
14].
The
re
a
r
e
ma
ny
pa
pe
rs
us
e
d
a
r
obus
t
c
on
t
ro
l
f
or
i
nduc
ti
on
mo
to
r
but
in
this
pap
e
r
c
ons
ider
t
he
best
be
cause
it
us
e
d
with
I
-
P
c
on
tr
oller
wi
th
who
le
ranges
of
va
riables
[15
-
19]
.
T
he
s
up
e
rc
onduct
in
g
in
duct
ion
m
ot
or
,
w
hich
de
ve
lop
e
d
a
n
a
nal
ys
is
m
odel
wit
h
e
qu
at
io
n
of
a
mo
t
or
vo
lt
age
ba
sed
on
the
non
-
li
ne
ar
c
urren
t
t
ha
t
relat
ed
to
H
TS
wi
ndon
gs
.
The
higher
ef
f
ic
ie
ncy
c
ontrol
of
the
mo
to
r
by
us
a
ge
of
be
hav
i
or
of
t
he
af
or
e
me
ntion
e
d
hyste
r
et
ic
.
They
got
a
good
res
ults
in
both
l
oad
a
nd
no
load
for
the
hyste
reti
c
r
otati
ng
c
hract
erist
ic
s
an
d
got
th
e
peak
val
ue
of
e
ff
ie
ci
enc
y
wh
e
n
t
he
vol
ta
ge
is
decr
easi
ng
afte
r
r
otati
ng
sync
hro
nous
of
the
mo
to
r.
The
ch
ar
act
ersit
ic
s
of
high
te
m
per
at
ur
e
suo
per
c
on
du
ct
or
inducti
on
mo
t
or
has
bee
n
in
dicat
ed
that
the
HTS
el
ect
ric
powe
r
wit
h
a
synch
r
onous
at
the
ef
fici
enc
y
is
mor
e
than
90%
an
d
r
at
ed
co
ndioti
on
20
kW.
T
he
c
har
ace
risti
cs
ha
ve
be
en
te
ste
d
an
d
rep
li
cat
e
d
reli
ed
on
e
q
ui
valent
ci
rcu
it
of
nonl
inear
el
ect
rical
.
The
res
ults
was
co
mf
or
t
able
of
e
xtre
mely
orga
nize
d
f
or
perform
ance
of
sy
nc
hro
nous re
gen
e
rati
on [2
0
-
21].
The
in
duct
io
n
mo
t
or
s
has
bee
n
us
ed
for
c
onversi
on
betwee
n
mecha
nical
a
nd
el
ect
rical
(elect
romecha
nical
)
a
nd
a
r
e
s
how
in
m
os
t
pr
ocesses
of
pro
du
ct
io
n
f
or
tw
o
t
hir
ds
of
the
c
on
s
umpt
ion
of
industrial
el
ect
ric.
Ind
uction
mo
to
rs
fa
ults
can
dis
play
i
n
huma
n
los
s
es,
sto
p
entire
sect
or
s
of
a
plant,
op
e
rati
onal
dis
ast
ers
an
d
ca
usi
ng
ec
onomi
c.
The
te
c
hn
i
qu
es
are
crit
ic
al
fo
r
dia
gnos
is
of
fau
lt
in
i
nduction
mo
to
rs. A
hy
bri
d
s
ys
te
m
that
u
ses
data
g
ot
f
r
om
c
urren
t
se
nsors
a
nd v
ib
rat
ion
to
d
isc
over
fail
urs
at
ea
rly
ste
p.
The
fail
ur
e
s
w
ere
c
orrectl
y
due
to
the
loa
d
with
unbala
nc
ed
way
in
the
mo
to
r
helix
an
d
in
the
m
otor
sh
a
ft
[22
].
T
he
str
uc
tre
of
cr
yoge
ni
c
inducti
on
m
ot
or
wen
t
unde
r
water
with
na
tural
gaz
f
or
operati
on
L
N
G
sp
ra
y
pump.
T
he
in
duct
ion
m
oto
r
tor
que
of
in
duc
ti
on
m
otor
dissimi
la
r
from
t
he
r
oom
te
m
pe
ratur
e
co
ndit
ion
s
to
desig
n
s
pecific
at
ion
s
of
t
he
inducti
on
m
otor
in
e
n
vi
ronme
nt
in
cr
ygge
ni
c
man
ner.
T
he
desig
n
of
c
ryog
e
nic
relat
ed
to
resis
ti
vity
var
ia
ti
on
for
r
otor
bar
s
and
sta
tor
windin
gs
[
23]
.
T
he
te
chn
i
qu
e
of
direct
to
rque
c
on
t
ro
l
(D
TC
)
f
or
a
t
wo
le
vel
in
ve
rter
ga
ve
five
ph
ase
in
du
ct
io
n
mo
to
r
(F
P
I
M
)
for
op
e
rati
on
i
n
l
ow
s
pee
d
de
man
ds
the
harmo
nic
volt
age
el
imi
nation
w
ould
ge
ne
rate
a
cu
rr
e
nt
of
distor
te
d
sta
tor.
T
he
a
nal
ysi
s
with
a
the
oret
ic
al
man
ner
is
impl
emented
t
o
dis
cov
e
r
res
ults
of
virtua
l
vecto
r
s
on
fl
ux
res
pons
e
of
FP
IM
a
nd
to
r
qu
e
with
s
peed
var
ie
s
t
o
help
in
ch
oosin
g
flux
ba
nd
width,
V
Vs,
ef
fici
en
t
formati
on
of
sect
or
s
an
d
hy
ste
resis
to
rque
ba
nd
width [
24].
The
fa
ults
of
be
arin
g
are
th
e
main
r
oot
for
t
he
fail
ures
of
i
nductio
n
m
otor.
T
he
meth
ods
of
diag
nosis
of
fa
ult
has
be
en
exa
mine
d
on
te
sts
of
la
bs
wh
ic
h
i
nf
le
xi
ble
a
nd
c
os
tl
y.
T
he
t
hr
ee
–
phase
s
quirre
l
cage
inducti
on
m
otor
is
sim
ulate
d
by
m
odel
ing
of
m
ulti
ple
c
oupled
ci
rcu
it
s.
T
he
a
nalysis
is
done
by
t
he
e
f
fecti
ng
of satu
rati
on of
the moto
r. T
he
r
es
ults o
f
e
xperimental
a
gr
e
e w
it
h
t
he resul
ts of sim
ulati
on
[25]
.
2.
MO
DLING O
F THE S
YS
T
EM
Ther
e
are
th
ree
phase
machi
ne
s for spee
d o
f t
he
sta
tor
by
=
120
Wh
e
re
is
the
numb
e
r
of
po
l
es
an
d
is
the
fr
e
quen
cy
in
.
Fig
ure
1
des
cribes
t
he
Pr
e
-
ph
a
s
e
ci
rcu
it
relat
ed
to
the
stat
or.
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S
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694
I
nt J
P
ow Elec
& Dri
Sy
st
V
ol
.
11
, N
o.
1
,
Ma
r
20
20
:
24
–
33
26
Figure
1
.
P
has
e
ci
rcu
it
of stat
or side
The
e
quat
ion o
f
el
ect
rical
ma
chine
a
s s
how
n i
n
Fi
gure
(
2
)
i
s
=
+
+
….…
………
………
…
….(1)
=
………
..……
…. …..
(
2)
The
e
quat
ion o
f
el
ect
rical
torq
ue
is
=
2
2
+
2
………
…..…
……….
.(3)
The
e
quat
ion o
f
mec
ha
nical
torq
ue
is
=
2
2
+
………
……
……
… .(4
)
By taki
ng La
place t
ran
s
f
or
m
for eq
uatio
n
(
1)
and
get
(
)
=
(
)
(
+
)
+
(
)
…….
. ……
……. .(
5)
But we
h
a
ve fr
om
e
quat
io
n
(
2)
=
(
)
…………
……
… …
….(6)
Substi
tuti
ng equati
on (6) i
n (
5),
we get
(
)
=
(
)
(
+
)
+
(
)
……..…
...
…
..(7
)
(
)
=
(
)
−
(
)
(
+
)
………
……
…
….(8)
By taki
ng La
place
trans
f
or
m
for eq
uatio
n
(
4)
and
get
(
)
=
2
+
………
……
……
……..(
9)
The
el
ect
rical
t
orq
ue
is
=
2
………
……
…………
……
… (1
0)
The
el
ect
rical
t
orq
ue
is e
qu
al
t
o
the
mec
ha
nical
torqu
e
=
2
(
)
=
(
2
+
)
(
)
………
……
…
….. (
11)
Evaluation Warning : The document was created with Spire.PDF for Python.
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t J
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ow Elec
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ys
t
IS
S
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88
-
8
694
Desig
n of
H∞
f
or
i
nductio
n m
oto
r
(
A
mmar
Iass
Is
ma
el
)
27
=
(
2
+
−
2
)
(
)
……
………
…
…...(
12)
The
tra
nsfer
fu
nction i
s
(
)
(
)
=
1
2
+
−
2
………
……
…………
…
(13)
We
hav
e
=
(
)
−
(
)
+
………
….…
……
…….
(14)
Substi
tuti
ng equati
on (1
4)
i
n (
13) , we
w
il
l
ge
t
(
)
(
)
=
3
+
(
+
)
2
+
(
+
)
………
…(
15)
With
par
a
mete
rs
= 0.0
19 ,
=
0
.
5
,
=
4
.
2
,
=
8
=
3
The fin
d
tra
nsf
er fu
nction i
s
(
)
(
)
=
0
.
0
00
12
8
0
.
00
06
7
3
+
0
.
71
9
5
2
+
The res
pon
se
of
ou
t
pu
t as
s
hown in Fi
gure
3
.
Figure
2.
Induc
ti
on
mo
tor
Figure
3.
The
ou
t
pu
t
f
or
ste
p i
nput
3.
IP CONT
ROL
LE
R
DESI
G
N
The
I
P
fee
db
a
ck
co
ntr
oller
f
or
the
cl
os
ed
-
l
oop
s
ys
te
m
w
it
h
is
sho
wn
i
n
Fig
ur
e
4.
T
he
tran
sfe
r
functi
on
with
cl
os
ed
-
lo
op
s
yst
em.
In
te
gr
al
pro
portio
nal
con
t
ro
ll
er
(
I
-
P
)
is
ad
va
nce
f
orm
of
propo
r
ti
on
al
integral c
ontrol
le
r.
In t
his met
hod of co
ntr
oller the i
nteg
ral
par
t i
s i
n
fee
df
orward
path
and
propo
rtion
al
par
t i
s
in
fee
db
ac
k path.
T
he disad
va
ntage
in
P
-
I
co
ntr
oller is
that hig
h
ma
ximum
o
f pea
k
overs
hoot.
T
o decea
se that
maxim
um
of
pe
ak ov
e
rs
hoot
we
ca
n use t
his I
-
P c
on
t
ro
ll
er.
We ca
n dr
i
ve
t
he
c
on
t
ro
l l
ow
of I
-
P c
ontrolle
r
as.
(
)
=
(
)
(
)
(
)
=
(
)
−
(
)
(
)
=
(
)
−
(
)
−
(
)
(
)
=
(
)
−
(
)
[
−
]
0
1
2
3
4
5
6
7
0
0
.
2
0
.
4
0
.
6
0
.
8
1
1
.
2
1
.
4
x
1
0
-4
S
t
e
p
R
e
s
p
o
n
s
e
T
i
m
e
(
s
e
c
o
n
d
s
)
A
m
p
l
i
t
u
d
e
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S
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:
2088
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8
694
I
nt J
P
ow Elec
& Dri
Sy
st
V
ol
.
11
, N
o.
1
,
Ma
r
20
20
:
24
–
33
28
Figure
4.
I
-
P c
on
t
ro
ll
er
dia
gram
4.
The
∞
CON
T
R
OL PR
OBL
EM
Fo
r
t
he
pu
rpos
e
of
sel
ect
io
n
in
this
pa
pe
r,
∞
methods w
il
l
be
require
d.
T
hi
s
gets
vie
w
is
def
i
ned
by
the
identific
at
ion
t
hat
2
and
∞
m
et
hodo
l
og
ie
s
a
re
al
ike
in
that:
bo
t
h
are
in n
e
ed
of
the
re
su
lt
s
to
two
Ri
ccat
i
equ
at
io
ns,
both
play
as
c
on
t
rol
le
rs
of
sta
te
-
dimens
i
on
e
qual
to
the
ge
ner
al
i
zed
pla
n
t,
P,
a
nd
both
giv
e
a
n
ide
a
to
str
uctu
re
i
n
their
c
ontrolle
r
s
that
a
re
al
rea
dy
see
n
i
n
L
Q
G
c
ontrol
[
12].
It
is
sig
nifica
nt
to
kn
ow
tha
t
H
∞
con
t
ro
ll
ers
give
a
sub
-
opti
m
al
co
ntr
oller,
wh
ic
h
co
ntrast
s
with
H
2
co
nt
ro
l
t
hat
giv
es
ide
ntica
l
an
d
sp
eci
al
con
t
ro
ll
e
rs
. I
t
mu
st
be n
oted
t
hat (
s
)
is
oft
en dr
oppe
d
as
a
usa
ge.
The fo
rm
ulati
on
of the
ge
ner
a
l pro
blem
of
H
∞ proble
ms
is il
lustrate
d b
y
[
]
=
(
)
[
]
=
[
11
(
)
12
(
)
21
(
)
22
(
)
]
[
]
………
…
…. (1
6)
=
(
)
The ge
ner
al
iz
e
d plant P
h
a
s s
how
n by
=
[
1
2
1
11
12
2
21
22
]
………
……
……….
.(17).
The
par
a
mete
r
s
v,
the
mea
s
ur
e
d
var
ia
bles
,
u,
the
c
ontr
ol
va
riables,
z
the
er
ror
si
gn
al
t
o
be
minimi
zed
,
w,
the
si
gn
al
of
exoge
nous
su
c
h
as
dist
urbance
s.
T
he
sc
he
mati
c
of
the
ge
ner
al
iz
ed
pla
nt
m
ode
l
can
be
s
how
n
i
n
Fi
gure
5.
Figure
5.
The
Gen
e
rali
zed
pl
ant m
od
el
By men
ti
onin
g
to
S
kogesta
d
a
nd
P
os
tl
et
hwai
te
[
2]
,
t
he
li
nea
r
tra
nsfer
f
unct
ion
al
t
ransf
orm
at
ion
f
r
om
w
to
z th
r
ough
the close
d
-
lo
op tra
nsfer
f
un
ct
ion
will
b
e
as
=
(
,
)
Wh
e
re
(
,
)
=
11
+
12
(
−
22
)
−
1
21
………
(18)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Desig
n of
H∞
f
or
i
nductio
n m
oto
r
(
A
mmar
Iass
Is
ma
el
)
29
5.
MIX
E
D SE
N
SITIVIT
Y
H
∞ CONT
ROL
w
ith
I
-
P
CONTROLL
E
R
M
ixe
d
se
ns
it
iv
it
y
(MS)
c
on
t
r
ol
is
the
trans
f
er
f
un
ct
io
n
to
fin
d
a
co
ntr
oller
that
giv
e
s
the
neces
sar
y
cl
os
ed
-
lo
op
se
ns
it
ivit
y
tra
nsf
er
functi
ons
T
,
S
an
d
KS.
T
is
the
tra
nsfer
f
un
ct
io
n
c
losed
-
lo
op
whic
h
is
cal
culat
ed
f
r
om:
=
(
+
)
−
1
…………
……
…
…….
(19)
S is the
sensi
ti
vity
functi
on
w
hich
is
calc
ulate
d from:
=
(
+
)
−
1
………
……
……
……. (
20)
These
quantit
ie
s (19 ) a
nd
(20
)
are
the
fee
dback c
onfig
ur
at
i
on sho
wn in
Fi
gure
6.
Figure
6. Fee
dback
con
fig
ur
a
ti
on
of one
de
gree f
ree
dom.
Fr
om Fi
gure
3, can
obta
in
(
)
an
d
(
)
can
be se
en:
(
)
=
(
)
(
)
+
(
)
[
(
)
−
(
)
]
………
…….
.. (21)
(
)
=
[
(
)
−
(
)
−
(
)
)
]
(
)
(
)
………
……
...(22)
These
tw
o
e
qu
at
ion
s
cal
culat
e
the
cl
os
e
d
-
l
oop
in
a
dd
it
io
n
to
the
re
quire
ment
t
hat
K
sta
bili
zes
to
reject
distu
r
ba
nces
t
o
t
he
s
yst
em,
a
nd
the
m
aximum
si
ngul
ar
value
of
S
s
hould
be
s
mall
to
reject
noise
.
F
or
reducti
on c
on
t
r
ol en
e
r
gy that
makes
the
max
imum
sin
gu
la
r value
of
KS
s
mall
.
The
rob
us
t
sta
bili
ty
with
ad
di
ti
on
al
pe
rtu
rbat
ion
s,
ma
ke
t
he
value
of
m
aximum
si
ngul
ar
KS
s
mall
rom aims
of th
e p
e
r
f
ormance
,
it
can be s
how
n
that t
he great
d
eal
of trad
e
-
off bet
wee
n
c
ompeti
ng
ob
je
ct
ives.
6.
H
-
I
NFI
NITY
SYNTHE
SIS
The
c
on
t
ro
ll
er
K
is
to
be
tu
ned
su
c
h
t
hat
the
H
-
in
finity
betwee
n
the
outp
uts
an
d
i
nputs
an
d
t
he
sy
ste
m
in
cl
os
e
lo
op
is
sta
ble
of
the
matri
x
a
re
le
ss
tha
n
on
e.
I
f
this
c
ondit
ion
is
a
gr
ee
d,
t
hen
the
ou
t
pu
t
of
the
con
t
ro
ll
er
is
sa
id
to
ha
ve
a
r
obus
t
performa
nce
syst
em,
w
hich
mea
ns
th
at
fo
r
t
he
ra
nge
of
un
ce
rtai
n
model
par
a
mete
rs
t
he
co
ntr
ol
of
cl
ose
lo
op
meet
s
the
re
quire
d
pe
rformance
de
s
c
riptio
n.
The
μ
-
synthe
sis
pr
oc
ess
to
ob
ta
in
th
e
rea
l
co
ntr
ollers
was
do
ne
by
us
in
g
the
hi
nfsyn.m
inst
ru
ct
ion
in
M
AT
L
AB®.T
his
inst
ru
ct
io
n
util
it
ie
s
a
mix
ed
se
ns
it
ivit
y
te
chn
iq
ue,
wh
i
ch
decr
ea
ses
t
he
c
os
t
functi
on
c
on
ta
ini
ng
the
weig
hts
of
three
performa
nces
f
rom
a
bove
a
nd
this
c
os
t
funct
ion
s
hould
be
le
ss
th
an
on
e
t
o
meet
pe
rfo
rm
ance
sp
eci
ficat
ion
s
as sho
wn in e
quat
ion (
23).
‖
(
)
(
)
̇
(
)
‖
<
1
………
……
…………
….
...
.
(
23)
Wh
e
re
S
is
the
se
ns
it
ivit
y
t
ra
ns
fe
r
f
unct
ion
if
the
s
ys
te
m
is
cl
os
e
d
lo
op,
a
nd
T
is
the
c
ompleme
ntar
y
sensiti
vity
func
ti
on
.
The
ge
ner
al
iz
e
d
plant
tra
nsfer
functi
on
matri
x,
P,
t
hat
symb
olize
s
the
s
ys
te
m
in
Fig
ure
6
and
is
use
d
for
the
co
ntr
oller
c
ombinati
on
proces
s
is
see
n
in
E
qu
at
io
n
(24).
On
ce
this
com
bin
at
i
on
proces
s
was
rea
li
zed
for
ea
ch
of
c
on
trolle
rs
ve
rific
at
ion
of
their
pe
rformance
is
r
eal
iz
ed
to
co
nfi
rm
the
pe
rfo
r
mance
s
pecific
at
ion
s
wer
e
matche
d.
In
Fig
ur
e
7,
1
2
are
and
respe
ctively.
P is
def
in
ed as
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
I
nt J
P
ow Elec
& Dri
Sy
st
V
ol
.
11
, N
o.
1
,
Ma
r
20
20
:
24
–
33
30
=
[
−
0
−
]
………………
…………
….
.
(24)
It
is
si
gnific
ant
to
not
e
th
at a
l
l
w
ei
ghts,
wi,
shoul
d
be
st
able
[2]
.
Figure
7.
S/K
S
f
r
om o
f MS
fo
r
trac
king
7.
PERFO
R
MANC
E
A
NA
L
Y
SIS
Confirmat
io
n
was
do
ne
t
o
make
certai
n
t
hat
eac
h
co
ntr
oller,
K
,
disc
overe
d
by
the
μ
-
s
ynthesis
appr
oach
a
gre
es
rob
us
t
sta
bi
li
ty
req
ui
rem
ents
an
d
t
he
performa
nce
s
pecifica
ti
ons.
The
c
on
t
ro
ll
er
s
are
nominall
y
sta
bl
e
with
no
pla
nt
uncertai
nt
y
and
th
ere
s
houl
d
be
no
po
le
s
on
the
rig
ht
-
half
pla
ne
f
or
the
nominal
cl
os
e
d
lo
op
plant.
T
he
perf
or
ma
nc
e
chec
k
was
to
ma
ke
ce
rta
in
t
he
value
of
(
23)
was
le
ss
t
ha
n
one.
Anothe
r
a
ppr
oa
ch
incl
ud
es
a
nalyzin
g
t
he
N
matri
x.
T
he
lowe
r
f
racti
onal
tran
sf
orma
ti
on
of
t
he
P
matri
x
detai
le
d
in
(24)
and the
contr
ol
le
r.
{
∆
1
∆
2
∆
3
1
2
3
}
=
[
11
21
12
22
]
{
∆
1
∆
2
∆
3
1
2
}
………
……
………
…..(2
5)
Nominal
performa
nce c
hecks
that the
nomi
na
l plant is c
ontrolle
d rela
ti
ng
to the pe
rform
ance s
pecifica
t
ion
s
.
No
min
al
perfo
rma
nce
‖
N
22
‖
∞
<
1
……
…………
(
26)
Robust
sta
bili
t
y
a
nd
r
obus
t
pe
rformance
to
make
certai
n
that
the
syst
em
is
sta
ble
in
cl
ose
d
l
oop
a
n
d
agr
ees
the
give
n per
forma
nce
requireme
nts
over
the
giv
e
n r
ang
e
of
uncert
ai
n
pa
ramete
rs.
No
min
al
perfo
rma
nce
‖
N
11
‖
∞
<
1
……
……….
.(2
7)
The
final
c
he
ckin
g
is
r
obust
performa
nce,
w
hich
ma
kes
certai
n
pe
rfo
rma
nce
s
pecifi
cat
ion
s
a
re
agr
ee
d for all
uncertai
n pla
nts.
No
min
al
perfo
rma
nce
‖
N
‖
∞
<
1
………
……
…
……..(
28)
The
c
rite
ria
of
performa
nce
use
d
to
desc
ribe
the
pe
rforma
nc
e,
wei
gh
ts
in
so
me
ca
ses
we
re
dif
fe
ren
t
than
the
pe
rformance,
wei
gh
t
s
us
e
d
to
deter
mine
the
perf
orma
nce
chec
ks.
W
her
e
is
the
per
t
urbati
on
pl
ant
from
the
nomi
nal
an
d
is
the
nominal
plant
.
T
he
nomi
na
l
plant
ha
d
a
sy
ste
m
gain
of
2
a
nd
a
ti
me
const
ant
of
0.
35
sec
onds
.
Th
e
was
de
te
rmi
ned
by
gai
n
uncertai
nt
y
m
ulti
plied
the
no
minal
pla
nt.
T
he
li
ne
so
li
d
pl
otte
d
in
Fig
9
i
s
the
uncert
ai
nty
weig
ht
boun
ding
the
maxim
um
e
rro
r
f
or
al
l
value
s
of
fr
e
qu
e
ncies
by
plo
tt
ing
t
he
m
ulti
plica
ti
ve
uncertai
nty
tra
ns
f
er
f
un
ct
io
n,
a
nd
we
ca
n
see
that
in
Fig
ur
es
8
an
d
9
.
The
s
ys
te
m
is
nominall
y
sta
ble
if
only
i
f
the
values
of
22
le
ss
t
han
one
an
d
can
be
s
een
t
he
nomin
al
performa
nce
by
pl
otti
ng
t
he
H
-
i
nf
i
nty
nor
m
as
s
how
n
in
Fig
ur
e
10
.
F
or
the
rob
us
t
st
abili
ty
,
11
is
le
ss
or
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Desig
n of
H∞
f
or
i
nductio
n m
oto
r
(
A
mmar
Iass
Is
ma
el
)
31
equ
al
one
f
or
a
ll
fr
eq
ue
ncies
and
t
hat
the
s
yst
em
is
r
obus
t
sta
ble
.
T
he
h
-
i
nf
i
nity
no
rm
of
11
can
bee
see
n
i
n
Figure
11.
T
he
-
synthe
sis co
nt
ro
ll
er is
foun
d t
o
ha
ve r
obus
t
performa
nce
w
hich
ca
n bee
se
en
in
Fig
ure
12
Figure
8.
Tra
nsfer
f
un
ct
io
n b
oundin
g o
f
M
ulti
plica
ti
ve un
ce
rtai
nty t
he
max
im
um er
r
or for
the
set
p
ara
mete
r r
ang
e
.
Figure
9. Bo
de
d
ia
gram
of t
he
pe
rfo
rma
nce
weig
ht
.
Fig
ure
10.
Th
e
22
of
H
-
infi
ni
ty
of
i
s le
ss
tha
n
one
for
all
fr
eque
n
cies.
Fig
ure
11.
Th
e
11
of
H
-
infi
ni
ty
nor
m
is
le
ss
th
an
one
for
all
fr
equ
enc
i
es
for the
-
s
ynthe
sis c
on
trol
l
er.
Figure
12.
Struc
t
ure
d
singul
ar
v
alue
and
th
e
m
aximum
singul
ar
v
a
lue
and
of
the N
ma
tri
x
is
le
ss
th
a
n
one
fo
r
a
ll
fre
quencie
s
8.
CONCL
US
I
O
N
This
pa
pe
r
sho
wed
a
meth
od
to
desi
gn
a
robu
st
c
ontrolle
r
s
for
a
n
in
du
ct
ion
m
otor.
T
hi
s
pa
per
ha
s
sh
ow,
from
t
he
r
esulta
in
ti
me
an
d fr
e
quenc
y domai
n,
w
hich
the
rob
us
t co
ntr
ol meth
od
w
it
h
I
-
P c
ontoll
l
er can
be
s
uccess
fu
ll
y
of
in
du
ct
io
n
mo
t
or.
T
he
dyna
mic
beh
a
vi
or
of
i
nductio
n
m
otor
is
show
with
the
tr
ansf
e
r
10
-4
10
-2
10
0
10
2
-
7
0
-
6
0
-
5
0
-
4
0
-
3
0
-
2
0
-
1
0
0
M
a
g
n
i
t
u
d
e
(
d
B
)
B
o
d
e
D
i
a
g
r
a
m
F
r
e
q
u
e
n
c
y
(
r
a
d
/
s
)
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
-
2
0
-
1
5
-
1
0
-5
0
5
10
M
a
g
n
i
t
u
d
e
(
d
B
)
B
o
d
e
D
i
a
g
r
a
m
F
r
e
q
u
e
n
c
y
(
r
a
d
/
s
)
S
1
/
W
p
10
-2
10
0
10
2
10
4
10
6
-
6
0
0
-
5
0
0
-
4
0
0
-
3
0
0
-
2
0
0
-
1
0
0
0
RS
F
r
e
q
u
e
n
c
y
(
r
a
d
/
s
)
S
i
n
g
u
l
a
r
V
a
l
u
e
s
(
d
B
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
I
nt J
P
ow Elec
& Dri
Sy
st
V
ol
.
11
, N
o.
1
,
Ma
r
20
20
:
24
–
33
32
functi
on
m
otor
is
sh
ow
n
with
the
trans
fer
f
unct
ion.
T
he
the
ory
beh
i
nd
t
he
rob
us
t
co
ntr
ol
with
the
a
pplyi
ng
of
conditi
ons
a
re
very
c
omf
or
ta
ble
f
or
e
ac
h
ste
p
of
r
obust
c
ontr
ol
to
co
ntr
ol
the
pe
rforman
ce
an
d
r
obus
t
ne
ss
to
analyze
dif
fere
nt
pa
rameter
s
of
the
s
ys
t
em.
T
he
c
ondi
ti
on
of
sta
bil
it
y
for
perfor
mance,
nomi
na
l
and
rob
us
tness
a
re
ve
r
y
c
omf
or
t
able
a
nd
al
l
t
he
y
a
re
le
ss
t
ha
n
one
an
d
is
c
omfo
rtable
wi
t
h
man
y
var
ia
bl
es
of
par
a
metrs
of th
e sy
at
em
w
it
h I
-
P c
ontrolle
r
.
REFERE
NCE
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ro
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t
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r
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rnational
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Pow
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usi
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ckste
pping
of
flywhe
el
ene
r
gy
storag
e
sys
tem
and
DF
IG
for
power
smoothi
n
g
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nts
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ernati
onal
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f
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r
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otor
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or
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S
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W
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X.
Ch
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Y
.
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B
.
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t
pre
dictive
cur
r
e
nt
con
trol
for
in
duct
ion
mot
or
in
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ng
fra
m
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"
20
16.
[19]
H.
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u
,
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B.
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,
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ng
,
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t
fau
l
t
-
tolera
n
t
co
ntrol
d
esign
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induc
ti
on
mo
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with
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lt
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Ta
ke
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oh
ar
u
Kara
shim
a,
N
aoyuki
Ame
mi
y
a,
Masa
aki
Yos
hika
wa,
Yos
hit
a
ka
Itoh,
Toshihi
s
a
T
eraza
wa
,
an
d
Yos
him
asa
Ohashi,
“Hyste
ret
i
c
Ro
tating
Chara
c
te
rsti
cs
o
f
HTS
Induc
t
io
n/
Synchronous
Motor,
”
IE
EE
Tr
a
nsacti
ons on Ap
pli
ed
Superc
ond
uct
i
vi
t
y
,
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[21]
Tom
ohar
u
Kara
s
him
a
,
T
aketsune
Naka
mur
a, Ke
n
ic
hi
Ike
da
,
N
aoy
uki
Ame
mi
ya
,
Masaa
ki
Yos
hik
awa
,
Yos
hit
aka
Itoh,
“E
xp
eri
m
e
nta
l
and
Analyti
ca
l
Studie
d
on
H
ighl
y
Eff
icient R
ege
nar
at
iv
e
Ch
ar
ac
t
eri
sti
cs
of a
2
0
-
kW
Cl
ass
HTS Induc
ti
on
/ S
ynchr
onous Motor”
,
IE
EE
Tr
a
nsacti
ons on
app
li
ed
supercondu
ct
i
vi
t
y
,
vol. 27, I
ss
ue
4,
2017
.
[22]
G.
A.
Cru
z, R. D.
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,
F.
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B
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o
and
A.
C.
L
i
ma
Filho
,
“A
Hy
brid
Sys
te
m
Bas
ed
on
Fuz
zy Log
ic
to
Fai
lure
Diagnosis
in
Ind
uct
ion
Motors,”
IEE
E
Latin Ame
rica
Tr
ansacti
on
s
,
vol. 15, Issue
8,
pp
.
1480
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9,
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[23]
Hui
Min
Ki
m,
Ki
Wook
L
ee,
Do
Gyun
Kim
,
Jong
H
oon
Par
k,
and
Gw
an
Soo
Park
,
“
Desi
gn
of
Cryogeni
c
Induc
ti
on
Motor
Submerge
d
in
L
ique
fi
el
d
Na
tural
Gas,”
IEEE
Tr
a
nsacti
ons on
Ma
gnet
i
cs
,
vol. 54, I
ss
ue
3,
2018
.
[24]
Saiful
la
h
Paya
m
i
and
Ran
ja
n
K.
Behe
ra
,
”An
I
mp
rove
d
DTC
Tec
hnique
for
Low
Speed
Oper
at
ion
of
a
F
ive
-
Phas
e
Induc
ti
on
Motor
”,
I
EEE
Tr
ansacti
on
on
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l
E
le
c
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s
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3513
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[25]
Mansour
Ojaghi
,
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and
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z,
“
Analytic
Model
for
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t
ion
M
otors
under
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c
al
i
za
ed
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ari
ng
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s,”
IE
EE
Tr
ansacti
on
on
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ersion
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18.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Desig
n of
H∞
f
or
i
nductio
n m
oto
r
(
A
mmar
Iass
Is
ma
el
)
33
BIOGR
AP
HI
ES OF
A
UTH
ORS
Amma
r
Iss
a
r
ece
ive
d
his
B
.
Sc
fro
m
Univer
sity
of
Baghda
d
in
Ira
q
in
2001,
MS
c
f
r
om
Univer
sity
Te
nag
a
nosiona
l
(unit
en)
in
Ma
la
ysia
at
2013
,
work
at
co
ll
eg
e
of
engi
n
ee
ring
Univer
sity
of
Diyal
a
,
Ir
aq
as
a
ss
ista
nt
l
ec
tur
e. His
cur
ren
t
r
ese
a
rch
in
te
r
ests
in
clud
e
power
e
le
c
tr
onic
,
e
le
c
trica
l
ca
r, re
n
able
en
er
gy.
La
ft
a
E
.
Jumaa
Alkura
wy2
re
ceive
d
the
B.
S.
,
a
nd
M.S.
d
egr
e
e
in
Con
trol
and
sys
te
ms
from
Te
chno
logy
Uni
ver
sity,
B
aghdad,
Ira
q
,
in
1996
and
2003
resp
e
ct
iv
el
y.
He
re
ceive
d
th
e
Ph.D.
degr
ee
in
E
le
c
tric
al
and
Comput
er
Engi
n
ee
r
ing
f
rom
Univer
sity
of
Miss
ouri
in
Colum
bia,
US
A,
in
2013.
Sinc
e
2
003,
I
hav
e
b
ee
n
with
Univer
si
ty
of
Diyala,
Co
lle
ge
of
eng
ineeri
n
g,
Diya
la
,
Ira
q
as
a
le
c
ture
r
.
Hi
s
cur
ren
t
rese
arch
in
te
rests
in
cl
u
de
mode
l
ing,
co
ntrol
,
Num
eri
c
al
an
a
lysis
and
nonli
ne
ar
Nisree
n
Kha
ma
s
3
recei
v
ed
the
B
.
S.,
and
M.S.
d
e
gre
e
in
Con
trol
and
sys
te
ms
fro
m
T
ec
hnology
Univer
sity,
Bag
hdad,
Ira
q
,
.
she
r
ec
e
ive
d
th
e
Ph.D.
degr
ee
in
Elec
tri
c
al
and
Compu
te
r
Engi
ne
eri
ng
fro
m
Technol
ogy
U
nive
rsity
,
Baghd
ad,
Ira
q
,
,
I
h
ave
bee
n
with
Univ
e
rsity
of
Diy
ala,
Coll
ege
of
eng
ine
er
ing,
Diy
ala
,
Ira
q
as
a
lec
ture
r.
Her
cur
r
ent
r
ese
arc
h
intere
sts
in
cl
ude
mode
li
ng
,
cont
r
ol,
Num
erica
l
an
al
ysis a
nd
nonli
n
ea
r
Evaluation Warning : The document was created with Spire.PDF for Python.