Intern
ati
o
n
a
l
Jo
u
r
n
a
l
of
P
o
we
r El
ec
tr
on
i
c
s
an
d D
r
i
v
e
S
y
stem
(I
JPE
D
S)
V
o
l.
11
, N
o
. 2, Jun
e
20
20
, pp
. 76
2
~
77
3
I
SSN
:
208
8-8
6
9
4
, D
O
I:
10.
115
91
/i
jp
e
d
s.v
1
1
.i2
.
p
p76
2-7
73
7
62
Jo
urn
a
l
h
o
me
pa
ge
: h
t
t
p
:/
/ijpe
d
s.
i
a
e
s
c
o
re.
c
o
m
Design an
d imp
l
ementation of va
riable and constant load for
induction m
o
tor
Sa
lam Wa
ley
Sh
neen
1
,
H
a
sh
mia
Sh.D
a
kheel
2
,
Z
a
in
ab
B
.
Abd
u
ll
a
3
1
Energ
y
an
d R
e
new
a
ble
En
ergie
s
Te
ch
no
lo
gy
C
e
nter,
Un
iv
ers
ity
o
f
Tech
no
lo
gy
,
I
r
aq
2,
3
Departm
e
nt of
Electro
me
chan
ical,
Un
iv
e
r
s
i
ty
o
f
Tech
no
lo
gy
, Ir
aq
A
r
ticle In
fo
A
B
S
T
RAC
T
A
r
tic
le
h
i
st
o
r
y:
Rec
e
i
v
ed
Ju
l
19
,
20
19
Re
vise
d De
c 2,
2
0
1
9
Acc
e
pt
e
d
Fe
b 4, 2
0
2
0
T
o
de
si
gn
a
n
d
im
p
l
e
m
e
n
ta
ti
on
of v
a
ria
b
le a
nd c
o
n
s
ta
nt wi
th
n
o
loa
d
fo
r
in
du
cti
o
n
mo
to
r
(
I
M
)
th
at is
th
e
g
o
al i
n
th
is
w
o
r
k
. Th
is
p
a
p
e
r
w
a
s
i
n
cl
ud
i
n
g
t
h
ree parts, f
i
rs
t
t
h
e s
i
mul
a
t
i
on
mode
l
wit
h
no
load
for
IM
,
Second the
simulation model
wi
th c
o
nst
a
nt
load
fo
r
IM, Thir
d the
simul
a
ti
on
model
wit
h
variab
le load
fo
r IM
. In
a
d
ditio
n
,
th
is wo
rk in
clud
es co
mp
a
r
a
tiv
e
b
e
tween
t
w
o di
fferent co
ntr
o
l
l
ers (PI
and fuzz
y
lo
gi
c c
ontro
l (FL
C
)
.
The si
mul
a
tion
resu
lts c
l
early
th
e i
m
plemen
tat
i
o
n
of v
a
riab
le
an
d
con
s
tan
t
with
n
o
load
for
IM.
The
simulati
on
respon
s
e
o
f
th
e s
y
s
t
e
m
ac
h
i
ev
es
b
e
tter
re
su
lts
wh
en
cho
o
s
i
n
g
to
u
s
e
ty
pe
fuz
z
y-P
I
con
t
roller
te
ch
nique
co
mp
a
r
is
on w
ith
c
o
nv
e
n
ti
on
a
l
PI c
o
n
t
ro
lle
r a
nd
im
pro
v
e t
h
e
p
e
rfo
r
m
a
nc
e of
t
h
e syste
m
at
differen
t
op
erat
io
n
co
nd
itio
n
s.
Ke
yw
ords:
FLC
IM
PI
Tr
an
sfer
fun
c
tio
n
Th
is
is a
n
o
p
en
acces
s a
r
ticle
un
d
e
r the
C
C
B
Y
-SA
licens
e
.
Corres
p
o
n
din
g
A
u
t
h
or:
Sa
la
m
Wa
le
y Sh
neen
,
Energ
y
a
n
d
Re
ne
wa
bl
e E
n
erg
i
es Tec
hnol
o
g
y
C
e
nt
er,
Uni
v
ersi
t
y
o
f
Tech
nol
og
y,
52
In
dust
r
y
st
re
et
, Ba
g
hda
d, Ira
q
.
Ema
i
l
:
s
a
la
m_w
a
le
y7
3@y
a
ho
o.c
o
m
1.
IN
TR
O
DUCTION
The
3-ph
ase
IM
is
impo
rtan
t
o
f
e
l
e
c
trical
ma
ch
ines
th
at
wide
l
y
use
d
i
n
d
i
ffe
ren
t
in
du
stri
al a
ppl
ica
t
io
ns
[
1
].
Th
ey
p
e
rfor
m
t
h
eir
cha
r
ac
ter
i
stic
fo
r dec
a
des
and
adap
t them
s
e
l
v
es
at
different
operat
e
condi
ti
ons
[2],
such as
oil
refin
e
r
i
es,
ele
c
tr
ic
p
o
w
e
r
s
t
at
io
n
s
, and
f
a
c
t
ories
becaus
e
th
e
i
r
si
mple
in
d
e
s
i
g
n
,
h
i
g
h
efficien
cy,
g
o
o
d
self-st
a
rtin
g,
g
o
o
d
po
wer fa
cto
r
,
low
manufa
c
tur
i
ng co
sts re
lat
i
v
e
ly,
an
d
smal
l
va
lue of
inert
i
a [3]. The
disad
v
antag
e
s
of IM
h
a
ve
represented in
n
o
n-l
i
near multivariable i
n
additi
o
n
to complex of math
emat
ical model, so IM
i
n
he
rentl
y
unable t
o
operate
at d
i
ffer
e
nt
rang
e of
s
p
eed
,
the
r
efore
to
s
o
lv
e
th
ese p
r
ob
lems
i
s
u
s
ed
mu
lt
i
typ
e
s
of
co
ntro
llers s
u
ch
as P
I
con
t
ro
llers.
Very
comp
r
e
hen
s
iv
e re
marks
era
th
at g
i
v
e
s
a
ver
y
effi
c
i
ent
meth
od
to
sev
e
ra
l
ma
n
i
pu
lat
e
p
r
ob
le
ms
in
sid
e
the
real w
o
rl
d
.
Th
ese
con
t
r
o
ll
er
s
are
s
i
mp
l
i
c
i
ty
,
r
e
li
abil
it
y.
R
o
bu
s
t
o
f
t
h
e
sy
stem
s and
tun
e
d
p
r
o
p
erly
th
er
efore
th
ey b
eco
m
e
s
im
po
rtan
t
in
in
du
st
r
i
al
app
l
ica
t
io
ns
.
Ho
we
v
e
r,
PI c
ontro
ll
er c
a
n
't o
ffe
r th
e
go
od
c
ontro
l o
v
e
r
all perfo
rm
an
ce
in
run
n
ing
con
d
ition
[4].
Th
e au
th
ors
of
[5-7
] ar
e pr
es
ent
hy
brid
co
ntro
l
s
y
s
t
em b
y
u
s
ing
F
L
C an
d
co
nv
en
tion
al
c
o
n
t
rollers
by
us
in
g
ma
the
m
ati
c
a
l
o
f
IM
an
d
th
ese
studies
dea
l
s
with the
stru
cture
of m
o
de
l t
o
ob
ta
in
h
i
g
h
-p
e
rfo
rm
anc
e
t
r
a
c
k
i
n
g
of IM.
In [8] propos
es speed con
t
rol of
IM
by
us
in
g
conv
en
tio
n
al
te
ch
niq
u
e
s
(P
I and
P
I
D)
co
n
t
rolle
r
s
with
v
ector
control
te
ch
niqu
e
a
t
fu
ll lo
a
d
cond
it
io
n an
d
dis
c
us
s
simulatio
n
r
e
su
lts
w
i
th
th
es
e
con
t
ro
llers
an
d
wi
tho
u
t an
y
co
n
t
roller
.
Th
e
study
[9
] p
r
o
p
o
s
es
sy
stem t
o
co
ntro
l on
s
p
e
e
d
of
IM
by
u
s
ing
fee
d
back
clos
e
lo
o
p
s
y
s
t
em
with
fu
zzy-P
ID
co
n
t
ro
ller
.
This
sy
stem h
a
s
o
t
her
ad
van
t
ages
tha
t
comb
i
n
atio
n
between
3-ph
ase
s
t
ep-u
p tr
ans
f
ormer and
3-p
h
ase
d
r
iv
e
to
ab
le
c
o
ntrol any
3-ph
as
e ma
chin
e o
n
a
1
-
ph
a
s
e su
pp
ly
,
als
o
stud
y
[1
0] ref
e
rs
s
p
eed
con
t
ro
l of
IM
by us
in
g MA
TLAB
To
ol
box
a
n
d
Sim
u
l
i
n
k
m
o
de
l
t
o
d
e
v
e
l
o
p
e
d
t
h
i
s
m
o
de
l by
u
s
i
ng
F
L
C wh
ich
avai
lab
l
e
cons
tan
t
sp
eed
a
t
varies
loa
d
s con
d
i
tio
ns
. M
a
n
y
stud
ies
h
a
d
prop
os
ed dif
f
ere
n
t
app
r
oa
ch
to
res
o
lve
th
e
d
o
w
n
s
i
de
o
f
(P
I
con
t
ro
ller)
.
Th
e
u
s
ag
e
o
f
ar
t
i
ficial
in
te
l
l
ig
en
ce te
chniqu
es (A
IT) s
o
on
e
o
f
th
es
e techn
i
qu
es
a
r
e
v
e
ry
i
m
po
rta
n
t
for
con
t
rol
l
i
ng n
o
n
-
line
a
r
sy
ste
m
wi
th
ou
t
in
d
e
p
e
nde
nt o
n
be
ha
v
i
o
r
s of i
n
te
rn
al
sy
st
em
suc
h
a
s
(FLC) t
h
at
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
Desi
g
n
a
n
d
i
m
pl
eme
n
tat
i
o
n o
f
v
a
ria
b
l
e
an
d con
s
t
a
nt l
o
ad f
o
r
i
n
d
u
ct
io
n
m
o
tor
(
Sal
am
W
a
l
e
y
S
h
n
ee
n
)
7
63
p
e
rmits d
e
s
i
gn
er
s to add
r
ess effi
c
a
c
i
ou
sly difficu
lt clos
ed
lo
op
s
y
s
t
em in
ord
e
r to
redu
c
e
tim
e
as
well as co
sts, su
pp
orts
no
n-l
i
n
e
a
r
syste
m
wh
ic
h
c
a
n
b
e
usin
g i
n
m
o
t
o
r c
o
n
t
ro
l fiel
ds [1
1].
PI c
o
nt
ro
l
l
e
r
c
a
n
b
e
t
une
d
the
ga
i
n
by
(AIT), (FL
C
)
an
d on
lin
e
tun
e
d
with chan
g
i
ng c
o
n
d
itions
o
f
s
y
s
t
em
[1
2],
th
e
co
n
t
rolle
r
g
a
in
s
are
th
e b
e
st
adv
a
nt
a
g
e o
f
thes
e
co
ntr
o
ller
s
b
ecaus
e
wh
ich
a
l
lo
w
u
s
ing
the
h
u
man
ex
p
e
ri
e
n
c
e
fo
r
th
e gen
e
rat
i
o
n
of th
e tuning
law [13
]
. This s
t
u
d
y
p
r
ov
id
e
s
fu
zzy-P
I
co
ntroller
that
F
L
C adjus
t
p
a
r
a
me
ters
of P
I
a
n
d co
mp
arativ
e
w
i
th
co
nv
entio
n
a
l P
I
co
ntrol
l
e
r
at
differen
t
o
p
erat
io
n
c
o
n
d
i
t
i
o
ns in
clude
(n
o
lo
a
d
,
c
o
n
s
ta
n
t
a
n
d
va
ri
a
b
le
loa
d
s) o
f
IM
in
ord
e
r
to
i
m
prove
o
p
e
r
a
t
i
on of
t
h
i
s
m
o
to
r a
n
d
obt
a
i
n
hi
gh
pe
rfo
rm
a
n
ce
at re
a
l
tim
e.
2.
MA
THEMA
T
I
C
A
L
MOD
EL O
F
IM
:-
T
h
e e
q
ui
v
a
l
e
n
t
circ
u
it of IM for (q
a
n
d
d
wi
nd
in
g
c
i
rc
u
i
t) whi
c
h
can
b
e
use
d
t
o
a
n
a
l
y
s
i
s
th
e m
ode
l of
IM
sho
w
s
in F
i
gu
re
1,
wh
il
e
po
wer
circu
i
t
o
f
th
e
3-p
h
ase
IM
sh
ows
in F
i
gu
re
2 [1
4
,
1
5
].
(a)
(
b
)
F
i
gu
r
e
1.
Eq
ui
val
e
nt
ci
rc
ui
t
o
f
I
M
F
i
gu
re 2.
P
o
we
r
c
i
r
c
ui
t
o
f
3-
p
h
ase I
M
Dynam
i
c
model
of IM can
repr
esent
by writi
ng deferenti
a
l
equa
t
i
on for
el
ectri
cal
and
mech
an
i
cal
quant
ities (voltage and
to
rqu
e
)
a
n
d
c
a
n
sho
w
n in
m
a
th
em
a
t
ic
al
m
ode
l o
f
IM
i
n
clu
d
e t
h
e
e
q
ua
tio
ns be
l
o
w
[3]
.
A-El
ec
tr
ic
al s
y
stem equa
ti
o
n
s
(1
)
(2
)
He
re
,
,
0
1
10
B
-
Flu
x
l
i
n
k
a
g
e
-c
ur
ren
t rel
a
t
i
o
n
s
Fo
r d
-
ax
is:
(3
)
(4
)
Fo
r q
ax
is:
(5
)
(6
)
Wh
er
e
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-86
94
In
t
J
Po
w
Ele
c
&
Dri
Sy
st,
Vol.
1
1
,
No
. 2
,
Jun
e
2
020
:762
–
77
3
76
4
C-
Mechan
ical syst
em equation
s:-
2
(7
)
Wh
er
e
,
∗
∗
(8
)
(9
)
3.
Ind
u
ct
io
n m
o
to
r a
nd c
o
n
t
ro
l
l
er
T
h
i
s
pa
p
e
r
p
r
opose
s
op
e
r
a
t
io
n
of IM
a
t
d
i
ffe
ren
t
c
o
n
d
iti
on
s su
c
h
a
s
(no
l
o
a
d
,
c
o
n
s
ta
n
t
a
n
d
v
a
ria
b
le
loa
d
s)
w
i
tho
u
t
co
ntrol
l
er and
by
u
s
ing
eac
h
of P
I
and
f
u
zzy-P
I co
n
t
roll
er to
dev
e
lop
p
e
rforman
c
e
of
I
M
at d
i
ffer
e
nt o
p
erat
io
n
co
nd
it
ion
s
,
th
e f
o
l
l
o
w
i
ng
st
eps
i
n
th
is
p
a
p
e
r
pr
es
en
t
in
th
e f
l
o
w
c
h
ar
t w
h
i
c
h s
h
o
w
s
in
F
i
g
u
r
e
3
.
Fi
gu
re
3.
Fl
o
w
cha
r
t f
o
r
pe
rf
o
r
ma
nce
of
mo
de
l
3
.
1
.
S
i
m
u
l
a
t
i
o
n
o
f
in
du
c
t
io
n mo
t
o
r
T
h
e
3
-
pha
se
volt
a
g
e
s
a
n
d fre
q
u
e
nc
y
a
r
e
i
n
p
u
t
s
of a
sq
u
i
rre
l
ca
ge
IM, wh
il
e
th
e 3
-
ph
a
s
e c
u
rre
nts,
t
o
rqu
e
a
nd
rot
o
r spe
e
d
a
r
e
o
u
tp
ut
s
o
f
IM
m
o
d
e
l [1
4].
Sim
u
l
i
nk m
o
del
of IM sho
w
s in
Fi
gu
re 4.
Fi
gu
re
4.
Si
m
u
li
nk mo
de
l
of I
M
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
Desi
g
n
a
n
d
i
m
pl
eme
n
tat
i
o
n o
f
v
a
ria
b
l
e
an
d con
s
t
a
nt l
o
ad f
o
r
i
n
d
u
ct
io
n
m
o
tor
(
Sal
am
W
a
l
e
y
S
h
n
ee
n
)
7
65
The
para
me
te
r
s
o
f
t
h
e
I
M
p
r
o
pos
e
i
n
t
h
i
s
pa
per
a
s
s
h
ow
n i
n
Ta
ble
1.
T
a
bl
e 1.
pa
r
a
m
e
t
e
r
s
o
f
I
M
p
a
r
a
m
et
er
s
v
a
l
u
es
P (
AV)
3*7
4
6
V (
line-
line)
220
(
r
.
m.s
)
f (
H
z)
60
R
s
(
Ω
)
0.
4
35
L
s
(H) 2*2
e
-
3
R
r
(
Ω
) 0.
8
16
L
r
(H)
2
e
-3
L
m
(H
) 69.31e
-
3
J (kg.
m^
2)
0.
0
89
F
c
0
Pole
pai
r
2
Where:
P=
po
we
r
,
V =
V
o
lta
g
e
, f
=
fre
q
u
ency
,
R
s
= stator resist
ance,
L
s
= s
t
ator
ind
u
c
t
a
n
ce,
R
r
=
r
o
t
o
r re
s
i
s
t
a
n
ce
,
L
r
=
r
o
tor
ind
u
ctan
ce
,
L
m
= mu
tu
al in
du
cta
n
ce, J= iner
tia
,
F
c
= fri
ction
f
acto
r
.
3
.
2
.
P
I
con
t
ro
ll
er
P
I
co
ntroller
can
p
r
op
ose high
p
e
rformanc
e
on
ly
wh
en th
e
co
n
t
roller
s
y
s
t
em op
era
t
es at op
e
r
at
in
g
po
in
t, so
th
e
P
I
co
ntro
ller
do
es no
t freq
u
e
ntly
pro
p
er
ly
tu
ne
at op
era
t
in
g
con
d
ition
ch
ang
e
s
a
n
d var
i
ation
s
of
p
a
ram
e
ters
,
in o
r
der
to
de
v
e
lo
p a
u
t
o
m
a
tic
t
u
ni
ng of PI co
n
t
ro
ll
er p
a
ra
m
e
te
rs [13
]
.
PI c
ontro
l
l
er d
r
iv
e
s
pla
n
t
to c
ontro
l
wei
g
h
t
e
d
su
m
m
a
t
i
on o
f
erro
r
and
in
teg
r
atio
n
of
v
a
lu
es
. T
h
e co
nv
ention
al
o
r
lin
ear
P
I
con
t
r
o
ller
h
a
s d
e
scrib
e
d
in
10
.
(1
0)
Wh
e
r
e Kp is
t
h
e
p
r
o
p
o
r
ti
on
al ga
in
a
nd
Ki
i
s
i
n
te
g
r
a
l
ga
i
n
o
f
co
ntr
o
ller
w
h
ile
erro
r
sign
a
l
e(
t) i
s
the di
ffe
re
nc
e
bet
w
ee
n
th
e
reference
r(t
)
an
d the process
output c(
t
)
[8]
.
(1
1)
Tab
l
e 2. in
dicat
e
s
effect
o
f
p
a
ra
m
e
t
e
rs
for PI on
co
ntroller
s
y
s
t
e
m
, wher
eas
Figure 5 r
e
fers t
o
block
di
agram of
this controller.
Ta
ble
2.
e
ffe
ct
of
pa
ra
met
e
rs
of
P
I
p
ar
a
m
et
e
r
s t
rise
t
ov
er sh
o
o
t
t
tu
nin
g
e
rr
o
r
k
p
D
e
c
.
I
n
cr
.
S
m
al
l
cha
nge
D
e
c
.
k
i
D
e
c
.
I
n
cr
.
I
n
c
r
.
el
im
inat
e
Whe
r
e:
D
e
c.
= d
ecr
es
e ,
In
c
r
=
in
cre
a
s
e
,
F
i
g
u
r
e
6
s
h
ows
P
I
-
c
ont
rol
l
e
r
st
ruc
t
ur
e
(k
p,
k
i
)
a
r
e i
n
p
u
t
of
P
I
-
c
o
n
t
r
ol
le
r
a
n
d
(
u
)
i
s
out
put
[
1
6
,
17
].
F
i
gu
re
5.
S
i
m
u
l
i
nk a
n
d
bl
oc
k
di
ag
ra
m
of
P
I
cont
rol
l
e
r
Fi
gu
re
6.
The
st
ruc
t
u
r
e of
P
I
c
ont
r
o
ll
e
r
3.
3.F
u
zzy
-PI c
o
ntrol
l
e
r
The
(F
LC)
i
s
o
n
e
of
best
a
p
pli
c
at
ions
whe
r
e
t
h
e
f
u
zz
y
t
h
e
o
r
y
c
a
n
a
ppl
y su
c
cessf
ul
l
y
, s
o
i
t
ca
n
s
o
l
v
e
p
r
o
b
l
em
s in
no
n
lin
e
a
r co
n
t
ro
l sy
st
em
bu
t
t
h
e sys
t
em
mod
e
l is co
mp
le
x
t
o
bu
ild
th
er
e
f
or
e kno
w
l
ed
ge
o
f
t
h
e
pr
o
c
ess
is i
m
p
o
r
t
a
n
t t
o
o
b
t
a
in t
h
e
fuz
z
y
r
u
le
s. (
F
LC)
c
o
n
s
i
s
t
s
of
3 st
e
p
s:
1
)
f
u
zzi
fi
ca
t
i
on
2
)
e
v
a
l
ua
ti
on
of
co
n
t
ro
l
ru
le
s
3)
d
e
fu
zz
if
ic
at
io
n [18
]
. (F
L
C
)
h
a
v
e
th
e ad
va
n
t
a
g
es
mo
r
e
t
h
a
n
th
e c
l
a
s
sica
l c
o
n
t
r
o
l
.
Th
ey
are
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
2
,
Jun
e
2
020
:762
– 77
3
76
6
i
n
cl
udi
ng
w
i
d
e
ra
nge
of
o
p
e
rat
i
n
g
ca
se
s.
C
h
ea
pe
r t
o
i
m
pro
v
e a
n
d
ea
si
e
r
i
n
n
e
u
r
al
l
a
ng
ua
ge
e
x
pre
ssi
ons
.
M
a
md
an
i
is typ
e
o
f
(FLC
)
c
a
n
u
s
e
in t
w
o
sy
st
em
s.
Th
e fi
rst
is
mu
l
tip
le
i
n
p
u
t
s
mu
lt
ip
le
ou
t
p
u
t
s
wh
i
l
e
th
e
o
t
h
e
r
i
s
mu
ltip
le
in
pu
t
and
si
g
n
a
l ou
t
p
u
t
syste
m
.
Th
e i
n
tere
st o
f
(FLC
)
i
s
ad
op
te
d
o
p
e
rat
o
rs
e
x
p
e
r
i
m
e
n
t
o
r
k
now
le
dg
e
of
t
h
e sy
st
em
i
n
a
h
e
uri
s
tic
w
a
y
and in d
e
s
i
gn
pr
o
c
e
s
s, th
e
t
h
re
sh
o
l
d
s
of fu
z
z
y li
ngu
al
v
a
r
i
a
b
le
s
are
oft
e
n
sel
e
c
t
i
on
ra
nd
oml
y
so a
n
i
n
co
rrec
t c
ont
roll
e
r
val
u
es
rea
c
h
t
o
u
n
st
a
b
l
e
mo
de,
an
o
p
p
o
si
t
e
con
s
eq
ue
n
c
e, b
r
e
a
k
d
o
w
n
a
n
d sepa
rat
i
o
n [19
,
2
0
].
F
i
gu
re 7
re
fers t
o
bl
oc
k di
ag
ram of (F
L
C
) [2
1].
F
i
gu
re
7. Bl
oc
k di
a
g
ram of (F
LC)
The
mai
n
g
o
al
es of
(fuz
zy
-P
I)
co
nt
rol
l
e
r
a
r
e
to de
crea
se
cont
rol
pl
a
n
ner
com
p
li
ca
t
i
on a
nd
de
ve
lo
p
dy
namic
a
nd st
at
i
c
p
e
rforma
nces o
f
the
syst
em. E
s
se
n
t
i
a
l
l
y
for syst
ems
de
si
gni
ng
a
r
e com
p
l
e
x
.
Th
e
para
met
e
rs a
r
e
di
ffi
c
u
l
t
t
o
ob
t
a
i
n
in t
h
is st
a
t
e
.
The (PI)
c
ont
rol
l
e
r
i
s
desi
gne
d to
set
pa
ramet
e
rs K
p
a
nd Ki
orderl
y t
o
mee
t
suit
abl
e
req
u
i
r
ed c
h
ara
c
t
e
ri
st
ic
s
i
n
c
l
ude
ri
se
ti
me,
ma
xim
u
m va
lue
of
o
v
ers
h
oot
, st
ea
d
y
st
at
e
error a
n
d
se
tt
l
i
ng
t
i
m
e. T
h
e
r
e
f
o
r
e,
(FLC)
co
ntr
o
l
si
g
n
al
ac
cordi
n
g
t
o
the
int
e
g
r
al
an
d
p
r
op
o
r
t
i
onal
ac
ti
ons
of
the P
I
-
c
ontroll
er [13]
.
(F
LC)
has
(2) i
n
puts
ar
e
repr
es
en
t
e
d
er
ro
r e
(
k
)
an
d
c
h
ang
e
of
e
r
ro
r
Δ
e(k
)
.
e(
k)
=
r
(
k)
−
y(
k),
Δ
e(
k) =e(
k
)
−
e(
k
−
1)
wh
e
r
e
(r )
ind
i
ca
te
d
to
a
p
p
lied
se
t
po
in
t
i
n
pu
t
a
n
d
(y)
d
e
no
te
to
p
l
a
n
t o
u
tp
u
t
,
(
k
)
ind
i
c
a
te
p
r
e
s
en
t
sta
t
e w
h
ere
a
s
(
k
−
1
)
i
s
pre
v
i
o
u
s
c
a
se
o
f
t
h
i
s
s
y
st
em,
whil
e
o
u
t
p
ut
of (FLC
) is
gra
d
ua
l c
h
a
nge
i
n
va
lue
o
f
Δ
e(k
)
[2
2],
F
i
gu
re 8 i
nduc
at
es t
o
blo
c
k di
ag
ra
m
of (
f
u
zzy
-P
I )
c
o
n
t
roll
er [23]
.
Fi
gu
re
8.
B
l
oc
k di
ag
ra
m
of (fuzz
y
–
P
I) c
ont
rol
l
e
r
4.
S
I
MUL
I
NK MOD
EL
AND
S
I
MUL
A
TIO
N
R
E
SU
LT
S
4.1.Si
m
u
li
n
k
m
o
de
l
F
i
gure 9
S
h
o
w
s simul
a
t
i
on
mode
l
of IM
wi
t
h
o
u
t
co
nt
rol
l
e
r
at
va
ri
abl
e
c
o
ndit
i
o
n
s o
f
l
o
a
d
(
no l
o
a
d
,
con
s
t
a
nt
a
nd v
a
ria
b
le
l
o
a
d
) as
foll
ows
.
Fi
gu
re
9. Si
m
u
li
nk M
odel
of
I
.
M wi
t
h
o
u
t Co
nt
rol
l
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
De
si
g
n
and
i
m
ple
m
e
n
t
a
t
i
o
n
of
vari
a
b
l
e
an
d c
o
n
s
t
a
nt
l
o
ad
f
o
r
i
n
d
u
ct
i
on
m
o
t
o
r (Sal
am
W
a
l
e
y
S
h
n
e
e
n
)
7
67
S
i
mul
a
t
i
o
n
M
o
de
l
of I.M
wi
t
h
P
I
C
ont
rol
l
e
r
at
va
ri
abl
e
l
o
a
d
s
(n
o
l
o
a
d
,
c
o
nsta
nt a
nd
va
ri
abl
e
l
o
a
d
s
)
a
s
sho
w
n
i
n
Fig
u
r
e
10
. In
ad
d
ition
,
S
i
mu
l
i
n
k
M
o
d
e
l
of
I.M
w
ith
PI
Con
t
ro
lle
r
a
t
v
a
r
i
ab
l
e
lo
ad
s
(
no l
o
ad,
con
s
t
a
nt
a
nd v
a
ria
b
le
l
o
a
d
) as
sh
ow
n i
n
Fi
g
u
r
e
11
.
Fi
gu
re
1
0
.
Si
m
u
li
nk
m
odel
of I.
M wi
t
h
P
I
- C
ont
rol
l
er
Fi
gu
re 1
1
. Si
m
u
l
i
n
k
m
odel
o
f
I.
M wi
t
h
(f
uz
z
y
-P
I)
C
ont
r
o
l
l
e
r
4.2.Si
m
u
lati
o
n
r
e
sul
t
s
The
simul
a
t
i
o
n
res
u
lt
s i
n
cl
u
d
e,
at
no
loa
d
, at
c
onst
a
nt
l
o
ad
wi
th
PI c
ont
rol
l
e
r
a
n
d
wi
th fuz
z
y
-P
I
(F
LP
I)
c
ont
r
o
l
l
e
r
.
4.2.
1.T
h
e
si
m
u
l
a
ti
on re
su
l
t
s
a
t
n
o
l
o
a
d
i
n
c
l
ud
e:
The
si
m
u
la
ti
on
re
sul
t
s
di
scu
ss th
ree
di
ffe
rent
sta
t
e
s
, t
h
e
fi
rst i
n
cl
u
d
es
ope
ra
ti
o
n
o
f
mot
o
r wi
t
h
out
any
c
ont
rol
l
e
r
whi
l
e
t
w
o
othe
r st
at
es
di
sc
uss
t
h
e
pe
rfo
r
ma
n
c
e wi
t
h
t
w
o
t
e
c
h
ni
que
s
ha
d
r
e
pre
s
e
n
te
d
i
n
P
I
an
d
f
u
zzy
-PI con
t
ro
l
l
e
r
.
Fir
s
t
,
simu
la
tion
r
e
s
u
lts
w
i
t
hou
t c
o
n
t
ro
l at
no
l
o
a
d
and
t
h
e simu
lat
i
on
r
e
sp
on
se
of
th
e sy
ste
m
a
t
no
l
o
ad wi
t
h
out
a
n
y
co
nt
rol
l
e
r
s c
a
n be
s
h
ow
i
n
the
F
i
gu
re 1
2
.
Se
con
d
p
a
rt
inc
l
u
d
e
s s
i
mu
l
a
ti
o
n
r
e
su
lts w
ith
PI c
o
n
t
ro
ll
er
at
n
o
lo
ad
;
Fi
g
u
re
1
)
s
how
s t
h
e s
i
mu
la
ti
on
r
e
s
ponse of
the
system.
Thi
r
d
part
di
scuss t
h
e res
p
o
n
se
of t
h
e s
y
st
em
b
y
usi
n
g
fuzz
y
-
PI (FL
P
I) c
ont
rol
l
e
r
a
t
no l
o
ad
con
d
i
t
i
on
,
t
h
e si
mula
t
i
on
res
u
l
t
s of thi
s
pa
rt
c
a
n
be
s
h
ow
n
i
n
F
i
gure
14.
(a
)
(b
)
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6
94
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n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
2
,
Jun
e
2
020
:762
– 77
3
76
8
(c
)
(d
)
F
i
gure
12. S
i
mul
a
t
i
on re
s
pons
e
o
f
t
h
e
sy
st
em
at
n
o
l
o
a
d
w
i
t
h
o
u
t
c
ont
rol
l
e
r,
(a
) Si
m
u
la
ti
o
n
resp
o
n
se of
t
h
e
Vs
&
Es,
(b) Si
m
u
la
t
i
on res
p
on
se
o
f
i
/
p & o/
p, (c)
S
i
mul
a
t
i
o
n
re
sponse
o
f
Te
, (d
)
S
i
m
u
l
a
t
i
o
n
resp
o
n
se
of
o/
p
(a)
(b
)
(c)
(d
)
Fi
g
u
r
e
13
. Si
mu
la
ti
o
n
r
e
sp
on
se
of
th
e syst
em a
t
no
l
o
a
d
w
i
t
h
P
I
c
o
n
t
ro
l
l
e
r
, (
a
)
Si
mu
la
ti
o
n
r
e
sp
on
se of
the
V
s
& Es,
(
b
)
S
i
m
u
l
a
t
i
o
n
re
sp
on
se
o
f
i
/
p
&
o/
p,
(c
) S
i
m
u
l
a
t
i
on
re
spo
n
se
o
f
T
e
,
(d)
Si
m
u
la
ti
on
r
e
sp
onse
o
f
o/
p
(a)
(
b
)
(c)
(d)
Fi
g
u
r
e
14
. Si
mu
la
ti
o
n
r
e
sp
on
se
of
th
e syst
em a
t
no
l
o
a
d
w
i
t
h
F
L
P
I
c
o
n
t
ro
l
l
er
,
(
a
)
Sim
u
la
t
i
o
n
re
sp
on
s
e
of th
e
Vs & Es, (b
) Si
mu
l
a
ti
on
re
sp
o
n
se
of
i
/
p &
o/
p,
(c) Si
m
u
l
a
t
i
on
res
p
ons
e
of Te
, (d
) Si
m
u
la
ti
on res
p
o
n
se
o
f
o/
p
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
De
si
g
n
and
i
m
ple
m
e
n
t
a
t
i
o
n
of
vari
a
b
l
e
an
d c
o
n
s
t
a
nt
l
o
ad
f
o
r
i
n
d
u
ct
i
on
m
o
t
o
r (Sal
am
W
a
l
e
y
S
h
n
e
e
n
)
7
69
4.2.
2.
T
h
e S
i
m
u
l
a
ti
on
re
s
u
l
t
s
a
t
c
o
n
s
tan
t
l
o
ad
in
cl
u
d
e
:
F
i
rst,
si
m
u
la
ti
o
n
res
u
l
t
s wi
th
o
u
t
c
ont
rol at
co
nsta
nt l
o
a
d
a
n
d
t
h
e
simul
a
t
i
on
re
sp
onse
of th
e
sy
st
em
a
t
no
l
o
a
d
wi
t
hou
t
an
y c
ont
rol
l
e
r
s
c
a
n
be
sho
w
i
n
t
h
e
F
i
g
u
re
15
.
S
e
c
o
nd
par
t
i
n
cl
u
d
es si
m
u
la
t
i
on re
sul
t
s
wi
t
h
P
I
cont
rol
l
e
r at
c
onst
a
nt
l
o
ad;
Fi
gu
re
1
6
sho
w
s t
h
e
sim
u
l
a
t
i
on
re
s
pon
se
o
f
t
h
e
syste
m
.
Thi
r
d
pa
rt
di
sc
uss t
h
e
r
e
s
pon
se of the s
y
ste
m
by
u
s
i
n
g fu
zzy
-
P
I (FLP
I)
c
o
n
t
ro
lle
r
at con
s
ta
n
t
l
o
a
d
co
nd
iti
o
n
,
th
e si
mu
la
tio
n
re
su
lt
s
of thi
s
pa
rt
ca
n
be
sh
ow
n
i
n
F
i
g
u
re
17.
(a)
(b)
(
c
)
(d)
F
i
g
u
re
15. S
i
mul
a
t
i
on re
spo
n
s
e
o
f
the
sy
st
em
at
co
nsta
nt
l
o
a
d
wi
t
h
o
u
t
c
ont
rol
l
er,
(a
) S
i
mul
a
t
i
o
n re
spo
n
se
of the
Vs
& Es
,
(b
) S
i
mul
a
t
i
on
res
p
onse
of i
/
p
& o
/
p, (c)
Si
mula
t
i
on
res
p
ons
e
of Te
,
(d
) Si
mul
a
t
i
o
n resp
o
n
se
of o/
p
(a)
(b)
(c)
(d)
F
i
g
u
r
e
16
.
S
i
mu
l
a
ti
o
n
r
e
sp
on
se
of
th
e sys
t
em a
t
con
s
ta
n
t
lo
a
d
w
ith
PI
c
o
n
t
ro
lle
r,
(a
) S
i
mul
a
t
i
o
n re
spo
n
se
of the
Vs
& Es
,
(b
) S
i
mul
a
t
i
on
res
p
onse
of i
/
p
& o
/
p, (c)
Si
mula
t
i
on
res
p
ons
e
of Te
,
(d
) Si
mul
a
t
i
o
n resp
o
n
se
of o/
p
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
2
,
Jun
e
2
020
:762
– 77
3
77
0
(a)
(b)
(c)
(d)
F
i
gu
re 1
7
. S
i
m
u
l
a
t
i
o
n
re
spo
n
s
e
o
f
the
sy
ste
m
at
c
o
nsta
nt l
o
a
d
wi
t
h
F
L
PI
co
nt
rol
l
e
r, (a)
Si
mula
ti
on
re
sp
o
n
se
of
t
h
e
Vs &
E
s
,
(
b
)
S
i
m
u
l
a
t
i
o
n
re
sp
o
n
se
of i/
p
&
o/
p, (c
) Si
mul
a
t
i
on
re
sp
o
n
se
of Te,
(d)
S
i
mul
a
t
i
on re
spo
n
se
of o/
p
4.2.
3.
T
h
e S
i
m
u
l
a
ti
on
re
s
u
l
t
s
a
t
vari
a
bl
e
l
o
ad
in
cl
u
d
e
:
F
i
rst, si
m
u
la
t
i
o
n
resul
t
s
wi
t
h
out
co
nt
rol
a
t
va
ria
b
le
l
o
a
d
a
n
d
the
si
mul
a
ti
on
res
p
o
n
se
of
t
h
e syste
m
at
no
l
o
a
d
wi
t
hou
t
an
y c
ont
rol
l
e
r
s
c
a
n
be
sho
w
i
n
t
h
e
F
i
g
u
re
18
.
S
e
c
o
nd
par
t
i
n
cl
u
d
es si
m
u
la
t
i
on re
sul
t
s
wi
t
h
P
I
cont
rol
l
e
r at
v
a
ri
abl
e
loa
d
; fi
gu
re
(1
9) sho
w
s t
h
e
si
mula
t
i
on res
p
o
n
se o
f
t
h
e syst
em
.
Thi
r
d pa
rt
di
sc
uss
t
h
e
sy
st
em
by
using
fu
z
z
y
-
P
I
(
F
LP
I
)
con
t
ro
ll
er
a
t
v
a
r
i
a
b
le
l
o
ad
co
nd
iti
o
n
, the
sim
u
la
tion
r
e
su
lts
o
f
th
i
s
p
a
rt
c
a
n
be sh
ow
n i
n
F
i
gu
re
2
0
.
(a)
(b
)
(c)
(d
)
Fi
gu
re
1
8
.
Si
m
u
la
ti
on
res
p
o
n
s
e
o
f
t
h
e
syst
em
at
va
ria
b
l
e
l
o
a
d
wi
tho
u
t
c
ont
r
o
ll
er,
(a
) S
i
mul
a
t
i
o
n re
spo
n
se
of the
Vs
& Es
,
(b
) S
i
mul
a
t
i
on
res
p
onse
of i
/
p
& o
/
p, (c)
Si
mula
t
i
on
res
p
ons
e
of Te
,
(d
) Si
mul
a
t
i
o
n resp
o
n
se
of o/
p
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
De
si
g
n
and
i
m
ple
m
e
n
t
a
t
i
o
n
of
vari
a
b
l
e
an
d c
o
n
s
t
a
nt
l
o
ad
f
o
r
i
n
d
u
ct
i
on
m
o
t
o
r (Sal
am
W
a
l
e
y
S
h
n
e
e
n
)
7
71
(a)
(b
)
(c)
(d
)
Fig
u
r
e
19
.
Simu
la
tio
n
re
sp
on
se
of
th
e
syste
m
at
v
a
r
i
ab
le
lo
ad
wi
th
PI
con
t
ro
ll
er
,
(a
) S
i
mul
a
t
i
o
n re
spo
n
se
of the
Vs
& Es
,
(b
) S
i
mul
a
t
i
on
res
p
onse
of i
/
p
& o
/
p, (c)
Si
mula
t
i
on
res
p
ons
e
of Te
,
(d
) Si
mul
a
t
i
o
n resp
o
n
se
of o/
p
Th
is
p
a
r
t
in
clu
d
e
s
t
h
e
sim
u
latio
n r
e
su
lt
s
o
f
th
e
sy
s
t
em
b
y
us
in
g fu
z
z
y
-
PI
c
o
n
t
ro
l
l
e
r
Figu
re
20 s
how
s
ea
ch of
FIS, m
e
mbe
r
shi
p
s, ru
l
e
s,
sur
f
a
ce vie
w
ers r
e
spectively
.
(a)
(b)
(c)
(d)
(e)
(f
)
Evaluation Warning : The document was created with Spire.PDF for Python.