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.
11, N
o.
1, Mar
ch 20
20,
p
p.
263~
2
7
4
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v11
.
i
1.pp
2
63-
27
4
263
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
j
p
eds.i
a
esco
re
.com
Comparativ
e Study of two contr
ol strate
g
ies proportional
integ
r
al
and fuzzy logic for th
e
control of a doubly fed induct
ion
generator dedicated to
a win
d application
Chebel
A
hlem
1
,
B
e
nrete
m
A
2
, D
ob
re
v I
3
, Bark
a
t I
4
1,
2
,
L
a
borat
ory
:
E
lectrom
echani
cal E
ngi
n
eering
, Bad
ji
-M
o
khtar-An
n
ab
a
Univer
s
i
t
y
, A
l
g
eria.
3,
4
Dy
n
F
l
u
i
d
L
a
b
o
rator
y
, Ar
t
s et
M
ét
iers-
P
ari
s
T
e
c
h
,
1
51
,
bd
Th
e
H
ospital,
F
rance.
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
Jan
1
7, 201
9
R
e
v
i
s
e
d
Jul
8
,
2
019
Ac
ce
p
t
ed
No
v
1
5
,
2
019
Th
is
p
aper
g
iv
e
s
a
o
bs
erve
e
v
a
lu
ati
on
of
a
w
hole
wi
nd
e
n
e
rg
y
co
nv
e
r
sio
n
dev
i
ce,
t
he
g
adget
p
r
im
aril
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b
a
sed
on
a
DF
IG;
to
g
o
v
ern
ind
e
pen
dently
t
he
acti
v
e
an
d re
act
iv
e
po
wers
a
v
ecto
r
m
anage with
s
t
a
to
r
f
l
u
x
o
ri
entat
i
on
o
f
th
e
DF
IG
i
s
used
.
A
co
m
p
arati
v
e
hav
e
a
l
oo
k
at
w
ere
a
c
h
i
eved
a
m
o
ng
the
tradi
t
ional
PI
c
ontrol
l
e
r
and
fu
z
z
y
lo
gi
c
m
a
nag
e
t
o
i
n
v
e
stigat
e
i
t
s
d
y
n
a
m
i
c
and
s
t
at
ic
p
erf
o
rman
ces.
Th
is
r
e
s
earch
p
ai
nt
ing
s
i
nclu
des
t
h
e
e
xa
m
i
na
ti
on
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f
a
secti
o
n
e
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rlier,
t
o
o
f
f
e
r
e
f
f
ecti
v
e
ass
i
stance,
t
o
all
th
ose
wh
o
ha
v
e
t
o
m
a
ke
sel
ecti
ons
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eg
ardin
g
t
h
e
p
lann
in
g
and
im
p
l
ement
a
ti
on
o
f
w
i
n
d
e
l
ectrici
ty
pro
j
ect
s.
T
he
p
rim
a
ry
g
oal
i
s
t
o
m
o
d
e
l
t
h
e
wi
nd
chai
n
and
th
e
u
sage
o
f
st
yl
es
of
t
echn
i
q
u
es
f
or
t
he
m
an
ipulat
e
of
t
his
gen
e
rat
o
r
t
o
m
ak
e
cert
ai
n
an
awes
om
e
law
w
e
b
egan
w
it
h
th
e
m
o
deling
of
t
h
e
w
in
d
ch
ai
n
th
en
t
he
m
o
d
e
li
ng
o
f
t
he
D
F
I
G
an
d
t
h
en
t
he
u
sag
e
o
f
t
h
e
t
w
o
strateg
i
es
f
or
t
h
e
regulat
i
on
o
f
the
l
a
tt
e
r
.
t
h
e
co
mplete
d
evice
is
m
odel
e
d
and
si
mulat
e
d
ins
i
de
th
e
M
a
tlab
/
S
i
muli
nk.
T
h
e
o
v
e
rall
p
erf
o
rm
ance
a
n
d
rob
u
s
t
n
e
s
s
a
r
e
an
aly
z
ed
and
com
p
ar
ed
b
y
u
s
i
n
g
M
a
tl
ab
/S
im
ulin
k
.
The re
s
ults
acqu
i
red
sh
o
w
th
e
g
r
eat
perf
o
r
man
ces
o
f
th
e
f
u
zzy
l
o
g
i
c
t
o
pro
v
e
the
p
l
easan
t
of
t
h
e
s
t
re
ng
th
a
nd
t
he
s
t
a
b
i
l
i
t
y
of
w
i
n
d
s
t
r
e
n
g
t
h
.
K
eyw
ord
s
:
A
c
ti
ve
a
nd r
eac
tive
p
o
w
e
r
D
o
u
b
l
y
f
e
d
in
d
u
ct
ion
ge
ner
a
t
o
r
Fu
zz
y
l
ogi
c
P
r
op
or
tio
na
l
Integra
l
(
P
I
)
Vect
o
r
co
n
t
r
ol
Wi
n
d
pow
e
r
Th
is
is a
n
o
p
en acces
s a
r
ti
cle u
n
d
e
r t
h
e
CC
B
Y
-S
A
li
cens
e
.
Corres
pon
d
i
n
g
Au
th
or:
C
h
eb
el
Ah
l
e
m
Lab
o
rato
ry: El
ectro
mech
ani
cal Eng
ineeri
n
g
,
Ba
dji-
Mo
kh
tar
-
A
nnaba
U
n
i
ve
rsit
y,
23000, A
l
g
eria.
Em
ail:
chb
l
a
h
l
e
m
@
gma
i
l
.
co
m
1.
I
N
TR
OD
U
C
TI
O
N
Win
d
t
u
r
b
i
ne
g
e
n
era
t
or
i
s
u
nder
s
to
o
d
a
n
d
e
xp
l
o
i
t
e
d
f
or
a
l
o
ng
t
ime
,
i
t
tur
n
e
d
i
nt
o
o
n
e
of
t
he
f
i
r
st
assets
e
xp
l
o
ite
d
by
w
a
y
o
f
t
h
e
m
an
a
ft
e
r
t
he
s
treng
t
h
o
f
w
oo
d,
a
nd
i
t
t
urned
in
t
o
u
se
d
for
the
pro
p
u
l
s
i
ons
o
f
the shi
p
s
a
n
d
t
h
e corn t
urb
i
ne
s
in
ter alia.
It was b
ut neg
lec
t
e
d
a
t
some
po
i
n
t of t
he
c
en
t
u
ry w
i
t
h the
i
n
co
m
e
of
foss
il
ene
r
gies
b
e
s
ide
s
t
he
h
ydr
oelec
t
r
i
c
ity.
Insi
de
t
he
S
eve
n
t
ie
s
af
t
e
r
the
o
i
l
c
r
isis
a
nd
the
f
i
r
s
t
al
ar
ms
bec
a
u
s
e
of
t
he
w
ar
ming
o
f
p
la
n
e
t,
a
n
ew
i
n
t
ere
s
t
i
s
c
arr
i
e
d
t
o
w
i
nd
p
o
w
e
r,
due
t
o
t
h
e
va
ri
ou
s
t
e
c
h
n
i
ca
l
ble
ssin
g
s
of
w
i
n
d
s
t
r
e
ng
t
h
t
e
c
h
n
o
l
og
y
e
r
a
(st
e
ppe
d
forw
a
r
d
var
e
l
ec
t
r
i
c
ity
,
d
e
cre
a
se
d
p
o
we
r
fl
u
c
tu
a
t
i
ons
a
nd
bet
t
er
power
p
e
r
form
anc
e
),
v
ariab
l
e
vel
o
c
i
t
y
opera
t
i
o
n
t
h
a
t
is
c
a
rr
i
e
d
out
b
y
us
in
g
a
con
v
ersi
o
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s
ys
tem
is
con
t
in
u
a
l
l
y
u
t
iliz
e
d
b
y
c
o
n
t
em
porar
y
MW
w
i
n
d
t
u
rb
i
n
es
[
1]
.A
dd
i
t
iona
lly
t
he
d
e
v
e
l
o
p
m
e
nt
o
f
re
ce
nt
tech
n
o
l
o
gy
r
e
t
u
rns
the
c
o
nv
e
r
sio
n
o
f
t
h
is
i
n
c
re
asin
gly
w
o
r
t
hw
hi
le
e
lec
t
r
i
c
i
t
y
a
nd
ec
o
n
o
m
ica
lly
a
g
g
re
ssi
v
e,
i
n
the
w
o
rl
dw
i
d
e
sca
l
es,
w
i
n
d
pow
er
m
a
i
nt
a
i
ns
a
g
row
t
h
o
f
30%
i
n
k
e
e
pi
ng
w
i
t
h
a
nnum
f
o
r
t
h
e
r
ema
i
ni
ng
d
e
c
a
d
e
.
B
e
c
a
u
s
e
o
f
t
h
e
u
n
i
q
u
e
b
l
e
s
s
i
n
g
s
o
f
t
h
e
D
F
I
G
,
i
t
i
s
t
u
r
n
in
g
i
n
to
t
he
m
ain
c
o
nfig
ur
ati
o
n
o
f
w
in
d
pow
e
r
tech
n
o
l
o
gy. T
h
e
v
e
c
t
or c
on
tro
l
a
pp
ro
ac
h
i
s
use
d
t
o
s
t
udy
t
he
g
e
nera
tor,
a
nd the
D
F
I
G
r
otor
i
s
c
o
n
n
e
c
te
d
to a
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.
11,
N
o.
1
, Ma
r
202
0
:
263
–
27
4
26
4
alter
n
a
t
i
n
g
ex
cita
t
i
o
n
w
h
ose
freq
u
enc
y
,
s
ecti
o
n
a
n
d
im
por
tance
can
b
e
tai
l
ored
[
2
]
.
Wi
th
t
he
D
F
I
G,
gene
ra
ti
o
n
c
a
n
b
e
a
c
c
o
m
p
l
i
she
d
i
n
vari
a
b
l
e
v
el
oc
it
y
start
i
n
g
fr
o
m
s
ub-s
ync
hr
on
ous
p
ace
t
o
s
u
perb
syn
c
hro
n
o
u
s
p
a
ce
((±
30%)
arou
n
d
the
s
ync
hr
on
ou
s
pac
e
)
[2,
3].
A
m
anag
e
stra
te
gy
m
u
st
b
e
ad
va
nc
ed
t
o tak
e
adva
n
t
a
g
e
of
t
hese
b
e
n
e
f
i
t
s
w
ithi
n
t
he
f
ie
ld
o
f
w
i
n
d
s
t
r
eng
t
h
t
ec
h
nol
og
y
thi
n
k
i
ng
o
f
t
h
e
c
omp
l
e
x
i
t
y
o
f
t
h
e
st
r
u
c
t
ure
o
f
t
he
D
F
I
G
and
th
e
first-clas
s
of
t
he
e
lectr
i
c
i
t
y
t
o
b
e
ge
ne
rate
d,
due
t
o
t
h
e
sh
orta
ge
o
r
sca
r
cit
y
o
f
con
t
ro
l
of
t
he
a
sset
pro
d
u
c
e
d
.
Re
gar
d
i
n
g
t
h
e
re
ac
ti
ve
pow
e
r
s
w
h
il
st
t
h
e
g
e
n
erat
o
r
i
s
con
n
e
ct
e
d
t
o
t
h
e
com
m
uni
t
y
,
ma
ny
d
i
f
fic
u
l
t
i
e
s
g
e
t
u
p,
w
hic
h
i
ncl
u
de
t
h
e
l
o
w
pow
e
r
c
o
mp
one
n
t
a
n
d
t
he
h
a
r
m
o
n
i
c
po
l
l
ut
i
on.
U
s
in
g
a
n
i
n
n
e
r
f
u
n
ct
iona
l
m
ode
c
o
n
t
rol
l
e
r
p
red
i
c
t
i
v
e
of
t
he
s
pe
c
i
fi
c
cre
a
t
i
o
n
a
nd
a
sso
ci
a
t
io
n
h
a
d
b
een
stud
ie
d,
i
n
w
h
i
c
h
a
s
u
ita
b
l
e
e
n
erg
y
r
e
a
c
tio
n
is
a
c
q
u
i
red
b
y
m
ea
ns
o
f
a
sses
s
me
nt
w
i
t
h
th
o
s
e
of
t
he
t
r
a
d
itio
na
l
proce
dure
stre
ng
th
r
eac
t
i
on
w
he
n
t
h
e
trad
i
t
iona
l
P
I
c
o
n
tr
o
l
l
e
r
is
u
se
d.
H
ow
ever
,
i
t
i
s
h
a
rd
t
o
use
o
n
e
due
t
o
the
c
o
mp
lex
i
ty
i
n
the
i
r
st
r
u
c
t
ures
[
4].
O
n
t
h
i
s
pa
per,
a
n
al
t
e
r
na
tive
me
t
h
od
has
be
e
n
p
r
o
pose
d
t
he
u
se
o
f
a
fuz
z
y
c
omm
o
n
se
nse
c
o
nt
r
o
ll
er
o
p
timiz
e
d
t
o
chec
k
t
h
e
ac
t
i
ve
a
n
d
r
e
act
i
v
e
p
o
wers
a
c
r
oss
the
r
o
t
o
r
c
i
rcu
it.
Ther
efore, we f
a
vored to use thi
s
ty
pe
of
co
ntr
o
l
l
e
r
(
fuzz
y)
un
de
r
n
ea
th
m
a
ny a
dva
nt
a
g
es
that
it
has,
l
i
k
e
[5]:
F
u
z
z
y
c
o
n
t
r
o
l
l
e
r
s
c
a
n
c
o
v
e
r
a
f
a
r
w
i
d
e
r
v
a
r
i
e
t
y
o
f
o
p
e
r
a
t
i
n
g
c
o
ndi
ti
on
s
an
d
mi
ght
opera
t
e
w
i
t
h
un
ique
v
a
r
ie
t
i
e
s
o
f
n
o
ise
a
n
d
di
stur
ba
nce
,
w
hic
h
i
s
w
h
y
th
ey
a
r
e
e
x
t
r
a
st
ro
ng
t
h
a
n
P
I
c
on
t
r
o
l
l
e
rs.
Dev
e
l
opi
ng
a
f
u
z
z
y
c
o
n
t
r
o
l
l
e
r
i
s
l
e
s
s
h
i
g
h
l
y
p
r
i
c
e
d
t
h
a
n
g
r
o
w
i
n
g
a
c
o
n
t
r
o
l
l
e
r
base
d
on
a
m
o
d
e
l
or
o
th
er
c
ont
r
o
lle
r.
F
uz
zy
c
o
nt
roll
e
r
s
are
cu
sto
m
i
z
a
b
l
e
b
ec
au
se
i
t
i
s
l
e
ss
c
o
mpli
cat
ed
t
o
re
co
gn
ize
a
n
d
trade
the
i
r
p
o
l
ic
i
e
s.
T
h
a
t
no
lo
nge
r
ha
n
d
ies
t
u
se
t
he
a
ppr
o
a
ch
o
f
t
h
e
h
u
m
a
n
opera
to
r
,
b
u
t
a
re
a
lso
e
xpr
essed
i
n
n
at
ura
l
l
i
n
guis
t
i
c
t
erm
s
.
It
is
s
m
oot
h to
l
e
a
r
n
h
ow
f
uz
z
y
c
on
t
r
o
ller
s
p
a
i
nt
i
ngs
a
n
d
t
he
w
a
y
t
o
c
re
ate t
h
em
a
n
d
o
bser
ve
t
hem
to
a
c
oncr
e
te
software.
The
w
o
r
k
pre
se
nte
d
in t
h
is pa
p
er is
use
d
i
n e
x
p
l
oi
t
a
tio
n of
t
he
fuz
zy l
og
ic t
he
ory
w
h
i
l
e a
n
o
p
t
im
ize
d
fuz
z
y
l
o
g
ic
c
o
n
tr
ol
ler
is
d
es
i
gne
d
s
o
o
ne
c
an
a
d
j
u
s
t
the
sta
t
or
a
ct
i
v
e
a
n
d
r
eac
tive
p
o
w
e
rs
f
l
o
a
t
o
f
a
DFIG
con
n
ec
ted
to a
n e
ffe
c
tive
gri
d
[6].
2.
MODELING OF THE
WI
ND
TURB
INE
Win
d
m
ills
p
ro
duce
e
l
ec
tric
a
l
p
ow
e
r
t
he
u
se
o
f
w
i
nd
s
t
re
n
g
t
h
t
o
ru
n
an
e
l
e
ct
ri
c
g
e
n
e
rat
o
r.
A
n
ai
r
moti
o
n
p
asses
over
t
h
e
pr
ope
ller
s
,
gene
ra
ti
n
g
l
i
f
t
a
nd
e
x
e
r
t
i
n
g
a
r
o
t
at
io
n
a
l
f
o
rc
e
.
T
he
r
ota
t
ing
b
l
ad
es
r
ot
at
e
a
slug
g
i
sh
s
ha
ft
o
f
t
h
e
nace
ll
e
,
w
hi
c
h
e
n
t
er
s
a
gear
box.
T
he
m
ul
t
i
p
l
i
er
i
ncre
ases
t
he
r
ate
of
r
o
t
at
ion
a
n
d
transm
its
it
t
o
t
he
g
e
n
era
t
or
,
w
h
ic
h
ma
kes
use
of
m
ag
ne
t
i
c
fie
l
ds
t
o
tran
sfor
m
the
ro
tat
i
o
n
a
l
e
le
ctr
i
ci
t
y
i
nt
o
elec
tr
ical e
ner
g
y
[7].
P
rec
e
pt of
p
o
w
e
r
transfor
ma
t
i
on
of a
w
in
d tur
b
i
n
e,
as
prove
n
i
n
F
ig
ure
1.
F
i
g
u
re
1
.
P
r
i
n
ciple
of
th
e
e
nerg
y
trans
f
orm
a
ti
on
o
f
a
w
i
nd
tu
rb
ine.
We
c
a
n
d
e
t
e
r
m
i
ne
t
he
p
ow
e
r
a
vaila
b
l
e
(theor
e
t
i
c
a
l
p
ow
er),
due
t
o
t
h
e
wi
n
d
t
h
roug
h
a
p
pl
yin
g
t
he
the
o
ry
o
f the
mom
e
nt
um
and
t
h
e the
o
r
e
m
of
B
e
r
n
o
u
l
l
i
:
1
2
.
.
.
(
1
)
: surface swept
b
y the
blades [
]
;
ρ
: de
nsit
y of t
he
a
ir ρ
=
1
.225
kg/
;
:
pac
e
of the
w
i
nd [
/s] ;
the m
e
c
h
a
n
ica
l
e
lec
t
r
i
c
ity
o
f t
h
e
w
i
n
d
tur
bi
n
e
is the
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
C
o
m
p
a
r
a
t
ive
S
t
u
d
y
o
f
two
c
o
ntr
o
l
st
ra
t
e
gi
e
s
pro
p
o
rti
o
na
l
i
n
t
e
g
r
a
l
and f
u
zz
y
(Chebe
l Ah
l
e
m
)
26
5
,
.
.
.
(
2
)
the m
a
xim
u
m qua
n
t
i
t
y
of k
i
n
etic
e
n
e
r
gy i
s
d
efine
d
by t
h
e
l
i
m
i
t
of
B
e
t
z
:
=
.
=
0
.59
.
(
3
)
the p
o
w
e
r c
o
effic
i
e
n
t is d
ef
ine
d
by
:
=
(
4
)
The
ev
ol
u
t
i
o
n of t
he
de
p
e
nds
a
t
the pe
rspec
tive
o
f
or
i
e
n
ta
t
i
on
o
f
t
he
b
la
de
s β
and
s
p
ec
if
ic
s
p
e
e
d
λ
:
λ
=
.
(5
)
λ : e
xpresses
th
e
conne
c
t
ion
b
e
tw
ee
n ve
lo
ci
t
y
a
t
the s
t
o
p
of
th
e
bl
a
d
es a
n
d
t
he spe
e
d
of t
h
e w
i
nd
;
:
N
umbe
r of re
v
o
l
ut
i
o
n
s
bef
ore
t
h
e
m
u
lti
p
l
i
e
r;
R: ra
y of
t
he b
lade
s of
t
he
a
ero
gener
a
tor;
Cp (
λ,
β
)
i
s
c
a
l
l
e
d
t
h
e co
ef
fi
c
i
en
t
re
ac
ti
vi
t
y
po
w
er.
(λ
,β
)
=
0
.
5
9
3
(
6
)
We c
an
e
xpre
sse
d t
h
e
po
w
e
r
coef
fic
i
e
n
t
Cp
by
[8,
9]:
e
x
p
(
7
)
=
.
.
(
8
)
The
stren
g
t
h c
o
effi
c
i
e
n
t and
the
r
efore
the
to
rque
dec
rea
s
e by
w
ay
o
f gre
a
ter
tha
n
λ
by w
a
y of
grow
i
n
g the
p
i
t
c
h
att
i
t
ude
[
10]
.
W
h
ere:
:
=
ρ.
.
,
(
9
)
:
Cou
p
l
es on
t
h
e
slow
a
xis
(si
d
e ha
rnesses)
;
The
role
o
f
t
h
e
m
u
lt
i
p
l
i
e
r
i
s
t
o
t
r
a
nsm
i
t
the
sp
ee
d of
t
he
b
lad
e
s
t
o t
h
e ge
ner
a
t
o
r
F
i
g
u
r
e
2.
F
i
gure
2. S
tructure
of
the
w
i
n
d
sys
tem
.
there
f
ore,
we can
m
odel
the
m
u
l
t
i
p
l
i
e
r
by
t
h
e fo
llow
i
n
g
e
qu
a
t
i
o
ns
:
C
(
10)
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.
11,
N
o.
1
, Ma
r
202
0
:
263
–
27
4
26
6
=
(
11)
w
ith:
G
:
The
r
epor
t
/
ra
ti
o
of t
h
e
s
peed-
i
nc
rea
s
in
g
gear
.
J=
+
(
12)
to
d
e
t
e
r
m
i
ne
t
he
e
vo
l
u
t
i
on
o
f
t
h
e
m
ec
han
i
c
a
l
p
ac
e
w
ith
p
art
of
th
e
f
u
ll
tor
que
(
)
i
m
plem
ented
t
o
t
he
rot
o
r, w
e
use the
essen
tia
l e
q
uat
i
o
n
o
f
t
he
d
ynam
i
c
s
:
J
=
(
13)
t
h
e
c
o
effi
ci
e
n
t
o
f
t
h
e
m
ul
tipl
i
er
l
ink
s
t
h
e
m
e
c
h
ani
cal
v
e
l
o
c
it
y
t
o
t
h
e
w
i
de
v
arie
ty
o
f
rev
o
l
u
t
i
o
ns
o
f
t
h
e
t
u
rb
in
e
and
co
n
n
ec
ts
t
he
tor
que
o
n t
h
e slow
a
xis t
o
t
he
t
or
q
u
e
o
n
t
h
e
q
uic
k
a
x
i
s.
In
w
hi
ch:
J
i
s
t
h
e
w
hol
e
in
e
r
tia
,
wh
i
c
h
se
e
m
s
on
t
h
e
r
oto
r
o
f
t
he
g
e
n
e
r
at
o
r
.
Thi
s
t
orq
u
e
t
a
kes
u
nder
con
s
i
d
era
tio
n,
t
he
e
lec
t
r
o
ma
g
n
et
i
c
c
o
u
p
l
e
(
C
e
m
)
prod
uc
e
d
t
hr
ou
g
h
th
e
g
e
n
e
ra
t
o
r,
t
he
c
ou
pl
e
o
f
v
isc
o
u
s
fric
ti
on
s (Cv
i
s) a
nd cou
p
l
es
it
(C
r
)
.
(
14)
The
coef
ficie
n
t
of visc
o
us fr
i
c
t
i
o
ns F
m
odel t
h
e
re
sist
ive
tor
q
ue
d
ue
t
o
fric
t
i
o
n
s as:
(
15)
One
can
m
o
d
e
l
the
t
r
ee
like
fo
ll
owi
ng:
Ω
Ω
(
16)
a
nd
: The
w
in
d c
o
u
p
l
e
and
the
e
l
e
c
trom
ag
ne
tic
c
o
u
p
l
e
.
an
d
:
T
he
i
ne
r
tia
of the
g
e
nera
to
r
a
nd
tha
t
o
f
the t
u
rb
i
n
e.
and
:
The
c
oe
ffic
ie
nt o
f v
i
sco
u
s fr
ic
tio
ns
o
f t
h
e
t
u
r
b
ine
a
nd
tha
t
o
f
th
e
ge
ne
ra
t
o
r
.
Ω
: N
u
m
b
er
of
revol
ut
i
ons
o
f t
h
e
gene
rat
o
r
(fa
s
t
ax
is)
.
We
p
u
t
:
(
17)
(
18)
F
r
om
w
here,
t
h
e
m
e
c
h
anica
l
e
qua
t
i
o
n
bec
ome
s
:
Ω
Ω
(
19)
3.
T
U
RB
IN
E S
I
MULAT
I
ON RES
UL
TS
F
i
gure
3
show
s
the
pro
f
ile
o
f
the
w
i
n
d
t
ha
t
w
i
l
l
b
e
a
p
p
l
i
e
d
for
t
he
w
in
d
t
u
rbi
n
e
its
l
ow
v
a
l
ue
i
s
arou
nd
(8m
/
s)
.
The
s
i
m
u
l
a
ti
o
n
r
esu
l
t
s
s
h
o
w
s
t
he
i
nf
lue
n
ce
o
f
th
e
va
r
i
at
ion
o
f
t
he
m
ec
han
i
ca
l
vel
o
c
i
t
y
a
s
a
cha
r
ac
t
e
ris
tic
o
f
t
h
e
wi
nd pa
ce
on the
ele
c
t
r
i
c
a
l stren
g
t
h
p
ro
d
uce
d
i
n
F
i
gur
e
4.
Thr
o
u
g
h
t
h
e
e
v
o
l
ut
i
o
n
of
t
h
e
p
ow
e
r
c
oe
ff
i
c
ie
n
t
F
i
g
ure
s
5
,
w
e
a
r
e
a
b
le
t
o
n
o
te
t
ha
t
t
h
i
s
one
i
s
appr
ox
im
ate
l
y
it
s
t
h
e
o
ret
i
ca
l
ma
ximum
va
lu
e.
T
his
c
o
e
f
fic
i
e
n
t
i
s
o
b
t
a
ine
d
f
or
a
f
i
x
e
d
a
ngle
β
(
β
=
2
0
)
t
ha
t
gi
ves
u
s
a
n
o
p
tim
al
λ
.
I
t
i
s
n
o
t
e
d
t
h
a
t
i
t
rea
c
hes
a
m
a
xim
u
m
va
l
u
e
of
0
.5.
Thi
s
s
im
ul
a
t
i
o
n
e
f
fe
cts
s
h
o
w
t
he
relia
bi
l
ity
o
f th
e
ma
nipula
tio
n
w
ith
ou
t servo
con
t
ro
l
l
i
n
g
o
f
t
h
e
win
d
p
ac
e.
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
C
o
m
p
a
r
a
t
ive
S
t
u
d
y
o
f
two
c
o
ntr
o
l
st
ra
t
e
gi
e
s
pro
p
o
rti
o
na
l
i
n
t
e
g
r
a
l
and f
u
zz
y
(Chebe
l Ah
l
e
m
)
26
7
F
i
gure
3. Wi
nd
profi
l
e
i
m
p
l
e
m
ented
to
t
he
t
urb
i
ne.
F
i
gure
4.
T
he m
ec
hani
ca
l
spe
e
d
and
the
p
o
w
e
r
produc
e
d
.
F
i
gur
e 5.
The
pow
er
coe
ffic
i
e
n
t
a
n
d
t
he
s
pe
cific
spee
d
.
4.
MODELING OF TH
E
DFIG
I
t
i
s
essen
t
ia
l
t
o
a
p
p
l
y
a
p
ar
ti
cula
r
a
n
d
sim
p
le
m
ode
l
for
a
hi
ghe
r
il
lus
t
r
a
tio
n
o
f
t
he
b
e
h
a
v
ior
of
a
dua
l-fe
e
d
i
n
d
u
c
t
i
o
n
g
e
n
er
at
o
r
.
The
tw
o-sec
t
i
o
n
mode
ls
(
d
,
q
)
gi
ve
n
b
y
w
ay
o
f
t
h
e
pa
rk
t
ra
ns
form
ati
on
a
r
e
used [11].
4.1.
Mod
el of
D
F
IG in
th
e
refe
r
e
n
tial (
d
,
q
)
The
D
F
IG
i
s
u
s
e
d
a
s
the
ge
ne
ra
t
o
r
se
l
e
c
t
ed
f
or
t
he
w
i
n
d
sy
stem
in
a
dd
it
io
n,
t
he
D
F
I
G
c
o
ntr
o
lle
d
b
y
in
verter
s
thr
o
u
gh
i
t
s
rot
o
r
o
p
e
rates
o
v
e
r
a
numbe
r
±30%
v
ariat
i
on
a
cro
s
s
t
h
e
syn
c
h
r
onou
s
p
a
c
e
.
T
hi
s
d
e
si
re
perm
its
t
he
c
o
nve
r
t
ers
d
i
me
nsio
ne
d
t
o
t
r
a
ns
it
3
0%
o
f
n
o
mina
l
e
n
ergy.
C
on
s
e
qu
ent
l
y
,
i
t
i
s
goi
ng
t
o
b
e
fi
na
nc
i
a
l
[1
2].
The
m
o
del
o
f
t
he
D
F
I
G
is
e
xpr
esse
d
in
t
h
e
(
dq)
re
fer
e
nc
e
fr
am
e
via
t
h
e
fo
l
l
ow
in
g
e
q
uat
i
on
s
[1
3-
1
5
]
.
We
h
ave
:
θ
θ
θ
⟹
θθ
θ
So
:
⟹
ω
=
ω
s
-ω
r
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.
11,
N
o.
1
, Ma
r
202
0
:
263
–
27
4
26
8
4.2
.
El
ectric equ
a
ti
ons
⎩
⎪
⎪
⎨
⎪
⎪
⎧
(
20)
W
ith
resp
e
c
tive
l
y:
,
,
a
nd
a
re the
d
irec
t
and
qua
drat
ure
stat
or a
nd ro
tor
vo
lta
ge
s of
t
he
tw
o
-phase sys
tem
.
a
nd
a
re
t
he pu
l
sa
ti
o
n
s
of
t
he
sta
tor a
nd ro
tor
elec
t
r
i
c
a
l
m
agni
t
u
d
es.
4.
3
.
M
ag
neti
c
eq
u
a
ti
o
n
s
⎩
⎨
⎧
(
21)
W
ith
:
,
,
a
nd
: A
r
e
stat
or
an
d
r
otor flow
direc
t
a
n
d
i
n
squ
a
rin
g
o
f
the
di
p
h
a
si
c
s
y
st
e
m
;
:
Th
e st
at
o
r
c
yc
l
i
c
i
nd
uct
a
n
c
e;
: The
rot
o
r
cyclic
i
n
duc
t
a
nce
;
:
Cyc
lic
m
ut
ua
l
i
n
d
u
c
t
a
n
ce
be
tw
ee
n sta
t
or a
nd rot
o
r.
4
.
4.
M
e
c
h
a
n
ic
al
e
quat
i
on
Ω
Ω
(
22)
W
ith
resp
e
c
tive
l
y:
:
T
he e
l
e
ctrom
a
gne
t
i
c
co
up
le
;
:
The
resistive tor
que;
: The
coe
ffic
ie
n
t
o
f v
i
sco
u
s fr
ict
i
o
n
o
f
t
he
D
F
I
G
;
:
The
ine
r
t
i
a
of
t
he r
evo
l
v
i
ng
parts
;
Ω
: N
um
ber
of
r
evo
l
ut
ion
s
o
f t
h
e
axi
s
of
the
DFIG.
The
ex
pre
s
si
on
of the
elec
tro
m
agne
tic
co
u
p
l
e
i
s
give
n t
h
ro
ug
h
:
⎩
⎪
⎨
⎪
⎧
(
23)
4.5.
Ac
t
ive and
reac
t
ive
powe
rs
(
24)
(
25)
5.
VECT
OR
C
O
N
TROL
O
F TH
E AC
T
I
VE
AND
R
EACT
IVE PO
WERS
O
F
T
H
E DFIG
The
a
rrange
me
nt o
f
the
(20)
and
(2
1)
o
ffe
rs t
he
e
xpress
i
on
of
t
he r
otor
vo
l
t
a
ge
s in l
i
n
e
w
i
t
h
t
he
rot
or
curr
ents v
ia
:
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
C
o
m
p
a
r
a
t
ive
S
t
u
d
y
o
f
two
c
o
ntr
o
l
st
ra
t
e
gi
e
s
pro
p
o
rti
o
na
l
i
n
t
e
g
r
a
l
and f
u
zz
y
(Chebe
l Ah
l
e
m
)
26
9
⎩
⎪
⎨
⎪
⎧
(
26)
w
e
c
a
n
pre
se
nt
t
he e
qua
t
i
o
n
o
f
t
or
que
is a
s
f
ol
l
o
w
s
:
(
27)
w
e
c
a
n
desc
r
ibe
d
the
f
urn
i
s
h
e
d
a
cti
v
e a
n
d re
ac
t
i
ve
e
ne
rg
y as
f
o
ll
o
w
s
:
(
28)
ado
p
t
i
ng
th
e b
e
l
i
e
f
of a
ne
gl
igi
b
le
s
ta
t
o
r
re
si
s
t
anc
e
R
s a
nd
th
e s
t
at
or
f
l
ux i
s
c
on
s
t
an
t
an
d orie
nt
a
t
e
d
alo
n
g
the
axi
s
,
we
d
educ
e
:
A
nd
0
0
(
29)
the s
t
at
or
acti
v
e
and r
eac
tive
e
n
e
r
g
y
m
ay
b
e expre
s
se
d as
f
o
llo
ws:
(
30)
The
c
l
osi
n
g eq
ua
ti
on
s dis
p
lay
that
t
he
ac
t
ive
and
rea
c
t
i
ve p
o
w
e
rs c
an be
c
o
nt
r
o
lle
d
via r
o
tor
curr
ents.
Th
us, the
rot
or
volta
ge
s i
n
sid
e
the
d
-q a
xis
ma
y
be
w
ritt
e
n
as
foll
ow
s
:
(
31)
:
t
he
lea
ka
ge
c
oeffici
en
t,
i
t
i
s
g
ive
n
b
y
:
=
1
5.1.
PI c
on
tr
ol of
th
e
D
F
IG
We
w
i
ll
es
ta
bl
i
s
h
a
m
a
na
ge
l
o
o
p
on
e
v
e
r
y
pow
er
w
ith
a
n
im
p
a
rtia
l
r
e
g
u
la
t
o
r
(PI
)
e
ven
as
com
p
en
sat
i
ng
for
the
d
i
st
urb
a
nce
t
e
rm
s
d
u
e
t
o
t
h
e
fac
t
c
urre
nts
a
nd
v
o
l
t
a
ges
a
r
e
li
nk
ed
b
y
w
a
y
of
a
s
w
itc
h
fu
nc
ti
o
n
of
first orde
r.
B
eca
use
the
slip
c
os
t
i
s
l
ow
.
The
pro
por
ti
o
n
al
I
n
t
egra
l
co
ntr
o
l
l
e
r
(
P
I)
i
s
s
t
i
ll
t
he
m
a
x
im
um
gene
ral
l
y
u
sed
for
co
ntr
o
l
lin
g
t
h
e
D
F
I
G
[
16],
as
w
ell
as
i
n
l
o
ts
o
f
b
u
s
i
nes
s
m
a
n
age
str
u
c
t
ur
es
.
It
i
s
s
i
m
p
l
e
a
n
d
q
u
i
c
k
t
o
p
u
t
i
n
t
o
e
f
f
e
c
t
e
v
e
n
a
s
pro
v
i
d
i
n
g i
d
e
a
l
perfor
m
a
n
ce
[17].
Re
g
u
l
at
ors
eve
r
y
a
x
i
s
po
s
i
t
i
o
n
is
t
o
ge
t
rid of
t
he
g
ap
a
m
ong
t
he
a
c
t
i
v
e
a
n
d
rea
c
ti
ve
s
tre
n
g
t
h
re
fer
e
nce
s
a
nd
the
me
asure
d
act
i
v
e
a
nd
r
eac
ti
ve
s
tre
n
g
t
h.
T
he
s
yn
t
h
es
i
s
o
f
P
I
c
on
t
r
ol
ler
s
i
s
offe
red
i
n
[
1
8
].
5.2.
Dire
ct
c
on
trol of
act
i
ve
an
d
reac
t
i
v
e p
o
we
r
s
Th
is
a
p
p
roa
c
h
u
ses
tw
o
P
I
c
o
n
tr
ol
ler
s
t
o
co
ntr
o
l
t
h
e
s
y
s
t
e
m
;
w
e
c
a
n
c
on
fi
g
u
re
a
m
a
n
i
p
ula
t
e
l
o
op
of
eve
r
y
e
n
erg
y
(
P
s
a
nd
Q
s
)
w
ith
a
n
i
nde
p
e
nde
n
t
c
o
n
tro
l
ler
at
t
he
same
t
i
m
e
as
c
o
m
p
e
nsat
in
g
fo
r
the
pert
urba
ti
on
p
h
rases.
B
ec
aus
e
o
f
t
h
e
l
o
w
s
lip
p
rice
,
w
e
n
e
g
lec
t
t
he
t
erm
s
c
ou
p
l
i
n
g
am
ong
th
e
tw
o
m
a
ni
p
u
la
t
e
axe
s
.
We a
cqu
i
re
a
v
ector
c
o
n
t
ro
l wit
h
a
n un
m
a
rrie
d con
t
ro
ller
i
n
line
w
i
t
h
a
xi
s,
show
n
in F
igure
6, [19, 20
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
o
w
E
l
e
c
&
D
r
i
S
yst
V
o
l.
11,
N
o.
1
,
Mar
202
0
:
263
–
27
4
27
0
F
i
gur
e
6.
B
l
o
c
k
d
i
a
gr
am
o
f
th
e
dir
e
c
t
c
o
n
tr
ol
5.
3.
I
n
d
i
r
ect
c
on
t
r
ol
o
f
ac
t
i
v
e
a
n
d
r
e
a
ct
ive
p
o
wer
5.
3.
1.
I
nd
irec
t
c
o
n
t
r
o
l
lo
op
s
wi
t
h
ou
t
t
h
e
powe
r
I
t
i
s
nece
ssa
r
y
t
h
a
t
t
he
r
o
t
or
c
ur
r
e
nts
ir
q
a
n
d
i
r
d,
r
e
s
pe
c
t
ive
l
y
t
he
p
ix
o
f
t
h
e
ac
ti
ve
a
nd
r
e
act
iv
e
pow
e
r
s
of
t
he
s
ta
tor
,
P
s
a
n
d
Qs,
m
a
i
nt
a
i
n
the
i
r
c
ont
e
m
p
o
r
a
r
y
r
e
feren
ces, [
19
]
.
F
i
gur
e
7.
R
e
p
r
e
sen
t
at
i
on
o
f
a
b
l
o
c
k
d
ia
gr
am
of
in
dir
e
ct
c
on
tr
ol
i
n
ope
n
l
o
o
p
5.
3.
2.
I
nd
irec
t
c
o
n
t
r
o
l
lo
op
s
wi
t
h
t
h
e
p
ow
ers
We
ar
e
a
bl
e t
o
c
om
pr
ise
a
n
e
xtr
a
m
ani
p
u
l
a
t
e
l
o
o
p
t
o
the
p
o
w
e
r
s
i
n
o
rd
e
r
to
di
sp
os
e
of
the
s
t
a
t
i
c
e
r
r
o
r
w
h
i
l
s
t
m
a
i
nt
a
i
ni
n
g
t
he
d
y
n
a
m
ics
of
t
he
m
a
c
hi
ne,
to
e
nha
n
ce
the
pr
ece
d
i
n
g
c
on
tr
o
l
F
i
g
ur
e
8
[20]
.
F
i
gur
e
8.
R
e
p
r
e
sen
t
at
i
on
o
f
a
b
loc
k
d
ia
gr
a
m
o
f
in
dir
e
ct
c
on
tr
ol
i
n
close
d
l
o
o
p
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
C
o
m
p
a
r
a
t
ive
S
t
u
d
y
o
f
two
c
o
ntr
o
l
st
ra
t
e
gi
e
s
pro
p
o
rti
o
na
l
i
n
t
e
g
r
a
l
and f
u
zz
y
(Chebe
l Ah
l
e
m
)
27
1
5.4.
S
i
m
u
l
atio
n
r
e
su
lts
The
di
sti
n
ct
c
u
r
ves
r
ece
ive
d
w
it
h
the
a
i
d
of
c
ontro
l
l
ing
t
h
e
ac
ti
v
e
a
nd
r
ea
ct
i
v
e
po
we
r
ge
n
e
ra
t
e
d
in
t
h
e
s
t
a
t
o
r
o
f
t
h
e
D
F
I
G
a
r
e
s
u
p
p
l
i
e
d
i
n
F
i
g
u
r
e
9
a
n
d
1
0
.
W
e
a
r
e
ab
le
t
o
s
e
e
t
h
e
go
o
d
r
e
s
ponse
o
f
t
he
e
nerg
y
manipula
t
e
of
the DFIG
.
F
i
gure
9.
A
ctiv
e pow
e
r
P
s [Watt]
F
i
g
u
r
e
1
0
.
React
iv
e po
wer Qs
[
VAR]
6.
FU
Z
Z
Y
CO
NT
ROL OF TH
E
D
FIG
F
u
zz
y
l
o
gi
c
su
cc
ee
ds
i
n
s
u
pp
lyi
ng
e
x
ce
pti
o
nal
perfor
m
a
n
ce
w
i
t
h
o
u
t
r
esort
i
n
g
t
o
t
h
e
m
a
them
at
ica
l
mode
l
o
f
the
s
ys
tem
,
t
r
u
ly w
i
t
h t
h
e
ai
d of inc
orp
o
ra
t
i
n
g
t
he
i
n
form
ati
o
n of t
he pr
o
fess
io
na
ls.
The
r
e
f
ore,
f
uzz
y
ma
nage
proc
e
d
ures
t
o
a
posi
t
i
v
e vo
l
u
m
e
the
a
bi
l
i
t
y
o
f hum
a
n
r
ea
s
o
ni
ng
[21
].
A
s
p
rove
n
i
n
F
igure
11
,
the
fuzz
y
m
a
n
i
p
u
l
a
t
e
is
b
ase
d
a
t
t
h
e
M
a
m
d
an
i
m
o
d
e
l.
T
hi
s
m
e
c
h
an
ism
is
su
bd
iv
id
ed
i
nto
sev
e
ral
l
e
v
e
ls:
a.
I
n
itia
l
i
zat
i
o
n
i
s
t
he
d
e
f
in
it
io
n
of
l
in
guis
t
i
c
v
a
r
iab
l
es
a
nd
p
h
ra
se
s;
b
u
i
l
d
t
he
m
em
bership
fe
a
t
ures
a
nd
the
ru
le
b
ase.
b.
F
u
zz
i
f
i
c
a
t
i
on
i
s
t
he c
o
nvers
io
n of
u
n
i
q
u
e
i
n
p
u
t
fa
c
t
s i
n
to
f
u
z
z
y val
u
e
s
m
e
m
be
rshi
p fu
nc
t
i
o
n
s.
c.
The
in
fere
nce
i
s
e
val
u
a
t
i
o
n
of
p
o
l
i
c
i
e
s
o
f
t
h
e
r
ule
of
t
h
u
mb
b
a
s
e
a
n
d
c
o
m
b
i
n
e
t
h
e
c
o
n
s
e
q
u
e
n
c
e
s
o
f
e
ach
r
ule.
d.
D
e
fuzz
ifica
t
i
o
n is c
onve
rt t
he
outp
u
t i
n
for
m
a
t
i
o
n to
n
on-
fu
zz
y
val
u
es.
F
i
gur
e 1
1
.
Bl
o
c
k dia
g
ra
m
of
f
uzz
y
co
n
t
ro
l
A
bloc
k
d
i
agr
a
m
w
h
ere
i
n
fuzz
y
c
o
ntr
o
l
l
e
r
s
a
r
e
incl
u
d
e
d
i
n
t
o
the
D
F
I
G
ve
ctor
m
ana
g
e
b
l
oc
k
i
s
show
n
i
n
f
i
g
ur
e
12.
E
ach
f
uz
zy
c
o
n
t
r
o
lle
r
g
i
ves
u
n
b
i
a
sed
c
o
n
t
ro
l
o
f
t
he
a
c
t
i
v
e
a
nd
rea
c
t
i
ve
p
ow
e
r
s.
F
igure
13
ill
us
trates
t
he
l
ayo
u
t
o
f
t
h
e
fu
zz
y
c
o
n
t
r
o
l
l
e
r
.
The
pr
ofi
t
s
a
n
d
a
r
e
sca
l
e
fac
t
ors
(norm
a
lizat
io
n).
To
atta
i
n
a
p
p
r
opr
i
a
te
c
on
tro
l
w
e var
y
t
hese
e
le
m
e
nts.
I
ndee
d
, the
y
w
ill
de
term
ine
t
h
e
p
e
r
f
o
r
m
a
nce
of the
c
on
tro
l
.
Usu
a
l
l
y
,
w
e
p
i
ck
a
f
e
w
p
a
r
a
m
et
ers
wh
i
c
h
i
n
cl
ud
es
l
i
n
gui
st
i
c
v
a
r
ia
b
l
e
s
,
m
e
m
b
er
ship
f
u
n
ct
ion
s
,
and
in
fere
nce
tec
h
n
i
q
u
e
an
d
defuz
z
i
f
ica
t
i
on
st
ra
t
e
g
y
t
ha
t
al
low
s
y
o
u
to
l
ay
ou
t
a
fu
z
z
y
co
nt
roll
e
r
f
or
t
h
e
ma
nip
u
la
t
i
o
n
o
f
e
l
ec
trica
l
d
r
i
ve
s
[2
2].
We
t
ake
as
i
n
p
u
t
s
the
e
rror
and
its
s
pi
no
ff,
at
t
he
s
am
e
time
a
s
t
he
ou
tpu
t
i
s
t
h
e
c
o
m
m
a
nd
i
t
se
lf.
T
h
e
tr
ian
g
u
lar
an
d
tra
p
ez
oi
d
a
l
me
mb
ershi
p
f
e
a
t
u
re
s
are
us
ed
i
n
a
no
rma
l
i
z
ed
speec
h
u
n
i
ver
s
e
insi
de
t
h
e
i
n
t
er
val
[-1;
1]
f
or
e
very
v
ar
i
a
b
l
e
,
a
s
prove
n
in
F
igures
1
4
a
n
d
1
5
,
r
e
spec
t
i
v
e
ly
f
or
in
put
s (
m
istake
s,
errors
v
arian
t
)
and o
u
t
p
ut (i
n
p
u
t
proc
e
dure
)
.
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.
11,
N
o.
1
, Ma
r
202
0
:
263
–
27
4
27
2
F
i
gure
1
2
. F
uz
z
y
con
tro
l
of D
F
IG
.
F
i
gure
1
3
.
D
e
sig
n
o
f a
fuzz
y c
ontr
o
l
l
er
.
F
i
gure
1
4
.
Mem
b
ershi
p
f
uncti
o
ns of error
an
d
change
o
f
error
F
i
g
u
r
e
15.
Mem
ber
s
h
i
p
fu
nc
t
i
o
n
s
o
f
ou
t
pu
t
The
su
bse
t
s
fu
zz
y m
e
m
b
ershi
p
w
a
s
note
d
a
s fo
l
l
ow
s
:
BN
:
Bi
g-N
e
gat
i
ve
;
SN
: Sm
all-N
e
ga
tive
;
AZ:
Ab
ou
t
-
Zero
;
SP
: Sm
a
l
l-P
o
siti
ve
;
BP
: B
i
g-
P
osi
t
i
v
e.
The
fuz
z
y
r
eg
ula
t
i
o
ns,
for
fi
gur
in
g
o
u
t
o
u
t
pu
t
va
ria
b
le
o
f
the
c
ontro
l
l
er
a
s
a
cha
r
ac
teri
st
i
c
o
f
en
ter
varia
b
l
e
s ar
e gr
oupe
d w
i
th
in
T
ab
le
1
.
Ta
b
l
e 1.
Infere
n
ce
ma
trix
Δu
e
BN
S
N
A
Z
S
P
BP
Δe
BN
B
N
BN
S
N
S
N
A
Z
SN
B
N
SN
S
N
A
Z
S
P
AZ
B
N
S
N
A
Z
SP
B
P
SP
B
N
AZ
S
P
SP
B
P
B
P
A
Z
SP
SP
B
P
B
P
7.
SIMU
L
A
TION
R
ESULT
S
F
i
gures 1
6,
17,
18 show
t
ha
t
t
h
e
pe
rform
a
nc
e
of fuzz
y
l
o
g
i
c
is
qu
i
t
e
g
o
od
in c
ompa
r
i
son
w
ith
P
I
con
t
ro
l
l
er.
Evaluation Warning : The document was created with Spire.PDF for Python.