I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
w
er
E
lect
ro
nics
a
nd
Driv
e
Sy
s
t
e
m
s
(
I
J
P
E
DS
)
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2021
,
p
p
.
1
9
8
7
~
1
9
9
8
I
SS
N:
2088
-
8694
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
p
ed
s
.
v
1
2
.
i
4
.
pp
1
9
8
7
-
1
9
9
8
1987
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
S
enso
r
less
no
nlin
ea
r
slidin
g
m
o
de
co
ntrol o
f
t
he in
d
uction
m
a
chine
a
t
v
ery
l
o
w
speed using
FM
-
M
RAS obs
erv
er
M
o
k
hta
r
T
o
ua
m
1
,
M
o
ha
m
med Chena
f
a
2
,
So
u
f
y
a
ne
Chekro
un
3
,
Ra
m
z
i Sa
li
m
4
1
,
2,
4
De
p
a
rtm
e
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
,
L
a
b
o
ra
to
ry
o
f
A
u
to
m
a
ti
c
s &
S
y
st
e
m
s
A
n
a
l
y
sis
(
LAA
S
)
,
P
o
ly
tec
h
n
ic
Na
ti
o
n
a
l
S
c
h
o
o
l
o
f
Ora
n
M
a
u
rice
A
u
d
in
,
A
l
g
e
ria
3
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
,
Un
iv
e
rsity
M
u
sta
p
h
a
S
tam
b
o
u
li
o
f
M
a
sc
a
ra
,
M
a
sc
a
r
a
-
A
lg
e
ri
a
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
A
p
r
1
0
,
2
0
21
R
ev
i
s
ed
Sep
3
,
2
0
21
A
cc
ep
ted
Sep
1
0
,
2
0
21
T
h
e
in
d
u
c
ti
o
n
m
o
to
r
is
c
o
m
p
lex
b
e
c
a
u
se
it
s
d
y
n
a
m
ic
is
n
o
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li
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e
a
r,
m
u
lt
iv
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riab
le
a
n
d
h
ig
h
ly
c
o
u
p
le
d
.
In
a
d
d
it
i
o
n
,
t
h
e
in
d
u
c
ti
o
n
m
o
to
r
(IM
)
c
o
n
tro
ll
e
r
d
e
sig
n
c
a
n
b
e
d
e
g
ra
d
e
d
d
u
e
t
o
w
id
e
ra
n
g
e
s
o
p
e
ra
ti
n
g
sp
e
e
d
sp
e
c
iall
y
in
l
o
w
a
n
d
n
e
a
r
-
z
e
ro
sp
e
e
d
s
a
n
d
a
lso
to
v
a
riatio
n
o
f
in
terv
a
l
p
a
ra
m
e
ters
su
c
h
a
s
th
e
sta
to
r
re
sista
n
c
e
c
h
a
n
g
e
b
e
c
a
u
se
o
f
sta
t
o
r
h
e
a
ti
n
g
d
u
ri
n
g
o
p
e
ra
ti
o
n
.
Ou
r
c
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tr
ib
u
ti
o
n
is
th
e
u
se
o
f
a
n
o
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li
n
e
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r
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d
in
g
m
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e
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o
n
tro
l
u
sin
g
a
f
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z
z
y
m
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tu
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f
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re
n
c
e
a
d
a
p
ti
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e
sy
ste
m
o
b
se
rv
e
r
b
a
se
d
o
n
tw
o
f
u
z
z
y
a
d
a
p
tatio
n
m
e
c
h
a
n
is
m
s
to
e
stim
a
te
b
o
th
r
o
to
r
sp
e
e
d
a
n
d
sta
t
o
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re
sista
n
c
e
.
T
h
e
p
ro
p
o
se
d
w
o
rk
wa
s
v
e
ri
f
ied
a
n
d
c
o
m
p
a
re
d
b
y
si
m
u
latio
n
a
n
d
tes
ted
in
v
a
rio
u
s
ra
n
g
e
s
o
f
sp
e
e
d
w
it
h
m
o
to
r
a
n
d
re
g
e
n
e
ra
ti
n
g
re
g
io
n
s
o
f
o
p
e
ra
ti
o
n
.
T
h
e
re
su
lt
s
sh
o
w
th
a
t
th
e
p
ro
p
o
se
d
a
p
p
r
o
a
c
h
h
a
s
p
r
o
v
e
d
g
o
o
d
e
ffe
c
ti
v
e
n
e
ss
in
trac
k
in
g
a
n
d
o
b
se
rv
a
ti
o
n
.
K
ey
w
o
r
d
s
:
Fu
zz
y
lo
g
ic
I
n
d
u
ctio
n
m
o
to
r
Mu
t
u
al
MR
AS
Sen
s
o
r
les
s
Sli
d
in
g
m
o
d
e
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Mo
k
h
tar
T
o
u
a
m
Dep
ar
t
m
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
L
ab
o
r
ato
r
y
(
L
AA
S),
P
o
l
y
tec
h
n
ic
Natio
n
a
l Sch
o
o
l o
f
Or
a
n
B
P
.
1
5
2
3
E
l M
n
ao
u
er
,
3
1
0
0
0
Or
an
-
Alg
er
ia
E
m
ail:
m
o
k
h
tar
to
u
a
m
@
g
m
ai
l.c
o
m
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
in
d
u
s
tr
y
i
s
o
f
te
n
i
n
ter
este
d
in
r
ed
u
cin
g
th
e
n
u
m
b
er
o
f
s
en
s
o
r
s
a
m
o
n
g
th
e
m
t
h
e
in
d
u
c
t
io
n
m
o
to
r
s
p
ee
d
s
en
s
o
r
s
.
Sin
ce
t
h
e
p
u
b
licatio
n
o
f
th
e
s
u
r
v
e
y
b
y
[
1
]
th
en
[
2
]
-
[
4
]
,
s
ig
n
i
f
ica
n
t
in
te
r
ests
o
n
s
en
s
o
r
less
s
lid
in
g
m
o
d
e
co
n
tr
o
l
o
f
i
n
d
u
c
t
io
n
m
o
to
r
h
av
e
b
ee
n
d
ev
elo
p
e
d
in
t
h
e
co
n
tr
o
l
r
esear
c
h
d
u
e
t
o
th
e
p
o
s
s
ib
ilit
y
to
i
m
p
le
m
en
t
t
h
is
co
n
tr
o
l
in
in
d
u
s
tr
ial
ap
p
licatio
n
s
u
s
i
n
g
n
e
w
p
o
w
er
elec
tr
o
n
ics
tech
n
o
lo
g
y
an
d
av
ailab
il
it
y
ch
ea
p
an
d
f
ast
co
m
p
u
tatio
n
.
Desp
ite
th
e
i
m
p
o
r
ta
n
t
d
ev
elo
p
m
e
n
t
s
o
f
th
e
s
e
n
s
o
r
les
s
co
n
t
r
o
l
la
w
s
ab
o
v
e
b
u
t
th
e
y
s
u
f
f
er
f
r
o
m
lar
g
e
co
m
p
u
t
atio
n
ti
m
e,
co
m
p
lex
it
y
,
p
ar
a
m
eter
s
v
ar
iatio
n
,
a
n
d
li
m
i
ted
b
an
d
w
id
th
co
n
tr
o
l
i
n
th
e
lo
w
a
n
d
n
ea
r
-
ze
r
o
s
p
ee
d
r
e
g
io
n
s
esti
m
atio
n
.
I
n
th
is
p
ap
er
,
a
n
o
n
lin
ea
r
s
lid
in
g
m
o
d
e
s
p
ee
d
a
n
d
r
o
to
r
f
lu
x
co
n
tr
o
l
co
m
b
i
n
ed
w
it
h
a
s
t
ab
le
f
u
zz
y
m
u
tu
al
m
o
d
el
r
ef
er
e
n
ce
ad
ap
tiv
e
s
y
s
te
m
(
FM
-
M
R
A
S)
s
p
ee
d
an
d
s
tato
r
r
esis
tan
ce
e
s
ti
m
ati
o
n
f
o
r
th
e
in
d
u
ctio
n
m
o
to
r
d
r
iv
e
h
as
b
ee
n
d
e
v
elo
p
ed
.
B
y
co
m
b
in
a
tio
n
t
h
e
id
ea
s
o
f
[
5
]
-
[
8
]
,
th
e
p
r
o
p
o
s
ed
FM
-
MR
A
S
u
tili
ze
s
t
w
o
m
o
d
el
s
ca
lled
as
r
ef
er
en
ce
a
n
d
ad
j
u
s
tab
le
m
o
d
els
w
h
o
s
e
b
ased
o
n
th
e
r
o
to
r
f
lu
x
er
r
o
r
s
v
ec
to
r
s
[
9
]
-
[
1
2
]
.
T
h
en
,
th
ese
er
r
o
r
s
ar
e
u
s
ed
d
r
iv
e
a
d
ap
tatio
n
m
ec
h
an
i
s
m
s
b
ased
o
n
th
e
f
u
zz
y
lo
g
ic
t
h
at
g
en
er
ates
in
p
ar
allel
th
e
esti
m
ated
s
p
ee
d
an
d
s
tato
r
r
esis
ta
n
ce
,
th
i
s
p
ar
allel
esti
m
atio
n
i
s
d
esi
g
n
ed
b
ased
o
n
th
e
co
n
ce
p
t
o
f
h
y
p
er
s
tab
ili
t
y
[
6
]
in
o
r
d
er
to
m
ak
e
t
h
e
s
y
s
te
m
as
y
m
p
to
tica
l
l
y
s
tab
le
.
T
h
e
i
m
p
o
r
tan
t
ad
v
a
n
tag
e
o
f
u
s
i
n
g
f
u
zz
y
lo
g
ic
is
r
o
b
u
s
t
n
es
s
ag
a
in
s
t
p
ar
am
eter
v
ar
iatio
n
s
.
T
h
e
w
h
o
le
p
r
o
p
o
s
ed
s
y
s
te
m
r
o
b
u
s
tn
e
s
s
,
s
tab
il
it
y
,
ef
f
ec
tiv
e
n
e
s
s
i
n
tr
ac
k
i
n
g
is
tes
ted
in
s
i
m
u
latio
n
.
Fi
n
all
y
,
s
o
m
e
co
m
m
e
n
ts
ar
e
p
r
esen
ted
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
iS
y
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2021
:
1987
–
1
9
9
8
1988
2.
M
AT
H
E
M
AT
I
CAL M
O
DE
L
O
F
I
ND
UC
T
I
O
N
M
O
T
O
R
T
h
e
m
o
d
el
u
s
ed
is
th
e
m
o
d
el
w
h
o
s
e
elec
tr
ical
q
u
an
tit
ies
ar
e
all
ex
p
r
ess
ed
in
a
f
ix
ed
f
r
a
m
e
lin
k
ed
to
th
e
s
tato
r
an
d
w
h
ich
w
i
ll b
e
q
u
ali
f
ied
m
o
d
el
(
,
)
.
T
h
e
m
o
d
el
is
g
iv
en
b
y
[
1
3
]
,
[
14]
.
{
̇
=
(
)
+
.
=
ℎ
(
)
(
1
)
W
ith
{
=
[
]
=
[
]
=
[
1
2
3
4
5
]
(
2
)
T
h
e
s
tate
v
ec
to
r
x
is
co
m
p
o
s
ed
o
f
t
w
o
elec
tr
ical
s
tate
s
(
,
)
an
d
t
w
o
m
a
g
n
e
tic
s
tate
s
(
,
)
an
d
a
s
tate
r
ep
r
esen
tin
g
t
h
e
r
o
tatio
n
al
s
p
ee
d
o
f
th
e
r
o
to
r
,
th
is
s
p
ee
d
w
ill
b
e
p
r
esen
ted
b
y
a
m
ec
h
a
n
ical
eq
u
atio
n
,
an
d
ℎ
ar
e
f
u
n
ct
io
n
s
o
f
th
e
v
ar
iab
les
x
.
Hen
ce
th
e
n
o
n
lin
ea
r
s
y
s
te
m
is
o
f
o
r
d
er
5
.
{
̇
1
=
−
1
+
3
+
4
5
+
̇
2
=
−
2
+
4
−
3
5
+
̇
3
=
1
−
1
3
−
4
5
̇
4
=
2
−
1
4
+
3
5
̇
5
=
(
2
3
−
1
4
)
−
1
(
3
)
w
it
h
=
+
1
(
1
−
)
;
=
1
;
=
;
Γ
=
1
(
1
−
)
;
=
;
=1
-
2
W
h
er
e
is
th
e
s
tato
r
r
esis
tan
ce
;
is
th
e
r
o
to
r
r
esis
tan
ce
;
is
th
e
s
tato
r
in
d
u
c
tan
ce
;
is
th
e
r
o
to
r
in
d
u
cta
n
ce
;
is
th
e
m
u
t
u
al
in
d
u
ctan
ce
;
r
o
to
r
tim
e
co
n
s
tan
t;
is
th
e
leak
ag
e
co
ef
f
icie
n
t;
is
th
e
n
u
m
b
er
o
f
p
o
le
p
air
s
;
is
m
o
m
e
n
t o
f
i
n
er
t
ia;
is
th
e
lo
ad
to
r
q
u
e.
3.
NO
NL
I
N
E
AR
SL
I
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.
1
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Def
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.
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Fig
u
r
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1
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d
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o
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ed
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t
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Fig
u
r
e1
.
C
h
atter
i
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t
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itc
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y
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te
m
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n
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h
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lid
in
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u
r
f
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e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
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b
al
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a
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6
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[
1
8
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=
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=
(
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(
6
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is
a
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tan
t
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ac
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d
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itio
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.
3
.
2
.
Select
io
n o
f
t
he
co
ntr
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Ou
r
g
o
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is
to
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en
er
ate
a
c
o
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tr
o
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la
w
[
]
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s
i
n
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th
e
s
lid
i
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co
n
tr
o
l
th
eo
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y
.
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h
e
s
tates
co
n
s
id
er
ed
f
o
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th
e
i
n
d
u
c
tio
n
m
o
to
r
co
n
tr
o
l a
r
e:
Sp
ee
d
an
d
r
o
to
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f
lu
x
(
,
)
.
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n
th
e
co
n
tr
o
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m
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t
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r
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k
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1
9
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0
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(
3
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d
(
10
)
,
th
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d
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m
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t o
f
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lc
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l
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s
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iv
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s
.
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2
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(
4
+
3
)
(
11
)
Su
c
h
as
.
x
x
x
x
x
x
x
x
xx
x
x
x
ì
ï
=+
ï
ï
ï
=+
í
ï
ï
ï
=+
ï
î
1
1
3
2
4
2
2
3
1
4
22
3
1
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
iS
y
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2021
:
1987
–
1
9
9
8
1990
T
h
e
s
y
s
te
m
(
11
)
ca
n
b
e
r
ea
r
r
a
n
g
ed
i
n
to
th
e
f
o
llo
w
in
g
m
atr
ix
f
o
r
m
.
43
1
1
34
2
2
s
s
mm
F
U
D
S
u
xx
F
S
u
L
x
L
x
F
S
(
12
)
w
it
h
{
1
=
(
1
−
1
−
)
2
−
1
1
−
5
(
1
+
)
−
1
1
̇
−
1
̈
2
=
(
2
+
−
2
)
+
(
3
+
(
2
−
3
−
)
1
+
5
2
)
(
13
)
T
o
ch
ec
k
th
e
L
y
ap
o
n
o
v
’
s
s
tab
ilit
y
co
n
d
it
io
n
,
o
n
e
m
u
s
t h
a
v
e
.
̇
=
−
(
)
(
14
)
E
q
u
alizin
g
(
12
)
an
d
(
14
)
w
e
will h
a
v
e
.
=
−
−
1
(
)
−
−
1
(
15
)
A
cc
o
r
d
in
g
to
(
5
)
th
e
co
n
tr
o
l la
w
co
m
p
o
n
en
t
s
ar
e
g
i
v
en
b
y
.
{
=
−
−
1
=
−
−
1
(
)
(
16
)
4.
F
U
Z
Z
Y
M
UT
UA
L
M
RASO
B
SE
RV
E
R
4
.
1
.
M
RAS
ba
s
ed
ro
t
o
r
s
peed
esti
m
a
t
io
n
T
h
e
p
r
in
cip
le
o
f
s
p
ee
d
esti
m
a
t
io
n
b
y
MR
AS
b
ased
o
n
r
o
to
r
f
lu
x
co
n
s
is
t
s
in
co
m
p
ar
in
g
th
e
o
u
tp
u
ts
o
f
t
w
o
f
lu
x
est
i
m
a
to
r
s
o
b
tain
ed
b
y
d
i
f
f
er
e
n
t
f
o
r
m
u
latio
n
s
.
T
h
e
f
ir
s
t
est
i
m
a
to
r
is
b
ased
o
n
th
e
s
tato
r
eq
u
atio
n
s
d
ef
in
i
n
g
a
m
o
d
el
i
n
v
o
ltag
e
c
alled
th
e
r
ef
er
e
n
ce
m
o
d
el.
T
h
i
s
m
o
d
el
is
u
s
ed
to
esti
m
ate
t
h
e
co
m
p
o
n
en
t
s
f
lu
x
an
d
f
r
o
m
th
e
m
ea
s
u
r
e
m
e
n
t
o
f
v
o
ltag
e
s
an
d
s
tato
r
cu
r
r
en
ts
;
b
ein
g
i
n
d
ep
en
d
en
t
o
f
th
e
s
p
ee
d
to
esti
m
ate
it a
cc
o
r
d
in
g
to
t
h
e
f
o
l
lo
w
i
n
g
[
5
]
,
[
7
]
,
[
2
1
]
.
=
[
]
=
{
[
]
−
[
]
−
[
]
}
(
17
)
T
h
e
s
ec
o
n
d
,
ca
lled
ad
j
u
s
tab
le
o
r
ad
ap
tiv
e
m
o
d
el,
is
d
escr
ib
ed
b
y
th
e
r
o
to
r
eq
u
atio
n
s
to
esti
m
atet
h
e
co
m
p
o
n
e
n
t
s
f
l
u
x
an
d
; B
ein
g
ex
p
licitl
y
li
n
k
ed
to
s
p
ee
d
,
h
e
d
ef
i
n
es a
cu
r
r
en
t
m
o
d
el
is
b
ei
n
g
as.
̂
=
[
̂
̂
]
=
{
−
1
[
1
0
0
1
]
−
̂
[
0
−
1
1
0
]
}
[
̂
̂
]
+
[
]
(
18
)
Su
c
h
as
̂
is
th
e
r
o
to
r
p
u
ls
atio
n
w
it
h
:
̂
=
.
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.
T
h
e
d
if
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er
en
ce
b
et
w
ee
n
th
e
co
m
p
o
n
en
t
s
o
f
th
e
r
o
to
r
f
lu
x
d
eliv
er
ed
at
th
e
o
u
tp
u
ts
o
f
th
e
t
w
o
m
o
d
el
s
is
u
s
ed
to
d
r
iv
e
an
ad
ap
tatio
n
m
ec
h
a
n
is
m
w
h
o
s
e
o
b
j
ec
tiv
e
is
to
g
e
n
er
ate
t
h
e
v
al
u
e
o
f
t
h
e
e
s
ti
m
ated
s
p
ee
d
w
h
itch
t
h
e
n
r
ea
p
p
lied
to
th
e
in
p
u
t o
f
t
h
e
ad
j
u
s
tab
le
m
o
d
el
w
it
h
.
=
(
̂
−
̂
)
(
19
)
an
d
̂
=
(
+
)
(
20
)
F
ig
u
r
e
2
,
s
h
o
w
s
th
e
s
t
r
u
c
tu
r
e
o
f
a
cl
a
s
s
i
ca
l
MRA
S
s
p
e
e
d
e
s
t
im
a
t
o
r
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I
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12
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I
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P
o
w
E
lec
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Dr
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I
SS
N:
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8
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694
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f
o
r
th
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s
a
k
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f
s
i
m
p
licit
y
.
Af
ter
s
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v
er
al
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t
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m
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ts
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zz
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b
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(
NB
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n
eg
a
tiv
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b
ig
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P
B
:
p
o
s
itiv
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b
ig
,
NS:
n
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ati
v
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s
m
a
ll
,
P
S:
p
o
s
itiv
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s
m
all
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Z
E
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ze
r
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eq
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al
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w
a
s
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av
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f
o
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th
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w
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r
th
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ea
t
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t
o
f
th
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m
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th
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Ma
x
-
Min
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f
Ma
m
d
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w
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th
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n
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m
et
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d
o
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d
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f
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ter
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f
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h
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el
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le
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ase
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as
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y
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f
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h
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in
f
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m
atr
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w
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n
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le
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cc
o
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d
in
g
to
th
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n
tr
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co
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)
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)
or
(
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)
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∆
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.
T
ab
le
1
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I
n
f
er
en
ce
m
atr
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x
d
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f
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b
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th
f
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zz
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tr
o
ller
s
∆
NB
NS
ZE
PS
PB
∆
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NB
NB
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PB
PS
NS
ZE
NS
ZE
PS
ZE
ZE
PB
PB
ZE
PS
NB
PS
ZE
PS
PB
NS
NB
PB
PB
PS
NS
NS
NB
5.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
I
n
o
r
d
er
to
d
em
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s
tr
ate
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alid
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th
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g
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er
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r
m
an
ce
o
f
th
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p
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p
o
s
ed
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en
s
o
r
less
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m
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-
b
ased
co
n
tr
o
l
s
y
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te
m
a
s
s
o
ciat
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w
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th
FM
-
MR
AS
o
b
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er
v
er
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s
o
m
e
s
elec
ted
s
i
m
u
lat
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ar
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p
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esen
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n
d
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th
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o
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t
w
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tlab
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m
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li
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t.
T
h
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v
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ti
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ated
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cin
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a
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iatio
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o
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th
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ce
s
p
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g
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m
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l
tan
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tato
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ce
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p
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less
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c
tio
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t
o
ac
cu
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atel
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m
ate
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er
y
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w
s
p
ee
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s
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h
e
s
tato
r
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esi
s
tan
ce
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s
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ti
m
ated
co
n
cu
r
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en
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it
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th
e
s
p
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ti
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p
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ate
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o
r
th
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f
l
u
ctu
a
tio
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in
s
tato
r
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esis
t
an
ce
.
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h
e
s
tu
d
y
i
s
ap
p
lied
f
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r
b
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th
in
d
u
ctio
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m
o
to
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o
p
e
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atin
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m
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e
m
o
to
r
m
o
d
e
an
d
th
e
r
e
g
en
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g
m
o
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t
h
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m
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o
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th
e
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s
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ted
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itiv
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to
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u
e
w
h
en
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u
n
n
in
g
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e
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h
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p
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n
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f
t
h
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ac
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ar
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s
h
o
w
n
i
n
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ab
le
2
.
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h
e
ac
cu
r
ac
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o
f
s
p
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esti
m
a
tio
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h
a
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ee
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ied
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p
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s
,
t
w
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en
ch
m
ar
k
s
ar
e
p
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o
p
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s
ed
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d
d
is
cu
s
s
ed
in
t
h
is
p
ap
er
as t
w
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ca
s
e
s
tu
d
ie
s
.
-
T
h
e
f
ir
s
t,
d
esig
n
ated
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ca
s
e
1
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,
s
h
o
w
s
t
h
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o
p
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o
f
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m
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t o
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ab
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to
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s
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I
n
t J
P
o
w
E
lec
&
Dr
iS
y
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2021
:
1987
–
1
9
9
8
1994
5
.
1
.
Ca
s
e
1
:
hig
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s
peeds
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pe
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t
io
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c
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r
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10.
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r
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11
.
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esp
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x
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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694
I
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Vo
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12
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4
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Dec
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er
2021
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1996
A
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