In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
3, S
ep 2019,
pp.
1
1
6
7
~1
1
7
7
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
3.pp1167-1177
1167
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Real-time implementation of a
novel hybrid fuzzy sliding m
ode
contr
o
l of a BLDC motor
Al
i
Mo
usmi,
Ah
me
d
Abbo
u
,
Y
a
s
sin
e
El Ho
um
M
o
h
a
m
e
d V
Un
iv
e
r
s
i
t
y
, M
ohamm
ad
ia S
cho
o
l
’
s o
f
En
g
i
n
eers
,
Moro
cco
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
No
v
2
1
,
2
018
Re
vise
d Mar
1,
201
9
Ac
ce
p
t
ed
M
ar 1
9
,
2
019
Th
is
p
aper
p
resent
s
a
no
vel
hyb
rid
con
t
ro
l
o
f
a
B
LD
C
moto
r
usin
g
a
m
i
x
e
d
s
l
i
d
i
n
g
m
o
d
e
a
n
d
f
u
z
z
y
l
o
g
i
c
c
o
n
t
r
o
l
l
e
r
.
T
h
e
o
b
j
e
c
t
i
v
e
i
s
t
o
b
u
ild
a
f
a
s
t
a
nd
rob
u
s
t
c
o
n
t
r
o
ller
w
h
i
c
h
overco
m
e
clas
si
cal
c
o
n
t
r
ol
lers’
in
con
v
e
ni
ences
a
nd
exp
l
o
i
t
the
f
a
st
r
es
po
nse
o
f
b
ru
s
h
less
d
c
m
o
to
rs
c
hara
ct
erized
by
a
n
in
te
n
s
e
t
o
r
q
u
e
a
n
d
f
a
s
t
r
e
s
p
o
n
s
e
t
i
m
e
.
F
i
r
s
t
t
h
e
p
a
p
e
r
s
t
u
d
y
p
r
o
s
a
n
d
c
on
s
of
b
oth
sliding
mode
a
nd
f
uzzy
l
ogi
c
c
o
n
t
r
o
l
l
e
r
s
.
T
h
e
n
t
h
e
n
o
v
e
l
c
o
n
t
r
o
ller
and
i
t
s
st
abili
t
y
dem
o
n
s
trati
o
n
are
prese
n
ted
.
F
i
n
ally
t
h
e
p
ropo
sed
co
n
tr
ol
le
r
me
t
h
o
d
is
us
e
d
fo
r t
h
e s
p
eed
c
ont
rol
of
a
BLDC
moto
r 3KW.
T
h
e
ob
t
ain
e
d
resul
ts
a
re
com
p
are
d
w
it
h
th
os
e
o
f
a
f
uzzy
l
og
ic
a
nd
a
c
on
vent
io
nal
s
l
idi
n
g
m
o
d
e
con
t
ro
ller.
It
a
llow
s
to
s
how
p
erf
o
rm
an
ce
o
f
t
he
p
rop
o
s
e
d
cont
r
oller
in
t
e
r
ms
of
s
p
e
e
d
r
es
po
ns
e
and
re
acti
o
n
agai
ns
t
d
i
s
t
u
r
bances,
wh
ich
is
i
mproved
more
th
an 5
tim
es witho
u
t
lo
si
ng st
ab
ilit
y
o
r alterin
g
t
racki
n
g
accu
racy.
K
eyw
ord
s
:
Br
ush
l
e
s
s
D
C
m
o
t
or
(
BLD
C
)
Fuz
z
y lo
g
i
c
co
ntr
o
l (F
LC
)
H
ybri
d
c
o
n
t
r
ol
ler
S
lid
ing
mode
c
ontro
l
(S
MC)
Sp
ee
d
co
nt
rol
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
A
li M
o
usm
i
,
D
e
pa
rtem
ent o
f
E
lectr
i
c
a
l E
n
gi
nee
r
in
g,
Mo
ham
e
d V
Uni
v
ersi
t
y
,
Mo
ham
m
a
d
i
a
S
choo
l’s of
E
n
g
ine
e
rs,
Ibn
S
i
na,
B, P
7
65
A
gda
l Ra
ba
t
,
Morocco.
Em
ail:
am
ousm
i
@gma
i
l
.
c
o
m
1.
I
N
TR
OD
U
C
TI
O
N
BLD
C
mo
to
rs,
a
l
so
k
no
wn
a
s
p
e
rma
n
ent
-
mag
n
e
t
DC
s
yn
ch
rono
us
m
o
t
o
r
s
ha
ve
a
s
erie
s
of
adva
n
t
a
g
e
s
l
i
k
e
t
h
e
s
i
m
p
le
s
t
r
uc
tur
e
,
fa
ste
r
t
or
que
r
es
po
ns
e,
h
ig
h
e
f
fi
ci
en
cy
,
h
i
gh
e
r
s
pe
ed
r
ang
e
s,
n
oi
sel
e
ss
opera
tio
n
an
d
lon
g
e
r
l
ife
time
.
C
om
bi
n
i
n
g
a
l
l
t
hese
b
e
n
e
f
i
t
s
m
a
kes
BLD
C
motors
be
m
or
e
sui
t
a
b
le op
t
i
on for
in
dus
try,
such
as e
lec
t
ric ve
h
i
cles,
rob
o
t
i
cs,
and
h
o
m
e
app
l
i
an
ce
s [1,
2]
. Com
p
are
d
to i
n
d
u
ct
i
on m
ach
i
n
e
s
,
the
spee
d
an
d
i
n
te
ns
it
y
of
t
he
e
l
ectric
tor
que
i
s
an
u
n
d
e
n
ia
b
l
e
adv
a
n
ta
ge
o
f
brus
hle
ss
m
o
tor
s
.
To
b
e
n
e
f
i
t
f
r
o
m
tha
t
,
ta
ki
ng
i
n
to
a
c
c
o
u
n
t
its
n
o
n
-l
i
n
ea
r
na
tur
e
a
nd
mo
del
i
n
g
e
r
ro
rs
,
o
n
e
h
as
t
o
bu
ild
a
co
nt
ro
l
l
e
r
as
f
ast
as
pos
si
b
l
e
overc
o
m
in
g t
h
e
pro
b
l
em
s
of
p
a
r
a
m
e
t
r
i
c
u
n
ce
rta
i
n
t
i
e
s.
S
e
ve
ral
c
o
ntro
l
law
s
h
ave
be
en
u
se
d
for
sp
e
e
d
co
n
t
ro
l
o
f
e
lec
t
r
ic
m
ot
ors
inc
l
ud
i
ng
BL
D
C
M,
P
ID
c
o
nt
roll
e
r
[
3
,
4
],
s
l
i
d
i
ng
m
od
e
c
ont
rol
l
e
rs
(
SM
C
)
[
5
,
6
]
,
Fu
z
z
y
l
o
g
i
c
c
ontr
o
l
l
ers
(F
LC
)
[7,
8]
a
nd
a
d
apta
t
i
v
e
con
t
ro
l
[9
]
e
t
c
.
B
u
t
g
i
ve
n
t
h
e
l
i
m
ita
tio
ns
o
f
ea
ch
c
ontr
o
l
l
er
,
r
esea
rche
rs
a
re
c
ons
t
a
nt
ly
e
xp
l
o
ring
a
l
l
m
oder
n
t
e
c
hni
qu
e
s
a
nd
i
t
s
d
if
fe
rent
p
o
s
si
bl
e
c
o
mbi
n
a
t
ion
s
i
n
o
r
d
e
r
t
o
set
u
p
a
no
n-l
i
ne
ar,
effic
i
ent
a
nd
ro
bu
st
s
pe
e
d
con
t
ro
l
l
er w
hic
h
o
ve
rcom
es th
e
d
isad
va
nta
g
e
s
of co
n
v
en
t
i
ona
l
p
r
o
p
o
rtio
na
l,
de
r
iva
t
ive
a
n
d
inte
gral r
eg
u
l
ators.
F
o
r
exa
m
ple,
P
I
contro
ll
e
r
,
t
h
e
most
p
op
u
l
ar
i
n
i
n
dustry,
r
e
qui
res
a
li
n
e
a
r
ized
s
yst
e
m
mode
l
a
n
d
i
t
i
s
ver
y
li
m
i
te
d i
n
te
r
ms
o
f a
d
ap
ta
ti
o
n
to l
o
a
d
v
aria
ti
o
n
s an
d
para
me
t
r
i
c u
n
c
e
r
t
a
in
ti
es.
S
l
i
d
i
n
g
m
ode
c
on
tro
l
i
s
a
va
riab
le
s
t
r
uc
ture
c
o
n
tro
l
t
ha
t
h
a
s
g
ro
wn
c
o
n
s
i
d
erab
ly
i
n
re
c
e
n
t
d
e
cad
es
[1
0-1
2
].
T
hi
s
i
s
m
a
i
n
l
y
due
t
o
its
s
imple
s
t
ruc
t
ur
e,
t
he
f
a
s
t
c
o
n
ve
r
g
enc
e
pro
p
e
r
ty
i
n
fin
i
te
tim
e,
a
nd
i
t
s
g
r
ea
t
rob
u
st
n
e
ss
a
g
a
i
n
s
t
m
o
del
i
n
g
e
rrors
a
nd
so
m
e
t
ypes
of
e
xter
na
l
d
i
s
t
u
rb
ance
s
[
1
2].
The
pr
i
n
c
i
ple
of
s
l
i
d
i
n
g
mode
c
on
t
r
ol
i
s
t
o
c
on
stra
in
t
he
s
y
s
tem
s
t
a
t
etra
jec
t
or
y
to
r
ea
c
h
a
g
i
ve
n
s
u
rfa
c
e
,
cal
led
a
sl
id
i
ng
s
u
rfa
ce
or
slid
i
ng
variab
l
e
,
and
th
e
n
r
em
ain
t
h
ere
.
T
he
m
ajor
d
isa
d
v
a
nta
g
e
o
f
t
h
is
c
on
tro
l
i
s
its
d
i
s
c
o
nti
n
u
o
u
s
na
ture,
in
prac
t
i
c
e
i
t
i
n
d
u
ces
h
i
gh
freq
u
e
n
c
y
s
w
itc
hi
ng
kn
ow
n
a
s
c
hat
t
eri
n
g
p
h
e
nome
n
o
n
o
nc
e
th
e
sli
d
in
g
s
u
rface
i
s
re
ac
h
e
d
.
I
n
f
act
,
th
ese
co
mmu
t
at
io
ns
c
a
n
e
x
c
i
t
e
u
n
w
an
ted
dyn
ami
cs
w
hic
h
m
a
y
d
e
s
t
a
bil
i
ze
,
de
ter
i
or
a
t
e
or
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
1
6
7
–
1
177
1
168
e
v
e
n
d
e
s
t
r
o
y
t
h
e
s
t
u
d
i
e
d
s
y
s
t
e
m
.
T
h
e
r
e
a
r
e
v
a
r
i
o
u
s
m
e
t
h
o
d
s
t
o
r
e
d
u
c
e
th
is
p
he
nom
en
o
n
,
the
be
st
kno
w
n
o
f
w
h
ic
h
is
t
he
e
qu
i
v
ale
n
t
c
o
nt
r
o
l
[
1
3]
w
it
h
r
e
place
me
n
t
o
f
t
h
e
d
i
scon
tin
uou
s
fu
n
c
ti
on
b
y
a
c
o
n
t
i
n
uo
us
a
ppr
ox
i
m
a
tio
n
in
v
ic
in
i
t
y
o
f
t
h
e
s
l
id
ing
surf
ace
(
satura
ti
o
n
fu
nc
t
i
o
n
o
r
si
gm
oid
f
unc
tio
n)
.
A
n
o
t
h
e
r
m
e
th
o
d
i
s
to
u
se
h
igh
or
de
r
sli
d
ing
m
o
des
[
14-
16]
,
w
hose
pr
inc
i
ple
is
t
o
re
ject
t
he
d
i
s
c
o
nt
i
n
u
iti
es
byc
o
n
tro
l
lin
g
a
n
d
c
a
nce
l
in
g als
o
the
u
pper
der
i
v
a
ti
ves
of t
he sl
i
di
n
g
v
a
r
i
a
b
l
e.
O
n t
h
e ot
he
r
h
a
nd,
se
v
er
a
l
w
a
y
s o
f
o
p
tim
i
z
i
ng t
h
e
S
M
C
d
i
sc
on
t
i
nu
o
u
s
m
e
m
b
r
a
ne
g
a
i
n
us
i
n
g
inte
l
l
i
g
e
n
t
al
g
o
r
i
th
m
s
w
e
r
e
u
se
d,
e
.
g
,
by
c
ombi
n
i
n
g
S
M
C
w
i
t
h
f
u
z
z
y
l
o
g
i
c
[
1
7
-
1
9
]
o
r
w
i
t
h
P
a
r
t
i
c
l
e
S
w
a
r
m
[
2
0
]
,
e
t
c
.
T
h
e
g
e
n
e
r
a
l
p
r
inc
i
pl
e
of
t
hi
s
ki
nd
o
f
regul
ato
r
i
s
to
r
e
duce
t
h
e
ga
i
n
a
s
w
e
a
ppr
oa
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s
t
he
s
l
i
di
n
g
s
ur
fac
e
a
n
d
t
o
pa
s
s
the
bat
o
n
to
t
he
s
o-
ca
ll
e
d
e
q
u
iva
l
e
n
t
c
o
n
t
r
o
l
pa
rt
t
o
c
o
nt
r
o
l
the
sys
t
em
o
nc
e
t
h
e
sl
i
d
i
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g
sur
f
ac
e
i
s
r
ea
ch
ed.
I
t
d
ec
r
e
a
s
e
s
t
he
c
ha
tter
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g
phe
n
o
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b
u
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r
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a
u
se
t
he
d
i
s
c
o
n
t
in
uou
s
me
mbr
a
ne
e
ns
ur
i
ng
per
f
or
ma
nce
a
g
ai
nst
par
a
me
tr
ic
unc
er
tai
n
tie
s
is
w
e
a
kene
d.
Fu
zz
y
Logi
c
co
nt
rol
i
s
o
n
e
o
f
th
e
mo
st
popu
l
a
r
st
rat
e
g
i
es
f
o
r
m
a
n
ag
i
ng
unce
r
tai
n
c
on
tr
ol
s
ys
tem
s
,
ba
se
d
o
n
t
he
f
uzz
y
s
et
t
he
or
y
i
n
t
r
o
d
u
c
e
d
b
y
ZA
D
I
H
i
n
1
96
5
[
21]
;
I
t
is
a
no
t
h
er
a
p
p
r
o
a
c
h
t
h
a
t
w
or
ks
w
it
h
o
u
t
kn
ow
i
n
gt
hes
y
s
t
e
m
m
ode
l
,
w
he
r
e
t
h
e
com
m
a
nd
is
c
a
l
c
u
l
a
te
d
bas
e
d
on
h
eur
i
s
tic
k
now
l
e
dge
w
it
h
out
know
in
g
the
sys
t
em
p
a
r
am
ete
r
s.
I
t
has
bee
n
s
uc
ce
ssful
l
y
a
pp
l
i
e
d
f
o
r
d
if
f
e
r
e
nt
i
ndu
st
ri
a
l
p
ro
c
e
sses
c
on
t
r
ol
[
1
3
]
,
t
h
e
r
e
sults
s
h
o
w
t
h
at
t
he
f
uzz
y
c
on
tr
o
l
l
e
r
,
d
e
s
pite
i
ts
lit
t
l
e
l
ong
r
e
s
p
o
n
s
e
t
i
m
e
,
g
i
v
e
s
a
p
e
r
f
e
c
t
p
u
r
s
u
i
t
w
i
t
h
o
u
t
an
yo
v
e
rsho
ot
.
Thi
s
p
a
p
e
r
p
r
e
se
nt
s
a
hyb
ri
d
c
o
nt
roll
er
c
o
m
b
i
ni
ng
p
erf
o
rma
n
ce
s
o
f
t
w
o
c
om
ma
nd
t
ype
s
;
i
t
fa
v
o
r
i
z
e
the
sl
i
d
i
n
g
m
o
de
c
ontro
l
l
er
a
t
t
h
e
d
y
n
am
i
c
r
egim
e
a
n
d
t
h
e
fuzz
y
l
og
ic
c
ontr
o
l
l
er
a
t
sta
t
i
c
r
egim
e,
b
y
u
s
i
ng
a
se
l
e
c
t
i
on
f
u
nc
t
i
o
n
a
ll
ow
i
ng
a
ver
y
s
m
o
o
t
h
c
o
mm
utat
i
on
be
t
w
een
t
he
t
w
o
c
on
tr
o
l
ler
s
.
T
h
e
paper
i
s
o
r
g
a
n
i
z
e
d
a
s
f
o
l
l
o
w
s
:
i
n
t
h
e
s
e
c
o
n
d
s
e
c
t
i
o
n
t
h
e
b
r
u
s
h
l
e
s
s
m
o
t
o
r
m
o
d
e
l
a
n
d
i
t
s
oper
a
t
i
n
g
p
r
i
nc
i
p
le
a
r
e
p
r
e
se
nt
e
d
.
The
th
ir
d se
c
t
i
on
pr
ese
n
t
s
t
he
t
he
o
r
y
of
c
la
ssica
l
slid
i
ng m
o
de,
d
e
ter
m
i
n
at
i
on
of
b
r
u
sh
les
s
m
ot
or
c
o
n
t
r
o
l
l
a
w
usin
g
th
is
c
om
ma
nd
t
ype
a
nd
d
isc
u
ssio
n
o
n
h
i
s
pr
oble
m
s.
I
n
the
fo
ur
t
h
s
ec
ti
on,
t
h
e
f
uzz
y
P
I
contr
o
l
l
er
a
nd
i
ts
im
pl
e
m
e
n
ta
t
i
o
n
a
r
e
p
r
e
se
n
t
e
d
.
The
f
i
ft
h
se
c
tio
n
pr
ese
n
ts
t
he
p
r
op
ose
d
c
on
tr
o
l
ler
a
n
d
i
t
s
sta
b
i
l
ity
s
t
u
d
y
.
Th
e
las
t
s
e
c
ti
on
w
i
l
l
p
r
e
se
nt
a
nd
d
i
scuss
t
h
e
ex
pe
r
i
me
nt
a
l
r
e
s
u
lts
us
in
g
a
B
L
D
C
m
otor
3
K
W
,
8
0
V
,
300
0r
pm
.
2.
MO
DELI
N
G
O
F
B
R
USHLES
S
D
C
MOTO
R
The
e
q
u
i
vale
n
t
m
ode
l
o
f
t
he
B
LD
CM
d
r
i
ve
s
ys
tem
w
i
t
h
t
he
ass
u
mpt
i
on
o
f
t
h
r
e
e-
phase
s
ym
me
tr
ic
sta
t
or
w
indi
n
g
s
is
s
how
n
i
n
F
i
gur
e
1.
F
i
gur
e
1.
T
he
f
ull
br
id
ge
d
r
i
vi
ng
c
i
r
c
ui
t
of
B
LD
C
m
o
tor
The
t
e
r
m
in
a
l
v
ol
t
a
ge
e
qu
at
i
o
n
of
t
hr
ee-
p
h
ase
sta
t
or
w
ind
i
ng
sis
e
x
pr
essed
a
s
:
(
1
)
(
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Rea
l
-
tim
e
im
pl
em
e
n
t
a
ti
on
o
f
a nove
l
hy
br
id fu
zzy
sl
i
d
i
ng m
ode
c
o
n
t
r
o
l
o
f
a BL
D
C
m
o
t
o
r
(
A
li
Mousm
i
)
1
169
Whe
r
e
R
i
s t
h
e
st
a
t
or
r
e
s
i
s
t
a
n
c
e,
L
is
the
s
t
at
or
i
nd
uc
ta
nce,
V
a
,
V
b
a
nd
V
c
ar
e
t
he
t
er
mina
l
vol
tage
s
o
f
the
t
h
ree
-
pha
se
s
ta
tor
wi
n
d
in
g
respe
c
t
i
ve
l
y
;
i
a
,
i
b
a
n
d
i
c
a
r
e
t
h
e
s
t
a
t
o
r
c
u
r
r
e
n
t
s
;
e
a
,
e
b
a
n
d
e
c
a
r
e
t
h
e
p
h
a
s
e
b
a
c
k
EMF
s
;
T
em
a
nd
Ω
r
e
pr
esent
e
l
ectr
o
m
a
g
n
e
tic
t
or
que
a
n
d
r
oto
r
a
ngu
lar
velo
c
it
y r
e
spec
ti
ve
ly
.
T
h
e
con
t
ro
ll
ed
b
ru
shl
e
ss
D
C
mo
t
o
r
con
s
i
s
ts
o
f
a
th
re
e
ph
a
s
e
wi
n
di
ng
s
st
ato
r
a
nd
a
p
erma
n
e
nt
ma
g
n
e
t
rot
o
r
Fi
gu
re
1
a
n
d
it
s
wi
ndi
ng
s
are
s
t
ar
c
onn
ec
t
e
d
.
T
h
e
m
o
t
o
r
i
s
oper
a
t
e
d
i
n
t
w
o
phase
s
c
o
n
duc
t
i
o
n
m
ode
i
n
w
h
ic
h
e
a
c
h
p
hase
v
o
l
t
a
ge
i
s
e
n
er
g
i
z
e
df
or
a
n
inte
r
v
al o
f
12
0
°e
lec
t
r
i
cal acc
ord
i
ng
to t
h
e ro
torel
e
c
t
r
i
c
a
l
pos
i
tio
n.
Bas
ic
a
l
l
y
,
ther
e
are
si
x
di
ffe
r
e
n
t
s
ec
tor
s
,
in
w
hich
j
u
s
t
tw
o
pha
s
e
s
a
r
e
pow
e
r
ed;
o
n
e
i
s
con
n
e
c
t
e
d
t
o
t
he
pos
i
tive
ter
m
in
al of
t
h
e DC
b
us +
V
DC
an
d
th
e
o
t
h
er
to
-
V
DC
.
The
r
o
t
o
r
p
o
s
iti
on
i
s
de
t
er
mi
ned
usin
g thr
ee H
a
ll
E
f
f
e
c
t
s
e
n
s
o
r
s
i
n
s
t
a
l
l
e
d
i
n
t
h
e
s
t
a
t
o
r
w
i
t
h
a
s
h
i
f
t
o
f
1
2
0
°
e
l
ectr
i
c
a
l
.
Tab
l
e
1
give
s
the
d
i
ff
er
ent
poss
i
b
ili
t
i
es
t
o
sup
p
l
y
the
mot
o
r
acc
or
di
ng
t
o
t
he
r
ot
or
pos
it
ion.
Tab
l
e
1. T
ruth tab
le
o
f Ha
ll
E
ffe
c
t
se
n
sor
s
a
nd
ga
te sta
te
Seq
Hal
l
S
e
n
sor
s
A
ctive
switc
h
e
s
P
h
a
s
e
s
c
urr
e
nts
C
B
A
C
B
A
1
1
0
1
Q
1
-Q4
OF
F
D
C
-
D
C
+
2
1
0
0
Q
5
-Q4
D
C
+
D
C
-
OF
F
3
1
1
0
Q
5
-Q2
D
C
+
O
F
F
D
C
-
4
0
1
0
Q
3
-Q2
OF
F
DC+
D
C
-
5
0
1
1
Q
3
-Q6
D
C
-
DC+
OF
F
6
0
0
1
Q
1
-Q6
D
C
-
O
F
F
D
C
+
3.
BL
D
C
MOTO
R
CONTRO
L
S
CHE
M
E
3.
1.
S
i
mplific
at
ion
of th
e
m
odel
The
br
us
h
l
e
s
s
m
o
t
o
r
ca
n
be
m
od
e
l
e
d
a
s
F
i
g
u
r
e
2
a
nd
F
i
g
u
r
e
3
:
F
i
gur
e
2.
T
he
B
LD
C
motor
cir
c
u
i
t
F
i
gur
e
3.
T
he
B
LD
C
motor
cir
c
u
i
t
in
s
eq
ue
nc
e
1
Co
n
s
i
d
er t
h
e
f
irst
seq
u
e
n
c
e c
h
ara
c
t
e
ri
z
e
d
by:
(
3
)
The
t
h
r
e
e
pha
se
s
of
t
he
m
ot
or
a
r
e
s
ymm
e
tr
ic
al
(
R
a
= R
b
a
nd L
a
= L
b
).
S
o
:
(
4
)
Wher
e
M
is
t
h
e
m
utua
l
s
t
a
t
or
i
nd
uc
tanc
e.
A
nd
b
y
pos
i
ng
(
5
)
We
o
b
t
a
i
n
a
n
e
xpr
ess
i
on
w
h
ic
h
i
s
t
he
s
am
e
a
s
t
he
e
l
e
c
t
r
i
ca
l
equ
a
t
io
n
o
f
t
he
D
C
ma
chine:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
1
6
7
–
1
177
1
170
(
6
)
I
n
t
he
s
a
m
e
w
a
y,
s
tu
dy
i
ng
t
h
e
ot
he
r
z
o
nes,
l
ead
u
s
t
o
t
he
e
le
c
t
r
i
c
a
l
e
qua
t
i
o
n
o
f
a
D
C
m
otor
.
Th
e
control
o
f
t
h
e
s
elf
-
d
r
i
v
e
n
B
LD
C
mo
tor
is
t
h
e
refo
re
s
imilar
to
a
s
epa
r
at
el
y
e
x
c
i
t
e
d
DC
m
o
t
or
w
h
e
r
e
th
e
s
p
e
e
d
i
s
dir
e
c
tly
p
r
o
por
t
i
ona
l
t
o
t
he
v
o
l
tage
a
pp
lied
t
o
t
h
e
motor
ter
m
ina
l
s.A
n
d
t
o
c
ha
n
g
e
this
vo
l
t
age,
i
n
th
is
p
aper
,
w
e
a
tta
ck
t
he
a
r
m
s
of
t
he i
nver
t
er
b
y a
P
WM
s
i
gna
l
of
w
h
i
c
h
w
e
var
y
t
he du
t
y
cy
c
l
e
t
o
ob
ta
in
t
he
d
es
i
r
ed
v
o
l
t
a
ge
a
n
d
t
he
d
e
s
ir
ed
s
p
e
ed
acc
or
di
n
g
l
y
.
3.
2.
Fi
rst o
r
de
r sl
idi
n
g
m
o
de
S
lid
i
n
g
m
ode
i
s
a
t
ype
o
f
va
r
i
a
b
le
s
tr
u
c
t
u
r
e
c
o
n
tr
ols.
I
t
c
o
n
si
s
t
s
o
n
def
i
ni
n
g
a
s
ta
ble
d
y
n
am
ic
re
l
a
ti
on
sh
ip
b
et
wee
n
t
h
e
s
y
s
t
e
m
s
t
at
e
v
a
ri
ab
l
e
s
ca
ll
ed
s
l
i
d
i
n
g
su
rf
ac
e
t
h
e
n
f
o
r
ce
i
t
s
t
ra
je
c
t
o
r
y
to
c
o
nverg
e
to
th
is
s
ur
fac
e
a
n
d
s
ta
y
th
er
e
.
T
he
e
v
o
l
ut
io
n
o
f
t
he
s
yst
e
m,
s
ubmi
tt
ed
t
o
a
co
nt
rol
l
a
w
th
a
t
m
ak
e
s
i
t
st
ay
o
n
th
e
gi
ve
n
sur
f
a
ce,
t
he
r
e
f
o
r
e
n
o
l
o
nger
de
pe
nds
o
n
t
h
e
sy
s
t
em
i
t
s
elf
o
r
dis
t
ur
ba
nce
s
o
f
w
h
i
c
h
it
m
ay
b
e
su
b
m
itt
e
d
,
bu
t
o
n
l
y
d
e
p
en
ds
on
t
h
e
pr
o
p
e
r
ti
e
s
o
f
this
s
ur
fac
e
.
The
fir
s
t-
or
d
e
r
sl
id
i
ng
m
ode
c
on
t
r
o
l
t
a
k
es
t
h
e
f
ol
l
o
w
i
ng
f
o
r
m
:
u=
u
di
s
c
= K
si
gn
(
S
)
(7
)
C
ons
ide
r
i
ng
a
no
n
l
i
n
e
a
r
sys
t
e
m
i
n
t
h
e
c
a
n
o
n
i
cal
f
or
m
of
B
r
u
n
ovs
k
y
[
10]
:
(
8
)
1
...
n
n
xx
i
s
th
e
sys
t
em
state
v
e
c
t
o
r
and
1
xy
A
ne
cessa
r
y
c
on
d
iti
on
f
or
t
h
e
e
st
a
b
l
i
shm
e
n
t
o
f
a
s
l
idi
n
g
r
e
gi
m
e
i
s
t
h
a
t
t
h
e
s
l
i
d
i
n
g
v
a
r
i
a
b
l
e
h
a
s
a
r
e
l
a
t
i
v
e
de
gree
eq
u
a
l
t
o
1 c
o
mpa
r
ed
t
o
the
con
t
ro
l u [
9
].
S
o
c
o
n
s
i
der
th
e
fol
l
ow
i
ng
li
n
e
a
r
s
lid
i
n
g
var
i
a
b
le
[
1
0
]
:
(
9
)
Wh
wew
e=y
-
y
re
f
a
nd
c
n-1
=1
The
coe
f
f
i
c
i
e
n
ts
c
iar
e
c
hose
n
s
uc
h
t
h
a
t
t
he
p
ol
y
nom
i
a
l
(
10)
i
s
a
polyn
om
ia
l
of
H
ur
w
itz.
(
10)
I
f
S
(
e
,
t
)
s
atisfies
t
he
c
o
n
d
i
t
i
o
n
on
t
h
e
rela
t
i
ve
d
egre
e,
t
h
e
c
on
tr
ol
u
a
ppea
r
s
in
t
he
e
x
p
ress
io
n
of
its
f
i
r
st
tim
e
de
r
i
vat
i
ve
,
and
:
(
11)
Ma
ny
st
ud
ies
w
e
r
e
p
e
r
for
m
ed
i
n
or
der
t
o
r
educe
or
e
lim
i
n
ate
the
c
hat
t
er
i
ng,
O
ne
o
f
the
m
c
ons
i
s
t
s
i
n
r
e
plac
in
g
the
sig
n
f
u
n
c
t
i
o
n
b
y
a
s
m
o
o
t
h
f
u
nct
i
o
n
i
n
v
ic
i
n
it
y
of
t
he
s
l
i
d
i
ng
sur
f
a
c
e
,
f
or
e
xa
mp
le
s
a
t
ur
a
t
i
o
n
fu
n
c
tio
n,
s
igm
o
id
f
u
n
c
t
i
o
nse
t
c;
t
hus
t
he
s
li
d
i
n
g
r
e
g
ime
r
e
sul
t
i
n
g
i
s
c
o
n
f
ine
d
i
n
a
ne
i
g
h
b
o
r
hoo
d
o
f
t
he
s
l
i
di
n
g
sur
f
ace
w
he
r
e
o
n
l
y
the
e
q
u
i
v
a
l
e
n
t
c
om
m
a
nd
a
cts
[7]
.
T
he
c
omm
a
nd
t
ak
e
s
t
h
e
f
o
l
lo
w
i
n
g
f
o
r
m
:
u=
u
di
s
c
+
u
di
s
c
(
12)
Where u
eq
an
d u
di
s
c
repr
ese
n
t r
e
spec
t
i
ve
ly
e
q
u
i
v
a
l
en
t an
d
d
i
sc
o
n
ti
nu
o
u
s co
m
m
a
nds.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Rea
l
-
tim
e
im
pl
em
e
n
t
a
ti
on
o
f
a nove
l
hy
br
id fu
zzy
sl
i
d
i
ng m
ode
c
o
n
t
r
o
l
o
f
a BL
D
C
m
o
t
o
r
(
A
li
Mousm
i
)
1
171
The
eq
u
i
va
le
nt
c
om
m
a
nd
c
a
n
be
d
e
f
i
n
ed
a
s
the
a
v
er
a
g
e
v
a
l
u
e
of
t
h
e
d
isc
o
nti
n
uo
us
c
on
t
r
o
l
[
7
]
.
It
s
e
xpr
ess
i
on
is
f
ou
n
d
b
y
a
n
n
u
ll
in
g
the
sli
d
ing
sur
f
ace
der
i
va
t
i
v
e.
T
he
i
de
a
o
f
t
h
i
s
c
o
mm
and
is
t
ha
t
fa
r
fr
om
t
he
sl
id
ing
sur
f
ace
t
he
d
i
s
c
ont
i
n
u
ous
p
or
ti
on
i
s
r
e
spo
n
s
i
b
l
e
f
o
r
co
nver
g
in
g
t
h
e
sta
t
e
tr
a
j
e
c
t
o
r
y
t
o
t
he
s
ur
fa
c
e
,
b
u
t
w
h
e
n
t
he
t
r
a
je
c
t
or
y
is
s
uf
f
i
c
i
e
n
tl
y
ne
ar
f
r
o
m
i
t
(
r
e
ach
in
g
t
h
e
vic
i
nit
y
p
r
e
fixe
d
ε)
,
t
h
e
di
sc
o
n
t
i
n
uo
us
c
ontr
o
l
be
g
i
ns
t
o
d
i
m
i
n
i
sh
a
n
d
v
a
n
is
h
com
p
le
t
e
l
y
w
he
n
the
sur
f
a
ce
v
a
l
ue
b
ec
o
m
e
s
z
er
o;
s
o
t
h
a
t
,
qui
va
le
n
t
c
o
m
m
a
nd
a
c
ts
a
lo
ne
a
nd
m
a
ke
s
i
nvar
i
a
n
t
t
h
e
s
l
i
d
ing
s
u
r
f
ace
.
S
o
,
to
e
l
i
m
ina
t
e
the
c
o
nt
r
o
l
d
i
sco
n
t
i
n
uous
m
em
br
a
n
e
and
the c
h
a
t
te
r
i
ng
p
h
e
n
ome
non
t
h
er
e
f
or
e
,
w
e
r
e
plac
e the
f
unc
t
i
on s
i
g
n (
S
)
by ano
t
her
con
t
in
uo
us f
u
n
c
t
i
o
n
a
t
S
=
0,
li
ke
fu
nc
t
i
o
n
s
a
t
(
S
)
.
A
p
p
l
y
i
ng
the
c
o
mm
and
w
i
t
h
f
or
m
in
(
12)
,
w
e
have:
(
13)
Th
e
equ
i
v
a
l
e
nt
c
o
m
man
d
h
a
s
a
s
a
go
al
t
o
ma
k
e
i
nv
a
r
i
a
nt
t
he
s
l
i
d
i
n
g
s
u
r
f
a
c
e
w
h
e
n
t
he
s
lid
in
g
m
o
d is
e
s
t
a
blis
hed,
g
e
n
e
r
al
ly
s
e
e
k
s
t
o
m
a
ke
nul
l
t
h
e
sli
d
in
g
sur
f
a
c
e
d
eriva
t
i
v
e
i
f
it
i
s
app
lie
d a
l
on
e
. Its
e
xpre
s
sio
n
i
s
:
n-
2
1(
i
+
1
)
i
0
ub
(
x
,
t
)
(
(
,
)
c
e
)
eq
fx
t
Wha
t
m
ake
s
t
h
e
e
volu
t
i
o
n
of
s
lid
i
ng
sur
f
ace
f
u
n
c
t
i
o
n
on
l
y
d
e
p
en
di
ng
on
u
disc
:
(
14)
3.
3.
D
e
t
e
rmin
at
i
o
n
of
t
h
e
c
on
t
r
ol
l
a
w
f
or
t
h
e
m
o
t
or
BLD
C
C
ons
ide
r
i
ng t
h
e first
seq
u
enc
e
,
wher
e:
i
a
=I,
i
b
=-I,
i
c
=0, e
a
=-e
b
=
E
m
:
F
r
om
e
qua
t
i
on
(
2
)
t
h
e
ele
c
tr
o
m
agnet
i
c
tor
q
ue
e
xpr
essi
o
n
b
ec
ome
s
:
em
2.
e
.
I
T
=
(
15)
Ω
We have
E
m
=K
e
Ω,
s
o
:
em
e
t
T
=
2K
.I
=K
.I
(
16)
Re
plac
ing
i
n
t
h
e
s
ystem
m
e
c
h
anica
l
e
q
u
a
t
i
o
n
(
17)
:
em
L
dΩ
T
=
J
+
B
Ω
+
T
(
17)
dt
We fin
d
:
L
tt
t
T
Jd
Ω
B
I=
+
Ω
+
(
1
8
)
Kd
t
K
K
Wh
i
c
h
gi
ves
:
2
2
tt
dI
J
d
Ω
B
d
Ω
=+
(
1
9
)
dt
K
d
t
K
dt
Re
plac
ing
(
1
9)
i
n
(
6
)
:
2
ab
3
24
2
11
1
1
UC
CC
dΩ
d
Ω
=
-
-
Ω
-
(
2
0
)
dt
C
C
dt
C
C
With
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
116
7
– 1
177
1
172
L
12
3
t
3
tt
t
t
RT
LJ
R
J
+
L
B
R
B
C=
,
C
=
,
C
=
+
K
a
n
d
C
=
KK
K
K
The
sl
id
i
ng s
u
rfa
ce
is cho
sen
as:
1
de
S=
+
K
e
(
2
1
)
dt
e
=
ω
r
–
ω is the
er
r
o
r in speed.
The
sl
id
i
ng s
u
rfa
cede
r
i
v
a
t
ive
is
:
2
1
2
dS
d
e
d
e
=
+
K
(
22)
dt
d
t
dt
1
dS
d
Ω
U
=g
(
Ω
,
)
-
(
2
3
)
dt
d
t
C
W
ith
:
2
3
rr
2
4
11
2
11
1
C
dΩ
d
Ω
C
C
dΩ
dΩ
g
(
Ω
,
)
=
+
K
+
(
-
K
)
+
Ω
+
(
2
4
)
dt
dt
dt
C
d
t
C
C
Lyap
u
n
ov th
e
o
r
e
m:
The
r
e
is
a
c
on
t
i
nu
ou
sl
y
d
i
ffe
r
ent
i
a
b
l
e
f
u
n
c
t
i
on,
p
osi
t
iv
e
de
fin
ite
V
:
(
x
,
t)
↦
V
(
x
,
t
)
s
u
c
h
t
h
a
t
t
i
m
e
deri
va
ti
ve
o
f
V
i
s
s
em
i-defin
i
t
e
n
ega
t
i
v
e
if,
and
on
ly
i
f
0
is
a
s
t
abl
e
e
qui
libri
u
m
p
oin
t
.
Fo
r
t
h
e
s
t
at
e
t
r
aj
ect
o
r
y
to co
n
v
e
r
ge
t
o
w
a
r
ds the
s
lid
i
ng surfa
ce
:
Ch
oos
i
n
g the
ne
x
t
L
yap
u
nov
func
t
i
o
n
:
2
1
V=
S
(
25)
2
S
o
t
ha
t, the
s
urfa
ce
S
=
0 is a
ttr
acti
v
e
ove
r
t
h
e
ent
i
re
oper
a
tin
g
range
, it su
ffi
ces
t
ha
t
the de
r
i
va
t
i
ve
w
i
t
h respec
t
to t
ime
of
V
is ne
ga
t
i
ve
:
•
S.
S
<
0
(26)
To
s
o
l
ve
t
he
c
hat
t
eri
n
g
phe
n
o
me
no
n
d
u
e
t
o
t
he
d
isc
o
nti
n
u
ous
n
a
t
ur
e
o
f
t
he
c
omm
a
nd,
t
he
m
ost
c
o
m
m
on
w
a
y
is to
r
e
place
t
h
e
s
i
g
n
func
tio
n
w
i
t
h
a
no
t
h
er
c
on
t
i
n
uou
s
fun
c
ti
o
n,
f
or
e
xam
p
le the
s
a
t
f
u
n
c
t
i
o
n
a
nd
t
h
e
ad
di
t
i
o
n
of
s
o-
ca
lle
d
eq
ui
va
len
t
c
omm
a
nd
w
h
i
c
h co
n
t
rols t
he
s
yste
m
at S
= 0.
So
:
eq
u=K
.
s
a
t
(
S
)
+
u
(
2
7
)
Wi
t
h
:
K
> 0
an
d u
eq
is t
he
e
q
u
i
v
ale
n
t c
o
mm
and
calcu
la
te
d by
c
ance
lin
g
the
sl
i
d
i
ng s
u
rfa
ce
d
eriv
a
t
i
v
e.
2
rr
eq
1
1
1
2
1
1
3
4
2
d
Ω
dΩ
dΩ
u=
C
+
K
C
+
(
C
-
C
K
)
+
C
Ω
+
C
(
2
8
)
d
t
dt
dt
Re
plac
i
ng u
in
(
23),
w
e
fin
d:
1
dS
K
.
s
a
t
(
S
)
=
-
(
2
9
)
dt
C
Wh
ic
h
m
e
ans that
t
he
Lya
p
u
n
ov
stab
i
l
i
t
y
co
nd
i
t
i
o
n is c
hec
k
ed.
In the
i
deal
cas
e
, the
syst
e
m
pre
s
e
n
t
s
n
o par
a
m
e
tric
uncer
t
a
int
ies
:
dS
S=
0
=
0
dt
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Rea
l
-
tim
e
im
pl
em
e
n
t
a
ti
on
o
f
a nove
l
hy
br
id fu
zzy
sl
i
d
i
ng m
ode
c
o
n
t
r
o
l
o
f
a BL
D
C
m
o
t
o
r
(
A
li
Mousm
i
)
1
173
I
f
t
he
s
yste
m
has
pa
r
a
m
e
tr
ic
unce
r
ta
in
t
i
e
s
,
(
23)
b
e
c
om
es:
1
dS
dΩ
U
=g(
Ω
,
)
+Δ
g-
(
30)
dt
d
t
C
Wit
h
Δ
g
is
t
he
t
er
m
r
e
pr
e
s
e
n
t
i
ng
par
a
me
t
r
ic
unc
er
tai
n
tie
s.
Wh
i
c
h m
eans
th
a
t
at
S=
0:
dS
=
Δ
g
0
(
31)
dt
S
o
t
he
s
t
a
t
e
t
r
a
j
e
ct
or
y
en
ds
u
p
le
avi
n
g
th
e
sli
d
i
ng
sur
f
a
ce.
A
n
d
a
sta
t
ic
e
r
r
or
a
ppea
r
s
ther
efor
e
.
3.
4.
Fuz
z
y
l
o
g
i
c
contro
l
l
er
To
day,
f
uzz
y
r
egu
l
at
i
o
n
i
s
a
m
ajor
b
r
a
nc
h
of
r
e
g
ula
t
i
o
n
tec
h
n
o
l
ogy
.
Th
e
fu
z
z
y
co
nt
roll
er
h
as
ac
h
i
ev
ed
t
h
e
g
re
at
est
su
c
c
e
s
s
i
n
i
n
d
u
s
t
r
i
a
l
an
d
co
mmerc
i
al
a
p
p
l
ic
a
t
i
o
ns
o
f
fuzz
y
me
t
h
o
d
s.
F
uzz
y
c
on
t
r
ol
ler
s
a
r
e
no
n
l
i
n
e
a
r
regu
la
tors.
T
h
re
e
p
h
ases
o
f
tr
e
a
tm
en
t
t
a
ke
p
lac
e
i
n
a
f
uzz
y
r
e
g
u
l
a
t
or
F
i
gur
e
4,
F
uzz
i
f
i
c
a
ti
o
n
,
I
n
fer
e
nce
an
d
D
e
f
u
zz
if
ica
tio
n
[1
0]
.
F
i
gur
e
4.
F
uzz
y
l
o
g
i
c
c
o
n
t
r
o
ll
er
3.
5.
Fuz
z
y
l
o
g
i
c
contro
l
l
er
i
mpl
e
m
e
nta
t
i
o
n
A
t
t
he
b
e
g
i
n
ni
ng
w
e
p
r
o
ce
e
d
ed
t
o
a
n
o
r
m
alizat
i
on
of
t
h
e
i
np
u
t
-
o
u
t
pu
t
s
,
ie
t
h
e
i
npu
t
s
a
nd
o
u
t
pu
t
of
the
fuzz
y
c
o
n
t
r
o
l
l
e
r
a
r
e
a
ll
t
r
a
nsf
o
r
m
ed
t
o
a
val
u
e
be
tw
ee
n
-
1
an
d
1 ;
fo
r
t
h
a
t
,
we
d
iv
i
d
ed
o
n
the
m
a
ximum
va
lue
s
t
ha
t
t
h
e
er
r
o
r
and
i
t
s
t
i
m
e
d
er
i
v
a
t
i
v
e
c
a
n
take.
T
h
e
ou
t
pu
t
a
l
s
o
t
a
k
es
v
a
l
ue
s
betw
ee
n
-
1
a
n
d
1
,
bef
o
r
e
be
in
g
mult
i
p
lie
d
by a
gai
n
t
ha
t
will be
in
t
e
g
ra
t
e
d t
o
g
iv
e
the
dut
y
c
y
c
l
e
va
l
u
e
t
h
a
t
a
t
t
ac
ks
t
he
e
n
g
ine
.
F
i
gur
e
5.
S
c
h
em
e
of
t
he
f
uzz
y
l
o
g
i
c
c
o
n
t
r
o
ll
er
i
n
sim
u
li
nk
e
n
v
i
r
o
nne
me
nt
G_
e=3
,
33
.1
0
-4
:in
pu
t
e
r
r
o
r
gain,
to
m
ake
it
b
etw
e
e
n
-
1
and
1
w
e
div
i
de
d
i
t
o
n
t
he
m
axim
u
m
t
he
s
peed
v
a
l
ue.
G
_de
=
3
.
1
0
-2
:der
iva
t
ive
ga
i
n
o
f
t
h
e
er
ror,
h
e
r
e
we
h
ave
use
d
j
u
s
t
t
h
e
diffe
r
e
n
c
e
(
e
(k
)
-
e
(
k
-
1
))
th
e
step
ca
l
c
u
l
a
t
i
o
n
t
i
me
i
s
co
ns
tan
t
a
nd
e
qua
l
to
1
0
-4
s
,
3
3
i
s
t
h
e
m
a
x
i
m
u
m
v
a
l
u
e
o
f
t
h
i
s
d
i
f
f
e
r
e
n
c
e
fo
u
nd
f
r
o
m
an
ope
n-
l
o
op
te
st.
G
_
o
u
t
=
2,
5
.
1
0
-2
: with
a calcu
lati
on
s
t
e
p
of
0
.1
ms
4.
T
H
E
P
R
OP
O
S
ED
M
E
T
H
O
D
S
lid
i
n
g
m
ode
c
on
t
r
ol
h
a
s
t
h
e
a
d
v
an
ta
ge
o
f
be
ing
a
b
le
t
o
dr
ive
t
he
s
yst
e
m
in
f
i
n
i
t
e
ti
m
e
,
but
t
h
e
ch
a
t
t
e
ring
p
rob
l
e
m
w
hi
ch
can
o
nly
b
e
r
educ
e
d
t
o
d
e
t
r
i
m
en
t
of
s
t
a
tic
p
r
e
cis
i
o
n
lim
it
s
i
t
s
p
erf
o
rm
ance
.
S
o
,
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
116
7
– 1
177
1
174
b
e
n
e
fi
t
f
r
o
m
i
ts
q
u
i
c
k
r
e
s
pons
e,
w
e
p
r
o
p
o
s
e
i
n
t
hi
s
p
a
p
e
r
t
o
c
o
m
b
in
e
t
w
o
l
a
ws
o
f
co
nt
rol
,
t
h
e
s
l
i
di
ng
m
o
d
e
i
n
the
trans
i
e
n
t
re
gi
m
e
a
n
d
a
f
uz
zy
c
o
n
tro
ller
tha
t
w
i
l
l
take
o
ve
r
a
s
m
u
c
h
a
s
w
e
a
p
p
r
o
a
c
h
t
h
e
s
t
a
t
i
c
r
e
g
i
m
e
.
S
o
,
w
e
c
an
e
nj
oy
t
h
e
com
p
lem
e
n
t
ary
pe
rform
anc
e
o
f
t
h
ese
tw
o
c
o
n
t
r
o
l
ler
s
’
t
ype
s,
by
pro
v
i
din
g
a
q
u
i
c
k
r
eac
tio
n
aga
i
ns
t
dis
t
urb
a
nc
es
a
nd
c
h
an
ges
o
f
i
nstruc
t
i
ons,
m
o
reo
v
e
r
t
he
c
o
m
m
and
ac
cura
cy
w
i
ll
be
p
ro
v
i
d
e
d
by
f
uzz
y
con
t
ro
l
l
er.
The
i
d
ea
is
t
o
r
e
d
u
ce
t
he
e
rr
or
o
f
the
spe
e
d
u
p
t
o
a
sa
tis
fac
t
o
r
y
va
l
u
e
by
r
el
yin
g
m
a
i
nly
o
n
t
h
e
S
M
C orga
n, a
nd the
n
s
t
a
rt
t
o r
e
lay gr
a
dua
l
l
y
to t
he
F
uz
zy c
o
n
t
r
oller
.
The
c
o
m
b
i
n
a
t
i
o
n
o
f
t
he
se
t
w
o
c
on
tro
lle
rs
w
ill
be
p
ro
v
i
de
d
b
y
a
s
i
m
p
l
e
f
u
n
c
t
i
o
n
(
3
4
)
,
w
h
i
c
h
a
l
l
o
w
s
to se
l
ec
t or
g
iv
e
the
adva
n
t
a
g
e
to the
m
os
t f
a
vora
b
le
com
m
a
nd d
ep
endi
ng
o
n
th
e
e
r
ro
r.
4.1.
Set
t
in
g
up
the co
m
ma
nd
a
nd
s
t
a
b
ili
t
y
d
i
s
cussi
o
n
We
h
av
e
:
1
dS
u
d
Ω
==-
+
g(
Ω
,
)
(
32)
dt
C
d
t
A
p
p
l
y
i
ng
the
fol
l
o
w
i
ng
c
om
m
a
nd
F
u
zzy
u
=
(1
-
α
)K
.
s
i
g
n
(
S
)
+
α
u
(
3
3
)
Wi
t
h
α
i
s
t
h
e
sele
ct
io
n
para
me
ter
calc
u
la
t
e
d base
d on t
h
e
err
o
r
e.
I
n
th
i
s
w
o
rk,
we
c
a
l
c
u
l
a
te i
t u
s
i
ng t
h
e
fo
l
l
ow
in
g
func
t
i
on
:
1
α=
(
3
4
)
1+
γ
.
e
e
i
s
t
h
e
s
p
e
e
d
e
r
r
o
r
.
γ
i
s
a
p
o
s
i
t
i
v
e
c
o
n
s
t
a
n
t
w
h
i
c
h
a
l
l
o
w
s
s
e
t
t
i
n
g
o
f
the
s
p
ee
d
er
ror.
e
se
ui
l
i
s
the
va
l
u
e
from
wich α
becomes l
e
s
s
t
h
an
0
.
1
.
F
i
rst
w
e
f
ix the
p
ara
m
e
t
er γ by
cho
o
s
i
ng a
thr
e
sho
l
d o
f
e
seu
i
l
such
u
s
:
se
u
i
l
se
ui
l
s
eui
l
e
>
e
α
<
0
.
1
(3
5)
19
α
=
0.
1=
γ
=
1+
γ
.
e
e
It m
eans that a
s
l
ong
as
e
> e
s
e
uil
the
com
m
a
nd ta
ke
s m
o
re
t
han 90
%
from
the
S
MC a
n
d
1
0% from
the
S
MC
.
Re
plac
ings
(
3
3
)
in
(32):
Fu
z
z
y
11
dS
1
1
dΩ
=-
(
1
-
α
)
K
.
s
i
gn(
S
)
-
α
u
+
g(
Ω
,
)
(
36)
dt
C
C
dt
A
c
c
o
rdi
n
g
to
t
he
c
o
n
v
e
r
ge
nc
e
c
o
n
d
i
t
i
on
(
25),
if
t
he
c
on
d
i
t
i
o
n
(
3
5
)
is
s
a
t
isf
i
e
d
,
the
s
t
ate
tr
a
j
ect
ory
con
v
er
ge
nce
t
o
w
a
r
d
s
S
=
0 is e
nsur
ed:
Fuzz
y
1
dΩ
(1
-
α
)K
>
-
α
u
+
C
.
g
(Ω
,
)
(3
7
)
dt
A
c
c
o
rdi
n
g
to t
he
s
e
l
ec
ti
o
n
fu
n
c
t
i
on
α tak
i
ng
int
o ac
co
un
t t
h
e
c
o
ndi
t
i
on
i
n (3
7
)
,
i
f
:
α
< 0.
1
we
h
ave:
Fu
z
z
y
1
dΩ
0
.
9
>
(
1
-
α
)
K
>
-
α
u
+
C
.g
(
Ω
,
)
(
3
8
)
dt
So
,
i
f
:
11
Fuzz
y
CC
d
Ω
K
>
u
+
.g
(Ω
,
)
(3
9
)
90
.
9
d
t
We
guar
a
ntee
t
h
e inc
l
us
io
n of
t
he
sta
te
t
r
a
jec
t
or
y
in a
dom
a
i
n
w
h
er
e:
seu
i
l
e<
e
In this paper,
K
i
s
equal
to
1
.2 .
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
Re
al-
t
im
e
im
pl
em
ent
a
t
i
on o
f
a
nov
e
l
hy
br
id fu
zzy
sl
id
ing m
ode co
n
t
rol o
f
a
BL
D
C
m
o
tor (Ali
Mousm
i
)
1
175
5.
EXP
E
RIMENT RESULTS
I
n
a
l
l
e
x
p
e
r
i
e
n
c
e
s
a
B
L
D
C
m
o
t
o
r
w
i
t
h
a
x
i
a
l
f
l
u
x
i
s
u
s
e
d
,
3
K
W
,
8
0
V
,
8
p
ol
e
s
(
F
i
gure
6)
,
an
i
n
v
er
t
e
r
w
h
ic
h can oper
a
t
e
a
t
12 kH
z
m
a
xim
a
l
sw
i
t
c
h
i
n
g
freq
u
e
n
c
y
b
a
s
ed o
n IG
B
T
s, a dsP
ac
e
c
a
r
d
D
S
1104 o
p
e
r
a
tin
g
at 20
MH
z a
n
d
a
PC w
i
t
h
Con
t
ro
l D
i
sk i
nterf
ace
fo
r
da
t
a
ac
qu
isi
ti
on.
F
i
gure
6. E
x
p
e
r
im
e
n
ta
l pla
t
fo
rm
of system
To
e
va
lua
t
e
the
pro
pose
d
c
on
t
r
o
ller
per
f
o
r
m
a
nce
s
,
one
c
om
pare
d
i
t
s
be
ha
v
i
or
w
it
h
t
h
e
fuz
z
y
con
t
ro
l
l
er
a
pp
lie
d
a
l
o
n
e.
(
F
i
gure
7),
(F
i
gur
e
8)
a
nd
(F
ig
ur
e
9)
pr
esen
t
re
spect
i
v
e
l
y
t
h
e
s
p
ee
d
re
sp
o
n
se
o
f
t
h
e
p
r
op
o
s
ed
,
th
e
f
u
zzy
l
og
ic
a
nd
c
onv
e
n
ti
on
al
s
l
i
di
ng
m
o
d
e
c
o
n
t
r
ol
le
rs
fo
l
l
ow
i
n
g
a
s
p
ee
d
re
fer
e
nce
of
1
5
0
0
rpm
,
t
he
m
ot
or
a
t
the
be
gin
n
i
ng
i
s
a
t
r
e
st.
(F
igure
1
0
),
(
F
i
gur
e
1
1
),
(
F
i
gure
12)
a
nd
(
F
ig
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13)
r
espe
c
t
i
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e
l
y
gi
ve
:
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h
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o
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i
a
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l
e
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efe
r
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e
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rom
0,
1
5
00
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h
en
2
5
0
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r
pm
,
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l
ut
io
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h
e
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elec
tio
n
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i
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he
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om
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a
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o
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t
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t
a
nd
t
h
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t
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f
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h
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o
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olle
r
F
L
C
a
nd
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M
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(
F
i
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e
14)
and
(F
ig
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1
5
)
vi
su
a
l
i
z
e
a
c
o
m
p
a
r
is
on
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e
n
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zzy
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ors
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ns
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a
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urbanc
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of
1
5V
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t
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h
e
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er
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our
ce,
t
he
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e
h
a
v
ior
o
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e
l
e
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tio
n
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i
on
a
nd
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h
e
o
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t
p
u
t
o
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th
e
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pose
d
r
egu
l
ator
a
re
give
n
i
n
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igure
16)
a
nd (
F
ig
ure
17).
F
i
gure
7.
S
pe
ed r
espo
nse of t
he
pro
pose
d
c
ontr
o
l
l
er
F
i
gur
e 8.
S
peed
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of t
h
FL
C
F
i
gure
9.
S
pee
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re
s
po
nse
of
t
h
SM
C
F
i
gure
1
0
. S
pe
e
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re
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varia
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le
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o
n
s
i
gn
F
i
gure
1
1
.
S
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lecti
on
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nc
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Fi
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u
r
e
12
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m
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put
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4
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8
10
0
50
0
10
00
15
00
20
00
Tim
e
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s
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d
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ig
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m
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300
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
116
7
– 1
177
1
176
F
i
gure
13. S
M
C
a
nd F
LC
c
o
nt
roll
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u
tp
ts
F
i
gure
1
4
. Rea
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pro
pose
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o
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tr
ol
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e
r a
g
ai
ns
t
a
di
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urba
nc
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F
i
gur
e 1
5
.
S
e
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c
t
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n
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tio
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Fi
g
u
r
e 16
. Co
m
m
a
n
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put
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i
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.
The
F
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tio
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6.
CONCL
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Th
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p
a
p
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pos
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a
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w
h
ybr
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t
r
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lle
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se
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o
n
f
uz
z
y
l
o
g
i
c
a
nd
slid
i
ng
m
o
de
t
h
e
ories.
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h
e
aim
i
s
t
o
se
t
up
a
c
o
n
t
ro
l
l
e
r
t
hat
ca
n
e
x
p
l
oi
t
the
fas
t
re
spo
n
se
o
f
Brus
hle
ss
m
o
tors.
The
new
c
o
n
t
r
o
ller
i
s
des
i
g
n
e
d
i
n a w
a
y to c
om
bin
e
t
h
e
com
p
l
em
entar
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ad
v
a
n
ta
ge
s of t
h
ese t
w
o
com
m
a
n
d
l
a
w
s
and re
m
o
vi
ng t
h
e
i
r
di
sa
d
v
a
n
ta
ges.
A
f
ter
t
h
e
new
c
o
n
t
r
o
ller
'
s
pr
esen
tat
i
on
a
n
d
it
s
s
tab
i
li
ty
d
isc
u
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ion,
one
u
sed
it
to
c
o
n
tr
ol
a
B
r
u
s
hl
es
s
DC
m
o
t
o
r
,
t
h
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n
d
i
s
cu
sse
d
and
c
o
mp
ared
i
t
s
p
e
r
f
o
rman
c
e
w
ith
t
h
o
se
o
f
fu
zz
y
log
i
c
a
n
d
sl
id
in
g
m
ode
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on
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l
l
e
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s
.
The
ex
pe
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m
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nta
l
r
e
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ul
t
s
s
h
o
w
t
h
e
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u
peri
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o
n
t
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l
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m
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o
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e
a
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i
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g
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t
di
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tu
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an
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a
n
d
s
t
at
i
c
a
c
c
ur
a
cy
.
ACKNOW
LEDG
E
MEN
T
S
The
authors
w
o
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l
d
li
ke
t
o
ac
kn
ow
ledge
t
he
f
ina
n
cial
s
upp
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of
the
na
ti
o
n
a
l
c
en
ter
for
sc
i
e
ntific
a
nd
techn
i
cal r
esea
r
c
h in Morocc
o
(CN
R
S
T).
REFE
RENCES
[1
]
T.
S
h
i
,
Y.
G
uo
,
P.
S
on
g,
a
n
d
C
.
Xia
,
“
A
ne
w
a
p
pro
a
c
h
o
f
min
i
miz
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g
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o
m
m
u
t
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io
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ip
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r
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l
ush
l
e
ss
dc
mo
to
r
bas
e
d
o
n
d
c–d
c
c
on
vert
er,
”
IEEE
Tr
an
s
.
Ind. Elect
ron
.
,
vol.
57,
no.
1
0
,
p
p
.
3
4
8
3
–34
90
,
O
c
t
. 2
01
0.
[2
]
Z.
Q
.
Zh
u
an
d
D.
H
owe,
“
Electri
cal
m
achi
n
es
a
nd
d
riv
e
s
f
o
r
ele
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tri
c
,
hy
bri
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,
and
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u
el
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vehicl
es,
”
Pr
o
c
. I
E
E
E
,
vol
.
9
5
,
no
.
4,
pp.
7
46
76
5
,
A
pr.
2
0
07.
[3
]
Al
i.
M
ou
sm
i
,
A
hme
d
.
Ab
bo
u
a
n
d
Ya
ssin
e
E
l
H
o
u
m
,
‘
T
ra
pe
z
o
ida
l
c
o
n
tro
l
o
f
brush
l
es
s
DC
m
oto
r
b
as
ed
on
DS
P
F
283
35
’,
IEEE Int
e
rn
ation
a
l
Co
nfer
ence
onW
ir
eless
T
ech
nol
o
g
ies
,
Emb
e
dded
a
n
d
Int
e
ll
igent
Sys
t
ems
(
W
IT
S
)
,
mor
o
cco
20
17.
D
O
I:
10.
1109/W
I
T
S
.
2017.
79
346
02
.
[4
]
M.
A
.
S
h
ams
e
ld
in,
and
A
.
M
.
A.
G
hany
,
M
.
A
.
A
.
G
h
a
ny
,
“P
erfo
rm
a
nce
S
t
u
d
y
o
f
E
n
h
anced
N
on
-Li
n
ear
P
ID
Cont
rol
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pplied
o
n
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rus
h
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e
s
s
D
C
M
o
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r,
”
In
t
e
rna
t
i
o
n
a
l
Jo
urn
a
l o
f
Po
wer Elect
ro
ni
cs
and
D
r
i
ve S
y
stem
(
I
JPEDS)
,
vol
.
9
,
n
o.
2,
p
p
.
536
–5
45
,
2
0
18
[5
]
H.
S
.
Ch
o
i
,
Y.
H
.
Park
,
Y.
S
.
C
h
o,
a
n
d
M
.
L
ee,
“
Glob
al
s
l
i
d
i
n
g
-
m
o
d
e
c
o
n
t
r
o
l
i
m
p
r
o
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e
d
d
e
s
i
g
n
f
o
r
a
b
r
u
s
h
l
e
s
s
D
C
mo
to
r
,
”
IEEE Cont
rol
S
y
st
ems
M
a
gazin
e,
v
o
l.
2
1
,
p
p.
27-3
5
,
2001
.
[6
]
L.
P
.
G
uo,
J
.
Y.
H
u
ng,
R
.
M.
N
elm
s
b
,
“
Co
m
p
arativ
e
eval
uat
i
on
of
s
li
d
i
ng
m
od
e
f
u
zzy
c
ont
rol
l
er
a
n
d
P
ID
c
on
t
r
oller
fo
r a b
oos
t
con
v
erter”,
El
e
c
t
r
i
c
Power Syst
ems
Re
search
, vo
l
. 8
1,
n
o
.
1, pp
. 99
-
10
6
, Jan.
20
11
.
[7
]
M.
A
Fn
aeich
.
F.Bet
i
n
.
G
-A
.
Cap
o
li
no,
a
n
d
F
.
F
n
aeich,
“
F
uzzy
l
o
g
ic
a
nd
s
liding-
m
o
d
e
c
on
tro
l
s
ap
plei
d
to
s
ex-phase
induction
machi
n
e
w
ith
o
p
e
n ph
a
s
e
s
,”
IEE
E
T
r
a
n
s. Ind
El
ectron
.
,
vol.
5
7
,
n
o.
1
,
pp.
354
-36
4
,
Jan.
20
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Evaluation Warning : The document was created with Spire.PDF for Python.