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.
4, D
e
c
e
m
ber
201
9,
pp.
1758~
17
71
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
4.pp1758-1771
1758
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
Advanced contr
ol structures for
induction mot
ors with ide
a
l
current lo
op response usin
g field
orien
t
ed
control
V
o
Tha
nh Ha
1
,
Ngu
y
en Tung La
m
2
,
Vo Thu Ha
3
, V
o
Qu
an
g V
i
n
h
4
1
Fa
cul
t
y
o
f
E
l
e
c
trica
l
a
nd
E
l
e
c
trica
l
E
n
g
ine
e
rin
g
,
U
n
iversi
ty o
f
T
ransp
o
rt
a
nd C
o
mm
uni
cati
o
ns, V
i
e
tn
a
m
.
2
S
c
h
ool
o
f
El
ec
t
r
i
c
a
l
Eng
in
e
e
ri
ng
, Ha
n
o
i
Uni
v
e
rsi
t
y
of
S
c
i
e
n
c
e
a
nd Te
c
h
n
o
l
ogy,
V
iet
n
a
m
.
3
F
a
c
u
l
t
y
of E
l
e
c
t
rica
l
Engi
ne
e
r
in
g,
U
ni
ve
rsi
t
y
o
f
E
co
nom
i
c
s
- Te
chnology f
or
Industr
ies
, Vietnam
.
4
F
acul
t
y
of
Contr
o
l
an
d A
u
t
o
m
a
tion,
Elec
t
r
i
c P
o
w
e
r U
n
i
v
e
r
sit
y
,
V
ie
t
n
a
m
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
A
pr 17,
2
0
1
9
Re
vise
d Ju
l 2
2
,
201
9
A
c
c
e
pte
d
A
ug 3,
201
9
F
i
el
d
ori
e
nt
ed
c
on
tro
l
(
FOC)
i
s
w
i
del
y
u
sed
f
o
r
hi
gh
p
erf
o
rm
anc
e
i
n
d
u
cti
on
m
o
t
o
r
(IM)
electrical
d
riv
e
s
ystem
s
.
T
y
p
i
call
y
,
FOC
us
es
l
i
n
ear
c
on
trols
and
sp
ace
v
ect
or
m
o
d
u
l
atio
n
(S
VM
)
t
o
c
o
n
t
r
o
l
t
h
e
f
u
n
d
a
men
t
al
c
omp
o
n
ent
s
o
f
the
sta
t
or
v
ol
ta
g
e
s.
T
hi
s
work
s
h
o
ws
t
ha
t
ba
se
d
o
n
a
f
a
s
t
a
n
d
p
recise
i
nn
er
curren
t
l
o
op
resp
on
se
o
n
e
m
ay
f
lex
i
bly
em
pl
oy
d
i
f
f
e
rent
a
d
v
an
ce
d
con
t
rol
m
e
th
ods,
t
o
ach
ieve
h
ig
h
p
e
rf
orm
a
nce
o
u
t
e
r
loops
(
sp
eed
a
n
d
f
lu
x
c
o
nt
rol
)
.
In
t
h
i
s
pap
e
r,
nov
el
a
p
p
ro
ach
es
b
as
ed
o
n
de
ad
-b
eat
s
ch
e
m
e
f
o
r
t
he
c
urrent
lo
op
c
om
bi
n
i
ng
w
i
t
h
e
xact
l
i
n
earizat
io
n
,
b
ac
k
s
t
e
pp
ing
con
t
rols,
a
n
d
f
a
t
n
e
s
s
-
bas
e
d
m
e
th
ods
f
or
t
h
e
out
er
l
oop
are
pro
p
o
s
ed.
By
c
o
m
pari
ng
wit
h
c
l
as
s
i
cal
PI
c
on
tro
l
,
th
e
p
r
op
ose
d
m
e
t
ho
d
sh
ows
the
ou
tsta
n
d
i
n
g
f
e
a
t
u
r
e
s
of
s
y
s
te
m
resp
on
se
s
uch
as
f
as
t
,
accurat
e
a
nd
d
e
c
o
upl
in
g
p
r
op
e
r
t
i
es
.
Th
e
perf
o
r
m
a
nce
eval
uat
i
on
i
s
g
i
ven
b
y
e
x
p
erim
ental
results.
K
eyw
ord
s
:
F
i
eld
or
ien
t
e
d
c
on
t
r
o
l
B
ack
st
epp
i
ng
Exac
t
line
a
riza
t
i
o
n
D
e
a
dbea
t
c
on
tr
ol
Fl
a
t
n
e
s
s
-b
ased
co
n
t
r
ol
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:
N
g
u
y
en
T
ung
Lam
,
S
c
hoo
l
o
f
Ele
c
t
rica
l
En
gine
erin
g,
Ha
n
o
i
U
n
iv
ersi
t
y
of
S
c
i
e
n
c
e
an
d
Tech
nol
ogy,
N
o
.1,
D
a
i
Co
V
iet R
o
a
d
,
H
a
i
Ba
Trung,
H
a
n
o
i
,
V
i
etna
m.
Em
ail:
l
a
m.
ng
uye
n
t
u
ng@
h
u
s
t
.e
du.v
n
1.
I
N
TR
OD
U
C
TI
O
N
N
o
w
a
days,
as
y
n
chr
o
n
o
u
s
e
l
e
c
t
rica
l
dr
ive
s
b
a
s
ed
o
n
fie
l
d-orien
t
e
d
c
o
ntro
l
(FO
C
)
ha
ve
b
e
e
n
w
i
de
l
y
use
d
i
n
in
dus
t
r
ial
a
p
p
lica
tio
ns
[
1].
Based
on
t
h
is
m
e
t
h
od,
w
e
c
an
f
i
nd
in
d
u
ct
ion
m
o
tors
h
a
v
e
s
i
m
i
l
a
r
cha
r
ac
t
e
ris
tics
to
s
e
p
ara
t
e
exc
ita
t
i
o
n
D
C
m
o
tor
s
i
n
t
e
rm
o
f
gen
er
a
tin
g
m
a
gne
t
i
c
fie
l
d
an
d
torq
ue
[
1-
4].
In
t
h
e
F
O
C
struc
t
u
r
e,
w
he
n
t
h
e
st
a
t
or
v
o
l
tage
c
on
tro
l
s
at
isfies
t
h
e
r
e
quirem
e
n
t
o
f
“
f
ast
–
ac
cu
ra
cy
–
d
ec
ou
pl
in
g
”
pro
p
er
t
i
e
s
i
n
c
u
rre
nt
r
e
s
po
ns
e,
t
he
i
n
duc
t
i
o
n
m
o
t
or
c
a
n
b
e
co
ns
idere
d
a
s
fed
by
a
c
urre
nt
s
o
u
rce
i
n
ver
t
e
r
w
i
t
h
c
o
n
t
r
o
l
l
a
b
l
e
c
u
r
r
e
n
t
,
w
h
i
c
h
l
e
a
d
s
t
o
o
r
d
e
r
r
e
d
u
c
t
i
o
n
o
f
t
h
e
m
o
d
el
o
f
in
d
u
ct
ion
m
o
tor
dri
v
e
from
4
th
to 2
th
o
rder
[
1]
.
The
ar
ticle
p
rese
n
t
s
d
i
ffere
n
t
m
e
t
ho
ds
t
o
de
si
gn
the
inne
r
lo
o
p
(
sta
t
or
c
u
rre
n
t
l
oo
p)
a
n
d
ou
ter
loo
p
(flu
x
an
d
spe
e
d
l
oo
ps).
F
i
r
st
l
y
,
de
ad
bea
t
c
ontr
o
l
w
i
t
h
f
in
it
e
r
e
s
po
nse
is
e
m
p
lo
ye
d
for
th
e
curr
ent
loo
p
s
[5-7]
.
S
e
cond
l
y
,
exa
c
t
l
i
n
ea
riza
t
i
o
n
is
u
ti
lize
d
t
o
t
r
ans
f
orm
the
no
n-
li
nea
r
d
yn
am
i
c
s
o
f
c
urre
nt
m
o
d
e
l
i
n
t
o
l
i
nea
r
in
put-
o
u
t
pu
t
rela
ti
on
sh
ip,
th
us
it
is
a
ble
t
o
a
p
p
l
y
c
o
mm
on
l
i
ne
ar
c
on
t
r
ols
to
t
he
c
ur
re
nt
m
o
d
el
[
8,
9
].
I
n
add
i
tio
n,
t
o
de
m
ons
t
r
ate
curr
ent
per
f
orm
a
nce
s
,
a
c
l
a
s
sic
a
l
P
I
c
ur
rent
c
o
n
t
r
oller
is
a
ls
o
de
sig
n
e
d
[
10-
13]
f
or
benc
hm
ar
kin
g
pur
pose.
T
h
e
c
lo
se
d-l
o
op
c
u
rrent
r
e
s
po
nse
base
d
o
n
d
ea
dbea
t
,
e
x
act
line
a
riza
tio
n
co
ntr
o
l
i
s
e
v
al
u
a
t
e
d
t
o
i
de
n
tif
y
t
h
e
mo
st
s
ui
t
a
bl
e
c
ont
ro
l
fo
r
t
h
e
cu
rre
n
t
lo
o
p
s. The
suc
ce
ss
in des
i
g
n
in
g a
co
n
t
ro
l for
t
h
e
curr
ent
lo
o
p
s
ca
n
lea
d
t
o
th
e
assum
p
ti
o
n
o
f
i
d
e
a
l
c
u
r
r
ent
l
o
o
p
r
e
s
p
o
n
s
e
t
h
a
t
r
e
s
u
l
t
s
i
n
t
h
e
s
y
s
t
e
m
o
r
d
e
r
reduc
tio
n.
S
ubse
q
uen
t
l
y
,
t
h
e des
i
g
n
c
on
t
r
o
l
of the
e
l
e
c
trica
l
d
r
i
ve sys
t
e
m ou
ter
l
oop
s
bas
e
d
o
n
r
ed
uc
in
g
or
der
mode
l
c
a
n
b
e
per
f
orm
e
d
i
n
v
a
r
i
ous
m
et
h
o
d
s.
T
he
c
la
ssic
a
l
P
I
c
on
tr
ol
l
e
r
c
a
n
on
l
y
b
e
e
ffe
c
t
i
v
e
ar
ou
nd
th
e
opera
tin
g
p
o
in
t.
W
he
n
o
p
e
r
ati
n
g
i
n
a
w
i
d
e
r
a
nge
t
he
s
ys
tem
perf
o
r
ma
nce
ca
n
be
d
e
g
rade
d
[1
0-
13]
.
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
Adv
ance
d
c
ont
ro
l struc
t
ure
s
f
o
r i
n
d
u
c
tio
n
m
o
tors
wi
t
h
ide
a
l c
u
rre
n
t
lo
op
re
sp
onse
… (
V
o
T
h
a
nh
H
a
)
1
759
N
o
w
a
da
ys,
th
e
no
n-l
i
nea
r
c
on
tro
l
w
i
t
h
a
b
rup
t
d
e
v
el
o
p
me
nts
in
h
a
r
d
w
a
re
a
re
i
ncreasingly
cons
idered
i
n
prac
t
i
c
a
l a
p
plic
a
tio
ns.
Du
e
to
f
l
a
t
p
r
o
p
ert
y
o
f
th
e
IM
w
i
t
h
roto
r
sp
e
e
d
and
fl
ux
a
re
s
e
l
ect
e
d
a
s
th
e
ou
tpu
t
s,
t
h
e
f
l
a
tn
e
ss-
base
d
pr
inc
i
p
l
e
is
u
se
d
for
sp
ee
d
an
d
fl
ux
c
o
n
t
ro
l.
B
y
si
m
p
l
y
r
ed
uci
n
g
t
h
e
orde
r
o
f
t
he
g
o
v
ern
i
n
g
e
qu
a
t
i
o
ns,
the
de
si
g
n
ed
s
pe
ed
a
nd
flu
x
r
efere
n
ce
t
r
aj
ector
ie
s
ca
n
be
c
hoos
i
n
g
ba
se
d
on
t
he
a
m
p
l
i
t
u
d
e
c
o
ns
train
t
o
f
curr
ent
[
14-
1
8
]
.
N
ot
i
n
g
tha
t
t
he
I
M
mode
l
is
o
f
s
t
ric
t
f
ee
dbac
k
f
orm
,
b
acks
t
ep
p
i
n
g
c
ontr
o
l
me
th
od
[
19-
21]
w
h
ic
h
m
a
ke
s
sure
t
ha
t
the
err
o
r
be
t
w
e
e
n
se
t
va
lues
a
n
d
r
eal
v
a
l
ues
satisfy
Lya
p
unov’s
s
t
abil
ity
i
s
al
s
o
dep
l
oye
d
for
s
p
ee
d
a
n
d
fl
ux
l
oo
ps.
Eva
l
ua
ti
on
of
d
y
n
a
m
ic
r
espo
n
s
e
b
e
t
w
e
e
n
d
i
f
f
e
r
e
n
t
s
p
e
e
d
a
n
d
f
l
u
x
c
o
n
t
r
o
l
st
r
u
c
t
ures
b
ase
d
on ri
pp
le t
orque
per
form
an
ce
[22-2
5
].
The
a
dva
nc
e
d
s
truc
t
u
res
f
o
r
F
O
C
of
t
he
i
n
d
u
ct
i
o
n
mot
o
r
w
i
t
h
i
de
al
c
ur
rent
l
oop
a
r
e
ve
rifie
d
ac
cord
in
g
e
x
p
e
r
i
me
nt
a
l
r
esu
l
t
s
.
These
res
u
l
t
s
a
r
e
o
b
ta
ine
d
f
rom
t
he
a
sse
ssm
e
nt
o
f
c
u
rre
nt
l
oo
p
re
spo
n
se
,
spee
d,
f
lu
x
a
n
d
th
e
pe
rfor
ma
nce
of
e
lec
t
r
i
c
a
l
dri
v
e
be
t
w
een
F
O
C
s
t
r
uctures
such
a
s
ha
rm
on
ic
d
i
s
to
rti
o
n
,
rip
p
le
t
orq
u
e,
a
nd
m
a
x
r
ip
pl
e
t
o
rq
ue
.
The
re
ma
inder
o
f
t
h
i
s
pa
p
er
i
s
orga
nize
d
as
f
o
l
l
o
ws.
The
m
a
t
h
e
m
atica
l
mode
l
of
t
he
d
rive
s
ys
t
e
m
w
ith
i
dea
l
l
y
c
o
n
t
r
ol
p
erf
o
rma
n
ce
o
f
t
h
e
s
t
a
to
r
sy
st
em
w
i
l
l
b
e
p
re
sent
e
d
i
n
se
cti
on
2.
S
ubse
que
ntl
y
,
the
de
si
g
n
m
e
t
ho
d
o
f
s
ta
t
o
r
curre
nt
c
o
n
t
r
ol
a
n
d
o
u
t
e
r
l
oop
b
y
n
o
n
li
ne
a
r
m
e
t
hod
is
d
i
s
cusse
d
in
s
ec
t
i
o
n
3
a
nd 4.
T
h
e
e
ff
ici
e
ncy
of
t
he
p
ro
pos
ed
m
eth
o
d
i
s
ve
ri
fi
e
d
b
y
si
mu
l
a
tio
n
as
w
e
l
l
a
s
i
mpl
e
ment
ati
on
a
r
e
s
h
o
w
n
i
n
s
e
c
t
i
o
n
5
a
n
d
s
e
c
t
i
o
n
6
,
r
e
s
p
e
c
t
i
v
e
l
y
.
T
h
e
f
i
n
a
l
s
ec
ti
on
w
i
l
l
s
umm
a
r
i
z
e
t
h
e
r
esea
rch
and
gi
ves
some directions for futur
e
w
orks
2.
MATHE
M
A
T
ICAL MODEL OF TH
R
EE PHASE IN
D
U
CT
ION M
O
TOR
I
n
s
ync
hr
on
ou
s
coord
i
nate
,
the
t
h
re
e-pha
se
i
n
duc
t
i
o
n
m
o
t
or
can
b
e
d
escri
b
ed
b
y
th
e
f
o
l
l
o
w
i
ng
dy
nam
i
c
a
l
[1].
11
1
1
11
1
1
1
sd
sd
s
s
q
s
d
sr
r
s
sq
s
sd
sq
m
s
q
sr
s
rd
m
rd
sd
rr
p
rd
sq
L
di
ii
u
dt
T
T
T
L
di
ii
i
u
dt
T
T
L
dL
i
dt
T
T
z
d
ki
m
dt
J
w
ss
w
ss
s
s
ss
ww
ss
s
s
y
y
w
y
ì
æö
ï
--
÷
ï
ç
÷
ï
ç
=-
+
+
+
+
÷
ï
ç
÷
÷
ç
ï
èø
ï
ï
ï
æö
ï
--
ï
÷
ç
÷
ï
ç
=-
-
+
-
+
÷
ï
ç
÷
÷
ç
ï
ï
èø
í
ï
ï
ï
=-
+
ï
ï
ï
ï
ï
ï
ï
ï
=-
ï
ï
ï
î
(
1
)
W
ith
22
3
;
2
s
qp
m
m
sr
rr
d
r
iz
L
L
k
TL
J
In
w
hi
c
h
,
;
s
ds
q
ii
a
r
e
dq
c
om
p
one
n
t
s
o
f
t
he
s
ta
t
o
r
cur
r
e
n
t;
m
i
i
s
e
l
ec
troma
gne
t
i
c
c
u
rre
nts;
,
s
ww
a
r
e
me
cha
n
ic
al
a
nd
s
y
nchro
n
o
u
s
s
pee
d
,
r
e
spec
t
i
ve
ly
;
''
,
rd
rq
yy
are
dq
c
ompo
ne
nt
s
of
t
he
r
o
t
or
f
l
u
x
;
s
i
s
t
o
tal
leaka
g
e
fac
t
or
;
r
T
is
r
ot
or
t
im
e
con
s
t
a
n
t
;
s
d
u
,
s
q
u
ar
e
dq
c
ompo
ne
nt
s
of
t
he
s
ta
t
o
r
v
o
l
t
age
;
s
L
is
s
tat
o
r
in
duc
ta
nce
,
L
m
:
t
o
r
q
u
e
l
o
a
d
;
W
m
:
t
o
rq
ue
m
ot
or.
I
t
c
an
b
e
se
en
t
h
a
t
the
ori
g
ina
l
s
ta
te
(
1
)
i
s
bi
l
i
ne
ar
a
nd
i
s
of
4
th
o
rd
e
r
.
Wh
e
n
c
on
si
d
e
ri
ng
t
h
e
c
u
rren
t
c
on
t
r
o
l
l
e
r
re
sp
on
se
i
s
pe
r
f
ect
,
th
e
i
n
du
ct
ion
mot
o
r
mod
e
l
c
a
n
b
e
re
d
u
ced
a
s:
1
rd
m
rd
sd
rr
p
rd
sq
L
dL
i
dt
T
T
z
d
ki
m
dt
J
w
y
y
w
y
ì
ï
ï
=-
+
ï
ï
ï
ï
í
ï
ï
ï
=-
ï
ï
ï
î
(2)
The
s
t
a
t
e (2)
is of
2
nd
o
r
d
e
r,
s
t
a
t
o
r
c
u
rr
e
n
t
i
sd
is use
d
to co
n
t
rol t
h
e
m
o
t
o
r
fl
ux a
n
d
i
sq
i
s
de
dica
t
e
d t
o
spee
d
con
t
ro
l
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.
10,
N
o.
4
, Dec
201
9 :
1
7
5
8
– 1
771
1
760
3.
STATO
R
C
U
RRENT CONTROL DES
I
G
N
3.1.
Deadb
eat con
t
rol
Th
e
id
e
a
l
dyna
mi
c
b
e
h
a
vi
o
r
c
an
b
e
a
c
hi
e
v
e
d
b
y
d
ead
b
e
a
t
r
e
s
pon
se
w
hic
h
m
ea
n
s
t
h
a
t
the
act
ua
l
val
u
e w
i
ll t
r
ac
k the
r
e
fe
renc
e
va
lue
a
f
ter o
n
e
sa
m
pl
in
g pe
riod,
or
,
if the
one
-ste
p de
la
y o
f
t
he c
on
tro
l
o
ut
p
u
t
is
take
n
i
n
t
o
acc
ou
nt,
afte
r
tw
o
sa
mpl
i
ng
peri
ods.
T
h
is
l
ea
ds
t
o
t
he
f
ac
t
t
h
a
t
c
l
o
se
d
lo
op
tr
ansfer
f
u
n
c
t
i
o
n
m
u
st
als
o
h
ave
the
for
m
o
f
a
p
o
l
y
nom
i
a
l
o
f
N
th
d
e
g
r
e
e
,
w
i
t
h
t
h
e
s
u
m
o
f
p
o
l
y
n
o
m
i
a
l
coefficients
e
qua
l
t
o
[1,5,
6].
A
c
c
o
rdi
n
g
to
[
1],
t
h
e
pro
b
l
em
o
f
de
si
g
n
i
ng
c
o
n
t
ro
l
l
e
r
t
ra
nsfer
f
u
n
c
t
i
o
n
i
s
n
o
w
r
e
p
l
a
c
e
d
b
y
f
i
n
d
i
n
g
a
po
lyn
o
m
i
a
l
of
m
a
trix co
n
tr
ol
l
e
r. Where
the
p
o
l
yn
om
ia
l
L
(
z
-1
)
has to fulf
i
l
l
:
()
()
00
1
11
1
sm
ij
ij
L
lb
B
==
=
=
åå
(
3
)
W
ith
:
l
i
c
oe
ffic
ien
t
s o
f
the
p
o
l
yn
om
i
a
l
L
(
z
-1
); B num
era
t
or o
f proc
ess trans
f
e
r
funct
i
ons
G
S.
b
j
coe
ffic
i
e
n
t
s
of t
he
p
oly
nom
ial
B
(
z
-1
),
nume
r
ator
o
f
G
S
(
z
-1
)
L
(1
)
,
B
(1)
sum
of pol
y
nom
ia
l
coe
f
fi
cie
n
ts of
L
(
z
-1
),
B
(
z
-1
)
A
c
c
o
rdi
ng
to t
o [1,
5
,6]
the s
t
ator
c
urr
e
nt c
ontr
o
l
w
ith
d
ea
d
b
e
a
t be
ha
v
i
or
as
sho
w
n as:
()
()
()
()
()
()
()
()
()
()
()
11
11
1
1
2
2
11
1
1
12
11
12
1
1
1
2
11
1
1
12
11
11
R
I
zL
z
L
z
zL
z
z
L
z
z
Lz
z
L
z
zL
z
z
L
z
--
--
-
-
--
--
-
-
éù
-F
-
F
êú
êú
êú
--
êú
=
êú
êú
F-
F
êú
êú
êú
--
êú
ëû
(4)
Wher
e
:
11
12
;
FF
tr
a
nsit
io
n m
a
trix
;
T
: sa
mpli
n
g
time
;
s
T
i
s
stat
o
r
ti
m
e
c
ons
tan
t
.
11
11
10
11
01
sr
sr
T
TT
T
TT
s
s
s
s
æö
-
÷
ç
÷
ç
-+
÷
ç
÷
÷
ç
èø
F=
æö
-
÷
ç
÷
ç
-+
÷
ç
÷
÷
ç
èø
;
11
11
11
r
r
T
T
T
T
T
T
ss
w
ss
ss
w
ss
--
F=
--
-
I
t
c
an
b
e
de
du
ce
d
t
h
a
t
t
he
c
on
tro
l
l
aw
s
do
n
ot
c
a
u
se
f
u
t
ure
er
r
ors
(stat
i
ona
ry
c
o
n
t
rol
error
s
)
,
t
he
po
lyn
o
m
i
a
l
s
L
1
(
z
-1
)
a
nd
L
2
(
z
-1
)
mu
st
not
c
o
n
t
a
i
n
t
h
e
co
ef
fi
ci
ent
l
0
.
Ad
di
ti
on
a
l
ly
,
to
e
li
mi
n
a
t
e
t
h
e
s
t
a
ti
on
a
r
y
control
errors
t
he
t
ransf
e
r
function
w
G
o
f
th
e
cl
osed
l
o
op
must
b
e
e
qua
l
I
u
n
d
e
r
s
ta
t
i
onar
y
c
o
n
d
i
t
io
ns
(
1
z
=
).
Ther
e
fore
,
it
c
a
n
be
seen
t
ha
t:
(
)
(
)
12
11
1
LL
==
(5)
Wit
h
t
h
e
c
on
d
i
t
i
o
n
s
(5)
we
c
ann
o
t
c
l
e
arl
y
d
e
f
i
n
e
t
h
e
c
o
ef
ficie
n
ts
o
f
po
l
y
nomia
l
s
L
1
(
z
-1
)
a
nd
L
2
(
z
-1
)
w
h
en
onl
y
t
h
e
t
o
t
a
l
c
o
e
ffic
i
e
n
t
p
o
l
y
n
o
mial
s
is
b
y
1.
T
he
re
fo
r
e
,
i
t
is
n
ece
ssa
r
y
t
o
h
a
v
e
s
ub-c
o
n
d
it
i
ons
t
o
be
able
t
o
de
term
ine
those
c
o
e
ffi
c
i
e
n
ts,
w
h
ic
h
i
s
t
he
c
o
n
d
i
t
ion
o
f
v
ol
t
a
ge
c
on
strai
n
t.
S
e
l
ecti
o
n
o
f
L
1
(z
-1
)
and
L
2
(z
-1
)
as se
c
ond-
de
g
r
ee
po
l
ynom
ia
l a
s
fo
l
lo
w
s
()
()
11
1
2
12
1
2
L
zL
z
l
z
l
z
--
-
-
==
+
(6)
The
co
ntro
l
l
e
r
(
6) c
an be
wr
i
t
t
e
n
in
f
orm
of discre
t
e e
q
ua
tio
ns
:
()
(
)
(
)
()
(
)
(
)
()
(
)
(
)
()
(
)
(
)
()
(
)
(
)
()
(
)
(
)
12
1
2
1
1
1
21
1
1
1
2
21
2
12
1
2
1
1
1
21
1
1
1
2
21
2
23
1
21
2
23
1
21
2
dd
d
d
d
dq
q
qq
q
q
q
qd
d
yk
l
y
k
l
yk
l
e
k
l
l
e
k
le
k
l
e
k
l
e
k
yk
l
y
k
l
yk
l
e
k
l
l
e
k
le
k
l
e
k
l
e
k
ì
ï
=-
+
-
+
+
-
F
-
ï
ï
ï
ï
-F
-
-
F
-
-
F
-
ï
ï
í
ï
=-
+
-
+
+
-
F
-
ï
ï
ï
ï
-F
-
+
F
-
+
F
-
ï
ï
î
(
7
)
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
Adv
ance
d
c
ont
ro
l struc
t
ure
s
f
o
r i
n
d
u
c
tio
n
m
o
tors
wi
t
h
ide
a
l c
u
rre
n
t
lo
op
re
sp
onse
… (
V
o
T
h
a
nh
H
a
)
1
761
The
co
ntro
l
l
e
r
(
7) c
an be
wr
i
t
t
e
n
in
t
he f
oll
o
w
i
n
g
for
m:
()
(
)
()
()
(
)
(
)
1
11
1
3
1
11
14
11
11
sd
d
r
d
sq
q
r
d
uk
h
y
k
k
uk
h
y
k
k
y
y
-
-
ì
éù
ï
¢
+=
-
F
+
ï
êú
ëû
ï
í
ï
éù
¢
+=
+
F
+
ï
êú
ï
ëû
î
(
8
)
Whe
r
e
l
1
and
l
2
ca
n
be
chose
n
a
s
fol
l
ow
s:
11
0
1
4
11
0
12
1
00
mi
n
;
;
1
qs
d
N
d
dq
hu
i
hu
ll
l
ee
ìü
ïï
-F
ïï
==
-
íý
ïï
ïï
îþ
(9)
W
ith
:
11
s
d
T
h
L
input matrix;
14
1
T
s
w
s
-
F=
.
The
co
ntro
l str
u
ct
ure
of
t
he
i
n
n
er
l
o
o
p
us
ing
t
h
e
de
a
d
-be
a
t
i
s
show
n i
n
F
ig
ure
1:
3~
IE
Indu
c
t
i
on m
o
t
o
r
3
2
t
u
t
v
t
w
u
s
α
u
sd
r
u
sq
r
i
s
α
i
su
SV
M
i
sq
i
sd
u
s
β
i
sv
i
sw
S
p
eed
m
e
a
s
u
re
i
sβ
F
l
ux
m
ode
l
E
q
. (7&8)
DC
u
I
nvert
e
r
u
sq
u
sd
De
a
dbea
t cur
r
e
nt contr
ol
S
a
tur
a
tio
n
F
i
gure
1.
C
o
n
tr
ol s
truct
u
re
of
t
h
e
c
u
rre
nt
v
ec
t
o
r
con
t
rol
l
er
w
i
t
h
d
ea
dbe
at
3.2.
Exact
lin
e
a
riz
a
ti
on
c
on
trol m
eth
o
d
U
s
in
g
t
h
e
s
t
a
t
e
feed
ba
c
k
o
r
the
c
o
ord
i
na
te
t
ransf
o
r
m
a
tio
n
t
h
e
e
xact
l
in
ear
i
z
ed
I
M
m
ode
l
ca
n
be
r
e
p
r
e
s
e
n
t
e
d
.
T
h
e
t
r
a
n
s
f
o
r
m
e
d
s
t
a
t
e
m
o
d
e
l
w
i
l
l
n
o
w
b
e
c
o
m
e
t
h
e
s
t
art
i
ng
p
o
i
n
t
f
o
r
t
h
e
co
n
t
rol
l
er
d
es
ig
n.
Be
s
i
de
s
the
ex
a
c
t
l
i
ne
ariza
tio
n
a
c
h
i
ev
ed
i
n
di
scre
te
s
ta
te
s
pa
c
e
,
t
h
e
i
npu
t
-
o
u
t
p
ut
d
e
c
ou
pl
i
n
g
rel
a
t
i
ons
a
re
to
t
a
l
l
y
gua
ran
t
ee
d.
B
a
s
e
d
o
n
t
h
is
r
es
ul
t
,
i
t
see
m
s
to
b
e
pos
si
b
le
t
o
re
pla
c
e
t
h
e
tw
o
di
m
e
nsi
o
nal
c
u
rrent
con
t
ro
l
l
er
by
a
coord
i
na
te
t
r
a
nsform
ati
o
n
an
d
tw
o
sepa
ra
te
c
urr
en
t
co
nt
rol
l
ers
f
o
r
b
o
t
h
d
a
nd
q
a
xes
[
1
,8,9]
.
A
c
c
o
rdi
n
g
to [1,
8,9]
t
he sta
te
-
f
ee
dbac
k
c
o
n
t
rol law
ca
n be
w
rit
te
n
a
s
:
-1
-1
-1
-
()()
()
()
-
(
)
u
L
x
g
x
L
xw
ax
L
x
w
(10)
The
(10)
can
b
e w
r
it
ten
i
n
de
t
aile
d
form
:
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.
10,
N
o.
4
, Dec
201
9 :
1
7
5
8
– 1
771
1
762
,
1
2
1
,
21
2
3
1
0
w
1
0w
w
00
0
0
u
rd
rr
d
c
dx
x
aa
aa
cT
dx
x
aa
a
a
(11)
W
ith
:
p
a
ramete
rs:
12
3
1
(
1)
1
(
1)
;;
;
;
;
s
ds
q
s
sr
s
r
ac
d
w
u
w
u
w
LT
T
T
Th
e
s
t
a
t
e-f
eedb
a
ck
c
ont
rol
l
a
w o
r
t
h
e
coo
rd
in
at
e
t
r
a
n
sfo
r
ma
t
i
on
law
can
b
e w
r
it
te
n i
n
de
t
aile
d
form
:
11
3
22
3
3
1
w[
w
w
]
1
w[
w
w
]
w
rd
sd
sd
s
q
s
q
s
m
rd
s
qs
q
r
s
d
s
d
s
m
s
ui
c
i
i
aL
ui
c
T
i
i
aL
(12)
The
co
ntro
l str
u
ct
ure
of
t
he
i
n
n
er
l
o
o
p
us
ing
t
h
e
m
e
th
o
d
of
exa
ct l
i
n
ear
i
z
a
t
io
n is sh
o
w
n
i
n
F
i
gur
e 2
E
q
.(
12)
s
j
e
1
w
2
w
F
l
ux
m
ode
l
*
sq
i
s
j
e
s
s
w
s
J
'
rd
y
w
w
is
d
R
is
q
R
S
t
at
e
f
e
ed
b
a
c
k
SV
M
su
i
sv
i
w
s
i
3~
s
i
s
i
s
i
*
sd
i
s
u
s
u
sd
u
sq
u
sd
i
sq
i
DC
u
w3
s
w
=
sd
i
sq
i
Exa
c
t
l
i
nea
r
i
zat
i
on of curre
nt
cont
rol
IE
Inve
rt
er
S
p
ee
d
m
eas
ure
F
i
gure
2. Co
n
tr
ol s
truct
u
re
of
the
c
u
rrent
v
ec
t
o
r
con
t
rol
l
e
r
w
i
t
h
m
eth
od
of e
xact l
i
n
ea
riza
t
i
o
n
4.
NONL
INEAR
CO
NTROL
DESIGN FOR OUTE
R
LO
O
PS
S
i
nce
the
de
ad
bea
t
c
o
n
tr
ol
ler
w
h
ic
h
forc
es
t
he
s
ta
t
o
r
c
u
rrent
t
o
i
t
s
de
si
r
e
d
va
l
u
e
in
f
i
n
ite
s
te
p
s
h
as
alre
ad
y
s
u
cce
s
s
fu
lly
b
ee
n
de
vel
o
ped
for
th
e
st
a
t
or
c
urr
e
nt
l
oo
p
i
n
p
r
e
v
i
o
u
s
s
e
c
ti
on
s,
t
he
r
emai
n
i
ng
o
bj
e
c
t
i
ve
of
t
h
i
s re
sear
ch
i
s
t
o
d
es
ig
n co
ntr
o
l
l
er
f
or
t
or
que a
n
d
flu
x l
o
ops.
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
Adv
ance
d
c
ont
ro
l struc
t
ure
s
f
o
r i
n
d
u
c
tio
n
m
o
tors
wi
t
h
ide
a
l c
u
rre
n
t
lo
op
re
sp
onse
… (
V
o
T
h
a
nh
H
a
)
1
763
4.1.
Flatn
e
ss-based cont
rol d
e
sig
n
The
a
s
ync
hro
n
ous
e
l
e
c
t
rica
l
dr
ive
str
u
c
t
ure
us
ing
f
l
a
t
ne
ss-
base
d
c
ontro
l
for
the
o
u
te
r
lo
op
(
s
pe
ed
a
n
d
fl
u
x
l
o
op) w
it
h
ide
a
l
per
form
anc
e
o
f s
t
a
t
or c
u
rre
nt
is s
h
ow
n in
F
i
gur
e 4. Ba
s
e
d
on [1,1
7],
t
h
e fla
t
o
u
t
p
u
t
i
s t
h
e
fl
u
x
a
nd spee
d
,
dd
r
,
thus w
e
obta
i
n the
fla
t
nes
s
-b
a
s
e
d
c
ontro
l
l
er
f
or
t
he flu
x
an
d
speed as f
o
llows:
Fl
ux and spee
d
referenc
e
tr
a
j
ecto
r
y desi
g
n
in
g
In or
d
er
t
o
gua
ra
ntee
d
i
f
f
er
en
t
i
a
b
le pr
ope
rt
y,
t
he
re
l
a
tio
ns
hi
p
b
e
t
ween
*
&
d
rd
rd
a
n
d
*
&
can
b
e
gi
ve
n a
s
f
ol
l
o
w
s
:
*
1
22
11
()
(
1
)1
rd
d
rd
s
s
G
Ts
T
s
(13)
*
2
22
22
()
1
()
1
s
G
s
Ts
T
s
(
14)
W
ith
:
**
,
rd
: r
e
fe
renc
e flux
an
d
spe
e
d;
,
d
rd
f
lu
x a
nd s
p
ee
d re
fer
e
nce
tra
j
e
c
t
or
y
Fee
d
f
o
rwa
r
d
co
nt
rol
d
e
s
i
gn
ing
In the
fla
t
sy
s
t
e
m
,
the in
pu
t va
l
u
e
i
s
**
,
Ts
d
s
q
ui
i
, t
h
e
i
n
put
v
al
u
e
**
;
s
ds
q
ii
are
c
o
m
p
u
t
ed
b
ased
o
n
t
h
e
fla
t
o
ut
p
u
t a
nd
the c
o
nstruc
te
d
tra
j
e
c
t
o
ries
:
*
**
rd
sd
r
d
r
d
iT
dt
(15)
*
1
*
*
2
L
sq
rd
d
hm
dt
i
h
(
16)
W
ith
L
m
:
est
i
ma
t
e
torq
u
e
loa
d
Fee
d
b
a
c
k co
ntrol
d
e
sign
in
g
In
f
act,
the
m
ode
l
s
t
a
t
e
of
I
M
is
not
a
bso
l
u
t
e
l
y
a
c
c
u
r
a
te
,
and
t
h
e
d
i
s
t
urba
nc
es
t
ha
t
have
n
e
g
at
i
v
e
effec
t
s on
t
he qua
l
ity of
the
f
l
a
t
ne
ss-
b
ased
c
on
tro
l
l
e
r.
F
or
t
h
i
s
r
e
a
so
n,
i
n
o
r
de
r
t
o
ens
ure
t
h
at
t
he
o
ut
p
u
t
m
a
tch
the
des
i
re
d
val
u
e,
a
dd
i
tio
na
l
c
l
o
s
e
d
l
o
op
co
ntr
o
l
is
r
eq
uire
d
u
si
ng
P
I
c
on
tro
ller
.
T
he
refor
e
,
t
h
e
P
I
c
on
tro
lle
r
for
the s
p
ee
d a
nd fl
ux l
o
op c
a
n
be
e
xpresse
d
as (17)
and
(18
)
:
1
1
(1
.
)
()
(1
)
dz
Rz
V
z
(17)
W
h
ere:
1
31
T
T
r
r
T
T
Vd
e
e
y
y
yy
-
-
»»
æö
÷
ç
÷
ç
-
÷
ç
÷
÷
ç
èø
An
d
1
1
1
1
1.
1
R
r
Vd
z
Gz
z
(
18)
W
h
ere:
11
da
=
: pa
ram
e
te
rs;
()
()
(
)
2
2
2
1
13
1
R
s
z
V
Vm
z
m
+
=
éù
++
-
+
êú
ëû
:
amp
l
ifi
c
at
io
n
co
e
ffi
ci
ent
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.
10,
N
o.
4
, Dec
201
9 :
1
7
5
8
– 1
771
1
764
IE
IM
3
2
u
s
α
u
sd
u
sq
i
s
α
i
su
i
sq
i
sd
u
s
β
i
sv
i
sw
i
sβ
Fl
u
x
m
odel
PT
(
13)&
(
1
4
)
F
lat
n
es
s ba
se
d co
n
t
r
o
l
o
f
o
uter
l
o
o
p
Eq
(
17)
Eq
(1
8
)
Eq
(1
5)&
(
16
)
D
e
a
dbe
at
curr
ent
c
ont
rol
(7
)&
(8
)
i
sq
I
nver
t
e
r
SVM
t
v
t
w
DC
u
t
u
Sp
e
e
d
m
e
a
s
ure
F
i
gure
3.
F
O
C
con
tro
l
struc
t
u
re
w
ith t
he de
a
d
bea
t
co
n
t
ro
ller
fo
r
t
h
e
IM’
stat
or c
urre
nt
l
o
o
p
and
the
fla
t
nes
s
-ba
s
e
d
c
ontro
l
l
er
f
or
t
he o
uter
l
oo
p
4.2.
B
a
c
k
st
ep
p
i
n
g
con
t
r
ol d
esign
Ba
c
k
ste
p
pi
n
g
a
ppr
oach
i
s
ba
sed
on
f
ee
dba
ck
c
on
t
r
o
l
l
e
r
d
e
si
gn
i
n
g
t
h
a
t
sat
i
sfi
e
s
Ly
ap
un
ov
’s
s
t
a
bilit
y
by
c
o
nstr
uc
ti
n
g
C
LF
s
(c
on
t
r
ol
L
ya
p
u
n
o
v
f
unc
t
i
o
n
s)
from
sub
s
yste
ms
[
19
-21
]
.
Th
e
as
yn
ch
ro
nou
s
e
l
ect
ri
c
a
l
dri
v
e
s
t
ruc
t
ure
usi
n
g
bac
k
ste
p
p
i
ng
c
on
tro
l
m
etho
d
for
t
h
e
o
u
t
er
l
o
o
p
w
ith
i
dea
l
ly
c
ontro
l
per
f
orm
a
nc
e
of
st
a
t
or c
urrent
i
s
show
n
i
n
F
ig
ure
4.
Flu
x
c
o
nt
rol
l
o
o
p
d
e
sign
i
ng
Ac
co
rd
ing
t
o
[1
9
]
u
si
n
g
th
e
bac
k
st
eppi
ng
c
on
t
r
o
l
m
e
t
hod
, t
h
e fl
u
x
c
on
tro
lle
r is e
xpresse
d
as foll
o
w
s
:
*
11
rd
sd
r
r
d
r
d
ic
T
z
T
dt
(19)
W
ith
:
1
c
: co
ns
ta
nt
;
*
1
rd
rd
z
:
e
rr
ors of
r
ot
or fl
u
x
;
*
;
rd
rd
:
ref
e
re
n
c
e an
d
a
c
t
u
al
f
lux
Wi
t
h
the
i
de
a
l
c
ontro
l
perfor
m
a
n
ce
of
s
ta
to
r
curr
ent
*
s
ds
d
ii
,
one can obtain:
*
*
11
rd
sd
r
r
d
r
d
cT
z
T
dt
i
(20)
Whe
r
e
*
s
d
i
is the
ac
t
u
a
l
c
o
n
t
rol s
i
gna
l o
f
t
he f
lux
contr
o
l
l
e
r
.
Spe
e
d
c
o
ntro
l l
o
o
p
de
si
gn
i
n
g
S
i
m
i
la
rl
y, the
spee
d
co
n
t
ro
ller
i
s
a
s follow
s
:
*
*
22
w
1
()
p
sq
z
d
ic
z
m
kJ
d
t
(24)
W
ith
:
2
c
:
co
ns
ta
nt
;
*
2
z
:
er
r
ors of spee
d
;
*
;
: r
e
fe
ren
c
e a
nd a
c
t
u
al s
pee
d
Wi
t
h
the
i
de
a
l
c
ontro
l
perfor
m
a
n
ce
of
s
ta
to
r
curr
ent
*
s
qs
q
ii
,
th
a
t
l
e
a
d
s
to
:
*
22
1
()
p
sq
L
z
d
ic
z
m
kJ
d
t
(25)
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
Adv
ance
d
c
ont
ro
l struc
t
ure
s
f
o
r i
n
d
u
c
tio
n
m
o
tors
wi
t
h
ide
a
l c
u
rre
n
t
lo
op
re
sp
onse
… (
V
o
T
h
a
nh
H
a
)
1
765
D
e
sig
n
o
f
se
t p
o
i
n
t
t
r
ajec
tory
fo
r fl
ux a
nd
sp
e
e
d
In
a
d
d
iti
on
t
o
t
h
e
goa
l
o
f
m
akin
g
t
h
e
se
t
po
in
t
r
e
fe
re
nc
e
e
n
ou
g
h
di
ff
e
r
e
n
t
i
a
b
l
e
lik
e
o
u
tp
ut
,
t
h
e
con
s
trai
n
t
s
of
o
u
t
put
c
o
u
l
d
b
e
t
a
ke
n
in
t
o
a
ccou
n
t
dur
in
g
tra
j
ec
tor
y
d
esi
gn
as
w
e
l
l
.
T
he
f
lu
x
an
d
spee
d
refere
nce
traje
c
t
or
y de
si
g
n
i
n
g by (
1
3) a
nd (14).
3
2
u
s
α
u
sd
u
sq
i
s
α
i
su
i
sq
i
sd
u
s
β
i
sv
i
sw
i
sβ
Fl
u
x
mo
d
e
l
De
a
d
b
eat
c
u
rre
n
t
contr
o
l
(7
)&(
8
)
Eq
(1
3)&
(
1
4
)
B
a
c
k
st
e
ppi
ng c
ont
r
o
l
of o
ut
er
l
oop
IE
IM
SVM
t
v
t
w
DC
u
t
u
Eq
(
20)&
(
25)
S
p
eed
m
eas
ur
e
Inve
r
t
e
r
F
i
gure
4.
F
O
C
con
tro
l
struc
t
u
re
with the deadbe
at controller
f
o
r
th
e
I
M
’
stat
or c
urre
nt
l
o
o
p
and
the
bac
k
s
t
e
p
p
i
ng c
o
ntr
o
ller
for
the o
u
te
r l
o
o
p
5.
EXPE
RIMENTAL
R
ESULT
S
In
o
rde
r
t
o
e
v
a
l
u
a
te
t
he
e
ffect
i
v
enes
s
of
s
t
a
t
o
r
cur
r
ent
c
ontr
o
l
a
n
d
spee
d
co
ntro
l
m
e
tho
d
s,
t
h
e
in
duc
t
i
on
m
o
to
r
i
s
opera
t
e
d w
i
t
h
IM’s
para
me
ters a
s show
n in
T
a
ble 1
:
Tab
l
e
1.
E
xperim
e
nta
l
w
i
t
h I
M
’
s
p
ara
m
e
t
ers
IM
p
a
r
am
e
t
e
r
s
S
y
m
bol
V
alue
Pow
e
r
P
dm
2.
2 kW
R
a
t
e
d
s
p
eed
N
dm
2880
r
p
m
Ra
t
e
d
vol
t
a
g
e
U
dm
400V
Pole
p
a
i
r
Z
p
1
P
o
wer
f
acto
r
co
s
φ
0
.
9
I
n
e
r
t
i
a
torque
J
0.
002K
g.
m
2
Th
is
s
e
c
t
io
n
give
s
ou
t
t
h
e
e
v
al
ua
ti
o
n
o
f
e
xpe
r
i
m
e
nt
a
l
r
esu
l
t
s
t
ha
t
i
n
c
l
ude
s
s
t
a
t
or
c
ur
rent
r
esp
o
n
se
,
speed,
f
lux
response
a
nd perfo
rm
ance of el
e
c
trica
l
d
rive.
The
eva
l
ua
ti
o
n
of
t
he
m
a
g
net
i
zat
i
on
of
t
he
s
qu
i
r
rel
c
a
ge
i
nd
uc
t
i
o
n
m
o
t
o
r
w
ill
be
done
by
ta
ki
n
g
t
h
e
fi
n
i
t
e
sam
p
lin
g
st
e
p
as
si
m
u
la
t
i
on
w
h
ic
h a
r
e
show
n in F
igur
e
5
and
Tab
l
e 2.
Tab
l
e
2. P
e
r
form
ance
c
om
pa
rison
o
f
t
he
sta
to
r c
u
rre
nt
l
o
o
p
F
O
C
c
ontrol
struc
t
ur
e
s
E
xac
t
l
i
n
ear
i
zat
io
n
De
ad
b
eat
Cu
r
r
e
n
t
s
i
sd
i
sq
i
sd
i
sq
Se
ttli
ng ti
m
e
(
s)
0
.0025
0
.0025
0
.001
0
.001
O
v
e
r
shoot
(
%)
1
5
25
1
0
2
0
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 El
ec &
D
ri S
y
s
t
Vo
l. 1
0
,
No
. 4
,
D
e
c
2
0
19
:
1
758
–
1
771
1
766
F
i
gur
e
5.
D
yna
mica
l
r
e
spo
n
se
s
of
t
he
s
tat
o
r
c
u
r
r
e
nt
s
lo
op
Th
is
a
r
e
r
esul
ts
i
n
the
F
i
gur
e
5
and
Ta
b
l
e
2,
w
e
can
t
he
t
he
c
u
r
r
e
n
t
c
on
t
r
o
l
ler
w
i
t
h
t
he
e
xa
c
t
li
nea
r
iza
t
io
n
m
e
th
o
d
h
a
s
t
he
l
ar
ge
ove
r
s
ho
o
t
a
nd
r
i
pple
c
u
r
r
ent
i
sq
.
B
e
s
i
de
s,
t
he
c
ur
r
e
n
t
s
i
sd
, i
sq
o
f
dea
d
bea
t
c
o
n
t
r
o
ller
sati
s
f
ies
“
f
ast
–
ac
cura
cy
–
d
ec
oup
l
i
n
g
”
pr
oper
tie
s
c
o
mpa
r
ed
t
o
the
e
x
ac
t
li
ne
ariza
t
i
o
n
tha
t
l
ea
ds
f
a
st
s
pee
d
r
e
s
p
ons
e
and
low
r
i
pp
le.
Whe
n
t
he
t
or
q
u
e
i
s
r
e
q
u
i
r
e
d
(
r
e
fer
e
nce
tor
q
ue
i
s
ma
t
c
h
w
i
t
h
a
c
t
ua
l
tor
q
ue
)
,
f
oll
o
w
e
d
by
t
h
e
pa
pe
r
pr
esen
ted
f
o
r
d
ynam
i
ca
l
r
e
s
p
o
n
se
e
val
u
a
t
i
o
n
of
F
O
C
c
on
tr
o
l
s
tr
u
c
t
ur
es
a
t
s
p
e
e
d
o
f
0
.
1
r
a
d
/s
a
nd 1
00
r
a
d/
s
ar
e
e
xpresse
d
thr
o
ugh
Figure
6, Figure
7
and Ta
bl
e
3:
Ta
b
l
e
3.
S
yste
m
r
e
spon
se
c
o
m
par
i
so
n
F
O
C
c
o
n
t
r
o
l
s
t
r
u
ct
u
r
es
D
ead
b
eat
-
F
l
a
t
n
e
s
s
Dead
b
eat
-
B
ack
s
t
ep
p
i
n
g
a
t
the
spe
e
d
o
f
0.
1
r
a
d/s
Flux se
ttling time
(s)
0.4
0.35
S
p
ee
d
se
ttl
ing
ti
m
e
(
s)
0
.
0
5
0.
05
a
t
th
e
sp
eed
o
f
1
0
0
r
a
d
/s
Flux se
ttling time
(s)
0.3
0.25
S
p
ee
d
se
ttl
ing ti
me (
s)
0.
25
0
.
1
5
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
Adv
ance
d
co
nt
ro
l stru
ct
ures for ind
u
c
t
i
o
n
m
o
t
o
rs
w
i
th i
d
e
a
l
curre
n
t
l
o
op
r
e
sp
onse
…
(
V
o T
hanh H
a
)
1
767
Fi
g
u
re
6
.
i
sd
c
u
r
r
e
nt
a
nd
spe
e
d
r
esponses
a
t
t
h
e
spe
e
d
of
0
.
1
r
a
d
/
s
F
i
gur
e
7.
i
sd
c
u
r
r
e
nt
a
nd
spee
d
r
e
sponses
a
t
t
h
e
spe
e
d
of
1
0
0
r
ad/s
Base
d
o
n
t
h
e
abo
v
e
resu
lts,
we
c
a
n
t
he
f
l
u
x
set
t
l
e
wit
h
i
n
0
.25s
,
the
lo
n
g
o
ver
spee
d
t
i
me
w
ith
w
i
d
e
spee
d
r
a
nge,
o
v
er
sh
oo
t
a
b
o
u
t
10%
t
o
2
5
%.
I
t
is
w
or
t
h
n
o
t
in
g
tha
t
the
ou
ter
lo
o
p
c
o
n
t
r
o
l
us
i
ng
bac
k
te
ppi
n
g
Evaluation Warning : The document was created with Spire.PDF for Python.