Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
7, N
o
. 1
,
Mar
c
h
20
16
,
pp
. 28
~44
I
S
SN
: 208
8-8
6
9
4
28
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
Constant Fr
equency
T
o
r
q
ue Cont
r
o
ller
for
DTC with Multilevel
Inverter
of Induction Machines
N
o
rj
u
lia Mo
ha
ma
d
N
o
rd
in
1
,
Na
zih
a
A
h
ma
d
A
z
li
2
, Nik
Rumz
i Nik I
d
ris
3
, Nur
Hu
d
a
Raml
an
4
,
Tole Su
tikn
o
5
1,2,3
Universiti Teknologi Ma
lay
s
ia, Faculty
of
El
ectrical Eng
i
neer
ing,
Skudai, Joho
r
Bahru, Malay
s
ia
4
Universiti
Mala
ysia
Pahang
, Fa
c
u
lt
y of
El
ec
tr
ic
al
and
El
ectron
i
cs
,
P
e
kan, Pahang
,
Malay
s
ia
5
Department of Electrical
Eng
i
n
eering
,
Un
iv
ersitas Ahmad Dahlan, Yog
y
ak
arta, I
ndonesia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Oct 22, 2015
Rev
i
sed
Jan
7, 2
016
Accepte
d
Ja
n 23, 2016
Direct
Torque
Control using m
u
l
tilev
e
l
inver
t
er (
D
TC-MLI) with
h
y
st
eresis
controller suffer
s
from high torque a
nd flux r
i
pple and v
a
riable switching
frequency
.
In
this paper, a
constant frequ
ency
tor
que
controller is
proposed to
enhanc
e the DTC-M
L
I perfor
m
ance. The op
erat
ional con
c
e
p
ts
of the
constant switch
i
ng frequ
ency
torque
controller of a DTC-MLI s
y
stem
followed b
y
th
e simulation results and
analy
s
is ar
e presented
.
The proposed
s
y
stem significantly
improves
the
DTC drive in term
s of d
y
nam
i
c
performance, smaller torque and
flux ri
pple, and
retains a constan
t
switchin
g
frequency
.
Keyword:
C
onst
a
nt
s
w
i
t
c
hi
n
g
fre
que
ncy
Di
rect
t
o
rq
ue
c
ont
rol
I
ndu
ctio
n m
a
c
h
in
es
Mu
ltilev
e
l in
v
e
rter
Tor
q
ue C
ont
r
o
l
l
e
r
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Norj
u
lia Bin
ti
Mo
h
a
m
a
d
No
rd
in
,
Depa
rt
m
e
nt
of
El
ect
ri
cal
Po
w
e
r E
ngi
neeri
n
g
,
Facu
lty of Electrical Eng
i
n
eerin
g
,
Un
iv
ersiti Tekn
o
l
o
g
i
Mal
a
ysia,
8
131
0 Sk
ud
ai,
Jo
hor
, Malaysia.
Em
a
il: n
o
r
j
u
lia@fk
e
.u
tm
.
m
y /
no
rju
lia@u
tm
.my
1.
INTRODUCTION
Si
nce i
t
has
b
een i
n
t
r
o
d
u
ce
d i
n
earl
y
1
9
80s
[
1
]
,
Di
rec
t
T
o
r
q
u
e
C
o
nt
rol
(D
TC
)
has
gai
n
ed
i
t
s
popularity in e
l
ectrical drives
res
earc
h
a
r
ea. Recently
, the
application of
high-powe
r
medium
voltage
in
AC
d
r
i
v
es
h
a
s sh
own
rap
i
d
d
e
v
e
lo
p
m
en
t.
Thu
s
, th
e u
s
e of
m
u
ltilev
e
l in
v
e
rters in
DTC sche
m
e
h
a
s b
e
come an
im
port
a
nt
st
r
u
ct
ure
f
o
r
f
u
rt
h
e
r
devel
opm
en
t
an
d i
m
pro
v
e
m
ent
.
N
u
m
e
rous t
e
c
hni
cal
p
a
pers
have
s
h
ow
n
a
su
perior p
e
rfo
rman
ce
of DTC
sch
e
m
e
u
s
ing
m
u
l
tilev
e
l
in
v
e
rters [2-3
4
]
.
By u
tilizin
g
the m
u
lt
ilev
e
l in
v
e
rter in
DTC
sch
e
m
e
, th
e cho
i
ces of
v
o
ltage v
ectors that can
b
e
used
to control t
h
e t
o
rque a
n
d fl
ux
are inc
r
ease
d
.
As a
res
u
lt,
m
o
re
preci
se
co
nt
rol
ca
n
be
o
b
t
a
i
n
ed.
Se
veral
c
ont
rol
m
e
thod
have
been
proposed for DTC schem
e
using m
u
ltilevel inverte
r
(DTC-ML
I);
hysteresis-bas
ed and
non-hysteresis
-base
d
s
u
ch as
pre
d
ic
tiv
e
con
t
r
o
l
st
r
a
teg
y
[1
1
,
15
,
17
,
18
, 2
0
, 2
2
, 26
, 27,
30
], sp
ace
vecto
r
m
odul
at
i
on
st
r
a
t
e
gy
[
2
, 4,
8
-
1
0
, 1
4
, 2
1
, 2
8
, 2
9
, 3
3
]
an
d fuzz
y
l
ogi
c
c
ont
rol
st
rat
e
gy
[
3
,
5
,
7, 1
9
, 3
1
, 3
4
-
3
6]
.
The
em
pl
oym
ent
of
hy
st
ere
s
i
s
-base
d
c
ont
rol
st
rat
e
gy
i
n
di
sc
ret
e
i
m
pl
em
ent
a
t
i
on
ha
s l
e
d
t
o
hi
g
h
to
rq
u
e
ripp
le ev
en
with
a
small h
y
steresis b
a
nd
.
Th
is is
d
u
e
t
o
th
e
d
e
l
a
y in
sam
p
lin
g
ti
m
e
. Besid
e
s th
at, it
creat
ed
a
vari
a
b
l
e
s
w
i
t
c
hi
n
g
f
r
eq
ue
ncy
of
t
h
e swi
t
c
hi
n
g
de
vi
ces
w
h
i
c
h
l
eads t
o
an
un
pr
edi
c
t
a
bl
e
harm
oni
c
s
current.
As a
resul
t
,
s
o
m
e
researc
h
e
r
s
pre
f
e
rre
d t
o
use
no
n
-
hy
st
eresi
s
-
b
ase
d
c
ont
rol
st
rat
e
gy
. Si
gni
fi
cant
im
pro
v
em
ent
s
are acc
om
pl
i
s
hed i
n
t
e
rm
s of
f
l
ux
a
n
d
t
o
rq
ue
ri
p
p
l
e
a
n
d
de
vi
ces s
w
i
t
c
hi
n
g
f
r
eq
ue
ncy
.
H
o
w
e
ve
r
i
t
i
nvol
ve
s a com
p
l
e
x
m
a
t
h
em
at
i
cal equat
i
ons a
n
d al
g
o
ri
t
h
m
whi
c
h has
l
e
d t
o
t
h
e co
m
p
l
e
xi
ty
of t
h
e DTC
-
MLI sch
e
m
e
a
n
d h
i
g
h
co
m
p
utatio
n
a
l bu
rd
en p
a
rticu
l
ar
ly wh
en th
e m
u
ltile
v
e
l inv
e
rter
’
s
lev
e
l is in
creased
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
1,
Mar
c
h
2
016
:
28
–
4
4
29
In [12
]
, t
h
e
DTC-MLI sch
e
me e
m
p
l
o
y
s a
m
u
l
tilev
e
l h
y
steresis con
t
ro
ller
.
It
shows
some sig
n
i
fican
t
im
pro
v
em
ent
s
, ho
we
ver t
h
e p
o
we
r
devi
ces s
w
i
t
c
hi
n
g
f
r
e
q
u
e
ncy
are
vari
es
and t
h
e t
o
rq
ue
and
fl
u
x
ri
p
p
l
e
ca
n
still b
e
con
s
i
d
ered as h
i
g
h
.
A
PI-con
stan
t
switch
i
ng
frequ
e
n
c
y
(PI-C
SF) t
o
rqu
e
con
t
ro
ller fo
r
DTC was
in
itially in
tro
d
u
ced i
n
[3
7,
38
].
Th
e PI-CSF torq
u
e
co
n
t
ro
ller
was rep
l
acin
g
th
e co
nv
en
tion
a
l
h
y
st
eresis
cont
rol
l
e
r
whi
l
e m
a
i
n
t
a
i
n
i
n
g
t
h
e
use
of
l
o
o
k
u
p
-
t
a
bl
e.
Ho
w
e
ver
i
t
has
bee
n
use
d
f
o
r
DT
C
wi
t
h
c
o
nve
nt
i
onal
3
-
pha
se i
n
vert
e
r
.
In th
is
work,
th
e PI-C
SF torq
u
e
con
t
ro
ller is
u
tilized
i
n
DTC
-
MLI syste
m
. Fig
u
re 1 sho
w
s a
pr
o
pose
d
sy
st
e
m
bl
ock di
a
g
r
a
m
.
The pr
o
p
o
s
ed co
nt
r
o
l
l
e
r
con
s
i
s
t
s
of a P
I
co
nt
r
o
l
l
e
r an
d a t
r
i
a
n
gul
a
r
carri
e
r
si
gnal
.
T
h
e c
onst
a
nt
s
w
i
t
c
h
i
ng
fr
eq
ue
ncy
i
s
o
b
t
a
i
n
e
d
by
com
p
ari
n
g
t
h
e
PI
co
nt
r
o
l
l
e
r
out
put
wi
t
h
t
h
e
triangular carrier signals. In this
schem
e
,
the
propose
d
cont
roller will
re
placed the
m
u
l
tilevel hysteresis
to
rq
u
e
con
t
ro
ll
er
.
Th
e
p
r
o
p
o
s
ed
system
is em
p
l
o
y
ed
a 5
-
lev
e
l cascad
ed
H-Bridg
e
m
u
ltil
ev
el in
v
e
rter
(CHMI)
as a power c
o
nve
rter
.
The
m
u
ltiple isolated DC s
o
urces
in CHMI are
particularly s
u
itable for a
n
electric
vehi
cl
e
(EV
)
a
ppl
i
cat
i
o
n si
nc
e t
h
e
po
we
r s
o
urce
f
o
r
an
EV
can
be
o
b
t
a
i
n
e
d
fr
om
t
h
e bat
t
e
ry
m
odul
es.
Fi
gu
re
1.
Pr
o
p
o
se
d sy
st
em
bl
ock
di
a
g
ram
In th
is p
a
p
e
r
,
th
e
o
p
e
ration
a
l con
cep
t
o
f
PI-CSF
t
o
rq
u
e
co
n
t
ro
ller u
tili
zed
i
n
DTC
-
MLI
system
fo
llowed
b
y
si
m
u
la
tio
n
resu
lts o
f
t
h
e propo
sed
system
is p
r
esen
ted. Fu
rtherm
o
r
e th
e experim
e
n
t
al resu
lts are
d
i
sclo
sed
t
o
v
a
lid
ate th
e sim
u
latio
n
resu
lts t
o
g
e
t
h
er w
ith th
e an
alysis on th
e
p
r
o
pos
ed
sy
st
em
perf
or
m
a
nce.
The
resul
t
s
ha
ve s
h
o
w
n t
h
at
su
peri
o
r
dy
na
m
i
c perf
orm
a
nce, sm
all
e
r t
o
r
que
an
d fl
u
x
r
i
ppl
es a
n
d
co
n
s
t
a
nt
devi
ce
swi
t
c
hi
ng
f
r
eq
ue
ncy
a
r
e ac
hi
eve
d
.
2.
MULTILEVE
L
INVERTE
R
A
5
-
lev
e
l cascad
e
d H-Bri
d
g
e
m
u
lt
ilev
e
l in
verter
(CHM
I) co
nsists
of 2
cells
of H
-
B
r
i
d
ge
i
n
ve
rt
e
r
connected in c
a
scade
d
form
with se
parated DC s
o
urce
s. Fig
u
r
e
2
shows
a
co
nf
igu
r
ati
o
n
of
5-
lev
e
l CH
MI
.
The
n
u
m
b
er o
f
v
o
l
t
a
ge l
e
vel
,
L, f
o
r C
H
M
I
c
a
n
be
det
e
rm
i
n
ed
by
2
1
(
1
)
Whe
r
e
m
i
s
a
num
ber
of cel
l
per
p
h
ase.
Ea
ch
H-
bri
dge c
e
l
l
pro
d
u
ce
d
V
jm
out
put
vol
t
a
ge, w
h
ere
j
denotes the
phases; a, b, c
.
Since
the cells are connected
in series, t
h
e total out
put
vol
tage for eac
h
pha
se
wo
ul
d
be
∑
(
2
)
∑
(
3
)
∑
(
4
)
V
aN
,
V
bN
and
V
cN
is th
e v
o
ltage o
u
t
p
u
t
p
e
r
ph
ase with
respect to
th
e n
e
u
t
ral,
N
. B
y
consi
d
eri
ng eac
h
cel
l
pr
od
uce {
-
V
DC
, 0,
V
DC
},
b
a
sed
o
n
(2
), (3
) and
(4), each
p
h
a
se
will p
r
o
d
u
ce a 5-lev
e
l
ou
tpu
t
vo
ltag
e
;
2
,
1
,0
,
1
,
2
(
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Const
ant Frequency
Tor
que
Contr
o
ller
for
DTC with
Mult
ilevel Inverter
of Induction …
(
N
.M. Nor
d
in)
30
I
n
sp
ace ph
asor
for
m
, th
e ou
tp
u
t
vo
ltag
e
,
V
S
, t
h
at
gene
rat
e
d
by
t
h
e
i
n
vert
e
r
can
be
de
fi
ne
d
as
(
6
)
Whe
r
e
a
=
e
j2
π
/3
and
a
2
=
e
j4
π
/3
.
I
n
d-
q f
o
rm
,
t
h
e out
put
v
o
l
t
a
ge
ca
n be
e
x
p
r
essed
a
s
2
(
7
)
√
(
8
)
Consi
d
eri
n
g equation (5),
(6)
and (7
), there ex
ist 125
co
m
b
i
n
atio
ns
o
f
ph
ase
vo
ltag
e
with
6
1
vo
ltage
v
ectors g
e
n
e
rat
e
d
for 5-lev
e
l CHMI. Th
e h
i
g
h
e
r th
e lev
e
l
o
f
m
u
ltilev
e
l
i
n
v
e
rter, th
e
h
i
gh
er th
e nu
m
b
er o
f
th
e
vol
t
a
ge
vect
o
r
gene
rat
e
d
,
t
h
us gi
vi
n
g
m
o
re deg
r
ees o
f
f
r
eed
om
i
n
choosi
n
g v
o
l
t
a
ge
vect
or
s f
o
r c
ont
rol
pu
r
poses
. Fi
g
u
r
e 3 a
nd Fi
gu
r
e
4 sh
o
w
s a v
o
l
t
a
ge vect
o
r
m
a
p o
n
d
-
q pl
an
e gene
rat
e
d
fr
o
m
5-l
e
vel
C
H
M
I
an
d
th
e conf
igu
r
ati
o
n of
t
h
e indu
ctio
n
m
ach
in
es fed
by 5-le
vel CHMI, res
p
ect
ively.
Fi
gu
re
2.
5
-
l
e
v
e
l
cascade
d
H-
bri
dge
m
u
l
tilev
e
l in
v
e
rter
(CHMI)
Fi
gu
re
3.
V
o
l
t
a
ge
vect
o
r
m
a
p on
d
-
q
pl
ane
Fi
gu
re
4.
3
-
p
h
a
s
e i
n
duct
i
o
n m
achi
n
e
fe
d
by
5
-
l
e
vel
C
H
M
I
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
1,
Mar
c
h
2
016
:
28
–
4
4
31
3.
STRU
CT
UR
E A
N
D
M
O
DELIN
G
OF THE
DTC
WITH
CO
NST
A
N
T
SWIT
CH
IN
G
FR
EQU
E
NCY
To
an
alyze th
e D
T
C
dr
iv
e i
n
ter
m
s o
f
its sw
itch
i
ng
f
r
e
quen
c
y, the inductio
n
m
ach
in
e
is m
o
d
e
led
u
s
ing
t
h
e fo
llowing
eq
u
a
tion
s
. Th
ese eq
u
a
ti
on
s are
written
i
n
g
e
n
e
ral referen
ce
fram
e
.
(
9
)
0
(
1
0
)
(
1
1
)
(12)
Th
e sup
e
rscript “g
” in th
e ab
ov
e equ
a
tio
ns d
e
n
o
t
es
th
at
th
e qu
an
tities are referred
to th
e ro
tati
ng
gene
ral re
fere
n
ce fram
e
. In th
e abo
v
e e
quati
ons
,
,
and
are
t
h
e st
at
or
vol
t
a
ge,
stator current and rotor
current, res
p
ec
tively.
,
,
and
are the stator
resistances,
rot
o
r
re
sistances,
stator flux linkages and
r
o
t
o
r f
l
ux lin
kag
e
s, r
e
sp
ectively.
is the
gen
e
ral re
fere
nce
spee
d a
n
d
is the
rot
o
r s
p
eed.
,
an
d
are the
stator s
e
lf-inducta
nce,
ro
to
r self-ind
uctan
ce an
d m
u
t
u
al
self-induct
a
nce respecti
v
e
l
y.
The t
o
rque
and m
echanical dynam
i
cs of the
in
du
ction
m
ach
in
es are m
o
d
e
led
as fo
llo
ws:
(
1
3
)
(
1
4
)
Whe
r
e
is th
e
electro
m
a
g
n
e
tic to
rqu
e
,
is the to
rqu
e
lo
ad
,
J
is th
e m
o
m
e
n
t
of i
n
ertia,
p
is
th
e
num
ber
of
p
o
l
e
an
d
is the m
echanical
rot
o
r
spee
d.
By u
s
in
g (9
)
–
(14
)
i
n
th
e statio
n
a
ry referen
ce fram
e, th
e p
o
sitiv
e and n
e
gativ
e torqu
e
slop
e are
obt
ai
ne
d by
[3
9, 4
0
]
⋅
(
1
5
)
⋅
(16)
Whe
r
e
σ
is the to
tal flu
x
lin
k
a
g
e
factor,
i
s
t
h
e st
at
or t
i
m
e
const
a
nt
and
is th
e roto
r tim
e
co
nstan
t
. In
(16
)
, it is assu
mes th
at th
e zero
vo
ltag
e
v
ect
ors are selecte
d
in orde
r to reduce the torque. T
h
e
instantane
ous stator flux fre
quency
can
be ob
tain
ed
in
term
s
o
f
th
e av
erage synchronous fre
quency a
nd
duty
ratio [38]. T
h
erefore
(15)
an
d
(1
6)
can
be
w
r
i
tten in th
e stato
r
fl
ux
re
fere
nc
e fram
e
as f
o
llows:
(
1
7
)
(18)
W
h
er
e
(
1
9
)
(
2
0
)
(
2
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Const
ant Frequency
Tor
que
Contr
o
ller
for
DTC with
Mult
ilevel Inverter
of Induction …
(
N
.M. Nor
d
in)
32
In (
1
7) a
nd (
1
8
)
, i
t
i
s
assu
m
e
d t
h
at
t
h
e q com
p
o
n
e
n
t
s
of t
h
e
part
i
c
ul
a
r
v
o
l
t
a
ge vect
o
r
are z
e
ro a
nd t
h
e
stator and rot
o
r fluxes are constant
which
means that the voltage vect
ors ar
e tan
g
e
n
tial to
th
e circu
l
ar stato
r
flux
lo
cu
s. Finally, th
e equ
a
tio
n (17
)
and
(18
)
are av
erag
ed
an
d sim
p
lifie
d
to g
i
v
e
(
2
2
)
4.
THE PROPOSED
CONTROLLER
The p
r
op
ose
d
t
o
r
q
ue co
nt
r
o
l
l
e
r i
s
em
pl
oy
ed as an
alternati
v
e to the
hysteres
is-b
ased
con
t
ro
ller wit
h
t
h
e be
nefi
t
of
ope
rat
i
n
g at
c
onst
a
nt
swi
t
c
h
i
ng
fre
q
u
ency
wi
t
h
l
o
w t
o
r
q
ue ri
ppl
e.
The
pr
o
pose
d
c
o
n
t
rol
l
e
r
con
s
i
s
t
of
6 t
r
i
a
ng
ul
ar
wa
vef
o
rm
generat
o
rs
, 6 c
o
m
p
arat
or
s an
d a p
r
o
p
o
rt
i
onal
-
i
n
t
e
g
r
al
(
P
I) c
o
nt
r
o
l
l
e
r.
Fi
gu
re
5 s
h
o
w
s
t
h
e c
o
nfi
g
u
r
at
i
o
n
o
f
t
h
e
pr
o
pose
d
t
o
rq
ue c
o
nt
rol
l
e
r
.
Figure 5. Proposed torqu
e
contro
ller
The si
x t
r
i
a
n
g
u
l
a
r w
a
ve
fo
rm
gene
rat
o
rs
ge
nerat
e
3 pai
r
s
of t
r
i
a
ng
ul
ar
wave
f
o
rm
s (carri
er si
gnal
s
)
with
th
e sam
e
mag
n
itu
d
e
bu
t
with
diffe
re
nt DC
o
f
f
s
et.
Eac
h
pair (C
Upper
and C
Lower
)
is 18
0°
o
u
t
o
f
ph
ase. In
p
r
i
n
cip
l
e, th
e
p
r
op
o
s
ed
co
n
t
ro
ller will p
r
odu
ce th
e sam
e
o
u
t
p
u
t
as an
8-lev
e
l h
y
steresis co
n
t
ro
ller in [12
]
,
whi
c
h can be
ei
t
h
er o
n
e of t
h
e fol
l
owi
ng t
o
r
q
ue err
o
r st
a
t
us;
3, 2,
1, +
0
.
5
, -
0
.
5
, -
1
, -
2
, -
3
. T
h
e n
u
m
ber of
l
e
vel
s
, h
o
w
eve
r
, m
u
st
be real
i
s
t
i
c
eno
u
g
h
f
o
r
im
pl
em
ent
a
t
i
o
n p
u
r
p
oses.
I
n
ot
he
r w
o
r
d
s, t
h
e hi
g
h
er t
h
e n
u
m
ber
o
f
lev
e
ls, t
h
e
faster in term
s
o
f
pro
c
essor
requ
irem
en
t is n
e
ed
ed fo
r i
m
p
l
e
m
en
tatio
n
.
By co
m
p
aring
the
t
r
i
a
ng
ul
ar
wa
v
e
fo
rm
s wi
t
h
t
h
e PI
co
nt
r
o
l
l
e
r
out
put
,
a c
o
n
s
t
a
nt
s
w
i
t
c
hi
n
g
f
r
eq
ue
ncy
can
b
e
achi
e
v
e
d
.
The i
n
st
a
n
t
a
ne
ous
val
u
e
o
f
t
h
e t
o
r
q
ue co
nt
rol
l
e
r
out
put
,
q(
t)
, i
s
gi
ven
by
(2
3
)
. A
s
f
o
r t
h
e ave
r
a
g
e
value
of the
ca
rrier signal pe
riod,
T
tri
, desi
gn
at
ed
by
d(
t
)
i
s
gi
ve
n
by
(
2
4).
3,
_
2,
_
_
1,
_
0.5,
0
0.5,
0
1,
_
2,
_
_
3,
_
(
2
3
)
(24)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
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-86
94
I
J
PED
S
Vo
l. 7,
No
.
1,
Mar
c
h
2
016
:
28
–
4
4
33
4.1. PI Contr
o
ler’s
P
a
rame
ter
Selection
The sel
ect
i
o
n of
param
e
t
e
rs val
u
e
of
PI c
o
nt
r
o
l
l
e
r
is i
m
p
o
r
tan
t
to
en
sure th
e prop
er
op
eration
o
f
to
rq
u
e
con
t
ro
ller.
Hen
ce, a lin
ear con
t
ro
l
syste
m
th
eo
ry
h
a
s b
e
en
u
s
ed
to carry ou
t
th
e lin
earizing
an
d
avera
g
i
n
g
pr
oc
ess f
o
r
t
h
e t
o
r
q
ue l
o
o
p
.
Fi
g
u
re
6 s
h
ow
s a sy
st
em
t
o
rq
ue l
o
o
p
.
Figure 6.
Torqu
e
loop
Aft
e
r t
h
e a
v
er
agi
n
g p
r
oces
s of (
1
5) a
nd (
1
6)
, a sim
p
l
i
f
i
e
d an
d ave
r
age
d
t
o
r
q
ue eq
uat
i
on can
b
e
written
as in
(19
)
. By in
trod
u
c
i
n
g
a sm
al
l p
e
rtu
r
b
a
tion in
T
e
,
d
and
ω
slip
fo
r lin
earizatio
n
in
(22
)
and
t
r
ans
f
o
r
m
e
d i
t
t
o
t
h
e
fre
qu
en
cy
dom
ai
n, t
h
e
sm
al
l
-
si
gnal
t
r
ans
f
er
f
unct
i
o
n a
nd
st
eady
s
t
at
e equat
i
o
n c
a
n
be
extracted
as fol
l
ows:
(
2
5
)
0
(
2
6
)
I
n
(25
)
,
fo
r
sim
p
l
i
city,
K
ω
sli
p
(s
)
can be neglected since t
h
e cont
ribu
tion
is relativ
ely s
m
all. Th
e
co
m
p
lete lin
earized
p
r
op
osed to
rqu
e
loop
is
sh
own
in Fi
g
u
re 7
.
Figure 7. Linearized
torque loop
Preferab
ly, in
o
r
d
e
r to ob
tain faster torqu
e
respo
n
s
e,
t
h
e
t
o
rq
ue l
o
o
p
ba
nd
wi
dt
h
s
h
o
u
l
d
b
e
as l
a
r
g
e
a
s
i
t
can.
Ho
we
v
e
r, t
h
e sel
ect
i
o
n
of
t
o
r
q
ue l
o
op
ba
n
d
wi
dt
h
an
d con
t
ro
ller’s p
a
ram
e
ters, i.e.,
propo
rtional g
a
in,
K
p
, and i
n
t
e
gr
al
gai
n
,
K
i
, ar
e l
i
m
i
t
e
d by
several
co
nst
r
ai
nt
s suc
h
as ha
rd
ware sam
p
l
i
ng t
i
m
e and carri
er
fre
que
ncy
.
Th
e param
e
ters o
f
1
.
5
k
W indu
ctio
n
m
ach
ines as liste
d in Table I are use
d
to calculate the num
e
rical
v
a
lu
es
of torque lo
op
tran
sf
er
fu
nct
i
o
n u
s
i
n
g
(1
9)
-
(2
0)
. I
n
sel
ect
i
ng t
h
e
p
r
o
p
o
rt
i
o
nal
gai
n
o
f
P
I
c
ont
rol
l
er, i
t
m
u
st be ensured that the a
b
s
o
lu
t
e
sl
o
p
e of cont
rol
si
g
n
al
, T
c
, is not exce
ed the a
b
s
o
lut
e
slope
of t
h
e
carrier
si
gnal
s
.
Tabl
e 1. In
d
u
ct
i
on
M
a
c
h
i
n
e
P
a
ram
e
t
e
rs
Para
m
e
ters
Values
Stator Resistance,
R
s
3
Rotor Resistance,
R
r
3.
793
Stator
self-
i
nductance,
L
s
0.
3222 H
Rotor
self-
i
nducta
nce,
L
r
0.
3308
H
M
u
tual inductance,
L
m
0.
3049 H
No.
of pole,
p
4
Stator
flux r
e
fer
e
nce,
ψ
s
0.
896 W
b
Voltage Vector
Magnitude,
V
s
ψ
s
120 V
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Const
ant Frequency
Tor
que
Contr
o
ller
for
DTC with
Mult
ilevel Inverter
of Induction …
(
N
.M. Nor
d
in)
34
Fo
r th
e po
sitive slop
e, as in
(1
7), th
e
fo
llowin
g
con
d
ition
m
u
st b
e
satisfied
:
〈
〉
(27)
Whe
r
e the val
u
e of
d
in
(27
)
i
s
calcu
lated
from (2
6
)
. For th
e n
e
g
a
tiv
e slop
e, as in
(18
)
, th
e fo
llowing
co
nd
itio
n m
u
st b
e
satisfied
:
〈
〉
|
|
(
2
8
)
As t
h
e ab
ove
m
e
nt
i
oned
,
t
h
e
t
o
rq
ue l
o
o
p
b
a
nd
wi
dt
h i
s
chose
n
depe
n
d
s
on t
h
e m
a
xim
u
m
band
wi
dt
h
l
i
m
i
t
e
d by
t
h
e
DSP
sam
p
l
i
ng
t
i
m
e
or t
h
e ca
r
r
i
e
r si
g
n
al
fre
q
u
ency
,
de
pe
ndi
ng
o
n
whi
c
h i
s
l
o
we
r.
It
i
s
de
s
i
rabl
e
t
o
have a hi
g
h
carri
er f
r
e
que
n
c
y
i
n
orde
r t
o
have a l
a
rge t
o
rq
ue l
o
o
p
ba
n
d
w
i
d
t
h
. H
o
we
v
e
r, t
h
e carri
e
r
si
gnal
s
are
g
e
n
e
rated
b
y
th
e
DSP
wh
ich
restricted to
its sam
p
lin
g
tim
e. In
o
t
her
word
s, t
o
rqu
e
loop
b
a
ndwid
th
is
restricted
to
the so
ftware sam
p
l
i
n
g
ti
m
e
a
s
well. To
m
a
in
tain
th
e lin
earity b
e
tween
T
c
and
d
, the
carrie
r
sig
n
a
ls are
bu
ild
with
eigh
t step
s p
e
r cy
cl
e. Fi
gu
re 8 s
h
o
w
s a ge
nerat
e
d car
ri
er si
g
n
a
l
un
der t
h
i
s
c
o
ndi
t
i
o
n
wi
t
h
a
75µs
so
ft
ware
sam
p
l
i
ng t
i
m
e. B
a
sed on t
h
e Fi
gu
re
8, i
t
sh
o
w
s t
h
a
t
t
h
e carri
e
r
f
r
e
que
ncy
i
s
1
6
67
Hz
an
d th
e ab
so
lu
t
e
slop
e
o
f
car
r
i
er
sign
al is
33
3,33
3.333
s
-1
.
Fi
gu
re
8.
Ge
ne
rat
e
d ca
rri
e
r
si
gnal
sam
p
l
e
d at
75µs
Th
e m
a
x
i
m
u
m propo
rtion
a
l
g
a
in
wh
ich
li
mited
b
y
th
e
max
i
m
u
m
p
o
s
i
tiv
e slop
es is
assu
m
e
d
to
b
e
occurre
d at z
e
ro rot
o
r s
p
ee
d,
ω
r
=0
, and
at
rated
slip
,
ω
e
=
ω
slip
= 7
.
33
rad/s. By sub
s
titu
tin
g
t
h
is
v
a
lu
e
an
d the
mach
in
es p
a
rameters v
a
lu
e in
to
(27
)
,
g
i
v
e
s
K
p
+
≤
3
6
.
8
5
.
T
h
e m
a
xim
u
m
pro
p
o
rt
i
o
nal
gai
n
w
h
i
c
h i
s
l
i
m
i
t
e
d by
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
1,
Mar
c
h
2
016
:
28
–
4
4
35
th
e m
a
x
i
m
u
m
ab
so
lu
te n
e
g
a
tiv
e slop
es is assu
m
e
d
to
b
e
occu
rred
at m
a
x
i
m
u
m
ro
to
r speed
. As in
th
is work,
th
e m
a
x
i
m
u
m
ro
t
o
r sp
eed
ach
i
ev
ab
le withou
t field
weak
en
ing
is app
r
ox
imatel
y 4
1
rad
/
s. By su
bstitu
tin
g
t
h
is
val
u
e a
nd t
h
e
m
achi
n
es pa
ra
m
e
t
e
rs val
u
e i
n
t
o
(
2
8),
gi
ves
K
p
-
≤
90
.5
6.
I
n
o
r
de
r t
o
ens
u
re t
h
e c
ont
rol
si
gnal
,
T
c
, is not exce
eding the absolu
te carrier signal slope
, K
p
i
s
chose
n
as
39
.5.
It
sh
oul
d b
e
not
e
d
t
h
at
, t
h
e ga
i
n
v
a
lu
e is ju
st an
in
itial v
a
lu
e th
at serv
e as a g
u
i
d
e
to
o
p
e
rate th
e p
r
opo
sed
con
t
ro
ller.
A fin
e
tun
i
ng
o
f
th
e
co
n
t
ro
ller shou
ld
b
e
don
e to
ach
iev
e
th
e ex
cellen
t
to
rq
u
e
resp
on
se. In
th
is
work
, th
e co
rresp
ond
ing
PI
cont
roller’s pa
ram
e
ters are chos
en as
K
p
=
37
.8
5 a
nd
K
i
= 61
6
9
.
5
5
.
T
h
e o
p
e
n
-l
oo
p
bo
de
pl
ot
o
f
t
h
i
s
PI
co
n
t
ro
ller settin
g
is sho
w
n
in Fig
u
re 9. Based
on
Fi
g
u
re
9, th
e cro
s
so
v
e
r freq
u
e
n
c
y fo
r
th
is p
a
rticu
l
ar
settin
g
i
s
ab
out
3.
0
5
k
H
z.
Figure 9. Bode p
l
ot of
the torqu
e
loop with
PI con
t
roller
5.
SIM
U
LATI
O
N
AN
D
E
X
PE
RIME
NTAL
RESULTS
The proposed syste
m
and
a
hysteresis-base
d syste
m
of DT
C
-
M
L
I f
o
r i
n
d
u
ct
i
on m
achi
n
e have bee
n
sim
u
l
a
t
e
d usi
n
g M
A
TL
AB
/
S
im
ul
i
nk. The
p
a
ram
e
t
e
rs of PI co
nt
r
o
l
l
e
r t
h
at
obt
ai
ne
d i
n
t
h
e pre
v
i
o
us s
ect
i
on
were
u
s
ed
i
n
t
h
e sim
u
latio
n
as well as i
n
the exp
e
rim
e
n
t
. To
sho
w
t
h
e
feasib
ility o
f
th
e p
r
op
osed syste
m
, an
expe
ri
m
e
nt
was al
so carri
ed
out
. Fi
gu
re 1
0
sho
w
s t
h
e
bl
oc
k di
ag
ram
of the ex
peri
m
e
nt
al
set
-
up.
A dS
PAC
E
DS
1104 c
ontroller card
base
d
on a
TMS
3
20F240 D
SP, ALTER
A DE
2
FP
GA boa
rd,
IGBT-base
d
5-le
vel
CHMI, a 1.5kW
s
q
uirrel-ca
g
e induc
tion machine coupl
e
d to a DC m
achine was
use
d
to exec
ute the
expe
ri
m
e
nt
. The DS
1
1
0
4
wa
s used t
o
i
m
plem
ent
t
h
e hy
st
eresis and the
propose
d
controller also to estim
a
te
t
h
e t
o
r
que a
n
d
st
at
or fl
u
x
at
a sam
p
l
i
ng pe
r
i
od
75µs
.
The
FPG
A
wa
s use
d
t
o
i
m
pl
em
en
t
t
h
e vol
t
a
ge
v
ect
or
selection table
as well as t
o
ge
nerate t
h
e
blanking tim
e for t
h
e
IGBT
.
The pa
ram
e
ters of the i
n
duct
ion m
achine as tabulat
ed i
n
Tabl
e I we
re u
s
ed i
n
bot
h si
m
u
l
a
t
i
on an
d
expe
ri
m
e
nt
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Const
ant Frequency
Tor
que
Contr
o
ller
for
DTC with
Mult
ilevel Inverter
of Induction …
(
N
.M. Nor
d
in)
36
Figure 10. Exp
e
r
i
mental set-up
block diagram
(a)
(
b
)
Figure 11. Simulation
results o
f
torque ripp
le.
(
a
) DTC-M
L
I
with h
y
s
t
er
es
is
-bas
ed controll
er.
(b) DTC-MLI
with PI-CSF contr
o
ller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
1,
Mar
c
h
2
016
:
28
–
4
4
37
(a)
(b
)
Figu
re
1
2
. E
x
p
e
rim
e
ntal results of
to
rq
ue rip
p
le. (a) DTC
-
M
L
I
wit
h
hy
steresis-
b
ase
d
c
o
ntr
o
ller.
(
b
) D
T
C-
M
L
I wit
h
P
I-C
SF c
ont
roller
Fi
gu
re
11 a
n
d
Fi
gu
re
12
sh
o
w
s a si
m
u
l
a
t
i
on an
d e
x
peri
m
e
nt
al
res
u
l
t
s
of
t
h
e t
o
r
q
ue ri
p
p
l
e
f
o
r
DTC
-
MLI with
h
y
steresis-b
ased
con
t
ro
ller with
Δ
T
=
0.
9N
.m
(o
r
10%
of t
h
e
ra
t
e
d t
o
rq
ue
) a
n
d
DTC
-
M
L
I
wi
t
h
P
I
-
CSF con
t
ro
ller. Based
on
th
e ex
p
e
rim
e
n
t
al
resu
lts, its clear
ly in
d
i
cates that th
e redu
ction
of to
rqu
e
ripp
le as
m
u
ch
as 26
%
in
th
e
DTC-M
L
I
with
PI-CSF con
t
ro
lle
r c
o
m
p
ared to the DTC-ML
I
with
hysteresis
-base
d
cont
rol
l
e
r.
Usi
n
g
t
h
e
PI
-C
SF
co
nt
r
o
l
l
e
r, t
h
e desi
gnat
e
d c
ont
rol
l
e
r
i
s
p
r
ope
rl
y
m
oni
t
o
r
e
d a
n
d
c
o
r
r
ect
ed t
h
e
lev
e
l o
f
erro
rs
to
en
su
re th
e PI con
t
ro
ller sign
al is
with
in
the ap
propriate carrier lev
e
l
h
e
n
ce su
itab
l
e
v
o
ltag
e
vector is selected either
to increase or decrease the to
rq
u
e
and bee
n
ap
pl
i
e
d co
ns
ecu
tiv
ely with
in
a carrier
wave
f
o
rm
peri
od
. H
o
weve
r
b
y
usi
n
g t
h
e
hy
st
eresi
s
-
b
ased
cont
rol
l
e
r,
t
h
e
vol
t
a
ge
vect
or
i
s
chose
n
bas
e
d
o
n
th
e co
m
p
arison
of th
e raw
erro
r si
g
n
a
l
with
th
e h
y
st
eresis b
a
nd
wh
ich
th
e sel
ected voltage
vector for
increasing
or
decreasing the t
o
rque is
a
ppl
i
e
d
fo
r t
h
e
ent
i
r
e
swi
t
c
hi
ng
pe
ri
od
.
Fi
gu
re
13 a
n
d Fi
gu
re
14 s
h
o
w
si
m
u
l
a
t
i
on and e
x
peri
m
e
nt
al
resul
t
s
o
f
st
ep res
p
ons
e f
o
r DTC
-
M
L
I
with
Hysteresis-b
ased
con
t
ro
ller and
DTC-MLI with
PI-CSF con
t
ro
ller resp
ectively. Based
on
th
e
expe
rim
e
ntal results,
DTC-M
L
I
with P
I-CS
F
co
ntr
o
ller
s
h
ows
5% faste
r
perform
a
nce com
p
ared t
o
the
DTC-
MLI with
h
y
steresis-b
ased
co
n
t
ro
ller.
I
n
D
T
C-M
L
I
with
PI-CS
F
c
o
ntro
ller, the
desi
g
n
ated c
o
ntr
o
ller fi
rst
filtered
and
p
r
o
cessed
t
h
e torq
u
e
erro
r t
o
ensu
re th
e la
rg
e
erro
r will ap
pro
p
riately trig
ger th
e correct
carrier
sig
n
a
l. As a resu
lt, th
e v
o
ltage v
ecto
r
with
t
h
e h
i
gh
est
torque increm
ent (or dec
r
em
en
t) is selected
fo
r larg
e
errors
he
nce
produce fa
ster t
o
rque re
sponse
. In c
ont
ra
st,
th
e raw
to
rqu
e
er
ro
r
si
gn
al in th
e
DTC-MLI with
h
y
steresis-b
ased
co
n
t
ro
ller is
d
i
rectly con
t
ro
lled
b
y
t
h
e hysteresis bands which
pr
odu
ce
a slo
w
er
r
e
spon
se.
Evaluation Warning : The document was created with Spire.PDF for Python.