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.
5, N
o
. 3
,
Febr
u
a
r
y
201
5,
pp
. 29
3
~
30
4
I
S
SN
: 208
8-8
6
9
4
2
93
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
FPGA-
B
a
s
e
d Im
plement
a
tion Di
rect Torque Con
t
rol of
Induction Motor
Saber
K
R
I
M
1
, S
o
ufie
n G
D
AIM
2
,
Abdell
a
t
if
MTIB
AA
3
,
Mo
ha
med Fa
ouzi M
I
MOU
N
I
4
1,2,3
Labora
t
or
y o
f
El
ectron
i
cs
an
d
Microelectronics (EuE),
Facu
lty
of Scien
ces of
Monastir
University
of
Monastir, Tunisia
4
Research
Unit o
f
industrial s
y
stems St
udy
and
renewable en
erg
y
(ESIER),
University
of
Monastir,
Tunisia.
3,4
Department of
Electr
i
cal
Engin
eering
,
National
Engineering Sch
ool of Monast
ir,
University
of
Monastir, Tunisia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug,
2014
Rev
i
sed
Jan 13, 201
5
Accepte
d
Ja
n 28, 2015
This paper prop
oses a digital implement
ation
of the direct tor
que contro
l
(DTC) of an Ind
u
ction Motor (I
M) with an observation str
a
teg
y
on the Field
Programmable Gate Array
(FPGA).
Th
e hard
ware solution b
a
sed on the
F
P
GA is
caract
e
r
is
ed b
y
f
a
s
t
pro
ces
s
i
ng s
p
eed
du
e to
the
par
a
ll
el
proces
s
i
ng.
In this stud
y
th
e FPGA is used to overcom
e th
e lim
ita
tion of t
h
e software
solutions (Digita
l Signal Processor (DSP), Microcontroll
er.
..)
. Al
so, the DTC
of IM has man
y
drawbacks such as for example; Th
e open
loop pure
integr
ation h
a
s f
r
om the problems of in
tegrat
io
n es
peci
al
l
y
at
t
h
e low s
p
eed
and th
e v
a
ria
tio
n of th
e s
t
ator r
e
s
i
s
t
anc
e
due
to
the
tem
p
er
ature
.
To
t
ack
l
e
thes
e probl
em
s
we us
e the
Slid
ing Mode Observer (S
MO). This
observer is
us
ed es
tim
ate th
e s
t
ator flux, th
e
s
t
ator current a
nd the s
t
ator res
i
s
t
ance
. The
hardware implementation meth
od is
based on Xilinx S
y
stem
Generator
(XSG)
which a modeling tool devel
oped b
y
Xilinx for the design of
implemented s
y
s
t
ems on FPGA;
from th
e design of the DTC with SMO fro
m
XSG
we can automatically
generate the VHDL code
.
The model
of the DTC
with SMO has b
een design
ed an
d simu
lated using XSG blocks, sy
nth
e
sized
with Xilin
x ISE
12.4 too
l
and im
plem
ented
on
Xi
linx Virtex
-V
FPG
A
.
Keyword:
Di
rect
T
o
r
q
ue
C
ont
r
o
l
I
ndu
ctio
n Mo
t
o
r
Field Program
m
able Gate Array
Real Tim
e
Slid
in
g m
o
d
e
ob
serv
er
VH
DL
Xi
l
i
nx Sy
st
em
Gene
rat
o
r
Copyright ©
201
5 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
:
Sabe
r KRIM
,
Lab
o
rat
o
ry
of
El
ect
roni
cs
an
d M
i
cr
oel
ect
ro
ni
cs (
E
uE
),
Fa
cul
t
y
of
Sci
e
nc
es o
f
M
o
nast
i
r
,
Nat
i
onal
En
gi
n
eeri
n
g Sc
h
ool
of
M
o
nast
i
r
,
U
n
i
v
e
r
si
t
y
of
M
ona
st
i
r
, Tunisia
E-m
i
a
l: k
r
im
sa
b
e
r@ho
tm
ail.f
r
1.
INTRODUCTION
W
i
t
h
t
ech
nol
o
g
i
cal
adva
nce
m
ent
i
n
t
h
e fi
el
d o
f
m
i
croelect
ro
ni
cs ne
w
di
gi
t
a
l
sol
u
t
i
ons
suc
h
as
FPG
As (
F
ield
Pro
g
r
am
m
a
ble Gate Ar
ray
)
or
ASIC
(A
p
p
li
cation Specific Integrated Ci
rc
uit) are a
v
ailable and
can
be
use
d
as
num
eri
cal
t
a
rg
et
s fo
r t
h
e i
m
pl
em
ent
a
t
i
on o
f
al
go
ri
t
h
m
s
com
m
a
nd. T
h
e i
nhe
re
nt
pa
ral
l
e
l
i
s
m
of
th
ese d
i
g
ital so
lu
tion
s
and
their h
i
g
h
calcu
l
a
tio
n
cap
acity mak
e
th
e calc
u
latio
n
ti
m
e
is
n
e
g
lig
ib
le in
sp
ite o
f
th
e co
m
p
lex
ity
o
f
th
e algo
rit
h
m
s
to
b
e
i
m
p
l
an
ted
.
T
h
ese
har
d
ware s
o
l
u
t
i
ons ca
n m
eet
t
h
e ne
w dem
a
nds
o
f
m
o
d
e
rn
co
n
t
rols, su
ch
as
redu
ctio
n of th
e
calcu
lati
on t
i
m
e, t
h
e p
r
oce
ssi
ng
pa
ral
l
e
l
i
sm
of t
h
ese h
a
rd
w
a
r
e
so
lu
tion
s
allows in
teg
r
ati
n
g
on
a sing
le target sev
e
ral algorith
m
s
th
at p
r
ov
id
e
v
a
ri
o
u
s
featu
r
es an
d
wh
ich
can
work i
nde
pe
ndently of each
other. For the cont
rol of
the
variable spee
d e
l
ectrical
m
achines,
vari
ous c
o
ntrol
al
go
ri
t
h
m
s
can be
use
d
.
Thes
e al
go
ri
t
h
m
s
oft
e
n
ha
ve se
ve
ral
nest
e
d
c
ont
rol
l
o
o
p
s.
I
n
o
u
r c
a
se
we
us
e t
h
e
DTC that contains a speed c
o
ntrol loop, stator fl
ux
regu
lato
r, electro
m
a
g
n
e
tic to
rqu
e
reg
u
l
ator and
th
e slid
ing
m
ode obse
r
ve
r
;
t
h
i
s
i
s
why
w
e
are i
n
t
e
rest
ed
i
n
t
h
e im
pl
em
ent
a
t
i
on
on F
P
GA
of
Di
rect
Tor
q
ue C
o
nt
r
o
l
based
on t
h
e sl
i
d
i
n
g
m
ode ob
ser
v
er fo
r co
nt
r
o
l
l
i
ng an i
n
duct
i
on m
o
t
o
r. D
u
ri
ng t
h
e
past
few y
ears se
vera
l
research
ers u
s
e th
e FPGA for co
n
t
ro
lling
electrical syste
m
[1
]-[7
]
. Most o
f
th
em
d
e
v
e
lop
th
e algo
rithm o
n
a
VH
DL
har
d
wa
re desc
ri
pt
i
o
n l
a
ng
ua
ge.
Fo
r t
h
e ha
r
d
wa
re i
m
pl
em
ent
a
t
i
on of t
h
e Di
rect
e Tor
q
ue C
o
nt
r
o
l
wi
t
h
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
5
,
No
.
3
,
Feb
r
uar
y
201
5 :
2
93 –
30
4
29
4
Sl
i
d
i
ng M
o
de
Obse
r
v
er
of a
n
i
n
d
u
ct
i
on m
o
t
o
r
on t
h
e FP
G
A
we
use
Xi
l
i
nx
Sy
st
em
Generat
o
r
(X
SG
)
t
ool
b
o
x
devel
ope
d
by
Xi
l
i
nx a
n
d a
d
d
e
d t
o
m
a
t
l
a
b/
sim
u
li
nk.
The
X
S
G a
d
vant
a
g
es
are t
h
e
rapi
d t
i
m
e
t
o
m
a
rket
, real
ti
m
e
an
d
p
o
rtab
ility. On
ce
th
e d
e
sign
and
sim
u
latio
n
o
f
th
e
propo
sed
algorith
m
e
is co
m
p
leted
we can
au
to
m
a
tical
ly
g
e
n
e
rate th
e VHDL co
d
e
in
Xilin
x
ISE.
The DTC
o
f
I
M
i
s
based on
t
h
e ori
e
nt
at
i
o
n
of t
h
e st
at
or f
l
ux by
a di
rect
act
i
on on t
h
e
st
at
es of t
h
e
swi
t
c
hes
o
f
t
h
e i
n
vert
er
[
8
]
-
[
1
1
]
.
T
h
e
DT
C
co
nt
r
o
l
ba
se
d
on
a
n
op
en
l
o
o
p
est
i
m
at
or o
f
st
at
o
r
fl
u
x
ha
vi
n
g
well-kno
wn
pro
b
l
em
s o
f
in
teg
r
ation
esp
ecially a
t
a
lo
w sp
eed
[1
2
]-[14
]; also
, it is sen
s
iti
v
e
to
th
e v
a
riatio
n
of
the m
achine param
e
ters such as st
ator
resis
t
ance [15]. T
o
sol
v
e thes
e
pr
obl
em
s
m
a
ny
obs
er
vat
i
o
n
m
e
t
h
o
d
s
are used, such
as th
e Ex
tend
ed
Kalm
an
Filter [16
]
b
u
t
t
h
e d
r
awb
ack of t
h
is ob
serv
er that th
e kn
owledg
e
o
f
l
o
ad
dy
nam
i
cs i
s
not
usual
l
y
pos
si
bl
e, M
o
d
e
l
R
e
ference
A
d
apt
i
v
e
Sy
st
em
(M
R
A
S)
[1
7]
, [
18]
;
t
h
e
dr
awba
c
k
o
f
th
is algo
rit
h
m
th
at it is
sen
s
itiv
e to
un
certain
ties of th
e in
du
ctio
n
m
o
to
r p
a
rameters, th
e lu
enb
e
rg
er
Ob
serv
er is used
fo
r state esti
m
a
t
i
o
n
of IM
[19
]
. In
th
is wo
rk
,
we propo
se to
u
s
e th
e adap
tiv
e slid
ing
m
o
d
e
obs
er
ver
fo
r t
h
e est
i
m
a
ti
on
of
t
h
e st
at
or
fl
u
x
,
st
at
or c
u
r
r
e
n
t
and
t
h
e a
d
apt
a
t
i
on
of t
h
e va
ri
at
i
on
of t
h
e s
t
at
o
r
resistance. Tha
t
is a powe
rful
observ
er that
can estim
ate sim
u
lt
aneously the stator fl
ux
, stator
c
u
rrent, rot
o
r
spee
d and m
o
tor
param
e
ters.
It is introduced to re
place
the
ope
n-loop esti
mator of stator flux. Furt
herm
ore it
has
bee
n
pr
ovi
ded
wi
t
h
an
ad
apt
a
t
i
on m
echa
n
i
s
m
of t
h
e
st
at
or
resi
st
ance.
Th
us, t
h
e ai
m
of t
h
i
s
pape
r i
s
fi
rst
,
to give
a fair c
o
m
p
arison
bet
w
een a
DTC
with an ope
n
lo
op
estim
ato
r
an
d
DTC
with
slid
in
g
m
o
d
e
ob
serv
er
at
t
h
e st
age of
adj
u
st
m
e
nt
of t
h
e st
at
or resi
st
ance. Sec
o
n
d
l
y
,
t
h
e pr
op
ose
d
m
odel
i
s
dev
e
l
ope
d usi
ng
Xi
l
i
n
x
Syste
m
Gen
e
rato
r for im
p
l
e
m
en
tatio
n
on
FPGA, t
o
enjoy
th
e p
e
rform
a
n
ces
o
f
FPGAs in
th
e fiel
d
of d
i
g
ital
cont
rol of electrical
m
achines in r
eal
t
i
m
e
.
The pe
rf
orm
a
nce of t
h
e pr
o
p
o
se
d
m
odel
i
s
pr
o
v
ed by
si
m
u
l
a
t
i
o
n
resu
lts, Resou
r
ces u
s
ed
and
ex
ecu
tion
tim
e.
2.
DIRE
CT TO
RQ
UE C
O
NT
ROL
OF
AN
I
N
D
U
C
TIO
N
MOTO
R
2.
1.
Induc
tion
Machine Model
The state m
ode
l of an induction m
ach
i
n
e ca
n
be e
x
p
r
esse
d a
s
f
o
l
l
o
ws:
.
dX
AX
B
U
dt
(1
)
Whe
r
e
A, B
,
X a
nd
U a
r
e t
h
e e
vol
ut
i
on
m
a
t
r
i
x
, t
h
e c
o
ntrol m
a
trix, s
t
ate vector
X
and the stator
voltage
respectively.
[]
00
0
00
0
S
r
Sr
r
rS
S
S
r
Sr
r
Sr
S
S
S
R
R
LL
R
LL
L
R
R
A
LL
R
L
LL
R
R
,
1
0
1
0
0
1
0
1
S
S
L
L
B
,
s
s
s
s
i
i
X
,
s
s
V
V
U
The st
at
e vect
or
X i
s
com
p
o
s
ed by
st
at
o
r
cur
r
ent
a
nd
fl
u
x
com
pone
nt
s.
The vect
or c
o
m
m
a
nd U i
s
constituted
by
the stator volta
ge c
o
m
pone
nts
.
2.
2.
Direct T
o
rque
Contr
o
l Principle
Direct to
rqu
e
co
n
t
ro
l of an
i
n
du
ction
m
ach
in
e is b
a
sed
on
th
e d
i
rect d
e
termin
atio
n
of th
e co
n
t
ro
l
seq
u
ence a
p
pl
i
e
d t
o
t
h
e s
w
i
t
c
hes o
f
a
vol
t
a
g
e
i
nve
rt
er. T
h
e
choi
ce
of se
q
u
e
nces i
s
bas
e
d
on t
h
e t
w
o hy
s
t
eresi
s
com
p
arat
ors
of
t
h
e st
at
or fl
ux
and el
ect
r
o
m
a
gnet
i
c
t
o
rq
ue [
20]
. T
h
e
vol
t
a
ge vect
or
Vs i
s
t
h
e o
u
t
p
ut
of a
t
h
ree
-
pha
se vol
t
a
ge i
nve
rt
er w
h
ose t
h
e st
at
e of t
h
e i
nvert
er s
w
i
t
c
hes are co
nt
r
o
l
l
ed by
t
h
ree B
ool
ea
n va
ri
abl
e
s Sj (
j
=
a, b
,
c).
Th
e v
o
ltag
e
v
e
cto
r
can
b
e
written
as:
24
33
s
ss
2
(.
.
)
3
v=
v
v
jj
Sa
b
VU
S
S
e
S
e
j
(3)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
FPG
A-
Ba
sed Im
p
l
em
en
t
a
tio
n D
i
rect To
rq
u
e
Con
t
ro
l
o
f
Indu
ctio
n Mo
to
r (
S
ab
er KRI
M
)
29
5
The com
p
one
n
ts of the
s
t
at
or v
o
l
t
a
ge
vect
or
S
S
S
V
V
V
,
and t
h
e st
at
or
fl
ux ve
ct
or
,
SS
S
i
n
C
onc
o
r
di
a r
e
fere
nce are
gi
ven
by
Eq
uat
i
o
n (
4
) a
n
d (
5
).
The cal
cul
a
t
i
o
n o
f
t
h
e
po
si
t
i
on a
n
d
m
odul
e of
t
h
e
st
at
or fl
ux
are
base
d o
n
t
h
e u
s
e of
com
p
o
n
e
n
t
s
,
SS
. The m
odul
e of t
h
e st
at
o
r
fl
u
x
an
d
its p
o
s
ition
are
g
i
v
e
n
b
y
Eq
u
a
t
i
o
n
(6
).
0
0
(v
)
(v
)
s
s
t
ss
s
t
ss
s
R
id
t
R
id
t
(4)
)
(
3
2
))
(
2
1
(
3
2
Sc
Sb
U
V
Sc
Sb
Sa
U
V
S
S
(5
)
22
ar
g
ss
s
s
Ss
s
ar
c
t
g
(6)
The el
ect
r
o
m
a
gnet
i
c
t
o
rq
ue i
s
ex
presse
d i
n
t
e
rm
s of t
h
e c
o
m
pone
nt
s o
f
st
at
or fl
ux
vec
t
or a
nd t
h
e
com
pone
nt
s
of
st
at
or c
u
rre
nt
vect
o
r
as:
3
()
2
es
s
s
s
Cp
i
i
(
7
)
The estim
ated
values
of the st
ator fl
ux and el
ectro
m
a
g
n
e
tic to
rq
u
e
are co
mp
ared
with
th
ei
r referen
c
e
val
u
es
Φ
sref, Teref respe
c
tively.
Switching states
ar
e selected by the swit
ching table,
where
C
E
is th
e erro
r
of electrom
a
gnetic torque
afte
r
hysteresis
bl
ock a
n
d
E
i
s
t
h
e
er
ro
r
of
t
h
e
st
at
or
fl
u
x
a
f
t
e
r
hy
st
eresi
s
bl
oc
k,
(
1
...
6
)
i
Si
means the sect
or (Ta
b
le
1)
[21]:
Tabl
e
1.
Swi
t
c
hi
n
g
t
a
bl
e
f
o
r
d
i
rect
t
o
r
q
u
e
c
o
nt
r
o
l
E
E
c
S1
S2
S3
S4
S5
S6
1
V2
V3
V4
V
5
V6
V1
1 0
V7
V0
V7
V
0
V7
V0
-1
V6
V1
V2
V
3
V4
V5
1
V3
V4
V5
V
6
V1
V2
0 0
V0
V7
V0
V
7
V0
V7
-1
V5
V6
V1
V
2
V3
V4
The st
ruct
ure
o
f
D
T
C
of a
n
i
n
duct
i
o
n m
o
t
o
r
i
s
gi
ve
n,
as s
h
o
w
n
by
t
h
e Fi
gu
re
1:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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J
PED
S
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l.
5
,
No
.
3
,
Feb
r
uar
y
201
5 :
2
93 –
30
4
29
6
In
verte
r
E
Sw
it
chi
n
g Ta
b
l
e
c
b
a
S
S
S
ref
Tr
e
f
+
-
+
sabc
i
c
b
a
S
S
S
O
p
en
lo
o
p
E
s
tim
a
to
r
PI
r
S
Te
m
ab
c
S
i
N
ref
S
V
abc
-
dt
i
R
v
S
S
S
S
)
,
(
)
,
(
)
,
(
s
s
s
s
s
s
arctg
32
es
s
s
s
Tp
i
i
H
y
s
t
eresis
co
mp
a
r
at
or
E
C
E
S
re
f
S
Fi
gu
re
1.
Sc
he
m
a
t
i
c
of co
n
v
e
n
t
i
onal
DTC
3.
DIRE
CT TO
RQ
UE C
O
NT
ROL
OF
AN
I
N
D
U
C
TIO
N
MOTO
R
WI
TH SLID
IN
G
MO
DE
OBSERVER
Th
e slid
ing
m
o
d
e
ob
serv
er
(
S
MO
)
is w
e
d
e
ly
u
s
ed
fo
r
n
o
n
lin
ear
system
s
d
u
e
to
its r
obustn
ess to
th
e
param
e
t
e
r vari
at
i
ons. T
h
e S
M
O i
s
use
d
t
o
cont
st
r
u
ct
t
h
e s
t
ate variables a
nd t
h
e stator
re
sistance. T
h
e diagram
of
t
h
e
SM
O i
s
sho
w
n i
n
Fi
gu
r
e
2.
No
nli
n
e
a
r
syst
e
m
Si
gn
(.)
h (
x
)
K
f (
x
, u
)
x
x
u
y
Fi
gu
re
2.
Pri
n
c
i
pl
e o
f
t
h
e
sl
i
d
i
n
g
m
ode o
b
se
r
v
er
The m
a
the
m
atical
m
odel
of t
h
e observe
d
stat
or curre
nt is
presented as:
11
1
1
1
0
1
1
0
S
r
r
Sr
SS
S
S
rS
S
S
r
S
S
r
S
S
S
Sr
S
Sr
S
R
R
R
LL
LL
L
L
R
R
R
L
LL
L
LL
ii
v
A
v
i
i
1
2
21
22
2
S
S
I
A
AA
I
(8
)
Th
e m
a
ti
matic
al
m
o
d
e
l of t
h
e ob
serv
ed
stator fl
u
x
is
g
i
v
e
n
b
y
th
e
fo
llo
wi
ng
system
:
1
31
32
41
4
2
2
1
0
0
0
1
0
SS
S
S
S
S
S
S
S
S
S
S
L
R
R
L
iv
I
AA
AA
v
I
i
(9
)
Whe
r
e:
11
1
2
21
22
A
A
A
A
,
31
3
2
41
42
A
A
A
A
and
1
1
2
2
()
()
S
S
s
i
gne
S
s
i
gne
S
I
I
: are th
e m
a
trix
es
o
f
g
a
in
s of the
ob
served
st
at
or cu
rre
nt
,
m
a
t
r
i
x
of gai
n
s of t
h
e
obse
r
ved st
at
o
r
fl
u
x
,
and t
h
e si
gn
vect
o
r
of t
h
e sl
i
d
i
ng m
ode sur
f
ace
respectively.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
FPG
A-
Ba
sed Im
p
l
em
en
t
a
tio
n D
i
rect To
rq
u
e
Con
t
ro
l
o
f
Indu
ctio
n Mo
to
r (
S
ab
er KRI
M
)
29
7
3.
1.
Determining
of the SM
O Charac
teristics
The sliding surface is based on the er
ror between the real
s
t
ator curre
n
t
s
i
and
s
i
, and the observe
d
stator c
u
rrent
s
i
an
d
s
i
as fo
llows:
1
2
2
2
1
1
1
1
()
SS
r
S
SS
r
r
ST
S
S
L
T
T
ii
ii
(10)
Whe
r
e:
T
ss
s
ii
i
and
T
ss
s
ii
i
are the real and
obse
r
ved stators curre
n
ts vectors
respectively.
r
r
r
R
L
T
: Ro
tor tim
e c
o
n
s
tan
t
.
Th
e m
a
trix
of
g
a
in
s related to th
e cu
rren
t
observ
e
r is as fo
llo
ws:
2
1
4
3
2
1
0
0
i
i
i
i
i
A
A
A
A
A
(1
1)
Whe
r
e
2
1
and
are t
w
o po
sitiv
e
co
n
s
tan
t
s, wh
ich
are
d
e
te
rm
in
ed
b
y
ap
p
l
ying
the stab
ility
con
d
ition
s
defi
ned
by
t
h
e
Ly
apu
n
o
v
ap
pr
oach
.
Th
e
g
a
in m
a
tri
x
o
f
th
e stator
flu
x
is as
fo
llows:
2
2
1
4
3
2
1
1
q
L
L
q
A
A
A
A
A
S
S
(12)
Whe
r
e
2
1
q
and
q
are t
w
o po
sitiv
e co
n
s
t
a
n
t
s.
Th
e stab
ility
o
f
th
e SM
O dep
e
nd
s
o
n
its co
nv
erg
e
n
ce to
ward
s its sli
d
ing
surface. To
stud
y the
stab
ility o
f
th
is ob
serv
er th
e fo
llo
wi
n
g
Lyapu
nov
fun
c
tion
i
s
u
s
ed
:
1
2
T
VS
S
(13)
Whe
n
the slidi
ng s
u
rface S=
0, the error bet
w
een t
h
e
real a
nd
observe
d
stator
curre
nt must bee zero,
0
SS
ii
and
th
e d
e
riv
a
te o
f
th
e lyapun
ov
fu
ctio
n is strictly n
e
g
a
tiv
e (
0
V
).
0
T
VS
S
(14)
The m
a
jor
drawbac
k
of the SMO obse
rver is
t
h
e c
h
at
t
e
ri
ng
phe
n
o
m
enon
. To
w
eaken t
h
i
s
phe
nom
e
non a saturation func
tion is used to
replace the
Ba
ng-Bang function. The sa
turat
i
on function is give
n
by the
syste
m
(15).
2
,
1
;
1
1
)
(
i
S
si
S
S
si
S
si
S
sign
i
i
i
i
i
(1
5)
Whe
r
e
is a
p
o
sitiv
e con
s
tan
t
with
a l
o
w v
a
l
u
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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I
J
PED
S
Vo
l.
5
,
No
.
3
,
Feb
r
uar
y
201
5 :
2
93 –
30
4
29
8
3.
2.
M
echa
n
ism of
A
d
a
p
t
a
t
i
on of
the S
t
ator
Resistan
ce
D
u
r
i
ng
o
p
e
r
a
tio
n th
e stator
r
é
sist
ance va
ry,
due
to the
temperat
ure
a
n
d
the
low spee
d operation. T
o
online
estim
a
t
e
of the
stator re
sistance anot
h
e
r term
ad
d
e
d
t
o
th
e lyapu
nov
fu
ctio
n.
2
1
22
T
S
S
VS
S
R
R
(16)
0
T
SS
S
VS
S
R
R
R
(17)
To
satisfy th
e co
nd
itio
n
o
f
th
e Equ
a
tion
(1
7), th
e
estimated stator resi
stance can be
expresse
d as
fo
llow:
*(
)
*
(
)
S
SS
S
S
SS
Rk
i
i
i
i
i
i
(1
8)
Wi
t
h
k
is a po
sitiv
e co
nstan
t
.
4.
USE
OF
X
I
LINX
SYSTEM GENERATOR
(
X
SG) IN T
H
E CONT
ROLLER DESIGN
4.
1.
Descripti
o
n of X
ilinx
System
Genera
to
r
Xilin
x
System
Gen
e
rat
o
r (XSG)
is a mo
d
e
ling
t
o
o
l
d
e
v
e
l
o
p
e
d
b
y
Xilin
x fo
r th
e
d
e
sign
of
im
pl
em
ent
e
d sy
st
em
s on FP
GA
. It
has a l
i
bra
r
y
of
vari
e
d
bl
oc
ks,
whi
c
h
can be a
u
t
o
m
a
t
i
cal
l
y
co
m
p
i
l
e
d i
n
t
o
an FP
G
A
[
22]
. In t
h
i
s
w
o
r
k
,
Xi
l
i
nx Sy
st
e
m
Generat
o
r
(
X
S
G
) i
s
used
t
o
im
pl
em
ent
the arc
h
i
t
ect
ure
of t
h
e
Direct To
rqu
e
Co
n
t
ro
l
o
f
indu
ctio
n Mo
t
o
r
with
slid
i
n
g m
ode
o
b
se
rve
r
o
n
F
P
G
A
.
I
n
t
h
e
fi
rst
st
e
p
,
we
b
e
gi
n
by
im
pl
em
ent
i
ng of t
h
e p
r
op
ose
d
arc
h
i
t
ect
ures
usi
n
g t
h
e
XS
G bl
ock
s
avai
l
a
bl
e o
n
t
h
e
Si
m
u
li
nk l
i
b
ra
ry
.
On
c
e
t
h
e Desi
g
n
of
t
h
e sy
st
em
i
s
com
p
l
e
t
e
d and gi
ves t
h
e
de
si
red si
m
u
l
a
t
i
on res
u
l
t
s
, t
h
e
VH
DL c
ode c
a
n be
gene
rat
e
d
by
t
h
e
XS
G t
o
ol
[
23]
.
The
desi
g
n
fl
ow
o
f
t
h
e
Xi
l
i
nx
Sy
st
em
Gene
rat
o
r i
s
gi
ven
by
fi
g
u
re
3.
Aft
e
r
gene
rat
i
o
n
of
VH
DL
co
de a
n
d
t
h
e
sy
nt
hes
i
s, we
can
ge
nerate th
e
b
itstrea
m
file. Th
en we can m
o
v
e
th
is
co
nfigu
r
ation file to
prog
ram
th
e FPGA [24
]
.
X
ilinx
S
y
ste
m
Gen
e
r
a
to
r
D
e
sig
n
G
e
re
r
a
tio
n of
V
H
DL
Cod
e
S
y
nthe
sis (B
itste
a
m
)
11
111
10
00
001
11
110
00
11
1
11
111
11
10
001
11
111
11
00
0
00
110
10
11
100
00
111
00
00
0
11
111
11
11
111
11
000
11
11
1
D
o
w
n
loa
d
into
FPG
A
Fi
gu
re
3.
C
o
nfi
g
u
r
i
n
g a
n
FP
G
A
4.
2.
Desig
n
of the Sliding
Mode Observ
er
using
X
S
G
4.
2.
1.
Design
of the
Currents Obs
erved
The
Desi
g
n
o
f
t
h
e
di
rect
c
o
m
pone
nt
o
f
t
h
e o
b
se
rv
ed s
t
at
or cu
rre
nt
vect
o
r
i
n
t
r
o
d
u
ced i
n
t
o
t
h
e
equat
i
o
n
sy
st
em
(8) gi
ven
by
Fi
g
u
re
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
FPG
A-
Ba
sed Im
p
l
em
en
t
a
tio
n D
i
rect To
rq
u
e
Con
t
ro
l
o
f
Indu
ctio
n Mo
to
r (
S
ab
er KRI
M
)
29
9
Fi
gu
re
4.
Desi
gn
o
f
t
h
e C
o
m
p
o
n
e
n
t
S
i
from
the XS
G
4.
2.
2.
Desig
n
of
Sliding
Surfa
ce, ga
in
Matrix an
d Sign Fu
ncti
on
The sliding surface, t
h
e saturation
function and the
gain
matrix are given in
equations (10), (11),
(12
)
and
(1
5),
are illu
strated
u
s
ing
XSG as sh
own
in Figure 5
.
(a)
(b
)
Figure
5. Desi
gn of slidi
n
g s
u
rface,
gain
matrix a
n
d sign
function
from
the
XSG
4.
3.
Simulati
on Re
sults
u
s
ing X
i
l
i
nx
S
y
s
t
em Ge
nerator
and Discussions
Th
e stru
cture
o
f
t
h
e
d
i
rect torqu
e
co
n
t
ro
l
with
th
e ad
ap
tativ
e slid
ing
m
o
de ob
serv
er of an
indu
ction
m
o
to
r is shown
in Figure
6
.
Inv
erter
E
S
w
itch
ing Ta
ble
c
b
a
S
S
S
ref
Tr
e
f
+
-
+
sabc
i
S
l
id
in
g Mo
d
e
Ob
ser
v
er
PI
r
S
Te
abc
S
i
N
ref
S
V
abc
-
S
R
E
Fig
u
re
6
.
Sch
e
matic o
f
a co
nv
en
tion
a
l
DTC
with
an
ad
ap
tativ
e slid
ing
m
o
d
e
o
b
serv
er
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.
5
,
No
.
3
,
Feb
r
uar
y
201
5 :
2
93 –
30
4
30
0
4.
3.
1.
T
h
e St
at
or
Re
si
stanc
e
i
s
Co
nst
a
nt
(
R
s=
5.
71
7
Ω
)
The si
m
u
l
a
ti
on
of t
h
e co
nve
nt
i
onal
DTC
wi
t
h
sl
i
d
i
ng m
ode
obse
r
ve
r i
s
achi
e
ve
d usi
ng t
h
e XSG
.
The
spee
d a
n
d
flu
x
refe
rences
use
d
in
the s
i
m
u
lation
res
u
lts are 150ra
d/s and
0.91wb
respectively. T
h
e
electrom
a
gnetic torque
refe
rence prese
n
ts the output of
PI controller of spee
d.
At time t = 0.5sec
a load
t
o
r
que
o
f
10
N
m
i
s
appl
i
e
d
.
0
0.
2
0.
4
0.
6
0.
8
1
0
20
40
60
80
100
120
140
160
t(
s
R
ot
or
S
p
eed
(
r
d
/
s
)
R
eal
s
peed
R
e
f
e
r
enc
e s
peed
E
s
t
i
m
a
t
ed S
pee
d
(a)
0
0.
2
0.
4
0.
6
0.
8
1
0
0.
2
0.
4
0.
6
0.
8
1
t(
s
)
S
t
at
or
F
l
u
x
(
w
b
)
(b
)
0
0.
2
0.
4
0.
6
0.
8
1
-5
0
5
10
15
20
25
t(
s)
E
l
ec
t
r
om
a
g
n
e
t
i
c
t
o
r
q
ue
(
N
m
)
R
eal
T
e
m
E
s
t
i
m
a
t
ed T
e
m
(c)
Fi
gu
re 7(a
)
.
Ev
ol
ut
i
o
n of
real
and
esti
m
a
ted
sp
eed
Fi
gu
re 7(
b
)
.
E
v
ol
ut
i
o
n of
t
h
e r
eal
an
d ob
ser
v
ed
stato
r
f
l
u
x
Fi
gu
re 7(c
)
.
Ev
ol
ut
i
o
n of
t
h
e r
eal
and estim
a
t
ed electrom
a
gnetic
t
o
r
que
0
0.
2
0.
4
0.
6
0.
8
1
-20
-10
0
10
20
t(
s
)
S
t
at
or
c
u
r
r
ent
(
A
)
R
eal
S
t
at
or
Cur
r
ent
O
b
s
e
r
v
e
d
S
t
at
or C
u
rr
ent
0.
47
0.
48
0.
49
0.
5
0.
51
0.
52
0.
53
0.
54
-5
0
5
0
0.
2
0.
4
0.
6
0.
8
1
-2
0
-1
0
0
10
20
t(
s
)
S
t
at
or
c
u
r
r
ent
(
A
)
R
eal
S
t
at
or
c
u
r
r
ent
O
b
s
e
r
v
ed S
t
a
t
o
r
c
u
r
r
ent
0.
4
5
0.
5
0.
5
5
0.
6
-5
0
5
10
Fi
gu
re 8(a
)
.
Va
ri
at
i
on of
t
h
e
real and obse
rved stator
current
S
i
Fi
gu
re 8(
b
)
:
V
a
ri
at
i
on of
t
h
e
obs
er
ved
an
d r
eal
st
at
or
current
S
i
4.
3.
2.
T
h
e St
at
or
Re
si
stanc
e
V
a
ri
e
s
fr
om
1
00%
(
R
s=2
*
5
.
7
17=
1
1
.
4
3
4
Ω
)
Th
e sim
u
latio
n
of th
e con
v
e
n
tio
n
a
l DTC with
an
op
en
lo
op
estim
a
t
o
r
an
d
th
e co
nv
en
tio
n
a
l DTC
with
a slid
ing
m
o
d
e
o
b
serv
er is ach
iev
e
d
usin
g th
e
XSG
at a low s
p
ee
d. T
h
e
ro
t
o
r
speed a
n
d stator flux
refe
rences
use
d
i
n
t
h
e si
m
u
lat
i
on res
u
l
t
s
ar
e 31.
4 ra
d/
s and 0.91 wb, res
p
ectively. At time t = 0.2sec
a load
t
o
r
que
o
f
10
N
m
i
s
appl
i
e
d
.
A
t
t
= 0.
4sec
t
h
e
st
at
or
resi
st
anc
e
i
n
crease
s
by
10
0%
.
(a) A
n
ope
n
l
o
op
est
i
m
at
or
(b
)
A slidi
n
g
m
ode
o
b
se
rve
r
Fi
gu
re 9.
Va
ri
at
i
on of
R
s
f
o
r DTC
wi
t
h
0
0.
5
1
1.
5
2
2.
5
5
6
7
8
9
10
11
12
t(
s
)
S
t
a
t
o
r
re
si
st
a
n
c
e
(O
h
m
)
DT
C re
s
i
s
t
a
n
c
e
M
a
c
h
i
n
e R
e
s
i
s
t
anc
e
0
0.
5
1
1.
5
2
2.
5
0
2
4
6
8
10
12
t(
s
)
S
t
at
or
r
e
s
i
s
t
anc
e
(
O
hm
)
R
e
a
l
r
e
si
sta
n
c
e
O
b
se
r
v
e
d
r
e
si
st
a
n
c
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
FPG
A-
Ba
sed Im
p
l
em
en
t
a
tio
n D
i
rect To
rq
u
e
Con
t
ro
l
o
f
Indu
ctio
n Mo
to
r (
S
ab
er KRI
M
)
30
1
(a) A
n
ope
n
l
o
op
est
i
m
at
or
(b)
W
i
t
h
a
slid
in
g m
o
d
e
ob
serv
er
Fig
u
r
e
10
.
Evolu
tio
n
of
th
e
st
ato
r
f
l
ux
f
o
r
DTC
w
ith
(a)
wi
t
h
out
a
d
j
u
st
m
e
nt
of t
h
e
st
at
or
resi
st
anc
e
v
a
r
i
ation
(b)
with
ad
ju
st
men
t
o
f
th
e stato
r
resistan
ce
variatio
n
Fig
u
r
e
11
. Evolu
tio
n
of
th
e st
ato
r
f
l
ux
tr
aj
ecto
r
i
es
(a) A
n
ope
n
l
o
op
est
i
m
at
or
(b
) W
i
t
h
a Slid
ing
M
o
de Obs
e
rve
r
Fi
gu
re 1
2
. Vari
at
i
on of
el
ect
ro
m
a
gnet
i
c
t
o
r
q
u
e
f
o
r DTC
wi
t
h
The si
m
u
l
a
t
i
on res
u
l
t
s
of
t
h
e
di
rect
t
o
rq
ue c
ont
rol
wi
t
h
sl
i
d
i
ng M
ode
O
b
s
e
rve
r
gi
ve
n
by
Fi
gu
re
7
a
n
d
8 show that the real and the
estim
a
ted variables are sim
i
l
a
r
.
In
Figur
e 7(
b)
and
7(
c)
i
t
c
a
n
b
e
s
e
e
n
t
h
a
t
t
h
e
stator
flux a
n
d the electrom
a
gnetic torque
a
r
e c
h
aracteriz
e
d
by
hi
gh
ri
pp
l
e
s d
u
e t
o
t
h
e
use
of
t
h
e
hy
st
eresi
s
com
p
arator.
Fig
u
re 9
sho
w
th
e sen
s
itiv
ity o
f
th
e
Direct To
rqu
e
Con
t
ro
l
o
f
an
In
du
ction Mo
to
r. In
Figu
re
9
(
a) we
can see
at t=0.4sec t
h
at the stator
resist
ance i
n
creases
2 tim
es the nom
i
nal stator resistanc
e
due
t
o
te
m
p
eratu
r
e, it
can
b
e
seen th
at in
th
e
case
of the
DTC
with
an
open loop e
s
tim
a
tor,
the stator resistance
use
d
i
n
t
h
e DTC
ke
pt
co
nst
a
nt
. B
y
cont
ra
st
, i
n
Fi
gu
re 9
(
b) t
h
e
o
b
ser
v
e
d
st
at
or
resi
st
ance co
n
v
er
ges ra
pi
dl
y
t
o
t
h
e
n
o
m
in
al v
a
lu
e, th
is is d
u
e
to
th
e on
lin
e ad
ap
tatio
n
of th
e stato
r
resistan
ce b
y
th
e slid
in
g
m
o
d
e
o
b
s
erv
e
r. Th
e
si
m
u
latio
n
resu
lts d
e
m
o
n
s
trates th
e rob
u
stness of th
e Slid
i
n
g
M
o
de
Ob
se
rve
r
a
g
ai
nst
t
h
e ab
ru
pt
l
y
vari
at
i
on
of
the m
achine pa
ram
e
tres.
In Fi
gure 10(a), at t = 0.4sec t
h
e real stator
flux is af
fect
ed
by
de va
ri
at
i
o
n
of
the stator resistance, it
decrease
s
a
b
ruptly to
0.72 wb, t
h
e e
r
ror
between the
real
and the
re
fere
nce
st
at
or
fl
ux
kept
co
nst
a
nt
.
Yet
,
i
n
0
0.
5
1
1.
5
2
2.
5
0
0.
2
0.
4
0.
6
0.
8
1
t(
s
)
S
t
at
or
f
l
ux
(
w
b
)
R
eal
s
t
at
or
f
l
ux
es
t
i
m
a
t
ed s
t
at
or
f
l
ux
0
0.
5
1
1.
5
2
2.
5
0
0.
2
0.
4
0.
6
0.
8
1
t(
s)
St
a
t
or
Fl
ux
(
w
b)
R
e
al
s
t
at
o
r
f
l
u
x
o
b
s
e
rv
ed s
t
a
t
or f
l
ux
0
0.
5
1
1.
5
2
2.
5
-5
0
5
10
15
20
25
30
t(
s)
E
l
ec
t
r
om
ag
net
i
c
t
o
r
q
u
e
(
N
m
)
Re
a
l
T
e
m
E
s
ti
m
a
te
d
T
e
m
0
0.
5
1
1.
5
2
2.
5
-1
0
0
10
20
30
t(
s)
El
ec
t
r
om
agne
t
i
c
t
o
r
q
u
e
(
N
m
)
Es
ti
m
a
te
d
T
e
m
R
eal
T
e
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
5
,
No
.
3
,
Feb
r
uar
y
201
5 :
2
93 –
30
4
30
2
th
e Fig
u
re 10(b
)
, th
e static error gradu
a
lly v
a
n
i
sh
es
due t
o
the prese
n
ce
of the
adaptive online
m
echanism of
the stator resist
ance
using
t
h
e Slid
in
g
Mod
e
Ob
serv
er.
In Figure 11(a
), we can noti
ce that
t
h
e st
ator fl
ux t
r
a
j
ect
ori
e
s i
n
cre
a
se due t
o
t
h
e va
ri
at
i
on of t
h
e
stator
resistanc
e
at t=0.4sec.
By co
n
t
rast, in Figu
r
e
11(
b)
t
h
e stator
f
l
ux
t
r
aj
ect
o
r
y is
k
e
p
t
con
s
tan
t
du
e to
t
h
e
prese
n
ce
of the
ada
p
tive
onli
n
e m
ech
an
is
m
o
f
th
e stato
r
resi
stan
ce
u
s
ing
the Slid
ing
M
o
de Ob
serv
er.
In
Figure
12(a), at t =
0.4sec the electrom
a
gne
tic to
rq
u
e
in
creases, and
th
e error b
e
tween
t
h
e
electro
m
a
g
n
e
tic to
rqu
e
and
the lo
ad
to
rqu
e
re
m
a
in
s co
n
s
ta
nt. H
o
we
ve
r, in Fig
u
re
12
(b
),
for the slidi
n
g
m
ode
obs
er
ver;
t
h
e e
l
ect
rom
a
gnet
i
c
t
o
r
q
ue i
s
kept
con
s
t
a
nt
.
4.
4.
FPGA
Imple
mentati
on Res
u
lts of the
Pr
op
osed
Appr
oach and
Discus
sions
On
ce t
h
e sim
u
latio
n
is co
m
p
le
ted
and
g
i
v
e
s t
h
e desired
results, we can g
e
nerate th
e
VHDL cod
e
an
d
sy
nt
hesi
zed
t
h
e
ha
rd
ware
bl
oc
k.
The
i
m
pl
ement
a
t
i
on
res
u
l
t
s
are
gi
ve
n
by
F
i
gu
re
13
an
d T
a
bl
e 2
.
T(
k
)
T
(
k
+1
)
T(
k
)
T
(k
+
2
)
T (
k
+2
)
T (
k
+2
)
T(
k
)
T (
k
+1
)
T (
k
+1
)
ADC
T
AD
C
T
AD
C
T
ex
T
ex
T
ex
T
(a
)
(b
)
(c
)
50µ
s
(b
)
Fi
gu
re 1
3
(
a).
R
TL schem
a
t
i
c of t
h
e c
o
nv
ent
i
onal
DTC with
a slid
ing
m
o
d
e
o
b
serv
er fro
m
Xili
n
x
ISE
Fi
gu
re
1
3
(
b
)
.
T
i
m
i
ng Di
ag
ram
f
o
r t
h
e
Im
l
e
ment
at
i
on
on
(a
): M
i
croc
ont
roller,
(
b
):
Digital Sig
n
al
Pro
cesso
r
(DS
P
)
,
(c
): Fie
l
d P
r
o
g
ram
m
able Gate
A
rray
(FP
G
A)
Tab
l
e 2
.
Resources Utilisatio
n
fo
r
t
h
e DTC with
SMO
Resourses
Used resources
Available resources
Nu
m
b
er
of bonded
I
/
O
68
640
Nu
m
b
er
of Slice
L
U
T
s
2087
4480
0
Nu
m
b
er
of Slices
Register
s
478
4480
0
Nu
m
b
er
of DSP48
E
s
8
128
Execution ti
m
e
:
ex
T
= 0.
94
µs
Th
e
Tab
l
e
2 sho
w
s th
e im
p
l
e
m
en
tatio
n
results in
term
o
f
th
e
u
s
ed
reso
urces and th
e execu
tio
n tim
e
of t
h
e
Di
rect
T
o
r
q
ue C
ont
rol
wi
t
h
SM
O
usi
ng t
h
e
FP
GA
Vi
rt
ex
-5
De
vi
ce. The R
TL sc
hem
a
ti
c of t
h
e C
D
TC
wi
t
h
SM
O i
s
gi
ve
n
by
Fi
g
u
r
e 1
3
(
a).
T
h
e
Fi
gu
re
13
(
b
),
sho
w
s
t
h
e
per
f
o
rm
ance o
f
c
o
m
put
i
ng t
i
m
e
fo
r t
h
e
h
a
rdware im
p
l
e
m
en
tatio
n
on
FPGA co
mp
ared
to
so
ft
ware so
lu
tions (Micro
con
t
ro
ller, Di
g
ital Sig
n
a
l
Processor).
T
AD
C
and
T
ex
are t
h
e an
alog
u
e
to
d
i
g
ital conv
ersio
n
tim
e and t
h
e exec
ution time respectivel
y.
In t
h
i
s
w
o
r
k
t
h
e exec
ut
i
on t
i
m
e equal
t
o
0.
94 µs. B
u
t
i
n
pape
rs [
25]
an
d [2
6]
, t
h
e sa
m
p
li
ng t
i
m
e
equal
t
o
1
0
0
µ
s
usi
n
g
t
h
e
d
S
PAC
E
1
1
0
4
(
d
i
g
i
t
a
l
si
gnal
pr
ocessi
n
g
an
d c
ont
rol
e
n
gi
nee
r
i
n
g).
I
n
pa
per
[
27]
,
th
e sam
p
lin
g
ti
m
e
eq
u
a
l to
50
0
µs. It can
b
e
seen
th
at th
e ex
ecu
tion
t
i
m
e
is to
o
i
m
p
o
rtan
t relative to
th
e
FPGA
du
e to th
e sequ
en
tial pro
ces
si
n
g
of t
h
e dS
PAC
E
.
5.
CO
NCL
USI
O
N
In
t
h
is
p
a
p
e
r, t
h
e
d
i
g
ital i
m
p
l
e
m
en
tatio
n
of
th
e Direct Torq
u
e
Con
t
ro
l wi
th
Slid
ing
M
o
d
e
Ob
serv
er
usi
n
g t
h
e FP
GA h
a
s bee
n
prese
n
t
e
d. T
h
e Sl
i
d
i
n
g m
ode
Obse
r
v
er
has been p
r
op
ose
d
t
o
im
pr
o
v
e t
h
e
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