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.
4, N
o
. 3
,
Sep
t
em
b
e
r
2014
, pp
. 28
1
~
28
9
I
S
SN
: 208
8-8
6
9
4
2
81
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
DSP-Based Sensorless Speed Co
ntrol of a P
erm
anen
t M
agn
et
Synchronous Motor using Sliding Mode Current Observer
R
a
ch
id
A
s
ko
ur,
Bad
r
Bou
o
ulid
I
d
ris
s
i
Depart
em
ent of
Ele
c
trom
ech
anic
al
Engi
ne
ering
,
Moula
y
Ism
a
ïl Universit
y
,
E
c
ole Nationale Sup
é
rieur
e
d’Arts
et
Mé
tie
rs, ENSAM-Me
knè
s,
Moroc
c
o
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Ja
n 30, 2014
R
e
vi
sed M
a
r
2,
2
0
1
4
Accepted
Mar 18, 2014
In this paper,
ex
perimental results
of 3-phase permanent magnet sy
nchronou
s
m
o
tor (P
M
S
M
)
s
e
ns
orles
s
s
p
eed control
are pres
ented
.
To es
t
i
m
a
te the
roto
r
position,
a slid
ing mode
curren
t
observer (SM
C
O) was implemented.
This
obs
erver es
tim
at
es
the ba
ck em
fs
of the m
o
tor in the s
t
a
tion
a
r
y
referen
c
e
frame using only
the measured
voltag
e
s and
currents of th
e
motor. These
em
fs were utiliz
ed to obtain the
roto
r position. T
h
e speed of the m
o
tor was
cal
cula
ted b
y
di
fferent
iat
i
ng the
rotor
position angle. The stab
ility
of th
e
proposed SMC
O
was verified using
Ly
apuno
v method to determine the
observer gain
. The saturation f
unction was ad
opted in order to reduce the
chattering pheno
menon caused by
the SM
CO. A vector contro
l method was
em
plo
y
ed to
a
c
h
i
eve
the
s
e
ns
orle
s
s
drive s
y
s
t
em
.
The
control
app
l
ica
tion was
develop
e
d in C
/
C++ languag
e
and impl
emented
using the Texas
Instruments
TMS320LF2812 digital signal pr
ocessor
(DSP).
This new proces
sor enables
intelligen
t
contr
o
l for motors. We used
to
test the drive th
e MCK2812 which
is a professional development kit av
ailab
l
e from Technosoft Co
mpan
y
.
Th
e
theore
tic
al f
i
ndi
ng is valid
at
ed
with
exp
e
rim
e
ntal r
e
s
u
lts
th
at
s
how the
effec
tiven
es
s
of
the r
eal
-tim
e
im
plem
enta
tion.
Keyword:
DSP real im
plementation
Fi
el
d o
r
i
e
nt
e
d
spee
d c
ont
r
o
l
PMSM sensor
less dr
iv
e
Slid
in
g m
o
d
e
cu
rren
t
ob
serv
er
Copyright ©
201
4 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
:
Rachid As
kour,
Depa
rtem
ent of Electrom
echanical Enginee
r
i
n
g,
Ecole
National
e
Su
pé
rieure
d
’
Arts et M
é
tiers
(E
NS
AM
),
Mar
j
an
e
I
I
,
BP 15
290
,
A
l
-
M
an
sour
, Mekn
ès, Mo
ro
cco
Em
a
il: rach
id
.ask
our@yah
oo
.fr
1.
INTRODUCTION
The
PMSM is
a good candi
date for hi
gh
perform
a
nce m
o
tion c
ont
rol
appli
cations because of
its
hi
g
h
t
o
r
que
t
o
i
n
ert
i
a
rat
i
o
,
hi
g
h
po
we
r
de
nsi
t
y
an
d
hi
g
h
effi
ci
e
n
cy
.
A
hi
g
h
pe
rf
orm
a
nce PM
SM
d
r
i
v
e i
s
b
a
sed
o
n
v
ect
or co
n
t
ro
l and
t
h
is requ
ires
kno
wled
g
e
of
t
h
e ro
to
r po
sition
.
In
d
e
ed
, th
e
stato
r
cu
rren
ts
of th
e
PMSM are co
ntro
lled
to g
e
n
e
rate co
n
s
tan
t
to
rq
u
e
u
s
i
n
g
t
h
e ro
tor po
sition
si
g
n
a
l. Th
erefore, th
e ro
t
o
r
p
o
sitio
n
m
u
st be obt
ai
n
e
d by
ei
t
h
er m
easurem
ent
or est
i
m
a
ti
on. Th
e angl
e of r
o
t
o
r po
si
t
i
on can
be m
easured w
i
t
h
an
opt
i
cal
enc
o
de
r, a
resol
v
er
o
r
wi
t
h
hal
l
sens
ors
.
It
i
s
po
p
u
l
a
r t
o
use a
n
e
n
co
de
r m
ount
e
d
o
n
t
h
e s
h
aft
- t
h
e
m
e
thod produc
es an accurate rot
o
r pos
ition angle.
If the rotor position is
available at every sam
p
ling tim
e of
th
e con
t
ro
l algo
rith
m
,
th
e speed
of th
e PM
SM can
b
e
easily calcu
lated
b
y
d
i
fferen
tiatin
g
t
h
e ro
tor po
sitio
n
angl
e.
Ho
we
ve
r, usi
ng t
h
e en
code
r m
a
ke t
h
e
m
o
t
o
r expe
nsive and m
echanically unre
liable. Also, the encode
r
is sen
s
itiv
e to
h
a
rsh
op
erating
con
d
ition
s
lik
e hu
m
i
d
ity
a
n
d
v
i
bration
s
. As a resu
lt, it is
d
e
sirab
l
e to
elimin
ate
th
e sen
s
or and
to
use estim
ate
s
of th
e ro
tor
po
sitio
n and
sp
eed
rath
er th
an
measu
r
em
en
ts.
There a
r
e seve
ral
m
e
thods to estim
a
te the roto
r position
of the PMSM.
Gene
rally, there are two
l
a
rge cat
eg
ori
e
s :
m
e
t
hods t
h
at
are based o
n
t
h
e m
a
gnet
i
c
sal
i
e
ncy
of t
h
e PM
SM
and m
e
t
hods t
h
at
est
i
m
a
t
e
t
h
e va
ri
abl
e
s
of i
n
t
e
rest
usi
ng t
h
e PM
SM
m
odel
[
1
]
.
M
a
gnet
i
c
sal
i
e
nc
y
m
e
t
hods u
s
e
t
h
e vari
at
i
o
n
of t
h
e
m
o
t
o
r'
s
i
ndu
ct
ance bet
w
een t
h
e d a
nd
q axe
s
[2]
.
B
u
t
t
h
es
e
m
e
t
hods are
rel
a
t
i
v
i
t
y
di
ffi
cul
t
t
o
im
pl
em
ent
an
d
are less portabl
e
from
one m
a
chine to a
not
her. Howeve
r,
t
h
ey
wo
r
k
well at low sp
ee
ds.
The sec
o
nd category
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
4
,
No
.
3
,
Sep
t
em
b
e
r
2
014
:
28
1 – 289
28
2
of est
i
m
ati
on i
s
based o
n
t
h
e PM
SM
m
odel
.
Several
est
i
m
a
ti
on m
e
t
hods base
d o
n
l
i
n
ear
or
no
n l
i
n
ea
r
o
b
s
erv
e
rs of t
h
e PM
SM are
p
r
esen
ted in the literatu
re [3
]-[6
].
Howev
e
r, in
all cases the im
p
l
e
m
en
tati
o
n
i
s
rel
a
t
i
v
el
y
di
ffi
cul
t
.
A speci
al
cl
ass of est
i
m
a
t
o
rs i
s
base
d on t
h
e sl
i
d
i
ng
m
ode cont
r
o
l
t
echni
que
s [7]
[
8
]
[
9]
.
Int
e
re
st
i
n
t
h
i
s
co
nt
r
o
l
ap
p
r
o
ach
has em
erg
e
d
due
t
o
i
t
s
r
o
b
u
st
ness a
g
ai
nst
param
e
t
e
r vari
at
i
o
n e
ffec
t
s u
nde
r
dy
nam
i
c con
d
i
t
i
ons
wi
t
h
a
m
i
ni
m
u
m
of i
m
plem
ent
a
t
i
on c
o
m
p
l
e
xi
ty
.
In
t
h
is wo
rk
, th
e ro
tor
p
o
s
iti
o
n
was
ob
tained
u
s
ing
a slidin
g
m
o
d
e
cu
rren
t
ob
serv
er.
Th
is m
e
th
o
d
u
tilizes th
e m
o
d
e
l
o
f
t
h
e
PMSM in
t
h
e stati
o
n
a
ry
referen
c
e fram
e an
d
esti
m
a
tes th
e ro
t
o
r po
sition
b
a
sed
on
the back em
fs [10]. The s
p
ee
d of th
e m
o
tor was calculated by pure di
ffe
re
ntiator. Because establishe
d back
e
m
fs are n
e
g
lig
ib
le at low sp
eeds,
we u
s
ed
Hall sen
s
ors in
fo
rm
atio
n
s
to
start th
e mo
tor. Th
e saturati
on
fu
nct
i
o
n was
a
d
o
p
t
e
d
i
n
o
r
de
r
t
o
re
duce
t
h
e
chat
t
e
ri
n
g
p
h
e
nom
eno
n
. The
SM
C
O
dy
nam
i
c
pe
rf
orm
a
nces
was
expe
rim
e
ntally verified in t
h
e case of
PM
SM
speed
vect
or c
ont
rol
.
T
h
e pa
per i
s
o
r
ga
ni
ze
d as fol
l
o
ws
. S
ect
i
o
n
2 de
scri
be
s t
h
e
PM
SM
sens
or
l
e
ss cont
rol
st
r
u
ct
u
r
e. T
h
e m
a
t
h
em
at
i
cal
backg
r
ou
n
d
i
s
p
r
e
s
ent
e
d i
n
Sect
i
on
3
.
In
th
is section, th
e PMSM m
o
d
e
l, th
e SMCO d
y
n
a
m
i
c
eq
u
a
tion
s
an
d th
e stab
ility a
n
alysis are reviewed.
Section 4 deals
with
t
h
e DSP real
im
p
l
e
m
en
tatio
n
.
An
ev
alu
a
tio
n of t
h
e resu
lts is presented
and
so
m
e
dig
ital
im
pl
em
ent
a
t
i
o
n as
pect
s a
r
e
di
scusse
d.
Fi
g
u
r
e
s s
how th
e effectiv
en
ess
of t
h
e im
p
l
e
m
en
ta
tio
n
.
2.
PMS
M
SENS
ORLESS
SPE
E
D C
O
NT
RO
L
Fi
gu
re 1 s
h
o
w
s a bl
ock
di
ag
r
a
m
of t
h
e sens
orl
e
ss
dri
v
e sy
st
em
of PM
SM
i
n
cl
udi
n
g
t
h
e SM
C
O
. Th
e
cont
rol
st
ruct
u
r
e i
s
base
d
on
t
h
e
Fi
el
d
Ori
e
nt
ed
C
o
nt
r
o
l
(FOC
)
[1
1]
. T
h
e
goal
o
f
F
O
C
i
s
t
o
dec
o
u
p
l
e
t
h
e
t
o
r
que a
n
d fl
u
x
p
r
o
d
u
ci
n
g
co
m
ponent
s
of t
h
e st
at
or cu
rre
nt
s al
l
o
wi
n
g
t
h
e
PM
m
o
t
o
r t
o
b
e
cont
rol
l
e
d i
n
suc
h
th
e sam
e
w
a
y as a sep
a
r
a
tely ex
cited
D
C
m
ach
in
e. In
t
h
e
sp
ecif
i
c case of
a
p
e
r
m
an
en
t
mag
n
e
t syn
c
h
r
o
nous
m
o
to
r witho
u
t
salien
t
po
les,
m
o
st o
f
th
e n
a
t
u
ral m
a
g
n
e
tic flu
x
is on th
e
d
ax
is.
In
o
r
d
e
r to
o
p
tim
ize th
e to
rque
pr
o
duct
i
o
n f
o
r
a gi
ven st
at
o
r
cur
r
ent
val
u
e, t
h
e appropriate strategy is to se
t refere
nce direct curre
nt isdref to
zero
.
T
h
e act
i
o
n
of
t
h
e c
u
r
r
e
n
t
re
gul
at
o
r
s i
s
t
h
en
t
o
shi
f
t
t
h
e
st
at
or c
u
rre
nt
vect
o
r
ont
o t
h
e
q a
x
i
s
.
In t
h
e se
ns
orl
e
ss d
r
i
v
e
sy
st
em
, Park an
d i
nve
rse
Par
k
t
a
nsf
o
rm
at
i
on ca
l
c
ul
at
i
ons a
r
e
base
d o
n
t
h
e
rot
o
r po
si
t
i
on est
i
m
a
ti
on
θ
b
y
th
e slid
ing
m
o
de o
b
serv
er. Also
, th
e ro
tor speed
estim
a
tio
n
N
i
s
obt
ai
ne
d
b
y
d
i
fferen
tiatin
g
θ
. In
addition, conve
ntional
m
odules
for vect
or control such as
spe
e
d and c
u
rrent PI
regulators, Clark and Park transf
orm
a
tion,
space vect
or P
W
M gene
ratio
n m
odule, and a three-phase
powe
r
inve
rter are i
n
clude
d as well
as the controlled PM
SM. Space vector PWM algorith
m
is used
for m
a
ximu
m
u
tilizatio
n
of
DC lin
k
vo
ltag
e
.
Fi
gu
re
1.
B
l
oc
k
di
ag
ram
of t
h
e sens
o
r
l
e
ss P
M
SM
dri
v
e sy
st
em
usi
n
g
SM
C
O
3.
MAT
H
EM
AT
ICAL
BA
CK
GRO
U
ND
3.
1. PM
SM
M
o
del
PM
SM
i
s
a cou
p
l
e
d a
nd n
o
n
l
i
n
ear sy
st
em
. Unde
r
vect
or control in curr
en
t loo
p
, it b
eco
m
e
s
a
d
ecoup
led
an
d lin
ear system wh
ich
lik
es
DC m
o
to
r.
Th
e PM
SM
m
odel in the stationary
re
fere
nce
fram
e
(
α β
can
be e
x
p
r
es
sed
by
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
DS
P-B
a
se
d
Se
nso
r
l
e
ss
Spee
d
C
o
nt
rol
of
a
P
e
rma
n
e
n
t
M
a
g
n
et
Sy
nc
hr
on
o
u
s M
o
t
o
r
…
(
R
achi
d Ask
o
ur)
28
3
(1
)
(2
)
Whe
r
e
L is st
ator sel
f
induc
t
ance,
R is
the
stator resistance, (
∝
,
, (
∝
,
and (
∝
,
are the
phase
currents
,
phase
voltages
a
n
d t
h
e
bac
k
em
f in
the
stationa
ry
refe
rence
f
r
am
e (
∝
, respectively.
T
h
e bac
k
e
m
f
i
s
gi
ve
n
by
:
.
.
(3
)
W
h
er
e
is the
e
l
ectrical angul
a
r
velocity,
i
s
t
h
e
fl
u
x
l
i
nka
ge
o
f
pe
rm
anent
m
a
gnet
a
n
d
is
the electrical
ro
t
o
r po
sitio
n.
3.2. Mathematical Model
of SMCO
The sl
i
d
i
n
g m
ode c
u
r
r
e
n
t
o
b
s
erve
r co
nsi
s
t
s
of a m
odel
ba
sed cu
rre
nt
o
b
s
erve
r an
d a
di
sco
n
t
i
n
u
o
u
s
cont
rol
ge
ne
rat
o
r
dri
v
en
by
er
ro
r bet
w
een es
t
i
m
a
t
e
d
m
o
t
o
r
cur
r
ent
s
a
nd a
c
t
u
al
m
o
t
o
r cu
rre
nt
s (Fi
g
u
r
e
2)
.
A
ban
g
ba
ng
co
nt
r
o
l
co
nsi
s
t
s
of
a s
u
m
m
a
t
i
o
n
poi
nt
t
h
at
c
a
l
c
ul
at
es t
h
e s
i
gn
o
f
t
h
e
er
r
o
r
bet
w
een
m
easur
e
d
current from
the
m
o
tor and es
t
i
m
a
t
e
d cur
r
ent
from
di
gi
t
i
zed
m
o
t
o
r m
odel
.
The com
put
ed
si
gn
of t
h
e e
r
r
o
r (+
1
or -
1
) i
s
m
u
l
t
i
p
l
i
e
d by
a sl
i
d
i
n
g m
ode ob
serve
r
gai
n
K.
The o
u
t
p
ut
o
f
t
h
e ba
ng
ba
ng c
ont
rol
l
e
r i
s
t
h
e
d
i
scon
tinu
o
u
s
co
n
t
ro
l Z. On
ce th
e d
i
g
itized
m
o
d
e
l is co
m
p
en
sated, th
e
n
e
x
t
step
is to
esti
m
a
te b
ack
emf
e
by
filterin
g
th
e
d
i
scon
tin
uou
s con
t
ro
l Z, as shown in
Figu
re 2. Val
u
es
e
and
e
(vect
or
c
o
m
p
onent of
e
) are
u
s
ed
for th
e esti
m
a
ted
th
eta calcu
latio
n
θ
.
Fig
u
re
2
.
Slid
i
n
g Mod
e
C
u
rren
t Ob
serv
er-Based
R
o
tor Fl
u
x
Po
sition
Esti
mato
r
The m
a
the
m
atical equations
for the
propos
e
d
SM
CO
in t
h
e station
a
ry
r
e
fere
nce
fram
e
(
α β
are
gi
ve
n as
f
o
l
l
o
ws:
∗
(4
)
∗
(5
)
Whe
r
e t
h
e sy
m
bol ^ indicates that a
va
riable is estim
at
e
d
a
n
d the
symbol
* i
ndicates
that a
varia
b
le is a
com
m
a
nd. The
di
sc
ont
i
n
u
ous
cont
rol
i
s
gi
ve
n
by
:
(6
)
Whe
r
e
(
>0) is
constant c
u
rrent observer gai
n
and the
sign
f
unct
i
o
n i
s
de
fi
ned
as
fol
l
o
ws:
1
0
1
0
(7
)
Th
e
go
al of
t
h
e d
i
sco
n
tinuo
us con
t
ro
l
is to
d
r
i
v
e cu
rren
t esti
m
a
t
i
o
n
erro
r to
zero. It is ach
i
ev
ed
b
y
pr
o
p
er sel
ect
i
on of
and corre
ct form
ation of estim
a
ted bac
k
em
f.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
4
,
No
.
3
,
Sep
t
em
b
e
r
2
014
:
28
1 – 289
28
4
In
im
p
l
e
m
en
tatio
n
,
t
h
e ab
ove fo
rm
u
l
atio
n
s
in
th
e con
tinuo
u
s
do
m
a
in
h
a
v
e
to b
e
tran
sfered to
t
h
e
d
i
screte form
;
th
erefore,
t
h
e slid
in
g
m
o
d
e
cu
rren
t ob
ser
v
er ca
n
be
fo
r
m
ul
at
ed by
t
h
e f
o
l
l
o
wi
ng
di
ffe
rence
equat
i
o
n:
1
∗
(8
)
.
(9
)
W
h
er
e th
e ma
t
r
ic
e
s
an
d
ar
e
gi
ve
n
by
and
1
;
is t
h
e curren
t
sam
p
lin
g
peri
od
an
d
is a 2x
2 un
ity m
a
tr
ix
.
In
ad
d
ition
,
t
h
e esti
m
a
ted
b
ack
em
f
̂
is o
b
t
ain
e
d
b
y
filterin
g
t
h
e d
i
sco
n
t
i
n
uou
s con
t
ro
l, Z, with
a
first o
r
d
e
r
low p
a
ss filter
(LPF) d
e
scrib
e
d
by:
̂
̂
(1
0)
Whe
r
e the
pa
ra
m
e
ter
i
s
defi
ned a
s
2
an
d
represen
ts t
h
e cu
t
o
ff pu
ls
ation
of th
e
filter. The cu
toff
fre
que
ncy
of t
h
e low pa
ss filter should
be de
signe
d
prope
rl
y according to
th
e fundam
ental freque
n
cy of the
tracke
d
stator
currents a
n
d t
o
filter
out t
h
e
high-fre
quenc
y
com
pone
nt of t
h
e di
sc
ontinuous c
ontrol
Z. T
h
e
di
scret
e
fo
rm
of (
1
0)
can
be
e
x
p
r
esse
d
by
:
̂
1
̂
2
̂
(1
1)
Fin
a
lly, th
e est
i
m
a
ted
ro
tor
po
sitio
n is d
e
rived
fro
m
th
e b
a
ck
em
f as fo
llows:
̂
̂
(1
2)
3.
3.
R
o
t
o
S
p
ee
d C
a
l
c
ul
a
t
i
o
n
Ro
to
r sp
eed is
calcu
lated
b
y
differen
tiatin
g
t
h
e
ro
t
o
r
po
sition
an
g
l
e as fo
llows:
(1
3)
Whe
r
e
′
i
s
t
h
e
s
p
eed
sam
p
l
i
ng
peri
od
.
In a
ddition, the
rotor spee
d is nece
ssa
ry to be
filtered out by the lo
w-pass filter in orde
r to reduce the
a
m
p
lifyin
g
no
ise g
e
n
e
rated
by th
e p
u
r
e d
i
fferen
tiator [12
]
. Th
e si
m
p
le first o
r
d
e
r lo
w-p
a
ss filter is u
s
ed, th
en
th
e actu
a
l
ro
t
o
r sp
eed
t
o
b
e
u
s
ed
is t
h
e
o
u
t
p
u
t
of th
e low-p
a
ss filter,
, gi
ve
n by
t
h
e f
o
l
l
o
wi
n
g
e
quat
i
o
n:
(1
4)
Whe
r
e
′
is th
e
LPF tim
e co
n
s
tan
t
and
is th
e
sp
eed
cu
t-off frequ
e
n
c
y.
3
.
4
.
Sta
b
ility Ana
l
y
s
is o
f
the
Sliding
Mo
de Current Observ
er
The slidi
ng
pl
ane S is realized on t
h
e state vari
ables
,
i.e., the stator
cu
rren
ts, b
y
the switch
i
ng
fun
c
tion
s
as:
0
(1
5)
It
i
s
necessa
ry
t
o
desi
gn t
h
e L
y
apu
n
o
v
fu
nct
i
on t
o
det
e
rm
i
n
e t
h
e re
qui
re
d
con
d
i
t
i
on
f
o
r t
h
e exi
s
t
e
nce
of
t
h
e sl
i
d
i
n
g
m
ode. Ly
ap
un
ov
f
u
nct
i
o
n
f
o
r
exi
s
t
e
nce
co
n
d
i
t
i
on
o
f
sl
i
d
i
n
g m
ode i
s
defi
ned
as:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
DS
P-B
a
se
d
Se
nso
r
l
e
ss
Spee
d
C
o
nt
rol
of
a
P
e
rma
n
e
n
t
M
a
g
n
et
Sy
nc
hr
on
o
u
s M
o
t
o
r
…
(
R
achi
d Ask
o
ur)
28
5
(1
6)
Whe
r
e slidi
ng surfaces
are
̅
and
̅
.
̅
and
̅
are t
h
e e
r
ror
betwee
n
est
i
m
a
t
e
d pha
s
e
cu
rre
nt
an
d
a
c
t
u
al
one
i
n
t
h
e
∝
and
ax
is
resp
ectiv
ely.
From
Lyap
u
n
o
v
st
ab
ility th
eo
ry,
th
e
o
b
s
erv
e
r is stab
le if t
h
e fun
c
tio
n V satisfy
V
> 0
and
< 0, i.e.,
̅
̅
̅
̅
0
(1
7)
Whe
r
e,
̅
̅
0
(1
8)
̅
̅
.
̅
∝
̅
.
̅
̅
∓
̅
̅
0
̅
0
∓
̅
̅
0
̅
0
(1
9)
Th
e
p
a
rt B
will b
e
n
e
g
a
tiv
e
d
e
fin
ite if t
h
e fo
llo
wi
n
g
satisfies:
|
|
,
(2
0)
As a
resu
lt, to
k
eep th
e sli
d
ing
m
o
d
e
o
b
serv
er stab
le,
th
e ob
serv
er
g
a
in
K sho
u
l
d satisfy th
e
in
equ
a
lity co
nd
itio
n
:
m
a
x
|
|
,
(2
1)
It is no
ted from
th
e abo
v
e
equ
a
tio
n th
at t
h
e
o
b
s
erv
e
r g
a
i
n
K sh
ou
ld
b
e
larg
er th
an
th
e ind
u
c
ed
b
a
ck
em
f.
3.
5. Red
u
ci
ng
Ch
at
teri
ng
Pr
obl
e
m
In
th
e im
p
l
e
m
en
tatio
n
o
f
slid
ing
m
o
d
e
con
t
ro
l th
eory in
real syste
m
s, th
e m
a
in
o
b
stacle is an
u
n
d
e
sirab
l
e phen
o
m
en
on
o
f
o
s
cillatio
n
with
fin
ite
freq
u
e
n
c
y and am
p
lit
u
d
e
,
wh
ich
is
k
nown as
‘ch
a
tterin
g
’
[13]. The c
h
attering is harm
ful b
ecause it leads to low co
ntrol
accuracy,
high wear of m
oving
m
echanical
part
s, a
n
d hi
gh
heat
l
o
sses i
n
el
ect
ri
cal p
o
w
er circu
its. To
so
lv
e th
e ch
attering
prob
lem
,
t
h
e sign
fun
c
tion
can
be re
placed
with its approximation
- a continuous form
. There a
r
e two di
ffere
n
t approac
h
es possi
ble, i.e
.
sat
u
rat
i
o
n an
d
si
gm
oi
d fu
nct
i
ons
(Fi
g
u
r
e 3
)
.
W
h
e
n
t
h
e am
pl
i
t
ude
of c
u
r
r
e
nt
err
o
r i
s
l
e
s
s
t
h
an
ε
, i
.
e., wi
dt
h
of
th
e bou
nd
ary layer, th
e d
i
scon
tin
uou
s con
t
ro
l Z ch
an
g
e
s to a saturatio
n
o
r
sig
m
o
i
d
fu
n
c
ti
o
n
.
Figure 3
.
Di
a
g
r
a
m
of sat
u
rat
i
o
n a
n
d
si
gm
oi
d
fu
nct
i
o
ns
The sat
u
rat
i
o
n
fu
nct
i
o
n ca
n
b
e
desc
ri
be
d as
fol
l
o
ws:
,
|
|
,
|
|
(2
2)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
4
,
No
.
3
,
Sep
t
em
b
e
r
2
014
:
28
1 – 289
28
6
There
e
x
ists
a great
variety of the
sigm
oid ty
p
e
fun
c
tio
ns.
So
m
e
of th
em
are listed
b
e
low
(no
r
m
a
lized
in
su
ch
way th
at
t
h
eir
values
are
betwee
n
1
):
m
s
ar
ct
a
n
m
s
|
|
m
s
/
(2
3)
In this
work, t
h
e sign function is
re
placed by the
saturation
function.
4.
DSP RE
AL
I
M
PLEME
N
T
A
TIO
N
4.
1. E
x
peri
me
ntal
Set
u
p
In
or
der t
o
ve
r
i
fy
t
h
e per
f
o
r
m
a
nce of t
h
e
pr
o
pose
d
SM
C
O
i
n
p
r
act
i
ce,
a pr
ofes
si
o
n
al
devel
opm
ent
kit (MCK2812) availa
ble from
Technos
oft
com
p
agny
has
bee
n
used for the a
ppli
cation
(Figure 4). The kit
i
n
cl
ude
s:
a)
a 3-
p
h
ases
A
C
po
we
r m
odul
e PM
5
0
:
i
t
co
nsi
s
t
s
o
f
a
5
0
W si
x M
O
SFE
T i
n
vert
er wi
t
h
i
n
t
e
grat
e
d
pha
s
e
s cu
rre
nt
se
ns
ors
i
n
al
l
3
pha
ses an
d
DC
v
o
l
t
a
ge, a
n
d
p
r
ot
ect
i
on
har
d
ware
.
b)
The TM
S
3
2
0
L
F
2
8
1
2
DSP
ba
sed de
vel
o
pm
ent
b
o
ar
d wi
t
h
on
-
boa
rd
peri
p
h
eral
s:
D
A
C
s
,
R
S
23
2
connector, etc.
[14].
c)
a Di
gi
t
a
l
M
o
t
i
on C
ont
rol
De
vel
o
pm
ent
soft
ware cal
l
e
d
D
M
C
D
-P
ro e
n
a
b
l
i
ng as
sem
b
ly
and C
codi
ng
,
real
-t
i
m
e deb
u
g
g
i
n
g,
dat
a
l
o
g
g
i
n
g a
n
d
ot
her
use
f
ul
feat
u
r
es.
d)
a Pi
t
t
m
a
n 34
41
seri
es 4-
pol
es
t
h
ree p
h
ases
pe
rm
anent
m
a
gnet
sy
nchr
on
o
u
s
m
o
t
o
r eq
ui
p
p
e
d
wi
t
h
5
00-lin
e
q
u
a
dratu
r
e i
n
crem
en
tal en
cod
e
r and
3
h
a
ll p
o
s
ition
sen
s
o
r
s. Th
e ch
aracteristics o
f
th
is
m
o
t
o
r are
gi
ve
n i
n
Ta
bl
e 1
.
Table
1. M
o
tor cha
r
acteristics
Motor para
m
e
te
r
Value
Rated voltage (
V
)
(
Y
-
c
onnexion)
19.
1
No
m
i
nal tor
que(
m
.N)
0.
029
M
a
x
i
mu
m c
u
r
r
e
n
t
(
A
)
Stator
inductance (m
H)
Stator resit
a
nce (
)
Rotor ti
m
e
constant (m
s
)
Electri
cal constant
(
m
s)
Rotor inertia (kg.
m
2
)
3.
64
0.
46
5.
25
7.
92
0.
09
0.
9.
10
-6
Fi
gu
re
4.
Ex
pe
ri
m
e
nt
al
set
up
4.
2. So
ftw
are Org
a
ni
s
a
ti
o
n
The
program
is de
velope
d m
a
inly
in C/C++ langua
ge a
n
d is
base
d on t
w
o m
odules :
initialization
and m
a
gnet
i
c
st
al
l
m
odul
e and t
h
e i
n
t
e
r
r
u
p
t
m
odul
e (Fi
g
u
r
e 5
)
. T
h
e i
n
t
e
rr
u
p
t
m
odu
l
e
han
d
l
e
s t
h
e
wh
ol
e
cont
rol
al
go
ri
t
h
m
.
It
’s
peri
o
d
i
cal
l
y
co
m
put
ed acc
or
di
n
g
t
o
a fi
xe
d
SV
P
W
M
peri
od
val
u
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
DS
P-B
a
se
d
Se
nso
r
l
e
ss
Spee
d
C
o
nt
rol
of
a
P
e
rma
n
e
n
t
M
a
g
n
et
Sy
nc
hr
on
o
u
s M
o
t
o
r
…
(
R
achi
d Ask
o
ur)
28
7
The
c
o
ntrol application use
a
specific real-tim
e en
v
i
ron
m
e
n
t, stru
ctured
on
two
lev
e
ls:
a)
a hi
gh p
r
i
p
ori
y
i
n
t
e
rru
pt
fu
nct
i
on t
r
i
gge
re
d every
1
0
0
s,
m
a
in
ly fo
r SVPWM g
e
n
e
ratio
n,
current c
o
ntrol and SMC
O
implem
entation,
b)
a lo
wer
priority in
terrup
t functio
n
tri
g
g
e
red ev
e
r
y 1
m
s
, for spee
d re
fere
nce a
n
d s
p
ee
d
cont
rol
i
m
p
l
e
m
en
tatio
n
.
St
art
Hard
w
a
re
& S
o
f
t
w
a
re
In
itiali
za
ti
on
M
a
g
n
e
t
ic
s
t
a
ll
Wa
i
t
i
n
g
loo
p
PW
M I
S
R
s
c
u
rrent & sp
e
e
d
loops
exe
c
u
t
ion
Figu
re
5.
Ge
ne
ral S
o
ftwa
re
Flowc
h
a
r
t
The c
hoice
of
the PW
M
fre
quency
depe
nds
on t
h
e m
o
to
r
electrical const
a
nt. In this a
pplication, the
P
W
M fre
que
ncy has bee
n
se
t to 20kHz.
After the in
itialization m
odule
has c
o
m
p
leted, a m
a
gnetic stall is
per
f
o
r
m
e
d by
appl
y
i
n
g
a
co
n
s
t
a
nt
v
o
l
t
a
ge
v
ect
or t
o
t
h
e
st
a
t
or
p
h
ase:
t
h
e
con
s
t
a
nt
phas
e
cu
rre
nt
s fl
owi
n
g
i
n
the coils create a fixed stator
flux. As a cons
eque
nce, the
roto
r flux
alig
ns itself n
a
tu
rally o
n
t
o
th
is stato
r
flu
x
(th
e
ro
t
o
r is stalled
in
th
is po
si
tio
n
)
.
Th
en
, a
waiting
loop
starts,
an
d
correspo
n
d
s
to
an
i
n
terru
p
tib
le co
mmu
n
i
cation
b
e
tween
th
e
DSP
m
onitor and t
h
e
gra
p
hical user inte
rface
. If the
use
r
send
s t
h
e start comman
d
,
th
e co
n
t
ro
l al
g
o
rithm
start
ex
ecu
ting
.
Th
e d
a
ta-l
o
g
g
i
ng
allo
ws
real-tim
e
d
e
b
ugg
ing
o
f
th
e ap
p
lication
.
4.
3.
Re
al
T
i
me Resul
t
s
Th
e ex
p
e
rim
e
n
t
s of th
e several con
d
ition
s
h
a
v
e
b
e
en
p
e
rfo
r
m
e
d
to
v
e
rify th
e
u
s
efu
l
n
e
ss
o
f
t
h
e
p
r
op
o
s
ed
sen
s
o
r
less con
t
ro
l
.
Thu
s
,
for th
e
first exp
e
ri
m
e
n
t
o
f
t
h
e estim
a
t
e
d
ro
tor
p
o
s
ition
,
th
e ru
nn
ing
PMSM
are tested
in
th
e con
d
ition
of 30
00
rp
m
(1
00
Hz
flux
ro
tatio
n
freq
u
e
n
c
y)
at lo
ad
con
d
itio
n
s
. To
ev
alu
a
te th
e
co
rrectn
e
ss
of th
e esti
m
a
ted
ro
tor po
sitio
n, an
en
cod
e
r attach
ed
t
o
th
e PM
SM is ad
op
ted
to
m
easu
r
e th
e ro
tor
flux
po
sitio
n
fo
r co
m
p
aring
to
th
e esti
m
a
ted
v
a
lu
e. Figur
e 6 sh
ow
s t
h
e ex
peri
m
e
nt
al
resul
t
s
of t
h
e se
ns
orl
e
ss
spee
d c
ont
r
o
l
a
t
30
0
0
rpm
at
l
o
ad
co
n
d
i
t
i
ons
.
Although t
h
ere are m
u
ch switching ri
ppl
e in th
e est
i
m
at
ed curre
nt
s owi
ng t
h
e
sl
i
d
i
ng m
ode
ope
ration, the
estim
a
ted current trace th
e actual current
with mi
nor e
r
rors acc
ording
to
the curre
n
t level as
shown in Figures 6(a
)
-(b). T
h
e curren
t error, reflectin
g
th
e
ch
attering
in
SMCO, wo
u
l
d
be d
e
term
in
ed
by th
e
cu
rren
t lev
e
l an
d
settin
gs o
f
t
h
e satu
ration
fu
n
c
tion
.
In
Figu
re 6(c), th
e esti
m
a
ted
b
ack
e
m
f h
a
s a sin
u
so
id
al
wave
form
that the rotor
posi
tion an
gle ca
n be calculated accurately. Fi
gure
6(d) s
hows that the est
i
m
a
ted
rot
o
r po
si
t
i
on m
a
t
c
hes
wi
t
h
t
h
e
real
rot
o
r p
o
si
t
i
on (e
nco
d
e
r th
eta)
with
sm
a
ll p
h
a
se sh
ift. In
Figu
re 6(f), the
esti
m
a
ted
sp
eed
m
a
tch
e
s ex
actly with
th
e referen
ce sp
ee
d (100Hz) at load conditions. So, the se
ns
orless
PMSM driv
e is effective.
I
n
t
h
e second
ex
p
e
r
i
m
e
n
t
, to
test th
e r
obu
stness o
f
t
h
e
propose
d
SMCO, t
h
e m
o
tor is acc
elerated and
decelerated be
tween 1500
- 4500rpm
(50-150Hz)
at
loa
d
conditions.
The estim
at
ed
rot
o
r spee
d obtaine
d
th
ro
ugh
estim
a
t
ed
ro
tor
p
o
s
itio
n is d
e
p
i
cted
i
n
Fi
g
u
re
7
.
As
o
b
s
erv
e
d, th
e esti
m
a
ted
sp
eed track
s th
e
referen
ce
spee
d accurate
ly regardless
of loa
d
c
o
nditions. The e
x
pe
ri
mental results
dem
onstrate that the sliding
m
o
d
e
obs
erver is vali
d a
n
d the
real-t
im
e im
ple
m
entation is s
u
cces
sful.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
4
,
No
.
3
,
Sep
t
em
b
e
r
2
014
:
28
1 – 289
28
8
(a)
(b
)
(c)
(d
)
(e)
(
f)
Fi
gu
re
6.
Se
ns
orl
e
ss
spee
d c
o
nt
r
o
l
at
3
0
0
0
r
p
m
(10
0
Hz)
(a)
∝
and
(Per
U
n
it) (b
)
and
(
P
er
Unit)
(c
)
∝
and
(Per Un
it)
(d
) Estim
a
t
ed
and E
n
coder the
t
a (ra
d)
(e)
Er
ro
r
of
the
t
a (ra
d)
(
f)
Estim
ated and
E
n
c
ode
r s
p
ee
d
(Hz
)
Figure
7. Real and estim
a
t
ed rotor s
p
eed (Hz
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
DS
P-B
a
se
d
Se
nso
r
l
e
ss
Spee
d
C
o
nt
rol
of
a
P
e
rma
n
e
n
t
M
a
g
n
et
Sy
nc
hr
on
o
u
s M
o
t
o
r
…
(
R
achi
d Ask
o
ur)
28
9
5.
CO
NCL
USI
O
N
Thi
s
pape
r
pre
s
ent
s
t
h
e
DS
P
im
pl
em
ent
a
t
i
o
n o
f
PM
SM
se
nso
r
l
e
ss s
p
ee
d
cont
rol
usi
n
g s
l
i
d
i
ng m
ode
cur
r
ent
o
b
se
rv
er. A
vect
or c
ont
rol
m
e
t
hod was em
pl
oy
ed t
o
achi
e
ve t
h
e
senso
r
l
e
ss d
r
i
v
e sy
st
em
. R
e
al
-t
im
e
resu
lts co
nfirm th
e effectiv
eness of th
e sen
s
o
r
less
d
r
i
v
e
imp
l
em
en
tatio
n
.
It is wo
rt
h
to
po
in
t ou
t th
at suitab
l
e
ch
o
i
ce
o
f
con
t
ro
l d
e
si
g
n
p
a
rameters (PI loop
g
a
i
n
s,
SMCO
g
a
i
n
and
filters con
s
tan
t
s)
m
u
st b
e
d
o
n
e
in
ord
e
r
to
ach
iev
e
sp
eed
closed loo
p
stab
ility an
d satisfacto
r
y
d
yna
m
i
c p
e
rfo
r
m
a
n
ces. On
t
h
e
oth
e
r
h
a
n
d
,
d
u
e
to
th
e
h
i
gh
p
e
rform
a
n
ce
o
f
TMS32
0
LF2
812
d
i
gital sig
n
a
l processor, all th
e fu
n
c
tion
a
lities req
u
i
red to
b
u
ild a
sens
orl
e
ss PM
SM
dri
v
e (t
he
con
v
ent
i
o
nal
m
odul
es for
v
ect
or co
nt
r
o
l
,
t
h
e vol
t
a
ge ca
l
c
ul
at
i
on, t
h
e
sl
i
d
i
n
g
m
ode ob
ser
v
er
, et
c.)
ha
ve
bee
n
c
ode
d i
n
C
/
C
++ l
a
ng
ua
ge.
The
use
of
a
hi
ghe
r l
e
vel
l
a
n
g
u
age
(es
p
eci
al
l
y
, t
h
e
use o
f
C
++ classes) eases g
r
eat
l
y
pro
g
ram
m
i
ng and i
s
w
e
l
l
sui
t
e
d t
o
m
a
nagi
n
g
va
ri
abl
e
s an
d co
nt
rol
l
i
n
g
pr
o
g
ram
fl
ow.
Fu
rt
he
r de
vel
opm
ent
suc
h
as ada
p
t
a
t
i
v
e
sens
orl
e
ss c
o
n
t
rol
o
r
c
h
at
t
e
ri
ng
re
duct
i
o
n c
a
n
be
easi
l
y
achi
e
ved
o
w
i
n
g t
o
t
h
e a
l
ready
devel
o
p
e
d s
o
ft
ware
f
r
a
m
ewor
k.
REFERE
NC
ES
[1]
Mihai Comanes
c
u. C
a
scad
ed EMF and Speed S
lid
ing Mode Ob
server for
the Nonsalient PMSM.
IECON 2010-3
6
th
Annual Con
f
erence on
IEEE In
d
u
strial Electronics Society
. 20
10; 792-797.
[2]
MJ Corley
, RD
Lorenz. Rotor
Position and
Velocity
Es
timation
for Permanent
Magne
t S
y
nchro
nous Machine
at
Standstill
and
Hi
gh Speed.
IEEE-
IAS Annua
l M
e
eting
. 1996; 1: 36
-41.
[3]
Y Yamamoto,
Y Yoshida,
T
Ashikaga
. Senso
r
less control of
PM Motor Usin
g Full Order Flux Observer.
I
E
EE
Transactions on
Indus
try Applica
tions.
2004
; 124: 743-749.
[4]
M Coma
ne
sc
u,
T Ba
tze
l
.
Re
duce
d
Orde
r Ob
se
rv
e
rs for Rotor
Po
sition Estima
tion of Nonsalient PMSM
.
IE
EE
International Electric
Machines &
Drives Conf
er
ence, I
E
MDC. 2
009.
[5]
Huang MC,
Moses AJ,
Anay
i F,
Yao XG.
Reduced Order Linear Kalman Filter T
h
eo
ry in
Applica
tion of Sensorles
s
Control for Permanent Magnet Synchronous
Motor (
P
MSM
)
.
IEEE Confere
n
ce on Industrial Ele
c
tron
ics a
nd
Applications. 20
06; 1-6.
[6]
J Solsona, MI
Valla
, C Mur
a
v
c
hik.
On Speed
and Rotor
Positi
on Estim
ation
i
n
Perm
anent M
a
gnet
AC Drive
s
,"
IEEE Transactio
ns on
Industrial Electronics
. 200
0; 47(5): 1176-1
180.
[7]
VI Utkin, JG Guldner, J Shi. Slid
ing M
ode Con
t
r
o
l in
El
ec
tr
omechanical S
y
stems.
Taylor and
Francis
. 1999
.
[8]
A Gouichiche,
MS Boucherit,
A Safa
, Y Messlem. Sensorless
Sliding Mode V
ector Con
t
rol of
Induction Moto
r
Drives.
International Journal of
Power El
ectronics and Drive
Sys
t
em (
I
JPEDS)
. 2
012; 2(3): 217-2
84.
[9]
H Glaoui,
A Ha
zzab
, B
Bouchi
ba, IK Bous
s
e
rh
ane.
S
p
eed
S
y
n
c
hronis
a
t
i
on of
web winding S
y
s
t
em
with S
lidin
g
Mode Control.
I
n
ternational Jou
r
nal of
Power
El
ectronics and Dr
ive System
(
I
JPEDS)
. 2013; 3(2):
155-169.
[10]
S Chi, Z Zh
ang,
L Xu. A Novel
Sliding Mode Observer w
ith Ad
aptiv
e F
eedba
ck
Gain for P
M
S
M
S
e
ns
orles
s
Vect
or
Control.
Power
Electronics
Sp
ec
ialists Conf
erenc
e
. 2007
: 2579-25
85.
[11]
R Askour, B Bo
uoulid Idrissi. Experimental Assessment of
Trapezoid
al Commut
a
tion and FOC Performances of 3-
P
h
as
e P
e
rm
anen
t M
a
gnet
Brus
hles
s
M
o
tor.
International Journ
a
l of Scie
n
ce a
nd Advanced T
echnolog
y
. 201
2;
2(11): 40-45
.
[12]
Texas Instrumen
t
. Dig
ital Motor
Control Softwar
e
librar
y
.
spru48
5a. 2003
.
[13]
KD Young, VI
Utkin, U
Ozguner. A contro
l engineer’s gui
d
e
to sliding mode control.
IEEE Transactions
On
Control Systems Technology
. 199
9; 7: 328-342.
[14]
Texas Instrumen
t
.
TMS320C28x DSP CPU and inst
ruction
set
reference guid
e
. spru430b. 2002
.
BIOGRAP
HI
ES
OF AUTH
ORS
Rachid ASKOUR
was
born in Cas
a
blan
ca
, M
o
rocco. H
e
re
cei
ved the
engin
eer
’s
degree from
Ecole Nation
a
le de l’Industrie Minérale, Ra
b
a
t, Morocco,
in
1996 and the
Master degree
(Diplôme des Etudes Approfondies) from Univ
ersité
des Scien
ces et Technolo
g
ies de Lille,
Lille, France,
in
2002. His sear
ch
inter
e
sted
power
electron
i
cs
and
contro
l
of electr
ical
machin
es.
Since 1997
, he
has been
working at
Eco
l
e Nati
onale Supérieur
e
d’Arts
et Métiers (ENSAM-
Me
knè
s),
Moulay
Isma
ïl Unive
r
sity
,
Me
knè
s,
Moroc
c
o
, wher
e he is
an as
s
i
s
t
ant P
r
ofes
s
o
r in the
Department o
f
Electromechanical Eng
i
neer
ing.
Badr
BOUOULID IDR
I
S
S
I
was born in M
a
rrakech
, Morocco. He
receiv
ed the Ph.D. degree
from Faculté Poly
technique de
Mons, Mons, Be
lg
ium, in 1997 and the engineer’
s
degree fro
m
Ecole Nation
a
le de l’Industr
ie
Minérale, R
a
bat, Morocco
, in 1
992. Since 199
9, he h
a
s been
working at E
c
ol
e Nation
a
le Sup
é
rieur
e
d’Arts
et Métiers (ENS
AM-M
eknès), Moulay
Ismaïl
Univers
i
t
y
, M
e
k
n
ès
, M
o
rocco, w
h
ere he is
a P
r
of
es
s
o
r in the Dep
a
rtm
e
nt of El
ec
t
r
om
echanic
al
Engine
ering,
in
t
h
e ar
eas
of
pow
er e
l
e
c
troni
cs
an
d el
ectr
i
c
a
l m
a
c
h
ines
. His
res
e
a
r
ch in
teres
t
s
are
mainly
electric
drives, sensorless drives, i
ndus
trial con
t
rol s
y
s
t
ems and DSP based con
t
rol
s
y
ste
m
s.
Evaluation Warning : The document was created with Spire.PDF for Python.