Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol
.
4
,
No
. 2,
J
une
2
0
1
4
,
pp
. 19
2~
20
3
I
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: 208
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4
1
92
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
Contr
o
l of Four
Switch
Thr
e
e
Phase Inverter
Fed Induction
Motor
Drives Based Speed and St
at
or
Res
i
stance Estimati
on
M. K. Me
tw
al
ly
Departement of
Electrical Eng
i
n
eering
,
Menouf
iy
a Un
iversity
, Faculty
of
Engin
e
ering, Menoufiya,
Eg
y
p
t
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 4, 2013
Rev
i
sed
Jan
9, 2
014
Accepte
d
Ja
n 26, 2014
This paper presents sensorless
position
and speed control for a four-switch
three-ph
ase inverter (FSTPI) fed
induc
tion motor
drive. Accurate
knowledge
of sta
t
or re
sista
n
c
e
is of utmost im
portance
for correct oper
a
tion
of a number
of speed sensorless induction motor cont
rol schemes in the low speed region
.
Since stator resistance
inevitab
ly vari
es with oper
a
ting
conditions, stable
and
accur
a
t
e
operat
i
on at near-
zero
s
p
eed requir
e
s
an appropriat
e
id
entifi
c
a
tion
algorithm for the stator resistan
ce. The pap
e
r proposes such an id
entificatio
n
algorithm, which is developed
for th
e rotor flux based mod
e
l refer
e
nce
adapt
i
ve s
y
s
t
em
(M
RAS
)
t
y
p
e
o
f
the
s
p
eed
es
ti
m
a
tor in
conjun
ction
with
a
rotor flux orien
t
ed control sch
e
me. In
this speed estima
tion method only
on
e
(out of the two avail
a
ble) degr
ee
of freedom
is utiliz
ed for speed e
s
tim
ation.
It is utilize the s
econd
av
ailab
l
e
degree of fr
eedo
m
as a mean
for
adapting th
e
s
t
ator res
i
s
t
an
ce
.
The paral
l
el s
t
a
t
or res
i
s
t
anc
e
an
d rotor s
p
eed identifi
c
a
tion
algorithm is d
e
v
e
loped
in a s
y
stematic
manner
,
u
s
ing Popov’s h
y
per stability
theor
y
.
It in
cr
eas
es
th
e com
p
lexit
y
of th
e
overal
l
con
t
r
o
l s
y
s
t
em
ins
i
gnific
a
nt
l
y
and enabl
e
s
c
o
rrect
speed estimation and
stable driv
e
operation at n
e
ar-zero speeds. The pr
oposed speed and positio
n estimato
r
with parallel stator resistance identif
ication for FSTPI fed induction motor at
ver
y
low speed
under h
i
gh
load operati
on
is
verified b
y
sim
u
lation
and
experimental res
u
lts.
The re
sults
show the robustness of the prop
osed method
with FST
PI.
Keyword:
I
ndu
ctio
n m
o
to
r
Four
switch three phase i
nve
rt
er
Sens
orl
e
ss
co
n
t
rol
M
odel refe
renc
e
ada
p
tive
syste
m
(MRAS)
Stator resistanc
e
identification
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
:
M. K. Metwally
Departem
ent of Electrical Engineering
,
Menoufiy
a Univ
ersity
,
Faculty of E
n
gineering,
Menoufiy
a, Eg
ypt.
Em
ail: m
ohkam
e
l2007@ya
hoo.com
1.
INTRODUCTION
The
i
nduct
i
on m
o
t
o
r has found
very
wi
de i
ndust
r
i
a
l
appl
i
cat
i
ons
due t
o
i
t
s
wel
l
-
known advant
ages
as
sim
p
le construction,
reliability and
low cost. Th
e m
o
st
popular high
perform
an
ce
induction m
o
tor control
m
e
t
hod
i
s
t
h
at
one known
as Fi
el
d-Ori
e
nt
ed
C
ont
rol
.
It
i
s
based on
a
d-q
reference fram
e
rotating
sy
nchronousl
y
wi
t
h
t
h
e
rot
o
r fl
ux
vect
or, whi
c
h al
l
o
ws
achi
e
vi
ng a
decoupl
ed cont
rol
bet
w
een
t
h
e fl
ux
and
th
e p
r
o
d
u
ced
to
rq
u
e
, lik
ewise to
a sep
a
rately ex
cited
DC m
o
to
r [1
].
In
Di
rect
Fi
el
d-Ori
e
nt
ed C
ont
rol
,
bot
h t
h
e i
n
st
ant
a
neous m
a
gni
t
ude and posi
t
i
on of t
h
e rot
o
r fl
ux
vect
or
are supposed t
o
be preci
sel
y
known. However, as
t
h
e rot
o
r fl
ux cannot
be di
rect
l
y
m
easured, effort
s
have been m
a
de t
o
est
i
m
at
e t
h
e rot
o
r fl
ux usi
ng vari
ous
ki
nds of observers, based on t
h
e m
easurem
ent
s
of t
h
e
st
at
or
current
s, t
h
e
st
at
or vol
t
a
ges a
nd
t
h
e m
o
t
o
r
speed. An i
m
port
a
nt
probl
em
is
that the exact
values of the
m
o
t
o
r
param
e
t
e
rs, from
whi
c
h t
h
e observer
and som
e
hi
gh
perform
ance cont
rol
sy
st
em
s
depend, are di
fferent
from
nom
i
n
al
val
u
es
and change
wi
t
h
respect
t
o
t
h
e t
e
m
p
erat
ure
and t
h
e
operat
i
ng condi
t
i
ons. Anot
her
quest
i
on
i
s
t
h
e need
of a speed
sensor t
o
provi
de
t
h
e rot
o
r speed
m
easurem
ent
,
necessary
t
o
regul
at
i
on
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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4
C
ont
r
o
l
of
Fo
u
r
Sw
i
t
c
h
Th
ree
Ph
ase
Invert
e
r
Fed
I
n
d
u
ct
i
o
n
Mot
o
r
Dri
ves
Base
d
Spee
d
…
(
M
. K
.
Met
w
a
l
l
y
)
19
3
purpose
as wel
l
as
observer operat
i
on. The presence
of t
h
i
s
sensor
increases the driv
e cost
and can reduce the
robust
n
ess
of t
h
e overal
l
sy
st
em
;
m
o
reover, i
n
som
e
cases
a speed sensor cannot
be m
ount
ed, such as m
o
t
o
r
d
r
iv
es in
a h
o
s
tile en
v
i
ro
n
m
en
t an
d
v
e
ry h
i
g
h
sp
eed
m
o
to
r d
r
iv
es.
Th
e
ex
ten
d
e
d
Kalm
an
filters fo
r sim
u
ltan
e
o
u
s
estim
atio
n
o
f
th
e ro
to
r flu
x
,
th
e sp
eed
an
d
so
m
e
m
o
to
r
param
e
ters
(frequently
only
the rotor resistance, the para
m
e
ter
subjected to the wide
st variation) have been
proposed
as a
pot
ent
i
a
l
sol
u
t
i
on t
o
t
h
e above
probl
em
s [2]
,
[3]
.
Unfort
unat
e
l
y
, t
h
i
s
approach has som
e
i
nherent
di
sadvant
ages, such as t
h
e i
n
fl
uence of noi
se and com
put
at
i
on burden.
In t
h
e l
a
st
y
ears, t
h
e sl
i
d
i
ng-m
ode observer has represent
e
d an at
t
r
act
i
v
e choi
ce for i
t
s
bei
ng qui
t
e
robust
t
o
di
st
urbances,
param
e
t
e
r devi
at
i
ons
and sy
st
em
noi
se
[4]
,
[5]
.
Adapt
i
v
e fl
ux
sl
i
d
i
ng-m
ode observers,
in
wh
ich
th
e m
o
to
r
sp
eed
is
estim
ated
b
y
ad
d
itio
n
a
l
equat
i
ons,
have been
desi
gned t
r
y
i
ng
t
o
reduce t
h
e
i
n
fl
uence of param
e
t
e
rs
variations [6]
-[8]
.
The
st
at
or resi
st
ance i
d
ent
i
f
i
cat
i
on
m
e
t
hods are by
far t
h
e m
o
st
frequent
l
y
m
e
t
and
i
t
i
n
cl
udes al
l
t
h
e
est
i
m
at
ors where an
updat
e
d st
at
or resi
st
ance
val
u
e
i
s
obt
ai
ned t
h
rough an
adapt
i
v
e m
echani
s
m
[9]
-[19]
.
Proport
i
onal
i
n
t
e
gral
(PI)
or i
n
t
e
gral
(I)
cont
rol
l
e
rs are
used for t
h
i
s
purpose. In pri
n
ci
pl
e,
t
w
o di
st
i
n
ct
sub-
categ
o
r
ies ex
ist. In
o
b
s
erv
e
r b
a
sed
system
s [1
1
]
-[1
2
]
, [1
5
]
,
[1
8
]
-[1
9
]
th
e
erro
r q
u
a
n
tity, wh
ich
serv
es as
an
i
nput
i
n
t
o
t
h
e
st
at
or resi
st
ance
adapt
a
t
i
on m
echani
s
m
,
i
s
det
e
rm
i
n
ed
wi
t
h
t
h
e
di
fference bet
w
een t
h
e
m
easured and t
h
e observed st
at
or current
.
In
MRAS b
a
sed
system
s [9
]-[1
0
]
, [1
3
]
-[1
4
]
, [1
6
]
-[1
7
]
th
e ch
o
i
ce o
f
th
e erro
r q
u
a
n
tity is
m
o
re
v
e
rsatile.
Th
e sch
e
m
e
o
f
[9
]
o
p
e
rates in
th
e
ro
tatin
g
referen
ce
fram
e
an
d
th
e
erro
r q
u
a
n
tity
is d
e
term
in
ed
with
t
h
e
di
fference bet
w
een
t
h
e rot
o
r
fl
ux d-axi
s
com
ponent
s obt
ai
ned
from
t
h
e
vol
t
a
ge and
current
m
odel
s
. The
m
e
thod of [10] is sim
ilar, except th
at it utilizes the rotor flux reference
and
only
one estim
ate of the rotor flux
d-axis com
ponent inform
ation of the
error quantity. The error quantity in
[13]
is
based on active power, while
t
h
e one i
n
[14]
i
s
obt
ai
ned as
a sum
of t
h
e product
s
of rot
o
r
current
and rot
o
r fl
ux d-q axi
s
com
ponent
s.
The
error
signal of
[17] utilizes an
erro
r in
the stator d-axis
current com
ponent
as the input
of the integral
co
n
t
ro
ller,
wh
ile th
e erro
r q
u
a
n
tity o
f
[1
8
]
is fo
rm
ed
in
su
ch
a way th
at th
e stato
r
resistan
ce id
en
tificatio
n
is
i
ndependent
of t
h
e t
o
t
a
l
l
eakage i
nduct
a
nce. From
t
h
e
poi
nt
of vi
ew of t
h
e m
e
t
hod of st
at
or
resi
st
ance
i
d
ent
i
f
i
cat
i
on proposed
i
n
t
h
i
s
paper, especi
al
l
y
re
l
e
vant
are
t
h
e M
R
AS
schem
e
s of
[9]
-[10]
, [16]
, as
di
scussed short
l
y
.
This
paper presents a m
odel reference adaptive syst
em
wo
rk
in
g
in
p
a
rallel with
a p
a
rticu
l
ar ad
ap
tiv
e
sch
e
m
e
. Th
is sch
e
m
e
is ab
le to
estim
ate eith
er th
e
m
o
to
r resistiv
e p
a
ram
e
ters o
r
th
e ro
to
r sp
eed
. Th
u
s
,
th
e
M
R
AS
al
l
o
w obt
ai
ni
ng
robust
rot
o
r fl
ux
est
i
m
at
i
on. M
o
re
over,
t
h
e confi
gurat
i
on wi
t
h
t
h
e adapt
i
v
e schem
e
for the estim
ation of stator resistance value allows to
im
plem
ent high accurate speed
controls, where there
is
t
h
e
need t
o
have const
a
nt
l
y
t
h
e ri
ght
val
u
es of
t
h
es
e param
e
t
e
rs t
o
preserve hi
gh l
e
vel
perform
ances. On t
h
e
ot
her hand, t
h
e confi
gurat
i
on wi
t
h
t
h
e rot
o
r speed est
i
m
at
i
on can be used for t
h
e i
m
pl
em
ent
a
t
i
on of
a
sensorl
e
ss cont
rol
.
Fi
nal
l
y
,
t
h
e val
i
d
i
t
y
of t
h
e
proposed al
gori
t
h
m
s
i
s
veri
fi
ed
by
m
eans
of si
m
u
l
a
t
i
on
and
experi
m
e
nt
al
resul
t
s
.
2.
SENSORLESS VECTOR CONTROL
r
ˆ
sl
ˆ
e
ˆ
r
ˆ
r
ˆ
r
r
s
R
*
r
Fi
gu
re
1.
B
l
oc
k
di
ag
ram
of s
e
ns
orl
e
ss
vect
o
r
c
ont
r
o
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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088
-86
94
I
J
PED
S
Vo
l. 4
,
No
. 2
,
Jun
e
2
014
:
19
2
–
20
3
19
4
Vect
or cont
rol
i
s
a m
e
t
hod
t
h
at
separat
e
s t
h
e
fl
ux and
t
o
rque current
s so
as t
o
l
i
n
earl
y
cont
rol
t
h
e
out
put
t
o
rque of an i
nduct
i
on m
o
t
o
r.
As such, vect
or
cont
rol
requi
res preci
se
knowl
e
dge of t
h
e angl
e of
rot
o
r
flu
x
.
No
rm
ally, with
v
ecto
r
co
n
t
ro
l,
th
e an
g
l
e
o
f
ro
to
r flu
x
is in
d
i
rectly
estim
ated
u
s
in
g
th
e m
o
to
r sp
eed
m
easured from
a
speed sensor at
t
ached
t
o
t
h
e rot
o
r
sh
aft
.
Al
t
hough a
vect
or cont
rol
l
e
r usi
ng
a speed
sensor
can accurately control a servo system
, various problem
s occurs as a resu
lt of the speed sensor. Therefore,
sensorl
e
ss vect
or cont
rol
,
whi
c
h can
cont
rol
t
h
e t
o
rque
wi
t
hout
a
speed sensor, has
becom
e
an
i
m
port
a
nt
research topic.
Al
t
hough
m
a
ny
m
e
t
hods
have
al
ready
been
proposed for speed est
i
m
at
i
on, t
h
e M
R
AS approach i
s
t
h
e m
o
st
attractive
m
e
thod because
in this m
e
thod,
the m
odels
are
sim
p
le and very
easy to im
plem
ent
[20]. Figure 1
shows a bl
ock
di
agram
of
a sensorl
e
ss
vect
or cont
rol
l
e
r
wh
ere estim
ated
speed is
used
for
the vector
control.
The
cont
rol
schem
e
of
i
nduct
i
on m
o
t
o
r dri
v
e
consi
s
t
s
of t
h
e
m
odel
i
ng of t
h
e
i
nvert
er, sensorl
e
ss cont
rol
al
gori
t
h
m
and t
h
e overal
l
sy
st
em
cont
rol
l
e
r, whi
c
h are di
scussed i
n
t
h
e fol
l
o
wi
ng subsect
i
ons.
2.
1. FST
P
I
T
o
pol
o
g
y
And
S
p
ace Vec
t
or
A
n
al
ysi
s
The FSTPI t
opol
ogy
consi
s
t
s
of
4 power swi
t
c
hes
t
h
at
provi
de
t
w
o of t
h
e
i
nvert
er out
put
phases.
Th
e th
ird
p
h
a
se is fed
b
y
th
e d
c
lin
k
fro
m
th
e cen
ter o
f
a sp
lit-cap
acito
r b
a
n
k
,
as sh
o
w
n
in
Fig
u
r
e 2
Fi
gu
re
2.
P
o
we
r C
i
rc
ui
t
of
4
-
s
w
i
t
c
h
3-
p
h
ase i
nve
rt
er
W
ith
resp
ect to
th
e
circu
it o
f
Fig
u
r
e
2
,
t
h
e phase vol
t
a
ges
at
t
h
e 3-phase
l
o
ad t
e
rm
i
n
al
s depend
on
t
h
e conduct
i
ng st
at
es of t
h
e power swi
t
c
hes. The cal
cul
a
t
i
ons of phase vol
t
a
ges are present
e
d i
n
Tabl
e 1.
Tabl
e
1. T
h
e
v
a
l
u
es
of
Li
ne-
z
ero
& Li
ne-
n
e
u
t
r
al
l
o
a
d
v
o
l
t
a
ges i
n
F
S
TP
I
Switch
on Vector
V
bo
V
co
V
an
V
bn
V
cn
3
5
1 1
V
dc
V
dc
-V
dc
/3 V
dc
/6 V
dc
/6
6
2
0 0
0
0
V
dc
/3 -V
dc
/6 -V
dc
/6
3
2
1 0
V
dc
0
0
V
dc
/2 -V
dc
/2
5 6
0 1
0
V
dc
0
-
V
dc
/2 V
dc
/2
The resultant space vector of the
inverter output voltage is calcula
ted using the following equations:
cn
V
2
a
an
aV
an
V
3
2
s
V
(
1
)
q
jV
d
V
s
V
(
2
)
The voltage space vector can be com
puted
with the aid of the gating signals S3
and S5:
5
S
2
a
aS
dc
V
3
2
s
V
3
5
.
0
(
3
)
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9
4
C
ont
r
o
l
of
Fo
u
r
Sw
i
t
c
h
Th
ree
Ph
ase
Invert
e
r
Fed
I
n
d
u
ct
i
o
n
Mot
o
r
Dri
ves
Base
d
Spee
d
…
(
M
. K
.
Met
w
a
l
l
y
)
19
5
W
h
ere a=
3
/
2
j
e
Thus, t
h
e ort
hogonal
com
ponent
s V
d
and V
q
are:
)
5
3
1
(
3
1
S
S
dc
V
d
V
(
4
)
)
5
3
(
3
1
S
S
dc
V
q
V
(
5
)
The num
erical calculation of the V
d
and V
q
, lead
s to
th
e fo
llo
win
g
im
p
o
r
tan
t
facts:
a)
The discrete voltage space vector
has four ac
tive vectors (unlike
the
six switch three
phase
i
nvert
er (SSTPI) whi
c
h has 6-act
i
v
e vect
ors wi
t
h
equal
m
a
gni
t
ude).
b)
These vect
ors have unequal
m
a
gni
t
udes.
c)
No zero vect
ors are found (unl
i
k
e t
h
e SSTPI i
nvert
er t
h
at
has 2-zero vect
ors).
Figure 3 shows the equivalent discrete volta
ge space vector of the FSTPI topology.
Fi
gu
re
3.
Eq
ui
val
e
nt
act
i
v
e
v
o
l
t
a
ge
vect
o
r
s
of
(F
STP
I
)
2.
2.
Speed Estimation Sc
he
me Base
d
on
MRAS
The speed estim
ator,
analyzed
in this
paper, is
the one origina
lly
proposed in [21]
and illustrated
in
Fi
gure
4, where t
h
e t
w
o l
e
ft
-hand si
de bl
ocks perform
i
n
t
e
grat
i
on of Equat
i
on (6) and (7). It
rel
i
e
s on
m
easured stator currents and
m
easured
st
at
or vol
t
a
ges and
i
s
com
posed of t
h
e
reference (vol
t
a
ge) and
t
h
e
adjust
abl
e
(current
) m
odel
.
The est
i
m
at
or ope
rates in the stationary
reference fram
e
(
α
,
β
) and i
t
i
s
descri
bed
wi
t
h
t
h
e fol
l
o
wi
ng equat
i
ons [21]
:
s
s
i
p
s
L
s
R
s
s
u
m
L
r
L
s
rV
p
)
ˆ
(
ˆ
(
6
)
s
rI
j
r
T
s
s
i
r
T
m
L
s
rI
p
ˆ
ˆ
1
ˆ
(
7
)
e
p
I
K
p
K
ˆ
(
8
)
rV
rI
rV
rI
s
rV
s
rI
e
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
(
9
)
A hat above a sym
bol in (6)-(9) de
notes estim
ated quantities, sym
bol
p
stands for
d
/
dt
,
Tr
is th
e
ro
to
r tim
e co
n
s
tan
t
an
d
)
/(
2
1
r
L
s
L
m
L
. All th
e p
a
ram
e
ters in
th
e m
o
to
r an
d
th
e estim
ato
r
are assu
m
e
d
to
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I
S
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:
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94
I
J
PED
S
Vo
l. 4
,
No
. 2
,
Jun
e
2
014
:
19
2
–
20
3
19
6
be
of t
h
e
sam
e
val
u
e,
except
for
t
h
e st
at
or resi
st
an
ce
(hence a
hat
above
t
h
e sy
m
bol
i
n
(6)). Underl
i
n
ed
variables are space vectors,
and sub-scripts
V
and
I
st
and for
t
h
e out
put
s of
t
h
e vol
t
a
ge (reference)
and
current
(adjust
a
bl
e) m
odel
s
, respect
i
v
el
y
.
Vol
t
a
ge, current
and fl
ux
are denot
ed wi
t
h
u
,
i
and
ψ
, respectively,
and subscri
p
t
s
s
and
r
st
and for st
at
or and rot
o
r,
resp
ectiv
ely. Su
p
e
rscrip
t
s
in space vector sym
bols denotes
the stationary
reference fram
e
.
As
is evident
from
(6)-(9) and
Figure 4, the
adap
tive m
echanism
(PI controller) relies
on an error
q
u
a
n
tity th
at rep
r
esen
ts th
e d
i
fferen
ce b
e
tween
th
e in
stan
tan
e
o
u
s
p
o
s
itio
n
s
o
f
th
e two
ro
to
r flu
x
estim
ates.
The second degree of freedom
, the difference in am
plit
udes of the two rotor flux estim
ates, is not
utilized.
Th
e p
a
rallel ro
to
r
sp
eed
an
d
stato
r
resistan
ce MRAS
estim
atio
n
sch
e
m
e
, wh
ich
will b
e
d
e
v
e
lo
p
e
d
in
th
e
n
e
x
t
section, will m
a
ke use of this second degree
of fr
eedom
to achieve sim
u
ltaneous estim
ation of the
two
q
u
a
n
tities. Th
e ro
le o
f
th
e referen
ce
an
d
th
e ad
j
u
stab
le m
o
d
e
l will b
e
in
terch
a
n
g
e
d
fo
r th
is p
u
r
p
o
s
e, sin
ce
th
e
rot
o
r fl
ux est
i
m
at
e of (7) i
s
i
ndependent
of st
at
or resi
st
ance.
s
s
U
s
s
I
)
,
(
ˆ
r
s
s
s
rI
T
i
)
,
,
,
(
ˆ
s
s
s
s
s
s
rV
R
i
u
s
rI
s
rV
ˆ
ˆ
e
Fi
gu
re
4.
B
a
si
c co
nfi
g
u
r
at
i
o
n
of
t
h
e
rot
o
r
fl
u
x
base
d
on
M
R
AS s
p
ee
d est
i
m
a
t
o
r
2.
3
.
Par
a
llel Rotor
Speed
an
d St
ator
Resis
t
ance es
timation
Parallel ro
to
r sp
eed
an
d
stato
r
resistan
ce estim
atio
n
sch
e
m
e
is b
a
sed
o
n
th
e co
n
cep
t o
f
h
y
p
e
rstab
ility
[21]
i
n
order t
o
m
a
ke t
h
e sy
st
em
asy
m
pt
ot
i
cal
l
y
st
abl
e
.
For t
h
e purpose of deri
vi
ng an adapt
a
t
i
on m
echani
s
m
it is v
a
lid
to
in
itially treat ro
to
r sp
eed
as a co
n
s
tan
t
p
a
ram
e
ter, sin
ce it ch
an
g
e
s
slo
w
ly co
m
p
ared
to
th
e
change i
n
rot
o
r fl
ux.
The st
at
or resi
stance
of the m
o
tor varies
with tem
p
er
at
ure, but
vari
at
i
ons are sl
ow
so
t
h
at
i
t
can be t
r
eat
ed as a
const
a
nt
param
e
t
e
r, t
oo. The confi
gurat
i
on of
t
h
e paral
l
e
l
rot
o
r speed and st
at
or
resi
st
ance
i
s
shown i
n
Fi
gure 5 and
i
s
di
scussed i
n
det
a
i
l
next
. Let
Rs
and
ω
denot
e t
h
e t
r
ue
val
u
es of t
h
e
stator resistance in the
m
o
tor and ro
tor
speed, respectively. Th
ese
are in general
different from
the
estim
ated
values. Consequently, a
m
i
sm
atch between the
estim
ated
and true
rotor flux space
vectors appears as
well.
Th
e erro
r eq
u
a
tio
n
s
fo
r th
e v
o
ltag
e
an
d
th
e cu
rren
t
m
o
d
e
l o
u
t
p
u
t
s can
th
en
b
e
written
as:
s
s
s
s
i
R
R
m
L
r
L
V
p
)
ˆ
(
(
1
0
a
)
V
j
V
s
rV
s
rV
V
ˆ
(10b)
s
rI
j
I
r
T
j
I
p
ˆ
ˆ
1
(
1
1
a
)
I
j
I
s
rI
s
rI
I
ˆ
(11b)
Sy
m
bol
s
s
rV
,
s
rI
in (10b), (11b) stand for true values
of the two rotor flux space vectors.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
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:
208
8-8
6
9
4
C
ont
r
o
l
of
Fo
u
r
Sw
i
t
c
h
Th
ree
Ph
ase
Invert
e
r
Fed
I
n
d
u
ct
i
o
n
Mot
o
r
Dri
ves
Base
d
Spee
d
…
(
M
. K
.
Met
w
a
l
l
y
)
19
7
s
s
U
s
s
I
s
rI
ˆ
s
rV
ˆ
e
ˆ
s
s
I
U
s
I
Rs
e
s
R
ˆ
Fi
gu
re
5.
St
r
u
c
t
ure
of
t
h
e M
R
AS sy
st
em
of
p
a
rallel rot
o
r
speed a
n
d stator resistance estimation
The sy
st
em
i
s
hy
per-st
a
bl
e i
f
t
h
e i
nput
and
out
put
of
nonl
i
n
ear bl
ock sat
i
s
fy
Popov'
s cri
t
e
ri
on
[21]
.
The adaptive m
echanism
for ro
t
o
r
speed est
i
m
at
i
on and st
at
or resi
st
ance
i
d
ent
i
f
i
cat
i
on i
s
gi
ven i
n
(12),
(13)
respectively.
0
1
1
0
ˆ
.
.
ˆ
J
e
p
I
k
p
K
s
rI
J
T
I
p
I
k
p
K
(
1
2
)
s
R
e
p
s
IR
k
s
pR
K
s
i
T
V
p
s
IR
k
s
pR
K
s
R
.
ˆ
(
1
3
)
W
h
ere
k
p
ω
,
k
I
ω
,
k
pRs,
k
IRs
, are
PI controller param
e
ters of roto
r speed and stator resistance adaptation
m
echanism
s
respectively.
The role
of
th
e
referen
ce an
d
th
e
ad
j
u
stab
le m
o
d
e
ls is
in
terch
a
n
g
eab
le in
th
e
p
a
rallel system
o
f
ro
to
r sp
eed
an
d
stator resistance
estim
ation. The
sp
eed and
stator resistance
can be
est
i
m
at
ed i
n
paral
l
e
l
usi
ng (12), (13)
at any speed.
The rotor
speed adaptation m
echanism
(1
2
)
is th
e sam
e
as
in the custom
ary
MRAS speed estim
ator
reviewed in Section
B. Stator
resistance adaptation
m
echanism
(13)
is,
at th
e first
sig
h
t
, sim
ilar to
th
e
o
n
e
o
f
[9
], [1
0
]
.
Ho
wev
e
r, stato
r
resistan
ce is
h
e
re estim
ated
in
th
e
statio
n
a
ry
referen
ce fram
e
(rath
er th
an
in
th
e ro
to
r
flu
x
o
r
ien
t
ed
referen
ce fram
e
), an
d
erro
r q
u
a
n
tity is
obtained
using two rotor flux space vect
or estim
ates (rather
than the refe
rence and a single estim
ated value,
as
in
[1
0
]
). Fu
rth
e
r, stato
r
resistan
ce an
d
ro
to
r sp
eed
estim
atio
n
o
p
e
rate in
p
a
rallel,
rath
er th
an
seq
u
e
n
tially as
in [16]. This is
enabled by utilizing
the second ava
ilable degree
of freedom
(the
difference in rotor
flux
am
pl
i
t
udes) i
n
t
h
e process of
stator resistance estim
ation.
3. SIM
U
L
A
T
I
ON
RES
U
LT
S
The proposed m
e
t
hod
was veri
fi
ed by
SIM
U
LINK/
M
A
TLAB
Program
.
The param
e
t
e
rs of
t
h
e
i
nduct
i
on
m
o
t
o
r used
i
n
t
h
e
si
m
u
l
a
t
i
on are
i
n
appendi
x I.
In al
l
si
m
u
l
a
t
i
ons, t
h
e
est
i
m
at
ed speed
was used for
vect
or cont
rol
l
e
r and present
e
d wi
t
h
t
h
e act
ual
speed for com
p
ari
s
on purpose.
Fi
gure 6 shows
t
h
e posi
t
i
on
waveform
s when
t
h
e
sensorl
e
ss posi
t
i
on
cont
rol
was
perform
ed usi
ng
the proposed m
e
thod
for FSTPI.
The position change
from
50°
to
100° at
t=2.5sec
and then
back to
50° at
=4sec.
The posi
t
i
on com
m
a
nd appl
i
e
d i
n
t
h
e posi
t
i
on cont
rol
l
e
r i
s
shown i
n
Fi
gure 6 upper di
agram
(bl
u
e) i
n
degrees the estim
ated
angle (red)
and the
actual rotor
a
ngl
e (bl
ack). The
l
o
ad t
o
rque
i
s
changed
from
0
t
o
100% rat
e
d at
t
=
1.5sec as shown i
n
Fi
gure 6 l
o
wer di
agra
m
.
The resul
t
s
show t
h
e robust
n
ess
of
t
h
e
sensorl
e
ss
posi
t
i
on cont
rol
duri
ng l
o
ad change
and posi
t
i
on change operat
i
ons.
Fi
gure
7 shows t
h
e act
ual
m
o
t
o
r
speed and est
i
m
at
ed speed duri
ng
l
o
ad change and posi
t
i
on change
operat
i
on (upper di
agram
)
and (l
ower
di
agram
)
show
s
t
h
e t
h
ree phase
m
o
t
o
r current
s
duri
ng t
h
e
sam
e
operat
i
on.
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
. 2
,
Jun
e
2
014
:
19
2
–
20
3
19
8
Fi
gu
re
6.
U
p
pe
r:
R
e
fere
nce
(
b
l
u
e),
est
i
m
a
t
e
d (re
d)
an
d act
ua
l
(bl
a
c
k
)
r
o
t
o
r
angl
es
i
n
°, L
o
wer:
t
o
r
que
cu
r
r
ent
iq
(A
)
Figure
7. Uppe
r: Act
u
al spee
d (black
)
an
d e
s
tim
a
ted speed
(
r
ed
) in
(
r
pm
),
Lo
wer: m
o
tor
cur
r
ents
Ia
bc i
n
(A
)
Fi
gu
re
8.
Act
u
al
st
at
or
resi
stance (blac
k
) and
estim
ated
st
ator resistance (red)
in
ohm
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
C
ont
r
o
l
of
Fo
u
r
Sw
i
t
c
h
Th
ree
Ph
ase
Invert
e
r
Fed
I
n
d
u
ct
i
o
n
Mot
o
r
Dri
ves
Base
d
Spee
d
…
(
M
. K
.
Met
w
a
l
l
y
)
19
9
Fi
gure
8 shows
t
h
e act
ual
st
at
or resi
st
ance
and t
h
e
est
i
m
at
ed resi
st
ance
usi
ng t
h
e proposed
estim
ation
algorithm
during
the tests de
picted
in Figure
6 in ohm
values
the
figure show the
accuracy of the
est
i
m
at
i
on al
gori
t
h
m
duri
ng l
o
ad
and posi
t
i
on change operat
i
ons.
Fi
gure
9 shows t
h
e speed waveform
s
when t
h
e sens
orl
e
ss speed cont
rol
was perform
ed at
very
l
o
w
speed operat
i
on.
The speed
change from
5rpm
t
o
50rpm
at
t=5sec. The
speed co
m
m
a
nd appl
i
e
d
i
n
t
h
e speed
cont
rol
l
e
r i
s
shown i
n
Fi
gure 9
upper di
agram
(red) i
n
rpm
t
h
e
est
i
m
at
ed speed (bl
u
e) and t
h
e act
ual
rot
o
r
speed (black). The
load torque
is changed from
0 to
90%
rat
e
d at
t
=
2sec as
shown i
n
Fi
gure
9 l
o
wer
di
agram
.
The resul
t
s
show t
h
e robust
n
ess
of t
h
e sensorl
e
ss sp
eed cont
rol
duri
ng l
o
ad change and speed
change
operat
i
ons at
very
l
o
w speed.
Fi
gu
re
9.
U
p
pe
r:
R
e
fere
nce
(
r
e
d)
, est
i
m
at
ed (bl
u
e) a
n
d act
u
a
l (blac
k
)
r
o
to
r
spee
ds i
n
rpm
,
Lo
wer: t
o
r
q
ue
current i
q
(A)
Figu
re 1
0
. U
p
p
e
r:
Act
u
al
r
o
to
r
a
ngle (blac
k
)
and
estim
at
ed r
o
to
r a
ngle
(re
d
)
in
°,
Lo
we
r:
Actual
rot
o
r
fl
ux
angle
(black) a
n
d estim
a
t
ed ro
to
r fl
ux
an
gle
(re
d)
in
°
Fi
gu
re
1
0
(
u
pp
er
di
agram
)
sh
ows
t
h
e
act
ual
rot
o
r
a
n
gle (bl
ack) and estimate rot
o
r a
n
gle
(re
d) duri
ng
l
o
ad
an
d s
p
ee
d c
h
a
nge
at
ve
ry
l
o
w s
p
ee
d
ope
rat
i
o
ns
als
o
the act
ual rot
o
r flux angle
(black) a
n
d estimated
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
. 2
,
Jun
e
2
014
:
19
2
–
20
3
20
0
rot
o
r fl
u
x
an
gle (re
d) a
r
e sh
o
w
n i
n
(lo
w
e
r
d
i
agram
)
.
The a
c
tual and e
s
timated angle are coincide
nce t
o
eac
h
ot
he
r whe
r
e t
h
e err
o
r i
s
ap
pr
o
x
i
m
at
el
y zero d
u
r
i
n
g l
o
a
d
cha
nge a
nd
spee
d ope
rat
i
o
ns w
h
i
c
h en
su
re t
h
e
effect
i
v
e
n
ess
o
f
t
h
e
p
r
o
p
o
se
d
m
e
t
hod at
ve
ry
l
o
w
sp
eeds
.
Figu
re 1
1
s
h
o
w
s the m
o
tor
cur
r
ent in t
h
e
stationary
re
fe
rence
fram
e
(
α
,
β
) (
u
ppe
r
di
ag
ram
)
and t
h
e
three
phase m
o
tor c
u
rre
n
ts Ia
bc (lower dia
g
ra
m
)
.
Figu
re
1
1
.
U
p
p
e
r: m
o
tor cu
rr
e
n
t in
stationa
ry
refe
re
nce f
r
am
e (
αβ
)
in
(A
),
Lo
wer: m
o
tor
cur
r
ents
Ia
bc i
n
(A
)
4.
EX
PERIMENTAL RESULTS
The experim
e
ntal setup is carried
out by a DSpace
1103 system
with
I/O
card for real tim
e
control
(sam
pling tim
e:
Ts= 5e-5).
An interface
board was
build
to receive
the gate-drive
signal, isolated
them
and
connect
ed
t
o
t
h
e four swi
t
c
hes whi
c
h were i
m
pl
em
ent
e
d
usi
ng i
n
t
e
grat
ed IGB
T
100A. The out
put
from
FSTPI
was connect
ed
t
o
a
t
h
ree phase
i
nduct
i
on m
o
t
o
r. The
experi
m
e
nt
al
resul
t
s
shown are
from
t
h
e IM
dri
v
e coupl
ed t
o
a separat
e
l
y
exci
t
e
d DC
generat
o
r works as a l
o
ad as shown i
n
Fi
gure 12. The m
achi
n
e was
operated
under sensorless position
and sp
eed control
algorithm
.
The torque
is applied by
the DC generator
under torque controlled
m
ode. An op
tional position
signal is
available
fro
m
an encoder with
1024 pulses
per
revol
ut
i
on.
Fig
u
r
e
12
. Exper
i
m
e
n
t
al Setu
p
Fig
u
re 13
sh
ows th
e d
y
n
a
mic b
e
h
a
v
i
ou
r
o
f
sen
s
o
r
less
p
o
s
ition
con
t
ro
l at 6
0
%
rated
lo
ad
wit
h
chan
ge i
n
p
o
si
t
i
on o
f
± pi
/
3
rad
.
The de
vi
a
t
i
on be
tween
actu
al an
d
estimated
ro
to
r
po
sitio
n
is abou
t
±
1°
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I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
C
ont
r
o
l
of
Fo
u
r
Sw
i
t
c
h
Th
ree
Ph
ase
Invert
e
r
Fed
I
n
d
u
ct
i
o
n
Mot
o
r
Dri
ves
Base
d
Spee
d
…
(
M
. K
.
Met
w
a
l
l
y
)
20
1
mech
an
ical during
transien
t
p
o
s
ition
ch
ange an
d
zero
in
stead
y state as sh
own
in
th
e lo
wer d
i
ag
ram
.
Th
e
respon
se ti
m
e
is li
mited
b
y
t
h
e b
a
n
d
wid
t
h
o
f
th
e sp
eed
co
n
t
ro
ller. Th
e
p
o
s
ition
con
t
ro
ller is p
r
opo
rtio
n
a
l
o
n
l
y. Good
p
e
rform
a
n
ce o
f
the syste
m
is ach
iev
e
d
n
o
ting
the cu
rren
t con
t
ro
ller li
m
ita
tio
n
to
ab
ou
t 100
% lo
ad
cur
r
ent
i
m
pose
d
by
t
h
e i
nve
r
t
er as s
h
ow
n i
n
t
h
e
m
i
ddl
e d
i
agram
of Fi
g
u
re
1
5
.
It
s
h
o
u
l
d be
n
o
t
e
d
t
h
at
t
h
e
resu
lts
p
r
esen
t
e
d
ind
i
cate th
e
p
o
t
en
tial o
f
th
e m
e
th
o
d
in
com
b
in
atio
n
with th
e si
g
n
a
l
p
r
o
c
essin
g
.
Fig
u
re
13
.
Senso
r
less po
sition
co
n
t
ro
l at
60% lo
ad
an
d ch
an
g
e
in
po
sitio
n of ± p
i/3 rad
.
Upp
e
r: Referen
ce
rot
o
r a
n
gle (bl
u
e), estim
ated rot
o
r a
n
gle (green), a
n
d actua
l rot
o
r a
n
gle (red); L
o
wer: e
r
ror bet
w
een actual
and estim
a
t
ed rotor a
ngles i
n
(°)
Fi
gu
re
1
4
.
U
p
p
e
r:
R
e
fere
nce
f
l
ux a
n
gl
e (se
n
s
o
r
-
ba
sed
)
(re
d)
, an
d e
s
t
i
m
a
t
e
d sens
orl
e
ss
fl
u
x
a
ngl
e
(
g
ree
n
)
,
Lower: e
r
ror between
refe
re
nce and estim
ated a
ngles
(°)
Fig
u
r
e
14
upper
d
i
agr
a
m
sh
o
w
s t
h
e co
m
p
ar
ison
b
e
t
w
een
th
e actu
a
l ro
tor
f
l
ux
ang
l
e (
r
e
d)
and
est
i
m
a
t
e
d rot
o
r
fl
u
x
a
ngl
e
(
g
r
een)
d
u
ri
ng
t
h
e t
e
st
depi
ct
e
d
i
n
Fi
gu
re
13
t
h
e er
r
o
r
bet
w
e
e
n t
h
e
t
w
o a
n
gl
e i
s
sh
own
in lower
d
i
ag
ram
±
2 degrees which confirm
the
effectiv
eness
o
f
t
h
e
use
d
c
ont
r
o
l
m
e
t
hod
.
Evaluation Warning : The document was created with Spire.PDF for Python.