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
. 31
5
~
32
5
I
S
SN
: 208
8-8
6
9
4
3
15
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
Speed Sensorless Vector Control
of Induction Motor Drive with
PI and F
u
zzy Controll
er
R
.
G
u
na
ba
lan*
,
V
.
S
u
b
b
i
ah*
*
* Depart
em
ent o
f
El
ectr
i
c
a
l
and
Ele
c
troni
cs
Eng
i
neering
,
Dr
. Siv
a
nthi Aditan
a
r C
o
lleg
e
of
Engin
e
ering, Tiruchend
u
r
** Depart
em
ent
of El
ectr
i
c
a
l
and
El
ectron
i
cs
Eng
i
n
eer
ing, PSG Colleg
e
of
Techno
log
y
, Co
imbator
e
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Sep 12, 2014
Rev
i
sed
D
ec 25
, 20
14
Accepte
d Ja
n
8, 2015
This paper d
i
rected th
e speed-sensorl
ess vector
control of
induction motor
drive wi
th P
I
an
d fuzz
y
contro
ll
ers
.
Natural obs
erver with fourth order state
s
p
ace m
odel is
em
plo
y
ed to e
s
tim
ate the s
p
e
e
d and rotor fl
uxes
of the
induction motor
.
The formation
of the na
tural o
b
server is similar to and as
well as its at
tr
ibute is id
enti
c
a
l to th
e indu
ction m
o
tor. L
o
ad torque
adapt
a
tion is
provided to es
tim
ate the torqu
e
a
nd rotor s
p
eed is
es
tim
ated
from the load torque, rotor
flu
x
es and stator
currents.
Ther
e
is no direct
feedback in
natu
ral observ
e
r and
also obs
erver
gai
n
m
a
trix is
absen
t
. Both
th
e
induction m
o
tor
and the observ
e
r are
char
ac
ter
i
zed b
y
st
ate
space m
ode
l
.
Simple fuzzy
lo
gic contro
ller and conve
ntion
a
l PI controllers
are used to
control th
e speed of the ind
u
ction motor in closed loop. MATLAB
simulations ar
e
made with PI
and fuzz
y
contro
llers and
the perf
ormance of
fuzz
y contro
ll
er
is better than
PI cont
roller in
view of torque ripples. Th
e
sim
u
lation result
s are obtained f
o
r vari
ous running conditions to
exhibit the
suitability
of this method for se
nsorless
vector
control. Exper
imental results
are provid
e
d f
o
r natual obser
ver based sens
orless vector
control with
conventional PI
controller.
Keyword:
Fuzzy c
ont
roll
er
I
ndu
ctio
n m
o
to
r
Natural ob
server
Sens
orl
e
ss
co
n
t
rol
Si
m
u
latio
n
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
:
R
.
G
u
n
a
bal
a
n,
Depa
rtem
ent of Electrical a
n
d
El
ect
ro
ni
cs E
n
gi
nee
r
i
n
g,
Ch
and
y
Co
llege of
En
g
i
n
eer
i
n
g, Tho
o
t
h
ukud
i 628
005
Ann
a
Un
iv
ersity,
Ch
en
n
a
i, TamilNad
u
,
INDIA.
Em
ail: guna
balanr@yahoo.co.in
1.
INTRODUCTION
In
d
u
ct
i
on m
o
t
o
rs are
pre
f
er
r
e
d fo
r m
o
st
of t
h
e i
ndust
r
y
appl
i
cat
i
o
ns be
cause o
f
t
h
e l
i
m
i
t
a
t
i
ons of
com
m
ut
ati
on and
rot
o
r s
p
eed
i
n
DC
dr
i
v
es. Th
e in
du
ction
m
o
to
r is in
fact
'b
ru
sh
less' an
d
can
op
erate with
sim
p
le control
m
e
thods not re
qui
ring a shaft
position tr
a
n
s
duce
r
.
W
i
t
h
no shaft position
feedbac
k
, the m
o
tor
rem
a
ins stable
only as long
as the
load torque
does not
exceed t
h
e brea
kdown torque
. At low s
p
eeds it is
p
o
s
sib
l
e
for
oscillato
ry in
stab
ilities to
d
e
velo
p
.
To
o
v
e
rco
m
e th
ese limita
tio
n
s
'field
-o
rien
ted
'
or
'v
ecto
r
'
cont
rol
has
be
en
devel
ope
d i
n
whi
c
h t
h
e
p
h
ase a
n
d
m
a
gni
t
ude
o
f
t
h
e
s
t
at
or c
u
r
r
ent
s
are re
g
u
l
a
t
e
d s
o
as t
o
main
tain
th
e op
ti
m
u
m
an
g
l
e
b
e
tween
stator
mmf an
d
ro
to
r
flux
. Th
is con
t
ro
l is b
a
sed
on
tran
sform
i
n
g
a th
ree
pha
se t
i
m
e
and fr
eq
ue
ncy
d
e
pen
d
e
n
t
sy
st
em
i
n
t
o
a t
w
o co-
o
r
d
i
n
at
e (
d
and
q axes
) t
i
m
e
i
nvari
ant
sy
st
em
.
These
projections
lead to a
struct
ur
e similar to
th
at of a sep
a
rately ex
cited
DC mo
tor con
t
ro
l.
Field
o
r
ien
t
atio
n
,
h
o
wev
e
r, requ
ires eith
er a sh
aft
p
o
s
ition
en
cod
e
r
o
r
an
in-b
uilt co
n
t
ro
l m
o
d
e
l wh
o
s
e p
a
rameters
are s
p
ecific to the m
o
tor.
Gene
ral
l
y
, t
w
o
t
y
pes o
f
fi
el
d
ori
e
nt
ed c
ont
ro
l
schem
e
s are avai
l
a
bl
e.
1.
D
i
rect
fi
el
d o
r
i
e
nt
ed c
o
nt
ro
l
2
.
In
d
i
rect field
o
r
ien
t
ed
co
n
t
ro
l. In
th
e d
i
re
ct sch
e
m
e
,
th
e in
stan
tan
e
ou
s p
o
s
ition
of ro
to
r fl
u
x
(
θ
e
) ha
s
t
o
be
m
easured
u
s
i
n
g fl
ux
se
nso
r
s
.
Thi
s
ad
ds t
o
t
h
e c
o
st
and
co
m
p
lex
ity o
f
th
e
d
r
iv
e syste
m
. In
the ind
i
rect
schem
e
, a
m
o
d
e
l
of t
h
e i
n
duc
t
i
on m
o
t
o
r i
s
r
e
qui
red t
o
cal
c
u
l
a
t
e
t
h
e re
fere
nce a
n
g
u
l
a
r sl
i
p
f
r
e
que
ncy
t
h
at
has
to
b
e
add
e
d
to
th
e m
easu
r
ed
ro
tor sp
eed. The su
m
is in
teg
r
ated
to
calcu
late th
e in
stan
tan
e
ou
s
po
sitio
n o
f
th
e
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 :
3
15 –
32
5
31
6
rot
o
r fl
ux
. Rot
o
r tim
e consta
nt (L
r
/R
r
) is u
s
ed
to
calcu
late th
e slip
frequen
c
y an
d
is sen
s
itiv
e to
te
m
p
eratu
r
e
and
fl
u
x
l
e
vel
.
To a
voi
d t
h
es
e com
p
l
i
cat
i
ons, di
f
f
er
en
t algorithm
s
are projecte
d
,
t
o
estimate both the
rot
o
r
fl
u
x
vect
or a
n
d/
o
r
r
o
t
o
r s
h
aft
spee
d. T
h
e i
n
duct
i
o
n m
o
tor
dri
v
es wit
h
out
mechanical speed se
ns
ors
ha
ve the
attractio
n
s
o
f
l
o
w co
st, h
i
g
h
reliab
ility, s
m
a
ller in
size
and
lack
of ad
d
i
t
i
o
n
a
l
wiri
ng
for
sen
s
ors o
r
d
e
v
i
ces
m
ount
ed
on
t
h
e s
h
aft
.
N
o
w
a
day
s
, a
n
u
m
b
er
o
f
est
i
m
ati
on t
e
c
hni
que
s
are a
v
ai
l
a
bl
e fo
r s
p
ee
d a
n
d fl
u
x
calcu
latio
n
.
The stan
d
a
rd sp
eed
estim
a
t
o
r
s
are Ex
tend
ed
Kalm
an
Filter
(EKF) [1
]
–
[6
],
Lu
en
b
e
rger ob
serv
er
[7]
–
[
9
]
and M
odel
R
e
fe
renc
e Ada
p
t
i
v
e Sy
st
em
(M
R
A
S)
[1
0]
. The i
n
i
t
i
a
l
sel
ecti
on of
noi
se c
ova
r
i
ance
matrices is n
o
t
easy in
EKF and
su
bsequ
e
n
tly th
e algo
ri
t
h
m
is com
p
licated.
The selec
tion
of
th
e ob
serv
er g
a
in
co
nstan
t
is
d
i
fficu
lt in
Lu
enb
e
rg
er ob
serv
er. Th
e
nu
m
b
er of
i
n
put
s t
o
t
h
e est
i
m
at
ors m
e
nt
i
oned
ab
o
v
e i
s
d
i
fferen
t
to
th
e n
u
m
b
e
r o
f
inpu
ts to
th
e in
ductio
n
m
o
to
r sin
ce th
ey u
tilize o
u
t
pu
t feed
back
. To
ov
ercome th
e
d
i
fficu
lties o
f
th
e abov
e estimato
r
s, natu
ral o
b
s
erv
e
r
p
r
o
p
o
s
ed
i
n
[11
]
is u
s
ed in
this p
a
p
e
r.
In
natu
ral
obs
erver, the dynamic behavi
or is exactly the sa
m
e
as
the
m
o
tor and there is no externa
l
feedbac
k
. T
h
e load
to
rq
u
e
ad
ap
tatio
n
is u
s
ed
to
esti
m
a
te
th
e lo
ad
to
rqu
e
from the active powe
r
erro
r. Fi
fth orde
r state space
m
o
d
e
l
was u
s
ed
in
[11
]
whereas fourth
ord
e
r in
du
ction
m
o
to
r
m
o
d
e
l is u
s
ed
in
th
is p
a
p
e
r to
reduce th
e
com
put
at
i
onal
bu
r
d
en
an
d t
h
e
eq
uat
i
o
n
s
are
sim
i
l
a
r t
o
Lue
n
ber
g
er
o
b
se
rve
r
.
Recent de
velopm
ents in the application of
cont
rol th
e
o
ry are suc
h
t
h
at the conventi
onal technique
s
for th
e d
e
si
gn
o
f
co
n
t
ro
llers
are b
e
ing
rep
l
aced
b
y
artificial in
tellig
en
ce
based
con
t
ro
llers. Th
e m
a
in
p
u
rpo
s
e
o
f
u
s
ing
artificial in
tell
ig
ence b
a
sed
con
t
ro
llers is
t
o
reduce the t
u
ning effo
rts a
ssociated
with the
con
v
e
n
t
i
onal
PI c
ont
r
o
l
l
e
rs
and
al
so t
o
obt
ai
n
t
h
e improved
res
p
onses. PID c
o
ntrollers a
r
e c
o
mmonly
in
ten
d
e
d
fo
r li
n
ear
syste
m
s an
d th
ey
provi
de a prefe
r
able
cost/be
n
efit ra
t
i
o [12].
Howe
ver, the
presence of
n
o
n
lin
ear effects li
m
i
ts th
eir perfo
r
m
a
n
ces.
Fuzzy
l
ogi
c c
ont
rol
l
e
rs (
F
L
C
’s) ha
ve t
h
e fol
l
o
wi
n
g
ad
v
a
nt
ages o
v
e
r
t
h
e co
nve
nt
i
o
n
a
l
cont
r
o
l
l
e
rs
[13
]
: th
ey are ch
eap
er to d
e
v
e
l
o
p, th
ey co
v
e
r
a wid
e
r
rang
e
o
f
op
erating
con
d
ition
s
, and
t
h
ey are m
o
re
read
ily
cu
sto
m
izab
le in
n
a
tural languag
e
term
s. App
licatio
n
o
f
PI-typ
e
fu
zzy con
t
ro
ller in
creases th
e
qu
ality facto
r
.
In
con
t
rast wit
h
trad
itio
n
a
l lin
ear and
non
lin
ear con
t
ro
l theo
ry, a
FLC is n
o
t
b
a
sed
o
n
a
m
a
th
e
m
atica
l
m
o
d
e
l
an
d is
wid
e
ly used
t
o
so
lv
e
pro
b
l
em
s u
n
d
e
r
u
n
c
ertain
and
v
a
gu
e env
i
ro
nmen
ts, with h
i
g
h
non
lin
earities.
In t
h
is pa
pe
r,
natural observer with re
duce
d
or
der
state space m
odel is proposed t
o
e
s
tim
a
te the
spee
d o
f
t
h
e i
n
duct
i
o
n m
o
t
o
r
and
fu
zzy
co
nt
rol
l
e
r i
s
em
pl
oy
ed i
n
st
ead
of
con
v
e
n
t
i
onal
P
I
co
nt
r
o
l
l
e
r f
o
r
spe
e
d
co
n
t
ro
l. Mean v
a
lu
e of th
e
ro
t
o
r fl
u
x
is
main
tain
ed
con
s
tan
t
b
y
em
p
l
o
y
in
g
PI con
t
ro
ller in
th
e
ro
tor flux
feedb
a
ck
p
a
t
h
. Si
m
u
latio
n
s
are p
e
rfor
m
e
d
for d
i
fferen
t ru
nn
ing
cond
itio
ns
to
stud
y th
e p
e
rform
a
n
ce of fu
zzy
cont
rol
l
e
r
o
v
er
PI
co
nt
r
o
l
l
e
r.
Ex
peri
m
e
nt
al
resul
t
s
are
pro
v
id
ed
with PI co
n
t
ro
ller to
v
a
lid
ate th
e
p
r
o
p
o
s
ed
m
e
t
hod.
2.
NAT
UR
AL O
B
SERVE
R
The arra
ngem
e
n
ts and the characteristics of the na
tu
ral observ
e
r are simi
lar to
th
e in
d
u
ctio
n
m
o
to
r
for th
e
sp
ecified
inpu
t vo
ltag
e
and
lo
ad
torqu
e
co
nd
itio
n.
Th
e m
a
j
o
r d
i
fferen
ce
b
e
tween
th
e
n
a
tural
ob
serv
er
an
d th
e con
v
e
n
tio
n
a
l
ob
server is th
at
fee
d
back is em
ployed only in t
h
e ada
p
tation algorithm
and
no
direct
feedbac
k
. So,
the conve
r
ge
nce rate of the natural obse
r
ve
r is faster tha
n
that of
the
m
o
tor in reaching the
st
eady
st
at
e behavi
ou
r. T
o
est
i
m
a
t
e
t
h
e rot
o
r
speed
, fo
u
r
t
h
or
der i
n
d
u
ct
i
o
n
m
o
t
o
r m
odel
in st
at
or fl
ux
or
i
e
nt
ed
refe
rence frame is used in this pape
r, where
a
s fifth or
de
r state space
m
odel is used
in [11]. The dq-axes
stator
currents a
n
d
rotor
fluxes a
r
e c
onsi
d
ere
d
as
st
ate varia
b
les.
The state s
p
ac
e represe
n
tation
of t
h
e three-pha
se
in
du
ctio
n m
o
to
r is as fo
llo
ws:
A
X
B
V
(
1
)
YC
X
(
2
)
Whe
r
e,
R
R
L
L
σ
L
0
L
σ
L
L
τ
ω
L
σ
L
L
0
R
R
L
L
σ
L
ω
L
σ
L
L
L
σ
L
L
τ
L
τ
0
1
τ
ω
0
L
τ
ω
1
τ
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4
Spee
d
Se
ns
orl
e
ss Vect
or
C
o
nt
rol
of
I
n
d
u
ct
i
o
n M
o
t
o
r
Dri
v
e
w
i
t
h
PI
a
n
d
Fu
zzy C
o
nt
rol
l
e
r
(
R
. G
u
n
a
bal
an
)
31
7
1
σ
L
0
0
1
σ
L
00
00
1000
0100
σ
1
- lea
k
age
c
o
efficient
X
i
i
φ
φ
Y
i
i
i
V
V
V
L
s
, L
r
–
stator an
d ro
tor self ind
u
c
tan
ce
respectiv
ely (H)
L
m
- m
u
tual
inductance
(H)
τ
-r
ot
o
r
t
i
m
e const
a
nt
=
r
-m
o
t
o
r
angu
lar v
e
lo
city (rad
/s)
Fi
gu
re 1 s
h
ow
s t
h
e st
ruct
ure
of t
h
e
nat
u
ral
obs
er
ver a
nd t
h
e sy
st
em
descri
be
d by
E
q
u
a
t
i
on (
1
)
a
n
d
Equ
a
tio
n (2
)
are ex
actly the sam
e
fo
rm
o
f
th
e i
n
du
cti
o
n m
o
tor m
odel a
n
d no e
x
ternal
feedbac
k
[11].
Esti
m
a
tio
n
o
f
th
e stator cu
rren
ts an
d th
e
ro
t
o
r flux
es can be written
b
y
t
h
e fo
llo
wi
n
g
equ
a
tio
ns:
A
X
B
V
(
3
)
Y
C
X
(
4
)
X
ı
̂
ı
̂
φ
φ
Y
ı
̂
ı
̂
ı
̂
Wh
ere, “^” represen
ts th
e esti
mated
q
u
a
n
tities.
Th
e l
o
ad to
rque is esti
m
a
ted
fro
m
th
e activ
e
p
o
wer erro
r
b
y
th
e
fo
llowing
eq
u
a
tion
[1
1
]
:
T
K
e
K
e
dt
(
5
)
e
V
ı
̂
i
V
ı
̂
i
(
6
)
Ro
to
r sp
eed
is esti
m
a
ted
from
th
e esti
m
a
te
d
stator
cu
rrent, ro
t
o
r flux
and
th
e estim
a
t
e
d
lo
ad
t
o
rq
ue
an
d it is rep
r
esen
ted
as fo
llows [1
4
]
:
ω
φ
ı
̂
φ
ı
̂
(
7
)
Whe
r
e n
p
is th
e no
.
of
p
o
l
e
p
a
i
r
s an
d J is
of inertia o
f
m
o
to
r l
o
ad system
(k
g.m
2
).
.
Fi
gu
re 1.
St
r
u
c
t
ure of
a nat
u
ra
l
ob
ser
v
er
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,
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.
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uar
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201
5 :
3
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32
5
31
8
Fi
gu
re
2.
C
l
ose
d
l
o
o
p
se
ns
orl
e
ss spee
d
co
nt
r
o
l
of
i
n
duct
i
o
n
m
o
t
o
r dri
v
e
wi
t
h
f
u
zzy
c
ont
r
o
l
l
e
r
The cl
ose
d
l
o
o
p
st
r
u
ct
u
r
e o
f
t
h
e nat
u
ral
obs
erve
r i
s
sh
o
w
n
i
n
Fi
g
u
re
2. T
h
e m
a
i
n
co
m
pone
nt
s ar
e
:
n
a
tural o
b
serv
er with
ad
ap
tiv
e lo
ad
torqu
e
esti
m
a
tio
n
,
calculation bloc
ks
of refe
re
nce current val
u
es, PI/
f
uzzy
cont
rol
l
e
rs
an
d
cu
rre
nt
re
g
u
l
a
t
e
d p
u
l
s
e
wi
dt
h m
odul
at
e
d
(
C
R
P
W
M
)
v
o
l
t
a
ge s
o
urce i
n
v
e
rt
er.
The
s
p
ac
e vect
o
r
m
odel
of t
h
e i
n
duct
i
o
n m
o
t
o
r
i
s
use
d
t
o
de
ri
v
e
t
h
e e
quat
i
ons
f
o
r
i
∗
and
i
∗
and a
r
e as
follows
[14]:
V
i
R
p
φ
j
ω
φ
(8
)
V
i
R
p
φ
j
ω
φ
(9
)
0
i
R
p
φ
j
ω
ω
φ
(1
0)
0
i
R
p
φ
j
ω
ω
φ
(1
1)
φ
L
i
L
i
(1
2)
φ
L
i
L
i
(1
3)
φ
L
i
L
i
(1
4)
φ
L
i
L
i
(1
5)
T
3
2
P
2
L
L
φ
i
(1
6)
T
3
2
P
2
L
L
φ
i
φ
i
(1
7)
Fro
m
Equ
a
tio
n (1
0):
i
p
φ
j
ω
ω
φ
R
(1
8)
By su
b
s
titu
ting in
Equ
a
tio
n (14
)
:
φ
L
p
φ
j
ω
ω
φ
R
L
i
(1
9)
Furt
her
aft
e
r
si
m
p
li
fi
cat
i
on,
p
φ
S
j
ω
ω
φ
L
S
i
(2
0)
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S
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:
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6
9
4
Spee
d
Se
ns
orl
e
ss Vect
or
C
o
nt
rol
of
I
n
d
u
ct
i
o
n M
o
t
o
r
Dri
v
e
w
i
t
h
PI
a
n
d
Fu
zzy C
o
nt
rol
l
e
r
(
R
. G
u
n
a
bal
an
)
31
9
Si
m
ilarly,
p
φ
S
j
ω
ω
φ
L
S
i
(2
1)
From
Eq
uat
i
o
n
(
2
0
)
a
n
d
E
qua
t
i
on
(2
1)
, t
h
e
g
e
neral
e
q
uat
i
o
n
i
s
re
prese
n
t
e
d
as:
p
φ
S
j
ω
ω
φ
U
i
whe
r
e,
US
L
;
S
(2
2)
p
φ
dr
e
j
φ
qr
e
S
r
j
ω
e
ω
r
φ
dr
e
j
φ
qr
e
U
i
ds
e
ji
qs
e
(2
3)
Sepa
rating real
and im
aginary pa
rts,
p
φ
dr
e
S
r
φ
dr
e
ω
e
φ
qr
e
ω
r
φ
qr
e
Ui
ds
e
(2
4)
For
c
onst
a
nt
fl
ux
o
p
e
r
at
i
o
n
,
p
φ
dr
e
0 an
d
φ
qr
e
0 an
d
i
ds
e
is calcu
lated
as fo
llows:
S
r
φ
dr
e
∗
Ui
ds
∗
S
r
L
m
i
ds
e
∗
(2
5)
i
ds
e
∗
i
ds
e
∗
L
m
(2
6)
Tor
q
ue
devel
o
ped
i
n
a
n
i
n
d
u
c
t
i
on m
o
t
o
r
T
e
P
2
L
m
L
r
φ
r
i
s
(2
7)
T
e
P
2
L
m
L
r
φ
dr
e
i
qs
e
φ
qr
e
i
ds
e
(2
8)
i
qs
e
∗
cont
rol
s
t
h
e a
v
erage
t
o
r
q
ue
d
e
vel
o
ped
,
i
qs
e
∗
L
r
P
2
L
m
φ
dr
∗
T
∗
(2
9)
i
qs
e
∗
L
r
n
p
L
m
φ
d
r
∗
T
∗
wh
er
e
n
p
is th
e po
le p
a
i
r
(3
0)
i
ds
e
∗
i
s
ge
nerat
e
d
b
y
com
p
ari
n
g t
h
e act
ual
fl
ux
w
i
t
h
t
h
e
set
re
fer
e
nce
fl
u
x
an
d
t
h
e e
r
r
o
r i
s
gi
ve
n t
o
t
h
e
PI c
o
nt
r
o
l
l
e
r
whi
c
h
gi
ves
t
h
e desi
red
val
u
e o
f
i
ds
e
∗
.
In ad
d
ition
,
it m
a
in
tain
s
th
e m
ean
v
a
l
u
e
o
f
ro
tor flux
as
constant. T
h
e
refe
rence c
u
rre
n
ts are tra
n
sform
e
d
into stationa
ry
refe
re
nc
e fram
e
by
rotor a
ngle
θ
e
. The t
w
o
pha
se d
q
-a
xes
st
at
or cu
rre
nt
s
are t
r
an
sf
orm
e
d i
n
t
o
t
h
ree
ph
ase refe
rence c
u
r
r
ent
by
2 t
o
3 co
n
v
ersi
on
b
l
ock
s
(
i
nv
er
se Clar
k
e
’
s
tr
an
sf
or
m
a
t
i
o
n)
.
3.
FUZ
Z
Y
LOGIC
CONT
ROLLER
Fuzzy
l
o
gi
c can be
descri
bed
sim
p
l
y
as “com
put
i
ng
with
words rath
er than
nu
m
b
ers’’; “co
n
t
ro
l wit
h
sentences rat
h
er than equations
’’.
A f
u
zz
y
cont
rol
l
e
r i
n
cl
udes em
pi
ri
cal
rul
e
s and i
s
usef
ul
i
n
op
erat
o
r
co
n
t
ro
lled p
l
ants. Fu
zzy con
t
ro
l is preferred
wh
ere
robu
st
c
ont
rol
i
s
desi
re
d, part
i
c
ul
arly
with
p
l
an
t p
a
rameter
variations and load disturba
nce eff
ects
.
T
h
ere is no des
i
gn procedure
in
fuzzy control suc
h
as root-locus
d
e
sign
, freq
u
e
n
c
y respon
se
d
e
sign
,
p
o
l
e p
l
ace
m
e
n
t
d
e
si
gn
or stab
ility
marg
in
s,
b
ecau
s
e th
e ru
les are o
f
ten
no
nl
i
n
ea
r. F
u
z
z
y
cont
r
o
l
l
e
rs
are bei
ng
use
d
i
n
vari
o
u
s co
nt
r
o
l
schem
e
s. In t
h
i
s
w
o
r
k
,
di
rect
co
nt
r
o
l
i
s
use
d
,
wh
ere th
e fu
zzy co
n
t
ro
ller i
s
in
th
e
forward
p
a
th in
a
feedbac
k
cont
rol system
. The p
r
ocess
ou
t
put
i
s
com
p
ared
with a re
fere
nce, a
n
d if t
h
ere is
a de
viatio
n, the con
t
ro
ller tak
e
s action
acco
r
d
i
ng
t
o
th
e
co
n
t
ro
l
strateg
y
. Triang
u
l
ar m
e
m
b
er
fun
c
tion
s
were u
s
ed
in
m
o
st o
f
th
e literatu
res [15
]
-[16
] wh
ereas Gau
ssian
me
m
b
ersh
ip
fun
c
tio
ns are selected
in
t
h
is pap
e
r as
t
h
ey
a
r
e sm
oot
h a
n
d
n
onze
r
o
at
al
l
p
o
i
n
t
s
. T
h
e c
ont
ro
l
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I
S
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:
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l.
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,
No
.
3
,
Feb
r
uar
y
201
5 :
3
15 –
32
5
32
0
si
gnal
s
are
er
r
o
r
(E
) a
n
d c
h
a
nge
i
n
er
ro
r
(C
E).
The
f
u
zzy
cont
rol
l
e
r
f
u
zz
i
f
i
e
s t
h
e i
n
p
u
t
si
gnal
s
an
d
ge
nerat
e
s
t
h
e cont
r
o
l
si
g
n
al
t
h
ro
u
gh t
h
e
eval
uat
i
on
of
cont
rol
r
u
l
e
s and
def
u
zzi
fi
cat
i
on.
Al
l
t
h
e i
nput
and o
u
t
p
ut
si
gnal
s
use Ga
ussi
a
n
m
e
m
b
ershi
p
fu
nct
i
o
n
s
. M
a
m
d
ani
t
y
pe i
n
fe
re
nce m
e
t
hod an
d m
ean of m
a
xi
m
u
m
(Thi
s m
e
t
hod
disre
g
ards the
sha
p
e of the
fuzzy se
t, bu
t th
e co
m
p
u
t
ation
a
l co
m
p
lex
ity is relativ
ely g
o
od) d
e
fu
zzi
ficatio
n
m
e
t
hod a
r
e
use
d
. T
h
e l
i
ng
ui
st
i
c
m
e
m
b
ershi
p
fu
nct
i
o
ns a
r
e
n
e
gat
i
v
e l
a
r
g
e
(
N
L)
,
negat
i
v
e
sm
al
l
(NS)
, zer
o (
Z
),
p
o
s
itiv
e sm
all
(PS) an
d po
sitiv
e larg
e
(PL).
Th
e
r
u
le m
a
tr
i
x
fo
r fu
zzy con
t
ro
l is g
i
v
e
n
in
Ta
ble
1. As
exam
ple,
the cont
rol rules for E
and
CE
are:
1
.
If E is
Z an
d CE is Z t
h
en co
n
t
ro
l si
g
n
a
l is Z
2.
If
E i
s
PS a
n
d C
E
i
s
Z t
h
e
n
cont
rol
si
gnal
i
s
PS
3
.
If E is
Z an
d CE is
NS t
h
en con
t
ro
l sign
al
is NS
Th
e m
e
m
b
ersh
ip
fun
c
tion
s
for th
e in
pu
t v
a
riab
le er
r
o
r, c
h
ange i
n
e
r
r
o
r
and t
h
e c
o
nt
ro
l
si
gnal
are
sho
w
n i
n
Fi
gu
r
e
3.
Tabl
e
1. R
u
l
e
t
a
bl
e f
o
r
f
u
zzy
cont
rol
CE
E
NL
NS
Z
PS
PL
NL
NL
NL
NS
NS
Z
NS NL
NS
NS
Z
PS
Z NS
NS Z
PS
PS
PS NS
Z
PS
PS
PL
PL
Z
PS
PS
PL
PL
Fi
gu
re 3.
F
u
zz
y
m
e
m
b
ershi
p
fu
nct
i
o
ns
4
.
S
I
MU
LA
TIO
N
R
E
SU
LTS
AND
D
I
SCU
S
S
I
O
N
S
Sim
u
l
a
t
i
ons ar
e do
ne i
n
M
A
TLAB
si
m
u
l
i
nk atm
o
sp
here.
The si
m
u
l
a
t
i
on bl
ock
s
of se
ns
orl
e
ss
vect
or
cont
rol
are c
o
n
s
t
r
uct
e
d i
n
M
A
TLAB
u
s
i
n
g p
o
we
r sy
st
em
block
s
et
s an
d si
m
u
li
nk l
i
b
ra
ri
e
s
. Nat
u
ral
o
b
se
rve
r
i
s
u
s
ed
to estim
a
t
e th
e sp
eed,
ro
tor fl
u
x
e
s and
stator cu
rrents. Con
v
e
n
tional PI con
t
ro
ller an
d fu
zzy con
t
ro
lle
r
are inv
e
stig
ated
. Th
e sim
u
lat
i
o
n
resu
lts are p
r
esen
ted
fo
r
d
i
fferen
t
ru
nn
i
n
g
con
d
ition
s
. Th
e
ratin
g
s
an
d
t
h
e
param
e
t
e
rs o
f
t
h
e i
n
d
u
ct
i
o
n m
o
t
o
r are
gi
ve
n i
n
Ta
bl
e
2.
Di
re
ct
fi
el
d
ori
e
nt
ed se
ns
orl
e
ss
ve
ct
or c
o
nt
rol
sc
hem
e
is u
s
ed
and
the ro
t
o
r ang
l
e is d
e
term
in
ed
fro
m
th
e esti
m
a
ted
ro
to
r flux
es. Th
e to
rqu
e
ad
ap
tation
g
a
in
s are
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Spee
d
Se
ns
orl
e
ss Vect
or
C
o
nt
rol
of
I
n
d
u
ct
i
o
n M
o
t
o
r
Dri
v
e
w
i
t
h
PI
a
n
d
Fu
zzy C
o
nt
rol
l
e
r
(
R
. G
u
n
a
bal
an
)
32
1
K
p
=0.08, K
I
=
0
.2. Fi
gu
re 4 a
nd Fi
gu
re 5 s
h
o
w
t
h
e si
m
u
l
a
t
i
on di
ag
ram
of sens
o
r
l
e
ss
vect
or co
nt
r
o
l
of
in
du
ctio
n
m
o
to
r
d
r
i
v
e with
PI con
t
ro
ller an
d
fu
zzy
c
ont
roller re
specti
v
ely. The induction m
o
tor
and t
h
e
natural observer are built with state space m
odel a
nd are
const
r
ucte
d by MATLAB
functions. In addition,
vari
ous
si
m
p
le bl
oc
ks a
v
ai
l
a
bl
e i
n
si
m
u
l
i
nk a
r
e
use
d
t
o
co
nst
r
uct
t
h
e ent
i
r
e sy
st
em
. PI cont
r
o
l
l
er i
s
con
s
t
r
uct
e
d
us
i
ng P
I
D bl
ock
avai
l
a
bl
e i
n
s
i
m
u
l
i
nk l
i
b
ra
ri
es. Th
e si
m
u
l
a
t
i
on
bl
oc
ks o
f
fuzzy
c
ont
rol
l
er ar
e
con
s
t
r
uct
e
d i
n
M
A
TLAB
us
i
ng f
u
zzy
t
ool
bo
x. F
u
zzy
co
n
t
ro
ller is framed
with
5
lin
gu
istic v
a
riables to
gene
rate the re
qui
red to
rq
ue r
e
fere
nce sig
n
al from
the sp
eed error. It also reduces
t
h
e c
o
m
put
at
i
onal
b
u
r
d
e
n
in
real tim
e.
The si
m
u
l
a
ti
on
resul
t
s
of spe
e
d
sens
orl
e
ss
ve
ct
or co
nt
r
o
l
of
i
n
d
u
ct
i
on m
o
t
o
r dri
v
e wi
t
h
PI
cont
r
o
l
l
e
r
an
d
fuzzy sp
eed
con
t
ro
ller fo
r d
i
fferen
t
runn
in
g
con
d
ition
s
are shown
i
n
Fig
u
re 6. Th
e m
o
tor is at n
o
l
o
ad
at
t
h
e t
i
m
e
of st
art
i
n
g
.
The s
p
e
e
d com
m
and i
s
set
at
500 r
p
m
.
At
t
= 1.5s,
a st
ep spee
d com
m
a
nd i
s
gi
ven t
o
i
n
crease
t
h
e
sp
eed
fr
om
50
0
rpm
t
o
75
0
r
p
m
.
At
t
=
3s, a
l
o
ad
of
1.
5
Nm
i
s
ap
pl
i
e
d
.
It
i
s
o
b
se
rve
d
fr
o
m
t
h
e
Figure 6(a) that the estimated sp
ee
d follows the actual speed.
At st
eady state, the differe
nce be
tween
estim
a
ted and actual speed is
zero.
During
starting as
wel
l
as change in speed, the pe
ak m
a
gnitude
of the
actu
a
l to
rqu
e
is less in
fu
zzy co
n
t
ro
ller
t
h
an
PI co
n
t
ro
ller
an
d also
t
h
e transien
t to
rqu
e
at
th
e ti
m
e
o
f
ch
an
g
e
in
sp
eed
is v
e
ry
h
i
gh
in
PI contro
lle
r a
nd i
t
i
s
su
pp
resse
d i
n
fuzzy
c
o
nt
ro
ll
er. T
h
e estim
ated a
nd act
ual torque
r
e
spon
ses ar
e sh
own
in
Figure 6
(
b
)
. Si
m
u
lations a
r
e also inve
stigated at
a speed
of
1000 rpm
and the result
s
are
descri
bed
i
n
Fi
gu
re
7.
Tabl
e
2. R
a
t
i
n
gs a
n
d
param
e
ters
of
i
n
duct
i
o
n m
o
t
o
r
Para
m
e
ters
Rat
i
n
g
s
Output
745.
6
W
Poles 4
Speed 1415
r
p
m
Voltage 415
V
Cur
r
e
nt 1.
8
A
R
s
19.
355
Ω
R
r
8.
43
Ω
L
s
0.
715
H
L
r
0.
715
H
L
m
0.
689
H
f
50
Hz
Fi
gu
re
4.
Si
m
u
l
a
t
i
on di
a
g
ram
of
spee
d
sens
o
r
l
e
ss
vect
or
co
nt
r
o
l
o
f
i
n
d
u
ct
i
o
n
m
o
t
o
r
dri
v
e
wi
t
h
PI
co
nt
r
o
l
l
e
r
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 :
3
15 –
32
5
32
2
Fi
gu
re
5.
Si
m
u
l
a
t
i
on di
a
g
ram
of
spee
d
sens
o
r
l
e
ss
vect
or
co
nt
r
o
l
o
f
i
n
d
u
ct
i
o
n
m
o
t
o
r
dri
v
e
wi
t
h
f
u
zzy
cont
rol
l
e
r
(a)
Estim
a
ted and
actual spee
d
re
sponse
(b
)
Est
i
m
a
t
e
d and
act
ual
t
o
r
q
ue
r
e
sp
onse
Fi
gu
re
6.
Si
m
u
l
a
t
i
on wa
ve
fo
r
m
for a s
p
ee
d
of
5
0
0
r
p
m
and
7
5
0
r
p
m
wi
t
h
1.
5
Nm
l
o
ad
0
1
2
3
4
5
0
20
0
40
0
60
0
80
0
10
00
12
00
Ti
m
e
(
s
)
S
p
eed (
r
pm
)
P
I
-
c
o
n
tr
o
lle
r
Ac
t
u
a
l
s
p
e
e
d
Es
t
i
m
a
t
e
d s
p
e
e
d
R
e
feren
c
e
sp
ee
d
0
1
2
3
4
5
0
20
0
40
0
60
0
80
0
10
00
12
00
Ti
m
e
(
s
)
S
p
e
e
d
(rp
m
)
F
u
z
z
y c
o
nt
r
o
l
l
e
r
A
c
t
u
a
l
sp
eed
E
s
t
i
m
a
t
e
d
sp
eed
R
e
fer
e
n
ce sp
eed
0
1
2
3
4
5
0
2
4
Ti
m
e
(
s
)
L
o
ad t
o
rque (
N
m
)
PI
C
o
n
t
r
o
l
l
e
r
0
1
2
3
4
5
-2
0
0
20
40
Ti
m
e
(
s
)
L
o
ad t
o
r
que (
N
m
)
E
s
ti
m
a
ted
lo
a
d
to
rq
u
e
A
c
t
u
al
l
o
ad t
o
r
q
u
e
0
1
2
3
4
5
0
2
4
Ti
m
e
(
s
)
L
o
ad t
o
rque
(N
m
)
Fu
zzy c
o
nt
r
o
l
l
e
r
0
1
2
3
4
5
-10
0
10
20
30
Ti
m
e
(
s
)
L
o
a
d
torqu
e
(N
m
)
A
c
tu
a
l
lo
a
d
t
o
rq
u
e
E
s
tim
a
t
e
d
lo
a
d
to
rq
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
Spee
d
Se
ns
orl
e
ss Vect
or
C
o
nt
rol
of
I
n
d
u
ct
i
o
n M
o
t
o
r
Dri
v
e
w
i
t
h
PI
a
n
d
Fu
zzy C
o
nt
rol
l
e
r
(
R
. G
u
n
a
bal
an
)
32
3
(a)
Estim
a
ted and
actual spee
d
re
sponse
(b
)
Est
i
m
a
t
e
d and
act
ual
t
o
r
q
ue
r
e
sp
onse
Fi
gu
re
7.
Si
m
u
l
a
t
i
on wa
ve
fo
r
m
for a s
p
ee
d
of
1
0
0
0
r
p
m
and
12
5
0
rpm
wi
t
h
2.
5
Nm
l
o
ad
5.
HA
R
D
W
A
RE RE
SULT
S A
N
D
DIS
C
USSI
ON
S
Three
-
phase s
qui
rrel
cage i
n
duct
i
o
n m
o
t
o
r
of
0.
74
6
k
W
(
1
H
P
) i
s
u
s
ed
f
o
r t
h
e e
x
peri
m
e
nt
al
set
up.
Brake drum
arra
ngem
e
nts are provide
d
for m
echani
cal loading. The central
p
r
ocessor un
it is
th
e
TMS32
0
F281
2 D
SP pr
o
cessor
an
d
it ex
ecu
t
e
s all
th
e
m
a
th
e
m
atical
calcu
l
a
tio
n
s
. Variou
s si
m
u
lin
k
b
l
o
c
k
s
like
n
a
tural ob
server an
d PI con
t
ro
llers are
b
u
ilt
in
VISS
IM.
TMS3
20
F28
1
2
DSP pro
c
essor sup
portin
g b
l
ock
s
are
avai
l
a
bl
e i
n
V
I
SSIM
.
In
VIS
S
IM
, t
h
e si
m
u
lat
i
on bl
ocks a
r
e con
v
ert
e
d i
n
t
o
C
-
co
des
usi
ng t
h
e t
a
rget
s
u
p
p
o
rt
fo
r TM
S
3
20
F
2
8
1
2
a
n
d c
o
m
p
i
l
e
d
usi
n
g
co
de c
o
m
poser
s
t
udi
o
i
n
t
e
r
n
al
l
y
an
d t
h
e
out
p
u
t
fi
l
e
i
s
d
o
w
n
l
oade
d
i
n
t
o
t
h
e DSP
p
r
oces
so
r t
h
r
o
u
gh J
-
t
a
g em
ul
at
or. T
h
ree n
u
m
b
ers
of LEM
cur
r
ent
sen
s
o
r
s and
vol
t
a
ge se
ns
o
r
s
are used t
o
measure
the
phase curre
nts a
n
d term
inal
v
o
ltag
e
s
o
f
t
h
e in
du
ction
m
o
to
r
resp
ecti
v
ely. Th
e
measured a
n
al
og c
u
rre
n
ts and voltages a
r
e
conve
r
ted int
o
d
i
g
ital
b
y
on
ch
ip
ADC with
1
2
b
it
reso
lu
tion
.
Th
e
feed
bac
k
si
g
n
a
l
s are l
i
nke
d t
o
D
SP
pr
oces
sor
usi
ng
2
6
p
i
n hea
d
er a
n
d
t
h
e p
r
oce
sso
r
est
i
m
a
t
e
s t
h
e
st
at
or
cur
r
ent
,
rot
o
r
f
l
ux, l
o
ad t
o
r
q
u
e
and s
p
ee
d. T
h
e p
r
oce
sso
r a
l
so ge
nerat
e
s t
h
e re
qui
red P
W
M
p
u
l
s
es t
o
enabl
e
th
e th
ree
p
h
ase IGBT inv
e
rter switch
e
s in
t
h
e In
tellig
en
t Po
wer Modu
le (IPM).
High
ly effectiv
e
o
v
e
r-cu
r
ren
t
an
d sho
r
t
-
circu
it p
r
o
t
ection
is realized
thro
ugh
th
e
u
s
e
of a
d
vance
d
c
u
rrent se
nse
IGBT c
h
ips t
h
at allow
cont
i
n
u
o
u
s
m
oni
t
o
ri
n
g
o
f
p
o
we
r de
vi
ce cur
r
ent
.
Sy
st
e
m
rel
i
a
bi
l
i
t
y
is furt
her e
nha
nced
by
t
h
e IPM
’
s
in
teg
r
ated
o
v
e
r te
m
p
er
atur
e an
d und
er vo
ltag
e
lo
ck
ou
t protectio
n
.
Th
e exp
e
r
i
m
e
n
t
al r
e
su
lts f
o
r
a step
ch
ang
e
in
sp
eed
of
1000
rp
m
to
1
2
5
0
r
p
m
f
o
r
a lo
ad o
f
2.5
N
m
are s
h
o
w
n i
n
Fi
gu
re
8.
The
act
ual
spee
d
o
f
t
h
e
m
o
t
o
r i
s
m
easured
by
p
r
o
x
i
m
it
y
senso
r
. T
h
e e
s
t
i
m
a
ted a
n
d
actual spee
d waveform
s for s
t
ep increase a
n
d dec
r
ease in
s
p
eed a
r
e
depic
t
ed in Figure 8(a) a
nd
Figure
8(b)
resp
ectiv
ely.
It is o
b
s
erv
e
d
t
h
at th
e esti
m
a
te
d
sp
eed
fo
llo
ws th
e actu
a
l sp
eed
and
m
a
tch
e
s with
th
e
simu
latio
n
wave
form
. The estim
a
ted speed
res
p
onse
with
res
p
ect to
the refe
re
nce spee
d of
1
2
5
0
rpm
(5
0
0
rpm
/
div
)
is
prese
n
t
e
d
i
n
Fi
gu
re
8(c
)
fo
r a
l
o
ad
o
f
2.
5
N
m
(1 Nm
/
d
i
v
).
It is inferred that drop i
n
s
p
e
e
d
occurs at t
h
e tim
e
of ap
pl
y
i
n
g
t
h
e l
o
ad an
d fu
rt
her t
h
e m
o
t
o
r ru
ns at
a const
a
nt
spee
d of
1
2
5
0
r
p
m
for a l
o
ad o
f
2.
5 N
m
. The
esti
m
a
ted
lo
ad to
rq
u
e
wav
e
fo
rm
is illu
strated
in
Figu
re
8
(
d
)
and
is eq
u
a
l is t
o
th
e app
lied
lo
ad
. The
expe
ri
m
e
nt
al
r
e
sul
t
s
are si
m
i
l
a
r t
o
t
h
e sim
u
l
a
t
i
on res
u
l
t
s
and t
h
e
per
f
o
rm
ance o
f
nat
u
ral
obse
r
ve
r i
s
pr
ov
e
d
expe
ri
m
e
nt
al
ly wi
t
h
PI
co
nt
r
o
l
l
e
r.
0
1
2
3
4
5
0
200
400
600
800
1000
1200
1400
1600
Ti
m
e
(
s
)
S
p
eed
(rp
m
)
PI
-
c
on
t
r
ol
l
e
r
A
c
t
u
a
l
sp
eed
E
s
ti
m
a
te
d
s
p
e
e
d
R
e
f
e
ren
c
e s
p
eed
0
1
2
3
4
5
0
200
400
600
800
1000
1200
1400
1600
F
u
zzy c
o
nt
r
o
l
l
e
r
Ti
m
e
(
s
)
Sp
e
e
d
(
r
p
m
)
Ac
t
u
a
l
s
p
e
e
d
E
s
ti
m
a
ted
sp
eed
R
e
f
e
ren
c
e
sp
eed
0
1
2
3
4
5
-2
0
2
4
6
P
I
-c
o
n
t
r
o
lle
r
0
1
2
3
4
5
-5
0
0
50
100
Ti
m
e
(
s
)
L
o
ad t
o
rque
(N
m
)
A
c
t
u
al
l
o
ad
t
o
r
que
E
s
ti
m
a
te
d
lo
a
d
to
rq
u
e
0
1
2
3
4
5
-2
0
2
4
6
Fu
zzy
c
o
nt
r
o
l
l
e
r
L
o
a
d
t
o
r
que
(
N
m
)
0
1
2
3
4
5
-10
0
10
20
30
Ti
m
e
(
s
)
E
s
tim
a
t
e
d
lo
a
d
to
rq
u
e
A
c
tu
a
l
lo
a
d
to
r
q
u
e
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 :
3
15 –
32
5
32
4
(a) Estim
a
ted
and
actual
s
p
ee
d response for a
step
sp
eed
o
f
10
00
r
p
m
an
d
125
0
rp
m
(b) Estim
ated and actual s
p
ee
d
response
for
a step
sp
eed
o
f
12
50
r
p
m
an
d
100
0
rp
m
(c)
Estim
a
ted speed
res
p
on
se
fo
r a
spee
d c
o
m
m
a
nd o
f
1
250
r
p
m
an
d a
lo
ad
of
2
.
5
N
m
(d) Estim
ated
lo
ad torqu
e
with
2
.
5
Nm
lo
ad
for a
spee
d of 1
2
5
0
rpm
Fi
gu
re 8
E
x
per
i
m
e
nt
al
resul
t
s
fo
r
a spee
d of
12
5
0
rpm
wi
t
h
2.
5 Nm
l
o
ad
5
.
CONC
LUSION
Th
e i
n
du
ction m
o
to
r and the n
a
t
u
ral
o
b
serv
er are m
o
d
e
lled
in
M
A
TLAB
with
state sp
ace and
si
m
u
latio
n
s
h
a
v
e
b
e
en
carried
ou
t fo
r
d
i
fferen
t runn
ing
con
d
ition
s
.
It is co
n
c
l
u
d
e
d
th
at
fo
urth
o
r
d
e
r in
du
ction
m
o
to
r
m
o
d
e
l is u
s
ed
an
d th
e
esti
m
a
ted
p
a
rameters su
ch as ro
t
o
r
sp
eed
and
lo
ad
torq
u
e
fo
llo
w th
e co
mman
d
val
u
e. P
I
co
nt
r
o
l
l
e
r and
fuzz
y
cont
rol
l
e
r
s
h
a
ve bee
n
us
ed in
th
e sp
eed
co
n
t
ro
l loo
p
to g
e
n
e
rate th
e to
rqu
e
refe
rence a
nd t
h
ei
r pe
rf
orm
a
nces have bee
n
com
p
ared. It
is v
a
lid
ated
th
at to
rq
u
e
ri
pple in fuzzy control
l
er is
less th
an
PI con
t
ro
ller. Th
e natu
ral ob
serv
er is si
m
p
le
an
d
sp
eed
y
an
d
is a su
itab
l
e esti
mato
r for sen
s
o
r
less
v
ector co
n
t
ro
l
of indu
ctio
n
m
o
to
r d
r
i
v
e.
Mean
v
a
lu
e
of th
e ro
tor
flux
h
a
s
b
e
en
main
tain
ed con
s
tan
t
b
y
em
pl
oy
i
ng r
o
t
o
r fl
u
x
feed
bac
k
.
T
o
val
i
d
at
e t
h
e
si
m
u
l
a
t
i
on,
har
d
ware
res
u
l
t
s
have bee
n
p
r
o
v
i
d
e
d
fo
r di
f
f
ere
n
t
r
unn
ing
co
nd
itio
n
s
.
REFERE
NC
ES
[1]
Salvator
e L, Stasi S, Tarchioni
L.
A new EKF-
based algorithm for flux
estimation in inductio
n
machines.
IEEE
Transactions on
Indus
trial Electronics
. 1993
; 40
(
5
): 496-504.
[2]
Kim YR, Seung-Ki Sul, Park
MH, Speed sen
s
orless vect
or
control of
induction motor using
Extended K
a
lman
Filter
.
IEEE Transactions on In
d
u
stry Applicatio
ns.
1994; 30
(5):1225-1233.
[3]
Kim
HW
, Sul SK. A New m
o
tor Speed Est
i
m
a
t
o
r Using Kalm
an Filter
in Low-
Speed rang
e.
I
E
EE Transactions on
Industry Appications.
1996; 43 (4
):498-504.
[4]
Shi KL, Chan
TF, Wong YK, Ho SL. Speed
estimation of
an
in
duction motor d
r
ive using an
op
timized
Extend
ed
Kalm
an Filt
er.
I
EEE Transactio
ns on
Industrial Electronics
. 200
2; 49 (1)
:
124-13
3.
Evaluation Warning : The document was created with Spire.PDF for Python.