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
. 37
6
~
39
2
I
S
SN
: 208
8-8
6
9
4
3
76
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
Hysteresis Current Control of Sw
itched Reluctance Motor in
Aircraft Applications
Ma
ged
N
.
F
.
Nas
h
ed
*,
Sa
m
i
a M
.
Ma
hm
oud**,
Mohse
n
Z
.
El-Sherif**,
Emad S. A
bdel-Aliem**
* Departm
e
nt
of
Power Ele
c
tron
i
c
and
En
erg
y
Co
nversion,
El
ectr
onics Rese
arch
I
n
stitute
, C
a
iro
,
E
g
y
p
t
** Departmen
t
o
f
Electr
i
cal
Engineer
ing
,
Shoubr
a Facu
lty
of Eng
i
neer
ing, Benha
University
, Cair
o, Eg
y
p
t
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Ja
n 21, 2014
Rev
i
sed
Mar
21
, 20
14
Accepted Apr 12, 2014
The switched r
e
luctance motor (SRM) drives
have been wid
e
ly
used in
aircr
a
ft applications
due
to the moto
r advantages like h
i
gh speed operation
,
simple construction, no windin
g
s on ro
tor. B
u
t high torque ripples and
acoustic noise
are main
disad
v
antag
e
s. Th
e
current h
y
s
t
eres
is chopping
control is
one of
the importan
t
c
ontro
l metho
d
s for SRM drives. Th
ese
disadvantages can be limited usin
g the
h
y
steresis or
chopping curr
ent
con
t
rol.
This control str
a
teg
y
m
a
kes the
torque of SRM m
a
intained wi
t
h
in a set of
h
y
ster
esis bands
b
y
apply
i
ng suitable
source vo
ltage. This p
a
per
introduces
two h
y
ster
esis control modes; hard
chopping
an
d soft chopping
mode. The
SRM drive s
y
stem is
modeled in Simulink model using
MATLAB/S
I
MULINK software
pack
age
.
Keyword:
Com
p
arator
Current c
o
ntrol
l
er
Har
d
c
h
op
pi
n
g
Hy
st
eresi
s
/
C
h
o
ppi
ng
Soft
ch
o
ppi
ng
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
:
Em
ad
S. Abd
e
l-Aliem
,
Assistant Lect
ure
r
Depa
rt
m
e
nt
of
El
ect
ri
cal
Engi
neeri
n
g
,
S
h
ou
b
r
a Fac
u
l
t
y
of
E
ngi
neeri
n
g
,
Ben
h
a
Un
iv
ersity,
1
0
8
Shou
br
a
Str
eet, Cair
o, Egyp
t, Po
stal code: 1
124
1
Em
a
il: e
m
ad
.sa
m
i@fen
g
.bu
.
ed
u.eg
1.
INTRODUCTION
One
of t
h
e m
o
st
appl
i
cat
i
o
n
s
of SR
M
i
n
ai
rcraft
i
s
usi
n
g t
h
e SR
M
coupl
e
d
wi
t
h
D
C
generat
o
r
through high s
p
eed
gear
box to dri
v
e the ge
nerat
o
r. T
h
is DC gene
rator may be interfaced
with a thre
e-phas
e
1
15V
lin
es thro
ugh
a fo
ur
-quad
r
an
t dr
iv
e to
b
e
u
s
ed
in
a
n
ot
her ai
rc
raft
a
p
p
l
i
cat
i
on. The
S
R
M
i
s
operat
e
d as a
sou
r
ce
of
t
o
rq
ue, a
n
d t
h
e
D
C
gene
rat
o
r
re
gul
at
es t
h
e
sy
ste
m
speed. T
h
e SRM is
dri
v
en by its c
o
nverter
synchronized
by the c
o
ntrol
and the
reso
l
v
er
on
th
e mo
tor’s
sh
aft. Th
is electric dri
v
e system
has bee
n
recogn
ized
to
p
r
ov
id
e
b
e
n
e
fits in
system
efficien
cy, we
i
g
h
t
an
d
size, and
flex
ib
ility in
sp
eed
con
t
ro
l of SRM.
Fi
gu
re
1 s
h
ow
s t
h
e
basi
c c
o
m
ponent
s
of
t
h
e m
o
t
o
r
d
r
i
v
e sy
st
em
. The
s
e com
p
o
n
ent
s
are
3-
p
h
6/
4
SR
M
,
asym
m
e
t
r
i
c
DC
-DC
I
G
B
T
c
o
n
v
e
r
t
e
r,
gear
bo
x,
DC
m
achine
works a
s
ge
nerat
o
r a
n
d also the ele
c
tronic
cont
rol t
h
at contain c
o
m
p
arator
,
an
d th
e cu
rren
t
con
t
ro
ller
.
The DC
-DC
c
o
n
v
e
r
t
e
r an
d SR
M
are expl
ai
ned i
n
det
a
i
l
s i
n
[1]
.
The
st
anda
rd
vol
t
a
ges o
f
t
h
e
con
v
e
r
t
e
r
used
i
n
ai
rcra
ft
are:
27
0
,
3
5
0
a
nd
54
0
V
[
2
]
.
T
h
e
SR
M
param
e
t
e
rs are
m
e
nt
i
oned i
n
A
ppe
n
d
i
x
(
A
)
.
Th
e co
m
p
arato
r
reg
u
l
ates the m
o
to
r p
e
rfo
rman
ce v
i
a com
p
arin
g
th
e m
easu
r
ed
ro
t
o
r
p
o
s
ition
θ
, s
w
i
t
c
hi
ng
t
u
r
n
-
on a
ngl
e
θ
on
, and sw
i
t
c
hi
ng t
u
rn
-o
ff an
gl
e
θ
off
[3]-[5]. T
h
e com
p
arator ca
n be im
ple
m
ente
d
expe
rim
e
ntally usi
n
g a
progra
mm
ed com
puter connected
t
o
a
con
t
ro
ller
th
at fo
llo
ws the comm
ands of t
h
e
si
m
u
lated
p
r
ogram
in
th
is com
p
u
t
er [6
]. R
o
tor po
sition
sen
s
o
r
is an
in
t
e
g
r
al
p
a
rt
o
f
SRM co
n
t
ro
l syste
m
m
ount
ed
on t
h
e rot
o
r t
o
d
e
t
e
r
m
i
n
e t
u
rn
-
on a
nd t
u
r
n
-o
ff a
n
gl
es t
o
e
x
ci
t
e
and
com
m
ut
ate t
h
e p
h
ase
wi
ndi
ng
s.
Usual
l
y
, o
p
t
i
c
al
enco
ders
, r
e
sol
v
e
r
,
or
hal
l
-
effect
se
ns
or
s
m
ount
e
d
o
n
t
h
e sha
f
t
are
used t
o
o
b
t
a
i
n
r
o
t
o
r
p
o
s
ition
informatio
n
[3
]-[4
]
, [7
]. Th
e SRM
an
d
t
h
e DC
ge
n
e
rat
o
r sp
eeds are n
e
v
e
r t
h
e sa
m
e
, so
, a
g
e
ar bo
x
syste
m
is u
s
ed
b
e
tween
th
e mo
tor an
d th
e
g
e
n
e
rat
o
r’s
ro
t
o
r
to protect it from
an excessive
wea
r
a
n
d tear. The
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
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:
208
8-8
6
9
4
Hyst
eresi
s
C
u
r
r
ent
C
o
nt
r
o
l
of
Sw
i
t
c
he
d Rel
u
ct
ance
Mot
o
r i
n
Ai
rcr
a
f
t
Ap
pl
i
c
at
i
ons
(
M
a
g
e
d
N
.
F. N
a
s
h
ed
)
37
7
gear sy
st
em
hel
p
s t
h
e ge
nerat
o
r
’
s r
o
t
o
r t
o
ru
n at
t
h
e gene
ra
t
o
r’
s rat
e
d s
p
e
e
d [
5
]
,
[6]
.
Thi
s
gear
bo
x i
s
essent
i
a
l
to
ensure th
at
th
e
g
e
n
e
rator speed
is con
s
tan
t
irre
s
p
ective
of
the SRM s
p
ee
d and airc
raft st
atus [2].
Fi
gu
re
1.
The
SR
M
dri
v
e sy
s
t
em
i
n
ai
rcraft
appl
i
cat
i
o
n
2.
PRINCIPLE OF
HYSTE
R
ES
IS CURRENT
CONT
ROL
Hy
st
eresi
s
/
c
h
o
ppi
ng c
u
rre
nt
cont
rol
i
s
a co
nt
r
o
l
st
rat
e
gy
use
d
wi
t
h
SR
M
for c
o
nt
r
o
l
l
i
ng t
h
e p
h
ase
’
s
cur
r
ent
s
t
o
be wi
t
h
i
n
a ba
nd
aro
u
nd a
re
fer
e
nce valu
e [8]
.
This strategy
is
prefe
r
able over
wide spee
d range
for SRM ope
ra
tion beca
use the desired
curre
n
t can be easily reached. T
h
e
control strategy based on turning
o
n
the switch
e
s o
f
th
e co
nv
erter wh
en
th
e p
h
a
se curren
t
is lo
wer t
h
an
a lo
wer
b
a
nd
limit, an
d
tu
rn
in
g
off
th
ese switch
e
s wh
en th
e
curren
t is ab
ov
e an
u
p
p
e
r
b
a
nd
l
i
m
i
t [9
],
[10
]
.
Th
e l
o
wer lim
i
t
an
d th
e upp
er limit
can be obtaine
d
accordi
ng to
the cont
rol re
quirem
ents and the switching fr
eque
ncy of the power conve
r
ter of
SRM [4].
The hy
st
eresi
s
cont
r
o
l
im
pl
em
ent
e
d t
h
r
o
u
g
h
usi
ng t
w
o m
ode
s;
soft
an
d
har
d
ch
op
pi
n
g
w
h
i
c
h ar
e
illu
strated
in
Fig
u
re 2(a),
2
(
b) [14
]
. Th
e soft ch
op
p
i
n
g
and
h
a
rd
ch
opp
i
n
g
that can
b
e
easily u
s
ed
with
th
e
asym
m
e
t
r
i
c
bri
dge
co
n
v
ert
e
r
.
Fi
gu
re
2c s
h
o
w
s t
h
e
asy
m
met
r
i
c
co
nve
rt
er
has t
w
o
swi
t
c
hes
per
p
h
ase
and
t
h
e
hy
st
eresi
s
ban
d
.
It
achi
e
ves
al
l
form
s of c
o
nt
r
o
l
,
i
n
cl
u
d
i
n
g h
a
r
d
a
nd s
o
f
t
cho
p
p
i
n
g [
1
1
]
. In c
h
op
pi
n
g
cont
rol
of
Fi
g.
2c;
t
h
e
pha
se cu
rre
nt
i
s
co
nt
r
o
l
l
e
d
be
t
w
een t
w
o l
e
ve
l
s
(i
.e., t
h
e
up
p
e
r l
i
m
i
t
and t
h
e l
o
we
r l
i
m
i
t
)
equal
to
i
ref,j
±
Δ
i/2
, wh
ere
i
ref,j
is the re
fere
nce c
u
rrent
of eac
h pha
se and
Δ
i/2
is th
e h
y
steresis b
a
nd
th
at has an
acceptable
range a
r
ound the
refere
nce c
u
rre
n
t [4].
(a)
Soft
choppi
ng
(
b
)
Ha
rd choppi
ng
(c
) Converter and
hysteresis
ba
nd
Fi
gu
re
2.
SR
M
d
r
i
v
e
usi
n
g
so
ft
ch
o
ppi
ng
an
d
har
d
c
h
op
pi
n
g
c
ont
rol
Thi
s
hy
st
eresi
s
curre
nt
co
nt
r
o
l
i
s
achi
e
ved w
i
t
h
a cl
osed-l
o
op c
ont
rol
by
one
of t
h
e t
w
o
m
odes o
f
a
cho
p
p
i
n
g act
i
o
n;
ha
r
d
c
h
o
p
p
i
n
g
m
ode o
r
s
o
f
t
cho
p
p
i
n
g m
ode.
a)
In s
o
ft
ch
o
ppi
ng m
ode:
Fi
g
u
re
2(a
)
, t
h
e p
h
ase v
o
l
t
a
ge i
s
swi
t
c
hed
bet
w
een
(zer
o) a
nd
(+U
)
value. For pha
s
e
of
indu
ctan
ce
L
1
, t
h
e lower switch
T
2
is lef
t
on
du
r
i
ng
phase cond
u
c
ting p
e
r
i
od
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
.
3
,
Sep
t
em
b
e
r
2
014
:
37
6 – 392
37
8
and t
h
e u
ppe
r
swi
t
c
h
T
1
is choppe
d accordi
ng t
o
the pulse
d
si
gnal. It allows not only control of
the current but
also
m
i
ni
m
i
ze t
h
e ri
ppl
e cur
r
e
nt
. Al
so
, i
t
prod
uces l
o
wer a
c
ou
st
i
c
noi
se and l
e
ss
electrom
a
gnetic interfe
renc
e
(EM
I
). T
h
ere
f
ore
,
so
ft switch
i
ng
is often
p
r
eferred fo
r
m
o
to
rin
g
ope
rat
i
o
n [
1
2]
.
b)
In
har
d
ch
o
ppi
ng m
ode:
Fi
g
u
r
e 2
b
, t
h
e
p
h
as
e vol
t
a
ge i
s
s
w
i
t
c
hed bet
w
een
(–
U) a
nd
(+U
)
val
u
e.
For phase
inductance
L
1
, bo
th switch
e
s
T
1
and
T
2
are s
w
i
t
c
h
i
ng
on
du
ri
n
g
t
h
e co
n
duct
i
n
g
peri
o
d
.
So
,
(+U) vo
ltag
e
is app
lied
to
cond
u
c
ting
p
h
a
se wh
en
T
1
and
T
2
a
r
e on, and (–U) vol
t
age is
appl
i
e
d w
h
en
T
1
and
T
2
a
r
e of
f be
fo
re t
h
e
pha
se cu
rre
nt
dr
o
p
s t
o
zer
o.
It
has l
a
rge
v
a
l
u
e o
f
cur
r
ent
ri
p
p
l
e
s.
It
ca
n
be a
ppl
i
e
d i
n
b
r
a
k
i
n
g
o
p
erat
i
o
n
[1
3]
.
3.
HA
RD
C
HOP
PING
C
O
NT
ROL OF CU
RRE
NT AT
N
O
-LO
A
D
The Si
m
u
l
i
nk bl
oc
k co
nt
r
o
l
di
ag
ram
when
hy
st
eresi
s
cur
r
ent
co
nt
r
o
l
(h
ard ch
o
ppi
n
g
)
i
s
used f
o
r
three phases 6/
4
SRM at
no
l
o
ad
is shown
in Figure 3.
Th
e
d
a
ta requ
ired
fo
r th
is m
o
to
r in
th
e fo
llowing b
l
o
c
k
cont
rol
di
ag
ra
m
i
s
m
e
nt
i
oned i
n
Ap
pe
ndi
x
(A
). T
h
e m
o
st
si
gni
fi
ca
nt
p
a
ram
e
t
e
r i
n
t
h
i
s
dri
v
e sy
st
em
of t
h
e
h
y
steresis con
t
ro
ller is th
e h
y
steresis b
a
n
d
wh
ich
is d
e
si
re
d to be as sm
all as possible in orde
r to re
duce the
cu
rren
t
ripp
le. Also, selecting
th
e
p
r
op
er switch
i
ng
strateg
y
, dwell ang
l
e, vo
lta
ge s
o
u
r
ce, a
nd
swi
t
c
hi
n
g
an
g
l
es will imp
r
ov
e th
e ov
erall efficien
cy
of th
e
driv
e sy
st
e
m
. Th
e m
a
in
id
ea of cu
rren
t
co
n
t
ro
l is t
o
p
r
o
d
u
ce
a total torque
as steady as possible
in
no
n lin
ear op
erati
o
n
;
as if th
e
m
o
to
r o
p
e
rates in
lin
ear m
o
d
e
of
ope
rat
i
o
n.
Thi
s
l
i
n
eari
t
y
o
f
t
o
r
que
d
e
pe
n
d
s
o
n
c
h
o
o
si
ng
s
w
itch
i
n
g
an
g
l
es to
m
a
k
e
th
e curren
t
of th
e ph
ases at
co
mm
u
t
at
io
n
produ
cing
a to
tal cu
rren
t
n
earl
y
as d
c
cu
rren
t
in
o
r
d
e
r to
max
i
mize th
e
mo
tor to
tal to
rque. So
,
t
h
e u
s
ed
swi
t
c
hi
n
g
a
ngl
es
are
t
u
r
n
-
o
n a
ngl
e,
θ
on
=4
5º,
and
tu
rn
-of
f
ang
l
e,
θ
off
=80º.
Fi
gu
re
3.
Si
m
u
l
i
nk m
odel
usi
n
g
ha
r
d
c
h
o
p
p
i
n
g
co
nt
r
o
l
f
o
r
3-
p
h
6/
4
SR
M
at
no
-l
oa
d
3.
1.
H
a
rd Ch
oppi
n
g
C
o
ntr
o
l
w
i
th Sou
rce
V
o
l
t
age
o
f
22
0V
The p
h
ase
’
s i
n
duct
a
nces,
vol
t
a
ges an
d c
u
r
r
e
n
t
s
agai
n
s
t
rot
o
r p
o
si
t
i
on at
n
o
l
o
ad u
s
i
n
g ha
r
d
ch
o
ppi
ng
co
n
t
ro
l are
shown in Figu
re
4, wh
ere the rat
e
d
con
v
e
rter
vo
ltag
e
is 220
V, bu
t t
h
is
v
o
ltag
e
will b
e
in
creased
with
lo
ad
ed
mo
tor to
in
crease th
e g
r
ad
ien
t
o
f
m
o
to
r
p
h
ase
’
s cu
rre
nt
s pr
o
duci
ng
fl
at
-t
o
p
p
ed t
o
t
a
l
cu
rre
nt
. Th
e
har
d
c
h
op
pi
n
g
m
ode i
s
m
o
re
sui
t
a
bl
e
fo
r
br
aki
n
g
o
p
erat
i
o
n t
o
hol
d
o
n
t
h
e l
o
a
d
t
o
r
que
a
n
d
t
o
p
r
ovi
de
m
o
t
o
r
ope
rat
i
o
n at
z
e
ro
spee
d.
Th
e m
o
t
o
r cha
r
a
c
t
e
ri
st
i
c
s:
i
ndu
ct
ance,
pha
se
vol
t
a
ge
,
pha
se
cur
r
e
n
t
,
t
o
rq
u
e
, an
d
sp
eed
will b
e
o
b
t
ain
e
d
at u
s
i
n
g
t
h
e DC so
urce vo
ltag
e
v
a
l
u
es 220
,
3
5
0
an
d
54
0V. Th
e
last two
v
a
lu
es o
f
th
e
source voltage are used
in
ai
rc
raft
a
pplications.
M
o
t
o
r t
o
t
a
l
t
o
r
que
ve
rsu
s
r
o
t
o
r p
o
si
t
i
on
usi
n
g ha
r
d
ch
o
ppi
n
g
at
n
o
-l
oad
wi
t
h
so
urce
v
o
l
t
a
ge o
f
22
0
V
is sho
w
n
i
n
Fig
u
re
5
.
Th
e torqu
e
ripp
le is
sm
a
ll; also
, the to
rqu
e
b
ecomes
m
o
re stable. Th
e m
o
to
r
sp
eed
reaches
its ste
a
dy state afte
r a
num
ber
of revol
utions le
ss
tha
n
se
ve
n c
o
m
p
le
te revolut
i
ons
of t
h
e
rot
o
r; a
s
sho
w
n i
n
Fi
gu
re 6. M
o
t
o
r p
h
ase c
u
r
r
ent
v
e
rsus
p
h
ase fl
ux
-l
i
n
kage i
s
sho
w
n i
n
Fi
gu
re 7.
Ha
rd c
h
op
pi
n
g
T1
T3
D1
T5
T2
T4
T6
D2
D3
D4
D5
D6
P
o
s
i
t
i
on S
e
ns
or
220 V
Fl
u
x
C
u
rre
n
t
T
o
t
a
l
t
o
r
que
Sp
e
e
d
Th
e
t
a
I
_
m
easu
r
e
d
I_
r
e
f
P
u
l
ses
H
y
s
t
er
es
i
s
c
ont
r
o
l
l
e
r
H
yst
er
esis
c
ont
r
o
l
l
e
r
Thre
e
phas
e
6
/
4 S
R
M
po
w
e
r
g
u
i
C
o
nt
i
nuo
us
T
o
W
o
r
k
s
pac
e
t
Th
e
t
a
_
O
n
45
Th
e
t
a
_
O
f
f
80
I_
r
e
f
I_
m
e
a
Pu
lses
n
Th
e
t
a
Fl
ux
I
L
TL
m
A1
A2
B1
B2
C1
C2
A1
A2
B1
B2
C1
C2
TL
m
g
C
E
g
C
E
g
C
E
g
C
E
g
C
E
g
C
E
K
-
K
-
0
C
o
m
p
ar
at
o
r
Th
e
t
a
T
h
e
t
a_O
n
Th
e
t
a
_
O
f
f
I_
r
e
f
Cl
o
c
k
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Hyst
eresi
s
C
u
r
r
ent
C
o
nt
r
o
l
of
Sw
i
t
c
he
d Rel
u
ct
ance
Mot
o
r i
n
Ai
rcr
a
f
t
Ap
pl
i
c
at
i
ons
(
M
a
g
e
d
N
.
F. N
a
s
h
ed
)
37
9
co
n
t
ro
l m
a
k
e
s th
e env
e
lop
e
area in
t
h
is Figure 7
as m
a
x
i
mu
m
as p
o
ssib
l
e, th
at m
ean
s, m
o
to
r to
tal to
rq
u
e
no
t
decrease
d
a
s
rotor
position c
h
ange
s.
Fig
u
re 4
.
In
stan
tan
e
o
u
s p
h
a
ses
ind
u
c
tan
ces, v
o
ltag
e
s,
an
d
cu
rren
ts
v
e
rsu
s
ro
t
o
r po
sitio
n u
s
ing
h
a
rd
chop
p
i
n
g
cont
rol
at
U
dc
=2
20V
Fig
u
re
5
.
In
stan
tan
e
o
u
s to
tal t
o
rqu
e
v
e
rsu
s
ro
tor
p
o
s
ition
usin
g h
a
rd chopp
ing
co
n
t
ro
l at
U
dc
=220
V
Fig
u
re
6
.
Mo
tor sp
eed v
e
rsu
s
ro
t
o
r
po
sitio
n
u
s
ing
h
a
rd
chop
p
i
n
g
con
t
ro
l at U
dc
=220
V
2
000
2
100
22
00
2
300
240
0
2
500
260
0
2
700
280
0
29
00
300
0
0.
05
0.
15
0.
25
0.
35
0.
45
0.
55
0.
65
P
h
a
s
e
I
nduc
t
ace,
L
ph
(H
)
200
0
210
0
22
00
23
00
2
400
250
0
260
0
27
00
2
800
2
900
300
0
-24
0
-16
0
-8
0
0
80
16
0
24
0
P
h
ase V
o
l
t
a
g
,
V
ph
(V
)
200
0
210
0
22
00
23
00
24
00
250
0
260
0
270
0
280
0
29
00
3
000
0
0.
2
0.
4
0.
6
0.
8
1
1.
1
R
o
t
o
r
p
o
s
it
io
n
,
(d
e
g
)
P
h
as
e
Cu
r
r
en
t
,
I
ph
(A
)
L
A
L
B
L
C
V
A
V
B
V
C
I
A
I
B
I
C
0
200
400
60
0
800
100
0
12
00
1
400
160
0
18
00
20
00
2200
240
0
2
600
2
800
300
0
32
00
3
400
360
0
38
00
4
000
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
5
R
o
to
r
P
o
s
i
ti
o
n
,
(de
g
)
I
n
s
t
an
ta
n
e
o
u
s
T
o
ta
l To
r
q
u
e
,
T
e
(Nm
)
T
e
T
e(
av
)
Hard Chopp
ing
No-lo
a
d
U
dc
=
22
0 V
n =
19
60
r
p
m
0
20
0
40
0
600
80
0
10
00
1
200
14
00
16
00
18
00
20
00
2
200
24
00
260
0
28
00
3
000
32
00
34
00
36
00
3
800
40
00
0
20
0
40
0
60
0
80
0
10
00
12
00
14
00
16
00
18
00
20
00
R
o
to
r
P
o
s
i
ti
o
n
,
(de
g
)
M
o
t
o
r
S
p
e
e
d,
n (
r
pm
)
H
a
r
d
C
h
o
ppi
ng
No
-lo
a
d
U
dc
=
220
V
n
=
1
960
rpm
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
.
3
,
Sep
t
em
b
e
r
2
014
:
37
6 – 392
38
0
Fi
gu
re
7.
P
h
as
e fl
u
x
-l
i
n
ka
ge
vers
us
p
h
ase c
u
r
r
ent
usi
n
g
ha
rd
ch
o
ppi
ng
co
nt
r
o
l
at
U
dc
=22
0
V
3.
2.
H
a
rd Ch
oppi
n
g
C
o
ntr
o
l
w
i
th Sou
rce
V
o
l
t
age
o
f
35
0V
Th
e sim
u
latio
n
is rep
eated
i
n
th
is sectio
n
un
d
e
r th
e sam
e
co
nd
itio
ns as
b
e
fo
re
wh
ile allo
wing
th
e
pha
se cu
rre
nt
s
t
o
ove
rl
ap at
appl
i
e
d
hi
g
h
e
r
val
u
e
of s
o
urce
vol
t
a
ge 3
5
0
V
. M
o
t
o
r charact
eri
s
t
i
c
s;
pha
se
in
du
ctan
ce,
p
h
ase vo
ltag
e
, and
p
h
a
se cu
rrent v
e
rsu
s
ro
tor
po
sitio
n are
shown in
Figu
re
8. In
creasing
v
a
lu
e of
th
e sou
r
ce
v
o
l
t
a
g
e
will resu
lt in
an
in
crease o
f
th
e
g
r
ad
ie
n
t
o
f
th
e
p
h
a
se curren
t
. Th
e m
o
to
r to
tal to
rqu
e
v
e
rsus
ro
t
o
r po
sition
is sh
own
in
Figu
re
9
.
It is n
o
t
iced
th
at th
e to
tal to
rqu
e
reach
e
s to
stead
y
state faster th
an
th
e
case whe
n
the
source
voltage
is 22
0V. B
u
t the to
tal to
rqu
e
has larg
er
ripp
le.
Fig
u
re 8
.
In
stan
tan
e
o
u
s p
h
a
ses
ind
u
c
tan
ces, v
o
ltag
e
s,
an
d
cu
rren
ts
v
e
rsu
s
ro
t
o
r po
sitio
n u
s
ing
h
a
rd
chop
p
i
n
g
cont
rol
at
U
dc
=3
50V
Fig
u
re
9
.
In
stan
tan
e
o
u
s to
tal t
o
rqu
e
v
e
rsu
s
ro
tor
p
o
s
ition
usin
g h
a
rd chopp
ing
co
n
t
ro
l at
U
dc
=350
V
0
0.
0
5
0.
1
0.
1
5
0.
2
0.
2
5
0.
3
0.
3
5
0.
4
0.
45
0.
5
0.
5
5
0.
6
0.
6
5
0.
7
0.
7
5
0.
8
0.
8
5
0.
9
0.
9
5
1
1.
0
5
0
0.
1
0.
2
0.
3
0.
4
0.
5
P
h
as
e C
u
r
r
en
t
,
I
ph
(A
)
Ph
a
s
e
Fl
u
x
-
l
i
n
k
a
g
e
,
ph
(W
b
)
Har
d
Chopp
i
n
g
No-
l
oad
U
dc
=
22
0 V
n =
1960 r
p
m
20
00
2
050
2
100
2
150
2200
2250
2300
235
0
240
0
24
50
25
00
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
65
P
h
a
s
e
s
I
nduc
ta
nc
e
s
,
L
ph
(H)
20
00
2
050
2
100
2
150
2200
2250
2300
235
0
240
0
245
0
25
00
-
400
-
200
0
200
400
P
h
as
es
V
o
l
t
ag
es
,
V
ph
(V
)
2
000
2
050
2
100
2150
2200
2250
2300
2350
240
0
245
0
250
0
0
0.
2
0.
4
0.
6
0.
8
1
1.
1
R
o
tor
Pos
ition
,
(d
e
g
)
P
h
as
es
Cu
r
r
en
t
s
,
I
ph
(A
)
L
A
L
B
L
C
V
A
V
B
V
C
I
A
I
B
I
C
0
200
40
0
600
80
0
1
000
12
00
1400
16
00
180
0
2000
22
00
2400
2600
2
800
3000
3200
34
00
3600
3
800
40
00
4200
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
5
5.
5
R
o
to
r
P
o
s
i
ti
o
n
,
(d
e
g
)
I
n
st
a
n
t
a
ne
ou
s T
o
t
a
l
T
o
q
u
e
,
T
e
(N
m
)
T
e
T
e(
av
)
Har
d
C
hoppi
ng
No-
l
oa
d
U
dc
=
350 V
n
=
2170
rp
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Hyst
eresi
s
C
u
r
r
ent
C
o
nt
r
o
l
of
Sw
i
t
c
he
d Rel
u
ct
ance
Mot
o
r i
n
Ai
rcr
a
f
t
Ap
pl
i
c
at
i
ons
(
M
a
g
e
d
N
.
F. N
a
s
h
ed
)
38
1
From
Figure
10, t
h
e m
o
tor s
p
eed reac
hes it
s steady
state a
f
ter a
b
out eleven re
volutions. The stea
dy
st
at
e val
u
e of spee
d becom
e
s 21
70 r
p
m
th
at
in
creases fu
rt
h
e
r with
in
creasin
g
th
e supp
ly v
o
ltag
e
. Th
e p
h
a
se
fl
u
x
-l
i
n
kage
v
e
rsus t
h
e
pha
s
e
curre
nt
at
35
0V i
s
sh
ow
n i
n
Fi
g
u
re 1
1
. I
n
t
h
i
s
case wh
en t
h
e su
ppl
y
vol
t
a
g
e
equals
350V, t
h
e e
nvel
ope
area is large
r
t
h
a
n
that
case
wh
en
th
e su
pp
ly voltag
e
is equ
a
l t
o
2
20V.
Fi
gu
re
1
0
. M
o
t
o
r
spee
d
ve
rsu
s
r
o
t
o
r
posi
t
i
o
n
usi
n
g
ha
rd
ch
o
ppi
ng
co
nt
r
o
l
a
t
U
dc
=350
V
Fi
gu
re
1
1
.
Pha
s
e fl
u
x
-
l
i
nka
ge
ve
rsus
p
h
ase
c
u
r
r
ent
usi
n
g
ha
rd
ch
o
ppi
ng
co
nt
r
o
l
at
U
dc
=35
0
V
3.
3.
H
a
rd Ch
oppi
n
g
C
o
ntr
o
l
w
i
th Sou
rce
V
o
l
t
age
o
f
54
0V
Th
e sim
u
latio
n
for ob
tain
mach
in
e ch
aracteristics is rep
eated
at app
lied
h
i
g
h
e
r
v
a
lu
e
o
f
sou
r
ce
v
o
ltag
e
540
V.
Mo
to
r ch
aracteristics; p
h
a
se i
n
du
ctan
ce,
p
h
a
se vo
ltag
e
, an
d p
h
a
se curren
t
v
e
rsu
s
ro
t
o
r
positio
n
are sh
own
in Fig
u
re
1
2
. In
creasin
g
v
a
l
u
e
o
f
th
e source
v
o
l
t
a
g
e
will resu
lt
in
fu
rt
h
e
r i
n
crease in
the grad
ien
t
of
the phase
curre
nt.
Fig
u
re 12
. Instan
tan
e
o
u
s p
h
a
ses
ind
u
c
tan
ces,
vo
ltag
e
s,
an
d
cu
rren
ts v
e
rsu
s
ro
to
r po
sition
u
s
ing
h
a
rd
chop
p
i
n
g
cont
rol
at
U
dc
=5
40V
0
50
0
10
00
15
00
2
000
25
00
30
00
35
00
40
00
45
00
50
00
550
0
60
00
65
00
70
00
75
00
800
0
85
00
90
00
95
00
0
25
0
50
0
75
0
10
00
12
50
15
00
17
50
20
00
22
50
25
00
Ro
t
o
r P
o
s
i
t
i
on
,
(d
e
g
)
M
o
t
o
r S
p
eed
,
n
(rp
m
)
Ha
r
d
Ch
o
p
p
i
n
g
No
-
l
o
a
d
U
dc
=
35
0
V
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
35
0.
4
0.
45
0.
5
0.
55
0.
6
0.
65
0.
7
0.
75
0.
8
0.
85
0.
9
0.
95
1
1.
05
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
P
h
a
s
e C
u
r
r
en
t,
I
ph
(A
)
P
h
a
s
e
F
l
ux-
l
i
n
ka
ge
,
ph
(W
b
)
Hard
Cho
ppi
ng
No-l
oad
U
dc
=
350
V
n
=
2170 rpm
20
00
20
50
21
00
21
50
220
0
22
50
23
00
23
50
240
0
24
50
25
00
0.
15
0.
25
0.
35
0.
45
0.
55
0.
65
P
h
a
s
e I
n
d
u
c
t
an
e,
L
ph
(H
)
200
0
20
50
21
00
21
50
220
0
22
50
23
00
23
50
24
00
24
50
25
00
-6
00
-3
00
0
30
0
60
0
P
h
a
s
e Vo
l
t
ag
e,
V
ph
(V
)
200
0
20
50
21
00
21
50
220
0
22
50
23
00
23
50
240
0
24
50
25
00
0
0.
2
0.
4
0.
6
0.
8
1
1.
1
R
o
to
r
P
o
s
ition
,
(d
e
g
)
P
h
as
e C
u
r
r
e
n
t
,
I
ph
(A
)
L
A
L
B
L
C
V
A
V
B
V
C
I
A
I
B
I
C
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
:
37
6 – 392
38
2
The m
o
tor tota
l torque
versus rot
o
r
position is sh
own in Figure 13,
where
the steady state reache
s
f
a
ster
th
an
th
e tw
o
cases o
f
ap
p
l
ying
22
0V an
d
35
0V
bu
t
with
larg
er ri
p
p
l
es.
The m
o
tor spee
d reac
hes its
steady state va
lue of
2220 rpm
after
fifteen rev
o
lutio
ns
as
sho
w
n
Fi
gu
re
14. T
h
e steady
state speed be
com
e
s
22
2
0
rpm
t
h
at
i
n
creases f
u
rt
h
e
r wi
t
h
i
n
crea
s
i
ng su
p
p
l
y
vol
t
a
ge. T
h
e p
h
ase
fl
ux
-l
i
nka
ge v
e
rsus
pha
se cu
rre
nt
at 5
40V
is show
n in
Figu
r
e
15
.
Fig
u
re 13
. Instan
tan
e
o
u
s
to
tal
to
rqu
e
v
e
rsu
s
ro
t
o
r po
sitio
n u
s
ing
h
a
rd
chop
p
i
n
g
con
t
ro
l
at
U
dc
=540
V
Fi
gu
re
1
4
. M
o
t
o
r
spee
d
ve
rsu
s
r
o
t
o
r
posi
t
i
o
n
usi
n
g
ha
rd
ch
o
ppi
ng
co
nt
r
o
l
a
t
U
dc
=540
V
Fi
gu
re
1
5
.
Pha
s
e fl
u
x
-
l
i
nka
ge
ve
rsus
p
h
ase
c
u
r
r
ent
usi
n
g
ha
rd
ch
o
ppi
ng
co
nt
r
o
l
at
U
dc
=54
0
V
0
1000
2000
30
00
4000
500
0
6
000
7000
8000
90
00
10000
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
5
Rot
o
r
P
o
s
i
t
i
o
n
,
(d
e
g
)
M
o
to
r
T
o
t
a
l T
o
r
q
u
e
,
T
e
(N
m
)
T
e
T
e(
a
v
)
H
a
rd C
hoppi
ng
N
o
-l
oad
U
dc
=
540 V
n =
2220
r
p
m
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
8000
8500
900
0
9500
10000
0
250
500
750
1000
1250
1500
1750
2000
2250
R
o
t
o
r P
o
s
i
t
i
on,
(de
g
)
Mot
o
r
S
p
e
e
d,
n
(
r
p
m
)
Ha
r
d
C
hop
pi
n
g
No
-
l
oa
d
U
dc
=
54
0
V
0
0.
05
0.
1
0.
1
5
0.
2
0.
25
0.
3
0.
35
0.
4
0.
4
5
0.
5
0.
55
0.
6
0.
6
5
0.
7
0.
75
0.
8
0.
85
0.
9
0.
95
1
1.
05
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
P
h
as
e C
u
r
r
e
n
t
,
I
ph
(A
)
P
h
a
s
e
F
l
ux-
l
i
nka
ge
,
ph
(W
b
)
H
a
r
d
C
hop
pi
ng
N
o
-
l
oad
U
dc
=
54
0 V
n =
22
20
r
p
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Hyst
eresi
s
C
u
r
r
ent
C
o
nt
r
o
l
of
Sw
i
t
c
he
d Rel
u
ct
ance
Mot
o
r i
n
Ai
rcr
a
f
t
Ap
pl
i
c
at
i
ons
(
M
a
g
e
d
N
.
F. N
a
s
h
ed
)
38
3
4.
SOFT CHO
P
PING
C
O
NT
ROL OF CU
RRE
NT AT
N
O
-LO
A
D
The
Si
m
u
l
i
nk bl
oc
k c
ont
rol
d
i
agram
whe
n
u
s
i
n
g
hy
st
eresi
s
cu
rre
nt
c
ont
r
o
l
(so
f
t
c
h
o
p
p
i
n
g)
f
o
r
t
h
re
e
pha
ses 6/
4 SR
M
at
no l
o
ad i
s
sho
w
n i
n
Fi
gu
re 1
6
. T
h
e
d
a
t
a
requi
red
fo
r t
h
i
s
m
o
t
o
r i
n
t
h
e fol
l
o
wi
n
g
bl
oc
k
cont
rol
di
a
g
ra
m
i
s
obt
ai
ned
fr
om
Appen
d
i
x
(
A
).
In s
o
ft
cho
p
p
i
n
g m
ode for asy
m
m
e
tri
c
bri
d
ge
, t
h
e
l
o
wer
switches a
r
e le
ft on
during
phases c
o
nducting pe
riod
s a
nd the
uppe
r s
w
itches are
c
h
opped according
to the
p
u
l
sed
sign
al in
ord
e
r to
allows no
t on
ly co
n
t
ro
l o
f
th
e cu
rren
t bu
t also
min
i
m
i
ze th
e cu
rren
t
ripp
les.
Also
, it
pr
o
duces l
e
ss a
c
ou
st
i
c
noi
se a
nd l
e
ss el
ect
r
o
m
a
gnet
i
c
i
n
t
e
rf
erence
(EM
I
).
The
hy
st
eresi
s
ban
d
i
s
desi
re
d
t
o
be
as sm
a
ll as possible to re
duc
e
curr
en
t
ripp
les. Also
, selectin
g
th
e
p
r
op
er switch
i
n
g
strateg
y
, dwell an
g
l
e,
v
o
ltag
e
sou
r
ce, an
d
switch
i
ng an
g
l
es
will i
m
p
r
ov
e th
e ov
erall efficien
cy of th
e driv
e syst
e
m
. Th
e switch
i
ng
angles
are c
hosen s
u
c
h
that
the
so
urce cu
rren
t and
to
tal
to
rq
u
e
b
e
co
m
e
s h
a
s less ri
pp
le v
a
l
u
es. So, th
e
switching
use
d
angle are
turn-on angle,
θ
on
=4
5º,
and
turn
-of
f
ang
l
e,
θ
off
=80
º
.
Fi
gu
re 1
6
. Si
m
u
l
i
n
k
m
odel
us
i
ng so
ft
ch
o
ppi
ng
co
nt
r
o
l
f
o
r 3-
p
h
6/
4 SR
M
at
no
-l
oa
d
4
.
1
.
So
ft
C
h
opping Co
nt
ro
l
wit
h
So
urce
V
o
l
t
ag
e
o
f
220V
The m
achine c
h
aracteristics;
pha
se
s inducta
n
ces, voltages
and curren
ts ag
ain
s
t
ro
t
o
r positio
n
u
s
ing
soft
ch
o
ppi
ng
cont
rol
are s
h
o
w
n i
n
Fi
gu
re 1
7
, w
h
e
r
e t
h
e ra
t
e
d co
nve
rt
er v
o
l
t
a
ge i
s
22
0
V
,
but
t
h
i
s
v
o
l
t
a
g
e
wi
l
l
be i
n
crease
d
with loa
d
ed m
o
tor to i
n
crea
se t
h
e
gra
d
ient
of
m
o
to
r
ph
ases cu
rr
en
ts to
pr
odu
ce
f
l
at-
t
op
p
e
d to
tal
cu
rren
t. Th
e so
ft cho
p
p
i
ng
m
o
d
e
is m
o
re su
itab
l
e fo
r mo
toring
o
p
e
ratio
n. Th
e m
o
to
r ch
aracteristics will
be
obt
ai
ne
d at
so
u
r
ce
vol
t
a
ge
o
f
22
0,
3
5
0
a
n
d
5
4
0
V
.
Fig
u
re 17
. Instan
tan
e
o
u
s p
h
a
ses
ind
u
c
tan
ces,
vo
ltag
e
s,
an
d
cu
rren
ts v
e
rsu
s
ro
to
r po
sition
u
s
ing
so
ft
chopp
ing
cont
rol
at
U
dc
=2
20V
T1
T3
D1
T5
T2
T4
T6
D2
D3
D4
D5
D6
Thre
e
phase
6/4 S
R
M
Po
s
i
t
i
o
n
Se
n
s
o
r
22
0
V
Flux
C
u
rre
n
t
To
t
a
l
to
r
q
u
e
S
p
eed
Th
e
t
a
T
h
et
a
_
m
easu
r
e
d
H
yst
er
esis
C
ont
r
o
l
l
e
r
P
u
lses
po
w
e
r
g
u
i
C
o
nt
i
n
uo
us
T
o
W
o
r
ksp
a
c
e
t
Th
e
t
a
_
O
n
45
Th
e
t
a
_
O
f
f
80
I_
r
e
f
I_
m
e
a
P
u
lses
n
Th
e
t
a
Fl
u
x
I
L
TL
m
A1
A2
B1
B2
C1
C2
A1
A2
B1
B2
C1
C2
TL
m
g
C
E
g
C
E
g
C
E
g
C
E
g
C
E
g
C
E
K
-
K
-
0
C
o
m
p
ar
at
o
r
Th
e
t
a
Th
e
t
a
_
O
n
Th
e
t
a
_
O
f
f
I_
r
e
f
Cl
o
c
k
200
0
2100
2200
2300
2400
2
500
2600
2700
2800
2900
3000
0.
1
0.
25
0.
4
0.
55
0.
65
P
h
as
e I
n
d
u
ct
an
ce
,
L
ph
(H
)
2000
2100
2200
2300
2400
2
500
2600
2700
2800
2900
3000
-
240
-
120
0
120
240
P
h
as
e V
o
l
t
a
g
e
,
V
ph
(V
)
2000
2100
2200
2300
2400
2500
2600
2
700
2800
2900
3000
0
0.
2
0.
4
0.
6
0.
8
1
1.
1
Ro
t
o
r P
o
s
i
t
i
o
n
,
(de
g
)
P
h
a
s
e
C
u
rre
n
t
,
I
ph
(A
)
I
A
I
B
I
C
V
A
V
B
V
C
I
A
I
B
I
C
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
:
37
6 – 392
38
4
Th
e m
o
to
r t
o
tal to
rq
u
e
v
e
rsu
s
ro
t
o
r po
sition u
s
ing
soft chop
p
i
n
g
at no-load
with
so
urce vo
ltag
e
o
f
2
20V is sh
own
in
Figu
re
1
8
. Th
e to
rqu
e
ri
p
p
l
e is sm
a
ller th
an
th
at th
e case wh
en
h
a
rd
cho
p
p
i
ng
con
t
ro
l is
use
d
at 220V.
The m
o
tor s
p
e
e
d reac
hes its
steady state af
ter abou
t eig
h
t
revo
lu
tion
s
o
f
th
e ro
to
r as sho
w
n
in
Fi
gu
re
19
. T
h
e
p
h
ase fl
ux
-l
i
n
kage
ve
rs
us
ph
ase cu
rre
nt
i
s
sho
w
n i
n
Fi
g
u
r
e 2
0
.
Th
e en
v
e
l
ope a
r
ea
bec
o
m
e
s
lar
g
er th
an
u
s
i
n
g h
a
rd
ch
opp
in
g at 220
V.
Fig
u
re 18
. Instan
tan
e
o
u
s
to
tal
to
rqu
e
v
e
rsu
s
ro
t
o
r po
sitio
n u
s
ing
so
ft
chopp
ing
co
n
t
ro
l
at U
dc
=220
V
Fi
gu
re
1
9
. M
o
t
o
r
spee
d
ve
rsu
s
r
o
t
o
r
posi
t
i
o
n
usi
n
g
so
ft
c
h
o
ppi
ng
co
nt
r
o
l
a
t
U
dc
=220
V
Fi
gu
re
2
0
.
Pha
s
e fl
u
x
-
l
i
nka
ge
ve
rsus
p
h
ase
c
u
r
r
ent
usi
n
g
so
ft
ch
o
ppi
ng
co
nt
r
o
l
at
U
d
c =
2
20
V
0
25
0
500
75
0
10
00
125
0
1
500
17
50
20
00
22
50
25
00
275
0
3
000
32
50
35
00
37
50
40
00
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
5
Rot
o
r
P
o
s
i
t
i
on,
(d
e
g
)
M
o
to
r
T
o
ta
l T
o
r
q
u
e
,
T
e
(N
m
)
T
e
T
e(
a
v
)
S
o
ft
C
h
o
p
p
i
n
g
No
-
l
o
a
d
U
dc
=
22
0V
n =
19
60 r
p
m
0
250
500
750
1000
1250
1500
1750
2000
225
0
2500
2750
3000
32
50
3
500
3750
4000
4250
4500
4750
5000
0
250
500
750
1000
1250
1500
1750
2000
Ro
t
o
r P
o
s
i
t
i
on
,
(de
g
)
M
o
to
r S
p
eed
,
n
(
r
p
m
)
S
o
f
t
C
h
o
ppi
ng
No
-l
o
a
d
U
dc
=
2
20 V
0
0.
0
5
0.
1
0.
1
5
0.
2
0.
2
5
0.
3
0.
3
5
0.
4
0.
4
5
0.
5
0.
55
0.
6
0.
6
5
0.
7
0.
75
0.
8
0.
8
5
0.
9
0.
95
1
1.
05
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
P
h
a
s
e
Curre
nt
, I
ph
(A
)
Ph
a
s
e
Fl
u
x
-
l
i
n
k
a
g
e
,
ph
(W
b
)
S
o
f
t
C
hoppi
ng
N
o
-
l
oad
U
dc
=
220V
n =
1960 r
p
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Hyst
eresi
s
C
u
r
r
ent
C
o
nt
r
o
l
of
Sw
i
t
c
he
d Rel
u
ct
ance
Mot
o
r i
n
Ai
rcr
a
f
t
Ap
pl
i
c
at
i
ons
(
M
a
g
e
d
N
.
F. N
a
s
h
ed
)
38
5
4
.
2
.
So
ft
C
h
opping Co
nt
ro
l
wit
h
So
urce
V
o
l
t
ag
e
o
f
350V
The sim
u
lation is re
peated at applied
sour
ce
voltage 350V. Mot
o
r c
h
aracte
r
istics; phase
s
in
du
ctan
ces, ph
ases vo
ltag
e
s,
and
ph
as
es curren
t
s
v
e
rsu
s
ro
tor
p
o
s
ition
are
shown in
Figu
re 21
. By in
creasin
g
th
e v
a
lu
e of
so
urce vo
ltag
e
will
resu
lts
in
in
creasing of t
h
e
g
r
ad
ien
t
of
th
e
ph
ase cu
rren
t. Th
e m
o
to
r to
tal
torque
vers
us rotor position
is shown in Figure 22,
whe
r
e
the steady state of the to
tal torque reache
s
faster
th
an
app
l
y 22
0V,
bu
t it h
a
s larg
er
ripp
le v
a
l
u
e.
Fig
u
re 21
. Instan
tan
e
o
u
s p
h
a
ses
ind
u
c
tan
ces,
vo
ltag
e
s,
an
d
cu
rren
ts v
e
rsu
s
ro
to
r po
sition
u
s
ing
so
ft
chopp
ing
cont
rol
at
U
dc
=3
50V
Fig
u
re 22
. Instan
tan
e
o
u
s
to
tal
to
rqu
e
v
e
rsu
s
ro
t
o
r po
sitio
n u
s
ing
so
ft
chopp
ing
co
n
t
ro
l
at U
dc
=350
V
Fi
gu
re
2
3
. M
o
t
o
r
spee
d
ve
rsu
s
r
o
t
o
r
posi
t
i
o
n
usi
n
g
so
ft
c
h
o
ppi
ng
co
nt
r
o
l
a
t
U
dc
=350
V
2000
20
50
2100
2150
2
200
2250
230
0
2
350
2400
245
0
2
500
0.
1
0.
25
0.
4
0.
55
0.
65
P
h
a
s
e
I
n
duc
t
a
nc
e
,
L
ph
(H
)
2000
20
50
2100
215
0
2
200
2250
23
00
2350
2400
2
450
2500
-
400
-
200
0
200
400
P
h
as
e V
o
l
t
a
g
e,
V
ph
(V
)
3000
305
0
3100
3150
3
200
3250
33
00
3350
34
00
3450
350
0
0
0.
2
0.
4
0.
6
0.
8
1
1.
1
Ro
t
o
r
Po
s
i
t
i
o
n
,
(d
e
g
)
P
h
as
e C
u
r
r
e
n
t
,
I
ph
(A
)
L
A
L
B
L
C
V
A
V
B
V
C
I
A
I
B
I
C
0
250
500
75
0
1
000
125
0
15
00
1
750
2000
22
50
2
500
275
0
300
0
3
250
350
0
375
0
40
00
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
5
R
o
t
o
r P
o
s
i
t
i
on,
(de
g
)
M
o
to
r
T
o
ta
l T
o
r
q
u
e
,
T
e
(N
m
)
T
e
T
e(
a
v
)
S
o
f
t
C
hopping
N
o
-
l
oad
U
dc
=
350 V
n =
2170
r
p
m
0
50
0
10
00
15
00
20
00
25
00
30
00
35
00
40
00
45
00
50
00
55
00
60
00
65
00
0
20
0
40
0
60
0
80
0
10
00
12
00
14
00
16
00
18
00
20
00
22
00
Rot
o
r
P
o
s
i
t
i
on,
(d
e
g
)
M
o
t
o
r S
p
ee
d
,
n
(rp
m)
S
o
f
t
C
hop
ping
N
o
-
l
oad
U
dc
=
350 V
Evaluation Warning : The document was created with Spire.PDF for Python.