TELKOM
NIKA
, Vol. 11, No. 4, April 2013, pp. 1807
~18
1
2
ISSN: 2302-4
046
1807
Re
cei
v
ed
Jan
uary 5, 2013;
Re
vised Feb
r
uar
y 7, 2013;
Acce
pted Fe
brua
ry 20, 20
13
Permanent Magnet Tracking Position Sensor
Dega
ng Lv
*
1
, Ningzhi Jin
2
1,2
School of Electri
c
al & Electroni
c Engi
n
eerin
g,
Ha
rbi
n
University of Science & T
e
ch
nolo
g
y,
52 Xuefu Avenue, Ha
rbin,
Chin
a.
*Co
rre
sp
ondi
ng autho
r, e-mail: lvdegan
g619
@1
26.com
A
b
st
r
a
ct
In view
of the disa
dvant
ages
of tradition
al
posit
i
on se
nso
r
, a novel p
e
r
m
a
n
e
n
t ma
gn
e
t
tracking
positi
on s
ens
or is pr
op
osed. T
he
hal
l
co
mpo
n
ent is
use
d
to c
onvert th
e
ma
g
netic si
gn
al r
e
fl
ecting
the s
haft
velocity a
nd
p
o
sitio
n
into
an
electric
al si
gna
l by
the
co
nstruction and opti
m
i
z
at
io
n of ma
gnetic fi
eld. An
d
then th
e res
o
l
v
er-to-di
gital
c
onvers
i
on
is c
a
rried
o
u
t
by
arctang
ent so
as to o
b
tai
n
th
e sig
n
a
l
s of s
haft
positi
on a
nd ve
locity.
Ke
y
w
ords
:
pe
rma
n
e
n
t ma
gn
et, resolver-to-
digit
a
l conv
ersi
on, positi
on se
nsor
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
In the moto
r co
ntrol
syst
em, the p
o
sit
i
on
sen
s
o
r
i
s
gene
rally n
e
eded t
o
p
r
ov
ide the
informatio
n of the rotor po
sition and velo
city in
order f
o
r the motor
positio
n and
velocity control,
so the
po
sition sen
s
ors
become a
n
i
m
porta
nt
co
mpone
nt of the moto
r co
ntrol
system.
At
pre
s
ent, the
photoel
ectri
c
encode
r is a
comm
on po
si
tion sen
s
o
r
[1, 2]. The po
sition sen
s
o
r
is
widely used i
n
many fields. With the increa
se of
the deman
d of position dete
c
ti
on in most fie
l
ds,
the tradition
al position
sensor
s are unabl
e to meet the spe
c
ial re
quirem
ents of sev
e
ral
appli
c
ation
s
becau
se
of their i
nhe
re
nt defe
c
t.
In t
h
is
pap
er, a
pe
rman
ent
magnet t
r
a
c
king
positio
n se
nsor is d
e
si
gne
d. The de
sig
ned sen
s
or i
s
better tha
n
the photoele
c
tri
c
en
cod
e
r in
environmental suitability,
and has
simpl
e
structure
and fabrication process,
so i
t
can
repl
ace
the
photoel
ectri
c
encode
r.
2. Tracking
Position Sen
s
or Principle and Design
rr
B
rc
B
ri
n
g
ma
g
n
e
t
i
c
x
y
r
B
P
a
ra
l
l
e
l
u
n
i
f
o
rm
ma
g
n
e
t
i
c
f
i
e
l
d
Figure 1. Cro
ss Se
ction of
the Cylindri
c
a
l
Magnet Steel in a Uniform Magneti
c
F
i
eld
2.1. The Basi
c Principle of Trackin
g
Position Sens
or
The
cylind
r
ical or rin
g
m
a
gnetic ste
e
l is pla
c
ed i
n
a
p
a
rallel
unifo
rm mag
netic fi
eld to b
e
magneti
z
ed,
and the
axis
of the mag
n
e
t
ic steel
is
m
ade ve
rtical t
o
the di
re
ctio
n of the m
a
g
netic
field, as sho
w
n in Figure 1.
In the ideal state,
the surface of the ma
gnet
ic
steel is magnetized to
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ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No. 4, April 2013 : 1807 – 1
812
1808
a bipola
r
ma
gnetic field,
who
s
e
re
sidu
al magn
et
ic i
ndu
ction inte
nsity ca
n be
decompo
se
d
into
the radial a
n
d
tangential co
mpone
nts, as
is sho
w
n in
Equation (1)
and Figu
re 1.
sin
cos
r
rc
r
rr
B
B
B
B
(1)
From
Equatio
n (1), th
e rad
i
al mag
netic f
i
el
d of
mag
n
e
tic
steel
su
rf
ace
chan
ge
s with
the
co
sine l
a
w,
with which t
he pe
rma
n
e
n
t magn
et
tracking
po
sition sen
s
o
r
is desi
gne
d. T
w
o
orthog
onal
h
a
ll co
mpo
n
e
n
ts a
r
e
placed on
the
same
circumf
e
ren
c
e
in th
e pe
riph
ery
of the
magneti
c
fiel
d. The
hall
compon
ents sense the
r
adi
al mag
netic f
i
eld an
d g
e
n
e
rate
a volta
ge
sign
al refle
c
ti
ng the chan
g
e
s of the ma
gnetic fi
eld.
The an
gula
r
positio
n information an
d e
v
en
the sp
eed i
n
formatio
n of t
he rotating m
agneti
c
fi
eld i
s
obtai
ned
by solving th
e a
r
ctan
gent val
u
e
of two orthog
onal cosi
ne voltage si
gnal
s [3].
2.2. The Con
s
truc
tion of
Space Mag
n
etic Field
Magneti
c
mat
e
rial
s in
clud
e
isotro
pic
and
ani
sotropi
c
material
s. After bei
ng ma
g
netize
d
,
the magn
etic prop
ertie
s
o
f
the anisot
r
opic
m
a
terial
s are better
and the
rem
anen
ce o
n
the
surfa
c
e
of th
e ma
gnet i
s
more
than
th
e isotro
pi
c m
a
terial
s.
Ho
wever, a
di
re
ction of
mag
n
e
t
ic
orientatio
n is
con
s
id
ere
d
when the
ani
so
tropic ma
te
ria
l
magnet i
s
b
e
ing ma
gneti
z
ed. O
n
ly wh
en
the directio
n
of external
m
agneti
c
field i
s
con
s
is
te
nt
with the
dire
ction of mag
n
e
tic o
r
ientatio
n
,
woul
d
it ca
n achi
eve
the
best mag
neti
z
ing
effect,
while the
ma
g
netizin
g effe
ct of the
isot
ro
pic
magnet
is al
ways u
n
iform
i
n
eve
r
y di
re
ction. Th
us,
th
e
ani
sotropi
c material
s are more
ap
plica
b
le
to the paralle
l magnetizi
n
g
of the bipolar magnet st
e
e
l in this desi
gn so a
s
to increa
se the air-
gap l
ength
of
the trackin
g
positio
n
sen
s
or,
while
the isotro
pic
mat
e
rial
s are
mo
re appli
c
abl
e to
the radial
cha
r
ge ma
gneti
s
m of multipolar mag
net ste
e
l.
The rin
g
or cylindrical ma
gnet steel of ani
sotropi
c m
a
terial
s nee
d
to be magn
etized in
the parallel m
agneti
c
field,
whe
r
e the
direction
of
the
parall
e
l mag
n
e
tic field
sho
u
l
d be
con
s
i
s
te
n
t
with the mag
netic ori
entati
on dire
ction
o
f
the magnet steel, as Fi
gu
re 2 sh
ows.
Figure 2. Gen
e
ral Vie
w
of Parallel Ma
gn
etizing
In the ideal st
ate, the spa
c
e distri
bution
of magneti
c
lines fo
r a ma
gnetized ri
ng
magnet
steel i
s
sho
w
n in Fig
u
re
3, whe
r
e th
e m
agnet
steel i
s
6mm in
out-diamete
r, 3m
m in in-diam
e
ter
and 3mm in
height, and I
n
the positive
half period
a
nd neg
ative half spa
c
e, th
e magneti
c
field
distrib
u
tion of
the positive
half cycle a
n
d
the
negativ
e half cycle
are exa
c
tly symmetrical. T
h
e
waveforms
of radi
al an
d t
ange
ntial ma
gnetic fiel
d a
r
e
sho
w
n i
n
Figure 4, o
n
a ci
rcumfere
nce
who
s
e ce
nter
is
the ce
nter of
the
mag
net
steel
with th
e ra
diu
s
of
6.
6mm. In the i
deal
state, th
ere
is no relativ
e
position d
e
viation between
the ma
gnetic
steel and the hall
compo
nent
and
betwe
en th
e
hall
comp
one
nts,
so th
e a
m
plitude
of
th
e radial
mag
netic fiel
d the
hall
co
mpo
n
ent
is se
nsitive to
is the sa
me
as the am
plitude of
the ta
ngential m
a
g
netic field the
hall com
pon
ent
is insen
s
itive to, and the ph
ase differen
c
e betwe
en th
em is only 90
°.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Perm
anent M
agnet Trackin
g
Position Se
nso
r
(Deg
ang
Lv)
1809
Ma
gn
et
ic fl
ux
d
e
n
s
it
y
（
T
）
C
i
r
c
u
m
f
e
r
e
n
c
e
d
i
s
p
l
a
c
e
me
n
t
(
mm)
Ra
d
i
a
l
m
a
g
n
e
tic
f
i
e
l
d
T
a
n
g
e
n
ti
a
l
m
a
g
n
e
tic
f
i
e
l
d
Figure 3. Space Di
strib
u
tio
n
of Magnetic
Line
s of Mag
netic Steel
Figure 4. Rad
i
al and Tan
g
e
n
tial Magnet
Field
w
h
en
R=
6
.
6mm
2.3. The Opti
mation of M
a
gne
tic Field
In the design
of perman
e
n
t
magnet tracking
p
o
sition
sen
s
o
r
, there
is gene
rally positio
n
deviation in t
he axial direction for the in
stallation
of h
a
ll eleme
n
ts, as
sho
w
n in
Figure 5. In this
ca
se, the ma
gnetic field
sensed by the
hall eleme
n
ts is diffe
rent.
Certai
n mea
s
ures m
u
st b
e
taken
to mini
mize th
e e
r
ror of th
e
sen
s
ed
mag
netic field be
ca
use of t
he evitable
in
stallati
on
deviation. Th
e erro
r can b
e
decrea
s
e
d
by putting
the ring co
re on
the perip
hery
of hall eleme
n
ts
.
The optimai
o
n
of axial magneti
c
field of the
core i
s
analy
z
ed q
ualitatively by the softwa
r
e
ANSOFT.
Figure 5. Dist
ribution of Ma
gnetic Fiel
d in Diffe
rent Axial Position
s on a Circu
m
feren
c
e
with
R=5.5mm
Suppo
se the
positio
n deviation of hall element
s
onl
y exists in the axial dire
ction of the
surfa
c
e
of m
agneti
c
st
eel. In the o
u
tsid
e of ma
gnet
i
c
steel
with th
e oute
r
di
am
eter of
6mm,
the
inner dia
m
ete
r
of
3mm
and
the h
e
ight
of 3mm,
o
ne
h
a
ll elem
ents i
s
pl
aced
on
a
ci
rcumferen
c
e
who
s
e
ce
nter is the
axis
center
of the
magnet
steel
with the
ra
di
us
of 5.5mm,
while
the
other
hall elem
ents is pla
c
e
d
on
a ci
rcumfere
nce
wh
ose
center i
s
1m
m
away from
the axis
ce
nte
r
of
the magn
et steel with the radiu
s
of 5.5m
m. The distri
b
u
tion of magn
etic field inten
s
ity vectors o
n
the surfa
c
e
of hall eleme
n
ts is sho
w
n
in Figur
e 5.
The Z-axi
s
comp
one
nt of magnetic field
intensity o
n
a
ci
rcumferen
c
e of the
axi
s
cente
r
of
the
magnet
ste
e
l
is
ze
ro, b
u
t it is not
ze
ro
o
n
any other
circumfere
nce. Thus, the p
r
oj
ects of
ma
gn
etic field inte
nsity vectors
in X-Y plane
are
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02-4
046
TELKOM
NIKA
Vol. 11, No. 4, April 2013 : 1807 – 1
812
1810
not equal, th
at is, the pro
j
ect of magnetic fi
eld int
ensity on a ci
rcu
m
fere
nce
who
s
e
cente
r
is
1mm a
w
ay from the
axis
center i
s
mu
ch smalle
r
th
an
th
a
t
on
a c
i
r
c
umfe
r
e
n
c
e
w
h
os
e ce
n
t
e
r
is
the axis ce
nter, as
sho
w
n
in Figure 6.
Figure 6.Top
View of Magn
etic Di
stributi
on in Di
fferent Axial Pos
i
tions
on a
Circ
umferenc
e
with
R=5.5mm
Distri
bution
of mag
netic field inte
nsi
t
y ve
ctors in
differe
nt ax
ial po
sition
s on
two
circumfe
ren
c
es i
s
sh
own i
n
Fig
u
re
7,
where
the
rin
g
co
re
is pla
c
ed in
the
out
side
of m
agn
etic
steel. Th
e project
s
of mag
netic field i
n
tensity ve
cto
r
s in X-Y
plan
e are
sh
own i
n
Figu
re 8,
where
the proje
c
t deviation is si
gnifica
ntly decre
ased a
fter the iron core is placed, and the error of
magneti
c
fiel
d compo
nent
se
nsed by t
he hall
elem
e
n
ts i
s
effectiv
ely wea
k
e
n
e
d
. Thu
s
, be
si
des
the method to
improve the i
n
stallatio
n
de
viation,
the method to ap
pl
y the ring core can
de
cre
a
s
e
the axial deviation and o
b
tain a goo
d pe
rforma
nce.
Figure 7. Dist
ribution of Ma
gnetic Fiel
d in
Different Axia
l Positions o
n
a Circumfere
nce
with R=5.5m
m (with iro
n
core
)
Figure 8. Bottom View of M
agneti
c
Di
stri
bution
in Different A
x
ial Positions
on a Circu
m
feren
c
e
with R=5.5m
m (with iro
n
core
)
2.4. The Arc
t
angen
t
Meth
od based
Re
solv
er-to-Di
g
ital Conv
ersion
In this p
ape
r, the origi
nal
sign
al of th
e po
sition
se
nso
r
i
s
de
co
ded by th
e a
r
ctan
gent
method [4]. T
he impl
ement
method
of a
r
ctan
gent i
s
t
o
solve the
p
hase an
gle
a
c
cordi
ng to
the
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TELKOM
NIKA
ISSN:
2302-4
046
Perm
anent M
agnet Trackin
g
Position Se
nso
r
(Deg
ang
Lv)
1811
input sin
e
an
d co
sine
sig
nals, that is,
to so
lve the arcta
ngent
value of the sine a
nd cosine
sign
als,
1
sin
ta
n
cos
V
V
, so
as to g
e
t the
positio
n an
gl
e
θ
. We
can
get more a
c
cura
cy angl
e
positio
n by th
e an
alysi
s
o
n
stable
e
rro
r [
5
] and
dyna
m
i
c e
r
ror [6] an
d e
rro
r
com
p
ensation. Fi
g
u
re
9 sho
w
s the circuit st
ru
cture of resolver-t
o-di
gital
conv
ersi
on with th
e arcta
nge
nt method.
Arc
ta
ng
en
t
me
t
h
od
d
sin
d
cos
de
rivato
r
d
n
12-
bi
t
A/
D
Po
sit
i
on
t
r
an
s
duc
e
r
Po
l
a
ri
ty
tra
n
sfo
r
ma
t
i
o
n
dsp
fil
t
er
sca
l
e
r
d
Figure 9
.
Circuit Structure of Arctang
ent
3. Experimental Re
sults
and Applica
t
ion
Two o
r
thog
o
nal linea
r hall
sen
s
o
r
s
sen
s
e t
he ma
gn
etic field co
m
pone
nts which re
sults
from two
-
pol
e
ring m
agn
etic ste
e
l an
d th
us o
u
tput two
pha
se o
r
tho
gonal
co
sine
voltage si
gna
ls,
as
sh
own in
Figu
re
10. I
t
can
be
se
en from the
tested
wavef
o
rm
s that
th
e two
si
gnal
s i
s
compl
e
tely orthogon
al with
the phase di
fference of 90
0
，
whi
c
h
will be then decoded to obtai
n
the positio
n si
gnal.
Figure 10. Waveform
s of Output Signal
s of Hall Sen
s
ors
Figure 11. Te
st Platform of Position Sen
s
or
Fi
gure 12. Te
st Wavefo
rm of Angular Po
sition
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ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No. 4, April 2013 : 1807 – 1
812
1812
The expe
rim
ental platform
is esta
blish
e
d
for
the test
of the trackin
g
positio
n se
nso
r
, as
sho
w
n i
n
Fig
u
re
11. The
output waveform of a
ngul
ar p
o
sition
fo
r the h
a
ll effe
ct ba
sed t
r
a
c
king
positio
n
sen
s
or i
s
sh
own i
n
Fig
u
re
12.
The
cu
rve b
e
t
ween
the
rot
a
tion
spe
ed
a
nd the
a
r
mat
u
re
voltage of
DC moto
r for the de
sig
ned t
r
ackin
g
p
o
siti
on sen
s
o
r
is
sho
w
n i
n
Fig
u
re
13, whe
r
e the
sep
a
rately e
x
cite DC mo
tor with the
rated ex
citin
g
cu
rrent of
0.3A
and the
rated
spe
e
d
of
2400
r/min is
use
d
.
Figure 13. Cu
rve betwe
en the Rotatio
n
Speed
a
nd the
Armature Voltage of DC Motor
4. Conclusio
n
A novel tra
c
king
po
sition
sen
s
o
r
i
s
d
e
sig
ned
whi
c
h provides a
new
sol
u
tio
n
for the
spe
ed an
d p
o
sition m
e
a
s
urem
ent of motor
c
ontrol
system. Th
e experim
ent
and ap
plication
results
sh
ow
that the re
sol
u
tion an
d p
r
e
c
isi
on
of th
e
desi
gne
d po
sition se
nsor
can compl
e
tel
y
meet the re
q
u
irem
ents of
the motor
co
ntrol sy
stem, and can repl
ace the
phot
oele
c
tric
en
coder
with the sam
e
resolution a
nd pre
c
i
s
ion,
so
it is of gre
a
t practi
cality in engin
eeri
n
g.
Ackn
o
w
l
e
dg
ement
This p
r
oje
c
t is su
ppo
rted b
y
National Na
tural Scie
nce Found
ation of
China (511
0
7023
)
Referen
ces
[1] Yu
Qing
gua
ng
，
Liu Ku
i
，
W
a
ng Ch
on
g. Cho
i
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e
n
cod
e
r an
d Me
asure of Sp
ee
d an
d Roto
r
Place of S
y
nc
h
r
ono
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[2] Z
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Sh
i
y
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，
Ai Hua
，
H
a
n
Xu
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p
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w
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han
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iv
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arc T
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unctio
n
Us
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Assembl
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i
n
F
i
xe
d-p
o
int DS
P Based
on D
i
fferentia
l Evol
ution A
l
gor
ith
m
.
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ngi
neer
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g an
d
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6-92
8.
[5] Shigeo
Morimoto
, Masay
u
ki Sanada.
Sinusoidal curr
ent drive syst
em
of
per
m
anent m
a
gnet
synchro
nous
motor w
i
th l
o
w
resoluti
on
pos
ition s
ensor
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o
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the
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[6]
Jianr
ong B
u
, Lon
g
y
a
Xu.
Near-Z
ero S
p
eed Perf
orma
nce Enh
anc
e
m
ent of PM S
y
nc
hro
n
o
u
s
Machines Assisted by
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w
-
Cost Hall Effect
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Ap
p
lied P
o
w
e
r Ele
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nfe
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