TELKOM
NIKA
, Vol.13, No
.2, June 20
15
, pp. 381 ~ 3
9
0
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v13i2.991
381
Re
cei
v
ed
No
vem
ber 1
2
, 2014; Re
vi
sed
March 17, 20
15; Accepted
April 5, 2015
Analysis and Simulation on Torque Ripples of
Brushless DC Motor
Qian Weik
an
g
1
, Shi Yutao
2
Schoo
l of Optical-Electric
al a
n
d
Comp
uter En
gin
eeri
ng, Un
iv
ersit
y
of Sh
an
g
hai for Scie
nce
and
T
e
chnolog
y, S
han
gh
ai, Chi
n
a
2000
93
e-mail: q
w
k
a
n
g
@
sh1
63.net
1
, sy
t_alex@163.com
2
A
b
st
r
a
ct
Becaus
e of
its small s
i
z
e
,
hig
h
re
lia
bil
i
ty, effi
ciency, a
nd
its outp
u
t torque
char
acteristics,
brush
l
ess DC
motor (B
LDCM
) had b
een w
i
d
e
ly use
d
in
ma
ny field of ro
bo
tics, precisio
n i
n
struments an
d
equ
ip
me
nt, etc. How
e
ver, its
inh
e
r
ent el
ectr
omag
netic torq
ue rip
p
le l
i
m
ite
d
the scop
e
of its applic
atio
n
,
w
h
ich w
a
s the focus an
d diffic
u
lty of its rese
arch in re
c
ent
years. T
h
is arti
cle fi
rst describ
ed the ca
uses
of
brush
l
ess DC
motor tor
q
u
e
rippl
e, an
d the
n
torqu
e
rip
p
l
e
ge
nerate
d
b
y
four PW
M mo
du
latio
n
s w
a
s
ana
ly
z
e
d
to
ge
t opti
m
u
m
co
ntrol sc
he
me, fi
n
a
lly
the
MAT
L
AB / SIMULINK sim
u
lati
on
mo
d
e
l
ve
ri
fi
ed
the
ana
lysis of the
results. T
h
is pa
per prov
id
ed the m
o
st intuiti
o
n
i
stic exhi
bitio
n
.
Ke
y
w
ords
:
Brushl
ess DC
mo
tor, T
o
rque rip
p
le, MAT
L
AB/SIMULINK
1. Introduc
tion
Brushle
ss DC motor (BL
DCM
) is on
e
type
of permanent mag
net synch
r
o
n
ous moto
r,
whi
c
h i
s
wildl
y
used i
n
ma
ny fields. It has g
ood
sp
e
ed re
gulatio
n
cha
r
a
c
teri
sti
cs,
su
ch a
s
h
i
gh
efficien
cy, long life, lo
w
noise, high
spe
ed
ran
g
e
,
good
outp
u
t ch
ara
c
te
ristics a
nd ot
her
advantag
es [1]. The
appli
c
ation
s
of
brushl
ess
DC (BLDC) moto
rs an
d drive
s
have gro
w
n
signifi
cantly due to their
high po
we
r d
ensity and
e
a
sy co
ntrol
method in
re
cent yea
r
s in
the
applia
nce in
d
u
stry and the
automotive in
dustry [2].
Ho
wever, it
h
a
s th
e di
sa
dvantage
of to
rque
ri
ppl
e, a
nd thi
s
will
re
duce the
reliability of
power tra
n
smissi
on
syst
em. What m
entione
d abo
ve rest
rict
s the appli
c
atio
ns in the hi
g
her
accuracy
sy
stem. The
mai
n
cau
s
e
of th
e d
r
awba
ck
i
s
the
existe
n
c
e
of ind
u
cto
r
. Beca
use of
the
indu
ctor, the curre
n
t cann
ot chang
e immediately at
the time of commutation. So that it cause
s
the com
m
uta
t
ion torqu
e
ri
pple. The
proce
dure
ha
s been inve
st
igated compl
e
tely in [3]-[4].
What’
s
mo
re,
the existen
c
e of indu
ced
emf and
swit
chin
g metho
d
which, in ce
rtain conditio
n
s
cau
s
e the fo
rward bia
s
of diode
s conn
e
c
ted to ina
c
tivepha
se an
d lead to cu
rre
n
t flow in ina
c
tive
pha
se
and
m
a
ke
s to
rqu
e
ri
pple [5].
Due
to the infl
u
e
n
c
e
of the to
rq
ue
ripple, th
e
hot topi
c
of t
h
e
pre
s
ent
study
of BLDM i
s
comm
utation
torque
rip
p
le
sup
p
re
ssion,
and the
way to su
pp
re
ss th
e
torque
rippl
e i
s
the imp
r
ove
m
ent of PWM
mode.
Different modul
atio
ns of PWM
u
s
ed in B
L
DCM
will g
ene
rate
differe
nt torque
rip
p
le.
There
a
r
e
four types of
PWM
mod
u
lation
propo
se
d
inclu
d
ing Hp
wm-Lon, Ho
n
-
Lp
wm,
p
w
m
-
on
a
nd on-pwm.
All four
m
odulatio
ns ca
n drive
the
m
o
tor
su
ccessfully, but the probl
e
m
is whi
c
h on
e
can g
ene
rat
e
the lowe
st torqu
e
rip
p
le.
By the calcul
ation, this pa
per
will analy
z
e t
he influe
n
c
e
s
of four types of PWM
mode on
the torque ripple duri
ng
commutation cl
early. Four
types of result will be compared to find t
he
lowe
st one.
To prove the
analysi
s
re
sult, the BLDCM sim
u
latio
n
model with
different PWM
mode
s
will b
e
built in m
a
tlab/simuli
nk.
Four type
s o
f
PWM mod
u
l
ation can b
e
applie
d to t
he
model, si
mul
a
tion re
sult
can present t
he con
c
lu
sio
n
intuitively and can p
r
ovi
de refe
re
nce
for
further
study of brushle
ss
DC moto
r.
2. Compone
nts And Principles of BL
DM Co
ntrol
Sy
stem
As sho
w
n in
the Fig
u
re
1,
BLDCM control syst
e
m
co
nsi
s
ts of five
comp
one
nts,
su
ch a
s
DC po
we
r, logic control, p
o
we
r drive,
ro
tor positio
n d
e
tection
syste
m
and motor.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 381 – 39
0
382
Fig
u
re 1. Block Dia
g
ra
m of BLDCM
Control System
In this control
system, power drive unit i
s
a
th
r
e
e-
p
has
e
in
ve
r
t
er
, it c
o
n
t
a
i
ns
s
i
x IG
BT
s
.
Furthe
r mo
re,
logic control unit and rotor position
d
e
te
ction sy
stem
are the mo
st i
m
porta
nt units.
The lo
gic co
ntrol u
n
it will
su
pply the
power to
ea
ch
pha
se
wi
nding,
and
the rotor po
si
tion
detectio
n
sy
stem contai
ns
three h
a
ll sen
s
ors
whi
c
h
ca
n provid
e the
informatio
n o
f
rotor p
o
sitio
n
and
spe
ed. T
hey ca
n
control the o
r
de
r a
nd time
of e
a
c
h p
h
a
s
e
con
ductio
n
of mo
tor stato
r
, the
n
the average
voltage of e
a
c
h p
h
a
s
e
win
d
ing
s
can
be
controlled. T
h
erefo
r
e the
system can
dri
v
e
and control th
e bru
s
hle
s
s DC motor [6].
3. The Math
e
m
atical Mod
e
l of BL
DCM
Assu
ming tha
t
the magnetic ci
rcuit i
s
un
satura
ted, ed
dy current an
d hystere
s
i
s
losse
s
are not
con
s
i
dere
d
. Thre
e-pha
se voltag
e equatio
n across the moto
r windi
ng
s is
as follo
ws:
c
b
a
c
b
a
c
cb
ca
bc
b
ba
ac
ab
a
c
b
a
c
b
a
c
b
a
e
e
e
i
i
i
p
L
M
M
M
L
M
M
M
L
i
i
i
R
R
R
u
u
u
0
0
0
0
0
0
(1)
Whe
r
e
c
b
a
u
u
u
,
,
are the thre
e-ph
ase vol
t
ages
；
c
b
a
i
i
i
,
,
are t
he thre
e-p
h
a
se
cur
r
e
n
t
s
；
c
b
a
e
e
e
,
,
are
the ba
ck e
m
fs
；
c
b
a
R
R
R
,
,
are th
e st
ator resi
stan
ces
；
c
b
a
L
L
L
,
,
are the
stator wi
ndin
g
s
self
-ind
uct
i
ons
；
cb
ca
bc
ba
ac
ab
M
M
M
M
M
M
,
,
,
,
,
a
r
e mu
tu
a
l
-
i
nd
uc
tio
n
s
be
tw
ee
n
the two-p
h
a
s
e windi
ng
s of stator;
p
is deri
v
ate operato
r
（
t
d
d
p
/
）
in (1).
Becau
s
e
of
three
-
ph
ase
windi
ng
s a
r
e
co
mpletely
symmetri
c
al
and th
e p
e
rmanent
magnet m
agn
etic pe
rme
abi
lity approxim
ates ai
r, mor
eover, it is a
star
wou
nd type. It can
can
be
assume
d tha
t
three
-
ph
ase
win
d
ing i
n
d
u
ctan
ce
a
n
d
mutual i
ndu
ctan
ce
are
consta
nt, furth
e
r-
more, th
ey h
a
ve nothi
ng
to do
with
th
e rotor po
sition. Th
en
eq
uation
s
can
be o
b
taine
d
as
follows
:
L
L
L
L
c
b
a
(2)
M
M
M
M
M
M
M
cb
ca
ba
bc
ac
ab
(3)
0
c
b
a
i
i
i
(4)
R
R
R
R
c
b
a
(5)
Con
s
id
erin
g above thre
e-pha
se voltag
e equatio
n is
c
b
a
c
b
a
c
b
a
c
b
a
e
e
e
i
i
i
p
M
L
M
L
M
L
i
i
i
R
R
R
u
u
u
0
0
0
0
0
0
0
0
0
0
0
0
(6)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Analysis a
nd
Sim
u
lation on Torqu
e
Rip
p
l
e
s of Bru
s
hle
ss
DC M
o
tor
(Qian
Wei
k
an
g)
383
The ele
c
trom
ech
ani
cal torque is:
m
c
c
b
b
a
a
e
i
e
i
e
i
e
T
(7)
Whe
r
e
m
is motor mechanical speed in (7).
4. Anal
y
s
is o
f
torque ripple
There are two main cau
s
e
s
of torqu
e
ri
pple,t
he first is the existe
n
c
e of alveol
u
s
, and the
se
con
d
is co
mmutation torque rip
p
le.Thi
s pap
er will fo
cu
s on the lat
t
er.
4.1.Commutation Princip
l
e of BL
DCM
The eq
uivale
nt circuit of
BLDCM is
shown
in Fig
u
r
e 2. Th
ere
are
six IGBT
s in the
equivalent
m
odel
namely
T1, T3, T
5
, T
4
, T6
and
T2.
They m
a
ke
up th
ree
-
ph
a
s
e i
n
verte
r
circuit
[7].
Figure 2. the Equivalent Ci
rcuit of BLDCM
IGBT will be
triggered a
c
cording to th
e ord
e
r
that i
s
cal
c
ul
ated
by the inform
ation of
rotor
po
sition
detectio
n
sy
stem. Only two of
three
pha
se
s are
active at any
time. The m
a
in
prin
ciple i
s
to let the corre
s
pondi
ng pha
se on wh
en th
e magneti
c
field is st
rong
e
s
t.
Based o
n
ele
c
trom
agn
etic
indu
ction pri
n
ciple, the ba
ck emf of each
phase is:
rlB
Z
e
D
(8)
Whe
r
e
r
is the distance bet
wee
n
the
stator and the rotor ce
nter;
l
is the length of the
magnet steel;
D
Z
is the num
ber of the eff
e
ctive co
ndu
ctors ab
out stator sin
g
le-p
hase;
B
is
magneti
c
ind
u
ction inte
nsit
y;
is the elect
r
ical a
ngul
ar
spe
ed of roto
r.
Con
s
id
erin
g (8), as the b
a
ck e
m
f of sin
g
le-p
ha
se wi
nding i
s
in proportio
n
to magneti
c
field inten
s
ity, the ba
ck emf
in condu
ctio
n time
of the
singl
e-p
h
a
s
e
windi
ng i
s
ma
ximal whe
n
t
he
spe
ed is
co
n
s
tant. At the same time, t
he ele
c
trom
a
gnetic to
rqu
e
is also maxi
mal. Acco
rdi
n
g
to
the an
alysi
s
, the rule
of
comm
utation
ca
n b
e
d
r
a
w
n li
ke
Figu
re 3.
Whe
r
e
k
is
ba
ck emf
coeffici
ent, the value is
m
D
rlB
Z
,
m
B
is the maximum
of magnetic f
i
eld inten
s
ity.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 381 – 39
0
384
Figure 3. The
Rule of Com
m
utation
4.2. Cause o
f
commuta
ti
on torqu
e
ripple
In an ideal si
tuation, back
EMF waveform is
trape
zoi
dal, the width
of its flat-top is 120
electri
c
al
an
g
l
e. At the sa
me time, the
pha
se
cu
rre
n
t wavefo
rm
is recta
ngul
ar who
s
e
wi
dth
is
also 1
20 ele
c
trial angle. O
n
ce the
state is not
like that
, it will genera
t
e the torque
ripple [8].
In a real–
w
o
r
ld situation, the existen
c
e
of
inducto
rs make the
current ca
nnot
chan
ge
immediately,
hen
ce th
e th
e ba
ck EMF
waveform o
r
curre
n
t waceform i
s
not li
ke that in
an
ideal
situation.So that it is the cause
of the commutation t
o
rque ripple.
The va
riation
of current
a
nd torque
du
ring th
e p
r
o
c
ess of
com
m
u
tation i
s
sh
own
in
Figure 4 in d
e
tail. In [9]-[11], the variation of
cu
rrent
corre
s
po
ndi
ng to differe
n
t
condition
s
wa
s
discu
s
sed in
detail.
Figure 4. wav
e
form of cu
rrent
and torq
u
e
durin
g co
m
m
utation
5. Influences
of PWM Mo
des on The
Torque
Ripp
le
As i
s
kno
w
n
to all, the
r
e
a
r
e
six
kind
s
o
f
state o
n
IG
BTs of
thre
e-pha
se i
n
verte
r
. They
are T1T
6
, T1T2, T3T
4
, T3T2, T5
T
4
and T5T6.
The IGBT which i
s
on
will
be
gi
ven PWM
si
gnal,
hen
ce th
e av
erag
e voltag
e
of stato
r
win
d
ing
ca
n be
controlle
d by
changi
ng the
PWM d
u
ty rat
i
o.
PWM mod
u
la
tions a
r
e divi
ded into two
categ
o
rie
s
, such
as
Hp
wm
-Lp
w
m mo
de
whi
c
h bel
ong
to
doubl
e-cho
p
PWM cont
rol modulatio
n, Hp
wm-Lon
m
ode
、
Hon
-
Lp
wm m
ode
、
p
w
m-on m
ode
and
on-p
w
m mo
d
e
that belong
to single-ch
op PWM c
o
n
t
rol modulatio
n. Due to the loss of dou
b
l
e-
cho
p
PWM control
mode
on IGBT i
s
t
w
ice a
s
m
u
ch a
s
that of
singl
e-cho
p
PWM
control
,
the
influen
ce of t
he PWM
mo
des
belo
ng t
o
sin
g
le-ch
o
p
PWM
contro
l modulatio
n
on commutati
on
torque
rippl
e wa
s analy
z
ed
in this pape
r. These fo
ur P
W
M mod
e
s a
r
e sh
own in F
i
gure 5 [12].
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Analysis a
nd
Sim
u
lation on Torqu
e
Rip
p
l
e
s of Bru
s
hle
ss
DC M
o
tor
(Qian
Wei
k
an
g)
385
Figure 5. Single-cho
p
PWM Control Mo
dulation
5.1. Analy
s
is
of The Com
m
utating Pr
ocess o
f
Up
per Bridg
e
-a
rms
Con
s
id
erin
g the circuit in Figure 2, the commu
tation
process fro
m
T1T2 state
to T3T2
state will
be
analyzed, th
at is to
say
T1 commu
tat
e
to T3. In t
he p
r
o
c
e
ss
of comm
utation,
para
s
itic di
od
e V4 is in a st
ate of stream.
(1)
Hp
wm-Lon a
nd pwm
-
o
n
modulatio
n
Acco
rdi
ng to
Figure 5, th
e
states du
rin
g
the commutat
i
on u
nde
r
Hp
wm-Lon
an
d
pwm
-
on
modulatio
n a
r
e same. In
th
e p
r
o
c
e
s
s of
comm
utation,
pa
ra
sitic
dio
de V4
is in
a
state of
st
rea
m
,
T3 i
s
given
P
W
M
sign
al a
n
d
T2
keep
s o
n
. Thu
s
th
ese
two
kin
d
s of
PWM m
odula
t
ion go
into th
e
same
categ
o
ry to be analyzed.
Assu
ming
tha
t
the termi
nal
volt
age of th
ree
-
ph
ase inv
e
rter is
d
U
.Considerin
g Fig
u
re 2,
the voltage o
f
A phase is
0V for the p
a
r
asiti
c
dio
de
V4 is in
a st
ate of stream
becau
se of
T3
PWM
sign
al.
The volta
ge
of B ph
ase i
s
d
U
whe
n
T
3
i
s
on
an
d the
voltage of
ph
ase
B i
s
0V
when T3 is off. So
that th
e vo
ltage of B phase
can be assumed as
d
DU
(D i
s
du
ty radio of
PWM sig
nal
). Then the vol
t
age of C ph
ase i
s
0V
by rea
s
on
of that T2 keep
s o
n
. Based o
n
(6
)
three
-
ph
ase voltage eq
uati
ons
can b
e
d
edu
ced a
s
fol
l
ows:
N
N
N
N
N
N
c
b
a
c
b
a
c
b
a
d
U
U
U
e
e
e
i
i
i
p
M
L
M
L
M
L
i
i
i
R
R
R
DU
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(9)
W
h
er
e
N
N
U
0
is the
voltage
of ne
utral p
o
int in
(9).
Con
s
ide
r
i
ng Fig
u
re 3,
k
e
e
c
b
whe
n
T3
T2 i
s
on. At the
sa
me time, it
ca
n be
a
s
sumin
g
that
k
e
a
for the c
o
mmutation time
is sh
ort. Com
b
ining (4) a
n
d
(9) , the voltage of neutral
point is:
k
DU
U
d
N
N
3
1
3
1
0
(10
)
Plugging
(10
)
into (9), the equatio
n ca
n be written a
s
follow:
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Vol. 13, No. 2, June 20
15 : 381 – 39
0
386
)
3
4
(
)
(
3
1
)
3
2
2
(
)
(
3
1
)
3
2
(
)
(
3
1
c
d
c
b
d
b
a
d
a
Ri
k
DU
M
L
dt
di
Ri
k
DU
M
L
dt
di
Ri
k
DU
M
L
dt
di
(11
)
Acco
rdi
ng to
the analysi
s
, it can be known that
0
)
0
(
,
)
0
(
)
0
(
0
b
c
a
i
i
i
i
be
fo
r
e
comm
utation.
At the same
time, the resi
stan
ce
of wi
n
d
ing can be i
gnored
when
the frequ
en
cy of
PWM sig
nal i
s
high. Con
s
i
derin
g (1
1), a
pproxim
ate value of three
-
pha
se current
is:
t
k
DU
M
L
i
i
t
k
U
M
L
i
t
k
DU
M
L
i
i
d
c
d
b
d
a
)
4
(
)
(
3
1
)
2
2
(
)
(
3
1
)
2
(
)
(
3
1
0
0
(12
)
Combi
ned
with (12
)
a
nd (7),the
electrome
c
h
a
n
ical
torq
ue
of BL
DCM du
ring
comm
utation
can b
e
derive
d
:
t
k
DU
M
L
k
n
ki
n
T
d
p
p
)
8
2
(
)
(
3
2
0
1
(13
)
The ele
c
trom
ech
ani
cal torque of BLDCM before
com
m
utation is:
0
0
2
)
(
ki
n
i
e
i
e
i
e
n
T
p
c
c
b
b
a
a
p
(14
)
Comp
ared (1
3) with (14), t
he value of the torque
rippl
e can b
e
obta
i
ned a
s
：
t
DU
k
M
L
k
n
T
T
T
d
p
)
2
8
(
)
(
3
1
0
1
(15
)
(2)
Hon
-
Lp
wm a
nd on-pwm modulatio
n
It is same
as th
e p
r
evi
ous sectio
n. Acco
rding
to figure 5,
the
states du
ring th
e
comm
utation
unde
r Hpwm-Lo
n
an
d pwm
-
on m
o
dulation a
r
e
same. In
the pro
c
e
ss of
comm
utation,
para
s
itic
dio
de V4 is i
n
a
state of st
rea
m
, T2 is give
n PWM
sign
a
l
and T3
ke
e
p
s
on. Thu
s
these two kin
d
s of
PWM modul
ation go into the sam
e
cate
gory to be an
alyzed.
Con
s
id
erin
g f
i
gure
1, like
that in previo
us
se
ction
th
e
voltage of
three pha
se can be
obtaine
d as
V
u
a
0
,
d
b
U
u
,
d
c
U
D
u
)
1
(
.
D
is al
so the
duty radio of
PWM si
gnal.
Like
the analytic
pro
c
ed
ure a
dopted a
bov
e, the el
ect
r
omagn
etic
to
rque duri
ng the
com
m
uta
t
ion
p
r
oc
es
s
is
:
t
DU
U
k
M
L
k
n
T
T
T
d
d
p
)
4
2
8
(
)
(
3
2
0
2
(1
6)
Comp
ared (1
5) with (16), t
he torqu
e
rip
p
le ca
n be written as follows:
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TELKOM
NIKA
ISSN:
1693-6
930
Analysis a
nd
Sim
u
lation on Torqu
e
Rip
p
l
e
s of Bru
s
hle
ss
DC M
o
tor
(Qian
Wei
k
an
g)
387
0
)
1
(
)
(
3
2
)
4
2
8
(
)
(
3
)
2
8
(
)
(
3
2
1
D
M
L
t
kU
n
t
DU
U
k
M
L
k
n
t
DU
k
M
L
k
n
T
T
d
p
d
d
p
d
p
(17
)
Hen
c
e the re
sult of analysi
s
is:
2
1
T
T
Obviou
sly, the commutati
on to
rqu
e
ri
p
p
le of
Hp
wm
-Lon
a
nd
pwm-on
mo
dula
t
ion i
s
lowe
r tha
n
th
at of Ho
n-L
p
w
m a
nd o
n
-p
wm mo
dulat
i
on du
ring
the
comm
utating
pro
c
e
s
s of u
pper
bridg
e
-arm
s.
5.2. Analy
s
is
of the Commutating Pr
ocess o
f
Lo
w
e
r
Bridg
e
-a
rms
Con
s
id
erin
g t
he
circuit in
figure
2, the
commutation
from T
1
T6
sta
t
e to T1T
2
state, that
is to say T6 comm
utate to T2 will be analyzed.
In the pro
c
e
s
s of commutatio
n
, para
s
itic di
ode
V3 is in
a
sta
t
e of stream,
Like th
e a
nal
ytic
pro
c
e
dure ado
pted
ab
ove, the torq
ue ri
pple
duri
n
g
the comm
utation pro
c
e
s
s can also be ca
lculate
d
as fol
l
ow:
(1)
Hp
wm-Lon a
nd on-pwm modulatio
n
t
DU
U
k
M
L
k
n
T
T
T
d
d
p
)
4
2
8
(
)
(
3
3
0
3
(1
8)
(2)
Hon
-
Lp
wm a
nd pwm
-
o
n
modulatio
n:
t
DU
k
M
L
k
n
T
T
T
d
p
)
2
8
(
)
(
3
4
0
4
(19
)
Compared (18) with (19), t
he torque ripple is
as
follows
：
0
)
1
(
)
(
3
2
)
2
8
(
)
(
3
)
4
2
8
(
)
(
3
4
3
D
M
L
t
kU
n
t
DU
k
M
L
k
n
t
DU
U
k
M
L
k
n
T
T
d
p
d
p
d
d
p
(20
)
Then the result of analysis is:
4
3
T
T
Thus,
du
ring
the commuta
ting p
r
o
c
e
s
s
of lower bri
d
ge-a
r
m
s
, th
e
co
mmutation
torq
ue
ripple
of Ho
n-Lp
wm
and
pwm
-
on
mo
dulation i
s
l
o
wer than th
a
t
of Hp
wm-L
on an
d o
n
-p
wm
modulatio
n.
So far,
con
c
l
u
sio
n
i
s
that t
he
co
mm
utation torque
rip
p
le
with p
w
m
-
on
mod
e
du
ring
comm
utation
is the lowest
among all fou
r
mode
s.
6. MATL
AB/
SIMULINK Simulation Mo
del
MATLAB pro
g
ram i
s
de
si
gned for
co
mputer
simul
a
tion [13]. It was u
s
e
d
to build a
simulatio
n
m
odel of BL
DCM a
c
cordin
g to the p
r
in
ciple
ado
pted
above. The
model of BL
DCM
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93-6
930
TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 381 – 39
0
388
control
syste
m
is sho
w
n i
n
Fig
u
re
6. I
n
this
a
nalysi
s
, the
sim
u
la
tion pa
ram
e
ters
were
set
a
s
f
o
llow.
The
st
at
or
win
d
ing r
e
si
st
a
n
ce
875
.
2
R
；
The
stator
win
d
ing ind
u
ct
ance
mH
L
5
.
8
; the ine
r
tia
moment
2
4
10
8
m
kg
J
; Pole pai
rs
2
p
;DC bus
voltage
wa
s
500V; Given
spe
ed
wa
s 3
000rad/s. At
la
st, the lo
ad
torqu
e
chan
ged from
m
N
0
to
m
N
3
after 0.5 se
co
nd.
In this
simula
tion model
, the p
w
m u
n
it contai
ned t
w
o co
mpon
ent
s such a
s
th
e HAL
L
unit and the pwm control. The functio
n
of HALL uni
t wa
s to receive the informa
t
ion of the rotor
positio
n.With
the inform
ation, the timin
g
of
com
u
tation could
be
achi
eved. Fol
l
owin
g that was
pwm
c
ontrol
unit.In this
unit PWM modulation c
o
ul
d be c
h
anged to observe
the v
a
riety about the
torque wavef
o
rm.
Figure 6. Simulation Mod
e
l
of BLDCM
7.Simulation Result
The si
mulati
on re
sult of
the BLDCM
model i
s
sh
own i
n
Figu
re 7. It is the sp
eed
waveform. As sho
w
n obvi
ously, the m
o
tor went
int
o
stea
dy stat
e after 0.2
seco
nd an
d speed
arrive
d at the given value. Becau
s
e of t
he fluct
uatio
n
of load torqu
e
, the spee
d fluctuated at
0.5
se
con
d
. Th
en
the
spe
e
d
re
turned
to th
e
stable
stat
e
a
fter le
ss than
0.2 second.
So far, it
gav
e a
con
c
lu
sio
n
that the simulat
i
on model
of
BLDCM is a steady control system.
0
0.
1
0.2
0.
3
0.4
0.
5
0.
6
0.
7
0.8
0.
9
1
-5
0
0
0
50
0
10
00
15
00
20
00
25
00
30
00
35
00
Figure 7. the Wavefo
rm of Simulation Result
In the simula
tion, PWM mode we
re ch
ange
d. The torqu
e
wavef
o
rm corre
s
po
nding to
four kin
d
of PWM mod
u
lati
ons(Hpwm-L
on, Hon
-
Lp
wm, pwm-on, o
n
-p
wm) i
s
sh
own in Fig
u
re
8.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Analysis a
nd
Sim
u
lation on Torqu
e
Rip
p
l
e
s of Bru
s
hle
ss
DC M
o
tor
(Qian
Wei
k
an
g)
389
0.915
0.
92
0.925
0.93
0.
935
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
5
5.
5
<
E
l
e
c
t
r
o
m
agneti
c
tor
q
ue T
e
(
N
*
m
)
>
0.
915
0.
9
2
0.
9
2
5
0.
9
3
0.
935
1
2
3
4
5
6
<
E
l
e
c
t
r
o
m
agnet
i
c
t
o
r
q
ue T
e
(
N
*
m
)
>
(a)
Hp
wm-Lon
(b) Hon-Lp
wm
0.
9
1
0.
915
0.
92
0.
925
0.
93
0.
935
0.
9
4
0
1
2
3
4
5
<
E
l
e
c
t
r
o
m
a
gnet
i
c
t
o
r
que
T
e
(
N
*m
)
>
0.
91
5
0.
92
0.
9
2
5
0.
93
0
.
935
1
2
3
4
5
6
<
E
l
e
c
t
r
o
m
agnet
i
c
t
o
r
que
T
e
(
N
*
m
)
>
(c)
pwm-on
(d) on-pwm
Figure 8. The
Waveform of
torque
Viewing Fi
gu
re(a), Fig
u
re
(b), Figu
re
(c)
and Fig
u
re
(d
) in Figure 7, i
t
is obviou
s
ly to see
that
the wave
form co
rre
sp
ondin
g
to pwm-on
mod
u
la
t
i
on i
s
the
mo
st ste
ady
(wit
hout b
u
rr
)am
ong
all mode
s. A
s
the a
nalysi
s
ab
ove, the
comm
utatio
n torqu
e
ri
pp
le with p
w
m
-
on mod
e
du
ring
comm
utation
is the l
o
we
st
among
all mo
des. T
h
u
s
th
e pwm-o
n
m
odulatio
n is t
he be
st
sele
ction
in B
L
DC
M co
nt
rol sy
st
em.
8. Conclusio
n
This pap
er
d
e
scrib
ed
th
e basi
c
com
p
o
nents of
the
BLDCM control syste
m
, it con
s
i
s
ted
of DC po
we
r,
logic control, power
drive
,
ro
tor po
sitio
n
dete
c
tion
system an
d m
o
tor. Th
en th
e
mathemati
c
al
model of BL
DCM
and the
rule of
com
m
utation were analyzed,
on that ba
sis the
c
o
nc
lus
i
on
w
a
s
ob
ta
in
ed
th
a
t
th
e
e
x
is
te
nc
e
o
f
w
i
nd
in
g ind
u
c
tan
c
e
w
a
s
th
e ca
us
e o
f
comm
utation
torqu
e
. Spe
c
ific
rea
s
o
n
wa
s that
the
cu
rrent can
not chang
e i
mmediately d
u
rin
g
comm
utation.
Thus it ma
ke the torqu
e
wavefo
rm fluctuate. Fu
rtherm
o
re, accordi
ng to the
analysi
s
the
way to sup
p
ress rippl
e torque was the i
m
provem
ent of PWM mod
e
.
Based
o
n
the
analy
s
is ab
o
v
e, the
com
m
utation to
rq
ue
ripple
corresp
ondi
ng to
Hp
wm
-
Lon mo
dulati
on, Ho
n-L
p
wm modul
atio
n, pwm
-
on modulatio
n
a
nd
on
-p
wm modulatio
n were
cal
c
ulate
d
. After comp
utation it was
kn
own that
the
commutatio
n
torque
ripp
le with pwm
-
on
mode du
rin
g
comm
utation
wa
s the lowe
st among all f
our mo
de
s.
At last, a
sim
u
lation m
odel
wa
s
esta
blished i
n
MAT
L
AB/SIMULINK. The
re
sult
told u
s
that the to
rqu
e
ri
pple
was l
o
we
st if
pwm
-
on
mod
u
la
tion
wa
s us
ed
in
th
e co
n
t
r
o
l
s
y
s
t
e
m
. It
c
o
u
l
d
verify the con
c
lu
sion d
r
a
w
n
previou
s
ly is righ
t. Com
pared with othe
r pape
r, the si
mulation mo
d
e
l
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0
390
whi
c
h
wa
s u
s
ed
to vertify the result is very
si
mple
and
prati
c
al,
it will hel
p u
s
und
erstand
th
e
conte
n
t better.Other
pape
r only pre
s
ent
ed the theo
re
ti
cal analy
s
is,
but this arti
cl
e let us see t
he
existen
c
e of
torrq
ue ri
pp
les
clea
rly. Mean
while
t
he differe
nce
of the re
su
lts we
re
sho
w
n
intuitively.
Ackn
o
w
l
e
dg
ements
The
re
sea
r
ch p
r
oje
c
t
wa
s
sup
port
ed by th
e
Huji
ang
F
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