TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 9, September
2014, pp. 67
4
2
~ 674
9
DOI: 10.115
9
1
/telkomni
ka.
v
12i9.472
0
6742
Re
cei
v
ed O
c
t
ober 1
1
, 201
3; Revi
se
d May 12, 20
14; Acce
pted Jun
e
10, 2014
Model Identification of Traveling Wave Ultrasonic Motor
Using Step Response
Shi Jingzhu
o
*
, Zhang Ca
ixia
Hen
an Un
ivers
i
t
y
of Scie
nce a
nd T
e
chnol
og
y,
No.26
3
Kai
y
u
a
n
Dad
ao, Lu
o
y
ang 4
7
1
003, C
h
in
a. F
a
x: +
86-
379-
642
31
91
0
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: sjzne
w
@
1
6
3
.com, 1726
64
7
98@
qq.com
A
b
st
r
a
ct
Ultraso
nic
mot
o
r
’
s
mo
del
ad
aptin
g to c
ontr
o
l a
p
p
licati
on
i
s
the fou
n
d
a
ti
on of th
e
mot
o
r
’
s h
i
g
h
perfor
m
a
n
ce c
ontrol. Ultras
o
nic motor
’
s fre
que
ncy-sp
e
ed
control
mo
del
gives a sig
n
ifi
c
ation to i
m
pr
ove
spee
d contro
l
perfor
m
a
n
ce.
T
h
is pa
per sh
ow
s the des
i
g
n of stepp
ing
respo
n
se ex
pe
riments, an
d a
l
so
expl
ains the
mode
l ide
n
tificati
on of USM by the w
a
y of
characteristic po
int
metho
d
. Cons
ideri
ng its time
-
varyin
g char
ac
teristic, mo
de
l
para
m
eters ca
n be fitted
usi
ng functi
ons w
i
th the i
n
d
epe
nde
nt varia
b
l
e
is
freque
ncy or spee
d. Cons
equ
ently, non-
lin
ea
rity can
reflect i
n
spee
d contro
l mo
de
l appr
op
riately.
Ke
y
w
ords
: ultr
ason
ic motor, spee
d c
ontro
l, mo
de
l,
identific
ation
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
The ultra
s
o
n
i
c motor (USM) is a ki
nd of spe
c
i
a
l motor wh
ich u
s
e the
inverse
piezoele
c
tri
c
effect of the piezoele
c
tric materi
al to make the
stator g
ene
rate me
cha
n
i
c
al
vibration
whi
c
h i
s
i
n
the
u
l
traso
n
ic fre
q
uen
cy ba
nd.
And the
roto
r is
driven
through
the f
r
ict
i
on
betwe
en the stator an
d ro
tor [1-4]. The
USM cont
ai
ns a se
rie
s
o
f
nonlinea
r proce
s
s su
ch a
s
piezoele
c
tri
c
ene
rgy co
nversi
on, fri
c
tion e
ner
gy tran
sfer
a
nd so on.
Those n
onli
near
cha
r
a
c
teri
stics ma
ke th
e USM become
a co
ntrolle
d
obje
c
t whi
c
h
is no
nlinea
r, time-varyin
g
a
n
d
stron
g
co
upli
ng, and it is d
i
fficult to rea
lize the motion
control
with high preci
s
io
n.
The math
em
atical mo
del
of the cont
ro
lled
obje
c
t is the importa
nt foundation
of the
control
syste
m
’s a
nalysi
s
,
de
sign
an
d
perf
o
rma
n
ce a
s
sessme
nt. We
mu
st get the
US
M’s
mathemati
c
al
model
whi
c
h
is suitable fo
r co
ntrol
a
ppli
c
ation
s
to im
prove the
performan
ce
of the
USM’s move
ment cont
rol
device and
study more
reasona
ble control st
rateg
y
[2], [5-7].
The
USM’s mod
e
ling p
r
obl
em
ha
s not
b
een
solved
mainly be
ca
use
of the
particula
rity and
compl
e
xity of its ope
ration
mech
ani
sm
and the
hist
o
r
y of the US
M’s research
is short. Mo
st of
the re
se
arch i
s
the
o
reti
cal
modelin
g a
n
d
nume
r
i
c
al m
odelin
g which
ado
pt finite e
l
ement m
e
tho
d
and othe
r m
e
thod
s [8-1
0]. They are b
a
se
d on t
he
theoreti
c
al
kn
owle
dge of p
i
ezo
e
le
ctric a
nd
friction a
nd try to establi
s
h the mo
de
l whic
h ca
n compl
e
tely describ
e the
USM’s
runni
ng
pro
c
e
ss.
We
have made
great p
r
og
re
ss and th
ese
model
s have
beco
m
e a p
o
we
rful tool f
o
r
analyzi
ng a
n
d
de
signi
ng t
he
USM. But
these
mod
e
ls
are
too
com
p
lex and
difficult to
be di
re
ctly
applie
d to th
e control. A
nd b
e
cau
s
e
of we
have
n
’
t thorou
gh
unde
rsto
od
USM’s no
nlinea
r
cha
r
a
c
teri
stics or the
nonli
near
rep
r
e
s
e
n
tation of the
model is
not
comp
reh
e
n
s
i
v
e enoug
h, so
these model
s still have the
potential to improve.
From
the
pe
rspe
ctive of
control
ap
plica
t
i
on, the
US
M’s m
odeli
n
g
ca
n
also a
d
opt othe
r
method
s, su
ch a
s
syste
m
identification. The
US
M's in
put a
n
d
output
sig
n
a
ls
can
refle
c
t the
dynamic
cha
r
acteri
stic
of the motor
system, and if
we sele
ct the approp
ri
ate form of the in
put
sign
al, the in
put an
d o
u
tp
ut sig
nal
can
compl
e
te
ly contain th
e
USM’s n
on-li
ne
ar
cha
r
a
c
teri
stics
whi
c
h a
r
e
ou
r con
c
erns [2
-3], [11]. So
we
can
u
s
e t
he inp
u
t an
d
output data
whi
c
h i
s
o
b
ta
ine
d
from the test to model the
USM’s mo
del
. And
the model ca
n be directly applie
d to control.
Speed
co
ntro
l is the
core
of the moto
r
motion
contro
l. In the USM
'
s
spe
ed
cont
rol, the
freque
ncy of the driving voltage is often
used a
s
a
control varia
b
l
e
to achieve
the regul
ation
o
f
spe
ed. Th
e
USM’s spee
d control
mo
del
with fr
e
q
uen
cy a
s
th
e inp
u
t varia
b
les is of g
r
eat
signifi
can
c
e f
o
r imp
r
oving
the spe
ed
control p
e
rf
o
r
mance. In this pa
per,
we
establi
s
he
d
the
USM’s
sp
eed
control mo
d
e
l whi
c
h a
p
p
r
opriately
cont
ains
nonlin
ea
r ch
aracte
risti
cs th
rou
gh th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Model Identifi
c
ation of Traveling Wave Ultraso
n
ic M
o
tor Using Step
Respon
se (S
hi Jing
zh
uo)
6743
identificatio
n
modelin
g m
e
thod. Th
e
model
with
f
r
equ
en
cy as input vari
ab
les, is
of great
signifi
can
c
e f
o
r improving the perfo
rma
n
c
e of
freq
uen
cy modulatio
n (FM)
spe
e
d
control.
2. Experiments Design F
o
r Identifica
tion
In this pape
r, we intende
d to estab
lish the USM’s frequen
cy-speed
control
model
throug
h the
identificatio
n
method,
so
the fr
e
quen
cy and
spe
ed which a
r
e mea
s
u
r
ed
by
experim
ents
are th
e input
and o
u
tput
sign
als,
resp
ectively. The
motor
spe
e
d
is the
out
put
respon
se
whi
c
h g
ene
rated
in a spe
c
ific f
r
equ
en
cy
of the inp
u
t sig
n
a
l. Adopting
different form
s of
input si
gnal,
the output
respon
se
will
be diffe
rent
. In orde
r to
make the
measured d
a
ta
compl
e
tely reflect the
ch
ara
c
teri
stics
of the
USM,
we m
u
st
u
s
e a
p
p
r
op
ria
t
e form of t
he
freque
ncy
si
gnal a
s
inp
u
t. The sele
ct
ed inp
u
t sig
nal mu
st be
sufficie
n
t to motivate all the
dynamic characteri
stics
of
the USM. It
mean
s that t
he fre
que
ncy
ran
ge
of the
input
sign
al
be
able to cove
r the part of ou
r con
c
e
r
n whi
c
h is
in the USM’s dynami
c
frequ
en
cy range. Step in
put
sign
al is
a co
mmon
sign
al
to meet the a
bove re
qui
re
ments. Th
e form of
step
signal i
s
sim
p
l
e
.
Beside
s it is
achi
eved ea
sily and ea
sy to analyz
e
a
nd re
se
arch.
So it is more
appropri
a
te
as
input si
gnal.
In this pa
per,
we u
s
e the
freque
ncy
step si
gnal a
s
input, and m
easure th
e st
ep
respon
se d
a
ta of speed u
nder the op
e
n
loop co
ntro
l
of the motor’s spe
ed to identify the motor’s
model.
In this pa
pe
r, Shinsei
US
R60, two
-
pha
se trav
eling
wave ultra
s
oni
c moto
r, is u
s
ed a
s
the
experim
ent m
o
tor. And the
homem
ade
H-bri
dge p
h
a
s
e
-
shift PWM
ci
rcuit i
s
u
s
ed
as d
r
ive control
circuit. DC tacho
-
ge
ne
rato
r is
coaxial ri
gid co
nne
ct
io
n with the mo
tor, and it is
use
d
to mea
s
ure
the motor’
s
speed. T
he fre
quen
cy of
the
driving volta
ge is set to a
desi
r
ed
value
by adju
s
ting
the
circuit. In
ord
e
r to
en
su
re
the a
c
cu
racy
of the id
entification,
we
ne
ed to
obtain
t
he exa
c
t valu
e of
the actual
dri
v
ing frequ
en
cy. In the experim
ent,
the waveform
of the motor’
s drive voltage
is
measured in
real-tim
e, a
nd the fre
q
u
ency va
lue i
s
obtain
ed b
y
processin
g
the re
cordi
n
g
waveform. In orde
r to make the m
e
asu
r
em
ent
d
a
ta can a
ccurately refle
c
t the dynamic
characteri
stics of the USM, ther
eby ensuring the credibility of the m
o
tor model which i
s
obtained
by identifying
. We n
eed
to
determine th
e pa
rame
te
rs of input
sign
al su
ch
a
s
step am
plitude
,
sampli
ng tim
e
, length of
data re
co
rd
s a
c
cordi
ng
to the prio
r
kno
w
le
dge a
nd the
control
perfo
rman
ce
before the ex
perim
ent.
USM'
s ope
rat
i
ng freq
uen
cy
is gen
erally l
a
rge
r
than it
s mech
ani
cal reso
nant fre
q
uen
cy,
the high
er th
e frequ
en
cy, the lower the
motor
sp
e
e
d
.
If the step a
m
plitude of freque
ncy in
pu
t is
too large, th
e sp
eed i
s
t
oo lo
w, and
the si
gnal
-to-noi
se
ratio
of the me
a
s
ured
sig
nal
will
decrea
s
e,
an
d it is not
co
ndu
cive to i
m
prove
t
he
accuracy
of the id
entificati
on. If the giv
e
n
freque
ncy i
s
too low, the
correspon
ding
desi
r
ed
sp
ee
d too high, th
en the variati
on of the mot
o
r’s
spe
ed
will be
large
an
d m
a
y make the
open
-loo
p ru
nning
USM
sudde
nly stall.
Experiment
with
the moto
r whose op
erating fre
que
ncy
ran
ge i
s
4
1
.
5-44
kHz
Th
e selecte
d
step rang
e of
the
freque
ncy in
put is 42.3
-
43.3kHz by trying t
he open
-loo
p o
peratio
n. US
M has
different
perfo
rman
ce
characte
risti
cs un
de
r the conditi
on of
different input frequen
cy
due to it h
a
s
compl
e
x nonl
inearity. The
r
efore, we ne
ed to mea
s
u
r
e the in
put and outp
u
t d
a
ta re
spe
c
tively
unde
r the co
n
d
ition of different input step
frequen
cy
in the experim
e
n
t, in order to
fully reflect the
motor’
s
cha
r
acteri
stics. In
the me
an
while, taki
ng i
n
to a
c
count
the un
ce
rtain
t
ies a
nd
ran
dom
pertu
rbatio
ns whi
c
h m
a
y occur in the t
e
sting
pr
ocess, we
ne
ed
measure
mul
t
iple set
s
of
data
unde
r e
a
ch freque
ncy to
e
liminate tho
s
e data
whi
c
h
has obvio
us deviation. T
he value
s
of the
step inp
u
t fre
quen
cy whi
c
h are
set in experim
ent a
nd the motor’s stea
dy-state spe
ed whi
c
h
corre
s
p
ondin
g
to the step input frequ
en
cy are sho
w
n i
n
Table 1.
Table 1. Te
sted Data of Steppin
g
Re
sp
onse
Number
Freque
nc
y
(
kHz)
Speed(r/min
)
1 43.1
22.4
2 43.2
20.3
5 43.3
18.5
13 42.7
37.1
14 42.8
32.6
15 42.9
30.3
17 42.4
53.6
18 42.5
46.9
19 42.6
43.2
21 42.3
62.8
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 67
42 – 674
9
6744
The data
re
cordin
g time n
eed to be l
o
n
g
eno
ugh to
contai
n the complete
step
respon
se
pro
c
e
ss. But the long
er the
time, the bigger the dat
a q
uantity. It will bring u
nne
ce
ssary bu
rde
n
to
the cal
c
ulati
on of model
identificatio
n and may
affect the a
c
cura
cy of identificatio
n. The
experim
ents
sho
w
that th
e time of the exper
im
ent
al motor’
s st
ep re
sp
on
se
not more th
an
100m
s, so th
e sele
cted le
ngth of the da
ta reco
rdi
ng time is 200
ms.
In the experi
m
ent, the dat
a re
cording i
s
complete
d throu
gh the A
/
D sam
p
ling,
and the
sampli
ng tim
e
directly affe
ct the a
c
cu
ra
cy of
ide
n
tification. Sampli
ng theo
rem
requires that t
h
e
sampli
ng fre
q
uen
cy sho
u
ld
be at least t
w
ice t
he cuto
ff frequen
cy of the obje
c
t. If the sampli
ng
time is too l
a
rge,
will m
a
ke the i
n
fo
rmati
on lo
ss too much
and redu
ce
the accu
ra
cy o
f
identificatio
n. And in the
ca
se
of the same
re
cordi
ng time, decrea
s
e the sa
mpling time will
increa
se th
e
amount
of d
a
ta. At the
same time,
be
cau
s
e
of the
limitations of
the h
a
rd
wa
re’s
respon
se
spe
ed and the computat
ion
speed, the sa
mpling time c
an not be too small. For the
experim
ent
motor, the re
quire
d contro
l respon
se
b
and
width is
not gre
a
ter t
han 5
00Hz.
And
further ta
king
into account
we ne
ed to o
b
tain
frequ
en
cy informatio
n from the m
easure
d
voltage
waveform, so the
sele
cted
sam
p
ling
freq
uen
cy i
s
1
0
M
H
z in
the expe
rime
nt to e
n
sure
th
e
measurement
accura
cy.
In the experi
m
ental, we capture the m
o
to
r’s d
r
ive voltage and ta
cho
gen
erato
r
output
voltage
sign
a
l
syn
c
hrono
u
s
ly, the m
e
a
s
ured
st
ep
re
spon
se
cu
rve i
s
sho
w
n
in
Fi
gure
1. In
ord
e
r
to make the
waveform cle
a
rly visible, the figure sho
w
s only a part
of the time data.
3. The Motor
’
s Model Identifica
tion Based on the
Step Respon
se
We n
eed to p
r
ep
ro
ce
ss the
s
e d
a
ta befo
r
e the mod
e
l identificatio
n. As se
en in Fi
gure
1,
the mea
s
u
r
ed
data contain
s
noi
se. T
he
noise be
com
e
s
m
o
re obvi
ous wh
en
the
amplitude of the
tacho
gen
erat
or’s outp
u
t signal i
s
smal
l. Takin
g
int
o
a
c
count th
e re
quired
b
and
width of
the
control
re
spo
n
se
is not
greater th
an
50
0Hz, we
ta
ke
low pa
ss filtering
for the
measured
sp
eed
sign
al a
nd th
e filter’
s
cuto
ff freque
ncy i
s
1
000
Hz. O
n
the
othe
r
hand, th
e
start time
of d
a
ta
recording e
a
r
lier tha
n
the action tim
e
of st
ep in
put to ensu
r
e the integri
t
y of
the data
measurement
. So there i
s
a se
ction
of zero
sp
eed
da
ta at the be
gi
nning
of the reco
rdin
g data
,
this
sectio
n i
s
u
s
ele
s
s for identificatio
n
.
If we re
se
rv
e that data, it
woul
d affe
ct the a
c
cura
cy
of
identificatio
n, and sho
u
l
d
be delete
d
. Meanw
hil
e
, the DC comp
one
nt existing in the
measurement
data, it will also affect the
accura
cy of identificatio
n and can be re
moved usi
ng
the
averag
e met
hod. After th
e prepr
ocessi
ng, we
obtai
n
ed ste
p
re
sp
onse data
of
spe
ed a
s
sh
o
w
n
in the in Figure 2. These da
ta can
be u
s
e
d
for the mod
e
l identificatio
n.
Figure 1. Tested Step Respon
se
Figur
e 2. Step Re
spo
n
se after Data
Pretreatm
ent
As me
ntione
d, USM i
s
a
kind of n
onlin
e
a
r a
nd time
-v
arying
obje
c
t
s
. In o
r
de
r to
achi
eve
high-perform
ance
control for
this kind of
object,
the cont
rol al
gorithm should
have the abilit
y of
online
corre
c
tion. It mean
s that
the
control
algo
ri
t
h
m i
s
self-a
d
apting.
Con
s
i
der it from
this
perspe
c
tive, the sel
e
cte
d
motor mod
e
l is se
co
nd-ord
e
r. It is used
f
o
r identification.
There are m
any method
s which use
step re
sp
o
n
se data to identify the model, such as
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Model Identifi
c
ation of Traveling Wave Ultraso
n
ic M
o
tor Using Step
Respon
se (S
hi Jing
zh
uo)
6745
area
meth
od,
ch
aracte
risti
c
p
o
int m
e
tho
d
, etc.
T
he
area m
e
thod
ca
n take full
ad
vantage
of da
ta
informatio
n of every point to identify the model,
an
d h
a
ve stro
ng a
b
ility to suppre
ss
noi
se. But it
is n
o
t an
opti
m
ization
alg
o
r
ithm, an
d it i
s
n
o
t sp
e
c
ific to the
sp
ecifi
ed o
r
de
r m
o
d
e
l. If the mod
e
l
orde
r is eq
ual
or clo
s
e to the orde
r of the actual
obje
c
t
,
we can obta
i
n more de
sirable re
sult
s by
usin
g the
are
a
metho
d
. Bu
t durin
g the
a
c
tual
c
ont
rol system de
sig
n
,
we often
u
s
e a
lo
w-ord
e
r
model to
sim
u
late the hi
g
h
-o
rde
r
obj
ect to simp
lify the control proce
s
s. The
n
the obtain
ed
low-
orde
r mod
e
l will inevitably have a deviation and th
e
model accu
racy is not hi
gh by usin
g the
area
metho
d
. Taki
ng i
n
to
accou
n
t the
measured
st
ep respon
se
cu
rve h
a
s
chara
c
te
risti
c
s of
dampin
g
and
oscill
ation, so we ca
n u
s
e cha
r
a
c
teri
stic poi
nt me
thod to ident
ify the motor’s
model. Thi
s
method is
sp
ecific to seco
nd-o
r
d
e
r un
d
e
rda
m
pin
g
model.
The tran
sfe
r
functio
n
of the USM’s fre
q
u
ency-sp
eed
control mo
del
can b
e
de
scri
bed a
s
:
2
0
22
00
()
2
s
Gs
K
e
ss
(1)
Whe
r
e:
1
/
Kh
f
,
1
h
is t
he
steady-st
a
te spee
d va
lue,
f
is a
given freq
uen
cy
step
value;
is the delay time;
K
a
nd
can b
e
obtained di
rectly
from the measu
r
ed d
a
ta.
and
0
are
mod
e
l p
a
ram
e
ters to
be i
dentified
,
whe
r
ein
12
/2
aa
;
02
1/
a
;
is dampi
ng
c
oeffic
i
ent;
0
is natural fre
q
uen
cy. For the
conveni
en
ce
of identifi
c
ation, th
e e
quation
(1
) i
s
norm
a
lized. Con
s
e
quently
,
we obtain
the stand
ard
uni
t tran
sfe
r
function
of th
e second
-o
rd
er
unde
rda
m
pin
g
model
2
0
1
22
00
()
2
Gs
ss
(2)
The step re
spon
se
time d
o
main expre
s
sion of
the n
o
rmali
z
e
d
obj
ect a
s
sho
w
n
in the
Equation (2) i
s
:
0
2
0
2
()
1
s
i
n
(
1
)
1
t
e
ht
t
(3)
Whe
r
e:
2
1
ta
n
.
Let
*
1
Y
and
*
2
Y
be re
spe
c
tively the
height of the
st
ep respon
se cu
rve’s first
and second
wave cre
s
t re
lative to the steady-state v
a
lue (i.e. 1),
and the interv
al time is
0
T
. By Equation (3
)
we can obtai
n:
2
1
*
1
Ye
(4)
2
3
1
*
2
Ye
(5)
From the a
b
o
v
e two equati
ons a
nd
0
T
, get:
*2
1
1
1+(
/
Y
)
(6)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 67
42 – 674
9
6746
0
2
0
2
1
T
(7)
The moto
r m
odel i
s
set a
s
the Equ
a
tio
n
(2
). We
ha
ve obtaine
d
model p
a
ram
e
ters
b
y
usin
g the ch
ara
c
teri
stic
p
o
int method
to identify and cal
c
ulat
e the mea
s
u
r
ed
freque
ncy a
n
d
spe
ed data. T
he model p
a
rameters are shown in Tabl
e 2.
Figure 3 a
n
d
Figure 4
sh
ow the
com
p
arison of
the identificatio
n model step resp
on
se
simulatio
n
re
sults with
th
e mea
s
u
r
e
d
values of th
e two
sets
of data. And
the
results
are
sat
i
sf
ie
d.
Figure 3. Tested and Simul
a
ted Step
Re
spo
n
s
e
Figure 4. Tested and Simul
a
ted Step
Re
spo
n
s
e
Table 2. Mod
e
l Paramete
rs Identified u
s
ing
Cha
r
a
c
teristi
c
Point Method
Number
ξ
ω
0
(rad/s)
K
(s
)
1 0.3373
887.533
0.5200
0.0138
2 0.3753
842.917
0.4707
0.0138
5 0.3241
837.550
0.4275
0.026
13 0.3912
825.563
0.8678
0.013
14 0.3744
865.378
0.7610
0.0137
15 0.4238
867.111
0.7064
0.0135
17 0.1999
738.785
1.2636
0.0172
18 0.2873
783.711
1.1021
0.019
19 0.3156
824.616
1.0137
0.021
21 0.2935
752.881
1.4855
0.022
Table 2 sho
w
s
that
the
motor
m
odel
para
m
et
ers
a
r
e time
-varyi
ng. It is
ca
used by th
e
USM’s n
onlin
earity. In orde
r to make the
model fu
lly re
flect the moto
r’s n
onlin
ear
cha
r
a
c
teri
stics,
the time-va
r
ying cha
r
a
c
teristics of p
a
rameters
nee
d to be
exp
r
esse
d in
th
e moto
r mo
del.
Because
of the motor
under differe
nt input frequency w
ill show diff
erent
characteristi
cs. So
we
can
con
s
ide
r
using the va
riation of mo
del par
amete
r
s alo
ng with
the chang
e of frequen
cy to
cha
r
a
c
teri
ze
the time-va
r
ying no
nline
a
rity. And
in the control p
r
ocess, the
given value
of
freque
ncy
is the o
u
tput
of the
sp
e
ed
co
ntrolle
r. If we
igno
re
t
he
d
y
namic proce
s
s of f
r
equ
en
cy
regul
ating, we can con
s
id
er the given value of
freq
uen
cy as the
actual value,
so the frequ
ency
value
is kno
w
n. The
r
efore,
the freq
uen
cy
f
ca
n be
u
s
ed
as va
riabl
e to
fit the pa
ram
e
ters
and
0
, and they are expre
s
sed
with
()
f
and
0
()
f
respectively. According to th
e chan
ge rul
e
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Model Identifi
c
ation of Traveling Wave Ultraso
n
ic M
o
tor Using Step
Respon
se (S
hi Jing
zh
uo)
6747
of
the
m
odel
para
m
eters, we ch
oo
se
th
e qu
adratic
p
o
lynomial fu
n
c
tion to
fit
an
d
0
to mak
e
the fitting fun
c
tion
be e
a
sy
to calcul
ate
online
with
th
e control
chip
su
ch
as DS
P, and o
b
tain
the
fitting function as sho
w
n in
Equation (8
) and (9
).
2
(
)
336.67384
15.65764
0.18186
f
ff
(8)
2
0
(
)
115374.
23674
5339.
94183
61.
36374
f
ff
(9)
The
com
pari
s
on
of the
be
fore a
nd
after fitting mo
de
l step
re
sp
on
se
cu
rve i
s
shown in
Figure 5. In the figure, the da
shed li
n
e
is t
he
resp
onse whi
c
h i
s
obtai
ned b
y
calculating
the
fitting data. It ca
n b
e
see
n
that both
coi
n
cid
e
b
a
si
call
y and th
e mo
del fitting effe
ct is go
od. T
he
model pa
ram
e
ter value
s
which a
r
e calculated from
t
he fitting function (8) a
nd (9) are sh
own
in
Table
3 Th
e relative erro
r i
s
the
relative
error
betwee
n
the ide
n
tified value
s
and
the fitted valu
es
of the model para
m
eters.
Figure 5. Step Re
spo
n
se with Fitting
Parameters
Figure 6. Step Re
spo
n
se with Fitting
Parameters
Table 3. Mod
e
l Paramete
rs Fitted by Freque
ncy Fitting Fun
c
tion
Number
f
0
f
(rad/s)
Value
Relative error
Value
Relative error
1 0.3442
2.0457%
858.000
3.3276%
2 0.3402
9.3525%
856.416
1.6014%
5 0.3326
2.6226%
851.380
1.6512%
13 0.3310
15.3885%
831.025
0.6616%
14 0.3407
9.0011%
845.207
2.3308%
15 0.3431
19.0420%
849.303
2.0538%
17 0.2817
40.9205%
768.024
3.9578%
18 0.3062
6.5785%
798.463
1.8823%
19 0.3202
1.4575%
816.424
0.9935%
21 0.2492
15.0937%
728.803
3.1981%
In the USM speed
cont
rol
system, the
measur
ed sp
eed value i
s
necessa
ry to con
s
titute
a cl
osed-l
oop
co
ntrol. Sin
c
e the
sp
eed
data i
s
kno
w
n, of course,
we
ca
n al
so
use
the
sp
ee
d
n
as the inde
p
ende
nt varia
b
le to fit
the model pa
ram
e
ters
and
0
, a
nd expre
s
sed
with
()
n
and
0
()
n
re
sp
ectiv
e
ly. Adopting the output
fitting function i
s
likely to get better contro
l effec
t
for som
e
of the co
ntrol
strategy. Acco
rding to
the id
entified mode
l param
eters,
we choo
se t
h
e
quad
ratic
pol
ynomial fun
c
tion to fit
and
0
. The fitting functio
n
s a
r
e
sho
w
n in Eq
uation (10)
and (1
1).
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 67
42 – 674
9
6748
2
(
)
0.29595
0.00359
7.00675
5
nn
e
n
(
10
)
2
0
(
)
847.
29469
1.
83959
0.
05952
nn
n
(
11
)
The
com
pari
s
on
of the
be
fore a
nd
after fitting mo
de
l step
re
sp
on
se
cu
rve i
s
shown in
Figure 6. The
model fitting para
m
eters which u
s
e the
spe
ed
n
as the indepe
ndent
variable a
r
e
sho
w
n in Ta
b
l
e 4.
Table 4. Mod
e
l Paramete
rs Fitted by Speed Fitting Fu
nction
Number
n
0
n
(rad/s)
Value
Relative error
Value
Relative error
1
0.3412
1.1562%
858.607
3.2592%
2
0.3400
9.4058%
860.085
2.0367%
5
0.3384
4.4122%
860.950
2.7938%
13 0.3327
14.9540%
833.592
0.9725%
14
0.3385
9.5887%
843.949
2.4762%
15 0.3404
19.6791%
848.354
2.1632%
17 0.2869
43.5218%
774.702
4.8617%
18
0.3101
7.9360%
802.549
2.4037%
19
0.3201
1.4259%
815.493
1.1064%
21 0.2447
16.6269%
727.717
3.3423%
4. Conclusio
n
In this pa
per, we
u
s
e th
e cha
r
a
c
teri
stic poi
nt met
hod to
ide
n
tify the USM
mod
e
l
according to
the freq
uen
cy step inp
u
t data an
d t
he
spe
ed o
u
tput
data, the
co
nclu
sio
n
s
are
as
follows
:
1) We nee
d
to select th
e approp
riat
e input sig
n
a
l form to sufficiently mo
tivate th
e
motor’
s characteri
stics by
usin
g the m
e
thod of
syst
em identific
ation to mod
e
l
the motor. T
he
step si
gnal i
s
a kind of inp
u
t
signal which
meet the req
u
irem
ent of identification;
2) Cha
r
a
c
teri
stic p
o
int met
hod i
s
a
kind
of
identificati
on metho
d
a
nd it aimed
a
t
the set
motor mod
e
l (se
c
o
n
d
-
orde
r unde
rd
amp
ed model
),
the identificatio
n effect is bet
ter;
3)
Re
sults of
identificatio
n
sho
w
that th
e
m
odel
pa
ra
meters a
r
e ti
me-varyin
g
. T
herefo
r
e,
we u
s
e the freque
ncy an
d
spe
ed a
s
ind
epen
dent vari
able
s
to fit th
e polynomi
a
l function fo
r the
model p
a
ram
e
ters,
re
spe
c
t
i
vely. And we
see
k
time
-va
r
ying rule
s to
prop
erly refle
c
t the no
nline
a
r
cha
r
a
c
teri
stics of the motor. It is simple t
o
impleme
n
t and ha
s go
od
result
s.
Referen
ces
[1]
Guo M, Hu J, Zhu H, Zhao
C, Dong S.
Three-
degr
ee-
of-freedom
u
l
tra
s
onic motor u
s
ing a 5-mm-
diam
eter pi
ezo
e
lectric c
e
rami
c tube.
IEEE Transactions
on Ult
rasonics, Ferroelectr
ics, and Frequenc
y
Contro
l
. 201
3; 60(7): 14
46-
14
52.
[2]
Shi J, Zhao F, Shen X, W
a
n
g
X. Cha
o
tic o
perati
on an
d chaos co
ntrol o
f
travelling
w
a
ve ultraso
n
i
c
motor.
Ultrasonics
. 201
3; 53(
6): 1112-
11
23.
[3]
T
o
monobu S
e
nj
yu, Mitsur
u N
a
kamur
a
. Math
ematica
l
mod
e
l
of ultras
onic
motors for sp
e
ed co
ntrol[C].
IEEE, Applie
d Pow
e
r Electron
ics Confer
ence
and Expos
itio
n, Dall
as, TX,
Unite
d
States
. 200
6.
[4]
Maas, Jürge
n
. Mode
l-bas
ed c
ontrol for ultras
onic motors.
IEEE/ASME Transactions on Mechatronics.
200
0; 5(2): 165
-180.
[5]
Xi
a, C
han
g-Li
a
ng, Qi,W
en-Ya
, Yang
Ro
ng,
Shi T
i
ng-N
a
.
Identific
atio
n a
n
d
mo
del
refere
nce
ada
pti
v
e
control
for u
l
trason
ic
motor
base
d
o
n
R
B
F
ne
ural
netw
o
r
k
.
Procee
din
g
s
of the
Ch
ines
e Soc
i
et
y o
f
Electrical E
ngi
neer
ing
.
2
004;
24(7): 11
7-1
2
1
.
[6] Shi,
Jin
g
zhu
o
,
Lü,Li
n.
Dyna
mi
c fu
zz
y
mo
de
lli
ng for sp
ee
d c
ontrol
of ultras
onic
motor
. Procee
din
g
s of
the Chi
nes
e Societ
y of Electri
c
al Eng
i
ne
eri
n
g
.
2011; 3
1
(33)
: 109-11
4.
[7]
Z
hang,Ji
anta
o
, Z
hang,T
i
emin,
Xi
e,Z
h
i
y
a
ng,
W
u
,W
ei.
Multivaria
ble
non
li
ne
ar mod
e
l of u
l
trason
ic moto
r
base
d
o
n
Ha
mmerste
i
n mod
e
l
an
d unifor
m
d
e
sig
n
. Proce
e
d
i
ngs
of the
W
o
rld C
o
n
g
ress
o
n
Intel
lig
ent
Contro
l and A
u
tomation. Jin
a
n
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799.
[8]
W
e
n
y
u Z
h
a
ng,
Jingz
huo S
h
i.
Mode
l Refer
e
nce Ad
aptiv
e
Spee
d Co
ntrol
of
2-PhasT
r
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TELKOM
NIKA
ISSN:
2302-4
046
Model Identifi
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