In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
1, Mar
ch 20
19,
p
p.
195~
2
1
0
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
1.pp
1
95-
21
0
195
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Motion control applic
ations
: observer b
a
sed DC motor
par
a
meters estimation for
novices
Br
an
esh M. Pilla
i,
Jac
kr
it
S
u
t
ha
korn
De
p
a
rtme
nt
of B
i
ome
d
ic
a
l
E
ng
in
eeri
ng,
F
aculty
o
f
E
ngineeri
n
g
,
M
ahi
d
o
l
U
n
i
versi
t
y,
T
hailand
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
Jun 29,
2018
Re
vise
d S
e
p 17,
201
8
Ac
ce
p
t
ed
Oc
t
3
, 2
0
18
Estim
atio
n
of
m
ot
or
i
nert
ia
a
nd
f
rictio
n
compon
ent
s
i
s
a
co
m
p
le
x
a
n
d
chal
lenging
t
a
sk
i
n
motion
contr
o
l
appl
i
cation
s
w
here
s
mall
s
iz
e
DC
m
otors
(<10
0W
)
are
u
s
ed
f
o
r
p
recis
e
c
o
n
t
r
ol.
It
i
s
ess
e
nt
ia
l
t
o
e
stim
a
t
e
t
h
e
a
c
c
u
r
a
t
e
f
r
ict
i
o
n
c
om
ponent
s
a
n
d
m
o
to
r
i
n
erti
a,
b
ecaus
e
t
h
e
p
aram
eters
p
rovi
ded
by
th
e
m
a
n
u
f
actu
r
er
a
r
e
n
ot
a
l
w
ays
accu
r
a
t
e
.
Thi
s
r
esearch
p
ro
po
se
s
a
S
e
ns
orles
s
m
et
h
o
d
of
d
e
t
ermi
nin
g
D
C
m
o
to
r
pa
ram
e
t
e
rs
,
i
n
clu
d
ing
m
o
m
e
n
t
of
i
n
e
rtia
,
to
rqu
e
c
o
e
ffi
cien
t
an
d
f
r
icti
on
a
l
c
om
ponen
t
s
usin
g
the
Dis
t
u
r
ba
nc
e
Observe
r
(
D
O
B)
a
s
a
torque
s
ens
o
r.
T
he
c
on
sta
n
t
v
e
lo
c
i
ty
m
ot
ion
t
es
t
an
d
a
no
vel
Revers
e
M
o
tio
n
A
ccelera
t
i
o
n
t
e
s
t
w
ere
co
nd
ucted
t
o
e
s
tima
te
f
ri
cti
onal
com
p
onen
t
s
and
m
o
ment o
f
i
n
ertia
o
f
t
h
e
m
ot
or.
Th
e
val
i
d
i
t
y
o
f
t
h
e
p
r
op
osed
no
vel
m
e
tho
d
w
as
v
erifi
e
d
b
y
e
x
p
erim
en
tal
resul
t
s
and
com
p
are
d
wi
th
con
v
en
tio
nal
accel
eratio
n
and
d
eceler
at
io
n
m
o
t
i
on
t
ests.
E
x
p
e
ri
m
e
nt
s
hav
e
been
car
ried
out
t
o
s
h
o
w
t
h
e
e
ff
ecti
v
enes
s
a
n
d
v
i
ab
ilit
y
of
t
h
e
e
stim
ated
param
e
ters
u
s
i
ng
a
Re
acti
o
n
Torq
ue
O
bs
erv
e
r
(RTO
B)
b
ased
f
ricti
on
com
p
ensat
i
o
n
met
ho
d.
K
eyw
ord
s
:
A
dva
nc
e m
o
t
i
o
n
c
on
tro
l
DC m
ot
or
par
am
eter
e
stima
t
i
o
n
D
i
stur
b
a
nce
ob
serve
r
F
r
ic
ti
o
n
c
o
m
p
e
n
s
a
t
i
o
n
R
e
verse
m
o
t
i
o
n
a
cc
elera
tio
n
S
e
nsor
l
e
ss se
n
s
or
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Jackr
it
Sutha
k
orn,
Ce
nter
f
or
B
io
me
dica
l a
nd R
o
b
o
t
ic
s
Tec
hno
lo
g
y
(
BA
RT L
A
B
),
D
e
pa
rtme
nt
o
f
Biome
d
ica
l
E
ngi
nee
r
i
n
g,
F
acul
t
y
of En
g
i
n
e
e
r
in
g, M
a
h
id
ol
U
niver
s
it
y,
99
9,
P
hut
t
a
mo
nt
h
on S
a
i 4,
S
a
l
aya
, N
akorn P
a
th
om
, 731
70,
Tha
ila
n
d.
Em
ail:
j
a
ckr
it.s
u
t
@
m
a
h
i
do
l.
ac.
th
1.
I
N
TR
OD
U
C
TI
O
N
Mo
t
i
o
n
co
n
t
ro
l
tec
h
n
i
que
s
h
a
ve
b
ee
n
s
i
gni
fi
c
a
n
tly
d
e
v
e
l
ope
d
i
n
recent
d
eca
d
es.
T
h
e
f
i
r
s
t
IEEE
Interna
tio
na
l
Wor
k
sh
o
p
o
n
A
dva
nc
ed
M
o
tio
n
C
o
ntr
o
l,
h
eld
in
1
9
9
0
e
mp
h
a
si
z
e
d
th
e
i
m
po
rt
an
c
e
o
f
ph
ysi
c
al
in
t
e
rpre
ta
ti
on
of
m
ot
i
on
c
o
n
t
ro
l.
M
o
t
i
o
n
con
t
ro
l
sys
t
em
s
pl
a
y
a
v
ita
l
r
o
l
e
i
n
m
a
n
y
i
nd
us
t
r
i
a
l
au
to
ma
ti
o
n
a
p
pli
c
at
ion
s
,
su
ch
a
s
p
o
s
i
t
i
o
n
co
nt
rol
,
v
el
o
c
it
y
co
nt
rol
,
a
c
c
e
l
e
r
a
t
i
on
c
ont
ro
l
,
f
o
r
ce
c
ont
ro
l
e
t
c
.
T
h
e
perform
ance
o
f
indust
r
i
a
l
r
obotic
a
ppli
cation
system
s
is
m
ai
nly
b
ase
d
o
n
posi
t
i
on
a
n
d
forc
e
c
o
nt
r
o
l
[
1
].
D
C
servom
o
t
ors
are
of
t
e
n
use
d
t
o
a
c
h
i
e
v
e
pr
ec
ise
p
o
s
i
t
i
o
n
a
n
d
t
orq
ue
c
o
n
tr
ol.
M
o
re
o
v
er,
i
n
m
ed
ica
l
r
ob
otic
s
app
l
ica
t
i
o
ns,
D
C
s
e
r
v
o
m
o
t
o
rs
a
re
w
i
d
el
y
use
d
due
t
o
i
t
s
sim
p
le
struc
t
ure
a
n
d
o
u
tsta
n
d
i
n
g
c
ontro
l
perform
ance at
l
o
w
cost [
2].
DC
s
e
r
vo
mo
t
o
rs
u
se
d
fo
r
con
t
ro
l
ap
pli
c
a
t
io
ns
s
hou
ld
i
n
c
o
r
p
o
rat
e
a
ccu
rat
e
c
on
t
r
ol
m
et
hod
s
t
o
o
bt
ai
n
t
h
e
d
e
si
re
d
re
sp
on
s
e
s.
C
on
t
r
o
l
l
e
r
p
a
ramet
e
rs
i
n
su
ch
a
ppl
i
cati
o
ns
h
a
v
e
t
o
b
e
t
u
ne
d
pr
oper
l
y
to
o
b
t
ai
n
t
h
e
des
i
red resp
on
se of
the
sy
st
e
m
[3].
Tuni
n
g
of c
o
n
t
ro
l
l
er p
ara
m
e
t
e
rs d
e
p
en
d
s
on
th
e p
hysi
c
al
p
a
r
amet
ers
o
f
th
e
syste
m
s.
T
here
fore
,
t
h
e
i
d
en
tif
i
c
at
i
on
of
a
ccur
a
te
p
h
y
s
i
c
a
l
p
ar
a
m
e
t
ers
of
s
yste
ms
i
s
im
por
tan
t
.
A
r
ma
ture
resistance
R
a
,
a
r
m
a
ture
i
nd
u
c
tance
L
a
a
n
d
b
ac
k
em
f
co
ns
t
a
nt
K
e
a
r
e
c
on
side
red
to
b
e
fixe
d
f
o
r
a
g
i
ve
n
D
C
motor.
O
nce
a
D
C
m
otor
i
s
i
n
o
pera
t
i
o
n
,
t
h
e
to
r
q
ue
c
ons
t
a
nt
K
t
ma
y
cha
nge
due
t
o
m
a
gne
tic
e
ffec
ts.
Mo
t
o
r
iner
tia
J
m
ay
c
ha
nge
d
ue
t
o
th
e
addi
tio
n or
re
m
ova
l
o
f
l
oa
d
s
t
o
the r
o
t
a
ry shaft [
4]
.
D
C
m
o
t
o
r
f
r
i
c
t
i
o
n
c
o
m
p
e
n
s
a
t
i
o
n
w
a
s
a
c
o
m
p
l
e
x
t
a
s
k
a
n
d
h
a
s
b
e
e
n
t
r
ie
d
b
y
m
an
y
r
e
sea
r
che
r
s.
Ho
we
v
e
r,
n
o
on
e
h
a
s
i
n
t
r
oduce
d
a
n
ef
fe
cti
v
e
st
ra
t
e
gy
f
o
r
f
ri
c
t
i
o
n
c
om
pe
n
s
at
io
n
of
s
m
a
l
l
siz
e
D
C
m
o
t
o
r
s
[5]-
[7].
T
here
i
s
no
re
sear
ch
a
vai
l
a
b
l
e
c
ons
i
d
eri
ng
the
f
o
u
r
p
arame
t
e
rs
(fric
ti
on
c
o
m
pone
n
t
s
(
T
f
a
nd
)
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
19
5 –
21
0
19
6
me
cha
n
ic
al pa
r
am
eter
J
a
n
d
e
l
ec
t
r
i
c
al
p
a
r
amet
er
K
t
) i
n
a
s
i
n
g
l
e
e
xpe
rime
n
t
.
I
n
o
rde
r
t
o ac
hi
e
v
e acc
urate forc
e
con
t
ro
l
ba
sed
frict
io
n
c
o
mpe
n
sa
t
i
o
n
,
i
t
i
s
es
s
e
nt
ia
l
to
i
de
n
tif
y
the
sys
t
em
p
a
r
am
eter
s
a
ccur
a
te
ly
a
n
d
d
e
a
l
wit
h
the
n
on-
li
near
frict
i
o
n
com
pone
n
t
s
[8]
.
I
n
th
is
r
ese
a
rc
h,
t
he
a
ut
hors
pro
pos
e
a
n
o
v
el
R
TO
B
m
ode
l
base
d
fric
ti
on
c
om
pe
nsa
t
i
o
n
me
t
hod
usi
n
g
a
P
I
D
c
o
n
t
r
o
l
l
er
.
If
the
fr
i
c
t
i
o
n
co
m
pone
n
t
s
a
n
d
m
echa
n
ic
al
p
ar
a
m
e
t
ers
o
f
t
he
s
y
s
t
e
m
are
ac
cu
ra
t
e
,
t
h
en
t
h
e
p
ropose
d
f
rict
io
n
comp
e
n
sa
t
i
on
m
et
hod
w
il
l
gi
ve
t
h
e
d
esi
r
e
d
s
y
s
t
e
m
cha
r
ac
t
e
ris
tics.
F
r
icti
ona
l
c
o
m
pone
n
t
s
a
l
s
o
m
ay
v
ary
w
i
t
h
w
e
a
r
and
te
ar
e
ffe
c
t
s
[
9
]
,
[
1
0
]
.
U
s
u
a
l
l
y
m
o
t
o
r
ma
nufac
t
u
r
e
rs
m
ay
s
u
ppl
y
t
h
e
para
me
ters
K
t
a
nd
J
.
H
o
w
e
ve
r,
f
or
s
m
a
ller
size
D
C
m
o
t
ors
(1
0-10
0
W
)
,
ma
nufac
t
u
r
e
rs’
give
n
va
l
u
es
f
or
c
om
m
e
rc
i
a
lly
a
vai
l
a
b
le
m
oto
r
s
m
ay
n
o
t
a
l
w
a
y
s
b
e
a
cc
u
r
at
e.
F
o
r
p
rec
i
se
con
t
ro
l
ap
p
l
i
c
a
t
i
o
ns,
t
h
e
acc
u
r
ac
y
of
t
he
m
o
t
or
p
ara
m
e
t
ers
is
v
e
r
y
import
a
nt
[
1
1
]-
[1
3].
Ma
nufac
ture
rs
do
no
t
norm
a
l
l
y s
u
pp
ly fric
t
io
n r
e
la
t
e
d para
me
t
e
rs.The
var
yin
g
pa
r
a
m
e
t
r
i
c
va
lue
of D
C m
o
tor
s
ca
n
a
l
s
o
be a
ttr
ib
u
t
ed
to
t
he
l
oa
d
c
o
nnec
t
e
d
w
i
t
h
t
he
m
o
t
or
[
14]
.
The
frict
io
n
c
o
m
pone
nts
pre
s
en
t
i
n
a
D
C
s
e
r
vo
m
o
t
o
r
ar
e
sta
tic
fric
ti
on,
c
ou
l
o
mb
f
ricti
o
n,
v
i
s
c
ous
f
rict
i
on a
nd S
t
ri
be
ck fri
ct
io
n.
Gen
e
ral
l
y
,
St
ri
b
e
c
k
f
ri
ct
ion
is
g
en
e
r
a
t
ed
u
si
ng
f
l
u
id
l
ub
ric
a
n
t
s
a
n
d
t
h
e
ef
f
ect
o
f
th
is
f
ri
ct
io
n
i
s
ig
nor
ed
i
n
t
h
is
r
e
s
e
a
rc
h.
C
o
u
l
o
m
b
fric
t
i
on
is
i
n
d
epe
n
den
t
o
f
ve
l
o
c
i
t
y
a
n
d
i
s
a
s
s
u
m
e
d
n
e
g
l
i
g
i
b
l
e
f
o
r
s
m
a
l
l
s
i
z
e
D
C
m
ot
ors.
T
he
s
t
a
tic
frict
ion
T
f
i
s
the
force
required
in
o
rder
t
o
s
t
ar
t
the
mo
t
i
on
fro
m
a
stan
d
st
ill
.
Th
i
s
fric
ti
on
is
a
l
s
o
ca
l
l
e
d
a
s
t
h
e
br
e
a
kaw
a
y
frict
i
on.
W
he
n
t
h
e
m
o
t
or
s
t
a
rts
to
r
ota
t
e,
v
i
s
c
ous
f
r
i
c
t
ion
a
p
pe
a
r
s
and
it
i
ncre
ases
w
ith
t
he
i
ncre
ase
of
v
e
l
oc
i
t
y.
T
he
e
stima
t
i
o
n
of
a
cc
urate
fr
iction
com
p
one
n
t
s
(
T
f
a
nd
)
and
the
me
cha
n
ic
al
p
a
r
am
eter
s
(
K
t
a
n
d
J
)
l
e
a
d
t
o
the
des
i
re
d
s
y
st
e
m
r
espon
se
[
15].
In
t
h
i
s
pa
per,
t
he
est
i
m
at
ion
o
f
st
a
t
i
c
fr
i
c
t
i
o
n,
vi
s
co
us fr
i
c
tio
n,
torq
u
e
cons
t
a
nt an
d
m
ot
or
i
n
ert
i
a a
r
e
discu
s
se
d i
n
de
t
a
i
l
.
S
e
ve
ral
me
tho
d
s
o
f
i
de
n
t
i
f
ic
ati
o
n
for
D
C
m
otor
p
ara
m
e
t
ers
have
be
en
p
rop
o
se
d
using
var
i
o
u
s
tech
n
i
q
u
es.
M
a
ny
re
sear
cher
s
have
p
r
o
p
o
se
d
m
e
th
od
s
of
f
in
d
i
n
g
m
echa
n
ic
al
p
ar
am
eters
o
f
D
C
m
o
t
o
r
s
[
1
6
-
21].
F
o
r
e
x
ampl
e
,
[
16]
t
he
g
ene
r
al
s
ystem
para
me
t
e
rs
i
de
nt
ifi
c
a
t
i
o
n
i
s
c
onsi
d
er
ed.
The
distr
i
b
u
t
i
on
-
b
ased
appr
oa
ch
[
1
7
]
is
u
se
d
to
i
de
n
t
i
f
y
pa
ram
e
ter
s
f
rom
di
sc
rete
tim
e
d
a
t
a
.
T
h
e
f
u
z
z
y
P
I
D
[
1
8
]
i
s
u
s
e
d
t
o
e
s
t
i
m
a
t
e
the
l
o
a
d
e
d
t
or
que
;
the
le
as
t-
squ
a
re
s
a
l
g
o
ri
t
h
m
is
i
m
p
lem
e
nte
d
[
19]-
[
21
]
to
e
s
t
i
m
at
e
sys
t
em
p
a
r
am
ete
r
s.
H
o
w
e
ve
r,
non
e
of
t
hem
can
b
e
effec
tive
l
y
use
d
f
or
s
mall
s
i
ze
D
C
m
otors.
I
n
[2
2],
the
impor
t
a
nc
e
o
f
est
i
ma
t
i
o
n
o
f
p
a
ram
e
ter
s
w
a
s
e
mpha
siz
e
d,
b
ut
t
here
w
ere
no
me
th
od
s
for
est
i
ma
t
i
n
g
t
he
m
otor
i
ne
rt
i
a
a
nd
th
e
fric
ti
ona
l
c
o
mpo
n
e
n
t
s
.
A
ltho
u
g
h
t
he
re
a
re
r
e
s
ear
ches
t
o
es
ti
m
a
t
e
t
h
e
v
i
sc
ous
fric
tio
n
o
f
D
C
m
o
t
o
rs
u
s
e
d
in
prec
ise
c
o
n
t
rol
ap
pl
ica
t
io
ns
s
uc
h
as
p
osit
io
n
co
ntr
o
l,
t
he
t
o
r
q
ue
c
oef
f
icie
n
t
a
nd
m
o
t
or
i
n
e
rtia
w
er
e
no
t
tak
e
n
in
to
c
o
n
s
i
de
rat
i
o
n
[
2
3
]-
[2
6].
In
[
2
7
]
,
l
oa
d
model
pa
ram
e
t
e
rs
w
e
r
e
obta
i
ned
u
s
i
ng
a
n
e
vo
l
u
ti
onar
y
a
l
gor
it
hm
bu
t t
h
e fric
t
i
o
n
coe
f
fici
en
t
o
f
t
he
m
otor
w
as
n
ot
c
o
n
s
i
de
red.
Tu
ni
n
g
t
he
c
o
n
tr
olle
r
par
a
m
e
ters
f
or
t
he
d
es
ired
s
ys
te
m
re
sp
ons
e
can
b
e
ach
i
e
v
e
d
on
l
y
w
i
t
h
ac
cura
t
e
l
y
e
s
t
i
m
ated
p
hy
sica
l
para
m
e
ters
o
f
the
s
y
s
t
em
.
In
m
oti
o
n
c
o
n
t
r
ol
a
pplica
tio
ns,
t
h
e
r
eal
t
ime
desired
syste
m
r
espo
n
s
e
is
n
o
t
a
ch
ie
va
ble
i
f
c
o
n
tr
oller
t
u
n
i
ng
i
s
d
one
base
d
o
n
ly
on
t
h
e
nom
i
n
al
m
otor
p
ar
a
m
eters
w
itho
u
t
c
o
n
s
i
d
e
rin
g
t
he
p
hy
sic
a
l
pa
ram
e
te
r
va
ria
t
i
o
ns
[
28].
T
h
e
a
l
g
ebra
ic
i
de
n
t
i
f
icat
i
on
m
e
tho
d
[
2
9
],
[
30]
a
re
t
o
e
s
t
i
m
a
t
e
t
h
e
p
a
r
a
m
e
t
e
r
s
f
o
r
a
c
o
n
t
i
n
u
o
u
s
t
i
m
e
s
y
s
t
e
m
.
T
h
e
r
e
c
u
rsi
v
e
l
e
ast
squ
a
re
m
e
t
hod
[
31
]
a
nd
t
h
e
in
verse
the
o
ry
w
i
t
h c
o
n
j
uga
t
e
gra
die
n
t m
e
th
od [3
2]
ar
e
use
d to
d
e
t
e
rmi
n
e sy
st
em p
a
r
ame
t
e
r
s.
In
t
hi
s
re
se
arc
h
,
t
h
e
t
o
rqu
e
c
o
e
ffi
c
i
ent
K
t
w
as
e
sti
m
a
t
e
d
u
s
i
n
g
t
he
c
onve
n
t
i
o
nal
D
C
m
ot
or
r
otor
s
t
a
ll
tes
t
.
The
fr
ic
t
i
on
c
o
m
p
one
n
t
s
w
e
re
i
de
n
t
i
f
ie
d
b
y
c
on
duc
tin
g
t
h
e
c
o
n
s
t
a
n
t
vel
o
c
ity
m
o
tio
n
tes
t
[
3
3
].
H
e
r
e
,
t
he
di
st
urba
nce
o
b
s
erve
r
(D
O
B
)
is
u
se
d
a
s
a
t
o
r
qu
e
se
ns
or.
D
O
B
i
de
n
tif
i
e
s
the
t
o
ta
l
me
ch
anica
l
l
oa
d
a
n
d
the
effec
t
o
f
s
y
s
t
e
m
p
a
r
am
eter
c
han
g
e
t
h
at
i
s
c
ons
i
d
ere
d
a
s
th
e
to
t
al
d
i
s
tu
rb
an
ce
o
f
t
h
e
mo
to
r
[
3
4
]
,
[
3
5
]
.
In
o
r
d
e
r
to
e
st
im
ate
the
m
o
t
o
r
ine
r
t
i
a
,
t
he
a
u
t
h
o
rs
p
r
o
p
o
se
a
R
TO
B
base
d
nov
el
R
e
v
e
r
se
M
oti
o
n
Ac
ce
l
e
ra
ti
on
t
e
s
t
.
R
T
O
B
s
u
b
trac
ts
t
he
i
de
n
t
i
f
ie
d
par
a
m
e
ters
f
rom
the
d
i
s
t
urb
a
nce
t
o
r
q
u
e
an
d
he
nc
e
o
u
t
p
uts
the
re
ac
tio
n
t
o
rq
ue
app
l
ied t
o
t
he
sys
t
e
m
[36]-
[
3
9
]
.
The
es
t
i
m
a
t
e
d
mot
o
r
i
n
er
ti
a
usin
g
Re
ve
r
s
e
Mo
tio
n
A
c
c
e
ler
a
ti
on
t
es
t
was
co
mp
a
r
ed
w
i
t
h
con
v
e
n
t
i
ona
l
a
c
c
e
lera
tio
n
a
n
d
dece
lera
ti
on
t
e
sts
resu
lt
s.
T
he
r
esu
l
t
s
o
f
t
h
ese
three
test
s
w
e
re
a
nalyz
e
d
a
n
d
c
o
mp
a
r
ed
i
n
sect
ion
3
.
T
h
e
e
st
i
m
ate
d
p
a
r
am
et
ers
we
re
v
a
l
i
d
at
ed
b
y
c
o
n
duc
t
i
ng
a
for
ce
c
o
n
t
ro
l
base
d
fr
i
c
t
i
o
n
com
p
en
sat
i
o
n
tes
t
.
Ex
perim
e
nt
s
w
h
er
e
c
a
rr
ie
d
ou
t
to
s
h
o
w
t
he
i
m
p
o
r
t
a
n
ce
a
nd
va
lid
i
t
y
o
f
the
a
ll
e
s
tim
ated
para
me
ters
u
s
i
ng
R
e
act
i
o
n
T
o
rq
ue
O
bse
r
ve
r
(RTO
B)
b
ase
d
f
r
i
ct
io
n
c
o
m
p
e
ns
at
io
n
t
e
c
h
n
i
qu
e
a
s
e
xpl
ain
e
d
in
sect
io
n
4.
T
he
p
r
o
pose
d
i
ner
tia
v
a
l
ue
s
w
e
r
e
c
ompa
red
w
i
t
h
t
he
c
o
nve
n
t
i
ona
l
test
r
esul
ts
u
s
i
ng
t
he
s
am
e
fric
ti
on c
o
m
p
e
n
sa
to
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Mo
ti
on
con
t
r
o
l
app
lic
a
tio
ns: obs
e
r
v
e
r b
a
se
d
DC motor p
a
r
a
mete
rs
es
ti
m
a
ti
o
n
fo
r… (Bra
nes
h
M.
Pil
l
ai)
19
7
2.
MO
DE
LI
NG
2.
1.
D
C
m
ot
or
m
od
elin
g
U
s
in
g
K
i
r
c
hh
o
f
f’
s
vo
l
t
age
la
w
i
n
c
ir
c
u
it
as
s
how
n
in
F
i
gur
e
1.
F
i
gur
e
1.
E
lect
r
i
c
a
l
m
ode
l
of
a
D
C
m
o
t
o
r
(1
)
A
nd,
e
b
K
e
(2
)
a
t
m
I
K
T
(3
)
Mo
t
o
r
tor
q
ue
i
s
e
x
pr
essed
as,
l
f
m
T
B
T
dt
d
J
T
(4
)
Where,
R
a
-
Arma
t
u
r
e
r
esista
n
ce;
L
a
-
A
r
m
a
tur
e
i
n
d
u
c
ta
n
c
e
;
I
a
-
Armatu
re
c
u
r
ren
t;
K
t
-
To
rqu
e
c
o
e
f
f
icient;
J
-
M
o
men
t
o
f
in
ert
i
a
of
mo
to
r;
K
e
-
Bac
k em
f con
s
ta
n
t;
V
a
-
A
r
m
a
tur
e
vol
t
a
ge;
e
b
-
Back
e
m
f;
-
A
ngu
lar
s
p
ee
d
;
T
m
-
Moto
r
to
rq
u
e
;
T
i
-
Lo
ad
t
o
r
qu
e
;
Tf
-S
t
a
tic
f
ric
t
i
o
n
torq
ue;
B
-
Vi
scou
s
f
r
i
c
t
i
on
c
o
e
ffic
i
ent
.
T
L
co
n
s
i
s
t
s
o
f
e
x
t
e
r
n
al
a
pp
l
i
e
d
t
or
q
u
e
a
n
d
a
l
l
t
h
e
d
i
s
t
ur
b
a
nc
e
ef
fec
t
s
of
t
he
sys
t
em
a
s
show
n
i
n
F
ig
ur
e
2(
a
)
.
(
4
)
c
a
n
b
e
r
e
written a
s
fo
l
lows.
L
m
T
T
J
(5
)
L
a
t
T
I
K
J
(6
)
Where
T
L
cons
i
s
ts
o
f
i
n
er
t
i
a
tor
q
ue,
exter
n
a
l
t
or
q
u
e
and
t
o
r
que
d
ue
t
o
C
o
u
l
o
mb
and
viscou
s
f
r
i
c
tion
.
B
T
T
T
f
l
L
(7
)
The
in
pu
t
to
t
he
m
ot
or
i
s
th
e
r
e
fe
r
e
nc
e
c
u
r
r
e
nt
Ia
a
nd
i
s
co
nt
r
o
l
l
e
d
a
cco
rdi
n
g
to
t
h
e
P
W
M
vol
t
a
ge
pu
lses
[
40]
,
[4
1]
.
Wi
th
t
he
T
L
m
ot
o
r
t
o
r
qu
e
ca
n
not
b
e
di
r
e
c
t
ly
c
on
t
r
oll
e
d
usi
n
g
Ia
.
Th
ere
f
ore
,
f
or
c
o
r
r
ect
fu
n
c
tio
na
li
ty,
T
L
m
ust
be
c
o
m
pensa
t
e
d
a
s
s
how
n
in
F
igur
e
2(
b)
.
T
L
i
s
r
e
f
e
r
r
ed
t
o
as
‘
D
i
s
t
ur
ba
nc
e
T
o
r
que
’
a
s
th
is
t
or
q
u
e
d
i
stur
bs
t
he
o
u
t
pu
t
t
o
r
q
ue.
To
m
e
a
sur
e
t
h
i
s
dis
t
ur
b
ance
t
or
que
a
n
d
c
o
m
p
e
nsa
t
e
f
o
r
it
,
t
h
e
‘
D
i
s
tur
b
a
n
ce
O
b
ser
v
e
r
’
i
s
i
n
t
r
o
d
u
c
e
d
[
4
2
]
a
s
show
n
in
F
i
gur
e
2(
c).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
19
5 –
21
0
19
8
(
a
)
(b)
(
c
)
(d)
F
i
gure
2.
(
a) Bl
o
c
k
d
iagra
m
o
f
D
C
m
o
t
o
r
(
b
)
B
lo
c
k
di
a
g
r
a
m
o
f
s
e
r
vomot
or (
c)
D
ist
u
r
b
a
n
ce
ob
s
erve
r c
o
n
t
r
o
l
bl
oc
k
(d)
Re
acti
o
n tor
que
o
bs
erve
r c
ont
r
o
l
b
l
oc
k
2.2.
Distur
ban
ce obse
rver
mod
eling
In
(
6
)
ha
s
t
w
o
pa
ram
e
te
rs,
na
me
d
mot
o
r
i
n
e
r
t
i
a
a
n
d
torq
ue
c
o
n
sta
n
t
.
T
h
ese
t
w
o
p
a
ra
me
t
e
rs
m
ay
b
e
cha
nge
d
d
u
e
to
s
ever
al
p
r
oper
tie
s.
I
ne
rti
a
m
a
y
b
e
c
h
an
ge
d
d
u
e
t
o
t
h
e
m
ech
a
n
ica
l
c
on
fig
u
ration
o
f
the
m
o
tion
syste
m
.
The
to
rque
c
oe
ffic
ie
nt
w
il
l
va
r
y
a
c
c
ord
i
n
g
t
o
t
h
e
rot
o
r
p
o
s
i
tio
n
o
f
t
h
e
e
le
c
t
ric
m
o
t
o
r
due
t
o
ir
r
e
gu
lar
di
stri
b
u
t
i
on
o
f
m
a
g
ne
t
i
c
flu
x
on
t
h
e surface
o
f
t
h
e r
o
tor
[43
]
,
[44].
J
J
J
n
(8)
t
tn
t
K
K
K
(9)
J
n
-
N
o
m
i
n
a
l
m
o
t
o
r
i
n
e
r
t
i
a
;
J
-I
nertia
v
a
r
ia
t
i
o
n
;
K
tn
- N
o
mina
l
t
o
r
que
c
oeffi
c
i
e
n
t
;
t
K
-V
a
r
iatio
n
o
f
t
or
que
coeff
i
cient.
F
rom
(6)-(9) it
ca
n
be determ
i
n
e
d that,
n
a
tn
dis
J
I
K
T
(10)
I
n
(
10
)
,
t
he
unkn
ow
n
val
u
e
o
f
T
di
s
i
s
ca
l
c
u
l
a
t
ed
u
sin
g
t
he
k
n
o
w
n
v
a
l
ues
at
r
ight
h
a
n
d
side
.
Fr
o
m
(11),
T
dis
i
s
c
a
l
c
u
la
te
d
a
s
f
o
l
l
o
w
s
.
a
t
f
l
dis
I
K
J
B
T
T
T
(11)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Mo
ti
on
con
t
r
o
l
app
lic
a
tio
ns: obs
e
r
v
e
r b
a
se
d
DC motor p
a
r
a
mete
rs
es
ti
m
a
ti
o
n
fo
r… (Bra
nes
h
M.
Pil
l
ai)
19
9
N
o
r
m
ally,
dis
t
ur
ba
nc
e
t
o
r
q
ue
c
on
sis
t
s
of
a
ll
i
n
t
er
na
l
tor
q
u
e
s,
exter
n
a
l
t
or
que
s,
f
r
i
c
t
i
on
t
o
r
q
ue
s
an
d
tor
que
s
due
t
o
par
a
me
t
e
r
va
r
i
atio
ns,
w
h
ich
m
u
st
h
a
v
e
c
o
m
p
ensa
te
d
fo
r
t
o
obt
ai
n
th
e
acc
u
r
at
e
ou
tpu
t
t
o
r
q
u
e
.
T
h
e
est
i
m
a
t
ed
d
istu
rb
an
ce
t
o
r
q
u
e
di
s
T
ˆ
i
s
ob
t
a
in
ed
fro
m
th
e
v
e
lo
c
i
t
y
res
po
n
s
e
and
the
t
o
r
que
c
ur
r
e
nt
I
a
. It is
e
s
tim
ated
t
hr
o
u
g
h
a
f
ir
s
t
-
o
r
d
e
r
l
ow
-
p
ass
fi
l
t
e
r
a
s
sh
ow
n
i
n
F
i
g
ur
e
2
(
c
)
w
her
e
di
s
G
d
e
no
t
e
s
th
e
c
u
t
-
off
f
r
e
que
n
c
y
of
t
h
e
l
o
w
-
p
as
s
fi
lt
e
r
.
T
h
e
pur
p
o
se
o
f
th
e
lo
w
-
pass
f
ilte
r
is
t
o
fil
t
e
r
o
u
t
n
oi
se
a
risi
ng
f
rom
di
ff
er
e
n
tia
ti
o
n
[
45]
,
[46]
.
2.
3.
R
e
act
i
on
t
or
qu
e
ob
ser
v
er
mod
e
li
n
g
The
di
stur
ba
nc
e
o
b
ser
v
er
i
s
u
s
e
d
not
o
nl
y
f
o
r
di
s
t
ur
ba
nce
c
o
m
p
e
nsat
io
n
bu
t
al
so
f
o
r
r
e
a
c
t
i
on
t
o
r
qu
e
est
i
m
a
t
io
n
.
T
he
d
ist
u
rb
an
c
e
o
b
s
erv
e
r
i
s
a
bl
e
t
o
e
sti
m
a
t
e
t
h
e
re
ac
tion
t
o
r
q
ue
w
i
t
h
o
u
t
us
i
ng
a
t
o
r
q
ue
s
e
n
sor
by
ide
n
ti
fyi
n
g
t
h
e
i
n
t
e
r
n
al
d
is
tu
rba
n
ce
o
f
t
h
e
sys
t
e
m
[
47].
Whe
n
t
he
m
o
t
or
i
s
r
u
n
n
i
ng
w
it
h
a
l
o
ad,
t
h
e
loa
d
tor
que
e
xer
t
e
d
on
t
h
e
m
o
t
o
r
d
u
e
t
o
t
h
e
l
o
a
d
is
o
b
t
a
i
ne
d
f
r
o
m
e
q
uat
i
o
n
(
1
2)
.
A
s
s
how
n
i
n
F
ig
ur
e
2(
d)
,
all
t
h
e
di
st
ur
ba
nce
co
m
pone
n
t
s
ar
e
r
e
m
ove
d
at
t
he
r
ea
cti
o
n
to
r
que
o
bser
v
e
r
;
h
e
n
c
e
,
t
h
e
R
T
O
B
o
u
t
p
u
t
i
s
t
h
e
e
s
tim
ated
l
oa
d
tor
que
.
)
(
a
t
f
dis
l
I
K
J
B
T
T
T
(
1
2
)
3.
DC MOTO
R
PARAME
TER
E
STI
M
ATI
O
N
MET
H
ODS
3.
1.
Ex
perimenta
l
S
etu
p
I
n
t
he
e
x
p
e
r
im
e
n
t,
a
s
show
n
i
n
F
ig
ur
e
3,
t
he
s
ys
tem
com
p
o
s
e
d
o
f
l
-
DOF
m
ain
m
o
tor,
m
a
n
u
f
ac
ture
d
by Ma
xo
n
R
E
-
m
ax
29
a
nd
th
e
m
o
t
o
r
spec
if
ic
ati
o
ns
a
r
e
l
i
s
t
e
d
i
n
T
a
b
le
1
a
nd
a
mo
tor
dr
i
v
er
S
E
-
H
B
-
40-
1
w
i
t
h
d
r
i
v
e
r
I
C
(
I
R
F
4
9
0
5
S
/
L
)
a
l
o
n
g
w
i
t
h
a
c
u
r
r
e
n
t
s
e
n
s
o
r
,
w
h
i
c
h
c
a
n
c
ar
r
y
a
c
u
r
r
e
nt
o
f
up
t
o
4
0A
p
ea
k
loa
d
.
The
c
u
r
r
e
nt
s
e
n
s
o
r
in
st
a
l
l
e
d
i
n
t
he
s
yste
m
is
t
o
e
s
t
i
m
a
te
t
he
a
c
t
ua
l
c
u
r
r
e
nt
o
f
t
h
e
m
a
in
m
o
t
or
.
The
mot
o
r
dr
iver
i
s
ope
r
a
ted
b
y
t
h
e
P
WM
s
igna
l
s
g
e
n
e
r
ate
d
b
y
the
pr
oce
s
sor
.
A
n
enc
o
de
r
c
o
u
p
l
ed
w
ith
t
h
e
m
ain
mot
o
r
doe
s
pos
i
tio
n
se
ns
in
g.
Tab
l
e
1.
D
C
Motor
spec
if
i
c
at
i
ons
P
a
r
a
me
t
e
r
Va
lue
Units
Ra
t
e
d
output
67.
2
W
Ra
t
e
d/
m
a
x
torque
21.
5/14
6
m
N
m
E
n
c
o
d
e
r
r
e
solution
512
P
ulse
/r
e
v
F
i
gur
e
2.
O
ne
D
O
F
r
ota
t
i
o
n
a
l
m
a
nipu
l
a
t
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
ow
E
l
e
c
&
Dr
i
S
y
st,
Vol.
10,
N
o.
1
,
Mar
c
h
2
0
1
9
:
19
5
–
210
20
0
3.
2.
Estim
a
ti
on o
f Torque
C
o
e
f
f
icient
(
K
t
)
It
i
s
i
m
p
o
rtan
t
to
i
de
n
tify
the
e
x
ac
t
K
t
o
f
D
C
m
otor
,
si
nc
e
t
h
e
g
i
ven
va
l
u
e
f
r
o
m
ma
nu
f
a
c
t
ur
er
s
m
a
y
no
t
be
a
n
e
x
a
c
t
r
epr
e
se
nta
t
i
o
n
of
K
t
f
or
t
he
l
oa
de
d
D
C
m
ot
or
.
The
c
h
a
n
ge
o
f
t
h
e
tor
q
ue
c
oef
f
i
c
i
e
n
t
is
a
ls
o
c
o
n
s
i
d
er
ed
a
s
a
d
i
s
t
ur
ba
nce
t
o
t
he
m
otor
.
T
h
e
in
p
u
t
pow
e
r
P
o
f
t
h
e
D
C
m
o
t
o
r
c
a
n
e
x
p
r
e
s
s
e
d
i
n
t
e
r
m
s
o
f
tor
que
a
nd
a
n
g
u
la
r
ve
l
o
c
ity
.
P
(
1
3
)
The
power
P
a
l
s
o
c
a
n
be
r
e
p
r
e
se
n
t
e
d
u
s
i
ng
ar
ma
t
u
r
e
v
o
lta
ge
V
a
a
nd
a
r
m
a
tu
r
e
c
ur
r
e
nt
I
a
.
a
a
I
V
P
(
1
4
)
a
t
I
K
(
1
5
)
F
r
om
(
14)
a
nd
(
15)
i
t
can
b
e
show
n
as
t
a
K
V
(
1
6
)
He
n
c
e
,
t
h
e
a
ngu
l
a
r
v
e
lo
c
ity
i
s
d
i
rec
tly
p
roport
i
o
n
a
l
to
t
h
e
a
rm
ature vo
lt
a
g
e, and t
h
e
a
r
m
a
ture
c
urren
t
is
a
n
in
de
pe
n
d
e
n
t
var
i
a
b
le
i
n
th
is
r
ela
t
i
o
nsh
i
p.
W
he
n
t
h
e
D
C
m
o
t
o
r
i
s
r
u
nni
ng
und
e
r
n
o
l
o
ad
c
o
ndi
tio
n
s
,
th
e
K
t
v
a
l
ue
d
oe
s
no
t
va
r
y
.
H
o
w
e
v
e
r
,
K
t
m
a
y
v
a
r
y
wh
en
t
h
e
m
o
t
o
r
i
s
lo
a
d
ed
.
T
h
e
ch
a
nge
o
f
K
t
o
f
t
h
e
l
o
ad
ed
m
o
tor
wa
s
de
t
e
rm
ined
u
s
i
ng
t
h
e
co
n
v
en
t
i
o
n
a
l
ro
t
o
r
sta
l
l
te
st
.
F
i
g
ur
e
4
sh
ow
s
t
h
e
se
t
u
p
use
d
f
or
a
r
o
t
o
r
s
t
a
ll
tes
t
[
4
8
]
.
T
his
expe
r
i
me
nt
w
a
s
c
o
n
d
u
c
t
e
d
t
o
m
e
a
s
ur
e
m
o
t
o
r
tor
q
u
e
s
a
g
a
i
n
s
t
a
r
a
n
g
e
o
f
a
r
m
a
t
u
r
e
c
u
r
r
e
n
t
s
.
I
n
th
is
t
e
s
t,
t
orq
u
e
c
oeffic
i
e
n
t
w
a
s
ob
t
a
ine
d
f
ro
m
t
h
e
sl
ope
o
f
th
e
gr
ap
h
o
f
F
igur
e
8,
b
y
p
l
o
t
tin
g
t
h
e
var
i
a
t
i
on
of
tor
que
a
ga
i
n
st
t
he
a
r
m
a
t
ur
e
cur
r
ent.
T
he
t
or
q
u
e
c
o
ef
f
i
c
i
ent
K
t
f
ou
n
d
u
si
ng
(
15)
f
r
o
m
F
i
g
u
r
e
5
(
a
)
is
0
.
2
56
Nm/A.
Fi
g
u
re
3
.
R
o
t
o
r
s
t
a
l
l
t
e
s
t
3.
3.
Estima
tio
n
o
f Frict
i
o
n
Co
m
p
o
nen
t
s
The
a
u
t
h
or
s
pr
op
ose
use
o
f
D
i
s
t
u
r
b
a
n
c
e
O
bse
r
ver
(
D
O
B
)
[
1
]
,
[
40]
i
n
a
cl
ose
d
l
oo
p
co
n
t
r
o
l
syst
e
m
,
to
e
stim
ate
the
di
stur
ba
nce
s
t
or
q
u
e
to
f
i
n
d
t
h
e
fr
ic
t
i
on
c
o
m
pon
e
n
ts.
The
di
st
ur
ba
nc
e
o
b
ser
v
er
i
de
nt
if
i
e
s
the
to
ta
l
m
e
c
h
an
ic
a
l
l
oad
tor
que
a
nd
t
h
e
e
f
fe
c
t
s
o
f
s
ys
t
e
m
par
a
m
e
te
r
s
a
s
r
e
pr
e
s
ente
d
in
e
qua
ti
o
n
(
11)
.
The
fri
c
t
i
o
n
c
o
mpon
e
n
t
s
w
e
r
e
est
i
ma
t
e
d
b
y
c
ondu
c
t
i
n
g
a
c
o
n
s
t
a
n
t
v
el
oci
t
y
m
o
t
i
o
n
tes
t
[
4
8
]
,
[
40]
,
w
h
en
t
he
m
otor
is
r
u
n
n
i
n
g
a
t
a
c
o
n
s
t
an
t
ve
l
o
c
ity.
T
h
e
ac
ce
l
e
rati
on
o
f
t
h
e
m
o
to
r
i
s
z
e
r
o
a
n
d
h
e
n
c
e
th
e
r
e
i
s
n
o
ef
fe
ct
o
n
the
m
o
tor
iner
tia
J
[
48
].
T
h
e
t
o
r
qu
e
c
o
e
ffi
c
i
en
t
wa
s
0
.
0
256
N
m/
A
f
o
r
m
t
h
e
p
r
e
vi
ou
s
l
y
d
i
s
c
u
s
s
e
d
r
o
t
o
r
s
t
a
l
l
t
e
s
t
.
T
h
e
t
e
st
w
as
c
o
ndu
c
t
ed
w
it
h
n
o
-
l
o
a
d
con
d
iti
on
s
a
nd
th
e
r
efo
r
e
th
e
ext
e
rn
a
l
t
o
r
q
u
e
i
s
ze
ro
.
T
h
e
DOB
o
u
t
pu
t
gi
ve
n
as,
B
T
T
f
dis
(
1
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
M
o
t
i
o
n
c
o
n
t
r
o
l
app
l
i
ca
t
i
ons:
obs
erve
r
b
a
sed
D
C
m
o
t
o
r
par
am
e
t
e
rs es
tim
a
t
i
o
n fo
r… (B
ra
ne
sh
M.
Pil
l
ai)
20
1
A
P
I
D
base
d
D
O
B
in
corp
or
a
tin
g
a
t
u
ne
d
vel
o
c
i
t
y
c
o
n
tr
olle
r
w
a
s
u
se
d
to
o
bta
i
n
a
b
e
tter
ve
loc
i
t
y
respo
n
se
w
i
t
h
thi
s
c
o
n
s
t
an
t
ve
l
o
c
i
t
y
t
es
t
[47]
.
The
c
o
rre
spond
i
ng
e
x
per
i
m
e
nta
l
p
ar
am
eter
v
a
l
ue
s
w
e
re
s
how
n
in
T
a
b
le
2
.
Th
e
tes
t
w
as
c
on
duc
te
d
w
i
t
h
d
i
ffe
ren
t
c
o
n
sta
n
t
ve
lo
cit
i
es
r
a
n
g
i
ng
f
ro
m
+
500
0
r
p
m
t
o
-5000
rp
m.
F
i
gure
5(b)
a
n
d
(
c
)
s
h
o
w
t
h
e
ve
loc
i
ty
r
esp
o
n
se
a
nd
the
ob
serve
r
o
u
t
pu
t
(d
i
s
tu
rb
a
n
c
e
to
rq
u
e
).
I
n
th
is
t
e
s
t
,
a
s
show
n
i
n
e
q
u
a
t
i
o
n
(18),
the
D
O
B
o
u
t
pu
t
c
ons
ists
o
f
fr
ict
i
o
n
c
om
po
ne
nt
s
and
the
c
h
a
n
ge
o
f
i
n
ert
i
a
e
f
fe
ct
o
f
the s
y
stem
J
.
This
J
effec
t
exis
ts
o
n
l
y
withi
n
t
he
a
c
cele
r
ati
on p
e
r
i
o
d
.
J
B
T
T
f
dis
(
1
8
)
F
o
r
t
h
e
e
s
tim
ati
on
of
f
ric
t
i
on
c
o
mp
o
n
e
n
ts,
on
ly
t
he
lin
e
a
r
vel
o
c
i
t
y
r
egi
o
n
wa
s
c
o
ns
ider
ed,
a
n
d
ac
cele
r
at
io
n is
z
e
r
o dur
ing
the
per
i
o
d
.
Tab
l
e
2. Expe
rime
nta
l
par
am
eters
P
a
ra
m
e
te
r
V
a
l
u
e
U
n
i
t
s
Motor I
n
e
r
t
i
a
(J
n
)
13.
5
g
cm
2
T
o
rque
C
o
e
f
f
ic
ie
nt
(
K
t
)
0.
256
N
m
/
A
K
P
C
onst
a
nt: P
I
D
0.
01
K
I
C
onst
a
nt:
PID
10
-4
K
D
C
onsta
nt
:
PID
0.
006
C
u
t
-
of
f
fre
que
n
c
y
of l
ow
p
a
ss
fil
t
e
r
(
G
di
s
)
0.
003
H
z
(a)
(b)
(c)
(d)
F
i
gure
5.
(
a
)
Tor
que
r
espo
nse
a
g
ain
s
t
curr
en
t (b)
V
e
loc
i
t
y
r
esp
onse o
f
t
he
c
on
st
a
n
t
vel
o
c
i
ty te
s
t (
c
)
D
i
st
urba
nce
ob
ser
v
er
outp
u
t f
o
r differe
nt
v
e
l
oci
tie
s (d)
Measur
e
d
fric
tio
n
tor
q
ue
O
b
se
rver
o
u
t
p
u
t
is
a
ve
rage
d
from
10
sec
o
nds
t
o
3
0
s
e
c
o
n
d
s
fr
om
F
i
gur
e
5(b).
A
v
e
r
ag
e
d
o
bser
ver
ou
tpu
t
a
ga
i
n
st
t
he
c
orr
e
spo
n
d
i
ng
v
e
l
oc
it
y
is
r
e
d
ra
w
n
i
n
F
i
gure
5(d)
,
for
c
l
o
c
kw
ise
an
d
a
n
t
i
c
l
o
ckw
i
se
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
19
5 –
21
0
20
2
direc
t
i
o
ns.
The
ant
i
c
l
o
c
k
w
i
se
d
ire
c
t
i
on
sh
o
w
s
a
hig
h
e
r
fri
ctio
n
f
o
r
the
gi
ven
D
C
m
ot
o
r
.
S
t
ati
c
f
r
i
c
t
i
o
n
T
f
i
s
ave
r
age
d
f
or
bot
h
d
i
r
ect
i
o
n
s
a
nd
c
a
n
b
e
ca
lc
ul
a
t
e
d
a
s
sh
o
w
n
in
F
i
gur
e
5(d).
H
o
w
e
ver
,
T
f
f
or
e
a
c
h
dire
c
t
i
o
n
is
a
l
so
c
a
l
cu
l
a
bl
e.
T
h
e
c
al
cul
a
t
e
d
av
e
r
ag
e
st
a
t
ic
f
ri
ct
io
n
v
a
l
u
e
T
f
is 0.037
5N
m
.
The vi
s
c
o
us fric
t
i
on c
o
effic
i
en
t
B
w
a
s
m
a
them
ati
call
y
i
de
n
tifie
d
by
u
s
i
ng
a
sta
nda
r
d
c
urv
e
f
it
ti
n
g
m
o
d
el
f
ro
m
F
i
gure
5(
b),
and
e
s
t
i
m
a
te
d
us
i
n
g
bo
th
t
he s
tan
d
a
r
d li
near
re
g
ressi
on m
e
th
o
d
a
nd
the m
e
th
o
d
o
f ev
a
l
ua
tio
n
[4
9],
and
expre
s
s
e
d in (1
9
)
.
0002573
.
0
B
(
1
9
)
The
va
lid
it
y o
f
t
hese
e
st
i
m
ate
d
f
ric
t
i
on c
o
m
p
o
n
e
n
t
s
is
p
r
o
v
e
n i
n t
h
e
fr
i
c
tio
n c
o
mpe
n
sat
i
o
n
s
ect
io
n 4 (
B
).
3.4.
Estimation
o
f
mot
o
r in
ert
i
a
(
J)
I
n
(
11),
the
i
n
er
tia
o
f
t
h
e
motor
J
s
u
b
je
c
t
ed
t
o
var
i
at
i
ons
i
s
descr
i
b
e
d.
T
h
i
s
vari
a
t
i
o
n
i
s
a
l
s
o
con
s
i
d
ere
d
a
s
a
d
i
stur
ba
nce
of
t
h
e
D
C
mo
tor.
I
de
nt
i
f
i
c
a
t
io
n
a
n
d
c
om
p
e
nsa
t
i
o
n
of
t
h
e
c
ha
n
g
e
of
i
nert
ia
impro
v
e
t
h
e
D
C
m
otor
r
ob
ustness
in
ope
rati
on.
H
ow
ev
er
,
bot
h
i
d
e
n
t
i
f
y
i
ng
an
d
co
mpe
n
sa
tin
g
th
e
inert
i
a
varia
t
i
o
ns
a
re
i
m
por
tan
t
t
as
k
s
.
There
a
r
e
n
o
s
t
r
ai
g
h
tforw
a
rd
m
e
thods
f
or
t
h
i
s
[16-2
1
]
.
To
overc
om
e
this
barr
i
e
r,
i
n
this
r
ese
a
rc
h,
t
he
a
ut
hor
s
pro
p
o
se
a
R
TO
B
base
d
ine
r
t
i
a
c
a
l
c
u
la
t
i
o
n
a
nd
c
om
pe
n
s
at
ion
te
c
h
niq
u
e
.
Estim
at
io
n
o
f
m
otor
i
nert
ia
e
st
ima
t
ed
i
n
thr
e
e
differ
en
t
w
a
ys
:
c
o
n
v
e
n
tio
n
a
l
a
cce
lera
ti
on,
d
e
celer
at
i
o
n
m
o
tio
n
tes
t
and
n
o
v
el
R
e
v
er
se
Mo
tio
n
A
c
c
e
lera
tio
n
t
e
s
t
.
3.4.
1. A
cce
l
e
rati
on
motion
te
st
In
t
hi
s
t
e
st
,
t
h
e
DC
m
o
t
o
r
i
s
at
t
ach
e
d
w
i
t
h
a
p
l
an
e
t
ary
g
earh
e
a
d
of
r
a
t
io
2
46
:
1
b
roug
ht
t
o
i
t
s
r
a
t
e
d
spee
d
from
i
n
i
tia
l
ze
ro
s
peed
.
As
s
hown
in
F
igure
6(
a),
the
ac
c
e
l
e
r
a
t
i
o
n
o
f
t
he
m
ot
or
w
as
c
alcula
t
e
d
b
y
di
vid
i
ng t
h
e
rat
e
d
spee
d
to t
he
tim
e ta
k
e
n to r
eac
h it
s ra
t
e
d s
pee
d
.
on
A
ccelerati
on
Accelerati
J
Inertia
Motor
Torque
)
(
(kg-m
2
)
(
20)
Dire
ct
c
a
l
cu
la
t
i
o
n
o
f
t
h
e
ac
c
e
ler
a
t
i
o
n
t
orqu
e
is
n
ot
p
oss
i
b
l
e
w
i
t
h
t
he
c
o
nve
nti
o
nal
me
tho
d
.
In
t
h
i
s
expe
r
i
me
n
t
,
th
e
aut
h
ors
use
d
R
TO
B
as
t
he
t
orq
u
e
se
nsor
.
The
a
c
c
e
l
era
t
i
on
t
o
rque
i
s
t
h
e
out
pu
t
o
f
t
he
t
orq
u
e
sens
or.
The
calc
u
l
a
t
e
d m
o
t
o
r
iner
tia
v
al
ue
f
ro
m
this tes
t us
in
g
equa
tio
n (
20)
is 16.
7 g
cm
2
.
3.4.
2. D
ece
l
e
rati
on
Mot
i
o
n
Test
The
p
o
w
e
r
su
pp
l
y
t
o
t
h
e
m
o
tor
is
d
isco
n
n
e
c
te
d
w
h
en
t
he
m
otor
i
s
r
u
n
n
i
n
g
at
i
t
s
r
at
ed
s
p
eed
.
Th
e
motor
s
p
ee
d
t
h
en
r
edu
c
es
t
o
z
e
r
o
from
i
t
s
s
te
a
dy
s
p
ee
d
a
s
s
how
n
i
n
F
i
gur
e
6(
b),
the
dy
na
mic
tor
que
e
qua
t
i
on
for
this
t
e
s
t
bec
o
m
e
s
(21).
0
B
T
J
f
(
2
1
)
The
tim
e
doma
i
n
s
o
l
u
ti
o
n
o
b
t
aine
d f
o
r e
qua
t
i
o
n
(
21)
i
s
ex
pre
s
se
d as
b
el
ow
w
ith a
ca
l
cu
la
ble c
o
ns
t
a
nt
A
.
)
/
(
J
B
f
Ae
B
T
t
(
2
2
)
The
calc
u
la
t
e
d m
o
t
o
r
i
n
ert
i
a
in
t
he de
c
e
l
e
r
at
i
on m
o
ti
on t
e
st
i
s
1
4
.
2 g
cm
2
.
3.4.
3. R
ever
se m
oti
o
n
ac
cele
r
ati
o
n
test
Th
is
i
s
a
n
ove
l
m
e
tho
d
i
n
t
ro
d
u
ce
d
by
t
h
e
a
u
th
ors
t
o
e
s
t
i
m
a
t
e
t
h
e
m
o
t
o
r
in
e
r
ti
a
.
H
er
e,
R
TOB
i
s
u
se
d
as
a
t
or
que
s
e
n
so
r
.
T
he
c
a
l
c
u
la
t
e
d
va
lue
s
f
or
m
ot
or
p
a
r
am
et
e
r
s
va
lue
s
(
K
t
,
T
f
a
n
d
B
)
w
e
r
e
u
s
e
d
f
o
r
t
h
i
s
t
e
s
t
.
A
D
O
B
b
ase
d
r
ob
us
t
ve
loc
i
ty
c
o
n
tr
ol
l
e
r
w
a
s
use
d
t
o
a
c
h
ieve
a
c
c
ura
t
e
v
el
oc
it
y
re
s
ponse
s
.
Th
e
t
e
st
w
as
con
d
u
cte
d
b
y
re
versin
g
the
m
o
tor
dire
c
t
i
on
s
udde
nly
w
h
ere
a
s
i
t
was
ru
nn
ing
a
t
s
t
ead
y
st
at
e
sp
eed
.
Th
e
con
t
ro
l
l
er
g
o
v
e
r
n
s
the
imm
e
dia
t
e
c
h
an
ge
o
f
t
h
e
d
i
re
ct
ion
a
s
s
h
o
wn
i
n
Fi
gure
6(
c),
the
m
o
t
o
r
ac
ce
ler
a
ti
on
to
the
o
p
p
o
s
i
te
d
i
r
ect
io
n
s
t
a
r
ts
a
t
t
1
a
nd
e
nd
s
at
t
2
.
At
t
2
,
t
h
e
m
o
t
o
r
ap
pr
oache
s
a
s
tea
d
y
sta
t
e
spe
e
d
in
t
he
op
p
o
site
d
ire
c
t
ion.
T
h
i
s
d
i
r
e
c
t
i
o
n
varia
t
i
on
resul
t
s
in
a
v
a
r
ia
tio
n
o
f
t
orq
u
e
,
a
nd
f
r
o
m
the
s
e
var
i
a
t
ions
t
he
motor
i
n
ert
i
a
i
s
d
ir
ect
ly e
stim
a
t
ed.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
M
o
t
i
o
n
c
o
n
t
r
o
l
app
l
i
ca
t
i
ons:
obs
erve
r
b
a
sed
D
C
m
o
t
o
r
par
am
e
t
e
rs es
tim
a
t
i
o
n fo
r… (B
ra
ne
sh
M.
Pil
l
ai)
20
3
The
RTO
B
o
u
t
p
u
t
o
f
Rever
s
e
m
o
ti
on
a
cce
le
rati
on
te
st
dis
T
ˆ
c
ons
i
s
ts
o
f
o
n
l
y
t
he
c
h
a
ng
e
o
f
m
otor
iner
tia.
The
k
n
o
w
n
d
is
t
u
r
b
a
n
ce
c
om
po
ne
nts
w
e
re
e
lim
i
n
a
t
e
d
i
n
t
h
e
i
n
n
e
r
l
oop
o
f
t
h
e
RTOB
a
s
e
xpl
a
i
n
e
d
i
n
F
i
gure
2(d)
.
J
T
dis
ˆ
(
2
3
)
F
r
om
(
8),
dis
T
ˆ
in (
2
3
)
is e
xpresse
d
a
s
)
(
ˆ
n
dis
J
J
T
(
2
4
)
(a)
(b)
(c)
(d)
F
i
gure
4.
(
a)
V
eloc
i
t
y &
acc
el
era
tion
resp
ons
e
of a
cce
lera
tio
n
m
o
tio
n
tes
t
(
b)
V
eloci
t
y r
e
spo
n
se
o
f
dece
lera
ti
o
n
mot
ion
te
st (c
)
Ve
l
oc
i
t
y
resp
o
n
s
e
o
f r
e
ver
s
e
mot
i
o
n
acc
e
l
er
ation
te
st (d)
I
ne
rti
a
re
s
p
onse
of
reverse
motion a
c
c
e
le
r
a
ti
o
n
t
e
s
t
By
i
nte
g
rat
i
n
g
(24)
f
or
t
he t
im
e inter
v
a
l
t
1
to
t
2
, the
abo
ve
expr
ess
i
on
can
b
e
rew
r
itten
as fol
low
s
:
2
1
)]
(
)
(
)[
(
ˆ
1
2
t
t
n
dis
t
t
J
J
dt
T
(
2
5
)
Mo
tor
inert
i
a
J
c
an
b
e c
a
lcu
l
a
t
ed
f
rom
the
ri
gh
t ha
nd
s
i
de
k
now
n pa
ram
e
te
rs of
(
26).
2
1
ˆ
)]
(
)
(
[
1
1
2
t
t
dis
n
dt
T
t
t
J
J
(
2
6
)
F
r
om
(
26)
a
nd F
i
g
u
r
e
6
(
d
) the
ca
l
c
ula
t
e
d
m
ot
or iner
tia
is 1
9
.1
g c
m
2
.
4.
EXPE
RIMENTS
AN
D
R
E
S
U
L
T
S
A
nove
l
ap
pr
oa
ch,
RTO
B
b
a
s
e
d
fric
t
i
o
n
c
o
mpe
n
sa
tio
n
mode
l
i
s
i
nt
r
o
d
u
ce
d
i
n
t
his
rese
arc
h
t
o
eva
l
ua
t
e
t
he
e
stim
at
ed
f
r
i
c
t
io
na
l
a
n
d
i
n
erta
i
l
v
a
l
ues.
T
he
b
loc
k
di
a
g
ram
of
t
he
p
ro
po
se
d
sys
t
em
i
s
sh
ow
n
i
n
F
i
gure
7.
I
n
o
r
der
to
a
ch
ie
v
e
t
he
a
cc
urate
in
e
r
t
i
a
l
v
a
l
ue
,
this
r
esea
rch
derive
d
t
h
e
i
n
n
o
v
at
i
v
e
(
26)
.
The
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
ow
E
l
e
c
&
Dr
i
S
y
st,
Vol.
10,
N
o.
1
,
Mar
c
h
2
0
1
9
:
19
5
–
210
20
4
si
gn
ifica
n
c
e
o
f
this
e
q
u
a
tio
n
is
t
h
a
t
i
t
c
o
m
pensa
t
e
s
f
or
(
24)
v
a
l
ue
b
e
t
w
e
e
n
t
hat
o
f
t
he
m
a
n
u
f
ac
tur
e
r
and
a
c
tua
l
i
ner
tia
.
F
i
gur
e
5.
R
TO
B
ba
se
d
f
r
i
ct
i
on
com
p
en
sat
i
o
n
m
odel
4.
1.
S
t
ab
i
lit
y
A
n
al
ys
i
s
F
r
i
c
tion
some
t
i
m
e
s
ca
use
s
r
educe
d
t
r
a
cki
n
g
pe
r
f
or
ma
nce
i
n
c
o
n
tr
ol
s
ys
tem
s
w
he
n
i
t
i
s
unc
ompe
nsa
t
e
d
.
T
h
is
s
e
c
t
i
o
n
a
n
al
yze
s
t
he
s
ta
bi
l
i
t
y
o
f
t
h
e
s
y
s
t
e
m
w
h
e
n
t
he
f
r
i
c
t
i
o
n
i
s
c
ompe
nsat
ed.
Th
e
sim
p
li
fie
d
t
r
a
nsfe
r
f
u
nct
i
o
n
(
27)
b
e
t
w
e
e
n
t
he
i
npu
t
T
dis
a
nd
o
u
tp
ut
i
s
d
er
ive
d
f
r
o
m
F
i
gur
e
7.
T
h
e
e
xper
i
m
e
nta
l
v
alue
s
use
d
f
or
t
he
M
A
TLA
B
simu
lat
i
ons
a
r
e
lis
t
e
d
in
T
a
b
l
e
3
.
T
h
e
st
abi
l
ity
o
f
th
e
sy
stem
i
s
a
n
al
yze
d
u
s
i
ng
r
oot
l
oc
us
p
l
o
t
for
(
27)
s
h
o
w
n
i
n
F
i
g
u
r
e
8
.
The
tr
a
n
sf
er
f
unc
t
i
on
gai
n
K
i
s
chan
ge
d
f
r
o
m
1
to
10
0
00, re
s
u
l
t
i
n
g
i
n
s
ta
ble c
h
ar
acte
r
ist
i
cs o
f t
h
e syste
m
.
This
il
l
u
s
t
r
a
t
e
s
tha
t
t
he
f
r
i
c
t
i
o
n
co
m
p
ensa
ted
sys
t
em
is
st
ab
l
e
.
Th
e
e
f
fec
t
s
o
f
t
h
e
p
arame
t
er
c
h
a
ng
e
we
re
a
n
a
ly
z
e
d
f
o
r
t
he
fr
i
c
t
io
n c
o
mpe
n
sa
te
d
s
y
s
t
em
t
o me
asur
e
t
h
e
st
ab
ili
ty
[
50
].
))
(
)
(
)(
(
)
(
)
))
(
(
(
2
2
2
I
d
p
dis
t
tn
dis
f
dis
tn
t
I
d
p
di
s
tn
dis
f
di
s
K
K
s
sK
BG
K
K
G
s
Js
B
T
G
s
sK
K
K
K
s
sK
G
s
YK
G
T
T
(
27)
Where,
Y
is
t
he
c
ur
r
e
nt
s
e
n
sor
ou
t
p
u
t
g
a
i
n.
T
h
e
syst
e
m
p
aramet
ers
J,
B
a
nd
T
f
w
e
r
e
a
ssum
e
d
t
o
b
e
c
h
ange
d
by
w
i
t
h
r
e
s
pect
t
o
t
h
e
i
r
nomi
n
a
l
va
lue
s
.
T
he
s
u
b
scr
i
pt
n
i
s
use
d
t
o
de
n
o
te
t
he
nomina
l
v
a
l
ue
s.
J
J
J
n
(
2
8
)
B
B
B
n
(
2
9
)
f
fn
f
T
T
T
(
3
0
)
The
s
y
s
t
em
f
r
e
que
nc
y
r
e
sp
on
se
i
s
a
n
al
yze
d
u
s
i
n
g
b
o
d
e
pl
o
t
t
o
o
l
in
M
ATLAB
to
i
d
e
nt
ify
t
h
e
ef
fe
ct
of
par
am
eter
c
ha
n
g
e.
F
ig
ur
e
8 (
a
)
&
(
b
)
sho
w
s t
h
e
r
oot
loc
us pl
ot
a
n
d
bod
e
p
l
ot
o
f
in
e
r
ti
a
ch
ang
e
r
e
s
pe
ct
iv
ely
a
n
d
a
r
r
o
w
s
i
ndic
a
te
t
ha
t
the
r
e
sp
on
se
s
va
r
y
w
i
t
h
J
.
W
h
e
n
J
ele
m
ent
inc
r
ea
se
s
,
t
he
c
on
j
u
gate
r
oo
ts
m
o
v
e
a
l
o
n
g
i
m
a
gi
nar
y
a
x
e
s,
b
u
t
t
he
s
ystem
r
e
ma
ins
s
t
ab
le.
Th
e
ef
fec
t
o
f
J
is
n
eg
lig
ib
le
f
or
l
ow
freque
nc
ies
a
n
d
is
s
ign
i
fica
n
t
f
o
r
h
i
ghe
r
fr
e
que
ncie
s
(
p
r
a
ct
ic
al
f
r
e
que
nc
i
e
s)
[
33
].
T
h
e
ref
o
re,
t
h
e
estimatio
n
of
a
n
acc
u
r
ate
J
i
s
imp
o
r
tant fo
r
a stable sy
s
t
em.
In
F
igu
r
e
8
(c
)
&
(
d
),
t
h
e
re
i
s
no
sub
s
tanti
a
l
ef
f
e
ct
on
stab
il
it
y
a
n
d
f
r
e
que
ncy
r
e
sp
ons
es
w
he
n
ch
a
ngi
ng
B
e
l
e
m
e
n
t.
I
t
is
e
vi
de
nt
t
ha
t
t
h
e
e
f
fe
ct
i
s
s
i
g
n
i
f
i
can
t
o
n
l
y
for
l
o
w
fr
e
que
nc
ies.
F
igur
e
8
(
e
)
a
nd
(
f
)
show
t
he
r
e
s
p
o
n
se
s
cor
r
e
sp
on
di
n
g
t
o
f
T
elem
en
t.
T
he
a
na
l
y
s
i
s
of
t
he
e
f
f
ec
t
o
f
p
ar
a
m
e
t
e
r
c
ha
nge
v
al
i
d
a
t
es
t
h
at
s
e
l
ect
in
g
t
h
e
c
o
rre
c
t
J
an
d
f
T
va
lue
s
a
r
e
v
i
t
a
l
f
or
a
s
ta
b
l
e
s
y
s
t
em
,
a
nd
he
nce
t
h
e
f
r
i
c
tio
n
co
mp
en
s
a
t
e
d
sys
t
em
’s stabi
l
i
t
y
d
e
p
en
ds o
n
them
.
Evaluation Warning : The document was created with Spire.PDF for Python.