Indonesian J
ournal of Ele
c
trical Engin
eering and
Computer Sci
e
nce
Vol. 1, No. 2,
February 20
1
6
, pp. 319 ~
328
DOI: 10.115
9
1
/ijeecs.v1.i2.pp31
9-3
2
8
319
Re
cei
v
ed Au
gust 11, 20
15
; Revi
sed
No
vem
ber 2
4
, 2015; Accepte
d
De
cem
ber
15, 2015
Nonlinear Servomotor in Single Pulse Simulation of
Electrical Disch
arge Machining System Modeling
Has
san Le
e*
1
, Az
li Yah
y
a
2
, Nor Hisha
m
Kham
is
3
, Shahrullail Samion
4
1,3
F
a
culty
of Electrical En
gin
e
e
rin
g
, Univers
i
ti T
e
knologi Ma
l
a
y
s
ia, Skud
ai 8
131
0, Johor, M
a
la
ysi
a
2
F
a
cult
y
of Bio
scienc
es an
d Medic
a
l Eng
i
n
eeri
ng, Un
iv
ers
i
ti T
e
knologi M
a
la
ysi
a
, Skud
ai
8131
0, Johor,
Malay
s
ia
4
F
a
cult
y
of Me
chan
ical En
gi
n
eeri
ng, Univ
ers
i
ti
T
e
knologi M
a
la
ysi
a
, Skud
ai
8131
0, Johor,
Mala
ysi
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: hassan
l
e
y
@
g
mail.c
o
m
1
, azli@fke.utm.m
y
2
, hisham@fke.utm.my
3
,
sy
ahruls@fkm.utm.my
4
A
b
st
r
a
ct
Electrical D
i
sc
harg
e
Machi
n
i
ng, EDM is a nonc
onv
entio
n
a
l an
d hig
h
pr
ecisio
n mach
in
ing. EDM
system
is consider
ed
a combination of s
e
r
v
o system
and EDM
proc
es
s. The serv
o
system
precis
ely
controls
the g
ap betw
een
el
ectrode
an
d w
o
rkpi
ece for
th
e co
ntinu
ous
e
l
ectrical
disc
ha
rges
occurre
nc
e.
Machi
n
in
g perf
o
rmanc
e and s
t
ability de
pe
nd
on the per
for
m
ance
of
servo
system. Th
e E
D
M serv
o syst
em
usua
lly
mo
del
e
d
as a
lin
ear s
ystem, w
h
ich i
gnor
es the
non
line
a
riti
es of th
e motor. An as
sumptio
n
that t
h
e
non
lin
eariti
e
s
are i
n
sig
n
ific
a
n
t in E
D
M sys
tem
mode
l
ma
y lea
d
s to
mo
deli
n
g
errors
a
nd res
u
lt i
n
p
oor
control
perfor
m
ance. In this
study
, nonlinear EDM serv
o
system
mode
l
was presented and the
dynam
i
c
respo
n
se of th
e mo
de
l w
a
s ana
ly
z
e
d
and
compar
ed w
i
th the line
a
r mo
del. Si
mu
latio
n
result show
s a
slightly d
i
fferen
c
e in system r
e
spo
n
se a
nd a
controll
er
use
d
in lin
ear
mo
d
e
l is less effici
ent for a nonl
in
ear
EDM serv
o sy
stem
mod
e
l. T
he r
e
sults
are
very us
eful
for
contro
l strate
g
y
an
d c
an c
ont
ribute
to
a b
e
tter
mac
h
i
n
in
g perf
o
rmanc
e an
d st
ability of EDM
app
licati
ons.
Ke
y
w
ords
: EDM system
, PID controller, DC
servom
otor, E
D
M proces
Copy
right
©
2016 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
Electri
c
al Di
scha
rge M
a
ch
ining, EDM i
s
a non
co
nventional ma
chining p
r
o
c
e
ss fo
r
cutting co
mpl
i
cated shap
e
or fine hole that would
b
e
difficult to
prod
uce with
ordina
ry cutting
tools with
out any conta
c
t b
e
twee
n elect
r
ode an
d
wo
rkpiece duri
ng
machi
n
ing [1
-2]. The history
of EDM tech
nique
s wa
s d
i
scovere
d
by Jo
sep
h
Pr
iestly in 1770. In 1943, Dr.
B. R. Lazare
n
ko
and Dr. N. I.
Lazare
n
ko de
veloped a co
ntrolled p
r
o
c
e
ss of ma
chini
ng difficult-to-machi
ne met
a
ls
by vapori
z
ing
material fro
m
the su
rfa
c
e of me
tal [2-5]. In EDM system mod
e
l
s
can b
e
arra
nged
in two main
group
s, servomotor sy
stem
and EDM pro
c
e
ss
as sho
w
n in
Figure 1.
The
servo
m
otor
system
con
s
i
s
ts of t
w
o
maj
o
r
su
bsy
s
tem
;
a p
e
rm
ane
nt mag
net
DC m
o
tor with
its
controlle
r an
d a lead-scre
w load. The l
ead-scre
w lo
ad con
s
i
s
ts o
f
gear, lead-scre
w shaft and
ram. T
he fe
edba
ck
sign
al in thi
s
mo
del i
s
the
g
ap voltag
e
which
is calcu
l
ated from E
D
M
pro
c
e
ss. E
D
M pro
c
e
s
s m
odel in
clud
es three
su
b
s
y
s
tem
s
, bre
a
kdown mod
e
l, material
rem
o
val
rate and inve
rse area [6-7]
Figure 1. Model of EDM System
An
ele
c
tri
c
al
spa
r
k
i
s
u
s
e
d
as
a
n
e
r
o
d
in
g
tool to remo
ve the material. The metal removal
pro
c
e
ss i
s
pe
rforme
d by a
pplying of pul
sed hi
gh fre
q
uen
cy dire
ct curre
n
t throu
gh ele
c
tro
de
to
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
1, No. 2, February 201
6 : 319 – 328
320
workpi
ece. The ele
c
trod
e motion is con
t
rolled by
the
machin
e so i
t
positione
d is not to cont
act
the wo
rkpie
c
e [8-1
0]. Wh
en the
gap
b
e
twee
n ele
c
trode a
nd
wo
rkpie
c
e i
s
suff
iciently small
10
–
50
μ
m, the gap is sai
d
bei
ng cont
rolle
d
by the serv
o system, an electri
c
al
spa
r
k o
c
curs in the
gap. In thi
s
pro
c
e
ss,
current is conve
r
ted into
i
n
ten
s
e heat with
extremely
hi
g
h
temp
eratu
r
e
s
rea
c
hin
g
8
0
0
0
° to
120
00°
C that
co
uld
melting al
mo
st anythin
g [2
], [11-15]. Th
e ga
p b
e
twe
e
n
an
electrode
an
d
a
workpi
ece
is a
d
ju
sted
a
nd mai
n
tain
ed
us
in
g se
r
v
omo
t
o
r
s
y
s
t
em a
t
a
cr
itic
a
l
ga
p
for the conti
nuou
s o
c
currence of
sp
ark disch
a
rge.
The ma
chin
ing stability
and p
r
od
ucti
vi
ty
depe
nd on
t
he
p
e
rfo
r
man
c
e of servo
m
otor system
[
16-2
2
]. Since
the
gap
bet
wee
n
el
ectro
d
e
and
wo
rkpie
c
e is cann
ot b
e
mea
s
u
r
e
d
dire
ctly, the a
v
erage
voltag
e ga
p
(
Vg
)
is impleme
n
ted as
the feed
ba
ck
sign
al to m
o
n
i
tor the
gap
which
re
pre
s
e
n
t
s voltage
dro
p
o
c
curred
du
ring
disch
a
rg
e
pha
se. After t
hat the e
rro
r
voltage bet
ween the
Vg
a
nd the
refere
nce volta
ge i
s
use
d
a
s
an
i
npu
t
of EDM controller. The con
t
rol gain (
Kc
)
and the level of
Vs
are ma
nually pre
s
et manually by the
EDM ma
chin
e operator [2
3-25].
Previou
s
stu
d
ies
use line
a
r mo
del
s to
simula
te th
e se
rvo sy
stem, so the
effect of
nonlin
earitie
s of DC
se
rv
omotor i
s
n
o
t
represent
ed
. Nonlin
eariti
e
s that o
c
cu
r in
servom
o
t
or
operation
sh
ould
be m
o
d
e
lled to
eval
uate the
reli
ability of the
co
ntrolle
r u
s
ed to
co
ntrol
the
electrode
po
sition. In this pape
r, nonlin
ear
servo
sy
stem mo
del
use
d
is exp
e
c
ted to repre
s
ent
the no
nline
a
rities that
nat
urally o
c
cu
r
durin
g
the
m
o
tor
ope
ratio
n
, so
that th
e influe
nce
of
nonlin
earitie
s to the EDM
system
ca
n
be ob
se
rved.
D
C
se
r
v
o
m
oto
r
mo
de
l w
ill b
e
c
a
rr
ie
d ou
t
usin
g the t
r
an
sfer fu
nctio
n
approa
ch
accordin
g
wi
th a
PID co
ntroll
ers for po
sition
controlled
an
d
will be p
r
e
s
e
n
ted in line
a
r
and
nonlin
ear m
odel. T
he sim
u
lation
is then impl
emented
usi
n
g
Matlab sim
u
li
nk. Dynamics re
sponse
of each m
o
del will be
analysed and
compared. T
h
e
dynamic
re
sp
onse of EDM
system mod
e
l is simul
a
te
d to identify the effects of
nonlin
earitie
s in
servo
system
to the EDM system model.
2. Rese
arch
Metho
d
2.1. DC Serv
omotor Mod
e
l
DC
se
rvomot
or is
a pe
rm
anent ma
gne
t DC moto
rs
that are m
odi
fied to wo
rk
usin
g a
clo
s
ed lo
op
control syste
m
in which the sh
aft
position or ang
u
l
ar velocity a
r
e the co
ntrol
variable
s
[26-27]. A control
l
er ca
n be u
s
ed to dire
ct the operation o
f
the
servo m
o
tor by sen
d
i
n
g
positio
n o
r
ve
locity si
gnal
s
to drive
s
th
e
motor. In
mo
delling
the
DC m
o
tor, th
e
aim i
s
to
find
the
governi
ng dif
f
erential e
q
u
a
tions that e
x
press t
he m
o
tor cha
r
act
e
ristics a
nd re
late the appli
ed
voltage to th
e torqu
e
p
r
o
duced by th
e roto
r. The
DC
motor
equivalent
ci
rcuit i
s
sho
w
n in
Figure 2.
Figure 2. DC
motor eq
uival
ent circuit
The voltage
balan
ce e
qua
tion of DC m
o
tor armature
circuit ba
sed
on Kirchhoff’s law i
s
expre
s
sed a
s
:
(
1
)
The torq
ue b
a
lan
c
e eq
uati
on of DC mot
o
r ba
sed o
n
Ne
wton’
s law is expre
s
sed
as:
(
2
)
Whe
r
e,
is armatur
e
cu
rr
ent (A);
is
equivalent indu
ctan
ce of armature
circuit (H);
is
equivalent re
sista
n
ce of armature
circuit
(
Ω
);
is termi
nal voltage of
armatu
re ci
rcuit (V);
is
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IJEECS
ISSN:
2502-4
752
Nonli
nea
r Servom
otor in Single Pulse Sim
u
la
tion of Electri
c
al Di
sch
a
rge
…
(Ha
s
san Lee
)
321
back el
ectro
m
otive
force (Vs/rad);
is t
he ine
r
tia mo
ment of the
rotor (K
g.m
2
);
is the to
rqu
e
coeffici
ent of DC moto
r (Nm/A) and
is angula
r
velocit
y
(rad/s).
The tran
sfe
r
functio
n
of DC servom
otor
model i
s
obta
i
ned by co
mb
ining eq
uatio
n 1 and
2. The La
pla
c
e T
r
an
sform
of both equ
a
t
ions give
s th
e simuli
nk m
odel de
picte
d
in Figure 3. The
angul
ar po
siti
on,
θ
of the motor is obtai
n
ed by taking
t
h
e integral of the motor vel
o
city,
.
Figure 3. Line
ar DC motor
Simulink Mo
d
e
l
2.2. Nonline
a
r DC Serv
omotor Model
DC
se
rvomot
or i
s
al
ways
having n
onlin
earit
ie
s that
need to
be
consi
dered in
controlle
r
desi
gn. In
prese
n
ce of thi
s
n
onlin
eariti
e
s
beh
avi
our, it is difficult to tune
a
controlle
r
as the
nonlin
ear effe
cts a
r
e difficu
lt to predict a
nd vary
w
i
th
th
e
s
y
s
t
em loa
d
[2
8
-
30
]. T
h
e
p
e
r
f
or
manc
e
of controlle
r
will not be
cl
ose to
optim
al and
not
b
e
sati
sfacto
ry. The nonli
n
ear effe
cts a
r
e
domina
n
t at low moto
r sp
e
eds a
nd grad
ually get
less promi
nent wit
h
highe
r mot
o
r sp
eed.
Wh
en
a DC motor
operates i
n
two di
re
ction
s
and hig
h
p
r
e
c
isi
on
control
is nee
ded fo
r the ap
plication,
the a
s
sumpti
on that
the
n
online
a
r
effects on
the
sy
stem a
r
e
negli
g
ible m
a
y le
a
d
to in
suffe
ra
bly
high mod
e
llin
g errors and
result in po
or
control pe
rformance [31-33
].
Figure 4. Forc
e vs
veloc
i
ty for fric
tion [28]
2.2.1. Friction
Figure 4
sho
w
ed
fri
c
tion
s
of the m
o
tor
torque.
Static or sti
c
tion
fri
c
tion
ch
aract
e
rizes a
starting
point
over which the motor to
rque mu
st
cross with the
purp
o
se of
smooth
moti
on.
Stiction is th
e
effect wh
ere, if
the interfa
c
e ha
s re
main
ed still for an
y length of time, the amo
unt
of force
req
u
i
r
ed
to
start t
he
relative m
o
tion i
s
g
r
eat
er th
an th
e a
m
ount
req
u
ired to
su
stain
it.
Visco
us o
r
ki
netic fri
c
tion
rep
r
e
s
ent
s a
torqu
e
that
alway
s
in th
e op
posite
di
rectio
n of
sh
aft
rotation. However, the viscous fri
c
tion i
s
prop
ortion
al to the angula
r
velocity and
in the model
it
is al
ways con
s
ide
r
ed
a
s
a l
i
near fun
c
tion
with
re
spe
c
t
to the
chan
g
e
of the
ang
u
l
ar velo
city [6
].
Coul
omb o
r
dry frictio
n
re
pre
s
ent
s a
consta
nt torq
u
e
that is
alwa
ys in the o
p
p
o
site di
re
ctio
n of
shaft rotation
. It can b
e
modele
d
a
s
a current
so
urce in
pa
rall
el to the
mot
o
r
with
con
s
t
a
nt
curre
n
t. Moreover directi
on of this current
equal
s the motor’s current dire
ction every time.
Coul
omb fri
c
t
i
on is
expre
s
sed im
po
sed
as a
sig
num f
unctio
n
de
pe
ndent o
n
the
rotational
sp
e
e
d
[34] as belo
w
:
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02-4
752
IJEECS
Vol.
1, No. 2, February 201
6 : 319 – 328
322
1,
0
0,
0
1,
0
In orde
r to
simplify applications
and
reflect the
re
al nonlin
ea
r
friction of th
e motor
accurately, a simplified fri
c
t
i
on model [35
]
was exp
r
essed in the Equ
a
tion (3
) as b
e
low:
.
.
(
3
)
Whe
r
e,
is the coul
omb fri
c
tion torque (Nm);
is viscous fri
c
tion to
rque
(Nm
)
;
is the
angul
ar velo
city of
the rotor (rad/
s);
sgn
ω
is signum fun
c
tio
n
of angula
r velocity.
The
co
ulom
b
friction
cau
s
e
s
m
e
chani
sm
s to
be
resi
st
ant to m
o
ve f
r
om
re
st. A
rotational
syst
em
will n
o
t st
art
to move
app
arently
until t
he d
r
iving
torque i
s
l
a
rge
enou
gh to
b
r
eak the
stati
c
fri
c
tion
torq
ue.
Such cha
r
a
c
teristi
cs of
co
ulomb fri
c
tion
form dead
zone no
nlinea
rity in the system [30, 34]. The
dead
zon
e
no
nlinea
rity is depictin
g in Figure 5.
Figure 5. Dea
d
zon
e
nonli
n
e
arity
2.2.2. Backla
s
h
The
sp
eed
required
by th
e loa
d
i
s
too
low
a
s
com
pare
d
to
the
nominal
spee
d of th
e
motor. In
such cases,
ge
ars a
r
e
introdu
ced b
e
tw
e
en t
he m
o
tor an
d
the l
oad, th
u
s
red
u
ci
ng
by a
fac
t
or,
n
the
angula
r
vel
o
city of the load itself. W
hen a ge
ar i
s
inserte
d
in
servo
syste
m
,
backla
s
h i
s
e
x
perien
c
e
d
o
n
its output d
ue to t
he cou
p
ling bet
wee
n
the co
gwhe
els of the g
e
a
r.
This give
s ri
se to nonlinea
rities and di
scontinuitie
s
in the force/velo
city relation
sh
ips. Backla
sh
is
the term that is comm
onl
y used to de
scribe a
n
y
sort of coupli
n
g that has
sla
ck
whe
n
it is
unloa
ded. De
vices
su
ch a
s
gea
r train
s
, or mech
ani
cal linkag
e
s th
at contain pin
n
ed hing
es,
will
exhibit backla
s
h to so
me e
x
tent or another a
s
illust
ra
ted in figure 6
(
b).T
he nonli
near E
D
M se
rvo
system m
o
d
e
l usu
a
lly fixed with le
ad
scre
w loa
d
a
s
sho
w
n in f
i
gure
6(a
)
. A leadscre
w
load
contai
ning th
e motor a
nd l
ead
scre
w ge
ars, le
ad
scre
w sh
aft and ram to hold a
n
elect
r
od
e. The
cal
c
ulatio
n of
the me
ch
an
ical
system
i
nertia
s
fo
r th
e lea
d
scre
w lo
ad i
s
ca
rrie
d
o
u
t u
s
i
n
g
Ne
wton’
s se
cond la
w of motion [6, 36].
(a)
(b)
Figure 6. (a)
Servomoto
r
lead
scre
w loa
d
(b
) Input-output for element with back
las
h
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IJEECS
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752
Nonli
nea
r Servom
otor in Single Pulse Sim
u
la
tion of Electri
c
al Di
sch
a
rge
…
(Ha
s
san Lee
)
323
2.3. PID Con
t
roller
The PID cont
rolle
r is a co
mmon contro
ller us
ed in EDM syste
m
[37]. It includes thre
e
term
p
a
ramet
e
rs comp
ri
se
d
of pro
porti
onal (P),
i
n
te
gral
(I) an
d
derivativ
e
(D). PID controll
er
algorith
m
do
es n
o
t ne
ed
com
p
licated
mathemat
i
c
s
an
d can b
e
cal
c
ul
ated more ea
sily.
The
relation
shi
p
b
e
twee
n co
ntrol sign
al and
pro
c
e
ss e
r
ror in PID controller is p
r
e
s
e
n
ted in equ
a
tion
4 belo
w
:
(
4
)
Based
on th
e Equation
(4), the p
r
op
o
r
tional g
a
in
(
) is de
pen
d o
n
the present
error
value and ha
ve direct relat
i
onship to the
cont
roll
er
se
nsitivity. The integral g
a
in (
) depen
ds o
n
the summatio
n
over time o
f
the present
error
an
d the previou
s
error. The de
ri
vative gain (
)
will considered
the current error
and
the duration of erro
r. By inserting nonlin
eari
t
ies of f
r
iction,
dead
zon
e
a
nd ba
ckl
ash to the linea
r servomoto
r
m
o
del that con
necte
d to lea
d
scre
w lo
ad
will
rep
r
e
s
ent a
complete n
onli
near E
D
M se
rvo system m
odel [38]. Th
e dead
zo
ne
nonlin
earity can
be ap
pea
red
as a
ch
ara
c
te
ristic
betwee
n
the ov
erall
system in
put
and o
u
tput.The man
u
factu
r
er
data for a
p
a
rticul
ar DC
servo
m
otor a
nd exp
e
rim
e
ntal data
in
pape
r [6] a
r
e u
s
ed
for t
h
e
simulatio
n
pu
rpo
s
e
s
. A co
mplete nonli
n
ear mo
del of DC
servo
m
ot
or is
sho
w
n in
Figure 7.
Figure 7. Simulink of Servo
System mod
e
l
2.4. EDM Process Mo
del
EDM pro
c
e
s
s blo
ck is a
model for EDM discha
rge phen
ome
non [6], [39-41]. The
simulatio
n
of
EDM p
r
o
c
e
ss
co
nsi
s
ts
of material
removal rate
model, b
r
ea
kdown mod
e
l
and
voltage ave
r
a
ge g
ap m
odel
. The m
a
the
m
atical
material re
moval
ra
te (M
RR) m
o
del i
s
devel
o
ped
usin
g Dime
n
s
ion
a
l Analysis to examine
the most
effective param
eters
on the
material rem
o
val
rate or effici
e
n
cy of the ma
chini
ng a
c
cording to the Equation (5) a
s
below:
∁
(
5
)
Whe
r
e
is experime
n
tal dim
ensi
onle
s
s co
nstant,
is a material p
r
op
erties fa
ctor,
r
e
pr
es
e
n
t
gap voltage,
is ga
p cu
rrent,
rep
r
e
s
e
n
t discha
rge
pulse on
-time, and
is
r
e
pr
es
e
n
t
spa
r
ki
ng fre
q
uen
cy. Then
by integratin
g and the
n
d
i
viding the surface a
r
ea
of electrode,
the
positio
n of the wo
rkpie
c
e (
ξ
) is
obtained. After that th
e pos
itio
n of workpi
ece is
subtracte
d
from
the ele
c
trod
e
positio
n (z) establi
s
h
e
d
in se
rvo
bl
ock. Then th
e re
sult is
u
s
ed i
n
empi
rical
brea
kd
own model to cal
c
ulate ignitio
n
delay time (
) [42-44]. In this
s
u
bs
y
s
tem,
can b
e
cal
c
ulate
d
according to no
nlinea
r model
as acco
rdin
g
to the equation 6 as follo
w
1
.
0
4
1
0
.
(
6
)
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02-4
752
IJEECS
Vol.
1, No. 2, February 201
6 : 319 – 328
324
Whe
r
e, the
gap po
sition
δ
is no
nline
a
r
ly related to
the ignition
delay time t
d
and to a le
ss
importa
nt poi
nt on
diele
c
tri
c
fluid
flushin
g
velo
city
. Ignition d
e
lay i
s
in
(µ
s) and
the ga
p
width
in
(µm) fo
r
a typical
flushing
velocity of
1
m
/s [45
-
48].
Next, ignition
delay time
is used
as inp
u
t of
averag
e gap
voltage mode
l. For the reg
u
lation of
the
gap bet
wee
n
electrode a
n
d
workpi
ece th
e
averag
e gap
voltage is e
m
ployed a
s
an indire
ct
measured fa
ctor [49
-
50].
An averag
e gap
voltage (
Vg
) i
s
cal
c
ul
ated a
c
cordi
ng to the Equation (7
) as bel
ow:
(
7
)
A complete
si
mulink m
odel
of the EDM
pro
c
e
ss
and
simulatio
n
pa
ramete
rs i
s
shown in
Figure 8. The
numeri
c
al d
a
t
a in paper [5
1]
are u
s
ed fo
r the simul
a
tion purpo
se
s.
Figure 8. Simulink of EDM
pro
c
e
ss m
o
d
e
l
3. Results a
nd Analy
s
is
Simulation of EDM syste
m
model tha
t
c
onsi
s
t of nonlin
ear
servo system a
nd EDM
pro
c
e
ss m
o
d
e
l has
been
carrie
d out u
s
ing MAT
L
AB Simulink in
orde
r to ana
lyse the sy
stem
respon
se fo
r singl
e pulse machi
n
ing p
r
oce
s
s. At first, linear and n
online
a
r serv
omotor mo
de
l is
simulate
d in
open lo
op sy
stem to analy
s
e the dyn
a
m
i
c re
sp
on
se o
f
each mo
del.
At steady sta
t
e
,
nonlin
ear
se
rvomotor mo
d
e
l have sho
w
s a lo
we
r ma
ximum elect
r
ode velo
city comp
ared to a
linear mod
e
l
as illu
strated
in Figu
re
9. The
sett
ling
time for n
o
n
linear servo
m
otor m
odel
also
slightly highe
r com
pare to linear m
odel that indica
tes
nonlin
ear effe
ct in resulting
slower sy
ste
m
respon
se.
Figure 9. Angular velo
city vs time
Figure 10 an
d 11 illustrate
the temporal
veloci
ty and p
o
sition of the electrode in a
close
d
loop
syste
m
with
a PID co
ntrolle
r
resp
ectively
.
For li
nea
r m
odel
syste
m
, the
cont
roll
er i
s
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IJEECS
ISSN:
2502-4
752
Nonli
nea
r Servom
otor in Single Pulse Sim
u
la
tion of Electri
c
al Di
sch
a
rge
…
(Ha
s
san Lee
)
325
sufficie
n
tly controlle
d the
electrode vel
o
city and
po
sition a
nd gi
ve fast sy
ste
m
re
spo
n
se
with
zero ste
ady state error.
Ho
wever, fo
re n
online
a
r
m
o
d
e
l system,
si
milar
controll
er give
s a
sli
ghtly
different in
sy
stem respon
se. The n
onlin
earitie
s
effe
ct cau
s
e
d
the
controlle
r a
r
e
not at optimu
m
p
e
r
for
m
a
n
c
e
w
i
th
s
l
ow
e
r
sys
te
m re
sp
o
n
s
e
c
o
mp
ar
e
to
lin
ea
r s
y
s
t
em mo
de
l an
d h
a
v
in
g h
i
ghe
r
steady
state error.
Figure 10. Te
mporal ele
c
trode velo
city vs
time for clo
s
ed lo
op serv
o system
Figure 11. Te
mporal ele
c
trode po
sition
vs
time for cl
ose
d
loop
servo system
Figure 12. Te
mporal ele
c
trode po
sition
of EDM syste
m
model
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ISSN: 25
02-4
752
IJEECS
Vol.
1, No. 2, February 201
6 : 319 – 328
326
Figure 12 illustrates the si
mulati
on response of electrode po
sition from the complete
EDM
system
model
at fixed
t
d
= 2
μ
s.
Time for ele
c
trode
po
sitio
n
to
settle d
o
wn
at
clo
s
e
d
to
referen
c
e ga
p
(21.13
μ
m
)
i
s
m
e
a
s
ured.
At this g
ap t
he p
o
sitio
n
i
s
sai
d
b
e
ing
controlle
d by t
he
servo
syste
m
and the
discharg
e
ph
ase
is takes
pla
c
e. Tem
poral
electrode
po
sition for li
ne
ar
EDM sy
stem
model i
s
ad
justed from i
n
itial positio
n
,
280
μ
m to 17.5
μ
m in 10
μ
s c
o
mpa
r
ed
t
o
nonlin
ear
mo
del ne
ed lo
n
ger time
whi
c
h i
s
ap
proxi
m
ately at 90
μ
s
to meet 17.5
μ
m. It c
a
n be
con
c
lu
de that
a nonline
a
r
EDM syste
m
model give
in
sufficie
n
t con
t
rol perfo
rma
n
ce a
nd sl
ower
respon
se
system du
e to
hi
gher
steady
state e
r
ror a
nd lo
nge
r
set
t
ling time
co
mpared to
lin
ear
EDM s
y
s
t
em
model. Ho
we
v
e
r,
nonlinear
model
showi
ng more
st
abl
e sy
st
em
co
mpared t
o
linear
model ba
sed
on the
lowe
r in overshoo
t value. The
linear control strategy in t
h
is case
is less
ef
f
e
ct
iv
e t
o
ensure t
he non
linear E
D
M sy
st
em
model performs
well
and need to be improved.
4. Conclusio
n
This
work p
r
ese
n
ts a no
n
linear E
D
M system model
that con
s
ist
s
of nonlin
ea
r se
rvo
system mo
de
l and EDM proce
s
s model.
The main go
al
of this stud
y was to inve
stigate the effect
of nonli
nea
rities i
n
se
rvo
system mo
del
to th
e
EDM
system
mod
e
l
. Dynami
c
re
spo
n
se from
a
linear
se
rvom
otor mod
e
l is use
d
to comp
are with
the n
online
a
r serv
omotor mo
del
. An Open loo
p
test for a m
o
tor mo
del
wa
s impleme
n
ted
in ord
e
r to i
d
entify a nonli
near
beh
avio
r of servomot
or
model. An ad
equate PID
controlle
r that
had be
en
p
r
o
v
ed in linea
r DC
se
rvomot
or mod
e
l wa
s
inse
rted into
the nonli
nea
r DC
se
rvomo
t
or mod
e
l. A clo
s
ed l
oop t
e
st was then
impleme
n
ted
in
orde
r to
obtai
n the dyn
a
mi
c respon
se
o
n
the E
D
M
system. As
a re
sult fro
m
the
clo
s
ed l
oop
test
indicates that slower re
spo
n
se system with
poor control strategy fo
r
nonlinear EDM system and
linear PID c
o
ntroller is
insuffic
i
ent for controlling a nonlinear ED
M s
y
s
t
em model and need to be
improve
d
. Th
e simul
a
tion
of nonline
a
r
model i
s
re
prese
n
ted
clo
s
ely to the re
al EDM ma
chine
operation.
Referen
ces
[1]
Androm
eda
T
,
A Ya
h
y
a, N
H
Kham
is. Gap
Resp
ons
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L
i
ne
ar a
n
d
No
n
-
Lin
ear
Disch
a
r
ge M
ode
l i
n
Electrical D
i
sc
harg
e
Machi
n
i
ng S
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Ho K
H
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New
m
a
n
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f
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ectri
c
al
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arg
e
machi
n
in
g (ED
M).
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rn
a
t
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ona
l
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u
r
na
l of
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ne T
ools
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re
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)
: 1287-1
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0
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i
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ng (EDM)
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eda
M, et
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h
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und
amenta
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e Proc
ess
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[5]
Schumac
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M
, R Krampitz, JP Kruth.
Historical P
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m
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n
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e Push
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y
a A. D
i
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y
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r KP, et al. Nu
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her
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EDT
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a
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e
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[12]
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i
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Jo
urn
a
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ria
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e
chno
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a A,
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udies
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ical D
i
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arge
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o
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nt.
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i
als Res
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[14]
F
onseca J, JD Marafon
a
. T
he effect of
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oni
s
a
tio
n
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l
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i
scha
r
ge mach
ini
n
g
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nce.
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o
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l Jo
urna
l of Advan
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ed Man
u
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r
ing T
e
ch
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y
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)
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[15] Jian
g
Y, et
a
l
. Adaptiv
e
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ont
r
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l for
smal
l-h
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