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)
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2
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n
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20
2
5
,
p
p
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401
~
4
1
1
I
SS
N:
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.
v
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i
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pp
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411
401
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o
th
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tstan
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g
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n
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th
e
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t
d
a
y
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t
h
e
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ru
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les
s
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(BLDC)
m
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h
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a
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tl
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e
s
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e
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m
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n
tro
l
sy
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m
u
ti
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z
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g
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ATLAB/S
imu
l
in
k
so
ftwa
re
.
Th
e
m
a
in
a
im
o
f
th
is
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ro
jec
t
is
to
c
o
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tro
l
t
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p
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a
n
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ime
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ID
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r.
T
h
e
a
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d
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m
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e
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d
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rro
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d
in
c
re
a
se
s th
e
sta
b
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f
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m
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ey
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s
:
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r
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C
m
o
to
r
s
MA
T
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AB
/S
im
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lin
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PID
co
n
tr
o
ller
s
Stab
ilit
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Un
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al
b
r
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T
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is i
s
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o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
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r th
e
CC B
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-
SA
li
c
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se
.
C
o
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r
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s
p
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A
uth
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r
:
T
ir
u
n
ag
ar
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ar
g
av
a
R
am
u
Dep
ar
tm
en
t o
f
E
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an
d
E
lectr
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n
ics E
n
g
in
ee
r
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g
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ML
R
I
n
s
titu
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o
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T
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Du
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1.
I
NT
RO
D
UCT
I
O
N
B
r
u
s
h
less
d
ir
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t
cu
r
r
en
t
(
B
L
DC
)
m
o
to
r
s
h
av
e
em
er
g
e
d
as
k
ey
co
m
p
o
n
en
ts
in
n
u
m
er
o
u
s
in
d
u
s
tr
ial,
au
to
m
o
tiv
e,
an
d
co
n
s
u
m
er
ap
p
licatio
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s
b
ec
au
s
e
o
f
th
ei
r
h
ig
h
ef
f
icien
cy
,
co
m
p
ac
t
s
ize,
an
d
p
r
ec
is
e
co
n
tr
o
llab
ilit
y
[
1
]
.
B
L
DC
m
o
to
r
s
h
av
e
a
n
u
m
b
e
r
o
f
b
en
ef
its
o
v
er
co
n
v
en
ti
o
n
al
b
r
u
s
h
ed
D
C
m
o
to
r
s
,
s
u
ch
as
h
ig
h
er
p
o
wer
-
to
-
weig
h
t
r
atio
s
,
b
etter
d
e
p
en
d
a
b
ilit
y
,
an
d
lo
wer
m
ain
ten
an
ce
n
ee
d
s
[
2
]
,
[
3
]
.
T
h
e
m
o
to
r
s
p
ee
d
r
eg
u
latio
n
is
o
n
e
o
f
th
e
m
o
s
t
im
p
o
r
tan
t
c
o
m
p
o
n
en
ts
o
f
B
L
DC
m
o
to
r
co
n
tr
o
l
s
in
ce
it
h
as
a
d
ir
ec
t
im
p
ac
t
o
n
s
y
s
tem
ef
f
icien
cy
an
d
p
er
f
o
r
m
an
ce
.
Nu
m
er
o
u
s
co
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tr
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l
al
g
o
r
ith
m
s
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d
m
eth
o
d
s
h
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b
ee
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ev
elo
p
ed
to
ac
co
m
p
lis
h
p
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is
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s
p
ee
d
co
n
tr
o
l; n
ev
er
th
eless
,
th
e
p
r
o
p
o
r
tio
n
al
in
teg
r
al
d
er
i
v
ativ
e
(
PID
)
c
o
n
tr
o
ller
co
n
tin
u
es
to
b
e
o
n
e
o
f
t
h
e
m
o
s
t p
o
p
u
lar
b
ec
au
s
e
o
f
its
ea
s
e
o
f
u
s
e
a
n
d
p
r
ac
ticality
[
4
]
,
[
5
]
.
B
y
m
o
d
if
y
i
n
g
t
h
e
co
n
tr
o
l
s
ig
n
al
in
r
esp
o
n
s
e
to
s
y
s
tem
f
ee
d
b
ac
k
,
th
e
PID
c
o
n
tr
o
ller
f
u
n
ctio
n
s
.
T
h
e
PID
co
n
tr
o
ller
ca
n
ef
f
icien
tl
y
r
eg
u
late
th
e
s
p
ee
d
o
f
B
L
DC
m
o
to
r
s
b
y
c
o
n
tin
u
ally
m
o
d
if
y
in
g
th
e
ap
p
lie
d
v
o
ltag
e
o
r
cu
r
r
en
t
th
an
k
s
to
th
is
co
n
tr
o
l
m
eth
o
d
,
wh
ich
in
cl
u
d
es
th
e
p
r
o
p
o
r
tio
n
al
co
m
p
o
n
en
t
(
P),
th
e
in
te
g
r
al
o
f
th
e
er
r
o
r
o
v
er
tim
e
(
I
)
,
an
d
th
e
d
er
iv
ativ
e
o
f
th
e
er
r
o
r
(
D)
[
6
]
,
[
7
]
.
E
n
h
an
ci
n
g
PID
-
co
n
tr
o
lled
B
L
DC
m
o
to
r
s
y
s
tem
s
'
p
er
f
o
r
m
an
ce
h
as
b
ee
n
th
e
s
u
b
ject
o
f
r
ec
en
t
r
esear
c
h
[
8
]
,
[
9
]
.
Op
tim
izin
g
PID
co
n
tr
o
ller
p
ar
am
eter
s
to
m
in
im
ize
s
tead
y
-
s
tate
er
r
o
r
,
s
h
o
r
ten
s
ettlin
g
tim
e,
an
d
en
h
an
ce
o
v
er
all
s
y
s
tem
s
tab
ilit
y
h
as b
ee
n
th
e
s
u
b
ject
o
f
n
u
m
er
o
u
s
s
tu
d
ies
[
1
0
]
,
[
1
1
]
.
Fu
r
th
er
m
o
r
e,
in
o
r
d
er
to
a
d
a
p
tiv
ely
m
o
d
if
y
co
n
tr
o
ller
p
ar
a
m
eter
s
in
r
ea
l
-
tim
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
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t J Ap
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Vo
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1
4
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2
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20
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5
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41
1
402
d
ep
en
d
i
n
g
o
n
s
y
s
tem
d
y
n
am
i
cs,
s
o
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ticated
PID
tu
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tr
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g
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l
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eth
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d
s
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d
au
to
-
tu
n
in
g
alg
o
r
ith
m
s
[
1
2
]
,
[
1
3
]
.
B
L
DC
m
o
to
r
s
y
s
tem
s
ca
n
n
o
w
p
r
ec
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ely
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ag
e
s
p
ee
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ac
k
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o
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itio
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k
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teg
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n
o
f
PID
c
o
n
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o
l
with
s
o
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h
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ticated
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en
s
o
r
tech
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o
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o
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ies
s
u
ch
as
en
co
d
er
s
an
d
Hall
ef
f
ec
t
s
e
n
s
o
r
s
[
1
4
]
-
[
1
7
]
.
Ad
d
itio
n
ally
,
th
e
r
esp
o
n
s
iv
en
ess
an
d
tr
an
s
ie
n
t
p
er
f
o
r
m
a
n
ce
o
f
PID
-
co
n
tr
o
lled
B
L
DC
m
o
to
r
s
y
s
tem
s
h
av
e
b
ee
n
im
p
r
o
v
ed
b
y
th
e
ad
d
itio
n
o
f
f
ee
d
f
o
r
war
d
co
n
tr
o
l
tech
n
iq
u
es
an
d
p
r
e
d
ictiv
e
alg
o
r
ith
m
s
,
allo
win
g
f
o
r
q
u
ic
k
an
d
p
r
ec
is
e
s
p
ee
d
ad
ju
s
tm
en
ts
in
d
y
n
am
ic
wo
r
k
in
g
c
o
n
d
itio
n
s
[
1
8
]
-
[
2
0
]
.
E
v
e
n
with
th
ese
d
e
v
elo
p
m
en
ts
,
B
L
DC
m
o
to
r
s
y
s
tem
s
s
till
f
ac
e
d
if
f
icu
lties
in
r
ea
ch
in
g
id
ea
l
s
p
ee
d
co
n
tr
o
l
p
er
f
o
r
m
an
ce
,
esp
ec
ially
in
ap
p
licatio
n
s
wh
er
e
ac
cu
r
ac
y
,
r
esp
o
n
s
iv
en
ess
,
an
d
e
n
e
r
g
y
ef
f
icien
cy
a
r
e
cr
u
cial
[
2
1
]
,
[
2
2
]
.
Stro
n
g
c
o
n
tr
o
l
s
tr
ateg
ies
an
d
ad
ap
tiv
e
tu
n
in
g
tech
n
iq
u
es
ar
e
r
eq
u
ir
ed
f
o
r
PID
-
co
n
tr
o
lled
B
L
DC
m
o
to
r
s
y
s
tem
s
b
ec
au
s
e
o
f
f
ac
to
r
s
s
u
ch
as
m
ec
h
a
n
ical
lo
ad
ch
a
n
g
es,
s
y
s
tem
n
o
n
lin
ea
r
ities
,
an
d
d
is
tu
r
b
an
ce
s
th
at
ca
n
im
p
ac
t p
er
f
o
r
m
a
n
ce
[
2
3
]
-
[
2
5
]
.
2.
M
E
T
H
O
D
2
.
1
.
M
a
t
hema
t
ica
l
m
o
del o
f
B
L
D
C
A
p
er
m
an
e
n
t
m
a
g
n
et
o
n
th
e
r
o
to
r
ca
u
s
es
s
o
m
e
v
ar
iatio
n
s
,
b
u
t
o
th
er
wis
e,
th
e
d
ev
el
o
p
m
en
t
o
f
a
B
L
DC
m
o
to
r
m
o
d
el
is
co
m
p
a
r
ab
le
to
th
at
o
f
a
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
e.
T
h
e
m
ater
ial
o
f
th
e
m
ag
n
et
af
f
ec
ts
th
e
f
lu
x
lin
k
ag
e
f
r
o
m
th
e
r
o
t
o
r
,
l
ea
d
in
g
t
o
co
m
m
o
n
o
cc
u
r
r
e
n
c
es
o
f
m
a
g
n
etic
f
lu
x
lin
k
ag
e
s
atu
r
atio
n
in
th
ese
m
o
to
r
s
.
Un
lik
e
tr
ad
itio
n
al
th
r
ee
-
p
h
ase
m
o
to
r
s
,
a
B
L
DC
m
o
to
r
ca
n
b
e
p
o
wer
e
d
b
y
a
v
o
lta
g
e
s
o
u
r
ce
th
at
d
o
es
n
o
t
h
a
v
e
to
b
e
s
in
u
s
o
id
al.
As
lo
n
g
as
th
e
p
ea
k
v
o
ltag
e
r
e
m
ain
s
b
elo
w
th
e
m
o
to
r
'
s
m
ax
im
u
m
v
o
ltag
e
lim
it,
alter
n
ativ
e
wav
ef
o
r
m
s
s
u
ch
as
s
q
u
ar
e
wav
es
ca
n
b
e
u
s
ed
.
T
h
e
ar
m
atu
r
e
win
d
in
g
m
o
d
el
o
f
th
e
B
L
DC
m
o
to
r
is
d
escr
ib
ed
b
y
(
1
)
,
(
2
)
,
an
d
(
3
)
.
=
+
+
(
1
)
=
+
+
(
2
)
=
+
+
(
3
)
W
h
er
e
is
ar
m
atu
r
e
s
elf
-
in
d
u
c
tan
ce
[
H]
,
R
is
r
esis
tan
ce
[
Ω
]
in
a
r
m
atu
r
e,
,
,
ar
e
p
h
ase
v
o
lta
g
e
[
V]
at
ter
m
in
al,
,
,
ar
e
in
p
u
t c
u
r
r
en
t
[
A]
o
f
m
o
to
r
,
a
n
d
,
,
ar
e
m
o
t
o
r
b
ac
k
-
E
MF
[
V]
.
2.
2
.
P
I
D
co
ntr
o
ller
T
h
er
e
ar
e
t
h
r
ee
s
u
b
b
lo
ck
s
in
th
e
C
ONT
R
OL
L
E
R
_
MO
D
b
lo
ck
as
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
es
e
b
u
ild
in
g
b
lo
ck
s
ar
e
all
f
i
n
ite
s
tate
m
ac
h
in
es.
T
h
e
d
u
ty
o
f
k
ee
p
th
e
n
ec
ess
ar
y
cu
r
r
e
n
t
f
lo
win
g
th
r
o
u
g
h
ea
ch
m
ac
h
in
e.
T
h
e
C
ONT
R
OL
L
E
R
_
MO
D
b
lo
ck
ass
u
m
es
co
n
tr
o
l
an
d
o
p
en
s
th
e
n
ec
ess
ar
y
v
o
ltag
e
s
o
u
r
ce
in
v
er
ter
(
VSI
)
g
ates
to
estab
lis
h
an
d
m
ai
n
tain
th
e
d
esire
d
cu
r
r
e
n
t
o
n
ce
t
h
e
esti
m
ate
b
lo
ck
h
as
p
r
o
d
u
ce
d
th
e
r
ef
e
r
en
ce
.
T
h
e
in
v
er
ter
'
s
co
n
s
tr
u
ctio
n
with
B
L
DC
m
o
to
r
is
d
is
p
lay
ed
f
o
r
r
ef
er
en
ce
as
s
h
o
wn
in
Fig
u
r
e
2
.
E
ac
h
m
ac
h
in
e
em
p
lo
y
s
s
tr
aig
h
tf
o
r
war
d
lo
g
ic
.
Fo
r
e
x
am
p
le,
th
e
m
ac
h
in
e
m
an
ag
in
g
th
e
U
p
h
ase
ch
ec
k
s
wh
eth
er
th
e
ac
tu
al
cu
r
r
en
t
in
p
h
ase
R
(
I
R
)
ex
ce
ed
s
th
e
d
esire
d
cu
r
r
en
t
(
I
R
STAR).
I
f
it
d
o
es,
tr
an
s
i
s
to
r
Q4
is
tu
r
n
ed
o
n
.
Oth
er
wis
e,
tr
an
s
is
to
r
Q1
is
ac
tiv
ated
.
2
.
3
.
B
L
DC
m
o
t
o
r
T
h
e
f
iv
e
v
a
r
iab
les
d
er
iv
ed
f
r
o
m
(
1
)
,
(
2
)
,
an
d
(
3
)
a
r
e
ce
n
tr
al
to
th
e
s
tate
-
s
p
ac
e
m
o
d
el
c
alcu
latio
n
s
.
Af
ter
f
u
r
th
er
p
r
o
ce
s
s
in
g
,
th
ese
v
ar
iab
les
p
r
o
d
u
ce
a
to
tal
o
f
2
5
o
b
s
er
v
ab
le
o
u
t
p
u
ts
.
T
h
e
b
lo
ck
also
r
ec
eiv
es
v
o
ltag
e
v
alu
es
ap
p
lied
to
th
e
win
d
in
g
s
,
alo
n
g
with
lo
ad
to
r
q
u
e
d
ata.
I
n
s
tead
o
f
u
s
in
g
th
e
Sim
Po
wer
Sy
s
tem
s
b
lo
ck
s
et,
wh
ich
r
eq
u
ir
es
s
u
b
s
tan
tial
co
m
p
u
tatio
n
al
p
o
we
r
an
d
m
em
o
r
y
,
in
p
u
t
v
alu
es
ar
e
s
o
u
r
ce
d
f
r
o
m
g
en
er
al
Simu
lin
k
b
lo
ck
s
.
Sin
ce
s
o
lv
in
g
d
if
f
er
e
n
tial
eq
u
atio
n
s
is
n
ec
es
s
ar
y
f
o
r
o
u
tp
u
t
ca
lcu
latio
n
s
,
o
n
ly
n
u
m
er
ical
v
alu
es a
r
e
u
s
ed
.
Fig
u
r
e
3
d
is
p
lay
s
th
e
Simu
lin
k
d
i
ag
r
am
f
o
r
th
e
B
L
DC
m
o
to
r
.
2
.
4
.
Sim
uli
nk
m
o
del o
f
t
he
B
L
D
C
m
o
t
o
r
T
h
is
b
r
u
s
h
less
DC
m
o
to
r
m
o
d
el
h
as
a
co
n
v
en
tio
n
al
s
etu
p
.
Mo
to
r
s
p
ee
d
is
co
n
tr
o
lled
b
y
an
o
u
ts
id
e
f
ee
d
b
ac
k
lo
o
p
,
wh
ile
cu
r
r
en
t
is
r
eg
u
lated
b
y
an
in
ter
io
r
f
e
ed
b
ac
k
lo
o
p
.
T
h
e
m
o
to
r
an
d
d
r
iv
er
s
u
b
s
y
s
tem
'
s
s
er
v
o
m
o
to
r
b
lo
ck
b
alan
ce
s
m
ec
h
an
ical
an
d
elec
tr
ical
p
o
w
er
an
d
m
o
d
els
th
e
in
n
er
c
u
r
r
en
t
f
ee
d
b
ac
k
lo
o
p
.
Mo
d
elin
g
th
e
cu
r
r
en
t
s
witch
in
g
r
eg
u
lated
b
y
th
e
m
o
to
r
d
r
iv
er
is
ty
p
ically
n
o
t
r
e
q
u
ir
ed
f
o
r
s
y
s
tem
d
esig
n
,
b
u
t
it
is
v
ital
to
m
ak
e
s
u
r
e
th
e
to
r
q
u
e
-
s
p
ee
d
c
h
ar
ac
ter
is
tics
an
d
cu
r
r
en
t
p
u
lled
f
r
o
m
th
e
DC
s
u
p
p
ly
ar
e
c
o
r
r
ec
t.
I
n
ac
tu
ality
,
th
e
m
ax
im
u
m
d
r
iv
i
n
g
cu
r
r
en
t
d
eter
m
i
n
es
th
e
v
ec
to
r
o
f
m
a
x
im
u
m
to
r
q
u
e
v
alu
e
s
.
I
t
is
as
s
u
m
ed
th
at
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
S
p
ee
d
c
o
n
tr
o
l o
f B
LDC
mo
to
r
u
s
in
g
P
I
D
co
n
tr
o
ller
(
Tir
u
n
a
g
a
r
i
B
h
a
r
g
a
va
R
a
mu
)
403
th
e
s
y
s
tem
th
at
u
s
es
th
e
m
o
to
r
an
d
d
r
iv
er
will
tak
e
ca
r
e
o
f
m
ak
in
g
s
u
r
e
th
e
m
o
to
r
d
o
esn
'
t
o
v
er
h
ea
t
b
y
r
u
n
n
i
n
g
at
h
ig
h
to
r
q
u
e
an
d
s
p
ee
d
co
m
b
in
atio
n
s
f
o
r
ex
te
n
d
ed
p
er
i
o
d
s
o
f
tim
e.
T
o
m
atch
th
e
d
a
tash
ee
t
v
alu
es,
th
r
ee
m
o
to
r
an
d
d
r
iv
er
m
ask
s
ettin
g
s
m
u
s
t
b
e
ad
ju
s
ted
.
T
h
ese
ar
e
th
e
tim
e
co
n
s
tan
t
f
o
r
th
e
in
n
er
-
lo
o
p
cu
r
r
e
n
t
co
n
tr
o
ller
a
n
d
t
h
e
p
r
o
p
o
r
tio
n
a
l
an
d
in
te
g
r
al
g
ai
n
s
f
o
r
th
e
s
p
ee
d
f
ee
d
b
ac
k
c
o
n
tr
o
ller
.
T
h
e
d
atash
ee
t
s
tates
th
at
th
e
n
o
-
lo
ad
tim
e
co
n
s
tan
t
in
t
h
is
ca
s
e
is
5
m
s
.
An
in
n
e
r
co
n
tr
o
l
lo
o
p
s
h
o
u
ld
,
as
a
g
e
n
er
al
r
u
le,
b
e
at
least
ten
tim
es
q
u
ick
er
th
an
th
e
o
u
ter
l
o
o
p
.
T
h
is
in
d
icate
s
th
at
th
e
p
r
esen
t
co
n
tr
o
ller
'
s
tim
e
co
n
s
tan
t
is
0
.
5
m
s
.
On
ce
th
is
v
alu
e
h
as
b
ee
n
estab
lis
h
e
d
,
th
e
p
r
o
p
o
r
tio
n
al
ter
m
is
r
aised
u
n
til
th
e
s
p
ee
d
tim
e
co
n
s
tan
t
is
r
o
u
g
h
ly
5
m
s
.
W
h
en
ex
ec
u
tin
g
a
s
p
ee
d
s
tep
u
n
d
er
lo
ad
,
th
e
in
teg
r
al
g
ain
s
h
o
u
ld
t
h
en
b
e
estab
lis
h
ed
an
d
in
cr
ea
s
ed
u
n
til
th
e
s
tead
y
-
s
tate
er
r
o
r
is
elim
in
ate
d
,
wh
ich
s
h
o
u
ld
tak
e
ab
o
u
t
5
m
s
.
T
h
e
5
m
s
in
c
r
ea
s
e
tim
e
u
n
d
er
n
o
lo
ad
m
u
s
t
th
en
b
e
r
ec
o
v
er
ed
with
s
o
m
e
f
in
e
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ates
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li
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a
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n
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o
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e
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t
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n
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s
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r
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o
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Fig
u
r
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d
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ch
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e
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o
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t
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o
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o
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th
e
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o
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m
ay
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tr
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g
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le
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tain
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o
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n
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er
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er
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ig
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t
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e
a
n
o
ticea
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le
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h
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g
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s
p
ee
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o
r
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o
m
m
an
d
s
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Fig
u
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5
.
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lectr
o
m
ag
n
etic
t
o
r
q
u
e
v
s
tim
e
ch
ar
ac
ter
is
tics
with
PID
co
n
tr
o
ller
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7
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th
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n
tr
o
ller
Fig
u
r
e
7
.
T
o
r
q
u
e
v
s
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e
ch
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ac
ter
is
tics
wi
th
o
u
t PI
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co
n
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o
l
ler
Fig
u
r
e
8
.
Sp
ee
d
v
s
tim
e
ch
ar
a
cter
is
tics
wi
th
o
u
t PI
D
co
n
tr
o
ll
er
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406
As
s
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u
r
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r
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m
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ar
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P
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o
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ller
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o
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th
e
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eg
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ter
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in
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o
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elp
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s
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s
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y
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u
o
u
s
ly
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teg
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atin
g
th
e
er
r
o
r
o
v
er
tim
e.
T
h
e
PI
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n
tr
o
ller
p
r
o
v
id
es
im
p
r
o
v
ed
r
esp
o
n
s
iv
en
ess
an
d
b
etter
ad
a
p
tatio
n
to
v
ar
y
in
g
lo
a
d
co
n
d
itio
n
s
,
r
esu
ltin
g
in
m
o
r
e
p
r
ec
is
e
co
n
tr
o
l
o
v
er
s
p
ee
d
an
d
to
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q
u
e.
As
s
h
o
wn
in
Fig
u
r
es
1
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d
1
2
,
s
p
ee
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v
s
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e
ch
ar
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m
ay
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h
i
b
it
s
o
m
e
d
eg
r
ee
o
f
s
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ilit
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u
t
th
er
e
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ld
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e
o
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er
s
h
o
o
t
o
r
u
n
d
er
s
h
o
o
t
in
r
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o
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s
e
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u
d
d
en
ch
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n
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e
s
in
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r
s
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ee
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m
m
an
d
s
.
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h
e
P
co
n
t
r
o
ller
p
r
o
v
id
es
p
r
o
p
o
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tio
n
al
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n
tr
o
l,
m
ea
n
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g
th
e
to
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q
u
e
o
u
tp
u
t
is
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ir
ec
tly
p
r
o
p
o
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tio
n
a
l
to
th
e
s
p
ee
d
er
r
o
r
.
Ho
wev
e
r
,
it
lack
s
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teg
r
al
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d
d
er
iv
ativ
e
ac
tio
n
s
,
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ich
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ld
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lt
in
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tead
y
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s
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er
r
o
r
s
an
d
s
lo
wer
r
esp
o
n
s
e
to
d
is
tu
r
b
an
ce
s
.
Fig
u
r
e
9
.
T
o
r
q
u
e
v
s
tim
e
ch
ar
ac
ter
is
tics
wi
th
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co
n
tr
o
ller
Fig
u
r
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1
0
.
Sp
ee
d
v
s
tim
e
c
h
ar
ac
ter
is
tics
wi
th
PI
co
n
tr
o
ller
Fig
u
r
e
1
1
.
T
o
r
q
u
e
v
s
tim
e
c
h
a
r
ac
ter
is
tics
with
P c
o
n
tr
o
ller
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I
n
t J Ap
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g
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SS
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2252
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8
7
9
2
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o
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s
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D
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r
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r
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1
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.
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v
s
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e
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h
ar
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ter
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th
P c
o
n
tr
o
ller
3
.
1
.
M
a
t
hema
t
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na
ly
s
is
T
h
e
tim
e
d
o
m
ai
n
s
p
ec
if
icatio
n
s
ar
e
r
is
e
tim
e,
p
ea
k
tim
e,
d
elay
tim
e,
s
ettlin
g
tim
e,
o
v
er
s
h
o
o
t,
a
n
d
s
tead
y
-
s
tate
er
r
o
r
.
T
h
e
tim
e
it
tak
es
f
o
r
a
s
ig
n
al
to
c
r
o
s
s
a
p
r
ed
eter
m
in
ed
lo
wer
v
o
ltag
e
th
r
esh
o
ld
a
n
d
th
en
a
p
r
ed
eter
m
in
e
d
u
p
p
e
r
v
o
ltag
e
t
h
r
esh
o
ld
is
k
n
o
wn
as
t
h
e
r
is
e
tim
e.
I
n
b
o
t
h
a
n
alo
g
an
d
d
ig
it
al
s
y
s
tem
s
,
th
is
is
a
cr
u
cial
p
ar
am
eter
.
I
t
ch
ar
ac
ter
izes
th
e
am
o
u
n
t
o
f
tim
e
a
s
ig
n
al
s
p
en
d
s
in
th
e
tr
an
s
itio
n
al
s
tag
e
b
etwe
en
two
v
alid
lo
g
ic
lev
els
in
d
ig
ital
s
y
s
tem
s
.
Peak
tim
e
is
th
e
am
o
u
n
t
o
f
tim
e
n
ee
d
ed
b
y
th
e
r
ea
ctio
n
to
r
ea
ch
its
in
itial
p
ea
k
,
wh
ich
is
th
e
p
ea
k
o
f
th
e
f
ir
s
t
o
s
cillatio
n
cy
cle
o
r
f
ir
s
t
o
v
er
s
h
o
o
t.
T
h
e
am
o
u
n
t
o
f
tim
e
it
tak
es
f
o
r
a
r
esp
o
n
s
e
to
r
ea
ch
h
alf
o
f
its
u
l
tim
ate
v
alu
e
d
u
r
in
g
its
in
itial
o
s
cillatio
n
cy
cle
is
k
n
o
wn
as
t
h
e
d
elay
tim
e.
T
h
e
am
o
u
n
t
o
f
tim
e
it
tak
es
f
o
r
th
e
o
u
tp
u
t
o
f
a
co
n
tr
o
l
s
y
s
tem
to
attain
an
d
r
em
ain
with
in
a
g
iv
en
er
r
o
r
r
an
g
e
f
o
llo
win
g
an
in
p
u
t
s
tim
u
lu
s
is
k
n
o
wn
as
th
e
s
ettlin
g
tim
e.
I
t
'
s
a
cr
u
cial
s
ig
n
o
f
th
e
s
tab
ilit
y
an
d
p
er
f
o
r
m
an
ce
o
f
a
co
n
tr
o
l
s
y
s
tem
.
B
y
d
e
d
u
c
tin
g
th
e
s
tead
y
-
s
tate
v
alu
e
f
r
o
m
th
e
p
ea
k
r
esp
o
n
s
e
v
alu
e
an
d
d
iv
id
in
g
th
e
r
esu
lt
b
y
th
e
s
tead
y
-
s
tate
v
alu
e
g
iv
e
s
th
e
o
v
er
s
h
o
o
t
an
d
is
o
f
ten
r
ep
o
r
ted
as
a
p
er
ce
n
ta
g
e.
I
t
is
p
o
s
s
ib
le
to
p
r
o
g
r
am
co
n
tr
o
ller
s
to
p
r
e
v
en
t
o
v
er
s
h
o
o
t,
b
u
t
d
o
in
g
s
o
t
y
p
ically
e
n
tails
r
ed
u
cin
g
co
n
tr
o
l
ef
f
o
r
t
as
th
e
s
etp
o
in
t
g
ets
clo
s
er
.
R
ea
ch
in
g
th
e
tar
g
et
v
alu
e
m
ay
ta
k
e
lo
n
g
er
as
a
r
esu
lt.
T
h
e
d
is
cr
ep
an
cy
b
etwe
en
a
co
n
tr
o
l
s
y
s
tem
'
s
in
ten
d
ed
a
n
d
ac
tu
al
o
u
tp
u
t a
f
t
er
it h
as a
ch
iev
ed
a
s
tead
y
-
s
tate
is
k
n
o
wn
as st
ea
d
y
-
s
tate
er
r
o
r
.
a.
W
ith
o
u
t PI
D
c
o
n
tr
o
ller
˗
R
is
e
tim
e
:
u
s
u
ally
lo
n
g
er
b
ec
a
u
s
e
o
f
s
lu
g
g
is
h
r
esp
o
n
s
e
wh
e
n
th
e
co
n
tr
o
ller
is
n
o
t a
d
ju
s
ted
.
L
o
n
g
er
s
ettlin
g
tim
e
as a
r
esu
lt o
f
s
tead
y
-
s
tate
er
r
o
r
a
n
d
o
v
er
s
h
o
o
t b
ein
g
u
n
c
o
n
tr
o
llab
le.
˗
Peak
tim
e
:
a
lo
n
g
er
tim
e
to
ac
h
iev
e
th
e
p
ea
k
o
v
er
s
h
o
o
t a
n
d
a
h
ig
h
er
o
v
er
s
h
o
o
t m
ay
o
cc
u
r
.
˗
Ov
er
s
h
o
o
t:
a
h
ig
h
er
o
v
er
s
h
o
o
t
co
u
ld
r
esu
lt
f
r
o
m
a
lac
k
o
f
co
n
tr
o
l.
Dep
e
n
d
in
g
o
n
t
h
e
d
y
n
am
ics
o
f
th
e
s
y
s
tem
an
d
ch
an
g
es in
lo
ad
,
t
h
er
e
m
ay
b
e
a
co
n
s
id
er
a
b
le
s
tead
y
-
s
tate
in
ac
cu
r
ac
y
.
b.
P
c
o
n
tr
o
ller
˗
R
is
e
tim
e
:
Mu
ch
th
e
s
am
e
as
o
r
m
ar
g
in
ally
b
etter
th
an
s
y
s
tem
s
with
o
u
t
PID
co
n
tr
o
l.
Alt
h
o
u
g
h
it
m
ay
b
e
m
ar
g
in
ally
b
etter
th
an
s
y
s
tem
s
with
o
u
t PI
D
co
n
tr
o
l,
s
tead
y
-
s
tate
er
r
o
r
is
s
till
a
p
o
s
s
ib
ilit
y
.
˗
Peak
tim
e
:
C
o
m
p
ar
ab
le
to
s
y
s
t
em
s
th
at
d
o
n
'
t u
s
e
PID
.
˗
Ov
er
s
h
o
o
t:
T
h
e
a
m
o
u
n
t o
f
o
v
e
r
s
h
o
o
t m
ay
v
ar
y
b
ased
o
n
th
e
co
n
tr
o
ller
g
ain
.
˗
Stead
y
-
s
tate
er
r
o
r
:
I
m
p
r
o
v
ed
co
m
p
ar
ed
to
s
y
s
tem
s
with
o
u
t
PID
co
n
tr
o
l,
b
u
t
s
tead
y
-
s
tate
er
r
o
r
m
ay
s
till
ex
is
t.
c.
PI
c
o
n
tr
o
ller
˗
R
is
e
tim
e
: G
en
er
ally
im
p
r
o
v
e
d
co
m
p
a
r
ed
to
P c
o
n
tr
o
ller
a
n
d
s
y
s
tem
s
with
o
u
t PI
D
co
n
tr
o
l
.
˗
Settli
n
g
tim
e
: T
y
p
ically
r
ed
u
c
ed
d
u
e
t
o
th
e
elim
in
atio
n
o
f
s
t
ea
d
y
-
s
tate
er
r
o
r
b
y
t
h
e
in
teg
r
al
ac
tio
n
.
˗
Peak
tim
e
: Sim
ilar
to
P c
o
n
tr
o
ller
o
r
s
lig
h
tly
im
p
r
o
v
e
d
.
˗
Ov
er
s
h
o
o
t: R
ed
u
ce
d
c
o
m
p
a
r
e
d
to
P c
o
n
tr
o
ller
an
d
s
y
s
tem
s
with
o
u
t PI
D
co
n
tr
o
l.
˗
Stead
y
-
s
tate
er
r
o
r
: E
lim
in
ated
o
r
s
ig
n
if
ican
tly
r
ed
u
ce
d
d
u
e
to
th
e
in
teg
r
al
ac
tio
n
.
d.
PID
c
o
n
tr
o
ller
˗
R
is
e
t
im
e
:
I
m
p
r
o
v
ed
c
o
m
p
ar
e
d
to
PI
co
n
tr
o
ller
an
d
s
y
s
tem
s
with
o
u
t
PID
co
n
tr
o
l,
th
an
k
s
to
th
e
d
er
iv
ativ
e
ac
tio
n
.
˗
Settli
n
g
tim
e
:
T
y
p
ically
f
u
r
th
er
r
ed
u
ce
d
co
m
p
ar
e
d
to
PI
co
n
tr
o
ller
d
u
e
to
en
h
an
ce
d
co
n
tr
o
l
o
v
e
r
o
v
er
s
h
o
o
t.
˗
Peak
tim
e
: G
en
er
ally
s
im
ilar
to
PI
co
n
tr
o
ller
o
r
s
lig
h
tly
im
p
r
o
v
ed
.
˗
Ov
er
s
h
o
o
t: R
ed
u
ce
d
c
o
m
p
ar
e
d
to
PI
co
n
tr
o
ller
an
d
s
y
s
tem
s
with
o
u
t PI
D
co
n
tr
o
l
d
u
e
to
th
e
d
am
p
in
g
ef
f
ec
t
o
f
th
e
d
e
r
iv
ativ
e
ac
tio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
4
,
No
.
2
,
J
u
n
e
20
2
5
:
40
1
-
41
1
408
˗
Stead
y
-
s
tate
er
r
o
r
:
Vir
tu
ally
elim
in
ated
d
u
e
to
th
e
co
m
b
in
ed
ac
tio
n
s
o
f
p
r
o
p
o
r
tio
n
a
l,
in
teg
r
al,
an
d
d
er
iv
ativ
e
ter
m
s
.
T
h
e
tim
e
d
o
m
ain
s
p
ec
if
icatio
n
with
f
o
r
m
u
la
is
g
iv
e
n
in
Fig
u
r
e
1
3
.
T
h
e
s
im
u
latio
n
r
esu
l
t
v
alu
es
o
f
r
is
e
tim
e,
p
ea
k
tim
e,
tr
an
s
ien
t tim
e
,
an
d
s
ettlin
g
tim
e
f
o
r
P,
PI,
PID
,
an
d
with
o
u
t
PID
co
n
t
r
o
ller
s
ar
e
s
h
o
wn
in
T
ab
le
1
.
T
h
e
p
o
s
itiv
e
p
ea
k
,
n
eg
ativ
e
p
ea
k
,
a
n
d
s
tead
y
-
s
tate
d
if
f
er
en
ce
v
alu
es
f
o
r
d
if
f
e
r
en
t
co
n
t
r
o
ller
s
ar
e
s
h
o
wn
in
T
ab
le
2
.
Fig
u
r
e
1
3
.
Fo
r
m
u
la
f
o
r
tim
e
d
o
m
ain
s
p
ec
if
icatio
n
T
ab
le
1
.
Simu
latio
n
r
esu
lts
C
o
n
t
r
o
l
l
e
r
R
i
se
t
i
me
P
e
a
k
t
i
me
Tr
a
n
s
i
e
n
t
t
i
me
S
e
t
t
l
i
n
g
t
i
me
P
I
D
0
.
0
1
6
0
.
0
3
3
0
.
0
8
7
1
.
0
0
0
PI
9
.
8
8
8
×
1
0
^
(
-
4)
3
.
6
2
6
×
1
0
^
(
-
3)
0
.
0
2
8
1
.
0
0
0
P
1
.
6
4
8
×
1
0
^
(
-
3)
3
.
6
2
6
×
1
0
^
(
-
3)
0
.
0
2
7
1
.
0
0
0
W
i
t
h
o
u
t
P
I
D
5
.
6
0
3
×
1
0
^
(
-
3)
8
.
8
9
9
×
1
0
^
(
-
3)
0
.
0
2
0
1
.
0
0
0
T
ab
le
2
.
Stead
y
-
s
tate
d
if
f
er
en
c
e
o
f
s
im
u
latio
n
C
o
n
t
r
o
l
l
e
r
P
o
si
t
i
v
e
p
e
a
k
N
e
g
a
t
i
v
e
p
e
a
k
S
t
e
a
d
y
-
st
a
t
e
d
i
f
f
e
r
e
n
c
e
P
I
D
1
5
0
3
.
5
5
5
1
4
9
8
.
5
2
6
5
.
0
2
9
PI
1
5
0
4
.
3
8
8
1
4
8
4
.
5
7
3
1
9
.
8
1
5
P
1
4
9
1
.
4
0
6
1
4
8
0
.
8
3
7
1
0
.
5
6
9
W
i
t
h
o
u
t
P
I
D
1
3
5
6
.
7
3
9
1
3
2
9
.
0
3
1
2
7
.
7
0
8
4.
CO
NCLU
SI
O
N
T
o
s
u
m
u
p
,
a
d
d
in
g
a
PID
co
n
tr
o
ller
to
a
B
L
DC
m
o
to
r
i
m
p
r
o
v
es
b
o
th
its
co
n
tr
o
l
ac
c
u
r
ac
y
an
d
o
p
er
atio
n
al
s
tab
ilit
y
.
Sp
ee
d
v
s
.
to
r
q
u
e
ch
ar
ac
te
r
is
tics
co
u
ld
s
h
o
w
o
s
cillatio
n
s
an
d
i
n
s
tab
ilit
y
with
o
u
t
PID
co
n
tr
o
l,
r
esu
ltin
g
in
u
n
ev
en
p
er
f
o
r
m
a
n
ce
.
B
u
t
with
a
PID
c
o
n
tr
o
ller
,
th
e
m
o
t
o
r
ca
n
m
ain
t
ain
m
o
r
e
s
tab
le
an
d
s
m
o
o
th
er
s
p
ee
d
v
s
.
to
r
q
u
e
c
h
a
r
ac
ter
is
tics
,
wh
ich
g
u
ar
an
tees b
etter
r
esp
o
n
s
iv
en
ess
,
m
o
r
e
ac
cu
r
ate
co
n
t
r
o
l,
a
n
d
g
r
ea
ter
f
lex
ib
ilit
y
u
n
d
er
d
if
f
e
r
en
t
lo
a
d
cir
c
u
m
s
tan
ce
s
.
As
a
r
esu
lt,
B
L
DC
m
o
to
r
s
y
s
tem
s
'
ef
f
icien
cy
an
d
d
ep
en
d
a
b
ilit
y
ar
e
g
r
ea
tly
in
cr
ea
s
ed
b
y
th
e
u
s
e
o
f
a
PID
co
n
tr
o
ller
.
T
o
s
u
m
u
p
,
ad
d
in
g
a
PID
co
n
tr
o
ller
to
a
B
L
DC
m
o
to
r
im
p
r
o
v
es
b
o
th
its
co
n
tr
o
l
ac
cu
r
ac
y
an
d
o
p
er
atio
n
al
s
tab
ilit
y
.
Sp
ee
d
v
s
.
to
r
q
u
e
c
h
ar
ac
ter
is
tics
co
u
ld
s
h
o
w
o
s
cillatio
n
s
an
d
in
s
tab
ilit
y
with
o
u
t
PID
co
n
tr
o
l,
r
esu
ltin
g
in
u
n
ev
en
p
er
f
o
r
m
a
n
ce
.
B
u
t
w
i
t
h
a
P
I
D
c
o
n
t
r
o
l
l
e
r
,
t
h
e
m
o
t
o
r
ca
n
m
a
i
n
t
a
i
n
m
o
r
e
s
t
a
b
l
e
a
n
d
s
m
o
o
t
h
e
r
s
p
e
e
d
v
s
.
t
o
r
q
u
e
c
h
a
r
a
c
t
e
r
is
ti
c
s
,
w
h
i
c
h
g
u
a
r
a
n
t
e
es
b
e
t
t
e
r
r
e
s
p
o
n
s
i
v
e
n
e
s
s
,
m
o
r
e
a
cc
u
r
a
t
e
c
o
n
t
r
o
l
,
a
n
d
g
r
e
a
t
e
r
f
l
e
x
ib
i
l
i
t
y
u
n
d
e
r
d
i
f
f
e
r
e
n
t
l
o
a
d
ci
r
c
u
m
s
t
a
n
c
es
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
T
h
er
e
ar
e
n
o
s
o
u
r
ce
s
o
f
f
u
n
d
i
n
g
ag
en
cy
th
at
h
av
e
s
u
p
p
o
r
te
d
th
e
wo
r
k
.
So
,
a
u
th
o
r
s
s
tate
n
o
f
u
n
d
in
g
in
v
o
lv
ed
.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
T
E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
t
r
ib
u
to
r
R
o
les
T
a
x
o
n
o
m
y
(
C
R
ed
iT)
to
r
ec
o
g
n
ize
in
d
iv
i
d
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
ate
co
llab
o
r
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
S
p
ee
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c
o
n
tr
o
l o
f B
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to
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(
Tir
u
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a
r
i
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h
a
r
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a
va
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a
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409
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m
e
o
f
Aut
ho
r
C
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So
Va
Fo
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Vi
Su
P
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ev
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R
av
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u
m
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[
1
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[
3
]
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8
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[
9
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1
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1
2
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1
3
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a
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st
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ield
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d
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A.P
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-
5
2
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e
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rn
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d
h
is
P
h
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fro
m
K
L
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iv
e
rsity
.
Dr.
Ch
e
e
rla h
a
s a
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e
x
ten
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e
p
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b
li
c
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ti
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re
c
o
rd
,
with
n
u
m
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ro
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s p
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p
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ste
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m
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c
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ic
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s
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ll
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tern
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re
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a
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sp
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ializa
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wire
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m
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icro
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tch
a
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s,
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ica
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m
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n
tati
o
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a
n
d
t
h
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tern
e
t
o
f
th
in
g
s
(Io
T).
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c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
sre
e
v
a
rd
h
a
n
c
h
e
e
rla@k
lu
n
iv
e
rsit
y
.
in
.
Dr
.
Ra
v
i
K
u
m
a
r
K
a
l
la
k
u
n
ta
is
c
u
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n
tl
y
se
rv
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g
a
s
a
n
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ss
o
c
iat
e
p
ro
fe
ss
o
r
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t
h
e
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p
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rtme
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t
o
f
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tro
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ics
a
n
d
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o
m
m
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n
ica
ti
o
n
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g
i
n
e
e
rin
g
a
t
Ko
n
e
ru
Lak
sh
m
a
iah
E
d
u
c
a
ti
o
n
F
o
u
n
d
a
ti
o
n
,
G
re
e
n
F
ield
s,
Va
d
d
e
sw
a
ra
m
,
A.P
.
-
5
2
2
3
0
2
.
He
e
a
rn
e
d
h
is
P
h
.
D.
fro
m
K
L
Un
iv
e
rsity
.
He
h
a
s a
n
e
x
ten
siv
e
p
u
b
li
c
a
ti
o
n
re
c
o
rd
,
with
n
u
m
e
ro
u
s
p
a
p
e
rs i
n
e
ste
e
m
e
d
jo
u
rn
a
ls
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n
d
c
h
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p
ters
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c
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d
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m
ic
b
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k
s.
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d
it
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o
n
a
ll
y
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h
e
h
a
s
p
re
se
n
ted
a
wid
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ra
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g
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o
f
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m
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d
re
se
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rc
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p
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p
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rs
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t
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th
n
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ti
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n
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l
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d
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tern
a
ti
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l
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o
n
fe
re
n
c
e
s.
His
a
re
a
s
o
f
sp
e
c
ializa
ti
o
n
in
c
lu
d
e
ima
g
e
p
r
o
c
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ss
in
g
,
m
a
c
h
in
e
lea
rn
in
g
,
m
u
lt
i
d
isc
ip
li
n
a
ry
a
re
a
s,
a
n
d
th
e
i
n
tern
e
t
o
f
th
i
n
g
s
(Io
T).
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
ra
v
i.
e
n
g
g
3
8
@k
l
u
n
i
v
e
rsity
.
in
.
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