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.
3, S
ep 2019,
pp.
1
4
1
9
~1
4
2
6
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
3.pp1419-1426
1419
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
A piecewise affi
ne PI controller
for bu
ck converter generated
DC moto
r
Moh
d
I
k
h
mil
Fadz
riz
a
n
Moh
d
Han
i
f
,
Mohd Helmi S
u
id
, M
o
hd A
sh
r
a
f
Ah
m
a
d
Facul
t
y
o
f
Elect
r
i
cal
a
nd Elect
ronics Engineering
, Uni
versiti
M
alaysi
a P
a
han
g
,
Malays
ia
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Sep
2
9
,
2
018
Re
vise
d Jan
1
6
, 2019
Ac
ce
p
t
ed
M
ar1
3
,
2
019
Th
is
p
aper
p
res
e
nt
s
a
new
Pi
ecewi
s
e
A
ffi
ne
P
rop
o
rti
o
n
a
l-In
teg
r
a
l
(
P
A
-
P
I
)
con
t
ro
ller
f
o
r
a
n
g
u
l
ar
v
el
ocit
y
t
r
ack
in
g
of
a
b
u
c
k
con
v
ert
e
r
g
e
nerated
DC
m
o
t
o
r
.
A
S
a
f
e
E
x
p
e
r
i
m
e
n
t
a
t
i
o
n
D
y
n
a
m
i
c
s
(
S
E
D
)
a
l
g
o
r
i
t
h
m
i
s
e
m
p
l
o
ye
d
a
s
a
dat
a
-driv
e
n
op
timi
zati
o
n
t
o
o
l
t
o
fin
d
t
he
o
p
t
imal
P
A
-
PI
c
ontro
l
ler
param
e
ters
su
ch
t
h
a
t
th
e
i
n
t
e
gral
s
quare
o
f
error
and
i
n
p
u
t
are
redu
ced.
T
h
e
e
s
s
ent
i
al
f
eatu
r
e
of
t
h
e
P
A
-
P
I
c
ont
ro
ller
i
s
t
h
a
t
t
h
e
param
e
t
e
rs
o
f
p
r
opo
rtio
na
l
a
n
d
i
n
t
e
g
r
a
l
g
a
i
n
s
a
r
e
a
d
a
p
t
i
v
e
t
o
t
h
e
e
r
r
o
r
v
a
r
i
a
t
i
o
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s
a
c
c
o
r
d
i
n
g
t
o
th
e
P
i
ecewis
e
Affi
ne
(
P
A
)
f
uncti
on.
M
o
r
eov
e
r,
t
he
p
ro
po
sed
P
A
f
u
n
ctio
n
is
e
xp
ect
ed
t
o
pro
v
i
d
e
bett
er
c
o
n
t
r
ol
accuracy
t
han
th
e
o
t
h
e
r
ex
istin
g
vari
abl
e
s
t
ruct
ure
PID
con
t
ro
ller.
In
o
rder
t
o
verif
y
t
he
e
f
f
ecti
v
en
ess
of
t
he
P
A
-
P
I
c
ontrol
ler,
a
wi
del
y
k
nown
bu
ck
c
onv
erter
generat
e
d
D
C
m
ot
or
i
s
con
s
i
d
ered.
T
he
perf
o
r
man
ces
o
f
the
pro
p
o
s
ed
c
o
n
tro
l
l
e
r
are
o
b
s
e
rved
i
n
t
e
rms
o
f
t
h
e
integral
sq
uare
o
f
error
and
i
n
p
u
t,
a
n
d
t
he
r
es
po
nses
o
f
the
ang
u
l
a
r
v
e
l
ocity
a
nd
d
u
t
y
rati
on
i
nput.
T
h
e
sim
u
latio
n
results
v
erif
y
t
h
at
t
h
e
p
rop
o
s
e
d
P
A
-
P
I
c
on
tr
o
l
le
r
yi
eld
s
h
igh
e
r
con
t
rol
accuracy
t
han
th
e
ot
her
exi
s
t
i
n
g
c
on
tro
l
l
e
r
s
of
b
u
c
k
con
v
ert
e
r
gener
a
t
e
d
D
C
m
o
t
or.
K
eyw
ord
s
:
Piec
ewise
Affine
P
r
o
p
o
r
tio
n
a
l-
Integral
Buc
k
c
on
ve
rter
D
C m
o
t
o
r
S
a
fe
E
xperim
e
nta
t
io
n
D
ynam
i
cs (
S
E
D
)
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:
Mo
hd
A
s
hraf A
hm
ad,
F
a
cult
y
o
f
E
l
e
c
t
rica
l
and
E
l
e
c
t
r
on
ics En
gi
nee
r
in
g,
Uni
v
ersi
ty
M
al
ays
i
a
Paha
ng,
P
e
kan,
266
0
0
, P
a
ha
ng, Ma
l
a
y
sia
.
Em
ail:
ma
shr
a
f@
ump.
ed
u.m
y
1.
I
N
TR
OD
U
C
TI
O
N
Rec
e
n
t
l
y,
v
ar
ious
a
p
p
lic
a
tio
ns,
such
a
s
ro
bo
tic
m
ani
p
u
l
a
t
or
,
dr
on
e
s
,
c
o
n
v
e
yor
b
e
lts,
and
e
l
e
c
tr
ic
cra
n
es,
r
e
quire
a
h
i
g
h
pre
c
is
ion
D
C
m
o
t
ors
.
M
e
a
nw
hi
le,
t
h
er
e
ar
e
large
numbe
rs
o
f
st
a
ndar
d
p
u
l
se
w
idt
h
modu
la
ti
o
n
(
P
W
M)
a
ppl
ica
t
i
ons
f
or
D
C
m
o
t
o
r
e
x
ecu
t
i
on.
N
eve
r
the
l
ess,
t
hi
s
t
e
c
h
ni
q
u
e
d
e
gra
d
e
s
t
he
p
re
cis
i
o
n
mo
t
i
on
o
f
t
h
e
DC
m
ot
o
r
o
wi
n
g
t
o
in
t
r
ac
t
a
b
l
e
swit
c
h
in
g
st
rat
e
gy
t
h
a
t
r
e
s
ul
tin
g
t
o
j
e
r
k
resp
on
se
i
n
th
e
vo
lt
age
and
curr
ent
of the
D
C
motor
[1].
A
s
a
s
o
lu
ti
on
t
o
th
e
p
r
obl
e
m
,
a
D
C
-D
C buc
k
c
o
nve
rter i
s
ad
o
p
te
d t
o
prov
i
de
a
sm
oo
t
h
t
ra
ck
in
g
mo
ti
o
n
o
f
t
h
e
DC
m
o
t
or.
In
p
art
i
cu
lar
,
i
t
can
t
rack
t
h
e
r
eq
ui
re
d
t
r
aj
ec
to
ry
o
f
b
o
th
a
ng
ul
ar
vel
o
c
i
t
y
a
n
d
p
osit
i
o
n
tra
j
e
c
t
o
ry
t
hro
u
gh
reg
u
la
t
i
n
g
a
n
in
p
u
t
vo
ltage
onl
y.
I
n
othe
r
w
o
rds,
t
he
s
elec
t
i
on
of
go
o
d
c
ontr
o
l
s
c
hem
e
i
s
ve
ry
i
m
porta
nt
t
o
pr
ov
ide
a
hi
g
h
p
r
ecis
i
o
n
o
f
m
o
ti
on of
t
he
D
C
motor
fe
d
by
t
h
e
D
C
-
D
C
buc
k
co
nv
erte
r.
To
t
he
b
es
t
o
f
our
k
n
o
w
l
e
d
ge,
a
variet
y
of
a
ppr
oa
ches
h
a
v
e
be
e
n
p
r
o
p
o
se
d
in
r
eg
ula
t
in
g
buc
k-
con
v
er
t
e
r
ge
ne
rated
D
C
m
oto
r
.
F
i
r
s
tly,
a
fee
dbac
k
c
o
n
tro
l
l
e
r
w
i
th
e
ne
rg
y
shap
i
ng
a
nd
d
a
m
p
i
n
g
i
n
jec
t
i
on
[2
]
is
u
se
d
to
c
o
n
t
rol
a
4
th
o
rde
r
m
ode
l
o
f
b
u
c
k
co
nver
t
e
r
g
e
n
er
ated
D
C
mo
t
o
r.
N
ext,
a
f
la
t
ness
based
m
e
thod
i
s
ado
p
t
ed
f
or
a
n
g
u
l
a
r
v
e
l
oc
i
t
y
trac
k
i
n
g
o
f
t
h
e
D
C
m
ot
or
f
e
d
by
t
h
e
D
C
-D
C
b
u
c
k
c
o
nver
t
e
r
i
n
[1],
[
3]
a
nd
[4]
.
H
e
r
e
,
t
h
e
co
ntr
o
l
l
er
d
esig
n
i
n
[
4]
i
s
der
i
ve
d
from
t
he
s
im
p
l
i
f
i
ed
2
nd
o
r
d
er
m
ode
l,
w
hi
l
e
t
he
c
o
n
tro
ller
i
n
[
1]
and
[3]
a
r
e
de
rive
d
from
t
he
4
th
o
rder
m
od
el.
M
o
re
over,
a
s
l
i
d
i
ng
mo
d
e
c
on
tro
lle
r
w
i
t
h
d
e
l
ta
m
o
dul
at
i
on
base
d G
P
I
is repor
ted
in [5].
In
p
a
r
t
i
c
ul
a
r
, t
he
s
i
m
pl
if
ie
d
mat
he
ma
ti
c
a
l
m
o
d
el i
n [4] i
s
appli
e
d
. Further
more, a
bac
k
ste
p
pi
n
g
c
on
tro
l
l
e
r
w
ith
n
o
n
-ada
p
t
i
v
e
a
n
d
ada
p
t
i
ve
m
ec
han
i
s
m
s
i
s
d
e
si
gne
d
base
d
on
4
th
o
rd
er
m
o
d
el
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
141
9
– 1
426
1
420
[6].
T
he
ir
w
or
k
c
l
aim
s
t
hat
t
h
e
a
d
ap
t
i
ve
m
e
c
ha
nism
i
s
s
i
g
n
i
f
ica
n
t
i
n
i
m
p
r
ov
in
g
t
h
e
c
ont
rol
per
f
orm
a
nce
eve
n
w
ith l
oad tor
q
u
e
v
a
r
iat
i
ons.
O
t
her
c
o
ntrol s
t
r
a
teg
i
es of
D
C
mot
or fe
d
b
y
D
C
-D
C bu
c
k
c
on
v
e
rter
a
r
e
LQ
R
an
d
PI
c
ontroll
ers
[7],
t
wo-stage
c
on
t
r
ol
w
i
t
h
di
ff
ere
n
ti
al
f
l
a
tn
es
s
[8],
H
∞
co
ntroller
[
9
],
r
obus
t
cont
r
o
l
law
with
ac
t
i
ve
d
istur
b
a
n
ce
reje
ct
i
o
n
[10],
neur
al ne
t
w
o
r
k
con
tro
lle
r
[1
1],
and
hy
b
r
id P
I w
ith F
uzzy
c
on
tro
l
ler
[12].
Base
d
o
n
t
he
s
ta
t
e
d
co
n
t
ro
l
sc
hem
e
s,
m
ost
of
t
h
e
c
o
n
tro
l
l
e
r
tec
hn
i
ques
have
e
m
p
l
o
ye
d
t
h
e
m
ode
l-
base
d
c
o
n
t
r
o
l
s
c
he
me
s,
w
hich
a
re
s
ynthe
siz
e
d
b
ase
d
o
n
t
h
e
2
nd
o
r
4
th
o
r
d
e
r
m
o
d
e
l
.
N
e
v
e
r
t
h
e
l
e
s
s
,
i
t
i
s
h
a
r
d
t
o
em
plo
y
t
he c
o
n
tr
olle
r
de
r
i
ve
d fr
om
t
he mo
d
e
l
i
n
re
a
l
e
xp
erim
ent
o
f
bu
ck
-c
on
v
e
rt
er
g
e
n
e
r
at
e
d
D
C
mot
o
r
pl
an
t
ow
i
ng
t
o
s
om
e
j
u
st
ifica
t
io
ns
.
These
are
th
e
unm
ode
l
e
d
dy
na
mic
p
ro
bl
em
s,
i
na
ccur
a
cy
o
f
t
h
e
s
i
mpl
i
f
i
e
d
m
ode
l,
a
n
d
m
as
s
i
ve ga
p
be
t
w
e
en
r
ea
l
app
l
ic
ati
o
ns
an
d
c
o
n
t
r
ol t
h
e
o
r
y
.
Th
en
c
e
,
a
d
a
t
a
-d
riv
e
n
co
nt
roll
er,
wh
i
c
h
is
d
er
ive
d
fro
m
the
ou
t
put
a
nd
inp
u
t
dat
a
o
f
th
e
pla
n
t
i
n
t
he
a
bsen
ce
o
f
a
n
y
kn
o
w
l
e
dg
e
of
t
h
e
p
l
a
nt,
ma
y
bec
o
me
a
p
ro
m
i
si
ng i
d
ea
. Me
a
nw
h
ile,
the
da
ta-dri
ve
n P
I
D c
o
nt
r
o
l
s
chem
e i
s
mos
t
l
y
pre
fer
r
ed an
d
e
s
t
a
b
lis
he
d
c
o
nt
roll
e
r
s
t
r
u
c
t
u
re
o
w
i
ng
t
o
it
s
si
mp
li
c
i
ty
i
n
d
e
si
gn
a
nd
easy
t
o
be
i
m
p
le
me
nt
e
d
[
13].
More
ov
e
r
,
th
e
c
o
n
t
r
o
l
ac
cura
cy
o
f
t
h
e
sta
n
da
rd
P
ID
c
o
n
tr
ol
s
chem
e
ca
n
be
e
n
h
a
n
c
e
d
b
y
upgr
a
d
i
n
g
it
t
o
n
on
line
a
r
P
I
D
[1
4]–[
19]
.
Th
e
r
efo
r
e,
i
t
is
s
ign
i
fi
ca
nt
t
o
a
sse
ss
t
h
e
e
f
f
ec
t
i
v
e
n
e
s
s
of
t
h
e
d
a
t
a-
dri
v
en
n
on
l
i
n
ear
P
ID
c
o
n
t
rol
l
er
f
or
i
n
p
u
t
trac
k
i
n
g
o
f t
h
e
ang
u
l
ar
v
el
oci
t
y
of
DC m
otor
f
e
d
b
y t
h
e
DC-DC b
uc
k-c
o
nv
erter
.
The
pa
pe
r
pr
e
s
en
ts
t
he
d
a
t
a
-
base
d
P
i
e
ce-
w
i
se
A
ff
i
n
e
P
I
c
ontro
l
l
e
r
f
o
r
i
npu
t
t
r
ack
ing
of
a
n
gul
ar
vel
o
c
i
t
y
o
f
D
C
m
otor
f
ed
by
the
D
C
-
D
C
b
u
c
k
co
nve
r
t
e
r
.
S
p
e
c
ifica
l
l
y
,
t
h
e
P
i
e
c
e
w
i
s
e
A
f
f
i
n
e
P
I
,
w
h
i
c
h
i
s
i
n
the
fam
i
l
y
o
f
var
i
a
b
le
s
tr
uct
u
re
P
ID,
is
e
x
p
e
c
te
d
t
o
p
ro
v
i
de
b
e
tt
e
r
c
ontro
l
ac
cu
ra
c
y
t
han
t
h
e
si
g
m
oi
d
b
a
sed
P
I
D
in
[
19]
.
This
i
s
be
ca
u
s
e
our
p
ro
p
o
se
d
var
i
a
b
le
s
truc
t
u
re
,
w
h
i
c
h
i
s
i
n
a
p
i
e
c
e
-
w
i
s
e
a
f
f
i
n
e
f
o
r
m
,
i
s
m
o
r
e
gene
ra
l
a
n
d
n
o
t
r
estr
ict
t
o
t
he
s
i
g
mo
id
f
un
c
t
i
o
n.
T
henc
e,
i
t
pr
o
f
fer
s
h
ig
h
pos
sib
i
l
ity
t
o
e
nha
nc
e
the
c
o
nt
r
o
l
ac
cura
cy by
usin
g
t
h
e
t
i
me
-var
y
i
ng P
I
gai
ns ac
c
ord
i
n
g
to
th
e
c
h
a
n
ges
of
a
ng
u
l
ar
ve
l
oc
ity
e
r
r
o
r
w
ith r
e
s
pect
t
o
the
op
t
i
m
a
l
P
i
e
cew
i
s
e
A
f
fine
f
u
n
ct
ion.
M
or
eover
,
t
he
s
t
u
d
y
i
n
[
19]
d
oes
no
t
inc
l
u
d
e
s
a
n
ex
pl
ic
i
t
d
e
s
c
r
ip
tio
n
of
d
ata
-
drive
n
c
ontro
ller
tu
n
i
n
g
,
w
h
i
l
e
i
n
t
hi
s
st
u
dy,
a
c
om
ple
te
d
ata
-
d
r
ive
n
c
o
n
tr
ol
s
yn
t
h
e
s
i
z
e
is
s
how
n.
Spe
c
ifica
l
l
y
,
a
safe
e
x
p
er
i
m
enta
tio
n
dy
na
m
i
c
s
(
SED
)
a
lgor
it
hm
[
2
0
]
i
s
e
mplo
ye
d
t
o
o
b
t
a
i
n
the
P
i
ec
ew
is
e
A
f
fine
P
I
ga
in
s
t
h
a
t
m
inim
iz
e
t
h
e
a
n
g
u
l
a
r
v
e
l
oc
ity
e
r
r
or.
The
S
ED
a
l
g
o
r
it
hm
i
s
w
i
de
l
y
e
s
t
a
b
lis
hed
to
b
e
a
sign
ifica
n
t
o
p
t
imiz
a
tio
n
t
o
ol
o
w
i
ng
t
o
i
t
s
c
a
p
ab
i
l
i
t
y
i
n
so
lv
i
n
g
v
a
rie
t
y
of
opt
i
m
iz
a
tio
n
p
r
ob
l
e
ms
w
i
t
h
f
a
s
t
con
v
er
ge
nce
s
p
eed
e
ve
n
for
lar
g
e
n
u
m
b
er
o
f
pa
ram
e
te
rs
t
un
i
ng
[2
1]–
[
25]
.
N
e
xt
,
th
e
pro
p
o
s
ed
d
a
t
a-
based
P
i
ec
ew
ise
A
f
fi
ne
P
I
c
o
n
t
r
o
lle
r
desi
g
n
i
s
veri
fie
d
t
o
a
w
i
de
l
y
e
s
t
a
b
l
i
she
d
m
ode
l
of
b
uck
-
c
o
n
v
erter
ge
n
e
r
a
ted
D
C
m
o
t
or
[
1].
The
c
o
n
t
ro
l
p
e
r
f
orm
a
nc
es
o
f
the
P
i
e
ce-
w
i
se
A
ffi
ne
P
I
con
t
r
o
l
l
e
r
b
a
sed
SED
a
r
e
an
aly
z
e
d
i
n
term
s
of
d
u
t
y
cycle
i
n
p
u
t
e
n
e
r
gy
a
nd
a
n
g
u
l
ar
v
e
l
oc
i
t
y
tra
j
e
c
tor
y
trac
k
i
ng
.
Lastl
y
,
a
pe
rform
anc
e
c
omp
a
riso
n
betw
ee
n
the
P
i
ece
w
i
se
A
ffi
n
e
P
I
c
ontro
ller
b
a
se
d
S
E
D
and
the
c
o
n
v
e
n
t
i
o
n
a
l
P
I
[
7
]
a
n
d
t
h
e
s
i
g
m
o
i
d
b
a
s
e
d
P
I
[1
9]
i
s
prese
n
te
d.
2.
B
U
CK
C
ONVE
R
TER GEN
E
RAT
ED DC MOTOR
Th
e co
mpl
e
t
e
4
th
orde
r
m
athem
a
tica
l
m
odel
of
b
uc
k c
o
n
v
erter
gene
rate
d
D
C
m
ot
or
,
w
h
ich
is
t
a
k
e
n
f
r
om
[1],
is
g
iven by
D
C
B
A
H
(
1
)
wher
e
.
0
,
1
0
0
0
,
0
0
0
,
0
0
0
1
0
0
1
0
1
0
0
1
D
C
L
U
B
J
K
L
K
L
R
L
C
C
L
L
R
A
e
M
M
M
E
M
M
M
L
The
de
tai
l
e
d
of
the
varia
b
le
s
o
f
the
p
l
a
nt i
n (1)
is gi
v
en
i
n
T
a
b
l
e
I
.
N
o
te
t
h
a
t
th
e
i
n
p
u
t
u
(
t
) of the
p
l
a
n
t
i
s
a
du
ty
r
ati
o
]
1
0
[
,
δ
, wh
i
l
e
t
h
e
a
ngul
a
r
v
e
l
o
c
i
t
y
ω
i
s t
h
e o
u
t
pu
t
of
th
e
p
l
a
nt
y
(
t
).
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
A piecewi
se affine PI
contr
o
ller
f
o
r
buck
convert
e
r gener
a
t
e
d DC mo
tor (Mohd Ikhmil
F.
Mohd Hanif)
1
421
T
a
bl
e 1
.
Va
r
i
a
b
l
es o
f bu
c
k
c
on
v
e
r
t
er g
en
e
r
at
ed
DC
mo
t
o
r
V
a
ri
a
b
l
e
s
Sym
bol
V
a
l
ue
U
nit
Ind
u
c
t
or
o
f
DC
m
o
t
or
L
M
8.
9×
10
-3
H
Re
sistor of DC
mo
t
or
R
M
6
O
h
m
El
ect
r
o
ma
g
n
e
t
i
c s
o
u
r
ce
K
E
0.
051
7
V
s
/ra
d
Ta
c
hoge
n
e
r
a
tor
g
a
in
K
M
0.
051
7
Nm
/A
Mo
me
n
t
o
f
in
er
t
i
a
J
M
7.
95×
10
-6
K
g
-
m
2
Inp
u
t volta
ge
U
e
24
V
Ind
u
c
t
or
L
1.
33×
10
-6
H
Re
sistor
o
f
c
o
il
w
i
ndings
R
L
0.
2
O
h
m
Ca
p
a
c
itor
C
470×
10
-6
F
3.
PROB
LEM
F
ORM
U
LAT
I
ON
F
i
gur
e
1
sh
ow
s
the
P
i
e
cew
is
e
A
f
fi
ne
P
I
contr
o
l
l
er
(
P
A
-P
I)
f
or
b
uck
co
n
v
er
t
e
r
gene
r
a
te
d
D
C
m
otor
.
Here,
t
h
e
sym
b
ols
r
(
t
),
u
(
t
),
y
(
t
)
and
e
(
t
)
ar
e
t
h
e
des
i
red
a
n
g
u
l
ar
v
e
l
oc
it
y
trajec
to
r
y
,
t
h
e
co
n
t
rol
in
p
u
t,
t
h
e
a
c
tua
l
a
n
g
u
l
ar
v
e
l
oc
i
t
y
r
e
spo
n
se,
an
d
t
h
e
er
r
o
r
betw
ee
n
de
si
r
e
an
d
ac
tua
l
a
ng
u
l
a
r
v
e
l
oc
i
t
y
,
r
e
spe
c
t
i
ve
l
y
.
T
h
e
pla
n
t
H
is
de
f
i
ned
a
s
t
he
b
uc
k
c
o
nver
t
er
ge
n
e
r
a
t
e
d
D
C
m
o
tor
s
y
s
t
em
a
s
p
r
e
s
ente
d i
n
t
he
pr
e
v
i
ous
sect
i
o
n.
The
P
A
-
P
I
c
ont
r
o
l
l
e
r
i
s
e
xpr
essed
by
s
t
I
t
P
s
C
)
(
)
(
)
(
(
2
)
wh
ere
,
w
t
e
w
,
w
t
e
w
,
w
t
e
w
w
t
e
M
c
w
t
e
M
c
w
t
e
M
c
t
P
P
l
P
l
P
P
P
P
P
l
P
l
P
l
P
P
P
P
P
P
)
(
)
(
)
(
if
if
if
)
)
(
(
)
)
(
(
)
)
(
(
)
(
1
2
1
1
0
1
1
1
2
1
0
1
0
(
3
)
wh
ere
)
2
1
(
)
(
)
(
1
1
l
..
.,
,
,
k
w
w
/
c
c
M
P
k
P
k
P
k
P
k
P
k
a
r
e
t
h
e
s
e
g
m
e
n
t
s
l
o
p
e
s
,
R
)
1
0
(
l
...,
,
,
k
w
P
k
a
r
e
t
h
e
g
i
v
e
n
i
n
p
u
t
p
o
i
n
ts
f
or
t
h
e
g
ain
P
(
t
)
sa
t
i
sf
y
i
ng
P
l
P
P
w
w
w
1
0
a
n
d
c
o
n
n
ect
i
ng
t
h
e
l
i
n
e
s
e
g
m
e
nts
,
a
nd
)
1
0
(
l
.
..,
,
,
k
c
P
k
a
r
e
t
h
e
o
u
t
p
u
t
p
oin
t
s
c
o
r
r
e
s
pond
i
n
g
t
o
e
a
c
h
i
n
put
p
oin
t
.
F
o
r
s
i
m
ple
n
o
t
at
ion,
l
et
d
efi
n
e
T
1
0
]
[
P
l
P
P
P
w
w
w
w
.
Th
e
i
llu
stra
t
i
on of t
h
e
pie
c
e
w
i
s
e
af
f
ine
f
u
n
c
tio
ns
fo
r
t
h
e
ga
in
P
(
t
)
i
s
s
how
n i
n
F
ig
ur
e
2
.
I
n
t
h
i
s
s
t
u
d
y
,
i
t
i
s
a
s
s
u
m
e
d
t
h
a
t
P
(
t
)
i
s
o
n
e
-to
-
one
m
a
p
t
o
e
(
t
)
an
d
P
(
t
)
=
0
if
e
(
t
)
=
0.
T
h
e
n
ce,
0
0
P
c
for
0
0
P
w
.
Not
e
t
ha
t
a
si
mi
la
r
pie
c
e
-
wi
se
a
f
f
i
n
e
f
u
nct
i
o
n
i
s
ap
pl
ie
d
to
int
e
gr
al
g
ain
I
(
t
)
.
N
e
x
t
,
t
h
e
c
o
n
t
r
o
l
pe
r
f
or
m
a
nc
e
assessme
n
t
f
o
r
th
e
c
ontr
o
l
sy
st
e
m
b
lo
c
k
d
ia
gr
am
i
n
F
i
gur
e
1
is
g
i
v
en
b
y
F
i
gur
e
1.
C
o
n
tr
ol
s
ystem
b
l
oc
k
dia
g
r
a
m
of
buc
k
c
o
n
v
e
r
ter
gene
r
a
ted
D
C
m
otor
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
4
1
9
–
1
426
1
422
F
i
gur
e
2.
P
i
e
ce
w
i
se
a
f
f
i
ne
f
un
cti
o
n
for
the
ga
in
P
(
t
)
,
)
(
)
(
))
(
,
)
(
(
0
0
2
2
2
1
f
f
t
t
t
t
dt
t
u
dt
t
e
t
I
t
P
Q
(
4
)
Where
t
0
∈0
∪
R
,
a
nd
t
f
∈
R
+
.
Note
t
h
a
t
th
e
ti
m
e
i
n
t
erva
l
[
t
0,
t
f
]
co
rres
p
ond
s
to
t
h
e
p
erio
d
for
th
e
pe
r
f
or
m
a
nc
e e
v
al
ua
ti
o
n
.
The
symb
ols
ꞷ
1
a
n
d
ꞷ
2
c
or
r
e
sp
on
d
to w
ei
g
h
t
i
ng
coe
f
fic
i
e
n
ts,
w
h
ic
h ar
e
g
i
ve
n
by t
h
e
d
e
si
gn
e
r
.
Th
e
f
i
rst
t
e
r
m
i
n
(3
)
co
rres
pon
d
s
t
o
th
e
t
r
ac
ki
ng
e
rr
or
,
w
h
ile
t
he
s
ec
on
d
me
ans
the
c
o
nt
r
o
l
i
n
p
u
t
en
e
r
g
y
.
H
e
r
e
,
t
h
e
v
a
lu
e
s
o
f
ꞷ
1
a
n
d
ꞷ
2
a
r
e
s
e
l
e
c
t
e
d
i
n
a
s
i
m
i
l
a
r
w
a
y
t
o
t
h
e
s
t
a
n
d
a
r
d
L
i
n
e
a
r
Q
u
a
d
r
a
t
i
c
Re
gu
la
tor
(LQR) pr
ob
l
e
m.
F
inal
ly,
the
pro
b
l
e
m
statem
ent i
s
de
s
c
r
i
be
d
b
y
:
Pr
ob
lem
3.
1.
C
ons
i
d
er
t
he
c
on
tr
o
l
s
ys
tem
bloc
k
dia
g
r
a
m
in
F
ig
ur
e
1.
T
h
e
n,
f
ind
th
e
P
A
-PI
co
ntro
ll
er
C
(
s
)
in
(2
)
su
ch
t
h
a
t
th
e
control
p
e
rfo
rman
ce
a
sses
s
men
t
Q(P(t),I(t))
i
s
m
i
nim
i
z
e
d
bas
e
d
on
t
h
e
u
(
t
)
and
y
(
t
)
d
a
ta.
Rema
rk
3
.1
.
T
he
p
r
o
p
o
sed
P
A
-
P
I
con
t
r
o
ll
er
i
s
e
x
pec
t
e
d
t
o
pr
o
duce
b
e
t
t
e
r
c
o
n
t
r
o
l
perfo
rman
ce
f
rom
o
u
r
pr
e
v
i
o
us
v
er
s
i
on
of
s
i
g
m
o
i
d
b
a
s
ed
P
I
in
[
19]
.
Thi
s
i
s
be
cause
t
he
n
o
n
l
i
ne
ar
P
I
gains
in
t
he
pr
o
pose
d
P
A
-
PI
a
r
e
not
r
estr
i
c
ted
t
o
o
nl
y
si
gm
oid-
base
d
f
unc
t
i
o
n
.
T
h
ough
i
t
loo
k
s
t
h
a
t
we
c
a
n
han
d
l
e
ge
ne
r
a
l
cla
s
s
o
f
n
on
l
i
ne
ar
s
u
b
s
y
s
t
e
m
s
P
I
g
ains
b
y
a
d
o
p
t
i
n
g
s
o
m
a
ny
bas
i
s
f
u
nct
i
on
s
(such
as
p
i
e
ce-
wise
a
ffine
fun
c
ti
o
n
s).
4.
PA-
P
I CONTRO
LLE
R
B
A
S
E
D
S
A
FE
E
XPE
R
IMENTATI
ON
DYN
AMIC
S
In
t
h
i
s
sec
tio
n,
t
he
m
ai
n
s
o
lu
t
i
o
n
o
f
the
P
r
o
b
lem
3.1
is
e
x
p
l
a
i
ne
d.
F
ir
st
ly
,
an
o
ver
v
iew
of
t
he
S
af
e
Ex
pe
r
i
me
n
t
a
t
i
on
D
ynam
i
c
s
(
S
E
D
)
a
lgor
i
t
h
m
i
s
pr
esen
te
d.
S
econd
l
y
,
it
is
s
how
n
o
n
how
t
o
a
ppl
y t
h
e
S
E
D
for
tu
n
i
n
g
t
he
p
a
r
a
m
e
t
e
r
s
of
P
A
-P
I
such
t
ha
t
t
h
e
c
ontr
o
l
per
f
o
r
m
a
nc
e
s
i
nde
x
i
n
(
4)
i
s
r
e
duc
e
d
.
4.
1.
Ov
erv
i
e
w
o
f
sa
f
e e
x
pe
ri
me
nta
t
i
o
n dy
na
m
i
cs
S
a
f
e
E
x
p
e
r
i
m
e
n
t
a
t
i
o
n
D
y
n
a
m
i
c
s
(
S
E
D
)
i
s
a
g
a
m
e
t
h
e
o
r
e
t
i
c
m
e
t
h
o
d
t
h
at
d
ef
in
e
s
e
ac
h
e
l
eme
n
t
o
f
t
h
e
de
sig
n
v
ar
ia
bl
e
a
s
a
p
l
a
yer
[
2
0]
.
H
e
r
e
,
the
r
a
nd
om
m
oti
on
of
e
a
ch
p
l
a
y
e
r
i
s
d
ec
id
ed
b
ased
o
n
p
r
e
-
d
e
t
e
rmi
n
e
d
pr
oba
b
ili
t
y
suc
h
tha
t
an
o
p
tim
al
goa
l or
d
esi
gn
var
i
a
b
l
e
is a
c
h
ie
ve
d,
w
hic
h
c
or
r
e
spo
n
d
s t
o
the
m
in
im
um
v
a
l
u
e
of
t
he
l
oss
f
u
nc
tio
n.
I
n
par
ticu
l
ar
,
l
e
t
the
opt
i
m
iz
at
ion
pr
o
b
l
em
i
s
give
n
by
)
(
mi
n
x
x
L
n
R
(
5
)
wh
ere
x
∈
R
n
i
s
t
h
e
de
sig
n
v
ar
i
a
ble,
a
n
d
L :R
n
→
R
i
s
de
n
o
t
e
d
b
y
th
e
lo
s
s
f
unc
tio
n.
T
he
S
ED
a
lg
or
i
t
hm
i
t
e
ra
t
i
v
e
l
y
upda
t
e
s
x
∈
R
n
u
s
i
ng
the
u
pda
te
d
law
,
E
r
,
E
r
x
r
λ
-
x
f
τ
x
i
i
i
1
1
2
if
if
)
(
)
1
(
(
6
)
fo
r
τ
=
0,
1
,
…
wher
e
r
1
an
d
r
2
ar
e
i
nde
pe
nd
e
n
t
r
a
ndom
num
ber
s
w
h
i
c
h
u
n
i
f
o
r
m
ly
d
i
s
t
r
ibu
t
e
d
b
e
t
w
ee
n
t
h
e
r
a
nges
o
f
[
0,
1
]
,
E
i
s
a
sc
a
l
ar
t
ha
t
de
fi
ne
s
the
pr
oba
b
i
l
i
t
y
of
u
s
i
n
g
t
h
e
n
ew
u
p
d
a
te
d
des
i
g
n
v
ar
i
a
ble,
λ
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A
pi
e
c
e
w
ise
a
f
f
i
ne P
I
c
ontr
o
l
l
e
r
for b
u
ck
c
o
n
v
erter ge
ner
a
te
d D
C
m
o
tor
(Mo
hd I
k
hm
i
l
F.
Mohd H
a
n
i
f)
1
423
repr
esents the
ste
p
size
g
a
i
n of t
he
de
s
i
g
n v
a
riab
le,
x
i
is
th
e
i
-t
h
el
emen
t
o
f
x
∈
R
n
,
x
̄
i
is
the
i
-
t
h elem
e
n
t o
f
x
̄
∈
R
n
,
and
x
̄
∈
R
n
,
i
s
d
en
ot
ed
a
s t
h
e c
u
rre
n
t
b
e
st
d
e
s
i
g
n
v
a
ri
a
b
l
e
v
ec
t
o
r. In
(6
)
,
the f
u
nct
i
on
f
i
s gi
ven b
y
,
x
r
λ
x
,
x
r
λ
x
x
,
x
r
λ
x
x
r
λ
x
x
f
i
i
i
i
lo
2
up
2
lo
up
2
lo
2
up
if
if
if
)
(
(
7
)
wher
e
x
up
and
x
1o
a
r
e
p
re
-define
s
u
ppe
r
a
n
d
l
o
w
e
r
bou
nd
v
a
l
ue
s
of
d
es
ig
n
varia
b
l
e,
r
espe
ctive
l
y.
T
h
e
impor
ta
nt
f
ea
t
u
re
o
f
S
E
D
is
t
ha
t
it
can
p
ro
vi
de
a
s
ta
b
l
e
c
onve
r
ge
nc
e
due
t
o
its
c
a
p
a
b
ili
t
y
t
o
ke
e
p
t
h
e
b
e
s
t
des
i
g
n
v
a
r
ia
bl
e
d
u
r
i
ng
the
t
u
n
i
ng
p
ro
c
e
ss.
M
or
eo
ver
,
t
h
e
S
ED
u
s
e
s
a
f
i
x
e
d
i
n
t
e
r
v
a
l
s
t
e
p
s
i
z
e
,
w
h
i
c
h
i
s
in
de
pen
d
e
n
t
of
t
he
n
um
ber
o
f
iter
a
t
i
o
n
s.
T
he
refore,
it
w
i
l
l
b
e
use
f
ul
d
a
t
a-d
r
i
v
e
n
o
p
t
imiza
tio
n
to
ol
f
or t
he
c
ase
when
d
i
s
tur
b
a
n
ce
s
or
uncer
ta
int
i
es
o
r
st
oc
ha
stic
d
e
l
a
y
o
ccur
d
u
ri
n
g
the
t
uni
ng
p
ro
c
e
s
s
.
In
t
hi
s
stud
y
,
t
h
e
pro
pose
d
S
ED
a
lgori
t
hm
t
e
r
m
i
na
t
e
s
us
i
ng
pre
-
spec
ifie
d
st
op
p
i
n
g
criteri
on
τ
ma
x
w
it
h
t
h
e
s
o
l
u
tio
n
)
(
min
arg
)}
1
(
)
1
(
)
0
(
{
x
x
x
x
x
x
L
*
τ
...,
,
,
.
4.2.
A
p
p
licat
ion
of S
ED to tu
n
e
PA
-
PI
c
on
t
r
oller
I
n
t
hi
s
sec
t
i
o
n,
i
t
is
d
esc
r
ibe
d
o
n
h
o
w
to
e
mplo
y
the
S
E
D
a
l
g
o
r
ithm
in
S
ec
t
i
on
4
.
1
f
or
t
un
i
n
g
t
h
e
pro
pose
d
P
A
-
P
I
c
ontro
l
l
er
o
f
buc
k
c
o
nver
t
e
r
g
ene
r
ate
d
D
C
m
o
tor
.
I
nit
i
a
l
l
y
,
t
h
e
des
i
gn
v
aria
bl
e
w
ith
r
espec
t
to t
he
P
A
-
P
I
c
on
tro
l
l
e
r ga
ins
is
d
efi
n
ed
b
y
T
1
1
]
[
I
l
I
P
l
P
c
c
c
c
υ
(
8
)
wher
e
ρ
R
υ
for
l
ρ
2
.
N
e
xt
,
a
l
ogar
i
t
h
m
i
c
func
t
i
o
n
i
s
ut
i
l
iz
e
d
f
or
e
v
e
ry
e
l
e
me
n
t
o
f
ρ
R
x
t
o
prov
ide
a
fa
st
d
e
s
ign
va
ria
b
le
s
e
a
rc
hing.
I
n
p
a
rt
icu
l
ar,
th
e
ne
w
set
t
i
ng
o
f
t
he
d
e
s
ig
n
va
riab
le
i
s
T
T
2
1
]
10
10
10
[
]
[
2
1
ρ
x
x
x
ρ
υ
υ
υ
w
it
h
the
loss
func
t
i
o
n
)
]
10
10
10
([
T
2
1
ρ
x
x
x
L
.
Lastly,
the
step-
by-s
t
ep pr
o
cedure to apply
t
he S
ED a
l
gor
ith
m
to PA
-
P
I
c
ontr
o
lle
r is sta
te
d
as foll
o
w
:
St
e
p
1
:
S
et
t
he
ini
tia
l
desi
g
n
v
ar
i
a
bl
e
x
(0)
with pre
-specified
τ
ma
x
a
nd
i
i
υ
x
log
for
i
=
1
,
2
,
…
,
ρ
.
Select
St
e
p
2
:
E
xecut
e
t
he S
ED
a
lgor
i
t
hm
in (
6
) by
set
t
i
n
g the
de
si
gn va
r
i
ab
l
e w
i
t
h
υ
in (8)
and
L
:=
Q
.
St
e
p
3
:
Af
t
e
r
τ
ma
x
i
t
e
rati
o
n
s, obta
i
n
t
h
e
o
p
t
ima
l
d
es
ig
n var
i
a
b
l
e
ρ
*
R
x
a
nd app
l
y to
C
(
s
)
i
n
(
2
)
.
5.
NUMERICAL RESULTS
I
n
t
his
sec
t
ion
,
t
he
e
f
f
ec
tive
n
ess
of
t
he
p
r
opose
d
P
A
-
PI
c
on
tro
ll
er
b
a
s
ed
S
ED
i
s
p
r
ese
n
t
e
d
.
T
he
mode
l
of
t
he
buc
k-c
o
n
v
e
r
ter
gene
rate
d
D
C
m
otor
i
n
(9)
is
u
sed.
The
de
sire
d
a
n
g
u
la
r
ve
l
o
c
ity
u
sed
in
t
his
nume
r
ica
l
e
x
a
m
p
l
e
i
s
b
a
sed
on
t
h
e
ta
nge
nt
h
y
p
e
r
b
o
l
i
c
f
un
cti
o
n
f
r
o
m
[1
9
]
.
The
des
i
gn
va
ria
b
le
o
f
P
i
e
c
e
w
i
se
Af
fine
P
I
controll
er
C
(s)
is
g
ive
n
i
n
t
h
e
sec
o
n
d
c
o
l
umn
o
f
T
ab
le
II
w
i
th
T
]
15
12
9
6
3
0
[
I
P
w
w
and
0
0
0
I
P
c
c
.
O
u
r
aim
i
s
t
o
ob
t
a
in
t
he
o
p
tima
l
ρ
R
υ
t
hat
mi
ni
mi
z
e
s
th
e
lo
ss
f
u
n
c
ti
on
Q
i
n
(3
)
f
o
r
10
1
ω
,
1
2
ω
,
t
0
=
0
,
t
f
=
0.25
a
n
d
τ
ma
x
=
1
0
0
0
.
The
c
o
effic
i
e
n
t
s
o
f
t
h
e
S
E
D
ar
e
set
a
s
E
=
0
.
7
a
n
d
λ
=
0.01
w
i
t
h
x
up
=
3
a
n
d
x
lo
=
-
3
.
N
o
t
e
t
h
a
t
t
h
e
i
n
i
t
i
a
l
d
e
s
i
g
n
v
a
r
i
a
b
l
e
i
n
T
a
b
l
e
I
I
i
s
s
e
l
e
c
te
d
base
d
on
t
he
v
al
ues
of
c
on
ve
nt
ion
a
l
P
I
c
ontro
l
l
e
r
i
n
[7]
.
F
or
e
xam
p
l
e
,
the
v
a
lue
of
t
h
e
p
r
o
p
o
r
t
i
ona
l
ga
in
f
rom
[7]
,
w
hic
h
i
s
0.00
6
9
,
is
m
ul
t
i
p
lie
d w
i
th
w
P
t
o o
b
t
ai
n t
h
e
fi
rst fi
ve
v
al
ues
o
f
ve
c
t
or
υ
(0)
in the
c
o
l
umn
4
of
T
able
II.
The
o
p
t
im
a
l
d
esi
gn
varia
b
l
e
ρ
*
R
υ
i
s
ta
b
u
la
te
d
in
T
a
b
l
e
2
.
Base
d
on
the
obta
i
ne
d
ρ
*
R
υ
,
the
resul
t
i
ng
P
i
ece
w
i
se
A
ff
ine
fu
nct
i
o
n
f
o
r
the
pro
port
i
ona
l
a
nd
i
n
te
gral
g
a
i
ns
c
a
n
b
e
o
b
se
rve
d
i
n
F
i
gur
es
3
a
nd
4,
r
e
s
pe
ct
i
v
e
l
y.
N
ot
e
t
h
a
t
,
the
pro
port
i
ona
l
g
a
in
r
equ
i
re
s
hi
gh
m
agn
i
tu
de
o
f
ga
i
n
f
or
t
he ang
u
l
a
r
v
e
l
oci
t
y
e
r
r
or
range
s
0
–
3
a
n
d
1
3
–
15.
M
ea
nw
h
ile,
t
h
e
inte
g
r
al
g
a
i
n
requ
ire
s
h
igh
m
a
gn
it
ude
o
f
ga
in
f
or
t
he
a
ng
u
l
ar
v
e
l
o
c
i
t
y
e
r
r
o
r
b
e
t
w
e
e
n
0
a
n
d
3
.
I
t
s
h
o
w
s
t
h
a
t
b
y
e
m
p
l
o
y
i
n
g
t
i
m
e
v
a
r
y
i
n
g
P
(
t
)
and
I
(
t
)
g
a
in
s
acc
ord
i
ng
t
o
t
h
e
cha
nge
s
o
f
e
rror,
it
w
ill
o
f
fer
m
o
re
r
oom
s
for
t
h
e
c
o
n
t
ro
l
l
e
r
i
m
p
rovem
e
nt.
More
over,
F
igure
s
5
a
n
d
6
s
how
the
r
e
s
p
o
n
ses
of
t
he
a
n
gul
a
r
v
e
l
oc
it
y
an
d
t
h
e
du
ty
r
ati
o
f
or
t
h
e
P
A
-P
I
contro
l
l
e
r
i
n
com
p
ar
is
on
t
h
e
con
v
e
n
t
i
ona
l
P
I
a
nd
S
igmo
i
d
-P
I
contro
l
l
ers.
N
ot
e
tha
t
,
t
h
e
r
e
fe
ren
c
e
i
s
r
epre
se
n
t
ed
b
y
t
h
e
do
t
b
l
ack
l
i
n
e,
t
h
e
PI
c
ont
r
o
lle
r
is
r
e
p
rese
nte
d
b
y
t
h
i
c
k
g
r
ey
line
,
t
he
s
igm
o
i
d
-ba
se
d
P
I
c
on
tro
l
l
e
r
is
r
epre
se
n
t
e
d
by
t
h
e
das
h
blac
k
l
i
ne
an
d
t
he
P
A
-
P
I
c
ontr
o
lle
r is r
epre
se
nte
d
b
y
t
h
e
th
ick
bl
a
ck li
n
e.
In gener
a
l, the r
espo
nse
s
c
l
a
r
i
fy tha
t
the
pro
p
o
sed
P
A
-P
I
base
d
S
E
D
yi
e
l
ds
b
e
t
ter
a
n
g
u
la
r
ve
loc
i
ty
t
ra
j
e
c
t
ory
trac
k
i
n
g
w
i
t
h
sl
igh
t
ly
m
i
n
imu
m
duty
rati
o t
h
a
n
o
t
h
er exis
t
i
ng m
e
t
h
ods. S
pe
c
i
fical
ly, from
t
h
e
m
a
gn
i
f
i
ed pic
ture, th
e
a
ctual
r
e
sponse of
y
(
t
)
is
m
uch
clo
s
er
t
o
the
re
fe
renc
e
r
(
t
)
t
h
an
o
t
h
e
r
c
ont
roll
e
r
s.
S
i
m
i
l
a
rl
y
,
t
h
e
r
es
po
nse
of
d
u
t
y
rati
o
o
f
the
PA-PI
controller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
141
9
– 1
426
1
424
is
s
li
g
h
tl
y
l
o
w
e
r
than
t
he
r
ece
nt
s
i
g
m
o
id
b
a
s
ed
P
I
contr
o
l
l
e
r.
This
i
s
s
u
p
por
ted
by
t
h
e
num
er
i
c
a
l
a
na
lys
i
s
o
f
the i
n
te
gr
al
s
q
u
ar
e
of
e
rror
and
in
p
u
t
as
t
a
b
ula
t
e
d
i
n
Tab
l
e
3.
I
t
i
s
s
how
n
tha
t
t
he
v
a
l
ue
s
of
t
he
i
n
t
e
g
r
a
l
squ
a
re
of
e
rror
and
inp
u
t
for
P
A
-
P
I
c
o
nt
roll
er are much lower than
o
t
h
er con
t
r
ol
l
e
rs.
Tab
l
e
2. P
A
-
P
I
de
s
ign
varia
b
l
e
s
υ
PA
-PI Pa
r
a
m
e
te
rs
x
(0)
)
0
(
10
)
0
(
x
υ
x*
*
10
*
x
υ
υ
1
P
c
1
-
1
.6
84
0
0.
020
7
-1.
0
1
8
7
0.
0958
υ
2
P
c
2
-1.
3
8
3
0
0.
041
4
-1.
3
4
6
7
0.
0450
υ
3
P
c
3
-1.
2
0
6
9
0.
062
1
-1.
3
8
8
7
0.
0409
υ
4
P
c
4
-1.
0
8
2
0
0.
082
8
-1.
3
1
2
3
0.
0487
υ
5
P
c
5
-0.
9
8
5
1
0.
103
5
-0.
9
7
4
2
0.
1061
υ
6
I
c
1
0.
0757
1
.
190
4
1.
5
320
34.
033
8
υ
7
I
c
2
0.
3767
2
.
380
8
1.
2
557
18.
018
3
υ
8
I
c
3
0.
5528
3
.
571
2
0.
8
146
6
.
5247
υ
9
I
c
4
0.
6778
4
.
761
6
0.
8
735
7
.
4739
υ
10
I
c
5
0.
7747
5
.
592
0
0.
3
712
2
.
3505
F
i
gure
3.
The
r
e
s
u
l
t
i
ng P
i
e
c
e
w
ise
A
ffi
ne
fu
n
c
t
i
on f
o
r
the
ga
i
n
P
(
t
)
F
i
gure
4.
T
he
r
esu
l
t
i
ng
P
i
ec
e
w
ise A
ffi
ne
f
u
n
ct
i
on for
the
ga
i
n
I
(
t
)
F
i
g
u
r
e
5
.
Resp
ons
es of t
h
e
an
gu
lar
vel
o
c
i
t
y
y
(
t
)
F
i
gure
6.
R
e
s
pons
e
s
o
f
the
an
gu
lar
vel
o
c
i
t
y
u
(
t
)
Ta
b
l
e
3.
P
e
rforma
n
ce
com
par
i
son
be
tw
ee
n
P
I
[7],
sigm
oid
b
a
sed
P
I
[19]
a
n
d
P
A-P
I
c
ontro
l
l
e
r
s
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A
pi
e
c
e
w
ise
a
f
f
i
ne P
I
c
ontr
o
l
l
e
r
for b
u
ck
c
o
n
v
erter ge
ner
a
te
d D
C
m
o
tor
(Mo
hd I
k
hm
i
l
F.
Mohd H
a
n
i
f)
1
425
C
ontrolle
r
P
I
[
7]
S
ig
m
o
id-
PI[
19]
P
A
-
P
I
25
0
0
2
)
(
.
dt
t
e
6.5190
0.027
8
0.0130
25
0
0
2
)
(
.
dt
t
u
0.0156
0
.016
2
0.0161
6.
CONCL
U
S
ION
Th
is
p
a
p
er
p
re
sen
t
s
a
P
i
e
c
e
w
i
s
e
A
f
fi
ne
P
ropor
ti
o
n
al-I
nte
g
ral
(P
A-PI)
contr
o
ller
b
a
sed
SED
f
o
r
buck
c
o
nv
e
r
t
e
r
g
e
ne
ra
t
e
d
D
C
m
ot
or.
It
j
u
s
t
i
f
i
e
s
tha
t
t
h
e
P
i
e
c
e
wi
se
A
ffine
P
r
op
o
r
ti
ona
l-Inte
gr
al
(
P
A
-
P
I)
c
ontr
o
l
l
er
has
i
m
pro
v
e
d
t
he
c
o
n
tr
ol
acc
urac
y,
i
n
term
s
of
t
he
r
esp
onse
s
o
f
t
he
a
n
g
u
l
a
r
veloc
ity
a
nd
duty
rat
i
o
i
np
ut,
a
n
d
t
h
e
int
e
g
r
al
s
qu
are
of
e
rro
r
a
n
d
i
np
ut
.
In
p
art
i
c
u
l
a
r,
t
h
e
P
A-P
I
contr
o
l
l
e
r
b
a
s
ed
S
ED
i
s
ab
le
t
o
c
l
ose
l
y
tra
c
k
the
desire
d
a
n
gu
lar
vel
o
c
i
ty
w
i
t
h
sma
l
l
d
u
t
y
ra
ti
o
inp
u
t
.
Th
is
fac
t
i
s
a
l
so
s
u
p
p
o
r
t
e
d
b
y
th
e
a
n
al
ys
is
o
f
t
h
e
in
t
e
gral
s
q
u
are
of
e
rr
o
r
a
nd
i
n
p
u
t
,
w
h
e
r
e
i
t
p
ro
duce
s
s
l
i
ght
ly
sma
l
le
r
va
lu
es
t
ha
n
the
c
o
n
v
en
t
i
o
n
a
l
P
I
an
d
the
sigm
oi
d
ba
se
d
P
I
c
ontro
l
l
ers.
T
he
nce,
t
h
i
s
fi
n
d
i
n
g
j
us
t
i
fies
t
h
e
e
ffe
ct
ive
n
e
ss
of
t
he
P
A-P
I
c
on
tro
l
le
r
in
offe
ri
ng m
o
re gene
r
ic c
l
a
ss o
f
v
ariab
l
e
stru
c
t
ure
PID
,
r
esult
i
n
g
in
m
or
e prosp
e
cts o
f
c
o
n
t
r
ol
ler
i
m
prove
me
n
t
.
ACKNOW
LEDG
E
MEN
T
S
The
a
u
th
or
w
oul
d l
i
ke
t
o e
x
press his t
h
a
nks
t
o
t
h
e
Resea
r
ch
a
nd
D
eve
l
o
p
m
e
nt D
e
p
artm
en
t un
der
the
gran
t
of RD
U
1
80
3
1
3
7
.
REFE
RENCES
[1]
F.
A
ntr
itter,
P
.
M
a
urer,
and
J.
R
eger,
“F
l
a
t
n
ess
ba
sed
control
of
a
b
uck
co
nv
erter
dri
v
en
D
C
mo
to
r,
”
in P
r
oc.
4
t
h
IFA
C
Sym
p
.
M
echa
t
ro
ni
c Syste
m
s
,
Heid
e
l
b
e
rg,
G
e
rm
any,
pp.
3
6
-
41
,
2
00
6.
[2]
J.
L
i
n
ares-Fl
o
res
and
H
.
S
i
r
a
-
Ram
i
re
z,
“
DC
m
o
t
or
v
elo
c
i
t
y
co
ntr
ol
t
hr
ou
gh
a
D
C
-
to
-DC
p
o
we
r
c
o
n
v
e
r
te
r,”
in
P
r
oc
.
IEEE 43
rd Con
f
. Deci
s
i
on
Contr
o
l
, A
t
l
an
t
i
s,
T
h
e
B
ahamas, vo
l
. 5
, p
p. 52
9
7
-5
30
2
,
2
0
0
4
.
[3]
J.
L
i
n
ares
-Flores
,
“
Co
nt
rol
su
ave
de
v
elo
c
idad
d
e
m
o
t
o
res
d
e
C
D
m
ed
ian
t
e
con
v
erti
do
res
d
e
pot
encia
CD/
C
D,”
Ph.D
. d
i
sserta
t
io
n
,
Secci´
o
n
de
M
ecatr´
onica
d
e
l
Dep
a
rtam
ento
d
e
In
gen
i
eria
E
l´
ec
tr
i
ca
del
C
I
NVE
S
TAVIP
N
,
M
e
xi
co
C
ity
,
Mexi
co,
2
00
6.
[4]
J.
L
in
ares
-Flo
res
and
H
.
S
ira-Ram
i
rez,
“
A
sm
ooth
s
t
art
e
r
f
o
r
a
DC
m
achi
n
e:
A
f
lat
n
ess
based
appro
ach,”
in
P
r
o
c
.
1
st
In
t. Conf. Elect
r.
Elect
ro
n
.
En
g
.
,
A
capu
l
co,
Mexi
co,
p
p.
5
8
9
-594,
2
0
0
4
.
[5]
J.
L
i
n
ares
-Flores
an
d
H.
S
ira-Ram
i
rez,
“
Sli
d
i
n
g
m
o
d
e
-del
ta
m
od
u
latio
n
GP
I
co
ntrol
of
a
D
C
mo
to
r
t
h
ro
ugh
a
b
u
c
k
con
v
erter,
”
in Proc.
2
nd
IFA
C
Sym
p
.
Syst.,
S
t
ruc
t
. Co
ntrol
,
O
a
xac
a
,
M
ex
ico,
p
p
.
405
-409
,
2
00
4.
[6]
H
.
E
l
F
a
d
i
l
a
n
d
F
.
G
i
r
i
,
“
A
c
c
o
u
n
t
i
n
g
o
f
D
C
-
D
C
p
o
w
e
r
c
o
n
v
e
r
t
e
r
d
ynamics
in
D
C
mot
o
r
velo
cit
y
a
d
a
pt
ive
con
t
rol,”
in
Pr
oc.
IEEE
In
t
.
Co
nf.
Contr
o
l
Ap
pl.
,
M
u
n
i
ch,
G
e
rm
any,
pp.
3
1
5
7
-
31
62
,
2
0
0
6
.
[7]
R.M
.
T.
R
aja
Ismai
l
,
M
.
A
.
A
hm
ad,
and
M
.
S.
R
am
li,
“
S
peed
c
o
n
trol
of
b
u
c
k-con
v
ert
e
r
dri
v
en
D
C
m
o
t
o
r
using
L
Q
R
and
P
I
:
A
com
p
arati
v
e
ass
e
s
s
m
e
nt,
”
i
n
Pro
c
. Int
e
rnationa
l Conf
erence
on
In
fo
rma
tion
Man
ag
e
m
e
n
t a
nd
En
gi
neeri
n
g
, pp
.
65
1
-6
55
, 20
0
9
.
[8]
R.
S
i
l
v
a
-Ort
igo
z
a,
J
.R.
Garci
a
-San
chez,
J
.
M
.
Alba
-M
art
i
nez,
V
.M
.
H
e
rnan
dez-Gu
zm´
a
n
,
M
.
M
a
rceli
n
o
-
Arand
a
,
H
.
Tau
d
,
and
R.
B
aut
i
st
a-Quintero,
“Two
-sta
ge
c
on
trol
d
e
s
ig
n
o
f
a
Bu
c
k
c
on
ve
rte
r
/DC
mo
to
r
system
w
ithout
veloc
i
t
y
measur
ements v
ia a Σ -
Δ
-mod
u
l
a
t
or,”
Math.
Prob
l
.
Eng
.
, v
ol
.
2
0
1
3
,
p
p
.
1-1
1
, 2
01
3.
[9]
M
.
Z.
M
.
T
u
m
ari,
M
.S
.
S
aeal
al,
M
.
R.
G
h
azali,
a
n
d
Y
.A.
W
a
h
a
b,
“
H-i
n
f
in
it
y
with
p
ol
e
placem
ent
c
o
nstrai
n
t
i
n
LM
I
regi
on
f
or
a
buc
k
-
con
v
erter
dri
v
en
D
C
m
o
t
o
r,
”
in
P
r
o
c
.
IE
EE
In
t.
Conf.
Po
wer
En
ergy
,
K
o
ta
K
i
n
ab
alu
S
a
bah,
Malaysia, p
p.
53
0
-53
5
, 20
1
2
.
[10]
H.
S
i
r
a-Ra
mi
rez
and
M
.
A.
O
liver-S
al
azar,
“
O
n
t
h
e
rob
u
st
c
on
tro
l
o
f
b
u
ck-co
n
v
e
rter
D
C-m
o
t
o
r
co
mb
in
ati
ons,”
IEEE Trans. P
o
wer
E
l
ectron.
,
v
o
l
.
2
8
,
n
o.
8
,
p
p
.
39
12-3
9
2
2
,
2
013.
[11]
O.
B
in
gol
a
nd
S
.
P
ac¸aci
,
“A
v
irt
u
al
l
abo
r
atory
for
neu
r
al
n
etw
ork
co
nt
roll
ed
D
C
m
o
t
o
rs
b
ased
on
a
DC-DC
bu
c
k
con
v
erter,
”
Int
.
J
.
E
n
g.
Educ.
,
vol.
28
,
n
o
.
3
,
p
p.
7
1
3
-72
3
,
201
2.
[12]
M
.
A
.
A
hm
ad,
R.M
.
T.
R
aj
a
Ism
a
il
,
and
M.S
.
R
am
li,
“Co
n
t
r
o
l
s
trat
e
gy
o
f
bu
c
k
c
on
vert
er
d
riv
e
n
DC
m
ot
or:
A
com
p
arat
iv
e assess
men
t
,
”
A
u
s
t
ral
i
a
n
J
.
B
a
si
c
Ap
pl
.
Sc
i
.
, vo
l
. 4
,
no
. 10
, p
p.
4
89
3
-
4
9
0
3
, 2
01
0.
[13]
M
.
A
.
A
h
m
ad
,
S.
A
zum
a
,
an
d
T.
S
u
g
i
e
,
“
P
erf
o
rmance
anal
ysi
s
o
f
m
o
del
-
free
P
I
D
t
u
n
i
ng
o
f
M
I
MO
s
y
s
t
e
m
s
b
as
ed
on
s
im
ult
a
neou
s
pert
urb
a
tio
n
stoch
a
st
ic
a
pp
roxi
m
a
ti
on,
”
E
x
per
t
Sys
t
ems
with
App
l
i
c
a
t
ions
,
vo
l.
4
1,
n
o
.
1
4
,
p
p.
63
61
-637
0,
2
0
1
4
.
[14]
I.
B
o
i
ko
,
“
V
ariab
l
e-st
ruct
ure
PID
con
t
rol
l
er
f
or
l
evel
p
roces
s,
”
Cont
ro
l E
ngin
eerin
g
Pra
c
ti
ce
,
v
o
l
.
2
1
,
n
o
.
5
,
p
p
.7
00
-70
7
, 2
01
3.
[15]
A.
At
e
s,
B
.
B
.
Alago
z
,
C.
Yerog
lu
,
an
d
H
.
A
li
soy,
“
Si
g
m
o
i
d bas
e
d
P
ID
c
ontrol
ler
im
p
l
em
en
t
a
tion
f
o
r
rotor
contro
l
,
”
Eu
ro
pean
Control
Confer
e
n
ce
(
E
CC)
,
p
p
. 4
58
-4
6
3
, 2
01
5.
[16]
M
.
R.
G
hazal
i, M.
A
.
Ah
m
a
d
,
M
.F.
M
a
t
J
u
s
o
f,
R
.M.T.
Raja
I
sm
ail
,
“
A
dat
a
-dri
ven
neu
r
oen
doc
ri
ne-P
ID
c
on
tro
ller
f
o
r
u
n
d
e
ract
uat
e
d
s
y
s
t
em
b
as
ed
o
n
s
a
fe
e
x
p
eri
m
entat
i
o
n
d
yna
m
i
cs
,”
i
n
Proc
.
of
14
th
IEE
E
Co
llo
qu
iu
m on
S
i
gn
al
Pr
ocessing and Its App
licati
o
n
s
,
p
p
.
6
1-6
6
, 2
01
8.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
4
1
9
–
1
426
1
426
[17]
M
.
A
.
S
h
a
m
s
e
l
d
i
n
,
M
.
S
a
l
l
a
m
,
A
.
M
.
B
a
s
s
i
u
n
y
,
a
n
d
A
.
A
.
G
h
a
n
y
,
“
A
n
o
v
e
l
se
lf-
t
un
ing
fra
c
t
io
na
l
or
de
r
PID
c
o
ntr
o
l
b
a
sed
on
opt
im
a
l
m
odel
re
f
e
renc
e
ad
apti
ve
s
ys
tem
,
”
In
t J P
o
wer E
l
ect
ronics
&
Dr
ive S
y
stem
,
vol.
10
,
no.
1
,
pp.
23
0 –
24
1,
20
1
9
.
[18]
P
.
V.
R
am
kumar,
M
.
S.
K
alav
ath
i
,
“
F
racti
ona
l
Orde
r
P
I
D
Co
nt
roll
e
d
I
n
t
erleav
ed
B
oo
st
c
o
n
v
e
rter
F
ed
S
hu
nt
A
c
t
i
v
e
Filt
er
System,”
In
ter
n
a
t
i
onal
Jo
ur
na
l o
f
Power
El
ectr
onics an
d
D
r
i
ve System
,
vol.
9,
no.
1
,
p
p
.
126-1
38,
2
0
1
8
.
[19]
M
.
A.
A
hmad
,
R.M
.
T.
R
a
j
a
Ismai
l
,
“
A
d
at
a-driven
s
igm
o
id
-based
P
I
c
o
n
trolle
r
for
bu
c
k
-c
on
verte
r
p
o
w
e
r
e
d
D
C
moto
r
,
”
in
Pr
oc.
of
I
EEE Sympo
s
ium
on Co
m
p
uter
App
l
ication
s
and
I
n
dustr
i
al El
ectron
i
cs
,
pp
.
81
-8
6
,
2
017
.
[20]
J
.
R.
M
arden
,
H
.
Yo
ung
,
G
.
A
rslan
,
a
nd
J
.
S
h
a
m
m
a
,
“P
ayo
f
f
based
dynamics
f
or
m
ulti-pl
ayer
w
eakly
acycl
ic
ga
me
s,”
in
Proc
.
of
46
th
I
EEE Conf
erence on Deci
s
i
on
and Contr
o
l
,
p
p
.
342
2–
34
27,
2
0
0
7
.
[21]
J
.
R
.
M
a
r
d
e
n
,
S
.
D
.
R
u
b
e
n
,
a
n
d
L
.
Y
.
P
a
o
,
“
A
m
o
d
e
l
-
f
r
e
e
a
p
p
r
o
a
c
h
t
o
wind
f
a
r
m
c
o
ntrol
us
in
g
g
a
me
t
he
o
r
e
t
ic
m
e
t
hod
s,
”
IEEE T
r
ans
actio
ns
on
Con
t
r
o
l
Systems T
echn
o
l
o
g
y
, v
ol
. 2
1, no
. 4
, pp
.
12
07
-12
1
4
, 20
1
3
.
[22]
M.F
.
F
.
K
ameru
l
B
i
eza
,
N.S.
A
b
d
u
l
Sh
uk
o
r
, M
.
A
.
Ah
mad
, M
.H.
Suid
,
M
.R
.
Gh
az
al
i,
M
.
F
.
Mat
Ju
so
f,
“
A
Si
mp
l
i
fy
F
u
zzy
L
ogi
c
Con
t
roll
er
B
ased
S
af
e
Ex
perim
e
ntation
D
ynami
cs
f
o
r
P
a
nt
og
raph-Cat
e
nary
S
ys
te
m
,
”
In
do
nesi
an
Jou
r
n
a
l
o
f
El
ectr
i
cal
E
n
g
i
neer
in
g
a
nd Com
puter
Science
, Vo
l
. 1
4
, no
. 2
,
2
0
1
9
.
[23]
N.S
.
A
b
d
u
l
S
hu
ko
r,
M
.A
.
Ah
ma
d
,
“
Dat
a
-driven
PID
controller
tuni
ng
b
ased
o
n
saf
e
e
xp
e
r
i
m
entatio
n
dy
nami
cs
f
or
co
nt
rol
o
f
d
ou
ble
-
p
e
nd
ul
um
-ty
p
e
o
v
erh
ead
c
r
a
n
e
,
”
L
ectu
r
e Notes in M
echa
n
i
c
al En
gi
neeri
n
g
,
p
p
.
295
-30
4
,
20
18.
[24]
M
.
R.
G
hazal
i, M.
A
.
A
h
m
a
d,
R
.M
.T.
Raj
a
I
sm
ail,
"
Dat
a
-Driv
e
n
P
I
D
c
o
nt
rol
f
o
r
DC/
D
C
buck-b
o
o
s
t
c
o
nv
erter-
i
n
v
e
rter-DC
Moto
r
b
a
sed
on
s
afe
exp
e
rim
e
n
t
ation
dy
nam
i
cs",
in
Proc
.
of
I
EEE In
ter
n
at
i
o
na
l
Confer
ence
on
Syst
ems, Pr
oces
s
and
Control
,
2
0
18
, Accep
ted
.
[25]
M
.
R.
G
h
azali
, M
.A.
A
h
m
a
d,
R
.M
.T.
Raja
I
sm
ail, "D
a
ta-dri
v
e
n
Neu
r
o
e
nd
oc
rin
e
-PID
T
un
in
g
Ba
se
d
o
n
S
a
f
e
E
x
p
e
ri
m
e
n
t
ati
on
Dy
nam
i
cs
f
or Con
trol
o
f
TIT
O
C
o
u
p
l
ed
T
an
k
Sy
st
e
m
with
S
toc
h
asti
c
Inpu
t
Delay",
L
ect
ur
e
Notes
in
M
e
c
h
an
ic
al
E
n
gine
e
r
in
g
, 2
01
9.
BIOGRAPHI
E
S
OF
AUT
HORS
Ir.
M
oh
d
Ikh
m
i
l
F
adzri
zan
M
o
h
d
Han
i
f
is
a
P
ro
f
e
ss
io
na
l
En
g
i
neer
w
it
h
th
e
Board
o
f
E
ng
i
n
eers
Mal
a
ysia
(
BE
M)
a
nd
a
M
ember
of
I
nstitution
o
f
E
ngi
n
eers
Mala
ysi
a
(IE
M)
.
H
e
i
s
current
ly
a
n
In
st
ru
m
e
nt
E
n
g
i
n
eer
o
f
O
p
erat
io
na
l,
I
n
t
egrit
y
a
n
d
E
ng
ineering
D
ep
art
m
ent
at
P
etrof
ac
M
a
l
a
ys
ia.
Ir.
I
k
h
mil
h
o
lds
Bachel
or
o
f
El
ectrical
E
n
g
in
eerin
g
(
Control,
I
nstrumentation
and
Au
to
ma
t
i
o
n)
f
r
o
m
U
n
iv
e
r
s
i
ti
T
e
k
ni
k
a
l
M
a
l
a
ys
ia
,
M
e
l
a
k
a
(
U
Te
M
)
i
n
20
0
7
.
H
e ha
s
m
o
re t
han
10
ye
a
r
s
of
w
o
r
ki
ng
e
x
p
e
r
ie
nc
e
in
I
nstrume
n
ta
t
i
o
n
a
n
d
Co
ntrol
e
n
gi
n
eerin
g
in
o
i
l
,
g
a
s
and
pe
troc
h
e
mic
a
l
i
n
d
u
stry
a
nd
a
lso
a
l
mo
st
2
y
e
a
r
s
of
w
o
r
k
i
ng
e
xp
er
i
e
nces
a
s
S
e
n
i
or
L
ectu
r
er
i
n
higher
e
ducat
ion
ins
titut
i
on
m
aj
o
r
i
n
Electri
cal
a
n
d
E
lectroni
c
s
(E&E)
eng
i
n
eering.
H
i
s
c
urrent
res
earch
i
n
t
erest
i
s
d
at
a
d
r
iven
p
iece
wi
se
a
ffi
ne
P
ID
c
on
tro
l
l
er
b
as
ed
o
n
S
a
f
e
E
x
p
erim
ent
a
ti
on
Dy
na
mic
s
a
lg
or
i
t
h
m
.
M
o
hd
H
elmi
S
u
i
d
recei
ved
the
B.E
n
g
(Ho
n
s
.
)
in
E
l
ectri
c
a
l
and
El
ectronics
E
n
g
ineeri
ng
f
r
o
m
U
n
i
v
ersiti
T
eknik
a
l
M
e
lak
a
i
n
20
07
.
In
2
0
1
4
,
h
e
rec
e
i
v
es
M
.
S
c
f
rom
S
c
ho
ol
o
f
El
e
c
t
r
on
ic
a
nd
E
l
ect
rical
E
ng
in
eeri
n
g
,
U
n
i
vers
it
y
S
a
in
s
M
a
lay
s
i
a
,
P
e
nang
.
He
i
s
curren
tly
,
a
lect
urer
i
n
F
acu
lt
y
of
E
lectri
cal
a
n
d
E
l
ectron
i
cs
E
n
g
in
eerin
g,
U
niv
e
rsi
t
y
M
al
ays
i
a
P
a
han
g
(
UM
P
)
.
His
cu
rrent
r
esearch
i
nteres
ts
a
re
d
ig
ital
i
m
age
p
r
o
ces
si
ng,
v
isi
o
n
f
or
r
o
b
o
tic
s
a
p
plic
a
t
io
n
a
n
d
co
m
p
u
t
ati
o
n
a
l i
n
t
e
ll
ig
e
n
ce.
M
o
hd
A
shra
f
A
h
m
a
d
recei
ved
h
i
s
first
deg
r
ee
i
n
B.Eng
E
l
ect
rical
M
echat
roni
cs
a
nd
M
ast
e
r
D
e
gree
in
M
.En
g
M
ech
atro
nics
a
n
d
A
ut
o
m
at
ic
C
o
n
t
r
ol
f
rom
Uni
v
ers
it
y
of
T
echno
lo
g
y
M
a
l
a
ys
ia
(
UTM)
i
n
2
006
a
nd
2
008
,
res
p
ecti
v
ely.
I
n
2
0
1
5
,
h
e
r
ece
ived
a
P
h.D
in
I
n
f
or
matics
(S
y
s
t
e
ms
S
c
i
ence)
f
rom
Kyoto
Un
iv
ersi
ty.
Curren
tl
y,
h
e
i
s
a
l
e
c
tu
rer
in
F
acul
t
y
o
f
E
l
ectrical
an
d Elect
ron
i
cs En
g
in
eerin
g
, Un
i
vers
it
y M
a
l
a
ysia P
ah
a
n
g (UM
P
).
His
current
researc
h
i
nteres
ts
are
m
o
del-f
r
ee
con
t
ro
l,
c
o
n
trol
o
f
mech
atro
nic
s
y
s
t
e
m
s,
non
li
n
e
ar
s
yst
e
m
identificat
ion
a
n
d
v
i
b
r
ati
on
cont
ro
l.
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