I
n
t
e
r
n
at
ion
al
Jou
r
n
al
of
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lec
t
r
ical
an
d
Com
p
u
t
e
r
E
n
gin
e
e
r
in
g
(
I
JE
CE
)
Vol.
15
,
No.
1
,
F
e
br
ua
r
y
20
25
,
pp.
252
~
259
I
S
S
N:
2088
-
8708
,
DO
I
:
10
.
11591/i
jec
e
.
v
15
i
1
.
pp
2
52
-
259
252
Jou
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Ar
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AB
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y
:
R
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ived
M
a
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2024
R
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vis
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p
11,
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T
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p
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f
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g
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p
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a
t
i
o
n
s
a
n
d
h
i
g
h
co
n
t
ro
l
accu
racy
.
K
e
y
w
o
r
d
s
:
As
tatis
m
C
ontr
ol
Dis
c
r
e
ti
z
a
ti
on
Dyna
mi
c
s
M
odulation
Th
i
s
i
s
a
n
o
p
en
a
c
ces
s
a
r
t
i
c
l
e
u
n
d
e
r
t
h
e
CC
B
Y
-
SA
l
i
ce
n
s
e.
C
or
r
e
s
pon
din
g
A
u
th
or
:
M
us
taf
a
qul
Us
a
nov
De
pa
r
tm
e
nt
of
Automation
a
nd
C
ontr
ol
of
T
e
c
hnol
ogica
l
P
r
oc
e
s
s
e
s
a
nd
P
r
oduc
ti
on
,
F
a
c
ult
y
of
C
ott
on
I
ndus
tr
y
T
e
c
hnology
,
T
a
s
hke
nt
I
ns
ti
tut
e
of
T
e
xti
le
a
nd
L
ight
I
ndus
tr
y
T
a
s
hke
nt,
Uz
be
kis
tan
E
mail:
us
a
nov6063334@gmail.
c
om
1.
I
NT
RODU
C
T
I
ON
One
of
the
ur
ge
nt
c
ha
ll
e
nge
s
of
moder
n
c
ontr
ol
theor
y
is
to
e
ns
ur
e
the
r
e
quir
e
d
be
ha
vior
of
the
c
ontr
ol
s
ys
tem
f
or
dyna
m
ic
plants
,
the
pa
r
a
mete
r
s
of
whic
h
c
ha
nge
wide
ly
in
the
pr
oc
e
s
s
of
the
f
un
c
ti
oning
of
the
s
ys
tem
[
1
]
–
[
4]
.
T
he
s
tanda
r
d
c
ont
r
ol
law
s
a
r
e
wide
ly
us
e
d
in
indus
tr
y,
a
lt
hough
they
a
r
e
r
e
latively
s
im
ple
f
or
their
im
pleme
ntation
in
c
ontr
ol
pr
o
blems
a
nd
a
r
e
r
e
li
a
ble,
they
a
r
e
li
ne
a
r
a
nd
ke
e
p
their
pa
r
a
mete
r
s
c
ons
tant
thr
oughou
t
the
e
nti
r
e
f
unc
ti
o
ning
c
yc
le
of
the
plant.
On
the
other
ha
nd
,
e
xis
ti
ng
a
nd
us
ing
indus
tr
ial
unit
s
a
r
e
nonli
ne
a
r
a
nd
non
-
s
tationar
y,
whic
h
s
igni
f
ica
ntl
y
c
ompl
ica
tes
the
s
olut
ion
of
the
pr
oblem
of
pr
oc
e
s
s
c
ontr
ol
in
r
e
a
l
t
im
e
.
E
xis
ti
ng
methods
f
or
r
e
s
e
a
r
c
hing
the
dyna
mi
c
s
of
a
c
ontr
ol
s
ys
tem
with
a
puls
e
-
width
modul
a
ti
on
(
P
W
M
)
modul
a
tor
a
r
e
ba
s
e
d
on
r
e
c
ur
r
e
nt
meth
ods
or
methods
us
ing
pha
s
e
plane
c
onc
e
pts
[
5]
–
[
7]
.
At
pr
e
s
e
nt,
ther
e
a
r
e
a
lar
ge
number
of
s
ys
tems
f
or
r
e
s
e
a
r
c
h
of
whic
h
we
ll
-
known
a
ppr
oa
c
he
s
a
r
e
not
s
u
it
a
ble,
or
f
unda
menta
l
dif
f
icult
ies
a
r
is
e
a
s
s
oc
iate
d
with
non
-
s
tanda
r
d
ope
r
a
ti
ng
modes
of
puls
e
-
width
modul
a
tor
s
.
I
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
Digit
al
adapt
ive
c
ontr
ol
w
it
h
puls
e
w
idt
h
modula
t
ion
of
s
ignal
s
(
I
s
amiddin
Siddi
k
ov
)
253
a
ddit
ion,
in
mul
ti
dim
e
ns
ional
c
ontr
ol
s
ys
tems
with
P
W
M
modul
a
tor
s
,
puls
e
r
e
pe
ti
ti
on
pe
r
iod
s
c
a
n
be
dif
f
e
r
e
nt,
that
is
,
the
modu
lator
ope
r
a
ti
ng
modes
a
r
e
a
s
ync
hr
onous
[
8
]
.
I
n
thi
s
c
a
s
e
,
the
r
e
s
e
a
r
c
h
methods
us
e
d
e
nc
ounter
s
ome
tr
oubles
a
s
s
oc
iate
d
with
t
he
c
a
lcula
ti
on
of
ou
tput
va
r
iable
s
f
r
om
the
mo
dulation
c
ha
r
a
c
ter
is
ti
c
s
of
pu
ls
e
e
leme
nts
,
whic
h
be
c
ome
s
a
n
a
ddit
ional
s
our
c
e
of
di
f
f
iculti
e
s
whe
n
s
tud
ying
the
ope
r
a
ti
ng
modes
of
pu
ls
e
pa
r
ts
of
the
c
ontr
ol
s
ys
tem
[
9]
–
[
12]
.
I
n
s
uc
h
s
it
ua
ti
ons
,
the
mos
t
pr
omi
s
ing
a
r
e
the
a
ppli
c
a
ti
ons
of
a
da
pti
ve
methods
ba
s
e
d
on
the
identif
ica
ti
on
o
f
the
c
ont
r
ol
plant
[
13]
–
[
16
]
.
T
h
e
dis
a
dva
ntage
s
of
thi
s
a
ppr
oa
c
h
a
r
e
the
c
ompl
e
xit
y
of
im
pleme
nti
ng
the
identif
ica
ti
on
p
r
oc
e
dur
e
,
r
e
qui
r
i
ng
lar
ge
c
omput
a
ti
ona
l
c
os
ts
a
nd
li
mi
ted
pos
s
ibi
li
ti
e
s
f
or
c
ha
nging
the
dyna
mi
c
pr
ope
r
ti
e
s
of
the
c
ontr
ol
s
ys
tem
[
17]
–
[
19]
.
Anothe
r
dis
a
dva
ntage
of
us
in
g
typi
c
a
l
li
ne
a
r
r
e
gulation
law
s
in
indus
tr
y
is
the
pr
e
s
e
nc
e
of
pha
s
e
de
lay
a
nd
high
s
e
ns
it
ivi
ty
to
int
e
r
f
e
r
e
nc
e
.
T
o
r
e
duc
e
thes
e
dis
a
dva
ntage
s
va
r
ious
methods
a
r
e
us
e
d,
s
uc
h
a
s
including
a
pha
s
e
-
a
he
a
d
f
il
ter
in
the
r
e
gulator
,
c
or
r
e
c
ti
ng
the
p
r
ope
r
ti
e
s
of
the
r
e
gulato
r
[
20
]
,
[
21
]
.
I
n
thi
s
c
a
s
e
,
in
the
ge
ne
r
a
ll
y
a
c
c
e
pted
s
c
he
me
f
or
c
onve
r
ti
ng
the
c
ont
r
ol
s
ignal
(
f
r
om
a
digi
tal
r
e
pr
e
s
e
ntation
int
o
a
pu
ls
e
-
width
s
ignal
of
a
given
powe
r
)
,
it
is
a
s
s
umed
that
a
puls
e
-
width
(
P
W
M
)
s
ignal
is
ge
ne
r
a
ted,
pr
opor
ti
ona
l
to
the
c
a
lcula
ted
va
lue
by
the
input
s
ignal,
a
nd
ga
in
o
f
the
r
e
c
e
ived
s
ignal.
On
the
other
ha
nd,
the
r
e
qui
r
e
d
P
W
M
s
ignal
is
r
e
pr
e
s
e
nted
by
a
s
e
que
nc
e
of
“
one
s
”
a
nd
“
z
e
r
os
”
with
a
g
iven
ope
r
a
ti
ng
c
yc
le
a
nd
a
f
r
e
que
nc
y
not
e
xc
e
e
ding
the
c
ontr
oll
e
r
f
r
e
que
nc
y,
whic
h
c
a
n
be
f
or
med
by
s
of
twa
r
e
a
t
the
output
of
the
mi
c
r
oc
ontr
o
ll
e
r
(
M
K)
.
T
his
l
e
a
ds
to
r
e
s
ult
s
in
lowe
r
ha
r
dwa
r
e
c
os
ts
a
nd
i
nc
r
e
a
s
e
d
r
obus
tnes
s
of
the
e
nti
r
e
c
ont
r
ol
s
ys
tem.
W
it
h
thi
s
a
ppr
oa
c
h,
the
M
K
doe
s
not
c
a
lcula
te
the
c
ontr
ol
s
ignal
it
s
e
lf
;
it
c
a
lcula
tes
the
duty
c
yc
le
of
the
a
ppr
op
r
iat
e
P
W
M
s
ignal
unde
r
the
input
s
ignal.
2.
M
E
T
HO
D
L
e
t
the
dyna
mi
c
s
of
a
li
ne
a
r
s
tationar
y
dis
c
r
e
t
e
c
ontr
ol
s
ys
tem
be
de
s
c
r
ibed
by
a
s
ys
tem
of
dif
f
e
r
e
nti
a
l
e
qua
ti
ons
:
x
(
i
+
1
)
=
Ax
(
i
)
+
Bu
(
i
)
;
y
(
i
)
=
Cx
(
i
)
(
1)
whe
r
e
,
x
∈
R
n
,
u
∈
R
m
,
y
∈
R
r
,
(
r
<
n
)
–
ve
c
tor
s
of
the
s
tate
,
c
ont
r
oll
e
d
a
nd
mea
s
ur
e
d
output
s
,
r
e
s
pe
c
ti
ve
ly.
A,
B
,
C
-
matr
ice
s
of
the
a
ppr
opr
iate
s
ize
s
of
the
obs
e
r
ve
d
a
nd
c
ontr
ol
led
in
f
luenc
e
s
.
I
t
is
r
e
qui
r
e
d
t
o
f
ind
a
n
a
lgor
it
hm
f
or
c
a
lcula
ti
ng
the
duty
c
yc
le
(
)
of
the
c
ontr
ol
P
W
M
s
ignal
in
thi
s
a
wa
y
that
the
c
los
e
d
-
loop
c
ontr
ol
s
ys
tem
is
s
us
taina
ble,
a
ll
owing
the
c
ontr
ol
s
ys
tem
to
be
given
the
p
r
ope
r
ti
e
s
o
f
As
tatis
m
a
nd
e
ns
ur
ing
the
ne
c
e
s
s
a
r
y
qua
li
ty
of
tr
a
ns
ient
pr
oc
e
s
s
e
s
dur
in
g
s
tep
c
ha
nge
s
in
e
xt
e
r
na
l
inf
luenc
e
s
.
I
t
is
known
that
the
duty
c
yc
le
of
a
puls
e
-
width
modul
a
ted
s
ignal
de
pe
nds
on
the
puls
e
dur
a
ti
on
(
)
a
nd
the
puls
e
r
e
pe
t
it
ion
pe
r
iod
a
c
c
or
ding
to:
(
)
=
⁄
.
T
a
king
thi
s
int
o
a
c
c
ount,
t
he
dis
c
r
e
te
model
o
f
the
P
W
M
s
ignal
c
a
n
be
r
e
pr
e
s
e
nted
by
a
dif
f
e
r
e
nc
e
e
qua
ti
on
of
the
f
oll
owi
ng
f
or
m:
(
+
1
)
=
(
)
,
(
2)
whe
r
e
,
(
)
-
dis
c
r
e
te
c
ontr
ol
s
ignal.
I
n
thi
s
c
a
s
e
,
if
take
in
to
a
c
c
ount
that
a
r
e
c
tangula
r
s
ignal
is
s
uppli
e
d
to
the
input
o
f
the
P
W
M
unit
,
a
nd
the
a
ve
r
a
ge
va
lue
of
the
c
ontr
ol
s
ignal
f
or
th
e
pe
r
iod
unde
r
c
ons
ider
a
ti
on
is
de
ter
m
ined
a
t
the
output
,
then
the
P
W
M
model
c
a
n
be
r
e
pr
e
s
e
nted
a
s
a
li
ne
a
r
-
dif
f
e
r
e
nc
e
c
ontr
ol
of
the
f
ir
s
t
or
de
r
,
i
.
e
.
(
+
1
)
+
(
)
=
(
)
,
whe
r
e
,
-
ti
me
c
ons
tant,
c
ha
r
a
c
ter
izing
the
iner
ti
a
of
the
p
r
oc
e
s
s
.
C
ons
ider
s
olvi
ng
the
p
r
oblem
of
r
e
s
e
a
r
c
hing
the
dyna
mi
c
s
of
a
c
ontr
ol
s
ys
tem
with
a
puls
e
-
width
modul
a
tor
.
T
he
c
ontr
ol
s
ys
tems
with
puls
e
width
modul
a
ti
on
be
long
to
the
c
las
s
of
no
nli
ne
a
r
s
ys
tems
.
I
n
thi
s
c
a
s
e
,
the
puls
e
-
width
mod
ulator
in
F
igur
e
1
is
one
of
the
main
e
leme
nts
of
moder
n
mi
c
r
oc
ontr
oll
e
r
s
int
e
nde
d
to
c
ontr
o
l
tec
hnologi
c
a
l
plants
.
T
he
c
a
lcula
ti
on
of
the
c
ontr
ol
s
ignal
f
or
the
P
W
M
c
ir
c
uit
is
c
a
r
r
ied
out
a
c
c
or
ding
to
the
f
ol
l
owing
r
e
c
ur
r
e
nc
e
r
e
lation
[
22]
:
∑
+
1
=
+
1
−
+
1
,
(
3)
+
1
=
+
∑
/
0
,
(
4)
+
1
>
,
ℎ
+
1
=
,
+
1
<
−
,
ℎ
+
1
=
−
,
+
1
<
∧
+
1
>
0
∧
≤
0
,
ℎ
+
1
=
0
,
+
1
=
+
1
>
−
∧
+
1
<
0
∧
≥
0
,
ℎ
+
1
=
0
,
+
1
=
(
5)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
15
,
No.
1
,
F
e
br
ua
r
y
20
25
:
252
-
259
254
w
he
r
e
+
1
is
t
he
in
pu
t
s
ig
na
l
o
f
t
he
mo
du
la
to
r
,
+
1
is
th
e
ou
t
pu
t
s
ig
na
l
o
f
th
e
m
od
u
la
to
r
.
is
th
e
o
ut
pu
t
s
ig
na
l
o
f
lev
e
l
,
li
mi
te
d
b
y
r
e
la
y
e
l
e
m
e
n
t
,
=
−
,
a
r
e
th
e
r
e
la
y
e
le
me
nt
of
the
de
a
d
z
o
ne
,
is
t
he
p
ul
s
e
d
ur
a
t
io
n
,
+
1
is
th
e
ou
tp
u
t
s
ig
na
l
o
f
t
he
m
od
u
lat
o
r
i
nt
e
g
r
a
ti
ng
e
le
men
t
.
0
is
t
he
ti
me
c
ons
ta
nt
of
th
e
mo
du
la
to
r
i
n
te
gr
a
t
in
g
e
l
e
m
e
n
t
,
+
1
is
the
output
s
ignal
of
the
s
u
mm
a
ti
on
e
leme
nt.
T
he
p
r
inciple
of
ope
r
a
ti
on
o
f
th
e
modul
a
tor
is
to
tr
a
ns
f
or
m
the
input
s
ignal,
i
.
e
.
e
r
r
o
r
s
ignal
int
o
a
s
e
que
nc
e
of
r
e
c
tangula
r
puls
e
s
.
I
n
thi
s
c
a
s
e
,
the
dur
a
ti
on
o
f
the
r
e
c
tangula
r
s
ignal
is
d
ir
e
c
tl
y
pr
opor
ti
ona
l
to
the
magnitude
o
f
the
e
r
r
or
s
ignal
,
a
s
s
hown
in
F
igur
e
2.
He
r
e
F
igur
e
2
(
a
)
a
s
a
wtooth
s
ignal
a
nd
F
igur
e
2(
b)
a
n
output
s
ignal
with
P
W
M
.
F
igur
e
1.
T
he
s
tr
uc
tur
a
l
s
c
he
me
of
the
modul
a
to
r
:
(
s
umm
a
ti
on
ope
r
a
ti
on)
;
(
int
e
gr
a
ti
on
ope
r
a
ti
on)
;
a
nd
(
li
m
it
ing
the
c
ontr
ol
s
ignal
of
a
r
e
lay
e
leme
nt
with
a
hys
ter
e
s
is
c
ha
r
a
c
ter
is
ti
c
)
(
a
)
(
b)
F
igur
e
2.
S
ignal
c
onve
r
s
ion
us
ing
P
W
M
:
(
a
)
s
a
wtooth
s
ignals
a
nd
(
b)
modul
a
ti
on
ou
tput
s
ignals
I
n
a
c
ontr
ol
s
ys
tem,
the
e
r
r
or
s
ignal
is
de
ter
mi
ne
d
by
the
dif
f
e
r
e
nc
e
be
twe
e
n
the
given
va
lue
a
nd
the
c
ur
r
e
nt
va
lue
of
the
c
ontr
oll
e
d
p
r
oc
e
s
s
.
T
he
output
s
ignal
of
the
c
ontr
o
l
plant
is
us
ua
ll
y
mea
s
ur
e
d
by
a
s
e
ns
or
,
a
nd
in
the
a
bs
e
nc
e
of
a
s
e
ns
or
,
the
va
lues
of
the
output
s
ignal
a
r
e
de
ter
mi
ne
d
f
r
om
the
mathe
matica
l
model
of
the
c
ontr
ol
plant.
I
n
thi
s
c
a
s
e
,
us
ing
the
c
onvolut
ion
theor
e
m,
the
va
lue
of
the
output
s
ignal
of
the
c
ontr
ol
plant
a
t
e
a
c
h
t
im
e
s
tep
is
c
a
lcula
ted
by
(
)
=
∫
(
)
(
−
)
0
,
whe
r
e
(
)
-
we
ight
f
unc
ti
on
,
de
ter
mi
ne
d
by
the
tr
a
ns
f
e
r
f
unc
ti
on
o
f
the
p
lant;
(
−
)
-
the
input
s
ignal
o
f
the
p
lant.
T
he
a
lgor
it
hm
ge
ne
r
a
tes
a
s
a
wtooth
s
ignal,
whic
h
is
c
ompar
e
d
with
the
e
r
r
or
s
ignal.
I
f
the
e
r
r
or
s
ignal
de
c
r
e
a
s
e
s
,
then
the
int
e
gr
a
tor
s
lows
down
the
gr
owth
of
the
e
r
r
o
r
s
ignal
a
nd
ove
r
s
hoots
the
tr
a
ns
ient
r
e
s
pons
e
of
the
c
ontr
ol
s
ys
tem.
T
he
e
r
r
or
s
ignal
c
ompens
a
ti
on
de
pe
nds
on
the
ti
me
c
on
s
tant
.
of
the
plant.
T
he
.
va
lue
is
a
c
c
e
pted
to
be
e
qua
l
to
the
puls
e
d
ur
a
ti
on
a
t
e
a
c
h
c
yc
le.
T
o
li
mi
t
the
outpu
t
s
ys
tem
of
the
c
ontr
oll
e
r
,
a
li
mi
tat
ion
on
the
dif
f
e
r
e
nti
a
ti
ng
c
omp
one
nt
in
the
f
or
m
[
,
−
]
is
us
e
d.
T
he
modul
a
to
r
ope
r
a
ti
on
a
lgo
r
it
hm
is
a
s
f
oll
ows
:
A
s
a
wtooth
s
ignal
is
s
uppli
e
d
to
the
modul
a
tor
,
whic
h
is
c
ompa
r
e
d
with
the
c
ont
r
ol
e
r
r
o
r
s
ignal.
I
f
the
c
ont
r
ol
s
ignal
is
gr
e
a
ter
than
the
s
ignal
f
or
m
e
d
in
the
a
lgor
it
hm,
then
the
outpu
t
is
logi
c
a
l
1,
c
or
r
e
s
pon
ding
to
the
s
upply
volt
a
ge
,
other
wis
e
0.
I
t
s
hould
be
noted
that
the
pr
opos
e
d
a
lgor
it
hm
f
or
c
a
lcula
ti
ng
the
va
l
ue
of
the
P
W
M
modul
a
tor
c
ontr
ol
s
ignal
,
im
plem
e
nted
in
mi
c
r
oc
ontr
oll
e
r
s
,
a
ppli
e
s
to
both
one
-
dim
e
ns
ional
a
nd
mul
ti
dim
e
ns
ional
c
ontr
ol
s
ys
tems
.
L
e
t
a
mul
ti
dim
e
ns
ional
c
ontr
ol
s
ys
tem
c
ons
is
t
of
two
pa
r
ts
,
including
puls
e
-
width
(
P
W
M
)
modul
a
to
r
s
a
nd
a
li
ne
a
r
c
onti
nuous
pa
r
t
of
the
s
ys
tem.
T
he
dur
a
ti
on
o
f
th
e
c
ur
r
e
nt
puls
e
va
lues
a
t
the
output
of
e
a
c
h
mod
ulator
is
de
ter
mi
ne
d
a
s
=
{
[
(
)
]
[
(
)
]
≤
;
[
(
)
]
>
,
,
whe
r
e
is
s
tep
dis
c
r
e
ti
z
a
ti
on
of
a
c
onti
nuous
s
ignal
a
t
the
modul
a
tor
ou
tput
;
is
modul
a
ti
on
c
ha
r
a
c
ter
is
ti
c
s
.
T
o
s
ynthes
ize
the
c
ontr
ol
a
lgor
it
hm,
us
e
a
dis
c
r
e
te
model
of
a
dyna
mi
c
plant,
de
s
c
r
ibed
by
a
s
ys
tem
of
dif
f
e
r
e
nc
e
e
qua
ti
ons
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
Digit
al
adapt
ive
c
ontr
ol
w
it
h
puls
e
w
idt
h
modula
t
ion
of
s
ignal
s
(
I
s
amiddin
Siddi
k
ov
)
255
(
+
1
)
=
(
)
+
(
)
(
)
=
(
)
+
(
)
(
6)
whe
r
e
,
,
a
r
e
numer
ic
matr
ice
s
;
,
a
r
e
matr
ice
s
c
ons
is
ti
ng
of
z
e
r
os
a
nd
one
s
;
is
ve
c
tor
of
the
s
tate
;
a
nd
is
ve
c
tor
o
f
mea
s
ur
e
d
output
s
.
T
o
i
mpar
t
the
pr
ope
r
ty
o
f
As
taticity
to
the
plant
model
of
the
c
ontr
ol
s
ys
tem,
a
n
a
ddit
ional
dis
c
r
e
te
int
e
gr
a
tor
is
in
tr
oduc
e
d
int
o
the
c
ontr
ol
loop:
(
+
1
)
=
(
)
+
ℎ
(
)
,
(
7)
whe
r
e
,
-
the
output
of
the
int
e
gr
a
to
r
;
ℎ
–
the
s
tep
of
t
he
dis
c
r
e
ti
z
a
ti
on.
T
he
n
the
dis
c
r
e
te
model
of
the
e
quivale
nt
plant
ha
s
the
f
oll
owing
f
o
r
m:
̅
(
+
1
)
=
̅
̅
(
)
+
̅
̅
(
)
̅
(
)
=
̅
̅
(
)
(
8)
whe
r
e
,
̅
-
e
xtende
d
ve
c
tor
of
mea
s
ur
e
d
output
da
ta,
a
nd
matr
ice
s
̅
,
̅
,
̅
a
r
e
de
f
ined
by
(
9)
:
̅
=
[
1
…
0
…
0
⋮
⋮
⋮
⋮
⋮
0
…
0
…
B
⋮
⋮
⋮
⋮
⋮
0
…
0
…
A
]
,
̅
=
[
0
…
1
…
0
]
,
̅
=
[
1
…
0
⋮
⋮
⋮
0
…
D
⋮
⋮
⋮
0
…
C
]
=
[
I
⋮
0
]
(
9)
whe
r
e
,
is
identit
y
matr
ix
.
S
hould
be
take
n
int
o
a
c
c
ount,
that
de
pe
nding
on
the
number
o
f
c
o
ntr
oll
e
d
va
r
iable
s
,
the
s
ize
s
of
the
matr
ice
s
̅
,
̅
,
̅
ha
ve
dif
f
e
r
e
nt
va
lues
.
W
he
n
s
olvi
ng
the
p
r
oblem
o
f
s
ynthes
izing
a
c
ontr
ol
a
lgor
it
hm
,
we
us
e
a
dis
c
r
e
te
c
ontr
oll
e
r
ba
s
e
d
on
a
c
ombi
na
ti
on
of
a
s
tate
c
ontr
oll
e
r
a
nd
a
L
ue
nbe
r
ge
r
obs
e
r
ve
r
of
mi
nim
a
l
c
ompl
e
xit
y
[
23]
–
[
25
]
:
(
)
=
̂
(
)
=
(
(
)
+
(
)
)
,
(
+
1
)
=
(
)
+
(
)
+
(
)
,
(
10)
whe
r
e
−
is
a
ve
c
tor
of
the
obs
e
r
ve
r
s
tate
,
̂
is
a
ve
c
to
r
of
e
s
ti
mate
s
of
plant
s
tate
va
r
iable
s
,
us
e
d
in
s
tate
c
ontr
oll
e
r
.
I
t
is
a
s
s
umed
that
the
matr
ice
s
(
,
,
,
,
)
s
a
ti
s
f
y
the
c
ondit
ions
.
−
=
,
+
=
,
(
11)
I
n
thi
s
c
a
s
e
,
the
poles
of
the
c
los
e
d
-
loop
c
ontr
ol
s
ys
tem
will
c
ons
is
t
of
the
poles
of
the
s
tate
c
ontr
oll
e
r
with
the
de
f
ini
ti
on
of
e
igenva
lues
a
nd
the
obs
e
r
ve
r
.
T
he
ve
c
tor
of
mea
s
ur
e
d
output
s
ha
s
a
c
a
nonica
l
s
tr
uc
tur
e
=
[
⋮
0
]
.
T
he
obs
e
r
ve
r
matr
ice
s
a
r
e
de
t
e
r
mi
ne
d
by
the
f
oll
owing
r
e
lations
:
=
[
−
]
,
=
[
−
]
,
=
[
0
−
]
,
=
=
−
(
22
+
12
)
+
21
+
11
,
=
=
22
+
12
(
12)
whe
r
e
,
is
s
ome
(
−
)
×
–
matr
ix,
de
f
ined
by
the
c
ontr
oll
e
r
;
(
,
=
1
,
2
̅
̅
̅
̅
)
a
r
e
blocks
of
matr
ix
obtaine
d
by
s
pli
tt
ing
ve
c
tor
int
o
two
c
omponent
s
(
1
)
=
a
nd
(
2
)
=
−
.
He
r
e
(
1
)
=
a
nd
(
2
)
=
−
c
oor
dinate
s
of
the
mea
s
ur
e
d
va
r
iable
,
(
1
)
=
a
nd
(
2
)
=
−
unmea
s
ur
e
d
c
oor
dinate
va
r
iable
s
.
B
a
s
e
d
on
the
matr
ice
s
12
a
nd
22
a
r
e
f
or
med
,
r
e
s
pe
c
ti
ve
ly.
M
a
tr
ice
s
a
nd
a
r
e
de
ter
mi
ne
d
us
ing
the
li
ne
a
r
-
qua
dr
a
ti
c
dis
c
r
e
te
opti
mi
z
a
ti
on
p
r
oc
e
dur
e
:
=
−
(
+
)
−
1
,
=
>
0
,
=
+
−
(
+
)
−
1
,
=
>
0
,
(
13)
=
−
22
12
(
+
22
12
)
−
1
,
=
>
0
,
=
22
12
+
−
22
12
(
+
12
12
)
−
1
12
12
(
14)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
15
,
No.
1
,
F
e
br
ua
r
y
20
25
:
252
-
259
256
E
ns
ur
ing
the
s
tabili
ty
of
the
c
los
e
d
-
loop
s
ys
tem
,
a
nd
the
r
e
quir
e
d
qua
li
ty
of
r
e
gulation
is
a
c
hieve
d
by
c
hoos
ing
the
we
ight
ing
c
oe
f
f
icie
nts
o
f
the
matr
ix
Q
,
=
≥
0
,
=
≥
0
.
L
e
t
us
r
e
pr
e
s
e
nt
the
c
ontr
oll
e
r
e
qua
ti
on
in
the
f
o
r
m
:
(
+
1
)
=
(
)
+
(
)
;
(
)
=
(
)
+
(
)
(
15)
T
he
n
the
mat
r
ice
s
,
,
,
a
nd
a
r
e
de
f
ined
by
(
16)
.
=
+
;
=
+
;
=
,
=
.
(
16)
T
hus
,
to
s
olve
the
pr
ob
lem
o
f
s
ynthes
izing
a
dis
c
r
e
te
c
ontr
oll
e
r
,
it
is
ne
c
e
s
s
a
r
y
to
f
ind
mat
r
ice
s
a
nd
us
ing
(
13)
,
a
nd
(
14
)
,
a
nd
the
r
e
maining
mat
r
ice
s
us
ing
(
1
2)
,
a
nd
(
16)
.
B
y
a
pplyi
ng
the
pr
opos
e
d
method
to
the
plant,
yo
u
c
a
n
obtain
a
s
olut
ion
to
the
s
ynthes
is
pr
oblem
in
the
f
or
m
of
dif
f
e
r
e
nc
e
e
qua
ti
ons
:
̅
(
+
1
)
=
̅
̅
(
)
+
̅
̅
(
)
;
(
)
=
̅
̅
(
)
+
̅
̅
(
)
(
17)
whe
r
e
̅
is
a
ve
c
tor
of
the
c
ont
r
oll
e
r
s
tate
.
T
he
dim
e
ns
ion
of
whic
h
is
de
ter
mi
ne
d
by
the
dif
f
e
r
e
nc
e
b
e
twe
e
n
the
dim
e
ns
ion
of
the
c
ontr
o
ll
e
d
plant
a
nd
the
n
umber
of
it
s
mea
s
ur
e
d
output
s
.
̅
,
̅
,
̅
,
̅
a
r
e
e
xtende
d
pa
r
a
mete
r
matr
ice
s
of
the
plant
.
T
o
f
ind
the
c
ompl
e
te
c
ontr
oll
e
r
e
qua
ti
on,
we
a
dd
a
dis
c
r
e
te
int
e
gr
a
tor
to
(
17)
.
I
n
thi
s
c
a
s
e
,
the
e
qua
ti
ons
of
the
de
s
ir
e
d
a
s
tatic
r
e
gulato
r
will
ha
ve
the
f
or
m:
(
+
1
)
=
[
1
0
1
×
2
̅
(
1
)
̅
]
(
)
+
[
0
ℎ
0
̅
(
2
)
̅
(
3
)
̅
(
4
)
]
(
)
,
(
18)
whe
r
e
̅
(
)
a
nd
̅
(
)
(
=
1
,
4
̅
̅
̅
̅
)
-
c
olum
ns
a
nd
e
leme
nt
s
of
the
c
or
r
e
s
ponding
matr
ice
s
.
T
he
e
qua
ti
on
(
18)
r
e
pr
e
s
e
nts
a
c
ontr
ol
a
lgor
it
hm
that
a
ll
ows
yo
u
to
c
a
lcula
te
the
P
W
M
c
ontr
ol
s
ignal
a
t
th
e
c
ur
r
e
nt
dis
c
r
e
ti
z
a
ti
on
s
tep
of
the
mea
s
ur
e
d
qua
nti
ti
e
s
.
App
lyi
ng
the
-
tr
a
ns
f
or
m
to
(
18)
a
nd
e
li
mi
na
ti
ng
the
̅
v
e
c
tor
,
we
obtain
the
f
o
ll
owing
r
e
lation:
(
)
=
(
)
(
)
+
(
)
(
)
+
(
)
(
(
)
−
(
)
)
,
(
19)
whe
r
e
,
(
)
,
(
)
,
(
)
a
r
e
the
tr
a
ns
f
e
r
f
unc
ti
ons
of
the
c
ontr
oll
e
r
.
T
he
c
ontr
ol
a
lgo
r
it
hm
a
ll
ows
us
to
mi
nim
ize
the
number
of
ope
r
a
ti
ons
.
T
he
c
ontr
ol
a
lgor
it
hm
a
ll
ows
us
to
mi
ni
mi
z
e
the
number
of
ope
r
a
ti
ons
.
T
he
p
r
opos
e
d
method
f
or
s
ynthes
izing
a
n
a
lgor
it
hm
f
or
a
c
ontr
ol
s
ys
tem
with
puls
e
-
width
modul
a
ti
on
by
e
li
mi
na
ti
ng
the
ope
r
a
ti
on
of
c
onve
r
ti
ng
a
n
a
na
logue
s
ignal
int
o
digi
tal
f
or
m
m
a
ke
s
it
pos
s
ibl
e
to
incr
e
a
s
e
the
a
c
c
ur
a
c
y
a
nd
r
e
li
a
bil
it
y
of
the
c
ontr
ol
s
ys
tem.
T
he
us
e
of
puls
e
s
ignals
a
s
c
ontr
ol
im
pa
c
ts
make
s
it
pos
s
ibl
e
to
im
a
gine
the
pul
s
e
-
width
modul
a
tor
a
s
a
li
ne
a
r
iner
ti
a
les
s
unit
,
whic
h
s
im
pli
f
ies
the
s
olut
ion
of
the
pr
oblem
of
s
ynthes
izing
a
c
ontr
ol
a
lgor
it
hm
a
nd
gives
it
pos
s
ibl
e
to
pr
ovide
the
va
l
ue
s
of
puls
a
ti
on
that
a
r
is
e
s
a
s
a
r
e
s
ult
of
qua
nt
iza
ti
on
of
a
c
onti
nuous
s
ignal.
3.
RE
S
UL
T
S
AN
D
DI
S
CU
S
S
I
ON
T
h
e
s
tr
uc
tu
r
e
s
c
h
e
m
e
o
f
a
d
yn
a
m
ic
pl
a
n
t
c
on
t
r
o
l
s
ys
te
m
w
it
h
a
P
W
M
m
od
ul
a
t
o
r
is
r
e
d
uc
e
d
a
s
s
h
own
i
n
F
i
gu
r
e
3
.
T
he
s
t
r
uc
t
ur
e
s
c
he
me
of
t
he
c
on
t
r
o
l
s
y
s
t
e
m
,
w
he
r
e
-
th
e
f
r
e
q
ue
n
c
y
o
f
t
he
P
W
M
s
i
gna
l
to
ge
ne
r
a
t
e
t
he
c
u
r
r
e
nt
c
o
nt
r
ol
s
ig
na
l;
i
s
c
on
t
r
o
l
s
ig
na
l
,
is
mo
vi
n
g
t
he
dr
i
ve
;
i
s
a
ng
u
la
r
d
is
p
la
c
e
men
t
o
f
th
e
v
a
l
ve
;
is
a
ng
ul
a
r
ve
loc
i
ty
o
f
t
he
r
o
to
r
;
a
n
d
i
s
lo
a
d
.
I
t
is
r
e
qu
ir
e
d
to
s
yn
th
e
s
iz
e
c
o
nt
r
ol
s
ys
te
ms
f
o
r
a
d
yna
m
ic
p
lan
t
w
it
h
a
dis
c
r
e
t
iz
a
t
io
n
s
t
e
p
ℎ
=
0
.
00
62
5
s
e
c
.
A
pp
l
yi
ng
the
p
r
op
os
e
d
c
o
nt
r
ol
a
l
go
r
it
hm
,
we
de
te
r
mi
ne
the
t
r
a
n
s
f
e
r
f
u
nc
ti
ons
o
f
th
e
c
on
t
r
o
ll
e
r
,
=
−
0
.
53
(
−
2
.
8
)
(
−
0
.
02
)
,
=
−
0
.
45
(
−
0
.
93
)
(
−
0
.
68
)
(
−
0
.
97
)
(
−
0
.
02
)
,
=
30
(
−
0
.
986
)
(
−
0
.
98
)
(
−
1
)
(
−
0
.
97
)
.
T
a
k
in
g
i
n
to
a
c
c
o
un
t
th
e
ne
g
a
t
iv
e
s
hi
f
t
o
f
the
a
r
g
u
men
ts
o
f
di
s
c
r
e
te
f
un
c
t
io
ns
,
th
e
e
q
ua
t
i
on
a
l
go
r
it
h
m
tak
e
s
th
e
f
o
l
lo
wi
ng
f
o
r
m:
(
)
=
1
.
99
(
−
1
)
−
1
.
009
(
−
2
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0
.
19
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−
3
)
−
0
.
53
(
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+
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.
53
(
−
1
)
−
3
.
44
(
−
2
)
+
1
.
44
(
−
3
)
−
4
.
5
(
)
+
11
.
75
(
−
1
)
−
10
.
1
(
−
2
)
+
2
.
85
(
−
3
)
+
30
(
)
−
59
.
6
(
−
1
)
+
30
.
18
(
−
2
)
−
0
.
58
(
−
3
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
Digit
al
adapt
ive
c
ontr
ol
w
it
h
puls
e
w
idt
h
modula
t
ion
of
s
ignal
s
(
I
s
amiddin
Siddi
k
ov
)
257
As
s
hown
in
F
igur
e
4
,
the
r
e
s
ult
s
of
the
s
im
ulat
ion
a
r
e
pr
e
s
e
nted
by
tr
a
ns
ient
pr
oc
e
s
s
e
s
f
or
the
va
r
iable
s
of
the
s
tabili
z
a
ti
on
loop,
obtaine
d
f
o
r
a
s
ingl
e
-
s
tage
load
a
ppli
e
d
a
t
a
c
e
r
tain
point
in
t
im
e
t
.
I
n
thi
s
c
a
s
e
,
the
e
qua
ti
on
(
19
)
wa
s
us
e
d
to
model
the
c
ontr
ol
a
lgor
i
thm
,
the
e
qua
ti
on
(
5)
wa
s
us
e
d
f
or
P
W
M
,
a
nd
a
z
e
r
o
-
or
de
r
f
ixator
with
leve
l
qua
nti
z
a
ti
on
wa
s
us
e
d
f
or
the
a
na
log
-
to
-
digi
tal
c
onve
r
ter
(
AD
C
)
.
T
he
gr
a
phs
it
c
a
n
be
s
e
e
n
that
the
qu
a
li
ty
of
s
tabili
z
a
ti
on
is
quit
e
s
a
ti
s
f
a
c
tor
y.
I
n
pa
r
ti
c
ular
,
in
te
r
ms
of
r
e
gulating
ti
me,
the
dyna
mi
c
e
r
r
or
doe
s
not
e
xc
e
e
d
5%
,
a
nd
the
e
r
r
o
r
i
n
the
s
tea
dy
s
tate
is
z
e
r
o.
F
igur
e
3.
T
he
s
tr
uc
tur
e
s
c
he
me
of
the
c
ontr
o
l
s
ys
tem
F
igur
e
4.
R
e
s
ult
s
of
a
na
lys
is
of
t
r
a
ns
ient
pr
oc
e
s
s
e
s
of
s
tabili
z
a
ti
on
loop
va
r
iable
s
:
(
)
is
a
ngular
ve
locity
of
the
r
otor
;
(
)
is
a
ngular
dis
plac
e
ment
of
the
va
lve;
(
)
is
movi
ng
the
dr
ive;
a
nd
(
)
is
c
ontr
ol
s
ignal
4.
CONC
L
USI
ON
T
he
pr
opos
e
d
a
lgor
i
thm
f
or
digi
tal
c
ont
r
ol
o
f
the
p
uls
e
width
of
a
P
W
M
s
ignal
s
hows
that
the
P
W
M
model
tur
ne
d
out
to
be
li
ne
a
r
a
nd
p
r
a
c
ti
c
a
ll
y
iner
ti
a
les
s
,
whic
h
make
s
it
e
a
s
y
to
take
thi
s
model
int
o
a
c
c
ount
whe
n
s
ynthes
izing
the
c
ontr
ol
a
lgo
r
it
hm
.
T
he
pul
s
e
width
c
a
lcula
ted
a
t
the
c
ur
r
e
nt
dis
c
r
e
ti
z
a
ti
on
s
t
e
p
f
r
om
the
mea
s
ur
e
d
va
r
iable
s
is
take
n
a
s
the
c
ontr
ol
P
W
M
s
ignal.
T
he
pr
opos
e
d
the
c
ont
r
ol
a
lgor
i
thm
b
a
s
e
d
on
a
hybr
id
a
ppli
c
a
ti
on
of
the
li
ne
a
r
-
qua
dr
a
ti
c
opti
mi
z
a
ti
on
pr
oc
e
dur
e
a
nd
the
theo
r
y
of
obs
e
r
ve
r
s
of
mi
nim
um
c
ompl
e
xit
y.
T
o
e
ns
ur
e
that
the
c
ondit
ions
o
f
As
taticity
a
r
e
met
,
the
dyna
mi
c
model
of
the
plant
is
s
uppleme
nted
with
a
dis
c
r
e
te
int
e
gr
a
tor
.
T
he
p
r
op
os
e
d
a
ppr
oa
c
h
a
ll
ows
it
pos
s
ibl
e
to
r
e
duc
e
ha
r
dw
a
r
e
c
os
ts
a
nd
incr
e
a
s
e
s
the
r
e
li
a
bil
it
y
of
the
c
ontr
ol
s
ys
tem
by
e
li
mi
na
ti
ng
digi
tal
-
to
-
a
na
logue
c
onve
r
s
ion
op
e
r
a
ti
ons
a
nd
f
or
m
ing
a
puls
e
-
width
modul
a
ted
s
ignal
with
s
lowne
s
s
pr
opor
ti
ona
l
to
the
c
a
lcula
ted
c
ontr
ol
s
ignal.
I
n
the
pr
opos
e
d
digi
tal
c
ontr
ol
a
lgor
it
hm,
the
f
or
med
c
ontr
ol
s
ignal
ob
taine
d
ba
s
e
d
on
c
a
lcula
ti
ng
the
du
ty
c
yc
le
of
a
puls
e
-
width
modul
a
ted
s
ignal
s
hows
that
the
P
W
M
model
be
c
omes
a
l
inea
r
a
nd
iner
ti
a
les
s
unit
.
T
his
a
ll
ows
you
to
ob
tain
a
high
-
qua
li
ty
modul
a
ted
c
ontr
ol
s
ignal,
pr
ovidi
ng
s
igni
f
ica
nt
s
uppr
e
s
s
ion
o
f
s
ignal
puls
a
ti
on
a
nd
high
c
ontr
ol
a
c
c
ur
a
c
y.
RE
F
E
RE
NC
E
S
[
1]
Q
.
L
i,
P
.
H
a
o,
J
.
W
a
ng,
a
nd
H
.
D
e
ng,
“
P
ul
s
e
-
w
id
th
-
modul
a
ti
on
-
ba
s
e
d
ti
me
-
de
la
y
c
ompe
n
s
a
ti
on
c
ont
r
ol
f
or
hi
gh
-
s
pe
e
d
on
/o
f
f
va
lv
e
s
,”
E
le
c
tr
oni
c
s
, vol
. 12, no. 17, Aug. 20
23, doi:
10.3390/e
le
c
tr
oni
c
s
12173627.
[
2]
X
.
L
a
ng,
Y
.
Z
ha
ng,
L
.
X
ie
,
X
.
J
in
,
A
.
H
or
c
h,
a
nd
H
.
S
u,
“
U
s
e
of
f
a
s
t
mul
ti
va
r
ia
te
e
mpi
r
ic
a
l
mode
de
c
ompos
it
io
n
f
or
os
c
il
la
t
io
n
t
,
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
15
,
No.
1
,
F
e
br
ua
r
y
20
25
:
252
-
259
258
moni
to
r
in
g
in
noi
s
y
pr
oc
e
s
s
pl
a
nt
,”
I
ndus
tr
ia
l
&
E
ngi
ne
e
r
in
g
C
he
m
is
tr
y
R
e
s
e
ar
c
h
,
vol
.
59,
no.
25,
pp.
11537
–
11551,
J
un.
2020,
doi
:
10.1021/a
c
s
.i
e
c
r
.9b06351.
[
3]
M
.
K
a
r
a
ba
c
a
k
a
nd
G
.
P
oyr
a
z
,
“
R
obus
t
a
da
pt
iv
e
c
ont
r
ol
of
p
ul
s
e
-
w
id
th
modul
a
te
d
r
e
c
ti
f
ie
r
s
ba
s
e
d
on
a
da
pt
iv
e
s
upe
r
-
twi
s
t
in
g
s
li
di
ng
-
mode
a
nd
s
t
a
te
f
e
e
db
a
c
k
c
ont
r
ol
le
r
s
,”
E
le
c
tr
ic
P
ow
e
r
C
om
pone
nt
s
and
Sy
s
te
m
s
,
vol
.
43,
no.
11,
pp.
1289
–
1296,
J
ul
.
20
15,
doi
:
10.1080/15325008.2
015.1027016.
[
4]
A
.
N
.
K
a
s
r
uddi
n
N
a
s
ir
,
M
.
A
.
A
hma
d,
a
nd
M
.
O
.
T
okhi
,
“
H
yb
r
id
s
pi
r
a
l
-
ba
c
te
r
ia
l
f
or
a
gi
ng
a
lg
or
it
hm
f
o
r
a
f
uz
z
y
c
ont
r
ol
de
s
ig
n
of
a
f
le
xi
bl
e
ma
ni
pul
a
to
r
,”
J
our
nal
of
L
ow
F
r
e
que
nc
y
N
oi
s
e
,
V
ib
r
at
io
n
and
A
c
ti
v
e
C
ont
r
ol
,
vol
.
41,
no.
1,
pp.
340
–
358,
M
a
r
.
2022,
doi
:
10.1177/146134842
11035646.
[
5]
R
.
B
r
a
nds
te
tt
e
r
,
T
.
D
e
ube
l,
R
.
S
c
he
id
l,
B
.
W
in
kl
e
r
,
a
nd
K
.
Z
e
ma
n,
“
D
ig
it
a
l
hydr
a
ul
ic
s
a
nd
‘
I
ndus
tr
ie
4.0,’
”
P
r
oc
e
e
di
ngs
of
th
e
I
ns
ti
tu
ti
on
of
M
e
c
hani
c
al
E
ngi
ne
e
r
s
,
P
ar
t
I
:
J
our
nal
of
Sy
s
te
m
s
and
C
ont
r
ol
E
ngi
ne
e
r
in
g
,
F
e
b.
2017,
vol
.
231,
no.
2,
pp.
82
–
93,
doi
:
10.1177/095965181
6636734.
[
6]
P
e
lu
s
i,
“
O
pt
im
a
l
c
ont
r
ol
a
lg
or
it
hms
f
or
s
e
c
ond
or
de
r
s
ys
te
ms
,
”
J
our
nal
of
C
om
put
e
r
Sc
ie
n
c
e
,
vol
.
9,
no.
2,
pp.
183
–
197,
F
e
b.
2013, doi:
10.3844/j
c
s
s
p.2013.183.197.
[
7]
Q
.
C
he
n,
X
.
L
a
ng,
L
.
X
ie
,
a
nd
H
.
S
u,
“
D
e
te
c
ti
ng
nonl
in
e
a
r
o
s
c
il
la
ti
ons
in
pr
oc
e
s
s
c
ont
r
ol
lo
op
ba
s
e
d
on
a
n
im
pr
ove
d
V
M
D
,”
I
E
E
E
A
c
c
e
s
s
, vol
. 7, pp. 91446
–
91462, 2019, doi:
10.1109/AC
C
E
S
S
.2019.2925861.
[
8]
S
.
B
a
l
di
,
A
.
P
a
p
a
c
hr
i
s
to
do
ul
ou
,
a
nd
E
.
B
.
K
o
s
ma
to
po
ul
o
s
,
“
A
da
p
ti
v
e
pu
l
s
e
w
i
dt
h
mo
dul
a
ti
o
n
d
e
s
i
gn
f
or
p
ow
e
r
c
o
nv
e
r
t
e
r
s
b
a
s
e
d
o
n
a
f
f
i
n
e
s
w
i
tc
h
e
d
s
y
s
t
e
m
s
,
”
N
o
nl
in
e
a
r
A
n
al
y
s
i
s
:
H
y
b
r
i
d
Sy
s
t
e
m
s
,
vo
l.
3
0,
p
p.
3
06
–
3
22
,
N
ov
.
20
18
,
doi
:
10
.1
01
6/
j.
na
h
s
.
20
18
.0
7.
00
2.
[
9]
M
.
A
.
A
hma
d,
R
.
M
. T
.
R
a
j
a
I
s
ma
il
,
M
.
S
.
R
a
ml
i,
N
.
M
.
A
bd G
ha
ni
,
a
nd
N
.
H
a
mba
li
,
“
I
nve
s
ti
ga
ti
ons
of
f
e
e
d
-
f
or
w
a
r
d
te
c
hni
que
s
f
or
a
nt
i
-
s
w
a
y
c
ont
r
ol
of
3
-
D
ga
nt
r
y
c
r
a
ne
s
ys
t
e
m,”
2009
I
E
E
E
Sy
m
pos
iu
m
on
I
ndus
tr
ia
l
E
le
c
t
r
oni
c
s
&
A
ppl
ic
at
io
ns
,
vol
.
77.
I
E
E
E
, pp. 265
–
270, Oc
t.
2009, doi:
10.1109/I
S
I
E
A
.2009.53564
45.
[
10]
S
.
M
.
G
ha
ma
r
i,
H
.
M
ol
la
e
e
,
a
nd
F
.
K
ha
va
r
i,
“
D
e
s
ig
n
of
r
ob
us
t
s
e
lf
‐
tu
ni
ng
r
e
gul
a
to
r
a
da
pt
iv
e
c
ont
r
ol
le
r
on
s
in
gl
e
‐
pha
s
e
f
ul
l‐
br
id
ge
i
nve
r
te
r
,”
I
E
T
P
ow
e
r
E
le
c
tr
oni
c
s
, vol
. 13, no. 16, pp. 36
13
–
3626, De
c
. 2020, doi:
10.1049/i
e
t
-
pe
l.
2020.0454.
[
11]
Q
.
G
a
o,
Y
.
Z
hu,
Z
.
L
uo,
a
nd
N
.
B
r
uno,
“
I
nve
s
ti
ga
ti
on
on
a
da
pt
iv
e
pul
s
e
w
id
th
modul
a
ti
on
c
ont
r
ol
f
or
hi
gh
s
p
e
e
d
on/
of
f
va
l
ve
,”
J
our
nal
of
M
e
c
hani
c
al
Sc
ie
nc
e
and T
e
c
hnol
ogy
, vol
. 34, no. 4,
pp. 1711
–
1722, Apr
. 2020, doi:
10.1007/s
12206
-
020
-
0333
-
y.
[
12]
C.
-
F
.
L
u,
C
.
-
H
.
H
s
u,
a
nd
C
.
-
F
.
J
ua
ng,
“
C
oor
di
na
te
d
c
ont
r
ol
o
f
f
le
xi
bl
e
AC
tr
a
n
s
mi
s
s
io
n
s
ys
t
e
m
de
vi
c
e
s
u
s
in
g
a
n
e
vol
ut
io
n
a
r
y
f
uz
z
y
le
a
d
-
la
g
c
ont
r
ol
le
r
w
it
h
a
dva
nc
e
d
c
ont
in
uous
a
nt
c
ol
on
y
opt
im
iz
a
ti
on,”
I
E
E
E
T
r
ans
ac
ti
ons
on
P
ow
e
r
Sy
s
te
m
s
,
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M
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R
us
ta
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G
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S
he
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va
,
A
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A
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J
uma
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S
.
F
a
iz
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“
D
e
ve
lo
pme
nt
of
mode
ls
a
nd
a
lg
or
it
hms
f
or
s
tu
dyi
ng
mul
ti
-
di
me
ns
io
na
l
s
ys
te
ms
w
it
h
la
ti
tu
de
-
im
pul
s
e
modul
a
ti
on,”
A
I
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e
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e
nc
e
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S
pe
c
tr
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ta
l
U
P
W
M
s
ig
na
l
s
ge
ne
r
a
t
e
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f
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om
r
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a
ti
ng
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A
li
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“
S
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he
s
is
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a
c
ont
r
ol
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ys
te
m
f
or
a
two
-
ma
s
s
e
le
c
tr
ome
c
ha
ni
c
a
l
obj
e
c
t,
”
A
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C
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r
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or
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a
c
ti
c
e
,
”
in
N
on
li
ne
ar
A
nal
y
s
is
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D
e
s
ig
n
of
P
has
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L
oc
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ont
r
ol
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S
A
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T
he
I
ns
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ti
on, S
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ut
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S
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to
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n
a
ut
oma
ti
c
c
ont
r
ol
s
ys
t
e
m
w
i
th
pul
s
e
-
w
id
th
modul
a
ti
on
a
c
c
or
di
ng
to
th
e
s
pe
e
d
c
r
it
e
r
io
n,”
2
020
I
nt
e
r
nat
io
nal
C
onf
e
r
e
n
c
e
on
I
nf
or
m
at
io
n
Sc
i
e
nc
e
and
C
om
m
uni
c
at
io
ns
T
e
c
hnol
ogi
e
s
(
I
C
I
SC
T
)
,
vol
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E
E
E
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C
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A
.
H
.
H
a
ns
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n,
M
.
F
.
A
s
mus
s
e
n,
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nd
M
. M
.
B
e
c
h,
“
H
a
r
dw
a
r
e
-
in
-
th
e
-
lo
op
va
li
da
ti
on
of
mode
l
pr
e
di
c
ti
ve
c
ont
r
ol
of
a
di
s
c
r
e
te
f
lu
id
pow
e
r
pow
e
r
t
a
ke
-
of
f
s
ys
te
m f
or
w
a
ve
e
ne
r
gy c
onve
r
te
r
s
,”
E
ne
r
gi
e
s
, vol
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8.
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I
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id
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D
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K
ha
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a
to
v,
G
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A
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,
U
.
K
huj
a
na
z
a
r
ov,
S
.
F
e
r
uz
a
xon,
a
nd
M
.
U
s
a
nov,
“
I
nve
s
ti
ga
ti
on
of
a
ut
o
-
os
c
il
a
ti
o
na
l
r
e
gi
me
s
of
th
e
s
ys
te
m
by
dyna
mi
c
nonl
in
e
a
r
it
ie
s
,”
I
nt
e
r
nat
io
n
al
J
our
nal
of
E
le
c
tr
ic
al
and
C
om
put
e
r
E
ngi
ne
e
r
in
g
,
vol
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14,
n
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1,
p
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I
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S
id
ik
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D
.
K
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a
to
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nd
G
.
A
li
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,
“
A
lg
or
it
hm
f
o
r
th
e
s
ynt
he
s
i
s
of
a
pr
e
di
c
ti
ve
c
ont
r
ol
s
ys
te
m
f
or
th
e
ta
pe
pul
li
ng
pr
oc
e
s
s
,”
E
3S W
e
b of
C
onf
e
r
e
nc
e
s
, vol
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a
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id
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a
s
hva
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,
a
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A
li
mova
,
“
N
e
ur
a
l
n
e
twor
k
opt
im
iz
e
r
of
pr
opor
ti
ona
l
-
in
te
gr
a
l
-
di
f
f
e
r
e
nt
ia
l
c
ont
r
o
ll
e
r
pa
r
a
me
te
r
s
,”
I
nt
e
r
nat
io
nal
J
our
nal
of
E
le
c
t
r
ic
al
and
C
om
put
e
r
E
ngi
ne
e
r
in
g
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vol
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3,
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T
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Y
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S
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a
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A
.
H
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D
a
vr
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O
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A
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M
uhi
ddi
n,
a
nd
U
.
H
u
z
a
n
a
z
a
r
ov,
“
F
or
ma
li
z
a
ti
on
of
th
e
c
ot
to
n
dr
yi
ng
pr
oc
e
s
s
ba
s
e
d
on
he
a
t
a
nd ma
s
s
t
r
a
ns
f
e
r
e
qu
a
ti
ons
,”
I
I
U
M
E
ngi
ne
e
r
in
g J
our
nal
, vol
. 2
1, no. 2, pp. 256
–
265, J
ul
. 2020, doi:
10.31436/i
iu
me
j.
v21i
2.1456.
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