Indonesi
an
Journa
l
of El
ect
ri
cal Engineer
ing
an
d
Comp
ut
er
Scie
nce
Vo
l.
23
,
No.
3
,
Septem
ber
20
21
,
pp.
1385
~
139
7
IS
S
N: 25
02
-
4752, DO
I: 10
.11
591/ijeecs
.v
23
.i
3
.
pp
1385
-
139
7
1385
Journ
al h
om
e
page
:
http:
//
ij
eecs.i
aesc
or
e.c
om
Enh
ancement
in
pn
eumatic
posi
tion
ing
syst
em
usin
g
nonli
ne
ar
ga
in
constr
ained
model
p
re
di
ctive
contr
oll
er
:
expe
riment
al
va
lid
ation
Siti
Fa
tima
h
S
ulaima
n
1
,
M.
F.
Ra
h
ma
t
2
,
A
hma
d
A
th
if
F
au
dz
i
3
,
Kh
air
uddin
Osm
an
4
,
N.
H.
S
un
ar
5
1
,4
Advanc
ed
Sen
sors
and
Embed
ded
Contro
l
Res
ea
rch
Group,
Ce
ntre
for
T
el
e
comm
unic
at
ion
Rese
arc
h
and
Innov
ation
(CeT
RI),
Facu
lty
of
E
lectr
oni
c
s
and
Com
pute
r
E
ngine
er
ing,
Univ
ersit
i
Te
kn
ika
l
Malay
s
ia
Mel
ak
a
2
,3,5
School
of
Ele
ct
ri
ca
l
Eng
ine
er
i
ng,
Univer
si
ti
Teknologi
Ma
lay
si
a
2,
3
,5
Cent
re
for
Ar
ti
ficia
l
Int
el
l
ige
n
ce
and
Robo
ti
cs
(CAIRO
),
Unive
rsiti
Te
knolog
i
Malay
s
ia
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
hist
or
y:
Re
cei
ved
M
ay
9
,
2021
Re
vised
Ju
l
1
8
,
2021
Accepte
d
J
ul
2
9
,
2021
The
issues
of
in
ac
cur
ate
posit
io
ning
control
h
av
e
m
ade
an
industri
al
use
of
pneumati
c
a
ct
u
at
or
r
emains
re
stric
t
ed
to
c
ert
a
in
app
li
c
at
ions
onl
y
.
Non
-
complia
nc
e
wit
h
s
y
stem
li
m
it
s
and
prope
rl
y
c
ontrol
the
op
erati
ng
s
y
st
em
may
al
so
degr
a
de
the
per
form
a
nce
of
pneumatic
positi
oning
s
y
stems
.
Thi
s
stud
y
proposed
a
new
appr
oac
h
to
enha
nce
pn
eumati
c
positi
o
ning
s
y
stem
while
consid
eri
n
g
the
constr
ai
nt
s
of
sy
st
em.
Fir
stl
y
,
a
m
at
h
ema
ti
c
al
m
odel
tha
t
r
epr
ese
nt
e
d
the
pneuma
ti
c
s
y
s
te
m
wa
s
det
ermined
by
s
y
s
te
m
ide
nti
f
icati
on
ap
proa
ch.
Second
l
y
,
m
odel
p
red
i
c
ti
ve
cont
ro
ll
er
(
MP
C)
was
deve
lop
ed
as
a
primar
y
cont
r
oll
er
to
control
the
pneuma
ti
c
positi
onin
g
s
y
stem,
which
t
ook
int
o
a
cc
ou
nt
the
constra
in
ts
of
the
s
y
s
tem
.
Next,
to
enha
nc
e
the
per
f
orm
anc
e
of
the
over
all
s
y
stem,
nonli
ne
ar
gai
n
f
unct
ion
was
inc
orpora
te
d
wi
thi
n
the
MPC
al
gorit
hm
.
Fin
all
y
,
th
e
per
form
anc
es
wer
e
compare
d
with
othe
r
con
trol
m
et
hods
such
as
constra
in
ed
MPC
(CMP
C),
proporti
ona
l
-
inte
gra
l
(PI),
and
p
red
ictive
fun
ctio
nal
con
trol
with
observe
r
(PF
C
-
O).
The
va
li
dation
bas
ed
on
real
-
ti
m
e
experim
ent
al
result
s
for
100
mm
positi
oning
control
rev
eale
d
th
at
the
inc
orpor
at
i
on
of
nonli
nea
r
gai
n
within
the
MPC
al
gorithm
improved
21
.
03%
and
2.
69%
of
the
spee
d
res
ponse
give
n
by
CMP
C
and
PFC
-
O,
and
red
u
ce
d
100%
of
th
e
over
shoot
give
n
by
CMP
C
and
PI
cont
rolle
r;
thus,
providin
g
fast
and
a
cc
u
rat
e
pn
eumati
c
positi
oning
cont
rol
s
y
st
em.
Ke
yw
or
d
s
:
Pn
e
um
atic
act
uator
Po
sit
io
n
c
on
tr
ol
Pr
e
dicti
ve
co
nt
ro
l
Syst
e
m
identific
at
ion
Transi
ent
re
spon
s
e
This
is
an
open
acc
ess
arti
cl
e
un
der
the
CC
BY
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Sit
i
Fatim
ah
Su
la
i
m
an
Ce
ntre
for
Tel
e
com
m
un
ic
at
ion
R
esea
rch
an
d
I
nnovat
ion
(C
eTR
I)
Faculty
of
Ele
c
tr
onic
s
an
d
C
om
pu
te
r
En
gin
e
erin
g
Un
i
v
ersit
i
Te
knikal
Ma
la
ysi
a
Me
la
ka
76100
D
ur
ia
n
Tu
nggal,
Me
la
ka,
Ma
la
ysi
a
Em
a
il
:
sitifatim
ahsu
la
im
an
@u
te
m
.ed
u.
m
y
1.
INTROD
U
CTION
The
pne
um
at
ic
syst
e
m
is
of
te
n
ass
ociat
ed
with
the
issues
of
nonlinea
riti
es
and
un
ce
rtai
nt
ie
s
su
ch
as
com
pr
essibil
it
y
of
ai
r
a
nd
fr
i
ct
ion
e
ff
ect
sur
rou
nd
i
ng
the
s
yst
e
m
[1
]
,
[
2].
Ther
e
f
or
e,
it
is
a
c
halle
ng
i
ng
ta
sk
to
con
t
ro
l
the
syst
e
m
for
a
certa
in
desire
d
perf
or
m
ance.
C
ont
ro
ll
in
g
the
syst
e
m
’s
posit
ion
al
so
bec
om
es
m
or
e
com
plica
te
d
with
the
nee
d
to
sim
ultaneou
sl
y
consi
de
r
the
accu
racy
of
s
yst
e
m
and
res
pons
e
tim
e.
V
ario
us
con
t
ro
ll
ers
we
re
re
porte
dly
pro
po
se
d
to
c
on
t
ro
l
t
he
pos
it
ion
of
pne
um
at
ic
syst
e
m
;
su
c
h
as
propor
ti
onal
-
integral
-
de
riva
ti
ve
(P
I
D
)
[
3],
po
le
-
p
la
cem
e
nt
[
4],
H
∞
loop
sh
api
ng
co
ntr
oller
[
5],
ada
pt
ive
con
t
ro
ll
er
[6
]
,
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
23
, N
o.
3
,
Se
ptem
ber
20
21
:
13
85
-
139
7
1386
fu
zzy
l
og
ic
[7
]
,
an
d
predict
iv
e
co
ntr
ol
[8
]
,
[
9].
H
owev
er,
m
os
t
of
these
r
eported
co
ntr
ol
le
rs
we
re
i
ncapable
to
si
m
ultaneou
sly
delive
r
high
-
s
peed
res
ponse
with
acc
ur
acy
.
It
is
al
s
o
c
ru
ci
al
to
a
ddress
t
he
c
onstrai
nts
of
the
syst
e
m
in
the
desig
n
of
c
on
t
ro
ll
er
for
the
act
ual
app
li
cat
ion
s
of
t
he
syst
e
m
.
The
non
-
com
pliance
with
the
pr
esc
ribe
d
c
on
strai
nts
m
ay
ca
us
e
dam
age
to
the
pne
um
atic
syst
e
m
and
its
com
po
ne
nts
a
nd
af
fects
the
overall
perform
ance
of
the
c
ontrol
s
yst
e
m
i
tse
lf.
Hen
ce
,
this
st
ud
y
reg
a
r
ded
the
sig
nificanc
e
of
co
ns
ide
ri
ng
t
he
const
raints
of
the
pn
e
um
at
ic
s
yst
e
m
du
rin
g
t
he
dev
el
op
m
en
t
of
the
c
ontr
oller.
T
his
stu
dy
propose
d
the
m
od
el
pre
dicti
ve
con
tr
oller
(
MPC
)
as
the
con
tr
ol
strat
egy
for
the
po
sit
io
ning
of
the
syst
e
m
.
M
PC
can
co
ns
id
ers
the
co
ns
trai
nts,
deals
with
m
ul
ti
var
ia
ble
con
t
ro
l
issue
,
an
d
al
s
o
su
it
able
f
or
si
ngle
-
in
put
an
d
s
ing
le
-
outp
ut
(SISO)
syst
em
a
nd
m
ulti
-
input
and
m
ulti
-
ou
t
pu
t
(MIMO
)
s
yst
e
m
[10
]
-
[
12]
,
w
hi
ch
e
xp
la
in
why
it
is
hig
hly
f
avou
rab
le
in
the
process
i
ndust
ries.
MPC
is
al
so
re
ported
use
d
to
con
t
ro
l
rob
ots
[13],
[
14]
.
Fi
gure
1
sho
ws
t
he
basic
st
ru
ct
ure
of
MPC
.
R
e
f
e
r
e
n
c
e
t
r
a
j
e
c
t
o
r
y
M
o
d
e
l
+
-
O
p
t
i
m
i
z
e
r
P
a
s
t
i
n
p
u
t
s
a
n
d
o
u
t
p
u
t
s
F
u
t
u
r
e
i
n
p
u
t
s
C
o
s
t
f
u
n
c
t
i
o
n
C
o
n
s
t
r
a
i
n
t
s
F
u
t
u
r
e
e
r
r
o
r
s
P
r
e
d
i
c
t
e
d
o
u
t
p
u
t
s
Figure
1.
Ba
sic
struct
ur
e
of
M
PC
[
11
]
MPC
in
Fig
ur
e
1
us
es
a
proce
ss
m
od
el
to
pre
dict
the
f
uture
ou
t
pu
t
base
d
on
the
previ
ou
s
and
cu
rr
e
nt
values
by
so
lvin
g
the
opti
m
al
fu
ture
co
ntr
ol
act
ion
s
at
each
sa
m
pli
ng
ti
m
e
instant
[1
1].
Th
e
optim
iz
er
consi
ders
the
c
os
t
f
unct
ion
an
d
the
co
ns
trai
nt
s
of
the
syst
e
m
to
cal
culat
e
the
co
ntr
ol
act
ion
s
.
In
pa
rtic
ular,
t
he
add
e
d
co
ns
trai
nts
in
MPC
pr
e
ven
t
the
wi
nd
-
up
ph
e
nom
eno
n.
W
it
h
the
use
of
MPC
as
a
s
trat
egy
to
con
tr
ol
the
po
sit
io
n
of
the
pneum
at
ic
syst
e
m
us
ed
in
this
stu
dy,
t
he
c
onstrai
nts
in
the
pne
um
at
ic
syst
e
m
can
be
consi
der
e
d
[
15]
.
The
em
plo
ym
e
nt
of
MPC
as
a
con
tr
ol
strat
egy
to
con
t
ro
l
the
posit
ion
of
pn
e
um
at
ic
syste
m
us
ed
in
this
stud
y
has
been
e
valuate
d
in
pr
e
vious
stud
ie
s
[
16]
,
[
17].
In
orde
r
to
ve
rify
the
eff
ect
iveness
of
the
strat
egy
in
ha
ndli
ng
syst
e
m
s
with
co
nst
raints,
c
on
st
ra
ints
we
re
ap
plied
to
t
he
in
put
of
t
he
syst
em
(co
nt
ro
l
si
gn
al
to
the
valves
).
From
the
st
ud
y,
they
fou
nd
t
hat
c
onstrai
ned
MPC
su
ccess
fu
ll
y
pr
oduce
d
acc
ur
at
e
tracki
ng
com
par
e
d
to
unc
onstrai
ne
d
MPC
[
16
]
,
[
17
]
.
H
oweve
r,
they
f
ound
th
at
the
i
nclusi
on
of
co
ns
trai
nts
in
the
MPC
al
gorithm
reduce
d
the
syst
e
m
resp
onse
and
ag
gr
e
ssivene
ss
of
the
pn
e
um
at
ic
syst
e
m
since
it
req
ui
res
m
or
e
com
pu
ta
ti
on
al
effor
t
to
opti
m
ise
the
cost
functi
on
(c
om
par
ed
to
the
unc
on
st
raine
d
cas
e)
[
16
]
,
[
17
]
.
These
fin
dings
w
ere
co
ns
ist
ent
with
sev
eral
pr
e
vious
st
ud
ie
s
[11],
wh
ic
h
dem
on
strat
ed
that
the
i
nclus
ion
of
const
raints
in
t
he
MPC
al
gori
thm
did
reduce
the
res
pons
e
t
i
m
e
in
the
syst
e
m
ou
tp
ut.
T
hus,
t
he
init
ia
l
us
e
of
const
raine
d
M
PC
was
i
nca
pa
ble
to
pro
vid
e
accu
rate
an
d
tim
e
ly
po
sit
io
ning
re
spo
ns
e
of
pneum
at
ic
syst
e
m
us
e
d
in
this
stu
dy
[16],
[
17
]
.
The
us
e
of
li
ne
ar
co
ntro
ll
er
to
con
tr
ol
a
syst
em
,
especial
ly
the
nonline
ar
s
yst
e
m
,
is
ty
pical
l
y
al
s
o
incapa
ble
to
si
m
ultaneou
sl
y
deliver
high
-
sp
ee
d
res
ponse
with
accurac
y
[1
8].
Des
pit
e
that,
this
stu
dy
co
nsi
der
e
d
that
t
he
syst
e
m
can
be
i
m
pr
ov
e
d
th
rou
gh
certai
n
m
od
ific
at
ion
s.
This
st
ud
y
fo
c
us
e
d
on
t
he
a
ppr
oac
h
a
dopte
d
by
Sera
j
i
[19],
co
ns
i
der
i
ng
that
its
im
ple
m
entat
ion
is
eff
ect
ive
a
nd
st
raig
htfor
ward.
Sera
j
i
[19]
i
m
pr
ove
d
the
co
nv
entional
P
ID
c
on
t
ro
ll
er
by
co
m
bin
ing
a
nonl
inear
gain
in
casca
de
and
a
li
near
fixe
d
-
gain
P
ID
con
tr
oller
in
orde
r
to
co
ntr
ol
the
robo
ti
c
ar
m
.
Con
seq
ue
ntly
,
the
con
t
ro
ll
er
is
a
bl
e
to
adap
t
its
r
esp
on
se
base
d
on
t
he
pe
rfo
rm
ance
of
the
cl
ose
d
-
l
oop
c
on
t
r
ol
syst
e
m
.
When
the
error
of
the
co
ntr
olled
var
ia
bl
e
is
la
rg
e,
the
gain
am
plifie
s
the
err
or
to
ge
ner
at
e
a
la
rg
e
cor
recti
ve
act
ion
to
rap
i
dly
dr
i
ve
t
he
syst
em
ou
t
pu
t,
res
ulti
ng
in
high
-
s
pee
d
r
esp
on
se
.
Wh
e
n
the
er
ror
di
m
inishes,
the
gain
is
autom
at
ic
ally
reduce
d
to
pre
ven
t
e
xcessi
ve
os
ci
ll
at
ion
s
a
nd
la
rg
e
over
s
hoots
in
the
r
esp
on
se
,
re
su
lt
ing
in
accurate
res
pons
e
with
ze
ro
s
te
ady
-
sta
te
er
r
or.
In
oth
e
r
w
ords
,
the
co
ntr
ol
le
r
posses
ses
t
he
a
dv
a
nta
ge
of
high
init
ia
l
gain
(
w
hich
deliver
s
hi
gh
-
sp
ee
d
respon
s
e)
an
d
low
gain
(that
pre
ve
nts
an
os
ci
ll
at
or
y
beh
a
viou
r
in
the
syst
e
m
resp
on
se
gi
ven
its
au
tom
a
ti
c
nonlin
ear
gain
a
dj
us
tm
ent).
In
an
ot
her
stu
dy,
Ra
hm
at
et
al.
[20]
f
ound
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
En
hance
men
t
in
pn
e
umatic
posit
ion
i
ng
syst
em
us
in
g
nonli
near
ga
i
n
c
on
s
traine
d
…
(
Siti
Fatim
ah
Sulai
man
)
1387
that
the
c
om
bi
nation
of
a
no
nlinear
gai
n
a
nd
the
PID
c
ontrolle
r
re
du
ces
the
ov
e
rs
hoot
a
nd
pro
duces
ac
cur
at
e
trackin
g
in
the
pneum
at
ic
posit
ion
in
g
syst
em
resp
on
se
,
w
hich
was
c
orr
oborat
ed
by
S
al
i
m
et
al.
[21
]
.
The
stud
y
al
s
o
de
m
on
strat
ed
the
en
hancem
ent
of
pne
um
atic
po
sit
io
ning
syst
e
m
in
the
tra
nsi
ent
res
ponse
of
the
syst
e
m
wh
ere
the
nonlinea
r
ga
in
functi
on
an
d
PID
co
ntr
oller
wer
e
c
om
bi
ned
to
c
on
t
ro
l
the
cy
li
nd
er
str
ok
e
of
pn
e
um
at
ic
syste
m
with
a
pay
load
of
m
axim
u
m
weigh
t
up
to
28
kg
at
the
en
d
of
the
pn
e
um
at
ic
cylinder
stroke.
T
he
ef
f
ect
iveness
of
t
he
pro
pose
d
appr
oach
by
Se
raj
i
[
19]
in
reducin
g
the
ove
r
sh
oot
an
d
pr
oducin
g
bette
r
trac
king
in
the
syst
em
per
f
or
m
ance
wa
s
pro
ven
us
i
ng
var
i
ou
s
a
ppli
cat
ion
s,
s
uc
h
as
in
r
obotics,
m
il
li
ng
syst
e
m
s,
and
w
ast
ewater
treat
m
ent
process
[
22
]
-
[
24
]
.
Give
n
s
uch
co
ns
ide
rati
ons,
t
his
stu
dy
inc
orporated
a
no
nlinear
gai
n
in
t
he
co
nv
e
ntio
nal
co
ns
trai
ne
d
MPC
(CMPC
)
as
a
ne
w
c
ontr
ol
strat
egy
to
im
pr
ove
sp
ee
d
re
spo
nse
an
d
acc
ur
ac
y
of
the
pne
um
atic
po
sit
io
ning
sy
stem
.
Since
this
stu
dy
involves
with
re
al
-
tim
e
i
m
p
leme
ntati
on
,
the
refor
e
,
this
s
t
ud
y
al
s
o
consi
der
e
d
t
he
us
e
of
ob
se
r
ve
r
in
t
he
desig
n
of
c
ontr
ol
str
at
egy.
Esse
ntial
ly
,
ob
se
rv
e
r
is
us
e
d
to
est
im
a
te
the
internal
sta
te
va
riable
of
the
r
eal
syst
e
m
[2
5]
.
This
st
ud
y
is
di
vid
e
d
int
o
6
sect
io
ns
.
T
he
bac
kgr
ound
of
the
stud
y
is
discu
s
sed
in
sec
tion
1.
Sect
io
n
2
prov
i
des
the
in
form
ation
ab
ou
t
the
pneum
at
ic
syst
e
m
e
m
plo
yed
in
this
stud
y
by
descr
i
bing
the
syst
e
m
’s
com
po
nen
ts
an
d
exp
la
inin
g
its
op
e
rati
on.
S
ect
ion
3
ex
pla
ins
the
exp
e
rim
ental
s
et
up
a
nd
the
proces
s
of
m
odel
li
ng
the
syst
e
m
us
ing
a
syst
e
m
identific
at
ion
te
ch
nique.
The
proce
dures
in
desig
ning
the
pro
po
se
d
co
ntr
ol
strat
egy
to
perform
the
con
tr
ol
ta
sk
are
pr
ese
nted
in
sect
ion
4.
Sect
ion
5
pr
es
ents
an
d
discu
s
ses
the
exp
e
ri
m
ental
resu
lt
s
of
the
propose
d
co
ntr
oller.
T
he
eff
ect
i
ven
es
s
of
the
pro
po
se
d
c
ontr
ol
strat
egy
in
c
om
par
ison
to
t
he
oth
e
r
c
on
tr
ollers
is
al
s
o
dem
on
strat
ed
in
sect
i
on
5
an
d
la
stl
y,
sect
i
on
6
c
oncl
ud
e
s
the
overal
l
fin
dings
of
the
stu
dy
.
2.
PNEU
M
ATI
C
S
YS
TE
M
D
ESCRIPT
IO
N
The
pne
um
at
ic
syst
e
m
us
ed
in
this
stu
dy
is
sh
ow
n
in
Fi
gure
2.
It
was
e
quip
ped
with
opti
cal
senso
r
(A
E
DR
-
8300
)
,
la
ser
st
ripe
r
od,
press
ur
e
se
ns
or
(
KOG
ANEI:
PS
U
-
EM
-
S)
)
,
valves
(
K
OGA
NEI
:
EB10ES
1
-
PS
-
6W)
,
an
d
pro
gr
am
m
able syst
e
m
o
n
c
hip
(P
S
oC)
c
ontr
ol
boar
d.
The
pn
eum
atic
syst
em
us
ed
in
t
his
stud
y
is
a
double
-
act
in
g
ty
pe
cy
li
nd
e
r
(
K
OGA
NEI
-
HA:
t
winport
cy
li
nd
ers
)
with
16
mm
rod
di
a
m
et
er
and
200
mm
rod
st
roke
le
ngth.
T
he
sc
hem
at
ic
diagr
am
of
the
syst
em
is
il
l
us
trat
ed
in
Fig
ur
e
3.
Figure
2.
The
pn
e
um
at
ic
syste
m
and
its
m
ain
c
om
po
ne
nts
Tw
o
valve
s
w
hich
w
ere
at
ta
ched
at
the
e
nd
of
the
cy
li
nder,
we
re
em
plo
ye
d
to
co
ntr
ol
the
inlet
and
ou
tl
et
ai
r
of
t
he
cy
li
nd
er.
I
n
t
his
stu
dy,
the
e
xtensi
on
a
nd
r
et
racti
on
of
t
he
cy
li
nd
er
st
rok
e
are
m
anipu
la
te
d
by
the
duty
cy
cl
e
of
a
pulse
-
widt
h
m
od
ulato
r
(PWM
)
si
gn
al
t
o
dr
i
ve
th
e
val
ve
s.
T
he
P
WM
m
od
el
in
this
s
tud
y
has
a
pr
eci
si
on
of
8
-
bit.
Wh
e
n
the
P
W
M
m
od
el
recei
ves
a
po
sit
ive
sig
nal
fr
om
the
plant
or
co
ntr
oller,
it
will
conve
rt
the
sig
nal
into
e
qu
i
va
le
nt
P
W
M
sig
na
l
and
se
nd
t
ha
t
sign
al
to
the
valve
1
to
pe
rfor
m
extensio
n.
If
the
P
W
M m
od
e
l r
ecei
ves
neg
at
iv
e
sig
nal, the
m
od
el
will
send t
he
si
gn
al
t
o valve
2
to
p
e
rfo
r
m
r
et
racti
on
.
S
t
r
i
p
e
c
o
d
e
O
p
t
i
c
a
l
e
n
c
o
d
e
r
P
r
e
s
s
u
r
e
s
e
n
s
o
r
V
a
l
v
e
s
P
S
o
C
m
i
c
r
o
c
o
n
t
r
o
l
l
e
r
b
o
a
r
d
G
u
i
d
e
r
o
d
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
23
, N
o.
3
,
Se
ptem
ber
20
21
:
13
85
-
139
7
1388
Figure
3.
The
pn
e
um
at
ic
syste
m
schem
atic
diag
ram
3.
MO
DEL
I
DENTIFI
CA
TI
O
N
Figure
4
sho
ws
the
ex
per
im
ental
set
-
up,
as
a
par
t
of
the
pro
cess
to
obta
in
t
he
m
at
he
m
atic
al
m
od
el
of
the
syst
e
m
.
In
this
stud
y,
a
m
at
hem
atical
mo
del
of
the
pne
um
atic
syst
e
m
was
ide
ntifie
d
by
m
eans
of
syst
e
m
identific
at
ion.
The
platf
orm
f
or
this
st
ud
y
was
MAT
LA
B/
Si
m
ulink
,
w
hich
was
eq
ui
pp
e
d
in
t
he
co
m
pu
te
r.
The
no
m
inal
pr
essu
re
us
ed
w
as
0.6
MPa
a
nd
a
natio
nal
in
strum
ent
(N
I
)
(P
CI/P
XI
-
62
21)
was
us
e
d
f
or
data
acqu
isi
ti
on
(DAQ)
syst
em
.
D
A
Q
s
y
s
t
e
m
P
n
e
u
m
a
t
i
c
s
y
s
t
e
m
P
e
r
s
o
n
a
l
c
o
m
p
u
t
e
r
(
e
q
u
i
p
p
e
d
w
i
t
h
M
A
T
L
A
B
s
o
f
t
w
a
r
e
)
A
i
r
c
o
m
p
r
e
s
s
o
r
s
y
s
t
e
m
Figure
4.
The
s
et
-
up
of
e
xperi
m
ent
A
total
of
2000
m
easur
em
ents
of
i
nput
an
d
ou
t
pu
t
data
w
ere
colle
ct
ed
at
sa
m
pling
ti
m
e
(
)
of
10
ms
du
ri
ng
e
xp
erim
ent.
The
input
data
c
on
t
ai
ns
20
00
data
po
i
nts
of
co
nt
inu
ous
ste
p
si
gn
al
a
pp
li
ed
to
the
valves
,
w
hile
the
ou
t
pu
t
da
ta
con
sist
of
2000
m
easurem
ents
of
cy
li
nd
e
r
stroke
po
sit
io
n
sig
na
l.
The
Au
t
oReg
ressiv
e
with
eX
og
e
nous
i
nput
(
ARX)
par
am
et
ric
m
od
el
was
cho
se
n
for
this
stud
y
since
it
sat
isfie
s
the
crit
eria
f
or
syst
e
m
identific
at
ion
.
T
he
id
entifi
ed
discret
e
sta
te
-
sp
ace
m
od
el
based
ARX
m
od
el
st
ru
ct
ure
util
iz
ed
thr
oughout
this
stu
dy
is
represe
nted
by
(
1).
=
[
0
1
0
0
0
1
0
.
1284
−
0
.
9976
1
.
8690
]
,
=
[
0
0
1
]
,
=
[
0
.
0016
0
0
]
,
=
[
0
]
(1)
C
h
a
m
b
e
r
1
C
h
a
m
b
e
r
2
V
a
l
v
e
1
V
a
l
v
e
2
P
r
e
s
s
u
r
e
s
e
n
s
o
r
C
y
l
i
n
d
e
r
S
u
p
p
l
y
p
r
e
s
s
u
r
e
(
0
.
6
M
P
a
)
E
x
h
a
u
s
t
O
p
t
i
c
a
l
e
n
c
o
d
e
r
E
x
t
e
n
d
R
e
t
r
a
c
t
S
t
r
o
k
e
I
2
C
C
o
u
n
t
e
r
P
W
M
A
D
C
P
S
o
C
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
En
hance
men
t
in
pn
e
umatic
posit
ion
i
ng
syst
em
us
in
g
nonli
near
ga
i
n
c
on
s
traine
d
…
(
Siti
Fatim
ah
Sulai
man
)
1389
The
ide
ntifie
d
m
od
el
fits
the
act
ual
plant
m
od
el
at
a
value
of
ap
pro
xim
a
t
el
y
91
.09
%.
The
loss
of
8.91%
m
ay
be
due
to
dea
d
-
z
one,
fr
ic
ti
on
a
nd
ai
r
le
a
kag
e
.
in
the
pn
e
um
at
ic
sys
tem
it
sel
f.
All
the
nonlinea
riti
es
in
this
stu
dy
ar
e
neg
le
ct
e
d
an
d
the
syst
em
util
iz
ed
is
assume
d
to
be
a
li
near
syst
em
.
As
the
m
od
el
in
(
1)
pr
ov
i
des
al
l
the
pole
s
insi
de
the
un
it
ci
rcle
(
0.1
887,
0.6
811
an
d
0.999
2),
it
is
consi
der
e
d
sta
ble.
4.
CONTR
OLL
ER
DE
SIG
N
This
sect
io
n
di
scusses
the
relevan
t
desi
gn
of
the
c
onve
ntio
nal
co
ns
trai
ned
MPC
(CMPC
)
to
c
ontr
ol
the
posit
io
n
of
pn
e
um
at
ic
syste
m
with
certai
n
m
od
ific
at
ions
f
or
en
ha
nced
perform
ance.
4.1.
MP
C
f
or
mulati
on
MPC
is
a
ty
pe
of
c
on
tr
oller
t
hat
is
desig
ne
d
base
d
on
a
m
at
he
m
at
ic
a
l
m
od
el
of
t
he
plant.
In
this
stud
y,
the
pne
um
atic
m
od
el
us
e
d
was
ta
ke
n
to
be
a
sta
te
-
sp
ace
m
od
el
,
and
the
pneum
at
i
c
syst
e
m
us
ed
in
this
stud
y
was
ass
um
ed
as
a
SISO
syst
e
m
.
The
de
te
rm
inist
ic
m
od
el
of
pneum
at
ic
syst
e
m
e
m
plo
ye
d
in
the
s
tud
y
with
inputs
a
nd
outp
uts
is
de
scribe
d
as
(
2)
a
nd
(
3).
(
+
1
)
=
(
)
+
(
)
(2)
(
)
=
(
)
+
(
)
(3)
W
he
re
,
,
,
a
nd
ar
e
syst
em
m
at
ri
ces
with
a
ppropr
ia
te
dim
ensi
on
s
,
is
t
he
sta
t
e
va
riabl
e
vecto
r
with
dim
ension
,
is
the
input
var
ia
ble
vecto
r,
an
d
is
the
process
outp
ut
vect
or.
In
this
stu
dy,
a
nd
=
1
sinc
e
t
he
s
yst
e
m
is
a
S
ISO
syst
e
m
.
Ma
trix
is
ass
um
ed
to
be
ze
r
o
in
orde
r
to
dem
on
s
trat
e
that
there
is
no
direct
f
eed
thr
ough
the
in
pu
t,
(
)
an
d
the
outp
ut,
(
)
.
This
is
due
to
the
pr
i
nciple
of
r
eced
ing
horizo
n
con
t
ro
l
it
sel
f,
in
wh
ic
h
only
a
curre
nt
inf
or
m
at
ion
of
the
plant
is
requir
ed
for
pre
dicti
on
an
d
c
on
t
ro
l
.
The
m
od
el
in
(2)
w
as
i
m
pr
ov
e
d
in
order
to
incl
ude
an
inte
gr
at
or
in
the
desi
gn.
The
dif
fer
e
nt
on
bo
t
h
sides
of
(2)
yi
el
ded
the
inc
rem
ental
sta
te
-
sp
ace
in
(
4),
∆
(
+
1
)
=
∆
(
)
+
∆
(
)
(4)
W
he
re
,
∆
(
+
1
)
=
(
+
1
)
−
(
)
,
∆
(
)
=
(
)
−
(
−
1
)
,
∆
(
)
=
(
)
−
(
−
1
)
∆
(
+
1
)
and
∆
(
)
de
note
the
differe
nce
of
the
sta
te
var
ia
ble,
a
nd
∆
(
)
de
no
t
es
the
di
ff
e
rence
of
t
he
con
t
ro
l
va
riabl
e.
A
new
sta
te
var
ia
ble
vector
in
(
5)
was
sel
ect
ed
in
order
to
c
onnect
the
s
ta
te
var
ia
ble
∆
(
)
to
the
outp
ut
(
)
.
(
)
=
[
∆
(
)
(
)
]
(5)
Con
si
der
i
ng
(4)
in
outp
ut,
(3)
can
be
wr
it
te
n
in
the
f
or
m
of
(
6),
(
+
1
)
−
(
)
=
(
(
+
1
)
−
(
)
)
(6)
Re
arr
a
ng
e
(
6)
base
d
on
(
4)
gi
ves
,
(
+
1
)
=
∆
(
)
+
∆
(
)
+
(
)
(7)
The
a
ugm
ente
d
sta
te
-
s
pace
m
od
el
as
ind
ic
at
ed
in
(
8)
c
an
be
ob
ta
ine
d
by
pu
tt
in
g
to
get
he
r
(4)
a
nd
(
7).
(
+
1
)
=
(
)
+
∆
(
)
,
(
)
=
(
)
(8)
W
he
re,
=
[
0
]
,
=
[
]
,
=
[
0
1
]
,
and
is
the
a
ugm
ented
m
od
el
,
0
is
the
zer
o
m
at
rix
with
dim
ensio
n
×
and
is
a
un
it
m
at
rix
wit
h
dim
ension
×
.
Con
side
rin
g
(1)
as
a
plant
m
od
el
,
the
a
ug
m
ented
m
od
el
of
the
pn
e
um
at
ic
syste
m
util
iz
ed
in
this
stu
dy
is
re
pr
ese
nted
as,
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
23
, N
o.
3
,
Se
ptem
ber
20
21
:
13
85
-
139
7
1390
=
[
0
1
0
0
0
0
1
0
0
.
1284
−
0
.
9976
1
.
869
0
0
0
.
0016
0
1
]
,
=
[
0
0
1
0
]
,
=
[
0
0
0
1
]
(9)
T
he
a
ugm
ente
d
m
od
el
in
(
9)
has
ei
ge
nv
al
ue
s
at
1,
0.9
992,
0681
1,
a
nd
0.188
7.
The
fir
st
is
from
the
au
gm
entation
of
the
pl
ant
m
od
el
,
w
hile
the
la
st
three
are
fro
m
the
or
i
gin
a
l
pn
e
um
at
ic
plant.
Con
se
quently
,
the
au
gm
ented
sta
te
-
sp
ace
m
od
el
has
one
in
te
gr
at
or
em
bedded
into
t
he
a
ugm
ented
sta
te
-
sp
ace
m
od
el
to
su
it
t
he
c
on
t
ro
ll
er
de
sign
pur
pose.
The
desig
n
of
MPC
is
base
d
on
opti
m
iz
ing
the
di
ff
e
ren
ce
of
t
he
con
t
ro
l
sig
nal
∆
(
)
withi
n
an
optim
iz
ation
window.
∆
(
)
,
or
so
ca
ll
ed
the
f
uture
co
ntr
ol
tra
j
ec
tory
is
denoted
by
(
10),
Δ
(
)
,
Δ
(
+
1
)
,
⋯
,
Δ
(
+
−
1
)
(10)
W
he
re
is
the
con
t
ro
l
horizo
n,
w
hich
is
use
d
to
dicta
te
the
nu
m
ber
of
par
am
et
ers
in
order
to
ca
ptur
e
the
fu
t
ur
e
co
ntr
ol
t
raj
ect
or
y.
Wh
e
n
the
sta
te
var
i
able
vector
(
)
at
sam
pling
tim
e
instant
is
ass
um
ed
avail
able
thr
ough
m
easur
em
ent,
the
c
urre
nt
plant
i
nfor
m
at
ion
is
prov
i
ded
by
the
sta
te
(
)
.
W
it
h
giv
en
in
form
at
ion
(
)
,
the
f
uture
sta
te
va
riables
a
re
de
no
te
d
as
(
11),
(
+
1
|
)
,
(
+
2
|
)
,
⋯
,
(
+
|
)
,
⋯
,
(
+
|
)
(11)
W
he
re
(
+
|
)
is
the
predict
ed
sta
te
va
riable
at
+
with
the
giv
e
n
c
urr
ent
pla
nt
in
for
m
at
ion
(
)
an
d
is
the
pr
e
dicti
on
horizo
n
or
t
he
le
ng
t
h
of
op
tim
iz
at
ion
window.
Gen
e
rall
y,
≤
.
In
t
his
st
udy,
an
d
wer
e
c
hosen
to
be
3
an
d
20,
resp
ect
ively
.
T
he
seq
ue
ntial
ly
cal
culat
ed
f
utu
re
sta
te
va
ria
ble
us
in
g
the
s
et
of
fu
t
ur
e
c
ontr
ol
par
am
et
ers
is
e
xpresse
d
,
(
+
1
|
)
=
(
)
+
∆
(
)
(
+
2
|
)
=
2
(
)
+
∆
(
)
+
∆
(
+
1
)
(
+
|
)
=
(
)
+
−
1
∆
(
)
+
−
2
∆
(
+
1
)
+
⋯
+
−
∆
(
+
−
1
)
(12)
T
he
s
ubsti
tuti
on
of
(
12)
i
nto
outp
ut
in
(
8)
pro
vid
es
the
pr
e
di
ct
ed
outp
ut
vari
ables,
as
sho
w
n
in
(
13)
,
(
+
1
|
)
=
(
)
+
∆
(
)
(
+
2
|
)
=
2
(
)
+
∆
(
)
+
∆
(
+
1
)
(
+
|
)
=
(
)
+
−
1
∆
(
)
+
−
2
∆
(
+
1
)
+
⋯
+
−
∆
(
+
−
1
)
(13)
Be
sides,
(13
)
c
an
al
s
o
be
wr
it
te
n
in
a
c
om
pact
m
at
rix
form
as,
=
(
)
+
ΦΔ
(14)
W
he
re
,
=
[
CA
C
A
2
⋮
]
,
Φ
=
[
0
⋯
0
⋯
0
⋮
⋮
⋮
⋮
−
1
−
2
⋯
−
]
I
n
t
his
stu
dy,
a
sta
te
est
i
m
a
t
or
or
an
ob
se
rv
e
r
syst
em
w
as
em
plo
ye
d
in
the
desig
n
of
c
ontrol
stra
te
gy.
Assum
ing
at
tim
e
,
the
in
for
m
at
ion
of
sta
t
e
var
ia
ble
(
)
wa
s
not
m
easur
a
ble
(
or
a
vaila
bl
e),
an
obser
ve
r
syst
e
m
will
be
us
e
d
to
est
im
ate
the
sta
te
var
i
able
(
)
f
ro
m
the
process
m
easur
em
ent.
Hen
ce,
the
f
uture
sta
te
var
ia
ble
in
(
12)
w
as
cal
culat
e
d
us
in
g
t
he
est
im
at
ed
sta
te
vari
ables
as
in
(
15
),
̂
(
+
1
)
=
̂
(
)
+
∆
(
)
+
(
(
)
−
̂
(
)
)
(15)
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
En
hance
men
t
in
pn
e
umatic
posit
ion
i
ng
syst
em
us
in
g
nonli
near
ga
i
n
c
on
s
traine
d
…
(
Siti
Fatim
ah
Sulai
man
)
1391
W
he
re
is
the
gain
m
at
rix.
T
he
po
le
-
place
m
ent
was
em
plo
ye
d
as
a
te
c
hn
i
qu
e
to
cal
culat
e
the
s
uitable
value.
The
pole
s,
w
hich
wer
e
us
e
d
to
fi
nd
the
s
uitable
ar
e
to
be
wer
e
m
ai
ntained
in
the
un
it
ci
rcle
in
ord
er
to
e
nsure
t
he
sta
bili
t
y
of
t
he
syst
e
m
.
The
value
of
pole
s
assi
gned
in
t
his
stu
dy
is
dem
on
str
at
ed
in
Table
1.
In
this
stud
y,
the
s
equ
e
nce
of
Δ
(
)
,
Δ
(
+
1
)
,
⋯
,
Δ
(
+
−
1
)
in
(10)
was
a
ppr
oxim
a
te
d
us
in
g
a
set
of
discrete
-
ti
m
e
Lag
uerre
f
un
ct
ion
s
.
The
set
of
discrete
-
ti
m
e
Lagu
e
rr
e
functi
ons
ex
pr
es
sed
a
vecto
r
f
orm
descr
ibe
d
in
(
16),
w
hile
(
17)
e
xpresse
d
its
di
ff
e
ren
ce
eq
uatio
n,
(
)
=
[
1
(
)
2
(
)
⋯
(
)
]
(16)
(
+
1
)
=
(
)
(17)
W
he
re
is
t
he
m
at
rix
with
di
m
ension
×
an
d
is
a
functi
on
of
pa
ram
et
ers
a
nd
.
The
init
ia
l
conditi
on
of
(
16)
is
giv
e
n
in,
(
0
)
=
√
×
[
1
−
2
⋯
(
−
1
)
−
1
−
1
]
(18)
is
the
scal
in
g
facto
r
of
the
Lag
uerre
netw
ork
a
nd
=
1
−
2
.
To
e
nsure
the
sta
bili
ty
of
t
he
netw
ork,
m
us
t
be
within
0
≤
<
1
.
In
this
st
udy,
the
valu
e
of
us
ed
is
0.1.
This
stu
dy
is
set
out
to
res
pect
the
act
uator
c
on
st
r
ai
nts
w
hile
br
i
ng
i
ng
a
nd
m
ain
ta
inin
g
t
he
po
sit
ion
of
the
cy
li
nd
er
str
ok
e
as
cl
os
e
as
poss
ible
to
the
desire
d
pos
it
ion
.
In
do
i
ng
so
,
the
m
anip
ul
at
ed
an
d
c
ontr
olled
var
ia
bles
bei
ng
co
ns
i
de
red
we
re
t
he
si
gn
al
to
the
val
ves
a
nd
t
he
posit
io
n
of
the
cy
li
nder
str
oke.
M
PC
was
use
d
in
this
stu
dy
to
determ
ine
the
fu
tu
re
adjustm
ents
of
the
sign
al
to
the
valve
.
MP
C
pr
e
dicte
d
the
fu
tu
re
pla
nt
ou
t
pu
ts
a
nd
pe
rfor
m
ed
the
con
t
ro
l
act
ion
s
acco
r
di
ng
ly
by
so
lvi
ng
the
optim
al
fu
tu
re
co
ntr
ol
act
ion
s
(c
os
t
functi
on
an
d
c
on
st
raints)
.
Th
e
cost
functi
on
that
r
eflect
the
c
on
t
r
ol
ob
j
ect
ive
of
this
stu
dy
is
de
fine
d
as,
=
∑
(
+
|
)
(
+
|
)
+
=
1
(19)
W
he
re
an
d
ar
e
the
weig
htin
g
m
at
rices
with
=
(
or
≥
0
)
an
d
wa
s
ch
os
e
n
to
be
0
.
1
(or
>
0
)
.
=
=
[
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
]
(20)
Wh
e
re,
=
[
0
0
0
1
]
S
ince
this
stu
dy
aim
s
to
br
in
g
an
d
m
ai
ntain
the
pr
e
dicte
d
ou
t
pu
t
as
cl
os
e
as
po
ssi
ble
to
the
set
-
point
s
ign
al
,
the
sta
te
var
ia
ble
(
+
|
)
in
(
19)
m
us
t
be
re
-
de
fin
ed
in
orde
r
to
include
the
set
-
point
sig
nal
in
t
he
c
ost
functi
on
e
qu
at
i
on.
Hen
c
e,
(21
)
is
t
he
new
e
quat
ion
of
the
sta
te
var
ia
ble
with
the
inclu
sio
n
of
set
-
po
i
nt
s
ign
al
(
)
within
the
opti
m
iz
at
ion
wind
ow,
(
+
|
)
=
[
∆
(
+
|
)
(
+
|
)
−
(
)
]
(21)
T
he
opti
m
a
l
so
luti
on
of
t
he
pa
ram
et
er
ve
ct
or
in
(
19)
base
d
on
m
inim
iz
at
ion
of
the
c
os
t
functi
on
is
represe
nted
as
(22),
=
−
Ω
−
1
(
)
(22)
W
he
re
,
Ω
=
∑
(
)
(
)
+
=
1
,
=
∑
(
)
=
1
U
pon
ob
ta
ini
ng
the
opti
m
al
s
olu
ti
on
of
the
pa
ram
et
er
vecto
r
,
the
c
ontrol
la
w
ca
n
is
reali
sed
as
,
Δ
(
)
=
(
0
)
(23)
The
c
ontrol
la
w
in
(
23)
ca
n
al
so
be
re
prese
nted
in
the
f
orm
of
li
near
sta
te
feedbac
k
c
ontr
ol
as
e
xpres
sed
in
(24),
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
23
, N
o.
3
,
Se
ptem
ber
20
21
:
13
85
-
139
7
1392
Δ
(
)
=
−
(
)
(24)
W
he
re
,
=
(
0
)
Ω
−
1
,
(
)
=
[
∆
(
)
(
)
]
H
ence
,
the
co
nt
ro
l
la
w
to
be
a
pp
li
ed
can
be
wr
it
te
n
as
,
(
)
=
∆
(
)
+
(
−
1
)
(25)
(
)
is
the
error
si
gn
al
betwee
n
the
predict
e
d
outp
ut
(
)
an
d
set
-
po
i
nt
signa
l
(
)
.
W
hen
an
ob
se
r
ve
r
is
us
e
d
in
the
des
ign
,
al
l
the
act
ual
sta
te
va
riab
le
(
)
will
be
re
placed
with
the
obser
ve
d
sta
te
va
riable
̂
(
)
.
4.2.
MP
C
with
co
nst
r
ain
ts
on
in
put
valv
e
s
Re
stric
ti
on
s
w
ere
giv
e
n
to
the
co
ntr
ol
sig
na
l
to
the
syst
em
’s
m
anipu
la
te
d
var
ia
ble
or
i
nput
valve
s
in
the
case
of
the
pn
e
um
at
ic
sys
tem
us
ed
in
t
hi
s
stud
y.
In
t
hi
s
stud
y,
a
co
nt
ro
l
sig
nal
was
def
i
ned
as
a
si
gn
al
expo
rted
f
ro
m
the
con
t
ro
ll
er
,
wh
ic
h
will
infl
uen
ce
the
s
yst
e
m
resp
ons
e
(i.e.
the
pos
it
ion
of
t
he
cy
li
nd
er
stroke)
.
Th
us
,
t
his
sig
nal
shoul
d
be
co
ntr
olled
to
en
sure
tha
t
would
al
ways
be
in
a
ra
ng
e
t
hat
is
al
lowed
by
the
syst
e
m
.
If
the
m
axi
m
u
m
a
llo
wa
ble
value
is
exceed
ed
,
an
ov
e
rs
hoot
m
igh
t
be
ge
ne
rated
in
the
syst
e
m
respo
ns
e.
T
his
ph
e
no
m
enon
m
ay
occu
r
fr
e
qu
e
ntly
as
the
syst
e
m
is
i
m
p
lem
ented
in
real
-
tim
e
env
iro
nm
ent.
The
m
axi
m
u
m
am
pli
tud
e
va
lue
al
lowe
d
f
or
t
he
e
xtensi
on
an
d
retract
ion
of
the
cy
l
ind
e
r
str
oke
duri
ng
op
e
rati
on
wer
e
set
to
+
255
(
f
or
val
ve
1)
an
d
-
255
(for
va
lv
e
2),
res
pecti
ve
ly
.
Hen
ce
,
t
he
sign
al
from
the
MPC
to
the
syst
em
’s
valves
wa
s
co
ns
trai
ne
d
withi
n
±
255.
S
uppo
se
that
the
li
m
i
ts
on
the
valve
s
co
ntr
ol
sig
na
ls
are
=
−
255
and
=
+
255
,
and
(
)
=
∑
∆
(
)
.
−
1
=
0
Con
s
eq
ue
ntly
,
the
ine
qual
it
y
const
raints
for
fu
t
ur
e
ti
m
e
,
=
1
,
2
,
…
can
be
e
xpresse
d
as:
−
255
≤
+
(
−
1
)
≤
+
255
(26)
W
he
re
,
=
[
∑
1
(
)
−
1
=
0
0
2
⋯
0
0
1
∑
2
(
)
−
1
=
0
⋯
0
⋮
⋮
⋮
⋮
0
1
0
2
⋯
∑
(
)
−
1
=
0
]
W
w
he
re
(
−
1
)
is
the
previ
ou
s
co
ntr
ol
sig
nal
a
nd
0
is
a
row
vecto
r
with
dim
ension
as
in
(
0
)
.
4.3.
The
desi
gn
of
n
on
li
ne
ar
gain
c
on
s
trai
ned
m
od
el
pr
edic
tive
c
ontr
oller
This
st
ud
y
inc
orp
or
at
ed
the
nonlinea
r
gai
n
in
a
co
ntr
oller
a
lgorit
hm
kn
ow
n
as
the
co
ns
tr
ai
ned
m
od
el
pr
e
dicti
ve
co
nt
ro
ll
er
(CMPC
)
as
a
ne
w
ap
proac
h
to
en
ha
nce
the
pe
rfo
rm
ance
of
pn
eum
atic
po
sit
ion
i
ng
syst
e
m
,
especial
ly
in
its
transient
respo
ns
e.
The
justi
ficat
ion
s
of
inc
orp
orat
ing
the
nonl
inear
gai
n
within
the
con
t
ro
ll
er
al
gorithm
as
a
new
appr
oach
f
or
t
his
stu
dy
inclu
ded
t
he
f
ollo
w
ing
:
1)
it
is
ch
al
le
ng
in
g
to
pr
ov
i
de
good
transie
nt
respon
se
with
the
us
e
of
li
ne
ar
co
ntro
ll
er
(which
in
this
case,
the
co
nventional
c
on
st
r
ai
ned
MPC
)
for
the
s
yst
e
m
(in
ot
her
w
ords,
it
is
im
po
s
sible
to
ac
hi
eve
high
s
pee
d
respo
ns
e
without
ov
e
rs
hoot
with
the
us
e
of
li
ne
ar
co
ntr
oller,
pa
rtic
ularly
in
r
eal
-
tim
e
env
iron
m
ent)
due
to
the
existe
nce
of
nonlinea
riti
es
an
d
un
ce
rtai
nties
in
the
syst
e
m
and
2)
the
inc
lusio
n
of
co
nst
raints
in
the
con
t
ro
ll
er
al
go
rithm
deg
ra
de
d
the
respo
ns
e
ti
m
e
of
the
syst
em
;
t
hu
s
,
m
aking
the
syst
e
m
slow
e
r.
This
stu
dy
al
s
o
co
ns
i
der
e
d
t
hat
the
us
e
of
li
near
c
on
tr
ol
le
r
rem
ai
ns
relevan
t
in
c
ontrolli
ng
the
po
sit
io
n
of
t
he
pn
e
um
at
ic
sy
stem
in
this
stud
y
a
nd
certai
n
m
od
ific
at
ions
can
im
pr
ove
the
pe
rfo
rm
a
nce
of
syst
e
m
.
Thu
s,
the
unde
rly
in
g
pri
nci
ple
to
this
pro
posed
con
t
ro
l
strat
e
gy
f
or
this
st
ud
y
was
to
e
m
plo
y
nonlinea
r
el
e
m
ents
in
the
li
near
co
ntro
ll
er
schem
e,
wh
ic
h
com
pen
sat
e
for
er
r
or
va
riat
ion
s
in
the
pne
um
atic
po
sit
io
ning
syst
e
m
,
wh
il
e
si
mu
lt
aneously
i
m
pro
ving
the
perform
ance
of
syst
e
m
.
Figu
re
5
il
lustrate
s
the
blo
c
k
diag
ram
of
the
pn
e
um
at
ic
po
sit
ion
in
g
syst
em
with
the
pr
opose
d
c
ontrol
stra
te
gy.
As
s
how
n
i
n
F
igure
5,
a
f
unc
ti
on
cal
le
d
no
nl
inear
gain
wa
s
em
plo
ye
d
in
this
stu
dy
to
c
om
pen
sat
e
the
no
nlinearit
ie
s
an
d
un
ce
rta
inti
es
in
the
sy
stem
par
am
et
e
rs.
It
was
uti
li
zed
to
c
on
tr
ol
t
he
e
rror
sig
nal
(
)
betwee
n
the
pr
edict
ed
outp
ut
(
)
an
d
set
-
po
i
nt
sig
nal
(
)
i
n
(24
).
It
is
of
utm
os
t
im
po
rta
nce
to
c
on
tr
ol
(
)
due
to
it
s
in
fl
uen
ce
on
t
he
f
or
m
at
ion
of
th
e
co
ntro
l
sig
na
l
to
the
pn
e
uma
ti
c
syst
e
m
.
T
his
te
ch
niq
ue
wa
s
e
m
plo
ye
d
in
t
his
stu
dy
to
a
dju
st
the
co
ntr
oller
gai
n
acc
ordin
g
to
t
he
ou
t
pu
t
pro
du
c
ed
f
ro
m
this
f
un
ct
io
n,
wh
ic
h
is
know
n
as
the scale
d err
or
(
)
as d
esc
ribed in
(
27).
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
En
hance
men
t
in
pn
e
umatic
posit
ion
i
ng
syst
em
us
in
g
nonli
near
ga
i
n
c
on
s
traine
d
…
(
Siti
Fatim
ah
Sulai
man
)
1393
(
)
=
(
)
×
(
)
(27)
W
he
re,
(
)
=
e
xp
(
)
+
e
xp
(
−
)
2
(28)
=
{
×
(
)
|
|
≤
|
|
>
Figure
5.
Bl
oc
k
diag
ram
of
the
pro
posed
co
nt
ro
l
strat
e
gy
The
value
of
nonlinea
r
gain
f
un
ct
io
n
(
)
in
(
28)
was
a
dju
ste
d
accor
ding
to
the
er
r
or
from
the
syst
e
m
,
wh
il
e
the
par
am
et
er
va
lues
of
bo
t
h
r
at
e
var
ia
ti
on
of
nonlinea
r
gain
(
)
an
d
var
ia
ti
on
of
er
ror
(
)
wer
e
sel
ect
ed
by
the
us
er
.
(
)
act
s
as
a
nonlinear
f
unct
ion
of
er
r
or
an
d
is
bo
unde
d
in
t
he
s
ect
or
as
descr
i
bed
in
(
29)
.
Fi
gure
6
il
lustrate
s t
he
rel
at
ion
s
hip
betw
een
an
d
.
0
≤
(
)
≤
(
)
(29)
Figure
6.
Re
la
ti
on
s
hip
bet
wee
n
an
d
The
inc
orp
or
at
ion
of
a
nonlinear
gain
func
ti
on
into
t
he
c
on
t
ro
ll
er
al
go
r
it
h
m
in
(25)
ge
ner
at
es
the
pro
po
se
d
c
on
t
r
ol
strat
egy
(
30).
T
his
stu
dy
pe
rfor
m
ed
the
f
ollow
i
ng
proce
dures
in
Fig
ure
7
to
determ
i
ne
the
par
am
et
er v
al
ue
s of
.
(
)
=
−
[
1
∆
1
(
)
+
2
∆
2
(
)
+
3
∆
3
(
)
+
4
(
(
)
×
(
)
)
]
+
(
−
1
)
(30)
As
s
how
n
i
n
Figure
7,
pri
or
to
the
sel
ect
ion
of
the
val
ue
of
pa
ram
eter
s
an
d
(28),
the
m
axi
m
u
m
valu
e
of
for
sta
bili
ty
m
us
t
be
ob
t
ai
ned
.
It
was
r
eveale
d
i
n
t
he
cl
os
ed
-
lo
op
sta
bili
ty
us
ing
Jur
y
sta
bili
ty
te
st
th
at
the
pe
rfor
m
ance
of
t
he
pro
po
s
ed
c
ontr
ol
s
yst
e
m
te
nd
to
un
sta
ble
w
he
n
≥
2
.
96
.
Th
us,
it
is
rec
omm
end
ed
t
hat
is
within
the
ra
nge
of
0
<
<
2
.
693
f
or
syst
em
sta
bili
ty
.
Ba
s
ed
on
t
he
pri
or
proce
dures
a
nd
te
sts,
t
he
rec
omm
end
ed
val
ue
of
an
d
w
ere
set
at
12
a
nd
0.1
,
res
pect
ively
.
Table
1
descr
i
bes
t
he p
aram
et
ers
of
t
he
prop
os
ed
con
trol strate
gy u
s
ed
in
this st
ud
y
.
Ba
sed
on
(
28)
,
w
hen
=
12
an
d
=
0.1
,
(
)
=
1
.
811
,
w
hich
im
plies
that
it
is
with
in
the
sta
ble
re
gion.
Ge
neral
ly
,
hi
gh
e
r
value
of
co
ntri
bu
te
s
the
hi
gh
e
st
over
sho
ot,
wh
ic
h
le
a
ds
t
o
P
n
e
u
m
a
t
i
c
s
y
s
t
e
m
C
o
n
v
e
n
t
i
o
n
a
l
M
P
C
w
i
t
h
o
b
s
e
r
v
e
r
s
y
s
t
e
m
N
o
n
l
i
n
e
a
r
g
a
i
n
S
e
t
-
p
o
i
n
t
(
i
n
p
u
t
)
S
t
r
o
k
e
p
o
s
i
t
i
o
n
(
m
m
)
+
-
N
o
n
l
i
n
e
a
r
g
a
i
n
,
k
n
l
(
e
)
0
1
E
r
r
o
r
,
e
+
e
m
a
x
-
e
m
a
x
+
0
.
1
0
-
0
.
1
0
1
.
8
1
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
23
, N
o.
3
,
Se
ptem
ber
20
21
:
13
85
-
139
7
1394
un
c
ontr
ollable
an
d
un
sta
ble
respo
ns
e
in
th
e
syst
e
m
.
In
a
dd
it
io
n,
util
isa
ti
on
of
t
his
te
c
hn
i
qu
e
aut
om
a
ti
cal
ly
adjusts
t
he
val
ue
of
acco
rd
i
ng
to
t
he
ge
ne
ra
te
d
val
ue
of
(
)
at
each
ti
m
e
inst
ant.
Wh
e
n
the
r
e
is
no
er
ror
pr
ese
nt,
(
)
=
1
. In ot
her
w
ords, the
con
t
ro
ll
er
syst
em
r
eact
s si
m
il
a
rly
to
ot
her co
nventio
nal MPC
w
it
hout
the
presence
of
in
the
co
ntr
ol
le
r
syst
e
m
.
Howev
e
r,
with
th
e
pr
ese
nce
of
e
rror
i
n
the
syst
e
m
and
inclu
sion
of
,
the
c
ontro
ll
er
sig
nal
will
be
a
dju
ste
d
a
ccordin
gly
to
t
he
val
ue
of
(
)
.T
he
key
ad
va
ntage
of
t
his
te
chn
iq
ue
is
th
e fact the
contr
oller
gain valu
e, expect
for
t
he
v
al
ue
s
of
an
d
, does
not re
quire t
un
i
ng.
Figure
7.
Proce
dures
to
deter
m
ine
the
pa
ra
m
et
er
values
of
nonlinear
gai
n
(
)
Table
1
.
Desc
ription
of
t
he
c
ontr
oller’s
pa
ra
m
et
ers
Co
n
trol
strateg
ies
Co
n
trol
p
ara
m
ete
r
s
Na
m
e
of
p
ara
m
et
e
r
Ab
b
reviatio
n
Valu
e
MPC
Predictio
n
h
o
rizon
20
Co
n
trol
h
o
rizon
3
Scalin
g
f
acto
r
of
Lagu
err
e
n
etwo
rk
0
.1
W
eig
h
tin
g
m
atr
ix
0
.1
Ob
serv
er
Ob
serv
er
p
o
les
-
0
.01
0
0
,
0
.0105
,
0
.01
1
0
,
0
.0115
No
n
lin
ear
g
ain
f
u
n
ctio
n
Variation
of
n
o
n
lin
ear
g
ain
12
Variation
of
err
o
r
0
.1
5.
RESU
LT
S
A
ND
DI
SCUS
S
ION
The
ca
pa
bili
ties
of
t
he
pro
po
s
ed
co
ntr
ol
strat
egy
(
NG
-
CM
PC)
to
c
on
t
ro
l
a
nd
to
im
pr
ov
e
the
transient
res
pons
e
perform
ance
of
the
pneu
m
at
ic
po
sit
ion
i
ng
syst
em
,
in
a
real
-
ti
m
e
env
iro
nm
ent
are
ev
al
uated
and
disc
us
se
d
in
this
sect
ion.
The
posit
ion
in
g
c
on
t
ro
l
perf
orm
ance
for
different
distances
us
in
g
t
he
pro
pose
d
con
t
ro
l
strat
e
gy
(NG
-
CM
PC
)
was
prese
nted
an
d
e
valua
te
d.
T
he
pe
rfor
m
ances
of
the
pr
opos
e
d
c
on
t
rol
strat
egy
wer
e
al
so
analy
sed
and
c
om
par
ed
to
the
existi
ng
m
et
ho
ds
of
si
m
il
ar
pn
eum
at
i
c
plant
syst
e
m
s
(r
efe
r
to
pneum
at
ic
s
yst
e
m
us
ed
in
this
stud
y)
in
order
to
deter
m
ine
the
i
m
pr
ov
em
ents.
A
s
a
m
pling
tim
e
of
10
ms
was
us
e
d
in
ex
per
im
enting,
a
nd
the
pro
po
se
d
co
ntr
ol
strat
egy
was
de
velo
ped
us
in
g
MA
TLAB/Si
m
ulink
.
T
he
con
t
ro
ll
er
pa
ra
m
et
ers
sta
te
d
in
Table
1
wa
s
us
ed
in
this
s
ect
ion
in
orde
r
to
per
f
or
m
validat
ion
.
In
thi
s
su
b
-
sect
ion
,
e
xp
e
rim
ents
wer
e
co
nducted
to
te
st
the
i
m
ple
m
ent
at
ion
of
the
propose
d
co
ntr
ol
strat
egy
(NG
-
CM
PC)
in
order
to
c
ontrol
thep
ne
um
a
ti
c
po
sit
ion
in
g
syst
e
m
at
diff
eren
t
distance
s.
Seve
ral
values
of
posit
io
n
dist
an
ce
(50
m
m
,
100
mm,
and
150
mm)
wer
e
pro
vid
e
d
f
or
com
par
is
on,
an
d
t
he
ste
p
sig
nal
w
as
ap
plied
as
t
he
in
pu
t
sign
al
.
Eac
h
te
st
was
cond
ucted
for
20
s.
T
he
perf
or
m
ances
of
the
NG
-
CM
PC
syst
e
m’s
transie
nt
(i.e.
ris
e
tim
e
(
)
,
set
tl
ing
tim
e
(
)
,
ov
e
rs
hoot
(
)
,
an
d
ste
ady
-
sta
te
er
ror
(
)
in
c
on
tr
olli
ng
the
pne
um
a
ti
c
po
sit
io
ning
sy
stem
s
for
al
l
di
sta
nces
we
re
then
c
om
par
ed
with
CM
PC
,
PFC
-
O,
a
nd
P
I.
Fi
gure
8
shows
a
com
par
at
ive
vi
ew
of
these
st
ep
te
sts
wh
e
re
the
po
sit
io
n
di
sta
nce
was
va
ried
f
ro
m
fu
ll
y
retract
ed
(0
m
m
)
to
near
fu
ll
y
retra
ct
ed
(
50
m
m
),
fu
ll
y
retract
ed
(0
m
m
)
to
the
act
uator
m
id
-
stroke
(
100
m
m
),
an
d
f
ully
retr
act
ed
(0
m
m
)
to
near
f
ully
exten
ded
(
150
m
m
).
Table
2
s
umm
arizes
the
data
obta
ined
in
Fi
gur
e
8.
The
ex
pe
rim
en
ta
l
res
ults
in
Fi
gure
8
a
nd
Ta
bl
e
2
dem
on
stra
te
an
inc
rease
i
n
t
he
res
pons
e
tim
e
of
and
for
al
l
strat
egies
as
the
po
sit
io
n
dista
nce
is
increa
s
ed.
I
n
oth
e
r
w
ords,
t
he
lo
nger
the
posit
io
ni
ng
distance
to
be
reache
d
by
the
cy
li
nd
er
str
ok
e,
the
longe
r
th
e
tim
e
ta
ken
by
al
l
strat
egies
to
achieve
it
s
s
te
ady
-
sta
te
value.
T
he
com
par
ison
betwee
n
the
c
ontr
oller
strat
eg
ie
s
sh
ows
that
NG
-
CM
PC
suc
cessf
ully
con
t
ro
ll
ed
the
pneum
at
ic
cy
li
nd
er
str
oke
the
fastest
in
order
t
o
achie
ve
a
po
sit
io
ning
distan
ce
of
50
m
m
,
10
0
m
m
,
and
F
i
n
d
t
h
e
c
l
o
s
e
d
-
l
o
o
p
c
h
a
r
a
c
t
e
r
i
s
t
i
c
e
q
u
a
t
i
o
n
o
f
I
P
A
p
o
s
i
t
i
o
n
i
n
g
c
o
n
t
r
o
l
s
y
s
t
e
m
D
e
t
e
r
m
i
n
e
m
a
x
i
m
u
m
v
a
l
u
e
o
f
n
o
n
l
i
n
e
a
r
g
a
i
n
,
k
n
l
(
e
m
a
x
)
u
s
i
n
g
J
u
r
y
s
t
a
b
i
l
i
t
y
c
r
i
t
e
r
i
o
n
S
e
l
e
c
t
k
a
n
d
e
m
a
x
b
a
s
e
d
o
n
k
n
l
(
e
m
a
x
)
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