Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 4
,
A
ugu
st
2016
, pp
. 16
73
~
1
680
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
4.9
652
1
673
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Model
Driven PI
D Controller in Wat
e
r Heater S
y
stem
T
o
mm
y H
o
n
d
i
ant
o
,
E
r
w
i
n S
u
san
t
o,
A
g
un
g S
u
ry
a
Wi
bo
w
o
Department of
Electrical Eng
i
n
eering
,
Telkom University
,
Ban
dung,
Indon
esia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Dec 7, 2015
Rev
i
sed
May 17
, 20
16
Accepted
May 30, 2016
PID controller h
a
s been widely
used as one of the basic prop
erty
con
t
rollers
in industr
y
.
How
e
ver,
tuning PID
paramete
rs is not simple and also has a few
problems in handling slow response sy
stem
s, such as boiler. Therefore, th
e
Model Driven PID (MD PI
D) control is designed
for solving thes
e problems,
especially
for p
l
ants or processes with
slow response. The MD PID is using
the m
odel of
th
e plan
t i
t
self
as the b
a
sic m
odel of
the
contro
ller
.
In th
is
research
, we will show the performance
of water
heater s
y
stem step response
with MD PID c
ontrolle
r com
p
a
r
ed to
the
conv
ention
a
l PID co
ntrolle
r (PI
controller). Th
e MD PID closed-loop s
y
stem
is exp
e
cted
to give fast
response, stable, and no
oversho
ot.
Keyword:
M
odel
dri
v
en
PID
RTD
Water heater
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
T
o
mmy H
o
n
d
i
an
to
,
Depa
rt
m
e
nt
of
El
ect
ri
cal
Engi
neeri
n
g
,
Telk
o
m
Un
i
v
ersity,
Jln
.
Telek
o
m
un
ik
asi, Teru
san Bu
ah
Batu
, Ban
dun
g 402
57
, In
don
esia.
Em
a
il: to
mmy
h
@
st
u
d
e
n
t
s.tel
k
o
m
u
n
i
v
e
rsity.ac.id
1.
INTRODUCTION
On
e of t
h
e m
o
st co
mm
o
n
con
t
ro
ller
u
s
ed is PID con
t
ro
ller. PID con
t
ro
ller is a classic co
n
t
ro
ller th
at
have
bee
n
wi
d
e
l
y
used t
o
c
o
nt
r
o
l
a pr
ocess
,
suc
h
as m
o
t
o
r spee
d c
ont
rol
,
p
o
si
t
i
oni
ng c
ont
rol
,
l
e
vel
cont
rol
,
t
e
m
p
erat
ure c
ont
rol
,
et
c.
H
o
we
ve
r,
due
t
o
i
t
s
si
m
p
l
e
st
uct
u
re
, P
I
D c
ont
rol
l
e
r al
s
o
bri
ng
som
e
i
ssues
i
n
d
i
fferen
t
areas. To
con
t
ro
l a
pro
cess
with rel
a
tiv
e slow respo
n
s
e, su
ch
as
bo
iler, it will leav
e so
m
e
o
v
e
rsh
o
o
t
fo
r a
l
o
ng
per
i
od.
T
h
ere
f
o
r
e
,
t
h
e
M
o
del
Dri
v
en
P
I
D (MD PID) contro
ller is presen
ted to
h
a
n
d
l
e slow
resp
o
n
se p
r
oce
ss t
o
m
i
nim
i
zing
o
v
ers
h
oot a
s
the expected actual poi
nt valu
e is rising
to
th
e set po
in
t
.
MD
PID con
t
ro
ller also
cap
ab
le to
con
t
ro
l n
on-stab
le syste
m
an
d
o
s
cillatio
n p
r
o
cess. MD
PID con
t
ro
ller is also
gi
ves
m
o
re si
m
p
l
e
co
nt
r
o
l
t
u
ni
ng
p
r
ope
rt
i
e
s.
M
D
PI
D co
nt
r
o
l
l
e
r i
s
pr
op
os
ed by
To
shi
b
a
R
e
search Tea
m
, i
t
i
s
desi
gn
ed by
com
b
i
n
i
ng M
odel
Dri
v
en
Con
t
rol (MDC) con
t
ro
ller syste
m
, PD feed
b
a
ck
,
Intern
al Mod
e
l Co
n
t
ro
l (IMC
)
, an
d
set po
in
t
filter.
Th
e
d
e
sign
ap
pro
ach techniq
u
e
s
of
MD
PI
D con
t
ro
lle
r is d
i
fferen
t co
m
p
are to
con
v
e
n
tion
a
l PID th
at
com
m
onl
y
usi
n
g
t
h
e
Zi
egl
e
r
-
N
i
c
h
o
l
s
[
1
]
,
[
2
]
m
e
t
hod
t
o
de
fi
ned
t
h
e c
o
nt
r
o
l
t
uni
ng
pa
ram
e
t
e
rs.
In
t
h
is research
,
we
d
e
sign
ed th
e MD PID co
n
t
ro
lle
r
system
an
d
si
m
u
lated
it in
water
heater system
.
The purpose
d
was to analyzed the MD
P
I
D
cont
r
o
l
l
e
r sy
s
t
em
wi
t
h
a pl
ant
or
pr
ocess a
nd c
o
m
p
ared t
o
t
h
e
co
nv
en
tio
n
a
l PI
D
con
t
r
o
ller. W
e
used
ph
ysic
ap
pr
o
a
ch
t
o
desi
g
n
t
h
e t
r
a
n
sfe
r
f
u
nct
i
on
m
odel
of t
h
e
wat
e
r
heater system
.
Resistance Tem
p
erature
Det
ect
or (R
T
D
) t
y
pe PT
10
0 wi
t
h
t
w
o wi
r
e
s i
s
u
s
ed as t
h
e se
ns
or
of
water
heater sy
ste
m
for m
easure
d
the
val
u
e
of t
h
e tem
p
er
ature as
the
pres
ent val
u
e (P
V
)
or
o
u
t
p
ut
an
d
as t
h
e
feed
bac
k
val
u
e
o
f
t
h
e
cl
os
ed
-
l
oo
p sy
stem
. The
res
u
lts of t
h
e ste
p
res
p
onse we
re a
n
alyzed a
n
d c
o
m
p
ared t
o
th
e step
resp
on
se of th
e conv
en
tion
a
l PID
co
n
t
ro
ller.
Th
e MD PID stabilit
y an
alysis,
step
resp
on
se
matlab
sim
u
lation of t
h
e system
, and MD P
I
D real
tim
e
result are
prese
n
ted.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
16
73
–
1
680
1
674
2.
R
E
SEARC
H M
ETHOD
The r
e
searc
h
chr
o
nol
ogi
cal
or
der i
n
t
h
i
s
pape
r a
r
e desi
gn t
h
e sy
st
em
m
odel
o
f
t
h
e
cont
rol
l
e
r
,
stab
ility an
alysis, sen
s
or co
nfi
g
uration
,
and
si
m
u
latio
n
an
al
ysis.
2.
1.
Hardw
a
re and
Software
Fi
gu
re 1 sh
o
w
s t
h
e over
a
l
l
sy
st
em
confi
g
u
r
at
i
on use
d
f
o
r
t
h
e researc
h
. T
h
e m
i
croco
n
t
r
o
l
l
e
r and PC
connected
by using serial com
m
unicati
on. Th
e read t
e
m
p
erat
ure pl
ot
t
e
d i
n
M
a
t
l
a
b soft
wa
r
e
. The o
u
t
p
ut
f
r
o
m
m
i
croco
n
t
r
ol
l
e
r i
s
P
W
M
t
o
t
r
i
gge
ri
n
g
t
h
e
he
at
i
ng p
r
oc
ress
base o
n
t
h
e
dut
y
cy
cl
e. Tem
p
arat
ure se
ns
or
(R
TD
)
is u
s
ed
to acquired
so
m
e
actu
a
l te
m
p
eratu
r
e
d
a
ta traj
ect
ory
from
the water
heater system
to
be a
n
alyzed.
Fi
gu
re
1.
Sy
st
em
C
onfi
g
u
r
at
i
o
n
fo
r R
e
sea
r
ch
2.
2.
MD
PI
D
Co
nt
roller
MD PID con
t
ro
ller has three p
a
rts,
PD
feed
b
a
ck
co
m
p
ensato
r, m
a
in
co
n
t
ro
ller, an
d set p
o
i
n
t
filter
[3]
.
Eac
h
part
s
ha
ve di
ffe
rent
fu
nct
i
o
ns.
Th
e t
uni
ng
pa
ra
m
e
t
e
rs used
ar
e
λ
and
α
. M
D
PI
D co
nt
r
o
l
l
e
r bl
oc
k
di
ag
ram
are sh
ow
n i
n
Fi
gu
re
2.
K
c
Q(s)
M(S)
P(S
)
F(s)
SP
(
s
)
In
p
u
t
Re
f
e
r
e
n
c
e
Ou
t
p
u
t
e
+
‐
+
+
+
‐
MAIN
CO
N
T
R
O
L
E
R
G(S
)
Fi
gu
re
2.
M
o
d
e
l
Dri
v
en
PI
D
B
l
ock
Di
ag
ram
2.
2.
1.
P
D
F
e
ed
ba
c
k
C
o
mp
e
n
sa
to
r
PD fee
d
back
b
l
ock F
(
s) i
s
use
d
f
o
r st
a
b
i
l
i
ze the pl
a
n
t
or
pr
o
cess P(s
)
an
d
d
e
si
gn t
h
e t
r
ans
f
er f
unct
i
o
n
G(s) in
first ord
e
r
with
d
ead
t
i
m
e
m
o
d
e
l as i
n
(1
).
T
h
e transfer
function of the
Propo
rtion
a
l-Deriv
a
ti
v
e
(PD)
bl
oc
k F
(
s
)
i
s
s
h
ow
n i
n
(2
).
(1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Mo
del
Dri
v
e
n
PID
C
o
nt
rol
l
e
r
i
n
W
a
t
e
r
Heat
er Syst
e
m
(
T
o
mmy
H
o
ndi
ant
o)
1
675
(2
)
B
y
usi
ng P
D
feed
bac
k
com
p
en
sant
or, t
h
e
pl
ant
i
s
com
p
en
sat
e
d i
n
t
o
FOT
D
(Fi
r
st
Or
der
,
Ti
m
e
Delay) m
o
d
e
l
as exp
r
essed in (3
).
(3
)
The
param
e
t
e
rs co
nst
a
nt
K
,
T, an
d L a
r
e g
a
i
n
, t
i
m
e const
a
nt
, an
d
dea
d
t
i
m
e
. These pa
r
a
m
e
t
e
rs were
use
d
f
o
r m
odel
i
ng t
h
e M
D
PI
D co
nt
r
o
l
l
e
r sy
st
em
. In t
h
i
s
re
search
, t
h
e
val
u
e o
f
K
,
T, a
n
d L we
re de
fi
n
e
d b
y
usi
n
g t
h
e m
odel
m
a
t
c
hi
ng
Ki
t
a
m
o
ri
m
e
t
hod
[4]
.
B
y
usi
ng t
h
i
s
m
e
t
hod
, t
h
e t
r
ansfe
r
f
unct
i
on o
f
t
h
e pl
a
n
t
have
to
b
e
kno
wn
.
In
t
h
is research
,
b
a
sed
on
th
e water
h
eater tran
sfer
fun
c
tion
m
o
d
e
l [5
] as in
(4
), th
e tran
sfer
fun
c
tion
i
s
defi
ned
.
(4
)
V
a
r
i
ab
le
s
k,
C,
a
n
d
R ar
e h
e
a
t
e
r
con
s
tan
t
,
th
e
r
m
a
l ca
pacitance, a
nd
therm
a
l resistance. For
,
and
by c
o
nsidering the
dead tim
e va
lu
e, eq
u
a
tion
(4) is sim
p
lify, wh
ere
,
, and
.
B
y
usi
n
g t
h
e
m
odel
m
a
t
c
hi
ng
Ki
t
a
m
o
ri
m
e
t
h
o
d
,
t
h
e
pa
ra
m
e
t
e
rs val
u
e
f
r
o
m
(3)
are
de
fi
ned
,
w
h
ere
th
e p
a
ram
e
ters v
a
lu
e are
,
, and
.
These
par
a
m
e
ters f
r
o
m
bl
ock
will b
e
t
h
e referen
ce
for all
th
e system
clo
s
ed
-l
o
o
p
p
a
rameter
in
m
a
in
co
n
t
ro
l
l
er and
set
po
int filter.
2.
2.
2.
Ma
in Co
ntro
ller a
n
d Set Po
i
n
t Filter
Main
con
t
ro
ller con
s
isted
o
f
Q-filter secon
d
o
r
d
e
r
and
first o
r
der m
o
d
e
l with
d
e
ad
tim
e
as th
e
po
sitiv
e
feedb
a
ck
. Th
e
eq
u
a
tion
of m
a
in
con
t
ro
ller is
sh
own
in (5) an
d (6
).
(5
)
(6
)
Th
e Q-filter seco
nd
ord
e
r
g
i
ve th
e co
n
t
ro
l syste
m
th
e stron
g
e
r ab
ility to
h
a
nd
le d
i
sturb
a
n
ce
o
f
t
h
e
sy
st
em
and i
nput
re
fere
nce
val
u
e cha
n
ges
wi
t
h
o
u
t
ove
r
s
ho
ot
. Pa
ram
e
t
e
rs K
c
, T
c
, a
nd L
c
are
gain, tim
e
con
s
t
a
nt
, a
n
d
d
ead t
i
m
e cont
r
o
l
l
e
r f
r
o
m
t
h
e acqui
red
pa
ra
m
e
t
e
rs fr
om
G(s) t
h
at
have
a
fol
l
o
wi
n
g
rel
a
t
i
on;
,
,
Set po
in
t
filter
eq
u
a
tion
is expressed
in (7
).
(7
)
.
2.
2.
3.
Tuning Par
a
meters
Param
e
ters
λ
and
α
a
r
e tu
nin
g
pa
ram
e
ters for M
D
P
I
D c
o
ntr
o
ller. T
uni
n
g
pa
ram
e
ter
λ
(lam
da) is
use
d
f
o
r t
u
ne
d
t
h
e spee
d res
p
ons
e o
f
t
h
e cl
o
s
ed-l
oo
p sy
st
e
m
and t
u
ni
n
g
param
e
t
e
r
α
(al
pha
) f
o
r
di
st
ur
bance
regu
latio
n p
e
rfo
r
m
a
n
ce.
Th
e op
ti
m
a
l
α
can
b
e
ob
tain
ed
as
in
(8
), b
y
can
celing
th
e
s
l
owest
pole of
the process a
n
d a
zero
of
t
h
e co
nt
r
o
l
l
e
r c
once
r
ni
n
g
t
h
e
α
[6]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
16
73
–
1
680
1
676
(8
)
In t
h
is resea
r
c
h
, t
h
e tu
nin
g
p
a
ram
e
ters for
M
D
PID con
t
ro
ller fo
r water h
eater
real-time si
m
u
latio
n
are
. The
co
nve
nt
i
o
nal
P
I
D c
ont
rol
l
e
r
we
used
as
co
m
p
ariso
n
is
Propo
rtion
a
l-In
tegral (PI)
cont
rol
l
e
r as s
h
o
w
n i
n
(
9
).
Ad
di
n
g
de
ri
vat
i
ve param
e
t
e
r t
o
t
h
e co
nt
rol
l
er i
s
not
re
qui
red
.
The w
a
t
e
r
heat
er
sy
st
em
respo
n
s
e i
s
m
ovi
n
g
sl
owl
y
, s
o
t
h
e
pre
d
i
c
t
i
v
e co
nt
r
o
l
fr
om
deri
vat
i
v
e pa
ram
e
t
e
r w
ont
gi
v
e
any
si
gni
fi
ca
nce c
h
ange
s.
The pa
ram
e
ter
s
of the PI controller we
use
d
are
and
.
W
h
e
r
e ‘u
’ is th
e
out
put
c
o
nt
r
o
l
l
e
r a
n
d
‘e
’ i
s
e
r
r
o
r
.
(9
)
2.
3.
Sy
stem Sta
b
ility
In
t
h
i
s
pa
per,
we a
n
al
y
zed
M
D
P
I
D
co
nt
r
o
l
l
e
r
by
u
s
i
n
g
ro
ot
l
o
c
u
s
m
e
tho
d
.
T
h
e c
ont
r
o
l
sy
st
em
dead
t
i
m
e
val
u
e are app
r
o
x
i
m
at
ed by
usi
ng
p
a
de ap
pr
o
x
i
m
at
i
on [
7
]
t
o
d
e
fi
ne t
h
e r
o
ot
l
o
cus t
r
a
j
ect
ory
.
B
y
app
r
oxi
m
a
t
e
t
h
e exp
one
nt
i
a
l
funct
i
o
n,
ro
ot
l
o
cu
s t
r
aject
ory
can be de
fi
ne
as sho
w
n i
n
(
1
0)
. The o
r
der
of t
h
e
ap
pro
x
i
m
a
te ex
pon
en
tial functio
n
is n
=
10
, so th
e clo
s
ed
l
o
op
t
r
a
n
sfe
r
fu
nct
i
o
n ca
n
b
e
ex
pre
ssed
i
n
(
1
1
)
.
Whe
r
e
and
ar
e n
u
m
e
rator a
n
d
den
u
m
e
rato
r coeficient res
p
ectively.
(1
0)
(1
1)
Fig
u
re
3
.
Model Dri
v
en PID
Ro
o
t
-Lo
c
u
s
Stab
ility
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
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8-8
7
0
8
Mo
del
Dri
v
e
n
PID
C
o
nt
rol
l
e
r
i
n
W
a
t
e
r
Heat
er Syst
e
m
(
T
o
mmy
H
o
ndi
ant
o)
1
677
(1
2)
From
t
h
e cl
ose
d
-l
oo
p t
r
a
n
s
f
er
fu
nct
i
o
n m
o
d
e
l
of M
o
del
D
r
i
v
en
PI
D c
ont
r
o
l
l
e
r, t
h
e r
o
ot
-l
ocu
s
g
r
a
p
h
i
s
sho
w
n i
n
Fi
gu
re 3
.
B
a
sed
on t
h
e r
oot
-l
oc
us fi
gu
re,
we c
oncl
ude t
h
at
t
h
e sy
st
em
perfo
rm
ance are no
r
m
al
ly
stable beca
use
all of t
h
e
poles
of the
control
sy
ste
m
are on t
h
e left si
de
of imaginary a
x
is
[8]
,
[9]
.
2.
4.
Resistance
Temperature
De
tector/PT100
Fi
gu
re 4.
R
T
D
PT1
0
0
Se
ns
or
Tw
o W
i
re
RTD is a devi
ce for
read the
te
m
p
erature value by
m
easuring the resistance
of the electrical cable.
The m
a
t
e
ri
al
o
f
R
T
D se
ns
or i
s
di
vi
de i
n
t
o
t
h
ree t
y
pes, c
o
o
p
e
r, ni
c
k
el
, an
d
pl
at
i
num
. Thes
e t
h
ree m
e
t
a
l ty
pes
have
va
riance
resistance. Plati
num
has t
h
e measurem
ent ra
nge to 650°C
, co
op
er
1
2
0
°
C, an
d n
i
ck
e
l
300
°C.
In
th
is research
, we use th
e RTD typ
e
PT1
0
0
with two wires.
There a
r
e also othe
r wire
co
nfigu
r
ation
s
av
ailab
l
e
with
three and
fo
ur
wires
[
1
0
]
. PT1
0
0
se
ns
or
has
t
h
e
pl
at
i
num
m
a
t
e
rial
wi
t
h
resistance 100
Ω
at the
refe
rence tem
p
erature
0°C
.
T
h
e
value
of
t
h
e
s
e
ns
or
resi
st
anc
e
cha
nge
s an
d
ri
se
up
0.
38
5
Ω
fo
r each
1
°
C in
cre
m
en
t to
th
e
m
easured te
m
p
erature.
In (12)
the
equation
of t
h
e l
i
nearity
m
easurem
ent
of t
h
e se
ns
or
i
s
sh
ow
n.
C
onst
a
nt
T i
s
t
h
e m
easured
t
e
m
p
erat
ure
,
T
ref
is t
h
e
r
e
fere
nce
te
m
p
erature
that equal t
o
0°C
.
Fi
gu
re
5.
PT
10
0 C
i
rc
ui
t
C
o
nfi
g
u
r
at
i
o
n [
1
1]
The
PT1
0
0
se
nso
r
has
dy
na
m
i
c resi
st
ance de
pen
d
i
n
g
on the m
easure
d
te
m
p
erat
u
r
e, t
h
erefore, it is
neede
d
a s
p
eci
fic circuit configurati
on
(Fi
g
ure 5) for m
easured t
h
e tem
p
er
at
ure val
u
e by
con
v
e
r
t
e
d
t
h
e s
e
ns
or
resistan
ce
v
a
lue in
to
vo
ltag
e
and
also can k
e
ep
its lin
earity. Th
e ci
rcuit co
nfigu
r
ation
is co
m
b
in
ing
th
e
Wheat
st
one
b
r
i
dge
a
n
d
O
p
er
a
t
i
onal
Am
pl
i
f
ier (
O
p-
Am
p) a
s
di
f
f
er
ent
i
a
l
a
m
pli
f
i
e
r. T
h
e
m
easurem
ent
range
of
th
e sen
s
or lin
earity is 0
°
C
-
200
°C
for
vo
ltage v
a
l
u
e
0
-
5
V
.
Th
e sen
s
o
r
circu
it resu
lts to its lin
earity are
shown
in
Tab
l
e 1.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
16
73
–
1
680
1
678
Tabl
e 1. Sens
o
r
Li
nea
r
i
t
y
Tem
p
°
C
R
T
D
(V
)
V
o
u
t
(V
)
N
o
n
lin
.
0 0.
0981
4
0.
0000
0
0.
000%
20
0.
1061
2
0.
4998
4
-
0
.
003%
40
0.
1140
9
0.
9997
8
-
0
.
004%
60
0.
1220
7
1.
4998
1
-
0
.
004%
80
0.
1300
5
1.
9998
9
-
0
.
002%
100
0.
1380
3
2.
5000
0
0.
000%
120
0.
1460
1
3.
0001
1
0.
002%
140
0.
1539
9
3.
5002
0
0.
004%
160
0.
1619
7
4.
0002
2
0.
004%
180
0.
1699
5
4.
5001
7
0.
003%
200
0.
1779
2
5.
0000
0
0.
000%
3.
R
E
SU
LTS AN
D ANA
LY
SIS
In t
h
i
s
sect
i
o
n
,
we e
xpl
ai
ne
d
t
h
e co
nt
r
o
l
l
e
rs’
per
f
o
r
m
a
nces resul
t
s
base
on
real
-t
i
m
e dat
a
acqui
si
t
i
o
n
and also
on m
a
them
a
tical analysis
i
n
m
a
tl
ab soft
ware
.
We c
o
m
p
are b
o
t
h
M
D
P
I
D c
o
nt
r
o
l
l
e
r a
nd c
o
nv
ent
i
ona
l
PID
co
ntr
o
llers
(P
I),
a
n
d
also
M
D
P
I
D
real-ti
m
e result.
3.
1.
MD PI
D
vs PI
Contr
o
ller Si
mulati
on
Fi
gu
re
6.
M
D
PID
v
s
P
I
C
ont
rol
l
e
r
The com
p
ari
s
on
of M
D
PI
D an
d PI c
o
nt
r
o
l
l
e
r
are s
h
own in Figure 6. T
h
e si
m
u
la
tion are
co
nd
itio
n
a
ly st
ate wh
ere th
e t
e
m
p
eratu
r
e of
water
h
eater sy
ste
m
is in
itia
ll
y at 2
5
°
C and
th
e d
e
si
red
ou
tp
u
t
o
f
th
e water tem
p
eratu
r
e is 40
°C
. Th
e ti
m
e
ran
g
e
of th
e si
m
u
lat
i
on i
s
fr
om
0
-
3
0
0
seco
nd
s.
The PI c
o
nt
rol
l
er are
sim
u
l
a
t
e
d based o
n
(9
) an
d t
h
e param
e
t
e
rs
and
are defi
ne
d. M
D
PI
D co
nt
r
o
l
l
e
r are si
m
u
l
a
t
e
d and al
s
o
changing t
h
e s
p
eed tuning
pa
ram
e
ter (
λ
) to
an
alyze th
e
d
i
fferen
ces
o
f
si
m
u
la
tio
n
resu
lt
s. Fo
r m
o
re d
e
tails o
f
t
h
e
si
m
u
l
a
t
i
ons
dat
a
, Tabl
e 2.
are
s
h
o
w
n.
Tabl
e
2. M
D
P
I
D
an
d P
I
C
o
nt
rol
l
e
r
St
ep R
e
s
p
o
n
se
A
n
al
y
s
i
s
Step In
fo
PI
MD
λ
=1
λ
=0.
75
λ
=0.5
Rise-Ti
m
e
92.
016
4s
74.
578
6s
59.
462
1s
47.
701
7s
Settling Ti
m
e
351.
01
97s
152.
75
77s
117.
99
46s
106.
79
00s
Overshoot
6.
8929%
0%
0.
0645%
2.
3073%
Undershoot
0 0
0
0
Pea
k
1.
0689
0.
9994
1.
0006
1.
0231
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Mo
del
Dri
v
e
n
PID
C
o
nt
rol
l
e
r
i
n
W
a
t
e
r
Heat
er Syst
e
m
(
T
o
mmy
H
o
ndi
ant
o)
1
679
Table
2 s
h
own that MD PID
and PI c
ont
roll
er reach
e
d
t
h
e
desire
d
output
value
alm
o
st at the sam
e
ti
m
e
, b
u
t
PI con
t
ro
ller resu
lt sh
own
so
m
e
o
v
ershoo
t fo
r a lon
g
e
r
p
e
ri
o
d
. Th
is is sh
own
fro
m
th
e larg
e
nu
m
b
er
o
f
th
e settlin
g ti
m
e
. PI con
t
ro
ller also reach
a h
i
g
h
e
r
p
e
ak
am
p
litu
d
e
t
h
an MD PID
co
n
t
ro
ller. Sel
ectin
g
sm
al
l
e
r speed
t
uni
ng
param
e
ters
(
λ
)
fo
r MD PID
con
t
ro
ller also
pr
ov
id
e th
e system
respons
to be
fa
ster,
but
th
e stab
ility d
ecrease.
In
sp
ite, th
e step
respon
s are still
to
ug
h
e
r th
an
PI co
n
t
ro
ller
b
a
se
o
n
Figu
re
6
.
Th
is can
be
occu
re
d
by
t
h
e l
acke
d
o
f
t
h
e ra
nd
om
sel
ect
ed pa
ram
e
t
e
rs i
n
t
h
e c
o
nve
nt
i
onal
PI
D c
o
nt
r
o
l
l
e
rs.
3.
2.
Wa
ter He
ate
r
Resul
t
w
i
th
MD
PI
D
The wat
e
r
heat
er sy
st
em
resul
t
by
usi
ng M
D
PID c
ont
rol
l
e
r
are sh
ow
n i
n
F
i
gu
re 7. T
h
e si
m
u
l
a
t
i
on of
wat
e
r h
eat
er s
y
st
em
i
s
use 40°C
as
desi
re
d
out
put
a
nd t
i
m
e
range
0-
4
5
0
. I
n
t
h
i
s
resea
r
ch
, we t
u
ne
d
t
h
e M
D
PI
D con
t
ro
ller
. Th
e
water
heater real tim
e
syste
m
is an
alyzed
b
y
p
l
o
ttin
g th
e
real time d
a
ta in
matlab
so
ftware.
It
i
s
show
n f
r
o
m
Fi
gure 7, t
h
e st
ep resp
on
se
sho
w
n st
a
b
l
e
per
f
o
r
m
a
nce of t
e
m
p
arat
ure c
ont
rol
w
h
e
n
the actual te
mparat
ure
value
reache
d
desi
red tem
p
erature value. T
h
e
r
e is
3.4%
ove
r
shoot in this
result
available a
n
d reached the
pea
k
at
41.36°C
.
The
ri
se tim
e of the
step
res
p
onse is
110.1 se
conds
.
Figure
7.
MD
PID Real-Tim
e Plot
4.
CO
NCL
USI
O
N
M
D
PI
D an
d
PI co
nt
r
o
l
l
e
r h
a
ve bee
n
si
m
u
l
a
t
e
d i
n
a desi
gne
d wat
e
r he
at
er sy
st
em
. By
addi
n
g
Q
-
filter b
l
o
c
k
seco
nd
o
r
d
e
r,
first
o
r
d
e
r m
o
d
e
l with
d
ead
tim
e
,
set po
in
t
filter, an
d PD feedb
ack b
l
o
c
k
d
i
ag
ram
,
MD PID con
t
ro
ller h
a
s sho
w
n
b
e
tter resu
lts co
m
p
are to
th
e si
m
u
latio
n
with
co
nv
en
tio
nal PID con
t
ro
ller (PI)
b
a
sed
o
n
th
e
rise ti
m
e
, settlin
g
tim
e, an
d
overshoo
t to
con
t
ro
l a slow
respo
n
s
e system
.
Ho
we
ver
,
M
D
PID co
nt
r
o
l
l
e
r desi
g
n
p
r
oce
ss, i
t
has t
o
be
careful
l
y
desi
gne
d. Sy
st
em
m
odel
i
ng i
s
req
u
i
r
e
d
t
o
def
i
ne t
h
e c
ont
r
o
l
l
er param
e
t
e
rs t
o
be a
p
p
l
y in
co
n
t
ro
ller. For co
nv
en
tio
nal PID, trial and
error
m
e
t
hod t
o
defi
ne c
ont
rol
l
e
r
p
a
ram
e
t
e
rs i
s
avai
l
a
bl
e wi
t
h
out
k
n
o
w
i
n
g t
h
e s
y
st
em
m
odel
.
I
t
can
be
defi
ne
d
by
usi
n
g t
h
e
kn
o
w
l
e
dge
o
f
c
o
m
m
on
cha
r
act
eri
s
t
i
c
o
f
pr
o
por
tio
nal, in
tegr
ator
, an
d
di
ffe
rential feature
s
.
Next
, M
D
PI
D
cont
r
o
l
l
e
r i
n
t
h
i
s
si
m
u
l
a
ti
on
pr
o
o
fe
d t
o
be a
b
l
e
t
o
gi
ve
s sat
i
s
fact
ory
res
p
o
n
se t
h
at
are
m
o
re st
abl
e
t
o
t
h
e set
poi
nt
f
o
r han
d
l
i
n
g pl
a
n
t
or pr
ocess
wi
t
h
rel
a
t
i
v
el
y
slow a
nd l
e
ss o
v
e
rsh
o
o
t
base
d on t
h
e
stab
ility an
alysis are sho
w
n
.
Fo
r
furth
e
r research
es, a m
o
re flex
ib
le m
e
th
o
d
b
y
u
s
ing
M
D
PID con
t
ro
ller fo
r m
u
ltiv
ariab
l
e con
t
rol
sy
st
em
can be im
pl
em
ent
e
d. In t
h
i
s
resea
r
ch, we s
h
ow
n
a real
t
i
m
e
sim
u
l
a
t
i
on of a
sim
p
l
e
SISO (
S
i
ngl
e
-
Inpu
t, Sing
le-Ou
t
p
u
t
) system
. Co
n
t
ro
lling
MIM
O
(M
u
lti-Inpu
t, Multi-Ou
tpu
t
) sy
ste
m
with
MD PID
co
n
t
ro
ller
will
b
r
i
n
g m
o
re com
p
lex
i
t
y
to
th
e alg
o
rith
m
s
b
u
t
still h
o
l
d
s
so
me of th
e MD
PID featu
r
es.
AC
KN
OWLE
DG
MENTS
Th
e au
t
h
or wish
es to
ack
nowled
g
e
Dr. Am
in
Su
yitn
o, Mu
roran
In
stitu
te of Tech
no
log
y
, fo
r th
e t
o
p
i
c
i
d
ea an
d
som
e
usef
ul
di
scus
si
on
wi
t
h
aut
h
o
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
16
73
–
1
680
1
680
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[1]
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BIOGRAP
HI
ES
OF AUTH
ORS
Tommy
Hondianto.
H
e
i
s
a
s
t
u
d
e
n
t
a
t
T
e
l
k
o
m
U
n
i
v
e
r
s
i
t
y
.
H
e
r
e
c
i
e
v
e
d
h
i
s
B
.
E
n
g
(
S
T
)
i
n
Electrical Eng
i
n
eering from Telkom University
, Indonesia in 2015. His research inter
e
st is
Control S
y
s
t
em
and Instrumentations.
Dr
.
Erw
i
n Susa
n
to.
Dr Erwin Susanto received
the Ph.
D de
gree
from Kuma
mo
t
o
Uni
v
e
r
si
ty
,
Japan in 2012.
Currently
, h
e
is
an Assistant Pr
ofessor at School of El
ectrical Engineering
,
Telkom Univers
i
ty
. Sin
ce 2014
,
he has been a h
ead of
Electron
ic S
y
stem Resear
ch Group. His
research
in
terest
is Control
S
y
st
e
m
theor
y
and
ap
plic
ations.
Agung Sur
y
a
Wibow
o
.
He receiv
e
d the master degree
from
STEI ITB, Ban
dung in 2012.
Currently
, he
is a lectur
er Scho
ol of Electr
i
ca
l
Engineering, Telkom Un
ivers
i
t
y
. His
res
ear
ch
inter
e
st is Con
t
r
o
l S
y
st
em
theor
y
and
appl
ica
tions
.
Evaluation Warning : The document was created with Spire.PDF for Python.