materi kuliah process control
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-
8/19/2019 Materi Kuliah Process Control
1/15
Chap.
5
Modeling
Considerations
for
Control
Purposes
tffiL
-
8/19/2019 Materi Kuliah Process Control
2/15
Cnap.
5
Modeling
Considerations
for
Control
Purposes
Fr Tt
Sterrn
FLrrt
5.5
Fcedback
loopc
ofr
stirrcd tank
heatcr.
-
8/19/2019 Materi Kuliah Process Control
3/15
Chap.
5
Modeling
Consideratbns
for
Control
Purposes
5.1
The
lnprt-Output Model
Every
chemical
process
and its
associated
variables
can be
pictorially as
shown
in
Figure
5.1.
The:main block
repres€nt
ess,
while
tho
arrowg
indicate
the
inputs and
outputs
of
the
p
A
mathematical
model that
is
convenient
and useful
to
system'deeigner
should conform
with
the
picture
above,
(i.
that, given
the vahicg
of
the
inputs,
it
provides
dire4ly
the
va
outputs).
In
particular,
thc
model
should
have
the
followi
form
for
evcry
output;
output
=.,(input
variables)
Using
Figurc
5.1, the
relationship
above
implies
that
-
8/19/2019 Materi Kuliah Process Control
4/15
82
Modeling
the
funamic
and
Static
Behavior
of
Chemica
balance as the
only
equation of
the
state
model,
v{-Fi(Tt-D+9-
dt
Pce
Thc amount
of hsat
Q
supplied
by the
steam
ir
grvcn
b
Q
=
UA,(T^_
T)
where
U is
the overall
heat
tranrfcr
coeflicient,
At
transfer,
and
I*
the
tcmperature
of the
steam.
tn
eq.
(4
its
equal and take
v
{*(
r, * 11'\7
=
Firt*uA,
ru
dt
U
pcp/
pce
or
-
8/19/2019 Materi Kuliah Process Control
5/15
t,,
[
,,,
1.s
n
Chap.
5 Modeling
Considerations for
Control
Purposes
r--
--
|
---
----1
lnput-output
model
Ffurt
5.2 Input-output
modcl of
a
ltirncd
tank
hcatcr.
-
8/19/2019 Materi Kuliah Process Control
6/15
84
Modeling
the
Dynamic
and
Static
Behavior of
Chemical
r-----
tti
o,.
?o,)
.u
*t
-
8/19/2019 Materi Kuliah Process Control
7/15
Chap.
5
Modeling
Considerations
for Control Purposes
Ifthe
system io
initially
(i.c.,
at t
-
0)
at
stcady ctate,
then
cir(r
-0;-g
and
Ii(t
-0)-0
rnd
it recultc
in
c1-
cr
-
0.
Equationr
(5.9r)
and
(5.9b)
reprcccnt the
input-output
mode
mixing
proocss,
and
ir
shown
schematically in Figure
5.3.
Ramrfrs
l.In
Examplce
5.1
and 5.2
the
output
variables
coincid
statc
variabla$
of
the
two
processes.
Cons€quently,
in
develop
the
input-output
modcl we
need
only
solvo
th
tial
equations
of
the mast
and
energy
balances.
This
is
true.
Thke
aB
sn
example
the
binary
distillation
colu
-
8/19/2019 Materi Kuliah Process Control
8/15
Chap.
5
Modeling
Considarations
for
Control
Purposes
tffiL
-
8/19/2019 Materi Kuliah Process Control
9/15
Chap.
5
Modaling
Considerations
lor
Gontrol
Purposes
r-t
T
I Controller l+---
Loop
2
FllrrG
5.3
Fccdba*
loopc
ofa
rtircd tank
heatcr.
-
8/19/2019 Materi Kuliah Process Control
10/15
Chap.
5
Modeling
Consideratbns
for
Control
Purposes
5.1
The
lnprt-Output Mod€l
Every
chemical
proccss
and
its
associated
variables
can be
pictorially
ar
shown
in
Figure
5.1. The
main
block
repres€nt
ess,
while
the
arrows
indicate
the
inputs and
outputs
of
the
p
A
mathematical
model that
is
convenient
and useful
to
system
deeigner
should conform
with
the
picture
above,
(i.
that,
given
the
valU6s
of
the
inputs,
it
provides
direcdy
the va
outpuls).
In
particular,
the
model
should
have
the followi
form
for
evcry
output;
output
=.,flinput
variables)
Using
Figurc
5.1, the
relationehip
above
implies
that
-
8/19/2019 Materi Kuliah Process Control
11/15
82 Modeling th€
Dynamic
and
Static
Behavior of
Chemica
balance as the
only
equation of
the
state
model,
v{-Fi(Tt-z1+.9-
dt
Pce
Thc smount
of hsat
Q
supplied
by
the
steam
ir
gvcn
b
Q
=
UA{T^-
T}
whcre
U is
the overall
heat
trancfcr
coeflicient,
At
transfer,
and
I*
the
tsmperature
of the
steam.
tn
eq.
(4
its
equal and take
v{*(
r,* L\7
=
Firt*uA,
rn
dt
\
pcp/
pce
or
ar
KTu
-
8/19/2019 Materi Kuliah Process Control
12/15
Chap.
5 Modeling
Consideradons for
Control
Purposes
r--
--
|
-------'l
lnput-output
model
Ffurr
5.2 Input-output
model of
a
crirrcd
tank
hcrrcr^
Ti
+
KTitt
t"
[,",',n
-
8/19/2019 Materi Kuliah Process Control
13/15
84
Modeling
the
DTnamic
and
Static
Behavior of
Chemical
r--*--
ri(r)
ri,
ro)
{ti
o,.
}o,)
an
*t
-
8/19/2019 Materi Kuliah Process Control
14/15
Chap.
5
Modeling
Considerations
for
Control Purposes
Ifthe
syEtcm ic
initially
(i.o.,
at I
-
0) at
stcady state,
then
cir(,-0)-0
and
li(t -0)-0
rnd
it rcsultr
in
c1- cz
-
0.
Equationr
(5.9a)
and
(5.9b)
reprcccnt the
input-output
mode
miring
pro@38,
and
is
shown
schematically in Figure
5.3.
&nur*s
l.In
Examplce
5.1
and 5.2
the
output
variables
coincid
state
varisblcs
of
the
two
processes.
Consequently,
in
develop
the
input-output
modcl
we
need
only
solvo
th
tial
equationg
of
the masr
and
energy
balances.
This
ig
true.
Tbke
aB
an
example
the binary
distillation
colu
-
8/19/2019 Materi Kuliah Process Control
15/15
Cnap.
5
Modeling
Considerations
for
Control
Purposes
Fr Tt
Sterrn
FLrrt
5.5
Fcedback
loopc
ofr
stirrcd tank
heatcr.
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