materi kuliah process control

8/19/2019 Materi Kuliah Process Control

1/15

Chap.

5

Modeling

Considerations

for

Control

Purposes

tffiL


2/15

Cnap.

5

Modeling

Considerations

for

Control

Purposes

Fr Tt

Sterrn

FLrrt

5.5

Fcedback

loopc

ofr

stirrcd tank

heatcr.


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


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


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.


6/15

84

Modeling

the

Dynamic

and

Static

Behavior of

Chemical

r-----

tti

o,.

?o,)

.u

*t


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


8/15

Chap.

5

Modeling

Considarations

for

Control

Purposes

tffiL


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.


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


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


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


13/15

84

Modeling

the

DTnamic

and

Static

Behavior of

Chemical

r--*--

ri(r)

ri,

ro)

{ti

o,.

}o,)

an

*t


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


15/15

Cnap.

5

Modeling

Considerations

for

Control

Purposes

Fr Tt

Sterrn

FLrrt

5.5

Fcedback

loopc

ofr

stirrcd tank

heatcr.

materi kuliah process control

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