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CBE / MET 43322 Feb 12

(Transfer functions and Block Diagrams)

Professor Douglas Cooper, author Loop Pro-Trainer

What are Valve CharacteristicsInherent Characteristics

• The three most common valve characterizations are equal percentage, linear, and quick opening

2Professor Douglas Cooper, author Loop Pro-Trainer

What are Valve CharacteristicsInstalled Characteristics

• In many process applications the pressure drop across a valve varies with the flow. In these instances an equal percentage valve will act to linearize the process.

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Equal percentage valves are the most commonly used control valves. • How do you know what inherent valve characteristic to choose to get a

linear installed characteristic?– The correct selection of valve characteristic to linearize the process

gain will ease the tuning process and make for a robust system.– Most times this selection is through experience, guesswork or the

valve manufacturer’s recommendation.Professor Douglas Cooper, author Loop Pro-Trainer

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Feedback Block DiagramTransmitter

Transducer

Valve

Energy Transfer Controller

Process

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Feedback Block Diagram

11s

11

sK

s+

+

si

sQ

sWVK

sMcK sM y-

sE+ sR

TK sC

sMor T

6

Feedback Block Diagram (simplified)

11s

1

sK

s+

+

si

sWVK

sMcK

-

sE+ sR

TK sC

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Closed Loop Transfer Function (let R(s)=0)

11s

1

sK

s+

+

si

sWVK

sMcK

-

sE+ sR

TK sC

sKKKsKs

ss TcVi

11

1

TcVi KKK

sK

sss

11

11

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Closed Loop Transfer Function (let R(s)=0)

11s

1

sK

s+

+

si

sWVK

sMcK

-

sE+ sR

TK sC

TcV

i KKKsK

sss

11

11

looptheinblocksallouputtoinputfrompathdirectonblocksall

ss

input

output

1

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Open Loop vs Closed Loop

Transfer Function (R(s)=0)

11s

1

sK

s

++

si

sWVK

sMcK

-

sE+ sR

TK sC

TcVi KKK

sK

sss

11

11

Open Loop:

Closed Loop:

11ss

s

i

TcV KKKKs

11

11

11

sKKKK

KKKK

TcV

TcV

1*

*

sK

*

* 1K tt

evse *

t

eAt 1

*1*

teAKt

10

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 1 2 3 4 5

time (t)

Y(t)

Open - loop

Closed - loop

t

time

AK *

A

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Transfer Functions (Chap 3-5)

11s

1

sK

s

++

si

sWVK

sMcK

-

sE+ sR

TK sC

11

s

GL

Define:

For heated, stirred tank:

..FTG

)()(ss

i

VV KG

1

sKGP

cc KG

TT KG

11s

1

sK

s

++

si

sWVK

sMcK

-

sE+ sR

TK sC

LG

PGVGcG

TG

)()(sRs

12

13

11s

skgsW C

LG sTo

11s

skg

s sW C

sG sTo

11s

CsTi

C

iTG sTo

14

sRSPG

sT seto

15

)(sWsTo

)(sTsT

i

o

)(sT

sTseto

o