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Chapter 8

Feedback Controllers

Error Signal

where

= set point (3-15 psig; 4-20mA; 1-5V)

= measured value of controlled variable

(or equivalent signal from transmitter)

(3-15 psig; 4-20mA; 1-5V)

Define

0;

e t R t B t

R t

B t

e t e t

= −

′ = −

;

0

Take Laplace Transform

R t R t R B t B t B

R B e t R t B t

E s R s B s

′ ′ = − = −

′ ′ ′ = − ⇒ = −

′ ′ ′ = −

Reverse or Direct Acting

Controller

• Direct-Acting (Kc < 0) : “output increases

as input increases"

• Reverse-Acting (Kc > 0) : “output increases

as input decreases"

Proportional Band (PB)

PB is the error (% of the range of controlled

variable) required to move the output from

its lowest to its highest value.

100%

c

PB

K

≡

• Chapter
• Chapter
• Chapter
• Chapter

Example 3: Liquid Level Control

• Control valves are air-to-open
• Level transmitters are direct acting

Chapter 8

Question: Type of controller action?

p =9 psig

10 psig

in order to make 170 gpm

o

p

q

=

=

at steady state

i o

q = q

( ) ( )

( ) ( ) ( )

where 0

1 0

c c

c

p t p K e t K

K e e R B

= + <

∞ → ∴ ∞ = − ∞ <

Chapter 8

INTEGRAL CONTROL ACTION

( )

0

: reset time (or integral time) - adjustable

(1) If ( ) 0, then ( ) varies continuously with time.

(2) If ( ) 0 for *, then

t

I

I

I

p t p e d

P s

E s s

e t p t

e t t t

p t

η η

τ

τ

τ

∫

0

( ) constant

t

s

I

p p e η d η

τ

∫

Reset Time

Reset time is the time that the integral mode repeats the

action of proportional mode.

I

t = τ

t *

t