Dynamic Behavior One - Process Control - Lecture Slides, Slides of Process Control

Download Dynamic Behavior One - Process Control - Lecture Slides and more Slides Process Control in PDF only on Docsity!

Dynamic Behavior of Closed-

Loop Control Systems

Chapter 11

4-20 mA

e t( ) = xsp ′^ ( )t −xm ′ ( )t (11-5)

or after taking Laplace transforms,

E s ( ) = X sp′^ ( )s − X m′ ( )s (11-6)

The symbol denotes the internal set-point composition expressed as an equivalent electrical current signal. This signal is used internally by the controller. is related to the actual composition set point by the composition sensor- transmitter gain Km:

xsp ′ ( )t

xsp ′ ( )t

xsp ′ ( )t

xsp ′^ ( )t = K m xsp ′ ( )t (11-7)

Thus

sp m (11-8) sp

X s K X s

Chapter 11

Composition Sensor-Transmitter (Analyzer)

We assume that the dynamic behavior of the composition sensor- transmitter can be approximated by a first-order transfer function:

τ 1

m (^) m m

X s (^) K X s s

Controller

Suppose that an electronic proportional plus integral controller is used. From Chapter 8, the controller transfer function is

c τI

P s K E s s

where and E(s) are the Laplace transforms of the controller output and the error signal e(t). Note that and e are electrical signals that have units of mA, while Kc is dimensionless. The error signal is expressed as

P ′ ( )s

p ′^ ( )t p′

Chapter 11

1. Summer 2. Comparator 3. Block - Blocks in Series

are equivalent to...

Chapter 11 ∴Y(s) = G(s)X(s)

Closed-Loop Transfer Function

for Load Change (Regulator

Problem)

1 2

sp

d p

d v p c m

d v p c

m s

m

d c v m

p

p

Y s

Y s X s X s

G s D s G s U s

G s D s G s G s G s K Y G Y s

G s D s G s G s G s G Y s

Y s G

D s G G

s

G G

= + ^ − 

General Expression of Closed-

Loop Transfer Function

1 where , : any two variables in block diagram : product of the transfer functions in the path from to : product of the transfer functions in the feedback loop.

f e

f

e

Y X

X Y

X Y

π π

π

π

=

Regulator Problem

open-loop transfer function

f d

e c v p m OL

X D

Y Y

G

G G G G G

π

π

=

=

=

= =

=

Chapter 11

I O

• Chapter
• Chapter
• Chapter
• Chapter
• Chapter
• Chapter