Feedback amplifiers

1. Chapter
8
Feedback Controllers

2. On-off Controllers
• Simple
• Cheap
• Used In residential heating and domestic refrigerators
• Limited use in process control due to continuous
cycling of controlled variable  excessive wear
on control valve.
Examples
•Batch process control (PLC = programmable logic controller)
•Solenoid in home heating unit
•Sprinkler systems
•Cruise control?

3. On-Off Controllers
Synonyms:
“two-position” or “bang-bang” controllers.
Controller output has two possible values.
Chapter
8
e = error =
set point – measured variable

4. Practical case (dead band)
Chapter
8
system never reaches steady-state
δ = tolerance

5. Chapter
8

6. Three Mode (PID) Controller
• Proportional
• Integral
• Derivative
Proportional Control
• Define an error signal, e, by e = Ysp – Ym
where
Ysp = set point
Ym = measured value of the controlled variable
(or equivalent signal from transmitter)
Chapter
8

7. Since signals are time varying,
e(t) = Ysp(t) - Ym (t)
n.b. Watch units!!
• For proportional control:
where,
p(t) = controller output
= bias value (adjustable)
Kc = controller gain (dimensionless, adjustable)
p
-
p
=
p
e(t)
K
+
p
=
p(t) c

Chapter
8
p

8. Figures 8.4, 8.5
in Text
Chapter
8
Standards (ISO/ISA)
3 – 15 psi
4 - 20 ma
0 – 10 VDC

9.  Proportional Band, PB
 Reverse or Direct Acting Controller
 Kc can be made positive or negative
 Recall for proportional FB control:
or
 Direct-Acting (Kc < 0)
“output increases as input increases"
p(t) Ym(t)
 Reverse-Acting (Kc > 0)
“output increases as input decreases"
c
K
%
100
PB 
e(t)
K
+
p
=
p(t) c
Chapter
8
 
)
t
(
Y
)
t
(
Y
K
p
)
t
(
p m
sp
c 



10. • Example 2: Flow Control Loop
Assume FT is direct-acting. Select sign of Kc so
that KcKv > 0
1.) Air-to-open (fail close) valve ==> ?
2.) Air-to-close (fail open) valve ==> ?
• Consequences of wrong controller action??
Chapter
8

11.  Transfer Function for Proportional Control:
Let
Then controller input/output relation can written as
Take Laplace transform of each side,
or
INTEGRAL CONTROL ACTION
Synonyms: "reset", "floating control"
I  reset time (or integral time) - adjustable
p
-
p(t)
(t)
p 

e(t)
K
(t)
p c


E(s)
K
(s)
P c


c
K
E(s)
(s)
P


s
1
E(s)
(s)
P
t
d
)
t
(
e
1
p
)
t
(
p
I
t
0
I 






 