1
Feedback Controllers: Week 1
Chapter 8
1
Figure 8.1 Schematic diagram for a stirred-tank blending
system.
P
D
I
2
“Normal”,
K
c
< 0
“Reverse”,
K
c
> 0
p
change wrt
y
m
not wrt
e
= error
Basic Control Modes
Next we consider the three basic control modes starting with the
simplest mode,
proportional control
.
Proportional Control
Chapter 8
In feedback control, the objective is to reduce the error signal to
zero where
( )
( )
( )
(8-1)
sp
m
e t
y
t
y
t
=
−
and
( )
error signal
e t
=
3
( )
( )
set point
measured value of the controlled variable
(or equivalent signal from the sensor/transmitter)
sp
m
y
t
y
t
=
=
(
y
sp
and
y
m
must have same units)
Although Eq. 8-1 indicates that the set point can be time-varying,
in many process control problems it is kept constant for long
periods of time.
For proportional control, the controller output is proportional to
the error signal,
Chapter 8
( )
( )
(8-2)
c
p t
p
K e t
=
+
where:
( )
controller output
bias (steady-state) value
p t
p
=
=
4
bias (steady state) value
controller gain (usually dimensionless)
c
K
=

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