Civil Engineering Reference
In-Depth Information
7.2 Proportional control
7.2.1 The operation of proportional control
Figure 7.4 shows the block diagram of a simple control system. The block
'controller' provides a transfer function whose input signal is the error, the
difference between the reference signal and the feedback signal. The control-
ler must operate upon this input in some way so as to generate a suitable
output signal to feed to the valve or other final control element. In the fol-
lowing, the commonly used types of control functions (PID) are discussed.
PID (proportional, integral and derivative)
controls are simple in principle.
They have played a very important role in the progress of automatic control
and are used as the most popular functions in process control applied in
various forms.
If a person is taking the role of control output decision based on the input
(error), he or she will naturally set a low output when the error (input) is
small and set a high output when the error is large. Such experience can be
regarded as proportional control. It is the simplest relationship between the
control output (
u
(
t
)) and input (
e
(
t
)), whereby the changes in input are multi-
plied by a suitable constant value (gain,
K
p
) to produce the output change:
u
(
t
) =
K
p
*
e
(
t
)+
u
o
(7-2)
where,
u
o
is a nominal control output without error. The gain constant cannot
normally be a pure number since the nature of the output signal is usually dif-
ferent from that of the input. The actual unit of the proportional gain varies
depending on the units of the controlled variable and control output.
Generally, the controller gain
K
p
is an adjustable parameter whose value
can be chosen and set by the operator. In theory the output signal may appar-
ently take any value but in practice its range is limited by the finite range
of controller output or finite range of the final control element: a valve or
damper can go only from fully closed to fully open. This fact can be regarded
as a saturation effect. It produces the practical input/output curves as shown
in Figure 7.5. The curves give the appropriate action for a heating duty; for
a cooling duty, normally a negative gain should be applied.
e(
t)
u(t
)
y(t
)
Actuator/
valve
r
Controller
Process
+
-
y'(t)
Sensor
Figure 7.4
Block diagram of a simple feedback control system.
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