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8.3 Basic control theory 93

8.3.3 Proportional controller

A controller whose action is proportional to the error signal is called a proportional
controller. This controller has the form
f
ftðÞ ¼ K p X set X m g ¼ K p etðÞ (8.2)
where K p is called the proportional constant. Fig. 8.5 shows an illustration of propor-
tional control action.
In general, both positive and negative control actions may occur. A dead-band
may be used to avoid frequent switching of the control action. Fig. 8.6 illustrates
a proportional controller with a dead-band and a cut-off at the controller limit.

f(t)

f(t) = K.e(t)

0 e(t)
FIG. 8.5
A typical proportional controller.

f(t)
Controller limit

0
Dead Band Error, e(t)

FIG. 8.6
A proportional controller with a dead-band and a limit.