First order Proportional control
Cuthbert Nyack
First order system with P control. The simplest controller
which can be used for feedback systems is a proportional
controller. This is basically an amplifier with gain K.
It produces an output m(t) = Ke(t). Its advantage is simplicity
but it has several disadvantages. The
applets on this page allow one to interactively investigate
the properties of proportional controllers.
Some of these are:-
The effect of K on the offset with a step input.
Since a finite error signal
e(t) is required to produce an m(t), then e(t) cannot
be zero. This means that there will always be a difference
between the desired value and the actual value.
The effect of K on the transient behaviour with a
ramp input. In this case, the difference between the desired
value and the actual value increases with time.
The solution for a unit step input is given by:-
and the solution for a unit ramp input is given by:-
The unit input step is shown as the
purple line. The output response
is shown in red. The horizontal
axis corresponds to 2 seconds.. Analysis of system
shows that the final value of the output tends to the
asymptotic value K/(K + 1).
In this case the slope of the output is different from that of the
input.
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COPYRIGHT © 1996 Cuthbert A. Nyack.