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.