The Proportional Controller

The easiest closed-loop controller scheme is one where the error signal is fed directly back into the controller and the new control output is determined by some fraction of the error.

$$u_{\mbox{new}} = u_{\mbox{old}} + K_p \varepsilon$$

For closed-loop controllers it is easiest to think in terms of the error, the difference between the commanded and measured values, of some quantity (like RPM) instead of the measured value directly. So we write the above as,

$$z = K_p \varepsilon$$

where $z$ represents the correction value to apply to the controller.

This proportional controller is very easy to implement, and is frequently used with good results. The controller does have a flaw in it; if the system is sitting at the desired output level (the set point) and is gets perturbed, the controller has a tendency to respond by oscillating about the set point. These oscillations cause the system to be at the set point on average, but it never settles down to stay there.