Correction of predominantly first-order processes

We consider processes for which the gain g and time constant τ have been determined experimentally (e.g. step test) or theoretically, having possibly neglected a second time constant, small in front of τ. It should be noted in particular that reality is represented by the $\frac{g}{1+\text{τ}p}$ model, but that this can only be an approximate representation, linked to a certain amplitude and time scale.

Consequently, when setting a desired response time for a looped system, it is important to bear in mind that this (slaved) response time must be compared with that of the non-slaved system, and that their time scales must be compatible with the measurement accuracy of the dynamic open-loop model....