Approximation Of Transport Lag Or Dead Time

Approximation of transport lag or dead time

If the dead time T is very small, then e^{- Ts} is frequently approximated by

Such approximations are good if the dead time is very small and, in addition, the input time function f(t) to the dead-time element is smooth and continuous. [This means that the second- and higher-order derivatives off(t) are small.]

A more elaborate expression to approximate e^-Ts is available and is

If only the first two terms in the numerator and denominator are taken, then

This approximation is also used frequently.