As discussed in the previous section the transfer function for a pure time delay is e–θs, where θ is the time delay. Some control system design techniques require a rational transfer function; the Padé approximation for dead time is often used in this case.
A first-order Padé approximation is
A second-order Padé approximation is
Consider the first-order + dead time transfer function, where the time-delay dominates the time constant
The first-order ...