A rational basis for the pole-zero map in controller discretization

Abstract

The pole-zero map, invariably introduced on an ad hoc basis, gives a very good frequency domain approximation in the range 0 ≤ ωT < 1, where T is sampling period, to the unrealizable digital controller transfer function C(z) which would result from mapping the corresponding analogue transfer function G c (s) under z = e sT ,i.e., s = (1/T) In z. A variation of the well known Tustin transformation emerges as a simple alternative.