An approximate root locus method in theSplane for sampled-data systems

An approximate
S
plane is derived from the
W
plane for analyzing sampled-data systems. Constant frequency and constant damping-ratio loci are first mapped onto the
W
plane. A simple transformation of the
W
-plane coordinates to
S
-plane coordinates is then constructed, and sampling frequency boundaries are specified wherein interpretation in the
W
plane becomes identical to that in the
S
plane. Hence
S
-plane results can be obtained quickly for those system frequencies within the specified boundaries.