Deadbeat sampled system direct synthesis

A direct synthesis method is presented for obtaining a discrete compensator to produce a finite-settling-time transient in response to a prescribed input with no intersample transient terms after the finite settling time. The method is applicable to a single constant-frequency sampler in a feedback system with any type of hold for any polynomial input. The method uses a fictitious sampler at the output with sample time
T/m
to scan the intersample times and to obtain criteria for deadbeat transients. The criteria are derived from root locus considerations but are applied to Laplace transforms containing both functions of
s
and functions of
z
so that the only operations are analytic ones.