DERIVATION AND APPLICATION OF THE FIRST TWO VALUES OF THE CONTROL SEQUENCE IN A SINGLE LOOP DEADBEAT SAMPLEDDATA SYSTEM
Annraoi de Paor
A modest contribution is made to the theory of single loop
deadbeat control, on a zeroorder hold basis, of a process
(asymptotically stable or unstable) by calculating 
explicitly in terms of the sdomain poles of the process, the
residues of its zerostate step response, and the proposed
sampling period, T,  the first two values of the control
sequence in the zerostate response of the closed loop system to
a step reference input. Since the resulting expressions are
tractable enough to be plotted as functions of T, and since
for realpole minimumphase systems they seem usually to
dominate the control sequence, it becomes possible to choose T
to limit exactly or at least give the order of magnitude of the
maximum control excursion and thus ameliorate one of the
difficulties which, as pointed out by Astram and Wittenmark
(1990), have given deadbeat control an unreservedly bad
reputation ie, the drastic increase in magnitude of
control signal with decrease in sampling period), and their
implied criticism of the lack of a sampling period guidance
formula. The work extends a previous study by the author (1990)
on Kalman's famous 1954 algorithm, and a later one (1993) which
gives guidance on sampling period selection for it and develops
a structural extension to cope with nonasymptotically stable
processes. Two examples of the present contribution are given
 one decisive, the other only indicative.
Keywords: deadbeat control, sampling period selection, limitation of control sequence excursion, optimum stability
