DERIVATION AND APPLICATION OF THE FIRST TWO VALUES OF THE CONTROL SEQUENCE IN A SINGLE LOOP DEAD-BEAT SAMPLED-DATA SYSTEM

Annraoi de Paor

   A modest contribution is made to the theory of single loop dead-beat control, on a zero-order hold basis, of a process (asymptotically stable or unstable) by calculating - explicitly in terms of the s-domain poles of the process, the residues of its zero-state step response, and the proposed sampling period, T, - the first two values of the control sequence in the zero-state 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 real-pole minimum-phase 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 dead-beat 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 non-asymptotically stable processes. Two examples of the present contribution are given - one decisive, the other only indicative.

Keywords: dead-beat control, sampling period selection, limitation of control sequence excursion, optimum stability

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