The use of pulse-width control for the on-off regulation of systems subject to sampling is investigated in this paper. The inherent inability of simple on-off control to achieve accurate, or dead-beat control in sampling systems is demonstrated, and methods for predicting and minimizing the limit-cycle behavior of these systems are given. It is then shown that if the on-off control is modified by allowing control of the “on” time during each sampling period, it is possible to achieve asymptotically stable dead-beat control. Sufficient conditions for the asymptotic stability in the large of pulse-width control systems are developed, using the “second method” of Lyapunov. Practical design of pulse-width controllers is developed from the theoretical results and experimental evaluation is given for some specific design problems.
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W. L. Nelson (1961) studied this question.