Word length of pulse transfer function for small sampling periods

Discrete-time systems composed of sampler, zero order hold and continuous-time plants are investigated. The well-known Astrom's et al. theorem in a reformulated version is first proved and then utilized for estimating the length of a digital word needed for recording the pulse transfer function parameters, in the case of small sampling periods. The estimated length, assuring a prescribed accuracy of the model, is somewhat larger than that obtained from Kaiser's condition of nondestabilization of the model. It is shown that only nonzero poles of the plant transfer function cause an increase of the word length; the zero poles and the zeros of the latter transfer function have no influence on this length. The calculations performed for several examples confirm the correctness of the proposed approach.