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 et al.´s (1984) 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 (1965) 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