Finite Word-Length Effects in Systems with Fast Sampling

Abstract

Discrete time systems composed of sampler, zero-order hold and continuous time plants are investigated. The well-known AstrÅström’set al.[1] theorem in a reformulated version is first proved and then utilised for estimating the length of a digital word needed for recording the pulse transfer function parameters, in the case of small sampling periods. It is shown that only non-zero poles of the plant transfer function cause an increase of the needed word-length; the zero poles and the zeros of the latter transfer function have no influence on this length. Next, the consequences for the control system design and regulator implementation are discussed. Finally, the identification of discrete time models under fast sampling and limited measurements accuracy is described. It is then shown that the identification accuracy of the shift operator and delta operator models is comparable. Considerations are illustrated by examples and simulations.