Improving the stability properties of the zeros of sampled systems with fractional order hold

Abstract

The paper discusses the limiting zeros, as the sampling period tends to zero, of sampled systems composed of a fractional order hold (FROH), a continuous-time plant and a sampler in cascade. The focus is on the evolution on the complex plane of the limiting discrete zeros with the gain β of the FROH. The classical root locus method is used, where β is the generalised gain. The appropriate β is determined to obtain the FROH that provides discretization zeros as stable as possible, or with improved stability properties even when unstable, for a given continuous-time plant. The FROH discretisation of continuous-time plants with relative degree two is analysed, and a straightforward method is developed to obtain the optimum value of β. The study is extended for sufficiently small, but finite, sampling periods and zero-free continuous-time plants.