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.
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