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

The paper discusses the limiting zeros, as the sampling period tends to zer o, of sampled systems composed of a fractional order hold (FROH), a continu ous-time plant and a sampler in cascade. The focus is on the evolution on t he complex plane of the limiting discrete zeros with the gain beta of the F ROH. The classical root locus method is used where beta is the generalised gain. The appropriate beta is determined to obtain the FROH that provides d iscretization zeros as stable as possible, or with improved stability prope rties even when unstable, for a given continuous-time plant. The FROH discr etisation of continuous-time plants with relative degree two is analysed, a nd a straightforward method is developed to obtain the optimum value of bet a. The study is extended for sufficiently small, but finite, sampling perio ds and zero-free continuous-time plants.