Comparative study of discretization zero dynamics behaviors in two multirate cases

Abstract

It is well known that the existence of unstable zero dynamics is recognized as a major barrier in many control systems. When the usual digital control with zero-order hold (ZOH) or fractional-order hold (FROH) input is used, unstable zero dynamics inevitably appear in the discrete-time model even though the continuous-time system with relative degree more than two is of minimum phase. This paper investigates the zero dynamics, as the sampling period tends to zero, of sampled-data models composed of a generalized sample hold function (GSHF), a continuous-time nonlinear plant and a sampler in cascade. More precisely, we show how an approximate sampled-data model can be obtained for nonlinear systems with two special GSHF cases such that sampled zero dynamics of the resulting model can be arbitrarily placed. Further, two GSHFs with appropriate parameters provide nonlinear zero dynamics as stable as possible, or with improved stability properties even when unstable, for a given continuous-time plant. It is also shown that the intersample behavior arising from the multirate input can be localised by appropriately selecting the design parameters based on the stability condition of the zero dynamics. The results presented here generalize well-known ideas from the linear to nonlinear cases.