Improving the Stability Behavior of Limiting Zeros for Multivariable Systems Based on Multirate Sampling

Abstract

It is well-known that existence of unstable sampling zeros is recognized as a major barrier in many control problems, and stability of sampling zeros, in general, depends on the type of hold circuit used to generate the continuous-time system input. This paper is concerned with stability of limiting zeros, as the sampling period tends to zero, of multivariable sampled-data models composed of a generalized sample hold function (GSHF), a continuous-time plant with the relative degrees being two and three, and a sampler in cascade. In particular, the main focus of the paper is how to preserve the stability of limiting zeros when at least one of the relative degrees of a multivariable system is more than two. In this case, the asymptotic properties of the limiting zeros on the basis of normal form representation of continuous-time systems are analyzed and approximate expressions for their stability are discussed as power series expansions with respect to a sufficiently small sampling period. More importantly, unstable sampling zeros of the sampled-data models mentioned above can be avoided successfully through the contribution of this paper, whereas a zero-order hold (ZOH) or a fractional-order hold (FROH) fails to do so. It is a further extension of previous results for single-input single-output cases to multivariable systems.