Modeling Method for Sampling Zeros of Sampled-data System with Time Delay in Generalized Sample Hold

Abstract

Unstable zeros are widely known to dramatically curb the performance of controllers and the direct applications of several control algorithms. Time delay is a crucial research topic due to the prevalence of communication and computational delays in the control process. In particular, time delay exacerbates the possibility of continuous-time systems with stable zeros transforming into discrete-time systems with unstable zeros. For continuous-time systems with a relative degree greater than or equal to two, at least one zero of the corresponding discrete-time system converges to either marginally stable or unstable locations as the sampling time approaches zero. This study investigates the sampling zeros of discrete-time systems in the case of a generalized sample hold function (GSHF) with time delay. Moreover, it presents a novel modeling method and stability conditions of the limiting zeros for the discrete-time system. The results demonstrate that the stable properties of zeros for the time delay systems can be preserved in the discretization process when GSHF is applied for signal reconstruction when zero-order hold fails to do so. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method in this study.