Improvement of the Asymptotic Properties of Zero Dynamics for Sampled‐Data Systems in the Case of a Time Delay

Cheng Zeng, Shan Liang, Jiaqi Zhong and Yingying Su

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: It is well known that the existence of unstable zero dynamics is recognized as a major barrier in many control systems, and deeply limits the achievable control performance. When a continuous‐time system with relative degree greater than or equal to three is discretized using a zero‐order hold (ZOH), at least one of the zero dynamics of the resulting sampled‐data model is obviously unstable for sufficiently small sampling periods, irrespective of whether they involve time delay or not. Thus, attention is here focused on continuous‐time systems with time delay and relative degree two. This paper analyzes the asymptotic behavior of zero dynamics for the sampled‐data models corresponding to the continuous‐time systems mentioned above, and further gives an approximate expression of the zero dynamics in the form of a power series expansion up to the third order term of sampling period. Meanwhile, the stability of the zero dynamics is discussed for sufficiently small sampling periods and a new stability condition is also derived. The ideas presented here generalize well‐known results from the delay‐free control system to time‐delay case.

Date: 2014
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https://doi.org/10.1155/2014/817534

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:817534

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