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

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 greaterthan or equal to three is discretized using a zero-order hold (ZOH),...

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Bibliographic Details
Published inAbstract and Applied Analysis Vol. 2014; no. 2014; pp. 924 - 935-1396
Main Authors Su, Yingying, Zeng, Cheng, Liang, Shan
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2014
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Hindawi Limited
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Summary: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 greaterthan or equal to three is discretized using a zero-order hold (ZOH), at least one of the zero dynamics of the resultingsampled-data model is obviously unstable for sufficiently small sampling periods, irrespective of whether they involvetime 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 thecontinuous-time systems mentioned above, and further gives an approximate expression of the zero dynamics in theform of a power series expansion up to the third order term of sampling period. Meanwhile, the stability of the zerodynamics is discussed for sufficiently small sampling periods and a new stability condition is also derived. The ideaspresented here generalize well-known results from the delay-free control system to time-delay case.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/817534