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 greater than or equal to three is discretized using a zero-order hold (ZOH)...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/817534 |
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| author | Cheng Zeng Shan Liang Jiaqi Zhong Yingying Su |
| author_facet | Cheng Zeng Shan Liang Jiaqi Zhong Yingying Su |
| author_sort | Cheng Zeng |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-314f9e106df1464d9fd89af6111305a2 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-314f9e106df1464d9fd89af6111305a22025-02-03T06:12:34ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/817534817534Improvement of the Asymptotic Properties of Zero Dynamics for Sampled-Data Systems in the Case of a Time DelayCheng Zeng0Shan Liang1Jiaqi Zhong2Yingying Su3College of Automation, Chongqing University, Chongqing 400044, ChinaCollege of Automation, Chongqing University, Chongqing 400044, ChinaCollege of Automation, Chongqing University, Chongqing 400044, ChinaCollege of Automation, Chongqing University, Chongqing 400044, ChinaIt 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.http://dx.doi.org/10.1155/2014/817534 |
| spellingShingle | Cheng Zeng Shan Liang Jiaqi Zhong Yingying Su Improvement of the Asymptotic Properties of Zero Dynamics for Sampled-Data Systems in the Case of a Time Delay Abstract and Applied Analysis |
| title | Improvement of the Asymptotic Properties of Zero Dynamics for Sampled-Data Systems in the Case of a Time Delay |
| title_full | Improvement of the Asymptotic Properties of Zero Dynamics for Sampled-Data Systems in the Case of a Time Delay |
| title_fullStr | Improvement of the Asymptotic Properties of Zero Dynamics for Sampled-Data Systems in the Case of a Time Delay |
| title_full_unstemmed | Improvement of the Asymptotic Properties of Zero Dynamics for Sampled-Data Systems in the Case of a Time Delay |
| title_short | Improvement of the Asymptotic Properties of Zero Dynamics for Sampled-Data Systems in the Case of a Time Delay |
| title_sort | improvement of the asymptotic properties of zero dynamics for sampled data systems in the case of a time delay |
| url | http://dx.doi.org/10.1155/2014/817534 |
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