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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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| 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 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. |
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| ISSN: | 1085-3375 1687-0409 |