Improving the Stability Behavior of Limiting Zeros for Multivariable Systems Based on Multirate Sampling
- 4 Downloads
It is well-known that existence of unstable sampling zeros is recognized as a major barrier in many control problems, and stability of sampling zeros, in general, depends on the type of hold circuit used to generate the continuous-time system input. This paper is concerned with stability of limiting zeros, as the sampling period tends to zero, of multivariable sampled-data models composed of a generalized sample hold function (GSHF), a continuous-time plant with the relative degrees being two and three, and a sampler in cascade. In particular, the main focus of the paper is how to preserve the stability of limiting zeros when at least one of the relative degrees of a multivariable system is more than two. In this case, the asymptotic properties of the limiting zeros on the basis of normal form representation of continuous-time systems are analyzed and approximate expressions for their stability are discussed as power series expansions with respect to a sufficiently small sampling period. More importantly, unstable sampling zeros of the sampled-data models mentioned above can be avoided successfully through the contribution of this paper, whereas a zero-order hold (ZOH) or a fractional-order hold (FROH) fails to do so. It is a further extension of previous results for single-input single-output cases to multivariable systems.
KeywordsLimiting zeros multirate input and hold multivariable systems sampled-data models stability
Unable to display preview. Download preview PDF.
- K. J. Åström and B. Wittenmark, Adaptive Control, 3rd ed., Courier Dover Publications, New York, 2008.Google Scholar
- K. J. Åström, Computer Controlled Systems, 3rd ed., Courier Dover Publications, New York, 2011.Google Scholar
- M. Ishitobi, “A stability condition of zeros of sampled multivariable systems,” IEEE Transactions on Automatic Control, vol. AC-45, pp. 295–299, 2000.Google Scholar
- C. Zeng, S. Liang, J. Zhong, and Y. Su, “Improvement of the asymptotic properties of zero dynamics for sampleddata systems in the case of a time delay,” Abstract and Applied Analysis, vol. 2014, pp. 1–12, 2014.Google Scholar
- M. Ishitobi, T. Koga, and S. Kunimatsu, “Asymptotic properties of zeros of multivariable sampled-data systems,” Proc. of Australian Control Conference, Melbourne, Australia, pp. 513–518, November 2011.Google Scholar
- C. Zeng, S. Liang, S. Gan, and X. Hu, “Asymptotic properties of zero dynamics of multivariable sampled-data models with time delay,” WSEAS Transactions on systems, vol. 13, pp. 23–32, 2014.Google Scholar
- C. Zeng and S. Liang, “Zero dynamics of sampled-data models for nonlinear multivariable systems in fractionalorder hold case,” Applied Mathematics and Computation, vol. 246, no. C, pp. 88–102, 2014.Google Scholar
- C. Zeng, S. Liang, Y. Zhang, J. Zhong, and Y. Su, “Improving the stability of discretization zeros with the taylor method using a generalization of the fractional-order hold,” International Journal of Applied Mathematics & Computer Science, vol. 24, no. 4, pp. 745–757, 2014.MathSciNetCrossRefzbMATHGoogle Scholar
- J. I. Yuz, G. C. Goodwin, and H. Garnier, “Generalized hold functions for fast sampling rates,” Proc. of 43rd IEEE Conference on Decision and Control (CDC’2004), Atlantis, Bahamas, 2004, pp. 761–765.Google Scholar
- S. Liang, X. Xian, M. Ishitobi, and K. Xie, “stability of zeros of discrete-time multivariable systems with gshf,” International Journal of Innovative Computing, Information and Control, vol. 6, no. 7, pp. 2917–2926, 2010.Google Scholar
- C. Zeng and S. Liang, “Time discretization for a 3-dof nonlinear mass-damper-spring mechanical vibration system via taylor approach and fractional-order hold,” ICIC Express Letters-B, vol. 6, no. 9, pp. 2515–2522, 2015.Google Scholar