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2014 | 24 | 4 | 745-757

Tytuł artykułu

Improving the stability of discretization zeros with the Taylor method using a generalization of the fractional-order hold

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
Remarkable improvements in the stability properties of discrete system zeros may be achieved by using a new design of the fractional-order hold (FROH) circuit. This paper first analyzes asymptotic behaviors of the limiting zeros, as the sampling period T tends to zero, of the sampled-data models on the basis of the normal form representation for continuous-time systems with a new hold proposed. Further, we also give the approximate expression of limiting zeros of the resulting sampled-data system as power series with respect to a sampling period up to the third order term when the relative degree of the continuous-time system is equal to three, and the corresponding stability of the discretization zeros is discussed for fast sampling rates. Of particular interest are the stability conditions of sampling zeros in the case of a new FROH even though the relative degree of a continuous-time system is greater than two, whereas the conventional FROH fails to do so. An insightful interpretation of the obtained sampled-data model can be made in terms of minimal intersample ripple by design, where multirate sampled systems have a poor intersample behavior. Our results provide a more accurate approximation for asymptotic zeros, and certain known results on asymptotic behavior of limiting zeros are shown to be particular cases of the ideas presented here.

Rocznik

Tom

24

Numer

4

Strony

745-757

Opis fizyczny

Daty

wydano
2014
otrzymano
2013-08-06
poprawiono
2014-03-24
poprawiono
2014-04-24

Twórcy

autor
  • College of Science, Guizhou Institute of Technology, No. 1 Caiguanlu, Yunyan, Guiyang Guizhou, 550003, China
  • College of Automation, University of Chongqing, No. 174 Shazhengjie, Shapingba, Chongqing, 400044, China
autor
  • College of Automation, University of Chongqing, No. 174 Shazhengjie, Shapingba, Chongqing, 400044, China
  • Key Laboratory of Dependable Service Computing in Cyber Physical Society, Ministry of Education, University of Chongqing, No. 174 Shazhengjie, Shapingba, Chongqing, 400044, China
autor
  • College of Automation, University of Chongqing, No. 174 Shazhengjie, Shapingba, Chongqing, 400044, China
autor
  • College of Automation, University of Chongqing, No. 174 Shazhengjie, Shapingba, Chongqing, 400044, China
autor
  • College of Automation, University of Chongqing, No. 174 Shazhengjie, Shapingba, Chongqing, 400044, China
  • Department of Electric and Electronic Information Engineering, Chongqing University of Science and Technology, No. 20 Daxuecheng, Shapingba, Chongqing, 401331, China

Bibliografia

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  • Bàrcena, R., de la Sen, M., Sagastabeitia, I. and Collantes, J.M. (2001). Discrete control for a computer hard disk by using a fractional order hold device, IEE Proceedings: Control Theory and Applications 148(2): 117-124.
  • Błachuta, M.J. (1998). On zeros of pulse transfer functions of systems with first-order hold, Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, FL, USA, Vol. 1, pp. 307-312.
  • Błachuta, M.J. (1999). On zeros of pulse transfer functions, IEEE Transactions on Automatic Control 44(6): 1229-1234.
  • Błachuta, M.J. (2001). On fast sampling zeros of systems with fractional-order hold, Proceedings of the 2001 American Control Conference, Arlington, VA, USA, Vol. 4, pp. 3229-3230.
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  • Hagiwara, T., Yuasa, T. and Araki, M. (1992). Limiting properties of the zeros of sampled-data systems with zeroand first-order holds, Proceeding of the 31st Conference on Decision and Control, Tucson, AZ, USA, pp. 1949-1954.
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  • Kabamba, P.T. (1987). Control of linear systems using generalized sampled-data hold functions, IEEE Transactions on Automatic Control AC-32(7): 772-783.
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  • Kaczorek, T. (2013). Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils, International Journal of Applied Mathematics and Computer Science 23(1): 29-33, DOI: 10.2478/amcs-2013-0003.
  • Karampetakis, N.P. and Karamichalis, R. (2014). Discretization of singular systems and error estimation, International Journal of Applied Mathematics and Computer Science 24(1): 65-73, DOI: 10.2478/amcs-2014-0005.
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  • Liang, S. and Ishitobi, M. (2004a). Properties of zeros of discretised system using multirate input and hold, IEE Proceedings: Control Theory and Applications 151(2): 180-184.
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  • Liang, S., Ishitobi, M. and Zhu, Q. (2003). Improvement of stability of zeros in discrete-time multivariable systems using fractional-order hold, International Journal of Control 76(17): 1699-1711.
  • Liang, S., Xian, X., Ishitobi, M. and Xie, K. (2010). Stability of zeros of discrete-time multivariable systems with GSHF, International Journal of Innovative Computing, Information and Control 6(7): 2917-2926.
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Bibliografia

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