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Rational approximation of fractional order systems by vector fitting method

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  • Control Theory and Applications
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Abstract

A novel method for approximating fractional order systems is presented. Vector fitting is involved in this method. As the basis of approximation of fractional order systems, approximation of fractional order operators is mostly achieved by curve fitting in frequency domain, such as the well-known Oustaloup’s method. However, these methods have several serious defects in principle. A new perspective based on system identification is adopted to deal with approximation of fractional order operators in this paper. Moreover, nonzero initial condition for approximating fractional order systems is considered. And the proposed assignment of initial values for the Caputo case offers an effective solution for the simulation with nonzero initial condition. Finally, numerical examples are given to verify the efficiency of the proposed method.

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Authors and Affiliations

  1. Department of Automation, University of Science and Technology of China, Hefei, Anhui, China

    Bin Du, Yiheng Wei, Shu Liang & Yong Wang

Authors
  1. Bin Du
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  2. Yiheng Wei
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  3. Shu Liang
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  4. Yong Wang
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Corresponding author

Correspondence to Yong Wang.

Additional information

Recommended by Associate Editor Choon Ki Ahn under the direction of Editor Duk-Sun Shim. This work is supported by the National Natural Science Foundation of China (No.61573332, No.61601431) and the Fundamental Research Funds for the Central Universities (No.WK2100100028).

Bin Du received his B.Eng. degree in Electrical Engineering from Nanjing University of Aeronautics and Astronautics in 2014. He is currently a Master candidate of Automation at University of Science and Technology of China. His research interests include fractional order systems nonzero initial condition and system identification.

Yiheng Wei received his Ph.D. degree in Automation from University of Science and Technology of China in 2015. He has been with University of Science and Technology of China since 2015, as a postdoctoral research associate. His research interests include fractional order systems identification, analysis and synthesis.

Shu Liang received his Ph.D. degree in Automation from University of Science and Technology of China in 2015. His research interests include fractional order systems and robust control.

Yong Wang received the B.Eng. degree in Automatic from the University of Science and Technology of China in 1982 and his M.Eng. and Ph.D. degrees in navigation, guidance, and control from Nanjing Aeronautical Institute, in 1985 and 1999 respectively. He has been with the Department of Automation, University of Science and Technology of China since 2001, where he is currently a Professor. He has published more than 260 refereed journal and conference papers. His research interests include active vibration control, vehicle guidance and control and fractional order dynamic and control.

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Du, B., Wei, Y., Liang, S. et al. Rational approximation of fractional order systems by vector fitting method. Int. J. Control Autom. Syst. 15, 186–195 (2017). https://doi.org/10.1007/s12555-015-0351-1

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  • DOI: https://doi.org/10.1007/s12555-015-0351-1

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