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An Estimation of Accuracy of Oustaloup Approximation

  • Krzysztof OprzędkiewiczEmail author
  • Wojciech Mitkowski
  • Edyta Gawin
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 440)

Abstract

In the paper a new accuracy estimation method for Oustaloup approximation is presented. Oustaloup approximation is a fundamental tool to describe fractional-order systems with the use of integer-order, proper transfer function. The accuracy of approximation can be estimated via comparison of impulse responses for plant and Oustaloup approximation. The impulse response of the plant was calculated with the use of an accurate analytical formula and it can be interpreted as a standard. Approach presented in the paper can be applied to effective tuning of Oustaloup approximant for given application (for example in FO PID controller). The use of proposed method does not require us to know time response of a modeled controller. The proposed methodology can be easily generalized to another known approximations. Results of simulations show that the good performance of approximation is reached for low order and narrow angular frequency range.

Keywords

Fractional order transfer function Oustaloup approximation 

Notes

Acknowledgements

This paper was partially supported by the AGH (Poland)—project no 11.11.120.815 and partially supported by the AGH (Poland)—project no 11.11.120.817.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Krzysztof Oprzędkiewicz
    • 1
    Email author
  • Wojciech Mitkowski
    • 1
  • Edyta Gawin
    • 2
  1. 1.Faculty of Electrotechnics, Automatics, Informatics and Biomedical Engineering, Department of Automatics and Biomedical EngineeringAGH University of Science and TechnologyKrakówPoland
  2. 2.Polytechnic InstituteHigh Vocational School in TarnówTarnówPoland

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