Step response of fractional order system depends on discretizing step?

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  • This topic has 2 replies, 2 voices, and was last updated 10 years ago by Ecook.
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  • #904
    Ecook
    Guest

    Hello, Aleskei.
    Right now I am using the fotf_gui to study the step response of the fractional order system

    s^{3.3}+2s^{2.2}+s^{1.1}+2
    ————————————————————————————————
    s^{7.7}+2.9s^{6.6}+2s^{6.6}+11.05s^{5.5}+14.075s^{4.4}+10.525s^{3.3}+4.55s^{2.2}+1.05s^{1.1}+0.1

    When the stimulus is specified with a step h=0.01, i.e. u=[0:0.01:160], the toolbox gives oscillatory results. But when the step is h=0.1, the results are better. Can you explain why this happen? Thank you very much.

    #906
    Aleksei
    Keymaster

    There might be a problem with the implementation of the solver. This part of FOMCON code belongs to the unmodified fotf toolbox code base. The solver *may* have some numerical issues that need to be addressed. I will review the code shortly. Meanwhile, kindly see the following references that document the implementation of the solver:

    [1] Y. Q. Chen, I. Petráš, and D. Xue, “Fractional order control – A tutorial,” in Proc. ACC ’09. American Control Conference, 2009, pp. 1397–1411.

    [2] D. Xue, Y. Chen, and D. P. Atherton, Linear Feedback Control: Analysis and Design with MATLAB (Advances in Design and Control), 1st ed.. Philadelphia, PA, USA: Society for Industrial and Applied Mathematics, 2008.

    [3] C. A. Monje, Y. Chen, B. Vinagre, D. Xue, and V. Feliu, Fractional-order Systems and Controls: Fundamentals and Applications, ser. Advances in Industrial Control. Springer Verlag, 2010.

    If you identify an explicit problem with the implementation, do not hesitate to file a bug.

    #908
    Ecook
    Guest

    Thank you for providing the good references. I’ll try to understand the solver from the references.
    Part of the denominator is missing in the post, so I’ll write it down again:

    s^{3.3}+2s^{2.2}+s^{1.1}+2
    ———————————————————-
    s^{7.7}+2.9s^{6.6}+2s^{6.6}+11.05s^{5.5}+14.075s^{4.4}
    +10.525s^{3.3}+4.55s^{2.2}+1.05s^{1.1}+0.1

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