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Volume 6 Issue 4
Jul.  2019

IEEE/CAA Journal of Automatica Sinica

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Ameya Anil Kesarkar and Selvaganesan Narayanasamy, "Asymptotic Magnitude Bode Plots of Fractional-Order Transfer Functions," IEEE/CAA J. Autom. Sinica, vol. 6, no. 4, pp. 1019-1026, June 2019. doi: 10.1109/JAS.2016.7510196
Citation: Ameya Anil Kesarkar and Selvaganesan Narayanasamy, "Asymptotic Magnitude Bode Plots of Fractional-Order Transfer Functions," IEEE/CAA J. Autom. Sinica, vol. 6, no. 4, pp. 1019-1026, June 2019. doi: 10.1109/JAS.2016.7510196

Asymptotic Magnitude Bode Plots of Fractional-Order Transfer Functions

doi: 10.1109/JAS.2016.7510196
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  • Development of asymptotic magnitude Bode plots for integer-order transfer functions is a well-established topic in the control theory. However, construction of such plots for the fractional-order transfer functions has not received much attention in the existing literature. In the present paper, we investigate in this direction and derive the procedures for sketching asymptotic magnitude Bode plots for some of the popular fractional-order controllers such as $PI^\alpha$, $[PI]^\alpha$, $PD^\beta$, $[PD]^\beta$, and $PI^\alpha D^\beta$. In addition, we deduce these plots for general fractional commensurate-order transfer functions as well. As applications of this work, we illustrate 1) the analysis of the designed fractional-control loop and 2) the identification of fractional-order transfer function from a given plot.


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    • To define basic fractional-order terms and develop their individual asymptotic magnitude Bode plots.
    • To utilize above plots for developing asymptotic magnitude Bode plots of: a) Fractional-order controllers such as PIα, [PI]α, PDβ, [PD]β , PIαDβ . b) General fractional commensurate-order transfer functions.
    • To illustrate the applications of these plots for: a) Performance analysis of designed fractional-order control loop. b) Identifying fractional-order transfer function from given asymptotic magnitude plot.


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