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Fractional order control of thermal systems: achievability of frequency-domain requirements

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Abstract

Fractional order models have been widely used in modeling and identification of thermal systems. General model in this category is considered as the model of thermal systems in this paper, and a fractional order controller is proposed for controlling such systems. The proposed controller is a generalization for the traditional PI controllers. The parameters of this controller can be obtained by using a recently introduced tuning method which can simultaneously ensure the following three requirements: desired phase margin, desired gain crossover frequency, and flatness of the phase Bode plot at this frequency. In this paper, it is found whether simultaneously achieving the mentioned frequency-domain requirements will be possible in the control of the considered thermal systems. Numerical examples are presented to show the usefulness of the obtained results.

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Notes

  1. It is worth noting that a more practical form for an IFD controller is obtained by replacing the derivative term \(s^{\mu }\) with the proper term \(s^{\mu }/(\gamma s^{\mu }+1)\), i.e., \(C(s)=k_1 \left( {1/s+k_2 s^{\mu }/(\gamma s^{\mu }+1)} \right) \) [19].

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Acknowledgments

This work was supported by the Iran National Science Foundation (INSF).

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Authors and Affiliations

  1. Electrical Engineering Department, Sharif University of Technology, Tehran, Iran

    Vahid Badri & Mohammad Saleh Tavazoei

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  1. Vahid Badri
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  2. Mohammad Saleh Tavazoei
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Correspondence to Mohammad Saleh Tavazoei.

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Badri, V., Tavazoei, M.S. Fractional order control of thermal systems: achievability of frequency-domain requirements. Nonlinear Dyn 80, 1773–1783 (2015). https://doi.org/10.1007/s11071-014-1394-1

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