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Fractional order [PI], [PD] and [PI][PD] controller design using Bode’s integrals

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Abstract

This paper is devoted to Bode’s integrals based design of fractional order [PI], [PD] and [PI][PD] controllers for integer order systems. The gain crossover frequency, the phase margin and the Nyquist plot slope adjustment in gain crossover frequency are considered as the design specifications for FO[PI] and FO[PD] controllers. To calculate the Nyquist plot slope, the Bode’s integrals are utilized. The FO[PI][PD] controller is constructed by series connection of the FO[PI] and FO[PD] controllers. To design the FO[PI][PD] controller, the measurement noise rejection and the integral time absolute error minimization are employed as the additional design requirements. Simulation results are presented to show the performance of the Bode’s integral based fractional order controllers.

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Authors and Affiliations

  1. Department of Electrical Engineering, Khomeinishahr Branch, Islamic Azad University, Isfahan, Iran

    Kianoush Ranjbaran & Mohammad Tabatabaei

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  1. Kianoush Ranjbaran
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  2. Mohammad Tabatabaei
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Correspondence to Mohammad Tabatabaei.

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Ranjbaran, K., Tabatabaei, M. Fractional order [PI], [PD] and [PI][PD] controller design using Bode’s integrals. Int. J. Dynam. Control 6, 200–212 (2018). https://doi.org/10.1007/s40435-016-0301-7

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  • DOI: https://doi.org/10.1007/s40435-016-0301-7

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