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On the Electronic Realizations of Fractional-Order Phase-Lead-Lag Compensators with OpAmps and FPAAs

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Fractional Order Control and Synchronization of Chaotic Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 688))

Abstract

It is well known that the fractional-order phase-lead-lag compensators can achieve control objectives that are not always possible by using their integer-order counterparts. However, up to now one can find only a few of publications discussing the strategies for parameters’ tuning of these compensators, with only simulation results reported. This is due in part to the implicit difficulties on the implementation of circuit elements with frequency responses of the form \(s^{\pm \lambda }\) that are named “fractances”. In this regard, there exist approximations with rational functions, but the drawback is the difficulty to approximate the required values with the ones of the commercially-available resistances and capacitors. Consequently, fractional compensators have not been appreciated by the industry as it is in the academia. Therefore, motivated by the lack of reported implementations, this chapter is structured as a tutorial that deals with the key factors to perform, with the frequency-domain approach, the design, simulation and implementation of integer-order and fractional-order phase-lead-lag compensators. The circuit implementations are performed with Operational Amplifiers (OpAmps) and with Field Programmable Analog Arrays (FPAA). Emphasis is focused in the obtaining of commercially-available values of resistances and capacitors. Therefore, the design procedure starts with the use of equations that provide the exact and unique solution for each parameter of the compensator, avoiding conventional trial-and-error procedures. Then, five OpAmp-based configurations for integer-order and fractional-order realizations are described in terms of basic analog building blocks, such as integrators or differential amplifiers, among others. The corresponding design equations are also provided. Then, six examples are presented for both, OpAmp-based and FPAA-based implementations with the simulation and experimental results discussed regarding other results reported in the literature.

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Acknowledgements

This work was supported in part by the National Council for Science and Technology (CONACyT), Mexico, under Grant 181201, 222843 and 237991; in part by the Universidad Autónoma de Tlaxcala (UATx), Tlaxcala de Xicothencatl, TL, Mexico, under Grant CACyPI-UATx-2015; and in part by the Program to Strengthen Quality in Educational under Grant P/PROFOCIE-2015-29MSU0013Y-02

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Authors and Affiliations

  1. Electronics and Telecommunications Department, Universidad Politécnica de Puebla, 72640, Cuanalá, Puebla, Mexico

    Carlos Muñiz-Montero

  2. Faculty of Electronics, Benemérita Universidad Autónoma de Puebla, Av. San Claudio y 18 Sur Jardines de San Manuel, 72592, Puebla, Mexico

    Luis A. Sánchez-Gaspariano & Víctor R. González-Díaz

  3. Department of Electronics, Universidad Autónoma de Tlaxcala, 90300, Apizaco, Tlaxcala, Mexico

    Carlos Sánchez-López

  4. Department of Computer Science, CINVESTAV, Av. Instituto Politécnico Nacional No. 2508 Col. San Pedro Zacatenco, 07360, Mexico City, Mexico

    Esteban Tlelo-Cuautle

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  1. Carlos Muñiz-Montero
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  2. Luis A. Sánchez-Gaspariano
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  3. Carlos Sánchez-López
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Correspondence to Esteban Tlelo-Cuautle .

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Editors and Affiliations

  1. Faculty of Computers and Information, Benha University Faculty of Computers and Information, AND Nanoelectronics Integrated Systems Center (NISC), Nile University, Egypt. , Benha, Egypt

    Ahmad Taher Azar

  2. Research and Development Centre, Vel Tech University Research and Development Centre, Chennai, Tamil Nadu, India

    Sundarapandian Vaidyanathan

  3. Department of Mathematics and CS, University of Tebessa Department of Mathematics and CS, Tebessa, Algeria

    Adel Ouannas

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Muñiz-Montero, C., Sánchez-Gaspariano, L.A., Sánchez-López, C., González-Díaz, V.R., Tlelo-Cuautle, E. (2017). On the Electronic Realizations of Fractional-Order Phase-Lead-Lag Compensators with OpAmps and FPAAs. In: Azar, A., Vaidyanathan, S., Ouannas, A. (eds) Fractional Order Control and Synchronization of Chaotic Systems. Studies in Computational Intelligence, vol 688. Springer, Cham. https://doi.org/10.1007/978-3-319-50249-6_5

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  • DOI: https://doi.org/10.1007/978-3-319-50249-6_5

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