| Peer-Reviewed

Floyd’s Modified Computational Method Applied to Calculate Step Response of a Regilator from Frequency Response

Received: 10 July 2019     Accepted: 12 August 2019     Published: 23 August 2019
Views:       Downloads:
Abstract

This work explains how to obtain the unit step time domain response by means of the frequency response of a regulator (gain and phase) using the Floyd’s Modified Computational Method. The preliminary condition is that the gain of the system tends to zero as the frequency tends to infinite. Floyd’s Method uses the Fourier’s Inverse Transform to achieve the Impulse Unit response. The Modified Method calculates the integral. This work details the mathematical developnent of Floyd’s Method. Authors introduce the integral of the Impulse Unit response to obtain the Step Unit response and also the linearization of the Method in order to approximate it and obtain an equation to do the computational calculation. We apply the modified method in a second order system, calculating its frequency response and its analytic step unit response by means of the MNatlab. Then we use the equation developed in this work by the linearization of Floyd‘s Modified Method applied in the frequency response of the system and compare with the step unit analytic response. The relative error is calculated and we can observe that Floyd’s Modified Method generates a step unit response in the time domain that has some time little retard and with values a little inferior to the analytic response. This behavior is attributed to the linearization and to do not use the complete frequency band of the system. However the final values are very exact. T.

Published in Science Journal of Circuits, Systems and Signal Processing (Volume 8, Issue 2)
DOI 10.11648/j.cssp.20190802.13
Page(s) 47-52
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Floyd’s Method, Impulse Unit Response, Step Unit Response, Frequency Domain, Time Domain, Fourier’s Inverse Transform

References
[1] GORDON, J. M. Basic Automatic Control Theory. First Edition, June 1957. D. Van Nostrand Company, INC. Princeton, New Jersey.
[2] CLOSE, M. C. Circuitos Lineares – vol. 2 Editora da Universidade de São Paulo. Livros Tecnicos e Cientificos. Editora AS. Rio de Janeiro, RJ. 1975.
[3] DORF, R, C. Sistemas Automaticos de Control: Teoria y Prática. Fundo Educativo Interamericano, AS. 1977.
[4] Ogata, Katsuhiko Engenharia de Controle Moderno, Prentice Hall do Brasil.
[5] Simon Haykin e Barry Van Veen, Sinais e Sistemas, Bookmaqn.
[6] Transformadas de Laplace, Coleção Schaum, Editora Mac Graw Hill do Brasil, LTDA.
[7] Digital Control of Dynamic Systems, Gene F. Franklin, J. David Powell, Michael L. Workman, Addison Wesley Publishing Company.
[8] John J D’Azzo, Constantine H. Houpis, Análise e Projeto de Sistemas de Controle Lineres, Editora Guanabara Dois.
[9] Élia Yathie Matsumoto, Matlab6.5 Fundamentos de Programação, Editora Érica.
[10] Erwin Kreyszig. Matemática Superior vols. 1, 2, 3 e 4, Livros Técnicos e Científicos Editora S. A.
[11] Ruel V. Churchill, Variáveis Complexas e Suas Aplicações. Mc Graw-Hill.
[12] Wilfred Kaplan, Cálculo Avançado vols, 1 e 2, Editora Edgard Blucher, LTDA.
[13] JosephA. Edminister, Circuitos Elétricos, Coleção Schaum. McGraw-Hill.
[14] Joseph J. Distefano e Allen R. Stubberud – Ivan J. Williams, Sistemas de Retroação e Controle, Coleção Schaum, Editora Mc Graw Hill do Brasil LTDA.
[15] George J. Thaler, Elementos de la Teoria de Servosistemas, Biblioteca Universal de Obras Tecnicas, Editorial Labor S. A.
[16] Paulo Alvaro Maya e Fabrizio Leonardi, Controle essencial, Pearson.
[17] John G. Truxal, Introductoy Systrem Engineerig, McGRAWLL-HILL KOGAKUSHA. LTD.
Cite This Article
  • APA Style

    Jose Flavio Feiteira, Jose Luiz Guarino, Rodrigo Guerra de Souza. (2019). Floyd’s Modified Computational Method Applied to Calculate Step Response of a Regilator from Frequency Response. Science Journal of Circuits, Systems and Signal Processing, 8(2), 47-52. https://doi.org/10.11648/j.cssp.20190802.13

    Copy | Download

    ACS Style

    Jose Flavio Feiteira; Jose Luiz Guarino; Rodrigo Guerra de Souza. Floyd’s Modified Computational Method Applied to Calculate Step Response of a Regilator from Frequency Response. Sci. J. Circuits Syst. Signal Process. 2019, 8(2), 47-52. doi: 10.11648/j.cssp.20190802.13

    Copy | Download

    AMA Style

    Jose Flavio Feiteira, Jose Luiz Guarino, Rodrigo Guerra de Souza. Floyd’s Modified Computational Method Applied to Calculate Step Response of a Regilator from Frequency Response. Sci J Circuits Syst Signal Process. 2019;8(2):47-52. doi: 10.11648/j.cssp.20190802.13

    Copy | Download

  • @article{10.11648/j.cssp.20190802.13,
      author = {Jose Flavio Feiteira and Jose Luiz Guarino and Rodrigo Guerra de Souza},
      title = {Floyd’s Modified Computational Method Applied to Calculate Step Response of a Regilator from Frequency Response},
      journal = {Science Journal of Circuits, Systems and Signal Processing},
      volume = {8},
      number = {2},
      pages = {47-52},
      doi = {10.11648/j.cssp.20190802.13},
      url = {https://doi.org/10.11648/j.cssp.20190802.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cssp.20190802.13},
      abstract = {This work explains how to obtain the unit step time domain response by means of the frequency response of a regulator (gain and phase) using the Floyd’s Modified Computational Method. The preliminary condition is that the gain of the system tends to zero as the frequency tends to infinite. Floyd’s Method uses the Fourier’s Inverse Transform to achieve the Impulse Unit response. The Modified Method calculates the integral. This work details the mathematical developnent of Floyd’s Method. Authors introduce the integral of the Impulse Unit response to obtain the Step Unit response and also the linearization of the Method in order to approximate it and obtain an equation to do the computational calculation. We apply the modified method in a second order system, calculating its frequency response and its analytic step unit response by means of the MNatlab. Then we use the equation developed in this work by the linearization of Floyd‘s Modified Method applied in the frequency response of the system and compare with the step unit analytic response. The relative error is calculated and we can observe that Floyd’s Modified Method generates a step unit response in the time domain that has some time little retard and with values a little inferior to the analytic response. This behavior is attributed to the linearization and to do not use the complete frequency band of the system. However the final values are very exact. T.},
     year = {2019}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Floyd’s Modified Computational Method Applied to Calculate Step Response of a Regilator from Frequency Response
    AU  - Jose Flavio Feiteira
    AU  - Jose Luiz Guarino
    AU  - Rodrigo Guerra de Souza
    Y1  - 2019/08/23
    PY  - 2019
    N1  - https://doi.org/10.11648/j.cssp.20190802.13
    DO  - 10.11648/j.cssp.20190802.13
    T2  - Science Journal of Circuits, Systems and Signal Processing
    JF  - Science Journal of Circuits, Systems and Signal Processing
    JO  - Science Journal of Circuits, Systems and Signal Processing
    SP  - 47
    EP  - 52
    PB  - Science Publishing Group
    SN  - 2326-9073
    UR  - https://doi.org/10.11648/j.cssp.20190802.13
    AB  - This work explains how to obtain the unit step time domain response by means of the frequency response of a regulator (gain and phase) using the Floyd’s Modified Computational Method. The preliminary condition is that the gain of the system tends to zero as the frequency tends to infinite. Floyd’s Method uses the Fourier’s Inverse Transform to achieve the Impulse Unit response. The Modified Method calculates the integral. This work details the mathematical developnent of Floyd’s Method. Authors introduce the integral of the Impulse Unit response to obtain the Step Unit response and also the linearization of the Method in order to approximate it and obtain an equation to do the computational calculation. We apply the modified method in a second order system, calculating its frequency response and its analytic step unit response by means of the MNatlab. Then we use the equation developed in this work by the linearization of Floyd‘s Modified Method applied in the frequency response of the system and compare with the step unit analytic response. The relative error is calculated and we can observe that Floyd’s Modified Method generates a step unit response in the time domain that has some time little retard and with values a little inferior to the analytic response. This behavior is attributed to the linearization and to do not use the complete frequency band of the system. However the final values are very exact. T.
    VL  - 8
    IS  - 2
    ER  - 

    Copy | Download

Author Information
  • Computational Modeling in Science and Technology, Universidade Federal Fluminense, Volta Redonda, Brazil

  • Computational Modeling in Science and Technology, Universidade Federal Fluminense, Volta Redonda, Brazil

  • Computational Modeling in Science and Technology, Universidade Federal Fluminense, Volta Redonda, Brazil

  • Sections