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), 2024. Published by Science Publishing Group |
Floyd’s Method, Impulse Unit Response, Step Unit Response, Frequency Domain, Time Domain, Fourier’s Inverse Transform
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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
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
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
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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}
}
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 -
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