<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The design method and the time-variant finite impulse response (FIR) architecture for real-time estimation of fractional and integer differentials and integrals are presented in this paper. The proposed FIR architecture is divided into two parts. Small-phase filtering, integer differentiation, and fractional differential and integration on the local data are performed by the first part, which is time-invariant. The second part, which is time-variant, handles fractional and global differentiation and integration. The separation of the two parts is necessary because real-time matrix inversion or an extensive analytical solution, which can be computationally intensive for high-order FIR architectures, would be required by a single time-variant FIR architecture. However, matrix inversion is used in the design method to achieve negligible delay in the filtered, differentiated, and integrated signals. The optimum output obtained by the method of least squares results in the negligible delay. The experimental results show that fractional and integer differentiation and integration can be performed by the proposed solution, although the fractional differentiation and integration process is sensitive to the noise and limited resolution of the measurements. In systems that require closed-loop control, disturbance observation, and real-time identification of model parameters, this solution can be implemented.</p>
</abstract>

The design method and the time-variant finite impulse response (FIR) architecture for real-time estimation of fractional and integer differentials and integrals are presented in this paper. The proposed FIR architecture is divided into two parts. Small-phase filtering, integer differentiation, and fractional differential and integration on the local data are performed by the first part, which is time-invariant. The second part, which is time-variant, handles fractional and global differentiation and integration. The separation of the two parts is necessary because real-time matrix inversion or an extensive analytical solution, which can be computationally intensive for high-order FIR architectures, would be required by a single time-variant FIR architecture. However, matrix inversion is used in the design method to achieve negligible delay in the filtered, differentiated, and integrated signals. The optimum output obtained by the method of least squares results in the negligible delay. The experimental results show that fractional and integer differentiation and integration can be performed by the proposed solution, although the fractional differentiation and integration process is sensitive to the noise and limited resolution of the measurements. In systems that require closed-loop control, disturbance observation, and real-time identification of model parameters, this solution can be implemented.

Design of Small-Phase Time-Variant Low-Pass Digital Fractional Differentiators and Integrators

Sensors and Systems, School of Engineering & Physical Sciences, Heriot-Watt University

Journal of Automation, Mobile Robotics and Intelligent Systems

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The design method and the time-variant finite impulse response (FIR) architecture for real-time estimation of fractional and integer differentials and...

Design of Small-Phase Time-Variant Low-Pass Digital Fractional Differentiators and Integrators

Published Online: Jun 23, 2024

Page range: 72 - 82

Received: Oct 03, 2023

Accepted: Feb 08, 2024

DOI: https://doi.org/10.14313/jamris/2-2024/15

Keywords
fractional differentiation, fractional integration, FIR filter, digital filter synthesis

© 2024 Mateusz Saków, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Design of Small-Phase Time-Variant Low-Pass Digital Fractional Differentiators and Integrators

Published Online: Jun 23, 2024

Page range: 72 - 82

Received: Oct 03, 2023

Accepted: Feb 08, 2024

DOI: https://doi.org/10.14313/jamris/2-2024/15

Keywordsfractional differentiation, fractional integration, FIR filter, digital filter synthesis

© 2024 Mateusz Saków, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
fractional differentiation, fractional integration, FIR filter, digital filter synthesis