Comparative study of op-amp-based integrators suitable for fractional-order controller design

Norbert Herencsar; Aslihan Kartci; Hacer A. Yildiz; Roman Sotner; Jan Dvorak; David Kubanek; Jan Jerabek; Jaroslav Koton

doi:10.1109/TSP.2019.8768843

Comparative study of op-amp-based integrators suitable for fractional-order controller design

Norbert Herencsar, Aslihan Kartci, Hacer A. Yildiz, Roman Sotner, Jan Dvorak, David Kubanek, Jan Jerabek, Jaroslav Koton

Department of Electronics and Communication Engineering

Brno University of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Citations (Scopus)

Abstract

In this paper, a fractional-order capacitor (FOC) of an order λ=0.89 (i.e. constant phase angle-80.1 degree) was emulated via Valsa RC network with five branches. The network component values were optimized using modified least squares quadratic method in a wide frequency range of 100 mHz-1kHz (i.e. 4 decades) and maximum relative phase error 0.78% was obtained. The design specification corresponds to a speed control system of an armature controlled DC motor, which is often used in control theory. Overall performance evaluation shows the product of evaluated key features (e.g. phase angle deviation and absolute values of relative phase, impedance, and pseudocapacitance errors) for the optimized FOC is 13.3% less than the one obtained via Valsa approximation. The behavior of Op-Amp-based non-inverting configurations of analogue fractional-order integral operator s-λ employing the optimized FOC, where 0<λ<1, is compared. The behavior of studied integrator circuits is confirmed by SPICE simulations using the readily available Texas Instruments TL072 low-noise Op-Amp macromodel, which is commonly used in electronics.

Original language	English
Title of host publication	2019 42nd International Conference on Telecommunications and Signal Processing, TSP 2019
Editors	Norbert Herencsar
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	740-743
Number of pages	4
ISBN (Electronic)	9781728118642
DOIs	https://doi.org/10.1109/TSP.2019.8768843
Publication status	Published - Jul 2019
Event	42nd International Conference on Telecommunications and Signal Processing, TSP 2019 - Budapest, Hungary Duration: 1 Jul 2019 → 3 Jul 2019

Publication series

Name	2019 42nd International Conference on Telecommunications and Signal Processing, TSP 2019

Conference

Conference	42nd International Conference on Telecommunications and Signal Processing, TSP 2019
Country/Territory	Hungary
City	Budapest
Period	1/07/19 → 3/07/19

Bibliographical note

Publisher Copyright:
© 2019 IEEE.

Keywords

DC motor
Fractional calculus
Fractional-order capacitor
Fractional-order controller
Fractional-order integrator
Op-Amp
Valsa RC network

Access to Document

10.1109/TSP.2019.8768843

Cite this

Herencsar, N., Kartci, A., Yildiz, H. A., Sotner, R., Dvorak, J., Kubanek, D., Jerabek, J., & Koton, J. (2019). Comparative study of op-amp-based integrators suitable for fractional-order controller design. In N. Herencsar (Ed.), 2019 42nd International Conference on Telecommunications and Signal Processing, TSP 2019 (pp. 740-743). Article 8768843 (2019 42nd International Conference on Telecommunications and Signal Processing, TSP 2019). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/TSP.2019.8768843

Herencsar, Norbert ; Kartci, Aslihan ; Yildiz, Hacer A. et al. / Comparative study of op-amp-based integrators suitable for fractional-order controller design. 2019 42nd International Conference on Telecommunications and Signal Processing, TSP 2019. editor / Norbert Herencsar. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 740-743 (2019 42nd International Conference on Telecommunications and Signal Processing, TSP 2019).

@inproceedings{4f1af791a7364f7b91ca15fddf1d8f7d,

title = "Comparative study of op-amp-based integrators suitable for fractional-order controller design",

abstract = "In this paper, a fractional-order capacitor (FOC) of an order λ=0.89 (i.e. constant phase angle-80.1 degree) was emulated via Valsa RC network with five branches. The network component values were optimized using modified least squares quadratic method in a wide frequency range of 100 mHz-1kHz (i.e. 4 decades) and maximum relative phase error 0.78% was obtained. The design specification corresponds to a speed control system of an armature controlled DC motor, which is often used in control theory. Overall performance evaluation shows the product of evaluated key features (e.g. phase angle deviation and absolute values of relative phase, impedance, and pseudocapacitance errors) for the optimized FOC is 13.3% less than the one obtained via Valsa approximation. The behavior of Op-Amp-based non-inverting configurations of analogue fractional-order integral operator s-λ employing the optimized FOC, where 0<λ<1, is compared. The behavior of studied integrator circuits is confirmed by SPICE simulations using the readily available Texas Instruments TL072 low-noise Op-Amp macromodel, which is commonly used in electronics.",

keywords = "DC motor, Fractional calculus, Fractional-order capacitor, Fractional-order controller, Fractional-order integrator, Op-Amp, Valsa RC network",

author = "Norbert Herencsar and Aslihan Kartci and Yildiz, {Hacer A.} and Roman Sotner and Jan Dvorak and David Kubanek and Jan Jerabek and Jaroslav Koton",

note = "Publisher Copyright: {\textcopyright} 2019 IEEE.; 42nd International Conference on Telecommunications and Signal Processing, TSP 2019 ; Conference date: 01-07-2019 Through 03-07-2019",

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Herencsar, N, Kartci, A, Yildiz, HA, Sotner, R, Dvorak, J, Kubanek, D, Jerabek, J & Koton, J 2019, Comparative study of op-amp-based integrators suitable for fractional-order controller design. in N Herencsar (ed.), 2019 42nd International Conference on Telecommunications and Signal Processing, TSP 2019., 8768843, 2019 42nd International Conference on Telecommunications and Signal Processing, TSP 2019, Institute of Electrical and Electronics Engineers Inc., pp. 740-743, 42nd International Conference on Telecommunications and Signal Processing, TSP 2019, Budapest, Hungary, 1/07/19. https://doi.org/10.1109/TSP.2019.8768843

Comparative study of op-amp-based integrators suitable for fractional-order controller design. / Herencsar, Norbert; Kartci, Aslihan; Yildiz, Hacer A. et al.
2019 42nd International Conference on Telecommunications and Signal Processing, TSP 2019. ed. / Norbert Herencsar. Institute of Electrical and Electronics Engineers Inc., 2019. p. 740-743 8768843 (2019 42nd International Conference on Telecommunications and Signal Processing, TSP 2019).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Herencsar, Norbert

AU - Kartci, Aslihan

AU - Yildiz, Hacer A.

AU - Sotner, Roman

AU - Dvorak, Jan

AU - Kubanek, David

AU - Jerabek, Jan

AU - Koton, Jaroslav

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N2 - In this paper, a fractional-order capacitor (FOC) of an order λ=0.89 (i.e. constant phase angle-80.1 degree) was emulated via Valsa RC network with five branches. The network component values were optimized using modified least squares quadratic method in a wide frequency range of 100 mHz-1kHz (i.e. 4 decades) and maximum relative phase error 0.78% was obtained. The design specification corresponds to a speed control system of an armature controlled DC motor, which is often used in control theory. Overall performance evaluation shows the product of evaluated key features (e.g. phase angle deviation and absolute values of relative phase, impedance, and pseudocapacitance errors) for the optimized FOC is 13.3% less than the one obtained via Valsa approximation. The behavior of Op-Amp-based non-inverting configurations of analogue fractional-order integral operator s-λ employing the optimized FOC, where 0<λ<1, is compared. The behavior of studied integrator circuits is confirmed by SPICE simulations using the readily available Texas Instruments TL072 low-noise Op-Amp macromodel, which is commonly used in electronics.

AB - In this paper, a fractional-order capacitor (FOC) of an order λ=0.89 (i.e. constant phase angle-80.1 degree) was emulated via Valsa RC network with five branches. The network component values were optimized using modified least squares quadratic method in a wide frequency range of 100 mHz-1kHz (i.e. 4 decades) and maximum relative phase error 0.78% was obtained. The design specification corresponds to a speed control system of an armature controlled DC motor, which is often used in control theory. Overall performance evaluation shows the product of evaluated key features (e.g. phase angle deviation and absolute values of relative phase, impedance, and pseudocapacitance errors) for the optimized FOC is 13.3% less than the one obtained via Valsa approximation. The behavior of Op-Amp-based non-inverting configurations of analogue fractional-order integral operator s-λ employing the optimized FOC, where 0<λ<1, is compared. The behavior of studied integrator circuits is confirmed by SPICE simulations using the readily available Texas Instruments TL072 low-noise Op-Amp macromodel, which is commonly used in electronics.

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Herencsar N, Kartci A, Yildiz HA, Sotner R, Dvorak J, Kubanek D et al. Comparative study of op-amp-based integrators suitable for fractional-order controller design. In Herencsar N, editor, 2019 42nd International Conference on Telecommunications and Signal Processing, TSP 2019. Institute of Electrical and Electronics Engineers Inc. 2019. p. 740-743. 8768843. (2019 42nd International Conference on Telecommunications and Signal Processing, TSP 2019). doi: 10.1109/TSP.2019.8768843

Comparative study of op-amp-based integrators suitable for fractional-order controller design

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Keywords

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