Generalizing Hybrid Integrator-Gain Systems Using Fractional Calculus

S. Ali Hosseini; Mohammad Saleh Tavazoei; Luke F. Van Eijk; S. Hassan Hosseinnia

doi:10.1109/CCTA49430.2022.9966184

Generalizing Hybrid Integrator-Gain Systems Using Fractional Calculus

S. Ali Hosseini, Mohammad Saleh Tavazoei, Luke F. Van Eijk, S. Hassan Hosseinnia

Mechatronic Systems Design

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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Abstract

The Hybrid Integrator-Gain System (HIGS) has recently gained a lot of attention in control of precision motion systems. HIGS is a nonlinear low pass filter/integrator with a 52° phase advantage over its linear counterpart. This property allows us to avoid the limitations typically associated with linear controllers, like the waterbed effect and Bode's gain-phase relation. In this paper, we generalize HIGS by replacing the involved integer-order integrator by a fractional-order one to adapt the phase lead from 0° (linear low pass filter) to 52° (HIGS). To analyze this filter in the frequency domain, the describing function of the proposed filter, i.e., the fractional-order HIGS, is obtained using the Fourier expansion of the output signal. In addition, this generalized HIGS is implemented in a PID structure controlling a double integrator system to validate the performance of the proposed filter in the time domain, in which by changing the fractional variable from zero to one, the output varies from the response of a linear control system to a nonlinear one.

Original language	English
Title of host publication	Proceedings 2022 IEEE Conference on Control Technology and Applications, CCTA 2022
Publisher	IEEE
Pages	1050-1055
ISBN (Electronic)	978-1-6654-7338-5
DOIs	https://doi.org/10.1109/CCTA49430.2022.9966184
Publication status	Published - 2022
Event	2022 IEEE Conference on Control Technology and Applications, CCTA 2022 - Trieste, Italy Duration: 23 Aug 2022 → 25 Aug 2022

Conference

Conference	2022 IEEE Conference on Control Technology and Applications, CCTA 2022
Country/Territory	Italy
City	Trieste
Period	23/08/22 → 25/08/22

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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Generalizing_Hybrid_Integrator-Gain_Systems_Using_Fractional_CalculusFinal published version, 1.73 MB

Cite this

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title = "Generalizing Hybrid Integrator-Gain Systems Using Fractional Calculus",

abstract = "The Hybrid Integrator-Gain System (HIGS) has recently gained a lot of attention in control of precision motion systems. HIGS is a nonlinear low pass filter/integrator with a 52° phase advantage over its linear counterpart. This property allows us to avoid the limitations typically associated with linear controllers, like the waterbed effect and Bode's gain-phase relation. In this paper, we generalize HIGS by replacing the involved integer-order integrator by a fractional-order one to adapt the phase lead from 0° (linear low pass filter) to 52° (HIGS). To analyze this filter in the frequency domain, the describing function of the proposed filter, i.e., the fractional-order HIGS, is obtained using the Fourier expansion of the output signal. In addition, this generalized HIGS is implemented in a PID structure controlling a double integrator system to validate the performance of the proposed filter in the time domain, in which by changing the fractional variable from zero to one, the output varies from the response of a linear control system to a nonlinear one. ",

author = "Hosseini, {S. Ali} and Tavazoei, {Mohammad Saleh} and {Van Eijk}, {Luke F.} and Hosseinnia, {S. Hassan}",

note = "Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.; 2022 IEEE Conference on Control Technology and Applications, CCTA 2022 ; Conference date: 23-08-2022 Through 25-08-2022",

year = "2022",

doi = "10.1109/CCTA49430.2022.9966184",

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booktitle = "Proceedings 2022 IEEE Conference on Control Technology and Applications, CCTA 2022",

publisher = "IEEE",

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Hosseini, SA, Tavazoei, MS, Van Eijk, LF & Hosseinnia, SH 2022, Generalizing Hybrid Integrator-Gain Systems Using Fractional Calculus. in Proceedings 2022 IEEE Conference on Control Technology and Applications, CCTA 2022. IEEE, pp. 1050-1055, 2022 IEEE Conference on Control Technology and Applications, CCTA 2022, Trieste, Italy, 23/08/22. https://doi.org/10.1109/CCTA49430.2022.9966184

Generalizing Hybrid Integrator-Gain Systems Using Fractional Calculus. / Hosseini, S. Ali; Tavazoei, Mohammad Saleh; Van Eijk, Luke F. et al.
Proceedings 2022 IEEE Conference on Control Technology and Applications, CCTA 2022. IEEE, 2022. p. 1050-1055.

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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AU - Hosseinnia, S. Hassan

N1 - Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

PY - 2022

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N2 - The Hybrid Integrator-Gain System (HIGS) has recently gained a lot of attention in control of precision motion systems. HIGS is a nonlinear low pass filter/integrator with a 52° phase advantage over its linear counterpart. This property allows us to avoid the limitations typically associated with linear controllers, like the waterbed effect and Bode's gain-phase relation. In this paper, we generalize HIGS by replacing the involved integer-order integrator by a fractional-order one to adapt the phase lead from 0° (linear low pass filter) to 52° (HIGS). To analyze this filter in the frequency domain, the describing function of the proposed filter, i.e., the fractional-order HIGS, is obtained using the Fourier expansion of the output signal. In addition, this generalized HIGS is implemented in a PID structure controlling a double integrator system to validate the performance of the proposed filter in the time domain, in which by changing the fractional variable from zero to one, the output varies from the response of a linear control system to a nonlinear one.

AB - The Hybrid Integrator-Gain System (HIGS) has recently gained a lot of attention in control of precision motion systems. HIGS is a nonlinear low pass filter/integrator with a 52° phase advantage over its linear counterpart. This property allows us to avoid the limitations typically associated with linear controllers, like the waterbed effect and Bode's gain-phase relation. In this paper, we generalize HIGS by replacing the involved integer-order integrator by a fractional-order one to adapt the phase lead from 0° (linear low pass filter) to 52° (HIGS). To analyze this filter in the frequency domain, the describing function of the proposed filter, i.e., the fractional-order HIGS, is obtained using the Fourier expansion of the output signal. In addition, this generalized HIGS is implemented in a PID structure controlling a double integrator system to validate the performance of the proposed filter in the time domain, in which by changing the fractional variable from zero to one, the output varies from the response of a linear control system to a nonlinear one.

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BT - Proceedings 2022 IEEE Conference on Control Technology and Applications, CCTA 2022

PB - IEEE

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Y2 - 23 August 2022 through 25 August 2022

ER -

Generalizing Hybrid Integrator-Gain Systems Using Fractional Calculus

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