State-Space Modelling of Loudspeakers using Fractional Derivatives

Alexander Weider King; Finn T. Agerkvist

State-Space Modelling of Loudspeakers using Fractional Derivatives

Alexander Weider King, Finn T. Agerkvist

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Abstract

This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response of a fractional harmonic oscillator, representing the mechanical part of a loudspeaker, showing the effect of the fractional derivative and its relationship to viscoelasticity. Finally, a loudspeaker model with a fractional order viscoelastic suspension and fractional order voice coil is fit to measurement data. It is shown that the identified parameters can be used in a linear fractional order state-space model to simulate the loudspeakers’ time domain response

Original language	English
Title of host publication	Proceedings of 138th International Audio Engineering Society (AES) Convention
Number of pages	10
Volume	9413
Publisher	Audio Engineering Society
Publication date	2015
Publication status	Published - 2015
Event	139th International Audio Engineering Society (AES) Convention - The Jacob Javits Center, New York City, United States Duration: 29 Oct 2015 → 1 Nov 2015 http://www.aes.org/events/139/

Conference

Conference	139th International Audio Engineering Society (AES) Convention
Location	The Jacob Javits Center
Country/Territory	United States
City	New York City
Period	29/10/2015 → 01/11/2015
Internet address	http://www.aes.org/events/139/

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title = "State-Space Modelling of Loudspeakers using Fractional Derivatives",

abstract = "This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response of a fractional harmonic oscillator, representing the mechanical part of a loudspeaker, showing the effect of the fractional derivative and its relationship to viscoelasticity. Finally, a loudspeaker model with a fractional order viscoelastic suspension and fractional order voice coil is fit to measurement data. It is shown that the identified parameters can be used in a linear fractional order state-space model to simulate the loudspeakers{\textquoteright} time domain response",

author = "King, {Alexander Weider} and Agerkvist, {Finn T.}",

year = "2015",

language = "English",

volume = "9413",

booktitle = "Proceedings of 138th International Audio Engineering Society (AES) Convention",

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note = "139th International Audio Engineering Society (AES) Convention ; Conference date: 29-10-2015 Through 01-11-2015",

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T1 - State-Space Modelling of Loudspeakers using Fractional Derivatives

AU - King, Alexander Weider

AU - Agerkvist, Finn T.

PY - 2015

Y1 - 2015

N2 - This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response of a fractional harmonic oscillator, representing the mechanical part of a loudspeaker, showing the effect of the fractional derivative and its relationship to viscoelasticity. Finally, a loudspeaker model with a fractional order viscoelastic suspension and fractional order voice coil is fit to measurement data. It is shown that the identified parameters can be used in a linear fractional order state-space model to simulate the loudspeakers’ time domain response

AB - This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response of a fractional harmonic oscillator, representing the mechanical part of a loudspeaker, showing the effect of the fractional derivative and its relationship to viscoelasticity. Finally, a loudspeaker model with a fractional order viscoelastic suspension and fractional order voice coil is fit to measurement data. It is shown that the identified parameters can be used in a linear fractional order state-space model to simulate the loudspeakers’ time domain response

M3 - Article in proceedings

VL - 9413

BT - Proceedings of 138th International Audio Engineering Society (AES) Convention

PB - Audio Engineering Society

T2 - 139th International Audio Engineering Society (AES) Convention

Y2 - 29 October 2015 through 1 November 2015

ER -

State-Space Modelling of Loudspeakers using Fractional Derivatives

Abstract

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