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State-Space Modeling of Loudspeakers Using Fractional Derivatives

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.

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Permalink: http://www.aes.org/e-lib/browse.cfm?elib=17970

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