Pascal Brunet and Bahram Shafai
Fractional Order System, Frequency Domain
With smartphones and tablets, loudspeakers play an ever important role in our everyday lives. Sound quality is paramount for clear communication and listening pleasure. In order to proper control the acoustic output of the loudspeaker a precise modeling and identification of the electromechanical part ('motor') is necessary. In this paper we show that the electrical impedance of the motor can be properly modeled and identified as a fractional order system. This is the main contribution of this paper. After showing the empirical evidence of fractional order behavior in actual loudspeaker measurement, we explain the related mathematical theory. We then describe a frequency domain subspace identification method adapted to fractional order systems. Finally by applying this identification method on the actual measured data, we show that the fractional order approach results in a better fit and a lower model complexity than the traditional integer order approach.
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