Identification of fractional-order transfer functions using exponentially modulated signals with arbitrary excitation waveforms
2020
This paper proposes a new identification method based on an exponential modulation scheme for the determination
of the coefficients and exponents of a fractional-order transfer function. The proposed approach has a broader
scope of application compared to a previous method based on step response data, in that it allows for the use of
arbitrary input signals. Moreover, it dispenses with the need for repeated simulations during the search for the
best fractional exponents, which significantly reduces the computational workload involved in the identification
process. Two examples involving measurement noise at the observed system output are presented to illustrate the
effectiveness of the proposed method when compared to a conventional output-error optimization approach based
on the polytope algorithm. In both examples, the proposed method is found to provide a better trade-off between
computational workload and accuracy of the parameter estimates for different realizations of the noise.
Keywords: Fractional order systems, system identification, transfer functions
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