Identifiability of fractional order systems using input output frequency contents

In this paper, issues related to the identifiability of a fractional order system having its input and output frequency contents are discussed. The effects of the commensurate order α in the identifiability of the model structure and model parameters are analytically studied. It is shown that both identifiabilities (model structure and model parameters) are reduced remarkably for smaller values of α. This phenomenon is observed even though the input signals are rich enough and system belongs to the model set. Our understanding is that the problem arises since differences among different members of the model set fall beyond the practically recognizable precision range. The issue is more problematic when α is smaller and measurements are noisy.