The characteristics of supercapacitors can be predicted accurately with less number of parameters using a fractional order model (FOM). But the digital implementation of the FOM requires equivalent integer order approximation. Then how can we claim that FOM is better?
Digitally it is always approximation; but depending on number of pole-zero interlaced will give you how closeness do you get represenation for a fractional Laplace variable. You are correct even with first principles of defining by generalizing repeated integration and repeated differentiation-to non-integer order, you get infinite terms-and say you want to use Grunwald-Letnikov formula-needs truncation. Therefore any digital representation of FOS will be approximation.
Thank You for your reply Shantanu sir..
Suppose if we set an accuracy limits and truncating the number of terms,
still the order of the function will be considerable. In fact, if we then compare
with RC ladder models, the complexity associated with the FOM will be higher.
Considering this, I think online implementation of FOM can be justified
only if the application demands are so stringent that the other models
are not suitable.
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