Fractional order derivatives may be implemented in the time domain for control purposes in many ways. An exhaustive study of the performance of 28 different alternatives is presented and compared with discretised Crone controllers. Placement of zeros and poles, impulse and step responses and frequency responses are addressed. No formula is clearly better than all others in all situations, but it is expected that this survey will allow the choosing of the best possibility for each particular case.
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Valério et al. (2005) studied this question.
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