Experiment design for system identification using fractional models of the second kind

Abstract This paper deals with the problem of experiment design in system identification using elementary fractional models of the second type. It is based on a frequency domain approach and answers the question what is the best sine input signal maximizing D-optimality criterion of the Fisher Information Matrix. A single parameter is assumed to be unknown: gain, pseudo-damping factor, natural frequency, or the commensurate differentiation order. Analogy with second order systems, with the differentiation order equal to one, is pointed out. This work extends the previous one (Abrashov et al., 2017) which dealt with elementary fractional systems of the first kind.