Experiment design for elementary fractional models

Experiment design is an important topic in system identification. It enables choosing the best input signal that allows computing parameters with minimum variance. Experiment design for system identification with fractional models is treated in this paper. Elementary fractional models of the second kind are considered, extending the previous results regarding models of the first kind. It allows choosing the best frequency(ies) of a sine input signal by minimizing the D-optimality criterion of the covariance-matrix. The case of a single unknown parameter is treated which can be either of the following: gain, pseudo-damping factor, natural frequency, or even the differentiation order. Then, all the combinations of two unknown parameters are considered. Finally, three and four unknown parameters are considered and the covariance matrix computed. It is shown that its optimum is difficult to obtain analytically in the general case. The particular case of second order (rational) systems, when the commensurate differentiation order equals one, is pointed out, as a special case in this study