A new IIR-type digital fractional order differentiator

A new least-squares approach to differintegration modeling

“…However, we intend to find approximations using finite orders ARMA models. There have been a lot of attempts to do it [4][5][6]8]. Here we propose a new LS identification algorithm different from that one proposed in [4].…”

“…Unfortunately, no definitive assertions can be made on the order of the ARMA models since no (6,6) amplitude (top, in dB) and phase (bottom, in radians) frequency response plots for the backward difference, with a ¼ 0:5. LS approach is the solid line, the exact model spectrum is the dash-dotted line, while as in [2] is the dashed line.…”

“…For them, ARMA models are only approximations that we call pseudo-fractional ARMA models [3]. In the last few years, a lot of attempts to obtain such models have been done (see [4][5][6][7][8][9]). However, it remains to clarify two important questions: (a) how to perform such modeling and (b) how to choose the most suitable orders.…”

Optimal Controllers with Complex Order Derivatives

“…Nevertheless, many aspects of this mathematical tool are still to be explored and further research efforts are necessary for the development of practical models. Furthermore, fractional derivatives (FDs) are more elaborated than their integer counterparts and their calculation requires some type of approximation [20][21][22][23][24][25][26].…”

Impulse response of a generalized fractional second order filter

“…An important step toward the application of fractional order filter is its numerical discretization, and there are two main kinds of discretization methods: the indirect method and the direct method. An effective impulse response invariant discretization method was discussed in [24,25,26,27,28]. The analytical impulse response of a fractional second order filter with form s 2 + as + b −γ is derived in [29], and its impulse response invariant discretization is obtained accordingly.…”