Frequency-band complex noninteger differentiator: characterization and synthesis

Comparative Study of Discrete Component Realizations of Fractional-Order Capacitor and Inductor Active Emulators

“…Hence, the performance of the 2nd to 5th-order approximations of the Continued Fraction Expansion (CFE) 26 are evaluated and compared with those o®ered by the 3rd and 5th-order Oustaloup's approximation. 27 The paper is organized as follows: in Sec. 2, the concept for emulating fractional-order capacitors and inductors is brie°y presented and the expressions of approximations of the integro-di®erential operator in the Laplace domain are presented and evaluated in terms of magnitude and phase response.…”

Discrete-Time Implementation and Experimental Validation of a Fractional Order PD Controller for Vibration Suppression in Airplane Wings

“…The approximation method consists in two steps: the first one involves the continuous-time fitting of the ideal fractional order PD controller with a higher order rational transfer function, while the second step requires the discretization of this fitted continuous-time approximation using any of the well know discretization techniques [13]. Even though a lot of continuoustime approximation methods have been developed, in this paper the Oustaloup Recursive Approximation method [19] is used because of its wide acceptance and efficiency. According to this method, the continuous-time rational transfer function is obtained as follows:…”

“…The poles and zeros are obtained based on a recursive distribution between a low and a high frequency, at well-chosen intervals, such that a constant ratio is obtained between two consecutive poles and zeros [19].…”

Robust Fractional Order Controllers for Distributed Systems

“…Because of its wide acceptance, simplicity and efficiency, the Oustaloup Recursive Approximation [13] method is selected in this paper. The fitted continuous-time approximation of the fractional order PID controller is then given as:…”