Studies on fractional order differentiators and integrators: A survey

Krishna, B. T.

doi:10.1016/j.sigpro.2010.06.022

Cited by 415 publications

(252 citation statements)

References 56 publications

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“…Therefore, the aim of this paper is to provide a useful comparative performance study o®ered by various orders of approximations of these stages. 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.…”

Section: S ð1þmentioning

confidence: 99%

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

Τσιριμώκου

Kartci

Koton

et al. 2018

J CIRCUIT SYST COMP

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Due to the absence of commercially available fractional-order capacitors and inductors, their implementation can be performed using fractional-order di®erentiators and integrators, respectively, combined with a voltage-to-current conversion stage. The transfer function of fractional-order di®erentiators and integrators can be approximated through the utilization of appropriate integer-order transfer functions. In order to achieve that, the Continued Fraction Expansion as well as the Oustaloup's approximations can be utilized. The accuracy, in terms of magnitude and phase response, of transfer functions of di®erentiators/integrators derived through the employment of the aforementioned approximations, is very important factor for achieving high performance approximation of the fractional-order elements. A comparative study of the accuracy o®ered by the Continued Fraction Expansion and the Oustaloup's approximation is performed in this paper. As a next step, the corresponding implementations of the emulators of the fractional-order elements, derived using fundamental active cells such as operational ampli¯ers, operational transconductance ampli¯ers, current conveyors, and current feedback operational ampli¯ers realized in commercially available discrete-component IC form,

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Section: S ð1þmentioning

confidence: 99%

“…5, are summarized in Tables 1 and 2. 26 Employing the Oustaloup's approximation method, the corresponding expression, for geometrically distributed frequencies over the band [! b ; !…”

Section: Approximation Of the Laplace Operatormentioning

confidence: 99%

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

Τσιριμώκου

Kartci

Koton

et al. 2018

J CIRCUIT SYST COMP

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“…The use of RC ladders [8,30] have been exercised since the mid-20th century for realizing fractional-order elements [1,7,10,11], but the approximation results were disappointing-having only a very limited bandwidth with a high number of components. An improved version of the RC ladder was introduced in [28] and has shown to be superior over its predecessors having only a small amount of components needed to perform as a CPE at a better bandwidth.…”

Section: Theory and Realization Of Fractional-order Elementsmentioning

confidence: 99%

“…2. The relationship between the resistors and capacitors with low and high cut-off frequencies are dictated by 10) respectively. Since the ladder will only approximate an FOI at frequencies ω min to ω max , a certain ripple will exist.…”

Section: Theory and Realization Of Fractional-order Elementsmentioning

confidence: 99%

Conceptual design of a selectable fractional-order differentiator for industrial applications

Gonzalez¹,

Dorčák

Monje

et al. 2014

Fract Calc Appl Anal

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In the past decade, researchers working on fractional-order systems modeling and control have been considering working on the design and development of analog and digital fractional-order differentiators, i.e. circuits that can perform non-integer-order differentiation. It has been one of the major research areas under such field due to proven advantages over its integer-order counterparts. In particular, traditional integer-order proportional-integral-derivative (PID) controllers seem to be outperformed by fractional-order PID (FOPID or PI λ D μ ) controllers. Many researches have emerged presenting the possibility of designing analog and digital fractional-order differentiators, but only restricted to a fixed order. In this paper, we present the conceptual design of a variable fractional-order differentiator in which the order can be selected from 0 to 1 with an increment of 0.05. The analog conceptual design utilizes operational amplifiers and resistor-capacitor ladders as main components, while a generic microcontroller is introduced for switching purposes. Simulation results through Matlab and LTSpiceIV show that the designed resistor-capacitor ladders can perform as analog fractional-order differentiation.

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“…However, at the same time, because of their unlimited memory, fractional order systems cannot be exactly implemented [10] and thus, they require a proper rational approximation [11], [12], [13] in a limited frequency range [14]. In this paper, a fractional order PD controller is designed for vibration suppression.…”

Section: Introductionmentioning

confidence: 99%

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

2017

APH

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Studies on fractional order differentiators and integrators: A survey

Cited by 415 publications

References 56 publications

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

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

Conceptual design of a selectable fractional-order differentiator for industrial applications

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

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