Active and Passive Realization of Fractance Device of Order 1/2

Krishna, B. T.; Reddy, K. Vijaya Kumar

doi:10.1155/2008/369421

Cited by 181 publications

(86 citation statements)

References 4 publications

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“…It was reported that such FOD can be represented using continued fraction expansions (CFE) [27] expressed by rational functions of the Laplace independent variable s -resulting in an infinite RC ladder network (see Fig. 1), [7,11]. However, by limiting the frequency range of application for the CPE, one can design a module composed of a finite number of components such as a finite ladder by truncating the CFE [22] that can approximately work as a CPE for the specific range of interest, and eventually become a practically-acceptable FOD [20,21] for various applications.…”

Section: Theory and Realization Of Fractional-order Elementsmentioning

confidence: 99%

“…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%

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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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Section: Theory and Realization Of Fractional-order Elementsmentioning

confidence: 99%

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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show abstract

“…These methods present a large array of approximations with varying order and accuracy, with the accuracy and approximated frequency band increasing as the order of the approximation increases. Here, a CFE method [24] was selected to model the fractional capacitors for PSPICE simulations. Collecting eight terms of the CFE yields a 4 th order approximation of the fractional capacitor that can be physically realized using the RC ladder network in Fig.…”

Section: Pspice Simulationsmentioning

confidence: 99%

Fractional-step Tow-Thomas biquad filters

Freeborn

Maundy

Elwakil

2012

NOLTA

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Abstract:In this paper we propose the use of fractional capacitors in the Tow-Thomas biquad to realize both fractional lowpass and asymmetric bandpass filters of order 0 < α 1 + α 2 ≤ 2, where α 1 and α 2 are the orders of the fractional capacitors and 0 < α 1,2 ≤ 1. We show how these filters can be designed using an integer-order transfer function approximation of the fractional capacitors. MATLAB and PSPICE simulations of first order fractional-step low and bandpass filters of order 1.1, 1.5, and 1.9 are given as examples. Experimental results of fractional low pass filters of order 1.5 implemented with silicon-fabricated fractional capacitors verify the operation of the fractional Tow-Thomas biquad.

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“…The original approach, developed by Oustaloup [26,27], is based on approximation of fractional systems in frequency domain. This approach is widely used, e.g., [11,22,25,32] and many others. However, this method has some flaws which cannot be neglected-when discretized, it does not guarantee stability of the system (the poles of discrete system are outside unit circle) (see, e.g., [30]).…”

Section: Introductionmentioning

confidence: 99%

On Digital Realizations of Non-integer Order Filters

Baranowski

Bauer

Zagórowska

et al. 2016

Circuits Syst Signal Process

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Typical approach to non-integer order filtering consists of analogue design and implementation. Digital realization of non-integer order systems is susceptible to problems such as infinite memory requirement and sensitivity to numerical errors. The aim of this paper is to present two efficient methods for digital realization of noninteger order filters: discrete time-domain Oustaloup approximation and Laguerre impulse response approximation. Properties of both methods are investigated with use of non-integer low-pass filter. Filters realized with presented methods are then used for filtering of EEG signal. Paper concludes with discussion of merits and flaws of both methods.Keywords Non-integer order filter · Fractional filter · Oustaloup method · discretization · Laguerre impulse response approximation Work realized in the scope of project titled "Design and application of non-integer order subsystems in control systems". Project was financed by National Science Centre on the base of decision no.

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Active and Passive Realization of Fractance Device of Order 1/2

Cited by 181 publications

References 4 publications

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

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

Fractional-step Tow-Thomas biquad filters

On Digital Realizations of Non-integer Order Filters

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