Continued Fraction Expansion Approaches to Discretizing Fractional Order Derivatives?an Expository Review

Chen, YangQuan; Vinagre, Blas M.; Podlubný, Igor

doi:10.1007/s11071-004-3752-x

Cited by 288 publications

(134 citation statements)

References 22 publications

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“…Signals were sampled with frequency of 50 Hz. This filter was originally used in postprocessing with non-integer filtration given by (9)- (12). Here we present it as a comparison with approximated filters.…”

Section: Example Of Filteringmentioning

confidence: 99%

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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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Section: Example Of Filteringmentioning

confidence: 99%

“…On the other hand, CFE method shows inferior quality in frequency characteristic representation [25]. Detailed analysis of CFE approximation in discrete time can be found in [12,44,45].…”

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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“…Fig. 2 Root-locus of G(j ω) for 1 <α < 2, K ≥ 0 ous operators of type s α adopts the Euler, Tustin, and Al-Alaoui generating functions [6][7][8].…”

Section: Approximations Of Fractional-order Operatorsmentioning

confidence: 99%

Fractional control of heat diffusion systems

2008

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The concept of differentiation and integration to non-integer order has its origins in the seventeen century. However, only in the second-half of the twenty century appeared the first applications related to the area of control theory. In this paper we consider the study of a heat diffusion system based on the application of the fractional calculus concepts. In this perspective, several control methodologies are investigated and compared. Simulations are presented assessing the performance of the proposed fractional-order algorithms.

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“…Sürekli kesir açılımı, Oustaloup, Carlson ve Charef yöntemleri gibi yaklaşımlar kesir dereceli türev ve uygulamalarında kullanılmaktadır [16], [17]. Bu çalışmada kesir dereceli türevlerin hesaplanmasında dördüncü mertebeden sürekli kesir açılım yaklaşık eşdeğer modelleri kullanılmıştır [18].…”

Section: Introductionunclassified

Image processing based object tracking application with fractional-order model reference controller

Kavuran¹,

Ateş²,

Alagöz³

et al. 2016

Pamukkale J Eng Sci

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Bu çalışmada doğru akım servo motorun pozisyon denetimi, kesir dereceli integratörle birlikte geleneksel model referans uyarlamalı denetleyici yapısı kullanılarak incelenmiştir. Denetleyici yapısındaki iyileşme, uyarlama kuralında kesir dereceli operatörlerin kullanılmasıyla sağlanmıştır. Gerçek zamanlı çalışan sistemin referans pozisyon bilgisi, kameradan alınan değerlere göre güncellenmiştir. Sistem çıkışı, öğrenme katsayısı değiştirilerek tamsayı ve kesir dereceli uyarlama kuralına göre karşılaştırmalı olarak kıyaslanmıştır. Elde edilen sonuçlara göre kesir dereceli yaklaşımın daha iyi sonuç verdiği gözlenmiştir.In this paper, position control application of DC servo motor is investigated by using conventional model reference adaptive control structure with fractional order integrator. Modification of the controller is achieved by fractional order integrator in adaptation rule. Object position for reference input of control system is updated in real time by the values obtained from camera of object tracking system. Results obtained for integer order integrator and fractionalorder integrator for model reference adaptive control system are compared and it is observed that the fractional-order integrator can provide faster adaptation for the system. Anahtar kelimeler: Kesir dereceli matematik, Model referans uyarlamalı denetim, Nesne takibi, Servo motor.

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Continued Fraction Expansion Approaches to Discretizing Fractional Order Derivatives?an Expository Review

Cited by 288 publications

References 22 publications

On Digital Realizations of Non-integer Order Filters

On Digital Realizations of Non-integer Order Filters

Fractional control of heat diffusion systems

Image processing based object tracking application with fractional-order model reference controller

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