Modeling and Identification of Fractional-Order Discrete-Time Laguerre-Based Feedback-Nonlinear Systems

Stanisławski, Rafał; Latawiec, Krzysztof J.; Galek, Marcin; Łukaniszyn, M.

doi:10.1007/978-3-319-09900-2_10

Cited by 11 publications

(3 citation statements)

References 17 publications

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“…Another approach has been the employment of an approximating filter incorporating discrete-Laguerre filters [9,15,19]. In the second case, applications are based on orthonormal basis functions (OBF) methods [2,8,16,18], and a number of other applications [5,12,13].…”

Section: Introductionmentioning

confidence: 99%

Modeling of Discrete-Time Fractional-Order State Space Systems Using the Balanced Truncation Method

Stanisławski

Rydel

Latawiec

2015

Theoretical Developments and Applications of Non-Integer Order Systems

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This paper presents a new method of approximation of linear time-invariant (LTI) discrete-time fractional-order state space systems by means of the Balanced Truncation Method. This reduction method is applied to the rational form of fractional-order system in terms of expanded state equation. As an approximation result we obtain rational and relatively low-order state space system. Simulation experiments show very high accuracy of the introduced methodology.

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Section: Introductionmentioning

confidence: 99%

Modeling of Discrete-Time Fractional-Order State Space Systems Using the Balanced Truncation Method

Stanisławski

Rydel

Latawiec

2015

Theoretical Developments and Applications of Non-Integer Order Systems

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“…Other avenues for warranting numerical stability need different approximation methods. One approach focused on using Laguerre functions to create an approximation of impulse response [7,8], which was used among the others in [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Practical Applications of Diffusive Realization of Fractional Integrator with SoftFrac

2021

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Fractional calculus has found multiple applications around the world. It is especially prevalent in the domains of control and electronics. One of the key elements of fractional applications is the fractional integral (or integrator) which is a backbone of famous PIλD controller. It gives advantages of traditional PID with a limited phase lag. The are, however, issues with implementation, which will allow good low-frequency behavior. In this paper, we consider a diffusive realization of a fractional integrator with the use of quadratures. We implemented this method in numerical package SoftFrac, and we illustrate how different quadratures work for this purpose. We show superiority of bounded domain integration with logarithmic transformation and explain issues with behavior for extremely low frequencies.

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“…For example, in Stanislawski et al [37,38] use Grünwald-Letnikow difference to design discrete filters. Another proposition of non-integer order discrete filter can be found in [13].…”

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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Modeling and Identification of Fractional-Order Discrete-Time Laguerre-Based Feedback-Nonlinear Systems

Cited by 11 publications

References 17 publications

Modeling of Discrete-Time Fractional-Order State Space Systems Using the Balanced Truncation Method

Modeling of Discrete-Time Fractional-Order State Space Systems Using the Balanced Truncation Method

Practical Applications of Diffusive Realization of Fractional Integrator with SoftFrac

On Digital Realizations of Non-integer Order Filters

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