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| Description
| - In the last two decades, a boom of fractional calculus applications started in many technical areas including automation and process control. The generalization of integrals and derivatives to arbitrary real order (FO - Fractional Order) simplifies solution of many problems especially in frequency domain. Unfortunately, switching into time domain is always quite difficult due to the necessity to approximate fractional elements by integer-order ones. For this purpose, often a high order zero/pole transfer function is employed. This paper extends the authors' previous work and summarizes the results of numerical optimization of zero/pole positions for two important fractional elements: fractional integro-differential operator and fractional pole. The optimization is done on a limited frequency band up to four decades. The quadratic difference between the frequency response of ideal FO element and its zero/pole approximation was taken as an optimality criterion. It is shown, that the optimization decreases markedly the criterion value compared to traditional methods. The paper main results are provided in a form of analytical functions parametrizing the zero/pole positions dependent on element order. Additionally, prospective applications of presented fractional elements are discussed from both controller synthesis and process modeling point of view.
- In the last two decades, a boom of fractional calculus applications started in many technical areas including automation and process control. The generalization of integrals and derivatives to arbitrary real order (FO - Fractional Order) simplifies solution of many problems especially in frequency domain. Unfortunately, switching into time domain is always quite difficult due to the necessity to approximate fractional elements by integer-order ones. For this purpose, often a high order zero/pole transfer function is employed. This paper extends the authors' previous work and summarizes the results of numerical optimization of zero/pole positions for two important fractional elements: fractional integro-differential operator and fractional pole. The optimization is done on a limited frequency band up to four decades. The quadratic difference between the frequency response of ideal FO element and its zero/pole approximation was taken as an optimality criterion. It is shown, that the optimization decreases markedly the criterion value compared to traditional methods. The paper main results are provided in a form of analytical functions parametrizing the zero/pole positions dependent on element order. Additionally, prospective applications of presented fractional elements are discussed from both controller synthesis and process modeling point of view. (en)
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| Title
| - Optimal Continuous Approximation of Basic Fractional Elements: Theory and Applications
- Optimal Continuous Approximation of Basic Fractional Elements: Theory and Applications (en)
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| skos:prefLabel
| - Optimal Continuous Approximation of Basic Fractional Elements: Theory and Applications
- Optimal Continuous Approximation of Basic Fractional Elements: Theory and Applications (en)
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| skos:notation
| - RIV/49777513:23520/11:43916108!RIV13-GA0-23520___
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| http://linked.open...avai/predkladatel
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| http://linked.open...avai/riv/aktivita
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| http://linked.open...avai/riv/aktivity
| - P(FR-TI1/077), P(GPP103/10/P208)
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| http://linked.open...vai/riv/dodaniDat
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| http://linked.open...aciTvurceVysledku
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| http://linked.open.../riv/druhVysledku
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| http://linked.open...iv/duvernostUdaju
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| http://linked.open...titaPredkladatele
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| http://linked.open...dnocenehoVysledku
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| http://linked.open...ai/riv/idVysledku
| - RIV/49777513:23520/11:43916108
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| http://linked.open...riv/jazykVysledku
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| http://linked.open.../riv/klicovaSlova
| - frequency band; optimization; fractional integrator; implementation; Fractional systems (en)
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| http://linked.open.../riv/klicoveSlovo
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| http://linked.open...ontrolniKodProRIV
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| http://linked.open...v/mistoKonaniAkce
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| http://linked.open...i/riv/mistoVydani
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| http://linked.open...i/riv/nazevZdroje
| - Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference
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| http://linked.open...in/vavai/riv/obor
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| http://linked.open...ichTvurcuVysledku
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| http://linked.open...cetTvurcuVysledku
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| http://linked.open...vavai/riv/projekt
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| http://linked.open...UplatneniVysledku
| |
| http://linked.open...iv/tvurceVysledku
| - Schlegel, Miloš
- Čech, Martin
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| http://linked.open...vavai/riv/typAkce
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| http://linked.open...ain/vavai/riv/wos
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| http://linked.open.../riv/zahajeniAkce
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| issn
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| number of pages
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| http://bibframe.org/vocab/doi
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| http://purl.org/ne...btex#hasPublisher
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| https://schema.org/isbn
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| http://localhost/t...ganizacniJednotka
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| is http://linked.open...avai/riv/vysledek
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