Influence of models approximating the fractional-order differential equations on the calculation accuracy

In recent years, the usage of fractional-order (FO) differential equations to describe objects and physical phenomena has gained immense popularity. Due to the high computational complexity in the exact calculation of these equations, approximation models make the calculations executable. Regardless...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Marciniak, Karol [verfasserIn] Saleem, Faisal [verfasserIn] Wiora, Józef [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Modeling errors Oustaloup filter Matsuda approximation Carlson approximation Continued fraction expansion approximation Modified Stability Boundary Locus approximation

Übergeordnetes Werk:	Enthalten in: No title available - 131
Übergeordnetes Werk:	volume:131

DOI / URN:	10.1016/j.cnsns.2023.107807

Katalog-ID:	ELV067147267

Internformat


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100	1		\|a Marciniak, Karol \|e verfasserin \|4 aut
245	1	0	\|a Influence of models approximating the fractional-order differential equations on the calculation accuracy
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520			\|a In recent years, the usage of fractional-order (FO) differential equations to describe objects and physical phenomena has gained immense popularity. Due to the high computational complexity in the exact calculation of these equations, approximation models make the calculations executable. Regardless of their complexity, these models always introduce some inaccuracy which depends on the model type and its order. This article shows how the selected model affects the obtained solution. This study revisits seven fractional approximation models, known as the Continued Fraction Expansion method, the Matsuda method, the Carlson method, a modified version of the Stability Boundary Locus fitting method, and Basic, Refined, and Xue Oustaloup filters. First, this work calculates the steady-state values for each of the models symbolically. In the next step, it calculates the unit step responses. Then, it shows how the model selection affects Nyquist plots and compares the results with the plot determined directly. In the last stage, it estimates the trajectories for an example of an FO control system by each model. We conclude that when employing approximation models for fractional integro-differentiation, choosing the appropriate type of model, its parameters, and order is very important. Selecting the wrong model type or wrong order may lead to incorrect conclusions when describing a real phenomenon or object.
650		4	\|a Modeling errors
650		4	\|a Oustaloup filter
650		4	\|a Matsuda approximation
650		4	\|a Carlson approximation
650		4	\|a Continued fraction expansion approximation
650		4	\|a Modified Stability Boundary Locus approximation
700	1		\|a Saleem, Faisal \|e verfasserin \|0 (orcid)0000-0003-2056-3196 \|4 aut
700	1		\|a Wiora, Józef \|e verfasserin \|4 aut
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912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
951			\|a AR
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allfields	10.1016/j.cnsns.2023.107807 doi (DE-627)ELV067147267 (ELSEVIER)S1007-5704(23)00728-1 DE-627 ger DE-627 rda eng Marciniak, Karol verfasserin aut Influence of models approximating the fractional-order differential equations on the calculation accuracy 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In recent years, the usage of fractional-order (FO) differential equations to describe objects and physical phenomena has gained immense popularity. Due to the high computational complexity in the exact calculation of these equations, approximation models make the calculations executable. Regardless of their complexity, these models always introduce some inaccuracy which depends on the model type and its order. This article shows how the selected model affects the obtained solution. This study revisits seven fractional approximation models, known as the Continued Fraction Expansion method, the Matsuda method, the Carlson method, a modified version of the Stability Boundary Locus fitting method, and Basic, Refined, and Xue Oustaloup filters. First, this work calculates the steady-state values for each of the models symbolically. In the next step, it calculates the unit step responses. Then, it shows how the model selection affects Nyquist plots and compares the results with the plot determined directly. In the last stage, it estimates the trajectories for an example of an FO control system by each model. We conclude that when employing approximation models for fractional integro-differentiation, choosing the appropriate type of model, its parameters, and order is very important. Selecting the wrong model type or wrong order may lead to incorrect conclusions when describing a real phenomenon or object. Modeling errors Oustaloup filter Matsuda approximation Carlson approximation Continued fraction expansion approximation Modified Stability Boundary Locus approximation Saleem, Faisal verfasserin (orcid)0000-0003-2056-3196 aut Wiora, Józef verfasserin aut Enthalten in No title available 131 (DE-627)352827580 1007-5704 nnns volume:131 GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 131
spelling	10.1016/j.cnsns.2023.107807 doi (DE-627)ELV067147267 (ELSEVIER)S1007-5704(23)00728-1 DE-627 ger DE-627 rda eng Marciniak, Karol verfasserin aut Influence of models approximating the fractional-order differential equations on the calculation accuracy 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In recent years, the usage of fractional-order (FO) differential equations to describe objects and physical phenomena has gained immense popularity. Due to the high computational complexity in the exact calculation of these equations, approximation models make the calculations executable. Regardless of their complexity, these models always introduce some inaccuracy which depends on the model type and its order. This article shows how the selected model affects the obtained solution. This study revisits seven fractional approximation models, known as the Continued Fraction Expansion method, the Matsuda method, the Carlson method, a modified version of the Stability Boundary Locus fitting method, and Basic, Refined, and Xue Oustaloup filters. First, this work calculates the steady-state values for each of the models symbolically. In the next step, it calculates the unit step responses. Then, it shows how the model selection affects Nyquist plots and compares the results with the plot determined directly. In the last stage, it estimates the trajectories for an example of an FO control system by each model. We conclude that when employing approximation models for fractional integro-differentiation, choosing the appropriate type of model, its parameters, and order is very important. Selecting the wrong model type or wrong order may lead to incorrect conclusions when describing a real phenomenon or object. Modeling errors Oustaloup filter Matsuda approximation Carlson approximation Continued fraction expansion approximation Modified Stability Boundary Locus approximation Saleem, Faisal verfasserin (orcid)0000-0003-2056-3196 aut Wiora, Józef verfasserin aut Enthalten in No title available 131 (DE-627)352827580 1007-5704 nnns volume:131 GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 131
allfields_unstemmed	10.1016/j.cnsns.2023.107807 doi (DE-627)ELV067147267 (ELSEVIER)S1007-5704(23)00728-1 DE-627 ger DE-627 rda eng Marciniak, Karol verfasserin aut Influence of models approximating the fractional-order differential equations on the calculation accuracy 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In recent years, the usage of fractional-order (FO) differential equations to describe objects and physical phenomena has gained immense popularity. Due to the high computational complexity in the exact calculation of these equations, approximation models make the calculations executable. Regardless of their complexity, these models always introduce some inaccuracy which depends on the model type and its order. This article shows how the selected model affects the obtained solution. This study revisits seven fractional approximation models, known as the Continued Fraction Expansion method, the Matsuda method, the Carlson method, a modified version of the Stability Boundary Locus fitting method, and Basic, Refined, and Xue Oustaloup filters. First, this work calculates the steady-state values for each of the models symbolically. In the next step, it calculates the unit step responses. Then, it shows how the model selection affects Nyquist plots and compares the results with the plot determined directly. In the last stage, it estimates the trajectories for an example of an FO control system by each model. We conclude that when employing approximation models for fractional integro-differentiation, choosing the appropriate type of model, its parameters, and order is very important. Selecting the wrong model type or wrong order may lead to incorrect conclusions when describing a real phenomenon or object. Modeling errors Oustaloup filter Matsuda approximation Carlson approximation Continued fraction expansion approximation Modified Stability Boundary Locus approximation Saleem, Faisal verfasserin (orcid)0000-0003-2056-3196 aut Wiora, Józef verfasserin aut Enthalten in No title available 131 (DE-627)352827580 1007-5704 nnns volume:131 GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 131
allfieldsGer	10.1016/j.cnsns.2023.107807 doi (DE-627)ELV067147267 (ELSEVIER)S1007-5704(23)00728-1 DE-627 ger DE-627 rda eng Marciniak, Karol verfasserin aut Influence of models approximating the fractional-order differential equations on the calculation accuracy 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In recent years, the usage of fractional-order (FO) differential equations to describe objects and physical phenomena has gained immense popularity. Due to the high computational complexity in the exact calculation of these equations, approximation models make the calculations executable. Regardless of their complexity, these models always introduce some inaccuracy which depends on the model type and its order. This article shows how the selected model affects the obtained solution. This study revisits seven fractional approximation models, known as the Continued Fraction Expansion method, the Matsuda method, the Carlson method, a modified version of the Stability Boundary Locus fitting method, and Basic, Refined, and Xue Oustaloup filters. First, this work calculates the steady-state values for each of the models symbolically. In the next step, it calculates the unit step responses. Then, it shows how the model selection affects Nyquist plots and compares the results with the plot determined directly. In the last stage, it estimates the trajectories for an example of an FO control system by each model. We conclude that when employing approximation models for fractional integro-differentiation, choosing the appropriate type of model, its parameters, and order is very important. Selecting the wrong model type or wrong order may lead to incorrect conclusions when describing a real phenomenon or object. Modeling errors Oustaloup filter Matsuda approximation Carlson approximation Continued fraction expansion approximation Modified Stability Boundary Locus approximation Saleem, Faisal verfasserin (orcid)0000-0003-2056-3196 aut Wiora, Józef verfasserin aut Enthalten in No title available 131 (DE-627)352827580 1007-5704 nnns volume:131 GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 131
allfieldsSound	10.1016/j.cnsns.2023.107807 doi (DE-627)ELV067147267 (ELSEVIER)S1007-5704(23)00728-1 DE-627 ger DE-627 rda eng Marciniak, Karol verfasserin aut Influence of models approximating the fractional-order differential equations on the calculation accuracy 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In recent years, the usage of fractional-order (FO) differential equations to describe objects and physical phenomena has gained immense popularity. Due to the high computational complexity in the exact calculation of these equations, approximation models make the calculations executable. Regardless of their complexity, these models always introduce some inaccuracy which depends on the model type and its order. This article shows how the selected model affects the obtained solution. This study revisits seven fractional approximation models, known as the Continued Fraction Expansion method, the Matsuda method, the Carlson method, a modified version of the Stability Boundary Locus fitting method, and Basic, Refined, and Xue Oustaloup filters. First, this work calculates the steady-state values for each of the models symbolically. In the next step, it calculates the unit step responses. Then, it shows how the model selection affects Nyquist plots and compares the results with the plot determined directly. In the last stage, it estimates the trajectories for an example of an FO control system by each model. We conclude that when employing approximation models for fractional integro-differentiation, choosing the appropriate type of model, its parameters, and order is very important. Selecting the wrong model type or wrong order may lead to incorrect conclusions when describing a real phenomenon or object. Modeling errors Oustaloup filter Matsuda approximation Carlson approximation Continued fraction expansion approximation Modified Stability Boundary Locus approximation Saleem, Faisal verfasserin (orcid)0000-0003-2056-3196 aut Wiora, Józef verfasserin aut Enthalten in No title available 131 (DE-627)352827580 1007-5704 nnns volume:131 GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 131
language	English
source	Enthalten in No title available 131 volume:131
sourceStr	Enthalten in No title available 131 volume:131
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topic_facet	Modeling errors Oustaloup filter Matsuda approximation Carlson approximation Continued fraction expansion approximation Modified Stability Boundary Locus approximation
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author	Marciniak, Karol
spellingShingle	Marciniak, Karol misc Modeling errors misc Oustaloup filter misc Matsuda approximation misc Carlson approximation misc Continued fraction expansion approximation misc Modified Stability Boundary Locus approximation Influence of models approximating the fractional-order differential equations on the calculation accuracy
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topic_title	Influence of models approximating the fractional-order differential equations on the calculation accuracy Modeling errors Oustaloup filter Matsuda approximation Carlson approximation Continued fraction expansion approximation Modified Stability Boundary Locus approximation
topic	misc Modeling errors misc Oustaloup filter misc Matsuda approximation misc Carlson approximation misc Continued fraction expansion approximation misc Modified Stability Boundary Locus approximation
topic_unstemmed	misc Modeling errors misc Oustaloup filter misc Matsuda approximation misc Carlson approximation misc Continued fraction expansion approximation misc Modified Stability Boundary Locus approximation
topic_browse	misc Modeling errors misc Oustaloup filter misc Matsuda approximation misc Carlson approximation misc Continued fraction expansion approximation misc Modified Stability Boundary Locus approximation
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title	Influence of models approximating the fractional-order differential equations on the calculation accuracy
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title_full	Influence of models approximating the fractional-order differential equations on the calculation accuracy
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title_sort	influence of models approximating the fractional-order differential equations on the calculation accuracy
title_auth	Influence of models approximating the fractional-order differential equations on the calculation accuracy
abstract	In recent years, the usage of fractional-order (FO) differential equations to describe objects and physical phenomena has gained immense popularity. Due to the high computational complexity in the exact calculation of these equations, approximation models make the calculations executable. Regardless of their complexity, these models always introduce some inaccuracy which depends on the model type and its order. This article shows how the selected model affects the obtained solution. This study revisits seven fractional approximation models, known as the Continued Fraction Expansion method, the Matsuda method, the Carlson method, a modified version of the Stability Boundary Locus fitting method, and Basic, Refined, and Xue Oustaloup filters. First, this work calculates the steady-state values for each of the models symbolically. In the next step, it calculates the unit step responses. Then, it shows how the model selection affects Nyquist plots and compares the results with the plot determined directly. In the last stage, it estimates the trajectories for an example of an FO control system by each model. We conclude that when employing approximation models for fractional integro-differentiation, choosing the appropriate type of model, its parameters, and order is very important. Selecting the wrong model type or wrong order may lead to incorrect conclusions when describing a real phenomenon or object.
abstractGer	In recent years, the usage of fractional-order (FO) differential equations to describe objects and physical phenomena has gained immense popularity. Due to the high computational complexity in the exact calculation of these equations, approximation models make the calculations executable. Regardless of their complexity, these models always introduce some inaccuracy which depends on the model type and its order. This article shows how the selected model affects the obtained solution. This study revisits seven fractional approximation models, known as the Continued Fraction Expansion method, the Matsuda method, the Carlson method, a modified version of the Stability Boundary Locus fitting method, and Basic, Refined, and Xue Oustaloup filters. First, this work calculates the steady-state values for each of the models symbolically. In the next step, it calculates the unit step responses. Then, it shows how the model selection affects Nyquist plots and compares the results with the plot determined directly. In the last stage, it estimates the trajectories for an example of an FO control system by each model. We conclude that when employing approximation models for fractional integro-differentiation, choosing the appropriate type of model, its parameters, and order is very important. Selecting the wrong model type or wrong order may lead to incorrect conclusions when describing a real phenomenon or object.
abstract_unstemmed	In recent years, the usage of fractional-order (FO) differential equations to describe objects and physical phenomena has gained immense popularity. Due to the high computational complexity in the exact calculation of these equations, approximation models make the calculations executable. Regardless of their complexity, these models always introduce some inaccuracy which depends on the model type and its order. This article shows how the selected model affects the obtained solution. This study revisits seven fractional approximation models, known as the Continued Fraction Expansion method, the Matsuda method, the Carlson method, a modified version of the Stability Boundary Locus fitting method, and Basic, Refined, and Xue Oustaloup filters. First, this work calculates the steady-state values for each of the models symbolically. In the next step, it calculates the unit step responses. Then, it shows how the model selection affects Nyquist plots and compares the results with the plot determined directly. In the last stage, it estimates the trajectories for an example of an FO control system by each model. We conclude that when employing approximation models for fractional integro-differentiation, choosing the appropriate type of model, its parameters, and order is very important. Selecting the wrong model type or wrong order may lead to incorrect conclusions when describing a real phenomenon or object.
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title_short	Influence of models approximating the fractional-order differential equations on the calculation accuracy
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Due to the high computational complexity in the exact calculation of these equations, approximation models make the calculations executable. Regardless of their complexity, these models always introduce some inaccuracy which depends on the model type and its order. This article shows how the selected model affects the obtained solution. This study revisits seven fractional approximation models, known as the Continued Fraction Expansion method, the Matsuda method, the Carlson method, a modified version of the Stability Boundary Locus fitting method, and Basic, Refined, and Xue Oustaloup filters. First, this work calculates the steady-state values for each of the models symbolically. In the next step, it calculates the unit step responses. Then, it shows how the model selection affects Nyquist plots and compares the results with the plot determined directly. In the last stage, it estimates the trajectories for an example of an FO control system by each model. We conclude that when employing approximation models for fractional integro-differentiation, choosing the appropriate type of model, its parameters, and order is very important. 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Influence of models approximating the fractional-order differential equations on the calculation accuracy

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