Eine selbstkonsistente Carleman Linearisierung zur Analyse von Oszillatoren Article Swipe
Harry Weber
,
Wolfgang Mathis
·
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.5194/ars-15-223-2017
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.5194/ars-15-223-2017
Die Analyse nichtlinearer dynamischer Schaltungen ist bis heute eine herausfordernde Aufgabe, da nur selten analytische Lösungen angegeben werden können. Daher wurden eine Vielzahl von Methoden entwickelt, um eine qualitative oder quantitative Näherung für die Lösungen der Netzwerkgleichung zu erhalten. Oftmals wird beispielsweise eine Kleinsignalanalyse mit Hilfe einer Taylorreihe in einem Arbeitspunkt durchgeführt, die nach den Gliedern erster Ordnung abgebrochen wird. Allerdings ist diese Linearisierung nur in der Nähe des stabilen Arbeitspunktes für hyperbolische Systeme gültig. Besonders für die Analyse des dynamischen Verhaltens von Oszillatoren treten jedoch nicht-hyperbolische Systeme auf, sodass diese Methode nicht angewendet werden kann Mathis (2000). Carleman hat gezeigt, dass nichtlineare Differentialgleichungen mit polynomiellen Nichtlinearitäten in ein unendliches System von linearen Differentialgleichungen transformiert werden können Carleman (1932). Wird das unendlichdimensionale Gleichungssystem für numerische Zwecke abgebrochen, kann bei Oszillatoren der Übergang in eine stationäre Schwingung (Grenzzyklus) nicht wiedergegeben werden. In diesem Beitrag wird eine selbstkonsistente Carleman Linearisierung zur Untersuchung von Oszillatoren vorgestellt, die auch dann anwendbar ist, wenn die Nichtlinearitäten keinen Polynomen entsprechen. Anstelle einer linearen Näherung um einen Arbeitspunkt, erfolgt mit Hilfe der Carleman Linearisierung eine Approximation auf einem vorgegebenen Gebiet. Da es jedoch mit der selbstkonsistenten Technik nicht möglich ist, das stationäre Verhalten von Oszillatoren zu beschreiben, wird die Berechnung einer Poincaré-Abbildung durchgeführt. Mit dieser ist eine anschließende Analyse des Oszillators möglich.
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- Type
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- Language
- de
- Landing Page
- https://doi.org/10.5194/ars-15-223-2017
- https://www.adv-radio-sci.net/15/223/2017/ars-15-223-2017.pdf
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https://doi.org/10.5194/ars-15-223-2017Digital Object Identifier
- Title
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Eine selbstkonsistente Carleman Linearisierung zur Analyse von OszillatorenWork title
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articleOpenAlex work type
- Language
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dePrimary language
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2017Year of publication
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2017-09-21Full publication date if available
- Authors
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Harry Weber, Wolfgang MathisList of authors in order
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https://doi.org/10.5194/ars-15-223-2017Publisher landing page
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https://www.adv-radio-sci.net/15/223/2017/ars-15-223-2017.pdfDirect link to full text PDF
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YesWhether a free full text is available
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goldOpen access status per OpenAlex
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https://www.adv-radio-sci.net/15/223/2017/ars-15-223-2017.pdfDirect OA link when available
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Physics, Gynecology, MedicineTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.angegeben | 17 |
| abstract_inverted_index.anwendbar | 157 |
| abstract_inverted_index.erhalten. | 39 |
| abstract_inverted_index.möglich. | 215 |
| abstract_inverted_index.Übergang | 132 |
| abstract_inverted_index.Allerdings | 61 |
| abstract_inverted_index.Berechnung | 203 |
| abstract_inverted_index.Schwingung | 136 |
| abstract_inverted_index.Verhaltens | 82 |
| abstract_inverted_index.angewendet | 94 |
| abstract_inverted_index.numerische | 125 |
| abstract_inverted_index.Oszillators | 214 |
| abstract_inverted_index.Schaltungen | 5 |
| abstract_inverted_index.Taylorreihe | 48 |
| abstract_inverted_index.abgebrochen | 59 |
| abstract_inverted_index.analytische | 15 |
| abstract_inverted_index.dynamischen | 81 |
| abstract_inverted_index.dynamischer | 4 |
| abstract_inverted_index.entwickelt, | 26 |
| abstract_inverted_index.qualitative | 29 |
| abstract_inverted_index.stationäre | 135, 195 |
| abstract_inverted_index.unendliches | 110 |
| abstract_inverted_index.Arbeitspunkt | 51 |
| abstract_inverted_index.Oszillatoren | 84, 130, 152, 198 |
| abstract_inverted_index.Untersuchung | 150 |
| abstract_inverted_index.abgebrochen, | 127 |
| abstract_inverted_index.beschreiben, | 200 |
| abstract_inverted_index.entsprechen. | 164 |
| abstract_inverted_index.nichtlineare | 103 |
| abstract_inverted_index.quantitative | 31 |
| abstract_inverted_index.vorgegebenen | 182 |
| abstract_inverted_index.vorgestellt, | 153 |
| abstract_inverted_index.(Grenzzyklus) | 137 |
| abstract_inverted_index.Approximation | 179 |
| abstract_inverted_index.Arbeitspunkt, | 171 |
| abstract_inverted_index.hyperbolische | 73 |
| abstract_inverted_index.nichtlinearer | 3 |
| abstract_inverted_index.polynomiellen | 106 |
| abstract_inverted_index.transformiert | 115 |
| abstract_inverted_index.wiedergegeben | 139 |
| abstract_inverted_index.Arbeitspunktes | 71 |
| abstract_inverted_index.Linearisierung | 64, 148, 177 |
| abstract_inverted_index.anschließende | 211 |
| abstract_inverted_index.beispielsweise | 42 |
| abstract_inverted_index.durchgeführt, | 52 |
| abstract_inverted_index.durchgeführt. | 206 |
| abstract_inverted_index.herausfordernde | 10 |
| abstract_inverted_index.Gleichungssystem | 123 |
| abstract_inverted_index.Netzwerkgleichung | 37 |
| abstract_inverted_index.selbstkonsistente | 146 |
| abstract_inverted_index.Kleinsignalanalyse | 44 |
| abstract_inverted_index.Nichtlinearitäten | 107, 161 |
| abstract_inverted_index.selbstkonsistenten | 189 |
| abstract_inverted_index.Poincaré-Abbildung | 205 |
| abstract_inverted_index.nicht-hyperbolische | 87 |
| abstract_inverted_index.unendlichdimensionale | 122 |
| abstract_inverted_index.Differentialgleichungen | 104, 114 |
| cited_by_percentile_year | |
| corresponding_author_ids | https://openalex.org/A5007568797, https://openalex.org/A5058996739 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 2 |
| corresponding_institution_ids | https://openalex.org/I114112103 |
| citation_normalized_percentile.value | 0.1560042 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |