Reconstruction of integrated equations of periodically driven phase-locked loop system from scalar time series
Purpose of this work is to develop a reconstruction technique for the equations of a phase-locked loop system under periodic external driving from a scalar time series of one variable. Methods. Instead of the original model, we reconstructed a time-integrated model. So, since it is not necessary to...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Saratov State University
2022-08-01
|
| Series: | Известия высших учебных заведений: Прикладная нелинейная динамика |
| Subjects: | |
| Online Access: | https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2022/07/and_2022_4_sysoeva-et-al_391-410_1.pdf |
| _version_ | 1828189595124105216 |
|---|---|
| author | Sysoeva, Marina Vyacheslavovna Kornilov, Maksim Vyacheslavovich Takaishvili, Lev Vyacheslavovich Matrosov, Valerij Vladimirovich Sysoev, Ilya V. |
| author_facet | Sysoeva, Marina Vyacheslavovna Kornilov, Maksim Vyacheslavovich Takaishvili, Lev Vyacheslavovich Matrosov, Valerij Vladimirovich Sysoev, Ilya V. |
| author_sort | Sysoeva, Marina Vyacheslavovna |
| collection | DOAJ |
| description | Purpose of this work is to develop a reconstruction technique for the equations of a phase-locked loop system under periodic external driving from a scalar time series of one variable. Methods. Instead of the original model, we reconstructed a time-integrated model. So, since it is not necessary to evaluate the second derivative of the observable numerically, the method sensitivity to observation noise has significantly decreased. The external periodic driving is approximated with a trigonometric polynomial of time, the antiderivative of which is also a trigonometric polynomial. The assumption about continuity of an unknown nonlinear function is used to construct the target function for optimization. Results. It is shown that the proposed approach gives a significant advantage over the previously developed approach to the reconstruction of non-integrated equations, allowing to achieve acceptable parameter estimates with measurement noise being about 10% of the RMS deviation of the signal even in the presence of external driving. Conclusion. The described approach significantly extends the possibilities of reconstruction of phase-locked loop systems, allowing systems to be reconstructed under arbitrary periodic driving and at the same time significantly increasing noise resistance. |
| first_indexed | 2024-04-12T08:09:26Z |
| format | Article |
| id | doaj.art-c5ef137e467a4ca4a6527b93e36324d8 |
| institution | Directory Open Access Journal |
| issn | 0869-6632 2542-1905 |
| language | English |
| last_indexed | 2024-04-12T08:09:26Z |
| publishDate | 2022-08-01 |
| publisher | Saratov State University |
| record_format | Article |
| series | Известия высших учебных заведений: Прикладная нелинейная динамика |
| spelling | doaj.art-c5ef137e467a4ca4a6527b93e36324d82022-12-22T03:41:03ZengSaratov State UniversityИзвестия высших учебных заведений: Прикладная нелинейная динамика0869-66322542-19052022-08-0130439141010.18500/0869-6632-2022-30-4-391-410Reconstruction of integrated equations of periodically driven phase-locked loop system from scalar time seriesSysoeva, Marina Vyacheslavovna0Kornilov, Maksim Vyacheslavovich1Takaishvili, Lev Vyacheslavovich2Matrosov, Valerij Vladimirovich3Sysoev, Ilya V.4Yuri Gagarin State Technical University of Saratov, ul. Politechnicheskaya, 77, Saratov, 410054, RussiaSaratov State University, ul. Astrakhanskaya, 83, Saratov, 410012, RussiaSaratov State University, ul. Astrakhanskaya, 83, Saratov, 410012, RussiaLobachevsky State University of Nizhny Novgorod, 603950 Nizhny Novgorod, Gagarin Avenue, 23Saratov State University, ul. Astrakhanskaya, 83, Saratov, 410012, RussiaPurpose of this work is to develop a reconstruction technique for the equations of a phase-locked loop system under periodic external driving from a scalar time series of one variable. Methods. Instead of the original model, we reconstructed a time-integrated model. So, since it is not necessary to evaluate the second derivative of the observable numerically, the method sensitivity to observation noise has significantly decreased. The external periodic driving is approximated with a trigonometric polynomial of time, the antiderivative of which is also a trigonometric polynomial. The assumption about continuity of an unknown nonlinear function is used to construct the target function for optimization. Results. It is shown that the proposed approach gives a significant advantage over the previously developed approach to the reconstruction of non-integrated equations, allowing to achieve acceptable parameter estimates with measurement noise being about 10% of the RMS deviation of the signal even in the presence of external driving. Conclusion. The described approach significantly extends the possibilities of reconstruction of phase-locked loop systems, allowing systems to be reconstructed under arbitrary periodic driving and at the same time significantly increasing noise resistance.https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2022/07/and_2022_4_sysoeva-et-al_391-410_1.pdfreconstructionphase-locked loop systemperiodic driving |
| spellingShingle | Sysoeva, Marina Vyacheslavovna Kornilov, Maksim Vyacheslavovich Takaishvili, Lev Vyacheslavovich Matrosov, Valerij Vladimirovich Sysoev, Ilya V. Reconstruction of integrated equations of periodically driven phase-locked loop system from scalar time series Известия высших учебных заведений: Прикладная нелинейная динамика reconstruction phase-locked loop system periodic driving |
| title | Reconstruction of integrated equations of periodically driven phase-locked loop system from scalar time series |
| title_full | Reconstruction of integrated equations of periodically driven phase-locked loop system from scalar time series |
| title_fullStr | Reconstruction of integrated equations of periodically driven phase-locked loop system from scalar time series |
| title_full_unstemmed | Reconstruction of integrated equations of periodically driven phase-locked loop system from scalar time series |
| title_short | Reconstruction of integrated equations of periodically driven phase-locked loop system from scalar time series |
| title_sort | reconstruction of integrated equations of periodically driven phase locked loop system from scalar time series |
| topic | reconstruction phase-locked loop system periodic driving |
| url | https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2022/07/and_2022_4_sysoeva-et-al_391-410_1.pdf |
| work_keys_str_mv | AT sysoevamarinavyacheslavovna reconstructionofintegratedequationsofperiodicallydrivenphaselockedloopsystemfromscalartimeseries AT kornilovmaksimvyacheslavovich reconstructionofintegratedequationsofperiodicallydrivenphaselockedloopsystemfromscalartimeseries AT takaishvililevvyacheslavovich reconstructionofintegratedequationsofperiodicallydrivenphaselockedloopsystemfromscalartimeseries AT matrosovvalerijvladimirovich reconstructionofintegratedequationsofperiodicallydrivenphaselockedloopsystemfromscalartimeseries AT sysoevilyav reconstructionofintegratedequationsofperiodicallydrivenphaselockedloopsystemfromscalartimeseries |