Comparative analysis of frequency characteristics for constructing digital models options of components of electrical complexes aperiodic units
Meeting the ever-increasing requirements for sensorless electric drives from technological processes can be achieved through the use of digital twins, which are a digital (discrete) model of a dynamic system. The use of discrete models always entails both some loss of accuracy in the time domain and...
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| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
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Tomsk Polytechnic University
2024-06-01
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| Series: | Известия Томского политехнического университета: Промышленная кибернетика |
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| Online Access: | https://indcyb.ru/journal/article/view/51/40 |
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| author | Alexander S. Glazyrin Evgeniy I. Popov Semen S. Popov Vladimir A. Kopyrin Sergey N. Kladiev Andrey P. Leonov Nataliya A. Voronina Vladimir Z. Kovalev |
| author_facet | Alexander S. Glazyrin Evgeniy I. Popov Semen S. Popov Vladimir A. Kopyrin Sergey N. Kladiev Andrey P. Leonov Nataliya A. Voronina Vladimir Z. Kovalev |
| author_sort | Alexander S. Glazyrin |
| collection | DOAJ |
| description | Meeting the ever-increasing requirements for sensorless electric drives from technological processes can be achieved through the use of digital twins, which are a digital (discrete) model of a dynamic system. The use of discrete models always entails both some loss of accuracy in the time domain and distortion in the frequency domain. To preserve the accurate properties of the model, the sampling frequency must be chosen to comply with the requirements of the Kotelnikov–Shannon–Nyquist theorem. However, in practice, the choice of sampling period is limited by the processing power of the digital signal processor. As a rule, the main element of the components of electrical engineering complexes is a first-order aperiodic link. As a result, the aim of the paper is to determine the limits of applicability in the frequency domain of existing methods of transition to the Z-region using the analog prototype method by conducting a comparative analysis of the integral error in approximating the frequency characteristics of the analog prototype with digital models of the aperiodic link for each of the methods. It was established that an increase in the sampling period leads to a discrepancy between digital models and their analogue prototypes in terms of the integral error for any upper limit of the viewing window in the mid and high frequencies. This, in its turn, leads to the loss of information about such physical processes in a real system, such as the bandwidth range or the change in the phase of the signal at the output of a dynamic system. With appropriate assumptions about the stationarity of the dynamic system, the Tustin method can be recommended as the main one for constructing digital models for most engineering problems. However, when signs of non-stationarity of a dynamic system appear or increased requirements for the synthesis of regulators, according to the authors, it is worth paying attention to analytical models of dynamic systems. |
| format | Article |
| id | doaj-art-b0a84e88c92148ddaa9098877bdf6aba |
| institution | Kabale University |
| issn | 2949-5407 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | Tomsk Polytechnic University |
| record_format | Article |
| series | Известия Томского политехнического университета: Промышленная кибернетика |
| spelling | doaj-art-b0a84e88c92148ddaa9098877bdf6aba2025-08-20T03:32:11ZengTomsk Polytechnic UniversityИзвестия Томского политехнического университета: Промышленная кибернетика2949-54072024-06-0122172810.18799/29495407/2024/2/51Comparative analysis of frequency characteristics for constructing digital models options of components of electrical complexes aperiodic unitsAlexander S. Glazyrin0Evgeniy I. Popov1Semen S. Popov2Vladimir A. Kopyrin3Sergey N. Kladiev4Andrey P. Leonov 5Nataliya A. Voronina6Vladimir Z. Kovalev7National Research Tomsk Polytechnic University, Tomsk, Russian Federation; Yugra State University, Khanty-Mansiysk, Russian FederationIndustrial University of Tyumen, Tyumen, Russian FederationNational Research Tomsk Polytechnic University, Tomsk, Russian Federation; «NPF Mechatronica-Pro» LTD,Tomsk, Russian FederationIndustrial University of Tyumen, Tyumen, Russian FederationNational Research Tomsk Polytechnic University, Tomsk, Russian FederationNational Research Tomsk Polytechnic University, Tomsk, Russian FederationNational Research Tomsk Polytechnic University, Tomsk, Russian FederationYugra State University, Khanty-Mansiysk, Russian Federation; National Research Tomsk Polytechnic University, Tomsk, Russian FederationMeeting the ever-increasing requirements for sensorless electric drives from technological processes can be achieved through the use of digital twins, which are a digital (discrete) model of a dynamic system. The use of discrete models always entails both some loss of accuracy in the time domain and distortion in the frequency domain. To preserve the accurate properties of the model, the sampling frequency must be chosen to comply with the requirements of the Kotelnikov–Shannon–Nyquist theorem. However, in practice, the choice of sampling period is limited by the processing power of the digital signal processor. As a rule, the main element of the components of electrical engineering complexes is a first-order aperiodic link. As a result, the aim of the paper is to determine the limits of applicability in the frequency domain of existing methods of transition to the Z-region using the analog prototype method by conducting a comparative analysis of the integral error in approximating the frequency characteristics of the analog prototype with digital models of the aperiodic link for each of the methods. It was established that an increase in the sampling period leads to a discrepancy between digital models and their analogue prototypes in terms of the integral error for any upper limit of the viewing window in the mid and high frequencies. This, in its turn, leads to the loss of information about such physical processes in a real system, such as the bandwidth range or the change in the phase of the signal at the output of a dynamic system. With appropriate assumptions about the stationarity of the dynamic system, the Tustin method can be recommended as the main one for constructing digital models for most engineering problems. However, when signs of non-stationarity of a dynamic system appear or increased requirements for the synthesis of regulators, according to the authors, it is worth paying attention to analytical models of dynamic systems.https://indcyb.ru/journal/article/view/51/40digital modelaperiodic unitz-transformamplitude frequency characteristicsphase frequency characteristicstustin methodintegral error |
| spellingShingle | Alexander S. Glazyrin Evgeniy I. Popov Semen S. Popov Vladimir A. Kopyrin Sergey N. Kladiev Andrey P. Leonov Nataliya A. Voronina Vladimir Z. Kovalev Comparative analysis of frequency characteristics for constructing digital models options of components of electrical complexes aperiodic units Известия Томского политехнического университета: Промышленная кибернетика digital model aperiodic unit z-transform amplitude frequency characteristics phase frequency characteristics tustin method integral error |
| title | Comparative analysis of frequency characteristics for constructing digital models options of components of electrical complexes aperiodic units |
| title_full | Comparative analysis of frequency characteristics for constructing digital models options of components of electrical complexes aperiodic units |
| title_fullStr | Comparative analysis of frequency characteristics for constructing digital models options of components of electrical complexes aperiodic units |
| title_full_unstemmed | Comparative analysis of frequency characteristics for constructing digital models options of components of electrical complexes aperiodic units |
| title_short | Comparative analysis of frequency characteristics for constructing digital models options of components of electrical complexes aperiodic units |
| title_sort | comparative analysis of frequency characteristics for constructing digital models options of components of electrical complexes aperiodic units |
| topic | digital model aperiodic unit z-transform amplitude frequency characteristics phase frequency characteristics tustin method integral error |
| url | https://indcyb.ru/journal/article/view/51/40 |
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