Analysis of frequency-robust multivariable dynamical systems
We consider the problem of studying the sensitivity of ellipsoidal frequency estimates of quality of multivariable dynamic systems to parameter variations. To solve the problem, we use the apparatus of sensitivity functions of extreme elements of singular value decomposition of real-valued transfe...
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| Format: | Article |
| Language: | English |
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Saint Petersburg National Research University of Information Technologies, Mechanics and Optics (ITMO University)
2023-06-01
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| Series: | Naučno-tehničeskij Vestnik Informacionnyh Tehnologij, Mehaniki i Optiki |
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| Online Access: | https://ntv.ifmo.ru/file/article/22037.pdf |
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| author | Roman O. Omorov Akylai Akunova Taalaibek A. Akunov |
| author_facet | Roman O. Omorov Akylai Akunova Taalaibek A. Akunov |
| author_sort | Roman O. Omorov |
| collection | DOAJ |
| description | We consider the problem of studying the sensitivity of ellipsoidal frequency estimates of quality of multivariable
dynamic systems to parameter variations. To solve the problem, we use the apparatus of sensitivity functions of
extreme elements of singular value decomposition of real-valued transfer matrices. The joint usage of the apparatus of
frequency sensitivity with the method of state space allowed us to construct the models of sensitivity. On the basis of the
obtained models, the ellipsoidal estimates of the frequency sensitivity functions for the state, output and error of linear
multivariable continuous systems in the form of the majorant and minorant of these functions have been determined.
The singular value decomposition of matrices composed of frequency parametric sensitivity functions has been applied
to the calculations. The obtained ellipsoidal estimates have the property of minimum sufficiency due to the substantial
possibilities of the singular value decomposition of matrices. This approach made it possible to use the elements of
the left singular basis corresponding to the extreme singular values, to select in the state, output, and error spaces the
subspaces characterized for each frequency value by the largest and smallest normal variation of the amplitude-frequency
response. Using the right singular basis made it possible to identify the subspaces in the parameter space which produce
the largest and the smallest normal variation of the amplitude-frequency response. The proposed approach has solved the
problem of the “optimal nominal” — the choice of the nominal value of the vector of primary physical parameters of the
control object aggregates that deliver the smallest value of ellipsoidal estimates of the frequency sensitivity functions
to the multivariable controlled process. Such parameters include: dimensions of various parts and characteristics of
their manufacturing accuracy, physical properties of materials as well as various values determining their design. The
approach made it possible to compare the course of multidimensional controlled processes by ellipsoidal estimates of
the frequency parameter sensitivity. |
| first_indexed | 2024-03-13T04:04:18Z |
| format | Article |
| id | doaj.art-79d94b2909854474bce2ec44b1902767 |
| institution | Directory Open Access Journal |
| issn | 2226-1494 2500-0373 |
| language | English |
| last_indexed | 2024-03-13T04:04:18Z |
| publishDate | 2023-06-01 |
| publisher | Saint Petersburg National Research University of Information Technologies, Mechanics and Optics (ITMO University) |
| record_format | Article |
| series | Naučno-tehničeskij Vestnik Informacionnyh Tehnologij, Mehaniki i Optiki |
| spelling | doaj.art-79d94b2909854474bce2ec44b19027672023-06-21T10:07:02ZengSaint Petersburg National Research University of Information Technologies, Mechanics and Optics (ITMO University)Naučno-tehničeskij Vestnik Informacionnyh Tehnologij, Mehaniki i Optiki2226-14942500-03732023-06-0123345546410.17586/2226-1494-2023-23-3-455-464Analysis of frequency-robust multivariable dynamical systemsRoman O. Omorov0https://orcid.org/0000-0003-3555-1323Akylai Akunova1https://orcid.org/0000-0003-0684-4063Taalaibek A. Akunov2https://orcid.org/0000-0002-0923-9777D.Sc., Professor, Corresponding Member of the National Academy of Sciences of the Kyrgyz Republic, Machinery Researching and Automatics Institute of Kyrgyz Republic National Academy of Sciences, Bishkek, 720071, Kyrgyz Republic, sc 6602708366PhD, Chief Researcher, Machinery Researching and Automatics Institute of Kyrgyz Republic National Academy of Sciences, Bishkek, 720071, Kyrgyz Republic, sc 7801308323PhD, Chief Researcher, Machinery Researching and Automatics Institute of Kyrgyz Republic National Academy of Sciences, Bishkek, 720071, Kyrgyz Republic, sc 6508211498We consider the problem of studying the sensitivity of ellipsoidal frequency estimates of quality of multivariable dynamic systems to parameter variations. To solve the problem, we use the apparatus of sensitivity functions of extreme elements of singular value decomposition of real-valued transfer matrices. The joint usage of the apparatus of frequency sensitivity with the method of state space allowed us to construct the models of sensitivity. On the basis of the obtained models, the ellipsoidal estimates of the frequency sensitivity functions for the state, output and error of linear multivariable continuous systems in the form of the majorant and minorant of these functions have been determined. The singular value decomposition of matrices composed of frequency parametric sensitivity functions has been applied to the calculations. The obtained ellipsoidal estimates have the property of minimum sufficiency due to the substantial possibilities of the singular value decomposition of matrices. This approach made it possible to use the elements of the left singular basis corresponding to the extreme singular values, to select in the state, output, and error spaces the subspaces characterized for each frequency value by the largest and smallest normal variation of the amplitude-frequency response. Using the right singular basis made it possible to identify the subspaces in the parameter space which produce the largest and the smallest normal variation of the amplitude-frequency response. The proposed approach has solved the problem of the “optimal nominal” — the choice of the nominal value of the vector of primary physical parameters of the control object aggregates that deliver the smallest value of ellipsoidal estimates of the frequency sensitivity functions to the multivariable controlled process. Such parameters include: dimensions of various parts and characteristics of their manufacturing accuracy, physical properties of materials as well as various values determining their design. The approach made it possible to compare the course of multidimensional controlled processes by ellipsoidal estimates of the frequency parameter sensitivity.https://ntv.ifmo.ru/file/article/22037.pdflinear multivariable systemellipsoidal estimatefrequency parametric sensitivitysensitivity modelsingular value decomposition |
| spellingShingle | Roman O. Omorov Akylai Akunova Taalaibek A. Akunov Analysis of frequency-robust multivariable dynamical systems Naučno-tehničeskij Vestnik Informacionnyh Tehnologij, Mehaniki i Optiki linear multivariable system ellipsoidal estimate frequency parametric sensitivity sensitivity model singular value decomposition |
| title | Analysis of frequency-robust multivariable dynamical systems |
| title_full | Analysis of frequency-robust multivariable dynamical systems |
| title_fullStr | Analysis of frequency-robust multivariable dynamical systems |
| title_full_unstemmed | Analysis of frequency-robust multivariable dynamical systems |
| title_short | Analysis of frequency-robust multivariable dynamical systems |
| title_sort | analysis of frequency robust multivariable dynamical systems |
| topic | linear multivariable system ellipsoidal estimate frequency parametric sensitivity sensitivity model singular value decomposition |
| url | https://ntv.ifmo.ru/file/article/22037.pdf |
| work_keys_str_mv | AT romanoomorov analysisoffrequencyrobustmultivariabledynamicalsystems AT akylaiakunova analysisoffrequencyrobustmultivariabledynamicalsystems AT taalaibekaakunov analysisoffrequencyrobustmultivariabledynamicalsystems |