Regions of robust relative stability for PI controllers and LTI plants with unstructured multiplicative uncertainty: A second-order-based example
This example-oriented article addresses the computation of regions of all robustly relatively stabilizing Proportional-Integral (PI) controllers under various robust stability margins α for Linear Time-Invariant (LTI) plants with unstructured multiplicative uncertainty, where the plant model with mu...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-08-01
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| Series: | Heliyon |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844023061327 |
| _version_ | 1797732911013691392 |
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| author | Radek Matušů Bilal Senol Libor Pekař |
| author_facet | Radek Matušů Bilal Senol Libor Pekař |
| author_sort | Radek Matušů |
| collection | DOAJ |
| description | This example-oriented article addresses the computation of regions of all robustly relatively stabilizing Proportional-Integral (PI) controllers under various robust stability margins α for Linear Time-Invariant (LTI) plants with unstructured multiplicative uncertainty, where the plant model with multiplicative uncertainty is built on the basis of the second-order plant with three uncertain parameters. The applied graphical method, adopted from the authors’ previous work, is grounded in finding the contour that is linked to the pairs of P–I coefficients marginally fulfilling the condition of robust relative stability expressed using the H∞ norm. The illustrative example in the current article emphasizes that the technique itself for plotting the boundary contour of robust relative stability needs to be combined with the precondition of the nominally stable feedback control system and with the line for which the integral parameter equals zero in order to get the final robust relative stability regions. The calculations of the robust relative stability regions for various robust stability margins α are followed by the demonstration of the control behavior for two selected controllers applied to a set of members from the family of plants. |
| first_indexed | 2024-03-12T12:21:23Z |
| format | Article |
| id | doaj.art-20dc2116e28d4cc9b7d3ac6e4f5f2d4e |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-03-12T12:21:23Z |
| publishDate | 2023-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-20dc2116e28d4cc9b7d3ac6e4f5f2d4e2023-08-30T05:53:07ZengElsevierHeliyon2405-84402023-08-0198e18924Regions of robust relative stability for PI controllers and LTI plants with unstructured multiplicative uncertainty: A second-order-based exampleRadek Matušů0Bilal Senol1Libor Pekař2Centre for Security, Information and Advanced Technologies (CEBIA–Tech), Faculty of Applied Informatics, Tomas Bata University in Zlín, nám. T. G. Masaryka 5555, 760 01, Zlín, Czech Republic; Corresponding author.Software Engineering Department, Faculty of Engineering, Aksaray University, Bahçesaray Mahallesi, 68100, Aksaray, TurkeyDepartment of Automation and Control Engineering, Faculty of Applied Informatics, Tomas Bata University in Zlín, nám. T. G. Masaryka 5555, 760 01, Zlín, Czech Republic; Department of Technical Studies, College of Polytechnics Jihlava, Tolstého 1556, 586 01, Jihlava, Czech RepublicThis example-oriented article addresses the computation of regions of all robustly relatively stabilizing Proportional-Integral (PI) controllers under various robust stability margins α for Linear Time-Invariant (LTI) plants with unstructured multiplicative uncertainty, where the plant model with multiplicative uncertainty is built on the basis of the second-order plant with three uncertain parameters. The applied graphical method, adopted from the authors’ previous work, is grounded in finding the contour that is linked to the pairs of P–I coefficients marginally fulfilling the condition of robust relative stability expressed using the H∞ norm. The illustrative example in the current article emphasizes that the technique itself for plotting the boundary contour of robust relative stability needs to be combined with the precondition of the nominally stable feedback control system and with the line for which the integral parameter equals zero in order to get the final robust relative stability regions. The calculations of the robust relative stability regions for various robust stability margins α are followed by the demonstration of the control behavior for two selected controllers applied to a set of members from the family of plants.http://www.sciencedirect.com/science/article/pii/S2405844023061327Robust controlRobust relative stabilityRobust performancePI controllersUnstructured multiplicative uncertaintyH-Infinity norm |
| spellingShingle | Radek Matušů Bilal Senol Libor Pekař Regions of robust relative stability for PI controllers and LTI plants with unstructured multiplicative uncertainty: A second-order-based example Heliyon Robust control Robust relative stability Robust performance PI controllers Unstructured multiplicative uncertainty H-Infinity norm |
| title | Regions of robust relative stability for PI controllers and LTI plants with unstructured multiplicative uncertainty: A second-order-based example |
| title_full | Regions of robust relative stability for PI controllers and LTI plants with unstructured multiplicative uncertainty: A second-order-based example |
| title_fullStr | Regions of robust relative stability for PI controllers and LTI plants with unstructured multiplicative uncertainty: A second-order-based example |
| title_full_unstemmed | Regions of robust relative stability for PI controllers and LTI plants with unstructured multiplicative uncertainty: A second-order-based example |
| title_short | Regions of robust relative stability for PI controllers and LTI plants with unstructured multiplicative uncertainty: A second-order-based example |
| title_sort | regions of robust relative stability for pi controllers and lti plants with unstructured multiplicative uncertainty a second order based example |
| topic | Robust control Robust relative stability Robust performance PI controllers Unstructured multiplicative uncertainty H-Infinity norm |
| url | http://www.sciencedirect.com/science/article/pii/S2405844023061327 |
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