Periodic Regulation of Linear Time-Delay Systems via Youla-Kučera Parametrization
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| Format: | Preprint |
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2025
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| _version_ | 1866908376392269824 |
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| author | Yüksel, Can Kutlu Vyhlídal, Tomáš Niculescu, Silviu-Iulian |
| author_facet | Yüksel, Can Kutlu Vyhlídal, Tomáš Niculescu, Silviu-Iulian |
| contents | The paper proposes an alternative way to achieve the Internal Model Principle (IMP) in contrast to the standard way, where a model of the signal one wishes to track/reject is directly substituted into the closed-loop. The proposed alternative approach relies on an already-existing stabilizing controller, which can be further augmented with a Youla-Kučera parameter to let it implicitly admit a model of a signal without altering its stabilizing feature. Thus, with the proposed method, the standard design steps of realizing IMP are reversed. The validity and potential of the proposed approach are demonstrated by considering three different types of time-delay systems. It is shown through simulations that all considered unstable systems, despite the infinite-dimensional closed-loop, can be straightforwardly periodically regulated by augmenting their stabilizing PI controllers. Thanks to a specifically chosen structure for the Youla-Kučera parameter, the required tuning can be done by solving a set of linear equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17792 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Periodic Regulation of Linear Time-Delay Systems via Youla-Kučera Parametrization Yüksel, Can Kutlu Vyhlídal, Tomáš Niculescu, Silviu-Iulian Systems and Control Rings and Algebras 93B55 G.1.3; I.6.4 The paper proposes an alternative way to achieve the Internal Model Principle (IMP) in contrast to the standard way, where a model of the signal one wishes to track/reject is directly substituted into the closed-loop. The proposed alternative approach relies on an already-existing stabilizing controller, which can be further augmented with a Youla-Kučera parameter to let it implicitly admit a model of a signal without altering its stabilizing feature. Thus, with the proposed method, the standard design steps of realizing IMP are reversed. The validity and potential of the proposed approach are demonstrated by considering three different types of time-delay systems. It is shown through simulations that all considered unstable systems, despite the infinite-dimensional closed-loop, can be straightforwardly periodically regulated by augmenting their stabilizing PI controllers. Thanks to a specifically chosen structure for the Youla-Kučera parameter, the required tuning can be done by solving a set of linear equations. |
| title | Periodic Regulation of Linear Time-Delay Systems via Youla-Kučera Parametrization |
| topic | Systems and Control Rings and Algebras 93B55 G.1.3; I.6.4 |
| url | https://arxiv.org/abs/2505.17792 |