Spectral design of robust delayed resonator by double-root assignment

Kuře, Matěj; Vyhlídal, Tomáš; Michiels, Wim; Boussaada, Islam

doi:10.1016/j.ifacol.2018.07.201

Cited by 10 publications

(7 citation statements)

References 13 publications

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“…The delayed resonator scheme by Olgac and Holm-Hansen (1994) consists in guaranteeing vibration suppression by ensuring the overall system to have zeros at ±jω, and we adapt that scheme here by placing zeros of multiplicity two at ±jω using Theorem 7.5. For a different adaptation, we refer to Kuře et al (2018). 2…”

Section: Hypergeometric Functions and Multiplicity-induced-dominancymentioning

confidence: 99%

Stability, Delays and Multiple Characteristic Roots in Dynamical Systems: A Guided Tour

Niculescu,

Boussaada,

et al. 2021

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This paper presents a guided tour of some specific problems encountered in the stability analysis of linear dynamical systems including delays in their systems' representation. More precisely, we will address the characterization of multiple roots of the corresponding characteristic function with a particular emphasis on the way these roots are affected by the system's parameters and the way that they can be used to control. The paper covers several approaches (perturbation techniques, hypergeometric functions) leading to some methods and criteria (frequency-sweeping, multiplicity-induced-dominancy) that can be implemented (software toolboxes) for analyzing the qualitative and quantitative properties induced by the delays and other parameters on the system's dynamics. A particular attention will be paid to the so-called partial pole placement method based on the multiplicity-induced-dominancy property. The presentation is as simple as possible, focusing more on the main intuitive ideas and appropriate mathematical reasoning by analogy in the presentation of the theoretical results as well as their potential use in practical applications. Illustrative examples complete the paper.

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Section: Hypergeometric Functions and Multiplicity-induced-dominancymentioning

confidence: 99%

Stability, Delays and Multiple Characteristic Roots in Dynamical Systems: A Guided Tour

Niculescu,

Boussaada,

et al. 2021

Preprint

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“…In the AVS application, we adapt the delayed resonator scheme proposed by Olgac and Holm-Hansen (1994) with a single root at ±iω. Recently the concept has been adjusted by Kuře et al (2018) with double roots at ±iω in order to enhance the robustness. Let us note that the solution in Kuře et al (2018) required two time delays.…”

Section: Application Case Studies: Vibration Suppression and Flexible...mentioning

confidence: 99%

“…Recently the concept has been adjusted by Kuře et al (2018) with double roots at ±iω in order to enhance the robustness. Let us note that the solution in Kuře et al (2018) required two time delays. Here, we provide a solution with a single delay.…”

Section: Application Case Studies: Vibration Suppression and Flexible...mentioning

confidence: 99%

“…The main goal of this paper is to investigate whether MID holds for ∆ when assigning a pair of complex conjugate roots instead of a real root. Designing a system to have a pair of dominant complex conjugate roots may have several practical interests, as highlighted in Kuře et al (2018), in which a robust delayed resonator is designed by assigning double imaginary roots. The questions we address in this paper are the following.…”

Section: Introductionmentioning

confidence: 99%

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Spectral dominance of complex roots for single-delay linear equations

et al. 2020

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“…The author's team recently proposed a modified DR [24] where the acceleration based delayed feedback is extended by a non-delay path in order to widen the applicable vibration suppression frequency range. Another contribution of the authors' team is in the design of a robust DR by optimizing the delay distribution [25], see also [26]. DR velocity feedback was considered in [15] and [16] where it was applied and tuned for torsional vibration suppression.…”

Section: Introductionmentioning

confidence: 99%