An extension of the structured singular value to nonlinear systems with application to robust flutter analysis

Iannelli, Andrea; Lowenberg, Mark H; Marcos, Andrés

doi:10.1007/s13272-020-00469-4

Cited by 3 publications

(2 citation statements)

References 33 publications

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“…A thorough discussion of the find- ings, together with a broad overview of the insights that can be gained and their critical interpretation, is also provided in order to clearly present the potential benefits of this novel analysis approach. Preliminary results of this work were presented in [18].…”

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confidence: 99%

On the effect of model uncertainty on the Hopf bifurcation of aeroelastic systems

2021

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This paper investigates the effect of model uncertainty on the nonlinear dynamics of a generic aeroelastic system. Among the most dangerous phenomena to which these systems are prone, Limit Cycle Oscillations are periodic isolated responses triggered by the nonlinear interactions among elastic deformations, inertial forces, and aerodynamic actions. In a dynamical systems setting, these responses typically emanate from Hopf bifurcation points, and thus a recently proposed framework, which address the problem of robustness from a nonlinear dynamics viewpoint, is employed. Briefly, the notion of robust bifurcation margin extends the concept of $$\mu $$ μ analysis technique from the robust control theory. The main contribution of this article is a systematic investigation of the numerous scenarios arising in the study of nonlinear flutter when uncertainties in the model are accounted for in the analyses. The advantages of adopting this framework include the possibility to: quantify relevant information for the determination of the nonlinear stability envelope; gain a more in-depth understanding of the physical mechanisms triggering subcritical and supercritical Hopf bifurcations; and reveal properties of the nominal system by identifying isolated branches not straightforward to detect with conventional numerical approaches.

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Section: Introductionmentioning

confidence: 99%

On the effect of model uncertainty on the Hopf bifurcation of aeroelastic systems

2021

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“…Preliminary results of this work were presented in [24]. Notation: [x; y] denotes vertical concatenation of two vectors x ∈ R n and y ∈ R m .…”

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Computation of Bifurcation Margins Based on Robust Control Concepts

Iannelli

Lowenberg

Marcos³

2020

SIAM J. Appl. Dyn. Syst.

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This article proposes a framework which allows the study of stability robustness of equilibria of a nonlinear system in the face of parametric uncertainties from the point of view of bifurcation theory. In this context, a branch of equilibria is stable if bifurcations (i.e. qualitative changes of the steady-state solutions) do not occur as one or more bifurcation parameters are varied. The work focuses specifically on Hopf bifurcations, where a stable branch of equilibria meets a branch of periodic solutions. It is of practical interest to evaluate how the presence of uncertain parameters in the system alters the result of analyses performed with respect to a nominal vector field. Note that in this article bifurcation parameters have a different meaning than uncertain parameters. To answer the question, the concept of robust bifurcation margins is proposed based on the idea of describing the uncertain system in a Linear Fractional Transformation fashion. The robust bifurcation margins can be interpreted as nonlinear analogs of the structural singular value, or µ, which provides robust stability margins for linear time invariant systems. Their computation is formulated as a nonlinear program aided by a continuation-based multi-start strategy to mitigate the issue of local minima. Application of the framework is demonstrated on two case studies from the power system and aerospace literature.

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Periodic compensation of continuous time plant with structured uncertainties

Chakraborty,

Dey

2023

International Journal of Control

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An extension of the structured singular value to nonlinear systems with application to robust flutter analysis

Cited by 3 publications

References 33 publications

On the effect of model uncertainty on the Hopf bifurcation of aeroelastic systems

On the effect of model uncertainty on the Hopf bifurcation of aeroelastic systems

Computation of Bifurcation Margins Based on Robust Control Concepts

Periodic compensation of continuous time plant with structured uncertainties

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