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CEAS EuroGNC 2019

An extension of the structured singular value to nonlinear systems with application to robust flutter analysis
Andrea Iannelli Department of Aerospace Engineering, University of Bristol, United Kingdom
Mark Lowenberg Department of Aerospace Engineering, University of Bristol, United Kingdom
Andrés Marcos Department of Aerospace Engineering, University of Bristol, United Kingdom
Abstract:
The paper discusses an extension of µ (or structured singular value), a well established technique for the study of linear systems subject to structured uncertainty, to nonlinear polynomial problems. Robustness is a multifaceted concept in the nonlinear context, and in this work the point of view of bifurcation theory is assumed. The latter is concerned with the study of qualitative changes of the steady-state solutions of a nonlinear system, so-called bifurcations. The practical goal motivating the work is to assess the effect of modeling uncertainties on flutter when considering the system as nonlinear. Flutter is a dynamic instability prompted by an adverse coupling between aerodynamic and elastic forces. Specifically, the onset of flutter in nonlinear systems is generally associated with Limit Cycle Oscillations emanating from a Hopf bifurcation point. Leveraging µ and its complementary modeling paradigm, namely Linear Fractional Transformation, this work proposes an approach to compute margins to the occurrence of Hopf bifurcations for uncertain nonlinear systems. An application to the typical section case study with linear unsteady aerodynamic and hardening nonlinearities in the structural parameters will be presented to demonstrate the applicability of the approach.
Keywords: Optimization; Robust control
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Andrea Iannelli, Mark Lowenberg, Andrés Marcos: An extension of the structured singular value to nonlinear systems with application to robust flutter analysis. Proceedings of the 2019 CEAS EuroGNC conference. Milan, Italy. April 2019. CEAS-GNC-2019-034.
BibTeX entry:

@Incollection{CEAS-GNC-2019-034,
    authors = {Iannelli, Andrea and Lowenberg, Mark and Marcos, Andrés},
    title = {An extension of the structured singular value to nonlinear systems with application to robust flutter analysis},
    booktitle = {Proceedings of the 2019 {CEAS EuroGNC} conference},
    address = {Milan, Italy},
    month = apr,
    year = {2019},
    note = {CEAS-GNC-2019-034}
}