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Stepped and swept control-based continuation using adaptive filtering

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Abstract

This paper introduces a new online method for performing control-based continuation (CBC), speeding up the model-less identification of stable and unstable periodic orbits of nonlinear mechanical systems. The main building block of the algorithm is adaptive filtering which can ensure the non-invasiveness of the controller without the need for offline corrective iterations. Two different strategies, termed stepped and swept CBC, are then developed for performing the continuation steps. A beam featuring different artificial stiffness and damping nonlinearities is considered for the experimental demonstration of the proposed developments. The performance of the CBC strategies are compared in terms of running time and identification accuracy.

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Acknowledgements

G.A. is grateful to the F.R.S.-FNRS for funding this research by the FRIA grant. L.R. acknowledges the financial support of the Royal Academy of Engineering, Research Fellowship #RF1516/15/11.

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Authors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, University of Liège, Allée de la Découverte, 9, 4000, Liège, Belgium

    Gaëtan Abeloos

  2. Department of Mechanical Engineering, Imperial College London, London, United Kingdom

    Ludovic Renson

  3. Bio, Electro and Mechanical Systems Department, Université Libre de Bruxelles, Brussels, Belgium

    Christophe Collette

  4. Department of Aerospace and Mechanical Engineering, University of Liège, Liège, Belgium

    Christophe Collette & Gaëtan Kerschen

Authors
  1. Gaëtan Abeloos
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  2. Ludovic Renson
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  3. Christophe Collette
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  4. Gaëtan Kerschen
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Corresponding author

Correspondence to Gaëtan Abeloos.

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Funding

This research was funded by the Fond de la Recherche Scientifique (F.R.S.-FNRS) under the Fonds pour la Formation á la Recherche dans l’Industrie et l’Agriculture (FRIA) grant.

Conflict of interest

The authors declare that they have no conflict of interest.

Availability of data and material

The data collected and used in this research is available on the University of Liège Open Repository and Bibliography (ORBi) at the address https://orbi.uliege.be/handle/2268/259361.

Code availability

The Simulink files used for the experiments and the post-processing scripts are available on the University of Liège Open Repository and Bibliography (ORBi) at the address https://orbi.uliege.be/handle/2268/259361.

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Abeloos, G., Renson, L., Collette, C. et al. Stepped and swept control-based continuation using adaptive filtering. Nonlinear Dyn 104, 3793–3808 (2021). https://doi.org/10.1007/s11071-021-06506-z

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