Experimental bifurcation analysis of an impact oscillator—Tuning a non-invasive control scheme

Bureau, Emil; Schilder, Frank; Santos, Ilmar; Thomsen, Jon Juel; Starke, Jens

doi:10.1016/j.jsv.2013.05.033

Cited by 43 publications

(59 citation statements)

References 13 publications

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“…The control signal generated by the controller is fed into the electromagnetic actuators after splitting and amplification; please refer to [1] for details. Ideally, for every chosen excitation amplitude A, frequency f and input vector c ∈ R 11 of Fourier modes, the controlled experiment settles onto a globally unique response independent of the initial state.…”

Section: A Mechanical Non-linear Oscillator Experimentsmentioning

confidence: 99%

“…A zero problem is now constructed as follows. Assume that X(A, f, c) is a sufficiently large discrete sample of the response that the controlled experiment settles onto for the input A, f and c, and that F is a function computing the first 11 Fourier modes of such a sample as in (1). Then,…”

Section: A Mechanical Non-linear Oscillator Experimentsmentioning

confidence: 99%

“…Stability is indicated in gray-scale along the response curve, black corresponds to asymptotically stable responses, while gray indicates instability. Extensive studies of the dynamics of this experiment and of a fitted one-degree of freedom model of the oscillator were conducted in [1,2,18].…”

Section: A Mechanical Non-linear Oscillator Experimentsmentioning

confidence: 99%

“…In [1,2] we have implemented and tested bifurcation analysis directly in a non-linear mechanical oscillator experiment using control based continuation [3,4,5,6], that is, tracking stable and unstable responses under variations of forcing frequency and amplitude. In these experiments we used a harmonically excited impact oscillator with control forces applied via electromagnetic actuators as a test specimen and developed methods for tuning the control parameters and for determining stability of steady-state responses.…”

Section: Introductionmentioning

confidence: 99%

“…Here, we will provide information about the details of the implementation of the toolbox CONTINEX developed for this type of experiment as well as for equation-free analysis [7,8,9,10,11]. We will motivate the algorithmic developments with new experimental results collected with the set-up used in [1,2]. The presented methods are able to extract bifurcation diagrams directly from strongly non-linear experiments, and the toolbox CONTINEX is freely available for download [12].…”

Section: Introductionmentioning

confidence: 99%

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Experimental bifurcation analysis—Continuation for noise-contaminated zero problems

Schilder

Bureau

Santos

et al. 2015

Journal of Sound and Vibration

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Noise contaminated zero problems involve functions that cannot be evaluated directly, but only indirectly via observations. In addition, such observations are affected by a non-deterministic observation error (noise). We investigate the application of numerical bifurcation analysis for studying the solution set of such noise contaminated zero problems, which is highly relevant in the context of equation-free analysis (coarse grained analysis) and bifurcation analysis in experiments, and develop specialized algorithms to address challenges that arise due to the presence of noise. As a working example, we demonstrate and test our algorithms on a mechanical non-linear oscillator experiment using control based continuation, which we used as a main application and test case for development of the the Coco compatible Matlab toolbox Continex that implements our algorithms.

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Section: A Mechanical Non-linear Oscillator Experimentsmentioning

confidence: 99%

Section: A Mechanical Non-linear Oscillator Experimentsmentioning

confidence: 99%

Section: A Mechanical Non-linear Oscillator Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Experimental bifurcation analysis—Continuation for noise-contaminated zero problems

Schilder

Bureau

Santos

et al. 2015

Journal of Sound and Vibration

Self Cite

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Continuation methods for lab experiments of nonlinear vibrations

2023

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In this work, we will give an overview of our recent progress in experimental continuation. First, three different approaches are explained and compared which can be found in scientific papers on the topic. We then show S‐Curve measurements of a Duffing oscillator experiment for which we derived optimal controller gains analytically. The derived formula for stabilizing PD‐controller gains makes trial and error search for suitable values unnecessary. Since feedback control introduces higher harmonics in the driving signal, we consider a harmonization of the forcing signal. This harmonization is important to reduce shaker‐structure interaction in the treatment of nonlinear frequency responses. Finally, the controlled nonlinear testing and harmonization is enhanced by a continuation algorithm adapted from numerical analysis and applied to a geometrically nonlinear beam test rig for which we measure the nonlinear forced response directly in the displacement‐frequency plane.

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Identification of Backbone Curves and Nonlinear Frequency Responses using Control-based Continuation and Local Gaussian Process Regression

Renson

2020

Nonlinear Structures &Amp; Systems, Volume 1

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Control-based continuation (CBC) is a general and systematic method to probe the dynamics of nonlinear experiments. In this paper, CBC is combined with a novel continuation algorithm that is robust to experimental noise and enables the tracking of important nonlinear dynamic features such as backbone and nonlinear frequency response curves. The method uses Gaussian process regression to create a local model of the response surface on which standard numerical continuation algorithms can be applied. The local model evolves as continuation explores the experimental parameter space, exploiting previously captured data to actively select the next data points to collect such that they maximise the potential information gain about the feature of interest. The method is demonstrated experimentally on a nonlinear structure featuring harmonically-coupled modes. The regression model is also exploited to estimate the uncertainty of the identified features.

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Experimental bifurcation analysis of an impact oscillator—Tuning a non-invasive control scheme

Cited by 43 publications

References 13 publications

Experimental bifurcation analysis—Continuation for noise-contaminated zero problems

Experimental bifurcation analysis—Continuation for noise-contaminated zero problems

Continuation methods for lab experiments of nonlinear vibrations

Identification of Backbone Curves and Nonlinear Frequency Responses using Control-based Continuation and Local Gaussian Process Regression

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