Stepped and Swept Control-Based Continuation using Adaptive Filtering

Abeloos, Gaëtan; Renson, Ludovic; Collette, Christophe; Kerschen, Gaëtan

doi:10.1007/s11071-021-06506-z

Download

Article (Scientific journals)

Stepped and Swept Control-Based Continuation using Adaptive Filtering

Abeloos, Gaëtan; Renson, Ludovic; Collette, Christophe et al.

2021 • In Nonlinear Dynamics

Peer reviewed

Permalink
https://hdl.handle.net/2268/259361

DOI
10.1007/s11071-021-06506-z

Files (4)Send to Details Statistics Bibliography Similar publications

Files

Full Text

main.pdf

Author preprint (5.47 MB)

Download

Annexes

codes.zip

Publisher postprint (14.53 kB)

Post-processing scripts

Download

models.zip

Publisher postprint (1.05 MB)

Simulink models for the experiments

Download

data.zip

Publisher postprint (9.6 GB)

Raw data

Download

All documents in ORBi are protected by a user license.

Send to

RIS BibTex APA Chicago Permalink X Linkedin

Details

Keywords :

Control-Based Continuation; Adaptive Filtering; Feedback Stabilization; Invasiveness Cancellation

Abstract :

[en] 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.

Disciplines :

Aerospace & aeronautics engineering

Author, co-author :

Abeloos, Gaëtan ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Renson, Ludovic; Imperial College London > Department of Mechanical Engineering

Collette, Christophe ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Active aerospace struct. and adv. mecha. systems

Kerschen, Gaëtan ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Language :

English

Title :

Stepped and Swept Control-Based Continuation using Adaptive Filtering

Publication date :

2021

Journal title :

Nonlinear Dynamics

ISSN :

0924-090X

eISSN :

1573-269X

Publisher :

Kluwer Academic Publishers, Netherlands

Peer reviewed :

Peer reviewed

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]

Available on ORBi :

since 29 April 2021

Statistics

Number of views

205 (29 by ULiège)

Number of downloads

255 (22 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

Bibliography

Keller, H.B.: Numerical solution of bifurcation and nonlinear eigenvalue problems. In: Rabinowitz, P. (ed.) Applications of Bifurcation Theory, pp. 359–384. Academic Press, New York (1977)
Seydel, R.: A continuation algorithm with step control. In: Numerical Methods for Bifurcation Problems, pp. 480–494. Springer, Berlin (1984)
Doedel, E., Kernévez, J.: Auto: Software for Continuation Problems in Ordinary Differential Equations with Applications. Applied Mathematics. California Institute of Technology, California Institute of Technology, Pasadena (1986)
Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. John Wiley & Sons, London (2008)
Pyragas, K.: Continuous control of chaos by self-controlling feedback. Phys. Lett. A 170(6), 421–428 (1992). 10.1016/0375-9601(92)90745-8 DOI: 10.1016/0375-9601(92)90745-8
Sieber, J., Gonzalez-Buelga, A., Neild, S.A., Wagg, D.J., Krauskopf, B.: Experimental continuation of periodic orbits through a fold. Phys. Rev. Lett. 100(24), 244101 (2008). 10.1103/PhysRevLett.100.244101 DOI: 10.1103/PhysRevLett.100.244101
Sieber, J., Krauskopf, B.: Control based bifurcation analysis for experiments. Nonlinear Dyn. 51, 356–377 (2008). 10.1007/s11071-007-9217-2 DOI: 10.1007/s11071-007-9217-2
Barton, D.A., Burrow, S.G.: Numerical continuation in a physical experiment: investigation of a nonlinear energy harvester. J. Comput. Nonlinear Dyn. 6(1), 011010 (2011). 10.1115/DETC2009-87318 DOI: 10.1115/DETC2009-87318
Bureau, E., Schilder, F., Santos, I., Thomsen, J.J., Starke, J.: Experimental bifurcation analysis for a driven nonlinear flexible pendulum using control-based continuation. In: 7th European Nonlinear Dynamics Conference (2011)
Bureau, E., Schilder, F., Ferreira Santos, I., Juel Thomsen, J., Starke, J.: Experimental bifurcation analysis of an impact oscillator—Tuning a non-invasive control scheme. J. Sound Vib. 332(22), 5883–5897 (2013). 10.1016/j.jsv.2013.05.033 DOI: 10.1016/j.jsv.2013.05.033
Barton, D.A., Sieber, J.: Systematic experimental exploration of bifurcations with noninvasive control. Phys. Rev. E 87, 052916 (2013). 10.1103/PhysRevE.87.052916 DOI: 10.1103/PhysRevE.87.052916
Renson, L., Gonzalez-Buelga, A., Barton, D.A., Neild, S.A.: Robust identification of backbone curves using control-based continuation. J. Sound Vib. 367, 145–158 (2016). 10.1016/j.jsv.2015.12.035 DOI: 10.1016/j.jsv.2015.12.035
Renson, L., Shaw, A.D., Barton, D.A., Neild, S.A.: Application of control-based continuation to a nonlinear structure with harmonically coupled modes. Mech. Syst. Signal Process. 120, 449–464 (2019). 10.1016/j.ymssp.2018.10.008 DOI: 10.1016/j.ymssp.2018.10.008
Kleyman, G., Paehr, M., Tatzko, S.: Application of control-based-continuation for characterization of dynamic systems with stiffness and friction nonlinearities. Mech. Res. Commun. 106, 103520 (2020). 10.1016/j.mechrescom.2020.103520 DOI: 10.1016/j.mechrescom.2020.103520
Gomes, B., de Cesare, I., Guarino, A., di Bernardo, M., Renson, L., Marucci, L.: Exploring the dynamics of nonlinear biochemical systems using control-based continuation. bioRxiv p. 695866 (2019)
Barton, D.A.: Control-based continuation: bifurcation and stability analysis for physical experiments. Mech. Syst. Signal Process. 84(B), 54–64 (2017). 10.1016/j.ymssp.2015.12.039 DOI: 10.1016/j.ymssp.2015.12.039
Renson, L., Barton, D.A., Neild, S.A.: Experimental tracking of limit-point bifurcations and backbone curves using control-based continuation. Int. J. Bifurc. Chaos 27(1), 1730002 (2017). 10.1142/S0218127417300026 DOI: 10.1142/S0218127417300026
Renson, L., Sieber, J., Barton, D.A., Shaw, A.D., Neild, S.A.: Numerical continuation in nonlinear experiments using local Gaussian process regression. Nonlinear Dyn. 98, 2811–2826 (2019). 10.1007/s11071-019-05118-y DOI: 10.1007/s11071-019-05118-y
Sokolov, I.J., Babitsky, V.I.: Phase control of self-sustained vibration. J. Sound Vib. 248(4), 725–744 (2001). 10.1006/jsvi.2001.3810 DOI: 10.1006/jsvi.2001.3810
Mojrzisch, S., Twiefel, J.: Phase-controlled frequency response measurement of a piezoelectric ring at high vibration amplitude. Arch. Appl. Mech. 86(10), 1763–1769 (2016). 10.1007/s00419-015-1032-5 DOI: 10.1007/s00419-015-1032-5
Peter, S., Scheel, M., Krack, M., Leine, R.I.: Synthesis of nonlinear frequency responses with experimentally extracted nonlinear modes. Mech. Syst. Signal Process. 101, 498–515 (2018). 10.1016/j.ymssp.2017.09.014 DOI: 10.1016/j.ymssp.2017.09.014
Scheel, M., Peter, S., Leine, R.I., Krack, M.: A phase resonance approach for modal testing of structures with nonlinear dissipation. J. Sound Vib. 435, 56–73 (2018). 10.1016/j.jsv.2018.07.010 DOI: 10.1016/j.jsv.2018.07.010
Scheel, M., Weigele, T., Krack, M.: Challenging an experimental nonlinear modal analysis method with a new strongly friction-damped structure. J. Sound Vib. 485 (2020). 10.1016/j.jsv.2020.115580
Denis, V., Jossic, M., Giraud-Audine, C., Chomette, B., Renault, A., Thomas, O.: Identification of nonlinear modes using phase-locked-loop experimental continuation and normal form. Mech. Syst. Signal Process. 106, 430–452 (2018). 10.1016/j.ymssp.2018.01.014
Peter, S., Leine, R. I.: Excitation power quantities in phase resonance testing of nonlinear systems with phase-locked-loop excitation. Mech. Syst. Signal Process. 96, 139–158. 10.1016/j.ymssp.2017.04.011
Karaağaçlı, T., Özgüven, H.N.: Experimental identification of backbone curves of strongly nonlinear systems by using response-controlled stepped-Sine testing (RCT). Vibration 3(3), 266–280 (2020). 10.3390/vibration3030019 DOI: 10.3390/vibration3030019
Karaağaçlı, T., Özgüven, H.N.: Experimental modal analysis of nonlinear systems by using response-controlled stepped-sine testing. Mech. Syst. Signal Process. 146 (2021). 10.1016/j.ymssp.2020.107023
Widrow, B., Williams, C.S., Glover, J.R., McCool, J.M., Hearn, R.H., Zeidler, J.R., Kaunitz, J., Dong, E., Goodlin, R.C.: Adaptive noise cancelling: principles and applications. Proc. IEEE 63(12), 1692–1716 (1975). 10.1109/PROC.1975.10036 DOI: 10.1109/PROC.1975.10036
Haykin, S.: Adaptive Filter Theory, 3rd edn. Prentice Hall, New Jersey (1996)
Guillaume, P., Verboven, P., Vanlanduit, S., Auweraer, H.V.D., Peeters, B.: A poly-reference implementation of the least-squares complex frequency-domain estimator. Proc. IMAC 21, 183–192 (2003)
Kerschen, G., Peeters, M., Golinval, J.C., Vakakis, A.F.: Nonlinear normal modes, Part I: a useful framework for the structural dynamicist. Mech. Syst. Signal Process. 23(1), 170–194 (2009). 10.1016/j.ymssp.2008.04.002 DOI: 10.1016/j.ymssp.2008.04.002
Li, Y., Dankowicz, H.: Adaptive control designs for control-based continuation in a class of uncertain discrete-time dynamical systems. JVC/J. Vib. Control 1–18 (2020). https://doi.org/10.1177/1077546320913377
Matheron, G.: Principles of geostatistics. Econ. Geol. 58, 1246–1266 (1963) DOI: 10.2113/gsecongeo.58.8.1246
Detroux, T., Renson, L., Masset, L., Kerschen, G.: The harmonic balance method for bifurcation analysis of nonlinear mechanical systems. Conf. Proc. Soc. Exp. Mech. Ser. 1, 65–82 (2016). 10.1007/978-3-319-15221-9_5 DOI: 10.1007/978-3-319-15221-9_5