Details
| Original language | English |
|---|---|
| Article number | e202300009 |
| Journal | GAMM Mitteilungen |
| Volume | 46 |
| Issue number | 2 |
| Publication status | Published - 4 Jun 2023 |
Abstract
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.
Keywords
- control-based continuation, feedback control, force harmonization, nonlinear vibrations
ASJC Scopus subject areas
- Materials Science(all)
- General Materials Science
- Physics and Astronomy(all)
- General Physics and Astronomy
- Mathematics(all)
- Applied Mathematics
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In: GAMM Mitteilungen, Vol. 46, No. 2, e202300009, 04.06.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Continuation methods for lab experiments of nonlinear vibrations
AU - Tatzko, Sebastian
AU - Kleyman, Gleb
AU - Wallaschek, Jörg
N1 - Funding Information: The authors thank the German Research Foundation (DFG) for the support within the priority program SPP 1897 “Calm, Smooth and Smart.” Open Access funding enabled and organized by Projekt DEAL.
PY - 2023/6/4
Y1 - 2023/6/4
N2 - 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.
AB - 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.
KW - control-based continuation
KW - feedback control
KW - force harmonization
KW - nonlinear vibrations
UR - http://www.scopus.com/inward/record.url?scp=85159063943&partnerID=8YFLogxK
U2 - 10.1002/gamm.202300009
DO - 10.1002/gamm.202300009
M3 - Article
AN - SCOPUS:85159063943
VL - 46
JO - GAMM Mitteilungen
JF - GAMM Mitteilungen
SN - 0936-7195
IS - 2
M1 - e202300009
ER -