H∞ optimization of positive position feedback control for mitigation of nonlinear vibrations

Feedback control; Numerical methods; Position control; Structural dynamics; Closed-form expression; Duffing oscillator; Harmonic Balance method; Non-linear vibrations; Optimal controls; Positive position feedback; Resonant vibrations; Vibration analysis

Abstract :

[en] This paper investigates the potential of using positive position feedback control for the mitigation of nonlinear vibrations. Closed form expressions for the H 8 optimal control parameters that minimize the maximal response of the structure are firstly derived for the linear case and then extended to the nonlinear case. The resonant vibration of a Duffing oscillator is considered to illustrate the proposed tuning of the optimal control parameters and the harmonic balance method is employed to approximate the analytical solutions. Numerical simulations are performed to demonstrate and validate the proposed method.

Disciplines :

Mechanical engineering
Aerospace & aeronautics engineering

Author, co-author :

Zhao, Guoying; Université Libre de Bruxelles - ULB > Department of Bio-, Electro- and Mechanical Systems > Precision Mechatronics Laboratory

Paknejad, Ahmad; Université Libre de Bruxelles - ULB > Department of Bio-, Electro- and Mechanical Systems > Precision Mechatronics Laboratory

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

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

Collette, Christophe ; Université Libre de Bruxelles - ULB > Department of Bio-, Electro- and Mechanical Systems > Precision Mechatronics Laboratory

Language :

English

Title :

H∞ optimization of positive position feedback control for mitigation of nonlinear vibrations

Publication date :

2018

Event name :

ISMA 2018 - 28th international conference on Noise and Vibration Engineering

Event organizer :

KU Leuven

Event place :

Leuven, Belgium

Event date :

From 17-09-2018 to 19-09-2018

Audience :

International

Main work title :

Proceedings of ISMA2018 and USD2018

Editor :

Desmet, Wim

Pluymers, Bert

Moens, David

Rottiers, Ward

Publisher :

KU Leuven, Leuven, Belgium

ISBN/EAN :

9789073802995

Pages :

143-151

Available on ORBi :

since 20 June 2019

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114 (8 by ULiège)

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Scopus citations^®
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Bibliography

F.-Y. Wang and Y. Gao, Advanced Studies of Flexible Robotic Manipulators. 2003.
M. Darecki et al., “Flightpath 2050,” Flightpath 2050 Eur. Vis. Aviat., p. 28, 2011.
G. Habib, T. Detroux, R. Viguié, and G. Kerschen, “Nonlinear generalization of Den Hartog's equal-peak method,” Mech. Syst. Signal Process., vol. 52-53, no. 1, pp. 17-28, 2015.
J. P. Den Hartog, Mechanical Vibrations. Dover Publications, 1985.
G. Zhao, N. Alujevic, B. Depraetere, and P. Sas, “Dynamic analysis and H 2 optimisation of a piezo-based tuned vibration absorber,” J. Intell. Mater. Syst. Struct., vol. 26, no. 15, pp. 1995-2010, 2015.
N. W. Hagood and A. von Flotow, “Damping of structural vibrations with piezoelectric materials and passive electrical networks,” J. Sound Vib., vol. 146, no. 2, pp. 243-268, Apr. 1991.
A. Preumont, Vibration Control of Active Structures, an introduction, vol. 179. Dordrecht: Springer Netherlands, 2011.
G. S. Agnes and R. D. Kriz, “Performance of Nonlinear Mechanical, Resonant-Shunted Piezoelectric, and Electronic Vibration Absorbers for Multi-Degree-of-Freedom Structures by Electronic Vibration Absorbers for Multi-Degree-of-Freedom Structures,” 1997.
M. Febbo and S. P. Machado, “Nonlinear dynamic vibration absorbers with a saturation,” vol. 332, pp. 1465-1483, 2013.
G. Habib and G. Kerschen, “A principle of similarity for nonlinear vibration absorbers,” Phys. D, vol. 332, pp. 1-8, 2016.
T. Asami and O. Nishihara, “Closed-Form Exact Solution to H[sub 8] Optimization of Dynamic Vibration Absorbers (Application to Different Transfer Functions and Damping Systems),” J. Vib. Acoust., vol. 125, no. 3, p. 398, 2003.
L. Meirovitch, Dynamics and Control of Structures. John Wiley & Sons, Inc, 1990.
D. Wagg, S. Neild, C. W. S. To, and S. K. Lau, Nonlinear Vibration with Control, vol. 58, no. 4. 2010.
T. Detroux, L. Renson, L. Masset, and G. Kerschen, “The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems,” pp. 1-34, 2016.
G. Kerschen, K. Worden, A. F. Vakakis, and J.-C. Golinval, “Past, present and future of nonlinear system identification in structural dynamics,” Mech. Syst. Signal Process., vol. 20, no. 3, pp. 505-592, 2006.