Abstract
A tuned mass damper (TMD) is implemented for the suppression of delay-induced vibrations. An inverted pendulum subject to proportional-derivative feedback control is considered as primary system. A TMD is then attached to it, in order to enlarge the stable region in the space of the control gains and mitigate vibrations induced by time delay in the feedback loop. Stability and bifurcation analysis enable us to evaluate the performance of the absorber both in terms of linear stability and of robustness against external perturbations. Results illustrate that, although the TMD is able to enlarge the stable region and suppress vibrations, in order to be efficient it requires a fine tuning and the knowledge of the system parameters, including time delay. Bifurcation analysis showed that the implementation of the TMD does not significantly improve the behavior of the system in terms of robustness of the system equilibrium because of the existence of subcritical bifurcations.
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References
S. Beregi, D. Takács, Analysis of the tyre–road interaction with a non-smooth delayed contact model. Multibody Syst. Dyn. 1–17 (2017)
J.L. Cabrera, J.G. Milton, On-off intermittency in a human balancing task. Phys. Rev. Lett. 89(15), 158, 702 (2002)
A. Casalotti, A. Arena, W. Lacarbonara, Mitigation of post-flutter oscillations in suspension bridges by hysteretic tuned mass dampers. Eng. Struct. 69, 62–71 (2014)
S. Chatterjee, On the design criteria of dynamic vibration absorbers for controlling friction-induced oscillations. J. Vib. Control. 14(3), 397–415 (2008)
J.P. Den Hartog, Mechanical vibrations (Courier Corporation, 1985)
N. Enayati, E. De Momi, G. Ferrigno, Haptics in robot-assisted surgery: challenges and benefits. IEEE Rev. Biomed. Eng. 9, 49–65 (2016)
K. Engelborghs, T. Luzyanina, D. Roose, Numerical bifurcation analysis of delay differential equations using dde-biftool. ACM Trans. Math. Softw. (TOMS) 28(1), 1–21 (2002)
G. Habib, G. Kerschen, Suppression of limit cycle oscillations using the nonlinear tuned vibration absorber. Proc. R. Soc. A 471(2176), 20140,976 (2015)
G. Habib, G. Kerschen, G. Stépán, Chatter mitigation using the nonlinear tuned vibration absorber. Int. J. Non-Linear Mech. 91, 103–112 (2017)
G. Habib, G. Rega, G. Stépán, Stability analysis of a two-degree-of-freedom mechanical system subject to proportional-derivative digital position control. J. Vib. Control. 21(8), 1539–1555 (2015)
G. Habib, G. Rega, G. Stépán, Delayed digital position control of a single-dof system and the nonlinear behavior of the act-and-wait controller. J. Vib. Control. 22(2), 481–495 (2016)
T. Insperger, J. Milton, G. Stépán, Acceleration feedback improves balancing against reflex delay. J. R. Soc. Interface10(79), 20120,763 (2013)
T. Insperger, G. Stépán, Act-and-wait control concept for discrete-time systems with feedback delay. IET Control. Theory Appl. 1(3), 553–557 (2007)
T. Insperger, G. Stépán, Semi-discretization for time-delay systems: stability and engineering applications, vol. 178 (Springer Science & Business Media, 2011)
W. Michiels, S.I. Niculescu, On the delay sensitivity of smith predictors. Int. J. Syst. Sci. 34(8–9), 543–551 (2003)
A.H. Nayfeh, Order reduction of retarded nonlinear systems-the method of multiple scales versus center-manifold reduction. Nonlinear Dyn. 51(4), 483–500 (2008)
P. Nwagoum Tuwa, P. Woafo, Analysis of an electrostatically actuated micro-plate subject to proportional-derivative controllers. J. Vib. Control. 24(10), 2020–2029 (2018)
F. Sadek, B. Mohraz, A.W. Taylor, R.M. Chung, A method of estimating the parameters of tuned mass dampers for seismic applications. Earthq. Eng. Struct. Dyn. 26(6), 617–635 (1997)
G. Stépán, Retarded dynamical systems: stability and characteristic functions (Longman Scientific & Technical, 1989)
B. Varszegi, D. Takacs, G. Stépán, S.J. Hogan, Stabilizing skateboard speed-wobble with reflex delay. J. R. Soc. Interface 13(121), 20160,345 (2016)
Y. Yang, J. Munoa, Y. Altintas, Optimization of multiple tuned mass dampers to suppress machine tool chatter. Int. J. Mach. Tools Manuf. 50(9), 834–842 (2010)
L. Zhang, G. Stépán, Hopf bifurcation analysis of scalar implicit neutral delay differential equation. Electron. J. Qual. Theory Differ. Equations 2018(62), 1–9 (2018)
Acknowledgements
The author would like to acknowledge the financial support of the European Union, H2020 Marie Skłodoska-Curie Individual Fellowship, Grant Agreement 704133 (PIEZOMACH) and of the Higher Education Excellence Program of the Ministry of Human Capacities in the frame of Biotechnology research area of Budapest University of Technology and Economics (BME FIKP-BIO).
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Habib, G. (2019). Suppression of Time-Delayed Induced Vibrations Through the Dynamic Vibration Absorber: Application to the Inverted Pendulum. In: Belhaq, M. (eds) Topics in Nonlinear Mechanics and Physics. Springer Proceedings in Physics, vol 228. Springer, Singapore. https://doi.org/10.1007/978-981-13-9463-8_6
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DOI: https://doi.org/10.1007/978-981-13-9463-8_6
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