Suppression of Time-Delayed Induced Vibrations Through the Dynamic Vibration Absorber: Application to the Inverted Pendulum
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.
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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