On the Stability of Digital Position Control with Viscous Damping and Coulomb Friction

Budai, Csaba; Kovâcs, László

doi:10.3311/ppme.10537

Cited by 5 publications

(2 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [19], the effect of the additional viscous damping was investigated while this current paper focuses on how the effect of virtual damping can modify the dynamic behavior of sampled-data systems. The main objective of this paper is not related to traditional controller design approaches, i.e., how to tune the gains to achieve best performance.…”

Section: Introductionmentioning

confidence: 99%

Combined effects of sampling and dry friction on position control

et al. 2019

Self Cite

View full text Add to dashboard Cite

This paper studies the combined effect of sampling and dry friction on the dynamics of mechanical systems subjected to position control using discretetime state feedback. This paper aims to highlight that even in case of a single degree-of-freedom mechanical subsystem, the controlled system cannot be characterized by a model with a single dominant frequency and some of the upper harmonics become relevant resulting multi-frequency vibrations. The presented stability analysis of the frictionless system gives insight into

show abstract

Section: Introductionmentioning

confidence: 99%

Combined effects of sampling and dry friction on position control

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…Besides vibration mitigation, friction damping has acquired high technical relevance because of its stabilizing effect on otherwise unstable self-excited vibrations. These are the consequence of destabilizing negative damping contributions which can be encountered in various applications: flutter vibrations of airfoils [3], chatter in machining processes [4,5] like in rolling mills [6], in control tasks [7][8][9], in robotics [10], and in brake squeal [11]. The driving example for the current work is cascade flutter vibrations of turbomachinery blades [12,13].…”

mentioning

confidence: 99%

Analysis of the non-periodic oscillations of a self-excited friction-damped system with closely spaced modes

2021

View full text Add to dashboard Cite

It is widely known that dry friction damping can bound the self-excited vibrations induced by negative damping. The vibrations typically take the form of (periodic) limit cycle oscillations. However, when the intensity of the self-excitation reaches a condition of maximum friction damping, the limit cycle loses stability via a fold bifurcation. The behavior may become even more complicated in the presence of any internal resonance conditions. In this work, we consider a two-degree-of-freedom system with an elastic dry friction element (Jenkins element) having closely spaced natural frequencies. The symmetric in-phase motion is subjected to self-excitation by negative (viscous) damping, while the symmetric out-of-phase motion is positively damped. In a previous work, we showed that the limit cycle loses stability via a secondary Hopf bifurcation, giving rise to quasi-periodic oscillations. A further increase in the self-excitation intensity may lead to chaos and finally divergence, long before reaching the fold bifurcation point of the limit cycle. In this work, we use the method of complexification-averaging to obtain the slow flow in the neighborhood of the limit cycle. This way, we show that chaos is reached via a cascade of period-doubling bifurcations on invariant tori. Using perturbation calculus, we establish analytical conditions for the emergence of the secondary Hopf bifurcation and approximate analytically its location. In particular, we show that non-periodic oscillations are the typical case for prominent nonlinearity, mild coupling (controlling the proximity of the modes), and sufficiently light damping. The range of validity of the analytical results presented herein is thoroughly assessed numerically. To the authors’ knowledge, this is the first work that shows how the challenging Jenkins element can be treated formally within a consistent perturbation approach in order to derive closed-form analytical results for limit cycles and their bifurcations.

show abstract