Hopf bifurcation calculation in neutral delay differential equations: Nonlinear robotic arms subject to delayed acceleration feedback control

Bártfai, András; Dombóvári, Zoltán

doi:10.1016/j.ijnonlinmec.2022.104239

“…15 Bifurcation diagram of the system in Eq. (8) the saddle-node bifurcation is qualitatively similar to the one represented in Figs. 1, 2, 4 or 12.…”

Section: Multi-dof System: Aeroelastic Fluttersupporting

confidence: 74%

“…In reality, very few, if any, physical systems of engineering relevance have globally stable solutions, and unexpected behavior can occur even in well-understood systems, in the case of large perturbations. This issue is demonstrated by numer-ous examples such as wheel shimmy [1][2][3], machining processes [4,5], robot control [6][7][8], flutter instability [9,10], break squeal [11,12], traffic jams [13,14], pressure relief valves [15], electric blackouts [16,17], human balance [18,19], turbulent flows [20][21][22] and prey-predator ecosystems [23,24], to name a few.…”

Section: Introductionmentioning

confidence: 99%

Predicting saddle-node bifurcations using transient dynamics: a model-free approach

Habib

2023

Nonlinear Dyn

4

0

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This paper proposes a novel method for predicting the presence of saddle-node bifurcations in dynamical systems. The method exploits the effect that saddle-node bifurcations have on transient dynamics in the surrounding phase space and parameter space, and does not require any information about the steady-state solutions associated with the bifurcation. Specifically, trajectories of a system obtained for parameters close to the saddle-node bifurcation present local minima of the logarithmic decrement trend in the vicinity of the bifurcation. By tracking the logarithmic decrement for these trajectories, the saddle-node bifurcation can be accurately predicted. The method does not strictly require any mathematical model of the system, but only a few time series, making it directly implementable for gray- and black-box models and experimental apparatus. The proposed algorithm is tested on various systems of different natures, including a single-degree-of-freedom system with nonlinear damping, the mass-on-moving-belt, a time-delayed inverted pendulum, and a pitch-and-plunge wing profile. Benefits, limitations, and future perspectives of the method are also discussed. The proposed method has potential applications in various fields, such as engineering, physics, and biology, where the identification of saddle-node bifurcations is crucial for understanding and controlling complex systems.

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“…In reality, very few, if any, physical systems of engineering relevance have globally stable solutions, and unexpected behavior can occur even in well-understood systems, in the case of large perturbations. This issue is demonstrated by numerous examples such as wheel shimmy [1][2][3], machining processes [4,5], robot control [6][7][8], flutter instability [9,10], break squeal [11,12], traffic jams [13,14], electric blackouts [15,16], human balance [17,18], turbulent flows [19][20][21] and prey-predator ecosystems [22,23], to name a few.…”

Section: Introductionmentioning

confidence: 99%

Predicting Saddle-Node Bifurcations Using Transient Dynamics: A Model-Free Approach

Habib

¹

2023

Preprint

1

0

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This paper proposes a novel method for predicting the presence of saddle-node bifurcations in dynamical systems. The method exploits the effect that saddle-node bifurcations have on transient dynamics in the surrounding phase space and parameter space, and does not require any information about the steady-state solutions associated with the bifurcation. Specifically, trajectories of a system obtained for parameters close to the saddle-node bifurcation present local minima of the logarithmic decrement trend in the vicinity of the bifurcation. By tracking the logarithmic decrement for these trajectories, the saddle-node bifurcation can be accurately predicted. The method does not strictly require any mathematical model of the system, but only a few time series, making it directly implementable for gray- and black-box models and experimental apparatus. The proposed algorithm is tested on various systems of different natures, including a single-degree-of-freedom system with nonlinear damping, the mass-on-moving-belt, a time-delayed inverted pendulum, and a pitch-and-plunge wing profile. Benefits, limitations, and future perspectives of the method are also discussed. The proposed method has potential applications in various fields, such as engineering, physics, and biology, where the identification of saddle-node bifurcations is crucial for understanding and controlling complex systems.

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Hybrid vibration absorber for self-induced vibration suppression: exact analytical formulation for acceleration feedback control

Bartos,

Habib

2023

Meccanica

0

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Hybrid vibration absorbers (HVAs) are an effective solution for vibration mitigation. They combine the passive vibration absorption mechanism of tuned mass dampers (TMDs) with feedback-controlled actuators, similar to active mass dampers. This enables them to overcome the performance of both systems in terms of vibration mitigation effectiveness and energy consumption, respectively. This study evaluates the vibration suppression capabilities of an HVA against self-excited oscillations. A single-degree-of-freedom host system encompassing a negative damping term is considered. First, the possibility of enhancing the stability properties of an optimally tuned TMD through a feedback controller is evaluated. The analysis shows that this approach cannot improve the absorber’s performance. Subsequently, simultaneous optimization of all the HVA parameters is considered. Our results reveal that this approach significantly enhances the system’s performance. All analysis is carried out analytically without resorting to approximations. Finally, the absorber is numerically applied to suppress friction-induced vibrations and galloping instabilities.

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Hopf bifurcation calculation in neutral delay differential equations: Nonlinear robotic arms subject to delayed acceleration feedback control

Cited by 6 publications

References 33 publications

Predicting saddle-node bifurcations using transient dynamics: a model-free approach

Predicting saddle-node bifurcations using transient dynamics: a model-free approach

Predicting Saddle-Node Bifurcations Using Transient Dynamics: A Model-Free Approach

Hybrid vibration absorber for self-induced vibration suppression: exact analytical formulation for acceleration feedback control

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