Tolerance of start-up control of rotation in parametric pendulum by delayed feedback

Yokoi, Yoshifumi; Hikihara, Takashi

doi:10.1016/j.physleta.2011.02.022

Cited by 19 publications

(12 citation statements)

References 22 publications

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“…Hence, for capturing pendulum rotation, we can neglect the dynamics of the base structure and the vibration source and replace it by a prescribed base motion thereby giving rise to a parametrically forced pendulum. This simplifies further study of the system and development of control strategies to ensure initiation of rotation [4,[16][17][18][19]. Control strategies are required for an effective harvester since a stable rotating solution is always accompanied by other attractors resulting in a limited basin of attraction (for rotation) and special initial conditions are required to ensure a rotating response.…”

Section: Introductionmentioning

confidence: 99%

Energy extraction from vortex-induced vibrations using period-1 rotation of an autoparametric pendulum

Das

Wahi

2018

Proc. R. Soc. A.

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We propose and analyse the feasibility of extracting energy from vortex-induced vibrations using rotating motion of an attached pendulum. The resulting autoparametric pendulum system is studied primarily to understand the effect of pendulum motion on the performance of the harvester which is typically ignored to result in a simple parametric pendulum. We find that rotating motions are possible only for small values of the pendulum mass when compared with the effective mass of the vibrating structure. However, the pendulum motion reduces the basin of attraction as well as the range of system parameters corresponding to the existence of rotary solutions. This significantly alters the harvester performance. By contrast, the evolution of the pendulum coordinates (angular position and velocity) remains largely unaffected by this interaction. Hence, for the purpose of design of controllers to robustly initiate/maintain rotation from arbitrary disturbances, the simplification to a parametric pendulum is reasonable while for the design of the harvester, this exercise is completely unsatisfactory.

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Section: Introductionmentioning

confidence: 99%

Energy extraction from vortex-induced vibrations using period-1 rotation of an autoparametric pendulum

Das

Wahi

2018

Proc. R. Soc. A.

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“…To address this shortcoming, delayed-feedback control, proposed in [24], was introduced in [25] with the aim of initiating the rotational motion regardless of the initial condi-40 tions and avoiding bifurcations that destabilize the rotation motion of pendulum while maintaining stable rotation. It was used for start up control of pendulum in [26], and the tolerance of start up control and delayed feedback control for maintaining periodic rotation was investigated in [27] and [28]. Its variant control strategy, extended time-delayed feedback which was proposed in [29], was 45 used in [30] to control bifurcation for the parametric pendulum under harmonic excitation.…”

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confidence: 99%

Rotating a pendulum with an electromechanical excitation

Teh

Woo

et al. 2015

International Journal of Non-Linear Mechanics

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“…However, in Yokoi and Hikihara (2011), delayed feedback control was implemented to an experimental setup of a parametric pendulum to maintain periodic rotations. Wang and Jing (2004) used the Lyapunov function method to design a controller of a pendulum system able to lead the chaotic motion to a desired periodic motion.…”

Section: Introductionmentioning

confidence: 99%

On nonlinear dynamics of a parametrically excited pendulum using both active control and passive rotational (MR) damper

Tusset

Janzen

Piccirillo

et al. 2017

Journal of Vibration and Control

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This paper presents two control strategies for a parametrically excited pendulum with chaotic behavior. One of them considers active control obtained by nonlinear saturation control (NSC) and the other a passive rotational magnetorheological (MR) damper. Firstly, the active control problem was formulated in order to design the external torque for the pendulum, considering the NSC. Numerical simulations were carried out in order to show the effectiveness of this method for the active control of the pendulum oscillation. The ability of the control of the proposed NSC in suppression of the chaotic behavior, considering the proposed parameters, was tested by a sensitivity analysis to parametric uncertainties. In the case of the passive rotational MR damper, firstly the influence of the introduction of the MR in a pendulum was performed considering the 0-1 test. Different electric currents are applied to suppress the chaotic behavior of the system. The numerical results showed that the simple introduction of a passive rotational MR damper without electric current did not change the chaotic behavior of the system. However, it is possible to keep the pendulum oscillating with periodic behavior using the rotational MR damper with energizing discontinuity.

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Tolerance of start-up control of rotation in parametric pendulum by delayed feedback

Cited by 19 publications

References 22 publications

Energy extraction from vortex-induced vibrations using period-1 rotation of an autoparametric pendulum

Energy extraction from vortex-induced vibrations using period-1 rotation of an autoparametric pendulum

Rotating a pendulum with an electromechanical excitation

On nonlinear dynamics of a parametrically excited pendulum using both active control and passive rotational (MR) damper

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