Chaos control of chaotic pendulum system☆

Wang, Ruiqi; Jing, Zhujun

doi:10.1016/j.chaos.2003.10.011

Cited by 37 publications

(27 citation statements)

References 25 publications

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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. Theoretical results were illustrated by numerical simulations which show the effect of the control.…”

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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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

View full text Add to dashboard Cite

show abstract

“…Chaotic dynamics appear frequently in nature and in nonlinear dynamical systems [9,10]. In [11], the nonlinear dynamic responses of the rotating continuous flexible shaft-rigid disk system with rub-impact between the disk and the stator were investigated. Time series, phase plane portrait, Poincaré map, bifurcation diagrams, and Lyapunov exponents were used to analyze the dynamic behavior of the system.…”

Section: Introductionmentioning

confidence: 99%

Chaotic Vibration Prediction of a Free-Floating Flexible Redundant Space Manipulator

Wang

2016

Shock and Vibration

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The dynamic model of a planar free-floating flexible redundant space manipulator with three joints is derived by the assumed modes method, Lagrange principle, and momentum conservation. According to minimal joint torque’s optimization (MJTO), the state equations of the dynamic model for the free-floating redundant space manipulator are described. The PD control using the tracking position error and velocity error in the manipulator is introduced. Then, the chaotic dynamic behavior of the manipulator is analyzed by chaotic numerical methods, in which time series, phase plane portrait, Poincaré map, and Lyapunov exponents are used to analyze the chaotic behavior of the manipulator. Under certain conditions for the joint torque optimization and initial values, chaotic vibration motion of the space manipulator can be observed. The chaotic time series prediction scheme for the space manipulator is presented based on the theory of phase space reconstruction under Takens’ embedding theorem. The trajectories of phase space can be reconstructed in embedding space, which are equivalent to the original space manipulator in dynamics. The one-step prediction model for the chaotic time series and the chaotic vibration was established by using support vector regression (SVR) prediction model with RBF kernel function. It has been proved that the SVR prediction model has a good performance of prediction. The experimental results show the effectiveness of the presented method.

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“…In Wang and Jing [12] it was implemented the Lyapunov function method for projecting a controller to a pendulum system with chaotic motion to a desired periodic motion like period-1, period-2 and period-4. The major advantage pointed in [11] was the time consumption of control, which is shorter than the OGY and SOGY methods.…”

Section: Introductionmentioning

confidence: 99%

Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism

et al. 2015

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The nonlinear dynamics behavior analyzed, in this paper, consists in a pendulum vertically excited on the support by a crankshaft -slider mechanism. The novelty is the obtainment and analysis of a mathematical model for the pendulum dynamics, under an excitation of a crank-slider, which is based on an extension of the mathematical model of the classical parametric pendulums. Through the modeling, it was verified that the nonlinear dynamics of the pendulum, excited by the crankshaft -slider mechanism approaches to that of harmonic excitation, when one considered the length of the shaft is sufficient larger than the radius of the crank. The nonlinear dynamic analyses focused on observation of different kinds of motion for different values of dimensionless parameters of the adopted mathematical model. These parameters, includes the frequency of excitation, the amplitude and the geometry of the crankshaft -slider mechanism. The adopted method of analyses used tools, such as, Lyapunov exponents, parameter space plots, basins of attractions, bifurcation diagrams, phase portraits, time histories and Poincaré sections. The kinds of motion include results on fixed point, oscillations, rotations, oscillations-rotations and chaotic motions.

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Chaos control of chaotic pendulum system☆

Cited by 37 publications

References 25 publications

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

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

Chaotic Vibration Prediction of a Free-Floating Flexible Redundant Space Manipulator

Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism

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