Rotation control of a parametrically excited pendulum by adjusting its length

Reguera, Florencia; Dotti, F; Machado, Sebastián P.

doi:10.1016/j.mechrescom.2016.01.011

Cited by 32 publications

(15 citation statements)

References 21 publications

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“…It was proved that the chaos in mechanical systems can be controlled. Reguera et al [17] presented a control law for the variable length pendulum to keep the pendulum in a stable rotation when the pivot was in sinusoidal and stochastic excitations.…”

Section: Introductionmentioning

confidence: 99%

An Improved Principle of Rapid Oscillation Suppression of a Pendulum by a Controllable Moving Mass: Theory and Simulation

Zhang

Liu

et al. 2019

Shock and Vibration

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An improved principle is proposed in this paper to achieve a more efficient amplitude suppression of an oscillating pendulum by a controllable moving mass. By establishing the governing equation of the pendulum with a moving mass, several suppression rules are presented to stipulate the motion parameters of the moving mass. The damping ratio is introduced to quantify the suppression effects generated by the mass intermittent motion. With the verification of the accuracy of the present model, some simulation has been taken to get the maximum damping ratio and solve the problem of the nonsynchronous motion. The simulation results show that the new principle is a more powerful control method for the oscillation problem of a pendulum. It is suggested that the new method should carry out the relevant active control experiment in the future research.

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Section: Introductionmentioning

confidence: 99%

An Improved Principle of Rapid Oscillation Suppression of a Pendulum by a Controllable Moving Mass: Theory and Simulation

Zhang

Liu

et al. 2019

Shock and Vibration

View full text Add to dashboard Cite

show abstract

“…It was concluded that the system exhibited chaotic properties in the domain of higher-level stability. A control scheme for a vertically excited parametric pendulum with variable length is presented in [16]. It offers two energy sources: a vibrating machine and sea waves simulated by a stochastic process [16].…”

Section: Introductionmentioning

confidence: 99%

“…A control scheme for a vertically excited parametric pendulum with variable length is presented in [16]. It offers two energy sources: a vibrating machine and sea waves simulated by a stochastic process [16]. For the pendulum to be controlled, a telescopic adjustment of the pendulum length [16] is used during the motion.…”

Section: Introductionmentioning

confidence: 99%

Modeling, Simulation, and Analysis of a Variable-Length Pendulum Water Pump

2021

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Due to the long-term problem of electricity and potable water in most developing and undeveloped countries, predominantly rural areas, a novelty of the pendulum water pump, which uses a vertically excited parametric pendulum with variable-length using a sinusoidal excitation as a vibrating machine, is presented. With this, more oscillations can be achieved, reducing human effort further and having high output than the existing pendulum water pump with the conventional pendulum. The pendulum, lever, and piston assembly are modeled by a separate dynamical system and then joined into the many degrees-of-freedom dynamical systems. The present work includes friction while studying the system dynamics and then simulated to verify the system’s harmonic response. The study showed the effect of the pendulum length variability on the whole system’s performance. The vertically excited parametric pendulum with variable length in the system is established, giving faster and longer oscillations than the pendulum with constant length. Hence, more and richer dynamics are achieved. A quasi-periodicity behavior is noticed in the system even after 50 s of simulation time; this can be compensated when a regular external forcing is applied. Furthermore, the lever and piston oscillations show a transient behavior before it finally reaches a stable behavior.

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“…Furthermore, authors have shown that this control technique can also be used via stability plots and by using Mathieu equation. In another work [31], authors have presented a control approach for a parametrically excited pendulum system in view point of energy extraction from an oscillatory motion and sea currents. They have shown that the stable rotations can be obtained regardless of the forcing conditions and for every set of initial conditions.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Response of an Inverted Pendulum System in Water under Parametric Excitations for Energy Harvesting: A Conceptual Approach

et al. 2020

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In this paper, we have investigated the dynamic response, vibration control technique, and upright stability of an inverted pendulum system in an underwater environment in view point of a conceptual future wave energy harvesting system. The pendulum system is subjected to a parametrically excited input (used as a water wave) at its pivot point in the vertical direction for stabilization purposes. For the first time, a mathematical model for investigating the underwater dynamic response of an inverted pendulum system has been developed, considering the effect of hydrodynamic forces (like the drag force and the buoyancy force) acting on the system. The mathematical model of the system has been derived by applying the standard Lagrange equation. To obtain the approximate solution of the system, the averaging technique has been utilized. An open loop parametric excitation technique has been applied to stabilize the pendulum system at its upright unstable equilibrium position. Both (like the lower and the upper) stability borders have been shown for the responses of both pendulum systems in vacuum and water (viscously damped). Furthermore, stability regions for both cases are clearly drawn and analyzed. The results are illustrated through numerical simulations. Numerical simulation results concluded that: (i) The application of the parametric excitation control method in this article successfully stabilizes the newly developed system model in an underwater environment, (ii) there is a significant increase in the excitation amplitude in the stability region for the system in water versus in vacuum, and (iii) the stability region for the system in vacuum is wider than that in water.

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Rotation control of a parametrically excited pendulum by adjusting its length

Cited by 32 publications

References 21 publications

An Improved Principle of Rapid Oscillation Suppression of a Pendulum by a Controllable Moving Mass: Theory and Simulation

An Improved Principle of Rapid Oscillation Suppression of a Pendulum by a Controllable Moving Mass: Theory and Simulation

Modeling, Simulation, and Analysis of a Variable-Length Pendulum Water Pump

Dynamic Response of an Inverted Pendulum System in Water under Parametric Excitations for Energy Harvesting: A Conceptual Approach

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