Dynamics of a system of coupled inverted pendula with vertical forcing

Bhadra, Nivedita; Banerjee, Soumitro

doi:10.1016/j.chaos.2020.110358

Cited by 2 publications

(2 citation statements)

References 36 publications

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“…A detailed overview of vibrational stabilization is given in [2]. Vibrational stabilization of the Kapitza pendulum (KP) has been widely studied within the framework of the Mathieu equation [3], [4], [5], [6], [7], [8]. A summary of various techniques applied to this problem along with intuitive explanations are given in [9].…”

Section: Introductionmentioning

confidence: 99%

Vibrational Stabilization of the Kapitza Pendulum Using Model Predictive Control with Constrained Base Displacement

Ahrazoğlu,

Aseem Ul Islam,

Goel

et al. 2023

2023 American Control Conference (ACC)

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Section: Introductionmentioning

confidence: 99%

Vibrational Stabilization of the Kapitza Pendulum Using Model Predictive Control with Constrained Base Displacement

Ahrazoğlu,

Aseem Ul Islam,

Goel

et al. 2023

2023 American Control Conference (ACC)

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“…The pendulum in an inverted position is a multivariate, high-order, nonlinear, strong coupling, and natural unstable system (Nivedita and Soumitro, (2020); Gonzalez and Rossiter, (2020)). The implementation of an inverted pendulum system can effectively reflect many typical problems in control, such as nonlinear, robustness, stabilization, follow-up, and tracking problems (Junkun et al (2020); Atilla and Firat, (2020)).…”

Section: Introductionmentioning

confidence: 99%

A Self-Stabilized Inverted Pendulum Made of Optically Responsive Liquid Crystal Elastomers

Cheng

Zhou

2022

Front. Robot. AI

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The inverted pendulum system has great potential for various engineering applications, and its stabilization is challenging because of its unstable characteristic. The well-known Kapitza’s pendulum adopts the parametrically excited oscillation to stabilize itself, which generally requires a complex controller. In this paper, self-sustained oscillation is utilized to stabilize an inverted pendulum, which is made of a V-shaped, optically responsive liquid crystal elastomer (LCE) bar under steady illumination. Based on the well-established dynamic LCE model, a theoretical model of the LCE inverted pendulum is formulated, and numerical calculations show that it always develops into the unstable static state or the self-stabilized oscillation state. The mechanism of the self-stabilized oscillation originates from the reversal of the gravity moment of the inverted pendulum accompanied with its own movement. The critical condition for triggering self-stabilized oscillation is fully investigated, and the effects of the system parameters on the stability of the inverted pendulum are explored. The self-stabilized inverted pendulum does not need an additional controller and offers new designs of self-stabilized inverted pendulum systems for potential applications in robotics, military industry, aerospace, and other fields.

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Dynamics of a system of coupled inverted pendula with vertical forcing

Cited by 2 publications

References 36 publications

Vibrational Stabilization of the Kapitza Pendulum Using Model Predictive Control with Constrained Base Displacement

Vibrational Stabilization of the Kapitza Pendulum Using Model Predictive Control with Constrained Base Displacement

A Self-Stabilized Inverted Pendulum Made of Optically Responsive Liquid Crystal Elastomers

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