Coupled inverted pendulums: stabilization problem

Семенов, Михаил Е.; Solovyov, Andrey M.; Popov, M. A.; Meleshenko, Peter A.

doi:10.1007/s00419-017-1323-0

Cited by 20 publications

(11 citation statements)

References 11 publications

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“…The presented paper continues investigations started in the works Semenov et al (2014, 2015a, 2015b, 2016, 2018), devoted to the solution to the problem of inverted pendulum stabilization in the cases of rigid (Semenov et al, 2014) and flexible rod (Semenov et al, 2015a; 2015b) and in the case of the system of two coupled inverted pendula (Semenov et al, 2018). Particularly, we present the generalization of results obtained in Semenov et al (2018) to the case when the number of pendula is arbitrary. These pendula are placed on a moving base, and forces applied to the base are treated as control.…”

Section: Introductionmentioning

confidence: 55%

“…Obtained numerical results show that the nonlinear material exhibits greater stability than the linear material. Developing the idea presented in Semenov et al (2018), in this study we consider both linear and nonlinear coupling between pendula assuming the number of pendula in the system is arbitrary. This makes it possible to obtain some conditions ensuring stabilization of this system in explicit analytic form and to consider a limit passage to the continuous case.…”

Section: Introductionmentioning

confidence: 99%

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Stabilization of coupled inverted pendula: From discrete to continuous case

Семенов

Solovyov

Meleshenko

2020

Journal of Vibration and Control

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This study is focused on the investigation of stabilization problem for the system of coupled inverted pendula. The corresponding algorithm of control is based on the feedback principles and demonstrates some features in the physical implementation of the stabilization process. In the discrete case, the wave-like motion appears and leads to an observable interference pattern. In the continuous case, the provided feedback algorithm allows to simulate the stabilization process for the initially unstable solid medium. In these case conditions, ensuring the stabilization process is presented in the form of corresponding physical restrictions on the wave motion. Also, within the small parameter method, we investigate the nonlinear oscillatory motion of the material (the solid medium is modeled by the proposed system with nonlinear coupling). Results of numerical simulation for the system under consideration are presented and discussed. Particularly, numerical results show that the nonlinear material exhibits greater stability than the linear one.

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Section: Introductionmentioning

confidence: 55%

Section: Introductionmentioning

confidence: 99%

Stabilization of coupled inverted pendula: From discrete to continuous case

Семенов

Solovyov

Meleshenko

2020

Journal of Vibration and Control

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“…Отметим, что проблеме стабилизации систем связанных неустойчивых осцилляторов посвящено совсем немного работ. Исследование возможности стабилизации таких систем при помощи горизонтальных движений проведено в [18][19][20]. Также представляет интерес другая задача -возможность управления различными конфигурациями цепочек с помощью вертикальных осцилляций точки крепления.…”

Section: Fig 1 Model Of a Vertical Pendulum With An Oscillating Mountunclassified

Coupled Pendulums System Under Control by Vertical Oscillations

Семенов

Пигарев

Малинина

et al. 2019

Journal of Siberian Federal University. Engineering &Amp; Technologies

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In this paper we propose a mathematical model consisting of two inverse pendulums with an elastic coupling (by spring). We propose a dynamic programmed control of the model motion, implemented through vertical oscillations of the common pendulums pivot point. We investigate dynamics of this mechanical system, and formulated a condition for identifying stability of the system. We constructed stability zones in the spaces of the original and dimensionless parameters. Also, we obtain evolution of stability zones depending on spring stiffness values. In conclusion, we presented results of numerical software experiments for various system configurations

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“…The theory of oscillations, which studies oscillations occurring in various systems, is an intensively developing field of modern mathematics and physics [1][2][3][4]. The main models of the theory of oscillations are the linear and nonlinear oscillators, rotators, RLC circuit, etc.…”

Section: Introductionmentioning

confidence: 99%