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Journal of Computer and Systems Sciences International

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01.04.2022 | CONTROL IN DETERMINISTIC SYSTEMS

Stabilization of a System of Unstable Pendulums: Discrete and Continuous Case

verfasst von: P. A. Meleshenko, V. A. Nesterov, M. E. Semenov, A. M. Solovyov, K. I. Sypalo

Erschienen in: Journal of Computer and Systems Sciences International | Ausgabe 2/2022

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Abstract

We study the dynamics of a system of unstable pendulums under the conditions of elastic links under the influence of an external driving force, which is treated as a control, i.e., the problem of controlling an unstable system with a deficit of control actions is presented. In addition, the case of nonlinear elastic bonds (with cubic nonlinearity) is presented. The transition from a discrete to a continuous system is considered, which describes a material that is a continuous analog of a discrete system, which is in a nonequilibrium and structurally unstable state. The dynamic characteristics of an unstable system and material (under the conditions of a deficit of control actions) are studied, and the values of the parameters that ensure its stabilization are identified. The necessary and sufficient conditions for stabilization of a system of inverted elastically bound pendulums are found, which are formalized in the form of restrictions on the stiffness coefficient of the elastic connection. For the continuum analog of the system under consideration, it is proved that in order to stabilize an unstable material, it is necessary that its parameters take values that satisfy the following condition: the time of passage of an elastic wave from one end of the system to the other and back should not exceed the period of its natural oscillations. The results of the computational experiments illustrating the theoretical constructions are presented.

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Titel: Stabilization of a System of Unstable Pendulums: Discrete and Continuous Case
verfasst von: P. A. Meleshenko
V. A. Nesterov
M. E. Semenov
A. M. Solovyov
K. I. Sypalo
Publikationsdatum: 01.04.2022
Verlag: Pleiades Publishing
Erschienen in: Journal of Computer and Systems Sciences International / Ausgabe 2/2022
Print ISSN: 1064-2307
Elektronische ISSN: 1555-6530
DOI: https://doi.org/10.1134/S1064230722020113

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