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Портал Begell Электронная Бибилиотека e-Книги Журналы Справочники и Сборники статей Коллекции
Journal of Automation and Information Sciences
SJR: 0.275 SNIP: 0.59 CiteScore™: 0.8

ISSN Печать: 1064-2315
ISSN Онлайн: 2163-9337

Выпуски:
Том 52, 2020 Том 51, 2019 Том 50, 2018 Том 49, 2017 Том 48, 2016 Том 47, 2015 Том 46, 2014 Том 45, 2013 Том 44, 2012 Том 43, 2011 Том 42, 2010 Том 41, 2009 Том 40, 2008 Том 39, 2007 Том 38, 2006 Том 37, 2005 Том 36, 2004 Том 35, 2003 Том 34, 2002 Том 33, 2001 Том 32, 2000 Том 31, 1999 Том 30, 1998 Том 29, 1997 Том 28, 1996

Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v34.i11.10
10 pages

The Synthesis of Stabilizing Control of a Rigid Body with Attached Elastic Elements

Alexander M. Kovalev
Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine, Donetsk, Ukraine
Alexander Zuyev
Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine
Vladimir F. Shcherbak
Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine, Donetsk, Ukraine

Краткое описание

We consider the problem of synthesis of nonlinear control law for a simulated mechanical system, which consists of a rigid carrying body and attached to it flexible beams. The system performs planar motion under controlling moment of forces applied to the carrying body. For obtaining a mathematical model in the form of a system of ordinary differential equations we make use of the modal method of discretization. The motion equations are presented in the Euler-Lagrange form with infinite number of elastic coordinates and a variable, which characterizes orientation of the carrying body. In order to obtain the nonlinear system we found control in the form of feedback, which provides asymptotical stability of the equilibrium state relative to definite combinations of elastic coordinates and orientation of the carrying body. For investigation we applied the approach of the Lyapunov control functions relative to a part of variables. We proved the Lyapunov stability of the complete system with respect to all phase variables. The question about realization of the obtained feedback for additional measurements of relative shears of a beam was studied. We show observability of the investigated system for different modes of motion. The results of numerical simulation are adduced.


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