Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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IssuesArchive of Issues2014-6pp.543-550

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I.M. Ananĺevskii and N.V. Anokhin, "Control of the spatial motion of a multilink inverted pendulum using a torque applied to the first link," J. Appl. Math. Mech. 78 (6), 543-550 (2014)
Year 2014 Volume 78 Issue 6 Pages 543-550
Title Control of the spatial motion of a multilink inverted pendulum using a torque applied to the first link
Author(s) I.M. Ananĺevskii (Moscow, Russia, anan@ipmnet.ru)
N.V. Anokhin (Moscow, Russia)
Abstract An approach to constructing a control for non-linear mechanical systems in which the number of degrees of freedom exceeds the dimension of the generalized control forces is developed. An n-link pendulum with two-degree-of-freedom joints, controlled by a torque applied to the first link, is considered as an example. Such a pendulum has 2n different equilibrium positions. A feedback control with an absolute value constraint, which transfers the pendulum from the neighbourhood of an arbitrary equilibrium position to this equilibrium position in a finite time, is constructed. For this purpose, the equations of motion of the pendulum are linearized in the neighbourhood of the equilibrium position under consideration, complete controllability of the linear model is established, and a control is constructed for it using the linear matrix inequality technique. The applicability of the control law obtained to the solution of the problem of controlling a non-linear multilink pendulum is verified.
Received 29 April 2014
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