Mechanics of Solids
A Journal of Russian Academy of Sciences

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Total articles in the database:		12804
In Russian (Изв. РАН. МТТ):		8044
In English (Mech. Solids):		4760

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Yu.G. Martynenko and A.M. Formal'skii, "Controlled Pendulum on a Movable Base," Mech. Solids. 48 (1), 6-18 (2013)

Year

2013

Volume

Number

Pages

6-18

DOI

10.3103/S0025654413010020

Title

Controlled Pendulum on a Movable Base

Author(s)

Yu.G. Martynenko (Institute of Mechanics, Lomonosov Moscow State University, Michurinskii pr-t 1, Moscow, 119192, Russia)
A.M. Formal'skii (Institute of Mechanics, Lomonosov Moscow State University, Michurinskii pr-t 1, Moscow, 119192, Russia, formal@imec.msu.ru)

Abstract

A plane motion of a multilink pendulum hinged to a movable base (a wheel or a carriage) is considered. The control torque applied between the base and the first link of the pendulum is independent of the base position and velocity and is bounded in absolute value. The coordinate determining the base position is cyclic. The mathematical model of the system permits one to single out the equations describing the pendulum motion alone, which differ from the well-known equations of motion of a pendulum with a fixed suspension point both in the structure and in the parameters occurring in these equations. The phase portrait of motions of a control-free one-link pendulum suspended on a wheel or a carriage is obtained. A feedback control ensuring global stabilization of the unstable upper equilibrium of the pendulum is constructed. Time-optimal control synthesis is outlined.

Keywords

pendulum, unstable equilibrium, controllability domain, time optimality, communication, vibration frequency

References

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Received

08 June 2011

Link to Fulltext

http://link.springer.com/article/10.3103/S0025654413010020

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