An inverted pendulum on a fixed and a moving base

The plane motions of a controlled single-link pendulum with a fixed suspension point and a pendulum with its suspension point located at the centre of a wheel which rolls without sliding along a flat horizontal surface are considered. The control torque, applied to the pendulum at the suspension poi...

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Bibliographic Details
Published in:Journal of applied mathematics and mechanics 2006-05, Vol.70 (1), p.56-64
Main Author: Formal'skii, A.M.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Physics
Solid dynamics (ballistics, collision, multibody system, stabilization...)
Solid mechanics
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Summary:The plane motions of a controlled single-link pendulum with a fixed suspension point and a pendulum with its suspension point located at the centre of a wheel which rolls without sliding along a flat horizontal surface are considered. The control torque, applied to the pendulum at the suspension point, is bounded in absolute magnitude. A controllability domain is constructed in the linear approximation for the one and the other pendulum, from all points of which the pendulum can be brought into the upper unstable equilibrium position without oscillations about the lower equilibrium. It is shown that the domain of controllability is greater for a pendulum mounted on a wheel, as a result it is more easily stabilizable. Control laws are constructed, under which the domain of attraction is identical to the controllability domain and is thereby the largest possible domain.
ISSN:0021-8928
0021-8928
DOI:10.1016/j.jappmathmech.2006.03.010