Asymptotic Stabilization of the Inverted Equilibrium Manifold of the 3-D Pendulum Using Non-Smooth Feedback

The 3-D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom; it is acted on by gravity and it is fully actuated by control forces. In , almost global stabilization of the inverted equilibrium manifold was studied using a smooth globally defined fee...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2009-11, Vol.54 (11), p.2658-2662
Main Authors: Chaturvedi, N., McClamroch, H.
Format: Article
Language:English
Subjects:
3-D pendulum
Adaptive control
Almost global stabilization
Angular velocity
Angular velocity control
Applied sciences
Asymptotic properties
Attitude control
Automatic control
Computer science
control theory
systems
Control systems
Control theory
Control theory. Systems
Convergence
equilibrium manifold
Exact sciences and technology
Feedback
Force control
Force feedback
Fundamental areas of phenomenology (including applications)
Gravity
gravity potential
Manifolds
Mathematical analysis
Mathematical model
non-smooth feedback
Pendulums
Physics
Solid dynamics (ballistics, collision, multibody system, stabilization...)
Solid mechanics
Stabilization
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Summary:The 3-D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom; it is acted on by gravity and it is fully actuated by control forces. In , almost global stabilization of the inverted equilibrium manifold was studied using a smooth globally defined feedback. Here, we study the problem of almost global stabilization of the inverted equilibrium manifold using non-smooth feedback of angular velocity and a reduced attitude vector of the 3-D pendulum. The importance of the non-smooth feedback is that the almost global domain of attraction is a geometrically simple set that excludes the hanging attitude manifold. Unlike the closed-loop for a 3-D pendulum with a smooth controller, the closed-loop designed in this paper does not exhibit a performance constraint. These new results are based on Lyapunov analysis of the non-smooth closed-loop 3-D pendulum.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2009.2031570