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U of M College of Engineering Control Seminar Series Sponsored by Eaton, Ford, General Motors, and Whirlpool |
Dynamics and Control of the 3D Pendulum
Professor N. Harris
McClamroch
Department of
Aerospace Engineering
University of Michigan
Abstract:
New 3D pendulum models are introduced and studied. The 3D pendulum consists of a rigid
body, supported at a fixed pivot, with three rotational degrees of freedom. The
pendulum is acted on by a gravitational force and control forces and moments;
the center of mass of the pendulum is assumed to be distinct from the location
of the pivot. The 3D
pendulum is a generalization of both the 1D or planar pendulum and the 2D or
spherical pendulum.
Several different 3D pendulum models are introduced and used to analyze
properties of the uncontrolled 3D pendulum dynamics, namely conservation
properties, equilibria, relative equilibria, and their local stability
properties. Variational
integrators that preserve long term accuracy of simulations indicate the presence
of chaotic solutions of the uncontrolled 3D pendulum. If the pendulum is asymmetric, several controllers are
introduced that provide asymptotic stabilization of an equilibrium. If the pendulum has a
single axis of symmetry, several controllers are introduced that provide
asymptotic stabilization of a relative equilibrium or an equilibrium. All of the results are developed
to reflect the non-Euclidean geometry of the configuration space, which is the
Lie group of rigid body rotations SO(3). Related experimental results are also summarized.
3:30 – 4:30 p.m.