Dynamics of an inverted pendulum with delayed feedback control
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Authors
Landry, Maria
Campbell, Sue Ann
Morris, Kirsten
Aguilar, Cesar O.
Subjects
inverted pendulum
time delay
feedback control
stability analysis
Hopf bifurcation
time delay
feedback control
stability analysis
Hopf bifurcation
Advisors
Date of Issue
2005
Date
Publisher
Society for Industrial and Applied Mathematics (SIAM)
Language
Abstract
We consider an experimental system consisting of a pendulum, which is free to rotate 360 degrees, attached to a cart. The cart can move in one dimension. We describe a model for this system and use it to design a feedback control law that stabilizes the pendulum in the uprigiht position. We then introduce a time delay into the feedback and prove that for values of the delay below a critical delay, the system remains stable. Using a center manifold reduction, we show that the system undergoes a supercritical Hopf bifurcation at the critical delay. Both the critical value of the delay and the stability of the limit cycle are verified experimentally. Our experimental data is illustrated with plots and videos.
Type
Article
Description
The article of record as published may be found at: http://dx.doi.org/10.1137/030600461
Series/Report No
Department
Applied Mathematics
Organization
Identifiers
NPS Report Number
Sponsors
Funder
Format
Citation
SIAM J. of Applied Dynamical Systems, V.4, no. 2, Pp. 333-351, 2005.
Distribution Statement
Approved for public release; distribution is unlimited.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.