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A new family of smooth strategies for swinging up a pendulum

Åström, Karl Johan LU ; Aracil, Javier and Gordillo, Francisco (2005)
Abstract
The paper presents a new family of strategies for swinging up a pendulum. They are derived from physical arguments based on two ideas: shaping the Hamiltonian for a system without damping; and providing damping or energy pumping in relevant regions. A two-parameter family of simple strategies without switches with nice properties is obtained. The main result is that all solutions that do not start at a zero Lebesgue measure set will converge to the upright position for a wide range of the parameters in the control law. Thus, the swing-up and the stabilization problems are simultaneously solved with a single, smooth law.
Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Swing up, Pendulum, Shaping Hamiltonians
host publication
Proceedings of the 16th IFAC World Congress
editor
Piztek, Pavel
publisher
Elsevier
external identifiers
  • scopus:79960727496
ISBN
0-08-045108-X
language
English
LU publication?
yes
id
9aa7fa46-6ee8-4c15-9cdb-98498fe21573 (old id 535680)
alternative location
http://www.esi2.us.es/~gordillo/PUBLI/prague1.pdf
date added to LUP
2016-04-04 10:12:48
date last changed
2022-01-29 19:59:05
@inproceedings{9aa7fa46-6ee8-4c15-9cdb-98498fe21573,
  abstract     = {{The paper presents a new family of strategies for swinging up a pendulum. They are derived from physical arguments based on two ideas: shaping the Hamiltonian for a system without damping; and providing damping or energy pumping in relevant regions. A two-parameter family of simple strategies without switches with nice properties is obtained. The main result is that all solutions that do not start at a zero Lebesgue measure set will converge to the upright position for a wide range of the parameters in the control law. Thus, the swing-up and the stabilization problems are simultaneously solved with a single, smooth law.}},
  author       = {{Åström, Karl Johan and Aracil, Javier and Gordillo, Francisco}},
  booktitle    = {{Proceedings of the 16th IFAC World Congress}},
  editor       = {{Piztek, Pavel}},
  isbn         = {{0-08-045108-X}},
  keywords     = {{Swing up; Pendulum; Shaping Hamiltonians}},
  language     = {{eng}},
  publisher    = {{Elsevier}},
  title        = {{A new family of smooth strategies for swinging up a pendulum}},
  url          = {{https://lup.lub.lu.se/search/files/5488761/625569.pdf}},
  year         = {{2005}},
}