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A family of smooth controllers for swinging up a pendulum

Åström, Karl Johan LU ; Aracil, Javier and Gordillo, Francisco (2008) In Automatica 44(7). p.1841-1848
Abstract
The paper presents a new family of controllers for swinging up a pendulum. The swinging up of the pendulum is 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 of the state space. A family of simple smooth controllers without switches with nice properties is obtained. The main result is that all solutions that do not start at a zero Lebesgue measure set 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. The properties of the solution can be modified by the parameters in the control law.... (More)
The paper presents a new family of controllers for swinging up a pendulum. The swinging up of the pendulum is 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 of the state space. A family of simple smooth controllers without switches with nice properties is obtained. The main result is that all solutions that do not start at a zero Lebesgue measure set 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. The properties of the solution can be modified by the parameters in the control law. Control signal saturation can also be taken into account using the Hamiltonian approach. (c) 2008 Elsevier Ltd. All rights reserved. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
swing-up, pendulum, shaping Hamiltonians, energy management
in
Automatica
volume
44
issue
7
pages
1841 - 1848
publisher
Pergamon
external identifiers
  • wos:000258054400019
  • scopus:45849147667
ISSN
0005-1098
DOI
10.1016/j.automatica.2007.10.040
language
English
LU publication?
yes
id
fd9412a5-6205-4ef4-8a4f-a5ee23064367 (old id 1253806)
date added to LUP
2008-10-28 14:49:52
date last changed
2017-09-10 03:55:09
@article{fd9412a5-6205-4ef4-8a4f-a5ee23064367,
  abstract     = {The paper presents a new family of controllers for swinging up a pendulum. The swinging up of the pendulum is 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 of the state space. A family of simple smooth controllers without switches with nice properties is obtained. The main result is that all solutions that do not start at a zero Lebesgue measure set 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. The properties of the solution can be modified by the parameters in the control law. Control signal saturation can also be taken into account using the Hamiltonian approach. (c) 2008 Elsevier Ltd. All rights reserved.},
  author       = {Åström, Karl Johan and Aracil, Javier and Gordillo, Francisco},
  issn         = {0005-1098},
  keyword      = {swing-up,pendulum,shaping Hamiltonians,energy management},
  language     = {eng},
  number       = {7},
  pages        = {1841--1848},
  publisher    = {Pergamon},
  series       = {Automatica},
  title        = {A family of smooth controllers for swinging up a pendulum},
  url          = {http://dx.doi.org/10.1016/j.automatica.2007.10.040},
  volume       = {44},
  year         = {2008},
}