A family of smooth controllers for swinging up a pendulum
(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:
https://lup.lub.lu.se/record/1253806
- author
- Åström, Karl Johan LU ; Aracil, Javier and Gordillo, Francisco
- organization
- publishing date
- 2008
- 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 Press Ltd.
- 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
- 2016-04-01 13:03:25
- date last changed
- 2024-05-23 04:50:05
@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}},
keywords = {{swing-up; pendulum; shaping Hamiltonians; energy management}},
language = {{eng}},
number = {{7}},
pages = {{1841--1848}},
publisher = {{Pergamon Press Ltd.}},
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}},
doi = {{10.1016/j.automatica.2007.10.040}},
volume = {{44}},
year = {{2008}},
}