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Limit cycles with chattering in relay feedback systems

Johansson, Karl Henrik; Barabanov, Andrey E. and Åström, Karl Johan LU (2002) In IEEE Transactions on Automatic Control 47(9). p.1414-1423
Abstract
Relay feedback has a large variety of applications in control engineering. Several interesting phenomena occur in simple relay systems. In the paper, scalar linear systems with relay feedback are analyzed. It is shown that a limit cycle where part of the limit cycle consists of fast relay switchings can occur. This chattering is analyzed in detail and conditions for approximating it by a sliding mode are derived. A result on existence of limit cycles with chattering is given, and it is shown that the limit cycles can have arbitrarily many relay switchings each period. Limit cycles with regular sliding modes are also discussed. Examples illustrate the results.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
sliding modes, relay control, oscillations, nonlinear dynamics, Discontinuous control, hybrid systems
in
IEEE Transactions on Automatic Control
volume
47
issue
9
pages
1414 - 1423
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • wos:000177921900001
  • scopus:0036740933
ISSN
0018-9286
DOI
10.1109/TAC.2002.802770
language
English
LU publication?
yes
id
457719cb-e0fd-42e4-b7c6-6104bb5340b5 (old id 162053)
date added to LUP
2007-06-21 15:59:51
date last changed
2017-08-13 04:26:49
@article{457719cb-e0fd-42e4-b7c6-6104bb5340b5,
  abstract     = {Relay feedback has a large variety of applications in control engineering. Several interesting phenomena occur in simple relay systems. In the paper, scalar linear systems with relay feedback are analyzed. It is shown that a limit cycle where part of the limit cycle consists of fast relay switchings can occur. This chattering is analyzed in detail and conditions for approximating it by a sliding mode are derived. A result on existence of limit cycles with chattering is given, and it is shown that the limit cycles can have arbitrarily many relay switchings each period. Limit cycles with regular sliding modes are also discussed. Examples illustrate the results.},
  author       = {Johansson, Karl Henrik and Barabanov, Andrey E. and Åström, Karl Johan},
  issn         = {0018-9286},
  keyword      = {sliding modes,relay control,oscillations,nonlinear
dynamics,Discontinuous control,hybrid systems},
  language     = {eng},
  number       = {9},
  pages        = {1414--1423},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Automatic Control},
  title        = {Limit cycles with chattering in relay feedback systems},
  url          = {http://dx.doi.org/10.1109/TAC.2002.802770},
  volume       = {47},
  year         = {2002},
}