Limit cycles with chattering in relay feedback systems
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/162053
- author
- Johansson, Karl Henrik ; Barabanov, Andrey E. and Åström, Karl Johan LU
- organization
- publishing date
- 2002
- 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
- 2016-04-01 16:44:25
- date last changed
- 2022-03-15 02:33:41
@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}}, keywords = {{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 = {{https://lup.lub.lu.se/search/files/4765935/625671.pdf}}, doi = {{10.1109/TAC.2002.802770}}, volume = {{47}}, year = {{2002}}, }