{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,1]],"date-time":"2025-03-01T06:13:44Z","timestamp":1740809624867,"version":"3.38.0"},"reference-count":13,"publisher":"SAGE Publications","issue":"15","license":[{"start":{"date-parts":[[2019,7,4]],"date-time":"2019-07-04T00:00:00Z","timestamp":1562198400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Transactions of the Institute of Measurement and Control"],"published-print":{"date-parts":[[2019,11]]},"abstract":"<jats:p> In this paper, limit cycle frequency, pulse width and stability analysis are examined using different methods for relay feedback nonlinear control systems with integer or fractional order plant transfer functions. The describing function (DF), A loci, a time domain method formulated in state space notation and Matlab\/Simulink simulations are used for the analysis. Comparisons of the results of using these methods are given in several examples. In addition, the work has been extended to fractional order systems with time delay. Programs have been developed in the Matlab environment for all the theoretical methods. In particular, Matlab programs have been written to obtain a graphical solution for the A loci method, which can precisely calculate the limit cycle frequency. The developed solution methods are shown in various examples. The major contribution is to look at finding limit cycles for relay feedback systems having plants with a fractional order transfer function (FOTF). However, en route to this goal new assessments of limit cycle stability have been done for a rational plant transfer function plus a time delay. <\/jats:p>","DOI":"10.1177\/0142331219860302","type":"journal-article","created":{"date-parts":[[2019,7,5]],"date-time":"2019-07-05T05:39:21Z","timestamp":1562305161000},"page":"4424-4435","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["Limit cycles in relay systems with fractional order plants"],"prefix":"10.1177","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4642-6272","authenticated-orcid":false,"given":"Ali","family":"Y\u00fcce","sequence":"first","affiliation":[{"name":"Engineering Faculty, Department of Electrical and Electronics Engineering, Inonu University, Turkey"}]},{"given":"Nusret","family":"Tan","sequence":"additional","affiliation":[{"name":"Engineering Faculty, Department of Electrical and Electronics Engineering, Inonu University, Turkey"}]},{"given":"Derek P","family":"Atherton","sequence":"additional","affiliation":[{"name":"University of Sussex, UK"}]}],"member":"179","published-online":{"date-parts":[[2019,7,4]]},"reference":[{"volume-title":"3rd IFAC Congress, Paper 28E","year":"1966","author":"Atherton DP","key":"bibr1-0142331219860302"},{"volume-title":"Stability of Nonlinear Systems","year":"1981","author":"Atherton DP","key":"bibr2-0142331219860302"},{"key":"bibr3-0142331219860302","unstructured":"Atherton DP (2011) An Introduction to Nonlinearity in Control Systems. Derek Atherton & Ventus Publishing ApS, ebook at bookboon.com."},{"key":"bibr4-0142331219860302","doi-asserted-by":"publisher","DOI":"10.1109\/ICFDA.2014.6967404"},{"key":"bibr5-0142331219860302","doi-asserted-by":"publisher","DOI":"10.3390\/machines2030176"},{"key":"bibr6-0142331219860302","doi-asserted-by":"publisher","DOI":"10.1049\/ip-d.1981.0005"},{"key":"bibr7-0142331219860302","doi-asserted-by":"publisher","DOI":"10.1049\/piee.1974.0168"},{"key":"bibr8-0142331219860302","doi-asserted-by":"publisher","DOI":"10.1080\/00207176608921414"},{"volume-title":"Proceedings of the Journ\u00e9es d\u2019\u00c8tudes des Vibrations AERA","year":"1950","author":"Hamel B","key":"bibr9-0142331219860302"},{"key":"bibr10-0142331219860302","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84996-335-0"},{"volume-title":"Relay Control Systems","year":"1984","author":"Tsypkin IZ","key":"bibr11-0142331219860302"},{"key":"bibr12-0142331219860302","doi-asserted-by":"publisher","DOI":"10.1016\/S1474-6670(17)55622-0"},{"key":"bibr13-0142331219860302","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.1971.4308335"}],"container-title":["Transactions of the Institute of Measurement and Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0142331219860302","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/0142331219860302","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0142331219860302","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,1]],"date-time":"2025-03-01T03:58:49Z","timestamp":1740801529000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0142331219860302"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,4]]},"references-count":13,"journal-issue":{"issue":"15","published-print":{"date-parts":[[2019,11]]}},"alternative-id":["10.1177\/0142331219860302"],"URL":"https:\/\/doi.org\/10.1177\/0142331219860302","relation":{},"ISSN":["0142-3312","1477-0369"],"issn-type":[{"type":"print","value":"0142-3312"},{"type":"electronic","value":"1477-0369"}],"subject":[],"published":{"date-parts":[[2019,7,4]]}}}