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The implementation of FO controllers requires the use of rational approximations, but such realizations produce distinct dynamic types of behavior. This study analyzes the accuracy in the prediction of LCs, namely their amplitude and frequency, when using several different algorithms. To illustrate this problem we use FO-PID algorithms in the control of systems with backlash.<\/jats:p>","DOI":"10.1177\/1077546315581572","type":"journal-article","created":{"date-parts":[[2015,4,23]],"date-time":"2015-04-23T21:22:14Z","timestamp":1429824134000},"page":"587-603","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":11,"title":["Limit cycle prediction of systems with fractional controllers and backlash"],"prefix":"10.1177","volume":"23","author":[{"given":"Ramiro S","family":"Barbosa","sequence":"first","affiliation":[{"name":"GECAD \u2013 Knowledge Engineering and Decision Support Research Center, ISEP\/IPP \u2013 Institute of Engineering\/Polytechnic of Porto, Porto, Portugal"}]},{"given":"JA Tenreiro","family":"Machado","sequence":"additional","affiliation":[{"name":"GECAD \u2013 Knowledge Engineering and Decision Support Research Center, ISEP\/IPP \u2013 Institute of Engineering\/Polytechnic of Porto, 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