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In the literature, several approaches have been introduced for tuning proportional-integral controllers by calculating the centroid of the stability region. However, all those approaches depend on graphical plottings which are time-consuming. Also, the design procedure has to be redone as the transfer function changes. Here, two new analytical methods are proposed to obtain the centroid of the stability region for the proportional-integral controllers to control a time delay process which can be modeled by a stable or unstable first-order plus dead-time model. The methods introduced eliminate the compulsory procedure of plotting the stability region. The efficiency of the suggested methods has been studied by conducting a robustness analysis and studying several simulation examples.<\/jats:p>","DOI":"10.1177\/09596518211048028","type":"journal-article","created":{"date-parts":[[2021,9,25]],"date-time":"2021-09-25T08:31:55Z","timestamp":1632558715000},"page":"818-831","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["Tuning proportional-integral controllers based on new analytical methods for finding centroid of stability locus for stable\/unstable first-order plus dead-time processes"],"prefix":"10.1177","volume":"236","author":[{"given":"Fadi","family":"Alyoussef","sequence":"first","affiliation":[{"name":"Department of Electrical and Electronics Engineering, Institute of Natural and Applied Sciences, Dicle University, Diyarbak\u0131r, 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