{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T05:20:56Z","timestamp":1741065656863,"version":"3.38.0"},"reference-count":31,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[2011,11,9]],"date-time":"2011-11-09T00:00:00Z","timestamp":1320796800000},"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":["Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering"],"published-print":{"date-parts":[[2012,5]]},"abstract":"<jats:p> The problem of tuning a two-parameter controller has been formulated as finding the centroid of the admissible region specified by the set of constraints that the controller should satisfy. The constraints can be as general as the closed-loop system stability or they may include several requirements on various stability, sensitivity, or performance measures. The design of stabilizing proportional\u2013derivative ( PD) controllers using the centroid of the stability region in the controller parameter space is considered as a case study. To this end, analytical formulas are derived to describe the stability boundaries of a class of integrating time delay systems, the stability region of which has a closed convex shape. The so-called centroid stable point is then calculated analytically and the resulting algebraic formulas are utilized to tune the controller parameters. Nonfragility and robustness of the designed control systems are then studied and simulation results are provided to evaluate the performance of the proposed tuning rules. <\/jats:p>","DOI":"10.1177\/0959651811427002","type":"journal-article","created":{"date-parts":[[2011,11,10]],"date-time":"2011-11-10T06:45:57Z","timestamp":1320907557000},"page":"685-698","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Constrained tuning of two-parameter controllers: a centroid approach"],"prefix":"10.1177","volume":"226","author":[{"given":"Mohammad A","family":"Rahimian","sequence":"first","affiliation":[{"name":"Electrical Engineering Department, Sharif University of Technology, Iran"}]},{"given":"Mohammad S","family":"Tavazoei","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, Sharif University of Technology, 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