{"id":853,"date":"2024-12-31T16:53:08","date_gmt":"2024-12-31T16:53:08","guid":{"rendered":"https:\/\/els-journal.net\/wp\/about\/"},"modified":"2025-04-27T08:30:53","modified_gmt":"2025-04-27T08:30:53","slug":"28204-locally-optimal-pi-controller-for-a-two-tank-system","status":"publish","type":"page","link":"https:\/\/els-journal.net\/wp\/?page_id=853","title":{"rendered":"28204 Locally Optimal PI Controller for a Two-Tank System"},"content":{"rendered":"\n\n\n<h3>Vol. 28, No. 2 &#8211; December 2024<\/h3>\n<h3>Locally Optimal PI Controller for a\nTwo-Tank System<\/h3>\n<h5>https:\/\/doi.org\/10.53314\/ELS2428068K<\/h5>\n<h5>Igor Kr\u010dmar, Velibor \u0110ali\u0107, Aleksandar Raki\u0107, and Petar Mari\u0107<\/h5>\n<h5><b>Abstract<\/b><\/h5>\n<h5>The paper provides an extensive experimental\nanalysis of an optimal PI controller for the two-tank system. The\ntwo-tank system is a benchmark hydrodynamic system. The PI\ncontroller has proportional action placed in a feedback path of the\nsystem, thus supporting aperiodic response of the system. The\noptimal PI controller tuning is based on transfer function of the\nsystem, and it minimizes surface between the error signal and the\ntime axis. The choice of the minimization criterion is adequate as\nthe system has aperiodic step response. The extensive\nexperimental analysis is performed on the laboratory testbed to\nassess the performance of the optimally tuned PI controller when\napplied to the two-tank systems in step response tasks, reference\ntracking tasks, and disturbance rejection tasks. The results of the\nexperiments verify the design procedure of the PI controller. The\ndesigned PI controller provides noticeable slow start of the system,\nthus forcing an actuator to operate on a border line of the dead\nzone for a significant period. To remedy the situation, a\nfeedforward modification of the controller is proposed. Gain of the\nfeedforward part is time varying. At the beginning of the system\noperation, it provides significant value of the control signal and\nsafe start of the system. On the other hand, as time advances, the\ngain of the feedforward part vanishes to zero. Although the\nfeedforward modification detunes optimal behavior of the system,\nit adds value to the operation of the system. Experimental analysis\nperformed on the laboratory testbed verifies utilities introduced\nby the feedforward controller modification.<\/h5>\n<h5>Full text:  <a class=\"fas fa-file-pdf\" href=\"https:\/\/els-journal.net\/wp\/wp-content\/uploads\/2024\/12\/2024-28-2-04.pdf\" target=\"_blank\" rel=\"noopener\"><\/a><\/h5>\n\n\n\n\n<a target=\"_blank\" href=\"http:\/\/www.scopus.com\/inward\/citedby.uri?partnerID=HzOxMe3b&#038;doi=10.53314\/ELS2428068K&#038;origin=inward\" ref=\"scopus-citedby\" rel=\"noopener\"><image src=\"http:\/\/api.elsevier.com\/content\/abstract\/citation-count?doi=10.53314\/ELS2428068K&#038;httpAccept=image%2Fjpeg&#038;apiKey=87124910cd33413b75b0a6f4e70d58bd\" border=\"0\" alt=\"cited by count\"\/><\/a>\n\n\n\n\nGoogle Scholar Citations <a target=\"_blank\" class=\"fas fa-external-link-alt\" href=\"http:\/\/scholar.google.com\/scholar?hl=en&#038;lr=&#038;cites=http:\/\/dx.doi.org\/ELS2428068K\" rel=\"noopener\"><\/a>\n\n\n\n\n<center> <span class=\"__dimensions_badge_embed__\" data-doi=\"10.53314\/ELS2428068K\" data-style=\"small_circle\"><\/span> <\/center> <script async src=\"https:\/\/badge.dimensions.ai\/badge.js\" charset=\"utf-8\"><\/script>\n\n\n\n\n<center>Google Scholar Citations <a target=\"_blank\" class=\"fas fa-external-link-alt\" href=\"http:\/\/scholar.google.com\/scholar?hl=en&#038;lr=&#038;cites=http:\/\/dx.doi.org\/10.53314\/ELS2428068K\" rel=\"noopener\"><\/a><\/center>\n\n\n\n\n<a target=\"_blank\" href=\"http:\/\/www.scopus.com\/inward\/citedby.uri?partnerID=HzOxMe3b&#038;doi=10.53314\/ELS2428068K&#038;origin=inward\" ref=\"scopus-citedby\" rel=\"noopener\"><image src=\"http:\/\/api.elsevier.com\/content\/abstract\/citation-count?doi=10.53314\/ELS2428068K&#038;httpAccept=image%2Fjpeg&#038;apiKey=87124910cd33413b75b0a6f4e70d58bd\" border=\"0\" alt=\"cited by count\"\/><\/a>\n\n\n\n\n<center><span class=\"__dimensions_badge_embed__\" data-doi=\"10.53314\/ELS2428068K\" data-style=\"large_rectangle\"><\/span><\/center><script async src=\"https:\/\/badge.dimensions.ai\/badge.js\" charset=\"utf-8\"><\/script>\n\n\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"parent":828,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-853","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/els-journal.net\/wp\/index.php?rest_route=\/wp\/v2\/pages\/853","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/els-journal.net\/wp\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/els-journal.net\/wp\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/els-journal.net\/wp\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/els-journal.net\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=853"}],"version-history":[{"count":4,"href":"https:\/\/els-journal.net\/wp\/index.php?rest_route=\/wp\/v2\/pages\/853\/revisions"}],"predecessor-version":[{"id":904,"href":"https:\/\/els-journal.net\/wp\/index.php?rest_route=\/wp\/v2\/pages\/853\/revisions\/904"}],"up":[{"embeddable":true,"href":"https:\/\/els-journal.net\/wp\/index.php?rest_route=\/wp\/v2\/pages\/828"}],"wp:attachment":[{"href":"https:\/\/els-journal.net\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=853"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}