{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T17:31:11Z","timestamp":1781112671728,"version":"3.54.1"},"reference-count":25,"publisher":"SAGE Publications","issue":"10","license":[{"start":{"date-parts":[[2024,1,28]],"date-time":"2024-01-28T00:00:00Z","timestamp":1706400000000},"content-version":"vor","delay-in-days":365,"URL":"http:\/\/www.sagepub.com\/licence-information-for-chorus"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CNS-1726865"],"award-info":[{"award-number":["CNS-1726865"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Transactions of the Institute of Measurement and Control"],"published-print":{"date-parts":[[2023,6]]},"abstract":"<jats:p>Allowing for a \u201cvirtual\u201d full actuation of a rotary inverted pendulum (RIP) system with only a single physical actuator has been a challenging problem. In this paper, a hybrid control scheme that involves a pole-placement feedback controller and an optimal proportional\u2013integral\u2013derivative (PID) or fractional-order PID (FOPID) controller is proposed to simultaneously enable the tracking control of the rotary arm and the stabilization of the pendulum arm in an input\u2013output feedback linearized RIP system. The PID controller is optimized first with the particle swarm optimization (PSO) to obtain three optimal gains, and then the other two parameters of the FOPID controller are optimized with the PSO. Compared to the optimized PID controller, the optimized FOPID controller improves the tracking and stabilizing accuracy by 53% and 29%, respectively, and demonstrates better adaptability for tracking different reference signals. Moreover, the hybrid FOPID controller exhibits 74.8% and 53% higher tracking accuracy than previous optimized model reference adaptive control PID (MRAC-PID) and linear\u2013quadratic regulator (LQR) controllers, respectively. The proposed hybrid controllers are also digitized with different rules and sampling times, showing a closer performance between the discrete-time and continuous-time hybrid controllers under smaller sampling times.<\/jats:p>","DOI":"10.1177\/01423312221146606","type":"journal-article","created":{"date-parts":[[2023,1,28]],"date-time":"2023-01-28T07:25:32Z","timestamp":1674890732000},"page":"1986-1998","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":16,"title":["Optimal fractional-order proportional\u2013integral\u2013derivative control enabling full actuation of decomposed rotary inverted pendulum system"],"prefix":"10.1177","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4170-099X","authenticated-orcid":false,"given":"Yi","family":"Yang","sequence":"first","affiliation":[{"name":"School of Engineering Technology, Purdue University, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haiyan H","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Engineering Technology, Purdue University, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Richard M","family":"Voyles","sequence":"additional","affiliation":[{"name":"School of Engineering Technology, Purdue University, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2023,1,28]]},"reference":[{"key":"bibr1-01423312221146606","doi-asserted-by":"publisher","DOI":"10.1177\/00202940211035406"},{"issue":"11","key":"bibr2-01423312221146606","first-page":"1","volume":"7","author":"Alsaedi A","year":"2015","journal-title":"Advances in Mechanical Engineering"},{"key":"bibr3-01423312221146606","doi-asserted-by":"publisher","DOI":"10.3934\/jimo.2017032"},{"key":"bibr4-01423312221146606","doi-asserted-by":"publisher","DOI":"10.1016\/S0957-4158(01)00075-7"},{"key":"bibr5-01423312221146606","doi-asserted-by":"publisher","DOI":"10.1177\/0142331219891571"},{"key":"bibr6-01423312221146606","doi-asserted-by":"publisher","DOI":"10.4028\/www.scientific.net\/SSP.177.84"},{"key":"bibr7-01423312221146606","doi-asserted-by":"publisher","DOI":"10.1177\/0959651818778218"},{"key":"bibr8-01423312221146606","doi-asserted-by":"publisher","DOI":"10.1007\/s13369-017-2618-8"},{"issue":"1","key":"bibr9-01423312221146606","first-page":"191","volume":"14","author":"Folea S","year":"2017","journal-title":"Acta Polytechnica Hungarica"},{"key":"bibr10-01423312221146606","doi-asserted-by":"publisher","DOI":"10.1109\/IECON.1991.239008"},{"key":"bibr11-01423312221146606","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/572424"},{"key":"bibr12-01423312221146606","doi-asserted-by":"publisher","DOI":"10.1109\/ICNN.1995.488968"},{"key":"bibr13-01423312221146606","doi-asserted-by":"publisher","DOI":"10.1109\/MED.2007.4433653"},{"key":"bibr14-01423312221146606","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-013-0335-y"},{"key":"bibr15-01423312221146606","volume-title":"La D\u00e9rivation Non Enti\u00e8re: Th\u00e9orie, Synth\u00e8se et Applications","author":"Oustaloup A","year":"1995"},{"key":"bibr16-01423312221146606","first-page":"2226","volume-title":"IEEE international conference on systems, man and cybernetics","author":"\u00d6zbek NS","year":"2010"},{"key":"bibr17-01423312221146606","doi-asserted-by":"publisher","DOI":"10.5772\/19412."},{"key":"bibr18-01423312221146606","volume-title":"Fractional Differential Equations","author":"Podlubny I","year":"1999","edition":"1"},{"key":"bibr19-01423312221146606","doi-asserted-by":"publisher","DOI":"10.1177\/0142331218822721"},{"key":"bibr20-01423312221146606","unstructured":"Slotine J-JE, Li W (1991) Applied Nonlinear Control. 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