{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T12:14:35Z","timestamp":1768306475162,"version":"3.49.0"},"reference-count":25,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T00:00:00Z","timestamp":1768003200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"national natural science foundation of China","doi-asserted-by":"crossref","award":["62203085"],"award-info":[{"award-number":["62203085"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In the framework of the traditional active disturbance rejection controller (ADRC), the state error feedback utilizes estimated values from the extended state observer, which may introduce phase lag. Therefore, academic researchers have proposed a modified version called the improved linear ADRC that employs output values from the plant for state error feedback except the output value from the extended state observer. However, there is limited literature exploring the relationship between traditional linear ADRC and improved linear ADRC. To address this gap, this article establishes mathmatical relationship between traditional linear ADRC and improved linear ADRC from the generalized PID control perspective, highlighting their distinctions in the frequency domain. Compared to the traditional ADRC, the improved ADRC incorporates differential terms and offers a novel approach to realize the generalized PID control via generalized PID interpretation. And to be more specific, the improved ADRC is a new way to realize the generalized PID control by three tuned parameters, and the number of parameters of the improved ADRC is fewer than that of the generalized PID control. From the time domain, numerical simulation results demonstrate that improved ADRC exhibits superior control performance by eliminating overshoot during set value tracking processes compared to the traditional ADRC. From the disturbance rejection simulations in direct current to direct current converter (DCDC), the improved ADRC can achieve better disturbance rejection performance than the traditional ADRC. The DC bus voltage drop values of the traditional ADRC are 55.8 V and 32 V; thus, the biggest voltage drop is 55.8 V, which is 7.44 times the the improved ADRC. The voltage rise of improved ADRC can be neglected compared to the voltage rise of the traditional ADRC. From the tracking performance perspective, the time to fully reach the reference value of the traditional ADRC is about 0.3 s, and the time to fully reach the reference value of the improved ADRC is about 0.15 s.<\/jats:p>","DOI":"10.3390\/s26020466","type":"journal-article","created":{"date-parts":[[2026,1,12]],"date-time":"2026-01-12T08:20:37Z","timestamp":1768206037000},"page":"466","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Generalized Proportional\u2013Integral\u2013Derivative Interpretation of a Class of Improved Two-Degree-of-Freedom Controllers"],"prefix":"10.3390","volume":"26","author":[{"given":"Wenfei","family":"Yu","sequence":"first","affiliation":[{"name":"School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6720-5604","authenticated-orcid":false,"given":"Ping","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China"},{"name":"The Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education, Dalian University of Technology, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shang","family":"Jiang","sequence":"additional","affiliation":[{"name":"The Department of Missile and Naval Gun, Dalian Naval Academy, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0002-6601","authenticated-orcid":false,"given":"Xu","family":"Fang","sequence":"additional","affiliation":[{"name":"School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China"},{"name":"The Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education, Dalian University of Technology, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"900","DOI":"10.1109\/TIE.2008.2011621","article-title":"From PID to Active Disturbance Rejection Control","volume":"56","author":"Han","year":"2009","journal-title":"IEEE Trans. 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