{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T03:22:45Z","timestamp":1767842565784,"version":"3.49.0"},"reference-count":42,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,2,24]],"date-time":"2021-02-24T00:00:00Z","timestamp":1614124800000},"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":"publisher","award":["51975234"],"award-info":[{"award-number":["51975234"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, a fractional-order active disturbance rejection controller (FOADRC), combining a fractional-order proportional derivative (FOPD) controller and an extended state observer (ESO), is proposed for a permanent magnet synchronous motor (PMSM) speed servo system. The global stable region in the parameter (Kp, Kd, \u03bc)-space corresponding to the observer bandwidth \u03c9o can be obtained by D-decomposition method. To achieve a satisfied tracking and anti-load disturbance performance, an optimal ADRC tuning strategy is proposed. This tuning strategy is applicable to both FOADRC and integer-order active disturbance rejection controller (IOADRC). The tuning method not only meets user-specified frequency-domain indicators but also achieves a time-domain performance index. Simulation and experimental results demonstrate that the proposed FOADRC achieves better speed tracking, and more robustness to external disturbance performances than traditional IOADRC and typical Proportional-Integral-Derivative (PID) controller. For example, the JITAE for speed tracking of the designed FOADRC are less than 52.59% and 55.36% of the JITAE of IOADRC and PID controller, respectively. Besides, the JITAE for anti-load disturbance of the designed FOADRC are less than 17.11% and 52.50% of the JITAE of IOADRC and PID controller, respectively.<\/jats:p>","DOI":"10.3390\/e23030262","type":"journal-article","created":{"date-parts":[[2021,2,24]],"date-time":"2021-02-24T20:53:21Z","timestamp":1614200001000},"page":"262","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Optimal Fractional-Order Active Disturbance Rejection Controller Design for PMSM Speed Servo System"],"prefix":"10.3390","volume":"23","author":[{"given":"Pengchong","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430070, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7006-2122","authenticated-orcid":false,"given":"Ying","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430070, China"}]},{"given":"Yibing","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430070, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7422-5988","authenticated-orcid":false,"given":"Yangquan","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Engineering, University of California, 5200 N.Lake Road, Merced, CA 95343, USA"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,24]]},"reference":[{"key":"ref_1","unstructured":"Krishnan, R. 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