{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,12]],"date-time":"2025-06-12T16:29:15Z","timestamp":1749745755057,"version":"3.38.0"},"reference-count":30,"publisher":"SAGE Publications","issue":"10","license":[{"start":{"date-parts":[[2022,1,12]],"date-time":"2022-01-12T00:00:00Z","timestamp":1641945600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52175101"],"award-info":[{"award-number":["52175101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51575328"],"award-info":[{"award-number":["51575328"]}],"id":[{"id":"10.13039\/501100001809","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":[[2022,6]]},"abstract":"<jats:p> A discrete-time-modified Bouc\u2013Wen model is proposed to describe the non-symmetrical and rate-dependent hysteresis of piezoelectric actuators for micro-vibration control applications. The modified model combines a non-symmetrical Bouc\u2013Wen model and a frequency-dependent dynamic module. A series of experiments are conducted to characterize the rate-dependent hysteresis of piezoelectric stack actuators under sinusoidal excitations at a range of 1 to 20\u2009Hz. The experimental results verify the validity of the modified model. The modified Bouc\u2013Wen model increases the complexity of Bouc\u2013Wen hysteresis nonlinear differential equation, which brings difficulties to parameter identification. To identify the parameters of Bouc\u2013Wen model, an improved hybrid differential evolution and Jaya (DE-Jaya) algorithm is introduced with a hybrid mutant operator and Jaya operator that tried to balance between convergence speed and solution accuracy. The improved algorithm is tested on benchmark functions and compared with other optimizations to prove its effectiveness. The comparison results show that hybrid DE-Jaya algorithm has better performance in convergence speed and solution accuracy. The identified discrete-time-modified Bouc\u2013Wen model is used as the secondary path in a filtered-x variable step-size affine projection algorithm (FXVSSAPA), and experimental verifications are done on a micro-vibration control platform. The experimental results show that the FXVSSAPA algorithm can converge to the steady-state error faster and verify the effectiveness of the proposed discrete-time-modified Bouc\u2013Wen model. <\/jats:p>","DOI":"10.1177\/01423312211069364","type":"journal-article","created":{"date-parts":[[2022,1,13]],"date-time":"2022-01-13T05:13:21Z","timestamp":1642050801000},"page":"1968-1978","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":8,"title":["Discrete-time rate-dependent hysteresis modeling and parameter identification of piezoelectric actuators"],"prefix":"10.1177","volume":"44","author":[{"given":"Muyao","family":"Shao","sequence":"first","affiliation":[{"name":"School of Mechatronic Engineering and Automation, Shanghai University, China"}]},{"given":"Yiru","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechatronic Engineering and Automation, Shanghai University, 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