{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,25]],"date-time":"2025-10-25T12:37:18Z","timestamp":1761395838011,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2020,9,6]],"date-time":"2020-09-06T00:00:00Z","timestamp":1599350400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51675228"],"award-info":[{"award-number":["51675228"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Program of Science and Technology Development Plan of Jilin Province of China","award":["20180101052JC, 20190303020SF"],"award-info":[{"award-number":["20180101052JC, 20190303020SF"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The piezoceramic actuated stages have rate-dependent hysteresis nonlinearity, which is not simply related to the current and historical input, but also related to the frequency of the input signal, seriously affects its positioning accuracy. Consider the influence of frequency on hysteresis modeling, a rate-dependent hysteresis nonlinearity model that is based on Krasnoselskii\u2013Pokrovskii (KP) operator is proposed in this paper. A hybrid optimization algorithm of improved particle swarm optimization and cuckoo search is employed in order to identify the density function of rate-dependent KP model, avoiding the blind search process caused by the high randomness of Levy\u2019s flight in the cuckoo search algorithm, and improving the parameter identification performance. For the sake of eliminating the hysteresis characteristics, an inverse feed-forward compensation control that is based on recursive method is proposed without any additional conditions, and a feed-forward compensation controller is designed accordingly. The experimental results show that, under different frequency input signals, as compared with the classic KP model, the proposed rate-dependent KP model can accurately describe the rate-dependent hysteresis characteristics of the piezoceramic actuated stages, and the recursive inverse feed-forward compensation control method can effectively mitigate the hysteresis behaviors.<\/jats:p>","DOI":"10.3390\/s20185062","type":"journal-article","created":{"date-parts":[[2020,9,6]],"date-time":"2020-09-06T23:12:49Z","timestamp":1599433969000},"page":"5062","update-policy":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Rate Dependent Krasnoselskii-Pokrovskii Modeling and Inverse Compensation Control of Piezoceramic Actuated Stages"],"prefix":"10.3390","volume":"20","author":[{"given":"Wenjun","family":"Li","sequence":"first","affiliation":[{"name":"College of Transportation, Jilin University, Changchun 130022, China"}]},{"ORCID":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/orcid.org\/0000-0002-8629-7882","authenticated-orcid":false,"given":"Linlin","family":"Nie","sequence":"additional","affiliation":[{"name":"College of Communication Engineering, Jilin University, Changchun 130022, China"}]},{"given":"Ying","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Communication Engineering, Jilin University, Changchun 130022, China"}]},{"ORCID":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/orcid.org\/0000-0003-1664-1024","authenticated-orcid":false,"given":"Miaolei","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Communication Engineering, Jilin University, Changchun 130022, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1177\/1045389X9200300109","article-title":"A Self-Sensing Piezoelectric Actuator for Collocated Control","volume":"3","author":"Dosch","year":"1992","journal-title":"J. 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