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A Hammerstein model is used to depict the rate-dependent hysteresis characteristics of piezoelectric actuators, in which a Bouc\u2013Wen model is to describe the static hysteresis characteristic, and a linear time-invariant system is to describe its rate-dependent characteristics. An inverse Bouc\u2013Wen model connected in series with the piezoelectric actuator is used to compensate the static hysteresis nonlinearity of piezoelectric actuators. Furthermore, an extended state observer\u2013based fractional order sliding-mode control is designed to deal with higher order unmodelled dynamics and inverse compensation errors. Moreover, the bounds of the estimation error of the extended state observer are estimated, and the convergence of the proposed control strategy is proved. Experimental results show that the proposed scheme can track both single and composite input signals within a certain frequency range. Compared with extended state observer\u2013based conventional sliding-mode controller, the proposed scheme has faster response time and smaller tracking error. <\/jats:p>","DOI":"10.1177\/0959651820934351","type":"journal-article","created":{"date-parts":[[2020,7,6]],"date-time":"2020-07-06T10:30:54Z","timestamp":1594031454000},"page":"39-51","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":16,"title":["Extended state observer\u2013based fractional order sliding-mode control of piezoelectric actuators"],"prefix":"10.1177","volume":"235","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3258-6494","authenticated-orcid":false,"given":"Shuyou","family":"Yu","sequence":"first","affiliation":[{"name":"Department of Control Science and Engineering, Jilin University, Changchun, China"}]},{"given":"Yangyang","family":"Feng","sequence":"additional","affiliation":[{"name":"Department of Control Science and Engineering, Jilin 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