{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T15:39:31Z","timestamp":1782229171086,"version":"3.54.5"},"reference-count":20,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2015,2,3]],"date-time":"2015-02-03T00:00:00Z","timestamp":1422921600000},"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":["61304251"],"award-info":[{"award-number":["61304251"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National High-tech R&amp;D Program of China","award":["2012AA041204"],"award-info":[{"award-number":["2012AA041204"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A modified Prandtl\u2013Ishlinskii (PI) model, referred to as a direct inverse asymmetric PI (DIAPI) model in this paper, was implemented to reduce the displacement error between a predicted model and the actual trajectory of a piezoelectric actuator which is commonly found in AFM systems. Due to the nonlinearity of the piezoelectric actuator, the standard symmetric PI model cannot precisely describe the asymmetric motion of the actuator. In order to improve the accuracy of AFM scans, two series of slope parameters were introduced in the PI model to describe both the voltage-increase-loop (trace) and  voltage-decrease-loop (retrace). A feedforward controller based on the DIAPI model was implemented to compensate hysteresis. Performance of the DIAPI model and the feedforward controller were validated by scanning micro-lenses and standard silicon grating using a custom-built AFM.<\/jats:p>","DOI":"10.3390\/s150203409","type":"journal-article","created":{"date-parts":[[2015,2,3]],"date-time":"2015-02-03T09:20:19Z","timestamp":1422955219000},"page":"3409-3425","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Improving Atomic Force Microscopy Imaging by a Direct Inverse Asymmetric PI Hysteresis Model"],"prefix":"10.3390","volume":"15","author":[{"given":"Dong","family":"Wang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peng","family":"Yu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Feifei","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ho-Yin","family":"Chan","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Kowloon, Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lei","family":"Zhou","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zaili","family":"Dong","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lianqing","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wen","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China"},{"name":"Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Kowloon, Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2015,2,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Krohs, F., Onal, C., Sitti, M., and Fatikow, S. 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