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By fabricating these actuators from a conductive thermoplastic elastomer, piezoresistive sensing is directly integrated. These sensor\u2010integrated actuators exhibit nonlinearities and hysteresis in their resistance change. To overcome this challenge, a novel approach that uses identified Wiener\u2013Hammerstein (WH) models is proposed to estimate the strain based on the resistance change. Three actuator types were investigated, namely, a bending actuator, a contractor, and a three degrees of freedom bending segment. By using the design freedom of additive manufacturing to set the porosity, the actuation and sensing behavior of a contracting actuator can be programmed. Furthermore, the WH models can provide strain estimation with on average high fits (83%) and low root mean square (RMS) errors (6%) for all three actuators, which outperformed linear models significantly (76.2\/9.4% fit\/RMS error). In these results, it is indicated that combining 3D\u2010printed graded porous structures and system identification can realize sensor\u2010integrated actuators that can estimate their strain but also tailor their behavior through the porosity.<\/jats:p>","DOI":"10.1002\/aisy.202300890","type":"journal-article","created":{"date-parts":[[2024,5,23]],"date-time":"2024-05-23T04:10:54Z","timestamp":1716437454000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["3D\u2010Printed Soft Proprioceptive Graded Porous Actuators with Strain Estimation by System Identification"],"prefix":"10.1002","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-9249-7906","authenticated-orcid":false,"given":"Nick","family":"Willemstein","sequence":"first","affiliation":[{"name":"Department of Biomechanical Engineering Faculty of Engineering Technology University of Twente  Drienerlolaan 5 7522 NB Enschede Netherlands"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7926-3262","authenticated-orcid":false,"given":"Herman","family":"van der Kooij","sequence":"additional","affiliation":[{"name":"Department of Biomechanical Engineering Faculty of Engineering Technology University of Twente  Drienerlolaan 5 7522 NB Enschede Netherlands"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2987-9541","authenticated-orcid":false,"given":"Ali","family":"Sadeghi","sequence":"additional","affiliation":[{"name":"Department of Biomechanical Engineering Faculty of Engineering Technology University of Twente  Drienerlolaan 5 7522 NB Enschede Netherlands"}]}],"member":"311","published-online":{"date-parts":[[2024,5,23]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1080\/11762320802557865"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1163\/156855312X626343"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/JSEN.2021.3055458"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1713450114"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1089\/soro.2015.0001"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/adfm.201303288"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1088\/1748-3182\/6\/2\/026007"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.3389\/frobt.2022.872007"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.1088\/1748-3190\/10\/3\/035003"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0090139"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1088\/1748-3190\/ac3adf"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/TMECH.2015.2493782"},{"key":"e_1_2_8_14_1","doi-asserted-by":"publisher","DOI":"10.1126\/science.aao6139"},{"key":"e_1_2_8_15_1","doi-asserted-by":"crossref","unstructured":"J.Sun J.Zhao in2020 IEEE\/RSJ Int. 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