{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T15:44:00Z","timestamp":1785426240650,"version":"3.56.0"},"reference-count":34,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T00:00:00Z","timestamp":1784851200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Innovation Program for Quantum Science and Technology","award":["2021ZD0300100"],"award-info":[{"award-number":["2021ZD0300100"]}]},{"name":"Shanghai Pilot Program for Basic Research\u2013Chinese Academy of Sciences, Shanghai Branch"},{"id":[{"id":"https:\/\/ror.org\/034t30j35","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Shanghai Science and Technology Major Project","award":["2019SHZDZX01"],"award-info":[{"award-number":["2019SHZDZX01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Low-frequency base vibration transmitted through supporting platforms can degrade the stability of precision payloads, optical instruments, and inertial measurement systems. In velocity-sensor-based active isolation platforms, displacement-related feedback states are unavailable. Direct velocity integration can drift under sensor bias, while raw lower-platform velocity feedforward can introduce measurement noise and out-of-band components. This paper proposes a dual extended state observer (ESO) reconstruction method combining equivalent-displacement feedback and lower-platform feedforward. The upper-platform ESO reconstructs feedback velocity and a bounded equivalent-displacement state, while the lower-platform ESO provides a smoothed velocity reference for feedforward compensation. The method was implemented on a plate-type active vibration isolation platform and evaluated using lower-to-upper-platform acceleration transmissibility over 0.1\u201310 Hz. Across three repeated 200 s records, the proposed ESO feedback\u2013feedforward condition achieved an integrated input\u2013output suppression ratio of 38.67\u00b10.46 dB, reduced the upper-platform output acceleration RMS to (1.31\u00b10.09)\u00d710\u22127 g, and provided a 48.92\u00b12.12 dB RMS reduction relative to the passive baseline. Direct nominal\u2013measured comparisons further showed that the reduced model captured the dominant passive and feedback-controlled dynamics. These results demonstrate that low-frequency active micro-vibration isolation can be achieved using only velocity measurements, without additional displacement sensors.<\/jats:p>","DOI":"10.3390\/s26154715","type":"journal-article","created":{"date-parts":[[2026,7,27]],"date-time":"2026-07-27T08:15:56Z","timestamp":1785140156000},"page":"4715","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Velocity-Sensor-Based Dual-ESO Reconstruction for Feedforward\u2013Feedback Low-Frequency Active Micro-Vibration Isolation"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-2845-4113","authenticated-orcid":false,"given":"Zhenyu","family":"Fan","sequence":"first","affiliation":[{"name":"Key Laboratory of Space Active Opto-Electronics Technology, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Hefei National Laboratory, Hefei 230088, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yong","family":"Xie","sequence":"additional","affiliation":[{"name":"Key Laboratory of Space Active Opto-Electronics Technology, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuzhang","family":"Zhu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Space Active Opto-Electronics Technology, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Hangzhou Institute for Advanced Study, Hangzhou 310024, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi","family":"Le","sequence":"additional","affiliation":[{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Hangzhou Institute for Advanced Study, Hangzhou 310024, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yifei","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Space Active Opto-Electronics Technology, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rui","family":"Xiu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Space Active Opto-Electronics Technology, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8114-705X","authenticated-orcid":false,"given":"Xindong","family":"Liang","sequence":"additional","affiliation":[{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Hangzhou Institute for Advanced Study, Hangzhou 310024, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Space Active Opto-Electronics Technology, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Hefei National Laboratory, Hefei 230088, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianjun","family":"Jia","sequence":"additional","affiliation":[{"name":"Key Laboratory of Space Active Opto-Electronics Technology, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Hefei National Laboratory, Hefei 230088, China"},{"name":"Hangzhou Institute for Advanced Study, Hangzhou 310024, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,7,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"100898","DOI":"10.1016\/j.paerosci.2023.100898","article-title":"Advances in spacecraft micro-vibration suppression methods","volume":"138","author":"Jiao","year":"2023","journal-title":"Prog. 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