{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T18:09:35Z","timestamp":1788199775885,"version":"build-2803163510"},"reference-count":26,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T00:00:00Z","timestamp":1777420800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Country Science and Technology Cooperation Project under the Shanxi Provincial Science and Technology Cooperation and Exchange Special Program","award":["202304041101007"],"award-info":[{"award-number":["202304041101007"]}]},{"name":"National Key Research and Development Program of China - Sub-project on Integration Technology of Laser Interferometry System and Inertial Sensors","award":["2024YFC2207100"],"award-info":[{"award-number":["2024YFC2207100"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Low-frequency seismic disturbances significantly limit the performance of precision engineering systems and active vibration isolation platforms. Model predictive control (MPC) is widely applied in such systems due to its ability to handle multi-variable dynamics and constraints. However, its performance strongly depends on model accuracy. To address this issue, this paper proposes a multilayer perceptron-enhanced model predictive control (MLP-MPC) framework for active vibration isolation. In the proposed approach, a multilayer perceptron (MLP) is trained offline to learn the mapping between the current system state and the free-response term in the MPC prediction equation. During online implementation, the trained MLP replaces the model-based free-response calculation while preserving the original quadratic programming structure of conventional MPC. The proposed method is evaluated on a single-degree-of-freedom active vibration isolation system under low-frequency sinusoidal excitation and measured seismic disturbances. The simulation results show that MLP-MPC achieves reduced running RMS tracking error and lower moving-window RMS error compared with conventional MPC and Proportional\u2013Integral\u2013Derivative (PID) control. The results suggest that integrating data-driven free-response estimation into predictive control provides a practical approach to enhancing the performance of low-frequency vibration suppression while maintaining computational feasibility.<\/jats:p>","DOI":"10.3390\/s26092770","type":"journal-article","created":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T12:31:56Z","timestamp":1777465916000},"page":"2770","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An Intelligent Model Predictive Control Framework for Low-Frequency Seismic Vibration Suppression in Active Isolation Systems"],"prefix":"10.3390","volume":"26","author":[{"given":"Qiuxia","family":"Fan","sequence":"first","affiliation":[{"name":"School of Automation and Software Engineering, Shanxi University, Taiyuan 030006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruidong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Automation and Software Engineering, Shanxi University, Taiyuan 030006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zefeng","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Automation and Software Engineering, Shanxi University, Taiyuan 030006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8843-1857","authenticated-orcid":false,"given":"Qianqian","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automation and Software Engineering, Shanxi University, Taiyuan 030006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chan","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Automation and Software Engineering, Shanxi University, Taiyuan 030006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Miaoshuo","family":"Li","sequence":"additional","affiliation":[{"name":"School of Automation and Software Engineering, Shanxi University, Taiyuan 030006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"061102","DOI":"10.1103\/PhysRevLett.116.061102","article-title":"Observation of Gravitational Waves from a Binary Black Hole Merger","volume":"116","author":"Abbott","year":"2016","journal-title":"Phys. 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