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Incorporating the MMR into a rotary generator significantly enhances the energy recovery efficiency of a vibration energy-harvesting system. This study develops an energy-harvesting system featuring an MMR in a permanent magnet synchronous motor (PMSM) electromagnetic damper, leveraging electromagnetic conduction to recover vibration energy. Utilizing the electromechanical analogy principle, an equivalent circuit model for the energy-harvesting system is developed, and a direct control method for the electromagnetic torque of the PMSM is proposed to achieve maximum power point tracking control. Considering the motion of MMR constitutes a state-dependent switching system, a \u201ctime-scale transformation\u201d method is designed to reconfigure the switching system with uncertain timings into one with fixed equivalent switching moments. In addition, an iterative optimization controller is proposed to ensure that the system operates at its maximum power point. Hardware-in-the-loop experiments are conducted to validate the effectiveness of the proposed iterative optimal control-based maximum power point tracking scheme.<\/jats:p>","DOI":"10.1177\/01423312251333172","type":"journal-article","created":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T02:28:39Z","timestamp":1750818519000},"page":"2077-2089","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["An iterative optimal control-based energy-harvesting scheme for PMSM electromagnetic damper with mechanical motion rectification"],"prefix":"10.1177","volume":"48","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-3941-4706","authenticated-orcid":false,"given":"Kaixin","family":"Cheng","sequence":"first","affiliation":[{"name":"School of Electrical Engineering, Dalian University of Technology, 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