The random vibration control strategy for multi-degree-of-freedom electro-hydraulic shaking tables (multi-DOF EHSTs) is a critical technology for engineering environmental simulation testing. Traditional three-variable control (TVC) commonly used in multi-DOF EHSTs fails to account for coupling effects and disturbances. Multi-DOF iterative learning control (ILC) can compensate for coupling effects. However, traditional multi-DOF ILC fails to account for disturbances and struggles to ensure monotonic decay of error. In this paper, frequency-domain-based iterative learning control (FILC) is proposed for the multi-DOF EHST. The proposed FILC can compensate for the coupling between the DOFs and mitigate the impact of periodic disturbances, while simultaneously achieving monotonic decay of iterative waveform tracking errors. Experimental results from a 2-DOF EHST demonstrate that the FILC algorithm significantly improves waveform tracking accuracy of random periodic acceleration signals compared to both TVC and traditional ILC.
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