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Purpose This study improves the robustness of the model-free controller based on a virtual structure. Additionally, the adverse interference between the proof-mass actuator resonance and a controlled object is investigated as it is not clarified in the previous studies. Methods and Results A virtual structure modeled as a SDOF system was inserted between the actuator and the actual controlled object. This achieved the indirect damping of the actual controlled object and model-free control. Vibration control simulations were conducted for various finite element models with a model-free    $${H}_{\infty }$$  H ∞ controller based on a virtual structure. The results demonstrate that the actuator resonance adversely affects the stability of the control system when the controlled object has a mode whose natural frequency is too close to that of the actuator. Therefore, a notch filter was applied to the model-free    $${H}_{\infty }$$  H ∞ controller design approach to suppress the resonance without affecting the damping performance. The improved controller with notch filter is more robust to the resonance of the actuator than the previous one. Conclusions The resonance of the proof-mass actuator adversely affects the stability of the control system composed of the previous model-free    $${H}_{\infty }$$  H ∞ controller when the low-order vibration mode of the actual controlled object is too close to the natural frequency of the actuator. Introducing a notch filter into the model-free approach based on a virtual structure effectively reduces the negative impact due to the resonance of the actuator and improves the robustness of the control system.

Stability Improvement of Model-Free Control Based on a Virtual Structure Against the Resonance of a Proof-Mass Actuator