The purpose of this study is to develop a simple and practical controller design method without modeling controlled objects. In this technique, modeling of the controlled object is not necessary and a controller is designed with an actuator model, which includes a single-degree-of-freedom virtual structure inserted between the actuator and the controlled object. The parameters of the virtual structure are determined so that indirect active vibration suppression is effectively achieved by considering the frequency transfer function from the vibration response of the controlled object to that of the virtual structure. Since the actuator model, which includes a virtually controlled object, is a simple low-order system, a controller with high control performance can be designed by traditional model-based optimal control theory. In this research, a mixed [Formula: see text] controller is designed considering both control performance and robust stability. The effectiveness of the proposed method is validated experimentally. The robustness of the controller is demonstrated by applying the same controller to various structures.

The purpose of this research is to construct a simple and practical controller design method, considering the actuator’s parameter uncertainty, without using a model of controlled objects. In this method, a controller is designed with an actuator model including a single-degree-of-freedom virtual structure inserted between actuator and controlled object, resulting in a model-free controller design. Furthermore, an [Formula: see text] control problem is defined so that the actuator’s parameter uncertainty is compensated by satisfying a robust stability condition. Because the actuator model including the virtual controlled object is a simple low-order system, and the actuator’s parameter uncertainty is considered, a controller with high robustness to the actuator’s parameter uncertainty can be designed based on traditional model-based control theory. The effectiveness of the proposed method is verified by both simulation and experiment.

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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.

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This study proposes a novel model-free vibration controller based on a virtual controlled object (VCO) considering actuator parameter uncertainty. A proof-mass actuator, which is modeled as a single-degree-of-freedom (SDOF) system, is employed. A VCO, which is defined as an SDOF system, is inserted between the actual controlled object and the actuator model. Considering frequency transfer characteristic from actual controlled object to VCO, setting appropriate parameters of the VCO realizes model-free control. A state equation to design the model-free controller is derived based on the two-degree-of-freedom (2DOF) system composed of the actuator model and the VCO. The actuator parameter uncertainty is quantitatively modeled in the 2DOF plant. Traditional mixed H2/H∞ control theory is applied for the uncertain plant to design a model-free controller with high damping performance and robustness to the actuator uncertainty. The effectiveness of the proposed controller is confirmed by vibration control experiments.

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