Parametric study on the optimal tuning of an inertial actuator for vibration control of a plate: Theory and experiments

This paper presents a theoretical and experimental tuning of the velocity feedback gain of a plate with an inertial actuator. The objective of the study is to analyse a direct velocity feedback control unit, which can be tuned locally and yet providing a global vibration reduction. This is achieved through the knowledge of the velocity signal and the actuator dynamics, without information on the plate dynamics. In practice, an electrical input is provided to the actuator, proportional to the local velocity of the structure, in such a way to generate active damping. The tuning is performed by maximising the power absorbed by the inertial actuator from the structure, and this is shown to be equivalent to the minimisation of the global level of vibration, estimated through the kinetic energy of the structure. Nine accelerometers have been used, and the performance for several values of different feedback gains has been investigated. Moreover, the influence of the frequency range of integration in the tuning of the velocity feedback gain is considered, and it is found experimentally that a broadband reduction up to 5 dB can be achieved, as expected from the numerical model. The absorbed power from the plate by the control unit is found to be negative below the first natural frequency of the inertial actuator, when the feedback control is implemented. This is due to the fact that, although a collocated velocity feedback is implemented, the control system is only conditionally stable because of the actuator dynamics. The performance of active control is found to reduce dramatically, if instability occurs for gains lower than the optimal one. For this reason, the work is enriched with a parametric study on the plate-actuator pair, in which the influence of the dynamic properties of the plate and the inertial actuator are investigated. The effectiveness of the active control is found to depend on the mass ratio between the actuator and the plate. In particular, for low mass ratios, the system well approximate the ideal case, in which a control force is proportional to the velocity of the plate, but for high mass ratios, a small amount of active damping can be introduced.