H2H2 optimal vibration control using inertial actuators and a comparison with tuned mass dampers

The optimum resonance frequency and the damping coefficient for passive Tuned Mass Dampers (TMD) have been determined using various optimality criteria in the past. In this study an active damping method using Inertial Actuators (IAs) is considered. Closed form expressions for the H2H2 optimal control parameters that minimise the kinetic energy of the primary structure are derived. It is shown that the resonance frequency of the IA should be as low as practically possible. However, for a given resonance frequency, an optimal pair exists of the passive damping coefficient of the IA and the feedback gain. Closed form expressions for these are provided in the paper. It is noted that the amount by which the described active approach outperforms an optimally tuned TMD having the same mass depends on the squared ratio of resonance frequencies of the IA and the primary structure.