H^∞Control of Multi-Degree-of-Freedom Structures by Hybrid Dynamic Vibration Absorber (Experimental Consideration of Robustness and Control Performances)

This study realizes robust vibration control for a multi-degree-of-freedom structure with a hybrid dynamic vibration absorber by applying H^∞ control. The controller for the hybrid DVA is shaped in frequency domain for a four-degree-of-freedom structure in order to control the vibration of the first and second modes as the reduced order model and to stabilize the third and forth modes as the residual model. The stroke of the hybrid DVA is taken into account as a constrained function in criteria. The active DVA is also designed by using just the same frequency weighting functions as used in the design of the hybrid DVA. The vibration control performance is clarified by carrying out numerical calculations and experiments. In experiments, the H^∞ controller designed in a continuous system is digitized, and is realized in a digital signal processor. It has been made clear that even the hybrid DVA and the active DVA have the same vibration control performance for both stationary and nonstationary random excitations, while the active DVA exhibits undershoot phenomena. Also, we have confirmed that the hybrid DVA has strong robustness against parameter variations of both the mass of the primary structure and the spring and damping constants of the hybrid DVA.