H^∞ control of multi-degree-of-freedom structure using active dynamic vibration absorber

In this study a robust controller for an active dynamic vibration absorber is designed for the purpose of vibration suppression of a four-degree-of-freedom structure by applying H^∞ control. First, we show the vibration control performance by the conventional H^∞ control theory is determined by the frequency weighting functions. The frequency response function on the stroke of the active DVA is necessary to be selected, since the active DVA and the primary structure interacts by the control force generated from the actuator. Secondly, we apply H^∞ control with pole assignment and show that the control design method can assign the poles of the controlled modes to the left of the specified vertical line on the complex plane. Their vibration control performances are clarified by numerical calculations and experiments. In experiments, the digitized H^∞ controller is realized in a digital signal processor. We have confirmed the strong robustness against parameter variations of the mass of the primary structure and the spring and the damping constants of the hybrid DVA.