H^∞Control of Multi-Degree-of-Freedom Systems Using Active Dynamic Vibration Absorber (A Criterion for Design of Frequency Weighting Function)

This paper proposes a design method using H^∞control theory concerning an active dynamic vibration absorber for multi-degree-of-freedom systems. In particular, the weighting functions of H^∞control are discussed as to which one is better. We finally propose the best weighting functions for vibration control, robust stability and stroke limits of the dynamic vibration absorber in two cases, namely, a hybrid dynamic vibration absorber and an active dynamic vibration absorber. The control object is a tower structure with four degrees of freedom, two vibration modes in the lower frequency domain as the reduced order model should be controlled, and another two higher modes as the residual model should be uncontrolled on the condition of robust stability without spillover. We have confirmed the strong robustness concerning parameter variations of the spring constant and the damping constant in the case of a hybrid dynamic vibration absorber. Also, it has been made clear that an active dynamic vibration absorber designed by H^∞control theory is effective against seismic disturbances such as the El Centro earthquake.