SUMMARYA recently developed hybrid mass damper (HMD) system and its application to a 36-storey high-rise building with a bi-axial eccentricity, located in Tokyo, are presented. This new HMD system utilizes a gear-type pendulum and a linear actuator. Here, the gear-type pendulum is employed to make the natural period of the auxiliary mass comparatively long while minimizing the height of the device, and the linear actuator, on the other hand, ensures smooth and noiseless operation of the system. There are several special features in the control method as well; two HMD systems are applied to control the transverse-torsional coupled vibration of the building, and also variable gain feedback (VGF) control technique has been developed to fully utilize the capacity of the HMD system from weaker to stronger external excitations.Free vibration tests as well as control of wind vibrations of the building induced by the Typhoon 9810 in 1998 were used to verify the performance of the control system. It was found that the maximum and the root-mean-square acceleration responses of the building were reduced to 63 per cent and 47 per cent of the corresponding uncontrolled accelerations. Finally, the control performance of the system was conÿrmed.

SUMMARYOptimal displacement feedback control law is derived for a vibration control of a single-degree-offreedom structure with an active tuned mass damper (ATMD). Analytical expressions of the linear quadratic regulator (LQR) feedback gains for the ATMD are derived by solving the Ricatti equation straightforwardly. Based on these solutions, it is found that if the sti ness of the tuned mass damper (TMD) is calibrated to satisfy a certain condition, the control law is simpliÿed to be composed of the feedback gains only for the displacement of the structure and the velocity of the auxiliary mass stroke, which is referred to as 'optimal displacement feedback control'. The mean-square responses of the structure as well as the auxiliary mass against Gaussian white noise excitations are evaluated by solving the Lyapunov equation analytically based on the stochastic optimal control theory. Using these analytical solutions, the optimal damping parameter for the auxiliary mass is also derived. Finally, the optimal displacement feedback control law is presented.

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SUMMARYA systematic design procedure and an algorithm are devised for variable gain feedback (VGF) control of buildings with active mass damper (AMD) systems. The limit of the stroke length of the auxiliary mass, which is considered to be one of the most important physical constraints for application of AMD systems to actual structures, is studied. A set of variable feedback gains is designed as a function of a single variable that indicates a trade-off between the reduction of the building response and the amplitude of the auxiliary mass stroke, and this variable is on-line controlled to keep the amplitude of the auxiliary mass stroke constant, and within its limits.A design method of static output feedback controller for modal control of buildings with non-classical damping is also presented. Next, an efficient control method for hybrid structural control is developed, with combined use of the VGF control and the static output feedback control. It is shown through numerical examples that the proposed control method effectively adapts the control performance according to the variation in the intensity level of the external excitations in such a manner that the amplitude of the auxiliary mass stroke is kept within its limits and the control power is restrained as well. The application range of the AMD systems is thereby improved significantly.