This study presents a synthesis method of a nonstationary optimal controller for reducing vibration of a time-varying object such as rope of elevator and crane. Moreover, from the viewpoint of wave propagation, we also propose a method of reducing vibration with controller to remove reflected waves. We deal with a rope of elavator of high-rise building as time-varying flexible system and construct the simultaneous model. For this system, controllers to reduce the vibration is designed by using weightings which depend on the velocity and displacement of rope of elevator, in addition, the reflected waves at both ends of its main-rope. The performance of reducing the vibration due to the rope-sway on a high-rise building is examined through numerical calculation. These controllers are compared with the stationary optimal controller for the case that the structure is subjected to artificial wind wave and Chi-Chi earthquake, and their usefulness are shown.
