Unified description of passive vibration control for buildings based on pole allocation applied to three‐degree‐of‐freedom model

Abstract

For a building with a passive control system, an inverse problem is formulated based on the pole allocation method in control theory. The structural system is simplified as a three-degree-of-freedom lumped-mass damped shear model. Through the selection of approximate model parameters, the simplified model can represent an earthquake-resistant structure, a base-isolated structure, an inter-storey-isolated structure, or a controlled structure with a tuned mass damper or viscous dampers. The natural frequencies and corresponding damping ratios in the three vibration modes are set as the initial control targets for the performance-based design. The newly introduced closed-form expression explains how the model parameters are related to the control target and generally proves the trade-off relationship in the passive control effect. Numerical examples demonstrate that pole allocation is arbitrary in selecting a solution. Nevertheless, only a limited solution can be applied to an actual building.