The design of passive energy dissipation systems, referred to as passive dampers, involves the determination of the required capacity of each damper installed at selected locations. Generally, dampers with an identical capacity are installed in various story units of a building. However, installing identical dampers in various story units does not achieve the optimal performance for the building and it may result in a conservative and more expensive design. In this paper, two design methods, based on the concepts of linear quadratic regulator (LQR) control theories, are presented for the design of the capacity of passive dampers. For most of the passive dampers, the force applied to the structure depends only on the displacement and velocity across the damper. From the standpoint of control theories, the passive control force depends only on the local measurements of the displacement (i.e., drift across the damper) and velocity. This type of controller is referred to as the decentralized controller. Consequently, LQR control theories for the design of active controllers are modified and applied to the design of passive dampers. Advantages of the proposed methods for different types of passive dampers are demonstrated through numerical simulations.
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