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Lyapunov-Based Control of a Bridge Using Magneto-Rheological Fluid Dampers

This study focuses on the effect of semi-active magneto-rheological fluid (MRF) dampers in reducing the response of a scaled bridge structure subjected to a random loading. A fluid-mechanics based model that can characterize the nonlinear dynamic behavior of MRF dampers is employed. A state-variable model for an integrated system of a scaled, two-span bridge and two MRF dampers is established. A feedback on-off control law is employed based on Lyapunov approach that guarantees the system stability for uncertain bounded input disturbances. An output feedback Lyapunov controller is implemented in the experimental study to verify the presented method. Both the theoretical and experimental studies show that the Lyapunov based control systems can effectively reduce the relative displacement between the deck and the abutment of the bridge when subjected to various input motions. In addition, when comparing to the experiment results, it is demonstrated that the proposed analytical model can predict the response of the system, accurately.