This paper presents vibration control of bridges deck under vertical earthquake component using active variable damper, where the damping coefficient of the device is varied to achieve the most reduction in the response. Standard control theory is difficult to apply in a straightforward fashion in this case because the equation of motion includes the damping coefficient, which needs to be controlled instantaneously. The equation is nonlinear in the sense that the control uses feedback information involving the structural response itself. Transfer matrix with Wilson's-θ integration method is used to determine the temporal dynamic response. Two algorithms for selecting the damping coefficient of variable dampers are presented and compared. They include an instantaneous optimal control algorithm for controlling the damping coefficients and a displacement-acceleration domain algorithm (bang-bang control). The effects of these control algorithms on the reduction of absolute acceleration and relative displacement are examined for deck bridges. Promising results are obtained in reducing seismic responses.
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