This study presents a complete formulation of a nonlinear controller using variable damping devices, which is used to control vibrations of building structures during large earthquakes. The control algorithm is formulated based on the idea of Lyapunov stability theory considering the inequality constraints associated with the function of the control device such that the control system is internally stable and asymptotic. The proposed nonliner control algorithm utilizes the full capacity of the control device to maximize the control effect. Because of its practicality, a boundary layer filter is introduced to the basic formulation. The control effect and basic performance are analyzed through numerical simulations on a three-story building model for an earthquake excitation. The results show that the effect of the proposed nonlinear control algorithm becomes greater for large excitations, thus verifying its applicability to building structures during large earthquakes.
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