Nonlinear sliding mode control of seismic response of building frames

A nonlinear continuous Sliding mode control strategy is presented to contro l the response of building frames to random ground motion. The control mech anism uses an active tuned mass damper placed at the top of the building fr ame, The control law is developed by considering uncertainties present in t he control force input and in the excitations produced by the ground motion . The control forces are obtained for two cases: (1) for the state vector c ontaining the structural displacement and velocity; and (2) for the state v ector containing the parameters governing the predominant frequencies of ex citations in addition to structural displacement and velocity. Using the pr oposed control strategy, responses of a 20-story building frame are control led for a narrow band ground excitation represented by its power spectral d ensity function. The responses, thus obtained, are compared with those obta ined by the conventional linear control strategies. It is shown that the no nlinear sliding mode control performs better than the conventional linear c ontrol strategies for the reduction of displacement response. Further, cont rolled responses are found to be highly sensitive to the variation of the s liding margin and weighing matrices used to obtain the sliding surface.