Nonlinear Sliding Mode Control of Seismic Response of Building Frames

A nonlinear continuous sliding mode control strategy is presented to control the response of building frames to random ground motion. The control mechanism uses an active tuned mass damper placed at the top of the building frame. The control law is developed by considering uncertainties present in the 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 containing the structural displacement and velocity; and (2) for the state vector containing the parameters governing the predominant frequencies of excitations in addition to structural displacement and velocity. Using the proposed control strategy, responses of a 20-story building frame are controlled for a narrow band ground excitation represented by its power spectral density function. The responses, thus obtained, are compared with those obtained by the conventional linear control strategies. It is shown that the nonlinear sliding mode control performs better than the conventional linear control strategies for the reduction of displacement response. Further, controlled responses are found to be highly sensitive to the variation of the sliding margin and weighing matrices used to obtain the sliding surface.