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Hybrid control system composed of a base isolation system and a magneto-rheological damper so-called smart base isolation is one of effective semi-active control system in controlling the seismic response of structures. In this paper, a design method is proposed for designing the smart base isolation system in order to achieve an effective performance under multiple earthquakes. The base mass, the base stiffness and the weighting parameter of H₂/linear quadratic Gaussian control algorithm, which is used to determine the desired control force, have been considered as the design variables and different earthquake records have been considered as design earthquakes. First, the optimum values of these variables under each of the considered earthquakes have been determined by using the genetic algorithm and then, an optimum control system has been designed with multiple earthquakes-based design approach. The defined design objective is minimizing the peak base drift while the peak inter-story drift has been constrained. For numerical simulation, smart base isolation system is designed for controlling a four-story shear frame. The results show that when the control system designed for a specific earthquake is subjected to another earthquake, difference between the performance of this control system and the optimal case under that earthquake is considerable. Hence, the specific earthquake-based design approach is an inappropriate design procedure for smart base isolation. Also, it has been found that control system designed based on multiple earthquakes-based design approach shows effective performance in controlling the response of structure under a wide range of earthquakes.

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