This paper considers the problem of designing a state-feedback controller with both passive base isolation (PBI) and active structural control (ASC). In order to improve control performance, state-feedback gains are designed based on the linear quadratic regulator (LQR) method that optimizes a new performance index containing absolute acceleration, and inter-story drifts and velocity. Simulations on a model of an eleven degree-of-freedom shear building for four earthquake accelerograms are used to verify this method. Comparison studies show that, compared with PBI, the combination of PBI and ASC improves control performance; and this method yields better control results than the conventional ASC, which considers relative displacement and relative velocity of each story. The results are also discussed from the viewpoint of control system structure regarding the location of system zeros. In addition, the effect of weights in the LQR on control performance is discussed. A method for selecting the weights is presented by using the infinity norm of a system as a criterion to visualize their effect.
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