Optimal Response-Related Weighting Matrices to Control Semi-Active Base Isolation Systems

In this paper, the performance of a semi-active base isolation system, including a magneto-rheological (MR) damper and base isolation system for different combinations of response-related weighting matrices, has been studied. To consider all possible sets of response-related matrices, seven H2/linear quadratic Gaussian (LQG) control designs have been considered. For a numerical simulation, a six-story shear frame has been subjected to different earthquakes, and the performance of the control system has been evaluated. The results show that the optimal force-related weighting parameter is identical for different sets of response-related weighting matrices and is also independent of earthquake records when minimizing the maximum base drift is considered as the design objective. Also, the results of different sets of response-related weighting matrices show that the optimal sets for the design objective of minimizing the maximum base drift are the velocity and displacement/velocity-related weighting matrices.