Optimum semi-active control with a limited number of magneto-rheological (MR) dampers and measurement sensors has certain requirements. Most important of them is the accurate estimation of control forces developed in the MR dampers from the observations made in the structure. Therefore, the observation strategy should form an integral part of the optimization problem. The existing literature on the subject does not address this issue properly. The paper presents a computationally efficient optimization scheme for semi-active control of partially observed building frames using a limited number of MR dampers and sensors for earthquakes. The control scheme duly incorporates the locations of measurement sensors as variables into the genetic algorithm (GA) based optimization problem. A ten-storied building frame is taken as an illustrative example. The optimum control strategy utilizes two well-known control laws, namely, the linear quadratic Gaussian (LQG) with clipped optimal control and the bang-bang control to find the time histories of voltage to be applied to the MR dampers. The results of the numerical study show that the proposed scheme of sensor placement provides the optimum reduction of response with more computational efficiency. Second, optimal locations of sensors vary with the response quantities to be controlled, the nature of earthquake, and the control algorithm. Third, optimal locations of MR dampers are invariant of the response quantities to be controlled and the nature of earthquake.

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