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In this paper, a modified linear-quadratic-Gaussian (MLQG) optimal control algorithm is proposed for controlling the seismic response of frame structures. Environmental loads (e.g., earthquakes) at the moment of calculation and exertion of control forces to structures, can not be measured. So these loads are not included in the conventional control algorithms, such as linear quadratic regulator and linear-quadratic-Gaussian control. Therefore the command of LQG optimal controller is merely a proportional feedback of estimated state of structure at the moment of exertion. This state approximation is performed by optimal state stimator or Kalman filter. In the proposed control algorithm, using a new variable, including control force andearthquake force, acceleration of gound motion, which is non-measurable duting exertion of control force, is considered in the state space equation of motion and also in both of Kalman Filter estimator and the optimal regulator. According to the proposed control algorithm, two ways are selected. So first command control are sum of the control force and ratios of the estimated state and measurement output of sensors, which are obtained and used in previous time step. The estimated state of system, used in the first command control, is calculated by the conventional and knownKalman Filter. but in second strategy of control, First, the Kalman Filter estimator is modified based on new state space equations, and then the estimated state of structure obtained from it, is used for calculation of command control. Numerical simulation of a seven-storey structure with active control system under several far-fault and near-fault earthquakes are performed to show effectiveness of two proposed controls on mitigation of structural responses and compare to those of a uncontrolled structure and a structure controlled with conventional control. Also sensitivity of some perforemance measures for controllers are investigated against changes of some controlling and perturbation parameters of systems or uncertainties. The alalysis results demonstrate that control performance of the proposed controllers, specially the second one, are better and also stable and robust under variations of uncertainties. So that the greatest reduction in maximum displacement (even up to 80 percent) compared to uncontrolled displacement of structure and meanwhile, very low energy consumption are attained by the second proposed control strategy.but in second strategy of control, First, the Kalman Filter estimator is modified based on new state space equations, and then the estimated state of structure obtained from it, is used for calculation of command control. Numerical simulation of a seven-storey structure with active control system under several far-fault and near-fault earthquakes are performed to show effectiveness of two proposed controls on mitigation of structural responses and compare to those of a uncontrolled structure and a structure controlled with conventional control. Also sensitivity of some perforemance measures for controllers are investigated against changes of some controlling and perturbation parameters of systems or uncertainties. The alalysis results demonstrate that control performance of the proposed controllers, specially the second one, are better and also stable and robust under variations of uncertainties. So that the greatest reduction in maximum displacement (even up to 80 percent) compared to uncontrolled displacement of structure and meanwhile, very low energy consumption are attained by the second proposed control strategy.

Keywords: LQG optimal control, Kalman filter, Active structural control, Structural dynamics, Earthquake

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