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In this paper a new approach to formulation of active control of structures based on energy concepts and use of Linear Quadratic Regulator (LQR) has been proposed. The suggested method eliminates the trial and error procedure in finding appropriate gain matrices in active control of structures. In this method the gain matrix is obtained by considering the energy of the structure and it remains constant for all types of earthquake input.
To show the efficiency of the proposed method, a three-story building with two active tendons in the first and third floors is considered. The proposed gain selection and other techniques reported in the literature for LQR controllers have been used to compare the response of the structure for three accelerograms. A comparison of the displacements and control forces shows that although the maximum displacement in the proposed method is negligibly more than classical LQR methods, but the control forces are considerably less than the classical methods. Comparison of the results for an earthquake with various levels of scaling also shows that the proposed method is not sensitive to the intensity of input earthquake.