Optimization of LQR method for the active control of seismically excited structures

This paper introduces an appropriate technique to estimate the weighting matrices used in the linear quadratic regulator (LQR) method for active structural control. For this purpose, a parameter is defined to regulate the relationship between the structural energy and control force. The optimum value of the regulating parameter, is determined for single degree of freedom (SDOF) systems under seismic excitations. In addition, the suggested technique is generalized for multiple degrees of freedom (MDOF) active control systems. Numerical examples demonstrate the robustness of the proposed method for controlled buildings under a wide range of seismic excitations.