Closed form solution for alongwind response of actively controlled tall buildings with LQG controllers

This paper derives a closed form solution for wind-induced response of actively controlled tall buildings with linear quadratic Gaussian (LQG) controllers to facilitate the real application of modern active control theory. The wind excitation acting on a tall building is decomposed into a number of component wind excitations in which any two component wind excitations are uncorrelated and each component wind excitation can be obtained as the output of a shaping filter with unit intensity white noise input. After the equations of motion of the system are established, the closed form solution for wind response of the system is then derived by combining the complex modal superposition method together with the pseudo-excitation method and the residue theorem. With the derived closed form solution, extensive parametric studies can be performed on wind-excited tall buildings with LQG controllers to seek beneficial weighting matrices so that the maximum wind response reduction can be achieved with reasonable control forces. The results from a numerical example demonstrate that if weighting matrices are selected appropriately, the modal damping ratios of the system can be significantly increased and the alongwind response of the building can be considerably reduced.