Optimal placement of output feedback controllers on slender civil structures at discrete locations

The dynamic responses of tall civil structures due to high winds and earthquakes are very important to the civil engineer. These dynamic responses can produce situations that can range from uncomfortable to unsafe. In recent years classical control theory has been used in civil engineering to reduce the dynamic response of tall civil structures. Many optimal control algorithms for civil structures involve full state feedback control. This method of control requires good estimates of the velocity and displacements throughout the structure. However, there are several important advantages of output feedback control: it takes less computational effort and it has the robustness of passive systems. In this paper, control algorithms are formulated for the selection of feedback gains and controller placement for flexible structures. In some cases, it is necessary to place controllers at discrete locations. For instance, for a tower there might be only several locations that are able to support the equipment needed for a feedback controller. For the placement of controllers at discrete locations in flexible structures, a method is proposed to select gains and placement simultaneously. The effectiveness of this algorithm is demonstrated for stochastic wind loads in the frequency domain.