Multiple Objective LQG Control of Wind-Excited Buildings

Abstract

A procedure for the design of controllers for tall buildings under wind loads is presented. It is assumed that there are constraints on the design, in terms of requiring that the root-mean square (RMS) values of certain displacements, velocities, or accelerations be within prescribed values. In addition, there are constraints on the RMS control force available. Under these conditions, the synthesis of a stabilizing controller is investigated. The solution process involves posing the search for a controller as a problem of constrained optimization for which the Lagrange multipliers are determined by an ellipsoid algorithm. These multipliers are directly related to the weights in the objective function of an associated Linear Quadratic Gaussian (LQG) optimal control problem. Thus the design problem may be seen to be one of optimal weight selection in the LQG setting. Two examples of tall buildings under wind loads, involving the design of active tuned mass dampers, are considered to illustrate the design process and to assess the performance of the controllers. Results on the performance of the designs and the control effectiveness are presented and discussed. The generality of the current procedure enables it to be applied directly to other kinds of structures like bridges, shell-like domes, cooling towers, tall chimneys, under earthquake or wind loads, and using either active mass dampers, active tendon control, or other technqiues as appropriate.