Generalized Linear Quadratic Gaussian Techniques for the Wind Benchmark Problem

This paper presents a comprehensive study of the stage-3 benchmark problem for response control of wind-excited tall buildings based on the linear quadratic gaussian (LQG) approach, and on its generalization, the k-cost-cumulant control method. For control design, the original nodal building model is first transformed into balanced modal space. The Hankel singular values (HSVs) and the power spectral density of the wind disturbances are calculated; and, based on them, a reduced-order model is derived by keeping the first six low-frequency modes. A balanced LQG (BLQG) controller is then determined by adopting the HSVs as a basis to choose the design weights. The main results of the paper are that the BLQG control design is able to come within 5–10% of the performance of the sample LQG controller supplied with the benchmark, but with control actions on the order of one-third less than the sample LQG, and with stability improvement features of a substantial nature over the range of stiffness perturbations specified in the benchmark. Finally, if the low authority BLQG controller is regarded as a one-cost-cumulant design, then with the appropriate use of the second-cost cumulant, the latter methodology is able to demonstrate how higher-authority controllers can give certain improvements in performance, but at the expense of significant investment in control action.