H∞ Norm Based Optimal Design of Vibration Control for Structural Perturbation Using Tuned Liquid Damper

In order to reduce the vibration of building structures excited by earthquakes, the mass ratio, frequency ratio, and damping ratio of a tuned liquid column damper (TLCD) are optimized. A five-story reinforced concrete structure building is selected for the numerical example with the consideration of parameter perturbation. The optimization objective is set to be the H∞ norm of the transfer function from the ground motion to the structural responses. The acquired optimal mass ratio, frequency ratio, and damping ratio of TLCD are 0.022 801, 0.909 070, and 0.098 655, respectively. With these optimal values, the robustness of the control system is verified. The results show that the control system has good robustness for structural parameter perturbation under seismic action in both frequency and time domain. The seismic reduction ratio is still kept above 7% even if the maximum system perturbation of mass, damping, and stiffness reach 30%.