H∞ robust control design of active structural vibration suppression using an active mass damper

A mathematical model of any real system is always just an approximation of the true, physical reality of the system dynamics. There are always uncertainties in the system modeling. This paper outlines a general approach to the design of an H∞ control of an active mass damper (AMD) for vibration reduction of a building with mass and stiffness uncertainties. Linear fractional transformation (LFT) is utilized in this paper for uncertainty modeling. To facilitate the computation of the H∞ controller, an efficient solution procedure based on linear matrix inequalities (LMIs) is employed. The controller uses the acceleration signal for feedback. A two-story building test-bed with an AMD is used to test the designed H∞ controller. Earthquake ground motion is introduced by a shaking table. A pair of diagonal shape memory alloy (SMA) wire braces are installed in the first floor to introduce stiffness uncertainty to the structure by controlling the temperature of the SMA wire brace. Masses are added to the structure to introduce mass uncertainty. Experiments were conducted and the results validate the effectiveness of the proposed H∞ controller in dealing with stiffness and mass uncertainties. (Some figures in this article are in colour only in the electronic version)