H∞ Control via State Feedback Applied to a Three-Story Building Subjected to Excessive Vibrations

Abstract

The dynamic loads from earthquakes and winds can destroy lives, cause collapse in civil structures, and interrupt basic services provided to the population. In this scenario, structural projects must be developed to diminish the damage induced by these actions. The objective of this paper is to design a controller based on H∞ optimization via state feedback to mitigate excessive vibrations in a three-story building caused by the joint action of wind and earthquake. The building is considered a rigid structure, shear building model. All research is based on computational simulation; research and experimental results will not be addressed. A qualitative and quantitative analysis is performed. The system presents large displacements and velocities through the numerical simulations of external actions, demonstrating a chaotic behavior, thus characterizing the total collapse or in parts of the structure. With the application of the H∞ control technique via state feedback, displacements and velocities have been reduced considerably, with a reduction of more than 75% in their maximum displacement. From the results presented, it is concluded that through state feedback and H∞ controller design, the system was stabilized and its H∞ norm was minimized, thus achieving the goal of the controller by avoiding catastrophes and financial losses.