Seismic upgrade of structures using the H∞ control problem for a general system interconnection paradigm

Abstract

This paper presents a novel approach for the modification and seismic upgrading of shear-frame structures by attaining and implementing optimal changes in stiffness, changes in mass, and added damping (referred to as the structural changes). A general system interconnection paradigm is proposed and presented. The paradigm is assigned with a passive controller that consists of the structural changes and has simulated feedback on the structural response and the seismic excitation. A newly formulated optimization problem is required to satisfy constraints on maximum total story accelerations and maximum interstory drifts. The objective is to minimize the H∞ norm of a singled out response of the general system interconnection closed-loop transfer function matrix, making it a single-input single-output transfer function case. The control problem is solved by utilizing the first-order steepest descent method, an H∞ synthesis algorithm, for calculating the free parameters of a passive controller which consists of the structural changes. Their method is further enhanced for seismic design needs, by imposing boundaries on the free parameters according to the dynamic response of the structure to given ground motion ensemble. Two numerical examples of a 9-story shear-frame structure and 10-story moment resisting frame are studied. Optimal changes in mass, stiffness, and damping are obtained, and results show significant improvement in the peak dynamic response. The results indicate the efficiency of the proposed procedure that possesses the capability of attaining optimal changes in all physical characteristics of the structure (mass, stiffness, and damping) while adhering to preassigned maximum response levels.