μ-Synthesis Control of a Seismic Excited Building

Abstract

In structural earthquake engineering, the earthquake protection of structures has considerably increased these last three decades since structural control appears as an efficient way for the energy dissipation due to dynamic loads. A number of papers investigated this field proving the potential of the active control to realize a significant reduction of the structures’ response that conduct to an important rising of the human safety and seismic structures protection. However, the several control approaches applied did not automatically consider the uncertainties that exist in the realistic case. That means that there are some variations in the coefficients of the structure model as mass, stiffness or damping and even in the structure dynamics which should be tacked into account since it could affect the controller design. The motivation of this study is to perform the µ-synthesis, a robust control successfully applied in many other fields, for its ability to explicitly include all these aspects in the same time in the control design procedure. The quantification of the uncertainties as well as the interpretation of the performance requirements in appropriate weighting functions are one of the great advantages of this robust control technique. Hence, this paper presents through simulations the response of a three floors building structure subjected to a seismic excitation, modeled by Kanai Tajimi Filter, where the active component consists in an active bracing system (ABS) attached to the second floor. A robust controller is designed with considering parametric and dynamic uncertainties (structured uncertainties). The designed µ-controller demonstrates its efficiency to considerably attenuate the building response by providing a significant disturbance reduction over low control effort energy when considering the parametric and dynamic (structured) uncertainties acting simultaneously in the control system. The robustness of the controller is evaluated by varying the considered uncertainties to their worst case variation.