Instantaneous Optimal Control of Building Frames

Abstract

A control algorithm based on the instantaneous optimal closed‐loop control technique is presented for the control of buildings subjected to earthquake excitations. It is proposed that the building frames be modeled using finite elements, with a two‐node six‐degree‐of‐freedom planar frame element as a basic tool for the example analysis. The instantaneous optimal closed‐loop control algorithm is derived in second‐order form using the Newmark integration scheme. The weighting matrices are so chosen that the instantaneous control technique is unconditionally stable. Examples of the optimal control of a three‐bay 10‐story steel building frame are illustrated using base isolators and active tendons. The input excitations chosen are based on the NS component of the ground acceleration record of the 1940 El Centro earthquake. Results on the reduction of the dynamic response and the control effectiveness of the passive, active, and hybrid control designs are presented and discussed.