A new active control performance index for vibration control of three-dimensional structures

Remarkable results have been reported about conventional active control algorithms during the last 30 years, but nearly all the existing literature considers 2-dimensional in plane structures to implement and verify the active control algorithms. To simulate the behavior of real buildings more accurately, more realistic and complex models should be used in the performance evaluation and design of controllers and their control algorithms. This paper presents a new performance index for active vibration control of three-dimensional structures. To analytically validate the proposed performance index, a six story three-dimensional structure is considered as an example with a fully active tendon controller system implemented in one direction of the building. Tier building formulation is used for three-dimensional dynamic analysis. The building is modeled as a structure composed of members connected by a rigid floor diaphragm such that it has three degrees of freedom at each floor, i.e., lateral displacements in two perpendicular directions and a rotation with respect to a vertical axis for the third dimension. The performance of the building with the active tendons controlled using a classical linear optimal control algorithm is compared to the performance of the proposed control algorithm under several far-fault and near-fault earthquakes using several performance measures. Comparison between the computational results shows that the proposed algorithm outperforms the performance of the classical linear optimal control algorithm for the actively controlled building.