Decentralized Control Strategies of Adjacent Building Structures Vibration under Earthquake Excitation

Abstract

A decentralized control scheme can effectively solve the control problem of civil engineering structure vibration under earthquake. This paper takes a research into the decentralized control scheme of adjacent buildings when the earthquake happens. It combines overlapping decentralized control method and linear matrix inequality (LMI) with $H_{\infty }$ control algorithm and puts forward the overlapping decentralized $H_{\infty }$ control method. A simplified dynamical model of structural vibration control has been established considering the topology structural features of adjacent buildings. The $H_{\infty }$ control algorithm is applied into each dynamically different subsystems and can be also served as the decentralized $H_{\infty }$ controllers. Therefore, by contracting decentralized $H_{\infty }$ controllers to original state space, overlapping decentralized $H_{\infty }$ controllers are obtained. In this manner, the adjacent buildings’ structure model is analyzed in terms of simulation and calculation which provides a comprehensive insight into vibration control. The results show that the centralized control, the decentralized control, and the overlapping decentralized control, based on linear matrix inequality, can be nearly effective in cases above satisfactorily. Besides, it can also reduce the computational cost as well as increase the flexibility of controller design.