Time delay H ∞ control of structures under earthquake loading

Abstract

In this paper, an H ∞ control algorithm is developed to reduce the earthquake response of structures with consideration of control force execution time delay. To achieve optimal control performance and assure control system stability, the strategy to select two control parameters γ and α is extensively investigated. It was found that the decrease of γ or increase of α results in significant reduction of structural responses. To obtain the same control results, a larger α has to be selected for stiff structures than for flexible structures. In addition, in active control of a real structure, control force execution time delay cannot be avoided. Relatively small delay times not only can render the control ineffective, but also may cause system instability. In this paper, explicit formulas for the maximum allowable delay time and critical control parameters are derived for the design of a stable H ∞ control system. Some solutions are also proposed to lengthen the maximum allowable delay time.