H a drift control of time-delayed seismic structures

In this paper, an optimal H (a) control algorithm was applied to the design of an active tendon system installed at the first story of a multi-story building to reduce its interstory drift due to earthquake excitations. To achieve optimal control performance and to guarantee the stability of the control system, an optimum strategy to select control parameters gamma and alpha was developed. Analytical expressions of the upper and the lower bounds of gamma and alpha were obtained for a single degree-of-freedom system with state feedback control. The selection ranges for both gamma and alpha are graphically defined so that the controlled system is always stable and the control performance is better than by the conventional LQR control algorithm. Numerical results from a controlled three-story building under real earthquake excitations demonstrate that the peak first interstory drift can be significantly reduced with maximum control force around 10% of the building weight. An optimum design flow chart was provided. In addition, for a time-delayed structure, this study gave explicit formulae to calculate the critical values of gamma and alpha. The system stability and control performance can thus be guaranteed even with time delay.