Optimal Control Method for Seismically Excited Building Structures with Time-delay in Control

Optimal control method for seismic-excited linear structures with time delay in control is investigated in this paper. Using zero-order holder, the continuous time differential equation with time delay can be transformed into a standard discrete time form that contains no time delay in terms of two cases that the time delay is integer and noninteger times of sampling period, respectively. The continuous time performance index is used in the design of the optimal controller and it is also transformed into discrete form. Then, the optimal controller can be designed according to the classical discrete LQR method. The controller obtained contains not only current step of state feedback but also a linear combination of some former steps of control. Because the optimal controller is obtained directly from the time-delay differential equation, it is prone to guarantee the stability of the controlled structures. Furthermore, this control method is available for case of large time delay. The performance of the control method proposed and system stability are both demonstrated by numerical simulation results. Simulation results demonstrate that the control method proposed in this paper is a viable and attractive control strategy for application to seismically excited linear structures.