Discrete Time-delay Optimal Control of Structures under Seismic Excitations using the Balanced Reduction Scheme

Abstract

The time-delay discrete-time equations are derived directly from the differential vibration equations for structures in state space, with discrete parameters obtained via the precise integration method. Then a state vector expansion method is used to transform these equations into ones which do not contain time-delay terms explicitly. Next, the order of this system is substantially reduced by using the balanced reduction method to form a dominant subsystem which is based on the eigenmodes of the state subspace with highest controllability. The controllers are then designed by the discrete time-delay optimal control theory, which contains the control terms not only of the current state but also of a few previous states, in order to reflect the effect of time delays. By using the proposed method, the order of the controller is very substantially reduced without causing any essential difference in the control effect. A numerical example for a shear-type building is presented and it shows the effectiveness of the proposed method even when time delays are quite large.

Keywords

Precise integration optimal control.

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