Time-delay control of structures

Time-delay causes unsynchronized application of the control forces which may not only degrade the performance of the control system but also even induce instability to the dynamic system. Time-delay control algorithm is developed in this paper to solve this practical problem. The control system is first formulated in discrete-time form. In the presence of time-delay, the motion equation of the discrete-time control system remains a difference equation which can be transformed into first-order difference equation by augmenting the state variables. Optimal time-delay control algorithm is derived based on the augmented system. The time-delay control forces are simply generated from the time-delay states multiplied by the constant feedback gain. Numerical simulation is illustrated to verify the feasibility of the proposed control algorithm. Since time-delay effect is incorporated in the mathematical model for the structural control system throughout the derivation of the proposed algorithm, system performance and dynamic stability are guaranteed.