Abstract
A modified instantaneous control algorithm with time-delay consideration for the active control of structures is developed in discrete-time formulation. The shift-invariant feedback gain matrix is obtained through an optimization process such that a prescribed instantaneous quadratic performance index is minimized. The effect of time-delay is taken into consideration by introducing a compensation scheme where the feedback gain matrix for the ideal control system is modified by the effective system matrix. It is proved that the real control system with time-delay compensation conserves the eigen-properties of the ideal control system with no time-delay. In the presence of time-delay, the equation of motion of the discrete-time control system remains a set of difference equations which makes the evaluation of the control system simple and straightforward. The feasibility of the proposed control algorithm is verified numerically through eigenvalue, frequency-domain and time-domain analyses by the tendon control of a structure. With the proposed control algorithm, the control system is still effective in spite of the presence of time-delay.
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