Effect of time-delay on multi-degree-of-freedom actively controlled civil engineering structures

We investigate the effect of time-delay on the stability and performance of actively controlled MDOF civil engineering structures. In particular, we present a stability analysis for the critical time-delay, i.e., the minimum time-delay when the controlled structure becomes unstable, for control systems with single and multiple actuators. It is shown that the time-delay problem is more serious for structures with closely-spaced modes. The phase-shift method for time-delay compensation has been investigated in the literature. However, this method may not guarantee the stability of the closed-loop system. In this paper, we show that the closed-loop system, using the phase-shift compensated gain matrix, becomes unstable when either the magnitude of the compensated time-delay is large or the active damping added to the structure is high