Time-delay effect and compensation on direct output feedback controlled mass damper systems

In active control, the control force execution time delay cannot be avoided or eliminated even with present technology, which can be critical to the performance of the control system. This paper investigates the influence of time delay on the stability of an SDOF system with an optimal direct output feedback controlled mass damper. An active mass damper system can take the form of a hybrid mass damper (HMD) or a fully active mass damper (AMD) depending upon imposed design constraints resulting from space, strength and power limitations. Explicit formulas and numerical solutions to determine the maximum delay time which causes onset of system instability are obtained. The control effect of the two-DOF HMD/AMD benchmark system with and without time delay is illustrated quantitatively in a continuous-time approach. In order to fit the digital implementation of the computer-controlled system in practice, the control gains will be compensated by using their discrete-time version to overcome the degradation of control effect due to time delay.