Closed Form Control Gains for Zero Assignment in the Time Delayed System

Control of the vibrating structures is desirable in various engineering applications for preventing fatigue and failure. It can be achieved by passive means using dynamic absorbers or by active means using sensors and actuators. In some cases, it is also not practical to apply a desirable control force in those locations at which the dynamics of the structure are to be controlled. In recent years, dynamic absorption schemes are investigated in which control strategies that absorb a steady state motion of a desired location in the structure have been developed. Such a vibration control strategy is termed as zero assignment. Unlike conventional full-state feedback control, which requires all the states of the system to be measured, zero assignment requires least numbers of sensors and actuators (depending on the number of dynamic absorption points) for estimating the control gains and, hence, it may provide economical engineering solution. However, while applying control strategy by active zero assignment, small time delay from the sensors and actuators in the feedback loop is unavoidable and they influence the control gains as well as the stability of the system. In this paper, we have developed vibration control strategy by active zero assignment and obtained closed form control gains for systems with and without time delays by using truncated and full Taylor series expansion. Some examples related to conservative and nonconservative systems as well as realistic distributed parameter systems are presented to demonstrate the active dynamic absorption and the effects of time delay on control gains. The effect of delay in the stability of the controlled system is also summarized.