Zero Assignment in Vibration: With and Without Time Delay

Abstract

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 dynamics of the structure to be controlled. In recent years, nodal control or dynamic absorption schemes are investigated in which control strategies to absorb a steady state motion of a desired location in the structure have been developed. Unlike conventional full-state feedback control which requires all the states of the system to be measured, nodal control strategy requires least numbers of sensors and actuators (depending upon the number of dynamic absorption points) for estimating the control gains and hence it may provide economical engineering solution. Nodal control problems are essentially a zero assignment problems in which a desired control is achieved by assigning zeroes to the prescribed locations in the structure. However while applying nodal control strategy by active means, 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 nodal control strategy and obtained control gains for systems with and without time delays. Some examples related to conservative and nonconservative systems as well as realistic distributed parameter systems are presented to demonstrate the nodal control strategy and the effects of time delay on control gains.