Active/Passive Vibration Control of Continuous Systems by Zero Assignment

Vibration absorption, by passive and active means, remains a priority for the engineering science community and industries. Passive and active control techniques for implementing dynamic absorbers as well as sensors/actuators combinations are being widely studied towards the development of cost effective and practical control strategies. Still several challenging issues are affecting the application and performance of feedback vibration control applications, such as inaccessibility of the state variables, time delay, modeling errors due to discretization etc. In this research, closed form solutions for the displacement, velocity and acceleration feedback control gains, for harmonically excited axially vibrating rods, are obtained, such that the steady state vibration at any desired location of the structure can be eliminated with the least numbers of sensors and actuators. Such a vibration control strategy is known as zero assignment problems in which the knowledge of all the state variables is circumvented. Depending upon the values and characteristics of the control gains, passive and active feedback control strategies thus can be identified and realized. Results of this paper would lead to the developments in the control strategies for more complex structures, feedback control incorporating time delay and implementation of piezoelectric actuators and sensors for vibration control.