Zero assignment in a time delayed continuous system for active vibration control

Active control of undesirable vibrations in structures, such as automobiles, rotors, air/space crafts, buildings, bridges etc., can be realized by pole and/or zero assignment. The Pole assignment problems in active control deals with reassigning a small set of unwanted eigenvalues and/or eigenvectors by using feedback control force to suitably chosen desired location, whereas the suppression of the amplitude of vibration at the desired location in the structure is known as zero assignment. Real time implementation of an active control strategy requires incorporation of the inherent time delay in the feedback loop for control gain computations. In this paper, methods for obtaining closed form solution of control gains for active zero assignment in a non-uniform distributed parameter system is presented while considering a small time delay in a feedback loop. The absorption strategy is demonstrated with examples. Effect of the time delay in control gains is studied and issues related to system stability are briefly discussed.