Noncolocated Control of a Damped String Using Time Delay

Recent research studies noncolocated control of flexible mechanical systems using time delay. The developments are limited to undamped flexible systems; damped flexible systems have not been considered. This paper investigates noncolocated vibration control of a viscously damped string using time delay. The control system is formulated in the Laplace transform domain. Based on the understanding of the system eigenstructure, a modified Bode plot of the feedback controller is introduced in a design region. The Bode plot designed, along with a specific time delay in the feedback loop, proper sensor and actuator positions, and proper control gain, guarantees stabilization of vibration of the damped string.