Design of Active Boundary Control to Suppress Vibrations in String

Abstract

Strings are commonly used in engineering structures but are highly susceptible to vibrations due to their low structural stiffness and damping. Suppressing these vibrations poses a significant challenge, as existing tools and technologies are limited. This study investigates the design of an active boundary control strategy to suppress the vibrations in a string. To achieve this, a dynamic model equipped with a displacement-type actuator and multiple displacement sensors was considered. A simple vibration control algorithm was proposed by designing a dynamic model with one degree of freedom. And the stability of the proposed algorithm was verified theoretically using this model. Based on the result for the simple case, a multi-input-multi-output control algorithm was designed in modal space. The numerical results show that the suppression of the vibration in the first three natural modes of the string using one boundary actuator, three displacement sensors, and the proposed control method was successful. Also, an experimental test bed was constructed to verify the practical validity of the proposed control method. The experimental results also demonstrate that the proposed control method can effectively suppress the three natural modes of string vibration. The effectiveness of the proposed control method has been verified both theoretically and experimentally.