Journal
JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY
Volume 19, Issue 1, Pages 40-50Publisher
KOREAN SOC MECHANICAL ENGINEERS
DOI: 10.1007/BF02916103
Keywords
axially moving system; exponential stability; boundary control; hyperbolic partial differential equation; Lyapunov method
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In this paper, an active vibration control of a translating tensioned string with the use of an electro-hydraulic servo mechanism at the right boundary is investigated. The equations of motion of the string are derived by using Hamilton's principle for the systems with changing mass. The control objective is to suppress the transverse vibrations of the string via a right-boundary control. An energy-based right-boundary control law, generating a specific current input to the servo-valve, is derived. It is revealed that a time-varying boundary force, as a function of the slope of the string at the right end and a suitably chosen damping coefficient of the actuator, can successfully suppress the transverse vibrations. The exponential stability of the closed loop system is proved. The effectiveness of the proposed control law is demonstrated via simulations.
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