Abstract
Dear editor, In this letter, the boundary tension constraint-based adaptive boundary control problem is investigated for a class of flexible string systems with unknown boundary disturbances and unknown parameters, with the purpose of suppressing transverse and longitudinal vibrations. Firstly, on the basis of the Hamiltonian principle, two partial differential equations for a transverse-longitudinal coupled string with spatiotemporally varying tension are derived. Secondly, the transverse and longitudinal adaptive boundary controllers are designed by constructing Lyapunov functions. A barrier Lyapunov function is adopted to confine the boundary tension within the constraint and disturbance observers are designed to estimate the unknown boundary disturbances. Finally, stability analysis of the closed-loop system is performed. The simulation results further illustrate the effectiveness of the proposed method.
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