Boundary control of a flexible crane system in two‐dimensional space.

A flexible crane system with vibrating and varying cable is investigated in two‐dimensional space. Two partial differential equations and four ordinary differential equations derived by the Hamilton's principle are used to describe the dynamics of the flexible crane system. The dynamic model of the crane system considers the variation of the tension of the cable. Boundary control design is given to suppress vibrations of the flexible crane system. The Lyapunov's direct method is employed to prove the uniform ultimate boundedness of the states of the cable system. The effectiveness and performance of the proposed control schemes are depicted via numerical simulations. [ABSTRACT FROM AUTHOR]