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Disturbance observer-based boundary control for a suspension cable system moving in the horizontal plane

This paper addresses the suppressing problem of cable vibration and the positioning control design for a suspension cable system of a helicopter with disturbances. Hamilton’s principle is applied to obtain a distributed parameter system for the suspension cable system of a helicopter. Two observers are employed to restrain the effect of unknown external disturbances. Based on the proposed disturbance observers and Lyapunov’s direct method, two boundary control laws are designed, which are provided by the actuators at the top and bottom boundaries of the suspension cable, respectively. Under the proposed control laws, the oscillation amplitude and the error between the bottom boundary payload and the desired point are proven to be uniformly ultimately bounded. Moreover, they will converge to a small neighbourhood of zero by selecting proper design parameters. Meanwhile, some sufficient conditions are provided to guarantee the validity of the proposed control laws. Finally, simulation results show the rationality and effectiveness of the control scheme developed in this paper.