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Boundary control for a vibrating string system with bounded input. (English) Zbl 1391.93119

Summary: In this study, we deal with the control problem of a vibrating string system under the condition of restricted input and external disturbance. The major objectives are the development of a boundary vibration control scheme for globally stabilizing the string system and simultaneously for compensating the effect of the input saturation, and the design of a disturbance observer for tracking the external disturbance. To this end, a boundary control is proposed based on smooth hyperbolic function to suppress the vibration and eliminate the input restriction effect, and a disturbance observer is employed to mitigate the external disturbance. The asymptotic stability of the controlled system is demonstrated employing the extended LaSalle’s invariance principle. In order to verify the control performance of the proposed control, simulation results are presented by the choice of proper control design parameters.

MSC:

93C20 Control/observation systems governed by partial differential equations
93D20 Asymptotic stability in control theory
74H45 Vibrations in dynamical problems in solid mechanics
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