Adaptive Control of a Flexible Varying-length Beam with a Translating Base in the 3D Space

摘要

This paper investigates a control scheme for a variable-length beam attached to a translating base under an unknown boundary disturbance. The axial beam motion is assumed pre-defined. A hybrid system consisting of a gantry, a trolley, and an expandible cantilever beam attached to the trolley is considered. Two control forces are applied to the trolley and the gantry, respectively, to position them and suppress the vibration of the beam. According to Hamilton’s principle, a nonlinear mathematical model is developed describing the dynamics of the transverse and lateral oscillations of the beam, trolley, and gantry. Based on this dynamic model, a robust adaptive control law is developed to handle the closed-loop stability of the axially moving system with unknown disturbances. Stability analysis using the Lyapunov method proves that the closed-loop system under the proposed control law is uniformly ultimately bounded. Finally, numerical simulations verify the proposed control laws’ effectiveness.