In this paper, vibration control of flexible-link manipulators is considered. A nonlinear partial differential equation describing the dynamics of a two-link planar manipulator with a flexible forearm is derived. Thereafter, utilizing the eigenfunctions corresponding to the boundary value problem at hand, a finite-dimensional approximation of the model is given. The controller design strategy is based upon an inner-loop controller which corresponds to the rigid body motion of the manipulator taking into consideration the vibrations of the manipulator and an outer-loop controller for further vibration damping and robustness enhancement of the closed-loop dynamics to parameter variations in the system. The measurement used in the outer-loop controller is obtained through an accelerometer mounted on the flexible forearm which can be easily attained in an experimental setup. The control methodology advocated in this paper are applicable to the multi-link flexible manipulators.

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