Adaptive input shaping for single-link flexible manipulators using an algebraic identification

This work proposes an adaptive control scheme applied to single link-flexible manipulators, which combines a feedback controller of the joint angle with an adaptive input shaper updated by an algebraic non-asymptotic identification. The feedback controller is designed to guarantee trajectory tracking of the joint angle, simplifying thus the input shaper, which can be designed for the arm dynamics only. The input shaper is updated by an algebraic identification of the natural frequency corresponding to the first vibration mode of the arm. In addition, the influence of the assumptions adopted to derive the algebraic identification on the performance of the estimation is studied. Finally, the proposed adaptive control strategy is implemented in practice.