Design of robust controllers and a nonlinear observer for the control of a single-link flexible robotic manipulator

Two robust nonlinear controllers along with a nonlinear observer have been developed in this study to control the rigid and flexible motions of a single-link robotic manipulator. The controllers and the observer have been designed based on a simplified model of the arm, which only accounts for the first elastic mode of the beam. The controllers consist of a conventional sliding mode controller (CSMC) and a fuzzy-sliding mode controller (FSMC). Moreover, the robust nonlinear observer has been designed based on the sliding mode methodology. namic model, used in assessing the performances of the controllers and the observer, considers the first two elastic modes of the beam. The inclusion of the second elastic mode has been done to investigate the effects of unstructured uncertainties on the overall performance of the closed-loop system. The digital simulations have demonstrated the capability of the observer in yielding accurate estimates of the state variables in the presence of modeling uncertainties. Moreover, they served to prove the viability of using the observer to provide on-line estimates of the state variables for the computation of the control signals. The results have illustrated robust performances of the controllers and the observer in controlling the rigid and flexible motions of the manipulator in the presence of both structured and unstructured uncertainties. This was achieved irrespective of the differences in the initial conditions between the plant and the observer. rmore, the structural deformations, incurred by the beam at the onset of its movement, have been shown to be significantly reduced by fuzzy-tuning the η -control parameter. The results have demonstrated the superiority of the FSMC over the CSMC in producing less oscillatory and more accurate response of the angular displacement at the base joint, in damping out the unwanted vibrations of the beam, and in requiring significantly smaller control torques.