Flexible manipulator state and input estimation using higher order sliding mode differentiator

This paper proposes a higher-order sliding mode differentiator to give an estimate for a highly nonlinear one-link flexible manipulator state. An Euler-Bernoulli cantilever beam models the manipulator, and the elastic movement is approximated using the assumed modes method based only on the first elastic mode. The Hamilton's principle yields the system nonlinear equations that are rearranged in the Brunovsky canonical form in order to derive the differentiator equations. This article evaluates, via the included numerical simulation results, the efficiency of the differentiator scheme to lower the estimation error and to shorten its required time to converge. It also evaluates its ability to reconstruct the unknown input to the system.