Robust regulation of a flexi-link manipulator based on a new modeling approach

A new methodology for modeling a flexible-link manipulator with an arbitrarily large (infinite) number of deflection modes is presented where dynamics representing flexibility is treated as uncertainty. The synthesis is performed based on only the certain dynamics of the manipulator. In other words, the proposed approach to modeling actually characterizes, in some sense, a reduced-order model of the system. It is shown that the uncertainty treated in this way is norm-bounded. Control of the tip position is pursued by utilizing the multi-objective H_∞ technique on the certain part of the dynamics. Robust regulation is obtained by minimizing the influence of the uncertainty on the tip position. The proposed strategy is applied to a single-link flexible arm and the simulation results verify the effectiveness of the analysis and design. Specifically, it is shown that by using the proposed scheme regulation of the tip position as achieved in a stable manner however by using the standard approach instability of the tip position occurs