An Analysis of Convergence Properties of Finite-Time Homogeneous Controllers Through Its Implementation in a Flexible-Joint Robot

A study of the stability of interconnected homogeneous systems, affected by singular perturbations, is presented by means of the implementation of finite-time composite control in a single-link flexible-joint robot. Previous results suggest that the implementation of finite-time convergent controllers leads to the arising of chattering. Now, throughout a practical example we show that the design of a controller making the whole system homogeneous avoids the undesired chattering and recovers the ideal finite-time convergence properties. Regrettably, information of the states of the fast dynamics is not commonly available, then the proposed strategy is not applicable at all. Nevertheless, the main interest of our study lays in the expansion of the panorama for a better understanding of the causes of chattering, which contributes to the development of chattering reduction techniques, and has attracted a lot of attention, nowadays.