Discontinuous dynamic position feedback for nonlinear systems

In this work, a dynamic feedback control law based on the well known “Twisting” algorithm is under study. Dynamic compensation is added to the Twisting algorithm, in order to use position feedback only, and keep properties such as finite time stability. Moreover, linear terms are considered to improve the robustness of the algorithm. In some mechanical applications, an observer or a differentiator design is required for control purposes when the whole state space is not available for measurement. An alternative solution for this problem is proposed: a finite time stable algorithm that uses dynamic position feedback. Indeed, this new proposal does not require to measure or estimate another signal but the position of the mechanical system. In the stability analysis, strict nonsmooth Lyapunov functions and homogeneity properties are used in order to show finite time stability and robustness. Based on the proposed algorithm, a control law for a one-link pendulum affected by Coulomb friction and bounded external perturbations is designed.