Continuous Twisting Algorithm for Third Order Systems

In this paper, two control schemes producing a continuous control signal are presented for a perturbed triple integrator: the Continuous Twisting Algorithm (3-CTA) and the Output Feedback Continuous Twisting Algorithm (3-OFCTA). The first one is a state feedback controller that ensures global finite-time stability of the origin, despite of Lipschitz, nonvanishing and matched disturbances. It provides steady state precision of fourth order of the output w.r.t. sampling step. The second one is an output feedback controller, which uses a third order Robust and Exact Differentiator as an observer. By requiring only information of the measurable output, the 3-OFCTA preserves all features of robustness, convergence and precision of the state feedback 3-CTA. Moreover, it is proven that a separation principle applies, so that the gains of the controller and of the observer can be selected independently to assure stability.