Global observers with finite-time and fixed-time convergence for a class of uncertain mechanical systems

Abstract

This paper proposes global sliding mode observers for a class of one-degree-of-freedom mechanical systems. For the observer design, besides the usual Coriolis and centrifugal forces, we consider uncertain dry frictions and disturbances. Moreover, the system is not required to be bounded-input bounded-state stable, rendering the observer design problem challenging. The observer design exploits the specific relationships between the inertia and Coriolis terms providing a sliding-mode observer, with global theoretically exact finite-time and fixed-time convergence to the velocities of the mechanical system. The efficiency of the proposed observer is validated through simulations on an inverted pendulum.