Robust tracking control for a class of uncertain mechanical systems

In this paper, it is proposed a control structure to solve the tracking problem in a class of uncertain mechanical systems. It is considered that the system is affected by unknown disturbances, discontinuous friction and uncertainties. The proposed control algorithm is based on the twisting control algorithm plus a nested signum term, moreover a disturbance estimator is used as feedback to the controller in order to compensate the non modelled parameters and uncertainties of the plant, also a velocity observer is proposed. Through the usage of Lyapunov tools, it is shown that the closed-loop nonlinear system is globally asymptotically stable and achieves zero steadystate position error, also, it is shown that while being asymptotically stable and homogeneous of degree q < 0, these systems approach the equilibrium point in finite time. Numerical simulations and real-time experiments carried out in a mass-spring-damper system show the performance and effectiveness of the control structure.