Robust tracking control for mechanical systems using only position measurements.

Abstract

A discontinuous control law is presented to solve the tracking problem for a class of second-order nonlinear systems and fully actuated n degrees of freedom (nDOF) mechanical systems. Moreover, the control algorithm can compensate for viscous friction, Coulomb friction, and bounded external perturbations. Only position measurements are available for feedback. In this way, this proposal does not require to measure or estimate another signal but the position of the mechanical system to achieve the tracking control objective, this is, the controller does not need velocity measurements as feedback; this constitutes the main contribution of the present approach. In the stability analysis, a strict Lyapunov function and its conditions are studied to prove asymptotic stability for second-order systems and Lagrangian systems. In a mass-spring-damper system is tested the closed-loop performance through numerical simulations. Also, simulations and real-time experiments are carried out in a (2DOF) Scara robot. As a result, the proposed discontinuous algorithm is proved to be suitable to solve the tracking problem, and also that the equilibrium points of the closed-loop system are globally stable.