Unknown friction

In this paper the robust tracking problem of a robot manipulator with two degrees of mobility and with unknown friction parameter, subject to variations within a given interval, is tackled. The design of a robust nonlinear controller is proposed such that a certain accuracy of the tracking is achieved and turns out to be a linear function of the diameter of the uncertainty interval. The suggested robust controller has an nonlinear feedback structure with a gain matrix which is a solution of a corresponding Hamilton-Jacobi equation and is a time varying matrix depending on current observations. Numerical simulations of this robust controller illustrate its effectiveness even in the case of the systems with essential nonlinearities and high uncertainty intervals. The results are compared with the sliding mode type and linear state feedback controllers