Comparison of Fractional Robust- and Fixed Point Transformations- Based Adaptive Compensation of\Dynamic Friction

Abstract

The features of fractional order robust and fixed-point transformation based adaptive controllers of a ``Ball-Beam System" are compared to each other. The speciality of this task is that the position of the ball along the beam is indirectly controlled via directly controlling the other axis, the tilting angle of the beam. It is assumed that this tilting axle suffers from considerable dynamic friction mathematically approximated by the LuGre model. By neglecting the internal physics of the tilting drive this system can be modeled as a ^{mathbf}$ order one because only the ^{mathbf}$ time-derivative of the ball's position can directly be influenced by the tilting torque. The system also has saturation since the available acceleration of the ball is limited by the gravitation. It is shown that little reduction of the order of the differential equation controlling the decay of the error metrics in a Sliding Mode / Variable Structure controller considerably improves the robust controller. However, really precise solution can be obtained by the adaptive controller. These statements are illustrated and substantiated via simulation.