Paper:

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

## József K. Tar^{*}, Imre J. Rudas^{*}, and Béla Pátkai^{**}

^{*}Institute of Intelligent Engineering Systems, John von Neumann Faculty of Informatics, Budapest Tech, H-1034 Budapest, Bécsi út 96/B, Hungary

^{**}Distributed Information and Automation Lab, Department of Engineering, University of Cambridge, Mill Lane, Cambridge CB2 1RX, UK

^{th}order one because only the 4

^{th}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.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.11 No.9, pp. 1062-1071, 2007.

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