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Vol: 55(69) No: 3 / September 2010

Extended Simulations for Convergence Stabilization of RFPT-based Adaptive Control of Underactuated Systems
József K. Tar
Institute of Intelligent Engineering Systems, Óbuda University, John von Neumann Faculty of Informatics, Bécsi út 96/B, H-1034 Budapest, Hungary, phone: +36-1-666-5543, e-mail: tar.jozsef@nik.uni-obuda.hu, web: http://www.uni-obuda.hu/
Imre J. Rudas
Institute of Intelligent Engineering Systems, Óbuda University, John von Neumann Faculty of Informatics, Bécsi út 96/B, H-1034 Budapest, Hungary, e-mail: rudas@uni-obuda.hu, web: http://www.uni-obuda.hu/
János F. Bitó
Institute of Intelligent Engineering Systems, Óbuda University, John von Neumann Faculty of Informatics, Bécsi út 96/B, H-1034 Budapest, Hungary, e-mail: bito@uni-obuda.hu, web: http://www.uni-obuda.hu/
Stefan Preitl
Department of Automation and Applied Informatics, “Politehnica” University of Timişoara, Faculty of Automation and Computers, Bd. V. Parvan 2, RO-300223 Timisoara, Romania, phone: +40-256-40-3224, e-mail: stefan.preitl@aut.upt.ro
Radu-Emil Precup
Department of Automation and Applied Informatics, “Politehnica” University of Timişoara, Faculty of Automation and Computers, Bd. V. Parvan 2, RO-300223 Timisoara, Romania, e-mail: radu.precup@aut.upt.ro, web: http://www.aut.upt.ro/~rprecup/


Keywords: adaptive control, Robust Fixed Point Transformations, parameter tuning, Cauchy sequences, simulations.

Abstract
The most sophisticated classical approaches in the adaptive control of Classical Mechanical Systems as “Adaptive Inverse Dynamics Controller (AIDC)”, “Adaptive Slotine Li Controller (ASLC)” are designed by the use of Lyapunov’s 2nd (“direct”) method. This method normally applies a quadratic Lyapunov function constructed of the tracking and parameter errors. In the lack of unknown external disturbances they normally guarantee global asymptotic stability, but require the use of complicated, slow, non-optimal tuning with high computational burden. Unknown external perturbations or the presence of not modeled, dynamically coupled subsystems can completely fob their parameter tuning. Recently an alternative problem tackling, the application of “Robust Fixed Point Transformations (RFPT)” was recommended for fully driven systems. Instead parameter tuning it operates with Cauchy sequences that are convergent only within a local basin of attraction. It can well compensate the simultaneous effects of modeling errors and unknown external disturbances. In this paper a new, more agile convergence stabilizing tuning is applied for the adaptive control of underactuated systems. The conclusions of the paper are illustrated by simulations. One of them applies common SCILAB codes with the simplest realization of Euler integration, the other uses the SCILAB SCICOS cosimulator’s professional integrator. It was found that the simple SCILAB code of very fast run can well be used for setting the proper control parameters, while the more sophisticated simulator of very long running time reveals subtle details. These different simulators lead to comparable results. Their combined application is an efficient way of designing a proper controller.

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