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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. References [1] A. M. Lyapunov, “A general task about the stability of motion” (in Russian), PhD Thesis, 1892. [2] A. M. Lyapunov, Stability of motion, Academic Press, New-York and London: 1966. [3] J.-J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall International, Inc., Englewood Cliffs, New Jersey, 1991. [4] J. K. Tar, I. J. Rudas, and J. Gáti, “Improvements of the Adaptive Slotine & Li Controller – Comparative Analysis with Solutions Using Local Robust Fixed Point Transformations,” Proc. 14th International Conference on Applied Mathematics (MATH’09), Puerto De La Cruz, Canary Islands, Spain, pp. 305–311, 2009. [5] J. K Tar, J. F. Bitó, I. J. Rudas, S. Preitl and R.–E. Precup, “An SVD Based Modification of the Adaptive Inverse Dynamics Controller,” Proc. 5th International Symposium on Applied Computational Intelligence and Informatics (SACI 2009), Timişoara, Romania, 2009, pp. 193–198, 2009. [6] J. K. Tar, I. J. Rudas, Gy. Hermann, J. F. Bitó, and J.A. Tenreiro Machado, “On the Robustness of the Slotine-Li and the FPT/SVD-based Adaptive Controllers,” Transactions on Systems and Control, vol. 3, no. 9, pp. 686–700, 2009. [7] J. K. Tar, I. J. Rudas, and K. R. Kozłowski, “Fixed Point Transformations-Based Approach in Adaptive Control of Smooth Systems”, in Lecture Notes in Control and Information Sciences 360 (Eds.: M. Thoma and M. Morari), Robot Motion and Control 2007 (Ed.: Krzysztof R. Kozłowski), Springer Verlag London Ltd., pp. 157–166, 2007. [8] J. K. Tar, J. F. Bitó, I. J. Rudas, K. R. Kozłowski, and J. A. Tenreiro Machado, “Possible Adaptive Control by Tangent Hyperbolic Fixed Point Transformations Used for Controlling the Φ6-Type Van der Pol Oscillator,” Proc. 6th IEEE International Conference on Computational Cybernetics (ICCC 2008), Stará Lesná, Slovakia, pp. 15–20, 2008. [9] T. Roska, “Development of Kilo Real-time Frame Rate TeraOPS Computational Capacity Topographic Microprocessors,” Plenary Lecture at the 10th International Conference on Advanced Robotics (ICAR 2001), Budapest, Hungary, August 22–25, 2001. [10] J. K. Tar, “Robust Fixed Point Transformations Based Adaptive Control of an Electrostatic Microactuator,” Acta Electrotechnica et Informatica, vol. 10, no. 1, pp. 18–23, 2010. [11] C. C. Nguyen, S. S. Antrazi, Z.-L. Zhou, and C. E. Campbell Jr, “Adaptive control of a Stewart platform-based manipulator,” Journal of Robotic Systems, vol. 10, no. 5, pp. 657-687, 1993. [12] J. Somló, B. Lantos, and P. T. Cát, Advanced Robot Control, Akadémiai Kiadó, Budapest, Hungary, 2002. [13] K. Hosseini-Suny, H. Momeni, and F. Janabi-Sharifi, “Model Reference Adaptive Control Design for a Teleoperation System with Output Prediction”, J Intell Robot Syst, DOI 10.1007/s10846-010-9400-4, pp. 1-21, 2010. [14] J. K. Tar, J. F. Bitó, and I. J. Rudas, “Replacement of Lyapunov\'s Direct Method in Model Reference Adaptive Control with Robust Fixed Point Transformations,” Proc. of 14th IEEE International Conference on Intelligent Engineering Systems (INES 2010), Las Palmas of Gran Canaria, Spain, pp. 231-235, 2010. [15] J. K. Tar, I. J. Rudas, J. F. Bitó, K. R. Kozłowski, and C. Pozna, “A Novel Approach to the Model Reference Adaptive Control of MIMO Systems,” Proc. of IEEE 2010 Robotics in Alpe-Adria-Danube Region (RAAD 2010) Conference, Budapest, Hungary, 2010. [16] J. K. Tar, J. F. Bitó, I. Gergely, and L. Nádai, “Possible Improvement of the Operation of Vehicles Driven by Omnidirectional Wheels,” Proc. of 4th International Symposium on Computational Intelligence and Intelligent Informatics (ISCIII 2009), Egypt, pp. 63–68, 2009. [17] J. K. Tar, I. J. Rudas, J. F. Bitó, S. Preitl, and R.-E. Precup, “Convergence stabilization by parameter tuning in Robust Fixed Point Transformation based adaptive control of underactuated MIMO systems,”, Proc. International Joint Conference on Computational Cybernetics and Technical Informatics (ICCC CONTI 2010), Timisoara, Romania, pp. 407-412, 2010. |