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Vol: 51(65) No: 1 / March 2006       Robust, Potential Limited Control for an Indirectly Driven Saturated System Jozsef K. Tar Institute of Intelligent Engineering Systems, Budapest Tech Polytechnical Institution, John von Neumann Faculty of Informatics, Bécsi út 96/B, H-1034 Budapest, Hungary, phone: +36-1-219-6543, e-mail: tar.jozsef@nik.bmf.hu, web: http://www.banki.hu/szervezeti_egysegek/cra/TarJozsef/tarjozsef.htm Imre J. Rudas Institute of Intelligent Engineering Systems, Budapest Tech Polytechnical Institution, John von Neumann Faculty of Informatics, Bécsi út 96/B, H-1034 Budapest, Hungary, phone: +36-1-219-6543, e-mail: rudas@bmf.hu, web: http://www.bmf.hu/rudas Stefan Preitl Department of Automation and Applied Informatics, "Politechnica" University of Timisoara, Faculty of Automation and Computers, Bd. V. Parvan 2, 300223 Timisoara, Romania, phone: +40-256-40-3229, e-mail: stefan.preitl@aut.upt.ro, web: http://www.aut.upt.ro/~spreitl Radu-Emil Precup Department of Automation and Applied Informatics, "Politechnica" University of Timisoara, Faculty of Automation and Computers, Bd. V. Parvan 2, 300223 Timisoara, Romania, phone: +40-256-40-3229, e-mail: radu.precup@aut.upt.ro, web: http://www.aut.upt.ro/~rprecup/ Keywords: robust control, variable structure / sliding mode control, chattering reduction. Abstract In this paper robust Variable Structure / Sliding Mode control of a 2 Degrees Of Freedom (DOF) Classical Mechanical System, a ball-beam system is considered. The control task has the interesting feature that only one of the DOFs of the system, i.e. the position of the ball is controlled via controlling the other axis, the tilting angle of the beam. Since the acceleration of the ball rolling on the beam depends on the gravitation and the tilting angle of the beam, and due to the phenomenology of Classical Mechanical Systems the directly controllable physical quantity is the rotational acceleration of the beam, this system is a 4th order one because it is the 4th time-derivative of the ball's position that can directly be influenced by the control. Another interesting feature of this system is its "saturation" since the rotational angle of the beam must be limited within the interval (-90°,+90°). Furthermore, due to the limitations in the centripetal and vertical acceleration the rotational speed of the beam also is limited. In the present approach a feedback control is applied in which the above limitations are achieved by the application of an angular potential and an angular velocity potential. The here applied robust control is based on the traditional concept of “error metrics”. The effects of friction at the beam’s axle are also investigated. References [1] P. A. Ioannou and J. Sun, Robust Adaptive Control, Prentice Hall, Upper Slade River, NJ, 1996. [2] J. -J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall International, Inc., Englewood Cliffs, New Jersey, 1991. [3] S.- J. Kim, S. -Y. Kim, and I. -J. Ha, “An efficient identification method for friction in single-DOF motion control systems, IEEE Transactions on Control Systems Technology, vol. 12, no. 4, pp. 555 – 563, July 2004. [4] L. Márton, Robust-Adaptive Control of Nonlinear Singlevariable Mechatronic Systems, PhD Thesis, Budapest University of Technology and Economics, Budapest, Hungary, 2005. [5] B. Armstrong-Hèlouvry, “Stick slip and control in low speed motion, “IEEE Transactions on Automatic Control”, vol. 38, no. 10, pp. 1483 – 1496, Oct. 1990. [6] C. Caundas de Wit, H. Ollson, K.J. Ã…strom and P. Lischinsky, “A new model for control of systems with friction”, IEEE Transactions on Automatic Control, vol. 40, no. 3, pp. 419 – 425 March 1995. [7] C. Caundas de Wit, “Comments on “A new model for control of systems with friction””, IEEE Transactions on Automatic Control, vol. 43, no. 8, pp. 1189 – 1190, Aug. 1998.