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Vol: 52(66) No: 1 / March 2007 Sector Sliding Mode Design for a Servo System Peter Korondi Dept. of Automation and Appl. Informatics, Budapest Univ. of Technology and Economics, PO Box: 91, H-1521 Budapest, Hungary, phone: (+36) 1-463 2184, e-mail: Korondi@elektro.get.bme.hu, web: http://www.aut.bme.hu/Portal/Munkatarsak.aspx Keywords: sliding mode control, sliding sector design Abstract Motion control has been a fruitful ground for applying Variable Structure Systems (VSS) theory. This paper provides an assessment of the state of the art of the relevant theoretical results for sliding mode control. The design of a sliding-mode controller consists of three main steps. First is the design of the sliding surface, the second step is the design the control law which holds the system trajectory on the sliding surface, and the third and key step is the chattering-free implementation. The main contribution of that paper is a new method for surface sector design to reduce the chattering. Experimental results of a DSP-controlled single-degree-of-freedom motion-control system are presented. References [1] V. I. Utkin, “Variable structure systems with sliding mode”, IEEE Transactions on Automatic Control, vol. AC-22, no. 2, pp. 212-222, 1977. [2] K-K. D. Young, “Controller design for manipulator using theory of variable structure systems”, IEEE Transaction on Systems, Man, and Cybernetics, Vol. SMC-8, February 1978, pp. 101-109. [3] A. Sabanovic and D. Izosimov, “Application of sliding modes to induction motor control”, IEEE Trans. Industrial Appl., vol. IA-17, no.1, pp. 41-49, 1981. [4] F. Harashima, H. Hashimoto and S. Kondo, “MOSFET Converter-fed position servo system with sliding mode control”, IEEE Trans. Industrial Electronics, vol. IE-32, no.3, pp. 238-244, 1986. [5] K. D. Young (editor), “Variable Structure Control for Robotics and Aerospace Applications”, pp. 157-172, Elsevier Science Publishers, 1993. [6] H. Hashimoto, K. Maruyama and F. Harashima, “A microprocessor based robot manipulator control with sliding mode”, IEEE Transactions on Industrial Electronics, vol. IE-34, no.1, pp. 11-18, 1987. [7] H. Hashimoto and Y. Ishikawa, “Robust digital sliding mode applied to motion control”, Proceedings of Japan/USA Symposium on Flexible Automation ASME, 1992, vol. l.1. pp. 25-30. [8] G. D. Andreescu, A. Popa and A. Spilca, “Two sliding mode based observers for sensorless control of PMSM”, Electr. Pow. Compo. Sys., vol. 30, pp. 121-133, Feb. 2002. [9] J. Vittek and S. J. Dodds, Forced Dynamics Control of Electric Drives, EDIS – Publishing Centre of Zilina University, Zilina, June 2003. [10] P. Korondi, H. Hashimoto and V. I. Utkin, “Direct torsion control of flexible shaft based on an observer based discrete-time sliding Mode”, IEEE Trans. on Industrial Electronics, vol. IE, no.2, pp. 291-296, 1998. [11] S. Boyd, L. E. Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Philadelphia PA: SIAM, 1994. [12] P. Gahinet, A. Nemirovski, A. J. Laub and M. Chilali, LMI Control Toolbox. The MathWorks, Inc., 1995. [13] C. W. Scherer and S. Weiland, Linear Matrix Iequalities in Control, ser. DISC course lecture notes, Technical University of Eindhoven, 2000. [14] P. Baranyi, “TP model transformation as a way to LMI based controller design,” IEEE Transactions on Industrial Electronics, vol. 51, no. 2, pp. 387–400, April 2004. [15] Z. Petres, B. Reskó and P. Baranyi, “TP model transformation based control of the TORA system”, Production Systems and Information Engineering, vol. 2, pp. 159–175, 2004. [16] A. G. Luk\'uyanov and V. I. Utkin, “Method of reducing equations of dynamic systems to regular form”, Automation and Remote Control, vol. 42, P.1, pp.413-420, 1981. [17] P. Korondi and H. Hashimoto, “Sliding mode design for motion control”, in Studies in Applied Electromagnetics and Mechanics, vol. 16, 12 pp., IOS Press, 2000. [18] V. I. Utkin, Variable Structure Control and Optimization. Berlin, Heidelberg, New York: Springer-Verlag, 1992. [19] K. Furuta, “Sliding mode control of a discrete system,” Systems and Control Letters, vol. 14, pp. 145-152, 1990. [20] V. I. Utkin and S.V. Dracunov, “On discrete-time sliding modes”, Preprints of IFAC Conference on Nonlinear Control, Capri, Italy, 1989. [21] P. Korondi, J-X. Xu and H. Hashimoto, “Sector sliding mode controller for motion control”, Proceedings of 8th Conference on Power Electronics and Motion Control, vol. 5, pp.5-254-5-259, 1998. |