In this paper, stabilization of an Active Magnetic Bearing (AMB) system with varying rotor speed using Sliding Mode Control (SMC) technique is considered. The gyroscopic effect inherited in the system is proportional to rotor speed in which this nonlinearity effect causes high system instability as the rotor speed increases. Also, transformation of the AMB dynamic model into a new class of uncertain system shows that this gyroscopic effect lies in the mismatched part of the system matrix. Moreover, the current gain parameter is allowed to be varied in a known bound as an uncertainty in the input matrix. SMC design method is proposed in which the sufficient condition that guarantees the global exponential stability of the reduced-order system is represented in Linear Matrix Inequality (LMI). Then, a new chattering-free control law is established such that the system states are driven to reach the switching surface and stay on it thereafter. The performance of the controller applied to the AMB model is demonstrated through simulation works under various system conditions.<\/p>\r\n","references":"[1] J. Y. Hung, W. B. Gao, and J. C. Hung, \"Variable Structure control: A\r\nSurvey,\" IEEE Trans. Industrial. Electronics, vol. 40, no. 1, pp. 2-22.,\r\n1993.\r\n[2] S. Spurgeon, and C. Edwards, Sliding Mode Control: Theory and\r\nApplications. London: Taylor and Francis, 1998.\r\n[3] X. Li, and R. A. DeCarlo, \"Robust Sliding Mode Control of Uncertain\r\nTime Delay Systems,\" Int. J. Control, vol. 76, no. 13, pp. 1296-1305,\r\n2003.\r\n[4] X. Z. Dong, \"State Feedback Sliding Mode Control for A Class of\r\nSystems with Mismatched Uncertainties and Disturbance,\" in Proc. 25th\r\nChinese Control Conference, Heilongjiang, 2006, pp. 938-942.\r\n[5] M. N. Ahmad, J. H. S. Osman, and M. R. A. Ghani, \"Proportional-\r\nIntegral Sliding Mode Tracking Controller with Application to a Robot\r\nManipulator,\" in 7th Conf. on Contr., Auto., Rob and Sys., ICARCV,\r\nSingapore, 2003, pp. 863-868.\r\n[6] Y. M. Sam, and J. H. S. Osman, \"Modeling and Control of Active\r\nSuspension System Using Proportional Integral Sliding Mode\r\nApproach,\" Asian Jour. Contr., vol. 7, no. 2, pp. 91-98, 2005.\r\n[7] J. H. Lee, P.E. Allaire, G. Tao, J. A. Decker, and X. Zhang,\r\n\"Experimental Study of Sliding Mode Control for a Benchmark\r\nMagnetic Bearing System and Artificial Heart Pump Suspension,\" IEEE\r\nTrans. on Contr. Sys. Mag, vol. 11, no. 1, pp. 128-138, 2003.\r\n[8] S. Sivrioglu, and K. Nonami, \"Sliding Mode Control With Time-\r\nVarying Hyperplane for AMB Systems,\" IEEE\/ASME Trans. on\r\nMechatronics, vol. 3, no. 1, pp. 51-59, 1998.\r\n[9] F. Matsumura, and T. Yoshimoto, \"System modeling and control design\r\nof a horizontal shaft magnetic bearing system,\" IEEE Trans. Magnetics,\r\nvol. MAG-22, no. 3, pp. 196-203, May 1986.\r\n[10] J. H. S. Osman, and P.D. Roberts, \"Two Level Control Strategy for\r\nRobot Manipulators,\" Int. Jour. of Control, vol. 61, no. 6, pp. 1201 -\r\n1222, 1995.\r\n[11] S. Boyd, L. El. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix\r\nInequality in Systems and Control Theory, Philadelphia: SIAM, vol. 15,\r\n1994.\r\n[12] J. G. VanAntwerp, and R. D. Braatz, \"A Tutorial on Linear and Bilinear\r\nMatrix. Int. Journal of Process Control, vol. 10, pp. 363 - 385, 2000.\r\n[13] D. Q. Zhang, and S. K. Panda, \"Chattering-free and fast-response sliding\r\nmode controller,\" IEEProc. -Contr. Theory Appl., vol. 146, no. 2, pp.\r\n171-177, March 1999.\r\n[14] J. Lofberg, \"YALMIP: A Toolbox for Modeling and Optimization in\r\n{MATLAB}\", in Proc. of the CACSD Conf., Taiwan, 2004. (Online).\r\nAvailable: http:\/\/control.ee.ethz.ch\/~joloef\/yalmip.php\r\n[15] J. F. Sturm, \"Using SeDuMi 1.02, a MATLAB toolbox for optimization\r\nover symmetric cones,\" Optimization Methods and Software- Special\r\nissue on Interior Point Methods, pp. 625-653, 1999. (Online). Available:\r\nhttp:\/\/sedumi.mcmaster.ca.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 13, 2008"}