Asymptotic Stabilization of an Active Magnetic Bearing System using LMI-based Sliding Mode Control
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.
[1] J. Y. Hung, W. B. Gao, and J. C. Hung, "Variable Structure control: A
Survey," IEEE Trans. Industrial. Electronics, vol. 40, no. 1, pp. 2-22.,
1993.
[2] S. Spurgeon, and C. Edwards, Sliding Mode Control: Theory and
Applications. London: Taylor and Francis, 1998.
[3] X. Li, and R. A. DeCarlo, "Robust Sliding Mode Control of Uncertain
Time Delay Systems," Int. J. Control, vol. 76, no. 13, pp. 1296-1305,
2003.
[4] X. Z. Dong, "State Feedback Sliding Mode Control for A Class of
Systems with Mismatched Uncertainties and Disturbance," in Proc. 25th
Chinese Control Conference, Heilongjiang, 2006, pp. 938-942.
[5] M. N. Ahmad, J. H. S. Osman, and M. R. A. Ghani, "Proportional-
Integral Sliding Mode Tracking Controller with Application to a Robot
Manipulator," in 7th Conf. on Contr., Auto., Rob and Sys., ICARCV,
Singapore, 2003, pp. 863-868.
[6] Y. M. Sam, and J. H. S. Osman, "Modeling and Control of Active
Suspension System Using Proportional Integral Sliding Mode
Approach," Asian Jour. Contr., vol. 7, no. 2, pp. 91-98, 2005.
[7] J. H. Lee, P.E. Allaire, G. Tao, J. A. Decker, and X. Zhang,
"Experimental Study of Sliding Mode Control for a Benchmark
Magnetic Bearing System and Artificial Heart Pump Suspension," IEEE
Trans. on Contr. Sys. Mag, vol. 11, no. 1, pp. 128-138, 2003.
[8] S. Sivrioglu, and K. Nonami, "Sliding Mode Control With Time-
Varying Hyperplane for AMB Systems," IEEE/ASME Trans. on
Mechatronics, vol. 3, no. 1, pp. 51-59, 1998.
[9] F. Matsumura, and T. Yoshimoto, "System modeling and control design
of a horizontal shaft magnetic bearing system," IEEE Trans. Magnetics,
vol. MAG-22, no. 3, pp. 196-203, May 1986.
[10] J. H. S. Osman, and P.D. Roberts, "Two Level Control Strategy for
Robot Manipulators," Int. Jour. of Control, vol. 61, no. 6, pp. 1201 -
1222, 1995.
[11] S. Boyd, L. El. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix
Inequality in Systems and Control Theory, Philadelphia: SIAM, vol. 15,
1994.
[12] J. G. VanAntwerp, and R. D. Braatz, "A Tutorial on Linear and Bilinear
Matrix. Int. Journal of Process Control, vol. 10, pp. 363 - 385, 2000.
[13] D. Q. Zhang, and S. K. Panda, "Chattering-free and fast-response sliding
mode controller," IEEProc. -Contr. Theory Appl., vol. 146, no. 2, pp.
171-177, March 1999.
[14] J. Lofberg, "YALMIP: A Toolbox for Modeling and Optimization in
{MATLAB}", in Proc. of the CACSD Conf., Taiwan, 2004. (Online).
Available: http://control.ee.ethz.ch/~joloef/yalmip.php
[15] J. F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization
over symmetric cones," Optimization Methods and Software- Special
issue on Interior Point Methods, pp. 625-653, 1999. (Online). Available:
http://sedumi.mcmaster.ca.
[1] J. Y. Hung, W. B. Gao, and J. C. Hung, "Variable Structure control: A
Survey," IEEE Trans. Industrial. Electronics, vol. 40, no. 1, pp. 2-22.,
1993.
[2] S. Spurgeon, and C. Edwards, Sliding Mode Control: Theory and
Applications. London: Taylor and Francis, 1998.
[3] X. Li, and R. A. DeCarlo, "Robust Sliding Mode Control of Uncertain
Time Delay Systems," Int. J. Control, vol. 76, no. 13, pp. 1296-1305,
2003.
[4] X. Z. Dong, "State Feedback Sliding Mode Control for A Class of
Systems with Mismatched Uncertainties and Disturbance," in Proc. 25th
Chinese Control Conference, Heilongjiang, 2006, pp. 938-942.
[5] M. N. Ahmad, J. H. S. Osman, and M. R. A. Ghani, "Proportional-
Integral Sliding Mode Tracking Controller with Application to a Robot
Manipulator," in 7th Conf. on Contr., Auto., Rob and Sys., ICARCV,
Singapore, 2003, pp. 863-868.
[6] Y. M. Sam, and J. H. S. Osman, "Modeling and Control of Active
Suspension System Using Proportional Integral Sliding Mode
Approach," Asian Jour. Contr., vol. 7, no. 2, pp. 91-98, 2005.
[7] J. H. Lee, P.E. Allaire, G. Tao, J. A. Decker, and X. Zhang,
"Experimental Study of Sliding Mode Control for a Benchmark
Magnetic Bearing System and Artificial Heart Pump Suspension," IEEE
Trans. on Contr. Sys. Mag, vol. 11, no. 1, pp. 128-138, 2003.
[8] S. Sivrioglu, and K. Nonami, "Sliding Mode Control With Time-
Varying Hyperplane for AMB Systems," IEEE/ASME Trans. on
Mechatronics, vol. 3, no. 1, pp. 51-59, 1998.
[9] F. Matsumura, and T. Yoshimoto, "System modeling and control design
of a horizontal shaft magnetic bearing system," IEEE Trans. Magnetics,
vol. MAG-22, no. 3, pp. 196-203, May 1986.
[10] J. H. S. Osman, and P.D. Roberts, "Two Level Control Strategy for
Robot Manipulators," Int. Jour. of Control, vol. 61, no. 6, pp. 1201 -
1222, 1995.
[11] S. Boyd, L. El. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix
Inequality in Systems and Control Theory, Philadelphia: SIAM, vol. 15,
1994.
[12] J. G. VanAntwerp, and R. D. Braatz, "A Tutorial on Linear and Bilinear
Matrix. Int. Journal of Process Control, vol. 10, pp. 363 - 385, 2000.
[13] D. Q. Zhang, and S. K. Panda, "Chattering-free and fast-response sliding
mode controller," IEEProc. -Contr. Theory Appl., vol. 146, no. 2, pp.
171-177, March 1999.
[14] J. Lofberg, "YALMIP: A Toolbox for Modeling and Optimization in
{MATLAB}", in Proc. of the CACSD Conf., Taiwan, 2004. (Online).
Available: http://control.ee.ethz.ch/~joloef/yalmip.php
[15] J. F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization
over symmetric cones," Optimization Methods and Software- Special
issue on Interior Point Methods, pp. 625-653, 1999. (Online). Available:
http://sedumi.mcmaster.ca.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:62417", author = "Abdul Rashid Husain and Mohamad Noh Ahmad and Abdul Halim Mohd. Yatim", title = "Asymptotic Stabilization of an Active Magnetic Bearing System using LMI-based Sliding Mode Control", abstract = "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.
", keywords = "Active Magnetic Bearing (AMB), Sliding ModeControl (SMC), Linear Matrix Inequality (LMI), mismatcheduncertainty.", volume = "2", number = "1", pages = "99-8", }
