Sliding Mode Control, with Integrator, for a Class of Mimo Nonlinear Systems

Anouar Benamor, Larbi Chrifi-alaui, Hassani Messaoud, Mohamed Chaabane
DOI: 10.4236/eng.2011.35050                

Abstract

In this paper, the robust control problem of general nonlinear multi-input multi-output (MIMO) systems is proposed. The robustness against unknown disturbances is considered. Two algorithms based on the Sliding Mode Control (SMC) for nonlinear coupled multi-input multi-output (MIMO) systems are proposed: the first order sliding mode control (FOSMC) with saturation (sat) function and the FOSMC with sat combined with integrator controller. Those algorithms were simulated and implemented on the three tanks test-bed system and the exprimental results confirm the effectiveness of our control design.

Keywords

Sliding Mode Control, Integrator, Nonlinear Systems, Coupled, Mimo, Uncertain, Liquid Level Control

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	V. Utkin, “Sliding Mode in Control and Optimization,” Springer-Verlag, Berlin, 1992
[2]	V. Utkin, J. Guldner and J. Shi, “Sliding Modes Control in Electromechanical Systems,” CRC press, Boca Raton, 1999.
[3]	L. Fridman, “An Averaging Approach to Chattering,” IEEE Transactions on Automatic Control, Vol. 46, No. 8, 2001, pp. 1260-1265. doi:10.1109/9.940930
[4]	H. Abid, M. Chtourou and A. Toumi, “Robust Fuzzy Sliding Mode Controller for Discrete Nonlinear Systems,” International Journal of Computers, Communications and Control, Vol. 3, No. 1, 2008, pp. 6-20.
[5]	S. Mahieddine-Mahmoud, L. Chrifi-Alaoui, V. van Assche, J.-M. Castelain and P. Bussy, “Sliding Mode Control Based on Field Orientation for an Induction Motor,” IEEE Industrial Electronics Society, IECON, North Carolina, 6-20 November 2005, pp. 181-186.
[6]	H. Hashimoto, H. Yamamoto, S. Yanagisawa and F. Harashima, “Brushless Servo Motor Control Using Variable Structure Approach,” IEEE Transactions on Industry Applications, Vol. 24, No. 1, 1988, pp. 160-170.doi:10.1109/28.87267
[7]	I. Eker and S. A. Akinal, “Sliding Mode Control with Integral Augmented Sliding Surface: Design and Experimental Application to an Electromechanical System,” Electrical Engineering, Vol. 90, No. 3, 2008, pp. 189-197. doi:10.1007/s00202-007-0073-3
[8]	A. Levant, “Chattering Analysis,” IEEE Transactions on Automatic Control, Vol. 55, No. 6, 2010, pp. 1380-1389.doi:10.1109/TAC.2010.2041973
[9]	C. Edwards and S. Spurgeon, “Sliding Mode Control: Theory and Applications,” Taylor-Francis, London, 1998.
[10]	J. J. E. Slotine and W. Li, “Applied Nonlinear Control,” Prentice-Hall International, New Jersey, 1991.
[11]	I. Eker snd S. A. Akinal, “Sliding Mode Control with Integral Action and Experimental Application to an Electromechanical System Application to an Electromechanical System,” IEEE-ICSC Congress on Computational Intelligence Methods and Applications, Istanbul, 2-14 December 2005, p. 6. doi:10.1109/CIMA.2005.1662303
[12]	S. Seshagiri and H. K. Khalil, “Robust Output Feedback Regulation of Minimum-Phase Nonlinear Systems Using Conditional Integrators,” Automatic, Vol. 41, No. 1, 2005, pp. 43-54. doi:10.1016/j.automatica.2004.08.013
[13]	R. Benayache, L. Chrifi-Alaoui, P. Bussy and J. M. Castelain, “Sliding Mode Control with Integral Corrector: Design and Experimental Application to an Interconnected System,” Mediterranean Conference on Control and Automation, Thessaloniki, 24-26 June 2009, pp. 831-836. doi:10.1109/MED.2009.5164647
[14]	T. Floquet, S. K. Spurgeon and C. Edwards, “An Output Feedback Sliding Mode Control Strategy for MIMO Systems of Arbitrary Relative Degree,” International Journal of Robust and Nonlinear Control, Vol. 21, No. 2, 2010, pp. 119-133. doi:10.1002/rnc.1579
[15]	K. Ogata, “System Dynamics,” Englewood Cliffs, New Jersey, 1978.