Explicit Feedback Linearization of Magnetic Levitation System

This study proposes the transformation of nonlinear
Magnetic Levitation System into linear one, via state and feedback
transformations using explicit algorithm. This algorithm allows
computing explicitly the linearizing state coordinates and feedback
for any nonlinear control system, which is feedback linearizable,
without solving the Partial Differential Equations. The algorithm is
performed using a maximum of N-1 steps where N being the
dimension of the system.

• Bhawna Tandon
• Shiv Narayan
• Jagdish Kumar

• Explicit Algorithm
• Feedback Linearization
• Nonlinear control
• Magnetic Levitation System.

[1] Valer Dolga, Lia Dolga, “Modeling and Simulation of a Magnetic
Levitation System” Annals of the Ordea University, Fascicle of
Management and Technological Engineering, Volume VI (XVI),2007.
[2] Ying Shing Shiao, “Design and Implementation of a controller for a
Magnetic Levitation System”, Proc. Natl. Sci. Counc. ROC (D), Vol. 11,
No. 2, pp. 88-94, 2001.
[3] Ehsan Shameli, Mir Behrad Khamesee, Jan Paul Huissoon, “NonLinear
controller design for a magnetic levitation device”, Microsyst Technol,
Vol. 13, pp. 831-835, Springer Verlag, 2006.
[4] W. Barie and J. Chiasoson, “Linear and nonlinear state space controllers
for Magnetic Levitation”, International Journal of System Science, Vol.
27, Issue 1, pp. 1153-1163, 1996.
[5] Issa Amadou Tall, “Explicit Feedback Linearization of Control
Systems”,48th IEEE Conference on Decision and Control, Shanghai, P.
R. China, pp. 7454-7459, December 2009.
[6] Issa Amadou Tall, “State Linearization of NonLinear Control Systems:
An Explicit Algorithm”,48th IEEE Conference on Decision and Control,
Shanghai, P. R. China, pp. 7448-7453, December 2009. [7] A.Isidori, “Nonlinear Control Systems”, 3rd edition, Springer, London,
1995.
[8] A.J.Krener, “On the Equivalence of control systems and the linearization
of nonlinear systems”, SIAM Journal on Control, Vol. 11, pp. 670-676,
1973.
[9] R.W. Brockett, “Feedback Invariants for nonlinear ayatems”, in
proceedings of IFAC Congress, Helsinski, 1978.
[10] H. Nijmeijer and A.J. Van Der Schaft, “Nonlinear Dynamical Control
Systems”, Springer-Verlag, New York, 1990.