Asymptotic differentiation of signals in the trajectory tracking control of a differentially flat nonlinear magnetic suspension system



Magnetic levitation, differential flatness, differentiation of signals, motion planning


This paper deals with the problem of time-varying desired position reference trajectory tracking tasks for an object in a differentially flat nonlinear magnetic levitation system using position measurements only. A novel scheme for signal differentiation is proposed for asymptotic estimation of velocity and acceleration. This differentiator can be utilized in many control applications of practical engineering systems where the differentiation of any signal is required. The differentiation of signals is combined with a differential flatness-based controller for asymptotic tracking of reference trajectories. Simulation results are provided to show the efficient performance of the proposed differentiator-control scheme. Two issues for reference trajectory tracking tasks are performed. The first one considers the rest-to-rest position transfer problem of the object from a nominal position to another, while the second one focuses on the sinusoidal position trajectory tracking problem.

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G. Schweitzer, E. Maslen. “Magnetic Bearings. Theory, Design and Application to Rotating Machinery”. Ed. Springer. Germany. 2010. pp. 1-26.

A. Hajjaji, M. Ouladsine. “Modeling and Nonlinear Control of Magnetic Levitation Systems.” IEEE Transactions on Industrial Electronics. Vol. 48. 2001. pp. 831-838.

F. Lin, L. Teng, P. Shieh. “Intelligent Adaptive Back-stepping Control System for Magnetic Levitation Apparatus.” IEEE Transactions on Magnetics. Vol. 43. 2007. pp. 2009-2018.

D. Cho, Y. Kato, D. Spilman. “Sliding mode and classical control magnetic levitations systems.” IEEE Control Systems Magazine. Vol. 13. 1993. pp. 42-48.

M. Lairi, G. Bloch. “Neural control of Maglev system”, Proceedings of MCEA’98. Marrakech. Morocco. 1998. pp. 472-475.

J. Slotine. “Applied Nonlinear Control”. NJ: Prentice-Hall. Englewood Cliffs.1991. pp. 1-405.

F. Zhao, S. Loh, J. May. “Phase-space nonlinear control toolbox: The maglev experience”. Proceedings of Hybrid Systems Workshop. Notre Dame. USA. 1997. pp. 1- 9.

C. Bonivento, L. Gentili, L. Marconi. “Balanced Robust Regulation of a Magnetic Levitation System”. IEEE Transactions on Control Systems Technology. Vol. 13. 2005. pp. 1036-1044.

L. Gentili, L. Marconi. “Robust nonlinear disturbance suppression of a magnetic levitation system.” Automatica. Vol. 39. 2003. pp. 735-742.

J. Yang, Y. Lee, O. Kwon. “Development of Magnetic Force Modeling Equipment for Magnetic Levitation System”. Proceedings of 2010 International Conference on Control Automation and Systems (ICCAS). Gyeonggi-do. Korea. 2010. pp. 29-33.

Z. Yang, K. Kunitoshi, S. Kanae, K. Wada. “Adaptive Robust Output-Feedback Control of a Magnetic Levitation System by K-Filter Approach.” IEEE Trans. on Industrial Electronics. Vol. 55. 2008. pp. 390-399.

C. Lin, M. Lin, C. Chen. “SoPC-Based Adaptive PID Control System Design for Magnetic Levitation System.” IEEE Systems Journal. Vol. 5. 2011. pp. 278- 287.

M. Feemster, Y. Fang, D. Dawson. “Disturbance Rejection for a Magnetic Levitation System.” IEEE/ ASME Trans. on mechatronics. Vol. 11. 2006. pp. 709- 717.

F. Suryawan, J. Doná, M. Seron. “Methods for trajectory generation in a magnetic-levitation system under constraints”. Proceedings of 18th Mediterranean Conference on Control & Automation. Marrakech. Morocco. 2010. pp. 945-950.

A. Yetendje, M. Seron, J. De Doná, J. Martínez. “Sensor fault-tolerant control of a magnetic levitation system.” International Journal of Robust and Nonlinear Control. Vol. 20. 2010. pp. 2108-2121.

H. Khalil. Nonlinear Systems. Prentice Hall. 3rd. Ed. New Jersey. USA. 2002. pp. 1-32.

M. Flies, J. Lé vine, P. Martín, P. Rouchon. “Flatness and detect of nonlinear systems: Introductory theory and examples.” International Journal of control. Vol. 61. 1993. pp. 1327-1361.

E. Chávez, F. Beltrán, A. Valderrábano, A. Favela. “Active Vibration Control of Vehicle Suspension Systems Using Sliding Modes, Differential Flatness and Generalized Proportional-Integral Control.” Rev. Fac. Ing. Univ. Antioquia. No. 61. 2011. pp. 104-113.

Quanser Inc. Magnetic Levitation Plant Manual. Markham. Ontario. Canada. 2006. http://www.quanser. com/. pp. 1-12.



How to Cite

Beltrán-Carbajal, F., Favela-Contreras, A., Valderrábano-González, A., & Silva-Navarro, G. (2013). Asymptotic differentiation of signals in the trajectory tracking control of a differentially flat nonlinear magnetic suspension system. Revista Facultad De Ingeniería Universidad De Antioquia, (66), 70–81. Retrieved from