A non-linear control method for active magnetic bearings with bounded input and output

Lam Tung Nguyen


Magnetic bearing is well-known for its advantage of reducing friction in rotary ma- chines and is placing conventional bearings where high-speed operations and clean- liness are essential. It can be shown that the AM is a nonlinear system due to the relation between the magnetic force and current/rotor displacement. In this paper, a mathematical model of a 4-DOF AMB supported by four dual electric magnets is presented. The control objective is placed in a view of control input saturation and output limitation that are meaningful aspect in practical applications. Backstepping algorithm based control strategy is then adopted in order to achieve the high dynamic performance of the bearing. The control is designed in such away that it takes input and output constraints into account by flexibly using hyperbolic tangent and barrier Lyapunov functions. Informative simulation studies are carried out to understand the operations of the machine and evaluate the controller quality.


N. F. Al-Muthairi and M. Zribi, “Sliding mode control of a magnetic levitation system,” Mathematical Problems in Engineering, vol. 2004, no. 2, pp. 93–107, 2004.

E. Maslen and G. Schweitzer, Magnetic Bearings - Theory, Design and Application to Rotating Machin- ery, 01 2009.

F. R. Ismagilov and V. E. Vavilov, “Superhigh-speed electric motor with unipolar magnetic bearing,” Russian Engineering Research, vol. 38, no. 6, pp. 480–484, Jun. 2018.

E. Gourc, S. Seguy, and L. Arnaud, “Chatter milling modeling of active magnetic bearing spindle in high-speed domain,” International Journal of Machine Tools and Manufacture, vol. 51, no. 12, pp. 928 – 936, 2011. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0890695511001465

C. R. Knospe, “Active magnetic bearings for machining applications,” Control Engineering Practice, vol. 15, no. 3, pp. 307–313, 2007.

B. Han, Z. Huang, and Y. Le, “Design aspects of a large scale turbomolecular pump with active magnetic bearings,” Vacuum, vol. 142, pp. 96 – 105, 2017. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0042207X16307515

T. Allison, J. Moore, R. Pelton, J. Wilkes, and B. Ertas, “7 - turbomachinery,” in Fundamentals and Applications of Supercritical Carbon Dioxide (sCO2) Based Power Cycles, K. Brun, P. Friedman, and R. Dennis, Eds. Woodhead Publishing, 2017, pp. 147 – 215. [Online]. Available: http://www.sciencedirect.com/science/article/pii/B9780081008041000074

D. Clark, M. Jansen, and G. Montague, “An overview of magnetic bearing technology for gas turbine engines,” NASA Technical Reports Server (NTRS), 09 2004. [Online]. Available: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20040110826.pdf

W. Zhang and H. Zhu, “Radial magnetic bearings: An overview,” Results in Physics, vol. 7, pp. 3756 – 3766, 2017. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S221137971730863X

L.-C.LinandT.-B.Gau,“Feedbacklinearizationandfuzzycontrolforconicalmagneticbearings,”vol.5, pp. 417–426, 1997.

N. Sarmah and R. Tiwari, “Identification of crack and internal damping parameters using full spectrum responses from a jeffcott rotor incorporated with an active magnetic bearing,” in Proceedings of the 10th International Conference on Rotor Dynamics – IFToMM, K. L. Cavalca and H. I. Weber, Eds. Cham: Springer International Publishing, 2019, pp. 34–48.

Q. Li, W. Wang, B. Weaver, and X. Shao, “Active rotordynamic stability control by use of a combined active magnetic bearing and hole pattern seal component for back-to-back centrifugal compressors,” Mechanism and Machine Theory, vol. 127, pp. 1 – 12, 2018. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0094114X1731635X

J. Sun, H. Zhou, X. Ma, and Z. Ju, “Study on pid tuning strategy based on dynamic stiffness for radial active magnetic bearing,” ISA Transactions, vol. 80, pp. 458 – 474, 2018. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S001905781830291X

A. M. A.-H. Shata, R. A. Hamdy, A. S. Abdelkhalik, and I. El-Arabawy, “A fractional order pid control strategy in active magnetic bearing systems,” Alexandria Engineering Journal, vol. 57, no. 4, pp. 3985 – 3993, 2018. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S1110016818301935

M. S. Kang, J. Lyou, and J. K. Lee, “Sliding mode control for an active magnetic bearing system subject to base motion,” Mechatronics, vol. 20, no. 1, pp. 171 – 178, 2010, special Issue on Servo Control for Data Storage and Precision Systems, from 17th IFAC World Congress 2008. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0957415809001615

A. Bonfitto, L. M. Castellanos Molina, A. Tonoli, and N. Amati, “Offset-Free Model Predictive Control for Active Magnetic Bearing Systems,” Actuators, vol. 7, no. 3, p. 46, 2018.

R. HE and K.-Z. LIU, “A Nonlinear Output Feedback Control Method for a 5DOF Active Magnetic Bearing System,” Transactions of the Society of Instrument and Control Engineers, vol. 41, no. 3, pp. 216–225, 2014.

Y. LI, Q. ZHANG, and X.-W. WANG, “The Terminal Sliding Mode Control of 4-DoF Active Magnetic Bearing Rotor System,” DEStech Transactions on Engineering and Technology Research, no. icmm, pp. 139–143, 2018.

S.-L. CHEN and Y.-H. HSIAO, “Smooth voltage controller and observer for a three-pole active magnetic bearing system,” Mechanical Engineering Journal, vol. 4, no. 5, pp. 16–00 718–16–00 718, 2017.

N. P. Q. Vo Thanh Ha, Le Trong Tan, Nguyen Duc Nam, “Backstepping Control of Two-Mass System Using Induction Motor Drive Fed by Voltage Source Inverter with Ideal Control Performance of Stator Current,” International Journal of Power Electronics and Drive System, vol. 10, no. 2, pp. 720–730, 2019.

I. A. Raptis and K. P. Valavanis, Linear and Nonlinear Control of Small-Scale Unmanned Helicopters. Springer Netherlands, 2011.

C. Hua, P. X. Liu, and X. Guan, “Backstepping control for nonlinear systems with time delays and appli- cations to chemical reactor systems,” vol. 56, pp. 3723–3732, 2009.

M. LIU, S. Xu, and C. Han, “A backstepping simple adaptive control application to flexible space struc- tures,” Chinese Journal of Aeronautics, vol. 25, p. 446452, 06 2012.

A. Golubev, A. Krishchenko, and N. Utkina, “Missile angle of attack tracking using integrator backstep- ping,” IFAC-PapersOnLine, vol. 52, pp. 724–729, 01 2019.

D.H.Nguyen,T.L.Nguyen,M.L.Nguyen,andH.P.Nguyen,“NonlinearControlofanActiveMagnetic Bearing with Output Constraint,” International Journal of Electrical and Computer Engineering (IJECE), vol. 8, no. 5, p. 3666, 2019.

DOI: http://doi.org/10.11591/ijpeds.v11.i4.pp%25p
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