Nonlinear Position-Flux Zero-Bias Control for AMB System with Disturbance

Authors

  • Arkadiusz Mystkowski Bialystok University of Technology, Department of Automatic Control and Robotics, Bialystok, Poland
  • Ewa Pawluszewicz Bialystok University of Technology, Department of Automatic Control and Robotics, Bialystok, Poland

Keywords:

Active magnetic bearing, control Lyapunov function, nonlinear flux controller, zero-bias control

Abstract

This study presents two novel nonlinear controllers for a single one-degree-of-freedom (1–DOF) active magnetic bearing (AMB) system operated in zero-bias mode with externally bounded disturbance. Recently developed controllers are complicated and inherently difficult to implement. The simple and low-order controllers proposed in this paper are designed using nonlinear feedback tools, including Lyapunov-based techniques and control Lyapunov functions (CLFs). The control objective is to globally stabilize the mass position of the nonlinear flux-controlled AMB system with control voltage saturation. The zero-bias AMB control model is derived from the voltage switching strategy. The developed CLF-based controllers are verified by numerical calculations.

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References

Z. Gosiewski and A. Mystkowski, “Robust control of active magnetic suspension: Analytical and experimental results,” Mechanical Systems & Signal Processing, vol. 22, pp. 1297-1303, 2008.

A. Mystkowski, “Mu-synthesis for magnetic bearings of flywheel,” Proc. in Applied Mathematics and Mechanics (PAMM), Wiley Online Library, vol. 9, pp. 631-632, 2009.

A Mystkowski, “-synthesis control of flexible modes of AMB rotor,” Acta Mechanica et Automatica, vol. 4, pp. 83-90, 2010.

Y. Ariga, K. Nonami, and T. Kamiyama, “Nonlinear zero-power control of an electrical power storing flywheel (derivation of nonlinear control ignoring the gyro-effect),” Journal of Japan AEM Society, vol. 8, pp. 403-410, 2000.

H. Bleuler, D. Yischer, G. Schweitzer, et al., “New concepts for cost-effective magnetic bearing control,” Automatica, vol. 30, pp. 871-876, 1994.

A. Charara, J. De Miras, and B. Caron, “Nonlinear control of a magnetic levitation system without premagnetization,” IEEE Trans. Contr. Syst. Technol., vol. 4, pp. 513-523, 1996.

R. P. Jastrzebski, A. Smirnov, A. Mystkowski, and O. Pyrhönen, “Cascaded position-flux controller for AMB system operating at zero bias,” Energies, vol. 7, pp. 3561-3575, 2014.

K. Z. Liu, A. Ikai, A. Ogata, and O. Saito, “A nonlinear switching control method for magnetic bearing systems - Minimizing the power consumption,” in Proc. of the 15th IFAC World Conference, Barcelona, Spain, 21-26 July 2002.

N. Motee, M. S. De Queiroz, Y. Fang, and D. M. Dawson, “Active magnetic bearing control with zero steady-state power loss,” in Proc. of ACC’2002, Anchorage, Alaska, USA, pp. 827-832, 8-10 May 2002.

A. Mystkowski, E. Pawluszewicz, and E. Dragašius, “Robust nonlinear position-flux zerobias control for uncertain AMB system,” Int. J. of Contr., vol. 88, pp. 1619-1629, 2015.

M. N. Sahinkaya and A. E. Hartavi, “Variable bias current in magnetic bearings for energy optimization,” IEEE Trans. on Mag., vol. 43, pp. 1052- 1060, 2007.

J. Lévine, J. Lottin, and J. C. Ponstart, “A nonlinear approach to the control of magnetic bearings,” IEEE Trans. Contr. Syst. Technol., vol. 4, pp. 524- 544, 1996.

P. J. Moylan and B. D. O. Anderson, “Nonlinear regulator theory and an inverse optimal control problem,” IEEE Trans. on Automatic Control, vol. 18, pp. 460-465, 1973.

I. G. Malkin, The Theory of Stability of Motion. Moscow: Gostekhizdat, 1952.

J. Willems, “Dissipative dynamical systems - Parts I and II,” Archive for Rational Mechanics and Analysis, vol. 45, pp. 321-393, 1972.

A. Bressan and B. Piccoli, Introduction to the Mathematical Theory of Control. Springfield: American Institute of Mathematical Sciences, 2007.

F. Clarke, “Lyapunov functions and feedback in nonlinear control, optimal control, stabilization and nonsmooth analysis,” Lecture Notes in Control and Information Science, vol. 301, pp. 267-282, 2004. [18] R. Marino and P. Tomei, Nonlinear Control Design – Geometric, Adaptive and Robust. UK: Prentice Hall International, 1995.

E. D. Sontag, Mathematical Control Theory, Deterministic Finite Dimensional Systems. 2nd ed., New York: Springer, 1998.

Z. Artstein, “Stabilization with relaxed controls,” Nonlinear Analysis, vol. 7, pp. 1163-1173, 1983.

E. D. Sontag, “Lyapunov-like characterization of asymptotic controllability,” SIAM Journal of Control and Optimization, vol. 21, pp. 462-471, 1983.

E. D. Sontag, “A universal construction of Artstein’s theorem on nonlinear stabilization,” Systems and Control Letters, vol. 13, pp. 117-123, 1989.

R. A. Freeman and P. V. Kokotović, “Inverse optimality in robust stabilization,” SIAM Journal of Control and Optimization, vol. 34, pp. 1365-1391, 1996.

R. A. Freeman and P. V. Kokotović, Robust Nonlinear Control Design – State–Space and Lyapunov Techniques. Boston: Birkhäuser, 1996.

R. A. Freeman and P. V. Kokotović, Design of ‘softer’ robust nonlinear control laws,” Automatica, vol. 29, pp. 1425-1437, 1993.

I. Kanellakopoulos, P. V. Kokotović, and A. S. Morse, “A toolkit for nonlinear feedback design,” Systems and Control Letters, vol. 18, pp. 83-92, 1992.

J. W. Helton and M. R. James, Extending ℋ∞ Control to Nonlinear Systems. Philadelphia: SIAM Frontiers in Applied Mathematics, 1999.

A. Isidori and W. Kang, “ℋ∞ control via measurement feedback for general nonlinear systems,” IEEE Trans. on Automatic Control, vol. 40, pp. 466-472, 1995.

P. Tsiotras and B. C. Wilson, “Zero- and low-bias control designs for active magnetic bearings,” IEEE Trans. Contr. Syst. Technol., vol. 11, pp. 889-904, 2003.

P. Tsiotras and M. Arcak, “Low-bias control of AMB subject to voltage saturation: state-feedback and observer designs,” Proc. of the 41st IEEE Conf. on Decision and Contr., Las Vegas, NV, USA, pp. 2474-2479, 10-13 December 2002.

G. Schweitzer and E. H. Maslen, Magnetic Bearings: Theory, Design, and Application to Rotating Machinery. Berlin Heidelberg: Springer– Verlag, 2009.

E. Maslen, P. Hermann, and M. Scott, “Practical limits to the performance of magnetic bearings: Peak force, slew rate and displacement sensitivity,” ASME Journal on Tribology, vol. 111, pp. 331- 336, 1989.

C. Knospe, “The nonlinear control benchmark experiment,” Proc. of the American Control Conference, Chicago, IL, pp. 2134-2138, 28-30 June 2000.

R. A. Freeman, “Global robustness of nonlinear systems to state measurement disturbances,” Proc. of the 32nd IEEE Conference on Decision and Control, San Antonio, Texas, USA, pp. 1507-1512, 15-17 December 1993.

J. D. Lindlau and C. Knospe, “Feedback linearization of an active magnetic bearing with voltage control,” IEEE Transactions on Control Systems Technology, vol. 10, pp. 21-31, 2002.

Z. Gosiewski and A. Mystkowski, “The robust control of magnetic bearings for rotating machinery,” Solid State Phenomena, vol. 113, pp. 125-130, 2006.

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Published

2021-07-30

How to Cite

[1]
Arkadiusz Mystkowski and Ewa Pawluszewicz, “Nonlinear Position-Flux Zero-Bias Control for AMB System with Disturbance”, ACES Journal, vol. 32, no. 08, pp. 650–656, Jul. 2021.

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