Stability Analysis for a Flywheel Supported on Magnetic Bearings with Delayed Feedback Control
Keywords:
Flywheel, magnetic bearing, PD controller, stability, time delayAbstract
In this paper, the model of the rotor dynamics of the flywheel is given using a rigid rotor supported on magnetic bearings. The phase lag of the control loop is modeled by a simple time delay. Limits of stability and the associated vibration frequencies are described in terms of nondimensional magnetic bearing stiffness and damping and nondimensional parameters of flywheel speed and time delay. Compared to the theoretical values, the simulation results and experimental measurements show the stability boundaries of the PD controller have the same qualitative tendencies.
Downloads
References
P. Poubeau, Satellite momentum wheel, United States Patent: 3955858, May 1976.
S. Michael, R. Thomas, and B. Enrico, “The challenges of miniaturisation for a magnetic bearing wheel,” Proceedings of 9th European Space Mechanisms and Tribology Symposium, Liege, Belgium, pp. 17-24, Sep. 2001.
G. Bernd, E. Markus, and K. R. Hans, “Gimballing magnetic bearing reaction wheel with digital controller,” Proceedings of the 11th European Space Mechanisms and Tribology Symposium, Lucerne, Switzerland, pp. 1-6, Sep. 2005.
B. C. Han, “Modeling and analysis of novel integrated radial hybrid magnetic bearing for magnetic bearing reaction wheel,” Chinese Journal of Mechanical Engineering, vol. 23, pp. 655-662, Nov. 2010.
L. Y. Xiang, S. G. Zuo, and L. C. He, “Electric vehicles to reduce vibration caused by the radial force,” The Applied Computational Electromagnetics Society, vol. 29, pp. 340-350, Sep. 2014.
A. F. Kacsak, G. V. Brown, and Q. H. Jansen, “Stability limits of a PD controller for a flywheel supported on rigid rotor and magnetic bearings,” AIAA Guidance, Navigation and Control Conference and Exhibition, San Francisco, California, pp. 5956, Aug. 2005.
J. Wu, Theory and Applications of Partial Functional Differential Equations. Springer, New York, 1996.
S. Guo, Y. Chen, and J. Wu, “Two-parameter bifurcations in a network of two neurons with multiple delays,” J. Differential Equations, vol. 244, pp. 444-486, Jan. 2008.
B. Hassard, N. Kazarinoff, and Y. Wan, Theory and Applications of Hopf Bifurcation. Cambridge University Press, Cambridge, 1981.
O. M. Ramahi, “Analysis of conventional and novel delay lines: A numerical study,” The Applied Computational Electromagnetics Society, vol. 18, pp. 181-190, Aug. 2003.
P. Orlov, T. Gazizov, and A. Zabolotsky, “Short pulse propagation along microstrip meander delay lines with design constraints: Comparative analysis of the quasi-static and electromagnetic approaches,” The Applied Computational Electromagnetics Society, vol. 31, pp. 238-243, Mar. 2016.
M. Hosek and N. Olgac, “A single-step automatic tuning algorithm for the delayed resonator vibration absorber,” IEEE Transactions on Mechatronics, vol. 7, pp. 245-255, July 2002.
H. Fazelinia, R. Sipahi, and N. Olgac, “Stability analysis of multiple time delayed systems using 'builiding block' concept,” Proceeding of the 2006 American Control Conference, Minnesota, USA pp. 2393-2398, 2006.
H. Fazelinia, R. Sipahi, and N. Olgac, “Stability robustness analysis of multiple time-delayed systems using "building block" concept,” IEEE Transactions on Automatic Control, vol. 52, pp. 799-810, May 2007.
B. Polajzer, J. Ritonja, and G. Stumberger, “Decentralized PI/PD position control for active magnetic bearings,” Electrical Engineering, vol. 89, pp. 53-59, Oct. 2006.
W. Zhang, J. W. Zu, and F. X. Wang, “Global bifurcations and chaos for a rotor-active magnetic bearing system with time-varying stiffness,” Chaos Solitons & Fractals, vol. 35, pp. 586-608, May 2008.
W. Zhang and J. W. Zu, “Transient and steady nonlinear for a rotor-active magnetic bearing system with time-varying stiffness,” Chaos Solitons & Fractals, vol. 38, pp. 1152-1167, Feb. 2008.
M. P. Aghababa and H. P. Aghababa, “Chaos suppression of rotational machine systems via finite-time control method,” Nonlinear Dynamics, vol. 69, pp. 1881-1888, Apr. 2012.
H. C. Gui, L. Jin, and S. J. Xu, “On the attitude stabilization of a rigid spacecraft using two skew control moment gyros,” Nonlinear Dynamics, vol. 79, pp. 2079-2097, Mar. 2015.
Z. W. Liu, R. S. Chen, and J. Q. Chen, “Using adaptive cross approximation for efficient calculation of monostatic scattering with multiple incident angles,” The Applied Computational Electromagnetics Society, vol. 26, pp. 325-333, Apr. 2011.
M. A. Pichot, J. P. Kajs, and J. P. Murhy, “Active magnetic bearings for energy storage systems for combat vehicles,” IEEE Transactions on Magnetics, vol. 37, pp. 318-323, Jan. 2001.
A. Palazzolo, System and methods for controlling suspension using a magnetic field, U.S. Patent: 6323614B1, 2001.
X. F. Chen, Research on vibration analysis and inhibitory control of magnetic suspension flywheel system, Ph.D., National University of Defense Technology, 2011.
H. W. Wang and J. Q. Liu, “Stability and bifurcation analysis in a magnetic bearing system with time delays,” Chaos, Solitons & Fractals, vol. 26, pp. 813-825, Mar. 2005.
J. C. Ji, “Stability and Hopf bifurcation of a magnetic bearing system with time delays,” Journal of Sound and Vibration, vol. 259, pp. 845- 856, Apr. 2003.
L. L. Zhang, S. A. Campbell, and L. H. Huang, “Nonlinear analysis of a maglev system with timedelayed feedback control,” Physica D, vol. 240, pp. 1761-1770, July 2011.
L. L. Zhang, Z. Z. Zhang, and L. H. Huang, “Double Hopf bifurcation of time-delayed feedback control for maglev system,” Nonlinear Dynamics, vol. 69, pp. 961-967, Mar. 2012.
