Research Papers

Lyapunov Sliding-Mode Observers With Application for Active Magnetic Bearing Operated With Zero-Bias Flux

[+] Author and Article Information
Arkadiusz Mystkowski

Department of Automatic Control and
Bialystok University of Technology,
Wiejska 45A,
Bialystok 15-351, Poland
e-mail: a.mystkowski@pb.edu.pl

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received May 24, 2017; final manuscript received November 6, 2018; published online December 19, 2018. Assoc. Editor: Heikki Handroos.

J. Dyn. Sys., Meas., Control 141(4), 041006 (Dec 19, 2018) (12 pages) Paper No: DS-17-1272; doi: 10.1115/1.4041978 History: Received May 24, 2017; Revised November 06, 2018

This study deals with sliding-mode nonlinear observers for a flux-controlled active magnetic bearing (AMB) operated with zero-bias flux. The Lyapunov sliding-mode observer (LSMO) feedback designs are performed for the nonlinear AMB dynamics due to control voltage saturation. The nonlinear observers are designed to estimate the magnetic flux and rotor mass velocity. The observer designs are incorporated in equivalence implementation of the nonlinear state-feedback controller. The main design tools such as sliding-mode control, Lyapunov-based control are used in this framework. The proposed observers are verified by means of numerical simulations, and stability and effectiveness of the proposed observer-based feedback designs are shown.

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Maslen, E. H. , 2000, “ Magnetic Bearings—Graduate Seminar Notes,” Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA.
Bahr, F. , Melzer, M. , Makarov, D. , Karnaushenko, D. , Schmidt, O. G. , and Hofmann, W. , 2012, “ Flux Based Control of AMBs Using Integrated Ultra-Thin Flexible Bismuth Hall Sensors,” 13th International Symposium on Magnetic Bearings, Arlington, VA, Aug. 6–9, pp. 1–15.
Lin, Z. , and Knospe, C. , 2000, “ A Saturated High Gain Control for a Benchmark Experiment,” American Control Conference, Chicago, IL, June 28–30, pp. 2644–2648.
Tsiotras, P. , and Arcak, M. , 2002, “ Low-Bias Control of AMB Subject to Voltage Saturation: State-Feedback and Observer Designs,” 41st IEEE Conference on Decision and Control, Las Vegas, NV, Dec. 10–13, pp. 2474–2479.
Maslen, E. H. , 2006, “ Self-Sensing for Active Magnetic Bearings: Overview and Status,” Tenth International Symposium on Magnetic Bearings, Martigny, Switzerland, Aug. 21–23, pp. 13–19.
Peng, C. , Fang, J. , and Xu, X. , 2015, “ Mismatched Disturbance Rejection Control for Voltage-Controlled Active Magnetic Bearing Via State-Space Disturbance Observer,” IEEE Trans. Power Electron., 30(5), pp. 2753–2762. [CrossRef]
Itkis, U. , 1967, Control Systems of Variable Structure, Wiley, New York.
Utkin, V. I. , 1977, “ Variable Structure Systems With Sliding Modes,” IEEE Trans. Autom. Control, 22(2), pp. 212–222. [CrossRef]
Spurgeon, S. K. , 2008, “ Sliding Mode Observers: A Survey,” Int. J. Syst. Sci., 39(8), pp. 741–764. [CrossRef]
Baloh, M. , Gang, T. , and Allaire, P. , 2000, “ Modeling and Control of a Magnetic Bearing Actuated Beam,” American Control Conference, Chicago, IL, June 28–30, pp. 1602–1606.
Rundell, A. E. , Drakunov, S. V. , and DeCarlo, R. A. , 1996, “ A Sliding Mode Observer and Controller for Stabilization of Rotational Motion of a Vertical Shaft Magnetic Bearing,” IEEE Trans. Control Syst. Technol., 4(5), pp. 598–608. [CrossRef]
Nguyen, Q. D. , and Ueno, S. , 2010, “ Improvement of Sensorless Speed Control for Nonsalient Type Axial Gap Self-Bearing Motor Using Sliding Mode Observer,” IEEE International Conference on Industrial Technology (ICIT), Vina del Mar, Chile, Mar. 14–17, pp. 373–378.
Shi, J. , Yan, Y. , Yu, S. , and Yu, X. , 2012, “ Dynamic Output Feedback Sliding Mode Control for Magnetic Bearing System Stabilization,” Tenth World Congress on Intelligent Control and Automation, Beijing, China, July 6–8, pp. 1547–1552.
Whittle, E. , Noshadi, A. , Shi, J. , and Kalam, A. , 2015, “ Experimental Study on Servo Linear Quadratic Gaussian and Observer-Based Sliding Mode Control for Active Magnetic Bearing System,” Power Engineering Conference (AUPEC), Australasian Universities, Wollongong, Australia, Sept. 27–30, pp. 1–6.
Tsiotras, P. , Wilson, B. , and Bartlett, R. , 2000, “ Control of a Zero-Bias Magnetic Bearing Using Control Lyapunov Functions,” 39th IEEE Conference on Decision and Control, Sydney, Australia, Dec. 12–15, pp. 4048–4053.
Jastrzebski, R. P. , Smirnov, A. , Mystkowski, A. , and Pyrhönen, O. , 2014, “ Cascaded Position-Flux Controller for AMB System Operating at Zero Bias,” Energies, 7(6), pp. 3561–3575. [CrossRef]
Mystkowski, A. , Pawluszewicz, E. , and Dragašius, E. , 2015, “ Robust Nonlinear Position-Flux Zero-Bias Control for Uncertain AMB System,” Int. J. Control, 88(8), pp. 1619–1629. [CrossRef]
Mystkowski, A. , and Pawluszewicz, E. , 2015, “ Remarks on Some Robust Nonlinear Observer and State-Feedback Zero-Bias Control of AMB,” IEEE 16th International Carpathian Control Conference, Szilvásvárad, Hungary, May 27–30, pp. 328–333.
Tsiotras, P. , and Wilson, B. C. , 2003, “ Zero– and Low–Bias Control Designs for Active Magnetic Bearings,” IEEE Trans. Control Syst. Technol., 11(6), pp. 889–904. [CrossRef]
Sontag, E. D. , 1983, “ A Lyapunov-Like Characterization of Asymptotic Controllability,” SIAM J. Control Optim., 21(3), pp. 462–471. [CrossRef]
Mazenc, F. , Queiroz, M. S. , Malisoff, M. , and Gao, F. , 2006, “ Further Results on Active Magnetic Bearing Control With Input Saturation,” IEEE Trans. Control Syst. Technol., 14(5), pp. 914–919. [CrossRef]
Lu, B. , and Wu, F. , 2004, “ Control Design of Switched LPV Systems Using Multiple Parameter-Dependent Lyapunov Functions,” American Control Conference, Boston, MA, June 30–July 2, pp. 3875–3880.
Schweitzer, G. , and Maslen, E. H. , 2009, Magnetic Bearings: Theory, Design, and Application to Rotating Machinery, Springer, Berlin.
Slotine, J. J. E. , Hedrick, J. K. , and Misawa, E. A. , 1987, “ On Sliding Observers for Nonlinear Systems,” ASME J. Dyn. Syst., Meas., Control, 109(3), pp. 245–252. [CrossRef]
Fichtenholz, G. M. , 1987, Differential- und Integralrechnung 3, 11th ed., Deutscher Verlag der Wissenschaften, Berlin (Translated From the Russian by Boll L. and Groger K.).
Arcak, M. , and Kokotović, P. , 2001, “ Observer-Based Control of Systems With Slope-Restricted Nonlinearities,” IEEE Trans. Autom. Control, 46(7), pp. 1146–1150. [CrossRef]
Torres, M. , Sira-Ramirez, H. , and Escobar, G. , 1999, “ Sliding Mode Nonlinear Control of Magnetic Bearings,” IEEE International Conference on Control Applications, Kohala Coast-Island, HI, Aug. 22–27, pp. 743–748.
Mystkowski, A. , and Pawluszewicz, E. , 2017, “ Nonlinear Position-Flux Zero-Bias Control for AMB System With Disturbance,” Appl. Comput. Electromagn. Soc. J., 32(8), pp. 650–656. http://www.aces-society.org/search.php?vol=32&no=8&type=2
Mystkowski, A. , 2010, “ Sensitivity and Stability Analysis of Mu-Synthesis AMB Flexible Rotor,” Solid State Phenom., 164, pp. 313–318. [CrossRef]
Mystkowski, A. , 2010, “ μ–Synthesis Control of Flexible Modes of AMB Rotor,” Acta Mech. Autom., 4(5), pp. 83–90. http://yadda.icm.edu.pl/baztech/element/bwmeta1.element.baztech-article-BPB2-0048-0014?printView=true


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Fig. 1

(a) One-degree-of-freedom AMB flux observer-based feedback control diagram and (b) magnetic hysteresis loop of the AMB actuator

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Fig. 3

Comparison of observer-based feedback responses: (a) observer (24) and (b) observer (29)

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Fig. 2

Scheme of 1DOF AMB

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Fig. 4

Comparison of estimate state x̂3 and true state x3: (a) observer (30) and (b) observer (38)

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Fig. 5

State-feedback and observer-based feedback responses with the observer (38)

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Fig. 6

(a) Flux estimation errors; (b) total fluxes ϕ1 and ϕ2; for observers (24), (30), (38) with controller (20) and for observer (29) with controller u=ν+uL; controller gains: k1=0.92,k2=9.94,k3=0.1

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Fig. 7

State-feedback and observer-based feedback fluxes and command voltages with the observer (29) and with control law u=ν+uL, for controller gains: k1=0.92,k2=9.94

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Fig. 8

State-feedback and observer-based feedback responses for IM and actual model (AM) with the observer (30) and (38)



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