Integral Sliding Mode Control with Exponential Approximation Law for an AMB Rotor System Considering the Alford Force
DOI:
https://doi.org/10.13052/2024.ACES.J.390910Keywords:
Active magnetic bearings, Alford force, Sliding mode control, Vibration controlAbstract
In order to deal with the nonlinear problems associated with the Alford force and active bearing rotor system in fluid machinery, an integral sliding mode control with exponential reaching law is proposed in this paper. An integral term is incorporated into the switching function, and an exponential approaching law, along with a boundary layer saturation function that replaces the symbolic function, is adopted to suppress the chattering and tracking error of sliding mode control. Simulation and experimental results show that, under the magnetic bearing force and Alford force, the system exhibits improved anti-disturbance performance compared to a PID controller. Moreover, the rotor amplitude is reduced by 33% when using this controller. The proposed controller demonstrates good dynamic performance and strong robustness, even when the parameters of the entire system are perturbed.
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References
G. Schweitzer and E. Maslen, Magnetic Bearing: Theory, Design, and Application to Rotating Machinery. Berlin: Springer, 2009.
J. S. Alford, “Protecting turbomachinery from self-excited whirl,” Journal of Engineering for Power, vol. 87, pp. 333-343, 1965.
A. Shata, R. Hamdy, and A. Abdel-Khalik, “A particle swarm optimization for optimum design of fractional order PID controller in active magnetic bearing systems,” IEEE MEPCON, 2016.
P. Anantachaisilp and Z. Lin, “Fractional order PID control of rotor suspension by active magnetic bearings,” Actuators, vol. 6, no. 1, 2017.
S. M. Raafat and R. Akmeliawati, “Intelligent H2/H∞
robust control of an active magnetic bearings system,” Al-Khwarizmi Engineering Journal, vol. 11, no. 2, pp. 1-12, 2015.
S. Ran, Y. Hu, and H. Wu, “Design, modeling, and robust control of the flexible rotor to pass the first bending critical speed with active magnetic bearing,” Advances in Mechanical Engineering, vol. 10, no. 2, pp. 1-13, 2018.
S. Ran, Y. Hu, H. Wu, and X. Cheng, “Resonance vibration control for AMB flexible rotor system based on μ
-synthesis controller,” Mathematical Problems in Engineering, pp. 1-16, 2018.
L. Di and Z. Lin, “Control of a flexible rotor active magnetic bearing test rig: A characteristic model based all-coefficient adaptive control approach,” Control Theory and Technology, vol. 12, pp. 1-12, 2014.
X. Guan, J. Zhou, C. Jin, and Y. Xu, “Disturbance suppression in active magnetic bearings with adaptive control and extended state observer,” Proceedings of the Institution of Mechanical Engineers Part I: Journal of Systems and Control Engineering, vol. 234, no. 2, pp. 272-284, 2020.
S. Y. Chen, and F. J. Lin, “Robust nonsingular terminal sliding-mode control for nonlinear magnetic bearing system,” IEEE Transactions on Control Systems Technology, vol. 19, no. 3, pp. 636-643, 2011.
V. V. Huynh and M. H. Q. Tran, “Integral sliding mode control approach for 3-pole active magnetic bearing system,” Applied Mechanics & Materials, vol. 829, pp. 128-132, 2016.
H. Rong and K. Zhou, “Nonlinear zero-bias current control for active magnetic bearing in power magnetically levitated spindle based on adaptive backstepping sliding mode approach,” Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science, 2016.
A. Mystkowski, “Lyapunov sliding mode observers with application for active magnetic bearing operated with zero-bias flux,” Journal of Dynamic Systems Measurement and Control, vol. 231, no. 20, 2018.
R. Rahmatullah and N. F. O. Serteller, “SMC controller design for DC motor speed control applications and performance comparison with FLC, PID and PI controllers,” in Intelligent Sustainable Systems (Lecture Notes in Networks and Systems), vol. 579. Singapore: Springer, 2023.
S. Chai, Y. Zhang, and Q. Qu, “An analysis on the air exciting-vibration force of steam turbine,” Engineering Science, vol. 3, no. 04, pp. 68-72, 2001.
W. B. Gao, Theory and Design Method for Variable Sliding Mode Control. Beijing: Science Press, 1996.
X. D. Guo and D. Bo, “A PMSM sliding mode control system based on a novel exponential reaching law,” Control Engineering of China, vol. 25, no. 10, pp. 1865-1870, 2018.
A. Wang, X. Jia, and S. Dong, “A new exponential reaching law of sliding mode control to improve performance of permanent magnet synchronous motor,” IEEE Transactions on Magnetics, vol. 49, no. 5, pp. 2409-2412, 2013.
Q. M. Wang, C. H. Jiang, and M. J. Xie, “Permanent magnet synchronous motor control with composite variable exponent reaching law,” Micromotors, vol. 54, no. 7, pp. 99-103, 2021.