Design-Oriented Benchmarking of Sliding Mode Controllers for a Magnetic Levitation System Under Actuator and Sensor Constraints

Öz

This study examined the control of a single-axis vertical magnetic levitation (MagLev) system under realistic implementation constraints. The system was considered due to its nonlinear dynamics and inherent open-loop instability, which make it suitable for evaluating practical control limitations. Actuator voltage and current saturation, parameter uncertainty, external disturbances, and measurement noise were explicitly incorporated into the analysis. For comparative evaluation, three control strategies were implemented: local linear state feedback control based on an LQR design, fixed-gain sliding mode control, and adaptive sliding mode control. Rather than relying on a single initial condition, controller performance was assessed over ranges of initial positions and velocities using a capture region framework. The effects of parametric uncertainty were systematically investigated through Monte Carlo–based numerical simulations. The results indicated that the linear controller exhibited zero successful captures over the evaluated initial condition grid, while sliding mode controllers achieved restricted but nonzero capture regions under nominal and disturbance conditions. The adaptive mechanism influenced transient behavior but did not substantially expand the feasible operating region due to actuator constraints. Measurement noise was found to degrade controller effectiveness in all cases. These findings emphasize the importance of jointly considering physical constraints and stability properties when evaluating control strategies for magnetic levitation systems.

Anahtar Kelimeler

• magnetic leviataion system
• sliding mode control
• adaptive sliding mode control
• actuator constraints
• capture region analysis
• nonlinear control

Kaynakça

1. [1] A. V. Starbino and S. Sathiyavathi, “Design of sliding mode controller for magnetic levitation system,” Computers & Electrical, Engineering vol. 78, pp. 184–203, 2019, doi: 10.1016/j.compeleceng.2019.07.007.
2. [2] P. Roy and B. K. Roy, “Sliding mode control versus fractional-order sliding mode control: applied to a magnetic levitation system,” Journal of Control, Automation and Electrical Systems, vol. 31, no. 3, pp. 597–606, 2020, doi:10.1007/s40313-020-00587-8.
3. [3] I. Iswanto and A. Ma’arif, “Robust integral state feedback using coefficient diagram in magnetic levitation system,” IEEE Access, vol. 8, pp. 57003–57011, 2020, doi:10.1109/ACCESS.2020.2981840.
4. [4] H. M. M. Adil, S. Ahmed, and I. Ahmad, “Control of MagLev system using supertwisting and integral backstepping sliding mode algorithm,” IEEE Access, vol. 8, pp. 51352–51362, 2020, doi:10.1109/ACCESS.2020.2980687.
5. [5] W. Bauer and J. Baranowski, “Fractional PIλD controller design for a magnetic levitation system,” Electronics, vol. 9, no. 12, art. 2135, 2020, doi:10.3390/electronics9122135.
6. [6] B. Ataşlar-Ayyıldız, O. Karahan, and S. Yılmaz, “Control and robust stabilization at unstable equilibrium by fractional controller for magnetic levitation systems,” Fractal and Fractional, vol. 5, no. 3, art. 101, 2021, doi:10.3390/fractalfract5030101.
7. [7] P. Majewski, D. Pawuś, K. Szurpicki, and W. P. Hunek, “Toward optimal control of a multivariable magnetic levitation system,” Applied Sciences, vol. 12, no. 2, art. 674, 2022, doi:10.3390/app12020674.
8. [8] A. Ma’arif, M. A. M. Vera, M. S. Mahmoud, E. Umoh, A. J. Abougarair, and S. N. Rahmadhia, “Sliding mode control design for magnetic levitation system,” Journal of Robotics and Control, vol. 3, no. 6, pp. 848-853, 2022, doi:10.18196/jrc. v3i6.12389.

9. [9] H. M. S. Yaseen, S. A. Siffat, I. Ahmad, and A. S. Malik, “Nonlinear adaptive control of magnetic levitation system using terminal sliding mode and integral backstepping sliding mode controllers,” ISA Transactions, 2022, doi: 10.1016/j.isatra.2021.07.026.
10. [10] A. Kerraci, M. F. Khelfi, and Z. Ahmed-Foitih, “An improved conditional integrator sliding mode controller based on swarm intelligence for a magnetic levitation system,” Turkish Journal of Electrical Engineering & Computer Sciences, vol. 32, no. 6, pp. 867–882, 2024, doi:10.55730/1300-0632.4107.
11. [11] M. Bulut and A. Dumlu, “Manyetik levitasyon sistemleri için doğrusal olmayan kontrol yöntemlerinin geliştirilmesi,” Journal of the Institute of Science and Technology, vol. 13, no. 2, pp. 960-972, 2023, doi:10.21597/jist.1189129.
12. [12] Y. Karabacak, A. Yaşar, and Î. Sarıtaş, “Doğrusal olmayan manyetik levitasyon sisteminin kontrolü için PID ve LQR kontrolcülerilerinin performans karşılaştırılması,” DEUFMD, vol. 25, no. 74, pp. 339–350, 2023, doi:10.21205/deufmd.2023257407.
13. [13] M. Abdollahzadeh, M. Pourgholi, “Adaptive fuzzy sliding mode control of magnetic levitation system based on interval type-2 fuzzy neural network identification with an Extended Kalman–Bucy filter,” Engineering Applications of Artificial Intelligence, vol. 130, 2024, doi: 10.1016/j.engappai.2023.107645.
14. [14] A. T. Vo, T. N. Truong, H.-J. Kang, and T. D. Le, “A fixed-time sliding mode control for uncertain magnetic levitation systems with prescribed performance and anti-saturation input,” Engineering Applications of Artificial Intelligence, 2024, doi: 10.1016/j.engappai.2024.108373.
15. [15] S. Hu, Y. Qin, and J. Yang, “Global fast terminal sliding mode control of magnetic levitation system based on improved extended state observer,” International Journal of Control, Automation and Systems, vol. 23, pp. 1469–1483, 2025, doi:10.1007/s12555-024-1010-1.
16. [16] A. Pandey, D. M. Adhyaru, G. Sharma and K. A. Ogudo,“Constrained and Unconstrained Control Design of Electromagnetic Levitation System with Integral Robust–Optimal Sliding Mode Control for Mismatched Uncertainties,” Energies, vol. 19, no. 2, art. 350, 2026, doi:10.3390/en19020350.
17. [17] M. Arucu, “Magnetic Levitation and Intelligent Transportation Systems: Superconductivity and Electrodynamics in Maglev Trains,” Journal of Intelligent Transportation Systems and Applications, vol. 8, no. 2, pp. 70–87, 2025, doi:10.51513/jitsa.1721729.
18. [18] L. E. J. Alkurawy and K. G. Mohammed, “Model predictive control of magnetic levitation system,” International Journal of Electrical and Computer Engineering (IJECE) vol. 10, no. 6, pp. 5802–5812, 2020, doi:10.11591/ijece. v10i6.pp5802-5812.
19. [19] H. M. Gutierrez and H. Luijten, “5-DOF real-time control of active electrodynamic MAGLEV,” IEEE Transactions on Industrial Electronics, vol. 65, no. 9, pp. 7468–7476, 2018, doi:10.1109/TIE.2018.2795520.
20. [20] A. Sharma, A. S. Alturki, and S. M. Amrr, “Extended State Observer Based Integral Sliding Mode Control for Maglev System With Fixed Time Convergence,” IEEE Access, vol. 10, pp. 93074-93083, 2022, doi:10.1109/ACCESS.2022.3204059.
21. [21] P. N. Vernekar and V. S. Bandal, “Sliding mode control for magnetic levitation systems with mismatched uncertainties using multirate output feedback,” International Journal of Dynamics and Control, vol. 11, no. 6, pp. 2958–2976, 2023, doi:10.1007/s40435-023-01151-3.
22. [22] A. M. Dongardive, R. H. Chile, and S. T. Hamde, “Advanced control strategy for magnetic levitation system: a higher order sliding mode observer approach,” International Journal of Dynamics and Control, vol. 12, no. 7, pp. 2498–2510, 2024, doi:10.1007/s40435-023-01363-7.
23. [23] A. Pandey and D. M. Adhyaru, “Robust-optimal control design for current-controlled electromagnetic levitation system with unmatched input uncertainty,” International Journal of Dynamics and Control, vol. 12, no. 8, pp. 2980–2990, 2024, doi:10.1007/s40435-024-01412-9.
24. [24] W. Li, K. Fan, and Z. Wu, “Magnetic levitation system control research based on improved linear active disturbance rejection,” Transactions of the Institute of Measurement and Control, vol. 46, no. 15, pp. 2959-2970, 2024, doi:10.1177/01423312241229838.
25. [25] L. Li, H. Ouyang, M. Ou and L. Gao, “Sliding model control of active magnetic bearing rotor system based on state observer,” Advances in Mechanical Engineering, vol. 16, no. 5, 2024, doi:10.1177/16878132241253666.
26. [26] K. P. Kamath, S. I. Bekinal, V.G. S. and M. Doddamani, “Review of control strategies for active magnetic bearings,” Cogent Engineering, vol. 12, no. 1, 2025, doi:10.1080/23311916.2025.2467145.
27. [27] S. Saha, S. M. Amrr, J. K. Bhutto, A. A. AlJohani and M. Nabi, “Fuzzy logic control of five-DOF active magnetic bearing system based on sliding mode concept,” Frontiers in Control Engineering, vol. 3, 2022, doi:10.3389/fcteg.2022.1008134.
28. [28] J. Vennemann, R. Brasse, N. König, M. Nienhaus and E. Grasso, “Super Twisting Sliding Mode Control with Compensated Current Controller Dynamics on Active Magnetic Bearings with Large Air Gap,” Electronics, vol. 12, no. 4, art. 950, 2023, doi:10.3390/electronics12040950.
29. [29] M. K. Hamzah, S. M. Raafat, and S. A. Al-Samarraie, “Event Triggered Based Sliding Mode Control for Magnetic Levitation System,” AIP Conference Proceedings, vol. 3232, 2024, doi:10.1063/5.0236666.
30. [30] L. Zheng, W. Nie and B. Xiang, “Vibration Analysis and Active Control of Rotor Shaft in Magnetically Suspended Air-Blower,” Machines, vol. 10, no.7, art. 570, 2022, doi:10.3390/machines10070570.
31. [31] Z. Xu, C. Trakarnchaiyo, C. Stewart and M. B. Kharmesee, “Modular Maglev: Design and implementation of a modular magnetic levitation system to levitate a 2D Halbach array,” Mechatronics, vol. 99, art.103148, 2024, doi: 10.1016/j.mechatronics.2024.103148.
32. [32] Q. Zhu, S. M. Wang and Y. Q. Ni, “A Review of Levitation Control Methods for Low- and Medium-Speed Maglev Systems,” Buildings, vol. 14, no. 3, art. 837, 2024, doi:10.3390/buildings14030837.
33. [33] J. de Jesús Rubio, L. Zhang, E. Lughofer, P. Cruz, A. Alsaedi and T. Hayat, “Modeling and control with neural networks for a magnetic levitation system,” Neurocomputing, vol. 227, pp. 113–121, 2017, doi: 10.1016/j.neucom.2016.09.101.
34. [34] G. García-Gutiérrez, D. Arcos-Aviles, E. V. Carrera, F. Guinjoan, E. Motoasca, P. Ayala and A. Ibarra, “Fuzzy logic controller parameter optimization using cuckoo search for a magnetic levitation system,” Applied Sciences, vol. 9, no. 12, art. 2458, 2019, doi:10.3390/app9122458.
35. [35] J. Zhang, X. Wang, and X. Shao, “Design and real-time implementation of Takagi–Sugeno fuzzy controller for magnetic levitation ball system,” IEEE Access, vol. 8, pp. 38221–38228, 2020, doi:10.1109/ACCESS.2020.2971631.
36. [36] W. Yang, F. Meng, S. Meng, S. Man and A. Pang, “Tracking control of magnetic levitation system using modelfree RBF neural network design,” IEEE Access, vol. 8, pp. 204563–204572, 2020, doi:10.1109/ACCESS.2020.3037352.
37. [37] Z. Zhang and X. Li, “Real-time adaptive control of a magnetic levitation system with a large range of load disturbance,” Sensors, vol. 18, no. 5, art. 1512, 2018, doi:10.3390/s18051512.
38. [38] V. I. Utkin, Sliding Modes in Control and Optimization. Springer, 1992.
39. [39] C. Edwards and S. K. Spurgeon, Sliding Mode Control: Theory and Applications. Taylor & Francis, 1998.
40. [40] A. Levant, “Higher-order sliding modes, differentiation and output-feedback control,” International Journal of Control, vol. 76, no. 9–10, pp. 924–941, 2003.
41. [41] Y. Shtessel, C. Edwards, L. Fridman, and A. Levant, Sliding Mode Control and Observation. Birkh¨auser, 2014. [42] H. K. Khalil, Nonlinear Systems, 3rd ed. Prentice Hall, 2002.
42. [43] J.-J. E. Slotine and W. Li, Applied Nonlinear Control. Prentice Hall, 1991.
43. [44] S. P. Bhat and D. S. Bernstein, “Finite-time stability of continuous autonomous systems,” SIAM Journal on Control and Optimization, vol. 38, no. 3, pp. 751-766, 2000, doi: 10.1137/S0363012997321358
44. [45] A. Polyakov, “Nonlinear feedback design for fixed-time stabilization of linear control systems,” IEEE Transactions on Automatic Control, vol. 57, no. 8, pp. 2106-2110, 2012, doi: 10.1109/TAC.2011.2179869.